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Step-by-step explanation:

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Answer:

See below

Step-by-step explanation:

Horizontal lines have ZERO slope

Vertical lines have 'undefined' slope

for this example  x = 1/2    includes the point and has undiefined slope

The given homogeneous system of equations can be represented as a matrix equation Ax = 0, where A is the coefficient matrix and x is the vector of variables.

To find the solution set in parametric vector form, we can perform row operations on the augmented matrix [A|0] and express the variables in terms of free parameters.

The augmented matrix for the given system is:

[3 3 6 | 0]

[-9 -9 -18 | 0]

[0 -7 -7 | 0]

Using row operations, we can transform this matrix to row-echelon form:

[3 3 6 | 0]

[0 -6 -12 | 0]

[0 0 -7 | 0]

Now, we can express the variables in terms of free parameters. Let x2 = t and x3 = s, where t and s are arbitrary parameters. Solving for x1 in the first row, we get x1 = -2t - 2s.

Therefore, the solution set in parametric vector form is:

x = [-2t - 2s, t, s], where t and s are arbitrary parameters.

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We know that Sarah will use (C) 3/8 cups of grape juice in each cup of water using simple mathematical operations.

A mathematical action is called an operation.

Mathematical operations include addition, subtraction, multiplication, division, and finding the root.

Most people agree that addition, subtraction, multiplication, and division are the four fundamental mathematical operations.

So, we know that:

Sarah uses 1/4 cup of grape juice for every 2/3 cup of water.

Sarah uses a certain amount of grape juice for every cup of water:

1/4 ÷ 2/3

1/4 * 3/2

3/8

Therefore, we know that Sarah will use (C) 3/8 cups of grape juice in each cup of water using simple mathematical operations.

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Correct question:
Sarah dilutes grape juice for her two-year-old sister. She uses 1/4 cup of grape juice for every 2/3 cup of water.

How much grape juice does Sarah use for each cup of water?

a. 1/6 cup

b. 3/4 cup

c. 3/8 cup

d. 1 1/2 cup

Answer:

-1 = s

Step-by-step explanation:

7 = -10s - 3

Add 3 to each side

7+3 = -10s - 3+3

10 = -10s

Divide each side by -10

10/-10 = -10s/-10

-1 = s

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.

Given the demand equations and the total cost function:

Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1

Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2

Total Cost: TC = 120 + 4Q

To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:

MR1 = MC:

16 - 0.2Q1 = 4

0.2Q1 = 12

Q1 = 60

MR2 = MC:

10 - 0.1Q2 = 4

0.1Q2 = 6

Q2 = 60

Substituting the quantities back into the demand equations, we find:

P1 = 16 - 0.1(60) = 10

P2 = 10 - 0.05(60) = 7

The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:

TR = P1 * Q1 + P2 * Q2

TR = (10 * 60) + (7 * 60)

TR = 600 + 420

TR = 1020

The total cost (TC) is given by the total cost function:

TC = 120 + 4Q

TC = 120 + 4(60 + 60)

TC = 120 + 480

TC = 600

Finally, the profit (π) can be calculated by subtracting total cost from total revenue:

π = TR - TC

π = 1020 - 600

π = 420

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

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Answer:

A

Step-by-step explanation:

when you substitute 4 in x and 3 in y, your result are 11 no 10

Answer:

The major field of anthroplogy and evolutionary and paleo anthropological perspectives on the origin of humankind

The equation defines function f is f(x) = - 1/4 x + 2.

To find the equation of function f, we need to eliminate the constant term of 14 in the equation y = f(x) + 14.

One way to do this is to subtract 14 from both sides of the equation:

y - 14 = f(x)

Now we can compare this with the given options for f(x):

A. f(x) = - 1/4 * x - 12

B. f(x) = - 1/4 * x + 16

C. f(x) = - 1/4 * x + 2

D. f(x) = - 1/4 * x - 14

We see that option C matches our equation: y - 14 = f(x) = - 1/4 x + 2. Therefore, the answer is:

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(a) Yes, the air in the house would exceed the long-term health standard if the groundwater is in equilibrium with the air in the house.

(b) The budget equation for TCE is dct/dt = k(c+ - CT) - Q(ca - CT).

(c) The characteristic time t for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation is given by t = Ahk/Q. For the given values, t = 1.4 years. A large value of t indicates a significant TCE problem.

(d) The minimum value of Q to keep CT below 20 ppm is 160 cfm. This is more than the residential requirement of 40 cfm.

(a) The Henry's Law constant for TCE is 0.4, which means that the concentration of TCE in air at equilibrium with water is 40% of the concentration in water. The groundwater concentration is 110 ppm, so the equilibrium air concentration would be 44 ppm. This exceeds the long-term health standard of 25 ppm.

(b) The flux of TCE through the floor is given by FT = k(c+ - CT), where k is a measured constant, c+ is the concentration of TCE in the groundwater, and CT is the concentration of TCE in the air in the house. The normal strategy for remediating vapor intrusion is to install fans in the house that ventilate the house with outside air. The outside ambient air has a concentration of ca. The budget equation for TCE is dct/dt = k(c+ - CT) - Q(ca - CT), where dct/dt is the rate of change of the concentration of TCE in the house, k is the flux constant, c+ is the concentration of TCE in the groundwater, CT is the concentration of TCE in the air in the house, Q is the ventilation rate, and ca is the concentration of TCE in the outside air.

(c) The characteristic time t for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation is given by t = Ahk/Q, where Ah is the area of the house, k is the flux constant, and Q is the ventilation rate. For the given values, t = 1.4 years. A large value of t indicates a significant TCE problem.

(d) The minimum value of Q to keep CT below 20 ppm is 160 cfm. This is more than the residential requirement of 40 cfm. The difference is due to the fact that the groundwater concentration is much higher than the ambient air concentration.

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Answer:

124 tiles

Step-by-step explanation:

2(20+40)

2(60)

120+4=124

Add the two angles and then subtract from 180* to find the missing angle

So,

145* + 15* = 160*

180* - 160* = 20*

Answer: x = 20*

Answer:

D. -2

Step-by-step explanation:

slope formula = \(\frac{y_{2}-y_{1} \\ }{x_{2} -x_{1} }\)

(-1,3)

\(x_{2}, y_{2}\)

(4,-7)

\(x_{1}, y_{1}\)

Plug in the numbers into the formula now

\(\frac{3-(-7)}{-1-4}\)

negative minus negative equals positive

\(\frac{10}{-5}\)

reduces to -2

Answer:

Purchase Price:

$432

Discount:

(432 x 30)/100 = $129.60

Final Price:

432 - 129.60 = $302.40

Step-by-step explanation:

Answer:

About $129

Step-by-step explanation:

30% of $432.43 rounds to 30% of $430 = .3 x 430 = About $129 dollars

Hope that helps!

Answer:

  f(2) = -13

Step-by-step explanation:

Evaluate the given formula with the given value of the variable.

  f(1) = -16 . . . . . . . . . . given

  f(n) = -29 -f(n-1) . . . . given

For n = 2, we have ...

  f(2) = -29 -f(2-1) = -29 -f(1) = -29 -(-16) . . . . put 2 in place of n and evaluate

  f(2) = -13

Answer:

$200

Step-by-step explanation:

30 * 5=150 +50=200

Answer:

89.25

Step-by-step explanation:

If you do 10.50

              x 8.5 you get 89.25.

Answer:

89.25

Step-by-step explanation:

10.5 x 8.5 on a calculator.

Answer:

B. w^14/t^14

Step-by-step explanation:

(w^8w^6)/(t^6^8) = w^14/t^14

Yes, it is evidence that population means are different because it does not cover 0. Zinc lozenges appear to be effective in reducing the average number of days of symptoms.

(a) Calculate x1 − x2 difference in sample means.
x1 − x2 = 7.2 - 4.1 = 3.1 days

Compute the unpooled s.e.(x1 − x2) standard error of the difference in means. (Round your answer to four decimal places.)
s.e.(x1 − x2) = √((1.6^2 / 23) + (1.4^2 / 25)) = √(1.1133) = 1.0551 days

(b) Compute a 95% confidence interval for the difference in mean days of overall symptoms for the placebo and zinc lozenge treatments. Use the unpooled standard error and use the smaller of n1 − 1 and n2 − 1 as a conservative estimate of degrees of freedom. (Round the answers to two decimal places.)

Using the t-distribution table and the conservative degrees of freedom (22), the critical t-value is approximately 2.074.
CI = (x1 - x2) ± t * s.e.(x1 - x2)
CI = 3.1 ± 2.074 * 1.0551
CI = 3.1 ± 2.1886
CI = (0.91, 5.29) days

(c) Complete the following sentence interpreting the interval which was obtained in part (b).
With 95% confidence, we can say that in the population of cold sufferers represented by the sample, taking zinc lozenges would reduce the mean number of days of symptoms by somewhere between 0.91 and 5.29 days, compared with taking a placebo.

(d) Is the interval computed in part (b) evidence that the population means are different? Fill the blank in the following sentence.

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Given:

A figure of a triangular prism.

Height of triangular base = \(9\dfrac{2}{3}\) yd

Base of triangular base = 4 yd

Height of prism = 4 yd.

To find:

The volume of the triangular prism.

Solution:

Volume of a triangular prism is:

\(V=Bh\)              ...(i)

Where, B is the area of triangular base and h is the height of the prism.

Area of triangular base is:

\(B=\dfrac{1}{2}\times base\times height\)

\(B=\dfrac{1}{2}\times 4\times 9\dfrac{2}{3}\)

\(B=2\times \dfrac{29}{3}\)

\(B=\dfrac{58}{3}\)

Putting \(B=\dfrac{58}{3}\) and h=4 in (i), we get

\(V=\dfrac{58}{3}\times 4\)

\(V=\dfrac{232}{3}\)

\(V=77.33...\)

\(V\approx 77.3\)

The volume of the triangular prism is 77.3 cubic yards. Therefore, the correct option is 2.

When performing a significance-test for comparing dependent means, several assumptions are necessary to make a valid inference- Normality, Equal variances, Independence,Random-sampling.

Some of these assumptions are:

Normality: The distribution of differences between the paired observations must be approximately normal.

This can be assessed using a normal probability plot or by conducting a normality test.

Equal variances: The variances of the paired differences should be approximately equal.

This can be assessed using the Levene's test.

Independence: The paired differences should be independent of each other.

This means that each observation in one sample should not influence the corresponding observation in the other sample.

Random sampling: The observations should be selected randomly from the population of interest.

This ensures that the sample is representative of the population.

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Answer:

2x^2 - 12*x/2= Area For Shaded Region

Step-by-step explanation:

This works because you find tha area of both and subtract the shaded area by the unshaded area

Answer: Expression for the area of shades region of the figure = 2\(x^{2}\) - 6x

Step-by-step explanation: Area of shaded region = Area of big rectangle - Area of small rectangle

Area of rectangle = length.breadth

Area of big rectangle = 2x.x                                  { . means multiply}

                                     = 2\(x^{2}\)

Area of small rectangle = 12.(x/2)

                                         =6x

∴ Area of shaded region = 2\(x^{2}\) - 6x

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The length of the similar tube will be 5041 cm.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that:-

The radius of the first tube will be calculated as:-

1200 = 2πr ( 13 )

r = 12 / 2π x 113

r = 14.7 cm

Now the length of the second tube will be:-

500 = 2π x 14.7 x L

L = 500 / 2π x 14.7

L = 5.41 cm.

Therefore the length of a similar tube will be 5041 cm.

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a. To construct a 95% confidence interval for B, we can use the estimated coefficient and its standard error. The formula for the confidence interval is:

B ± t * SE(B)

Where B is the estimated coefficient, SE(B) is the standard error of the coefficient, and t is the critical value from the t-distribution based on the desired confidence level and the degrees of freedom (n - 2).

b. Hypothesis test:

(i) The null hypothesis (H0): B = 20 (there is no effect of smoking on birth weight).

The alternative hypothesis (Ha): B ≠ 20 (there is an effect of smoking on birth weight).

(ii) The test statistic is calculated by dividing the estimated coefficient by its standard error:

t = (B - hypothesized value) / SE(B)

(iii) The p-value is the probability of observing a test statistic as extreme or more extreme than the calculated value, assuming the null hypothesis is true.

(iv) The level of significance is the predetermined threshold for rejecting the null hypothesis. Common levels are 0.05 and 0.01.

(v) The test is two-sided because the alternative hypothesis allows for both positive and negative effects of smoking on birth weight.

(vi) Based on the calculated test statistic and p-value, we can compare the p-value to the level of significance. If the p-value is less than the level of significance, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

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Answer:

s

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

point S

When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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Answer:

No

Step-by-step explanation:

The number which makes \(5x=10\) true is 2.

\(5(2)=10\)

\(10=10\)

Therefore, 2 is the true value for this. But, lets check an equation like this.

\(\frac{5x}{3}=10\)

We can use algebraic methods to solve this, first multiply 3

\(5x=30\)

Divide by 5

\(x=6\)

Because  6 > 2, the number 2 does not make the two equations equivalent.

Answer:

d.) 150 billion dollars

Step-by-step explanation:

As per the given bar graph, we can draw the following conclusions:

Net exports for United States = ~ -110 Billion Dollars (It means import of 110 Billion Dollars)

Net exports for Denmark = ~ -30 Billion Dollars (It means import of 30 Billion Dollars)

Net exports for China = ~ 115 Billion Dollars

Net exports for Germany = ~ 35 Billion Dollars

We have to find the sum of net exports of Germany and China:

\(\Rightarrow\) 35 + 115 = 150 Billion Dollars.

Hence, correct answer is d. 150 Billion Dollars.

Answer: d

Step-by-step explanation:

150 billion dollars