The compound interest rate charged is given as follows:
13% per year.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
P = 12000, A(t) = 22109.22, n = 1, t = 5.
Hence the interest rate is obtained as follows:
22109.22 = 12000(1 + r)^5
(1 + r)^5 = 22109.22/12000
1 + r = (22109.22/12000)^(1/5)
1 + r = 1.13
r = 1.13 - 1
r = 0.13.
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Polaris, the North Star, is very important in navigation because it does not appear to move in the sky.
True
False
Help meee
Which one is it?
Answer:
the number of shirts sold
Step-by-step explanation:
that's what the question is asking
Four more than the quotient of a number and 5 is equal to 2 . Use the variable w for the unknown number.
The unknown number's variable w is equal to -10.
How is a variable defined in mathematics?In mathematics, a variable is an alphabet or phrase that represents an unknown quantity, unknown value, or unknown number. The variables are used, particularly when dealing with algebraic expressions or algebra. As an example, the variables x and 9 are constants in the linear equation x+9=4.
The following information can be written as an equation to express it:
4 + w/5 = 2
By deducting 4 from both sides of the equation, we may isolate the variable on one side and solve for w:
w/5 = -2
Then, to find w, we can multiply both sides by 5.
w = -10
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the city's pr manager, who never took statistics, claimed the mean score of all ninth graders in the city was 81 . of course, that is incorrect. what
The mean score of all the ninth graders in the city is equal to 81.84 ( round to two decimal places )
Number of schools in the city = 3
Result of the mean score of the ninth grade students are
Glenwood 78 269
Central City 93 321
Lincoln High 66 161
Given mean score by PR manager = 81
Correct mean score is calculated as
= ( 78 × 269 + 93 × 321 + 66 × 161 ) / ( 269 + 321 + 161 )
= ( 20982 + 29853 + 10626 ) / 751
= 61461 / 751
= 81.84 ( round to two decimal places )
Therefore, the mean score of the ninth grade students of all the schools in the city is given by 81.84 ( round to two decimal places ).
The above question is incomplete , the complete question is:
In a city with three high schools, all the ninth graders took a Standardized Test, with these results: High School Mean score on test Number of ninth graders
Glenwood 78 269
Central City 93 321
Lincoln High 66 161
The city's PR manager, who never took statistics, claimed the mean score of all ninth graders in the city was 81 . Of course, that is incorrect.
a. What is the mean score for all ninth graders in the city? Round to two decimal places.
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1. Find f(4)
f(1)=8
f(n)=-2f(n-1)-4
The fourth term in the sequence is:
f(4) = -76
How to find the value of f(4)?Here we have a sequence where we know the first term:
f(1) = 8
And the recursive formula is:
f(n) = -2*f(n - 1) - 4
Using the recursive formula we can get the next terms:
f(2) = -2*f(2 - 1) - 4
= -2*f(1) - 4 = -2*8 - 4 = -20
f(3) = -2*f(3 - 1) - 4
= -2*-20 - 4 = 40 - 4 = 36
f(4) = -2*f(4 - 1) - 4
= -2*36 - 4 = -76
That is the value of the fourth term.
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Ken has just retired. His Roth IRA has a present value of $524,856.00 and has an interest rate of 3.4%, compounded annually. In addition, he receives a yearly pension of $32,615.12. Given that Ken plans to draw from his Roth IRA for the next fifteen years, find his total annual income.
Ken total annual income is $ 55,401.98.
What has compounded annually?
The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this.
The completely randomized design, in which participants are assigned to treatment groups at random, is the most basic type of experimental design. The main benefit of using this method is that it minimizes the influence of chance and eliminates bias. This approach makes use of probability theory, which gives statistical analysis a strong foundation.
Given that Roth IRA has a present value of $524,856.00. The rate of interest is 3.4% per annum.
A = P(1+r)^t
A = amount
P = principal
r = rate of interest
t = time
The amount after 15 years is
A = 524,856.00(1+3.4%)¹⁵
A = 866658.9925
The total interest is 866658.9925 - 524,856.00 = $341802.99
The average interest per annum is (341802.99 /15) =22786.866
The annual income is 22786.866 + 32,615.12 = 55,401.986
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hat
The distance around a circle is 36
meters long. What is the diameter of the
circle?
Answer: [tex]36/\pi[/tex] or approximately 11.4592
Step-by-step explanation:
The distance around a circle equals its circumference.
The circumference equation is: C = 2[tex]\pi[/tex] * r where r = radius.
Now, we know that the distance around the circle is 36 so C = 36
Using the equation, we have 36= 2[tex]\pi[/tex]*r
Now, we solve for r by dividing by 2[tex]\pi[/tex] to both sides.
r = [tex]36/2\pi[/tex] which equals [tex]18/\pi[/tex] which is approximately 5.7296
Now, since radius is half of the diameter, we need to multiply this by 2.
This finally gives us the answer of diameter = [tex]36/\pi[/tex] which is approximately 11.4592
A procedure for using sample data to find the estimated regression equation is
a. point estimation. b. interval estimation.
c. the least squares method. d. extrapolation.
Option C. the least squares method is a procedure for using sample data to find the estimated regression equation.
The procedure for using sample data to find the estimated regression equation is called the least squares method. This method involves finding the line that minimizes the sum of the squared vertical distances between the observed data points and the line. The estimated regression equation is used to predict the value of the dependent variable based on the value of the independent variable. This method is commonly used in regression analysis to model the relationship between two variables. It is a useful tool for making predictions and understanding the relationship between variables.
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Clarissa cycled at 12 1/2 miles per hour for 2 1/2 hours. How far did she travel?
She travel 31.25 miles we calculate it by multiply by speed and time
Speed indicates how quickly something or someone is moving. If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example because the distance is measured in metres (m) and the time is measured in seconds (s).The formula can be rearranged in three ways:
speed = distance ÷ time
distance = speed × time
time = distance ÷ speed
To calculate one of the variables (speed, distance or time) we need the other two.
As given in Question she cycled at speed 12 1/2 miles per hours
12 1/2 can be written as 12.5 miles per hours
and she cycled for 2 1/2 hours which can be written as 2.5 hours
and to find the distance how much she total travel we have to multiply the speed and time
distance = 12.5x2.5 = 31.25 miles
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4. Find the coordinates of the center and the measure of the diameter for a circle whose equation is
(x+4)² + (y + 5)² = 64
The general equation of a circle is (x-h)² + (y-k)² = r²
Where,
(h,k) = center of circler = radiusHere we are given the equation (x+4)² + (y+5)² = 64 and given this we are asked to find the diameter as well as the coordinates of the center.
Finding the coordinates of the center and diameter.Finding the center
If (h,k) = center, then the coordinates of the center are the given values of h and k but negative. This is because the values are being subtracted from x and y. (x-h)² + (y-k)² = r²
This means that, (x+4)² + (y+5)² = 64 is the same as saying (x-(-4))² + (y-(-5))² = 64 based off of the general equation of a circle.
Notice how the plugged in values are negative rather than positive.
In conclusion, we can say that the center is at (-4,-5) (see attached image below to check answer)
In the equation, 64 takes the place of r²
So r² = 64
Taking the square root of both sides we get r = 8
So the radius is 8.
To convert to diameter we multiply by 2
So diameter = 8 * 2 = 16
In conclusion, a circle with the equation (x+4)² + (y + 5)² = 64, has a center at (-4,-5) and a diameter of 16
a two-tailed test is a hypothesis test in which the rejection region is . a. only in the upper tail of the sampling distribution b. in both tails of the sampling distribution c. in one tail of the sampling distribution d. only in the lower tail of the sampling distribution
A two-tailed test is a hypothesis test in which the rejection region is option (B) in both tails of the sampling distribution
The hypothesis test is defined as the statistic approach checking the results of a research study support a particular theory when we apply that result to population
A two-tailed test is a hypothesis test that defined in which the critical area of the distribution is two sided, so the sample will be greater than or less than a certain range of values
Therefore, the rejection region of a two-tailed test is a hypothesis test is in both tails of the sampling distribution.
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y=-1/2x-1
y=1/4x-4
graphing method
The solution of the system of equations is (4, -3)
How to solve the system of equations graphically?Here we want to solve the next system of equations:
y = -(1/2)x - 1
y = (1/4)x - 4
Graphically.
To do so, we just need to graph both of these lines on the same coordinate axis and find the point where the lines intersect. Below is the graph of the system of equations, there we can see that the lines intersect at the point (4, -3), so that is the solution of the system.
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patricia's parents buy her too much stuff, so she had 3 times as many as her friend suzy. if patricia has 15 toy trucks, how many does suzy have?
The solution of units problem is Suzy has 5 toy trucks by using the equation 15 = 3 * Suzy's number of toy trucks
According to the given information:
If Patricia has 3 times as many toy trucks as Suzy, we can set up an equation where:
Patricia's number of toy trucks = 3 * Suzy's number of toy trucks
We know that Patricia has 15 toy trucks, so we can substitute that value into the equation:
15 = 3 * Suzy's number of toy trucks
Now we can solve for Suzy's number of toy trucks:
Suzy's number of toy trucks = 15 / 3
Suzy's number of toy trucks = 5
Therefore, Suzy has 5 toy trucks.
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Z
S
L
T
X
V
Figure 1.
Use the diagram to answer the question.
Which of the following are opposite rays?
The rays that are opposite are:
TX and TL
What is a ray?A ray is a line that points in one direction. It has one starting point and no end point.
It is important that we know the difference between a line and a ray.
A line has no endpoints or a starting point.
We have,
From the figure,
The rays are:
TS
TL
TV
TZ
All have a common starting point, T.
We see that,
TX and TS are perpendicular rays.
TS and TL are perpendicular rays.
TX and TL are opposite rays.
Now,
The rays that are opposite are:
TX and TL.
Thus,
TX and TL are opposite rays.
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three numbers a, b, and c between 0 and 1 are selected independently and at random. what is the probability that these numbers appear in increasing order?
The probability of selecting three numbers in increasing order is 1/3, which means that in one out of every three trials, we will select three numbers in increasing order.
Probability is a branch of mathematics that deals with the measurement of the likelihood or chance of an event occurring. In this problem, we are asked to find the probability of selecting three numbers in increasing order from a range of 0 to 1.
Let's compute the probability of selecting three numbers in increasing order. Since the total number of possible outcomes is infinite, we need to use a continuous probability distribution to compute the probability. In this case, we can use the uniform distribution, which assumes that each number between 0 and 1 is equally likely to be selected.
The probability of selecting "a" as the smallest number is a/1 = a.
The probability of selecting "a" as the largest number is (1-a)/1 = 1-a.
The probability of selecting "a" as the middle number is 2(1-a)a, which is the product of the probability of selecting "a" and the probability of selecting "b" or "c" from the remaining range.
Therefore, the probability of selecting three numbers in increasing order is the sum of these probabilities:
P(increasing order) = ∫₀¹ (a * (1 - a) + (1 - a) * a + 2a(1 - a))da
P(increasing order) = ∫₀¹ 2a(1 - a)da
P(increasing order) = 2∫₀¹ a - a²da
P(increasing order) = 2[(a²/2) - (a³/3)] from 0 to 1
P(increasing order) = 2[(1/2) - (1/3)] = 1/3
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#7. Tyler llenó su bañera, se bañó y luego drenó la bañera. La función B da la profundidad del agua,
pulgadas, t minutos después de que Tyler comenzó a llenar la bañera.
Explique el significado de cada declaración en esta situación.
a. B(0) = 0
b. B(1)
C. B(9) = 11
d. B(10) = B(22)
e. B(20) > B(40)
The explanation of each statement in each given situation is given below:
How to solve for thisa. B(0) = 0
depth in inches 0 minutes after filling began is 0; that is at time =0; depth =0
b. B(1) < B(7)
B(1) represents the function one minus after filling began
c. B(9) = 11
depicts that the depth in inches of water 5 minutes after filling is 11
d. B(10) = B(22)
depicts that the depth in inches of water 10 minutes after filling began is 22.
e. B(20) > B(40)
represents the function 20 minutes after filling began
These are the required answers
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The question translated in English is: "#7. Tyler filled his tub, took a shower, and then drained the tub. Function B gives the depth of the water,
inches, t minutes after Tyler started filling the tub.
Explain the meaning of each statement in this situation.
to. B(0) = 0
b. B(1) C.B(9) = 11
d. B(10) = B(22)
and. B(20) > B(40)"
please help me im a bit stck on this question
Pls show your work thank you will mark the Brainliest
Answer:
second option
Step-by-step explanation:
an exponential function modelling the situation has the form
y = a [tex](b)^{x}[/tex]
to find a and b use ordered pairs from the table
using (0, 11000 )
11000 = a [tex](b)^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then
a = 11000 , so
y = 11000 [tex]b^{x}[/tex]
using (1, 9350 )
9350 = 11000 [tex]b^{1}[/tex] = 11000b ( divide both sides by 11000 )
[tex]\frac{9350}{11000}[/tex] = b
b = 0.85
then exponential function is
y = 11000 [tex](0.85)^{x}[/tex]
what is the least number that can be made using each digit exactly once? explain why the value of the 4 is greater than the value of the 6
Answer: The least number that can be made using each digit exactly once is 123456789. The value of 4 is greater than the value of 6 because in the decimal system (base 10), the position of a digit determines its value. The leftmost digit represents the greatest place value (ones, tens, hundreds, etc.) and each subsequent digit represents a smaller place value. In the number 123456789, the 4 is in the thousands place, which has a greater value than the 6, which is in the tens place.
Therefore, the 4 has a greater value than the 6 because it represents a larger place value.
Step-by-step explanation:
What is the value of
3/10^3
Answer:
c
Step-by-step explanation:
9/10
raven is planning a bridal shower for her best friend. at the party, she wants to serve 3 beverages, 3 appetizers, and 2 desserts, but she does not have time to cook. she can choose from 19 bottled drinks, 12 frozen appetizers, and 8 prepared desserts at the supermarket. how many different ways can raven pick the food and drinks to serve at the bridal shower?
To get the total number of different ways, multiply 1,536 x 18 = 7,344.
7,344 different ways. Raven has 19 choices for drinks, 12 choices for appetizers, and 8 choices for desserts. The formula for calculating the number of different ways is 19 x 12 x 8 = 1,536. Since Raven needs to pick 3 drinks, 3 appetizers, and 2 desserts, the formula is 3 x 3 x 2 = 18. To get the total number of different ways, multiply 1,536 x 18 = 7,344.
The formula can be used to calculate the number of different ways to combine any number of choices. For example, if Raven had 24 choices for drinks, 15 choices for appetizers, and 7 choices for desserts, the formula would become 24 x 15 x 7 = 3,240. If Raven still had to pick 3 drinks, 3 appetizers, and 2 desserts, the total would be 3 x 3 x 2 = 18. Multiplying 3,240 x 18 = 57,720 different ways.
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I don’t know how to solve 20x³-25x²+4x-5
Answer: The equation 20x³-25x²+4x-5 can be factored by finding its roots, which are the values of x that make the equation equal to zero.
To find the roots, you can use one of the following methods:
Rational Root Theorem
Synthetic Division
Factor Theorem
Binomial Expansion
I would recommend using the Rational Root Theorem, which states that if a polynomial has a rational root, then it can be expressed as a product of linear factors with rational coefficients.
First, list out the possible rational roots of the equation: ±1, ±2, ±5, ±1/2, ±1/5.
Next, test each root by dividing the equation by (x-root), using synthetic division. If the remainder is zero, then the root is a factor of the equation. Repeat this process until you have found all of the roots.
Finally, factor the equation by grouping the roots into pairs and multiplying each pair to obtain a quadratic factor. Factor each quadratic and simplify the expression.
It is important to note that this is a rather advanced topic in algebra and finding the roots of polynomials can be quite challenging. If you need further assistance, I recommend seeking help from a tutor or textbook on algebra.
Step-by-step explanation:
Which of the following is equal to √16 x 4
A. √16 x √4
B. 32
C. √16/4
D. 64
Answer:
None
Step-by-step explanation:
Let's clarify that a radical symbol beside a number means what number squared (or to the power of 2) can give me the number in the symbol.
In this case it would be 4 because
[tex]4*4=16[/tex]
A method I use is to find the square root is dividing the number in the radical symbol 2 times
First by the original number, and then by the product of the last equation. It will not always work, but it works in some cases like this one.
[tex]\frac{16}{2} = 8\\ \\\frac{8}{2}=4\\ \\\sqrt{16}=4[/tex]
Second step, multiply 4 by 4, which equals 16.
Since the square root of 16 is 4, you can substitute 4 in the rest of the equations instead of the radical expression.
None of the following equations equal 16, which means none of the following equations if equal to [tex]\sqrt{16} *4[/tex]
in the sketch A is an x-intercept and B is the turning point of the parabola, f(x) =ax^2+bx+c the straight line AB is defined as g(x) =3x+6.D(-1\3:35/6) is a point of f and CD is perpendicular to t x-axis B in the y intercept of f and g
Determine the coordinates of B
The required coordinates of B are (0, 6) for the given parabola.
What is x-Intercept?The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.
To determine the coordinates of B, we can use the information given in the problem.
A is an x-intercept, which means that the y-coordinate of A is 0, and it can be found by setting x = 0 in the equation for f(x).
The line AB is g(x) = 3x + 6. This line is a straight line and it is perpendicular to the x-axis at B, which means that the x-coordinate of B is 0.
Therefore, we can set x = 0 in both equations to find the y-coordinate of B.
For f(x), we have:
f(0) = a × 0² + b × 0 + c = c
For g(x), we have:
g(0) = 3 × 0 + 6 = 6
Since the line AB passes through the turning point B, we know that the y-coordinate of B is equal to both f(0) and g(0). Therefore, we have:
c = 6
So, the coordinates of B are (0, 6).
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Select all the angle relationships in △
△
ABC that are correct.
In ΔABC, we can conclude that m∠A < m∠C and m∠B < m∠A < m∠C. Hence, options a. and d. are the accurate solutions.
The angle opposite to the longest side of the triangle is the largest angle of the triangle, similarly, the angle opposite to the smallest side of the triangle is the smallest angle of the triangle.
In the given ΔABC, we have,
The longest side = AB = 3.1
The angle opposite to side AB = m∠C
The smallest side = AC = 2.9
The angle opposite to side AC = m∠B
side CB = 3
The angle opposite to side CB = m∠A
We have,
side AC < side CB < side AB
m∠B < m∠A < m∠C
From the given relations in the options provided, we get,
a. m∠A < m∠C
d. m∠B < m∠A < m∠C
are correct interpretations.
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The complete question is -
Select all the angle relationships in △ABC that are correct.
Let A={2,4,6} and B={135}
R={(2,2),(4,4),(6,6)} is a relation on A. Express the relation
The relation:
{x = y : x, y ε A}.
And this relation is a function.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
A={2,4,6} and B={135}
R={(2,2), (4,4), (6,6)} is a relation on A.
That means, each value of set A connects to the same point.
The relation:
{x = y : x, y ε A}
Hence, {x = y : x, y ε A}.
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The frequency of people compared to the number of monthly text messages sent and received by a class are shown in the histogram.
A histogram titled Daily Text Messages. The x-axis is labeled Number of Sent Texts and has intervals of 1 to 15, 16 to 30, 31 to 45, 46 to 60, 61 to 75, 76 to 90, and 91 to 105. The y-axis is labeled Frequency and starts at 0, with tick marks every 2 units up to 12. There is a shaded bar for 1 to 15 that stops at 1, for 31 to 45 that stops at 3, for 46 to 60 that stops at 4, for 61 to 75 that stops at 4, for 76 to 90 that stops at 5, and for 91 to 105 that stops at 8. There is no shaded bar for the 16 to 30 interval.
Which of the following best describes the shape of the data, and why?
The data is symmetric because the majority of students sent fewer than 45 text messages.
The data is symmetric because some students have phones and some do not.
The data is skewed because most text messages are replied to and cause the number to be at least twice what it was originally.
The data is bimodal because the popular number of text messages to send is between 91 and 105.
The data is symmetric because some students have phones and some do not. The correct option is B.
What does histogram mean?A histogram is a simplified representation of the distribution of numerical data. The phrase was first used by Karl Pearson at the outset.
Rectangles are used in a histogram, a type of visual representation of statistical data, to show how frequently data points occur throughout a range of subsequent numerical intervals of equal width.
In the most common sort of histogram, the independent variable and dependent variable are shown along the horizontal axis and the vertical axis, respectively.
The histogram is a frequently used graphing tool. It is used to summarize data that is measured on an interval scale, whether it be continuous or discontinuous.
It is widely applied to give the primary properties of the data distribution a practical way to be illustrated.
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Answer: B. The data is symmetric because some students have phones and some do not.
Step-by-step explanation:
Find the area of the polygon in square units.
The area of the figure is solved to be
10 square unitsWhat is the area of ta kite?The area of a kite is solved using the formula
= P * q / 2
Where
p = length of long diagonal
q = length of short diagonal
Using the figure the length can be traced to be
p = 3 - -5 = 3 + 5 = 5
q = 6 - 2 = 4
Area of the figure
= 5 * 4 / 2
= 20 / 2
= 10 square units
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What coordinates did we plot when we graphed the function y = 3x - 4?
You should have 4 answers selected.
1. (-1, -7)
2. (-1, 8)
3. (0, -4)
4. (0, 9)
5. (1, -1)
6. (2, 2)
The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
we graphed the function y = 3x - 4
now, the required coordinates are, which satisfies the graph function.
as, we get,
(-1, -7), satisfies the graph function
(0, -4) , satisfies the graph function
(1, -1), satisfies the graph function
Hence, The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4
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A company makes short-sleeved and long-sleeved T-shirts. The company checks a random sample of 60 T-shirts of each type. It finds that 4 short-sleeved shirts have problems and 1 long-sleeved shirt has problems. How many T-shirts should the company predict have problems in a shipment of 3,000 shirts of each type?
The company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.
To predict the number of T-shirts with problems in a shipment of 3,000 short-sleeved and 3,000 long-sleeved T-shirts, we can use the proportion of T-shirts with problems in the random sample as an estimate of the proportion of T-shirts with problems in the population.
For short-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 4/60 = 0.067. For long-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 1/60 = 0.017.
To estimate the number of short-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of short-sleeved T-shirts in the shipment:
Estimated number of short-sleeved T-shirts with problems = 0.067 x 3,000 = 201
Similarly, to estimate the number of long-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of long-sleeved T-shirts in the shipment:
Estimated number of long-sleeved T-shirts with problems = 0.017 x 3,000 = 51
Therefore, the company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.
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