the solution set of a linear system involving variables x1; : : : ; xn is a list of numbers.s1; : : : ; sn/that makes each equation in the system a true statement when the values s1; : : : ; sn are substituted for x1; : : : ; xn, respectively.

Answer:

Section of the function which is constant is C

Step-by-step explanation:

Any line parallel to x-axis has a slope of zero and in this figure we can see that the section C only is parallel to x-axis and since it parallel to the x-axis it has a slope of zero hence the function at C is neither increasing because it doesn't have a positive slope nor is it decreasing because it doesn't have a negative slope so it remains constant.

There are 19 people who own a cat or a dog.

A number is a mathematical object used to represent quantity, measurement, or a count of something. It can be an integer (whole number), a rational number (fraction), an irrational number (such as pi), or a real number (which includes all rational and irrational numbers).

To find the number of people who own a cat or a dog, we need to add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs.

Let's start by finding the number of people who own only cats. We know that 16 people own cats, and 5 people own both cats and dogs. Therefore, the number of people who own only cats is:

16 - 5 = 11

Next, let's find the number of people who own only dogs. We know that 8 people own dogs, and 5 people own both cats and dogs. Therefore, the number of people who own only dogs is:

8 - 5 = 3

Finally, we can add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs:

11 + 3 + 5 = 19

So, there are 19 people who own a cat or a dog.

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The mean (μ) of the sample is 25 and the standard error (SE) is approximately 1.58.

To find the mean and standard error of a sample, we can use the formulas:

Mean (μ) = population mean = 25
Standard Error (SE) = √(variance / sample size)

Given that the population mean is 25 and the variance is 200, we can calculate the standard error as follows:

Standard Error (SE) = √(200 / 80)
SE = √2.5
SE ≈ 1.58

Therefore, the mean (μ) of the sample is 25 and the standard error (SE) is approximately 1.58.

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To dilute 40 quarts of 5% acid solution to a 2% solution, you need to add x quarts of water. To find x, we can use the following formula: Initial amount of acid × initial concentration = final amount of acid × final concentration We know the initial amount of acid is 5% of 40 quarts, which is 2 quarts.

So the formula becomes: 2 quarts × 5% = (40 + x) / 50 quarts × 2%Now we can solve for x:2 × 40 × 5% = (40 + x) / 50 × 2%400% / 2% = 40 + xx = 400 - 40x = 360 quarts Therefore, you need to add 360 quarts of water to 40 quarts of 5% acid solution to dilute it to a 2% solution.

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Step-by-step explanation:

\((1) \: \: \sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } \times \frac{ \sqrt[3]{64} }{ \sqrt[3]{3} } \times \frac{ \sqrt[6]{9} }{ \sqrt[3]{2} } \)

Note that the 1st two factors can be combined:

\( \sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } = \sqrt[3]{5 \times \frac{2}{5} } = \sqrt[3]{2} \)

We also know that the numerator in the 3rd factor can be rewritten as

\( \sqrt[3]{64} = 4\)

And the numerator in the 4th term can be rewritten as

\( \sqrt[6]{9} =({( {3})^{2} })^{ \frac{1}{6} } = \sqrt[3]{3} \)

So let's rewrite expression #1

\( \sqrt[3]{2} \times \frac{4}{ \sqrt[3]{3} } \times \frac{ \sqrt[3]{3} }{ \sqrt[3]{2} } \)

Notice that all the radical terms cancel out except for 4 therefore,

\(\sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } \times \frac{ \sqrt[3]{64} }{ \sqrt[3]{3} } \times \frac{ \sqrt[6]{9} }{ \sqrt[3]{2} } = 4\)

a) The steady-state level of capital-labor ratio is 0.1833 and output per worker is 0.55.

b) The steady-state consumption per worker is 0.33.

c) To increase the consumption per worker to the golden-rule level, the government can implement policies to increase the capital-labor ratio (k) to the golden-rule level (kG = 46.49).

d) The steady-state capital-labor ratio is 0.1333, output per worker is 0.4, and consumption per worker is 0.18.

a. To calculate the steady-state level of capital-labor ratio and output per worker, we can use the Solow model equations.

Steady-state capital-labor ratio (k):

In the steady state, investment equals saving, so we have:

sY = (d + n)k

0.40 * 3k = (0.15 + 0.07)k

1.2k = 0.22k

k = 0.22 / 1.2

k = 0.1833

Steady-state output per worker (y):

Using the production function, we have:

y = 3k

y = 3 * 0.1833

y = 0.55

Therefore, the steady-state level of capital-labor ratio is 0.1833 and output per worker is 0.55.

b. Steady-state consumption per worker:

In the steady state, consumption per worker (c) is given by:

c = (1 - s)y

c = (1 - 0.40) * 0.55

c = 0.60 * 0.55

c = 0.33

The steady-state consumption per worker is 0.33.

c. To increase the consumption per worker to the golden-rule level, the government can implement policies to increase the capital-labor ratio (k) to the golden-rule level (kG = 46.49). This can be achieved through measures such as promoting investment, technological progress, or increasing the saving rate.

d. If the saving rate increases to 55%, we can calculate the new steady-state levels of capital-labor ratio, output per worker, and consumption per worker.

Steady-state capital-labor ratio (k'):

0.55 * 3k' = (0.15 + 0.07)k'

1.65k' = 0.22k'

k' = 0.22 / 1.65

k' = 0.1333

Steady-state output per worker (y'):

y' = 3k'

y' = 3 * 0.1333

y' = 0.4

Steady-state consumption per worker (c'):

c' = (1 - 0.55) * 0.4

c' = 0.45 * 0.4

c' = 0.18

In this case, the steady-state capital-labor ratio is 0.1333, output per worker is 0.4, and consumption per worker is 0.18.

Regarding government policy, the saving rate increase in this scenario would lead to lower consumption per worker compared to the golden-rule level. Therefore, the government policy in this case would be different from that in (c), where they aim to achieve the golden-rule level of consumption per worker.

e. The difference in the levels of variables in (a), (b), and (d) can be explained as follows:

In (a), we have the initial steady-state levels where the saving rate is 40%. The economy reaches a balanced state with a capital-labor ratio of 0.1833 and output per worker of 0.55.

In (b), the steady-state consumption per worker is calculated based on the initial steady-state levels. It is determined by the saving rate and output per worker, resulting in a consumption per worker of 0.33.

In (d), when the saving rate increases to 55%, the economy adjusts to a new steady state. The higher saving rate leads to a lower consumption rate, resulting in a new steady-state capital-labor ratio of 0.1333, output per worker of 0.4, and consumption per worker of 0.18.

The difference in the levels of variables is driven by changes in the saving rate, which affects investment and capital accumulation. Higher saving rates lead to higher investment, which increases the capital-labor ratio and output per worker. However, it also reduces consumption per worker, as more resources are allocated to investment. The government policy to achieve the golden-rule level of consumption per worker would involve finding the optimal saving rate that maximizes long-term welfare, considering the trade-off between investment and consumption.

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Isoquants for f(K, L) = 1/2 min{K, L} that produce exactly 10 goods and 25 goods can be graphed, with labeled points.

For function f(K, L) = 1/2 min{K, L}, we can graph the isoquants that represent the combinations of capital (K) and labor (L) that produce exactly 10 goods and 25 goods.

An isoquant represents all the combinations of inputs (K and L) that yield the same level of output. In this case, the isoquants will be curves that connect different combinations of K and L, where the output is constant at either 10 goods or 25 goods.

To graph the isoquant for 10 goods, we plot points where f(K, L) = 10. For example, if we let K = 4 and L = 4, the minimum of K and L is 4, so f(K, L) = 1/2 * 4 = 2 goods.

Since this is less than 10, we need to increase either K or L. We can try K = 8 and L = 4, where the minimum of K and L is still 4, and f(K, L) = 1/2 * 4 = 2 goods. Again, this is less than 10, so we increase K or L further.

Continuing this process, we can plot a few more points and connect them to obtain the isoquant for 10 goods.

Similarly, we can graph the isoquant for 25 goods by plotting points where f(K, L) = 25. For each point, we determine the minimum of K and L, multiply it by 1/2, and check if the result is equal to 25. By plotting and connecting several such points, we obtain the isoquant for 25 goods.

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Answer:

Step-by-step explanation:

A. 2x = -6

    x = -3

 3 + y = 5

   y = 2

(-3, 2)

-9 - 2 = -11

 -11 = -11

3 + 2 = 5

5 = 5

B. 4x + 2y = 1

    6x + 4y = 1

-8x - 4y = -2

 6x + 4y = 1

-2x = -1

x = 1/2

4(1/2) + 2y = 1

2 + 2y = 1

2y = -1

y = -1/2

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

1 + 3 = 2 + 2

4 = 4

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

3 - 2 = 1

1 = 1

C.

-x + 32y = -25

4x + 8y = 100

-4x + 128y = -100

136y = 0

y = 0

-x = -25

x = 25

(25, 0)

32(0) - 25= -25

-25= -25

5(25) = 100 + 25 - 8(0)

125 = 125

D.

3x + 2y = 6

4x + 5y = -20

-12x - 8y = -24

12x + 15y = -60

7y = -84

y = -12

2(-12) + 3x = 6

-24 + 3x = 6

3x = 30

x = 10

(10, -12)

2(-12) + 3(10) = 6

-24 + 30 = 6

6 = 6

4(10) + 5(-12) + 20 = 0

40 - 60 + 20 = 0

 -20 + 20 = 0

0 = 0

Approximately 1.71 square inches of the tinted glass are red in the semicircular window. The area of the red portion was calculated using the radius of the semicircle and the angle of the triangle opposite to the 40° angle.

Since the window is semicircular, it can be divided into a half-circle and a triangle.

The half-circle will be colored green and the remaining portion, which is a triangle, will be colored red.

The central angle of the half-circle is 40°, which means that the angle of the triangle opposite to it is 140°.

We know that the sum of angles in a triangle is 180°, so the sum of the other two angles in the triangle is:

180° - 140° = 40°

Since the two angles are equal, each one is 20°.

To find the area of the red portion, we need to find the radius of the semicircle.

Let's assume that the diameter of the window is 10 inches. Then, the radius would be:

r = d/2 = 10/2 = 5 inches

The area of the half-circle (colored green) is:

A_green = 1/2 * pi * r^2

= 1/2 * pi * 5^2

= 39.27 sq. in. (approx.)

The area of the triangle (colored red) is:

A_red = 1/2 * base * height

= 1/2 * r * sin(20°) * 2

= r * sin(20°)

= 1.71 sq. in. (approx.)

Therefore, approximately 1.71 square inches of the tinted glass are red.

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The missing figure is in the image attached below

Answer:

B. not found in a toy store

Step-by-step explanation:

Given:

T = the set of things found in a toy store.

V = the set of things that cost more than $50.

T∪V = the set of things that found in a toy store or cost more than $50.

T∩V = the set of things that found in a toy store and cost more than $50.

The set T′ is the complement of the set T and it consists of the  set of things that are not found in a toy store.

The correct option is B

Answer:

Step-by-step explanation:

787.490566

Answer:

2 + 2 + 5 × 18 ÷ 2 + 745 - 345 ÷ 53  = 787.490566038

hope this helps

Step-by-step explanation:

what is the problem ?

the solution of such a system of 2 equations is the point, where they cross.

this point has the same coordinates for both equations, and that is called the solution.

and we can clearly see that point in the graph :

(-1, 1)

formally we can solve that way

y = 2x + 3

y = -x

therefore,

2x + 3 = -x

3x + 3 = 0

3x = -3

x = -1

y = -x = - -1 = 1

so, we get

(-1, 1) as solution.

There are several statistics that are robust to outliers: Median, Interquartile range, Winsorized mean and Trimmed mean.

These statistics are more suitable for datasets that contain outliers as they are less influenced by the extreme values and provide more accurate information about the central tendency and variability of the data.

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Based on the fact that Brielle mixed 8 cups of blue and 6 cups of yellow paint, the complete table to show a new mixture that matches this paint color is:

The original paint color is in the ratio:
8 : 6

This can be simplified to:

(8 : 6 ) / 2

4 : 3

For every 4 blue cups, there will be 3 yellow cups.

If there are 9 yellow cups then the number of blue cups would be:

= (9 x 4) / 3

= 12 blue cups

If there are 16 blue cups, there will be:
= (16  x 3) / 4

= 12 yellow cups

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Answer:

Name: alternate exterior angles

Relationship: they are congruent. (15x + 5)° = (14x + 11)

Value of x: 6

Missing angle measures: 95°

Here are the general steps for using the u-substitution method to evaluate a definite integral:

1. Identify a part of the integrand that looks like the derivative of another function.

This is usually denoted as u, and u should be a function that is easy to integrate.

2. Replace the selected part of the integrand with u. In other words, substitute u for the expression inside the integral.

3. Take the derivative of u with respect to the variable of integration, and then multiply by dx to obtain du.

4. Replace dx with the expression in terms of du, using the relationship you found in step 3.

5. Rewrite the entire integral in terms of u and du, and simplify as much as possible.

6. Evaluate the integral using u and the limits of integration. Replace u with the original expression, and then evaluate the expression at the upper and lower limits of integration.

7. Substitute the values obtained in step 6 into the original equation to get the final answer.

The u-substitution method is a powerful technique for evaluating definite integrals.

The general idea behind the u-substitution method is to replace a complicated expression inside the integral with a simpler expression, which is equal to the original expression.

Here are the general steps for using the u-substitution method to evaluate a definite integral:

Let's take an example to illustrate these steps:

Evaluate the definite integral ∫\((2x + 1)^(3/2) dx from x = 1 to x = 2.\)

Let u = 2x + 1.

Replace 2x + 1 with u in the integral to get ∫\(u^{3/2} dx.\)

Take the derivative of u with respect to x to get du/dx = 2, and then multiply by dx to obtain du = 2dx.

Replace dx with 1/2 du.

Rewrite the entire integral in terms of u and du to get ∫\(u^{3/2} (1/2) du.\)

Evaluate the integral using u and the limits of integration to get (2/5) \(u^{5/2}\) from 3 to 5.

Substitute the values obtained in step 6 into the original equation to get the final answer, which is\((2/5) [(5^{5/2}- 3^{5/2}].\)

Therefore, the value of the definite integral ∫\((2x + 1)^{3/2}\)dx from x = 1 to x = 2 is approximately 6.243.

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The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

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A a gang of 17 bandits stole a chest of gold coins, using Chinese Remainder Theorem the smallest possible number of coins in the chest is given as 7.

The Chinese Remainder Theorem in Mathematics states that, assuming that n and the divisors are pairwise coprime, one may utilise the remainders of n's division by the product of these other numbers to get the unique remainder of n's division by n. (no two divisors share a common factor other than 1).

Apply Chinese Remainder Theorem we get,

x≡3(mod17),

So, (x-3) is divided by 17

so, x = 20

x≡10(mod16),

(x-10) is divided by 16

x = 26

x≡4(mod11)

(x-4) is divided by 11

So, x = 15

x≡0(mod7)

(x-0) is divided by 7.

So, x=7

So smallest possible coin is 7.

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Answer:

B = 82 c = 82

Step-by-step explanation:

These add up to 360 and since 98 + 98 + 82 + 82 = 360 b and c = 82 Hope this helps!

Answer:

-15

Step-by-step explanation:

they are opposite angles so they are congruent

x+70=55

x=55-70

x=-15

Answer:

$4,541.74.

Step-by-step explanation:

The total amount accrued, principal plus interest, with compound interest on a principal of $2,500.00 at a rate of 12% per year compounded 12 times per year over 5 years is $4,541.74.

Answer:

x=5

Step-by-step explanation:

3x+9=24

putting x=5

3(5)+9=24

15+9=24

24=24

statement x=5 makes the open sentence 3x+9=24 true.

d. The extra variability is caused by variations in the df value.

T-statistics are used to test hypotheses about the mean of a population when the standard deviation of the population is unknown and the sample size is small.

The t-distribution is similar to the standard normal distribution (z-distribution) but it has flatter tails and is more spread out. This extra spread is caused by the fact that the t-distribution is based on the sample size, which is reflected in the degrees of freedom (df) value.

The larger the sample size, the closer the t-distribution is to the standard normal distribution, and the more similar the t- and z- statistics will be.

In contrast to this, as the sample size decrease, the t-distribution becomes more spread out and t- statistics are therefore more variable than z-scores.

This increased spread means that t-statistics have a higher chance of falling into the tails of the distribution, which leads to a greater likelihood of a type I error (rejecting a true null hypothesis) or a lower power (failing to reject a false null hypothesis).

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y=-8x + 89​

Slope m= 8

y- intercept = +89. For x= 0

The option that is not a factor of capacity planning is the option d

d) Proximity to suppliers

The process of ascertaining the production capacity an organization needs in order to meet changing demand for the products and services of the organization is known as capacity planning.

The factors considered in capacity planning are factors which include the capacity measurement approach, the economies of scale, preparedness to deal with the capacity in chunks, and activities towards identifying the best operating level.

Therefore, from the listed options, the option that is not a factor in capacity planning is the option (d) proximity to suppliers

Other aspects of the operations of an organization, such as supply chain management and logistics can be affected by the proximity of suppliers, but the proximity of suppliers is not directly linked to the determination process for the production capacity needed to meet the market demand.

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Answer:

S V W and if you rotate it the W would be an M

Step-by-step explanation: