Describe the pattern in your own words:;1;8;27;64;125 and write down the next five terms​

Answer: 8x²+4x-4

Step-by-step explanation:

(f+g)(x) is f(x)+g(x). Since we are given f(x) and g(x), we can directly add them together.

3x²-2x+4+5x²+6x-8                                  [combine like terms]

8x²+4x-4

Answer:

7x = 28

Step-by-step explanation:

Divide the 28 by the 7 to isolate the x

28 / 7 = 4

x = 4

The required number of children and adults for sitting in the theater are 300 and 50 respectively.

A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.

Let be consider number of children be x and that of adults is y.

We have,

x + y = 350-------(1)

y = 350 - x

And 5x + 10y = 2000------------------(2)

Put value of y in equation (2)

5x + 10( 350 - x) = 2000

5x + 3500 - 10x = 2000

-5x = -1500

x = 300

Then

y = 350 - x = 350 - 300 = 50

Thus, There will be 300 children and 50 adults in the  theater .

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Answer:

Option A ( 86 Degrees)

Step-by-step explanation:

To convert Celsius to Fahrenheit formula is:

\(F = \frac{9}{5} C + 32\)

\(F = \frac{9}{5} 30 + 32\)

\(F = 54 + 32\)

\(F = 86 Degree\)

Answer:

(0,5) and (2,6)

Step-by-step explanation:

FromFrom the given numbered list, the four members selected for the panel discussion are Keating, May, Bolt, and Engler.

To obtain a simple random sample size 4 from the numbered list of club members, we can use the random number table provided. Starting from the first column of the first row and working down each column, we select the first four numbers between 1 and 25.

According to the given random numbers: 03, 14, 05, 01, the corresponding members would be Keating (03), May (14), Bolt (05), and Engler (01). Therefore, the four members selected for the panel discussion would be Keating, May, Bolt, and Engler.

This selection process ensures randomness and provides an unbiased representation of the club membership for the panel discussion on the upcoming national election.

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Answer:

The sides from least to greatest are AB, BC, AC

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Answer: 25% i believe

Step-by-step explanation:

The probability that it lands inside the triangle is,

P = 25%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Since, the probability is equal to,

P = size of the event space/size of the sample space

Here, In this problem

size of the sample size = area of the rectangular dartboard = 648 square centimeters

And, size of the event space = area of the triangular part = 162 square centimeters.

Hence, the probability that it lands inside the triangle is,

P = 162 / 648

P = 0.25

P = 25%

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The matching for different kinds of telescopes is shown. (Refer to the matching shown below.)

A telescope is a tool used to view distant objects through the electromagnetic radiation that they emit, absorb, or reflect.

The term "telescope" now refers to a broad range of instruments capable of detecting different regions of the electromagnetic spectrum, and in some cases, other types of detectors, in addition to the original meaning of the word, which was only an optical instrument using lenses, curved mirrors, or a combination of both, to observe distant objects.

Refracting telescopes with glass lenses were the first practical telescopes ever made, and they were developed in the Netherlands at the start of the 17th century.

The matching according to the question:

Reflecting Telescopes: The Hubble Space Telescope, the largest telescope in the world, is currently the one most frequently used by professional astronomers.

Refracting Telescopes: In Galileo's telescopes, very large telescopes become "top-heavy," incoming light travels through glass, and the largest reflecting telescope in the world has a diameter of one meter.

Therefore, the matching for different kinds of telescopes is shown.

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Answer:

8

Step-by-step explanation:

The standard deviation of the data set is 3.17 (rounded to the nearest tenth).

To calculate the standard deviation of a set of data, you first need to calculate the mean (average) of the data set.

Mean = (17 + 18 + 22 + 16 + 18 + 14 + 13 + 23 + 20) / 9 = 18

Next, you need to calculate the variance of the data set.

Variance = [(17-18)^2 + (18-18)^2 + (22-18)^2 + (16-18)^2 + (18-18)^2 + (14-18)^2 + (13-18)^2 + (23-18)^2 + (20-18)^2] / (9-1) = 18.7

Standard deviation = √(18.7) = 3.17

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The median, however, would still be 24, since there are still an odd number of values and 24 is still the middle value. Therefore, the answer is:

The mean will increase and the median will not change.

To find the mean, we add up all the values and divide by the total number of values:

Mean = (16+18+20+24+24+24+24+31+32)/9 = 22

To find the median, we arrange the values in order from smallest to largest and find the middle value. In this case, the middle value is 24, since there are an odd number of values.

If we add one more vehicle with a rate of 4 mpg, the new list of values would be:

4, 16, 18, 20, 24, 24, 24, 24, 31, 32

The mean would now be:

Mean = (4+16+18+20+24+24+24+24+31+32)/10 = 22.7

So the mean would increase.

what is median?

In statistics, the median is a measure of central tendency that represents the middle value of a dataset when it is ordered from least to greatest (or greatest to least). To find the median, you simply arrange all the values in order and select the middle value. If there is an even number of values, then the median is the average of the two middle values. The median is often used as a measure of central tendency when the dataset has extreme values or outliers, as it is less sensitive to these values than the mean.

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Answer:

1. 87

A77

B24

C93

D47

E 31

F 48

2. 160

A10

B20

C30

D40

E 50

F 60

3. 68

A851

B295

C302

D574

E 112

F 638

4. 174

A3

B4

C5

D 6

E 7

F 8

5. a

A180-a

B180/2

C 179*a

D 179+a

E 60

F pi

Find the complementary angles of the following.

6. 53

A90

B32

C 25

D 45

E 18

F 37

7. 12

A46

B78

C98

D31

E 52

F 64

8. 73.5

A16.5

B34.2

C29.4

D17.7

E 57.9

F 11.3

9. 23.7

A66.3

B70.1

C42.5

D83.9

E 54.8

F 36.2

10. a

A90/a

Ba-90

Ca/2

D90-a

E 90-2

F a^2

Two of the angles are listed. Find the measure of the third angle in each triangle. Similar to example 6

11. 16,42

A256

B421

C107

D510

E 122

F 329

12. 90, 30

A23

B42

C47

D60

E 71

F 89

13. 43, 118

A12

B34

C19

D57

E 11

F 27

14. 60, 60

A15

B90

C29

D60

E 30

F 45

15. 14, 123

A73

B25

C38

D19

E 43

F 13

16. 68, 86

A45

B56

C26

D19

E 32

F 82

17. 55, 77

A18

B37

C62

D57

E 20

F 48

18. a, (a + 80)

A100 - 2a

B112 - 7a

C182 - 2a

D254 - 5a

E 311 - 3a

F 302 - 1a

19. x, (x + 20)

A189 - 7x

B167 - 1x

C114 - 5x

D160 - 2x

E 124 - 2x

F 142 - 1x

20. m, 2m

A172 - 2m

B187 - 7m

C124 - 4m

D143 - 1m

E 164 - 9m

F 180 - 3m

1. C

2. B

3. E

4. D

5. D

6. F

7. B

8. A

9. A

10. B

11. D

12. A

13. D

14. B

15. A

16. C

17. F

18. A

19. D

20. F

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

a) The area of the picture is the product of its dimensions:

  (18 cm)² = 324 cm²

__

b) The area of the board is 4 times that:

  board area = 4×324 cm² = 1296 cm²

__

c) The dimensions of the square board are the square root of its area:

  √1296 = √(4×324) = (√4)(√324) = 2×18 = 36 . . . . cm

The board is 36 cm square.

Cora would need a sample size of at least 1078 students to achieve a margin of error less than 0.03 for estimating the true proportion of high school students attending their home basketball games with 90% confidence.

To determine the sample size required to achieve a specific margin of error, we need to use the formula:

\(n = (z^2 * p * (1-p)) / E^2\)

n is the required sample size

z is the z-score corresponding to the desired confidence level (90% confidence level corresponds to a z-score of approximately 1.645)

p is the estimated proportion of students attending home basketball games (0.5, since exactly half attend)

E is the desired margin of error (0.03)

Plugging in the values into the formula:

\(n = (1.645^2 * 0.5 * (1-0.5)) / 0.03^2\)

n ≈ 1077.97

Rounding up to the nearest whole number, the required sample size would be approximately 1078 students.

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Answer:

A quadrilateral is a parallelogram if and only if opposite angles are equal.

So, to make the quadrilateral a parallelogram, we can set the following equalities:

(4x + 13) deg = (5x - 12) deg

(4y + 7) deg = (3x - 8) deg

Solving the first equation,

4x + 13 = 5x - 12

x = -5

Solving the second equation,

4y + 7 = 3(-5) - 8

4y + 7 = -17

4y = -24

y = -6

So, the values of x and y that make the quadrilateral a parallelogram are x = -5 and y = -6

Answer:

Peyton in the correct option

Step-by-step explanation:

The correct expression is given by Peyton.

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

Consider if m is any integer, then

gcd (a + m⋅ b, b) = gcd (a, b).

If m is a positive divisor, then

gcd (a/m, b/m) = gcd (a, b)/m.

So, if x and y are prime, then

gcd(x*y, b) = gcd(x, b) *  gcd(y, b).

First, find the greatest common factor of the given terms.

The greatest common factor or GCF is the largest factor that all terms have in common.

Then, Factor out the greatest common factor from each term.

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Answer:76

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume of gas varies directly as the cube of its radius.

Find k:

Volume of the smaller balloon:

The difference in volumes is the volume of released gas:

Answer:

What's the complex name

Pd(co2) (me3p)2

Answer:

1 hour

Step-by-step explanation:

12.5 + 6.25h

12.5 + 6.25 = 18.75

h = 1

Hopefully this helps you :)

pls mark brainlest ;)

Information is needed to evaluate the project's financial viability, considering factors such as the initial investment, expected cash flows, cost of capital, and project duration.

To calculate the year 1 operating cash flows (OCF), we need to subtract the year 1 costs from the year 1 revenues:

OCF = Year 1 Revenues - Year 1 Costs

OCF = $192,000 - $125,000

OCF = $67,000

To find the depreciation expense in year 3, we need to determine the depreciation method. The provided information is incomplete regarding the depreciation method, so we cannot calculate the depreciation expense in year 3 without knowing the specific method.

The change in Net Working Capital (NWC) in year 2 can be determined by multiplying the Net Working Capital percentage (given as a percentage of t+1 revenues) by the year 1 revenues and subtracting the result from the year 2 revenues:

Change in NWC = (Year 2 Revenues - Net Working Capital percentage * Year 1 Revenues) - Year 1 Revenues

Without the specific Net Working Capital percentage or Year 2 Revenues values, we cannot calculate the exact change in NWC in year 2.

The net cash flow from salvage (ATSV) is calculated by multiplying the Salvage Value percentage by the Initial Cost:

ATSV = Salvage Value percentage * Initial Cost

ATSV = 28% * $390,000

ATSV = $109,200

To calculate the project's NPV, we need the cash flows for each year, the cost of capital, and the project duration. Unfortunately, the information provided does not include the cash flows for each year, so we cannot calculate the project's NPV.

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The complete question is:

Below are your numerical inputs for the problem: 4 & Initial Cost (\$) & 390000 5 & Year 1 Revenues (\$) & 192000 6 & Year 1 Costs (\$) & 125000  7 & Inflation & 2.75% 8 & Project Duration (years) & 6 9 & Depreciation Method & 10 & Tax Rate & 11 & Net Working Capital (\% oft+1 Revenues) & MACRS 12 & Salvage Value (\$) & 28.00% 13 & Cost of Capital & 15.00% & 245000 How much are the year 1 operating cash flows (OCF)? How much is the depreciation expense in year 3 ? What is the change in Net Working Capital (NWC) in year 2? What is the net cash flow from salvage (aka, the after-tax salvage value, or ATSV)? What is the project's NPV? Would you recommend purchasing the ranch? Briefly explain.

The area of the triangle JHI is 8.75 square units.

From the given figure,

Area of a ΔJHI = Area of a rectangle - (Area of 3 triangles)

= 5×4 - (1/2 ×3×4 + 1/2 ×2×3 + 1/2 ×1×5)

= 20 - (6+3+2.5)

= 20 - 11.25

= 8.75 square units

Therefore, the area of the triangle JHI is 8.75 square units.

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The required answer is the y = 80

The best fit line equation in a scatter plot represents the relationship between two variables. It is also known as the regression line or the line of best fit. The equation of the best fit line is typically represented as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

To find the best fit line equation in a scatter plot,

1. Plot the data points on a scatter plot.
2. Visualize the trend or pattern in the data points.
3. Determine whether the relationship between the variables is linear, meaning that the data points roughly form a straight line pattern.
4. Use a statistical method, such as the least squares method, to find the line that minimizes the distance between the data points and the line.
5. Calculate the slope (m) and the y-intercept (b) of the best fit line.
6. Write the equation of the line using the values of m and b.

Using the least squares method, determine that the slope of the best fit line is 2 and the y-intercept is 70.

Therefore, the equation of the best fit line would be:

y = 2x + 70

This equation represents the expected test score (y) based on the number of hours studied (x). For example, if a student studies for 5 hours, estimate their test score by substituting x = 5 into the equation:

y = 2(5) + 70
y = 10 + 70
y = 80

So, according to the best fit line equation, if a student studies for 5 hours,  expect their test score to be around 80.

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Suppose someone built a gigantic apartment building, measuring 10 km×10 km at the base. Estimate how tall the building would have to be to have space in it for the entire world's population to live.

To find the height of the building, we need to divide the volume by the area of the base:

Height = Volume/Area of the base=\(770 billion m³/100 km²= 770000 m/10 km= 77 km\)

Therefore, the gigantic apartment building measuring 10 km x 10 km at the base would have to be 77 km tall to have space in it for the entire world's population to live. (77 km is approximately the height of the Earth's thermosphere, which extends from 80 km to 600 km above sea level.)

A hamburger chain advertises that it has sold 10 billion Bongo Burgers. Estimate the total mass of feed required to raise the cows used to make the burgers.

Therefore, the total mass of feed required to raise the cows used to make the burgers is 1.5 billion \(kg x 6.1 = 9.15\)billion kg.

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The answer to the question "Is the dependent variable continuous?" would be a. Yes, it is measured in interval form.

The question asks whether the dependent variable is continuous. In this context, a continuous variable is one that can take on any value within a certain range. The options provided are: (a) Yes, it is measured in interval form, (b) No, it is measured in variance form,

(c) Yes, it is measured, and (d) The error occurs when you reject the correct hypothesis during a hypothesis test. Among these options, the most appropriate answer is (a) Yes, it is measured in interval form.

This indicates that the dependent variable is continuous and can be measured on an interval scale, where the values can have a meaningful order and the differences between them are consistent.

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Answer:

10:04 AM

Step-by-step explanation:

1 hr and 59 minutes is 1 minute short of two hours therefore 8:05 + 2 = 10:05 - 1 = 10:04

Answer:

37cm = 370 millimeters

37cm = 0.37 meter

37cm = 0.00037 kilometers

Step-by-step explanation:

\(1cm = 10 millimeters \\\\1 cm = \frac{1}{100} meter\\\\1cm = \frac{1}{100000} kilometer\\\\\)

37cm = 370 millimeters

37cm = 0.37 meter

37cm = 0.00037 kilometers

Given that, in exercises 1-5, the given tableau represents a solution to a linear programming problem that satisfies the optimality criterion but is infeasible, we need to use the dual simplex method to restore feasibility.

The Dual Simplex method is a linear programming algorithm used to solve linear programming problems that have been modified in a way that the feasible region is unbounded. It is applied to maximization or minimization problems.

The procedure for restoring the feasibility of an infeasible solution using the Dual Simplex method is as follows:

Find the entry in the objective row of the current tableau with a negative coefficient.

Choose the pivot column as the column corresponding to the variable with the most negative coefficient. Determine the minimum ratio of the current solution to the non-negative entries in that column to identify the pivot row.

Update the tableau using the selected pivot row and pivot column through the usual pivoting procedure.

In the final tableau, if there are negative coefficients in the last row, the solution is infeasible. If there are no negative coefficients, the solution is feasible.

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