Question 4 13 points)
COMPARING METHODS
Solve the triangle with the given information. Round decimal answers to the nearest tenth:
m ZB = 98°
m ZC = 37°
a = 18

The value of K that will make the expressions equivalent is 10.

Considering the two expressions:

7 + (1/2)x - 3 + (3/4)x and 1 whole number (1/4)x + k - 6

we shall write the expression 7 + (1/2)x - 3 + (3/4)x in the form of the expression having k and then compare to know the value of k as follows;

(1/2)x + (3/4)x = (2x + 3x)/4

(1/2)x + (3/4)x = 5x/4

7 - 3 = 10 - 3 - 3

7 - 3 = 10 - 6

so;

7 + (1/2)x - 3 + (3/4)x = 5x/4 + 10 - 6

by comparison;

5x/4 is equal to the mixed fraction 1 whole number (1/4)x

k = 10 as obviously -6 is equal to -6.

Therefore, 10 is the value of k that will make expressions equivalent.

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9514 1404 393

Answer:

  9, the sum of the numbers given in the ratio

Step-by-step explanation:

The reduced ratio 2 : 7 means that two parts correspond to one length and 7 parts correspond to the other length. That is, there are a total of 2+7 = 9 parts in the full length of the segment.

It is convenient to think of the line segment as being divided into 9 equal parts.

_____

Additional comments

It is often helpful to consider the total number of "ratio units" in a given ratio. For example, in this problem, the shorter segment is 2/9 of the whole, and the longer one is 7/9 of the whole.

It can also be useful to consider what a "ratio unit" represents. If the whole segment is 27 inches long, then each of the 9 ratio units will represent 3 inches, for example. This means the division 2:7 is 2(3 in):7(3 in) = 6 in : 21 in.

Answer:

Since all three of the interior angles are the same degree, the three sides must be the same length. So, 3x - 5, 4x - 30, and 2x + 20 must be equal.

To solve for x, you can just set one of the sides equal to another one of the sides. I will do 3x - 5 and 4x - 30.

3x - 5=4x - 30

Add 5 to both sides.

3x = 4x - 25

Subtract 4x from both sides.

-x = -25

Divide both sides by -1.

x=25

:)

Answer:

[see below]

Step-by-step explanation:

The triangle shown is equilateral, as all three angles are marked congruent.

This means that the sides are equal to each other.

\(4x - 30 = 2x + 20\\\rule{150}{0.5}\\4x - 2x - 30 = 2x - 2x + 20\\\\2x - 30 = 20\\\\2x -30 + 30 = 20 + 30\\\\2x = 50\\\\\frac{2x=50}{2}\\\\\boxed{x = 25}\)

Hope this helps you.

The length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.

In mathematics, a scale factor is the proportion of related dimensions of an object to a description of that object.

Given that:-

The length and width of the outside edge will be:-

The sides are Dilated by factor 3 so the edges of the rectangle will be calculated as;-

Length = 3 ( 2x+4 ) = 6x + 12

Width   = 3 ( 3x+2 ) = 9x + 6

Therefore the length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.

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step 1

the probability of get 4 in one dice is

P=1/6

so

the probability of get 4 in two dices is

(1/6)*(1/6)=1/36

Answer:

9

Step-by-step explanation:

Answer:

x = 104

y = 74

Step-by-step explanation:

According to the figure, the quadrilateral has two pairs of parallel, opposite sides. That makes the quadrilateral a parallelogram.

In a parallelogram, opposite sides are congruent and opposite angles are congruent.

Because of congruent sides:

x - 7 = 97

x = 104

Because of congruent angles:

y = 74

The answer to the system of equations is (-7/11, 23/11), which stands for the intersection of the two lines.

It has one or more variables, and based on the values of the variables, it can either be true or false. Equations are frequently employed in a wide range of mathematical applications, from straightforward algebraic equations to more intricate differential equations used in calculus and physics. Equations are used to depict relationships between various mathematical objects or values. An essential part of addressing algebraic problems is to solve equations to determine the values of the variables that make the equation true.

given

We can solve one equation for one variable and then insert the expression into the second equation to apply the substitution method. For instance, we can resolve the first equation for y as follows:

y = 2x + 6

After that, we may enter the following expression in place of y in the second equation:

2x + 6 = -9x - 1

Then, we may find x:

11x = -7

x = -7/11

We may use one of the original equations to obtain the value of y once we have determined the value of x:

y = 2(-7/11) + 6 = 23/11

The answer to the system of equations is (-7/11, 23/11), which stands for the intersection of the two lines.

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To understand why either v_{-1} >> v_{2} and  v_{-1} >> v_{1} or  v_{2} and  v_{-1}  and v_{2} and  v_{1} n the mechanism for the decomposition of ozone, we need to consider the rate constants and the overall reaction rate.

In the given mechanism, v_{-1}   represents the rate constant for the formation of O atoms, v_{2}  represents the rate constant for the recombination of O atoms, and v_{1}   represents the rate constant for the recombination of O and O3 to form O2.

In the first scenario (a), where v_{-1} >> v_{2} and  v_{-1} >> v_{1} it suggests that the formation of O atoms (step v_{-1}  is significantly faster compared to both the recombination of O atoms (step v_{2} ) and the recombination of O and O3 (step v_{1}) . This indicates that the rate-determining step of the overall reaction is the formation of O atoms, and the subsequent steps occur relatively quickly compared to the formation step.

In the second scenario (b) v_{2} >> v_{-1}  and v_{2} >> v_{1}  it implies that the recombination of O atoms (step  ) is much faster compared to both the formation of O atoms (step  ) and the recombination of O and O3 (step  ). This suggests that the rate-determining step of the overall reaction is the recombination of O atoms, and the other steps occur relatively quickly compared to the recombination step.

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The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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Answer:

.125 | 1/8

__________

\(So,\;we\;have\;the\;following\;equation.\\\\1/2\;Divided\;By\;4=?\\\\So,\;if\;you\;solve\;the\;equation\;properly\;you\;should\;get\;0.125\\\\Just\;divide\;the\;two\;and\;you\;get\;your\;answer!\)

The value of E(X) is \(\frac{9}{4}\).

A variable with a value of 1 if event A occurs and a value of 0 otherwise is the indicator variable. With the exception of the fact that its argument is random as defined by the probability space, the indicator random variable is virtually identical to the indicator function.

Let \(X_{j}\)  be the indicator random variable of HH appearing at position j for j = 1,2,......,9. Notice that these aren't quite independent from each other, so if the binomial solution is entirely accurate, it gives the correct expected value.

But we can anyway use linearity of the expectation. As \($X=\sum_{j=1}^9 X_j$\), in another word, X, which is the total number of appearances of HH, is the sum of the ones that did occur, we get that

\($\mathbb{E}[X] = \mathbb{E} \left[\sum_{j=1}^9 X_j \right] \\=\sum_{j=1}^9 \mathbb{E}[X_j] \\= \sum_{j=1}^9 \frac{1}{4} \\= \frac{9}{4}.$\)

Therefore, the value of E(X) is \(\frac{9}{4}\) .

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Answer:

-43, -29, 29, 43

\\Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

The slope of the line is \(\frac{-7-8}{-5-4}=\frac{5}{3}\).

So, the equation is \(y+7=\frac{5}{3}(x+5)\).

Substituting x=0 to find the y-intercept, we get y=4/3.

Answer:

13v + 9

Step-by-step explanation:

(7v + 6) + (6v + 3) ← remove parenthesis

= 7v + 6 + 6v + 3 ← collect like terms

= 7v + 6v + 6 + 3

= 13v + 9

The point estimate for the population mean number of weeks it takes a worker aged 55 plus to find a job is 22.9 weeks, with a margin of error of approximately 4.18 weeks and a 95% confidence interval of (18.72, 27.08) weeks. The data is skewed to the right, and collecting data from a larger sample and accounting for other factors could improve the study.

The point estimate for the population mean number of weeks it takes a worker aged 55 plus to find a job can be found by calculating the sample mean. Adding up all the values in the data and dividing by the sample size of 39 gives a point estimate of 22.9 weeks.

To find the margin of error at 95% confidence, we need to first calculate the sample standard deviation. The sample standard deviation is 12.9 weeks. Using the formula for the margin of error at 95% confidence level, we get:

Margin of error = 1.96 * (12.9 / √(39)) ≈ 4.18 weeks

The 95% confidence interval estimate of the mean is given by

(22.9 - 4.18, 22.9 + 4.18) = (18.72, 27.08)

Therefore, we are 95% confident that the true population mean number of weeks it takes a worker aged 55 plus to find a job lies between 18.72 and 27.08 weeks.

To determine the degree of skewness in the sample data, From the data provided, the distribution appears to be skewed to the right, as there are a few very large values that pull the mean to the right of the median.

For a repeat of this study, it would be useful to collect data from a larger sample size to improve the precision of the estimates. Additionally, it may be useful to collect data on other factors that may affect job search time, such as education level, prior work experience, and industry.

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--The given question is incomplete, the complete question is given

" Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job contained in the file JobSearch are consistent with the AARP findings (AARP Bulletin, April 2008). a) Provide a point estimate of the population mean number of weeks it takes a worker aged 55 plus to find a job. b) At 95% confidence, what is the margin of error? c) What is the 95% confidence interval estimate of the mean? d) Discuss the degree of skewness found in the sample data. What suggestion would you make for a repeat of this study? Job Search Time (Weeks) 21 14 51 16 17 14 16 12 48 0 27 17 32 24 12 10 52 21 26 14 13 24 19 28 26 26 10 21 44 36 22 39 17 17 10 19 16 22 5 22"--

1) The value of P(A∩B) = 0.

2) The value of P(A|B) = 0.

3) P(A|B) is not equal to P(A). A and B are independent events.

4) The statement "Mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent." is not accurate.

5) We can conclude that mutually exclusive events have a probability of intersection of zero and are not independent.

1) Since A and B are mutually exclusive, they cannot occur at the same time, so P(A∩B) = 0.

2) The conditional probability of A given B is defined as the probability of A occurring given that B has occurred. Since A and B are mutually exclusive, if B has occurred, then A cannot occur. Therefore, P(A|B) = 0.

3) No, P(A|B) is not equal to P(A). Since B has occurred, the sample space has been reduced to only those outcomes in which B has occurred. Therefore, the probability of A given that B has occurred can only be determined from the portion of the sample space in which both A and B occur.

However, since A and B are mutually exclusive, this probability is zero. Therefore, P(A|B) ≠ P(A).

4) The statement is not accurate. Mutually exclusive events and independent events are different concepts. Two events are mutually exclusive if they cannot occur at the same time, whereas two events are independent if the occurrence of one event does not affect the probability of the other event.

If two events are mutually exclusive, they are not independent because the occurrence of one event precludes the occurrence of the other event.

5) Mutually exclusive events have a relationship where if one event occurs, the other cannot. In contrast, independent events are events where the occurrence of one event does not affect the probability of the other event occurring.

Therefore, we can conclude that mutually exclusive events and independent events are not the same concept, and we must be careful not to confuse them.

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Step-by-step explanation:

the distance is sqrt ( (-6)^2 + (-12)^2) = sqrt(  36 + 144) = sqrt( 180) = sqrt(36*5) = 6 * sqrt(5)

2/(2+4) = 2/6 = 1/3

-2 + (1/3)*6*sqrt(5) = -2 + 2* sqrt(5)

6 + (1/3)*6*sqrt(5) = 6 + 2* sqrt(5)

Yes, I can help them determine how they did within their respective groups. A higher Z-score indicates a faster time compared to the average for their group, while a lower Z-score indicates a slower time.

To do this, we will calculate the standard score or Z-score for each of them, which measures how many standard deviations above or below the mean their finishing time was. Calculation is as follows:

For Leo:

Z = (4948 - 4313) / 583 = 1.01

For Mary:

Z = (5513 - 5261) / 807 = 0.33

So, Leo finished 1.01 standard deviations above the mean for the Men, Ages 30 - 34 group, while Mary finished 0.33 standard deviations below the mean for the Women, Ages 25 - 29 group.

As for your second question, if the distributions of finishing times were not nearly normal, then the values of the standard score would change. This is because the standard score is calculated using the mean and standard deviation, which are important parameters of a normal distribution, these parameters may not accurately represent the data, and therefore the standard score would not be an accurate measure of relative performance.

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well, let's take a look at the table

is g(x) increasing from -2 to -1? hmmm from when x = -2 g(x) = 2, then when x = -1, g(x) = -3, hold the mayo!! it went from 2 to -3, that's just going down, so, nope is not.

is itdecreasing from -1 to 0?  hmmm x = -1, g(x) = -3, as x = 0, g(x) = 2, wait a second!!! it went from -3 to 2, it really went up, so nope, is not decreasing on that interval.

is it increasing from 0 to 1?  let's see, as x = 0, g(x) = 2, as x = 1, g(x) = 17, woahhh!!, it went from 2 and rocketted to 17, yeap, it is increasing as x = 0 to x = 1.

Answer:

B

Step-by-step explanation:

Answer:

$14.82/hr

It depends on where you are though.

Answer:

91 divided by 14 = 6.5 is the length

Step-by-step explanation:

Whenever given an area and 1 given length always divide the area by the length to find the missing length.

Answer:

An abacus is a calculation tool used by sliding counters along rods or grooves, used to perform mathematical functions. In addition to calculating the basic functions of addition, subtraction, multiplication and division, the abacus can calculate roots up to the cubic degree.

Answer: For first blank: GNS

P = N G = P S = R

The coordinates of the point on the directed line segment from (−3,4) to (3,8) partitions the segment into a ratio of 1 to 3 is given as follows:

(-1.5, 1).

The coordinates of the point are applied using proportions, as the fact that the point partitions the segment into a ratio of 1 to 3 means that the following equation is built:

Point - Initial Coordinate = 1/4(Final Coordinate - Initial Coordinate).

This equation is used to find both the x-coordinate and the y-coordinate of the point.

The x-coordinate of the point is obtained as follows:

x + 3 = 1/4(3 + 3)

x + 3 = 1.5

x = -1.5.

The y-coordinate of the point is obtained as follows:

y - 4 = 1/4(-8 - 4)

y - 4 = -3

y = 1.

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The slope of the tangent line to the parabola y = 3x^2 + 5x + 3 at the point (3, 45) is 23 that can be found by calculating the first derivative of the function with respect to x and then evaluating it at the given point.

First, let's find the first derivative of y with respect to x:
y = 3x^2 + 5x + 3
dy/dx = (d/dx)(3x^2) + (d/dx)(5x) + (d/dx)(3)
dy/dx = 6x + 5
Now that we have the first derivative, we can find the slope of the tangent line at the point (3, 45) by plugging in x = 3:
dy/dx = 6(3) + 5
dy/dx = 18 + 5
dy/dx = 23

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Answer:

B. x+60+90=180

Step-by-step explanation:

You selected the right choice yay!!

A line will always equal 180 and we are given three things that must equal 180. Also, what is on the top is the same as the bottom so x applies.

x+60+90=180

Answer:

8x5

Step-by-step explanation:

Just do 8x5 then you'll get your answer of 40. So he did it right because if you do 8x5 you'd get 40.

Answer:

Area of triangle=1/2 bh

b= 5in ,h = 8in

A= 1/2 ×5 × 8

= 20in.sq

Her answer was wrong because she forgot to multiply with 1/2 ....