A.54 pie cm^3

B.72 pie cm^3

C.126 pie cm^3

D.378 pie cm^3

There are  [tex]55[/tex] ways of these integers be selected to give a sum.

Given that:

It has [tex]12[/tex] consecutive integers .

Now,

Definition of consecutive integers :

" Consecutive integers are the integers that follow in the fixed sequence .

Consecutive integers is represented by  [tex]n,n+1,n+2,n+3,....[/tex] where [tex]n[/tex] is an integer."

By given :

we have [tex]12[/tex] consecutive integers .

Thus,[tex]n=1[/tex] and substitute the equation is,

[tex]1,(n+1),(1+2),(1+3),(1+4),(1+5),(1+6),(1+7),(1+8),(1+9),(1+10),(1+11)\\\\\implies 1,2,3,4,5,6,7,8,9,10,11,12[/tex]

Now,

Split all the integers into 4 equal parts,

Part 1:  Those integers are divisible by [tex]4[/tex] and the remainder be 0.

Then,  

   [tex]a=0(mod 4)[/tex]

Part 2:  Those integer producing the remainder [tex]1[/tex] when it is divisible by [tex]4[/tex].

Then,

   [tex]a=1(mod 4)[/tex]

Part 3:  Those integer producing the remainder [tex]2[/tex]  when it is divisible by[tex]4[/tex].

Then,

    [tex]a=2(mod 4)[/tex]

Part 4: Those integer producing the remainder [tex]3[/tex]  when it is divisible by[tex]4[/tex].

Then,

   [tex]a=3(mod4)[/tex]

Since, three of these integers be selected to give a sum which divides by [tex]4[/tex] is,

In any 12 consecutive integers there are [tex]12\div4[/tex]

i.e. exactly 3 numbers of each category of mod4 namely ,

[tex]0(mod4), 1(mod4), 2(mod4), 3(mod4)[/tex]

Thus, the  total combinations of above [tex]5[/tex] categories of sets of [tex]3[/tex] integers are

                 [tex]3C_1=3(1)=3[/tex]

            [tex]3C_1*3C_2=3(1)*3=9[/tex]

           [tex]3C_1*3C_1*3C_1=3*3*3=27[/tex]

           [tex]3C2 * 3C1 = 3*3 = 9[/tex]

           [tex]3C1 * 3C2 = 3*3 = 9[/tex]

Thus, sum of the total ways be [tex]12[/tex] consecutive integers of three integers is divisible by 4 is,

       [tex]3+9+27+9+9=55[/tex]

Hence, it has [tex]55[/tex] ways.

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Answer:

0.3085 = 30.85% probability that an individual man’s step length is less than 2.5 feet.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 2.7 feet and a standard deviation of 0.4 feet.

This means that [tex]\mu = 2.7, \sigma = 0.4[/tex]

Find the probability that an individual man’s step length is less than 2.5 feet.

This is the p-value of Z when X = 2.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.5 - 2.7}{0.4}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a p-value of 0.3085

0.3085 = 30.85% probability that an individual man’s step length is less than 2.5 feet.

Answer:

No

Not continous at x = 6

Step-by-step explanation:

When x = 6

G(6) = 1/(6 - 6) = 1/0

Dividing by 0 creates a discontinuity

Answer:

1/6

Step-by-step explanation:

Rhianna has 3/6 or 1/2 of a box of pencils

When she divides 3/6 among three people, you get 1/6

Each friend gets 1/6 of a box

Answer: Robert and Chris can skate 10 miles in 45 minutes.

Step-by-step explanation:

Let's start by finding the unit rate.

[tex]\frac{4}{18} =\frac{2}{9} \\\frac{18}{18} =1[/tex]

Robert and Chris can skate [tex]\frac{2}{9}[/tex] of a mile in 1 minute. Now we can multiply both by 45 to see how far the can go in 45 minutes.

[tex](\frac{2}{9}) (\frac{45}{1} )\\\frac{(2)(45)}{(9)(1)} \\\frac{90}{9} \\10[/tex]

45x1=45

The can skate 10 miles in 45 minutes.

Step-by-step explanation:

V should be written as (1/3) pi r^2 h

V = (1/3) pi r^2 h multiply by 3

3V = pi r^2 h Divide by pi

3V/ pi = r^2 h Divide by r^2

3V / (pi *r^2 ) = h

Answer:

2000 meters

Step-by-step explanation:

400 * 5

Answer:

1850 cents or $18.50

Step-by-step explanation:

50*8=400

3*35=105

5*269=1345 ($2.69 can be converted to 269 cents)

400+105+1345=1850

Answer:

y = 1(x - 5)² + 3

Step-by-step explanation:

The general formula of a quadratic equation is written as;

y = a(x − h)² + k

Where (h, k) are the x and y coordinates at the vertex.

Our vertex coordinate is (5, 3)

Thus;

y = a(x - 5)² + 3

Now,we are given another coordinate as (8, 12)

Thus;

12 = a(8 - 5)² + 3

12 = 9a + 3

9a = 12 - 3

9a = 9

a = 9/9

a = 1

Thus,the equation is;

y = 1(x - 5)² + 3

Answer:

36%

Step-by-step explanation:

Step-by-step explanation:

Loss percentage= loss/cost× 100%

250-180=70

70/180=0.3888

0.3888×100%=39%

Answer:

x^2 + 7x + 12 = 0

x^2 + 7x  = -12

(+3)(+4)=0

=−3

=−4

I also love r        o      blox

Hope This Helps!!!

Answer:

(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0

Step-by-step explanation:

Given

x² + 7x + 12 = 0

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 7x

x² + 2([tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] + 12 = 0

(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] + [tex]\frac{48}{4}[/tex] = 0 , that is

(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0

Given:

The function is:

[tex]f(x)=\dfrac{x+4}{x^2-25}[/tex]

To find:

The values that are NOT in the domain of the given function.

Solution:

We have,

[tex]f(x)=\dfrac{x+4}{x^2-25}[/tex]

This function is a rational function and it is defined for all real values of x except the values for which the denominator is equal to 0.

Equate the denominator and 0.

[tex]x^2-25=0[/tex]

[tex]x^2=25[/tex]

Taking square root on both sides, we get

[tex]x=\pm \sqrt{25}[/tex]

[tex]x=\pm 5[/tex]

So, the values [tex]x=-5,5[/tex] are not in the domain of the given function.

Therefore, the correct option is D.

Answer:

Not enough data

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

Perimeter = 2*width + 2*length

So

240 = 2w + 2l

120 = w + l

l = 120 - w

(a) Area = w*l

Substituting for l:

A = w(120 - w)

A = 120w - w^2

(b)

Finding the derivative:

A = 120w - w^2

A' = 120 - 2w

For a maximum area A' = 0, so:

120 - 2w = 0

2w = 120

w = 60 yards for maximum area.

(c)

Maximum area

= 120*60 - 60^2

= 3600 yd^2.

Answer:

Step-by-step explanation:

Use the formula P=MX+B

Answer:

C. -2x +3y-6=0

this is the answer

Answer:

cost of paint set = $ 13.64

cost of sketch book = $ 6.82

cost of brush = $ 4.55

Step-by-step explanation:

Let the cost of paint set is s.

cost of sketch book = s/2

cost of brush = s/3

Money spent = $ 28 - $ 3 = $ 25

So,

s +  s/2 + s/3 = 25

6 s + 3 s + 2 s = 150

11 s = 150

s = $ 13.64

cost of paint set = $ 13.64

cost of sketch book = $ 6.82

cost of brush = $ 4.55

[tex]\displaystyle\bf 4\sqrt{28} :3\sqrt{7} =4\sqrt{4} \cdot \sqrt{7} :3\sqrt{7} =4\cdot2:3=\boxed{\frac{8}{3} }[/tex]

Answer:

remember how the absolute value works:

|x| = x   if x ≥ 0

|x| = -x  if x < 0

Then we can rewrite:

|x| ≤ a

as:

-a ≤ x ≤ a

Now let's apply this to our case:

|3x + 5| ≤ 1

we can rewrite this as:

-1 ≤ 3x + 5 ≤ 1

We could solve this for x now, first subtracting 5 in the 3 sides:

-1 - 5 ≤ 3x + 5 - 5 ≤ 1 - 5

-6 ≤ 3x ≤ -4

now dividing by 3 in the 3 sides:

-6/3 ≤ 3x/3 ≤ -4/3

-2 ≤ x ≤ -(4/3)

So we rewrote the inequality without the absolute value part.

The last equation says z = 3, so that in the second equation we get

y + 2z = y + 6 = 5   ==>   y = -1

and in turn, the first equation tells us

x - 2y + 2z = x + 2 + 6 = x + 8 = 9   ==>   x = 1

So the solution to the system is (x, y, z) = (1, -1, 3).

Answer:

|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

If [tex]|Z| > 2[/tex], the value of X is considered to be unusual.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15.

This means that [tex]\mu = 100, \sigma = 15[/tex]

Sample of 3

This means that [tex]n = 3, s = \frac{15}{\sqrt{3}}[/tex]

Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

We have to find the z-score.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{115 - 100}{\frac{15}{\sqrt{3}}}[/tex]

[tex]Z = 1.73[/tex]

|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.

Answer:

I. Length, L = 9.552 meters

II. Width, W = 7.96 meters

Step-by-step explanation:

Let the length = L

Let the width = W

Given the following data;

Perimeter = 35 m

Translating the word problem into an algebraic equation, we have;

Length = 1.2W

To find the dimension of the room;

The perimeter of a rectangle is given by the formula;

P = 2(L + W)

Substituting into the formula, we have;

35 = 2(1.2W + W)

35 = 2(2.2W)

35 = 4.4W

Width, W = 7.96 meters

Next, we would find the length of the rectangle;

L = 1.2*W

L = 1.2 * 7.96

Length, L = 9.552 meters

Answer:

For that you should prove Ac²=Ab²+Bc²

Step-by-step explanation:

Use distance formula for finding each distance Ac,Ab and BC and prove "Ac²=Ab²+Bc²" as true

Answer:

a) Japan =0.599

US= 0.006

b) Japan

Variance= 0.475

Standard Deviation =0.69

USA

Variance =2.4

Standard Deviation= 1.55

Step-by-step explanation:

A represents the number of defendants found guilty in Japan in 10 trials

B represents the number of defendants found guilty in US in 10 trials

A represents a binomial function such that n=10,p=0.95 and B represents a binomial function such that n=10,p=0.60

a) Japan: P(A=10)=0.95^10=0.599

US: P(B=10)=0.60^10=0.006

b) Japan:

Expected number of guilty verdicts in 10 trials in Japan =  np=10*0.95=9.5

Variance: Var(A) = np(1-p) = 10*0.95*(1-0.95) = 0.475

Standard Deviation = sd(A)=√0.475=0.69

US:

Expected number of guilty verdicts in 10 trials in USA = np=10*0.60=6

Variance: Var(B)=np(1-p)=10*0.6*0.4=2.4

Standard Deviation sd(B)=√2.4=1.55

Answer:

(h o k) (3) = 3

(k o h) (-4b) = -4b

Step-by-step explanation:

An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.

This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.

Answer:

Monday: 7.25

Tuesday: 6.75

Wednesday: 5.2

Thursday: 6.1

Answer:

1,188,137,600 possible combinations

Step-by-step explanation:

The first three and last two digits can be any letter while the middle two digits can be any number.

26*26*26*10*10*26*26=1,188,137,600

1. 3

29-9=19

13+9=22

22-19=3

I don't know number 2, sorry.