Question is in image. The cone at the top is part of the question

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

The value of 'n' is 18 in the given equation 8n - 5 = 139.

We have to find the value of 'n'.

To do so, we need to solve the given equation.

Let us see how we can solve the given equation.8n - 5 = 139

We need to find the value of 'n'.

Let us bring the constant term to the right side by adding 5 to both the sides of the equation.8n - 5 + 5 = 139 + 5On simplifying, we get8n = 144Now, we need to isolate 'n' to find its value.

To do so, we divide both the sides by 8.8n/8 = 144/8On simplifying, we get n = 18

Therefore, the value of 'n' is 18.

Hence, the value of 'n' is 18 in the given equation 8n - 5 = 139.

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The right response is 400%. In other words, Johnny moves at four times the pace of Jane.

We must compare the speeds of Johnny and Jane in relation to one another in order to get their ratio. According to the issue, Jane moves at a pace that is 1/4 that of Johnny. In other words, Jane moves at a speed that is one-fourth that of Johnny.

We may compare the speeds as a fraction to figure out the ratio:

Johnny's speed divided by Jane's speed equals 4/1.

This indicates that Johnny is moving at a speed that is four times that of Jane. We can express Johnny's speed as 400% of Jane's speed in percentage terms.

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The final rule for g(x) is g(x) = 3|3x| + 12.

To stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3, we multiply the function by 3. This will result in a vertical stretching of the graph.

So, the rule for g(x) is g(x) = 3f(x).

Now, let's find the expression for g(x) using the given function f(x) = −|3x| − 4:

g(x) = 3f(x)

g(x) = 3(-|3x| - 4)

g(x) = -3|3x| - 12

This is the expression for g(x), which represents the transformed graph.

To reflect the graph of g(x) across the x-axis, we change the sign of the function. This means that the negative sign in front of the absolute value will become positive, and the positive sign in front of the constant term will become negative.

Therefore, the final rule for g(x) is g(x) = 3|3x| + 12.

Now, let's consider the graph of g(x). The graph will have the same shape as f(x), but it will be stretched vertically by a factor of 3 and reflected across the x-axis.

The original graph of f(x) = −|3x| − 4 is a V-shaped graph that opens downward and passes through the point (0, -4). The transformed graph of g(x) will have a steeper V-shape, opening downward, and passing through the point (0, 12) instead of (0, -4).

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The numerical length of the line segment RT is 6.

Length:

Length is the measuring unit used to identifying the size of an object or distance from one point to the other.

Given,

There is a point on the line segment RT.

And the values of the pots are,

RT = 3x, RS = 3x - 5 and ST = 3x - 1.

Now we need to find the length of the line segment RT.

To find the line of the line segment RT,

We have to add the length of the segments,

That can be written as,

=> RT = RS + ST

Now, we have to apply the values of the point to the equation, then we get,

=> 3x = 3x - 5 + 3x - 1

=> 3x = 6x - 6

=> 6x - 3x - 6

=> 3x - 6

=> 3x = 6

=> x = 2

If the value of x is 2, then the length of the line segment RT is,

RT = 3x => 3 x 2 = 6

Therefore, the length of the line segment RT is 6.

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Answer:

14 cabins

Step-by-step explanation:

16 ÷ 2 = 8 in 1 cabin

112 ÷ 8 = 14 cabins

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Answer:

3/8

Step-by-step explanation:

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The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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The Area of the poster will be \("216x^{2} +12x"\)

According to the question,

The length of poster,

6x inches

The width of poster,

8x+28x+2 inches

Now,

The Area of the poster will be:

= Length * Width

By putting the values, we get

= (6x) × (8x + 28x + 2)

= (6x) × (36x + 2)

= 216x² + 12x

Thus the above answer is right.

We can only add and subtract fractions that have the same bottom numbers. If fractions have the same bottom numbers, we can add them by just adding the top numbers and and keeping the original bottom number.

If they don't have the same bottom number, we have to find the least common denominator for those fractions which is simply the least common multiple of the two or how ever many fractions there are.

For example, to add 1/2 and 1/3, we find the least common

denominator, which is 6, and we want to get a 6 in the denominator.

When we have the same denominator, just add

the numerators and keep the original denominator.

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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The amount in the mother's bank account is 2450

From the question, we have the following parameters that can be used in our computation:

Amount each year = $700

Number of years = 3 1/2

Using the above as a guide, we have the following:

Amount = Amount each year * Number of years

substitute the known values in the above equation, so, we have the following representation

Amount = 700 * 3 1/2

Evaluate

Amount = 2450

hence the amount in the mother's bank account is 2450

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Answer:

18

Step-by-step explanation:

360÷20=18

twentycharactersignorethis

the building has 16 exterior walls

\(\\ \qquad\quad\sf\longmapsto ^nC_2=^nC_4\)

\(\boxed{\sf ^nC_r=\dfrac{n!}{r!(n-r)!}}\)

\(\\ \qquad\quad\sf\longmapsto \dfrac{n!}{2!(n-2)!}=\dfrac{n!}{4!(n-4)!}\)

\(\\ \qquad\quad\sf\longmapsto \dfrac{1}{2\times 1(n-2)!}=\dfrac{1}{4\times 3\times 2\times 1(n-4)(n-3)(n-2)!}\)

\(\\ \qquad\quad\sf\longmapsto 2=24(n-4)(n-3)\)

\(\\ \qquad\quad\sf\longmapsto 2=24\left\{n(n-3)-4(n-3)\right\}\)

\(\\ \qquad\quad\sf\longmapsto 2=24(n^2-3n-4n+12)\)

\(\\ \qquad\quad\sf\longmapsto 2=24(n^2-7n+12)\)

\(\\ \qquad\quad\sf\longmapsto 2=24n^2-168n+288\)

\(\\ \qquad\quad\sf\longmapsto 24n^2-168n=-286\)

\(\\ \qquad\quad\sf\longmapsto 24n^2-168n+286=0\)

\(\\ \qquad\quad\sf\longmapsto 12n^2-84n+143=0\)

\(\\ \qquad\quad\bf\longmapsto n=\dfrac{7}{3}\pm \dfrac{1}{3}\sqrt{3}\)

Answer:

n = 6

Step-by-step explanation:

There's a secret formula for this:

If nCx = nCy,

Then n = x + y.

Hence, for this question, n = 2 + 4 = 6

a) The only outcome that satisfies both events X and Y is the letter C.

b) The outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

c) The complement of event X is {D, E, F, G}.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The outcomes for each of the following events are:

(a) Event "X and Y": {C}

To satisfy both events X and Y, the letter selected must come before "D" (which includes the letters A, B, and C) and must be one of the letters in the word "CAGE" (which includes only the letter C). Therefore, the only outcome that satisfies both events X and Y is the letter C.

(b) Event "X or Y": {A, B, C, E, G}

The outcomes that satisfy event X are A, B, and C (since they come before "D"), and the outcomes that satisfy event Y are C, A, G, and E (since they are letters found in the word "CAGE"). Therefore, the outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

(c) The complement of event X: {D, E, F, G}

The complement of event X is the set of outcomes that do not satisfy event X. The outcomes that do not satisfy event X are D, E, F, and G (since they come after or are equal to "D"). Therefore, the complement of event X is {D, E, F, G}.

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Answer:

The function domain is:

{x|x ≥ -4}

Hence, option 4 is correct.

Step-by-step explanation:

Given the expression of the function

\(f\left(x\right)=\sqrt{x+4}\)

We know that the domain of the function is the set of input values for which the function is real and defined

We know that the value inside the radical expression must be greater than or equal to 0 so that the function remains defined.

so

\(x+4\ge \:0\)

subtract 4 from both sides

\(x+4-4\ge \:0-4\)

simplify

\(x\ge \:-4\)

Therefore, the function domain is:

{x|x ≥ -4}

Hence, option 4 is correct.

Answer: segundo

Step-by-step explanation:

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Gordon put 2 buckets of water and then 4/5 of a bucket of water.

If you add them you get that

The 2 buckets represent "wholes", you can express them as fractions, using the same denominator as the given fraction.

1 whole can be expressed as 5/5

2 wholes is then 10/5

Now add both measures:

You can express the answer

Buckets of water

Complete Question

Assisted-Living Facility Rent.Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486 (the Wall Street Journal, October 27, 2012). Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is s = $650. a. Develop a 90% confidence interval estimate of the population mean monthly rent.

Answer:

\(CI: 3388.39<X<3583.61\)

Step-by-step explanation:

Sample Size n=120

Mean \=x =3486

Standard Deviation \sigma=650

Confidence interval CI=0.9

Therefore

Level of sig \(\alpha=0.1\)

Therfore

The Critical Value from table is

Z_c=1.645

Generally the equation for Standard error is mathematically given by

\(S.E=\frac{\sigma}{\sqrt{n}}\)

\(S.E=\frac{650}{\sqrt{120}}\)

\(S.E=59.3366\)

Generally the equation for Margin error is mathematically given by

\(M.E= = Z_c * SE\)

\(M.E=1.65 * 59.34\)

\(M.E= 97.61\)

Therefore

\(CI= \=x \pm M.E\)

\(CI= 3486 \pm 97.61\)

Lower limit

\(LL= \=x-M.E=3486-97.6087\)

\(LL= 3388.39\)

Upper limit:

\(UL= \=x+E=3486+97.6087\)

\(UL= 3583.61\)

Therefore The  90% confidence interval estimate of the population mean monthly rent.

\(CI: 3388.39<X<3583.61\)

Answer: 2 1/3

Step-by-step explanation: 2 and 1/3.

14/6 = 2.3333... which is 2 1/3 as a mixed number.

Answer:

2 1/3

Step-by-step explanation:

simpliying this you would make it into 7/3 then divide each by thre then get 2 1/3

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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The grams of cocoa does it contains is 36.57 grams

From the question, we have the following parameters that can be used in our computation:

Weight of the chocolate bar = 69

Proportion = 53%

This implies that

Grams of cocoa = weight of the chocolate bar * Proportion

Substitute the known values in the above equation, so, we have the following representation

Grams of cocoa = 53% * 69

Evaluate the products

Grams of cocoa = 36.57

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Answer:

y=2047.05791602

y≈2047

Answer:

5

Step-by-step explanation:

because it takes 4 1/5 paint for each canvas 5 times 4 1/5 is 21.

Answer:

1/18

Step-by-step explanation:

Answer:

1/18

Step-by-step explanation:

1/3 / 6/1 =1/3 x 1/6 = 1/18

The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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There are 896 trips will it take him to haul all of the dirt away.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The rectangular hole is 8 feet wide, 16 feet long, and 7 feet deep.

Now,

Since, The rectangular hole is 8 feet wide, 16 feet long, and 7 feet deep.

And, His pickup truck can haul one cubic meter.

Hence, Number of trips will it take him to haul all of the dirt away will be;

⇒ 16 × 7 × 8 / 1

⇒ 896

Thus,  Number of trips = 896

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Answer:

x = 20 ft

Area of the living room = 400 ft²

Step-by-step explanation:

From the picture attached,

Length of rug = (x - 3) ft

Width of the rug = (x - 9) ft

Area of the rectangular rug = Length × Width

                                              = (x - 3)(x - 9)

187 = (x - 3)(x -9)

187 = x² - 12x + 27

x² - 12x - 160 = 0

x² - 20x + 8x - 160 = 0

x(x - 20) + 8(x - 20) = 0

(x - 20)(x + 8) = 0

x = -8, 20

Since, measure of 'x' can't be negative, measure of x will be 20 ft.

Therefore, area of the square living room = x²

                                                                     = (20)²

                                                                     = 400 ft²

Answer:

Note that orthogonal to the plane means perpendicular to the plane.

Step-by-step explanation:

-1x+3y-3z=1 can also be written as -1x+3y-3z=0

The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).

Let us find a point on this  line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively

Therefore, the vector equation is given as:

-1(x-0) + 3(y-0) + -3(z-5) = 0

-x + 3y + (-3z+15) = 0

-x + 3y -3z + 15 = 0

Multiply through by - to get a positive x coordinate to give

x - 3y + 3z - 15 = 0