Find the 6th term of the arithmetic sequence 3x+7, x+1, −x−5,...

Answer:

c

Step-by-step explanation:

Answer:

y= -8/11   x=-63/11

Step-by-step explanation:

Rewrite equation

Step: Solve6x+y=−10for y

Step: Substitute−6x−10 for y in 4x−3y=14

Step: Substitute  −8 /11  for x in y=−6x−10

y= −62 /11  --- (Simplify both sides of the equation)

___________________________________________

y= -8/11

x=-63/11

Dilation and rotation will not produce a congruent triangle

What is rotation ?

The rotation of a point with regard to the origin is described by the rotation formula. To get the position of the point after rotation, apply the rotation formula. Rotation is a circular movement about the specific axis or point of rotation. In general, there are two common directions for rotation: clockwise and anti-clockwise or counter-clockwise.

Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.

Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.

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The correct 98% confidence interval for the true proportion of graduates working in the field of study in which they obtained their degree is (0.811, 0.892).

To calculate the confidence interval, we need to use the formula for estimating proportions and the standard error of the proportion. The formula is:

Confidence interval = sample proportion ± z * standard error

Calculate the sample proportion

In this case, the sample proportion is the number of graduates working in their field of study (361) divided by the total number of graduates surveyed (424):

Sample proportion = 361/424 ≈ 0.852

Calculate the standard error

The standard error of the proportion is calculated using the formula:

Standard error = sqrt((sample proportion * (1 - sample proportion)) / sample size)

Using the given values, we have:

Standard error = sqrt((0.852 * (1 - 0.852)) / 424) ≈ 0.014

Determine the confidence interval

To find the z-value for a 98% confidence level, we look up the corresponding value in the z-table. The z-value for a 98% confidence level is approximately 2.33.

Substituting the values into the confidence interval formula, we have:

Confidence interval = 0.852 ± 2.33 * 0.014

Confidence interval ≈ (0.811, 0.892)

Therefore, the correct 98% confidence interval for the true proportion of graduates working in their field of study is (0.811, 0.892).

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The limit 9/4 is greater than 1, the series

\(\(\sum_{n=1}^{\infty} \frac{9^{n}}{(n+1) 4^{2 n+1}}\)\)  diverges by the Ratio Test.

To determine the convergence or divergence of the series,

\(\(\sum_{n=1}^{\infty} \frac{9^{n}}{(n+1) 4^{2 n+1}}\)\), we can use the Ratio Test.

The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. If the limit is greater than 1 or infinite, then the series diverges. If the limit is exactly 1, the test is inconclusive.

Let's denote aₙ as the nth term of the series:

\(\[a_n = \frac{9^n}{(n+1)4^{2n+1}}\]\)

Now, let's calculate the limit of the ratio

\(\(\lim _{n \rightarrow \infty} \frac{a_{n+1}}{a_n}\):\)

\(\[\lim _{n \rightarrow \infty} \frac{a_{n+1}}{a_n} = \lim _{n \rightarrow \infty} \frac{\frac{9^{n+1}}{(n+2)4^{2(n+1)+1}}}{\frac{9^n}{(n+1)4^{2n+1}}}\]\)

Simplifying the expression:

\(\[\lim _{n \rightarrow \infty} \frac{9^{n+1}}{(n+2)4^{2(n+1)+1}} \cdot \frac{(n+1)4^{2n+1}}{9^n}\]\)

\(\[\lim _{n \rightarrow \infty} \frac{9^{n+1}}{(n+2)9^n} \cdot \frac{(n+1)4^{2n+1}}{4^{2(n+1)+1}}\]\)

\(\[\lim _{n \rightarrow \infty} \frac{9^n \cdot 9}{(n+2)9^n} \cdot \frac{(n+1)4^{2n+1}}{4^{2n+2} \cdot 4}\]\)

\(\[\lim _{n \rightarrow \infty} \frac{9}{n+2} \cdot \frac{n+1}{4 \cdot 4} = \frac{9}{4} \lim _{n \rightarrow \infty} \frac{n+1}{n+2}\]\)

As n approaches infinity, the limit becomes:

\(\[\frac{9}{4} \cdot 1 = \frac{9}{4}\]\)

Therefore, the series is divergent.

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Complete Question:

Use the Ratio Test to determine whether the series is convergent or divergent.\(\(\sum_{n=1}^{\infty} \frac{9^{n}}{(n+1) 4^{2 n+1}}\)\) and evaluate the following limit \(\(\lim _{n \rightarrow \infty} \frac{a_{n+1}}{a_n}\):\)

Answer:

blue felt = 20*2.5 = 50

74-50=24 yards of red

24/20 = 1.2

each student gets 1.2 yards of red felt

So the answer is 1.2 Yards

Step-by-step explanation:

Answer:

Step-by-step explanation:

its rigt on E D G E U N I T Y :)

The absolute and relative error to the nearest thousandth are 12.000 cubic inches and 13.953% respectively

To calculate the absolute error, we subtract the estimated value from the actual value:

Absolute Error = |Estimated Value - Actual Value|

Absolute Error = |98 - 86|

Absolute Error = 12

The absolute error is 12 cubic inches.

To calculate the relative error, we divide the absolute error by the actual value and then multiply by 100:

Relative Error = (Absolute Error / Actual Value) * 100

Relative Error = (12 / 86) * 100

Relative Error ≈ 13.953

The relative error is approximately 13.953%.

Rounding both the absolute and relative error to the nearest thousandth, we have:

Absolute Error ≈ 12.000 cubic inches

Relative Error ≈ 13.953%

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Answer:

sequence B only

Step-by-step explanation:

Reflect around point N and then translate to the left the reflected figure from N to point B

If we had a polynomial-time algorithm for computing the length of the shortest TSP tour, then we would also have a polynomial-time algorithm for finding the shortest TSP tour by using the following approach: Generate all possible tours, For each tour, compute its length, The shortest tour is the one with the minimum length.

The first step, generating all possible tours, can be done in polynomial time. This is because the number of possible tours is a polynomial function of the number of cities.

The second step, computing the length of each tour, can also be done in polynomial time. This is because the length of a tour is a polynomial function of the distances between the cities.

Therefore, the overall algorithm for finding the shortest TSP tour is polynomial-time.

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The amount of money you need to save today is $4,926.

To calculate the amount of money you need to save today, you can use the formula for calculating future value with compound interest:

Future Value = Present Value * \((1 + Interest Rate)^T^i^m^e\)

In this case, the future value is $5,000, the interest rate is 1.75% (or 0.0175), and the time is 1 year. We need to solve for the present value.

Rearranging the formula, we have:

Present Value = Future Value /\((1 + Interest Rate)^T^i^m^e\)

Plugging in the values, we get:

Present Value = $5,000 / \((1 + 0.0175)^1\)

Present Value = $4,926

Therefore, you need to save $4,926 today in order to have $5,000 one year from now.

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The value of the voltage of the electricity is 6 + j + 2j²

From the question, we have the following parameters that can be used in our computation:

C = 2 - j

I = 3 + 2j

The formula of voltage is given as

V = CI

Substitute the known values in the above equation, so, we have the following representation

V = (2 - j) * (3 + 2j)

Open the brackets

So, we have

V = 6 + 4j - 3j + 2j²

Evaluate the like terms

V = 6 + j + 2j²

Hence, the voltage is 6 + j + 2j²

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The time when the food price is most and cheapest is obtained from the extremum value of the function.

The extremum of a function is a maximum or minimum value of the function.

The function that models the food-price is I(t) = 0.00009045·t⁵ + 0.001438·t⁴ - 0.0656·t³ + 0.4598·t² - 0.6270·t + 99.33

Where;

t = The number of years since 1984

I(3) = 100

The time when the food is cheapest or most expensive can be obtained by differentiating the function for food-price and equating the result to 0 as follows;

I'(t) = 0.00009045×5·t⁴ + 0.001438×4·t³ - 0.0656×3·t² + 0.4598×2·t - 0.6270 = 0

Factoring the result, using a graphing calculator, we get;

(t - 0.823)·(t - 5.131)·(t - 11.05)·(t + 29.72) = 0

The values of the minimum and maximum values are therefore';

I(0.823) = 0.00009045×0.823⁵ + 0.001438×0.823⁴ - 0.0656×0.823³ + 0.4598×0.823² - 0.6270×0.823 + 99.33 ≈ 99.08

I(5.131) = 0.00009045×5.131⁵ + 0.001438×5.131⁴ - 0.0656×5.131³ + 0.4598×5.131² - 0.6270×5.131 + 99.33 ≈ 100.67

I(11.05) = 0.00009045×11.05⁵ + 0.001438×11.05⁴ - 0.0656×11.05³ + 0.4598×11.05² - 0.6270×11.05 + 99.33 ≈ 96.38

I(-29.72) = 0.00009045×(-29.72)⁵ + 0.001438×(-29.72)⁴ - 0.0656×(-29.72)³ + 0.4598×(-29.72)² - 0.6270×(-29.72) + 99.33 = 1270.8

Therefore, the food price when the food was cheapest is $99.08

The time when the food is most cheapest where 0 ≤ t ≤ 10 is t = 0.823 years ≈ 1 years

Similarly, the food price when the food was most expensive in a 10 year time frame is $100.67

The time when the food is most expensive is t ≈ 5.131 years ≈ 5 years

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Answer: 360

Step-by-step explanation:

done

The maximum value of x = 18.8 approx. Hence the mathematical statement that represents the given situation is x² - 12x ⩽ 380. The correct option is b.

Given that an open box is to be formed out of a rectangular piece of cardboard whose length is 12cm longer than its width.

To form the box, a square of side 5cm will be removed from each corner of the cardboard. Then the edges of the remaining cardboard will be turned up.

If the box is to hold at most 1900 cm³ then the mathematical statement that represents the given situation is:

x² - 12x ⩽ 380. Hence, option (b) is the correct.

Consider the width of the rectangular cardboard be x cm.

Then its length would be x + 12 cm.

Now the square of 5cm is removed from each corner.

The height of the box would be 5 cm, as given.

Then, the length and width of the box would be (x + 12 - 10) cm and (x - 10) cm respectively.

Hence the base of the box would be x² - 20x + 100 cm².

Now we need to determine the maximum value of x so that the box can hold a maximum of 1900 cm³.

The volume of the box is given by length × width × height

x(x + 2) (5) ⩽ 1900x² + 10x - 1900

⩽ 0x² - 190x + 190 ⩽ 0(x - 10) (x - 19)

⩽ 0x ⩽ 19

[Since x > 0]

Therefore, x lies between 0 and 19.

When we plot the graph for the given expression, the curve intersects x-axis at x = 10 and x = 19.

Hence the value of x should be between 10 and 19.

Now let's determine the maximum value of x. For that, substitute x = 19 in the volume of the box.

We get the volume of the box to be 1901 cm³ which is greater than 1900 cm³.

The correct option is b.

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For your birthday, you plan to hang a piñata in your basement. You decide to attach two hooks on opposite walls, connect the hooks with a taut string, and hang the piñata from the point on the string exactly halfway between the hooks.

1.The first hook is located 4 feet east of the origin (x-coordinate) and 7.5 feet above the origin (z-coordinate), so its coordinates are (4, 0, 7.5).

2.The second hook is located 5 feet east of the origin (x-coordinate), 12 feet north of the origin (y-coordinate), and 8 feet above the origin (z-coordinate), so its coordinates are (5, 12, 8).

3.To find the point on the string that is exactly halfway between the hooks, we need to find the midpoint of the line segment joining the two hooks. We can use the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two hooks.

Substituting the values, we get:

Midpoint = ((4 + 5)/2, (0 + 12)/2, (7.5 + 8)/2)

= (4.5, 6, 7.75)

Therefore, the coordinates of the point on the string that is exactly halfway between the hooks are (4.5, 6, 7.75).

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Step-by-step explanation:

3.65<x<3.75

plsss mark brainliestt

Angela's use 6 cups of flour and Jaleel's use 19/3 cups of flour.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph shows the relationship between the number of cups of flour and the number of cups of sugar in Angela's brownie recipe.

And, The table shows the same relationship for Jaleel's brownie recipe.

Hence, The equation for Angela's brownie recipe is,

Two points on graph are (4, 2) and (2, 1)

⇒ y - 2 = (2 - 1)/ (4 - 2) (x - 4)

⇒ y - 2 = 1/2 (x - 4)

⇒ y - 2 = 1/2x - 2

⇒ y = 1/2x

And, The equation for Jaleel's brownie recipe is,

Two points on graph are (3/2, 1) and (3, 2)

⇒ y - 1 = (2 - 1)/ (3 - 3/2) (x - 4)

⇒ y - 1 = 2/3 (x - 4)

⇒ y - 1 = 2/3x - 8/3

⇒ y = 2/3x - 8/3 + 1

⇒ y = 2/3x - 5/3

So, For Jaleel and Angela buy a 12-cup bag of sugar.

The equation for Angela's brownie recipe is,

⇒ y = 1/2x

⇒ y = 1/2 × 12

⇒ y = 6

The equation for Jaleel's brownie recipe is,

⇒ y = 2/3x - 5/3

⇒ y = 2/3 × 12 - 5/3

⇒ y = 19/3

Thus, Angela's use 6 cups of flour and Jaleel's use 19/3 cups of flour.

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Answer:

94 marbles

Step-by-step explanation:

4512/48 = 94

Answer:

11, subtraction, 23 - 12 = 11

Answer:

possibly a dollar per pound so 2$ for 2 lbs

Step-by-step explanation:

Answer:Probably 2 dollar for 2 pounds

Step-by-step explanation:

because if you divide the 3 dollars that the 2 pounds of apples by 2 because is 2 pounds you get 1.50 and the question says he payed less for the apples you get like 1 and you multiplied by 2 because is 2 pounds you get 2 dollars

Answer:

The volume of the hemisphere is 496741.6 m³

Step-by-step explanation:

The volume of an sphere is given by:

In which  and r is the radius.

An hemisphere is half of an sphere, so it's volume is half the sphere's volume. So

In this question:

. So

The volume of the hemisphere is 496741.6 m³

Answer:

y=-(x+3)(x+1)(x-2)=-x^3-2x^2+5x+6

Step-by-step explanation:

If the zeros are:

x1=-3

x2=-1

x3=2

then the function is:

y = a (x-x1) (x-x2) (x-x3) = a (x+3) (x+1) (x-2)

y = a (x^3+2x^2-5x-6)

To find the value for "a" we use the information that, if x=1, then y=8:

y = a (1+2-5-6) = a (-8) = 8 therefore a=-1

So:

y=-(x+3)(x+1)(x-2)=-x^3-2x^2+5x+6

The car has traveled 240 miles in 4 hours. The correct answer is option b.

To calculate the distance traveled by the car, we can use the formula:

Distance = Speed * Time

In this case, the speed of the car is given as 60 miles/hour, and the time is given as 4 hours. Plugging these values into the formula, we get:

Distance = 60 miles/hour * 4 hours = 240 miles

Therefore, the car has traveled 240 miles in 4 hours.

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The likely terms that are the same based on the information include 3/4a³ and 0.75a³.

It should be noted an equation is used to show the relationship between the variables that are given.

In the question, the likely terms that are given include: 3d, 3/4a³, -6ad, and 0.75a³.

It should be noted that the expressions that are the same include 3/4a³ and 0.75a³. This is because 3/4 is the same as 0.75 in decimal.

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please mark this answer as brainlist

(A) The statement is true. The union of the edge sets of two different U, V-walks must contain a cycle. (B) The statement is false. The union of the edge sets of two different U, V-paths does not necessarily contain a cycle.

(A) The statement is true. If we have two different U, V-walks in a graph, the union of their edge sets will always contain a cycle. This is because a walk is a sequence of vertices and edges that allows revisiting vertices and reusing edges. By combining two different U, V-walks, we are essentially creating a closed loop or a cycle within the graph.

(B) The statement is false. The union of the edge sets of two different U, V-paths does not necessarily contain a cycle. A path is a sequence of vertices and edges where no vertex or edge is repeated. It allows traversing through the graph without revisiting any vertex or reusing any edge. If we combine two different U, V-paths, they may simply merge and extend the overall path without forming a cycle.

To illustrate this, consider a simple graph with three vertices A, B, and C, where there is a direct edge from A to B and another direct edge from B to C. If we consider two different U, V-paths from A to C, say A-B-C and A-C, their union (A-B-C-A-C) does not form a cycle. It is a connected path from A to C without any repeated edges or vertices.

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Step-by-step explanation:

Domain of the function is [-2, 4] whereas the range of the function is [-4, 2].

Marissa needs to score 94% on test five to have a mean of 90% for all five tests.

What is average?

Let's look at the average formula in more detail in this part and use some examples to illustrate how it may be used. The following is an example of the average formula for a specific set of data or observations: Average = (Sum of Observations) ÷ (Total Numbers of Observations).

Let's use the formula for finding the mean:

mean = (sum of all scores) / (number of scores)

We know that Marissa has taken four tests and has a mean score of 89%, so:

(4 x 89) + x = 5 x 90

Simplifying:

356 + x = 450

x = 94

Therefore, Marissa needs to score 94% on test five to have a mean of 90% for all five tests.

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Answer:

6 quarters and 6 dimes

Step-by-step explanation:

since there is 6 quarters it would be 6x$.25 which is $1.50, and each dime is worth 10 cents so 6x$.10 is $.60, and $1.50+$.60=$2.10