Therefore , large of a sample would be required in order to estimate the mean per capita income will be $3,838.
Test statistics – what are they?You can assess the degree to which the distribution of your data conforms to that predicted underneath the null hypothesis of the statistical test you are just using by utilizing a test statistic. The data distribution, which is determined by the confidence interval and deviation from the central tendency of each observation, represents the frequency of each observation.
Here,
First step is to find z 80% confidence level
At 80% confidence level the z will be:
α/2 = 1 - 80% = 1 - 0.80 = 0.20
α/2= 0.20 / 2 = 0.01
Zα/2= Z0.01= 1.28 from z table
Now let calculate the Sample size using this formula
Sample size = n= [( Z[tex]\alpha[/tex]/2* σ ) / E]^2
Let plug in the formula
n = (1.28*12.1/0.25)^2
n= 3,838.05
n=3,838.(Approximately)
Therefore , large of a sample would be required in order to estimate the mean per capita income will be $3,838.
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PLEASE HELP ME!!!!!!!!!!!!!
A state government borrows $2,000,000 at simple annual interest. Some of the money is borrowed at 6%, some at 7.5%, and some at 8.5%. Use a system of linear equations to determine how much (in dollars) is borrowed at each rate given that the total annual interest is $137,000 and the amount borrowed at 7.5% is four times the amount borrowed at 8.5%. Solve the system of linear equations using matrices.
If the amount borrowed at 7.5% is four times the amount borrowed at 8.5%. The amount borrowed is: $200,000, $800,000, $1,000,000.
How to find the amount borrowed?Now let find the amount borrowed
Let X+Y+Z = 2000000
0.06X + 0.075Y + 0.085Z = 137000
Y = 4Z
Substituting Y=4Z into the first and second equations:
X + 5Z = 2000000
0.06X + 0.075(4Z) + 0.085Z = 137000
X = 2000000 - 5Z
0.06X + 0.385Z = 137000
0.06(2000000 - 5Z) + 0.385Z = 137000
120000 - 0.3Z + 0.385Z = 137000
0.085Z + 120000 = 137000
0.085Z = 17000
Divide both side by 0.085Z
Z= 17,000/0.085
Z = 200000
So,
Y = 4Z
Y = 800000
X= 200,000 + 800,000
X = 1000000
Hence,
Z = 200000
Y = 800000
X = 1000000
Therefore the amount borrowed is: $200,000, $800,000, $1,000,000.
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What Is The Order?
For The Variable Expressions
Answer:
I think it’s 4/n and 4 divided by n. Sorry if it’s wrong!
Step-by-step explanation:
22. What are the values of w and x in the triangle below? Round the answers to the nearest tenth.
(1 point)
The values of x and w on the triangle are given as follows:
w = 14.4, x = 11.2.
How to obtain the values of x and w?The values of x and w are obtained applying the trigonometric ratios, as the triangle is a right triangle.
The three trigonometric ratios are given as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For the angle of 48º, we have that:
The adjacent side is w.The opposite side is of 16.Hence:
tan(48º) = 16/w
w = 16/tan(48º)
w = 14.4.
For the angle of 32º, we have that:
The adjacent side is 14.4 + x.The opposite side is of 16.Hence:
tan(32º) = 16/(14.4 + x)
tan(32º)(14.4 + x) = 16
x = (16 - 14.4tan(32º))/tan(32º)
x = 11.2.
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The difference of the ages of a sister and her younger brother is 6 years. The
numerical value of the product of their ages is equal 4 times the sum of their
Find the present ages of the sister and her brother.
Answer:
bother = 6 years ; sister = 12 years
Step-by-step explanation:
s = sister
b = brother
s - b = 6
s * b = 4(s+b)
s = b + 6
b(b+6) = 4(b+6 + b)
b² + 6b = 4(2b + 6)
b² + 6b = 8b + 24
b² + 6b - 8b - 24 = 0
b² - 2b - 24 = 0
(b-6)(b+4) = 0
b = 6
b = -4 (impossible because an age can’t be negative)
s = 6 + 6
s = 12
ASAP ASAP ASAP ASAP PLEASE
Which statement best explains why Kyle's survey may be biased?
• Two out of every three students entering Kyle's class didn't receive the survey.
• It wasn't possible for students to volunteer to take the survey.
• Only students who are taking one of Kyle's classes received the survey.
• Kyle gave the survey on paper instead of electronically.
Answer: the answer is c
Step-by-step explanation:
because Bru
find the probability of the given event. a single fair die is rolled. the number on the die is greater than 2.
The probability to get the numbers greater than 2 from the outcomes of the event of rolling a single fair die is equal to P(A) = 2/3.
As given in the question,
Event is rolling a single fair die.
Number of fair die to be rolled = 1
Possible outcomes = { 1, 2, 3, 4, 5, 6 }
Total number of possible outcomes = 6
Numbers greater than 2 on rolling a single fair die = { 3, 4. 5,6 }
Number of favourable outcomes = 4
Probability of getting a number greater than 2
= (Number of favourable outcomes) / (Total number of outcomes)
= 4 / 6
= 2 / 3
Therefore, the probability of getting a number greater than 2 while rolling a single fair die is equal to 2 / 3.
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Which of the following choices correctly names the figure below?
write the equation in slope -intercept form. What are the slope and y intercept?
-3x-10y=7
Answer: slope -intercept form = [tex]-\frac{3}{10} x-\frac{7}{10}[/tex] the slope = [tex]-\frac{3}{10}[/tex] and the y-intecept = [tex](0,-\frac{7}{10} )[/tex]
Step-by-step explanation: I used y=mx+b and filled it in with the infomation that I already knew. Hope this helps :)
7. Determine the midpoint
a) A (-4,6) B (2,-3)
The coordinates of the midpoint of line segment A (-4,6) and B (2,-3) is M (-1 , 3/2).
What is a line segment?A line segment is a measurable route between two points. Line segments can make up any polygon's sides because they have a set length.
Given:
Points A (-4,6), and B (2,-3)
Calculate the midpoint of the line segment by the formula given below,
[tex]M [(x_1 + x_2) / 2 \ \ , (y_1 + y_2)/2][/tex]
Substitute the values,
M [(-4 + 2) / 2 , (6 + (-3) / 2)]
M [(-2 / 2) , (3 / 2)]
M (-1 , 3/2)
Therefore, the coordinates of the midpoint of line segment A (-4,6) and B (2,-3) is M (-1 , 3/2).
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Im so confused on this like i think it was y=-5/3x but i dont know
Answer:
Below
Step-by-step explanation:
Slope , m, is calculated (y1-y2) / ( x1-x2) =
Using the first two points : (-5-0) / (-3 -0) = 5/3
slope = 5/3
the volume of a cube with length x is V(x)=x^3. The volume of the sphere with radius 1/2x is shown in the graph. Over the interval [1,2], which volume is increasing faster?
Answer:
The volume of the cube is increasing faster.
The volume of the cube with length : [x] is increasing faster.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that the volume of a cube with length [x] is V(x) = x³. The volume of the sphere with radius (1/2)x is shown in the graph.
We have the volume of the cube with length : [x] is -
V{C} = x³
Volume of the sphere with radius : (1/2)x is
V{S} = (4/3)πr³ = (4/3)π(x/2)³ = πx³/6
V{S} = πx³/6
Refer to the graph of the function attached of both the function. It can be seen that the function of the volume of the cube with length [x] is increasing faster.
Therefore, the volume of the cube with length : [x] is increasing faster.
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ABSTRACT REASONING In △EFG, the bisector of
∠F intersects the bisector of ∠G at point H. Explain
why FG — must be longer than FH — or HG . —
I have a job that pays me 40 dollars an hour. However, it's far away and I pay $250
a week on gas. I have another job that's closer, but it only pays 25 dollars an hour
and I only spend 100 dollars on gas a week. What should I do? Use math to
support your answer. (Calculate this problem on a monthly basis. On both jobs, he
would work 160 hours per month.)
Answer: The first job seems better.
Step-by-step explanation:
If 1 month = 4 weeks:
40 x 40 = 1600 per week
40 x 160 = 6400 per month
250 per week on gas
250 x 4 = 1000 per month on gas
1600 - 250 = 1350
6400 - 1000 = 5400
You would earn $1350 per week on the first job, and $5400 on this job.
_____________________________________________________
25 x 160 = 4000 per month
25 x 40 = 1000 per week
100 per week on gas
100 x 4 = 400 per month on gas
1000 - 100 = 900
4000 - 400 = 3600
$900 per week on the second job, and $3600 per month on this job.
Hello,
I hope you and your family are doing well!
To compare the two jobs and determine which one is more financially advantageous, you need to calculate the total income and total expenses for each job on a monthly basis.
For the first job, the total income is 40 dollars per hour * 160 hours per month = 6400 dollars per month. The total expenses are 250 dollars per week * 4 weeks per month = 1000 dollars per month. The net income is 6400 dollars per month - 1000 dollars per month = 5400 dollars per month.
For the second job, the total income is 25 dollars per hour * 160 hours per month = 4000 dollars per month. The total expenses are 100 dollars per week * 4 weeks per month = 400 dollars per month. The net income is 4000 dollars per month - 400 dollars per month = 3600 dollars per month.
Based on these calculations, the first job is more financially advantageous because it has a higher net income. You would earn an additional 1800 dollars per month by working the first job instead of the second job.
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Happy Holidays!
a fair die is rolled four times A4 is condsider success while all.other out comes are failures what is the probability of 2 succusses?
Answer:
P(Success1) =1/6
P(Success2) =1/6
P(2Success) =1/6 × 1/6 = 1/12
Heather works as a waitress at her family's restaurant she works every 2 hours every morning during the breakfast shift and returns to work each evening for the dinner shift in the last 4 days she worked 28 hours if Heather works the same number of hours each evening how many hours did she work during each dinner shift?
Heather worked 5 hours every evening during each dinner shift.
What is a Linear Equation?Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.
A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.
Let morning shift = m
evening shift = e
Representing the word problem in an equation;
4(m + e) = 28
Diving both sides by 4
m + e = 7
but she always works 2 hours in th morning shift
2 + e = 7
e = 7 - 2
e = 5
Therefore she worked 5 hours in the evening shift for 4 days.
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2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of which type of reaction?
The reaction described by 2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of oxidation - reduction reaction
What is Redox reaction?Any chemical process in which a participating chemical species' oxidation number changes is known as an oxidation-reduction reaction, often known as a redox reaction. The phrase refers to a broad range of procedures.
The equation of the reaction is written as
2H₂O + 2K → 2KOH + 2H₂
The reducing agent here is Potassium which is K it transformed from Potassium to Potassium Hydroxide. Potassium is electron donor
The oxidizing agent is water which ended up as Hydrogen molecule
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A grocery store has small bags of apples for $5 each and large bags for $8 each. If you buy 15 bags and spend $93, how many of each size bag did you buy?
Answer:
There are 9 small $5 bags and 6 large $8 bags
Step-by-step explanation:
9 x 5 = 45
6 x 8 = 48
45 + 48 = 93
7. Charlie went to Juarez, Mexico, on a shopping trip.
He bought silver rings at $5 each and bracelets at $8
each. If he bought a total of 19 items and spent $131,
how many bracelets and rings did he buy?
What’s the domain of this relation (-1,5) , (0,4), ( 1,2) , (3,-2)
Answer:
{-1, 0, 1, 3}
Step-by-step explanation:
A relation is a set of ordered pairs of numbers. The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. In this case, the relation is (-1,5) , (0,4), ( 1,2) , (3,-2), so the domain is the set of all the x-values in these ordered pairs, which is the set {-1, 0, 1, 3}. Therefore, the domain of the relation is {-1, 0, 1, 3}.
30. Choose all equations that are true.
48 X 1,000 = 4,800
48 x 1024,800
48 X 104
480,000
48 X 10³ = 4,800.00
48 X 10³ = 48,000
Answer: 1, 3
Step-by-step explanation:
An investor invested a total of $2900in two mutual funds. One fund earned a 8% profit while the other earned a 6% profit. If the investor's total profit was $194, how much was invested in each mutual fund?
The amount invested at 8% and 6% is 1000 and 1900 respectively.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, The person invested $2900 in two mutual funds and the total profit is $194.
Let the amount invested at 8% is x, then the amount invested at 6% is:
2900-x
Since the total profit is $194, it follows:
8% of x + 6% of (2900 - x) = 194
8x/100 + 6(2900 - x)/100 = 194
8x + 17400 - 6x = 19400
2x = 19400 - 17400
2x = 2000
x = 1000
The amount invested at 6% is:
2900 - 1000
= 1900
Hence, the amount invested at 8% and 6% is 1000 and 1900 respectively.
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You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period. How many hours x of television must you watch in the eighth week to meet your goal?
Television Viewing
Week....... Hours Watched
1 .......................1
2 .....................1.5
3 .....................0.5
4 .......................3
5 ......................1.5
6 ........................2
7 .......................0.5
There are 2 hours of television must you watch in the eighth week to meet your goal.
What is television?
The transmission of audio and video data electronically between a source and a recipient.
The primary use of television is to transmit shows for entertainment, information, and education. Television is a system for transmitting visual images and sound that are reproduced on screens.
Given: You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period.
Suppose x is the hours of watching television in the 8th week.
Let the average of watching television per week is 1.5.
⇒
[tex]\frac{1 + 1.5 + 0.5 + 3 + 1.5 + 2 + 0.5 + x}{8} = 1.5\\ \frac{10+x}{8}=1.5 \\10+x = 12\\x = 12-10\\x = 2[/tex]
Hence, there are 2 hours of television must you watch in the eighth week to meet your goal.
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Question 4
A seller at a farmer's market sells trays of large eggs and extra large eggs.
They sold a total of 75 trays of eggs in the past month.
•
They sold twice as many trays of large eggs as extra large eggs.
4.1. If they sold x trays of large eggs and y trays of extra large eggs, write
down two linear equations for the results above.
Answer:
They would have sold 8.2 eggs
Step-by-step explanation:
^
Select all expressions that equal the distance between the points on the number line
| 3 | + | -2 |
| -2 + 3 |
| -3 - 2 |
3 - ( -2 )
| 3 - ( -2 ) |
The expressions that are equal to the distance between point A and point B would be
| 3 | + | -2 |
| -3 - 2 |
3 - ( -2 )
| 3 - ( -2 ) |
What is a number line?
In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
In the given number line, the distance between point A and point B is 5.
Now we have to check each option
| 3 | + | -2 | = 3 + 2 = 5
| -2 + 3 | = | 1 | = 1
| -3 - 2 | = | -5 | =5
3 - ( -2 ) = 3+ 2 = 5
| 3 - ( -2 ) | = |3 + 2| = 5
Hence, the expressions that are equal to the distance between point A and point B would be
| 3 | + | -2 |
| -3 - 2 |
3 - ( -2 )
| 3 - ( -2 ) |
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3x+9-7=c+10+x
-4x+9=2x+10
7.
Which is a factored form of 8x³ + 27? (1 point)
O (2x+3)(2x+3)(2x + 3)
O (2x+3)(4x² - 6x +9)
○ (2x − 3)(4x² + 6x + 9)
O(2x-9)(4x² + 18x +81)
Answer:
B) (2x + 3)(4x² - 6x + 9)-----------------------------------
Given sum of cubes, use identity a³ + b³ = (a + b)(a² - ab + b²):
8x³ + 27 = (2x)³ + 3³ = (2x + 3)((2x)² - (2x)(3) + 3²) = (2x + 3)(4x² - 6x + 9)The matching choice is B.
Answer:
B) (2x + 3)(4x² - 6x + 9)
Step-by-step explanation:
Given expression:
[tex]8x^3+27[/tex]
Rewrite 8 as 2³ and 27 as 3³:
[tex]\implies 2^3x^3+3^3[/tex]
[tex]\textsf{Apply exponent rule} \quad a^nc^n=(ac)^n:[/tex]
[tex]\implies (2x)^3+3^3[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Sum of Cubes Formula}\\\\$a^3+b^3=(a+b)(a^2-ab+b^2)\\\end{minipage}}[/tex]
Therefore:
a = 2xb = 3Using the Sum of Cubes formula:
[tex]\begin{aligned}\implies (2x)^2+3^3&=(2x+3)((2x)^2-2x(3)+3^2)\\&=(2x+3)(4x^2-6x+9)\end{aligned}[/tex]
∆abc and ∆def satisfy the aaa correspondence. ∆abc and ∆def . is not a criterion for congruency of any two triangles.
Triangles ABC and DEF might or might not be congruent since the angle-angle-angle (AAA) postulate is not a requirement for congruency of any two triangles. This is due to the fact that the angle-angle-angle postulate only takes into account the triangles' angles and does not specify their side lengths, hence congruency for these triangles may or may not be true.
What is a congruent triangle?
Therefore, if two triangles have the same number of sides on each side, they are said to be congruent.
Additionally, we can determine if they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.
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Answer:
congruent
(AAA)
Step-by-step explanation:
Here is a system of equations.
y=2x-2
y=2x-1
Graph the system. Then write its solution. Note that you can also answer "No solution" or "Infinitely many" solutions.
For the system of equations y = 2x -2 and y = 2x - 1, There is no solution.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given pair of set of equations,
y = 2x -2,
y = 2x - 1.
The graph of the equations is shown below,
To find the solution for the equations,
The value of x and y can not be determined because lines are parallel to each other.
Therefore, Equations have no solution.
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determine if law of sines or law on cosines is the best choice substitute the values into the appropriate formula and solve
Answer:
Hi again, use the sine rule for length. answer: 82.42
Step-by-step explanation:
Review the proof of the identity cos(π − A) = −cosA.
cos(π − A)
Step 1: = cosπcosA − sinAsinπ
Step 2: = (−1)(cosA) + (sinA)(0)
Step 3: = −1cosA + (sinA)(0)
Step 4: = −cosA + 0
Step 5: = −cosA
At which step was an error made?
step 1
step 2
step 3
step 4
In the proof of given identity, cos(π - A) = -cos A. Therefore, step 1 is error made.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
The given identity is,
cos(π - A) = -cos A.
Use formula for cos(a − b) = cosa . cosb + sina . sinb
cos(π - A) = cosπcosA + sinAsinπ
= (−1)(cosA) + (sinA)(0)
= −1.cosA + (sinA)(0)
= −cosA + 0
= −cosA
Since, in the step 1 the formula is wrongly used,
Therefore, step 1 is error made.
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