Find the 11th term of the arithmetic sequence an=
24 – 7(n - 2)
2115

The best description for the solution to the given set of equations is "no solution" or "inconsistent."

The given set of equations consists of two linear equations in the form of y = mx + c, where m represents the slope and c represents the y-intercept.

Equation C: y = 4x + 8

Equation D: y = 4x + 2

Comparing the equations, we can see that both equations have the same slope, which is 4. However, their y-intercepts differ.

For Equation C, the y-intercept is 8, while for Equation D, the y-intercept is 2.

Since the slopes are the same, these equations represent parallel lines. Parallel lines never intersect, which means there is no solution to this set of equations.

Therefore, the best description for the solution to the given set of equations is "no solution" or "inconsistent."

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Answer:

The number of peanuts that will be needed to make all the sandwiches a child will eat by graduation  is approximately 141,667 peanuts

Step-by-step explanation:

The number of peanut butter sandwiches that an average American child will eat by the time she graduates from high school = 1500 peanut butter sandwiches

The number of sandwich taken every four days = 1 sandwich

The number of peanuts required to make 18-oz jar of peanut butter = 850 peanuts

The amount of peanut butter in an average sandwich = Two ounces

Therefore, we have by the time of graduation;

Each American child will have taken 1500 sandwiches

The 1500 sandwiches will have = 1500 × 2 ounce = 3,000 ounces of peanut butter

The number of 18-oz jars of peanut butter that will contain up to 3000-oz of peanut butter = 3000-oz/(18-oz) = 166.67 Jars

The number of peanuts required to make the 166.67 Jars of peanut butter = 850 peanuts/jar ×  166.67 Jars = 141666.67 ≈ 141,667 peanuts

The number of peanuts that will be needed to make all the sandwiches a child will eat by graduation  ≈ 141,667 peanuts.

The amount of fabric needed to cover 8 blocks is 192cm.

In order to determine the amount of fabric needed, the total surface area of the rectangular prism has to be determined. The total surface area of the rectangular prism is the sum of the areas its faces.

Total surface area of a rectangular prism = 2 (lw + wh + lh)

where:

2 x [(4 x 1/2) + (1/2 x 2) + (4 x2)] = 24cm

Fabric needed fo 8 blocks = 24 x 8 = 192cm

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Answer:

The amount of fabric needed to cover 8 blocks is 192cm.

How much fabric is needed to cover 8 blocks?

In order to determine the amount of fabric needed, the total surface area of the rectangular prism has to be determined. The total surface area of the rectangular prism is the sum of the areas its faces.

Total surface area of a rectangular prism = 2 (lw + wh + lh)

where:

l = length

w = width

h = height

2 x [(4 x 1/2) + (1/2 x 2) + (4 x2)] = 24cm

Fabric needed fo 8 blocks = 24 x 8 = 192cm

Step-by-step explanation:

Answer:

t

Step-by-step explanation:

Answer:t

Step-by-step explanation:the other person was right

Answer:

make x the subject of this equation

x/5 = a + g

x = 5 (a + g)

Answer:

\( \sf \: x = 5(a + g) \\ \)

Step-by-step explanation:

\( \sf \frac{x}{5} - g = a \\ \)

To remove ( - g) add 'g' to both sides.

\( \sf \frac{x}{5} = a + g \\ \)

To remove 5 multiply both sides by 5.

\( \sf \: x = 5(a + g) \\ \)

The chi-squared test is the most appropriate hypothesis test to determine whether the proportion of people who smoke is independent of region

To determine whether the proportion of people who smoke is independent of region, the most appropriate hypothesis test would be the chi-squared test for independence.

The chi-squared test for independence is used to analyze the association between two categorical variables. In this case, we have two categorical variables: smoking (smoker/non-smoker) and region (e.g., Northeast, Midwest, South, West). We want to investigate whether the proportion of smokers differs across regions.

The null hypothesis (H0) for this test would be that the proportion of people who smoke is independent of region, meaning there is no association between smoking and region. The alternative hypothesis (Ha) would be that the proportion of smokers is dependent on the region, indicating an association between smoking and region.

By conducting the chi-squared test for independence, we can calculate the test statistic and compare it to the critical value from the chi-squared distribution to determine whether we reject or fail to reject the null hypothesis. If the test statistic is significantly different from the critical value, we can conclude that the proportion of people who smoke is not independent of region.

Therefore, the chi-squared test for independence is the most appropriate hypothesis test.

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Answer:

S = $10.20

Step-by-step explanation:

s = 12 - .15 (12)

s = 12 - 1.80

s = $10.20

If 15% comes off the price, then 85% of the price is left to pay. (100 - 15 = 85)

12 x .85 = $10.20

Statement (c) is correct for a simple graph. Every trail is a path, and every path is a trail.

In graph theory, a simple graph is an undirected graph with no loops or multiple edges between the same pair of vertices. A path in a graph is a sequence of vertices where each consecutive pair is connected by an edge. A trail in a graph is a path that allows for repeated vertices and edges.

Statement (a) is not correct because not every path is a trail. A path does not allow for repeated vertices or edges, whereas a trail does.

Statement (b) is not correct because not every trail is necessarily a path. A trail may contain repeated vertices or edges, but a path does not.

Statement (d) is not correct because paths and trails do have a relation. A trail is a more general concept that encompasses paths by allowing for repetition of vertices and edges.

Therefore, statement (c) is the correct statement. In a simple graph, every trail is a path, and every path is a trail.

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Answer:

C) there are no solutions

Step-by-step explanation:

3x-6<3x+13

3x<3x+19

0<19

Answer:

D

Step-by-step explanation:

5(x-5)=353 + x

the first 5 is all his tests, in the parenthesis x is the average score, and -5 is the 5 points lower mentioned in the problem.

Answer:

B

Step-by-step explanation:

We are given that Markus scored 85, 92, 82, and 94 on his first four tests and x on his fifth.

We know that his score on the fifth test is five points lower than the average of all five tests.

To find the average, we add up all the values and divide by the number of values there are. Therefore, the average of all five tests is:

\(\displaystyle \frac{85+92+82+94+x}{5}\)

Simplify:

\(\displaystyle =\frac{353+x}{5}\)

His test score x is five points lower than the average. Hence:

\(\displaystyle x=\left(\frac{353+x}{5}\right)-5\)

Rewrite. We can add five to both sides:

\(\displaystyle x+5=\frac{353+x}{5}\)

And multiply both sides by five. Hence:

\(\displaystyle 5(x+5)=353+x\)

Thus, our answer is B.

Notes:

By solving the equation, we see that x = 82. So, Markus scored 82 points on his fifth test.

If that is true, then his average score of all fives tests will be:

\(\displaystyle \frac{85+92+82+94+82}{5}=87\)

82 is indeed five points fewer than 87, so our answer is correct and matches the given information.

The simplified form of the given expression is 4/√6. Therefore, option D is the correct answer.

A surd is an expression that includes a square root, cube root or other root symbol. Surds are used to write irrational numbers precisely – because the decimals of irrational numbers do not terminate or recur, they cannot be written exactly in decimal form.

The given expression is 6√2/√3 - 8/3√(3/2).

Here, 6√2/√3 - 8√3/3√2

= 6√2/√3 - 8/√3√2

= 6√2/√3 - 8/√6

= 12/√6- 8/√6

= 4/√6

Therefore, option D is the correct answer.

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Answer:

16A.) C

16B.) x=6; the students each paid $6 for their concert tickets.

Step-by-step explanation:

[Note: I know that this answer is lengthy, but the explanation is very simple and is worth reading]

16A.)

First, let's "figure out" the amount of money spent by the students. Each student paid $x for a ticket and $4 on parking. That means that the cost for one student would be $x + $4. To figure out how much it would cost 12 students, we can take the amount it costs 1 student and multiply it by 12. Again, since x + 4 is the cost for 1 student, 12( x + 4 ) would be the cost of 12 students. Next, let's figure out how much the adults paid for their tickets.

Now, let's find the cost the adults paid for the ticket. If the students paid $x and the adults paid four times as much for each of their tickets, then the cost of the ticket for the adults must have been $4x. Now, we know each adult paid $4x for a ticket and $6 on parking. That means that the cost for one adult would be $4x + $6. To figure out how much it would cost 4 adult , we can take the amount it costs 1 adult and multiply it by 4. Again, since 4x + 6 is the cost for 1 adult, 4( 4x + 6 ) would be the cost of 4 adults.

Since the 12 students paid 12(x+4) dollars for the concert and the 4 adults paid 4(4x+6) and since we know they spent the same amount of money, we can set 12(x+4) and 4(4x+6) equal to each other. This gives us the answer 12(x+4)=4(4x+6), or C, for question 16A.

16B.)

To solve the equation 12(x+4)=4(4x+6) means to solve for x. So, let's solve for x:

12 ( x + 4 ) = 4 ( 4x + 6 )   [Distribute the 12 on the left side]

12x + 48 = 4 ( 4x + 6 )   [Distribute the 4 on the right side]

12x + 48 = 16x + 24   [Subtract 12x from both sides]

48 = 4x + 24   [Subtract 24 from both sides]

24 = 4x   [Divide both sides by 4 to get the value of x]

6 = x

Now, for the second half of the question, what does x=6 mean? Well, if we look at the previous problem, x was the amount of money spent by the students for the concert ticket. So, the answer x=6 tells us that the students paid $6 for their concert tickets.

[Note: They didn't ask for the price of the adults' tickets, but if they did, we would have plugged in x=6 into the equation 4x to find that the cost of the adults' tickets were $24.]

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Answer: \(\frac{15}{2}\)

Step-by-step explanation:

\(\frac{2}{3}x-1=4\)

\(\frac{2}{3} x=4+1\)

\(\frac{2}{3} x=5\)

\(x=\frac{5}{\frac{2}{3} } =\frac{\frac{5}{1} }{\frac{2}{3} } =\frac{5*3}{1*2} =\frac{15}{2}\)

\(x=\frac{15}{2}\)

The application rate is 3 (per DM$).

The given below table shows the monthly production volume, direct materials, direct labor, and manufacturing overheads for the past three months at Gizzard Wizard (GW):

Month Prod. Volume DM ($)DL ($)MOH ($)May 1000$400.00$600.00$1200.00

June 400160.00240.00480.00

July 1600640.00960.001920.00

By using DM$ to apply overhead, we have to find the application rate. We know that the total amount of manufacturing overheads is calculated by adding the cost of indirect materials, indirect labor, and other manufacturing costs to the direct costs. The formula for calculating the application rate is as follows:

Application rate (per DM$) = Total MOH cost / Total DM$ cost

Let's calculate the total cost of DM$ and MOH:$ Total DM$ cost = $400.00 + $160.00 + $640.00 = $1200.00$

Total MOH cost = $1200.00 + $480.00 + $1920.00 = $3600.00

Now, let's calculate the application rate:Application rate (per DM$) = Total MOH cost / Total DM$ cost= $3600.00 / $1200.00= 3

Therefore, the application rate is 3 (per DM$).

Hence, the required answer is "The application rate for GW is 3 (per DM$)."

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The equation of the trend line is given as follows:

y = 1.33x + 20.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

Two points on the line in this problem are given as follows:

(0, 20) and (15, 40).

When x = 0, y = 20, hence the intercept b is given as follows:

b = 20.

When x increases by 15, y increases by 20, hence the slope m is given as follows:

m = 20/15

m = 1.33.

Hence the function is given as follows:

y = 1.33x + 20.

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Answer:

let x be the smaller number.

let x + 2 be the larger number.

4 times the smaller number is 2 more than 3 times the larger number.

in equation form, this becomes:

4x = 3 * (x+2) + 2

simplify this to get:

4x = 3x + 6 + 2 which becomes:

4x = 3x + 8

subtract 3x from both sides of this equation to get:

x = 8

this means that x+2 = 10

the smaller number is 8 and the larger number is 10.

4 times the smaller number is equal to 32.

3 times the larger number + 2 is equal to 32.

requirements of the problem check out ok, so the solution is good.

the smaller number is 8.

the larger number is 10.

Step-by-step explanation:

please mark me as the

Answer:

The first one would be m^30n^20p^30  

And the second one would be a^2 / d^4  

Step-by-step explanation:

For 1, you have to multiply the inner exponents by the outer one so you get (m^12n^8) times (m^18n^12p^30). Then you mutiply the two together, so you add the exponents, where you get m^30n^20p^30.

For 2, since you're dividing, you have to subtract the exponents so you get a^2d^-4, but since you shouldn't have the negative you turn it into a^2 / d^4

Hope this helps :)

Answer: C, the table.

Step-by-step explanation:

       In a function, there can only be one output (y) per input (x), but you can have multiple inputs (x) per one output (y).

       Using this logic, we see that the answer is;

                 C

The rate at which the top of the ladder is sliding down the wall when the top of the ladder is 7 feet from the ground is 105 ft/sec.

A 25 foot long ladder is leaning against a wall and sliding away at a rate of 15 ft/sec. We need to find how fast is the top of the ladder sliding down the wall when the top of the ladder is 7 feet from the ground.Let's assume the length of the ladder be 'L'.Therefore, L = 25 feet. The rate at which the ladder is sliding away from the wall is given by dL/dt. dL/dt = 15 ft/sec. Let the height of the wall be 'h'.

Therefore, h = 7 feet.We need to find the rate at which the top of the ladder is sliding down the wall. Let's assume this rate be 'x'.We know that, the ladder, wall, and the ground form a right-angled triangle.Let's assume that the distance between the base of the ladder and the wall be 'y'. Therefore, we have:x^2 + y^2 = L^2Differentiating with respect to time t, we get:2x(dx/dt)+2y(dy/dt)=0dx/dt=−y(dy/dt),Since the ladder is sliding down the wall, dy/dt is negative.dy/dt = -15 ft/sec.We need to find x when y = 7. y = 7.

Therefore, \(x=√(L2−y2)=√(252−72)=√(625−49)=√576=24\)ft.

Now, we can substitute the values in the equation we obtained for dx/dt.dx/dt = -y (dy/dt)= -7 × (-15) = 105 ft/sec.Hence, the rate at which the top of the ladder is sliding down the wall when the top of the ladder is 7 feet from the ground is 105 ft/sec.

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a) The stone takes 4 seconds to reach its highest point., b) The maximum height reached by the stone is 256 feet., c) The stone takes a total of 8 seconds before hitting the beach., d) The velocity of the stone on impact is -128 ft/sec.

To solve the problem, we can use the equations of motion for vertical motion under constant acceleration.

a) To find the time taken to reach the highest point, we can use the equation:

v = u + at,

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

At the highest point, the stone's final velocity will be 0 ft/sec (as it momentarily comes to a stop). The initial velocity is 128 ft/sec, and the acceleration due to gravity is -32 ft/sec^2 (negative because it acts in the opposite direction to the initial velocity).

Therefore, 0 = 128 - 32t.

Solving for t, we get t = 4 seconds.

b) To find the maximum height, we can use the equation:

s = ut + (1/2)at^2,

where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time taken.

At the highest point, the displacement is the maximum height. The initial velocity is 128 ft/sec, the acceleration is -32 ft/sec^2, and the time is 4 seconds.

Substituting the values, we get:

s = (128 * 4) + (1/2)(-32)(4^2) = 512 - 256 = 256 feet.

Therefore, the maximum height reached by the stone is 256 feet.

c) To find the time before the stone hits the beach, we need to consider the time it takes for the stone to reach the ground from the highest point. The time of flight is twice the time taken to reach the highest point.

Time of flight = 2 * 4 = 8 seconds.

d) The velocity of the stone on impact can be determined using the equation:

v = u + at,

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

At impact, the stone's final velocity will be the negative of the initial velocity (as it is moving in the opposite direction). Therefore, the velocity on impact is -128 ft/sec.

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The least common factor of 3 and 5 was chosen as the first step in order to combine the fractions 2/3 + 4/5, leading to option (A) Finding the least common denominator.

The smallest multiple that any two numbers have in common is called the lowest common multiple.

It implies that we can divide both numbers by that and that this is the lowest number by which both numbers may be divided.

The LCM of 2 and 8 is 8, for instance.

So, using the two fractions provided:

2/3 + 4/5

15 is the least frequent factor between 3:

(10 + 12)/15

Thus, we used LCM in the first phase.

Therefore, the least common factor of 3 and 5 was chosen as the first step in order to combine the fractions 2/3 + 4/5, leading to option (A) Finding the least common denominator.

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Complete question:
When adding 2/3 + 4/5, what step must be completed first?

A)Finding the least common denominator.

B)Reducing the fractions.

C)Adding the numerators, but keeping the denominators.

D)Adding the denominators, but keeping the numerators.

Answer:

Step-by-step explanation:

Surface area of sphere = 125 sq.ft

4πr² = 125

4*3.14*r² = 125

\(\sqrt{x} r^{2}=\frac{125}{4*3.14}\\\\r^{2}=9.95\\\\r=\sqrt{9.95}\\\\\)

r = 3.15 ft

Answer:

631 feet

Step-by-step explanation:

125 square feet = 4 • pi • radius sqaured. Dividing the surface area by 4 and pi, and then taking the square root of that result, gives the correct radius of 3.155 feet. Doubling the radius gives the correct diameter of 6.31 feet.

By using the property of similar triangles, it can be obtained that

Value of x is 7.2

What are similar triangles?

Two triangles are said to be similar if the corrosponding angles are equal and the corrosponding sides are similar.

The different axioms of similarity are-

SAS axiom, AA axiom, SSS axiom

By the property of similar triangles,

\(\frac{9}{9 + 6} = \frac{x}{12}\\x = \frac{9}{15} \times 12\\x = 7.2\)

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It is a good practice for a server or bartender to not take patrons' drink orders too quickly

A bartender a person who prepares or serves alcoholic and some non-alcoholic beverages from behind a bar.

Below are some of the duties or responsibilities of a bartender:

So therefore, it is a good practice for a server or bartender to not take patrons' drink orders too quickly

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a. The subspace generated by the vector system u has 2 dimensions. A basis for this subspace is {(1, 2, 6), (0, -1, -5)}. b. The parameter k that makes u = (2, 3, \(k^2 + 1\)) a linear combination of the basis w is k = ±√6. The coordinate vector [u]w with respect to the basis w is [u]w = (2, 1).

a. To find the number of dimensions and a basis for the subspace generated by the vector system u, we need to determine the linearly independent vectors among the given vectors. Let's perform Gaussian elimination to determine the linearly independent vectors:

Row 2 = Row 2 - 0 * Row 1

= (0, -1, -5)

Row 3 = Row 3 - 2 * Row 1

= (2, 3, 7)

Row 4 = Row 4 - Row 1

= (1, 0, -4)

Row 3 = Row 3 - 2 * Row 2

= (2, 3, 7) - 2 * (0, -1, -5)

= (2, 3, 7) - (0, -2, -10)

= (2, 5, 17)

Now, we have the following row-echelon form:

(1, 2, 6)

(0, -1, -5)

(0, 0, 0)

(0, 0, -10)

We can see that there are 2 pivot columns in this row-echelon form, which indicates that the subspace generated by the vector system u has 2 dimensions.

b. To find the parameter k such that u = (2, 3, k² + 1) is a linear combination of the basis w, we can set up the following equation:

(2, 3, k² + 1) = a(1, 2, 6) + b(0, -1, -5)

This equation gives us the following system of equations:

2 = a

3 = 2a - b

\(k^2 + 1 = 6a - 5b\)

From the first equation, we can deduce that a = 2. Substituting this value into the second equation, we get:

3 = 2(2) - b

3 = 4 - b

b = 4 - 3

b = 1

Now, we can substitute the values of a and b into the third equation:

\(k^2 + 1 = 6(2) - 5(1)\\k^2 + 1 = 12 - 5\\k^2 + 1 = 7\\k^2 = 7 - 1\\k^2 = 6\)

k = ±√6

Therefore, the parameter k that satisfies u = (2, 3, \(k^2 + 1\)) as a linear combination of the basis w is k = ±√6. The coordinate vector [u]w represents the coefficients of the linear combination of the basis vectors w that yield the vector u. Using the basis w = {(1, 2, 6), (0, -1, -5)}, we can express u as:

u = a(1, 2, 6) + b(0, -1, -5)

Substituting the values of a = 2 and b = 1, we get:

u = 2(1, 2, 6) + 1(0, -1, -5)

u = (2, 4, 12) + (0, -1, -5)

u = (2, 4, 12) + (0, -1, -5)

u = (2, 3, 7)

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Answer: D.) The inequality sign always opens up to the smaller number

Answer:

im going to go with D

Answer:

2 x ^2 − 2 x + 4 = 0

x ^2 − 2 x + 4 = 0

2 x ^2 − x = 0

Step-by-step explanation:

There is enough proof to indicate that the percentage of newsletter readers who possess a Rolls Royce is less than 69%.

The null hypothesis is that p = 0.69, meaning that 69% of the newsletter readers own a Rolls Royce. The alternative hypothesis is that p < 0.69, meaning that less than 69% of the newsletter readers own a Rolls Royce.

We can use a one-tailed z-test to test the hypothesis. Assuming a sample size of n = 100, if we observe fewer than 69 Rolls Royces in our sample, we can reject the null hypothesis.

Using a z-test, we can calculate the z-score by using the formula:

z = (p' - p) / sqrt(p * (1 - p) / n)

where p' is the sample proportion, p is the hypothesized proportion, and n is the sample size.

At a significance level of 0.10, the critical z-value is -1.28. If the calculated z-score is less than -1.28, we can reject the null hypothesis.

If we conduct a survey of 100 newsletter readers and find that 58 of them own a Rolls Royce, the sample proportion would be p' = 0.58. Calculating the z-score, we get:

z = (0.58 - 0.69) / sqrt(0.69 * 0.31 / 100) = -1.83

Since -1.83 is less than -1.28, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that fewer than 69% of the newsletter readers own a Rolls Royce.

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