At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph?
A) approximately 16%
B) at most 34%
C) at most 2.5%
D) at most 13.5%

The sum of complemenatry angles = 90

The sum of supplementary angles = 180

The value of the composite function (g ° h)(0) is equivalent to zero.

A function that is composed of further functions, each of which serves as the input to the next.

Given the function below;

g(x) = 5x

h(x) = √x

Determine the composite function (g o h)(x)

(g o h)(x) = g(h(x))

(g o h)(x) = g(√x)

g(√x) = 5√x

Substitute the value of x to have:

(g o h)(0) = 5√0

(g o h)(0) = 0

This gives the required value

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Problem #1

budget rent a car rented a basic car at a daily rate of $45.95 plus 40 cents per mile. Another company rents a basic car for $46.95 plus 20 cents per mile. For what mileage is the cost the same.

Define the variables

Let

x -----> number of miles

y -----> the total cost

we have

budget rent a car

y=40x+45.95 ------> equation 1

Another company

y=20x+46.95 -------> equation 2

Solve the system of equations

equate equation 1 and equation 2

40x+45.95=20x+46.95

solve for x

40x-20x=46.95-45.95

20x=1

x=0.05 miles

therefore

Let l and w be the length and width of the rectangle, respectively.

Therefore, according to the question,

Therefore, solving for l and w,

ANSWER

A. True

EXPLANATION

Let the complex number be z = a+ ib, so its complex conjugate is z* = a - ib, where a and b are real numbers. Let's find the product,

The product is,

Solve the products,

Simplify: note that the second and third terms are opposites, so they cancel out. Remember that i² is equal to -1,

Since a and b were real numbers, then the sum of their squares is also a real number.

Hence, this statement is true.

The ordered pair which can be plotted according to the given data in graph will be (6,21).

Plotting an ordered pair on graph of speed and time represents the motion of a particle accelerating from a speed at time 0 , u , to a speed v at time t .

According to given graph we have already plotted points as follows

(2, 7), (4, 15), (5,17)

Now by analysis of the given graph pattern we can conclude that the ordered pair which can be added to the given graph if (6, 21).

Note : - The Question is completed as below and the coordinate plane is attached too.

Maggie walks at a constant speed. Maggie plots points on the coordinate plane below to show amounts of time it takes her to walk certain distances.

Which of the following ordered pairs could Maggie add to the graph?

A. (1,3)

B. (3,10)

C. (6,21)

D. (3,1)

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Answer:

This is impossible.

Step-by-step explanation:

You didn't give us how much 1 yard is.

Answer: How much is one yard?

Step-by-step explanation:

Let be "x" Jon's current salary.

According to the information given in the exercise, the salary at the new job is 68,000 and this is 12% more than his salary at his current job.

To convert from percent to a Decimal number, you can divide by 100. Then:

Therefore, knowing that information, you can set up the following equation:

Now you can solve for "x" in order to find its value:

The answer is:

[tex] \sqrt{ \frac{4 {x}^{2} }{3y} } \\ = \frac{ \sqrt{4 {x}^{2} } }{ \sqrt{3y} } \\ = \frac{ \sqrt{4 } \times \sqrt{ {x}^{2} } }{ \sqrt{3y} } \\ = \frac{2x }{ \sqrt{3y} } [/tex]

ATTACHED IS THE SOLUTION

Answer:

The image is the answer

Step-by-step explanation:

To find f(-8), we just need to replace x by -8 on the function f(x) as:

At the same way g(-2) is equal to:

Finally, h(2/3) is equal to:

Answers: f(-8) = 23

g(-2) = 16

h(2/3) = 9

There are 40 animals in the shelter, 18 of that animals are cats.

We need to find the percent of the animals that are cats.

Then, 40 animals represent 100% in the shelter.

We can use the rule of three to find the cat's percent:

Therefore:

40 animals -------------- 100%

18 cats ------------------------ x

x = (18*100)/40

x =45

So, 45 % of the animals are cats.

$6,50,000 is the cost of the goods sold.

By dividing a company's cost of sales, or cost of goods sold, by its inventory turnover, one can determine how well it uses its inventory (COGS).

The number of times inventory is sold or used over a given time frame, like a year, is referred to as the inventory turnover in accounting. It is calculated to determine whether a company has an excessive amount of inventory in relation to its level of sales.

Inventory turnover is the count of times a company's stock is sold during the course of a month, a quarter, or (most frequently) a year of business.

We should apply the following formula to calculate the cost of goods sold:
Cost of goods sold / inventory equals inventory turnover.
Rearranging the equation and replacing the unknown values results in:

Inventory plus inventory turnover equals cost of goods sold.
Price of items sold = $5,000,000 divided by 13
$6,50,000 is the cost of the goods sold.

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Let's define first the variables.

let H be the number of bags of the type that cost 3.25 and P the number of bags of the type that cost 2.75.

since they sold a total of 156 bags we have that H+P=156

and from the other condition we obtain 3.25H+2.75P=455

now we can solve the system of equations.

from the first equation H=156-P

substituing the previous equality in the second one we obtain:

now that we have P, we can replace it in the first equation obtaining that H=50

then the answer will be that they sold 50 bags of $3.25 and 106 bags of $2.75

The value of x in the linear equation −0.28x − 15.3 = 1.92 is -61.5 option (B) -61.5 is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The linear equation one variable is:

−0.28x − 15.3 = 1.92

-0.28x = 1.92 + 15.3

-0.28x = 17.22

x = -17.22/0.28

x = -61.5

Thus, the value of x in the linear equation −0.28x − 15.3 = 1.92 is -61.5 option (B) -61.5 is correct.

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Answer:

its B -61.5

Step-by-step explanation:

i attched pictures to show you

 y = 2/3x + 7  is slope-intercept form of the equation .

What exactly does slope intercept mean?

the equation of the parallel line in slope intercept form y=mx+b so that we can clearly see the slope and y intercept

      2x-3y = -9

      3y = 2x + 9

         y = 2/3x + 9/3

          y = 2/3x + 3

compare equation y = mx + c  

  slope = 2/3  

to find c put x = -3 and y = 5

     y = mx + c  

      5 = 2/3 * (-3) + c

      5 = -6/3  + c

        c = 5 + 2  = 7

put the final equation together

           y = 2/3x + 7

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Answer:

[tex]8.808 \times 10^{-6}[/tex]

Step-by-step explanation:

Given expression:

[tex](2.6 \times 10^{-6})+(3.2 \times 10^{-2})(1.94 \times 10^{-4})[/tex]

The grouping of numbers by parentheses in a different way does not affect their product.  Also, changing the order or position of the product of two numbers does not change the end result.

[tex]\implies (2.6 \times 10^{-6})+(3.2 \times 1.94 \times 10^{-2} \times 10^{-4})[/tex]

Multiply the numbers 3.2 and 1.94:

[tex]\implies (2.6 \times 10^{-6})+(6.208\times 10^{-2} \times 10^{-4})[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies (2.6 \times 10^{-6})+(6.208\times 10^{-2-4})[/tex]

[tex]\implies (2.6 \times 10^{-6})+(6.208\times 10^{-6})[/tex]

Factor out the common term 10⁻⁶:

[tex]\implies 10^{-6}(2.6+6.208)[/tex]

Add the numbers 2.6 and 6.208:

[tex]\implies 10^{-6}(8.808)[/tex]

[tex]\implies 8.808 \times 10^{-6}[/tex]

Scientific notation is written in the form a × 10ⁿ , where 1 ≤ a < 10 and n is any positive or negative whole number.  Therefore, the final answer is in scientific notation.

The value of t must be less than -2/3, that is, the correct answer must be a negative number, in this case it would be the letter C) -3

given data:

The cost of house is $176000.

The percentage the house realtor requires is 5%.

That is,

Thus 5% of 176000 is 8800.

Thus, you need to give $8800 to the local realtor.

The distance between Destinee's house and Anna's house is 15.62 miles

To find the coordinate of the Anna's house, we can use the formula of midpoint on this. This is given as

[tex]midpoint(x,y) = \frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2}[/tex]

In the question, El Ticonzito's house is at midpoint between Destinee's house and Anna's house.

[tex]midpoint(x,y) = \frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2}\\-4 = \frac{2 + x_1}{2} = -8 = 2 + x_1\\x_1 = -8 - 2 = -10\\\\-2 = \frac{3 + y_1}{2} \\-4 = 3 + y_1\\-4 - 3 = y_1\\y_1 = -7[/tex]

The coordinate's of Anna's point is (-10, -7).

Let's use this to calculate the distance (d) between the two points.

[tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2} \\d = \sqrt{(-10-2)^2 + (-7 - 3)^2} \\d = \sqrt{(-12)^2 + (-10)^2} \\d = \sqrt{244}\\ d = 15.62 miles[/tex]

The distance between the two points is 15.62 miles

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Given:

Radius of the cirle = 11 ft

Angle = 150 degrees

π = 3.14

Let's find the area of the sector of the cicle.

To find the area of the sector, apply the formula:

Where:

π = 3.13

θ = 150 degrees

r = 11

Thus, we have:

Solving further:

Therefore, the sector area of the circle is 158.3 square feet.

ANSWER:

158.3 square feet.

parallel lines have the same slopes. Therefore,

Y can be found below

The image of the point after the transformation is (2, -7)

The given parameters are:

Point =  (-1, 3)

Transformation rule:

D₂ o T 4.-5

The above means that

When these transformations are combined, we have

(x, y) = (2x + 4, 2x - 5)

So, the mathematical representation of this transformation is

(x, y) = (2x + 4, 2x - 5)

Substitute the equation Point =  (-1, -3) in the equation (x, y) = (2x + 4, 2x - 5)

So, we have the following equation

(x, y) = (2(-1) + 4, 2(-1) - 5)

Evaluate the product

(x, y) = (2, -7)

Hence, the image is (x, y) = (2, -7)

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1. The lower limit of this confidence interval is $587.13.

2. The upper limit of this confidence interval is $841.25.

The lower limit describes the lowest price that entry-level road bikes will cost.

The upper limit refers to the highest price that entry-level road bikes can command.

Using the lower and upper limits, Randy can confidently estimate the range of the asking price of the used entry-level road bikes.

N = 14

Mean price, µ = $714.19

Sample deviation = $184.56

Confidence interval = 99%

The z-score of 99% confidence interval = 2.576

The margin of error = z-score x (standard deviation/√n)

= 2.576 x ($184.56/√14)

= $127.06

Lower Limit =  µ - margin of error

= $714.19 - $127.06

= $587.13

Upper Limit = µ + margin of error

= $714.19 + $127.06

= $841.25

Thus, Randy can estimate that the price of used entry-level road bikes is $714.19 ±$127.06 at a 99% confidence level.

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If we apply the first discount the shoes would have a price of:

To this pice we make the 20% discount, then:

Therefore, after the discounts the price would be $84

The like terms in the expression are 12n and 6n

Like terms are terms that have the same coefficients and in the same order of degrees.

In the expression:

12n - 6 + p + 6n

The like terms are 12n and 6n

we have the following:

where d is distance, t is time and v is velocity, replacing:

therefore, the distance is 13.2 miles

The first equation given in the question as, y = 1^x is not exponential.

What do you mean by exponential?

A mathematical function with the form f (x) = a^x is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's base and must be bigger than 0. The transcendental no., or roughly 2.71828, is the most often used exponential function on regular basis.

The equation, y = 1^x is not an exponential because for any integer value of x, y always equals to zero. Which makes it simple equation and not an exponential equation.

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The angle A is given 72 degree and angle C is given 90 degree.

The side b is 5.

Then the right triangle is given

Use the property , the sum of the angles of the property is the 180 degree.

Then the angle B is 18 degree.

Then to determine side a , use the tan trigonometric function.

The side a is 15.38.

Now to determine the side c, use the trigonometric function sin .

The side c is 16.18.