1. You are planning to hang lights around your windows for a party. The cost is
$4.00 for a 20-foot string of lights.

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

\(-\frac{28}{3}\)

Step-by-step explanation:

\(\frac{-3-(-1/5)}{(1/10)-(-1/5)}=-\frac{28}{3}\)

Answer:

x =15

Step-by-step explanation:

its a rectangle all interior angles must be equal to 90 so 6x=90

divide by 6 to get x on its own and you get 15

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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Step-by-step explanation:

n/2 + 3 < 20

50 >= 16- 2n

n / 2.83 > 100

Answer:

mhm

Step-by-step explanation:

that is right

The likelihood of having sets of twins is P(I/F)= 0.4615

Let

I = identical

F = fraternal

BB = both boys

BG = mixed

GG = both girls

a)P(BB) = P(I) P(BB|I) + P(F) P(BB|F)

= 0.30*0.5 + (1-0.30)*0.25

= 0.325  

b)P(I|GG) = P(I) P(GG|I) / P(GG)As

P(GG) = P(I) P(GG|I) + P(F) P(GG|F) = 0.30*0.5 + (1-0.30)*0.25 = 0.325

Then

P(I|GG) = P(I) P(GG|I) / P(GG)

= 0.30*0.50/0.325

= 0.461538462

Hence, the likelihood of having sets of twins is 0.4615.

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Answer:

a. The test statistic is 2 and we conclude that the new ad campaign is not signficantly better.

Step-by-step explanation:

They used to be able to sell to 50% of those who saw their ads. Test if the new campaign is better.

At the null hypothesis, we test is it is the same, that is, the proportion is the same.

\(H_0: p = 0.5\)

At the alternate hypothesis, we test if it is significantly better, that is, the proportion is above 50%.

\(H_1: p > 0.5\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that \(\mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5\)

They take a random sample of 100 potential buyers and find that they convinced 60 of these people to buy their product.

This means that \(n = 100, X = \frac{60}{100} = 0.6\)

Test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.6 - 0.5}{\frac{0.5}{\sqrt{100}}}\)

\(z = 2\)

The test statistic is 2.

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion above 0.6, which is 1 subtracted the by p-value of z = 2.

Looking at the z-table, z = 2 has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

The p-value of the test is 0.0228 > 0.01, which means that we cannot conclude that the new ad campaign is signficantly better, so the correct answer is given by option A.

Answer:

6pi

Step-by-step explanation:

Area of a circle = 2pi*r

d = 12

r = d/2

r=6

Area of semicircle = (2pi *r)/2 = pi*r

pi*6 = 6pi

Answer:18π cm^2

Step-by-step explanation:

diameter=12

Radius=diameter ➗ 2

Radius=12 ➗ 2

Radius=6

Area of semicircle=0.5 x π x radius x radius

Area of semicircle=0.5xπx6x6

Area of semicircle=18π cm^2

Answer:

272$

Step-by-step explanation:

You really should be clearer with your questions, but if your looking for the balance she has 272$

We have a deposit of $4000 at the end of each year.

The rate is 5% compounded annually (r = 0.05).

The number of periods is n = 10.

We have to calculate the present value of the annuity.

We will use the formula:

If we replace with our data, we get:

Now, we have to calculate the interest.

Answer:

16.8

Step-by-step explanation:

Set up a proportion.  

w = width and l = length

I would put the length and the width of the model in the first fraction and the length of the actual building on the right.

\(\frac{w}{l}\) =\(\frac{w}{l}\)

\(\frac{7}{58.7}\) = \(\frac{w}{140.9}\)  Multiply both sides of the equation by 58.7 and 140.9 and you get:

140.9(7) = 58.7x

986.3 = 58.7x  Divide both sides by 58.7

16.8023850085 = x  I will round to the nearest tenths' place

16.8

El supplemento y el complemento de cada ángulo son, respectivamente:

Caso A: m ∠ A' = 43°

Caso B: m ∠ A' = 31°

De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:

Ángulo y su complemento

m ∠ A + m ∠ A' = 90°

Ángulo y su suplemento

m ∠ A + m ∠ A' = 90°

Donde:

Ahora procedemos a determinar cada ángulo faltante:

Caso A: Complemento

47° + m ∠ A' = 90°

m ∠ A' = 43°

Caso B: Suplemento

149° + m ∠ A' = 180°

m ∠ A' = 31°

El enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.

The statement is written in Spanish and its answer is written in the same language.

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Answer:

e is 63 degrees

d is 31 degrees

Discuss measures that can be taken to develop the spirit of hard work

The statement "In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality" best describes the process used to solve the equations.

In the equation -3x + 6 = 21, to isolate the variable x, we subtract 6 from both sides of the equation, which yields -3x = 15. Then, we divide both sides by -3 to solve for x, resulting in x = -5. This process is applicable to equations where we aim to find the exact value of the variable.

Similarly, in the inequality -3x + 6 < 21, we want to find the range of values for x that satisfy the inequality. By subtracting 6 from both sides, we obtain -3x < 15.

However, since we performed the same operation on both sides of the inequality, the direction of the inequality sign remains the same.

Thus, the correct inequality is -3x < 15. To isolate x, we divide both sides by -3. However, since we reversed the inequality sign, we must also reverse it again, resulting in x > -5.

This process allows us to determine the range of values for x that satisfy the inequality.

Therefore, the statement accurately describes the process for solving both the equation and the inequality, highlighting the significance of reversing the inequality sign when manipulating inequalities.

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An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

One plane has a speed of 450 km/h and the other has a speed of 900 km/h.

Step-by-step explanation:

I am going to say that:

The speed of the first plane is x.

The speed of the second plane is y.

One plane is flying at twice the speed of the other.

I will say that y = 2x. We could also say that x = 2y.

Two airplanes leave an airport at the same time, flying in the same direction

They fly in the same direction, so their relative speed(difference) at the end of each hour is y - x = 2x - x = x.

If after 4 hours they are 1800 km apart, find the speed of each plane

After 1 hour, they will be x km apart. After 4, 1800. So

1 hour - x km apart

4 hours - 1800 km apart

4x = 1800

x = 1800/4

x = 450

2x = 2*450 = 900

One plane has a speed of 450 km/h and the other has a speed of 900 km/h.

It is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in
the graph intersecting the x- or y-axis at a different point.

Function is an operation that takes an input, performs some processing on it, and returns a result. It is a set of instructions that performs a specific task. Functions are typically used to perform repetitive tasks, like finding the sum of two numbers, adding two strings together, or finding the maximum of a list of numbers. Functions are essential to programming and can be used to make code more organized, reusable, and efficient.


The function f(x) = x is the parent function for linear equations. This equation is generally used to graph a line with a slope of 1 and a y-intercept of (0, 0). In order to translate this parent function, different transformations are applied to it.

A vertical translation down 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function down 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, -4).

A horizontal translation right 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function right 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (4, 0).

A horizontal translation left 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function left 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (-4, 0).

Finally, a vertical translation up 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function up 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, 4).

In conclusion, it is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in the graph intersecting the x- or y-axis at a different point.

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Answer:

3\(\sqrt[9]{Z}\)²

Step-by-step explanation:

Expression -

(27\(\sqrt[3]{Z}\)²) ^1/3

Transform the expression -

³\(\sqrt[3]{27}\)\(\sqrt[3]{Z}\)²

Simplify - //Note: ignore the ' * '//

3\(\sqrt[3]{*}\)\(\sqrt[3]{z}\)²

Simplify (Again) -

3\(\sqrt[9]{Z}\)²

Because the account is compounded continuously, Euler number is required

e = 2.7182818

if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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The inverse functions and the domains and ranges of the inverse functions can be presented as follows;

A. The inverse function of f(x) is; \(f^{-1}(x) = \frac{3-x}{7\cdot x}\)

B. f(g(x)) = \(\frac{3}{7\times \frac{(3-x)}{7\cdot x} + 1}\) = x

C. The inverse function reverses the effect of the function. The inverse function is therefore;

x \({}\)      y

10\({}\)     5

6\({}\)      8

5\({}\)      9

4\({}\)      13

2) Domain; 10, 6, 5, 4

Range; 5, 8, 9, 13

An inverse function maps the output, or y-value of a function to the input value or x-value of the function.

2. A. f(x) = 3/(7·x + 1)

The inverse function can be found as follows;

Let f(x) = y

y = 3/(7·x + 1)

(7·x + 1) = 3/y

7·x = (3/y) - 1 = (3 - y)/y

x = (3 - y)/(7·y)

Plugging in x = f⁻¹(x), and y = x, to get;

B. g(x) = (3 - x)/(7·x)

f(x) = 3/(7·x + 1)

f(g(x)) = 3/(7 × ((3 - x)/(7·x)) + 1) = 3/(((3 - x)/(x)) + 1) = 3/(3/x - 1 + 1)

3/((3/x - 1 + 1) = 3/(3/x) = 3 × x/3 = x

Therefore; f(g(x)) = 3/(7 × ((3 - x)/(7·x)) + 1) = x

C. The inverse of the function is the function that produces the input of the function from the function's output, therefore, the inverse of the function can be presented as follows;

x \({}\)     y

10\({}\)    5

6\({}\)     8

5\({}\)     9

4\({}\)     13

2) The domain is the set of the possible inputs of the function, and the range is the set of the possible outputs of the function.

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Answer:

42.4 is the correct answer to this question

Answer:

1. <

2. >

3. <

Step-by-step explanation:

Answer:

1. <

2. >

3. <

Step-by-step explanation:

Answer: 519 120

Step-by-step explanation:

84*84=7056

7056/7=1008

1008*515=519 120

Answer:

10x² - 9x

Step-by-step explanation:

(10x² - 10x - 6) + (x + 6)

10x² - 10x - 6 + x + 6

10x² - 9x - 6 + 6

10x² - 9x