What are the next two numbers in the sequence?
4, 16, 64, 256,

Answer:

The answer is 5,512.

Step-by-step explanation:

Multiply 53 times 13 times 8

Answer:

kbjlhbkhhhiljb jkbhiphouhkvguohyuhlj vguhbkhuobjk

Step-by-step explanation:

The dimensions of the rectangle that will allow for the most economical fence to be built is 50 feet and 25 feet in length and width respectively.

Given in the question,

Area = 1250 ft²

The three sides cost $3 per foot, and the fourth side costs $9 per foot.

Let x and y be the length and width of the rectangle.

Because the area is 1250 ft², therefore

xy = 1250, or

y = 1250/x            

Case 1: Three sides are (x,y,x) and the 4-th side is y.

The cost is

C = 3(2x +y) + 9y

  = 6x + 12y

  = 6x + 12(1250/x)

  = 6x + 15000/x

For C to be minimum, C' = 0. That is

6 - 15000/x² = 0

x² = 15000/6

x =  50 ft, y = 1250/50 = 25 ft

C = 6(50) + 15000/(50²) = $600

Case 2: Three sides are (y,x,y) and the 4-th side is x.

The cost is

C = 3(x + 2y) + 9x

   = 12x + 6y

   = 12x + 6(1250/x)

   = 12x + 7500/x

For C to be minimum, C' = 0.

12 - 7500/x² = 0

x² = 7500/12 = 625

x = 25 ft, y = 50ft

C = 12(25) + 7500/25 = $600

Thus, the Dimensions will be 25 feet and 50 feet.

Question:

A fence is to be built to enclose a rectangular area of 1250 square feet. the fence along three sides is to be made of material that costs ​$3 per foot. the material for the fourth side costs ​$9 per foot. find the dimensions of the rectangle that will allow for the most economical fence to be built.

To Learn more about Questions on Dimensions of Rectangle:

https://brainly.com/question/6768558

#SPJ4

Answer:

(-7. -8) Just flip the signs.

Answer:

\(\boxed {\boxed {\sf (-8,-7)}}\)

Step-by-step explanation:

When a point is reflected over y=-x, the following change occurs:

\((x,y)\)    ⇒  \((-y, -x)\)

We are given the point (7,8).

Essentially, we change the signs for both coordinates, then flip the x-coordinate and y-coordinate.

1. Change the signs

\((7,8)\)    ⇒    \((-7,-8)\)

2. Flip the x and y coordinates

\((-7,-8)\)   ⇒    \((-8,-7)\)

So the image of (7,8) after a reflection over y=-x is (-8,-7)

the length and breadth of the rectangle is L = 4, B =16

Let L and B stand for length and width, respectively.

a rectangle is 4 times a long as it is wide

L=4B …….(1) (1)

L1 and B1 should represent the revised length and width.

L1=(L+4)

B1=(B-1)

Area = L1 + B1 + 60.

=> (L+4)×(B-1)=60 …….(2) (2)

Using (1)-

=> (4B+4)×(B-1) =60

=> 4×(B^2–1) = 60

=> B^2–1 = 15

=> B^2 = 16

=> B = +4 or -4

B=4 inches because breadth is always positive.

L = 4 B = 16 inches.

To learn more about rectangle:

https://brainly.com/question/15019502

#SPJ4

The true statements are Function B has greater slope, Function A has greater y intercept and Function B has greater x intercept.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

We have to first find the linear equations of the functions.

Given for function A,

Let x be the number of hours.

Function A can be represented as f(x) = 4/5 + 2x

Equation in slope intercept form is y = mx + c, where m is the slope and c is the intercept along Y axis.

Y intercept is the point of the line where it touches the Y axis. x coordinate will be zero here.

x intercept is the point of the line where it touches the X axis. y coordinate will be zero here.

y = 2x + (4/5), in slope intercept form.

Here 2 is the slope and 4/5 is the y intercept.

When y = 0, 2x + (4/5) = 0, then x = -2/5

x intercept = -2/5

For function B,

we have when x = 0, f(x) = y = 2/3

y intercept = 2/3

Slope = [(2/3) - (-25/3)] / [0 - -3]

          = [27/3] / 3

          = 9 / 3

          = 3

Equation in slope intercept form of function B is,

y = 3x + 2/3

When y = 0, 3x + 2/3 = 0, then x = -2/9

x intercept = -2/9

So function B has greater slope as slope is 3 for B and 2 for A.

Function A has greater y intercept as y intercept for A is 4/5 and for B is 2/3.

Function B has greater x intercept as x intercept is -2/9 for B and -2/5 for A.

Hence the correct options are function B has greater slope, Function A has greater y intercept and Function B has greater x intercept.

Learn more about Slope here :

https://brainly.com/question/3605446

#SPJ1

(a) The surface area of the cylinder is

                 \(2\pi r(r+h) = 2\pi *6*(6+4) = 376.991\\\)  square centimeters

(b) The Volume of the cylinder is

                 \(\pi r^{2} h = \pi (6^{2} )*4 =452 .389\)  cubic centimeters

(c)  The more volume option is choice 1.

             \(\pi r^{2} h = \pi (12^{2} )*4 = 1809.557\\\\\pi r^{2} h = \pi (6^{2} ) *12 = 1357.168\\\)

Hope that helps!

Answer:

(a) The surface area of the cylinder is

2πr(r+h)=2π*6*(6+4)=376.991 square centimeters

(b) The Volume of the cylinder is

πr²h= π(6²)*4=452.389 cubic centimeters

(c)  The more volume option is choice 1.

πr²h= π(12²)*4=1809.557

πr²h= π(6²)*12=1357.168

The area of the rectangular pasture is found to be 80,000 ft².

Given:

Let the pasture's rectangular length be l feet.

Given that the rectangular pasture's length being 200 feet longer than its breadth, its width must be w = l200 feet.

The pasture's boundary is;

2(l + w) = 1200

2(l + l - 200) = 1200

2l - 200 = 600

l = 400 feet

Width; w = l - 200

w = 400 - 200 = 200 feet

Rectangular area;

A = l x w

A = 400 x 200

A = 80,000 ft²

Thus, the area of the rectangular pasture is found to be 80,000 ft².

To know more about the Rectangle, here

https://brainly.com/question/25292087

#SPJ4

Answer: we would need 7 bags of fertilizer to cover the area of the triangle.

Step-by-step explanation:

To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle can be found by taking the square root of the semi-perimeter multiplied by the difference of the semi-perimeter and each side length.

The semi-perimeter of the triangle is (2.1+1.8+2.7)/2 = 2.7

The area of the triangle is sqrt(2.7*(2.7-2.1)(2.7-1.8)(2.7-2.7)) = sqrt(2.70.60.9*0) = 1.35

Each bag of fertilizer covers 0.2 square miles, so we need to divide the area of the triangle by the area covered by each bag to find how many bags are needed: 1.35 / 0.2 = 6.75

Rounding up to the nearest whole number, we would need 7 bags of fertilizer to cover the area of the triangle.

Step-by-step explanation:

= ( 3x + 5 ) ( 4x² + 8x + 40 )

= 3x ( 4x² + 8x + 40 ) + 5 ( 4x² + 8x + 40 )

= 12x³ + 24x²+ 120x + 20x² + 40x + 200

= 12x³ + 24x² + 20x² + 120x + 40x + 200

= 12x³ + 44x² + 160x + 200

Answer:

12x^3 +44x^2 +160x +200

Step-by-step explanation:

Distribute:

(3x+5)(4x^2 +8x+40)

3x(4x^2 +8x+40) +5(4x^2 +8x+40)

Then it would be:

(12x^3 +24x^2 +120x) + (20x^2 + 40x +200)

therefore the soloution is:

12x^3 +44x^2 +160x +200

Answer:

32

Step-by-step explanation:

if you look at the diagram the dot goes up 1 each. It also makes another row which makes 4 rows total. Since 3 contains 7 dots and 3 rows we would do 8 in 4 rows. 8 x 4 is 32.

Hope this helped!

Answer: I got 16.3 degrees, initial answer was 16.26 I just rounded.

Step-by-step explanation: If you use Tan, Sin or Cos you can find the angle of the triangle. I used Tan which is Opposite side over the adjacent side, so Tan^-1 = (14/48).

The polar pairs in Option B and Option D are valid representations of (3, 120°).

Polar coordinates use an angle, usually measured in degrees or radians, and a distance from the origin to define the location of a point in a two-dimensional space. As opposed to this, rectangular coordinates use a point's x and y distances from the origin to define its location. While rectangular coordinates are more helpful for expressing linear motion or vectors, polar coordinates are frequently employed to describe rotational or circular motion.

Given that the coordinates are (3,120°).

To determine the coordinates we convert the polar coordinates to rectangular coordinates as follows:

x = rcos(theta)

y = rsin(theta)

To convert a rectangular coordinate to polar coordinates, we use the following formulas:

r = √(x² + y²)

theta = arctan(y/x)

Converting (3, 120°) to rectangular coordinates:

x = 3cos(120°) = -1.5

y = 3sin(120°) = 2.598

Converting (-1.5, 2.598) to polar coordinates:

r = √((-1.5)² + (2.598)²) = 3

theta = arctan(2.598/-1.5) = -60° + 360° = 300°

We observe that A and C do not have the same r value thus they are eliminated.

Now, for B:

x = 3cos(-240°) = -1.5

y = 3sin(-240°) = -2.598

r = √((-1.5)² + (-2.598)²) = 3

theta = arctan(-2.598/-1.5) = 60°

Trying option D:

x = 3cos(-60°) = 1.5

y = 3sin(-60°) = -2.598

r = √((1.5)² + (-2.598)²) = 3

theta = arctan(-2.598/1.5) = -60° + 360° = 300°

Thus, the polar pairs in Option B and Option D are valid representations of (3, 120°).

Learn more about polar coordinates here:

https://brainly.com/question/11657509

#SPJ1

By Limit comparison test the series ∞∑n=11n√n²+5 converges.

To use the limit comparison test, we need to find a series whose convergence or divergence is known and that is similar to the given series.

Let's consider the series ∞∑n=11n√n²+5 and choose a series that we know converges, such as ∞∑n=1 1/n².

We can now take the limit as n approaches infinity of the ratio of the nth term of the given series to the nth term of the chosen series:

limₙ→∞ (n√(n²+5))/(1/n²)

Simplifying the expression inside the limit, we get:

limₙ→∞ (n√(n²+5))/(1/n²) = lim(n→∞) n³√(1+5/n²)/1 = lim(n→∞) n³/√(n⁶+5n⁴)

Using L'Hopital's rule, we can take the derivative of the numerator and denominator separately with respect to n to get:

limₙ→∞n³/√(n⁶+5n⁴) = lim(n→∞) 3n²/3n⁵/²= lim(n→∞) 3n¹/²)/3n⁵/²) = 0

Since the limit is finite and nonzero, the given series and the chosen series have the same convergence behavior. Therefore, since we know that ∞∑n=1 1/n² converges (by the p-series test with p=2),

we can conclude that the given series ∞∑n=11n√n²+5 also converges.

Learn more about L'Hopital's rule : https://brainly.com/question/30763940

#SPJ11

In order to find a 99% confidence interval for the proportion of students who take notes, the student would need to follow certain steps. First, they would need to obtain a random sample of students and record whether or not each student takes notes. Based on this data, they would calculate the sample proportion, which is the number of students who take notes divided by the total number of students in the sample.

Next, they would use a statistical formula to calculate the margin of error, which is the amount by which the sample proportion could vary from the true proportion in the population. They would also use a table or calculator to find the critical value for a 99% confidence level.

Finally, the student would use these values to construct the confidence interval, which is the range of values that is likely to contain the true proportion of students who take notes in the population with 99% confidence. This interval would be expressed as a range of values, such as "between 0.55 and 0.75," and would indicate the level of uncertainty in the estimate based on the sample data.

To learn more about proportion click here: brainly.com/question/26617614

#SPJ11

The row numbers along the left side of the worksheet are 1, 2, 4, 5, 6. We can observe that there is a missing number in the sequence, specifically the number 3. Therefore, based on the pattern, we can deduce that row 3 is missing from the worksheet.

Based on the given information, the row numbers along the left side of the worksheet are 1, 2, 4, 5, 6, with a missing number in the sequence, which is the number 3.

The presence of the numbers 1, 2, 4, 5, and 6 indicates that rows corresponding to those numbers exist in the worksheet. However, there is no row with the number 3 mentioned in the sequence. Thus, we can conclude that row 3 is missing from the worksheet.

It is important to note that the missing row could be intentional or accidental, but based on the given information, we can deduce that there is a discontinuity in the row numbering, specifically the absence of row 3.

Learn more about  number from

https://brainly.com/question/27894163

#SPJ11

1234567890233572o7o5y345uo22u.3936584643728284/43794729237932972478864966666666666666666666666666666666663870434573428734907 goood luck!

Step-by-step explanation:

for the perimeter you have to say two brackets live plus height plus with plastic

Answer:

D

Step-by-step explanation:

(a) False. The set {x∈R^n | Ax=b} is not necessarily convex. It depends on the matrix A and the vector b. For example, if A is a non-convex matrix, then the set of solutions {x∈R^n | Ax=b} will also be non-convex.

(b) True. The set {(x₁,x₂) | x₂ ≤ 3x₁²} is convex. The inequality defines a downward parabolic region, and any line segment connecting two points within this region will lie entirely within the region. (c) False. Not all polygons on the R² plane are convex. For example, a polygon with a concave portion, such as a crescent shape, would not be convex.

(d) True. If S⊆R² is convex, then it must enclose a region of finite area. Convex sets do not have "holes" or disjoint parts, so they form a connected and bounded region. (e) False. If S₁⊆R² and S₂⊆R², and S₁∩S₂=ϕ (empty set), then S₁∪S₂ can be convex. If S₁ and S₂ are both convex sets that do not overlap, their union can still be a convex set. (f) True. If S₁⊆R² and S₂⊆R² are both closed sets, then their union S₁∪S₂ must also be closed. However, it may or may not be convex. The convexity of the union depends on the specific sets S₁ and S₂.

To learn more about vector click here: brainly.com/question/24256726

#SPJ11

Answer:

38 inches

Step-by-step explanation:

just add them all together.

Answer:

5 1/2 :)

Step-by-step explanation:

The statement ''the formula for finding the surface area of a cylinder is sa = πr2 πrh.'' is false because the formula for finding the surface area of a cylinder is given by: SA = 2πrh + 2πr^2 , where SA represents the surface area, r is the radius of the base, and h is the height of the cylinder.

The first term, 2πrh, represents the area of the curved surface of the cylinder (the lateral surface area), which is a rectangle that wraps around the cylinder. It is calculated by multiplying the height of the cylinder by the circumference of the base.

The second term, 2πr^2, represents the areas of the two circular bases of the cylinder.

By adding these two terms together, we obtain the total surface area of the cylinder.

Therefore, the correct formula for finding the surface area of a cylinder is SA = 2πrh + 2πr^2.

To know more about surface area refer here:

https://brainly.com/question/29298005#

#SPJ11

Answer:

the answer is 130

Step-by-step explanation:

Answer:

130

Step-by-step explanation:

when adding you positive number to a negative number you have to subtract. so to make it easier im going to change it from -240 +370 to

370-240 and solve

370-240=130

have a great day :D

distance between 2 points = root (x1-x2)²+(y1-y2)²

so root (-2-2)²+(5--3)² = 8.994 ≈ 9 units

An angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The angle is measured in a counterclockwise direction from the positive x-axis and is considered positive if it lies in the counterclockwise direction and negative if it lies in the clockwise direction.

The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located. An angle in a rectangular coordinate system is in a standard position if its vertex is at the origin of the plane. An angle is said to be in a standard position if its vertex is located at the origin of the coordinate system.

To summarize, an angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located.

Learn more about the rectangular coordinate system: https://brainly.com/question/4726772

#SPJ11

Answer:

x = 180 - 89 = 91

Step-by-step explanation:

Answer:

m‹N = 118.7

Step-by-step explanation:

61.3° + 118.7° = 180°

The formula you have given (SS₁ + SS₂) / (n₁+ n₂) is actually the formula for the unweighted average of the variances, which is not appropriate when the sample sizes and variances are different between the two samples.

The formula for pooled variance is:

pooled variance = (SS₁+ SS₂) / (df₁ + df₂)

where SS₁ and SS₂ are the sum of squares for the two samples, df₁ and df₂ are the corresponding degrees of freedom, and the pooled variance is the weighted average of the variances of the two samples, where the weights are proportional to their degrees of freedom.

Note that the denominator is df₁ + df₂ not n₁+ n₂. The degrees of freedom take into account the sample sizes as well as the number of parameters estimated in

Learn more about “ formula for pooled variance “ visit here;

https://brainly.com/question/31450664

#SPJ4