Answer:
a) x² - x - 12 = 0
Step-by-step explanation:
We have equation A = equation B
⇒ x² - 9 = x + 3
⇒ x² - 9 - x - 3 = 0
⇒ x² - x - 12 = 0
Let the variance of Y is 4x^2. What is the standard deviation of Y?
Select one:
a. none of the above
b. Square root of 4x^2
c. 2
d. 2x^2
e. x
Note: Answer D is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
The correct answer is option (b): Square root of 4x^2.
The standard deviation of a random variable Y is the square root of its variance. In this case, the variance of Y is given as 4x^2. Taking the square root of 4x^2, we get the standard deviation of Y as 2x.
Therefore, the correct answer is the square root of 4x^2, which is the standard deviation of Y.
Calculate:
1+2-3+4+5-6+7+8-9+…+97+98-99
The value of the given expression is 1370.
To calculate the given expression, we can group the terms in pairs and simplify them.
We have the following pattern:
1 + 2 - 3 + 4 + 5 - 6 + 7 + 8 - 9 + ... + 97 + 98 - 99
Grouping the terms in pairs, we can see that each pair consists of a positive and a negative term. The positive term increases by 1 each time, and the negative term decreases by 1 each time. Therefore, we can rewrite the expression as:
(1 - 3) + (2 + 4) + (5 - 6) + (7 + 8) + ... + (97 + 98) - 99
The sum of each pair in parentheses simplifies to a single term:
-2 + 6 - 1 + 15 + ... + 195 - 99
Now, we can add up all the terms:
-2 + 6 - 1 + 15 + ... + 195 - 99 = 1370
As a result, the supplied expression has a value of 1370.
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What is the surface area of a triangular with 6, 7cm 4cm 12cm
The surface area of the given triangle is approximately 33.74 square centimeters.
To calculate the surface area of a triangle, we need the lengths of two sides and the included angle between them. However, in this case, you provided the lengths of all three sides (6 cm, 7 cm, and 12 cm).
To determine the surface area, we can use Heron's formula, which is applicable to triangles with all three side lengths known.
Heron's formula states that the surface area (A) of a triangle with side lengths a, b, and c is given by:
[tex]A = \sqrt(s \times (s - a) \times (s - b) \times (s - c))[/tex]
where s is the semi perimeter of the triangle, calculated as:
s = (a + b + c) / 2
Plugging in the given side lengths, we have:
s = (6 cm + 7 cm + 12 cm) / 2 = 25 / 2 = 12.5 cm
Now we can substitute the values into Heron's formula:
[tex]A = \sqrt(12.5 cm \times (12.5 cm - 6 cm) \times (12.5 cm - 7 cm) \times (12.5 cm - 12 cm))[/tex]
[tex]= \sqrt(12.5 cm \times 6.5 cm \times 5.5 cm \times 0.5 cm)[/tex]
= √(1137.5 cm^4)
≈ 33.74 cm^2
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Millman’s golfing group is terrific for a group of amateurs. Are they ready to turn pro? Here’s the data. (Hint: Remember that the lower the score [in golf], the better!)
Milkman’s Group: size 9, average score 82, standard deviation 2.6
The pros: size 500, average score 71, standard deviation 3.1
Based on the average scores and standard deviations, it appears that Millman's group still has room for improvement before they can reach the level of professional golfers.
To determine whether Millman's golfing group is ready to turn pro, we can compare their performance to that of professional golfers. Based on the provided data, Millman's group consists of 9 amateurs with an average score of 82 and a standard deviation of 2.6.
On the other hand, the professional golfers consist of 500 individuals with an average score of 71 and a standard deviation of 3.1.
To make a meaningful comparison, we can look at the average scores of the two groups. The average score is an indicator of the overall performance, with lower scores being better in golf.
In this case, the professional golfers have an average score of 71, while Millman's group has an average score of 82. This suggests that the professional golfers perform better, on average, than Millman's group.
However, it is also essential to consider the standard deviation, which measures the variability of scores within each group. A smaller standard deviation indicates less variation and greater consistency in performance.
The professional golfers have a standard deviation of 3.1, while Millman's group has a standard deviation of 2.6. This suggests that Millman's group has slightly less variation in scores compared to the professional golfers.
Overall, based on the average scores and standard deviations, it appears that Millman's group still has room for improvement before they can reach the level of professional golfers.
The professional golfers demonstrate better performance, on average, and a slightly higher variability in scores compared to Millman's group. Therefore, it would be advisable for Millman's group to continue refining their skills and striving to improve their scores before considering turning pro.
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Michael has $15 and wants to buy a combination of cupcakes and fudge to feed at least three siblings. A cupcake costs $2, and a piece of fudge costs $3
This system of inequalities models the scenario:
2x + 3y <15
x+y≥ 3
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points).
***PLEASE MAKE IT EASY FOR ME SO ITS EASY TO TYPE*** 15 POINTS
Step-by-step explanation:
Part A: The graph of the system of inequalities consists of two lines and a shaded region.
The line 2x + 3y = 15 is a solid line (because of the "less than" symbol in the inequality) and is graphed using a straight line connecting two points. For example, when x = 0, y = 5, and when x = 7.5, y = 0.
The line x + y = 3 is a solid line (because of the "greater than or equal to" symbol in the inequality) and is graphed using a straight line connecting two points. For example, when x = 0, y = 3, and when x = 3, y = 0.
The shaded region represents the solution set. It is the area below the line 2x + 3y = 15 and above or on the line x + y = 3. This shaded region satisfies both inequalities simultaneously.
Part B: To determine if the point (5, 1) is included in the solution area, we substitute x = 5 and y = 1 into both inequalities:
2x + 3y < 15:
2(5) + 3(1) < 15
10 + 3 < 15
13 < 15
Since 13 is less than 15, the point (5, 1) satisfies the first inequality.
x + y ≥ 3:
5 + 1 ≥ 3
6 ≥ 3
Since 6 is greater than or equal to 3, the point (5, 1) satisfies the second inequality.
Since the point (5, 1) satisfies both inequalities, it is included in the solution area for the system.
Part C: Let's choose the point (2, 2) as another example from the solution set.
Interpretation in real-world context:
When we have x = 2 and y = 2, it means Michael decides to buy 2 cupcakes and 2 pieces of fudge. This combination of sweets satisfies the conditions set in the inequalities, ensuring that he can feed at least three siblings.
The point (2, 2) represents a valid solution in which Michael spends a total of $10 (2 cupcakes * $2/cupcake + 2 fudges * $3/fudge = $4 + $6 = $10). With this choice, he can afford to buy enough treats to feed his three siblings while staying within his budget of $15.
I WILL GIVE BRAINLIEST
Step-by-step explanation:
In a randomized block design blocked by gender, treatments should be assigned randomly within each gender block. The correct assignment maintains a distribution of one treatment for each gender. Looking at the given options, only one meets this criterion:
OA: (1f, 2f), B: (1m, 2m). C: (3f, 3m). D: (4f, 4m)
Each treatment group A, B, C, and D contains one male and one female, making the distribution of treatments blocked by gender.
which equation could use the find the length of the hypotenuse
0 6² + 11² - c²
0 6²+c² - 11²
Oc²-6²-11²
0 11²-6²-c²
Answer:
A. 6² + 11² = c²
Step-by-step explanation:
The correct equation to find the length of the hypotenuse in a right triangle is the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, if we assume that the length of one side is 6 and the length of the other side is 11, the correct equation would be:
A. 6² + 11² = c²
This equation can be simplified as follows:
36 + 121 = c²
157 = c²
Therefore, the correct equation to find the length of the hypotenuse in this case is A. 6² + 11² = c².
0.5(x-4)=4x-3(x-1)+37/5
Answer:
Multiply to remove the fraction, then set it equal to 0 and solve.
Exact Form: x = −124/5
Decimal Form: x = −24.8
Mixed Number Form: x = −24 4/5
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APQR-ASTU. Solve for x. Enter the number only.
The length of the unknown side x using the concept of similar triangles is: x = 4
How to find the side lengths of similar triangles?Similar triangles are referred to as triangles that have the same shape but different sizes. All equilateral triangles and squares of any side length are examples of similar objects. In other words, if two triangles are similar, their corresponding angles are the same and their corresponding side proportions are the same.
Now, we are told that triangle PQR is similar to Triangle STU and as such their corresponding sides are similar and therefore to find the missing side x, we have:
12/x = 15/5
x = (12 * 5)/15
x = 60/15
x = 4
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Mrs Johnson's latest test had an odd number of total marks. I got 84%. How many marks did I get?
Answer:168
Step-by-step explanation:Let's denote the total number of marks as "M."
Marks obtained = (84/100) * M
For example, if the total marks were 200, then:
Marks obtained = (84/100) * 200 = 168
Answer:
21
Step-by-step explanation:
If you got 84% then divide it by 100%. 100%/84%=21/25 check.
[tex] \frac{21}{25 } \times \frac{100}{1} = 84[/tex]
A particular type of vaccine comes in a Brand-1 and a Brand-2. Sixty-five percent
of all patients at a certain vaccination centre want the Brand-2.
i) Among ten randomly selected patients who want this type of vaccine, what
is the probability that at least six want the Brand-2?
ii) Among ten randomly selected patients, what is the probability that the
number who want the Brand-2 vaccine is within 1 standard deviation of
the mean value?
iii) The store currently has seven vaccines of each brand. What is the probability that all of the next ten patients who want this vaccine can get the brand
of vaccine they want from current stock?
i) Probability of at least six patients wanting Brand-2: P(X ≥ 6)
ii) Probability of number of patients within 1 standard deviation of mean: P(μ - σ ≤ X ≤ μ + σ)
iii) Probability that all ten patients get their desired brand from current stock: (7/14) * (6/13) * ... * (1/5)
i) The probability of at least six patients wanting Brand-2 out of ten randomly selected patients can be calculated using the binomial distribution. We need to sum the probabilities of six, seven, eight, nine, and ten patients wanting Brand-2.
The probability can be calculated as P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10), where X follows a binomial distribution with n = 10 and p = 0.65. The answer is the sum of these individual probabilities.
ii) To calculate the probability of the number of patients who want the Brand-2 vaccine being within 1 standard deviation of the mean value, we need to find the range of values that fall within one standard deviation of the mean.
We can use the normal approximation to the binomial distribution since n = 10 is reasonably large. We calculate the mean (μ) and standard deviation (σ) using μ = n * p and σ = √(n * p * (1 - p)), where p = 0.65. Then we calculate the probability of the number of patients falling within the range μ - σ to μ + σ.
iii) Since there are seven vaccines of each brand in stock, the probability that all ten patients who want the vaccine can get the brand they want from the current stock is equal to the probability of the first patient getting their desired brand (7/14) multiplied by the probability of the second patient getting their desired brand (6/13), and so on until the tenth patient (1/5). The final probability is the product of these individual probabilities.
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Suppose you have entered a 48-mile biathlon that consists of a run and a bicycle race. During your run, your average
velocity is 5 miles per hour, and during your bicycle race, your average velocity is 23 miles per hour. You finish the race
in 6 hours. What is the distance of the run? What is the distance of the bicycle race?
The distance of the run is miles.
The distance of the bicycle race is approximately 24.61 miles.
Let's assume the distance of the run is 'x' miles and the distance of the bicycle race is 'y' miles.
We know that average velocity is equal to the total distance divided by the total time taken.
We can use this information to form two equations based on the given average velocities and total time.
For the run:
Average velocity = Distance of the run / Time taken for the run
5 mph = x miles / T hours ---(Equation 1)
For the bicycle race:
Average velocity = Distance of the bicycle race / Time taken for the bicycle race
23 mph = y miles / (6 - T) hours ---(Equation 2)
Since the total time for the race is 6 hours, we can substitute (6 - T) for the time taken during the bicycle race.
Now, we can solve these equations simultaneously to find the values of 'x' and 'y'.
From Equation 1, we have:
5T = x
From Equation 2, we have:
23(6 - T) = y
Now, we substitute the value of 'x' in terms of 'T' from Equation 1 into Equation 2:
23(6 - T) = 5T
138 - 23T = 5T
138 = 28T
T = 138 / 28
T ≈ 4.93 hours
Substituting this value back into Equation 1, we can find 'x':
5(4.93) = x
x ≈ 24.65 miles
Therefore, the distance of the run is approximately 24.65 miles.
To find the distance of the bicycle race, we substitute the value of 'T' back into Equation 2:
23(6 - 4.93) = y
23(1.07) = y
y ≈ 24.61 miles
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This example using cluster sampling, how do we know whether these estimates are considered valid?
The estimates are not correct because we are to find the proportion and sample error of the given values. The proportion expresses the number of opposing votes to the total number of voters. Also, the sampling error follows the formula of [tex]SE = Z\sqrt{P(1 - P/n)}[/tex]
The right estimate to use
The exact formula used in the expression is quite different from the standard formula for calculating the standard error. We are supposed to find the root of the standard deviation but that is not the case as can be seen in the formula above.
So, the main issue with this formula is that the square root is not considered in the proportion formula used by the council, so it is not a valid estimate.
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Which statement can be concluded using the true statements shown?
If two angles in a triangle measure 90° and x degrees, then the third angle measures (90-x) degrees.
In triangle ABC, angle A measures 90 degrees and angle B measures 50°.
Angle C must measure 50 degrees.
Angle C must measure 40 degrees.
O Angle C must measure (90 - 40) degrees.
O Angle C must measure (90-30) degrees.
Answer:
Angle C must measure 40 degrees.
Step-by-step explanation:
All angles in a triangle add up to 180 degrees
(90-50)=40 degrees
We can check our answer by adding all the angles up
90+50+40=180
Angle C must be 40 degrees
Find the surface area of the prism.
A. 78 in2
B. 158 in2
C. 120 in2
D. 119 in2
Answer:
119in^2
Step-by-step explanation:
formula= 2(width×length+hight×length+hight×5
2×(5×8+3×8+3×5) = 119in^2
Use the following models to show the equivalence of the fractions 35 and 610 a) Set model
Answer:
0
Step-by-step explanation:
Use the following models to show the equivalence of the fractions 35 and 610 a) Set model
Snow Fall (Inches)
2.75
2.5
2.25
2
1.75
1.5
1.25
1
0.75
0.5
0.25
0
4
O A. 1.25
OB. 0.75
O C. 2.5
O D. 1.5
●
1
2
3
4
Time (hours after Midnight)
5
12. The graph above depicts the amount of snow accumulation from midnight to 5:00 a.m. The x-axis represents time (hours after midnight), and the y-axis represents the number of
inches of snow on the ground. How many inches of snow accumulated between 2:00 a.m. and 5:00 a.m.?
The amount of snow accumulated between 2 am and 5 am is: 1.25 inches
How to Interpret Linear Equation Graphs?The general formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
From the given graph attached, we see that the y-axis gives the amount of snow at different specific times.
Meanwhile the x-axis gives the time in hours after midnight
At 2am, the y-axis value is 1.25 inches, and as such at 2am snow accumulation was 1.25 inches.
At 5 am, the y-axis value reads 2.5 inches, and as such at 5am snow accumulation was 2.5 inches.
The difference in both snow accumulations is: 2.5 - 1.25 = 1.25
Hence, 1.25 inches snow accumulated between 2 am and 5 am.
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Can you use the ASA postulate or the AAS theorem to prove the triangles are congruent
In the figure, m<1 = (x+6)°, m<2 = (2x + 9)°, and m<4 = (4x-4)°. Write an
expression for m<3. Then find m<3.
A. 180° -(x+6)°
B. 180° -(4x-4)°
C. 180° - [(2x+9)° + (x+6)°]
D. 180° + (x+6)°
m<3=
The expression for m<3 is 349° - 7x.
To find the measure of angle 3 (m<3), we need to apply the angle sum property, which states that the sum of the angles around a point is 360 degrees.
In the given figure, angles 1, 2, 3, and 4 form a complete revolution around the point. Therefore, we can write:
m<1 + m<2 + m<3 + m<4 = 360°
Substituting the given angle measures, we have:
(x + 6)° + (2x + 9)° + m<3 + (4x - 4)° = 360°
Combining like terms:
7x + 11 + m<3 = 360°
To isolate m<3, we subtract 7x + 11 from both sides:
m<3 = 360° - (7x + 11)
m<3 = 360° - 7x - 11
m<3 = 349° - 7x
Therefore, the expression for m<3 is 349° - 7x.
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8.5 x 10[2] my assignment is about exponents
Answer:
850
Step-by-step explanation:
Our given expression is [tex]8.5*10^{2}[/tex]
To solve, simply use PEMDAS as it applies to the expression.
First, you do the exponent(s): [tex]10^2 = 100[/tex]
Then, you do multiplication: [tex]8.5*100=850[/tex]
So, your answer is 850.
Han make sparkling juice by mixing 1. 5 liter of juice and 500 milliliter of sparkling water
Han will have 2 liters (or 2000 milliliters) of sparkling juice after combining 1.5 liters of juice and 500 milliliters of sparkling water.
To make sparkling juice, Han mixes 1.5 liters of juice and 500 milliliters of sparkling water.
To add the quantities together, we need to convert the units to the same measurement. We can convert the liters to milliliters since 1 liter is equal to 1000 milliliters.
1.5 liters is equal to 1.5 x 1000 = 1500 milliliters.
Now we have 1500 milliliters of juice and 500 milliliters of sparkling water.
To find the total quantity of the sparkling juice, we add the volumes of juice and sparkling water together:
1500 milliliters + 500 milliliters = 2000 milliliters
Therefore, Han will have a total of 2000 milliliters (or 2 liters) of sparkling juice by mixing 1.5 liters of juice and 500 milliliters of sparkling water.
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Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.
To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.
The loan amount can be calculated by subtracting the down payment from the property value:
Loan amount = Property value - Down payment
= $170,000 - $20,000
= $150,000
Now we can calculate the LTV ratio:
LTV ratio = Loan amount / Property value * 100
= $150,000 / $170,000 * 100
= 88.24%
Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.
To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:
PMI payment = (Loan amount * PMI rate) / 12
= ($150,000 * 0.30%) / 12
= $450 / 12
= $37.50
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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment
Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.
30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%
15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
find AB using segment addition prostulate 2x-3 24 5x+6
Answer:
To find the length of AB using the segment addition postulate , we need to add the lengths of segments AC and CB.
AC + CB = AB
Substituting the given lengths:
2x-3 + 24 = 5x+6
Simplifying and solving for x:
21 = 3x
x = 7
Now that we know x, we can substitute it back into the expression for AB:
AB = 2x-3 + 24 = 2(7)-3 + 24 = 14-3+24 = 35
Therefore, the length of AB is 35.
Step-by-step explanation:
A given city is at 35°S and 200°W. How far is it from this city to A. the North Pole and B. the Equator C. the south pole
The distance from the given city to the South Pole is 125 degrees of latitude.
To determine the distance from the given city to various locations, we need to consider the latitude and longitude coordinates.
Distance to the North Pole:
The North Pole is located at 90°N latitude. Since the given city is at 35°S latitude, we need to calculate the difference in latitude between the city and the North Pole.
Distance to the North Pole = 90° - 35° = 55°
The distance from the given city to the North Pole is 55 degrees of latitude.
Distance to the Equator:
The Equator is located at 0° latitude. To determine the distance from the city to the Equator, we need to calculate the absolute value of the latitude of the city.
Distance to the Equator = |35°| = 35°
The distance from the given city to the Equator is 35 degrees of latitude.
Distance to the South Pole:
The South Pole is located at 90°S latitude. Since the given city is at 35°S latitude, we need to calculate the difference in latitude between the city and the South Pole.
Distance to the South Pole = 35° - (-90°) = 35° + 90° = 125°
The distance from the given city to the South Pole is 125 degrees of latitude.
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Select the correct answer.
Mr. Miller owns two hotels and is ordering towels for the rooms. He ordered 27 hand towels and 48 bath towels for a bill of $540 for the first hotel. He
ordered 50 hand towels and 24 bath towels for a bill of $416 for the other hotel.
What is the cost of one hand towel and one bath towel?
O A.
OB.
OC.
O D.
The cost of one hand towel is $4 and the cost of one bath towel is $9.
The cost of one hand towel is $9 and the cost of one bath towel is $4.
The cost of one hand towel is $5 and the cost of one bath towel is $8.
The cost of one hand towel is $8 and the cost of one bath towel is $5.
Answer: D: The cost of one hand towel is $8 and the cost of one bath towel is $5.
Step-by-step explanation:
Let's assume the cost of one hand towel is 'x' dollars and the cost of one bath towel is 'y' dollars.
For the first hotel, Mr. Miller ordered 27 hand towels and 48 bath towels, resulting in a bill of $540. This can be expressed as the equation:
27x + 48y = 540 ...(equation 1)
For the second hotel, Mr. Miller ordered 50 hand towels and 24 bath towels, resulting in a bill of $416. This can be expressed as the equation:
50x + 24y = 416 ...(equation 2)
To solve this system of equations, we can use any suitable method such as substitution or elimination. Let's use the elimination method:
Multiplying equation 1 by 2 and equation 2 by 3, we get:
54x + 96y = 1080 ...(equation 3)
150x + 72y = 1248 ...(equation 4)
Now, subtracting equation 4 from equation 3, we have:
(54x + 96y) - (150x + 72y) = 1080 - 1248
-96x + 24y = -168
Dividing both sides of the equation by -24, we get:
4x - y = 7 ...(equation 5)
Now, we have a system of equations:
4x - y = 7 ...(equation 5)
50x + 24y = 416 ...(equation 2)
Solving this system of equations, we find that x = 8 and y = 5.
Therefore, the cost of one hand towel is $8 and the cost of one bath towel is $5.
So, the correct answer is option D: The cost of one hand towel is $8 and the cost of one bath towel is $5.
Answer:
Step-by-step explanation:
Total cost of hand towels for first hotel = 27 * $5 = $135
Total cost of bath towels for first hotel = 48 * $8 = $384
Total cost of hand towels for second hotel = 50 * $5 = $250
Total cost of bath towels for second hotel = 24 * $8 = $192
Total cost of all hand towels = $135 + $250 = $385
Total cost of all bath towels = $384 + $192 = $576
Total number of hand towels = 27 + 50 = 77
Total number of bath towels = 48 + 24 = 72
Average cost of one hand towel = $385 / 77 = $5
Average cost of one bath towel = $576 / 72 = $8
Naomi wants to save $100,000, so she makes quarterly payments of $1,500 into an account that earns 4.4%/a compounded quarterly. (If you are using TVM Solver, please ensure you provide screenshots of your work or breakdown how you entered everything into the solver).
How long will it take her to reach her goal?
Would doubling her payment amount save her half the time needed to save? Support your statement.
Naomi will take approximately 93 quarters (around 23 years and 3 months) to save $100,000 by making quarterly payments of $1,500 with a 4.4% interest rate.
Doubling her payment amount would save her time, but the exact time saved would require recalculating with the new payment amount.
To calculate the time it will take for Naomi to reach her goal of $100,000, we can use the future value formula for a series of periodic payments:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value (goal amount) = $100,000
P = Payment amount per period = $1,500
r = Interest rate per period = 4.4% per year / 4 (quarterly compounding) = 1.1% per quarter
n = Number of periods (quarters) to reach the goal (what we need to find)
Plugging in the values, we have:
$100,000 = $1,500 * [(1 + 0.011)^n - 1] / 0.011
Simplifying the equation, we have:
[(1 + 0.011)^n - 1] = $100,000 * 0.011 / $1,500
[(1.011)^n - 1] = 0.073333...
Now, we can solve this equation for n using logarithms:
n = log(0.073333...) / log(1.011)
Using a financial calculator or an online calculator, we find that n ≈ 92.33 quarters.
Since Naomi is making quarterly payments, we round up to the next whole number, giving us a total of 93 quarters.
Therefore, it will take Naomi approximately 93 quarters (or around 23 years and 3 months) to reach her goal of $100,000.
Doubling her payment amount to $3,000 per quarter would indeed save her time in reaching her goal. The higher payment amount means she would accumulate the desired amount faster. However, to determine the exact time saved, we would need to recalculate using the same formula as above with P = $3,000. The time saved will depend on the specific calculation result.
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When parallel lines are intersected by a transversal, which of the following angle pairs are supplementary?
Answer:
if two parallel lines are cut by a transversal,then, exterior angles on the same side of the transversal are supplementary!
Step-by-step explanation:
I don't really know how to explain it but I hope this helped!
What function has the same range as f(x) = -2 x - 3 + 8
Answer:
Any equation that has the power of x at 1
Step-by-step explanation:
Since the function f(x) = -2x -3 +8 has an infinite range, so any other equation that only contains x^1 would work
What is the vertex for the graph of v - 3 = - (x+2)^2
The vertex for the graph of the equation [tex]v - 3 = - (x+2)^2 is (-2, 3).[/tex]
To find the vertex of the graph of the equation [tex]v - 3 = - (x+2)^2,[/tex] we can rewrite it in the standard vertex form: [tex]v = a(x - h)^2 + k,[/tex]
where (h, k) represents the vertex coordinates.
First, let's rearrange the given equation:
[tex]v - 3 = - (x+2)^2[/tex]
[tex]v = - (x+2)^2 + 3[/tex]
Comparing this with the standard vertex form, we can see that h = -2 and k = 3.
Therefore, the vertex of the graph is (-2, 3).
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NO LINKS!! URGENT HELP PLEASE PLEASE!!!
Answer:
[tex]\textsf{12)} \quad \text{a.}\;\;m \angle 1 = 107^{\circ}, \quad \text{b.}\;\;m \angle 2 = 107^{\circ}, \quad \text{c.}\;\;m \angle 3 = 73^{\circ}[/tex]
[tex]\textsf{13)} \quad EC = 6[/tex]
[tex]\textf{14)}\quad \text{a.}\;\;x = 33, \quad \text{b.}\;\; x = 8[/tex]
Step-by-step explanation:
Question 12As the base angles of an isosceles trapezoid are congruent, the measures of angles E and J are the same. Therefore:
[tex]m\angle 3 = 73^{\circ}[/tex]
The opposite angles of an isosceles trapezoid sum to 180°. Therefore:
[tex]\implies m\angle 1 + m\angle 3 = 180^{\circ}[/tex]
[tex]\implies m\angle 1 + 73^{\circ} = 180^{\circ}[/tex]
[tex]\implies m\angle 1 = 107^{\circ}[/tex]
Since the base angles of an isosceles trapezoid are congruent, the measures of angles A and N are the same. Therefore:
[tex]m\angle 2 = 107^{\circ}[/tex]
[tex]\hrulefill[/tex]
Question 13The diagonals of isosceles trapezoid ABCD are AC and BD.
Point E is the point of intersection of the diagonals. Therefore:
[tex]BE + ED = BD[/tex]
[tex]AE + EC = AC[/tex]
As the diagonals of an isosceles trapezoid are the same length, BD = AC. Therefore:
[tex]AE + EC = BD[/tex]
Given BD = 20 and AE = 14:
[tex]\implies AE + EC = BD[/tex]
[tex]\implies 14 + EC = 20[/tex]
[tex]\implies 14 + EC - 14 = 20 - 14[/tex]
[tex]\implies EC = 6[/tex]
[tex]\hrulefill[/tex]
Question 14The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides (legs) of the trapezoid.
The formula for the midsegment of a trapezoid is:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Midsegment of a trapezoid}\\\\$M=\dfrac{1}{2}(a+b)$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the midsegment.\\ \phantom{ww}$\bullet$ $a$ and $b$ are the parallel sides.\\\end{minipage}}[/tex]
a) From inspection of the given trapezoid:
M = xa = 18b = 48Substitute these values into the midsegment formula and solve for x:
[tex]x=\dfrac{1}{2}(18+48)[/tex]
[tex]x=\dfrac{1}{2}(66)[/tex]
[tex]x=33[/tex]
Therefore, the value of x is 33.
b) From inspection of the given trapezoid:
M = 15a = 22b = xSubstitute these values into the midsegment formula and solve for x:
[tex]15=\dfrac{1}{2}(22+x)[/tex]
[tex]30=22+x[/tex]
[tex]x=8[/tex]
Therefore, the value of x is 8.