For questions 3 - 4, determine the 8th term in the following sequences. 3) 1, 2, 4, 8, ... 4) a= 216, r=-6

The population of the average length in 2013 is (b) 4.08 minutes

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

The table of values

Using the least squares, we have the following summary

The regression equation is

y = mx + b

Where

m =  SP/SSX =  2.14/17.5 = 0.122

b = MY - bMX = 2.72 - (0.12*1.5) = 2.53867

So, we have

y = 0.12x + 2.54

In 2013, we have

y = 0.12 * 13 + 2.54

y = 4.1

Hence, the prediction is (b) 4.08 minutes

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The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).

To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).

In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:

(x₁ + x₂)/2 = 1

(y₁ + y₂)/2 = 3

We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:

(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2

(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6

Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:

x₁ + (2-x₁) = 2 => x₁ = 1

y₁ + (6-y₁) = 6 => y₁ = 3

So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.

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The factor of such equation described as having the number 3 as a root can be determined as; (x-3).

It follows from the task content that; we are required to determine a possible factor of a polynomial in the event that such polynomial has a root of 3.

The implication of a polynomial having a root of 3 is that; such a polynomial has 3 to be one of it's zeros.

Hence, a linear equation which holds for such polynomial is that; x = 3 and when expressed as a linear factor, the linear factor is; (x-3).

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Based on the above, the options that could be their individual weights are:

B. 3 1/4 pounds  and 5 1/2 pounds

C. 4 3/4 pounds and 4 pounds

E. 6 pounds and 2 3/4 pounds

From the question, we are going to analyze the options to see which ones satisfy the given equation:

A. 7 pounds and 3/4 pound:

7 + 3/4

= 7 3/4 pounds, and thus, it does not equal 8 3/4 pounds.

B. 3 1/4 pounds and 5 1/2 pounds:

3 1/4 + 5 1/2

= 8 3/4 pounds, and thus it satisfies the equation.

C. 4 3/4 pounds and 4 pounds:

4 3/4 + 4

= 8 3/4 pounds, thus satisfies the equation.

D. 8 pounds and 1/4 pound:

8 + 1/4

= 8 1/4 pounds, and thus does not equal 8 3/4 pounds.

E. 6 pounds and 2 3/4 pounds:

6 + 2 3/4

= 8 3/4 pounds, and thus it satisfies the equation.

Therefore, the options that satisfy the equation of 8 3/4 pounds are options B, C, and E.

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See text below

Two bags of flour have a total weight of 8  whole number 3/4 pounds. What could be their individual weights?

Select all that apply.

A. 7 pounds and 3/4 pound

B. 3 1/4 pounds  and 5 1/2 pounds

C. 4 whole number  3/4 pounds and 4 pounds

D. 8 pounds and 1/4 pound

E. 6 pounds and 2 whole number 3/4 pounds

Answer:

y = -9

Step-by-step explanation:

perpendicular to the y-axis means it is parallel to the x-axis.

so, it is a flat line, which means the slope is 0 (it has the save y value for every x value).

therefore the equation is

y = 0×x + b

of simply

y = b

to get b we look at the point we know about (0, -9).

-9 = b

aha !

so, the line equation is simply

y = -9

The number of sections of board that he can construct will be equal to 7.

We are given that:

A carpenter has 6 boards.

Length of each board = 7 / 8 yard long

Now, we will use multiplication.

Total length of cardboards available = 7 / 8 × 6 yards

Total length = 42 / 8 yards

Total length = 21 / 4 yards.

Now, 3/4 yard sections of board that he can construct will be:

Number of sections of board = 21 / 4 ÷ 3 / 4

Number of sections of board = 21 / 3

Number of sections of board = 7

Therefore, the number of sections of board that he can construct will be equal to 7.

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The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

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Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

The product of 3 and 10√28, in its simplest radical form is: 60√7.

Step-by-step explanation:

hope it helps

Answer:area=l×b

10×8=80cm* 2

perimeter =(l+b)2

10+8)*2

18×2

=36cm

Step-by-step explanation:

Answer:

read the explanation

Step-by-step explanation:

For A:

Perimeter is (10+8)*2=36

Area is 10*8=80

For B:

Perimeter is 10*4=40

Area is 10*10=100

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer: (-3, 0)

Step-by-step explanation:

         First, we will graph these equations. See attached. One has a y-intercept of 3 and then moves right one unit for every up down (we get this from the slope of 1). The other has a y-intercept of 4, and then moves down two units for every unit right (we get this from the slope of 1).

         The point of intersection is the solution, this is the point at which both graphed lines cross each other. Our solution is:

                         (-3, 0)     x = -3, y = 0

Answer:

(-3, 0)

Step-by-step explanation:

When we graph the equations:

y = x + 3,

y = -2 - 6,

we can see that they intersect at (-3, 0).

Therefore, that is the solution to the system.

— Extra note —

When graphing a line from a slope-intercept form equation (y = mx + b), we know the following:

m is the line's slope (rise over run)

b is the y-coordinate of the line's y-intercept

Answer:

7 girls can go in the first place, 6 in the second, etc.

7! ways is the number of ways to arrange the girls.

likewise the boys can be arranged in 7! ways

The total number of ways becomes 7! * 7!

7! * 7! = 25,401 600 ways

Answer:

x=2, z=4, y=-6

Step-by-step explanation:

Add

-9x-y+2z= -4

-6x+y+5z= 2

-9x-6x is -15x

-y+y is 0

2z+5z is 7z

-4+2 is -2

So the equation now looks like this: -15x+7z=-2

Subtract

-6x+y+5z= 2

-4x+y+5z= 6

So the equation will look like this:

-6x+y+5z= 2

-(-4x+y+5z= 6)

-6x+4x is -2x

y-y is 0

5z-5z is 0

2-6 is -4

So the equation now looks like this: -2x=-4

You can find x by dividing -2 on both sides:

x=2

So 2 is x

Now you can substitute x into 2

-15(2)+7z=-2

-30+7z=-2

7z=28

Divide 7 on both sides:

z=4

So now you can substitute z into 4 (For any of the three equation)

-4(2)+y+5(4)=6

-8+y+20=6

20 minus 8 is 12

y+12=6

Subtract 12 on both sides:

y=-6

So the answers are

x=2, z=4, y=-6

Hope this helps!

Answer:

26 inches

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

144 divided by 12 is 12

After calculating we found that: a) 95% of widget weights lie between 42 and 54 ounces.b) 97.35% of widget weights lie between 39 and 54 ounces and c) 0.3% of widget weights lie above 45 ounces.

a) Since the distribution is bell-shaped and the mean is 48 ounces with a standard deviation of 3 ounces, we can use the 68-95-99.7 Rule to determine that 68% of the widget weights lie within one standard deviation of the mean, 95% lie within two standard deviations of the mean, and 99.7% lie within three standard deviations of the mean. Thus, we know that 95% of the widget weights lie between:

48 - 2(3) = 42 ounces and 48 + 2(3) = 54 ounces.

b) To find the percentage of widget weights that lie between 39 and 54 ounces, we need to determine how many standard deviations away from the mean these values are.

39 ounces is 9 ounces below the mean, so it is (9/3) = 3 standard deviations below the mean.

54 ounces is 6 ounces above the mean, so it is (6/3) = 2 standard deviations above the mean.

Using the 68-95-99.7 Rule, we know that 99.7% of the widget weights lie within three standard deviations of the mean. Since 39 ounces is three standard deviations below the mean, we can conclude that 0.15% (or 0.003 x 100) of the widget weights lie below 39 ounces.

Likewise, since 54 ounces is two standard deviations above the mean, we know that 2.5% of the widget weights lie above 54 ounces. Thus, the percentage of widget weights that lie between 39 and 54 ounces is:

100% - 0.15% - 2.5% = 97.35%

c) We need to find the percentage of widget weights that lie above 45 ounces. Since 45 ounces is three standard deviations below the mean, we know that 99.7% of the widget weights lie above 45 ounces. Therefore, the percentage of widget weights that lie above 45 ounces is:

100% - 99.7% = 0.3%.

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Answer:

1= 25 minutes i believe

Step-by-step explanation:

Answer:

FV= $6,750

Step-by-step explanation:

Giving the following information:

Initial investment (P)= $5,000

Interest rate (r)= 5% simple interest

Number of periods (t)= 7 years

To calculate the future value of the investment, we need to use the following formula:

FV= (P*r*t) + P

FV= (5,000*0.05*7) + 5,000

FV= 1,750 + 5,000

FV= $6,750

To find the equation of the tangent plane and the normal line to the surface x⁴ + y⁴ + z⁴ = 3x²y²z² at the point (1, 1, 1), we follow these steps:

Find the gradient vector of the surface at the given point:

The gradient vector of the surface is given by:

∇f(x,y,z) = < ∂f/∂x, ∂f/∂y, ∂f/∂z >,

where f(x,y,z) = x⁴ + y⁴ + z⁴ - 3x²y²z²

So, we have:

∂f/∂x = 4x³ - 6y²z²,

∂f/∂y = 4y³ - 6x²z²,

∂f/∂z = 4z³ - 6x²y²

At the point (1,1,1), we have:

∂f/∂x = 4(1)³ - 6(1)²(1)² = -2,

∂f/∂y = 4(1)³ - 6(1)²(1)² = -2,

∂f/∂z = 4(1)³ - 6(1)²(1)² = -2.

Therefore, the gradient vector at (1,1,1) is: ∇f(1,1,1) = <-2, -2, -2>

Find the equation of the tangent plane:

The equation of the tangent plane to the surface at the point (1,1,1) is given by:

f_x(1,1,1)(x - 1) + f_y(1,1,1)(y - 1) + f_z(1,1,1)(z - 1) = 0,

where f_x, f_y, and f_z are the partial derivatives of f(x,y,z) with respect to x, y, and z, evaluated at (1,1,1). Substituting the values we found in step 1, we get:

-2(x - 1) - 2(y - 1) - 2(z - 1) = 0

Simplifying, we get:

x + y + z = 3

So, the equation of the tangent plane is x + y + z - 3 = 0.

Find the equation of the normal line:

The normal vector to the tangent plane is the same as the gradient vector of the surface at the given point, i.e., ∇f(1,1,1) = <-2, -2, -2>. So, the equation of the normal line passing through the point (1,1,1) is:

x - 1 = -2t,

y - 1 = -2t,

z - 1 = -2t

or

x = -2t + 1,

y = -2t + 1,

z = -2t + 1.

Therefore, the equation of the normal line to the surface x⁴ + y⁴ + z⁴ = 3x²y²z²  at the point (1,1,1) is:

x = -2t + 1,

y = -2t + 1,

z = -2t + 1.

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Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

Option D is the correct answer.

We have,

Edouard Manet's painting "Luncheon on the Grass" was first rejected by the Paris Salon in 1863, as it was considered scandalous due to the nudity of the female figure in the painting.

In response to this rejection,

Emperor Napoleon III ordered an exhibition to be held for all the rejected paintings, which was known as the Salon des Refusés (Salon of the Refused).

Thus,

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

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Answer:

Reptile, any member of the class Reptilia, the group of air-breathing vertebrates that only have:

Answer:

  $2418.07

Step-by-step explanation:

Problems involving the time-value of money are conveniently solved using a TVM app on a suitable calculator or spreadsheet. The result of doing that is shown in the attachment.

__

If you would like to compute the value of Emily's account by hand, the annuity formula is the one you want.

  A = Pn((1 +r/n)^(nt) -1)/r . . . . where r is the annual interest rate, n is the number of times per year it is compounded (12), t is the number of years (1/2), and P is the periodic payment into the acccount (400).

Using the given values in the formula, we have ...

  A = 400(12)((1 +0.036/12)^(12/2) -1)/0.036 = 4800×(1.003^6 -1)/0.036

  A ≈ 2418.07

At the end of 6 months, Emily will have saved $2418.07.

Answer:5 and 3

Step-by-step explanation: They are tho samples bc they are the ones tht are duplicated (x2)

The expression with the correct coefficients in each block is given as follows:

20x³ + 0x² - 7x.

The functions in the context of this problem are defined as follows:

The operation is given as follows:

f(x)g(x) + h(x).

Hence, to obtain the resultant function, we apply the definitions into the operation and the simplify, applying the distributive property and combining the like terms, as follows:

4x(5x² - 4) + 9x = 20x³ - 16x + 9x = 20x³ - 7x.

As there is no x² term, the coefficient of zero multiplies the term x².

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The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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