Todd and Garrett began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Todd took a test in Math and earned a 74.6, and Garrett took a test in English and earned a 68.8. Use the fact that all the students' test grades in the Math class had a mean of 70.6 and a standard deviation of 11.9, and all the students' test grades in English had a mean of 63.7 and a standard deviation of 8.6 to answer the following questions.

Required:
a. Calculate the z-score for Todd's test grade.
b. Calculate the z-score for lan's test grade.
c. Which person did relatively better?

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits at the bank.

This conclusion is based on the given premises that the bank is open during the time between 8:00 a.m. and 3:00 p.m. and that when the bank is open, people may make withdrawals or deposits. By combining these premises with modus ponens (a valid form of deductive reasoning), we can infer that if the time is within the bank's operating hours, then people may make withdrawals or deposits at the bank.

Answer: 5

Step-by-step explanation: 5 isn’t equal to all

Answer:

\(y=5x^2-80x+324\)

Step-by-step explanation:

Answer:

A. y = 12x + 50

B. x is the monthly price

C. y is the total amount

D. 5 months

Step-by-step explanation:

110 - 50 = 60

60/12 = 5

Answer: $0.67.

Step-by-step explanation:

To find the price per foot of the waxed paper, we need to convert the price from yards to feet and then divide the total cost by the length in feet.

Given:

Length of waxed paper roll = 2 yards

Cost of waxed paper roll = $4.02

1 yard is equal to 3 feet. Therefore, the length of the waxed paper roll in feet is:

Length in feet = 2 yards * 3 feet/yard = 6 feet

To find the price per foot, we divide the total cost by the length in feet:

Price per foot = Cost / Length in feet

Price per foot = $4.02 / 6 feet

Dividing gives us:

Price per foot = $0.67 per foot

Therefore, the price per foot of the waxed paper is $0.67.

The number of hours of television watched and the number of hours of exercise, correct to three decimal places is 3.940.

A decimal is any number expressed in base-10 notation, which includes a decimal point and the numbers 0 through 9. Decimals are used to represent fractions, numbers that are not whole numbers, and numbers that are exceptionally large or tiny.

To calculate the correlation coefficient between hours of television watched and hours of exercise, we will use the formula

r = (∑xy − (∑x)(∑y) / n) /\(\sqrt{((2x-x/n)(2y-2/n))}\)

where x is the number of hours of television watched and y is the number of hours of exercise.

Given the data provided, we have

x = 3, 14, 21, 28, 43

y = 38, 27, 36, 15, 30

Therefore,

∑x = 3 + 14 + 21 + 28 + 43 = 109

∑y = 38 + 27 + 36 + 15 + 30 = 156

∑xy = (3)(38) + (14)(27) + (21)(36) + (28)(15) + (43)(30) = 1291

∑x2 = 32 + 142 + 212 + 282 + 432 = 4552

∑y2 = 382 + 272 + 362 + 152 + 302 = 4644

n = 5 (number of members surveyed)

Substituting these values into the formula, we get

r = (1291 − (109)(156) / 5) /\(\sqrt{(4552-(109)2/5)(4644-(156)2/5)))}\)

r = (1291 − 17784 / 5) /\(\sqrt{(4552-10902/5)(4644-24336/5)}\)

r = (-16493 / 5) / \(\sqrt{(3456)(2036)}\)

r = -3298.6 / \(\sqrt{695936}\)

r = -3298.6 / 835.2

r = -3.94

Rounded to the nearest thousandth, r = -3.940.

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Regarding probability, the option with the correct statement is presented as follows;

When two events A and B are independent, the joint probability of the events can be found by multiplying the probability of the individual events.

The probability of an event is the ratio of the number of times the event occurs to the number of all possible events.

The probability of the union of mutually exclusive events is zero, therefore, we get;

P(A ∩ B) = 0

The union of two events consists of the possible outcomes that are in A or in set B or in set A ∩ B

The union of events A and B consists of all outcomes in the sample space that are contained in both event A and event B is incorrect

The joint probability of independent events A and B can be obtained from the product of the probability of event A and event B as follows;

P(A and B) = P(A) × P(B)

The correct option is therefore;

The probability of the union of two events is found from the sum of the probabilities of the two events minus the probability of the intersection of the two events, which can be presented as follows;

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A) + P(B) ≤ 2

P(A ∩ B) ≤ 1

The larger the value of P(A) and P(B) the larger the value of P(A ∩ B), such that we get; P(A ∪ B) ≤ 1

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Answer:

b

Step-by-step explanation:

In a 30-60-90 right triangle, the hypotenuse is twice the length of the short leg.

The hypotenuse is AB and is 18.

The short leg is BC and is 9.

The only choice with BC = 9 is b.

Answer: b

The expected value of your bet will be the negative $16.27 that mean loses.

Binomial distributions consist of n independent Bernoulli trials.

The expected value will be

E(X) = np

Suppose that you and a friend are playing cards and decide to make a bet.

If you draw two face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards replacing the first card, you win $50.

Otherwise, you pay your friend $20.

Then the probability of winning will be

p = (12 / 52)(12 / 52)

p = 9 / 169

Then the probability of loosing will be

q = 1 – p

q = 1 – 9/169

q = 160 / 169

Then the expected value will be

E(x) = (9/169) x 50 + (160/169) x (-20)

E(x) = -$16.27

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Answer:

I hit my toe

Step-by-step explain

. 0.85+[0.15+(-1/3)

Answer:

y = 3/4 x + 3

Step-by-step explanation:

slope of the line :

(0-3)/(-4-0)

-3/-4

3/4

y = 3/4 x + 3

Answer:

  86.75

Step-by-step explanation:

Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.

The grade for the course, with fourth test score x, will be ...

  0.20(63.5 +76 +87) +0.40x = 80

  0.40x +45.3 = 80

Solving for x, we get ...

  0.40x = 34.7 . . . . subtract 45.3

  x = 86.75 . . . . . . . divide by 0.4

The minimum score you need on the fourth test is 86.75.

<95141404393>

Answer: 0.3278

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!!

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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Answer:

The answer is 504 ft ^3 check my solution

Answer:

Option B.)

Step-by-step explanation:

Just took the test and got 100% :]

The system of logarithmic equation is graphed and the point of intersection of the equation is log₃ ( 5x ) = log₅ ( 2x + 8 ) is A ( 1.0 , 1.4 )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the solution to the logarithmic equation be represented as A

Now , the value of A is

log₃ ( 5x ) = log₅ ( 2x + 8 )

On simplifying , we get

log₃ ( 5x ) = log₁₀ ( 5x ) / log₁₀ ( 3 )

log₅ ( 2x + 8 ) = log₁₀ ( 2x + 8 ) / log₁₀ ( 5 )

Substituting the logarithmic quantities , we get

log₁₀ ( 5x ) / log₁₀ ( 3 ) = log₁₀ ( 2x + 8 ) / log₁₀ ( 5 )

On cross multiplying , we get

log₁₀ ( 5x ) / log₁₀ ( 2x + 8 ) = log₁₀ ( 3 ) / log₁₀ ( 5 )

( 5x ) / ( 2x + 8 ) = 3/5

On cross multiplying , we get

25x = 6x + 24

Subtracting 6x on both sides , we get

19x = 24

Divide by 19 on both sides , we get

x = 1.26

Therefore , the approximate values of the function on graphing is A ( 1.0 , 1.4 )

Hence , the solution of function from graphing is A ( 1.0 , 1.4 )

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Using proportional reasoning, we can predict that there will be 40 red candies in the large bag.

Using proportional reasoning, we can set up and solve the following equation to determine the number of red candies in the large bag:

P = Proportion of red candies in the large bag

R = Red candies in the small bag

R × (33/9) = P

12 × (33/9) = P

P = 40 red candies in the large bag

Therefore, using proportional reasoning, we can predict that there will be 40 red candies in the large bag.

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Answer:

(1, 24)

(2, 22)

(3, 20)

(4, 18)

(5, 16)

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

9  ---> numerator

10  ---> denominator

Answer:

108 ft²

Step-by-step explanation:

For the polygon on the left, we are given the length of one side (3 ft) and the total area (27 ft²). With this information, we can determine the length of the other side - 9 ft. I found this by dividing 27 ft² by 3 ft, giving me the final result of 9 ft.

Next, we have to find the other side of the polygon on the right so we can ultimately determine its area. It looks like there is a scale factor of 2 between the two polygons, since 3 × 2 = 6. We know that the bottom side of the left polygon is 9, so multiplying 9 by 2 should give us the bottom side of the polygon on the right. 9 × 2 = 18.

Now, we have the side lengths for the polygon on the right and can determine its area. What is 6 ft × 18 ft? Well, the answer is 107 ft², and this is the answer to the question.

Hopefully that's helpful! :)

The quotient evaluated in 7 is equal to the quotient of the two functions evaluated in 7, thus:

(f/g)(7) = f(7)/g(7) = 3

Here we know the functions:

f(x) = 2x + 1

g(x) = x - 2

The quotient evaluated in 7 is equal to the quotient between the two functions evaluated in x = 7, then here we will get:

f(7) = 2*7 + 1 = 14 + 1 = 15

g(7) = 7 - 2 = 5

Then the quotient gives:

(f/g)(7) = f(7)/g(7) = 15/5 = 3

That is the value.

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We have the following:

replacing:

Therefore, the table is

x y

-4 -7

-2 -1

0 5

2 11

The value of 3¾ft in yards would be = 1 6/25 yard

A mixed number is the type of number that is made up of three parts such as the whole number, a numerator and a denominator.

To convert to yards;

1 ft = 0.33 yard

3¾ = X yards

make x yards the subject of formula;

X yards = 3¾ × 0.33

X yards = 3.75×0.33

X yards = 1.24 yards

X yards in mixed number= 124/100 = 31/25 = 1 6/25 yard.

Note that the final value which is 124/100 is reduce to the lower figure by dividing through with 4 to arrive at the mixed number 1⁶/25

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The answer is 8/7

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

The multiplication of 4/5 and 10/7 is 8/7 in its simplest form.

To multiply 4/5 by 10/7,

We simply multiply the numerators (4 and 10) to get 40 as the new numerator and multiply the denominators (5 and 7) to get 35 as the new denominator.

Therefore, 4/5 x 10/7 = 40/35.

To simplify this fraction,

We can first find the greatest common factor (GCF) of the numerator and denominator,

Which is 5. We can divide both the numerator and denominator by 5 to get:

40/35 = (5 x 8) / (5 x 7)

          = 8/7

So the answer in simplest form is 8/7.

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Answer:

15 dollars

Step-by-step explanation:

We can write a ratio to solve

6 cones         9 cones

------------   = --------------

10 dollars       x dollars

Using cross products

6*x = 10 *9

6x = 90

Divide each side by 6

6x/6 = 90/6

x = 15

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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The effect that does NOT relate to one's driving ability is breathalyzer test results indicating a high BAC. Option B.

While the breathalyzer test measures the blood alcohol concentration (BAC), it is a method used to determine the level of alcohol in a person's system and is commonly used in assessing impairment for driving under the influence.

Therefore, it directly relates to one's driving ability and is not excluded from the effects on driving ability caused by a BAC of .2 percent.

On the other hand, options, lack of coordination, impaired gross motor skills, and impaired reactions all directly relate to one's driving ability as they affect the physical and cognitive abilities necessary for safe and efficient driving.

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