a steel sphere with a 3-inch radius is made by removing metal from the corners of a cube that has the shortest possible side lengths. how many cubic inches are in the volume of the cube?

The Number of small and large boxes shipped are 10 and 5 respectively.

Large boxes :

Volume = 18 cubic feets

Let number of large boxes = b

Small boxes :

Volume = 10 cubic feets

Number of small boxes = 2b

Total volume shipped = 190 cubic feet

To obtain total volume shipped :

(Number of small boxes × volume of small boxes) + (Number of large boxes × volume of large boxes

Writing as a system of equation :

(10 × 2b) + (18 × b)

20b + 18b = 190 cubic feets

38b = 190

b = 190 ÷ 38

b = 5

Hence,

Number of large boxes = 5

Number of small boxes = 2(5) = 10

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Answer:

Step-by-step explanation:

It is a representation of the functional relation with dependent and independent variables, normally, x- independent and f(x) - dependent variable.

We can write the given function as:

The value of x is 40 and the value of y is 25.

What is consecutive interior angles?

Pairs of angles that are between two lines and on the same side of the line that cuts through the two lines are referred to as consecutive internal angles. According to the theorem, if two lines are parallel, then successive interior angles are supplementary to one another.

Angles that add up to 180 degrees are referred to as supplementary angles.

As we know that the sum of three angles of triangle is 180 degrees.

So from the first figure we get,

2x + x + y + y + 10 = 180

3x + 2y = 170          ...(1)

From the second figure we get,

4x - y + x + 5 = 180         (Since they are consecutive interior angles)

5x - y = 175             ...(2)

After solving equation (1) and (2), we get

x = 40 and y = 25

There the value of x is 40 and the value of y is 25.

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The Nya will pay $46.42 for the sweater. The decimal equivalent of a 20 percent discount is 0.20. To calculate the savings in dollars, multiply the decimal discount by the item's price. For instance, if the item's original price is $24, you would multiply 0.2 by that amount to get $4.80.

We have been given that Nya wants to buy a sweater that had an original price of $55. The sweater is now discounted 20%.

the price of sweater after20% discount is 55-20% of 55

The price of the sweater after discount =55-(20/100*55)

The price of the sweater after discount=55-(0.20*55)

The price of the sweater after discount=55-11

The price of the sweater after discount=44

SO  The price of the sweater after discount is $44

Now let us find the price of sweater after adding 5.5% sales tax

The price of sweater after sales tax =44+(5.5/100*44)

The price of sweater after sales tax=44+(0.055*44)

The price of sweater after sales tax=44+2.42

The price of sweater after sales tax=46.42

$46.42 is paid for sweater after sales tax

Hence, The Nya will pay $46.42 for the sweater.

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The experimental design which is used in the study is Completely randomized design.

Completely Randomized design may be defined as a technique in which all the solutions are assigned at random so that each questions receive all the possible solutions. According to the question we know that the sample size is 100 volunteers who are suffering from chronic pain. Now, out of the 100 volunteers, 50 males and 50 females are chosen. Further out of the 50 males, 25 males are randomly assigned to the treatment group while the other 25 males are assigned to a control group. Since, the treatments are randomly assigned completely, each of the volunteers have an equal chance of receiving the treatments.

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The sample size needed will be equal to n = 149.

The (1 - α)% confidence interval for population proportion is given by

CI = p ± z(α/2)√p (1 - p)/n

The margin of error will be given as

MOE = z(α/2)√p (1 - p)/n

We know that approximately 73% people support the candidate and margin of error is 0.06.

The critical value of z for confidence level 94% is given by z = 1.65. Now, using the formula of Margin of Error.

MOE = z(α/2)√p (1 - p)/n

n = [z(α/2)√p (1 - p)/MOE]²

n = [1.65√0.73 (1 - 0.73)/0.06]²

n = 148.84

n = 149 approximately which is the required sample size.

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Answer:

the answer is 2 and one fourth

Step-by-step explanation:

because the 3s cancel out

The boxes of candy sold by Roger are 29/30.

According to the question,

We have the following information:

Roger sold 1/3 as much candy as Sally sold.

Sally sold [tex]2\frac{9}{10}[/tex] boxes of candy.

Now, first we will convert the boxes of candy sold by Sally from the mixed fraction.

(More to know: there are three kinds of fraction: mixed fraction, proper fraction and improper fraction. We need to change mixed fraction in most of the cases to solve the questions further.)

We have:

29/10

Now, we know that the boxes of candy sold by Roger is 1/3 of 29/10.

So, we have the following expression:

[tex]\frac{1}{3}* \frac{29}{10}[/tex]

29/30

Hence, the boxes of candy sold by Roger is 29/30.

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The polynomial is f(x) = x³ - 12x² + 64x + 128

Given,

The polynomial has 4, 4-4i, and 4+4i as its roots.

f(-1) equals -255

We have to find a polynomial of degree 3.

If x = 4 is a root, then:

(x - 4) is a factor of the polynomial.

If x = 4 - 4i is a root,

Then,

(x - 4 + 4i) is a factor of the polynomial.

If x = 4+4i is a root.

Now,

(x - 4 - 4i) is a factor of the polynomial.

All the three roots are of the same polynomial.

So,

The polynomial is the product of these factors.

f(x) = k(x - 4) (x-4+4i) (x-4-4i)

f(x) = k(x - 4) [(x-4)² - (4i)²]

f(x) = k(x- 4) [x² + 16 - 8x + 16]

f(x) = k(x - 4) [x² - 8x + 32]

f(x) = k[x³ - 8x² + 32x - 4x² + 32x - 128]

f(x) = k[x³ - 12x² + 64x + 128]

Now find "k", we know that f(-1) = -255.

f(-1) = k[(-1)³ - 12(-1)² + 64(-1) + 128]

-255 = k[-1 - 12 - 64 + 128]

-255 = k × -255

k = 1

That is, the polynomial is f(x) = x³ - 12x² + 64x + 128

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The equation that relates the number of chirps per minute x, and the outside temperature in degrees Fahrenheit is x = 4f -148. If the snowy tree cricket chirps 100 times in a minutes, the the outside temperature is 62 degrees Fahrenheit.

The number of chirps per minute is 148 less than 4 times the outside temperature in degrees Fahrenheit.

The number of chirps per minute = x

The outside temperature in degrees Fahrenheit = f

Then the linear equation will be

x = 4f - 148

Given that x = 100 chirps per minutes

Substitute the values in the equation

100 = 4f -148

4f = 100+148

4f = 248

f = 248/4

f = 62 degrees Fahrenheit.

Hence, the equation that relates the number of chirps per minute x, and the outside temperature in degrees Fahrenheit is x = 4f -148. If the snowy tree cricket chirps 100 times in a minutes, the the outside temperature is 62 degrees Fahrenheit.

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Answer:

5, 11, 8

Step-by-step explanation:

I did the quiz and got it correct :]

In general, one can obtain the volume of a sphere and a cube using the formulas below

In our case, we need to subtract the volume of the hollow sphere from the volume of the cube, as shown below

Rounding to the nearest hundredth,

The answer is 2778.37in^3

A perfect square is a number that is gotten by multiplying it by itself.

An example of a perfect square is 25 and one that is not is 7.

A square number, sometimes known as a perfect square, is an integer that is the square of another integer; in other words, it is the product of another integer and itself. For instance, 9 is a square number since it equals 3² and may be expressed as 3 × 3.

A perfect square is a number that can be written as the product of two integers or as an integer's second exponent. 25 is a perfect square because it is the product of the integer 5 and itself, 5 × 5 = 25. A perfect square is a positive integer formed by multiplying an integer by itself.

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Answer:

  y = -1/3x +1

Step-by-step explanation:

You want the slope-intercept form equation of the line through the points (-3, 2) and (-9, 4).

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x)

  m = (4 -2)/(-9 -(-3)) = 2/-6 = -1/3

The y-intercept is given by the formula ...

  b = y1 -m(x1)

  b = 2 - (-1/3)(-3) = 1

The slope-intercept equation of the line is ...

  y = mx +b

  y = -1/3x +1

ANSWERS

1. Domain: all real values

2. Zeros: 0 (with multiplicity 2) and 3

3. Not periodic. Symmetric about the point (1, 2)

4. Positive for x < 3; negative for x > 3

5. f → ∞ as x → -∞; f → -∞ as x → ∞

6. none

EXPLANATION

1. The domain of a function is the set of all the x-values for which the function exists. In this case, we have a polynomial function and, therefore, the domain is all real values.

2. To find the zeros of the function, we have to solve,

First, factor x² and -1 out. To do so, we have to divide each term by x² and by -1 - or, in other words, divide by -x²,

So, we have,

In this equation, we can see that if x = 0, then the equation is true. Also, if x = 3 the equation is true. So, these are the two zeros, with the particularity that x = 0 has multiplicity 2. This is because the factor related to that zero is x squared.

Hence, the zeros are 0 and 3. 0 has multiplicity 2.

3. As mentioned before, this is a polynomial function, which means that it is not a periodic function. A cubic function is an odd function, and it is symmetric about the origin. However, this function is not the parent function, x³, but it is symmetric about the point (1, 2).

4. We know that the function is zero at x = 0 and at x = 3. For x < 0, the function is positive,

For 0 < x < 3, the function is also positive. This is because x = 0 with multiplicity 2.

Then, since the function crosses the x-axis at x = 3 and that zero has multiplicity 1, we can conclude that the function is negative for x > 3.

Hence, is the function is positive for x < 3 and negative for x > 3.

5. As mentioned in part 4, the function is positive for all values of x less than 3, which means that the function goes to infinity as x goes to negative infinity.

Since for x > 3 the function is always negative, it goes to negative infinity as x goes to infinity.

6. A polynomial function has no restrictions in the domain and, therefore, has no asymptotes.

When seen as a function, a relationship exists between a set of inputs and outputs.

The number of bricks in the chimney exists 900.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Simply described, a function is an input-output connection where each input is coupled to exactly one output range, codomain, and domain are included in each function. A function exists generally denoted by f(x) where x exists the input.

Let x be the number of bricks in the chimney. The work done exists the rate multiplied by the time.

Using w = rt, we get

[tex]$x=\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5[/tex]

Expanding the above equation, we get

[tex]$\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5: \quad \frac{19 x}{18}-50$[/tex]

x = (19x / 18) - 50

Multiply both sides by 18

[tex]$x \cdot 18=\frac{19 x}{18} \cdot 18-50 \cdot 18[/tex]

Simplifying the above equation,

x × 18 = 19x - 900

Subtract 19x from both sides

x × 18 - 19x = 19x - 900 - 19x

Simplifying the above equation, we get

-x = -900

Divide both sides by -1

[tex]$\frac{-x}{-1}=\frac{-900}{-1}[/tex]

x = 900

Therefore, the value of x exists 900.

The complete question is:

Bricklayer Brenda would take nine hours to build a chimney alone, and bricklayer Brandon would take  hours to build it alone. When they work together, they talk a lot, and their combined output decreases by  bricks per hour. Working together, they build the chimney in  hours. How many bricks are in the chimney?

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The range of the given function is {-5,-1,4} which is the B option.

Given function:-

[tex]f(x) = x^2+4x-1[/tex]

Domain = {-2,0,1}

We have to find the range of the given function for the given domain.

Putting x = -2 in the given function, we get,

[tex]f(-2) = (-2)^2+4(-2)-1[/tex]

f(-2) = 4 - 8 - 1 = -5

Putting x = 0 in the given function, we get,

[tex]f(0) = (0)^2+4(0)-1[/tex]

f(0) = 0 + 0 -1 = -1

Putting x = 1 in the given function, we get,

[tex]f(1) = (1)^2+4(1)-1[/tex]

f(1) = 1 + 4 - 1 = 4

Hence, the range of the given function is {-5,-1,4}.

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The equation of the line that represents the information is y = $40.

The slope of the line is 0.

The equation that represents the total amount paid by Mr. Williams for the city water can be represented with a linear equation. A linear equation is an equation that is made up of a single variable that is raised to the power of one.

The form of a linear equation is:

y = ax + b

Where:

y = $40 + (x × 0)

y = $40

When shown on a graph, a linear equation can either slope upward, downward or have a slope of zero.

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In order to find 5a-3b, lets find 5a. This is given by

Similarly, -3b is given by

Then, by substituting our results into the expression 5a-3b, we get

This can can be done by adding entry by entry, that is

Therefore, the answer is

a) The probability that exactly 2 of them have never been married is[tex]0.0026 \text{ or }2.6*10^{-3}[/tex]

b) The probability that at most 2 of them have never been married is[tex]0.0029\text{ or }2.9*10^{-3}[/tex]

c) The probability that at least 13 of them have been married is [tex]0.0046 \text{ or } 4.6*10^{-3}[/tex]

a)  What is the probability that exactly 2 of them have never been married?

By applying binomial probability distribution method,

[tex]P(x)=^{n}C_{x}p^{x}q^{n-x}[/tex]

Substitute,

P(x) =Binomial probability =  51% = 0.51

x = No. of times of an outcome = 2

n = No. of trials = 15

q =  Probability of failure = 49% = 0.49

[tex]^{n}C_{x}[/tex] = No. of combinations

[tex]P(2)=^{15}C_{2}*(0.51)^{2}*(0.49)^{15-2}\\\\P(2)=\frac{15!}{13!2!} *(0.51)^{2}*(0.49)^{13}\\\\P(2)=0.0026 \text{ or }2.6*10^{-3}[/tex]

b) What is the probability that at most 2 of them have never been married?

By applying binomial probability distribution method,

[tex]P(x)=^{n}C_{x}p^{x}q^{n-x}[/tex]

Substitute,

P(x) =Binomial probability =  51% = 0.51

x = No. of times of an outcome = 0,1,2

n = No. of trials = 15

q =  Probability of failure = 49% = 0.49

[tex]^{n}C_{x}[/tex] = No. of combinations

[tex]P(0-2)=^{15}C_{0}*(0.51)^{0}*(0.49)^{15-0}+^{15}C_{1}*(0.51)^{1}*(0.49)^{15-1}+^{15}C_{2}*(0.51)^{2}*(0.49)^{15-2}\\\\P(0-2) = 2.253*10^{-5}+15*0.51*4.59987*10^{-5}+2.563*10^{-3}\\\\P(0-2)=0.0029 \text{ or }2.9*10^{-3}[/tex]

c)What is the probability that at  least 13 of them have been married?

By applying binomial probability distribution method,

[tex]P(x)=^{n}C_{x}p^{x}q^{n-x}[/tex]

Substitute,

P(x) =Binomial probability =  51% = 0.51

x = No. of times of an outcome = 13,14,15

n = No. of trials = 15

q =  Probability of failure = 49% = 0.49

[tex]^{n}C_{x}[/tex] = No. of combinations

[tex]P(13-15)=^{15}C_{13}*(0.51)^{13}*(0.49)^{15-13}+^{15}C_{14}*(0.51)^{14}*(0.49)^{15-14}+^{15}C_{15}*(0.51)^{15}*(0.49)^{15-15}\\\\P(13-15)= 105*(0.51)^{13}*(0.49)^{2}+15* (0.51)^{14}*(0.49)+(0.51)^{15}\\\\P(13-15)= 0.0046 \text{ or } 4.6*10^{-3}[/tex]

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Answer:

x25 - 24.1x square would be your answer

Step-by-step explanation:

By taking the quotient between the average depth of the oceans, we conclude that the atlantic ocean is 3.251 times deeper.

We know that the average depth of the arctic ocean is 3.953x10^3 feet and the average depth of the atlantic ocean is 1.2851x10^4 feet

Notice that both of these are in scientific notation.

To see how many times deeper is the atlantic ocean than the artic ocean we need to take the quotient between the average depth of the atlantic ocean and the average depth of the arctic ocean, this gives:

(1.2851x10^4)/(3.953x10^3) = (1.2851/3.953)*(10^4/10^3)

= 0.3251*(10^1) = 3.251

The atlantic ocean is 3.251 times deeper than the artic.

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Given that

There is a cylinder and we have to find the change in its volume if the radius is doubled and the height is halved.

Explanation -

Let the Initial radius be r and the height be h. Then the initial volume will be

Now applying the given changes,

new radius = 2 x r

new height = h/2

Then the new volume will be V,

Hence volume will be doubled. And option D is correct.

Final answer -

Question: Write the system of linear equations represented by the augmented matrix to the right use W, X, Y and Z for the variables :

Solution:

An augmented matrix is equivalent to a system of linear equations. In this case, the given matrix is represented by the following system of linear equations:

-1 w - 3x +5y +2z = 13

0w + 1x + 3y + 0z = 10

0w + 0x +y - 1z = 3

1w - 3x + 0y + 0z = -2

this is equivalent to:

w - 3x +5y +2z = 13

x + 3y = 10

y - z = 3

1w - 3x = -2

So that, the correct answer is:

w - 3x +5y +2z = 13

x + 3y = 10

y - z = 3

1w - 3x = -2

The quadrilateral in the picture is a square since all four sides are equal.

The angles are all equal and all are right angles.

Clearly, the quadrilateral is a square.

The scale factor K = 0.9 is smaller than 1, so this is a reduction.

If we have a dimension L, a change of scale of scale factor K gives the new length: K*L

Then:

if K > 1, we have an enlargement.

if K = 1, we have a preservation (nothing changes)

if  0 < K < 1, we have a reduction.

In this case, we have K = 0.9, this is smaller than 1, so we have a reduction.

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Answer:

x = 20

Step-by-step explanation:

X = 20 Because the values are Corresponding Angles This means that they are congruent

Answer:

9*X+5*3.25

Step-by-step explanation:

So, total 9 person; 4 person have their own shoe.

Cost for game = 9*X;

Cost for shoe = 5*3.25;

So the total cost = 9*X+5*3.25

Answer:

Step-by-step explanation:

2 subtraction symbols equals a plus

so the answer is 9