In a recent court case it was found that during a period of 11 years people were selected for grand jury duty and ​% of them were from the same ethnicity. Among the people eligible for grand jury​ duty, ​% were of this ethnicity. Use a significance level to test the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, p-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ p-value method and the normal distribution as an approximation to the binomial distribution.

The time taken to label 750 books if Clare labels books at 15 books per minute is 50 minutes.

In this situation, Clare volunteers at a library during the summer and has to label 750 books and she labels books at 15 books per minute and she takes no breaks.

Let the time taken to label the 750 books be represented by x.

This will be illustrated as:

1/x = 15/750

Cross multiply

(15 × x) = (750 × 1)

15x = 750

Divide

x = 750 / 15

x = 50

The time is 50 minutes.

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Complete question

Clare volunteers at a library during the summer and has to label 750 books. Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.

In accordance with algebra properties and relationship between logarithms and powers, the logarithm ㏒ₐ (108 / a³) is equal to the pseudolinear expression 2 · b + 3 · c - 3.

In this problem we must determine the base of a given set of logarithms by using algebra properties and relationships between powers and logarithms. Now we proceed to solve:

Step 1 - We get the following equations:

㏒ₐ 2 = b, ㏒ₐ 3 = c  

Step 2 - Now we add the other logarithm:

㏒ₐ (108 / a³)

Step 3 - By logarithm properties:

㏒ₐ 108 - ㏒ₐ a³

㏒ₐ (2² · 3³) - 3 · ㏒ₐ a

㏒ₐ 2² + ㏒ₐ 3³ - 3 · 1

2 · ㏒ₐ 2 + 3 · ㏒ₐ 3 - 3

Step 4 - By Step 1:

2 · b + 3 · c - 3

The logarithm ㏒ₐ (108 / a³) is equivalent to 2 · b + 3 · c - 3.

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Answer:

Here,

2x+3x=20x

or,5x=20x

or,5x-20x=0

or,15x=0(divide both sides by -15)

hence,x=0

The distance from the origin to point P graphed on the complex plane is d = [tex]\sqrt{29}[/tex]

Given,

In the question;

From the figure,

To find the distance from the origin to point P graphed on the complex plane .

Now, According to the question:

To see the graph,

The point P lie on the x- axis and y - axis .

x = 2 and y = -5

We know the formula of distance,

Distance (d) = [tex]\sqrt{x^{2} +y^2}[/tex]

d = [tex]\sqrt{2^2 + (-5)^2}[/tex]

d = [tex]\sqrt{4 + 25}[/tex]

d = [tex]\sqrt{29}[/tex]

Hence, The distance from the origin to point P graphed on the complex plane is d = [tex]\sqrt{29}[/tex]

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Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Divide the top and bottom on the fraction by 4

2x^2+6x

2(-5)^2+6(-5)

2(25)+6(-5)

50+6(-5)

50+(-30)

50-30

20

The train's speed was= 56.7 miles per hour

acc to our question-

Hence, The train's speed was= 56.7 miles per hour

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Answer:

Step-by-step explanation:

The correct statements are,

(1) The equation 2n = p should be 2p = n.

(2) The actual cost of the onions is $3.00 per pound.

(3) Potatoes cost $1.50 per pound.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mr. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes.

The equation will be formed as,

6p + 3n = 18

n = 2p

Substitute the value of n = 2p in the equation,

6p + 3(2p) = 18

6p + 6p = 18

12p = 18

p = $1.5

The cost of an onion is,

n = 2p

n = 1.5 x 2

n = $3

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If its a 28 day month then 671088640

29 days 1342177280

30 days 2684354560

and 31 days 5368709120

The current age of Jenny is 6 years.

Let the current age of Phil be = x years

So the current age of Bill is = 2x years

The current age of Jenny is = 2x-2 years

Sum of their ages is = x+2x+2x-2 = 5x-2 years

Now the age of their dad is = 2(5x-2) = 10x-4 years

Now after nine years,

Age of Phil = x+9

Age of Bill = 2x+9

Age of Jenny = 2x-2+9 = 2x+7

Sum of their ages = x+9+2x+9+2x+7 = 5x+25

New age of their father = 10x-4+9 = 10x+5

According to question, the required linear equation to solve the question is,

5x+25 = 10x+5

5x = 20

x = 4

Hence the Jenny's current age = 2*4-2 = 8-2 = 6 years

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Answer:

 D    is the answer I thinnk

Step-by-step explanation:

Answer:

  x = 3

Step-by-step explanation:

You want the equation of the line through points (3, -3) and (3, -6).

The two points have the same x-value, indicating the line through them is a vertical line. That will have an equation of the form x = c.

The x-value of the given points is 3, so the equation is ...

  x = 3

__

Additional comment

We note that the answer box is pre-filled with "y =". There is no "y =" equation that will go through these points. The slope is undefined, so the slope-intercept form of the equation cannot be used.

y-intercept: (0,60)

This is given in the table.

Slope: [tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

Using (1,50) and (2,40):

   [tex]m = \dfrac{40 - 50}{2-1} = \dfrac{-10}{1} = -10[/tex]

The slope is -10.

Using the slope-intercept form (y=mx+b) and the fact that we found m=-10 and b=60 from the table, the equation is:

   y = -10x + 60

The possible amount of time for which they could rent the meeting room is 1, 2, and 3 hours.

In the question,

It is given that,

Reservation fee is $49.

Additional fee is $5.80 per hour.

The math club can spend maximum of $72.20.

The inequality will be:

49 + 5.8*t < 72.20

5.8*t < 23.2

t < 4

Hence, the possible amount of time for which they could rent the meeting room is 1, 2, and 3 hrs.

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Answer: 76

Step-by-step explanation:

Based on the given conditions, formulate: 6+10*7

Calculate the product or quotient: 6+70

Calculate the sum or difference: 76

The ideal mechanical advantage of this car Jack: 30cm

What is Ideal mechanical advantage?

The length of the effort arm of a lever divided by the length of the resistance arm represents the optimal mechanical advantage. The IMA is typically calculated as the resistance force (Fr) divided by the effort force (Fe). IMA is also equal to the product of the load's travel distance (dr) and the distance over which the effort is applied (de).

The Handle of the car jack = 75cm

The car lifted by the jack = 2.5cm

According to the formula:

Ideal mechanical advantage =  The resistance force /  The effort force

or, (Fr/Fe)

IMA = 75 / 2.5

IMA = 30cm

Hence, Ideal mechanical advantage of the car jack = 30cm

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Answer: b= (0,4)

Step-by-step explanation:

The 'b' value in a line is the y-int. of a linear equation. That means you need to determine where the linear equation intersects with the y-axis. In this scenario it intersects at the point (0,4)

The test statistic's p-value is -2.785.

According to A publisher, 45% of its readers own a particular make of car.

Claim: An executive in marketing would like to test the claim that the percentage is different from what is reported.

[tex]H_{o}[/tex]: p = 0.45

[tex]H_{a}[/tex]: p ≠ 0.45

a random sample of 300 found that 37% of the readers owned a particular make of car.

= 37% × 300

= (37 ÷ 100) × 300

X = 111

n= 300

One sample proportion test should be used.

p-vector = x ÷ n,

p-vector = 111 ÷ 300

p-vector = 0.37

The test statistic's formula,

= [tex]\frac{p-q}{\sqrt{\frac{pq}{n} } }[/tex]

test statistic = [tex]\frac{0.37- 0.45}{\sqrt{\frac{0.45(1-0.45)}{300} } }[/tex]

≈ -2.7851

thus, the p-value of the test statistic is -2.7851.

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Options C and E are correct. The expression can be written in the forms of

We have the length of the room as 12 feet

The width of the room = [tex]10\frac{1}{2}[/tex] feet

The expansion of the = 12 +x

What is the area of a rectangle?

The area of a rectangle is given as lw = length x width

Hence we would have the following:

(12+x)10.5 = area

We would have to open the bracket as well

126 + 10.5x

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Complete question

1012 feet. The length of the room is being expanded by x feet. Choose an expression to represent the new area of the living room in square feet and the expanded form of the expression. Select all that apply.

A. 10.5(12x) square feet

B. (10.5 + 12 + x) square feet

C. 10.5(12 + x) square feet

D. 126x square feet

E. (126 + 10.5x) square feet

F. (22.5 + x) square feet

The range of values that satisfy the given inequalities, 8x - 11 > 5 and 15(6x+2) > -150, is x > -2 OR x > 2

From the question, we are to determine the range of values which satisfy the given inequalities.

The given inequalities are

8x - 11 > 5 and 15(6x+2) > -150

To determine the range of values that satisfy the inequalities, we will solve each of the inequalities separately

Solving 8x - 11 > 5

Add 11 to both sides

8x - 11 + 11 > 5 + 11

8x > 16

Divide both sides by 8

8x/8 > 16/8

x > 2

Solving 15(6x+2) > -150

Divide both sides by 15

15(6x+2)/15 > -150/15

6x + 2 > -10

Subtract 2 from both sides

6x + 2 - 2 > -10 - 2

6x > -12

Divide both sides by 6

6x/6 > -12/6

x > -2

Putting the two solutions together,

x > -2 OR x > 2

Hence, the solution is x > -2 OR x > 2

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P(x) is a polynomial function having rational coefficients that has given roots is: P(x) = x³ + 2x² + 4x + 8.

P(x) has given roots: -4 and 2i. ​

A radical is always preceded by a pair of plus & minus signs.

As a result, there would be another root -2i.

All of the roots are -4, -2i, + 2i.

As, the number of roots given are 3, thus the polynomial formed ill be cubic.

The roots in terms of the polynomial can be written as-

P(x) = (x - (-2))(x - 2i)(x + 2i)

P(x) = (x + 2)(x - 2i)(x + 2i)

Simplifying,

P(x) = x³ + 2x² + 4x + 8

Thus, P(x) is a polynomial function having rational coefficients that has given roots is P(x) = x³ + 2x² + 4x + 8.

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On that specific day, the US dollar was worth more than the Canadian dollar and less than the Australian dollar.

The equation u = 0. 99c depicts the value of the US dollar in relation to the Canadian dollar on a specific day.

From the equation,

For  Australian dollar; (from table)

u = 0.95 c   -->

a = 1/0.95 u

a = 20/19 u

(20/19u - u)/ u = 1/19   ....1

For Canadian dollar:

u = 0. 99c

c = 1/0.99 u --> c = 100/99 u

Thus,

(100 u / 99 - u)/ u = 1/99  .....2

From 1 and 2]

1/19 > 1/99

Thus, on that specific day, the US dollar was worth more than the Canadian dollar and less than the Australian dollar.

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The dimensions that represent a similar triangle to triangle QRS are given as follows:

B. 10 cm, 20 cm, 25 cm.

Similar triangles are two triangles that have the same angle measures.

These triangles will also have proportional side lengths, because of the sine/cosine/tangent relations in a right triangle and the law of sines for non-right triangles.

In this problem, we want a triangle that is similar to a triangle with the dimensions presented as follows:

s,. 6 centimeters,. 12 centimeters,. q,. 15 centimeters,. r,.

Hence all these dimensions have to be multiplied by the same scale factor.

Then, option B is correct, as the ratios between the lengths are given as follows:

10/6 = 20/12 = 25/15 = 5/3.

Meaning that all sides were multiplied by 5/3.

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Answer Answer is B, thank you, I just love to help.

Step-by-step explanation:

The change that Tamir would have to receive would be: $5.75

We would first have to solve for the total amount of the tickets that Tamir has received

This would be given as

32.5 + 26.5 dollars

= 59 dollars

Given that he has a 1/4 off in both of the tickets the amount that he would have to pay would be

59 - 1/4 * 59

59 - 14.75

= $44.25

This is the amount that he would have to pay for the coupons.

Given that he used a $50 bill, we would have to solve for his change.

This would be solved as $50 - $44.25

= 5.75

Hence his change is going to be $5.75

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The angle that is same side exterior angle to ∠ABC is ∠EFH.

When parallel line are cut by a transversal line, angle relationships are formed such as corresponding angles, vertically opposite angles, alternate angles, same interior angles, etc.

AD and EG are parallel to each other.

CH is a transversal line to the parallel lines.

Therefore, let's find the angle that has the same relationship as same side exterior angles as angle ABC.

Two angles that are exterior to the parallel lines and on the same side of the transversal line are called same-side exterior angles.

Same side exterior angles are supplementary.

Therefore,

∠ABC and ∠EFH are same side exterior angles.

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Answer:

Example 1 : Convert 2 feet into inches. Solution : Here, we convert bigger unit into smaller unit. So we have to multiply. 2 feet = 2 x 12 inches = 24 inches Example 2 : Convert 3.5 yards into inches. Solution : Here, we convert bigger unit into smaller unit…

Answer: no clue

Step-by-step explanation: i don't know Spanish lol