factor 42z+68.

simplify and factor 3(x - 2) + 9(x + 1) + 5(1 + 2x) + 2(3x - 4)

Answer:

When flipping a coin, there are two possible outcomes: heads or tails. The probability of getting heads on any one flip is 1/2, and the probability of getting tails is also 1/2.

To find the probability that all three coins will land on the same side (either all heads or all tails), we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

So, for each coin flip, there are two possible outcomes, and the probability of getting either outcome is 1/2. To find the probability that all three coins will land on the same side, we need to find the probability of getting either all heads or all tails.

The probability of getting all heads is:

(1/2) x (1/2) x (1/2) = 1/8

Similarly, the probability of getting all tails is also 1/8.

So, the probability of all three coins landing on the same side is:

1/8 + 1/8 = 2/8 = 1/4

Therefore, the probability that Matrix will flip 3 coins and all three coins will land on the same side is 1/8 or 0.125, which can also be written as a fraction or percentage.

Answer:

x = 7

Step-by-step explanation:

Since the two sides (9x - 25) of the triangle are congruent to each other, we can add them together

(9x - 25) + (9x - 25)

18x - 50

A triangle is 180 degrees when adding all three sides

So if 2 sides together equal 18x - 50 and the last side equals 104, then they should equal 180 total

18x - 50 + 104 = 180

Combine like terms

18x + 54 = 180

Subtract both sides by 54 to isolate the variable

18x + 54 - 54 = 180 - 54

18x = 126

Divide both sides by 18 to isolate the variable

18x ÷ 18 = 126 ÷ 18

x = 7

Check your work by plugging in the x value for the expression and adding all three sides to equal 180 degrees

9(7) - 25 + 9(7) - 25 + 104 = 180

Pemdas says to multiply first

63 - 25 + 63 - 25 + 104 = 180

38 + 38 + 104 = 180

76 + 104 = 180

180 = 180

The work is correct

The population density in Nevada in 2012 was approximately 24.9 people per square mile.

In order to find the population density in Nevada in 2012, we need to know the land area of Nevada in square miles. Assuming the land area of Nevada in 2012 was 110,622 square miles, we can calculate the population density as follows:

First, we need to find the population of Nevada in 2012:

Population in 2012 = Population in 2005 + (Population in 2005 x % increase)

Population in 2012 = 2.432 million + (2.432 million x 0.132)

Population in 2012 = 2.754944 million (rounded to the nearest thousand)

Next, we can calculate the population density:

Population density = Population / Land area

Population density = 2.754944 million / 110,622 square miles

Population density ≈ 24.9 people per square mile

Therefore, the population density in Nevada in 2012 was approximately 24.9 people per square mile.

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a. The probability is 4/10 or 0.4.

b. The combination formula: C(10, 5) = 252.

c. C(6, 3) = 20.

d. C(4, 2) = 6.

e. The probability is 120/252 ≈ 0.4762.

a. To calculate the probability that the person drawing the names is a Democrat, we divide the number of Democrats (4) by the total number of council members (10). Therefore, the probability is 4/10 or 0.4.

b. When there are no restrictions on the composition of the committee, we can calculate the number of ways it can be formed using combinations. Since there are 10 council members and we need to choose 5, the number of ways the committee can be formed is given by the combination formula: C(10, 5) = 252.

c. To determine the number of ways to choose 3 Republicans, we calculate the combination of 6 Republicans taken 3 at a time: C(6, 3) = 20.

d. Similarly, to calculate the number of ways to choose 2 Democrats, we use the combination formula with the 4 Democrats: C(4, 2) = 6.

e. To find the probability of selecting 3 Republicans and 2 Democrats, we need to calculate the total number of favorable outcomes and divide it by the total number of possible outcomes. The number of ways to select 3 Republicans from 6 and 2 Democrats from 4 is given by the product of their respective combinations: C(6, 3) * C(4, 2) = 20 * 6 = 120. The total number of possible outcomes is C(10, 5) = 252. Therefore, the probability is 120/252 ≈ 0.4762.

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Answer:

V=14.12 in³

Step-by-step explanation:

This is a tough one. To find the volume, you'll need the followimg equation:

\(\frac{4}{3} \pi {r}^{3}\)

The 3 next to the R is an exponent. An exponent involves multiplying the radius by itself. So it would look like this: 1.5×1.5×1.5

Next, you must multiply the result by 3.14. So it would be 3.375×3.14. And finally, you must multiply that result by 4 and divide by 3. So 10.59×4 to get 42.36 then divide that by 3. 42.36 divided by 3 is 14.2. (Answer can vary from time to time and you may need to round up)

Answer: SMART Goal: I will keep my locker clean and organized as a sign of respect for myself and to save time.

Achievable: Each week, I will clean out my locker by throwing away anything I don’t need and making sure everything is in its correct place.

Time-Based: I will organize my locker before school starts. I will clean it every week. By the end of the first semester, I’ll automatically know where everything in my locker can be found.

Step-by-step explanation:

In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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The area of the rectangle is changing at a rate of 20 ft²/sec when the length equals 10 feet and the width equals 8 feet.

Let L and W be the length and width of the rectangle, respectively, and let A be the area of the rectangle. Then we have:

We want to find dA/dt, the rate of change of the area A with respect to time t, when L = 10 ft and W = 8 ft.

We know that:

A = L*W

Taking the derivative of both sides with respect to time t, we get:

dA/dt = d/dt (L*W)

Using the product rule of differentiation, we get:

dA/dt = dL/dt * W + L * dW/dt

Substituting the given values, we get:

dA/dt = 5 ft/sec * 8 ft + 10 ft * (-2 ft/sec)

Simplifying, we get:

dA/dt = 40 - 20 = 20 ft²/sec

Therefore, the area of the rectangle is changing at a rate of 20 ft^2/sec when the length equals 10 feet and the width equals 8 feet.

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3000? maybe good luck

Answer:

6,000

Step-by-step explanation:

To find the volume, you have to solve the width x length x height.

So, 1 of the containers is 20(W) x 15(L) x 10(H) which equals to a volume of 3,000.Then we have another container with the same dimensions. That means we will add 3,000 because it's the same. 3,000 + 3,000 = 6,000

Hope this helped :)

Based on the given values, we can compute the expected returns and expected standard deviations for different weightings of the stocks in the portfolio. The results are as follows:

a. When w1 = 1.00, the expected return of the two-stock portfolio is 0.13, and the expected standard deviation is 0.03.

b. When w1 = 0.65, the expected return of the two-stock portfolio is 0.1095, and the expected standard deviation is 0.0214.

c. When w1 = 0.60, the expected return of the two-stock portfolio is 0.104, and the expected standard deviation is 0.0222.

d. When w1 = 0.30, the expected return of the two-stock portfolio is 0.074, and the expected standard deviation is 0.0262.

e. When w1 = 0.10, the expected return of the two-stock portfolio is 0.038, and the expected standard deviation is 0.0324.

To calculate the expected return of the two-stock portfolio, we use the weighted average of the individual expected returns based on the given weights. For example, in part (a), where w1 = 1.00, the expected return is simply equal to E(R1) = 0.13.

To calculate the expected standard deviation of the two-stock portfolio, we use the formula:

σ = √(w1^2 * E(a1)^2 + w2^2 * E(q2)^2 + 2 * w1 * w2 * E(a1) * E(q2) * ρ)

where E(a1) is the expected standard deviation of stock 1, E(q2) is the expected standard deviation of stock 2, and ρ is the correlation coefficient.

Regarding the risk-return graph, without the specific details of the graph options provided, it is not possible to determine which graph is correct for the given weightings and correlation coefficient. The graph would typically depict the risk-return tradeoff for different weightings and correlation coefficients, showing the relationship between expected return and expected standard deviation of the portfolio.

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The retail price is $354.65.

What is retail price?

The price at which a product's manufacturer ostensibly recommends that a retailer sell it is referred to as the list price, also known as the manufacturer's suggested retail price, recommended retail price, or suggested retail price of a product.

Given: An import/export business marks up imported merchandise by 105%.

A wicker chair imported from Singapore originally costs from the manufacturer $173.

We have to find the retail price.

Retail price = \(= 173 + 173*\frac{105}{100} \\\)

                   = 173 + 181. 65

Retail price  = 354.65

Hence,  Retail Price is $ 354.65.

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Answer:

90 minutes

Step-by-step explanation:

it will take twice as long therefore 90 minutes

The surface with the curved plane with grid lines is represent the plane in the hyperbolic geometry.

According to the statement

we have to find about the those surface which represent the plane in hyperbolic geometry.

So, For this purpose, we know that the

The hyperbolic plane is a plane where every point is a saddle point. In hyperbolic geometry, two parallel lines are taken to converge in one direction and diverge in the other.

And according to the statement, we have to find that the surface.

And from the given surfaces, The curved plane with the grid lines.

In this surface the grid lines are in the one plane and in combining form they represent the plane.

This surface represent the plane in hyperbolic geometry.

So, The surface with the curved plane with grid lines is represent the plane in the hyperbolic geometry.

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The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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Answer:

1176

Step-by-step explanation:

Answer:

8 > 8 - 2

Step-by-step explanation:

because that is just the other side of the same "coin".

8 - 2 < 8

data exactly the same thing as

8 > 8 - 2

Equation of the line passing through  (1, -9) and (1, 12) is y = -9

The equation to the line in  slope intercept form

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

calculation of slope, m for (1, -9) and (1, 12)

(y - y₁) /  (x - x₁)   = m

m = (-9 - 12) /  (1 - 1)

m = 1 / 0

m = undefined slope (this is the slope of vertical line)

equation of the line  (1, -9)

(y - -9) = 0

y + 9 = 0

y = -9

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Answer:

66.6%

Step-by-step explanation:

Step one

given

A coat at a store is originally priced at $54.99

The store marks down the price down to $32.99

Required

the percent decrease

Step two:

the percent decrease= change in price/ old price*100

the percent decrease= 54.99-32.99/54.99*100

the percent decrease= 22/ 32.99*100

the percent decrease= 0.666*100

the percent decrease= 66.6%

Answer:66.6%

Step-by-step explanation:Step one

given

A coat at a store is originally priced at $54.99

The store marks down the price down to $32.99

Answer:

6

Step-by-step explanation:

3x+11 = 29

3x =  29 - 11 = 18

x = 18/3 = 6

Answer:

\(\frac{12}{7}\)

Step-by-step explanation:

Cross multiply, then divide:

I hope this helps!

The value of t is 1.71 in the equation 7/3=4/t

Two or more expressions with an Equal sign is called as Equation.

The given equation is 7/3=4/t

Seven divided by three equal to four divided by t

We need to solve the value of t

Apply the cross multiplication

7t=12

Divide both sides by 7

t=12/7

t=1.71

Hence, the value of t is 1.71 in the equation 7/3=4/t

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We have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

To solve the given equations for the equilibrium values of C, NX, CF, r, and ε, let's go step by step.

First, we'll substitute equations (2), (3), (4), (5), (6), (7), (8), and (9) into equation (2) to eliminate the variables C, I, G, NX, CF, and T.

Equation (2) becomes:
Y = (1/2)(Y - T) + (2,000 - 100r) + 1,500 + (500 - 500ε)

Next, let's simplify the equation:

Y = (1/2)(Y - 1,000) + 2,000 - 100r + 1,500 + 500 - 500ε

Distribute (1/2) to the terms inside the parentheses:

Y = (1/2)Y - 500 + 2,000 - 100r + 1,500 + 500 - 500ε

Combine like terms:

Y = (1/2)Y + 3,500 - 100r - 500ε

Now, let's isolate Y by subtracting (1/2)Y from both sides:

(1/2)Y = 3,500 - 100r - 500ε

Multiply both sides by 2 to get rid of the fraction:

Y = 7,000 - 200r - 1,000ε

We now have one equation (10) in terms of Y, r, and ε.

Next, let's substitute equation (1) into equation (10) to solve for Y:

5,000 = 7,000 - 200r - 1,000ε

Subtract 7,000 from both sides:

-2,000 = -200r - 1,000ε

Divide both sides by -200:

10 = r + 5ε

This gives us equation (11) in terms of r and ε.

Now, let's substitute equation (11) into equation (5) to solve for NX:

NX = 500 - 500ε

Substitute r + 5ε for ε:

NX = 500 - 500(r + 5ε)

Simplify:

NX = 500 - 500r - 2,500ε

This gives us equation (12) in terms of NX, r, and ε.

Finally, let's substitute equation (12) into equation (6) to solve for CF:

CF = -100r

Substitute 500 - 500r - 2,500ε for NX:

CF = -100(500 - 500r - 2,500ε)

Simplify:

CF = -50,000 + 50,000r + 250,000ε

This gives us equation (13) in terms of CF, r, and ε.

To summarize, we have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

These equations represent the equilibrium values of Y, r, ε, NX, and CF in the given open economy.

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Answer:

(4,-1)

Step-by-step explanation:

x is 4 y is -1

Answer:

(2,1)

Step-by-step explanation:

Let's solve your system by elimination.

6x−7y = 5;−4x+7y=−1

6x−7y=5

−4x+7y=−1

Add these equations to eliminate y:

2x = 4

Then solve2x = 4for x:

2x = 4

(Divide both sides by 2)

x = 2

Now let's plug x in to solve for y.

6x - 7y = 5

6(2) - 7y = 5

12 - 7y = 5

subtract 12 on both sides.

-7y = -7

divide both sides by -1

y = 1

NOTES: The general equation of a circle is (x – h)2 + (y – k)2 = r2, where (h, k) represents the location of the circle's center, and r represents the length of its radius.

THE ANSWER IS A

1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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we have the next squared binomial

we have the next formula in order to expand a squared binomial

So we can expand

so the correct answer is the first one

Answer:

8 inches

Step-by-step explanation:

Length = 36 in

Ratio = 2:7

Small piece: