In a class of students, the following data table summarizes the gender of the studentsand whether they have an A in the class. What is the probability that a student whohas an A is a female?Female MaleHas an A24Does not have an A176

It is given that there are

run in 2 minutes.

So, we have to determine time required to run

Apply the unitary method,

For 5/4 miles required 2 minutes.

So , for 1 miles, time required

Therefore,for 3/2 miles , time required is

Hence the time required is 2.4 minutes.

The given solutions of the quadratic equation:

x = 4 and x = -1

First we make them factors of the equation:

x= 4 becomes:

and x = -1 becomes:

So (x-4) and (x+1) are the factors.

To get the general quadratic equation, we would expand the factors

The general quadratic equation:

There are 66.4 milliliters of acid in the solution

The amount of the solution of acid and water = 357

Percentage composition of acid in the solution = 18.6%

Amount of acid in the solution = (18.6/100) x 357

Amount of acid in the solution = 66.402 milliliters

Amount of acid in the solution = 66.4 milliliters (to the nearest tenth)

There are 66.4 milliliters of acid in the solution

The solution of the system of equations are  x = - 6 , y = 44 and z = 2

Given,

The system of equations;

3x + y - 2z = 22

x + 5y + z = 4

x = -3z

We have to solve the given equations;

Substitute x = -3z in both equations;

3x + y - 2z = 22

⇒ 3 × -3z + y - 2z = 22

⇒ - 9z + y - 2z = 22

⇒ - 11z + y = 22

And,

x + 5y + z = 4

⇒ - 3z + 5y + z = 4

⇒ 5y - 2z = 4  

Solve the equations  - 11z + y = 22  and 5y - 2z = 4  

We get,

⇒ y = 44 and z = 2

So, x = - 3z    

⇒ x = - 3 × 2

⇒ x = - 6

Thus, The solution of the system of equations are;

⇒ x = - 6 , y = 44 and z = 2

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Answer:

c for the first one and a for the second

A function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”

The input values make up the domain, and the output values make up the range.

The relation is given to be:

To classify a function, get the input and output values. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

The input values are: {7, 4, 0, 3, 1}

The output values are: {6, -6, -1, 3, 1}

Therefore, the relation is a function.

The correct option is OPTION A: Yes, because each first component corresponds to exactly one second component.

The domain is:

The range is:

The linear equation parallel to line u that passes through (7,9) is y = 2x - 5

Two lines are parallel if have the same slope, we know that line V is parallel to:

y = 2x + 8/9

Then line V will be of the form:

y = 2x + c

To find the value of c, we use the fact that the line passes through (7, 9), replacing these values we get:

9 = 2*7 + c

9 = 14 + c

9 - 14 = c

-5 = c

The linear equation is y = 2x - 5

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The amount of hardener added to 1 container of resin = 55mL.

The amount of hardener added to 14 containers is calculated as,

Thus 0.770 litres of hardener must be added to 14 containers of resin.

We can find W and L using the sine and the cosine functions:

Therefore:

Answer:

84.87 cm²

In the number 44,244, we can see two pairs of 4's.

The first pair (to the left) has a higher value than the second pair to the right, but the 4's have something in common: The leftmost 4 is ten times as high as the rightmost 4.

For this reason, we start the number as forty-four thousand and end up with forty-four.

The new picture is 64 ft squared. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

We are given the relation: Area of pic = constant * d^2, where d is distance from projector to wall.

For d = 10, we have A = 16 ft sqrd

Now given d = 20

what is A?

constant = 16/10*10

new A = [16/100] * 20*20 = 16 * 4 = 64 ft sqrd.

The new picture is 64 ft squared.

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Answer: 4 part yogurt 6 part blueberries

Step-by-step explanation: 2+3=5 5x2=10 3x2=6 2x2=4 6+4=10

The Solution:

Given that equal number of each brand of golf ball was ordered.

Let the number of each brand ordered be represented with n

Each swinger ball cost $2.10

So, the total cost of the swinger ball ordered is:

Each Supra ball cost $1.00

So, the total cost of the supra ball ordered is:

Given that the total cost of the Swinger balls exceeded the total cost of the Supra balls by $330.00. We have the linear equation below:

We are required to find the number of dozens of each brand of golf balls that were ordered.

So, we shall solve for n and then divide the value by 12.

Dividing both sides by 1.1, we get

Dividing 300 by 12 (since 1 dozen = 12 balls), we get

Therefore, the correct answer is 25 dozens.

To obtain the measure of segment AD, add the measurement of segment AC and segment CD.

Rewrite the fraction part as similar fractions. Multiply the numerator and teh denominator of the second fraction by 2 to obtain 8 in the denominator.

Add the whole numbers, 2 and 1. Add the numerators, 3 and 2, and then copy the common denominator, which is 8.

Therefore, the correct answer is the third option, 3 5/8 in.

the perimeter of a cuadrilateral is 2L+2W=68 where L is the length of the room

since L= 18 feet

we will have that

2(18)+2W=68

then

W=(68-36)/2= 32/2=16

The ratio of Perch to total fish is:

3 ( Number of perch that he caught)

------------------------------------------------------

9 ( The result of the addition of all values)

Simplifying, we have:

1

---

3

So, the answer would be 1 : 3

Solution:

Note that :

and If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. In this case, this statement is not true. We can conclude that it is not a right triangle.

Jeff needs 21 oz of gelatin and 14 cups of water to make 7 boxes

The table of values is given as

Boxes          Gelatin Powder (oz)        Water (cups)

3                                           9                        6

From the above table, we can see that

Gelatin Powder = 3 * Boxes

Water  = 2 * Boxes

When there are 7 boxes, the equations become

Gelatin Powder = 3 * 7

Water  = 2 * 7

Evaluate the products in the above equation

So, we have

Gelatin Powder = 21

Water  = 14

Hence, the amount of gelatin and water needed to make 7 boxes are 21 oz and 14 cups respectively

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Answer: D: jeff will use 21 oz of powder and 14 cups of water

Step-by-step explanation:

the chart says there are

3 boxes of gelatin ) 9 oz of powder ) 6 cups of water

that equals the same as

1 box of gelatin ) 3 oz of power ) 2 cups of water

so for every box of gelatin, there is 3oz of powder and 2 cups of water

if he wants to make 7 boxes.....

7x3oz=21 oz

7x2cups=14 cups

so the Answer is D

From the checks and calculation the tractor is not operating correctly.

Standard deviation refers to by how how much the data varies from the mean

Given data form the question

1% level of significance

variance was found to be 68mm2

A sample of 31 planting lines

a maximum variance of 55mm2

Definition of variables

1% level of significance is equivalent to 99% confidence interval

mean sample, μ = ?

standard deviation, SD = √variance = √68 = 8.246

Z score, Z = 2.576

sample size, n = 31

maximum variance, X = 55mm2

The formula in term s of Z is

Z = ( X - μ ) /  SD

2.576 = (55 - μ) / 8.246

(55 - μ) = 2.576 * 8.246

55 - μ = 21.242

μ = 55 - 21.242

μ = 33.758 mm²

For the tractor to be working correctly the difference between the mean and 2 * SD should not be more than the maximum variance which is 55mm²

55mm² ≥ mean ± 2 * SD

55mm² ≥  33.758 mm² ± 2 * 8.246

55mm² ≥ 50.25

Since 50.25 is less than the maximum variance the tractor is operating correctly

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According to the given data we have the following:

first linear function is defined by the equation 2x + 3y = 12

second linear function passes through the points (3,-2) and (-2, k)

the two linear functions have the same y-intercept

k?

To calculate k first we have to do the following:

we would have to use the formula y=mx +b

the two linear functions have the same y-intercept, therefore, b=12.

So, y=mx +12

As second linear function passes through the points (3,-2) we are going to substitue the x and y with 3 and -2.

So, -2=m*3+12

-2-12=m*3

-14=m*3

m=-14/3

m=-4

Finally we would calculate k by writiing the equation of the line that passes through each pair of points as follows:

y2-y1/x2-x1=m

So

So, k +2/-5=-4

k+2=20

k=20-2

k=18

The marginal cost in dollars of producing x units is given by the next equation:

a)

To find the marginal cost (in dollars per unit) when x= 9.

Then, we need to replace x=9 on the derivation of the cost equation:

So:

Where:

and, the derivate of a constant is equal to zero.

Replacing x= 9

Hence, the marginal cost is equal to:

b) Now, when the production increases 9 to 10. It's the same as the cost of producing one more machine beyond 9.

Then, it would be x=10 on the cost equation:

and x= 9

Then, we calculate C(10) - C(9) =

C)

Both results are equal.

Hence, the marginal cost when x=9 is equal to the additional cost when the production increases from 9 to 10.

From the given picture we can see

ACB is a right triangle at C

AC = b

CB = a

AB = c

Since mSince a = 5 ft

Then to find b and c we will use the trigonometry ratios

Substitute the value of sin 60

By using the cross multiplication

Divide both sides by root 3

To find b we will use the tan ratio

Substitute the value of tan 60

Switch b and root 3

The exact values of b and c are

a) The probability of exactly 21 particles arrive in a particular one minute period is 0.0426

b) The probability of exactly one particle arrives in a particular one second period is 0.2042

Probability is the ratio of the total number of conceivable outcomes to the number of outcomes in an exhaustive set of equally likely alternatives that result in a particular occurrence.

The probability is given by:

P(X=x) = (e⁻ⁿ nˣ)/x!

a)  The probability of exactly 21 particles arrive in a particular one minute period is given by :

P(X=21) = (e⁻16 × 16²¹)/21!

P(X=21) = (2.176746853×10¹⁸)/51090942171709440000

P(X=21) = 0.0426

b) The probability of exactly one particle arrives in a particular one second period is :

1 min = 16 particles

1 sec = 16/60 particles

1 sec = 0.2667 particles

P(X=1) = (e⁻⁽¹⁶/⁶⁰⁾ × (16/60)¹)/1!

P(X=1) = 0.2042

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Answer

Rotate 270 degrees clockwise about the origin → Translate 3 units right and 3 units up → Dilate by a scale factor of 3

Step-by-step explanation

Rotation 270 degrees clockwise about the origin transforms the point (x, y) into (-y, x). Applying this rule to the vertices of figure A, we get:

(-5, 5) → (-5, -5)

(-4, 4) → (-4, -4)

(-5, 1) → (-1, -5)

(-4, 1) → (-1, -4)

Translation 3 units right and 3 units up transform the point (x, y) into (x+3, y+3). Applying this rule to the previous points, we get:

(-5, -5) → (-5+3, -5+3) → (-2, -2)

(-4, -4) → (-4+3, -4+3) → (-1, -1)

(-1, -5) → (-1+3, -5+3) → (2, -2)

(-1, -4) → (-1+3, -4+3) → (2, -1)

Dilation by a factor of 3 transforms the point (x, y) into (3x, 3y). Applying this rule to the previous points, we get:

(-2, -2) → (3x-2, 3x-2) → (-6, -6)

(-1, -1) → (3x-1, 3x-1) → (-3, -3)

(2, -2) → (3x2, 3x-2) → (6, -6)

(2, -1) → (3x2, 3x-1) → (6, -3)

These vertices coincide with the vertices in figure B

On the first day, he biked x miles

The next day, he will bike

EFG is a triangle with vertices

E(-3,3), F(1,-1) and G(-3,-5).

First, let us evaluate the length of each side of the triangle using the distanec formula.

Since two sides of the triangle are equal, therefore, EFG is an isoscele triangle.

Answer:

y=−2/11x−20

Step-by-step explanation:

Answer:

2,842 feathers

Step-by-step explanation:

An emperor penguin has 76,634 feathers. The penguin has about 27 times as many feathers as a blue jay. About how many feathers does the blue jay have?

76,634/27 = 2,842 feathers

The sales tax formula is used to determine how much businesses need to charge customers based on taxes in their area. State and local governments across the United States use a sales tax to pay for things like roads, healthcare and other government services. Sales tax applies to most consumer product purchases and exists in most states.

The sales tax formula is simply the sales tax percentage multiplied by the price of the item. It's important for businesses to know how to use the sales tax formula so that they can charge their customers the proper amount to cover the tax. For consumers, it's good to know how the sales tax formula works so that you can properly budget for your purchases

The sales tax formula is as shown below:

Given that

Sales tax = 47

price of the dining room = 940

Sales tax rate= unknown

To find the sales tax rate, we would substitute into the formula above

Hence, the sales tax rate is 5%

Let:

Where:

k = Constant of proportionality

So: