A cube shaped aquarium with a side length of 1.2 meters is full of liquid. A fish swims in the container. What is the probability that the fish is at most 0.5 meters away from the center of the container?

Division of the monomial denominator by writing the fraction as the sum or difference of fractions is    [tex]8x+8 - \frac{1}{x^{3}}[/tex].

What is a polynomial equation?

Polynomial long division is a generalized variant of the well-known arithmetic operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.

We have,

                   [tex]\frac{8x^{4} + 8x^{2} - 1}{x^{3}}[/tex]

Break down the polynomial and divide:

                 [tex]= \frac{8x^{4} }{x^{3} } + \frac{8x^{2}}{x^{3}} + \frac{-1}{x^{3}}[/tex]

Calculating each division we get

                [tex]=8x+ 8x - \frac{1}{x^{3} }[/tex]

Therefore the final answer is

                 [tex]\frac{8x^{4} +8x^{3} −1}{x^{3}} = 8x+8 - \frac{1}{x^{3}}[/tex]

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If the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).

Let the given function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex]

Differentiating with respect to x, we get

d/dx((2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex])

= sin (2) (d/dx(2[tex]$$x^4[/tex] + 1) [tex]$$x^5[/tex] + d/dx ([tex]$$x^5[/tex])  (2[tex]$$x^4[/tex] + 1)

d/dx (2[tex]$$x^4[/tex] + 1) = 8x³

d/dx ([tex]$$x^5[/tex]) = 5[tex]$$x^4[/tex]

= sin (2) (8x³ + 5[tex]$$x^4[/tex] (  (2[tex]$$x^4[/tex] + 1)

Simplify

= sin (2) (8x³ + 5[tex]$$x^4[/tex] (  (2[tex]$$x^4[/tex] + 1)

= sin (2) (18[tex]$$x^8[/tex] +  5[tex]$$x^4[/tex]

Therefore, the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).

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The probability that the sample proportion surviving for at least 3 years will be less than 67% is of:

0.1131 = 11.31%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:

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

The proportion and the sample size are given as follows:

p = 0.73, n = 80.

Hence the mean and the standard error are given as follows:

The probability that the sample proportion surviving for at least 3 years will be less than 67% is the p-value of Z when X = 0.67, hence:

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

Z = (0.67 - 0.73)/0.0496

Z = -1.21

Z = -1.21 has a p-value of 0.1131.

Hence the probability is:

0.1131 = 11.31%.

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The number of dogs do they need to walk in order to pay for the box of treats is 4

The function that representing the profit is

y = 3x - 5

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Here the cost for buying a box of treat = $5

Substitute the value in the function and find the number of dog that they need to walk

5 = 3x - 5

3x = 5 + 5

3x = 10

x = 10 / 3

x = 3.33

x ≈ 4

Hence, the number of dogs do they need to walk in order to pay for the box of treats is 4

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The time the airforce plane needs to before the planes are 3510 miles apart is 8.32 hours.

Time is the duration of an event

Since a jet left paris and flew toward moscow at an average speed of 410 mph. an air force plane left three hours later and flew in the opposite direction with an average speed of 160 mph.

The distance flown by the jet is d = vt where

So, d = 410t

Also, the distance flown by the airplane is D = vt' where

So, D = 160t'

= 160(t + 3)

Since the total distance apart of the both jet and airplane is D' = d + D, we have

D' = 410t + 160(t + 3)

Given that D = 3510 miles, we have that

410t + 160(t + 3) = 3510

Soving for t, we have

410t + 160t + 480 = 3510

570t = 3510 - 480

570t = 3030

t = 3030/570

t = 5.32 hours

Since t' = t + 3, we have

t' = 5.32 + 3

= 8.32 hours

So, the airforce plane needs to fly for 8.32 hours.

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Answer:

B(a) = a/6 - 9

Step-by-step explanation:

The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.

What is the area of a trapezoid?

If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as

= [(a + b)h]/2

Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.

Therefore, 'b' is the parallel side of the base.

The given function that represents the area of the trapezoid is:

A(b) = [12(b + 9)]/2

Let, A(b) = a.

Therefore, a =  [12(b + 9)]/2

⇒ 2a = 12(b + 9)

⇒ a = 6(b + 9)

⇒ a = 6b + 54

⇒ 6b = a - 54

⇒ b = (a - 54)/6

⇒ b = a/6 - 9

If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:

B(a) = a/6 - 9

Answer: ZYH

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The value of C (8,5) is 56.

A combination is made up of n different items that are taken one at a time without repeating itself.

The given expression is C(8,5).

The expression C (8,5) can be denoted as ₈C₅.

The formula for selecting x thins from n things is:
ₙCₓ = n!/( (n-x)! x!)

Therefore, the value of ₈C₅ is:

₈C₅ = 8!/( (8-5)! 5 !)

     = 8!/( 3! ×5!)

      = (8×7×6×5!)/( 3! ×5!)

      = (8×7×6)/(3!)

      = (8×7×6)/(6)

      = 8×7

      =56

Hence, the value of C (8,5) is 56.

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Option B. The appropriate conclusion at the 5% significance level is to Reject the null hypothesis, the population mean is significantly different from 123

H0: mean = 123

H1 : mean ≠ 123

We have the p value of the statistics stated already in the question as p value = 0.0037.

The level is significance that we have been given in the question is 5% = 0.05

We are to test here if the true mean is different from 123.

Hence we would be testing the p value against the significance level.

We can see that P value is  < level of significance.

0.0037 < 0.05

Hence we would reject the null hypothesis.

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The amount of profit made by JMP is 102000.

Given,

In the question;

JMP made a profit of $85,000 last year.

If the profit margin increased by 20% this year.

To find the amount of profit made by JMP.

Now, According to the question:

Based on the given condition:

Formulate:

= 85000 x (20% + 1)

Calculate;

85000 x (0.2 + 1)

Calculate the sum or difference

85000 x 1.2

= 102000

Hence, The amount of profit made by JMP is 102000.

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A) The speed (in m/s) at which the ball hits the ground is; 23.43 m/s

B) The time (in s) that it takes the ball to remain in the air is; 3.67 s

C) The maximum height attained by the ball is; 16.51 m

A) The motion of the ball on the vertical axis is basically uniformly accelerated motion, with acceleration g = 9.81 m/s² and initial vertical velocity v_y = 18 m/s, so the vertical position of the ball at time t is:

y(t) = v_y*t - ¹/₂gt²

The formula for time when the ball hits the ground is;

t = 2v_y/g

t = (2 * 18)/9.81

t = 3.67 s

Thus, vertical velocity at time t is given by the formula;

v_y(t) = v_y - gt

v_y(t) = 18 - (9.81 * 3.67)

v_y(t) = -18 m/s (which shows it is in the opposite direction because of the negative sign)

Thus, the speed at which the ball hits the ground is the resultant of the vertical and horizontal velocity at time t;

v = √(v_x² + v_yt²)

v = √(15² + 18²)

v = 23.43 m/s

b) From a above, the time that the ball remains in the air is the time it takes to hit the ground which is t = 3.67 s

c) The time to reach maximum height is half the time it takes to reach the ground. Thus;

t = 3.67/2 = 1.835 s

Thus maximum height is given by the formula;

y(t) = v_y*t - ¹/₂gt²

y(1.835) = 18(1.835) - ¹/₂(9.81)(1.835²)

y = 16.51 m

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The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

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A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.

What is a combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

Here,

There are 4 numbers needed for the combination and one can pick between 0 and 32.

This means that there are 33 numbers that can be used for the lock including 0.

The number of possible combinations is:

= Number that can be used with no restrictions on the number combination lock limit

= 33 ⁴

= 1,185,921 combinations

Hence, If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.

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Step-by-step explanation:

Given the inequality 4x ≤ 28, determine the value of x.

4x ≤ 28

divide both sides by 4:

4x/4 ≤ 28/4

x ≤ 7

set builder notation: (-∞, 7]

answer:

The value of x is 7.

Step-by-step explanation:

4x ≤ 28 | divide both sides by 4

4x / 4 = x  and 28 / 4 = 7

therefore, x ≤ 7

Answer:

[tex]2,8,14,20[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]2[/tex] and the common difference is [tex]6[/tex], then each successive term in the sequence is [tex]6[/tex] more than the previous term:

[tex]a_n=6n-4[/tex]

Therefore, the first term is [tex]2[/tex], followed by [tex]8[/tex], [tex]14[/tex], and [tex]20[/tex].

Answer:

6

Step-by-step explanation:

the answer is 6

The loan given has a rate of 0.53%

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.

The formula of simple interest is given as;

S.I = P(1 + RT)

Substituting the values into the formula;

(9000 + 336) = 9000(1 + r * 7)

9336 = 9000 + 63000r

Collecting like terms

336 = 63000r

r = 0.0053

r = 0.0053 * 100

r = 0.53%

The rate on the loan is 0.53%

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Answer:

s = 89°

Step-by-step explanation:

Exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.

[tex] \therefore[/tex]

[tex] \rm \implies (v + 1) \degree + (v - 28) \degree = (v + 32) \degree \\ \\ \rm \implies 2v - 27 \degree = (v + 32) \degree \\ \\ \rm \implies 2v -v = 32 \degree + 27 \degree \\ \\ \rm \implies v = 59 \degree [/tex]

Sum of angles in a straight line is equal to 180°

[tex] \therefore[/tex]

[tex]\rm \implies v + 32 \degree + s = 180 \degree \\ \\ \rm \implies 59 \degree + 32 \degree + s = 180 \degree \\ \\ \rm \implies s + 91 \degree = 180 \degree \\ \\ \rm \implies s = 180 \degree - 91 \degree \\ \\ \rm \implies s = 89 \degree[/tex]

For given function  f(x) = 7/(x² - 5),

f(a + 4) = 7/(a² + 8x + 11)

In this question we have been given a function f(x) = 7/(x² - 5)

We need to evaluate f(a + 4)

Substitute x = a + 4 in given function.

f(a + 4)

= 7/((a + 4)² - 5)

=  7/(a² + 8x + 16 - 5)

=  7/(a² + 8x + 11)

Therefore, for given function  f(x) = 7/(x² - 5),

f(a + 4) = 7/(a² + 8x + 11)

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Answer:

Step-by-step explanation:

You want to know the numbers of dimes and quarters that make 475 cents using 25 coins.

Let q represent the number of quarters. Then 25-q is the number of dimes, and the total value of the coins is ...

  25q +10(25-q) = 475

Simplifying the above equation gives ...

  15q +250 = 475

  15q = 225 . . . . . . . subtract 250

  q = 15 . . . . . . . . . divide by 15; number of quarters

  25 -q = 10 . . . . number of dimes

The man has 10 dimes and 15 quarters.

The equation in slope intercept form of the line that passes through the graph is y = 2/3x + 2

From the graph, we have the points to be given as

(-3,0) and (0,2)

Start by calculating the slope of the points using the following slope equation

m = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-3,0) and (0,2)

So, we have

m = (2 - 0)/(0 + 3)

Evaluate

m = 2/3

The equation is then calculated as

y = m(x - x₁) + y₁

Where

(x, y) = (0, 2) and m = 2/3

So, we have

y = 2/3(x - 0) + 2

Expand

y = 2/3x + 2

Hence, the equation in slope intercept form of the line is y = 2/3x + 2

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Answer: candidate 2 has 90 votes

Step-by-step explanation:

165-75=90

The area of triangle using vertices is D)  A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

What is area of triangle using vertices ?

 The length of a triangle's three sides must first be determined if the triangle's vertices are known. The distance formula can be used to determine the length. when the vertices in the coordinate plane are known, the process to determine the triangle's area. Consider the triangle PQR, whose coordinates P, Q, and R are [tex](x_1,y_1)(x_2,y_2)[/tex], and [tex](x_3,y_3)[/tex] respectively.

If the triangle's area is zero and its vertices are P[tex](x_1,y_1)[/tex] Q[tex](x_2,y_2)[/tex], and R[tex](x_3,y_3)[/tex] then (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_2(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]] = 0 and its points are collinear.

Here the given vertices are, [tex](x_1,y_1),(x_1,y_2)[/tex] and [tex](x_3,y_3)[/tex] then the area of triangle is ,

=> A =  (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_2(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]]

=> A =  (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_1(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]]

=> A = (1/2)[ [tex]x_1y_2-x_1y_3+x_1y_3-x_1y_1+x_3y_1-x_3y_2[/tex]]

=> A = (1/2) [[tex]x_1y_2-x_1y_1+x_3y_1-x_3y_2[/tex]]

=> A = (1/2) [[tex]x_1(y_2-y_1)-x_3(y_2-y_1)[/tex]]

=> A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

Hence the correct option is D)  A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

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The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The linear function with a slope of 3 and y-intercept of 10 is y = 3x + 10.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Slope = 3

y-intercept = 10

The equation of a line is given as y = mx + c

m = slope

c = y-intercept

Now,

m = 3

c = 10

So,

The linear function with a slope of 3 and y-intercept of 10 is y = 3x + 10.

Thus,

The linear function with a slope of 3 and y-intercept of 10 is y = 3x + 10.

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Answer: 56 minutes

Step-by-step explanation:

7 = 7, 14, 28, 35, 42, 49, 56

8 = 8, 16, 24, 32, 40, 48, 56

7 and 8 have 56 in common so it would take them 56 minutes

Latrina will serve 640 hors d’oeuvres to the 240 people at her wedding .

In the question ,

it is given that

At Latrina's wedding

number of  hors d’oeuvres offering that 3 people will get = 8 offering

So, the number of offering of hors d’oeuvres that 1 person will get = 8/3  .

we need to find that

how many hors d’oeuvres will she serve for 240 people .

So ,

the number of  hors d’oeuvres offering that 240 people will get =(8/3)×240

= 8 × 80

= 640

Therefore , Latrina will serve 640 hors d’oeuvres to the 240 people at her wedding  .

The given question is incomplete , the complete question is

Latrina is planning to serve hors d’oeuvres at her wedding. She plans on offering 8 hors d’oeuvres for every 3 people. If she has invited 240 people to the wedding, how many hors d’oeuvres will she serve?

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There are  181440 number of different 10 letter words , (real or imaginary) that can be formed from the given letters   .

In the question ,

it is given that ,

the letters are X, W, C, V, R, Z, W, U, M, A ,

since the total number of letters = 10 ,

So , 10 letter can be arranged in 10! ways = 362880 ways

and we can also see that the letter W is repeated 2 times

So it can be arranged in 2! ways = 2 ways .

So , the total number of different 10 letters words that can be formed is calculated by dividing total number of possible arrangements by arrangement of each repeated letter ,

that is ,

= 362880 / 2

= 181440  .

Therefore  , There are 181440 number of different 10 letter words (real or imaginary)that can be formed from the given letters   .

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David share is £8

Vicky share is £28

From the question, we have

David and Vicky share £36 in the ratio 2:7.

David share = £36 *2/9 = £8

Vicky share = £36 *7/9 = £28

Multiplication:

The product of the numbers is what is obtained in mathematics when two or more numbers are multiplied. We frequently perform it since it is one of the fundamental mathematical operations. Using multiplication tables is the most straightforward use. In mathematics, adding a number repeatedly in relation to another is represented by multiplying two integers. These figures can be natural figures, whole figures, fractional figures, integer figures, or other figures. When m is multiplied by n, m is either added to itself n times or multiplied by n.

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By the concept of basic arithmetic, it is $3.64 more expensive per pound, to buy salmon at Super Grocery A than at Super Grocery B.

The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.

At Super grocery B, 3 pounds of Salmon cost = $ 24.63

So, 1 pound will cost = $ 24.63/ 3

= $ 8.21

At Super grocery A, 2 pounds of Salmon cost = $ 23.70

So, 1 pound will cost = $23.70/ 2

= $ 11. 85

To buy salmon at SuperGrocery A than at SuperGrocery B expense per pound is given by

= $11.85 - $ 8.21

$ 3.64

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