Is the sequence arithmetic? If so, identify the common difference.
14, 21, 42, 77, ...
yes; 7
yes; –7
yes; 14
no

Complete question :

The scatter plot shows the annual revenue for one airline. The equation of the trend line shown is y = 0.4x + 4.1, where x represents the number of years since 2000 and y represents the revenue in millions of dollars. What was the approximate difference between 2003 and 2007?

The difference in revenue was approximately million ______ dollars

Answer:

$1.6 million

Step-by-step explanation:

Given the trend line equation : y = 0.4x + 4.1

x = years since 2000 ; y = revenue in $ million ;

Approximate difference between 2003 and 2007

In year 2003 ; x = 2003 - 2000 = 3

y = 0.4(3) + 4.1

y = $5.3 million

In year 2007 ; x = 2007 - 2000 = 7

y = 0.4(7) + 4.1

y = $6.9 million

Aproximate difference :

$6.9 million - $5.3 million = $1.6 million

Answer:

The difference in revenue was approximately

1.6 million dollars.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

coefficient is a number before a letter in this case itz 5

Answer:

43

Step-by-step explanation:

just subract 60 and 17

Answer:

m=11

Step-by-step explanation:

Add 17 from 60

then divide 77 by 7

equals 11.

a) The number of ways to form a committee of 6 people from the department is 177,100.

b) The number of ways to form a committee of 6 people with an equal number of men and women is 54,600.

c) The number of ways to form a committee of 6 people with more women than men is 91,455.

a) To form a committee of 6 people from the department, we can choose 6 individuals from a total of 25 people (10 men + 15 women). The order in which the committee members are chosen does not matter, and we are not concerned with any specific positions within the committee. Therefore, we can use the concept of combinations.

The number of ways to choose 6 people from a group of 25 is given by the combination formula:

C(25, 6) = 25! / (6! * (25 - 6)!) = 25! / (6! * 19!) = 177,100

Therefore, there are 177,100 ways to form a committee of 6 people from the department.

b) In this case, we need to choose an equal number of men and women for the committee. We can select 3 men from the available 10 men and 3 women from the available 15 women. Again, the order of selection does not matter.

The number of ways to choose 3 men from 10 is given by the combination formula:

C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 120

Similarly, the number of ways to choose 3 women from 15 is:

C(15, 3) = 15! / (3! * (15 - 3)!) = 15! / (3! * 12!) = 455

To find the total number of ways to form a committee with an equal number of men and women, we multiply these two combinations:

Total = C(10, 3) * C(15, 3) = 120 * 455 = 54,600

Therefore, there are 54,600 ways to form a committee of 6 people with an equal number of men and women.

c) In this case, we need to form a committee with more women than men. We can choose 1 or 2 men from the 10 available men and select the remaining 6 - (1 or 2) = 5 or 4 women from the 15 available women.

For 1 man and 5 women:

Number of ways to choose 1 man from 10: C(10, 1) = 10

Number of ways to choose 5 women from 15: C(15, 5) = 3,003

For 2 men and 4 women:

Number of ways to choose 2 men from 10: C(10, 2) = 45

Number of ways to choose 4 women from 15: C(15, 4) = 1,365

The total number of ways to form a committee with more women than men is the sum of these two cases:

Total = (Number of ways for 1 man and 5 women) + (Number of ways for 2 men and 4 women)

     = 10 * 3,003 + 45 * 1,365

     = 30,030 + 61,425

     = 91,455

Therefore, there are 91,455 ways to form a committee of 6 people with more women than men.

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Answer:

-12x+3

Step-by-step explanation:

Multiply -3 to 4x first then do it for -1

So -3*4x = -12x and -3*-1 = 3

So -12x + 3

Hope this helps!

Answer:

the answer is -12x+3

From the given numbers, the greatest number is 23 × 10^126

The first number = 23 × 10^126

The second number = 23 × 10^86

The third number = 23 × 10^66

The fourth number = 23 × 10^3

The scientific notation is defined as the easiest method to represents the very smallest or the largest number. The scientific notation consist of a whole number multiplied by the power of ten

Here, the whole number is same in all cases, only the power of the 10 is different . To find the largest number we have to find the number with largest power of 10

The number with largest power of 10 = 23 × 10^126

Hence, the greatest number is 23 × 10^126

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The possible definitions of f(x) and g(x), considering the composition of the functions, are given as follows:

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

The functions for this problem are defined as follows:

As the composition of the functions is then given as follows:

\(h(x) = f(g(x)) = f(8x + 6) = \sqrt{8x + 6}\)

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Answer:

4,000 grams = 4 kilograms

Step-by-step explanation:

You have to divide the mass value by 1000.

Hope it helps :D

The amount of payment to be made into a sinking fund is $6,454.75 (rounded to the nearest cent) so enough will be present to accumulate $95,000 for 4.5 years with the given interest rate and compounding frequency.

A sinking fund is a type of investment used by organizations to set aside money over a period of time to pay off debts or fund future capital expenditures.

The main goal of a sinking fund is to reduce the risk of default by ensuring that there is enough money available to pay off debts when they come due. In this question, we are required to find the amount of payment to be made into a sinking fund so that enough will be present to accumulate the given amount.

Given information:
Present Value(PV)=0
Future Value(FV)=$95,000
Interest Rate(r)=4%/2=2% per half-year
Time(n)=4(1/2)*2=9 half years

The formula to find the payment size to be made into a sinking fund is:
PMT=FV/( ((1+r)^n-1) / r)

Substituting the given values in the formula:
PMT= $95,000/( ((1+2%)^(9*2)-1) / 2%)
PMT=$6,454.75

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The income elasticity for the household is -1.05.

Income elasticity measures how quantity demanded changes when there is a change in the income of a person / household

Income elasticity = percentage change in quantity demanded / percentage change in income

Income elasticity = -21% / 20 = -1.05

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Answer:

=35

Step-by-step explanation:

3(3) ^2 + 2(4)

= 3(9) + 8

= 35

Where you see a, substitute with 3 and where you see b, substitute with 4

Just follow the steps above.

\(\\ \sf\Rrightarrow 3a^2+2b\)

\(\\ \sf\Rrightarrow 3(3)^2+2(4)\)

\(\\ \sf\Rrightarrow 3(9)+8\)

\(\\ \sf\Rrightarrow 27+8\)

\(\\ \sf\Rrightarrow 35\)

Answer:

the meal cost $25.8 in total.

Step-by-step explanation:

9% of 20 is 1.8

20% of 20 is 4

20 + 1.8 + 4 = 25.8

May I have brainliest please? :)

An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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Based on the given algebraic expression, the value of b in 7.8b - 2.14 = -42.7 is -5.2

7.8b - 2.14 = -42.7

7.8b = -42.7 + 2.14

7.8b = -40.56

b = -40.56 / 7.8

b = -5.2

Check:

7.8b - 2.14 = -42.7

substitute the value of b into the equation

7.8(-5.2) - 2.14 = -42.7

-40.56 - 2.14 = -42.7

- 42.7 = -42.7

In conclusion, the solution to the algebraic expression 7.8b - 2.14 = -42.7 is b = -5.2

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If the IQ scores of adults in the United States follow a normal distribution with a mean of 98 and a standard deviation of 16 and Mensa is a high IQ society in which people who have IQs in the top 2% of the population can become a member, then the lowest IQ one could have in the U.S. and still be able to join Mensa is 130.8

To find the lowest IQ, follow these steps:

Therefore, the lowest IQ one could have in the U.S. and still be able to join Mensa is 130.8.

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Answer:

y  = 8x + 3

Step-by-step explanation:

The line we are describing here is line p;

 slope of line p = 8

  y- intercept = (0,3)

y-intercept of a line is the point where it crosses the y-axis. At this point, the x = 0

So;

  Slope of the line = 8

   y-intercept  =  3

Equation of the line;

       y  = mx + c

y and x are the coordinates

m is the slope

c is the y-intercept

      y  = 8x + 3

Answer:

pi

Step-by-step explanation:

First solve the integral

\(\int\ {(1+ cos x} )\, dx\)

\(\int\ {1} \, dx +\int\ {cos x} \, dx\)

\(\int\ {1} \, dx = x\) and \(\int\ {cos x} \, dx = sin x\)

x + sin x

Now consider the limit from 0 to π

\(\lim_{0 \to \\pi } (x+sin x)\)

(π +sin π) -(0 +sin 0)

sin π = 0 and sin 0 = 0

π-0

π

Answer:

\(\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx=\pi\)

Step-by-step explanation:

\(\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx\\\\=x+\sin x\biggr|^{\pi}_0\\\\=[\pi+\sin\pi]-[0+\sin0]\\\\=\pi\)

Remember your antiderivatives!

Answer:

6(4a + 5b) is the answer

In standard or decimal notation, the number 8.47 x 10^12 is written as 847 x 10^10. So there are 10 zeroes included in the standard or decimal notation of 8.47 x 10^12.

To convert from scientific notation to standard notation, we move the decimal point to the right or left by the number of places specified by the exponent . The exponent tells us how many places the decimal point should be moved.

The number 8.47 x 10^12 is written in scientific notation. In scientific notation, a number is expressed as a product of a coefficient and a power of 10. The coefficient is 8.47 in this case, and the power of 10 is 12.

The power of 10 indicates the number of zeros that are included in the number. In this case, 10^12 means 10 multiplied by itself 12 times, which is equal to 10,000,000,000,000.

Therefore, the number 8.47 x 10^12 is equal to 8.47 x 10,000,000,000,000.

= 847 x 10^10

So there are 10 zeroes included in the standard or decimal notation of 8.47 x 10^12.

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Answer:

-1

Step-by-step explanation:

-1

Answer:(6,-22)

Step-by-step explanation:

A for loop for print the integers 1 through 40, separated by spaces or new lines is represented by #include <iostream>

using namespace std;

int main(){ for(int count=1;count<=40;count++)

printf(" %d",count);}.

A for loop is a repetition control structure that allows you to efficiently write a loop that needs to execute a specific number of times. The structure for writing the " For loop" in C++ programming ,

#include <iostream> using namespace std; int main() { for (int i = 1; i <= 5; ++i) { cout << i << " "; } return 0; } .

We have to print the integers 1 through 40, separated by spaces or new lines. You may use only one variable, count which has already been declared as an integer. The required for-loop is written as the following: Input :

#include <iostream>

using namespace std;

int main(){

for(int count=1;count<=40;count++)

printf(" %d",count);}

Output : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

The for-loop description-

Hence, the required program code is founded.

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Answer:

Step-by-step explanation:

perimeter of a rectangle  = twice the length  plus  twice the width

P = 2L + 2W    equation 1      P = 86 ft

Given the length is seven feet more than the width

L = W + 7         equation 2

Substitute equation 2 into equation 1

P = 2(W+7) + 2W    =  86 ft

     2W +14 + 2W    =  86 ft

     4W    =  86  - 14

        W   =  72 / 4

        W   =  18 feet

The "errors-in-variables" problem, also known as measurement error, occurs in econometrics when one or more variables in a regression model are measured with error. In other words, the observed values of the variables do not perfectly represent their true values.

Consequences for the least squares estimator:

Attenuation bias: Measurement error in the independent variable(s) can lead to attenuation bias in the estimated coefficients. The least squares estimator tends to underestimate the true magnitude of the relationship between the variables. This happens because measurement errors reduce the observed variation in the independent variable, leading to a weaker estimated relationship.

Inconsistent estimates: In the presence of measurement errors, the least squares estimator becomes inconsistent, meaning that as the sample size increases, the estimated coefficients do not converge to the true population values. This inconsistency arises because the measurement errors affect the least squares estimator differently compared to the true errors.

Biased standard errors: Measurement errors can also lead to biased standard errors for the estimated coefficients. The standard errors estimated using the least squares method assume that the independent variables are measured without error. However, in reality, the standard errors will be underestimated, leading to incorrect inference and hypothesis testing.

To mitigate the errors-in-variables problem, econometric techniques such as instrumental variable (IV) regression, two-stage least squares (2SLS), or other measurement error models can be employed. These methods aim to account for the measurement errors and provide consistent and unbiased estimates of the coefficients.

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Answer:

its a fraction so it would be 3  3/7

Step-by-step explanation:

Working together, it will take Cleo and Phil 3

__

3

7

hours to paint the room.

Let x represent the number of hours it will take to paint the room while working together.

__x

8

1 __x

6

5 1

24( __x

8

1 __x

6

) 5 24(1)

3x 1 4x 5 24

7x 5 24

x 5 ___

24

7

or 3__

3

7

Answer:

hey thats kinda confusing but im sending this text insted of giving a wrong answer cuz i need points also SUB TO TECHNOBLADE

Step-by-step explanation:

"y" will represent the total cost per month

"x" will represent the number of movies watched in one month

There are two streaming plans:

Plan A

Has a monthly fee of $16 plus $2 per movie watched.

→ So if he watches no movies in a month, he will pay $16 and for each movie watched he will pay an extra $2

You can represent the monthly cost of plan A as follows:

Plan B

Has a monthly fee of $12 plus $3 for every movie watched.

The monthly cost of the plan can be expressed as follows:

For both equations the y-interceot represents the monthly fee of the plan and the slope of the line is the cost per movie.

To determine the number of movies (x) that would make both plans cost the same for one month using a graph, you have to draw both lines and determine the point where they intercept. The x-coordinate of said point will be the number of movies that make both plans cost the same.

To draw the lines you have to determine at least two points of the line.

The easiest point will be the y-intercept, for the second point, choose any value of x, replace it in the formula and calculate the corresponding value of y. Then plot both points and draw the line.

For plan A

y-intercept, x=0

The coordinates are (0,16)

Second point, for example, for x= 2 movies

The coordinates are (2,20)

For plan B

y-intercept, x=0

The coordinates are (0,12)

Second point, for example, for x=3

The coordinates are (3,21)

The red line represents the cost with respect to the number of movies for plan A

The purple line represents the cost with respect to the number of movies for plan B

Where both lines intercept indicates the point when both plans cost the same. Said point is (4,24), which means that when you watch x=4 movies both plans will cost $24 that month.

Answer:

3

Step-by-step explanation:

3 is the complete oposite of -1/3 in terms of slopes, therefore they are perpendicular to each other.