Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been experiencing problems as shown by its June contribution format income statement below:
Flexible
Budge
Actual
Sales (7,000 pools)
$265,000 $265,000
Variable expenses:
Variable cost of goods sold*
79,240
97,525
Variable selling expenses
19,000
19,000
Total variable expenses
98,240
116,525
Contribution margin
166,760
148,475
Fixed expenses:
Manufacturing overhead
Selling and administrative
Total fixed expenses
Net operating income (loss)
67,000
67,000
85,000
85,000
152,000
152,000
$ 14,760 $ (3,525)
Janet Dunn, who has just been appointed general manager of the Westwood Plant, has been given instructions to "get things under control. Upon reviewing the plant's income statement, Ms. Dunn has concluded that the major problem lies in the variable cost of goods sold. She has been provided with the following standard cost per swimming pool:
Direct materials
Direct labor
Variable manufacturing overhead
Total standard cost per unit
Standard
Quantity or
Hours
3.5 pounds
0.4 hours
0.3 hours
Standard Price or Rate
§ 2.10 per pound
$ 7.60 per hour
$ 3.10 per hour
Standard
Cost
$ 7.35
3.04
0.93
$ 11.32
During June, the plant produced 7,000 pools and incurred the following costs:
a. Purchased 29,500 pounds of materials at a cost of $2.55 per pound.
b. Used 24,300 pounds of materials in production. (Finished goods and work in process inventories are insignificant and can be ignored.)
c. Worked 3,400 direct labor-hours at a cost of $7.30 per hour.
d. Incurred variable manufacturing overhead cost totaling $8,400 for the month. A total of 2,400 machine-hours was recorded.
It is the company's policy to close all variances to cost of goods sold on a monthly basis
Required:
1. Compute the following variances for June:
a. Materials price and quantity variances
b. Labor rate and efficiency variances.
c. Variable overhead rate and efficiency variances.
2. Summarize the variances that you computed in (1) above by showing the net overall favorable or unfavorable variance for the month.
Answers
a. Materials price variance = (Standard price - Actual price) x Actual quantity
= ($2.10 - $2.55) x 24,300 pounds
= -$10,935 (Unfavorable)
b. Materials quantity variance = (Standard quantity - Actual quantity) x Standard price
= (3.5 pounds - 24,300 pounds) x $2.10 per pound
= -$48,465 (Unfavorable)
Labor rate and efficiency variances:
a. Labor rate variance = (Standard rate - Actual rate) x Actual hours
= ($7.60 - $7.30) x 3,400 hours
= $1,020 (Favorable)
b. Labor efficiency variance = (Standard hours - Actual hours) x Standard rate
= (0.3 hours - 3,400 hours) x $7.60 per hour
= -$23,600 (Unfavorable)
Variable overhead rate and efficiency variances:
a. Variable overhead rate variance = (Standard rate - Actual rate) x Actual hours
= ($3.10 - $8,400/2,400 hours) x 2,400 hours
= -$2,800 (Unfavorable)
b. Variable overhead efficiency variance = (Standard hours - Actual hours) x Standard rate
= (0.3 hours - 2,400 hours) x $3.10 per hour
= -$7,194 (Unfavorable)
Net overall favorable or unfavorable variance for the month:
To calculate the net overall variance, we sum up all the variances:
Overall Variance = Materials price variance + Materials quantity variance + Labor rate variance + Labor efficiency variance + Variable overhead rate variance + Variable overhead efficiency variance
= -$10,935 + (-$48,465) + $1,020 + (-$23,600) + (-$2,800) + (-$7,194)
= -$94,014 (Unfavorable)
Related Questions
How many ways can steve select a song
Answers
Using the combination formula, it is found that there are 3300 ways to choose the songs.
The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?
��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:
��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!
For the rock songs, we have three from a set of eleven, hence:
�11,3=11!3!8!=165C11,3=3!8!11!=165
For the alternative songs, we have four from a set of five, hence:
�5,4=5!4!1!=5C5,4=4!1!5!=5
For the rap songs, we have three from a set of four, hence:
�4,3=4!3!1!=4C4,3=3!1!4!=4
Since the songs are independent, the total number of ways is given by:
�=165×5×4=3300T=165×5×4=3300
hope this helps you
Using the combination formula, it is found that there are 3300 ways to choose the songs.
The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?
��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:
��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!
For the rock songs, we have three from a set of eleven, hence:
�11,3=11!3!8!=165C11,3=3!8!11!=165
For the alternative songs, we have four from a set of five, hence:
�5,4=5!4!1!=5C5,4=4!1!5!=5
For the rap songs, we have three from a set of four, hence:
�4,3=4!3!1!=4C4,3=3!1!4!=4
Since the songs are independent, the total number of ways is given by:
�=165×5×4=3300T=165×5×4=3300
hope this helps you
if rice is 0.75 x it with 9379372
Answers
Answer:
7034529
Step-by-step explanation:
Assuming you mean to multiply 0.75 by 9379372, the result would be:
0.75 x 9379372 = 7034529
Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
A. purchase price: $120, advertised price: $300
B. purchase price: $108, advertised price: $270
C. purchase price: $130, advertised price: $325
D. purchase price: $117, advertised price: $293
Answers
Required purchase price is $120 and advertised price is $300.
How much did Danielle purchase the antique dresser for?
Let's assume that Danielle purchased the antique dresser for $x.
According to the problem, she advertised it for 250% of her purchase price, which means she advertised it for,
250% of x = 2.5x
She sold the dresser for 15% less than the advertised price of 2.5x, so she sold it for,
(1 - 0.15) × 2.5x = 2.125x
We know that the selling price was $255, so we can set up the equation,
2.125x = 255
Solving for x,
x = 120
Therefore, Danielle purchased the antique dresser for $120.
What was her initial advertised price?
To find the initial advertised price, we can plug x = 120 into the expression 2.5x,
2.5x = 2.5 × 120 = 300
So, the initial advertised price was $300.
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What meaning of the statement this?
Answers
Every subgroup of Z is cyclic and is generated by a unique nonnegative integer. This property makes Z a particularly simple and well-behaved group for studying group theory.
What exactly is a "group theory"?Group theory is a branch of abstract algebra that studies mathematical structures called groups. Group theory provides a powerful framework for studying symmetry, structures, and transformations in various areas of mathematics, physics, chemistry, and other fields of science. It has applications in cryptography, coding theory, crystallography, quantum mechanics, and many other areas of science and engineering.
The set of integers subject to addition, or Z, is an example of an abelian group in group theory. A subset that also forms a group by addition is referred to as a subgroup of Z. It turns out that every Z subgroup is cyclic, i.e., created by a single element.
Let H be a subgroup of Z to be more precise. H is closed under addition since Z is an additive group, and it includes the identity element (0). We can demonstrate that H is produced by a, which means that every element in H can be written as a multiple of a, by looking at the lowest positive integer in H (if any), indicated as a. Thus, H becomes a cyclic subgroup with an as its generator.
Moreover, this generator a is exclusive to H. Assume that H contains a second positive integer b that likewise yields H. We can demonstrate that the set of multiples of a and b is indeed the same set, which suggests that a and b produce the same subgroup H. As a result, a = b, and H has a unique generator.
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He jogging track has a length of 792 yards how long is this in miles
Answers
By performing the division, the jogging track is 0.45 miles long.
What is division?Division is a mathematical operation that involves the splitting of a quantity into equal parts or groups.
According to given information:The problem asks us to convert a length of 792 yards to miles. To do this, we need to use a conversion factor to relate yards to miles. We know that there are 1760 yards in a mile, so we can use this relationship to convert the length in yards to miles.
To convert yards to miles, we divide the length in yards by the number of yards in a mile. This is because we want to cancel out the units of yards and be left with the corresponding number of miles.
So, 792 yards / 1760 yards/mile gives us the length of the jogging track in miles. We can simplify this expression by performing the division to get the result of 0.45 miles. Therefore, the jogging track is 0.45 miles long.
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A bag contains two Pennie’s,two nickels, two dimes and two quarters. If a coin selected at random from the bag, what is the probability that the coin selected will be worth less than 10 cents
Answers
8 coins in total and half are worth less then $0.10
Can someone help me solve this?
Answers
The values of x and y in the given figure are 10.5 and 15 respectively in the quadrilateral
We have to find the values of x and y in quadrilateral
4y+14+7y+1=180
Combine like terms
11y+15=180
Subtract 15 from both sides
11y=180-15
11y=165
Divide both sides by 11
y=15
The value of y is 15
Now 7x+1+105=180
7x+106=180
Subtract 106 from both sides
7x=180-106
7x=74
Divide both sides by 7
x=10.5
Hence, the values of x and y in the given figure are 10.5 and 15 respectively
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4.
Study Figure A and Figure B below.
Figure A
Figure B
In the table below, fill in the correct number
of faces, vertices, and edges for Figure A and
Figure B.
Figure A
Figure B
Number
of Faces
Number
of Vertices
Number
of Edges
Answers
A square prism has the following characteristics:
Number of faces: 6
Number of vertices: 8
Number of edges: 12
A cuboid has the following characteristics:
Number of faces: 6
Number of vertices: 8
Number of edges: 12
What is meant by square prism?
A square prism is a three-dimensional geometric shape with two parallel square bases and rectangular faces connecting the two bases. It has 8 vertices, 12 edges, and 6 rectangular faces.
What is meant by cuboid?
A cuboid is a three-dimensional geometric shape with six rectangular faces, where opposite faces are equal in size and shape. It has 8 vertices, 12 edges, and 6 rectangular faces. A cuboid is also known as a rectangular prism.
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Eulerize this graph in the most efficient way possible, considering the weights of the edges.
Answers
We can eulerize this graph in the most efficient way possible by making these vertices have even degree through adding an edge between them.
How do we Eulerize a graph?We can eulerize a graph by ensuring to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.
A good method to do this is by adding edges between pairs of vertices that have odd degree until all vertices have even degree.
In the scenario above, we can see that all vertices have odd degree except for the last vertex.
Hence , in order to make this vertex have even degree, we can add an edge from it to any other vertex with odd degree.
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Two identical baseballs are dropped. The first is dropped from a height of 121 feet and the second is dropped from a height of 225 feet. Find the two height functions and compare their graphs.
h1(t) = −16t2 + 121 is a vertical translation of h2(t) = −16t2 + 225.
The y-intercept of h1 is 4 ft greater than that of h2.
h1(t) = −4t2 + 121 is a vertical translation of h2(t) = −4t2 + 225.
The y-intercept of h1 is 104 ft less than that of h2.
h1(t) = −16t2 + 121 is a vertical translation of h2(t) = −16t2 + 225.
The y-intercept of h1 is 104 ft less than that of h2.
h1(t) = −4t2 + 11 is a vertical translation of h2(t) = −4t2 + 15.
The y-intercept of h1 is 4 ft greater than that of h2.
Answers
The correct answer is:
[tex]h1(t) = -16t^2 + 121[/tex] is a vertical translation of [tex]h2(t) = -16t^2 + 225.[/tex]
The y-intercept of h1 is 104 ft less than that of h2.
What is a y-intercept?
A function or relationship's graph meets the y-axis of the coordinate system at a point known as a y-intercept, sometimes known as a vertical intercept.
The height function for an object dropped from a height of h0 is given by:
[tex]h(t) = -16t^2 + h0\\\\h1(t) = -16t^2 + 121\\\\h2(t) = -16t^2 + 225[/tex]
To find the y-intercept of h1, we set t = 0 in the equation[tex]h1(t) = -16t^2 + 121:[/tex]
[tex]h1(0) = -16(0)^2 + 121 = 121[/tex]
Therefore, the y-intercept of h1 is 121 feet.
To find the y-intercept of h2, we set t = 0 in the equation [tex]h2(t) = -16t^2 + 225:\\\\h2(0) = -16(0)^2 + 225 = 225[/tex]
Therefore, the y-intercept of h2 is 225 feet.
The difference in their y-intercepts is:
225 - 121 = 104
Therefore, the y-intercept of h1 is 104 feet less than that of h2.
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Use your quadratic cost function and the following demand curve.
P = 900 - 0.03Q MR = 900 - .06Q
Calculate marginal cost (MC) and average cost (AC), price (P) and marginal revenue (MR) Graph MC, AC, P, and MR as a function of output (you may use Excel or graph these relationships by hand). Show the price and output that maximizes profit in this graph. Then use algebra to calculate the price and output (view output as a measure of desired run production for the season) that will maximize the firm’s profit. Calculate your profits at this price and output level.
Calculate the level of output that minimizes average cost. Show this solution on your graph above. Calculate your profits at this output level.
Calculate the price and level of output that maximizes total revenue. Show this solution on your graph above. Calculate your profits at this output level.
Assume that the demand and cost data above is for the N. Y. Yankees and Major League Baseball owners impose a lump sum tax of $4 million dollars to help equalize talent across high revenue and low revenue teams. How will the tax affect your profit maximizing output and the price you charge? How will the tax affect your profits? Explain.
Extra Credit
Now suppose that the league owners impose a “luxury tax” of 50 percent on costs that are above $200,000. Calculate your profit maximizing output and pricing levels, and your profits. Now assume the players’ association has it’s way and the tax is only 25 percent on costs that are above $500,000. Calculate your profit maximizing output and pricing levels, and your profits. (Hint: you may find it useful to find the output level where the luxury tax kicks in and then examine how this tax affects your cost structure at higher output levels). Graph your solutions to the “luxury tax” in your graph above.
Answers
To find MR, we take the derivative of the demand curve with respect to Q:
MR = dP/dQ = 900 - 0.06Q
How to solveTo find MC, we need to take the derivative of the quadratic cost function with respect to Q:
C(Q) = 500 + 10Q + 0.005Q^2
MC = dC/dQ = 10 + 0.01Q
To find AC, we divide the total cost by the quantity:
AC = C(Q)/Q = (500 + 10Q + 0.005Q^2)/Q = 500/Q + 10 + 0.005Q
To find P, we use the demand curve and solve for Q:
P = 900 - 0.03Q
Q = (900 - P)/0.03
Explanation:
To find P, we use the demand curve and solve for Q:
P = 900 - 0.03Q
Q = (900 - P)/0.03
To find MR, we take the derivative of the demand curve with respect to Q:
MR = dP/dQ = 900 - 0.06Q
Now we can graph MC, AC, P, and MR:
|
P | /MR
| /
| /
| /
| /
| /
| / AC
| /
MC |/
|------------- Q
Note:
The graph is a rough sketch and not drawn to scale. The MC curve is upward-sloping, the AC curve is U-shaped, the P curve is downward-sloping, and the MR curve lies below the P curve and is also downward-sloping.
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4. The Federal Reserve System
a. lends money to banks
b. functions as the bank for the government
Oc
Od.
d. all of these
5. What portion of its revenues does the United States spend on defense
Oa
c. aids the check-clearing process
a. about 10 percent
b. about 20 percent
c. about 40 percent
d. about 50 percent
Answers
4. The Federal Reserve System
d. all of these5. about 10 percent
What is the federal reserve?
The Fed is the renowned central bank of the United States, famous for their diverse and crucial functions which includes:
Providing short-term loans to banks: The Federal Reserve serves as a lender during critical times, acting seamlessly to help out other financial institutions in order meet the necessities required to stabilize within our economic system.
Govern through banking services provided: The account management of U.S government lies on this exceptional institution. It proficiently sponsors numerous activities such as payment processing and providing governmental services amongst others.
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How do I find angle P and angle BEC and angle PCA
Answers
The solution is : The measure of angle ADC is 115°.
Here, we have,
Let A, B, C represent the vertex angle measures of ΔABC.
Then the sum of angles in ΔADC is ...
A/2 +∠ADC + C/2 = 180°
Multiplying by 2 gives ...
A + C + 2×∠ADC = 360°
From the given information, we know ...
A + C + 50° = 180° . . . . . sum of angles in ΔABC
This lets us write an expression for (A +C):
A + C = 130° . . . . . . . . subtract 50° from the previous equation
Substituting for A+C, we get ...
130° + 2×∠ADC = 360°
2×∠ADC = 230° . . . . . . . . . subtract 130°
∠ADC = 115° . . . . . . . . . . . divide by 2
The measure of angle ADC is 115°.
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complete question:
The measure of an angle ABC is 50°,AD bisects angle BAC, and DC bisects angle BCA. The measure of angle ADC is what?
URGENT!! I WILL GIVE
BRAINLIEST!!!!!!!!!!!! AND 100 POINTS
Answers
Answer:
the function is decreasing.
the slope is -3/4 and the y-intercept is 7.
the function is linear and continuous.
y = -3/4 x + 7 3 this function.
Step-by-step explanation:
"the function is linear and discrete" is false. there are no interruptions or steps in the curve. it is a continuous curve.
the usual function form of a line is
y = ax + b
"a" being the slope, "b" being the y-intercept.
that is why the other statements are false.
Xzavier stops by Sweet Treats after school to get a birthday surprise for his mom. He has $11. The table shows the prices of his mom's favorite treats.
Sweet Treats
Candy Price per Pound
Chocolate-covered Cashews $13.88
Chocolate-Peanut Butter Cups $11.46
Chocolate-Caramel Bites $9.62
Gourmet Gummy Bears $8.24
After looking at the prices, Xzavier decides to get two different one-half pound bags of candy for his mom. Do not consider tax. If Xzavier spends the greatest amount possible for two different one-half pound bags of candy, which two candies did he buy?
A. chocolate-covered cashews and chocolate-caramel bites
B. chocolate-peanut butter cups and chocolate-caramel bites
C. gourmet gummy bears and chocolate-caramel bites
D. chocolate-peanut butter cups and gourmet gummy bears
Answers
Answer:
B. chocolate-peanut butter cups and chocolate-caramel bites
Step-by-step explanation:
Chocolate-peanut butter cups cost $11.46 per pound, so one-half pound costs $5.73.
Chocolate-caramel bites cost $9.62 per pound, so one-half pound costs $4.81.
$5.73 + $4.81 = $10.54, so B is the correct answer.
On the same coordinate plane mark all points (x,y) such that (A) y=x+5 (B) y=-(x+5) (C) y=|x+5|
Answers
The graph of the functions (A) y=x+5 (B) y=-(x+5) and (C) y=|x+5| are added as an attachment
Marking all points on the same coordinate planeFrom the question, we have the following parameters that can be used in our computation:
(A) y=x+5 (B) y=-(x+5) (C) y=|x+5|To mark all points on the same coordinate plane, we simply plot the graphs of the three functions on the same graph
Using the above as a guide, we have the following:
The graph of the functions (A) y=x+5 (B) y=-(x+5) and (C) y=|x+5| are added as an attachment
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PLEASE HELP ME! I WILL BE GIVING 50 POINTS!
Answers
The box plot that represents the data is given as follows:
Bottom plot.
What does a box-and-whisker plot shows?A box and whisker plots shows these five features from a data-set, listed as follows:
The minimum non-outlier value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum non-outlier value.The ordered data-set for this problem is given as follows:
2, 2, 4, 7, 7, 14, 16, 18.
The minimum and maximum values are given as follows:
Minimum of 2.Maximum of 18.The data-set has an even cardinality, hence the median is given by the mean of the two middle elements as follows:
Median = (7 + 7)/2 = 7.
(which removes the top two options).
The quartiles are given as follows:
First quartile -> median of 2, 2, 4 and 7 -> 3.Third quartile -> median of 7, 14, 16, 18 -> 15.Meaning that the last plot is correct. (the one that is already marked).
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HELPPPP IT IXL PLEASEE
Answers
Answer:
32
Step-by-step explanation:
m∠S = tan⁻¹(5/8) = 32⁰
30 50 50 301 10. What is the area of the right (37,92) triangle? 11. What is the area of the isosceles (37,52) triangle?
Answers
The area of the right triangle is 1702 sq units and the area of the isosceles triangle is 539.39 sq units
What is the area of the right triangle?The area of the right triangle is calculated as
Area = 1/2 * Base * Height
So, we have
Area = 1/2 * 37 * 92
Area = 1702
What is the area of the isosceles triangle?The area of the isosceles triangle is calculated as
Area = 1/2s²sin(c)
So, we have
Area = 1/2 * 37² * sin(52)
Evaluate
Area = 539.39
Hence, the value of the area is 539.39 sq units
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NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #1
Answers
The end behavior of f(x) is described as follows:
As x -> -∞, f(x) -> ∞.As x -> ∞, f(x) -> 0.How to obtain the end behavior of a function?The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.
The function for this problem is given as follows:
f(x) = 4(5/7)^x.
It is an exponential function with base with absolute value less than 1, hence the end behavior is given as follows:
Increases to the left of the graph -> As x -> -∞, f(x) -> ∞.Approaches the horizontal asymptote y = 0 at the right of the graph -> As x -> ∞, f(x) -> 0.More can be learned about the end behavior of a function at brainly.com/question/1365136
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A simple random sample of size n is drawn. The sample mean, x, is found to be 18.8, and the sample standard deviation, s, is
found to be 4.4.
Click the icon to view the table of areas under the t-distribution.
(a) Construct a 95% confidence interval about u if the sample size, n, is 34.
Lower bound:: Upper bound: [
(Use ascending order. Round to two decimal places as needed.)
(b) Construct a 95% confidence interval about μ if the sample size, n, is 61.
Lower bound: Upper bound:
(Use ascending order. Round to two decimal places as needed.)
How does increasing the sample size affect the margin of error, E?
A. The margin of error does not change.
B. The margin of error increases.
OC. The margin of error decreases.
Answers
a) The 95% confidence interval for a sample size of 34 is given as follows: (17.26, 20.34).
b) The 95% confidence interval for a sample size of 61 is given as follows: (17.67, 19.63).
c) Increasing the sample size, the margin of error decreases.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The margin of error is defined as follows:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
From this we get that it is inversely proportional to the square root of the sample size, hence if we increasing the sample size, the margin of error will decrease.
The mean and the standard error are given as follows:
[tex]\mu = 18.8, s = 4.4[/tex]
For a sample size of 34, we have 33 degrees of freedom, hence, using a t-table, the critical value is given as follows: 2.0345.
Hence the bounds of the interval are given as follows:
18.8 - 2.0345 x 4.4/sqrt(34) = 17.26.18.8 + 2.0345 x 4.4/sqrt(34) = 20.34.For a sample size of 61, we have 60 degrees of freedom, hence, using a t-table, the critical value is given as follows: t= 2.
Hence the bounds of the interval are given as follows:
18.8 - 2 x 4.4/sqrt(61) = 17.67.18.8 + 2x 4.4/sqrt(61) = 19.93.More can be learned about the t-distribution at https://brainly.com/question/17469144
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describe how to use the zero product property when solving a quadractic equation by factoring
Answers
X + 1 = 0, so x = -1, and x - 24 = 0, so x = 24. Consequently, the two answers to the equation are x = -1 and x = 24.
What is equation?It is a method for illustrating a notion, a connection, or a behaviour that often involves two or more variables. Equations can be used to explain several events, including economic models and physical principles. They can also be applied to problem-solving and forecasting. Symbols, integers, and mathematical operations like addition, subtraction, multiplication, and division are used to create equations.
An essential tool for factoring quadratic equations is the Zero Factor Property. Finding two terms, one of which is a factor of the constant term and the other of which is a factor of the coefficient of the squared term, whose product is equal to the constant term, is the fundamental principle behind the Zero Factor Property. With this knowledge, the given quadratic equation can be factored into two parts that equal zero.
One must first factor a quadratic equation into two factors that are equal to zero in order to solve it using the zero factor property. To do this, one needs determine the constant term's factors as well as the coefficient of the squared term's factors. The coefficient of the squared term is always obtained by multiplying the factors, which are always different integers.
The constant term's factors are always sums of numbers that result in the constant term. Once the elements are known, the equation can be factored into two factors that are equal to zero each.
Consider the equation [tex]x^2+5x-24=0[/tex], for instance. The factors of the constant term are -1 and 24, while the factors of the squared term's coefficient are 1 and 5. The equation then reads as (x + 1)(x - 24) = 0.
At this stage, the Zero Factor Property can be used to find x. Since all factors must be equal to zero, x can be solved for by setting all factors to zero. Thus, x + 1 = 0, resulting in x = -1, and x – 24 = 0, resulting in x = 24. Thus, x = -1 and x = 24 are the two answers to the problem.
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Complete questions as follows-
How do I use the zero factor property when solving a quadratic equation by factoring?
In investing $6,500 of a couple's money, a financial planner put some of it into a savings account paying 5% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 13% annual simple interest. The combined interest earned for the first year was $637. How much money was invested at each rate?
Answers
The pair made the following investments: The combined interest for the first year was $477 from a $2550 savings account earning 6% simple interest annually and a $3600 development plan earning 9% simple interest annually.
What is Simple interest?Borrowers are required to pay the lender's basic interest as a fee in exchange for a loan.
Compound interest is not taken into account in the calculation; just the initial principal is taken into account.
Simple interest applies to all loans, not just specific ones.
Also highlighted is the type of interest that banks provide their customers on their savings accounts.
So, we presumptively have $x invested in the savings account.
Consequently, $ was invested in the development plan.(6150 - x).
S.I. = (Prt)/100 is the formula for simple interest on a sum of money (P), compounded at a rate (r), over a time period (t).
We figure out the interest on both investments:
Contribution to a savings account:
Amount invested (P) = $x.
Rate of interest (r) = 6%.
Time for investment (t) = 1 year.
As a result, interest was received= (Prt)/100 = $(x*6*1)/100 = $ (6x)/100
We are aware that $477 in interest has been paid in total.
Thus, we can write the following equation using the interest from both investments added:
(6x)/100 + {9(6150 - x)}/100 = 477
or, 6x + 55350 - 9x = 47700,
or, 55350 - 47700 = 3x,
or, 3x = 7650,
or x = 7650/3 = 2550.
As a result, investments in:
Savings account = $x = $2550.
Development plan = $(6150 - x) = $(6150 - 2550) = $3600.
Therefore, the pair made the following investments: The combined interest for the first year was $477 from a $2550 savings account earning 6% simple interest annually and a $3600 development plan earning 9% simple interest annually.
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Correct question:
In investing $6,150 of a couple's money, a financial planner put some of it into a savings account paying 6% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $477. How much money was invested at each rate?
Choose the best answer below!
Answers
The range of [tex]f(x) = \frac{1}{3x+4}[/tex] is all real numbers except for 0 i.e. {y ∈ R, y ≠ 0} and there is no x-intercept in f(x) = 1/(3x - 4)
The range of the functionThe range of [tex]f(x) = \frac{1}{3x+4}[/tex] is all real numbers except for 0.
To see this, note that the denominator of [tex]f(x) = \frac{1}{3x+4}[/tex], can take any real value except -4/3, since division by zero is undefined.
Therefore, f(x) can take any value except 0, which means the range of f(x) is {y ∈ R, y ≠ 0}
The reciprocal that is a linear functionThe reciprocal of a is 1/a
From the list of options, we have
f(x) = 1/(x + 3)
The reciprocal is x + 3 and this is a linear function
So, the reciprocal of a function that is linear is f(x) = 1/(x + 3)
The asymptote of the reciprocalThe reciprocal function of the form f(x) = 1/x has a vertical asymptote at x = 0.
Similarly, the reciprocal function of the form f(x) = 1/(ax + b) has a vertical asymptote at x = -b/a.
Comparing the given functions with the above form, we can see that:
f(x) = 1/(x + (5/2)) is of the required form with a = 1 and b = 5/2.
So, it has a vertical asymptote at x = -(5/2)/1 = -5/2.
Therefore, the function with a vertical asymptote at x = -5/2 is option (a), f(x) = 1/(x + (5/2)).
The horizontal asymptote of the functionThe correct answer is (d) All of the above, as all functions a, b and c have a horizontal asymptote at y = 0, when solved by graphs
The true statement about the function f(x)As x approaches (5/3)^+ (from the right-hand side), the function f(x) approaches positive infinity.
So, the true statement is (b) f(x) -> oo
The x-interceptGiven that
f(x) = 1/(3x - 4)
So, we have
1/(3x - 4) = 0
This gives
1 = 0
This means that there is no x-intercept.
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10. Katherine has diabetes. At each meal, she must estimate the mass in grams of carbohydrates she plans to eat, then inject the appropriate amount of insulin. Katherine needs 1 unit of insulin for 15 g of carbohydrates. Katherine's lunch has 60 g of carbohydrates. How many units of insulin should Katherine inject?
Answers
Answer:
Katherine needs 1 unit of insulin for 15 g of carbohydrates.
Step-by-step explanation:
To find out how many units of insulin Katherine should inject for her lunch which has 60 g of carbohydrates, we can use the following proportion:
1 unit : 15 g = x units : 60 g
where x is the number of units of insulin Katherine should inject.
To solve for x, we can cross-multiply:
1 unit * 60 g = 15 g * x units
60 = 15x
x = 4
Therefore, Katherine should inject 4 units of insulin for her lunch.
z The Systeen of Somall particles of chass on Shown belowr is rotationrg at aver Is of the Particles are. Cocpected by Light Sloves that Camber Length eaed or shortened what is the new angular sleed if the stores are Shortened to 0.son? BACRICE I Lon Ou b Sen 3 h Fon Self down at
Answers
The new angular speed, ω₂, is four times the initial angular speed, ω₁.
How to solveTo solve this problem, we can use the conservation of angular momentum. The initial and final angular momenta should be equal:
I₁ω₁ = I₂ω₂
Where I₁ and I₂ are the initial and final moments of inertia, respectively.
Assuming the particles are connected in a circular arrangement, the moment of inertia can be calculated using:
I = n * m * r²
Where n is the number of particles and r is the distance from the center of rotation.
Now we have:
(n * m * L²)ω₁ = (n * m * (0.5L)²)ω₂
Simplifying the equation, we get:
ω₂ = 4ω₁
So the new angular speed, ω₂, is four times the initial angular speed, ω₁.
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A system of small particles, each with mass m, is connected by light strings of length L. The system is rotating at an initial angular speed ω₁. If the strings are shortened to 0.5L, what is the new angular speed, ω₂?
Which of the following best describes the equation below?
3(x + 12) + 5x = 8x - 36
A.
exactly one real solution, x = -1
B.
exactly one real solution, x =
C.
no real solutions
D.
infinite real solutions
Answers
The best description of the equation is no real solutions. Option C
How to solve for the equationTo solve the equation 3(x + 12) + 5x = 8x - 36, we can simplify the left-hand side by distributing the 3, and then combine like terms:
3x + 36 + 5x = 8x - 36
8x + 36 = 8x - 36
36 = -36
This equation is a contradiction, since there is no value of x that will make 36 equal to -36. Therefore, there are no real solutions to this equation.
The answer is (C) no real solutions.
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I need help. If you can answer this I will give you brainliest!!!!!
Answers
Answer:
B, C, E
Step-by-step explanation:
B:
[tex](\frac{3}{4})^2-\frac{6}{16} \\= \frac{9}{16} - \frac{6}{16} = \frac{3}{16}[/tex]
C:
[tex](\frac{3}{8})^2 / \frac{3}{4} \\= \frac{9}{64} / \frac{3}{4} = \frac{9}{64} *\frac{4}{3} = \frac{3}{16}[/tex]
E:
[tex]2*\frac{3}{4} - (\frac{3}{4})^2 - \frac{3}{4} \\= \frac{6}{4} - \frac{9}{16} - \frac{3}{4} = \frac{3}{4} - \frac{9}{16} = \frac{12}{16} - \frac{9}{16} = \frac{3}{16}[/tex]
Answer:
B, C, E
Step-by-step explanation:
B:
[tex](\frac{3}{4})^2-\frac{6}{16} \\= \frac{9}{16} - \frac{6}{16} = \frac{3}{16}[/tex]
C:
[tex](\frac{3}{8})^2 / \frac{3}{4} \\= \frac{9}{64} / \frac{3}{4} = \frac{9}{64} *\frac{4}{3} = \frac{3}{16}[/tex]
E:
[tex]2*\frac{3}{4} - (\frac{3}{4})^2 - \frac{3}{4} \\= \frac{6}{4} - \frac{9}{16} - \frac{3}{4} = \frac{3}{4} - \frac{9}{16} = \frac{12}{16} - \frac{9}{16} = \frac{3}{16}[/tex]
Schools in a large county are categorized into one of two regions: East or West. Administrators want to estimate the difference in the proportions of students participating in Advanced Placement programs in each region. They take a random sample of 50 East students and find that 20 of them have taken at least one AP class. A separate random sample of 80 West students shows 16 students that have taken at least one AP class.
They want to use these results to construct a 95%confidence interval to estimate the difference in the proportion of students taking an AP class in each region
(East−West). Assume that all of the conditions for inference have been met.
Which of the following is a correct 95% confidence interval based on their data?
(0.038, 0.362)
Answers
Based on the data, the appropriate 95% confidence interval is (0.039, 0.361), which is closest to the answer option (0.038, 0.362).
Define the term standard normal distribution?A specific type of ordinary dispersion with a mean of 0 and a standard deviation of 1 is known as a standard typical conveyance.
We may use the following calculation to create a 95% confidence interval for the variation in the proportion of students taking an AP class in each region:
(East - West) ± z*√[(East proportion)(1 - East proportion)/East sample size + (West proportion)(1 - West proportion)/West sample size]
where z* denotes the critical value of the standard normal distribution for the desired level of confidence, East proportion denotes the percentage of East students who took at least one AP class, West proportion denotes the percentage of West students who took at least one
AP class, East sample size denotes the sample size of East students, and West sample size denotes the sample size of West students.
Using the given data, we have East proportion = 20/50 = 0.4, West proportion = 16/80 = 0.2, East sample size = 50, and West sample size = 80.
The crucial value z* for a 95% confidence level can be calculated using a conventional normal distribution table or calculator and is roughly 1.96.
after entering each value into the formula:
(0.4 - 0.2) ± 1.96√[(0.4)(0.6)/50 + (0.2)(0.8)/80]
= 0.2 ± 0.161
As a result, the answer choice (0.038, 0.362) comes the closest to the right 95% confidence interval based on the data, which is (0.039, 0.361).
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2.4.4 Quiz: Parabolas with Vertices Not at the Origin
The vertex of this parabola is at (2, -4). When the y-value is -3, the x-value is
-3. What is the coefficient of the squared term in the parabola's equation?
10
-10
OA. -1
B. 1
10-
C. 5
OD. -5
(2,-4)
10
Answers
The coefficient of the squared term in the parabola's equation is: -5
How to find the equation of the parabola?We are given the following information in the question:
Vertex of parabola: (2,-4)
Also, (x = 3, y = -1) lies on the parabola.
The general equation of parabola is of the form:
y = a(x - h)² + k
where:
(h, k) is the vertex of the parabola
Putting h = 2, k = -4 in the equation, we get:
y = a(x - 2)² - 4
Now, putting x = -3 and y = -3 in the above equation, we get:
-3 = a(-3 - 2)² - 4
a = 1/25
The second parabola is of the form:
x = a(y + 4)² + 2
At -3, -3:
-3 = a + 2
a =-5
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