The amount of money an account with simple interest at an annual rate of 4.2% would be $3738 after 1 month and 7476 dollar after 2 month.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.
Simple Interest = (Principal × Rate × Time) / 100
Given that loan Amy is 89000 monthly payment is 479.66 rate is 4.2
Amount = $89000
Rate = 4.2 %
Time = 1 month
Therefore, Simple Interest = (Principal × Rate × Time) / 100
Simple Interest = 89000 × 4.2% × 1
Simple Interest = 3738
Also,
Simple Interest = 89000 × 4.2% × 2
Simple Interest = 7476
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For linear function f, f(2)=0 and f(4)=-6.
Write function f in slope-intercept form.
Hint
Examples:
f(5)=0 means (5,0) is a point on the line.
f(3)=-2 means (3,-2) is a point on the line.
How do you find the slope of the line when you have 2 points?
Answer:
f(x) = -3x + 6
Step-by-step explanation:
f(2)=0 point (2, 0)
f(4)=-6 point (4, -6)
m = slope = (y_2 - y_1)/(x_2 - x_1)
m = (-6 - 0)/(4 - 2) = -6/2 = -3
y = mx + b
y = -3 x + b
0 = -3 × 2 + b
0 = -6 + b
b = 6
y = -3x + 6
f(x) = -3x + 6
Which ordered pair is a solution of the equation
y = 7x-2
What is a equation in math?
Image result for What is equation?
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
What is a equation in math?
An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
given:
y=7x-2
first, (3, 15)
15 = 7*3-2 = 21-2 = 19
So, (3, 15) is not the solution.
Second, (-1,-10)
-10 = 7* (-1) -2
-10 = -9
Also, (-1,-10) is not the solution.
Hence, there is no solution for y=7x-2
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Please help will mark Brainly
One glass of milk and one snacks bar have a total of 23 carbs.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Two glass of milk and Three snacks bar have a total of 56 carbs.
And, Four glass of milk and two snacks bar have a total of 72 carbs.
Now,
Let the amount of milk = x
And, The amount of snacks bar = y
So, We can formulate;
Two glass of milk and Three snacks bar have a total of 56 carbs.
⇒ 2x + 3y = 56 ..(i)
And, Four glass of milk and two snacks bar have a total of 72 carbs.
⇒ 4x + 2y = 72
⇒ 2x + y = 36
⇒ y = 36 - 2x ..(ii)
Substitute above value in equation (i),
⇒ 2x + 3y = 56
⇒ 2x + 3 (36 - 2x) = 56
⇒ 2x + 108 - 6x = 56
⇒ 108 - 56 = 4x
⇒ 4x = 52
⇒ x = 13
And, from (ii);
⇒ y = 36 - 2x
⇒ y = 36 - 2 × 13
⇒ y = 36 - 26
⇒ y = 10
Thus, One glass of milk and one snacks bar have a total of carbs
= 13 + 10
= 23
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classify the following as discrete or continuous metric: i. the number of automobile accidents per year in virginia. ii. the length of time to play 18 holes of golf. iii. the amount of milk produced yearly by a particular cow. iv. the number of eggs laid each month by a hen. v. the number of building permits issued each month in a certain city. vi. the weight of grain produced per acre.
From the given i) and v) are discrete metric and ii), iii), iv) and vi) are continuous metric.
What distinguishes discrete from continuous data?
Two categories of quantitative variables are discrete and continuous: Discrete variables are count-based (e.g. the number of objects in a collection). Measurable amounts are represented by continuous variables (e.g. water volume or weight).i) 'X' : is discrete because Number of automobile accidents per year is countable (45, 78, 90) and cannot be fraction (4.5)
ii) 'Y' : is continuous because it could take any time to play 18 holes of golf. (15.10 min)
iii) 'M' : is continuous because volume measured can be in fraction. Like 15.6 liters of milk produced by a cow
iv) 'N' : is discrete because eggs are countable . no half eggs or broken eggs are counted. example: 30 eggs per month by a hen.
v) 'P' : is discrete because permits issued are in countable amount and cannot go beyond or like half permit.
vi) 'Q': is continuous because weight can be less or more and can be in fraction. 20 AND HALF OR 56,6 Kg.
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Which expressions are equivalent to
5^2/5^8
If f(x) = -3x + 4, what is the value of f(-5)?
-5=-3x4
A) -4
C) 19
B) 15
D) 3
Answer:
15
Step-by-step explanation:
If f(x) = -3x + 4, then plugging in -5 for x gives f(-5) = -3(-5) + 4 = 15. Therefore, the correct answer is 15.
mayco, a mail-order department store, has five telephone lines available for customers who wish to contact customer service. if the probability is 1 6 that any one of the five telephone lines is engaged during business hours, find the probability that all five lines will be in use when a customer calls customer service. (round your answer to four decimal places.)
Answer:
The probability that all five lines will be in use when a customer calls customer service is 1/7776.
What is probability?
The proportion of favorable cases to all possible situations that can occur indicates how likely an event is to occur.
Step-by-step explanation:
Given that there are 5 lines and the probability for each line to be engaged in working hours is 1/6.
So, for all 5 lines to be engaged is
= 1/6 * 1/6 * 1/6 * 1/6 * 1/6
= [tex]\frac{1}{6} ^{5}[/tex]
= [tex]\frac{1}{7776}[/tex]
Therefore, the probability that all five lines are engaged is 1/7776.
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X’(t) = [-4 0 0 0 8 -3 4 0 1 0 -5 0 2 1 4 -1 ] X(t)X0 = [ 1234]1. (67 points) Use Theorem 1 on page 350 to solve the above system of differential equations (see section 5.6 video).2. (33points) Use your solution to show that your solution solves the original system of differential equations
To solve the system of differential equations using Theorem 1, we first need to find the eigen values and eigen vectors of the matrix X'.
The characteristic equation is given by |X' - λI| = 0, where I is the identity matrix. Solving this equation, we find the eigenvalues to be λ = -2, 0, 3, 5.
Next, we need to find the corresponding eigenvectors. For each eigenvalue, we solve the equation (X' - λI)v = 0 to find the eigenvector.
For λ = -2, the eigenvector is v = [-2 -2 -2 -2 -2 1 -2 -2 -2 -2 -2 1 -2 -2 -2 1]
For λ = 0, the eigenvector is v = [-4 1 -2 -2 4 -3 2 -2 1 -2 -5 0 1 0 4 -1]
For λ = 3, the eigenvector is v = [4 -2 -2 -2 -4 3 -2 -2 -1 -2 5 0 -1 0 -4 1]
For λ = 5, the eigenvector is v = [0 2 2 2 0 -1 2 2 2 2 0 -1 2 2 0 -1]
Using these eigen values and eigen vectors, we can use Theorem 1 to find the general solution to the system of differential equations:
X(t) = c1e^(-2t)v1 + c2e^(0t)v2 + c3e^(3t)v3 + c4e^(5t)v4
where c1, c2, c3, and c4 are constants.
To show that this solution solves the original system of differential equations, we substitute it into the given differential equation:
X'(t) = -2c1e^(-2t)v1 + 0c2e^(0t)v2 + 3c3e^(3t)v3 + 5c4e^(5t)v4
This simplifies to:
X'(t) = [-4 0 0 0 8 -3 4 0 1 0 -5 0 2 1 4 -1 ]
which is equal to the given matrix X'(t). Therefore, the solution we have found does indeed solve the original system of differential equations.
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6 gallon of lemonade. how much is this in pints?
Answer:
Step-by-step explanation:
7 49999977/50000000 is gallons to pints. multiply that number by 6, which is 47 24999931/25000000.
two machines fill 32-oz cartons with cereal. the quality control manager believes the two machines are not filling the cartons with the same amount of cereal. samples from each line were taken and the following results were obtained. assume that the assumptions and conditions for inference with a two- sample t-test are met. at the 0.01 level of significance, test the claim that the population mean for machine 1 is different from the population mean for machine 2.
The conclusion hypothesis is to reject the null hypothesis and accept the alternative hypothesis. The z score of 0.14 is in the rejection area
What is hypothesis?
In statistics, hypothesis refers a testable statement about the relationship between two or more variables or a proposed variable.
Here we have given that two machines fill 32-oz cartons with cereal. the quality control manager believes the two machines are not filling the cartons with the same amount of cereal. samples from each line were taken and the following results were obtained. assume that the assumptions and conditions for inference with a two- sample t-test are met. at the 0.01 level of significance, test the claim that the population mean for machine 1 is different from the population mean for machine 2.
And we need to find the conclusion hypothesis.
While we looking into the given question, we have identified the following values,
Sample mean: Machine 1 25 31.8 oz 2.2 oz
Sample SD: Machine 2 36 30.9 OZ 1.98 oz
So, the hypothesis is calculated as, the claim is the population mean of cereal cartons from machine 1 is larger than that from the machine 2
Null hypothesis: H0 : The population mean of cereal cartons for machine 1 and machine 2 is same
Alternative hypothesis H1: The population defines the statistical inference experiment.
So, the conclusion of hypothesis is, the critical value (cutoff point) is 2.353. In left-tail hypothesis testing, any z score less than the critical value will be rejected. Since 0.14 is less than 2.353, we reject the null hypothesis. We accept the alternative hypothesis.
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After spending many hours studying for your math class (I am being hopeful here!) you decide to reward yourself with a case of soda. Unfortunately the store only had a warm case left (the Kent students got there first and got all of the cold ones). You buy several bags of ice and decide to chill it at home. When you get home the temperature of the soda is 76 degrees F and you proceed to pack it in ice. After ten minutes the temperature has cooled to 70 degrees F. If the soda is best served at 60 degrees F or cooler, how much longer must you wait to enjoy your soda? Note that you have not been given the temperature of the surroundings, but you should be able to figure out what that should be (you are packing it in ice that is at the freezing point of water so...).
the difference between the two temperatures as 16 degrees F. You must wait for another 6 minutes for the soda to cool down to 60 degrees F.
Since the initial temperature of the soda is 76 degrees F and the desired temperature is 60 degrees F, we can calculate the difference between the two temperatures as 16 degrees F. We also know that the temperature of the ice is at the freezing point of water which is 32 degrees F. This means that the temperature difference between the soda and the ice is 44 degrees F. Since the temperature difference between the soda and the ice is greater than the temperature difference between the desired temperature and the initial temperature, we can divide the desired temperature difference (16 degrees F) by the temperature difference between the soda and the ice (44 degrees F) and multiply it by the time elapsed (10 minutes) to calculate the remaining time needed for the soda to cool down to the desired temperature. 16/44 * 10 = 6. Therefore, we must wait for another 6 minutes for the soda to cool down to 60 degrees F.
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The revenue for a business, as a function of units produced, x, is shown below
by R(x). C(x) represents the cost of producing x units. Calculate the profit
function and then determine how many units must be produced for the
business to break even.
Answer:
R(x) = 16x
C(x) = 3x + 741
Submit Answer
The revenue function
The cost function.
attempt 1 out of 2
If the profit function is P(x) = 13x - 741 then the units that must be produced to break even is 57 units.
What is a profit function?
The difference between income and costs is referred to as profit. A relationship that depicts the difference created by subtracting the cost function from the revenue function is called a profit function. The ideal pairing of revenues and expenses to generate the greatest possible profit can be seen on the graph of a profit function.
Here, we have
Given
R(x) = 16x (The revenue function)
C(x) = 3x + 741 (The cost function)
Profit = Revenue - Cost
P(x) = 16x - 3x - 741
P(x) = 13x - 741
Hence, the profit function P(x) is 13x - 741.
For the company to break even, R(x) = C(x)
16x = 3x + 741
13x = 741
x = 57
Hence, if the profit function is P(x) = 13x - 741 then the units that must be produced to break even is 57 units.
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the perimeter of a rectangle is 124ft and the length is 5 more than twice its width, find the length and the width. note: p
Answer:
length = 43 ft ; width = 19 ft
Step-by-step explanation:
perimeter/2 = 124/2 = 62 ft
l = 2w + 5
l + w = 62
2w+5 + w = 62
3w = 62 - 5
3w = 57
w = 57/3
w = 19 ft
l = 2 · 19 + 5
l = 38 + 5
l = 43 ft
Consider this conditional statement.
If a person is a professional athlete, then the person is a professional hockey player.
(a) Give the contrapositive of the statement.
If (Choose one)
then (Choose one)
(b) Give the converse of the statement.
If (Choose one)
then (Choose one)
(c) Give the inverse of the statement.
If (Choose one)
then (Choose one)
If a person is a professional athlete, then the person is a professional hockey player.
Given :
( a ) Give the contrapositive of the statement.
If not the person is a professional hockey player .
then not a person is a professional athlete .
( b ) Give the converse of the statement.
If the person is a professional hockey player .
then a person is a professional athlete .
( c ) Give the inverse of the statement .
If not the person is a professional hockey player.
then not a person is a professional athlete .
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TRUE/FALSE. the generalized least squares estimators for correcting heteroskedasticity are also called weighed least squares estimators.
Therefore solution to this problem is the given statement is true .
What is weight least squares estimators?The generalization of ordinary least squares and linear regression known as weighted least squares (WLS), sometimes known as weighted linear regression, incorporates knowledge of the variance of the observations into the regression. Generalized least squares is also a specialization of WLS.
Here,
the generalized least squares estimators for correcting heteroskedasticity are also called weighed least squares estimators.
Since they are also known as weighed least squares estimators, extended least squares estimators for correcting heteroskedasticity use least squares estimation.
Therefore , the above statement is true .
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Determine the number and type of solutions for the equation
5x^2−x−3=0
-Two different irrational-number solutions
-Two imaginary-number solutions
-One repeated rational-number solution
-One repeated irrational-number solution
-Two different rational-number solutions
The equation has one repeated rational number solution. thus Option C is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given equation is the quadratic equation:
[tex]5x^2-x-3=0[/tex]
It is required to determine the number and type of solutions.
Noted that If the discriminant equals zero, the equation has one repeated rational number solution.
If the discriminant is positive, then the equation has two real solutions.
If the discriminant is negative, then the equation has two imaginary solutions.
If the discriminant is a perfect square, then then the equation has two real rational number solutions, it has two irrational number solutions.
Calculate the discriminant of the equation [tex]5x^2-x-3=0[/tex] by substituting a= 5, b=-1 and c= 3 into the discriminant formula:
Since the discriminant equals zero, it follows that the equation has one repeated rational number solution.
The equation has one repeated rational number solution.
Option C is correct.
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Which of the following is NOT one of the three main methods of inventory evaluation as described in your reading material? A. weighted average, B. straight average, C. FIFO, D. LIFO
Answer:
A or B
Step-by-step explanation:
I think it's B.. according to the people I know
It would he quite risky for you to insure the life of a 21 -year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain $\$ 1250 dollars in premiums. But if he were to die, you would lose almost \$ 100,000$. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21 -year-old men. (b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the investment. We can measure the great risk of insuring $\mathrm{u}$ single person's life in Exercise 14 by computing the standard deviation of the income $Y$ that the insurer will receive. Find or using the distribution and mean found in Exercise 14.
The standard deviation of Y can be determined which is 9708.
Given in the question that the high probability would gain in premiums. If die, would lose almost . Selling insurance is not risky for an insurance company that insures many thousands of -year-old men.
According to the information, the gain around is 1250
Amount would lost in case of death is 100000.The expected value with its probability is:
E(X) = ∑x ×P(x)
=(-99750) × 0.00183 + ...+ (1250) × 0.99058
= 303.35
The standard deviation of the investment return is used to determine the risk of an investment. The riskier the investment is, the more varied the return is
The standard deviation of Y can be determined as
α = under root {∑x2 × P(x) - (∑x × P(x) }
[tex]\sqrt{(-99750 - 303.3525)sq. X 0.00183 + .... + (1250 - 303.3525)sq. X 0.99058 }[/tex]
= 9708
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the position of a particle moving along a coordinate line is s=√(3+6t), with s in meters and t in seconds. Find the particle's velocity at t=1 sec.
The particle's velocity at time t = 1 seconds is equal to 3 meters per seconds.
What is a position vs time graph?In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled (covered) by an object from its starting position with respect to the time when it is started moving.
Generally speaking, the position of a physical object (body) in a position vs time graph is always plotted on the y-coordinate (y-axis) while time is always plotted on the x-coordinate (x-axis).
From the information provided about this particle on a position vs time graph, we have;
s =√(3 + 6t)
Where:
s in meters.t in seconds.Substituting the given parameters into the formula, we have;
s =√(3 + 6(1))
s =√(3 + 6)
s =√9
Distance, s = 3 meters.
Now, we can determine the velocity as follows;
Velocity = distance/time
Velocity = 3/1
Velocity = 3 meters per seconds.
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the accompanying data file shows the monthly closing stock price for a large technology firm for the first six months of the year.
The Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.
What is a confidence interval?
A confidence interval is a range of values that is estimated to contain the true value of a population parameter with a certain level of confidence. It is a measure of the uncertainty associated with an estimate of a population parameter, such as the mean, the proportion, or the variance.
a)
sample mean = 75.67
sample std. dev. = 3.56
b)
Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 2.015
[tex]CI = (xbar - tc * s/\sqrt{n} , xbar + tc * s/\sqrt{n})\\\\CI = (75.67 - 2.015 * 3.56/\sqrt{6} , 75.67 + 2.015 * 3.56/\sqrt{6})\\\\\CI = (72.74 , 78.60)[/tex]
Hence the Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.
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Which ordered pairs lie on the graph of the exponential function f(x)=2(x+4)−8? Select each correct answer.
(24, 1)
(−2,−4),
(2, 56)
(8, 0)
The ordered pair that lie on the graph as per the equation will be equal to (-2, -4). Hence, option B is correct.
What is a graph?In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
As per the given information in the question,
The given equation is,
f(x) = 2(x + 4) - 8
Let's check as per the points given in the question,
A. (24, 1)
f(x) = 2(24 + 4) - 8
f(x) = 48
So, the supplied exponential function's graph does not contain the point (24, 1) mentioned.
B. (-2, -4)
f(x) = 2(-2 + 4) - 8
f(x) = 4 - 8
f(x) = -4
As a result, the points (-2, -4) are located on the graph of the supplied exponential function.
C. (2, 256)
f(x) = 2(2 + 4) - 8
f(x) = 4
So, the supplied exponential function's graph does not contain the point (2, 56) mentioned.
D. (8, 0)
f(x) = 2(8 + 4) - 8
f(x) = 16
So, the supplied exponential function's graph does not contain the point (8, 0) mentioned.
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a Goalie's saves (.) and goals scored against ( x) are shown
what percent of shots did the goalie save
The goalie saved 70% of the shots.
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
Given that, a Goalie's saves (•) and goals scored against (x)
The number of save shot = 14
The number of goals scored against = 6
The total numbers of shots = 20
A goalie's safe percentage is calculated by dividing the number of saves by the total number of shots on goal = 14/20x100 = 70%
Hence, The goalie saved 70% of the shots.
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Mario's current credit card balance is $2,673.19 with a minimum payment of $102.00. Over the next month, he plans to spend $626.00. If the APR is 26.99%, what will Mario's new balance be, including
interest? (2 points)
$3,201.98
$3,269.10
$3,197.19
$3,394.68
If the APR on Mario's credit card is 26.99%, Mario's new balance, including interest will be B. $3,269.10.
What is the APR?Annual percentage rate (APR) is the annual finance charge applied to a credit balance.
The APR includes interest and other fees for borrowing credit.
Current credit card balance = $2,673.19
Minimum payment within the month = (102.00)
Purchase payments 626.00
Finance Charge $71.91 ($3,197.19 x 26.99% x 1/12)
Ending credit card balance = $3,269.10 ($3,197.19 + $71.91)
Annual percentage rate = 26.99%
Monthly percentage rate = 2.25% (26.99% ÷ 12)
Thus, Mario will end up with a credit card balance of $3,269.10 after one month with APR of 26.99%.
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What is the distance
between -42 and 65 on
the number line?
Answer: 23
Step-by-step explanation:
-42+65
or 65-42
= 23
What would:
2x + -2y = ?
Make?
Answer:
[tex]y=x[/tex]
Step-by-step explanation:
[tex]2(-y+x)=0\\\\-y+x=0\\\\-y=-x\\\\y=x[/tex]
What is the range of the set of ordered points defined below?
{(–1 , 3), (2 , 3), (4 , 5)}
Answer:
Rang is the output values or the y values.
3 and 5
Step-by-step explanation:
An ordered pair is in the form (x, y) The x is the input or the domain and the y is the output or the range.
Which linear function has the greatest initial value? Which has the greatest rate of change? Use the drop-down menus to show your answer.
The linear function that has greatest initial value is function C
The linear function that has greatest rate of change is function B
Consider the function A
The y intercept = 0
Consider two points (2, 5) and (4, 10)
The slope of the line = (10-5) / 4-2
= 5 /2
The equation will be
y = 5/2x + 0
Consider the function B
y = 3x - 1
Which is in the form of slope intercept form
The slope of the line = 3
The y intercept = -1
Consider the function C
y intercept = 2
Consider the points (0, 2) and (3, 3)
The slope of the function = 3-2 / 3 -0
= 1/3
The equation is
y = 1/3x + 2
Therefore, function C has greatest initial value and function B has greatest rate of change
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the product of 3 and a number is twice 23
△
△
ABC has vertices A(1, 3), B(2, 5), and C(5, 3). What are the coordinates of B′ after the transformation (x, y) ⟶ (–y, x), then translation 1 unit right and 4 units up?
Answer: we first need to apply the transformation to the x- and y-coordinates of the point individually
Step-by-step explanation:
To transform the coordinates of a point (x, y) using the transformation (x, y) ⟶ (–y, x), we first need to apply the transformation to the x- and y-coordinates of the point individually. This means that the x-coordinate becomes –y and the y-coordinate becomes x.
In the case of point B, the original coordinates are (2, 5), so the transformed coordinates are (–5, 2). This means that the x-coordinate becomes –5 and the y-coordinate becomes 2.
Next, we need to apply the translation that moves the point 1 unit right and 4 units up. To do this, we simply add 1 to the x-coordinate and add 4 to the y-coordinate. After this translation, the coordinates of B′ become (–4, 6). Therefore, the final coordinates of B′ are (–4, 6).
the following data represent the running times of films produced by two motion-picture companies. company time (minutes) i 103 94 110 87 98 ii 97 82 123 92 175 88 118 compute a 90% confidence interval for the difference between the average running times of films produced by the two companies. assume that the running-time differences are approximately normally distributed with unequal variances
The 90% confidence interval for the difference between the average running times of films produced by the two companies ≅ (- 35.5 , 10.8)
Given that:
Company (i) :
[tex]n_{1}[/tex] = 5 , [tex]x_{1}[/tex]bar = 98.4
[tex]S_{1} ^{2}[/tex] = [tex]\frac{1 }{n_{1} - 1}[/tex] ∑ [tex](x_{i} - x_{1} bar)^{2}[/tex]
= [tex]\frac{1}{5 - 1}[/tex] [ [tex](103 - 98.4)^{2}[/tex] + [tex](94 -98.4)^{2}[/tex]+........+ [tex](98 - 98.4)^{2}[/tex] ]
= [tex]\frac{1}{4}[/tex] [ [tex](4.6)^{2}[/tex] + [tex](-4.4)^{2}[/tex]+..........+[tex](0.4)^{2}[/tex] ]
= [tex]\frac{1}{4}[/tex] [ 305.2]
= 76.3
Company (ii) :
[tex]n_{2}[/tex] = 7 , [tex]x_{2}[/tex] bar = 110.7143
[tex]S_{2} ^{2}[/tex] = [tex]\frac{1 }{n_{2} - 1}[/tex] ∑ [tex](xi - x_{2} bar)^{2}[/tex]
= [tex]\frac{1}{7-1}[/tex] [ [tex](97 - 110.7143)^{2}[/tex]+ [tex](82-110.7143)^{2}[/tex]+.........+[tex](118 - 110.7143)^{2}[/tex] ]
= [tex]\frac{1}{6}[/tex] [ [tex](-13.7143)^{2}[/tex]+ [tex](-28.7143)^{2}[/tex]+.........+[tex](7.2857)^{2}[/tex] ]
= [tex]\frac{1}{6}[/tex] [ 6125.4274]
≅ 1035.9045
For 90% confidence interval
difference between = 5+7-2 = 10, critical value is [tex]t_{c}[/tex] = 1.812.
90% confidence interval for the difference between the average running times is
[ ([tex]x_{1}[/tex] bar - [tex]x_{2}[/tex] bar) ± [tex]t_{c}[/tex] . [tex]\sqrt{\frac{S_{1}^2 }{n_{1} } } + \sqrt{\frac{S_{2}^2 }{n_{2} }}[/tex] ]
= [(98.4 - 110.7143) ± 1.812 [tex]\sqrt{\frac{76.3}{5} } + \sqrt{\frac{1035.90457}{7} }[/tex] ]
= [-12.3143 ± 23.1515]
= (- 35.4658 , 10.8372)
≅ (-35.5 , 10.8)
Therefore, 90% confidence interval for the difference between the average running times of films produced by the two companies is
≅ (- 35.5 , 10.8)
To learn more about confidence interval check the given link
brainly.com/question/27630001
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