Three spherical balls with radius r are contained in a rectangular box. two of the balls are each touching 5 sides of the rectangular box and the middle ball. the middle ball also touches four sides of the rectangular box. What is the volume of the space between the balls and the rectangular box? This is a SAT question and is no calculator. Show all the work Answer is 4r^3(6-pi)

Answer:

60.96 cm

Step-by-step explanation:

1 feet = 12 inches

2 feet = x inches

Cross Multiply

x inches = 2 feet × 12 inches/1 feet

= 24 inches

From the question, we are told:

1 inch = 2.54cm

24 inches = y cm

Cross Multiply

y cm = 24 inches × 2.54cm/1 inch

y cm = 60.96 cm

Therefore, 2 feet is equivalent or equal to 60.96 cm

Answer:

the answers are below

Step-by-step explanation:

1. the populaton of ths study are the college students that are beng tested on the effect of alcohol on their emotions. college students are the main focus of this experiment.

2. The sample for this study is the 120 students from the University. the sample of a study is actually the number of participants in that study. this queston says that they are 120

3. the null hyothesis:

 h₀ : alcohol has no effect on college students emotions

4. the alternate hypothesis:

 h₁: there is effect of alcohol on college students emotions

5. The researcher would have to use a t test which is an inferential statistical test. A t test is used to test for the existence of statistical difference between two means that may have similar features

Answer:

9.2 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 57 = x/6

6 tan 57 = x

9.239189783 = x

9.2 =x

Answer:

x = 9.2

Step-by-step explanation:

Step 1: Find out what primary trigonometry ratio is needed

The give us the adjacent and the angle.  We need to find the opposite value so we will use tangent

Step 2: Plug in information and solve

[tex]tan(57)=\frac{x}{6} \\x=6tan(57)\\x=9.239[/tex]

Therefore x= 9.2

Answer:

-8

Step-by-step explanation:

slope is change in y divided by change in x

slope = (12-36)/(11-8)

slope = -24/3

slope = -8

Step-by-step explanation:

[tex] \frac{3}{4} = \frac{w}{28}[/tex]

[tex] \frac{3}{4} = \frac{w}{4 \times 7} [/tex]

[tex]3 = \frac{w}{7} [/tex]

[tex]w = 21[/tex]

[tex] \frac{13}{(x + 2)} = \frac{8}{(x - 1)} [/tex]

By cross - multiplication

[tex] \implies13 \times (x - 1) = 8 \times (x + 2)[/tex]

[tex] \implies13x - 13 = 8x + 16[/tex]

[tex] \implies13x - 8x = 16 + 13[/tex]

[tex] \implies5x = 29[/tex]

[tex] \implies \: x = \frac{29}{5} [/tex]

[tex] \implies \: x = 5.8[/tex]

Answer:

-7/2

Step-by-step explanation:

2/3(6x - 18) = -26

divide by 2/3 or multiply by 3/2 (same thing)

6x - 18 = -39

add 18 to both sides

6x = -21

divide by 6

x = -21/6

simplify

x = -7/2

Answer:

Step-by-step explanation:

If one pre calculus class lasts 1.75hours

32 class meetings will last 32*1.75 = 56 hours

Hence the number of hours that the precalculus meets in the semester is 56 hours. In order to know the number of minutes the same class meet, we will convert 56 hours to minutes.

Since 1 hour = 60 minutes

56hours = (56*60) minutes

56hours = 3360 minutes

Expressing 3360 in scientific notation means expressing it in exponential form.

3360 = 3.36 * 10³ minutes

Hence the precalculus class meets for  3.36 * 10³ minutes in a semester.

Answer:

7.5/2 = 3.75

3.75/5 = .75

he gets .75 pounds of candy

Answer:

rotation of 270°

Step-by-step explanation:

Consider the coordinates of of preimage and image of ABC

A(1, 0 ) → A'*0, - 1 )

B(6, - 7 ) → B'(- 7, - 6 )

C(0, - 4 ) C'(- 4, 0 )

What we note is the x- coordinate of the image is the y- coordinate of the preimage and the y- coordinate of the image is the negative of the x- coordinate of the preimage, that is

(x, y ) → (y, - x )

This is equivalent to a counterclockwise rotation about the origin of 270°

Step-by-step explanation:

A rational number is any number that can be divided (written as a fraction) by.

Examples: 1/2, 3, 5/9

*Irrational numbers: cannot be divided

Examples: π, 3.53465374765768957965...

Answer: A rational number is a number that can be expressed as the quotient (i.e. ratio or fraction) of two integers.

Step-by-step explanation: Integers are rational since any integer, n ,can be written as n/1 )Rational numbers are numbers that can be expressed as fractions whereas irrational numbers cannot be expressed as fractions A rational number is a number that terminates or ends. As in a perfect square like: 144; 36; 625 etc.More specifically, a rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero. 1.37, for instance, is rational because it can be expressed as 137 / 100.It is any whole number even if it's a negative number Any number that can be expressed as a fraction is a rational number whereas irrational numbers can't be expressed as a fractions.In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero. Since q may be equal to 1, every integer is a rational number.

Answer:

Step-by-step explanation:

Volume of the water is equivalent to the volume of a cylinder = πr²h where;

r is the radius of the cylindrical tank

h is the height of the water

Given parameters

radius of the cylindrical tank r = 1feet = 12 inches

height of the water inside the tank = 6inches

Volume of the water = πr²h

Volume of the water  = π(12)²*6

Volume of the water  = π*144*6

Volume of the water  = 864π in³

Hence the volume of the water is 864π in³

Answer:

[tex]\huge \boxed{\mathrm{2714.34 \ in^3 }}[/tex]

Step-by-step explanation:

The volume formula for a right cylinder is given as :

[tex]V=\pi r^2 h[/tex]

[tex]V \Rightarrow \sf volume[/tex]

[tex]h \Rightarrow \sf height[/tex]

[tex]r \Rightarrow \sf radius[/tex]

The radius 1 feet ⇒ 12 inches

The height of the water in the cylinder is 6 inches

[tex]V=\pi (12)^2 (6)[/tex]

[tex]V= 2714.336053...[/tex]

The volume of the water is 2714.34 cubic inches.

Answer:

1/8

Step-by-step explanation:

Given:

z = xy

z = 0

y = x

x =1

To find:

volume of the solid bounded by the graphs of the equations

Solution:

Compute integral of volume in the first octant:

[tex]Volume = V = \int\limits^1_0\int\limits^x_0 {z} \, dydx[/tex]

[tex]\int\limits^1_0\int\limits^x_0 {z} \, dydx = \int\limits^1_0\int\limits^x_0 {xy} \, dydx[/tex]

[tex]= \int\limits^1_0x\int\limits^x_0 {y} \, dydx[/tex]

= [tex]\int\limits^1_0[/tex] x y²/2 |ˣ₀  dx

= 1/2  [tex]\int\limits^1_0[/tex] x y² |ˣ₀  dx

= 1/2  [tex]\int\limits^1_0[/tex] x (x²-0²) dx

= 1/2  [tex]\int\limits^1_0[/tex] x³dx

=  [tex]\frac{1}{2} \frac{x^{3+1} }{3+1}[/tex] |¹₀

= (1/2) (x⁴/4) |¹₀

= 1/8 x⁴ |¹₀

= 1/8 (1⁴ - 0⁴)

= 1/8 (1)

V = 1/8

Answer:

941

Step-by-step explanation:

= 1, 2, 3...900 is the number of parents that are going to attend the ceremony.

we are given a random number of parents (0 1 2)

each of these random numbers have a probability of 1/3

so we multiply the numbers by their probability

E(X) = 0*1/3 + 1*1/3 +2*1/3

= 1

E(X²) = 0²*1/3 + 1²*1/3 + 2²*1/3

= 5/3

we calculate the variance

= E(X²)-[E(X)²

= 5/3 - 1²

= 2/3( got this by taking the lcm)

∑Xi with n = 900 will have  to be the number of parents attending this ceremony for all seniors

E|S| = 900 * 1

= 900

var |S| = 900*2/3

=600

we are usng normal distribution to solve this

μ = E(S) = 900

σ² = var(S) = 600

for a seating area wth 900 seats now we are to find the probability that all the parents present will have seats

s-μ/√σ

900 -900/√600

= 0

p(z≤0)

= 0.5

for a seating area wth 925 seats we are to fnd probability that all parents will be seated

= s-μ/√σ

= 925-900/√600

= p(z≤1.0208)

= 0.84623

going to the table of standard normal distribution we have

p(z≤1.644845)= 0.95

s-μ/σ≤1.644845 = 0.95

we cross multply

s-μ≤1.644845σ

we make s subject of the formula

s ≤ μ+1.644845σ = 0.95

we now μ = 900 and

σ = √600

900+1.644845*√600

=900 +40.388

=940.388

= 941

we have that the minimum number of seat requred for all parents n attendance to be seat is 941 at a probability of 0.95

We have the minimum number of seats required for all parents' attendance to be seat is 941 at a probability of 0.95.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

1, 2, 3, .....900 is the number of parents that are going to attend the ceremony.

A random number of parents (0, 1, 2)

The probability is 1/3.

[tex]\rm E(X) = 0 * \dfrac{1}{3} + 1*\dfrac{1}{3}+2*\dfrac{1}{3} = 1\\\\\\E(X^2) = 0^2*\dfrac{1}{3}+1^2*\dfrac{1}{3}+2^2*\dfrac{1}{3}= \dfrac{5}{3}[/tex]

Then the variance will be

[tex]\rm Var = E(X^2) -[E(X)]^2\\\\Var = \dfrac{5}{3} -1 \\\\Var = \dfrac{2}{3}[/tex]

∑Xi with n = 900 will have to be the number of parents attending this ceremony for all seniors

[tex]\rm E \left| S \right| = 900* 1 \\\\E \left| S \right| = 900[/tex]

And

[tex]\rm Var \left| S \right| = 900 * \dfrac{2}{3} \\\\Var \left| S \right| = 600[/tex]

Then by the normal distribution, we have

[tex]\rm \mu = E(S) = 900\\\\\sigma ^2 = Var (S) = 600[/tex]

For a seating area with 900 seats then the probability of the parents present will have seats.

[tex]\rightarrow \dfrac{S - \mu }{\sqrt{\sigma}}\\\\\\\rightarrow \dfrac{900-900}{\sqrt{600}}\\\\\\\rightarrow 0[/tex]

For a seating area with 925 seats then the probability of the parents present will have seats.

[tex]\rm \rightarrow \dfrac{S - \mu }{\sqrt{\sigma}}\\\\\\\rightarrow \dfrac{925-900}{\sqrt{600}}\\\\\\\rightarrow P(z \leq 1.0208) \\\\\rightarrow 0.84623[/tex]

From the standard normal distribution table, we have

[tex]\rm p(z\leq 1.644845) = 0.95\\\\\dfrac{S-\mu}{\sqrt{\sigma }} \leq 1.644845= 0.95\\\\S \leq \mu + 1.644845 \sqrt{\sigma }= 0.95\\\\S=900 + 1.644845*\sqrt{600}\\\\S= 941[/tex]

We have the minimum number of seats required for all parents' attendance to be seat is 941 at a probability of 0.95.

More about the normal distribution link is given below.

https://brainly.com/question/12421652

Answer:

3 days

Step-by-step explanation:

hiking = every 12 days = 1 day

swimming = every 9 days = 1 day

today = he did both exercise = 1 day

find:

how many days from now will you go both hiking and swimming again?

= 3 days

Answer:

≈ 11.66 units

Step-by-step explanation:

Given points:

To find:

The distance between two points is calculated by formula:

Answer is ≈ 11.66 units

Answer:

-1

Step-by-step explanation:

|-1 |= 1

-|-1| = 1

Answer:

-1

Step-by-step explanation:

The question should not be "find the absolute value". Finding the absolute value is part of this problem, but it is not the entire problem.

Think of absolute value of a number as the distance from that number to zero on the number line. A distance is not negative. It is only positive or zero. For example, the number 4 is 4 units from zero on the number line. Then the absolute value of 4 is 4. |4| = 4. Similarly, the number -4 is also 4 units from zero on the number line, so the absolute value of -4 is also 4. |-4| = 4. The absolute value of zero is zero since zero is at a distance of zero units from zero. An absolute value can only be zero or positive. It is never negative.

In your problem, you need to deal with the absolute value of -1 first. -1 is 1 unit from zero on the number line, so the absolute value of -1 is 1.

|-1| = 1

Your problem has one extra step which is the negative outside the absolute value.

-|-1| = -1

Answer:

m=1

Step-by-step explanation:

just expand the brackets using the distributive law and proceed to isolate x

Answer:

w ≥ 14

Step-by-step explanation:

Step 1: Solve

11 ≤ w - 3

11 + 3 ≤ w

14 ≤ w

Therefore w is bigger or equal to 14

Answer:

Step-by-step explanation:

[tex]11 \leqslant w - 3 \\ 11 + 3 \leqslant w \\ 14 \leqslant w[/tex]

Step 1 : Collect like terms and simplify

Answer =

w≤14

Answer:

£107,714  > £107,674

Step-by-step explanation:

Given

£107,714  and £107,674

Required

Determine the relationship between them using > or <

From the given parameters, we understand that

£107,714  is greater than £107,674

The keyword greater than is represented mathematically with  >

Hence:

£107,714  is greater than £107,674

becomes

£107,714  > £107,674

Answer:

The expected value and standard deviation of your total winnings are -$0.081 and $3 respectively.

Step-by-step explanation:

We are given that the game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green.

Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money.

Let the probability of the ball landing on red slot = [tex]\frac{18}{37}[/tex]

The probability of the ball landing on black slot = [tex]\frac{18}{37}[/tex]

The probability of the ball landing on green slot = [tex]\frac{1}{37}[/tex]

Now, it is stated that Gambler can place bets only on the red or black slot, so;

The probability of winning the bet will be = [tex]\frac{18}{37}[/tex]

and the probability of losing the bet will be = [tex]\frac{18}{37}+\frac{1}{37}[/tex]

                                                                        = [tex]\frac{19}{37}[/tex]

If the gambler wins he gets $3 and if he loses he will get -$3.

So, the expected value of gambler's total winnings is given by;

E(X) = [tex]\sum X \times P(X)[/tex]

        = [tex]\$3 \times \frac{18}{37} + (-\$3 \times \frac{19}{37})[/tex]

        = [tex]\$3 \times (-\frac{1}{37})[/tex]  = -$0.081

Now, the standard deviation of gambler's total winnings is given by;

S.D.(X) = [tex]\sqrt{(\sum X^{2} \times P(X))-(\sum X \times P(X))^{2} }[/tex]

So, [tex]E(X^{2})=\sum X^{2} \times P(X)[/tex]

                 = [tex]\$3^{2} \times \frac{18}{37} + (-\$3^{2} \times \frac{19}{37})[/tex]

                 = [tex]\$9 \times (\frac{18}{37}+\frac{19}{37})[/tex]  = $9

Now, S.D.(X) = [tex]\sqrt{\$9-(-\$0.081)^{2} }[/tex]

                     = [tex]\sqrt{8.993}[/tex]  = $2.99 ≈ $3

Hence, the expected value and standard deviation of your total winnings are -$0.081 and $3 respectively.

Answer:

D. x= 10/3

Step-by-step explanation:

|x+3| = 4x -7

1. x+3 > 0 or  x> -3

Since 10/3 is greater than -3, it is accepted correct

2. x+3 < 0 or  x < -3

Here we have 4/5 > - 3, it is contradicting with x< -3 so this is not correct

So there is one solution:

Answer:

(6,-4)

Step-by-step explanation:

That’s where they intersect

Answer:

Table 1 and 2 represent a function

Step-by-step explanation:

Given

Table 1

x 5 10 11

y 3 9 15

Table 2

x 5 10 11

y 3 9 9

Table 3

x 5 10 10

y 3 9 15

Required

Determine which of the tables represent that y is a function of x

For a relation to be a function; the x values must be unique.

In other words, each x value must not be repeated;

Having said that;

Analyzing Table 1

Table 1

x 5 10 11

y 3 9 15

Note that the x rows are unique as no value were repeated;

Hence, Table 1 is a function

Table 2

x 5 10 11

y 3 9 9

Note that the x rows are unique as no value were repeated;

Hence, Table 2 is a function

Table 3

x 5 10 10

y 3 9 15

Note that the x rows are not unique because 10 was repeated twice;

Hence, Table 3 is not a function

Answer:

x * (x+1)^2 = x(x+1)(x+1) = x(x^2 + 2x + 1) = x^3 + 2x^2 + x

Step-by-step explanation:

Is the "$" supposed to be there?

(x+1)^2 = (x+1)(x+1) = x^2 + 2x + 1

That's all I CAN do...I'm not that old yet... =\

Answer:x^(2)+2x^(2)+x hoped i helped

Step-by-step explanation:

Answer:

Hey there!

Are there any more options, because the probability is 7/12.

Also, this is a mutually inclusive event.

Let me  know if this helps :)

Answer:

32 1/2 inches

Step-by-step explanation:

Why this is true is the line is in the middle of 32 and 33 witch means it is 32 1/2

Answer:

9

Step-by-step explanation:

The absolute value of -3 is |-3|, which in turn is 3.  Thus we have

3(3), or 9.  The fourth answer choice is the correct one.

Answer:

Step-by-step explanation:

Answer:

< E = 42.1° is the answer

Answer:

Mean=80

Median=120

Mode=61

Step-by-step explanation:

Mean= sum of the data ÷ number of the data

= 720÷9

= 80

Median= the middle number

= 120

Mode= the number which is repeated

= 61

Hope it helps you :)