Somebody plz help!!

7. The length of a rectangle is 5 cm more than its width, w.
(For parts a) and b), write the starting formula then the simplified answer.)
a) Write an expression for the perimeter of the rectangle in terms of its width. (Perimeter=the sum of all sides of a shape)


b) Rearrange the formula to isolate for w.


c) The perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle?
(Show your substitution then state the values for width and length)

The approximate probability that the mean number of siblings in the sample of size 50 is at most 2 is 0.1562 or 15.62%.

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.

To answer this question, we need to use the central limit theorem, which states that the sample mean of a large enough sample from any population with a finite mean and variance will follow a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, we have a sample size of 50, which is considered large enough for the central limit theorem to apply. Therefore, the mean of the sample means will be equal to the population mean, which is 2.2, and the standard deviation of the sample means will be equal to the population standard deviation divided by the square root of the sample size, which is 1.4/sqrt(50) = 0.198.

To find the probability that the mean number of siblings in the sample of size 50 is at most 2, we need to calculate the z-score and use the standard normal distribution table or calculator. The z-score can be calculated as:

z = (2 - 2.2) / 0.198 = -1.01

Using the standard normal distribution table or calculator, we can find that the probability of getting a z-score of -1.01 or less is approximately 0.1562.

Therefore, the approximate probability that the mean number of siblings in the sample of size 50 is at most 2 is 0.1562 or 15.62%.

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The scale factor of triangle ABC to triangle LMN is 3, indicating that ABC is three times larger than LMN.

The scale factor of triangle ABC to triangle LMN can be determined by comparing the corresponding side lengths. Given that AB = 18, BC = 12, LN = 9, and LM = 6, we can find the scale factor by dividing the corresponding side lengths of the triangles.

The scale factor is calculated by dividing the length of the corresponding sides of the two triangles. In this case, we can divide the length of side AB by the length of side LM to find the scale factor. Therefore, the scale factor of ABC to LMN is AB/LM = 18/6 = 3.

This means that every length in triangle ABC is three times longer than the corresponding length in triangle LMN. The scale factor provides a ratio of enlargement or reduction between the two triangles, allowing us to understand how their dimensions are related. In this case, triangle ABC is three times larger than triangle LMN.

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Answer:

there is a math caulator

Step-by-step explanation:

Answer:

it would be .15%

Step-by-step explanation:

u have to move the decimal over two times to have a percent

:) brainliest?

Answer:

y>2x-4

y int = -4

over 2 right 1 (like staircase)

The line is dotted and shade to the left of graph

Step-by-step explanation:

You have the following sentence:

triangle ABC is right triangle, so angle ∠A measures 90°

In order to find a counterexample of the previous sentence, you simply determine which of the given triangle is a right triangle in which the measure of angle ∠A is not 90°.

You can notice that the option B is a right traingle where the angle A does not measure 90°, otherwise, angle ∠B measures 90°

a) The variable x is the average distance of Venus from the sun.

b) The equation for the given condition,

⇒ ⇒ 57.9 = 3.8 + x/2

c) The average distance of Venus from the sun = 108.2 million kilometers.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The average distance of Mercury from the sun = 57.9 million kilometers

And, This distance is 3.8 million kilometers more than half the average distance of Venus from the sun.

Now,

Since, The average distance of Mercury from the sun = 57.9 million kilometers

And, This distance is 3.8 million kilometers more than half the average distance of Venus from the sun.

Let the average distance of Venus from the sun = x

So, We can formulate;

⇒ 57.9 = 3.8 + x/2

Solve for x as;

⇒ 57.9 = 3.8 + x/2

⇒ 57.9 - 3.8 = x/2

⇒ x/2 = 54.1

⇒ x = 54.1 × 2

⇒ x = 108.2

Thus, The average distance of Venus from the sun = 108.2 million kilometers.

Therefore, a) The variable x is the average distance of Venus from the sun.

b) The equation for the given condition,

⇒ ⇒ 57.9 = 3.8 + x/2

c) The average distance of Venus from the sun = 108.2 million kilometers.

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Answer:

  095

Step-by-step explanation:

You want the bearing from C to D, given that the bearing from D to C is 85° west of north.

The bearing from C to D will be the opposite of the bearing from D to C.

Bearing is measured clockwise from north, so the bearing shown from D to C is -85°. Its opposite is found by adding 180°.

  180° +(-85°) = 95°

The 3-digit bearing of D from C is 095.

Answer:

see explanation

Step-by-step explanation:

The solution to the equations is at the point of intersection of the 2 lines.

If the system has no solution, this indicates the lines do not intersect and therefore must be parallel.

Answer:

250 cubic cm

Step-by-step explanation:

Side length = x

\(2x^{2} + 4x(10) = 120\)

\(x^{2} +2x - 30 =0\)
After factorization, we will get (x+6) ( x-5) = 0

side length should be positive, so we take x to be 5.
Dimensions will be 5 x 5 x 10 = 250 cubic centimeters.

Question:

What is the measure of an interior angle of a 21-gon?

Concept:

Define a 21-gon

A 21-gon is a 21 sided polygon also know as An icosikaihenagon

In the case of this polygon, the value of n is

We will then calculate the sum of interior angles of a 21-gon and then divide the sum by the number of sides n...

Therefore,

The formula we will use to calculate the measure of an interior angle of a 21-gon is given below as

The formula for the sum of interior angles is given below as

Hence,

We will have

Step 2:

Substitute the value of n=21 in the formula above, we will have

Hence,

The final answer = 162.86°

The solution of the inequality are n  ≤ -7 and n ≥ -12.

A compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality individually.

n + 2 ≤ −5 and  n + 6 ≥ −6

Hence,

n + 2 ≤ − 5

subtract 2 from both sides of the inequality

n + 2 - 2 ≤ − 5 - 2

n  ≤ -7

n + 6 ≥ −6

subtract 6 from both sides of the inequality

n + 6 ≥ −6

n + 6 - 6 ≥ −6 - 6

n ≥ -12

Therefore, n  ≤ -7 and n ≥ -12

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Answer:

h = \(\sqrt{84}\) cm

Step-by-step explanation:

The radius, height h and slant height form a right triangle.

radius r = 8 ÷ 2 = 4, hypotenuse = 10

Using Pythagoras' identity in the right triangle

h² + 4² = 10²

h² + 16 = 100 ( subtract 16 from both sides )

h² = 84 ( take the square root of both sides )

h = \(\sqrt{84}\) cm

The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

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Horizontal translation: 2 units right.

Vertical translation: 5 units up

Stretch/compression: stretched by a factor of 3.

Reflection: not reflected.

The correct statement is: 'A standard normal distribution has a mean of 0 and a standard deviation of 1 '

The correct answer is an option (b)

In this question, we need to complete given statement.

We know that the normal distribution is a symmetrical and bell-shaped distribution.

In standard normal distribution the mean, median and mode are all equal. Also, it always has a mean of zero and a standard deviation of one.

So,  A standard normal distribution has a mean of 0 and a standard deviation of 1 .

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Sample mean in sample b to be less variable and more representative of  population mean than sample mean in sample a.

Standard error measures the variability of sample means around the population mean.

It decreases as sample size increases.

Using the formula for the standard error of the mean,

Calculate the standard errors for each sample,

Standard error of sample a

= s/√(n)

= 850/√(9)

= 283.33

Standard error of sample b

= s/√(n)

= 850/√(36)

= 141.67

Where s is the sample standard deviation

And n is the sample size.

The standard error of sample b is smaller than the standard error of sample a.

Sample mean in sample b is more likely to be closer to true population mean than sample mean in sample a.

Therefore, sample mean b is more surprising as larger sample size makes it more likely and accurately represents population mean.

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The force is 1.6N and the distance between them is 1.3 meters

An inverse variation from force to the square of distance is represented s:

k = Fd^2

Where k represents the variation constant

When F = 10, d = 2.

So, we have:

k = 10 * 2^2

k = 40

Substitute k = 40 in k = Fd^2

Fd^2 = 40

When d = 5, we have:

F * 5^2 = 40

This gives

25F = 40

Divide by 25

F = 1.6

Hence, the force is 1.6N

In (a), we have:

Fd^2 = 40

When F = 25, we have:

25 * d^2 = 40

This gives

25d^2 = 40

Divide by 25

d^2 = 1.6

Take the square root of both sides

d = 1.3

Hence, the distance between them is 1.3 meters

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Answer: The answer will be D

Step-by-step explanation: I think the answer will be C because you can multiply this as I did to get the answer so its C

Answer:

1320

Step-by-step explanation:

Divide 7920 by 12 then multiply the quotient by 2

Answer:

1320

Step-by-step explanation:

7,920/12 = 660

660 x 2 = 1320

In general, the Divergence Test (nth term test) only allows us to determine whether a series diverges or not. It does not help us to determine the convergence of a series. Therefore, none of the other tests apply to this series.

The Divergence Test (nth term test) states that if the limit of the nth term of a series is not equal to zero, then the series diverges.

The series [infinity] 12 n n=1 is defined as follows:

[infinity] 12 n n=1 = 12¹ + 12² + 12³ + ...

The nth term of this series is given by:

aₙ = 12ⁿ As n → ∞, aₙ → ∞,

which means the limit of the nth term of the series does not exist.

Therefore, the series [infinity] 12 n n=1 diverges by the Divergence Test (nth term test).

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To compute the Laplace transform of the given function, we can use the linearity property of the Laplace transform and apply the transform to each term separately.

Using the Laplace transform pairs:

L{1} = 1/s

L{u(t)} = 1/(s+1)

L{e^(-6t)} = 1/(s+6)

L{cos(πt)} = s/(s^2+π^2)

Applying these transforms to the given function:

L{1 u^(5/2)(t) e^(-6t) cos(πt)} = L{1} * L{u^(5/2)(t)} * L{e^(-6t)} * L{cos(πt)}

Substituting the transform pairs:

= (1/s) * (1/(s+1)^(5/2)) * (1/(s+6)) * (s/(s^2+π^2))

Simplifying this expression, we can multiply the terms together:

= s / (s(s+1)^(5/2)(s+6)(s^2+π^2))

Therefore, the Laplace transform of the given function is:

L{1 u^(5/2)(t) e^(-6t) cos(πt)} = s / (s(s+1)^(5/2)(s+6)(s^2+π^2))

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Answer:

No, that would cost more than $180.

Step-by-step explanation:

6(10)+60(3)≤$180

60+180 = $240

$240≤$180

Hope this helps!

The capital includes :

Any financial contribution made to a business to assist in achieving and advancing its commercial goal is referred to as a capital investment. The phrase may also refer to a long-term purchase made by a company, such as one for land, equipment, businesses, etc.

When a corporation issues securities to equity investors and debt to bondholders, the total amount of debt and capital lease obligations are added to the amount of stock given to investors to determine the overall amount of money raised. This amount is referred to as invested capital. The balance sheet of the business does not include an item for invested capital because debt, capital leases, and stockholders' equity are all stated separately.

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Answer:

3p - q = 3(2-5) - (8x3) = -9 - 24 = -33. Therefore, 3p-q=-33.

the antiderivative of the function f(x) = 2 csc(x) cot(x) sec(x) tan(x) is F(x) = 2x + C.

To find the antiderivative F(x) of the function f(x) = 2 csc(x) cot(x) sec(x) tan(x), we can simplify the expression and integrate each term individually.

We know that csc(x) = 1/sin(x), cot(x) = 1/tan(x), sec(x) = 1/cos(x), and tan(x) = sin(x)/cos(x).

Substituting these values into the expression:

f(x) = 2 * (1/sin(x)) * (1/tan(x)) * (1/cos(x)) * (sin(x)/cos(x))

= 2 * (1/sin(x)) * (1/(sin(x)/cos(x))) * (sin(x)/cos(x)) * (sin(x)/cos(x))

= 2 * (1/sin(x)) * (cos(x)/sin(x)) * (sin(x)/cos(x)) * (sin(x)/cos(x))

= 2 * 1

= 2

The antiderivative of a constant function is simply the constant multiplied by x. Therefore:

F(x) = 2x + C

where C represents the constant of the antiderivative.

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To find the profit function, maximum profit quantity, and maximum profit for a firm with revenue\(R(q) = 15q - 0.5q^2\) and cost \(C(q) = q^3 - 13.5q^2\\\) + 50q + 40, we first subtract the cost from the revenue to obtain the profit function \(\prod(q) = R(q) - C(q)\). Then, we can determine the quantity where the profit is maximized by using the second derivative test. Finally, we can calculate the maximum profit by substituting the quantity found in part (b) into the profit function \(\prod(q)\).

a. The profit function \(\prod(q)\) is obtained by subtracting the cost function C(q) from the revenue function R(q). Therefore, \(\prod(q) = R(q) - C(q)\) =\((15q - 0.5q^2) - (q^3 - 13.5q^2 + 50q + 40\)). Simplifying this expression gives \(\prod(q)\) = \(-q^3 + 14q^2 - 35q - 40\).

b. To determine the quantity where the profit is maximized, we can use the second derivative test. The second derivative of the profit function \(\prod(q)\) is obtained by differentiating \(\prod(q)\) with respect to q twice. Taking the second derivative of \(\prod(q)\), we get \(\prod''(q) = -6q + 28\). To find the quantity where the profit is maximized, we set \(\prod''(q)\) equal to zero and solve for q: -6q + 28 = 0. Solving this equation gives q = 28/6 = 14/3.

c. Once we have found the quantity q = 14/3, we can substitute this value into the profit function Π(q) to find the maximum profit. Plugging q = 14/3 into \(\prod(q)\), we have \(\prod(14/3) = -(14/3)^3 + 14(14/3)^2 - 35(14/3) - 40\). Evaluating this expression gives the maximum profit value.

\(\prod(14/3) = -((14/3)^3) + 14((14/3)^2) - 35(14/3) - 40.\)

Simplifying this expression gives:

\(\prod(14/3) = -2744/27 + 2744/9 - 490/3 - 40.\)

Combining the terms and finding a common denominator:

\(\prod(14/3) = (-2744 + 8192 - 4410 - 1080)/27.\)

Further simplification:

\(\prod(14/3) = 958/27.\)

Therefore, the maximum profit at the quantity q = 14/3 is 958/27.

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The height of the tree is approximately 172.8 feet.

What is triangle ?

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry. The sum of the angles in a triangle is always 180 degrees, and the length of one side is always less than the sum of the lengths of the other two sides. Triangles are classified by their sides and angles into different types such as equilateral, isosceles, scalene, acute, obtuse, and right triangles.

According to the question:
Using the properties of similar triangles, we can set up the following proportion:

(54 + h) / 66 = h / 96

Cross-multiplying and solving for h, we get:

96(54 + h) = 66h

5184 + 96h = 66h

30h = 5184

h = 172.8

Therefore, the height of the tree is approximately 172.8 feet.


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Step-by-step explanation:

Box Number 5 should have 48 pink ribbons and 60 yellow ribbons. We can calculate this by first adding up the total number of pink and yellow ribbons in Sandy's first four boxes (4+16+12+36 = 68 pink ribbons, and 5+20+15+45 = 85 yellow ribbons). The ratio of pink to yellow ribbons in the first four boxes is 68:85, or 4:5.

To determine the amount of pink and yellow ribbons in Box Number 5, we can use the ratio from the first 4 boxes by multiplying 4 and 5 by any factor that will give us integers. This factor is 8, so we get 4 x 8 = 32 pink ribbons and 5 x 8 = 40 yellow ribbons, for a total of 48 pink ribbons and 60 yellow ribbons in Box Number 5.

Given   :  Sandy has four boxes filled with pink ribbons and yellow ribbons.

Box No.  Pink Ribbons  Yellow Ribbons

1                     4                      5

2                   16                    20

3                   12                    15

4                  36                    45

To Find : Relation between  Pink Ribbons and   Yellow Ribbons

Solution:

Pink Ribbons = x

Yellow Ribbons = Y

Box No.  Pink Ribbons x  Yellow Ribbons y

1                     4                      5

2                   16                    20

3                   12                    15

4                  36                    45

Slope = (20 - 5)/(16 - 4)

= 15/12

=5/4

y - 5 = (5/4)(x- 4)

=> 4y - 20 = 5x - 20

=> 4y  = 5x

=> 5x = 4y

5x = 4y  is the relations between  Pink Ribbons and   Yellow Ribbons