Malik used these steps to solve the system of equations. 2 x 4 y = 20. 5 x minus 3 y = 11. Step 1 6 x 12 y = 60. 20 x minus 12 y = 44. Step 2 Step 3 x = 4 Step 4 2 (4) 4 y = 20. 8 4 y = 20. 4 y = 12. Y = 3. Step 5 The solution is (4, 3). What needs to be done in step 2? Divide both sides of the equations in step 1 by the same number to eliminate one variable. Multiply both sides of the equations in step 1 by the same number to eliminate one variable. Add the equations in step 1 to eliminate one variable. Subtract the equations in step 1 to eliminate one variable.

Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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Step-by-step explanation:

\( \frac{1}{5} (10 - 15u) = 2 - 3u\)

Answer:

9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

9

Answer:

x = 8

Step-by-step explanation:

We can see that in the picture that they are similar triangles and that CA is four times VT, so that means that all the sides in triangle TUV are four times those in triangle ABC. We now know that TU is four times AB, and 8 times 4 is 32, so we can say that 5x - 8 = 32. Now, we can add by 8 on both sides to get that 5x = 40. Now, we divide by five on both sides to get that x = 8.

The 95% confidence interval for the true proportion of people who favor candidate is (0.419,0.481).

A random sample of 1000 people was condidered for testing.

Number of people in sample favoured candidate

= 450

So, sample proportion, p = 450/1000 = 0.45

Confidence level= 95% i.e, alpha = 1 - 0.95=0.05, From standard normal Z- table, the value of Z( 0.025) is equals to 1.96..

Confidence interval formula,

CL = p ± Z× √(p×(1-p)/n)

Lower bound of interval is ,

=0.45 - 1.96× √(0.45× (1-0.45)/1000)

= 0.45 - 1.96× √(0.45× 0.55/1000)

= 0.45 - 1.96× √(0.0002475)

=0.419165~ 0.419

So the Upper bound is

= p + Z×√(p×(1-p)/n)

= 0.45 + 1.96× √(0.45× (1-0.45)/1000)

= 0.45 + 1.96× √(0.0002475)

= 0.480835 ~0.481

Hence, the required confidence interval is (0.419,0.481).

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Using the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power, it can be seens that that the two expressions are equal to each other.

The properties of multiplication state that when multiplying two expressions with the same base, we can add their exponents together. This means that 3 to the fifth power x 3 to the third power is equal to 3 to the eighth power.

In mathematical notation, this looks like:

3^8 = 3^5 x 3^3

Using the properties of multiplication, we can add the exponents together:

3^8 = 3^(5+3)

Simplifying the exponent:

3^8 = 3^8

This shows that the two expressions are equal to each other. Therefore, we can conclude that 3 to the eighth power and 3 to the fifth power x 3 to the third power are the same value.

Note: The question is incomplete. The complete question probably is: Use the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power.

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Answer:

4

Step-by-step explanation:

30*4=120 because 12=3*4 and 30*4 is basically 3*4*10, and since it's asking for the scale factor, we test to see if 12*4=48, which it does.

The height of the tower is approximately 336.4 feet. To find the height of the tower, we can use trigonometric ratios in a right triangle formed by the tower, the person's line of sight, and the ground.

Let's label the height of the tower as "h" in feet. We can divide the right triangle into two smaller triangles: one with the angle of elevation of 42 degrees and the other with the angle of depression of 28 degrees.

In the triangle with the angle of elevation, the side opposite the angle of elevation is the height of the tower, h, and the side adjacent to the angle of elevation is the distance from the window to the tower, which is 350 feet. We can use the tangent function to relate the angle of elevation and the sides of the triangle:

tan(42 degrees) = h / 350

Similarly, in the triangle with the angle of depression, the side opposite the angle of depression is also the height of the tower, h, and the side adjacent to the angle of depression is the distance from the window to the tower, which is still 350 feet. Using the tangent function again, we have:

tan(28 degrees) = h / 350

We can solve these two equations simultaneously to find the value of h. Rearranging the equations:

h = 350 * tan(42 degrees)

h = 350 * tan(28 degrees)

Evaluating these expressions, we find that h is approximately 336.4 feet.

Therefore, the height of the tower is approximately 336.4 feet.

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Answer:

The number of tickets purchased typically varies from the expected value by 0.95 tickets.

Step-by-step explanation:

The standard deviation of the distribution is 0.95.

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

We have

P (X = 1)= 0.29

P (X = 2) = 0.44

P( X= 3) = 0.19

P (X = 4) = 0.06

P (X = 5) = 0.02

The expected value is given by the sum of each value multiplied by it's respective probability, hence:

E(X) = 0.29(1) + 0.44(2) + 0.19(3) + 0.06(4) + 0.02 (5)

E(X) = 2.08

As, The standard deviation is the square root of the total of the difference squared between each value and the mean, multiplied by the likelihood of each value.

\(\sigma\) = √0.29 (1- 2.08)² + 0.44(2- 2.08)² +.....+ 0.02 (5- 2.08)²

  = 0.95

Thus, the standard deviation is 0.95.

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The polygon with the given vertices after the dilation with a scale factor of -4 is graphed on the image given at the end of the answer.

A dilation is a type of transformation that multiplies each of the coordinates of the vertices of the image by the scale factor. Hence, the side lengths are changed, and thus the original polygon and the dilated polygon are not congruent.

The vertices of the original polygon are given as follows:

R(-7,-1), S(2,5), T(-2,-3), U(-3,-3).

The scale factor of the dilation is given as follows:

k = -4.

Hence each coordinate of the vertices are multiplied by -4, and the vertices of the dilated polygon are given as follows:

R'(28, 4), S'(-8, -20), T'(8, 12), U'(12,12).

The dilated polygon, with these vertices labeled, is shown by the image given at the end of the answer.

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Answer:

A

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here g(x) = f(x) - 2 ← with c = - 2 < 0

Then g(x) is the graph of f(x) shifted down 2 units

Length of Bridge = 7.26 metres

Distance between the 2 people = 26.04 metres

The figure is attached below, to give you a clearer idea of the situation of the bridge and the 2 people.

Distance between Q and the bridge = 25m

Angle = 73.8°

Since P is located on the bridge (south-east corner), we can find the length of the bridge using tan 73.8°.

tan θ = height/base

tan 73.8° = 25/length of bridge

Let length of bridge =x.

⇒ 3.442 = 25/x

⇒ x = 25/3.442 = 7.2632 ≅ 7.26 metres.

To find the distance between P and Q (the 2 people), we can use sin 73.8°.

sin θ = height/hypotenuse

sin 73.8° = 25/distance between P and Q

Let distance between P and Q = y

sin 73.8° = 25/y

⇒ 0.96 = 25/y

⇒ y = 25/0.96 = 26.04166 ≅ 26.04 metres

Therefore, the distance between the 2 people = 26.04 metres, and the length of the bridge over the river = 7.26 metres.

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Answer:

\(f(2) = 6\)

Step-by-step explanation:

Substitute x=2 into f(x) x times 3

\(f(2) = 2 \times 3\)

Calculate it

\(f(2) = 6\)

Answer:

26$ because 13+13 is 26 boom

Answer:

Why is | 7 | the absolute value of the number 7?

The absolute value of a number is how far away the number is from zero. The absolute value is ALWAYS positive.

What is the absolute value of -7?

The negative version of the number is also | 7 |

Step-by-step explanation:

Answer:

7 and -7

Step-by-step explanation:

Absolute value is the distance a number is from 0 on a number line. If you go back 7 spaces from positive 7 you will land at 0, and if you go up 7 spaces from -7 you will land at 0.

Answer:

12 my g

Step-by-step explanation:

Answer:

$8,978.36

I hope this helps you

The formula for the amount earned with compound interest after n years is given as:

A = P \((1 + R/n)^{nt}\)

The accumulated value at the end of 8 years is $8978.36

Option D is the correct answer.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P \((1 + R/n)^{nt}\)

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

The formula for the amount earned with compound interest after n years is given as:

A = P \((1 + R/n)^{nt}\) _______(1)

P = $6,530

R = 4%

n = 4

t = 8

Substituting in (1)

Now,

A = 6530 x \((1 + 0.04/4)^{32}\)

A = 6530 x \(1.01^{32}\)

A = 6530 x 1.37

A = $8978.36

Thus,

The accumulated value at the end of 8 years is $8978.36

Option D is the correct answer.

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The area under the standard normal curve between z=â1.16 and z=â0.03 is 0.3663.

To find the area under the standard normal curve between z = -1.16 and z = -0.03, we will use the following steps:

1. Look up the z-values in the standard normal distribution table (or use a calculator or online tool that provides the corresponding probability values).
2. Subtract the probability value for z = -1.16 from the probability value for z = -0.03.
3. Round your answer to four decimal places.

Step 1: Look up the z-values in the standard normal distribution table.
- For z = -1.16, the corresponding probability value is 0.1230.
- For z = -0.03, the corresponding probability value is 0.4893.

Step 2: Subtract the probability values.
Area = P(-0.03) - P(-1.16) = 0.4893 - 0.1230

Step 3: Round the answer to four decimal places.
Area = 0.3663

So, the area under the standard normal curve between z = -1.16 and z = -0.03 is approximately 0.3663.

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The capitalized cost for the solid waste treatment plant, based on a 6% MARR, is approximately $579 million.

To calculate the capitalized cost for the solid waste treatment plant, we need to determine the present value of all the costs over the project's lifespan.

The costs involved in the project are as follows:

Initial installation cost: $35 million.

Minor repair and renovation (R&R) after 10 years: $14 million.

Major R&R after 20 years: $18 million.

Operating and maintenance (O&M) costs each year, increasing at a compound rate of 6% per year.

First, let's calculate the present value of the O&M costs over the 20-year period: Using the TVM Factor Table calculator, the present value factor for a 6% MARR and 20 years is 10.206.

The total O&M costs over 20 years can be calculated as follows: O&M costs for the first year: $3 million. O&M costs for the subsequent years: $3 million * (1 + 0.06) + $3 million * (1 + 0.06)^2 + ... + $3 million * (1 + 0.06)^19.

Using the formula for the sum of a geometric series, the O&M costs over the 20-year period can be calculated as: O&M costs = $3 million * (1 - (1 + 0.06)^20) / (1 - (1 + 0.06)) = $3 million * (1 - 1.418519) / (-0.06) = $3 million * (-0.418519) / (-0.06) = $2.91038 million.

Now, let's calculate the present value of the costs: Present value of the initial installation cost: $35 million.

Present value of the minor R&R cost after 10 years: $14 million * 10.206 (present value factor for 6% MARR and 10 years) = $142.884 million. Present value of the major R&R cost after 20 years: $18 million * 10.206^2 (present value factor for 6% MARR and 20 years) = $371.001 million.

Present value of the O&M costs: $2.91038 million * 10.206 = $29.721 million. Finally, the capitalized cost of the solid waste treatment plant is the sum of all the present values: Capitalized cost = $35 million + $142.884 million + $371.001 million + $29.721 million = $578.606 million.

Rounding the final answer to the nearest whole number, the capitalized cost for the solid waste treatment plant is $579 million.

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The complete question is:

A new solid waste treatment plant is to be constructed in Washington County. The initial installation will cost $35 million (M). After 10 years, minor repair and renovation (R&R) will occur at a cost of $14M will be required; after 20 years, a major R&R costing $18M will be required. The investment pattern will repeat every 20 years. Each year during the 20 -year period, operating and maintenance (O\&M) costs will occur. The first year, O\&M costs will total $3M. Thereafter, O\&M costs will increase at a compound rate of 6% per year. Based on a 6% MARR, what is the capitalized cost for the solid waste treatment plant? Click here to access the TVM Factor Table calculator. $ Carry all interim calculations to 5 decimal places and then round your final answer to a whole number. The tolerance is ±25,000.

Answer:

it's option c 192 square units as area of parallelogram equals products of base and heights

The following are correct applications of the rule cited: a. ~A-B, -B/: A M.T. and e. (A v B) > C, D v F) - C, D v F) v (A v B) 1: ~CvC Dil. The rule mentioned here is a stated rule. The statement rule helps to prove new sentences from the previous ones.

Here are the descriptions of all the options: a. ~A-B, -B/: A M.T.A- assumptionB- premise -B - premise~A - ~ introductionTherefore, we can say that this is the correct application of the rule cited, A M.T.b. (A v B) (A( Bv C)), (A. (A v B)) (A v B) 1:: (A (B v C)) (A. (A v B)) H.S.

The application of this rule is incorrect as it does not follow the main operator. Instead, it states two different premises as a single premise. c. - (A.B)-(-A.- B), V (A.B) /:: (-A.- B) D.S. The application of this rule is incorrect as it does not follow the rule of simplification. The rule of simplification states that if a compound sentence comprises two parts, you can take the first or second part alone.

d. (A. B) = (C.D) 1: A (C.D) ( Simp.)The application of this rule is incorrect as it does not follow the rule of simplification. e. (A v B) > C, D v F) - C, D v F) v (A v B) 1:. ~CvC Dil. The application of this rule is correct as it follows the negation and disjunction. Therefore, we can say that the correct applications of the rule cited are A M.T. and ~CvC Dil.

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Answer: $2.10

Step-by-step explanation:

21(.10)=2.1

Answer:

(x + 9)(x + 3)

Step-by-step explanation:

Factor 27 so that the factors, when combined, will equal 12:

x² + 12x + 27

x                9

x                3

(x + 9)(x + 3) is your answer.

Check: Use the FOIL method. Multiply the first two terms, the outside terms, the inside terms, and then the last two terms. Combine like terms:

(x + 9)(x + 3) = x² + 3x + 9x + 27 = x² + 12x + 27 (√)

~

Answer:

(x+9)(x+3)

Step-by-step explanation:

first of all, you should learn this properly, because you'll have to go back to this over and over again. anyways

you need to find two numbers so that it adds up to 12, but also multiplies to 27.

The numbers 9 and 3 fit the situation

So you add 9x and 3x because it's the same thing as 12x. you're just splitting up the term 12x into two other terms.

so now it looks like x^2 + 9x + 3x + 27. now you factor the first two terms and last two terms

x ( x + 9 ) <---factor of first two terms

3 ( x + 9) <---factor of last two terms

x(x+9)+3(x+9)

you notice that (x+9) is common in both factorized parts

so, you add x and 3 from the outside

and you get (x +3 ) (x+9)

Answer:

6.4

Step-by-step explanation:

9.8 + 10.9 + x = 27.1

20.7 + x = 27.1

x = 6.4

We know perimeter of triangle=sum of sides

\(\\ \sf\longmapsto 9.8+10.9+x=2.71\)

\(\\ \sf\longmapsto x+20.7=2.71\)

\(\\ \sf\longmapsto x=2.7-20.7\)

\(\\ \sf\longmapsto x=|-18|\)

\(\\ \sf\longmapsto x=18ft\)

The mean is 0.8 and the standard deviation is 0.8579.

The experimental probability consists of many trials. When the difference between the theoretical probability of an event and its relative frequency get closer to each other, we tend to know the average outcome. This mean is known as the expected value of the experiment denoted by .

In a normal distribution, the mean is zero and the standard deviation is 1.

In a binomial experiment, the number of successes is a random variable. If a random variable has a binomial distribution, its standard deviation is given by: = √npq, where mean: = np, n = number of trials, p = probability of success and 1-p =q is the probability of failure.

In a Poisson distribution, the standard deviation is given by = √λt, where λ is the average number of successes in an interval of time t.

Sample space = n = 10

Probability of winning = p = 0.08

Probability of losing = q = 1 - p = 1 - 0.08 = 0.92

Mean, μ = np = 10×0.08 = 0.8

Standard deviation, σ =  \(\sqrt{npq}\)

∴ σ = \(\sqrt{10 * 0.08* 0.92} = \sqrt{0.736} = 0.8579\)

Thus, the mean is 0.8 and the standard deviation is 0.8579.

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Answer:

Radius: 4

Center(5,-2)

Step-by-step explanation:

Equation of circle is (x-h)² + (y-k)² = r²

(x-5)² + (y+2)² = 4²

-(-5): x-coordinates of the center

-(+2) : y-coordinates of the center

4: radius