The length of a Ping Pong table is 3 ft less that four times the width. The area of the
Ping Pong table is 85 square feet. What are the dimensions of the Ping Pong table?

Answer:

50%

Step-by-step explanation:

The given word :

E A C H

There are 2 vowels.

Using the hypergeometric distribution, it is found that there is a 0.1538 = 15.38% probability that the top three finishers in the contest will all be seniors.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that all of them are seniors is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,14,3,8) = \frac{C_{8,3}C_{6,0}}{C_{14,3}} = 0.1538[/tex]

0.1538 = 15.38% probability that the top three finishers in the contest will all be seniors.

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The percentage of the group that is between 62 and 65 inches tall is 47.725%

The given parameters are:

Calculate the z-scores for x = 62 and x = 65 using:

z = (x - μ)/σ

So, we have:

z = (62 - 62)/1.5 = 0

z = (65 - 62)/1.5 = 2

The percentage is then represented as:

P(62 < x < 65) = P(0 < z < 2)

Rewrite as:

P(62 < x < 65) = P(z < 2) - P(z < 0)

Evaluate

P(62 < x < 65) = 0.47725

Express as percentage

P(62 < x < 65) = 47.725%

Hence, the percentage of the group that is between 62 and 65 inches tall is 47.725%

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Answer:

Step-by-step explanation:

256x

Answer: 60/100 or 6/10 or 3/5

Step-by-step explanation:

We get 10+20+30=60.

We Covert to a fraction, 60/100

Reduce Down. 6/10

Reduce again, 3/5

Final answer is 3/5, the chance of it not being Red, White, or Blue is 3/5.

Answer:

What are the dementions? 9 and 2?

That would be 9*3.14*4 = 133.04

~ 133.04 units cubed

Step-by-step explanation:

Using the slope of the linear function, it is found that Mr. Mole descends 2.3 meters per minute.

A linear function is modeled by:

y = mx + b

In which:

In this problem, Mr. Mole's altitude in meters after t minutes is given by:

A = -2.3t - 7.

The rate of change is the slope of m = -2.3, hence, Mr. Mole descends 2.3 meters per minute.

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Answer:

Yes. 3/100 = 0.3

Step-by-step explanation:

3/100 converted to decimal form equals 0.3.

Answer:

No

Step-by-step explanation:

If you divide 100 by 3 you will end up with 0.03, not 0.3.

Hope this helps!

Answer:

u = 5 m/s

Step-by-step explanation:

Given

Required Formula

Solving

Answer:

573440 Kg

Step-by-step explanation:

[tex]\boxed{\bf Mass = density * volume}[/tex]

Find the volume of the solid cube

          Volume of solid cube = side³

                                              = 4 * 4 * 4

                                              = 64 m³

[tex]\sf Mass = 8960* 64\\[/tex]

        = 573440 Kg

Answer:

6

Step-by-step explanation:

3 x 2 x 1

first strip you can have 3 options

second only 2 options left

last one, only 1 choice

RBY

RYB

BRY

BYR

YRB

YBR

Answer:

6 flags

Step-by-step explanation:

The flag must have stripes of 3 different colors.

Ways to arrange each stripe :

Stripe 1 x Stripe 2 x Stripe 3

Answer:

Step-by-step explanation:

Two numbers have a sum of 23 and a difference of 5. What is the smaller of the two numbers.

x + y = 23

x - y = 5

(23 - 5) : 2 = 9

9 + 5 = 14

check

14 + 9 = 23

14 - 9 = 5

Answer:

the mean is 4.5

the median is 5

Step-by-step explanation:

Answer:

C) V = 14130 in³

Step-by-step explanation:

Volue of a sphere: 4/3πr³

Substitute the values from above into the formula to find the volume of the sphere:

V = 4/3πr³

V = 4/3*3.14*15³

V = 4/3*3.14*3375

V = 4/3*10597.5

V = 14130 in³

Hope this helps!

Answer:

equation 1, y = 14 - 6.5

From Alicia's house, the movie theater is 7.5 miles away

Step-by-step explanation:

the total miles is 14

Marisol already drove 6.5 so the remaining amount of miles to the movie theater is 14 - 6.45

Answer:

C - 35 gallons per minute

Step-by-step explanation:

350 / 10

Answer:

350/10 = 35 gallons per minute

Step-by-step explanation:

The correct answer is 12:16 P.M.

According to the problem,

∴ Time at which Dev finishes her lunch =

                  9:52 A.M.  + ( 1 hour and 48 minutes +  36 minutes )

                =   11:40 A.M. +  36 minutes = 12 : 16 P.M.

∴ Deb finish eating lunch at 12:16 P.M.

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Answer:

see explanation

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(- 4, - 7 ) → (4, - 7 )

Answer:

n>3

Step-by-step explanation:

n/3>1

3(n/3)>1(3)

n>3

Answer:

The expression is not factorable with rational numbers.

Hope this helps.

Answer:

-7

Step-by-step explanation: an easy way to find the y-intercept (the point at which the line crosses the y axis) is by identifying what part of the equation does not have an x value. in this problem, it would be -7. if it were to not have a number that is followed by an x the y-intercept is 0.

hope that helps!

Answer:

b 18 boys

Step-by-step explanation:

In order to solve this problem we must create a system of equations.

Creating a system of equations

Let x = number of boys and y = # of girls

We are given that in total there are 27 children which means # of boys + # of girls = 27 so we can say x + y = 27

We are also given that there are twice as many boys as girls so we can also say x = 2y ( as # of boys = twice the number of girls )

Solving the system

Now to find the # of boys and girls we must solve the system. To do so we are going to use the substitution method.

What is the substitution method?

The substitution method is where one of your variables ( x in this case ) is defined by an expression in which you can plug in or " substitute " it into the other equation ( we can substitute x = 2y into the other equation and solve for y )

Substitute equation 2 into equation 1

Equation 1 : x + y = 27

==> plug in x = 2y

y + 2y = 27

==> combine like terms

3y = 27

==> divide both sides by 3

y = 9

So there are 9 girls in the classroom

Solving for # of boys

To solve for the number of girls we plug in the # of girls (y=9) into one of the equations and solve for x

equation : x + y = 27

==> plug in y = 9

x + 9 = 27

==> subtract 9 from both sides

x = 18

There are 18 boys in the classroom

Checking our work:

Now that we have found the possible answers we can check our work. To do so we are going to want to plug in the values of x and y into both equations and if both are true our answer is correct

Equation 1 x + y = 27

==> plug in x = 18 and y = 9

18 + 9 = 27

==> simplify

27 = 27 ✓

equation 2 x = 2y

==> plug in x = 18 and y = 9

18 = 2(9)

==> multiply 2 and 9

18 = 18 ✓

Both are correct therefore we can conclude that there are 18 boys and 9 girls.

Since 30² = 900 and 40² = 1600, between 30 and 40 of the numbers Grogg enters will reduce to integers. Now just find which count is correct. We don't have to look far:

31² = 961

32² = 1024

so there 31 of the outputs of √1, √2, √3, ..., √1000 are integers.

Grogg will result to integers  with  31  outputs from √1, √2, √3, ..., √1000 .

An integer serves as the whole number which can be a positive or negative numbers , such as 6, 9, but it cannot be a fraction.

since, she is starting from √1, √2, √3, up to √1000 , then we know that

31² = 961, then we can find the correct count which is 31. so if she is to input those number into square root one after the other , she will have 31 count.

Therefore, Grogg will result to integers  with  31  outputs from √1, √2, √3, ..., √1000 .

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The initial horizontal component of the vector which represents the velocity of the ball is; Choice C; 11.4 ft./sec.

It follows from the task content that the velocity vector of the ball has magnitude 15.8 ft./sec. and is at an angle of 43.8° with the horizontal.

On this note, it follows from vector resolution that the horizontal component of the ball's velocity is;

V(x) = V cos 43.8⁰

V(x) = 11.4 ft./sec.

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Answer:

X= 38°

Y = 142°

Step-by-step explanation:

let the angle vertically opposite to 142° = w

therefore, w= 142° ( vertically opposite angles are equal)

hence,x+ w =180° ( two interior angles sum up to 180°)

x+ 142° = 180°

x= 180 - 142 = 48°

X = 38°

then calculating for Y

X + Y = 180° ( angles on a straight line sum up to 180°)

38+Y = 180

Y = 180- 38

Y = 142°

Answer:

D.(2, 2)

Step-by-step explanation: