A professional golfer is shopping for a new brand of golf ball. He likes most of the features of one particular brand, but he wants to make sure that the brand has a desirable spin rate (the rate at which the ball spins on its axis after being struck by a golf club). To test the spin rate of this new brand of ball, the golfer hits the brand of ball on 100 five-iron shots, and a computer measures the spin rate for each shot. The computer then produces the following histogram summarizing the 100 spin rates: 2520151050Frequency1010242421115000550060006500700075008000Spin rate (in revolutions per minute) Based on the histogram, find the proportion of spin rates in the sample that are greater than or equal to 7000 revolutions per minute. Write your answer as a decimal, and do not round your answer.

Answer: Polygon Q's area is 1/4 of Polygon P's area

======================================================

Explanation:

Imagine we had a square with side length 8. The area of this square is 8*8 = 64.

Now let's reduce each side of the square by the scale factor 1/2. So each new side is 8*(1/2) = 4. The area of this smaller square is 4*4 = 16.

Comparing the new area (16) to the old one (64), we see that the new area is 16/64 = 1/4 of the old area.

In other words,

new smaller area = (1/4)*(old larger area)

So this is one example to see why (1/2)*(1/2) = 1/4 is the area scale factor based on the linear scale factor of 1/2. In short, (1/2)^2 = 1/4. Whatever the original scale factor is, square it and you'll get the area scale factor.

Answer:

i think id say it is 10.5 i might be wrong though

Step-by-step explanation:

Answer:

14 lemonade serving

Step-by-step explanation:

1½+3=4½

In 4 liters we get 12 ⅓serving of lemonade

In ½ we get 1 serving of lemonade from the ½ we remain with to ⅙liters so we still add that as a serving

Total =12+1+1=14

Huh?? Can u attach a picture or some

Answer:

2 quarts of 100% antifreeze.

Step-by-step explanation:

5 quarts/ .40 * x/ 1

.40x= 5

x=2

2 quarts of pure antifreeze must be added to 5 quarts of a 40​% antifreeze solution to obtain a 50​% antifreeze​ solution.

Looking at the concentrations.

100% of x quarts is x quarts of antifreeze.

30% of 5 quarts is .3(5) quarts antifreeze.

Adding that we have 5+x quarts and we want

50% of that to be antifreeze so the total is

.5(x + 5)

x + .3(5) = .5(5+x)

x + 1.5 = 2.5 + .5x

x - .5x = 2.5 - 1.5

.5x = 1

x = 1/.5 = 2 quarts pure antifreeze.

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Let's consider the standard and usually used value of irrational numbers given in the question.

So, let's see the options:

A) GiveN:

[tex] \dfrac{\pi}{2} + \pi[/tex]

Let consider π = 3.14

[tex] \dfrac{3.14}{2} + 3.14[/tex]

[tex]1.57 + 3.14[/tex]

[tex]4.71 \: (approx.)[/tex]

B) GiveN:

[tex]2\pi - 1[/tex]

Here also, let's consider the value be 3.14

[tex]2 \times 3.14 - 1[/tex]

[tex]6.28 - 1[/tex]

[tex]5.28 \: (approx.)[/tex]

C) GiveN:

[tex]4 \sqrt{2} [/tex]

Let's consider the value of √2 be 1.414

[tex]4 \times 1.414[/tex]

[tex]5.6516 \: (approx.)[/tex]

D) GiveN:

[tex]8 - \sqrt{3} [/tex]

Let's consider the value of √3 be 1.732

[tex]8 - 1.732[/tex]

[tex]6.268 \: (approx.)[/tex]

So, we can see that we have got the approximate value of all the numericals, and the closest to 5.66 is 5.6516 which is the answer of Option C.

So, Correct answer is C

#CarryOnLearning

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Answer:

B. [tex] -\frac{3}{2} [/tex]

Step-by-step explanation:

Rate of change/slope is given as [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Use the coordinate pairs of any two points on the slope/line.

Let's use the following coordinates pairs:

[tex] (-2, 4) = (x_1, y_1) [/tex]

[tex] (0, 1) = (x_2, y_2)

Plug in the values into the formula, [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]:

[tex] m = \frac{1 - 4}{0 - (-2)} [/tex]

[tex] m = \frac{-3}{0 + 2} [/tex]

[tex] m = \frac{-3}{2} [/tex]

[tex] m = -\frac{3}{2} [/tex]

Answer:

-25

Step-by-step explanation:

Answer:

x=bc-35 over 90

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

10

-6

=6

Adding a negative number is simply subtraction.

10-4=6

Answer:

11.2 gallons.

Step-by-step explanation:

We have been given that a rectangular​ prism-shaped room is 18 ft by 10 ft and 8 ft high. We are asked to find the gallons of paint needed to paint the walls of room.    

Answer:54

4 1/2times 12

Convert 4 1/2 to an improper fraction.

9/2 times 12

Cancel the common factor of 2

9 times 6

Multiply

9 by 6 the you'll get 54

Answer:

y = 40

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

y+10 + 2y +50 = 180

3y+60 = 180

Subtract 60 from each side

3y+60-60 = 180-60

3y = 120

Divide each side by 3

3y/3 = 120/3

y = 40

Answer:

LM is 8

Step-by-step explanation:

LM --> (2x-16)+(x-9) =11

Solve for x

Plug in this value for LM equation to solve for LM:

LM is 8

Step-by-step explanation:

[tex] \frac{a}{b} = \frac{5}{4} \: \: \: \: \: \: \frac{b}{c} = \frac{3}{2} [/tex]

[tex] \frac{a}{b} \times \frac{b}{c} = \frac{5}{4} \times \frac{3}{2} [/tex]

[tex] \frac{a}{c} = \frac{15}{8} [/tex]

[tex] \frac{c}{a} = \frac{8}{15} [/tex]

Answer:

[tex]\huge\boxed{\sf \frac{a}{c} = \frac{15}{8} \ \ OR \ \frac{c}{a}= \frac{8}{15} }[/tex]

Step-by-step explanation:

[tex]\sf Given \ that\\\\\frac{a}{b} = \frac{5}{4} \\\\\frac{b}{c} = \frac{3} {2}\\\\Multiplying \ both \ of \ the \ above \ equations\\\\\frac{a}{b} * \frac{b}{c} = \frac{5}{4} * \frac{3}{2} \\\\\frac{a}{c} = \frac{5*3}{4*2} \\\\\bold{\frac{a}{c} = \frac{15}{8} }[/tex]

Hope this helped!

Answer:

2419.0265 meters

Step-by-step explanation:

To find the answer you must first find the circumference of the circle. The circumference formula is C = 2 \pi r. So if you plug in 77 you get 483.8053. Then multiply that by 5 and you will have your final answer.

Answer:

8 miles

Step-by-step explanation:

Given:

Time = 4 hours

Distance = 240 miles

To find:

The speed or the rate mile per hour for Mrs. Rice's drive.

Solution:

We know that,

[tex]Speed =\dfrac{Distance}{Time}[/tex]

On substituting the given values, we get

[tex]Speed =\dfrac{240}{4}[/tex]

[tex]Speed =60[/tex]

Therefore, the speed or rate is 60 mile per hour for Mrs. Rice's drive.

Answer:

The first angle is [tex]70^{o}[/tex].

Step-by-step explanation:

Let the measure of the second angle be represented by [tex]x^{o}[/tex].

Thus, the first angle = [tex](3x+10)^{o}[/tex]

Third angle = [tex]90^{o}[/tex]

Sum of angles in a triangle = [tex]180^{o}[/tex]

So that;

[tex]x^{o}[/tex] + [tex](3x+10)^{o}[/tex] + 90 = [tex]180^{o}[/tex]

[tex]x^{o}[/tex] + [tex]3x^{o}[/tex] + [tex]100^{o}[/tex] = [tex]180^{o}[/tex]

[tex]4x^{o}[/tex] = [tex]180^{o}[/tex] - [tex]100^{o}[/tex]

[tex]4x^{o}[/tex] = [tex]80^{o}[/tex]

divide both sides by 4 to have;

[tex]x^{o}[/tex] = [tex]20^{o}[/tex]

The first angle = [tex](3x+10)^{o}[/tex]

                        = ( 3 x 20 + 10)

                        = 60 + 10

                        = [tex]70^{o}[/tex]

Therefore, the first angle is [tex]70^{o}[/tex].

Step-by-step explanation:

Hey there!!!

Here,

Triangle BCM and triangle ABC are 2 isosceles triangle.

Solving in triangle BCM.

Angle CBM = 31° { it is the base angle.}

Angle CBM + 31° + angle BCM = 180° { sum of interior angle of a triangle is 180°}.

31°+31°+ angle BCM = 180°

Angle BCM = 180° - 62°

Therefore the measure of angle BCM = 118°.

Again,

Solving in triangle ABC.

Angle BCM + angle ACB = 180° { being linear pair}.

118°+ angle ACB = 180°

Angle ACB = 180°-118°

Therefore the measure of angle ACB is 62°.

Angle ACB = angle BAC (Base of an isosceles triangle).

Therefore the measure of angle BAC = 62°.

Now, To find x,

Angle BAC + angle ACB + angle x = 180° (sun of interior angle of a triangle is 180°).

62°+62°+angle x = 180°

Therefore the measure of angle x is 56°.

[tex]hope \: it \: helps...[/tex]

Answer:

actually a 56 pound bag cost =9

so one pound bag cost =9/56=0.16 cents

Step-by-step explanation:

Hey there! I'm happy to help!

To write a percentage as a decimal, you move the decimal place to the left two digits, so 15.8% as a decimal is 0.158.

To find the percentage of a certain number, you multiply it this percent by the certain number.

0.158×43000=6794

So, Sarah will have to pay $6,794.

Have a wonderful day! :D

Answer:

The answer to your question is 192 pretzels

Step-by-step explanation:

Data

number of pieces = 8

length of each piece = 2 ft

length of each pretzel = 1 in

number of pretzels = x

Process

1.- Convert ft to in

                        1 ft --------------- 12 in

                         2 ft --------------- x

                         x = (2 x 12) / 1

                         x = 24 ft

2.- Divide the length of each piece by the length of each pretzel

                       24/1 = 24 pretzels per piece

3.- Multiply the number of pretzels per the number of pieces

                       24 x 8 = 192 pretzels

Answer:

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. ... Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.

Step-by-step explanation:

Answer:

It looks like this question is not solvable. So, if this is absolutely correct, write "no solution".

Step-by-step explanation:

Below is the first step to attempt solving the equation.

The little twos at the top of each number are called exponents. This means a number times itself.

So,

537*537=288,369

15.9*15.9=252.81

74*74=5476

Now, take the 288,369*252.81 to get a total of 72,902,566.89 .

Since this answer is (obviously) not equal to the 5476 on the other side, the two are not equal.

Here's how you'd work it out on paper to show it isn't solvable.

(537*537)*(15.9*15.9)= (74*74)

(288,369)*(252.81)= 5476

72,902,566.89 ≠5476

So the answer would be:

Not solvable.

Given :

P( X = 70 ) = 0.62 .

P( X = 80 ) = 0.23 .

To Find :

We need to find If a person reaches their 70th birthday, what is the probability that they will live to age 80 .

Solution :

We need to find :

[tex]P(X=70 | X=80 )[/tex]

We know ,

[tex]P(x,y ) = \dfrac{P(x)}{P(y)}[/tex]

So ,

[tex]P(X=70 | X=80 )=\dfrac{P(X=80)}{P(X=70)}\\\\=\dfrac{0.62}{0.23}=0.371[/tex]

Hence , this is the required solution .

50 seconds per minute

The rate of entering customers per minute, if 4 customers entered a store over the course of 6 minutes, is 2 / 3.

It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

Given:

4 customers entered a store over the course of 6 minutes,

Calculate the rate of entering customers per minute as shown below,

The rate of entering customers per minute = total number of customer / total time

The rate of entering customers per minute = 4 / 6

The rate of entering customers per minute = 2 / 3

Thus, the rate of entering is 2 / 3.

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Answer:

x = 16.957

Step-by-step explanation:

(3/5)x - 6 = (-1/6)x + 7

Add (1/6)x to both sides. Add 6 to both sides.

(3/5)x + (1/6)x = 7 + 6

(18/30)x + (5/30)x = 13

(23/30)x = 13

Multiply both sides by 30/23.

x = 13/1 * 30/23

x = 390/13

x = 16.957

Answer:

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

Step-by-step explanation:

I had this question not to long ago and got it right

Answer:

23/100

0.23

Step-by-step explanation:

Hope it helps....

Answer:

23% as a fraction is 23/100.

23% as a decimal is 0.23

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

-5-3=-8

-8+2=-6

you subtract 3 from the Total temperature then and 2 to the answer