what is the slope of the line that passes through the points (-1,-7) and (-2,-5)

The given function is f(x) = 15(1.02)^x, where x is the number of years from the date at which money is initially deposited.

This means that $15 were initially deposited into the account, and the amount grows at an annual rate of 2% (which is represented by 1.02 being raised to the power of x).

Therefore, the correct answer is: $15 were initially deposited into the account, which grows at an annual rate of 2%.

Hope I helped you...

Hence, the sum of the given sequence 150+120+96+… is 609.6.

Part A: Mary seats are in the theater

To find the number of seats in the theater, we need to find the sum of seats in all the 35 rows.

For this, we can use the formula of the sum of n terms of an arithmetic sequence.

a = 20

d = 2

n = 35

The nth term of an arithmetic sequence is given by the formula,

an = a + (n - 1)d

The nth term of the first row (n = 1) will be20 + (1 - 1) × 2 = 20
The nth term of the second row (n = 2) will be20 + (2 - 1) × 2 = 22

The nth term of the third row (n = 3) will be20 + (3 - 1) × 2 = 24and so on...

The nth term of the nth row is given byan = 20 + (n - 1) × 2

We need to find the 35th term of the sequence.

n = 35a

35 = 20 + (35 - 1) × 2

= 20 + 68

= 88

Therefore, the number of seats in the theater = sum of all the 35 rows= 20 + 22 + 24 + … + 88= (n/2)(a1 + an)

= (35/2)(20 + 88)

= 35 × 54

= 1890

There are 1890 seats in the theater.

Part B:Determine the nth term of the geometric sequence. 1,3,9,27, …

The nth term of a geometric sequence is given by the formula, an = a1 × r^(n-1) where, a1 is the first term r is the common ratio (the ratio between any two consecutive terms)an is the nth term

We need to find the nth term of the sequence,

a1 = 1r

= 3/1

= 3

The nth term of the sequence

= an

= a1 × r^(n-1)

= 1 × 3^(n-1)

= 3^(n-1)

Hence, the nth term of the sequence 1,3,9,27,… is 3^(n-1)

Part C:Find the sum, if it exists. 150+120+96+…

The given sequence is not a geometric sequence because there is no common ratio between any two consecutive terms.

However, we can still find the sum of the sequence by writing the sequence as the sum of two sequences.

The first sequence will have the first term 150 and the common difference -30.

The second sequence will have the first term -30 and the common ratio 4/5. 150, 120, 90, …

This is an arithmetic sequence with first term 150 and common difference -30.-30, -24, -19.2, …

This is a geometric sequence with first term -30 and common ratio 4/5.

The sum of the first n terms of an arithmetic sequence is given by the formula, Sn = (n/2)(a1 + an)

The sum of the first n terms of a geometric sequence is given by the formula, Sn = (a1 - anr)/(1 - r)

The sum of the given sequence will be the sum of the two sequences.

We need to find the sum of the first 5 terms of both the sequences and then add them.

S1 = (5/2)(150 + 60)

= 525S2

= (-30 - 19.2(4/5)^5)/(1 - 4/5)

= 84.6

Sum of the given sequence = S1 + S2

= 525 + 84.6

= 609.6

To know more about geometric visit:

https://brainly.com/question/29199001

#SPJ11

Compound interest formula:

A = P (1+r/n)^nt

Where:

A = total amount

P = principal investment

r= interest rate in decimal form = 2/100 = 0.02

t= years

n= number of compounding periods in a year= 12

Replacing:

A = 30,000 (1+0.02/12)^4x12

A = 30,000 (1.001666667)^48

A= 32,496.45

Answer:

3.75

Step-by-step explanation:

Answer:

  6

Step-by-step explanation:

You want the x-coordinate of the midpoint of segment AB with endpoint coordinates A(21, 5) and B(-9, -13).

The midpoint of a line segment has coordinates that are the average of the endpoint coordinates:

  M = (A +B)/2

  M = ((21, 5) +(-9, -13))/2 = (12, -8)/2

  M = (6, -4)

The midpoint of AB is (6, -4).

The x-coordinate of the midpoint is 6.

Answer:

Step-by-step explanation:

Given,

Number of words Lucy can type in 5 minutes

= 300 words

So,

Number of words Lucy can type in 1 minute

\( = \frac{300}{5} \: words\)

= 60 words

Therefore,

Number of words Lucy can type in 27 minutes

= (60 × 27) words

= 1,620 words

Hence, Lucy can type 1620 words in 27 minutes.

The graph of g is Transformation up 7 units.

what is Transformation?

A graph transformation is a method for altering an existing graph or graphed equation to create a different version of the graph that follows. The modification of algebraic equations is a typical form of algebraic issue.

solution:

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

g(x) = f(x) + k

Also, we have the value of k to be

k = 7

From the question, we can interpret g(x) = f(x) + k as f(x) is shifted up by k units

This means that

g(x) = f(x) + k

So, we have

g(x) = f(x) + 7

Hence, the transformation is (a) translated up 7 units

To learn more about Transformation from the given link

https://brainly.com/question/1620969

#SPJ1

I got 6x+3..................................................                                              

Therefore, You can add approximately 0.228 gallons of water to the mix and still remain within the specified W/C ratio of 0.45.

The total weight of the mix is 22 + 41 + 57 + 8 = 128 lbs. To calculate the current W/C ratio, we need to convert the weight of water to gallons. One gallon of water weighs approximately 8.34 lbs. Therefore, the current weight of water is 8/8.34 = 0.96 gallons. The current W/C ratio is 0.96/128 = 0.0075. To remain within spec with a W/C ratio of 0.45, we can use the formula: (water weight + x)/(total weight) = 0.45, where x is the additional weight of water needed. Solving for x, we get x = (0.45 x 128) - 8 = 50.4 lbs. Converting to gallons, this is 50.4/8.34 = 6.05 gallons. Therefore, 6.05 gallons of water can be added to the mix and still remain within spec.
To determine how many gallons of water can be added to the mix and still remain within the specified W/C ratio of 0.45, follow these steps:
1. Calculate the required amount of water for the specified W/C ratio: Cement weight x W/C ratio = 22 lbs. x 0.45 = 9.9 lbs. of water.
2. Subtract the initial water content from the required amount: 9.9 lbs. - 8 lbs. = 1.9 lbs. of additional water needed.
3. Convert the additional water weight to gallons: 1.9 lbs. / 8.34 lbs./gallon (water density) ≈ 0.228 gallons.

Therefore, You can add approximately 0.228 gallons of water to the mix and still remain within the specified W/C ratio of 0.45.

To know more about addition visit :

https://brainly.com/question/4721701

#SPJ11

There are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

According to the given question.

Total number of items, n = 12

Total numbers of items to be selected, r = 5

Since, we have to determine the number of different groups of 5 items that can be selected from 12 distinct items. So, we will find the number of different groups by permulation formula i.e.

\(^{n} P_{r} = \frac{n!}{(n-r)!}\)

Where,

\(^{n} P_{r}\) is the total number of permutations.

n is the total number of objects.

r is teh total number of objects to be selected.

Therefore,

The number of different groups or permutaions of 5 items that can be selected from 12 distinct group

\(^{12} P_{5}\)

\(= \frac{12!}{(12-5)!}\)

\(= \frac{12!}{7!}\)

\(= \frac{12\times11\times10\times9\times8\times7!}{7!}\)

= 12 × 11 × 10 × 9 × 8

= 95040

Hence, there are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

Find out more information about permuation here:

https://brainly.com/question/1216161

#SPJ4

Answer:

-3/2

Step-by-step explanation:

you can use the rise over run method to find the slope of this line

There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

To know more about types of sampling visit :

https://brainly.com/question/12902833?referrer=searchResults

#SPJ4

The graph of the function:

Can be obtained by using the parent function:

Whose graph is shown below:

We must first turn x into -x by making a reflection over the y-axis. This way, the function becomes:

And the graph is:

Finally, we just add 4 to x to translate the graph 4 units to the right to get our desired function:

The graph is shifted 4 units to the right as shown:

Answer:

x = - 6 , x = 4

Step-by-step explanation:

the absolute value function always gives a positive value but the expression inside can be positive or negative , that is

2x + 2 = 10 or - (2x + 2) = 10

solving both

2x + 2 = 10 ( subtract 2 from both sides )

2x = 8 ( divide both sides by 2 )

x = 4

or

- (2x + 2) = 10

- 2x - 2 = 10 ( add 2 to both sides )

- 2x = 12 ( divide both sides by - 2 )

x = - 6

The simulation can be used to assess the likelihood of obtaining the observed proportion of seniors interested in the senior trip (42 out of 80) if the true proportion is actually 55%.

By simulating the survey process 200 times with a sample size of 80 and assuming a 55% interest rate, we can compare the distribution of simulated proportions to the observed proportion. If the observed proportion falls within the range of simulated proportions, it suggests that the claim made by the senior class president is plausible.

However, if the observed proportion is significantly different from the simulated proportions, it would cast doubt on the president's claim. The absolute difference value (0.450306) mentioned in the question is likely a measure of the discrepancy between the observed and expected proportions, indicating the extent of the deviation from the claim.

learn more about sample size at https://brainly.com/question/30647570

#SPJ1

The annual interest rate on the loan is 0.02 or 2%.

To find the annual interest rate on the loan, we need to use the formula for simple interest:

I = Prt

where:

I is the interest,

P is the principal (the amount of the loan),

r is the annual interest rate (expressed as a decimal),

t is the time in years

We know the following information:

I = $240

P = $4000

t = 3

We can use this information to set up the equation and solve for r:

240 = 4000 * r * 3

240 = 12000r

r = 240/12000

r = 0.02

Therefore, the annual interest rate on the loan is 0.02 or 2%.

To learn more about simple interest refer to:

brainly.com/question/25845758

#SPJ1

The missing side length is 17 and the side lengths 8, 15, and 17 form a Pythagorean triple.

Side lengths: 8, 15

Missing side length: 17

Yes, the side lengths form a Pythagorean triple. The side lengths 8, 15, and 17 form a Pythagorean triple because 8^2 + 15^2 = 17^2.

To answer this question, we first need to determine if the side lengths 8, 15 and the missing side length form a Pythagorean triple. To do this, we use the Pythagorean theorem which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side. If this is true, then the side lengths form a Pythagorean triple.

In this case, we can plug in the side lengths 8 and 15 into the Pythagorean theorem. 8^2 + 15^2 = 17^2. Since the equation is true, this means that the side lengths 8, 15 and 17 form a Pythagorean triple. Therefore, the missing side length is 17.

Learn more about length here

https://brainly.com/question/13194650

#SPJ4

Answer:

The set of all solutions. 

Logarithmic differentiation: This is a technique used to differentiate functions that are in the form of products and quotients. The logarithmic differentiation technique involves taking the natural logarithm of both sides of an equation before differentiating them.

In order to use logarithmic differentiation to differentiate the given functions, we must first find the natural logarithm of both sides. We then differentiate both sides with respect to x and simplify the expression. Let us differentiate each function separately.

y = x^(x)Taking the natural logarithm of both sides we get:

ln(y) = x ln(x)We now differentiate both sides of the equation with respect to x using the chain rule and simplify the expression as follows:

dy/dx * (1/y) = ln(x) + 1dy/dx = y (ln(x) + 1)

dy/dx = x^(x) (ln(x) + 1)ii. v = 6x (6nx + 1)

Taking the natural logarithm of both sides we get:

ln(v) = ln(6x) + ln(6nx + 1)

To know more about differentiation visit:

https://brainly.com/question/13958985

#SPJ11

We need to find which payment method gives us more money at the end of 100 days.

It is better to be paid by the payment method where there is an increase of  cents by 2 times in salary everyday.

First payment method

Earning $5 dollars per day for 100 days.

So, total amount at the end of 100 days is \(5\times 100=\$500\)

Second payment method

Earning 10 cents on day 1 and an additional 10 cents after each day.

So,

a = First element of sequence = 0.05$

r = Common ratio = \(\dfrac{0.10}{0.05}=\dfrac{0.20}{0.10}=2\)

n = Number of terms = 100

\(S_n=\dfrac{a(r^n-1)}{r-1}\\ =\dfrac{0.05(2^{100}-1)}{2-1}\\ =\$6.38\times 10^{28}\)

So, in the second payment method an \(\$6.38\times 10^{28}\) is earned.

Hence, the second payment method is better.

Learn more:

https://brainly.com/question/17147305

https://brainly.com/question/12719739

Answer:

6 ft

Step-by-step explanation:

Let the width = w

Then the length = 4w - 3

perimeter = 2(length + width)

perimeter = 2(4w - 3 + w)

perimeter = 2(5w - 3)

perimeter = 10w - 6 = 54

10w - 6 = 54

10w = 60

w = 6

Answer: The width is 6 ft

Answer:

0 Joules (No work)

Step-by-step explanation:

The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the car is 100 newtons, but the car does not move, so the distance over which the force is applied is 0 meters.

Therefore, the amount of work done on the car is 100 newtons * 0 meters = 0 joules. This means that no energy has been transferred to or from the car as a result of the force applied to it.

Answer:

1. Perimeter: 26 Area: 30

2. Perimeter: 20 Area: 25

3. Perimeter: 38 Area: 144

Step-by-step explanation:

Perimeter you add all the sides and area you multiply length times height.

Answer:

Circumference. hope this helped!

Answer:

i hope it's help

Step-by-step explanation:

5. x = -4

6.  x > 5/2

7.  x = -5

8.  x = 40/13 = 3.077

Answer:

($) 60 is the profit per item when the selling price is reduced by 20%

Step-by-step explanation: 20% of 700 is 140.

The original profit is 700 - 500 = 200. The selling price is 140 less, Subtract 140 from 200. That leaves a profit of 60. (Not necessarily dollars, as the currency was not given in the question.)