What is the graph of system of linear inequalities in two variables?

The answer is B.) The horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.

Statement which is true about the graph of the function that represents the average cost per person is the horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.

" Graph is defined as the pictorial presentation of the data on the coordinate plane along x-axis and y-axis."

" Average cost is defined as the ratio of the total cost for 'n' number of people to the 'n' number of people."

Formula used

Average cost = \(\frac{total cost}{number of people}\)

According to the question,

Cost of catering dinner per person = $11.95

Delivery and set up fixed cost= $25

'T' represents the total cost

'x' represents the total number of people

'y' average cost per person

As per the given condition we have,

Cost of catering dinner x persons = $11.95x

Total cost for 'x' number of people= $11.95x + $25

Substitute the value to get average cost we get,

Average cost = \(\frac{11.95x+25}{x}\)

                       = \(11.95 + \frac{25}{x}\)

As shown in the graph ,

Horizontal asymptote  y = 11.95

Hence, graph of the function that represents the average cost per person is the horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.

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(a) The sequence representing the cash prize awarded in terms of the place n is as follows: a(n) = 1310 - 90(n-1).

(b) The total amount of prize money awarded at the tournament is $10,440.

To calculate this, we can use the formula for the sum of an arithmetic series. The formula is given by:

Sum = (n/2)(first term + last term)

In our case, the first term (a1) is the cash prize for the first place, which is $1310. The last term (a12) is the cash prize for the twelfth place, which is $430.

Using the formula, we can calculate the sum as follows:

Sum = (12/2)(1310 + 430) = 6(1740) = $10,440.

Therefore, the total amount of prize money awarded at the tournament is $10,440.

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The Pythagorean Theorem is explained in this problem.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

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Answer:

50

Step-by-step explanation

I hope this helps

Answer:

Step-by-step explanation:

y = 2x + 4a/6b   y=(12xb+4b )/6b

6yb=12x+4a

a=(-12xb+6yb)/4=

a=3yb/2 -3xb

x=y/2-a/3b

b=2a/(3y-6x)

the solution is for every variable

Answer:

12 i think im not exactly shore

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

order of operations so

15-(3x4)

15-12

3

Amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).

As given in the question,

Amount  invested by Nathan is principal 'P' = $3,500

Interest rate 'r' = 3.5% compounded quarterly

Number of compounding periods per year for given quarterly 'n'  = 4

Time period 't'= 19 years

Amount of money in the account after 19 years when no deposits or withdrawals are done.

Let 'A' be the amount.

Formula used:

 \(A = P \times ( 1+ \frac{r}{n} )^{nt}\)

Substitute the value in the formula we get,

A = 3500 × [ 1 + (0.035/4) ]⁽⁴⁾⁽¹⁹⁾

   =  3500 × [ 1 + 0.00875]⁽⁴⁾⁽¹⁹⁾

   =  3500 × [ 1.00875]⁷⁶

   = 6,786.06 (approximately)

   = $6800 (nearest hundred dollars)

Therefore, amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).

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Answer:

I didn't Sanderstead sorry

Consider the traingle as per the attachment

In \({\triangle}\)ADB. By Pythagoras theorem:

\({:\implies \quad \sf x^{2}+4^{2}=AB^{2}}\)

\({:\implies \quad \sf AB^{2}=x^{2}+16\quad ...(i)}\)

Now, In \({\triangle}\)ADC. By Pythagoras theorem:

\({:\implies \quad \sf x^{2}+9^{2}=AC^{2}}\)

\({:\implies \quad \sf AC^{2}=x^{2}+81\quad ...(ii)}\)

Now, In \({\triangle}\)BAC. By Pythagoras theorem:

\({:\implies \quad \sf AB^{2}+AC^{2}=BC^{2}}\)

By (i) and (ii)

\({:\implies \quad \sf x^{2}+16+x^{2}+81=(BD+DC)^{2}}\)

\({:\implies \quad \sf 2x^{2}+97=(4+9)^{2}}\)

\({:\implies \quad \sf 2x^{2}=169-97}\)

\({:\implies \quad \sf 2x^{2}=72}\)

\({:\implies \quad \sf x^{2}=36}\)

\({:\implies \quad \sf x=\sqrt{36}=\boxed{\bf{6}}}\)

Hence, Option b) is correct

Pythagoras theorem:- It states that, in a right angled triangle the square of hypotenuse is equal to the sum of the square of base and square of perpendicular

Using the graph of the function we can see that f(x) = 2 when x = 9.

We want to find the value of x such that f(x) = 2.

To do so, we will use the graph of the function f(x).

To do so, we need to find y = 2 on the vertical axis, then find the correspondent value on the horizontal axis.

Once you find y = 2 on the vertical axis, move horizontally until you hit the graph of f(x), there you will move vertically to the horizontal axis to find the value of x.

We can see that f(x) = 2 when x = 9.

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Answer:

a: x = -4, b : x = -4, c : x = -3, d : x = -5

Step-by-step explanation:

Answer:

2^2 x 5 x 9.

Step-by-step explanation:

This will give you the answer because when multiplying all of this you will get 180. Answer B.

Answer:

8π

Step-by-step explanation:

A=180/360×π(4^2)

A=1/2×16π

A=8π

Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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Answer:

A. 100

Step-by-step explanation:

84

Step-by-step explanation:

c + 100 =180

c=180-100

c=80

100+96+d+c=360

100+96+d+80=360

276+d=360

d=360-276

d=84

Answer:

A, 8

Step-by-step explanation:

Use the equation 15+4x=47

Subtract 15 from both sides to get

4x=32

divide to get 8

x=8

The present value of $200 to be received 10 years from today, assuming a discount rate of 10 percent, is approximately $77.90.

To calculate the present value of $200 to be received 10 years from today, we can use the formula for present value:

\(PV = \frac{FV}{(1 + r)^n}\)

Where:

Future Value = $200

Discount Rate = 10% (0.10)

n = 10 years

Plugging in the values into the formula:

\(\begin{equation}\text{Present Value} = \textdollar200 \div (1 + 0.10)^{10}\end{equation}\)

Calculating the result:

\(\text{Present Value} = \frac{200}{(1.10)^{10}} \approx 77.90\)

Therefore, the present value of $200 to be received 10 years from today, assuming a discount rate of 10 percent, is approximately $77.90.

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Answer:prime

Step-by-step explanation:

I just took the test and got it right

To state the null hypothesis and alternative hypothesis for Megan's test, we need to know what type of data she will be collecting and what type of test she will be conducting.

Assuming she will be collecting data on the number of hours of sleep students are getting and conducting a one-tailed hypothesis test, the following are possible null and alternative hypotheses:

a.) Null hypothesis: The average amount of sleep students are getting is equal to or greater than eight hours per night.

Alternative hypothesis: The average amount of sleep students are getting is less than eight hours per night.

b.) Null hypothesis: Less than or equal to 50% of students are getting less than eight hours of sleep per night.

Alternative hypothesis: More than 50% of students are getting less than eight hours of sleep per night.

c.) Null hypothesis: There is no difference in the proportion of students getting less than eight hours of sleep between two groups (e.g., males vs. females, freshmen vs. seniors, etc.).

Alternative hypothesis: There is a difference in the proportion of students getting less than eight hours of sleep between two groups.

d.) Null hypothesis: The number of students getting less than eight hours of sleep is equal to or greater than a certain value (e.g., 30%).

Alternative hypothesis: The number of students getting less than eight hours of sleep is less than the specified value.

Note that in each case, the null hypothesis represents the status quo or the default assumption, while the alternative hypothesis represents Megan's research question or hypothesis. The choice of null and alternative hypotheses depends on the research question, the data being collected, and the type of hypothesis test being conducted.

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The child advocate collects data by randomly selecting 4 out of the 25 state orphanages. In each of the four selected orphanages, the child advocate surveys every child.

This approach allows the child advocate to obtain information from a representative sample of children in state orphanages. By surveying every child in the selected orphanages, the child advocate ensures that no child is excluded from the data collection process. This method provides a comprehensive understanding of the experiences, needs, and concerns of the children in the four chosen orphanages.

By collecting data in this manner, the child advocate can gather valuable insights that can inform policies and interventions to improve the well-being and support for children in state orphanages.

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(a) At a 5% level of significance, there is no evidence to support Lindsey's claim.

(b) At a 10% level of significance, there is evidence to support Lindsey's claim.

(c) In a statistical test of hypotheses, we say that the data are statistically significant at a level an if D. the p-value is less than a.

(a) To determine if there is evidence to support Lindsey's claim at a 5% level of significance, we compare the p-value to the significance level (α). If the p-value is less than α, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis. In this case, since the p-value is 0.056, which is greater than 0.05 (the significance level), there is no evidence to support Lindsey's claim.

(b) At a 10% level of significance, we compare the p-value to α = 0.10. If the p-value is less than 0.10, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis. Since the p-value is 0.056, which is less than 0.10, there is evidence to support Lindsey's claim at a 10% level of significance.

(c) In a statistical test of hypotheses, we determine if the data are statistically significant based on the p-value. The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true. If the p-value is less than the chosen significance level (α), typically 0.05, we say that the data are statistically significant at that level. So, the correct answer is D: the p-value is less than α.

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u = [2, -2]. The orthogonal complement W⊥ of W is the set of all vectors orthogonal to W. In this case, a basis for W⊥ is {[2, -2]}.

Rewrite the equation in standard form for vectors

The given equation is 2x - y = 0. We can rewrite it as y = 2x

Find a vector in W
We can choose any value of x and compute the corresponding y value to find a vector in W. Let x = 1, then y = 2(1) = 2.

So, one such vector in W is v = [1, 2].

Find a vector orthogonal to v

To find a vector orthogonal to v, we need to find a vector u = [a, b] such that the dot product of v and u is zero (v • u =

0). So, [1, 2] • [a, b] = 0. This translates to 1a + 2b = 0.

Find a basis for W⊥

Solve the equation 1a + 2b = 0 for a and b. We can set a = 2 and solve for b: 2(2) + 2b = 0, which gives b = -2.

Therefore, u = [2, -2].
The orthogonal complement W⊥ of W is the set of all vectors orthogonal to W. In this case, a basis for W⊥ is {[2, -2]}.

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Dividing the given ratio by 2, we get

8:6 = 8/2 : 6/2 = 4:3

Multiplying the given ratio by 2, we get

8:6 = 8*2 : 6*2 = 16:12

Then, the correct choices are A and C

Remi purchased approximately 150 pounds of pumpkins.

To find the number of pounds of pumpkins purchased by Remi, we can divide the total amount spent by the price per pound.

Let's assume that x represents the number of pounds of pumpkins purchased.

The total amount spent, $73.50, can be expressed as the product of the price per pound, $0.49, and the number of pounds purchased, x:

$73.50 = $0.49 × x

To solve for x, we divide both sides of the equation by $0.49:

x = $73.50 / $0.49 ≈ 150

Therefore, Remi purchased approximately 150 pounds of pumpkins.

By dividing the total amount spent by the price per pound, we found the quantity of pumpkins purchased.

In this case, Remi spent $73.50 and the price per pound was $0.49, resulting in the purchase of approximately 150 pounds of pumpkins. This information can be useful for budgeting, inventory management, and understanding consumer behavior at the local farm.

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Step-by-step explanation:

z=(21-17)/3

z=4/3

z=1.3333

\(\\ \sf\longmapsto z=\dfrac{Age-Mean}{Standard\: deviation}\)

\(\\ \sf\longmapsto z=\dfrac{21-17}{3}\)

\(\\ \sf\longmapsto z=\dfrac{4}{3}\)

\(\\ \sf\longmapsto z=1.3\)

Answer:

C. Reflection across the y-axis

Step-by-step explanation:

Reflection across y axis= (x,y) to (-x,y) so B (1,2) is now B'(-1,2). Hope this helped!