2.

What are complementary angles?

(b)

Give three examples of angles that are complementary..

3.

(a)What are acute angles?

(b)

Give examples of acute angles..

\(f^2(3) = 576\)

Given:

\(f(x) = (x +2)^2 -1\)

Solving for \(f^2(3)\):

\(f^2(3) = (f(3))^2 \\ f^2(3) = (((3) +2)^2 -1)^2 \\ f^2(3) = ((3 +2)^2 -1)^2 \\ f^2(3) = ((5)^2 -1)^2 \\ f^2(3) = (25 -1)^2 \\ f^2(3) = 24^2 \\ f^2(3) = 576\)

Answer:

156

Step-by-step explanation:

Hey There!

The angle that is equal to 156 and the angle labeled x are corresponding angles meaning that they are congruent angles. Therefore x=156

Answer:

69

Step-by-step explanation:

becuz

Answer:

The additive inverse of a real number is the opposite of that number on the real number line. For example, the opposite of −3 is 3. A number and its additive inverse have a sum of 0. The sum of any number and its opposite is equal to zero.

Answer: w = 20 l = 38

Step-by-step explanation:

l = 2w - 2 (based on given info)

p = 2l + 2w (formula for perimeter)

p = 116 (given)

116 = 2l + 2w

116 = 2(2w-2) + 2w (substitute in l)

116 =‘ 4w-4 + 2w

116 = 6w-4

w=20

l=2(20) - 2 = 38

The answer of the given question based on the Expression is , (1)  4.23 x 10⁴ , (2) 2 x 10³ , (3) 9.2 x 10⁶ , (4) 4 x 10³ , (5)  8 x 10⁷ , (6) 3.2 x 10⁷ ,

An expression is  combination of numbers, variables, and the mathematical operations like addition, subtraction, multiplication, and division. It can also include mathematical functions, parentheses, and exponents.

Expressions can be as simple as a single number or variable, such as "3" or "x". They can also be more complex, such as "2x + 5" or "sin(x)/x". An expression can be used to represent a mathematical relationship or to solve a problem.

In some cases, an expression can be simplified or evaluated to produce a single value or result.

42,300 = 4.23 x 10⁴

2,000 = 2 x 10³

9,200,000 = 9.2 x 10⁶

4,000 = 4 x 10³

80,000,000 = 8 x 10⁷

32,000,000 = 3.2 x 10⁷

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Based on the expression, the supplied question's response is,

(1). 4.23 x 10⁴,

(2). 2 x 10³,

(3). 9.2 x 10⁶,

(4). 4 x 10³,

(5). 8 x 10⁷,

(6). 3.2 x 10⁷.

The mathematical operations of addition, subtraction, multiplication, and division are all combined in an expression. It may also contain exponents, parenthesis, and mathematical functions.

Simple expressions like "3" or "x" are examples of simple expressions. More complicated formulas like "2x + 5" or "sin(x)/x" are also possible.

A mathematical relationship or a problem can be solved with an expression.

An expression may occasionally be assessed or condensed to generate a single value or outcome.

42,300 = 4.23 x 10⁴

2,000 = 2 x 10³

9,200,000 = 9.2 x 10⁶

4,000 = 4 x 10³

80,000,000 = 8 x 10⁷

32,000,000 = 3.2 x 10⁷

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Answer:

-6 < x <9

Step-by-step explanation:

-7 < X -1 <8

Add 1 to all sides

-7+1 < X -1+1 <8+1

-6 < x <9

Answer:

D

Step-by-step explanation:

The correlation coefficient is 0.9541. This can be determined from the information provided in the ANOVA table, specifically the regression sum of squares (SSR) and the total sum of squares (SST).

The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger relationship, and values closer to 0 indicate a weaker relationship.

To calculate the correlation coefficient, we can use the formula:

r = sqrt(SSR/SST)

From the ANOVA table provided, we can see that SSR = 12,323.64 and SST = 13,538.4. Plugging these values into the formula gives:

r = sqrt(12,323.64/13,538.4) = 0.9541

Therefore, the correlation coefficient for this model is 0.9541, indicating a strong positive linear relationship between the independent variable and the dependent variable

Complete Question:

Using the following information. Coefficients -12.8094 Intercept Independent variable 2.1794 ANOVA df SS MS F 1 90.0481 Regression Residual Total 12,323.64 1,214.762 13,538.4 12,323.64 136.8550 8 1° 9 What is the correlation coefficient? Multiple Choice 0.9103 0.9541 -0.9541

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Answer:

\(3\frac{11}{18}\) m/s

Step-by-step explanation:

Caden walks 150m in 1 minute

A student blocks his way and he has to stop for 1 minute

He then walks 500m in 1 minute.

1 minute = 60 seconds

Let's use 's' to stand for seconds and 'm' to stand for meters.

Average speed = Total distance ÷ total time taken.

Total distance = 150m + 500m = 650m

Total time taken = 60s + 60s +  60s = 180s

Average speed = 650m ÷ 180s = \(\frac{650}{180} = 3\frac{11}{18}\) m/s

Answer:

To estimate the proportion of customers who were "good" with the customer service, we can calculate the sample proportion based on the given data. Out of the 10 randomly selected responses, we count the number of "good" responses and divide it by the total number of responses.

Given responses: Good, Good, Bad, Good, Bad, Good, Bad, Good, Good, Bad

Number of "good" responses: 6

Total number of responses: 10

Sample proportion of customers who were "good" with customer service:

Proportion = Number of "good" responses / Total number of responses

Proportion = 6 / 10

Proportion = 0.6

Therefore, based on the sample, we can estimate that approximately 60% of the customers were "good" with their customer service.

Answer:

9.333333 (repeating decimal)

Answer:

9 1/3

Step-by-step explanation:

Answer:I believe the answer is 34

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Hope this helps

Engineers can be held most morally blameworthy for foreseeable harms resulting from technological innovations, engineers have a responsibility to anticipate the potential consequences of their work,

and to take steps to mitigate those consequences. If they fail to do so, and their work results in harm, they can be held morally blameworthy. When engineers develop new technologies, they have a responsibility to consider the potential consequences of their work.

They need to think about how their technology could be used, and whether it could be used to harm people or the environment.

They also need to consider how their technology could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their work results in harm, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

For example, engineers who develop new weapons systems have a responsibility to consider the potential consequences of their work. They need to think about how their weapons could be used,

and whether they could be used to kill or injure innocent people. They also need to consider how their weapons could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their weapons are used to kill or injure innocent people, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

It is important to note that engineers cannot be held morally blameworthy for unforeseeable harms. This is because they did not have the opportunity to anticipate the harm, and they could not have taken steps to prevent it.

For example, engineers who develop new medical treatments cannot be held morally blameworthy if the treatments have unforeseen side effects. This is because the engineers did not have the opportunity to anticipate the side effects, and they could not have taken steps to prevent them.

In conclusion, engineers can be held morally blameworthy for foreseeable harms resulting from technological innovations.

This is because they have a responsibility to anticipate the potential consequences of their work, and to take steps to mitigate those consequences.

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Answer: Z is less than Zc ∴ 1.342 < 1.96

Therefore, Null hypothesis is not Rejected.

There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.

Step-by-step explanation:

Given that;

U = 75

X = 78

standard deviation α = 10

sample size n = 20

population is normally distributed

PROBLEM is to test

H₀ : U = 75

H₁ : U ≠ 75

TEST STATISTIC

since we know the standard deviation

Z =  (X - U) / ( α /√n)

Z = ( 78 - 75 ) / ( 10 / √20)

Z = 1.3416 ≈ 1.342

Now suppose we need to test at ∝ = 0.05 level of significance,

Then Rejection region for the two tailed test is Zc = 1.96

∴ Reject H₀ if Z > Zc

and we know that Z is less than Zc ∴ 1.342 < 1.96

Therefore, Null hypothesis is not Rejected.

There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.

Testing the hypothesis, it is found that since the p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.

At the null hypothesis, we test if the mean is of 75, that is:

\(H_0: \mu = 75\)

At the alternative hypothesis, we test if the mean is different of 75, that is:

\(H_1: \mu \neq 75\)

The test statistic is:

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

In which:

For this problem, we have that:

\(X = 78, \mu = 75, \sigma = 10, n = 20\)

The value of the test statistic is:

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

\(z = \frac{78 - 75}{\frac{10}{\sqrt{20}}}\)

\(z = 1.34\)

Since this is a two-tailed test, the p-value of the test is P(|z| < 1.34), which is 2 multiplied by the p-value of z = -1.34.

Looking at the z-table, z = -1.34 has a p-value of 0.0901.

2(0.0901) = 0.1802

The p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.

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Answer: 3/2

Step-by-step explanation:

To find the slope of the line that passes through the points (2, 1) and (0, -2), we can use the formula:

m = (y2 - y1) / (x2 - x1)

where:

m = slope of the line

(x1, y1) = coordinates of the first point

(x2, y2) = coordinates of the second point

Plugging in the values we have, we get:

m = (-2 - 1) / (0 - 2)

m = -3 / -2

m = 3/2

Therefore, the slope of the line that passes through the points (2, 1) and (0, -2) is 3/2.

Step-by-step explanation:

P - 12.95 = 44

P = 56.95

is it right?

The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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The area of the circular garden that Jenny will have to mulch is 78.5 square feet.

To calculate the area of a circle, we use the formula A = πr^2, where A is the area and r is the radius of the circle. Given that the garden has a diameter of 10 feet, we can find the radius by dividing the diameter by 2. So the radius (r) is 10/2 = 5 feet.

Now we can substitute the value of the radius into the formula: A = 3.14 * 5^2 = 3.14 * 25 = 78.5 square feet.

Therefore, Jenny will have to mulch an area of 78.5 square feet in her circular garden.


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The number of prime factors of 3×5×7+7 is 3.

To find the number of prime factors, we need to calculate the given expression:

3×5×7+7 = 105+7 = 112.

The number 112 can be factored as 2^4 × 7.

In the first step, we factor out the common prime factor of 7 from both terms in the expression. This gives us 7(3×5+1). Next, we simplify the expression within the parentheses to get 7(15+1). This further simplifies to 7×16 = 112.

So, the prime factorization of 112 is 2^4 × 7. The prime factors are 2 and 7. Therefore, the number of prime factors of 3×5×7+7 is 3.

In summary, the expression 3×5×7+7 simplifies to 112, which has three prime factors: 2, 2, and 7. The factor of 2 appears four times in the prime factorization, but we count each unique prime factor only once. Thus, the number of prime factors is 3.

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Answer:

48

Step-by-step explanation:

First find the amount of the markup

40 * 20%

40 *.2

8

Add this to the original price

40+8 = 48

The measure of the base of the triangle is 10 millimetres

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

Area of the triangle = 80 square millimetres

Height of the triangle = 16 millimetres

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

The base of the triangle = 2 * Area/Height

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

The base of the triangle = 2 * 80/16

Evaluate

The base of the triangle = 10

Hence, the base is 10 millimetres

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Complete question

The area of the triangle is 80 square millimeters and the height of the triangle is 16 millimetres.

Calculate the length of the base

Answer:

n=900

Step-by-step explanation:

n/4= 225, so multiply by 4 to get n=900 (hopefully I understand the question correctly, if not, please let me know.)

Upon answering the query  As a result, the following is the system of equations' solution: x = -150, y = 120.

An equation in math is an expression that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between each of the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The sign and only one variable are frequently the same. as in, 2x - 4 equals 2, for instance.

To solve

\(Y/4 - x/5 = 6 ........ (1)\\x/15 + y/12 = 0 ....... (2)\\\)

After using the substitution approach to find the value for one of the variables, we can use that value to find the value for the other variable.

We can solve for x in terms of y using equation (2):

\(x = - (5/4) y ........ (3)\)

Equation (1) may now be changed to an equation in terms of y by substituting equation (3) for equation (1):

\(y/4 - (-5/4)y/5 = 6\\5y - 4y = 120\\y = 120\\x = - (5/4) (120) = -150\\\)

As a result, the following is the system of equations' solution:

x = -150, y = 120.

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Answer:

\((x + 3)(x - 5)(x-3)<0\)

Step-by-step explanation:

Given

\((x + 3)(x^2 - 8x + 15)<0\)

Required

Complete the factoring

\((x + 3)(x^2 - 8x + 15)<0\)

Expand

\((x + 3)(x^2 - 3x - 5x+ 15)<0\)

Factorize:

\((x + 3)(x(x - 3)-5(x-3))<0\)

Factor out x - 3

\((x + 3)(x - 5)(x-3)<0\)

The expression has been completely factored

The disposable income is 4,000, consumption is 3,500, government purchases is 1,000, and taxes minus transfers are 800, national saving is equal to. Therefore, S = 4,000 - 3,500 - 1,000 = 500.Hence, option b is correct.

National savings (S) can be calculated as: S = Y - C - G, where Y is income, C is consumption, and G is government purchases.

To determine S, we must first calculate Y.Y = C + I + G + NX, where I is investment, and NX is net exports.

The formula for calculating national savings is as follows: National savings (S) = Y - C - G

The following is a numerical representation of the above data:Y = C + I + G + NX = 3,500 + I + 1,000 + NX

Disposable income is 4,000, while taxes minus transfers are 800. Therefore, Y + TR - T = C + S.

Now, let's compute this value.

Substitute the given values in the equation4,000 + TR - 800 - T = 3,500 + S600 - T = S + 3500 - 1000S = 500

Substitute the value of S in the formula:S = Y - C - G

Therefore, S = 4,000 - 3,500 - 1,000 = 500Hence, option b is correct.

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Answer:4.62x10^13

Step-by-step explanation: