In each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference in two population means. Are the conditions for use of a T-model met?
1. In a random sample of 100 university students, the distribution of time spent at university recreational facilities is strongly skewed to the right. [ Select ] ["Conditions met; proceed with the hypothesis test.", "Conditions not met; do not proceed with the hypothesis test."]
2. In a random sample of 50 university students (37 females and 13 males), the distribution of time spent at university recreational facilities is strongly skewed to the right for females but not strongly skewed for males. [ Select ] ["Conditions met; proceed with the hypothesis test.", "Conditions not met; do not proceed with the hypothesis test."]
3. In a study of 100 brother-sister sibling pairs at the university, the distribution of time spent at university recreational facilities for the 100 males is compared to the 100 females; both distributions are fairly normal.

The number of each type of tickets sold are;

180 adults tickets

260 students tickets

60 children tickets

Let us solve to get the solution using 3 variables.

Let c be the number of children's tickets

Let s be the number of student tickets

Let a be the number of adult tickets

We are told that the total number of tickets was 500

Thus;

a + s + c = 500   ------(1)

The number of adult tickets was 3 times the number of children's tickets. Thus;

a = 3c   ------(2)

The total cost of the tickets was $8070. Thus;

18a + 15s + 12c = 7860  ----(3)

We conclude that solving these three equations simultaneously gives us;

a = 180 adults

s = 260 students

c = 60 children

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Answer: The solution here is found by establishing a system of linear equations.

A system of equations with x unknowns can be evaluated for an exact solution if the system has x equations.

Within the question, we are asked to discover the values of two different unknowns - dimes and nickels.

Therefore, we'll need two equations to obtain an exact solution, both of these will come directly from the problem itself.

Let d represent the number of dimes Diane has and let n represent the number of nickels.

Equation 1

We know from the given information that the total number of coins (both dimes and nickels) is equal to 19.

Subsequently, we can generate the equation d + n = 19.

Equation 2

We know that the individual value of a dime is $0.10 or 0.1 dollars, therefore the total value of the dimes is equal to the individual value of a dime multiplied by the total number of dimes.

The resultant expression for the total value of the dimes is (0.1)*d

We know that the individual value of a nickel is $0.05 or 0.05 dollars, therefore the total value of the nickels is equal to the individual value of a nickel multiplied by the total number of nickels.

The resultant expression for the total value of the nickels is (0.05)*n

We know that Diane only has dimes and nickels, and the total value of all her coins must be equal to the total value of the dimes plus the total value of the nickels. This value is given within the problem to be $1.55 or 1.55 dollars.

Subsequently, our second equation within the system is (0.1)*d + (0.05)*n = 1.55.

Now, we can solve the system of equations using whichever means is most convenient. For this example, I will solve the system by substitution

First, solve for one of the variables —> Equation 1 —> d + n = 19 —> d = 19 - n

Second, substitute the value of d into Equation 2 —> (0.1)*(19 - n) + (0.05)*n = 1.55

Recall that 0.1 = 1/10 and 0.05 = 1/20

Equation 2 —> (1/10)*19 - (1/10)*n + (1/20)*n = (31/20) —> (19/10) - (n/10) + (n/20) = (31/20)

Find the least common denominator of all fractions in the equation (20 in this case), convert the fractions to have like denominators, and solve.

(19/10)*(2/2) - (n/10)*(2/2) + (n/20) = (31/20) —> (38/20) - (2n/20) + (n/20) = (31/20) —> (38/20) - (n/20) = (31/20) —> (n/20) =(38/20) - (31/20) =(7/20) —>n = 7

Substitute solution into Equation 1 to solve for d

d + 7 = 19 —> d = 12

q+4+q + 10q+40 + 25q = 155

37q + 44 = 155

37q = 111

q = 3 (# of quarters)

d = q+4 = 7 (# of dimes)

p = d+q = 7+3 = 10 (# of pennies)

Step-by-step explanation:

a) The value in four years is 2,207,626

b) The growth rate percent is 102.5 %

c) It would attain the value in 11 years.

We know that a function has to do with a mathematical rule that is used for the establishment of a fact. We have from the question that the function that models the car is; V = 2000000(1.025)^n

Let us recall that n has to do with the number of years.

a) In four years, the value of the car would be;

V = 2000000(1.025)^4

V = 2,207,626

b) The growth rate percent of the function can  be obtained as;

1.025 * 100 = 102.5 %

c) To obtain the year in which the value of the car would reach 2624173.32, we have;

2624173.32 = 2000000(1.025)^n

2624173.32/2000000 = (1.025)^n

1.312 = (1.025)^n

ln1.312 = n ln (1.025)

n = ln1.312 /ln (1.025)

n = 0.272/0.025

n = 11

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The appropriate hypothesis test results that it reject the null hypothesis and accept the alternative hypothesis. The z score of -7.26 is in the rejection area

How to calculate hypothesis test?

The general form to calculate the hypothesis is by using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic.

Here the hypothesis test for the population mean μ, we use the t-statistic t = x  − (μ*s) / n

where the t-distribution with n - 1 degrees of freedom.

Here we have given that suppose that a particular NFL team claims that the mean weight of their defensive players is 315 pounds.

And we need to find  appropriate hypothesis test and make conclusions at significance level 0.08 and here we have to assume weights are normally distributed.

While we looking into the given question, we have identified that weights are normally distributed.

Then the value of the given data are written as

data = 315 ,

n= 15 ,

Mean = 300,

standard deviation = 8,

Significance level= 0.08

Then the hypothesis is written as,

The critical value (cutoff point) is 1.761.

Where in left-tail hypothesis testing, any z score less than the critical value will be rejected. Since -7.26 is less than 1.761, we reject the null hypothesis. We accept the alternative hypothesis

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Answer:

y=x/4 - 2

Step-by-step explanation:

First, find the slope:

m=(y2-y1)/(x2-x1)  ==> slope formula where m=slope

(x1, y1), (x2, y2) ==> (x1=-4, y1=-3) and (x2=4, y2=-1)

Now plug in known values back into the slope formula:

m=(-1-(-3))/(4-(-4))

m=(-1+3)/(4+4)

m=2/8  ==> simplify

m=1/4

y=mx+b  ==> slope-intercept equaiton form

-1=(1/4)(4)+b  ==> plug in the slope, m=1/4, and a known coordinate: (4,-1)

-1=1+b  ==> simplify

-1-1=1-1+b  ==> solve for b

b=-2

y=(1/4)x+(-2)  ==> plug in b=-2 and m=1/4 back into y=mx+b

y=x/4 - 2

Answer:

Therefore, the correct solution graph for the inequality is a line with no solution. This means that there is no value of x that satisfies both inequalities at the same time.

Step-by-step explanation:

To solve this inequality, we need to consider the two separate cases of 7x+2≥30 and 2x-3≤-11 separately.For the first case, 7x+2≥30, we can rewrite the inequality as 7x≥28, which simplifies to x≥4. This means that the solution for this inequality is x≥4.For the second case, 2x-3≤-11, we can rewrite the inequality as 2x≤-8, which simplifies to x≤-4. This means that the solution for this inequality is x≤-4.To find the combined solution for both inequalities, we need to take the intersection of these two solutions. The intersection of x≥4 and x≤-4 is the empty set, which means that there is no solution that satisfies both inequalities

To get the equation which combines with the graphed equation to create a system of equations whose solution set is comprised of the points (−1,−5) and (3,3) we need to plug the points into each equation choice.

Therefore , this is the first step to solve this equation.

The equations of degree 1 are known as linear equations.

These are the equations which are defined for a straight line in a coordinate system.

A linear equation is one that describes a straight line. The general form of a linear equation is  y= mx + b, where m denotes the slope and b its y-intercept.

Note:

The complete question is ,

A linear equation is graphed to the left. Which of the following equations combines with the graphed equation to create a system of equations whose solution set is comprised of the points (−1,−5) and (3,3)?

WHAT IS THE FIRST STEP IN SOLVING THIS PROBLEM?

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Both lines are not connecting each other. So there is no solution. So the pair of lines, identify the system of inconsistent.

In the given question, we have to check the following pair of lines, Identify the system by type.

(a) consistent

(b) inconsistent

(c) equivalent

As we know that;

A system is consistent if it has at least one solution. A consistent system is dependent if there are an endless number of possible solutions. Both equations show the same line on a graph when you plot the equations.

A inconsistent system has no solution. There is no solution because the graphs of the lines do not connect, making the graphs parallel.

Even if the vertices of two graphs differ or are rearranged, we will pronounce them equivalent if they have the same edge structure.

As we can see that in the graph that both lines are not connecting each other. So there is no solution. So the pair of lines, identify the system of inconsistent.

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The slope linear relationship (1,3) and (-2,-1) is 4/3.

What is  line?

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

Find the line y=m x+b passing through (1,3),(-2,-1).

Compute the slope [tex]$(1,3),(-2,-1): \quad m=\frac{4}{3}$[/tex]

Compute the y intercept: [tex]$\quad b=\frac{5}{3}$[/tex]

Construct the line equation [tex]$\mathbf{y}=\mathbf{m} x+b$[/tex]  where [tex]$m=\frac{4}{3}$[/tex]and [tex]$b=\frac{5}{3}$[/tex]

[tex]y=\frac{4}{3} x+\frac{5}{3}$$[/tex].

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Answer:

$1,127.49

Step-by-step explanation:

Compound interest formulas

Hence, if a two-year savings account containing $1,000 pays a 9% interest rate compounded daily, it will grow to $1,127.49 at the end of two years

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Kanoi and Ale'a can weed the same garden together in 22.22 minutes

Rate of work refers to amount to of work completed at a given time

Information from the question include

Kanoi can weed a garden in 40 minutes

Kanoi's rate = 1/40 per minute

Ale'a can weed the same garden in 50 minutes

Ale'a rate = 1/50 per minute

When both are working together the rate will be

1/40 per minute + 1/50 per minute

= 9/200 per minute

The time is solved

1 / 9/200

= 200/9

= 22.2222 minutes

= 22.22 minutes to the nearest hundredth

The time it will take both of them to weed is 22.22 minute

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The marginal rate of substitution (MRS) is a measure of how much of one good an individual is willing to give up in exchange for another good. In other words, it represents the slope of the indifference curve at a given point.

If Victoria's indifference curves are bowed outward, it means that as she moves from right to left along the horizontal axis, the MRS will decrease. This is because as she consumes more of one good, she becomes less willing to give up units of the other good in exchange. The MRS will continue to decrease until it reaches its minimum value at the point where the indifference curve is tangent to the budget line.

It's important to note that the MRS will only decrease if Victoria's indifference curves satisfy the other three properties of indifference curves:

If Victoria's indifference curves do not satisfy these properties, it is not possible to accurately determine the behavior of her MRS as she moves from right to left along the horizontal axis.

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Two line segments are said to be congruent if, regardless of their orientation or position, their lengths are the same.

If the matching sides and angles of two triangles are the same length, then the triangles are said to be congruent.

Two sides that are the same length make up an isosceles triangle .In addition, it contains two equal-sized angles located across from the two sides of equal length. A triangle with three identical sides is called an equilateral triangle.

So

According to the given information

Segment AD = Segment BC

Two line segments are said to be congruent if, regardless of their orientation or position, their lengths are the same.

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Based on the rating system and the summarize() and mean() functions, the code chunk to add is summarize(mean(Rating)) and the mean rating is 3.185933.

To determine the mean value for the variable Rating, you must add the code chunk summarize(mean(Rating)). Trimmed flavors df%>% summarize(mean(Rating)) is the right code. In this section of the code:

You can display summary statistics using the summarize() method. To generate specific statistics, you can combine the summarize() method with others like mean(), sd(), and max().

In this instance, you compute the mean value for the variable Rating using the mean() function.

The average score is 3.185933.

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The value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

-5x - 10y = 30 and - 3x + 3y = 27

Solve by using the elimination method,

Divide the equation - 3x + 3y = 27 by 3 and equation -5x - 10y = 30 by 5 on both sides,

(- 3x + 3y) / 3 = 27 / 3  and (-5x - 10y) / 5 = 30 / 5

-x + y = 9  and -x - 2y = 6

Subtract equation

-x + y = 9 - (-x - 2y = 6)

-x + y - 9 = x - 2y - 6

y = 3

and - x + 3 = 9, x = -6

Therefore, the value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.

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Answer:

  3x +3

Step-by-step explanation:

You want to simplify 2x+ (9+x) -6.

Like terms have the same constellation of variables. Here, there are terms containing x, and terms not containing x.

  2x+ (9+x) -6 = (2 +1)x +(9 -6) = 3x +3

The simplified expression is 3x +3.

Answer:3x+3

Step-by-step explanation:

First we remove the parenthesis because they are not needed in an addition problem to make it 2x+9+x-6

Then we sort and combine like terms, [2x+x]+[9-6]

After that, you add the coefficients of the the first term, which makes 3x and subtract 6 from 9 to get 3

This then leads you to 3x+3

the dimensions of a rectangle with area 64000 m2 whose perimeter is as small as possible. (give your answers in increasing order, to the nearest meter.)Length: 200 m and Width: 320 m

The area of a rectangle is given by the formula A = lw, where l is the length and w is the width. To find the dimensions of a rectangle with an area of 64000 m2 and a perimeter that is as small as possible, we can use the formula P = 2l + 2w. We can use this to create an equation with the area and solve for l and w: 64000 = lw, and 2l + 2w = P (min). Solving for l and w, we get l = 200 m and w = 320 m. Thus, the dimensions of the rectangle with an area of 64000 m2 and a perimeter that is as small as possible are 200 m by 320 m.

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The minimum usual value, μ-2σ is 17.8 and the maximum usual value, μ+2σ is 54.04

From the information, n = 108, p = 0.24

minimum usual value μ-2σ

maximum usual value μ+2σ

Find the mean, μ:

μ = np = 108 × 0.24 = 35.92

Find the variance, n(1-p):

n(1-p) = 108 ×( 1-0.24) = 82.08

Find the standard deviation, σ:

σ  = √82.08 = 9.06

minimum usual value, μ-2σ:

μ-2σ = 35.92 - (2×9.06) = 17.8

maximum usual value, μ+2σ:

μ+2σ = 35.92 + (2×9.06) = 54.04

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The range of the data set are

{10.2, 3.8, 21.9, 33.4, 31.8, 17.2} = 29.6

{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71} = 0.6

{6, 2, 14, 11, 28, 10, 19, 15, 11} = 26

The first data set is

{10.2, 3.8, 21.9, 33.4, 31.8, 17.2}

The range is the difference between the highest value and the smallest value

The highest value = 33.4

Lowest value = 3.8

The range = 33.4 - 3.8

= 29.6

The second data set is

{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71}

The highest value = 0.71

Lowest value = 0.11

The range = 0.71 - 0.11

= 0.6

The third data set is

{6, 2, 14, 11, 28, 10, 19, 15, 11}

Highest value = 28

Lowest value = 2

The range = 28 - 2

= 26

Therefore, the range of the each data set has been found

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Answer:

200

Step-by-step explanation:

The sum is 182.5, which is 200 to 1 significant figure.

The fraction of the book chung read on the second day is 17/40 and No, he didn't finish the book in two days

fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. In proper fractions the denominator is greater than the numerator but in improper, the denominator is lesser than the numerator.

Chung read 5/8 of a book

let's represents the volume pages of the book by x

therefore chung read 5/8 × x = 5x/8

on the second day, he read 1/5 less of the previous day = 5x/8-1/5x = 17x/40 i.e he read 17/40 of the book on the second day

the volume of pages left = x - (17×/40+5×/8)

x-22x/40

the fraction of remaining page left = (40-22)x/40

= 28x/40

divide through by 4

7/10 of x

therefore 7/10 of the book is still left to be read. This means chung didn't finish reading the book on the second day.

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Answer:

  (x, y) = (17, 10)

Step-by-step explanation:

You want the values of x and y given three angles written in terms of x and y at a transversal crossing parallel lines.

Angles at lower right of the points of intersection are corresponding angles, and are congruent:

  (9x -16)° = (8x +1)°

  x = 17 . . . . . . . . . . . . . divide by °, add 16-8x

The marked angles at the bottom form a linear pair, so are supplementary.

  (4y +3)° = 180° -(9x -16)°

  4y +3 = 180 -9(17) +16 = 43 . . . . . . use 17 for x and simplify

  4y = 40 . . . . . . subtract 3

  y = 10 . . . . . . divide by 4

Answer:

Your Answer is A.

Step-by-step explanation:

First look at the inequality graph.

We can note that its a variable is greater than 2. (p >2)

Then looking at our options.

Option A can be.

Option B can't be it since its greater than or equal to.

Option C can be.

Option D can't be since dividing or multiplying by a negative switches the signs greater than to less than or vice versa.

Leaving only option A or C.

Solve A and C.

5p + 4 > 14

5p > 10

p > 2

5p - 4 > 14

5p > 18

p > 18/5

The Cost make up of procedure 1 is $280000.

Cost make up of procedure 2 is 140000

The cost makeup will be calculated thus:

Cost make up of procedure 1

Labour (40%) 112000

Materials (45%) 126000

Overhead (15%) 42000

Total =[280000

Cost make up of procedure 2

Labour ( 60%) 84000

Materials (30%) 42000

Over head (10%) 14000

Total 140000

Working note:

Sales $600000

Less: Gross profit (sale *30%) $ 180000

COGS $420000

Procedure 1 ( COGS *2/3) $ 280000

Procedure 2 (COGS * 1/3) $ 140000

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Complete question

Blue Skies Inc. is a retail gardening company that is piloting a new strategic initiative aimed at increasing gross profit. Currently, the company’s gross profit is 25% of sales, and its target gross profit percentage is 30%. The company’s current monthly sales revenue is $600,000. The new initiative being piloted is to produce goods in-house instead of buying them from wholesale suppliers. Its in-house production process has two procedures. The makeup of the costs of production for Procedure 1 is 40% direct labor, 45% direct materials, and 15% overhead. The makeup of the costs of production for Procedure 2 is 60% direct labor, 30% direct materials, and 10% overhead. Assume that Procedure 1 costs twice as much as Procedure 2.

Determine what the cost of labor, materials, and overhead for both Procedures 1 and 2 would need to be for the company to meet its target gross profit.

Answer:

Step-by-step explanation:

We have two types of textbooks. Let's use "x" to represent the number of math textbooks and "y" to represent the number of history textbooks.

Altogether, the bookseller sold 240 math and history textbooks. So:

x + y = 240

Now, the number of history textbooks sold was 72 less than the number of math books sold. So:

y = x - 72

Now we can substitute for y in the equation and solve:

x + y = 240

x + (x - 72) = 240

2x - 72 = 240

2x = 312

x = 156

The bookseller sold 156 math textbooks.

Since y = x - 72, he must have sold 84 history textbooks.

Let's check our answers:

x + y = 240

156 + 84 = 240

That is true, so we did get the correct answers

Answer:

So the payoff balance of the car loan after 4 years will be approximately $22,169.73.

Step-by-step explanation:

payoff balance after 4 years can be calculated using the following formula:

Payoff balance = Principal * (1 + APR/n)^(nt) - [(Principal * (1 + APR/n)^(nt) * (APR/n)) / (1 + APR/n - 1)]
Where:
Principal is the loan amount, which is $28,550 in this case.
APR is the annual percentage rate, which is 8% in this case.n is the number of times per year that interest is compounded, which is usually 12 for monthly compounding.t is the number of years for which the loan is taken, which is 4 years in this case.
Plugging in the values, we get:
Payoff balance = $28,550 * (1 + 0.08/12)^(124) - [($28,550 * (1 + 0.08/12)^(124) * (0.08/12)) / (1 + 0.08/12 - 1)]
Payoff balance = $28,550 * 1.006669^48 - [$28,550 * 1.006669^48 * 0.006669] / 0.006669Payoff balance = $22,169.73

Answer: 5.08333 repeating three