If the rate of inflation is 2.6% per year, the future price p (1) (in dollars) of a certain item can be modeled by the following exponential function, where t is the
number of years from today.
p(t)=1200 (1.026)
Find the current price of the item and the price 8 years from today.
Round your answers to the nearest dollar as necessary.


Current price ?$

Price 8 years from today?$

Yes because in the second expression, you use the distributive property, multiplying the 3 by the 3a and the 4 in parentheses. This equals 9a+12, which is the other expression

Answer:

none

Step-by-step explanation:

None, 106 is from the numbers being added and it is a right angle

The area of the composite figure is equal to 12.28 square kilometers

The composite figure can be observed to be made up of a triangle and a semicircle, so we shall calculate for the area of both shape and sum the results to get the total area of the composite figure as follows:

area of triangle = 1/2 × 3 km × 4 km = 6 km²

area of complete circle = 3.14 × 2 km × 2 km = 12.56 km²

area of semicircle = (12.56 km²)/2 = 6.28 km²

total area of the composite figure = 6 km² + 6.28 km²

total area of the composite figure = 12.28 km²

Therefore, the area of the composite figure is equal to 12.28 square kilometers

Read more about area here:https://brainly.com/question/21135654

#SPJ1

Answer:

The correct function is y = 4(.25^x).

we know that general term for gp is  [tex]a_{n}[/tex] = a [tex]r^{n-1}[/tex]

where r = common ratio

a = first term

putting values we get

8th term = 8x 64/729

= 0.702

hence the 8th term is 0.702

Monthly you should deposit approximately $241 to accumulate ​$ 85,000 in 18 ​years.

Given that,

f = 85000

r = 6% = 0.06/12 = 0.005

n = 17×12 = 204

We know that, a = (f×r)/((1+r)ⁿ⁻¹)

a is the annuity.

f is the future amount.

r is the interest rate per time period.

n is the number of time periods.

Here,

a = (85000×0.005)/((1.005)²⁰⁴⁻¹)

a = 240.6356536

a ≈ $241

Therefore, monthly you should deposit approximately $241 to accumulate ​$ 85,000 in 18 ​years.

Learn more about the annual percentage rate here:

brainly.com/question/10795072.

#SPJ1

The recipe will need 21 cups of sauce and three and a half teaspoons of oregano for 7 servings. The correct option is C.

The sauce to oregano ratio for five servings is equal to 15 cups and 2.5 teaspoons, respectively. For a single portion of the recipe, this computes to 3 cups and 0.5 teaspoons.

It should be noted that to attain the correct amount needed for seven servings, simply multiply each part of the ratio by seven. Consequently, you should use 21 cups of sauce and three and one-half teaspoons of oregano. All together, this recipe requires 21 cups of sauce and three and a half teaspoons of oregano for 7 servings.

Learn more about word problem on

https://brainly.com/question/21405634

#SPJ1

A linear equation to find the cost for a new customer to rent a bay is y = 2x + 10.

The cost for a new customer to rent a bay for 6 hours is equal to $22.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about the amount of money top golf charges a new customer, the cost can be modeled by this linear equation:

y = mx + c

y = 2x + 10

When x = 6 hours, the cost can be calculated as follows;

y = 2x + 10

y = 2(6) + 10

y = $22.

Read more on slope-intercept here: brainly.com/question/4074155

#SPJ1

Answer:

To calculate the average annual percentage gain, we need to use the formula:

Average annual percentage gain = ((Ending value / Beginning value)^(1/n) - 1) x 100%

where:

- Ending value = the value of the investment at the end of the period

- Beginning value = the value of the investment at the beginning of the period

- n = the number of years

In this case, the beginning value of the stocks is not given, so we cannot calculate the exact average annual percentage gain. We only know the profit and the ending value. However, we can make an estimate assuming that the profit is equal to the gain, i.e., there were no transaction costs or other fees.

If the profit was $3,250 and the ending value was $10,500, then the beginning value was:

Beginning value = Ending value - Profit

Beginning value = $10,500 - $3,250

Beginning value = $7,250

The number of years is given as 4.

Using the formula above, we can estimate the average annual percentage gain as:

((10,500 / 7,250)^(1/4) - 1) x 100%

= (1.1267^(0.25) - 1) x 100%

= (1.0266 - 1) x 100%

= 0.0266 x 100%

= 2.66%

Therefore, the estimated average annual percentage gain is 2.66%.

Step-by-step explanation:

Answer:

Step-by-step explanation:The six sample minimums are 15, 15, 15, 18, 18, and 20.

To find the mean of all six sample minimums, we add them up and divide by 6:

(15 + 15 + 15 + 18 + 18 + 20) / 6 = 16.1667

So the mean of all six sample minimums is $16,166.67.

The population minimum is the smallest cost among the four cars, which is $15,000.

The sample minimum is a biased estimator of the population minimum. Since the samples are of size 2, the probability of obtaining the population minimum as the sample minimum is only 1/3 (when the minimum of the two cars selected is the population minimum). Therefore, the sample minimum tends to underestimate the population minimum.

The two inequalities that the graph represents are:

y < -x + 4

y ≤ ²/₃x - 4

An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

The first inequality is the one with the dashed line and a y-intercept of 4 and so since shaded below line, we will use the symbol <.

The slope from two coordinates on the line (0, 4) and (4, 0) is:

(0 - 4)/(4 - 0) = -1

Thus, inequality is:

y < -x + 4

The first inequality is the one with the solid line and a y-intercept of -4 and so since shaded below line, we will use the symbol ≤.

The slope from two coordinates on the line (0, -4) and (6, 0) is:

(0 + 4)/(6 - 0) = 2/3

Thus, inequality is:

y ≤ ²/₃x - 4

Read more about Inequality Graph at: https://brainly.com/question/11234618

#SPJ1

Answer:

meaning that you're answer would be $7.34 please make brainliest

Step-by-step explanation:

The surface area of each square pyramid, we used the formula Surface Area = Base Area + 4 x (1/2 x Base x Height of Face) is 1049.2mm², 1285.8mm² and 2100mm². The cost to cover each pyramid was $1.05, $1.29 and $2.10.

To calculate the surface area of each pyramid, we need to use the formula

Surface Area = Base x Height of face + 2 x ((Base/2) x Slant Height)

For the small pyramid, we have

Surface Area = 20 x 25 + 2 x ((20/2) x 26.46)

Surface Area = 500 + 2 x 10 x 26.46

Surface Area = 1049.2 mm²

Cost to cover the small pyramid

Cost = Surface Area x 0.001

Cost = 1049.2 x 0.001

Cost = $1.05

For the medium pyramid, we have

Surface Area = 20 x 40 + 2 x ((20/2) x 42.43)

Surface Area = 800 + 2 x 10 x 42.43

Surface Area = 1285.8 mm²

Cost to cover the medium pyramid

Cost = Surface Area x 0.001

Cost = 1285.8 x 0.001

Cost = $1.29

For the large pyramid, we have

Surface Area = 30 x 40 + 2 x ((30/2) x 50)

Surface Area = 1200 + 2 x 15 x 50

Surface Area = 2100 mm²

Cost to cover the large pyramid

Cost = Surface Area x 0.001

Cost = 2100 x 0.001

Cost = $2.10

To know more about surface area:

brainly.com/question/18727714

#SPJ1

The amount of sales tax he collected from the office services would be =$658.43

To calculate the amount of sales tax,the percentage tax amount should be determined as follows.

The total receipts from the office services = $1861.16

The amount that is for labor = $1240

The amount for parts = 1861.16-1240

= $621.16

The tax amount = 6/100 × 621.16

= 3726.96/100

= $37.27

Therefore the amount sale tax = 621.16+37.27 = $658.43

Learn more about percentage here:

https://brainly.com/question/24339661

#SPJ1

It seems there are two numbers missing between "15 cm summ" and "12 cm". Please provide the complete values so I can help you solve the problem.

The required statements that are true for the given function are mentioned below.

There are many possible statements that could be true for the function h, given the information provided. Here are a few examples:

is a linear function that passes through the points (-2, 2) and (8, 19).

h is a quadratic function that has a maximum value of 25 at x = 11.

h is a piecewise function that equals 1 for -3 ≤ x ≤ 0, 2x + 3 for 0 < x ≤ 4, and 19 - x for 4 < x ≤ 11.

h is a logarithmic function that equals 1 at x = -3 and approaches 25 as x approaches 11.

Each of these statements is consistent with the given domain, range, and function values at x = -2 and x = 8. There are many other possible statements that could be true for h as well.

Learn more about function here:

brainly.com/question/21145944

#SPJ1

The total time taken to walk the museum is t = 3/4 of an hour

Given data ,

Let the time spent at the first 3 exhibits = 3/4 + 3/4 + 3/4 = 9/4 hours

Let the time spent at the museum after the first 3 exhibits = 1 1/2 = 3/2 hours

Total time spent at the museum = 9/4 + 3/2 = (9/4 + 6/4) = 15/4 hours

Since the museum closes after you spend a total of 4 1/2 hours at the museum, we can subtract the total time spent at the museum from the closing time to find the time it took you to walk to the museum:

Closing time - Total time spent at the museum = 4 1/2 - 15/4

On simplifying the equation , we get

A = 9/2 - 15/4

On subtracting the fractions , we get

9/2 - 15/4 = (18/4) - (15/4) = 3/4

Hence , it took you 3/4 hour, or 45 minutes, to walk to the museum

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Let's call the cost of each video game "x". We can set up two equations based on the information given:

4x + 2(0.01) = 20.92 (the 0.01 represents the commission fee for each phone)

4x = 20.92 - 0.02

4x = 20.90

x = 5.225

So each video game costs $5.225.

We can double-check our answer using the information about the friend's sales:

4(5.225) + 3(0.01) = 23.44

20.90 + 0.03 = 23.44

23.44 = 23.44

So our answer is correct.

The value of x and y are,

x = 8 and y = 4

We have to given that;

Tim has $20 to buy snacks for 12 people in an office.

And., Tim is buying bags of pretzels that cost $1.50 per bag and bags of crackers that cost $2.00 per bag.

Let x represent bags of pretzels.

And, y represent bags of crackers.

Hence, We can formulate;

x + y = 12  .., (i)

And, 1.5x + 2y = 20  .. (ii)

From (i);

x = 12 - y

Plug in (ii):

1.5 (12 - y) + 2y = 20

18 - 1.5y + 2y = 20

18 + 0.5y = 20

0.5y = 2

y = 2/0.5

y = 4

And, x = 12 - 4

x = 8

Thus, The value of x and y are,

x = 8 and y = 4

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The real exchange rate is 0.75.

It is not possible to make a profit by buying apples in one country and selling them in another.

We have,

To find the real exchange rate, we need to compare the price of apples in the two countries in terms of their respective currencies.

In the U.S., a bushel of apples costs $15.00.

In Japan, the same apples cost 1,600 yen.

Using the exchange rate of 80 yen per dollar, we can convert the cost in yen to dollars:

1,600 yen / 80 yen per dollar

= $20.00

So, the price of a bushel of apples in Japan is equivalent to $20.00 in the U.S.

The real exchange rate is the ratio of the prices of the same goods in two different countries, taking into account the exchange rate.

In this case, the real exchange rate is:

Real exchange rate = Price in U.S. / Price in Japan

= $15.00 / $20.00

= 0.75

This means that it takes 0.75 U.S. dollars to buy the same goods in Japan which would cost 1 Japanese yen.

To determine if there is an arbitrage opportunity, we need to compare the real exchange rate with the actual exchange rate.

If the real exchange rate is greater than the actual exchange rate, there is an arbitrage opportunity for someone to buy the good in one country and sell it in another country for a profit.

However, if the real exchange rate is less than the actual exchange rate, there is no arbitrage opportunity.

In this case,

The real exchange rate is 0.75, while the actual exchange rate is 80 yen per dollar, or 0.0125.

Since the real exchange rate is less than the actual exchange rate, there is no arbitrage opportunity.

Therefore,

The real exchange rate is 0.75.

It is not possible to make a profit by buying apples in one country and selling them in another.

Learn more about exchange rates here:

https://brainly.com/question/29562028

#SPJ1

Answer:correct answers 0.42

2.73

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):

-6u^2 - 5u + 3 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -6, b = -5, and c = 3. Substituting these values, we get:

u = (5 ± sqrt(5^2 - 4(-6)(3))) / 2(-6)

u = (5 ± sqrt(109)) / (-12)

Therefore, either:

sin(θ) = (5 + sqrt(109)) / (-12)

or:

sin(θ) = (5 - sqrt(109)) / (-12)

Using trigonometric identities, the given expression, tan(x) × cos(x), simplified to a single trigonometry is sin(x)

From the question, we are to simplify the given trigonometric expression

From the given information

The given expression is

tan(x) × cos(x)

From trigonometric identities, we know that

tan(x) = sin(x) / cos(x)

Now,

Substituting this value in the given expression

tan(x) × cos(x)

We get

sin(x) / cos(x) × cos(x)

Simplifying further

sin(x) / cos(x) × cos(x) = sin(x)

Hence,

The simplified expression is sin(x)

Learn more on Simplifying trigonometric identities here: https://brainly.com/question/29722989

#SPJ1

The percent increase from 2013 to 2014 is given as follows:

39%.

The percent increase from 2013 to 2014 is obtained applying the proportions in the context of the problem.

The amounts were of 631 in 2013 and 877 in 2014, hence the percentage of 2014's amount relative to 2013's amount is given as follows:

877/631 x 100% = 139%.

The initial amount has a percentage of 100%, hence the percent increase from 2013 to 2014 is given as follows:

139% - 100% = 39%.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The dragging of the tiles to the appropriate places is given below.

1. 5.83 m/s > magnitude 4.5 m/s, direction angle 55˚ magnitude 3m/s, direction angle 135°

2. 4.05 m/s > magnitude 3.5 m/s, direction angle 35˚ magnitude 4 m/s, direction angle 150˚

3. 5.29 m/s > magnitude 6 m/s, direction angle 120˚ magnitude 2 m/s, direction angle 240˚

4. 3.32 m/s > magnitude 3 m/s, direction angle 70° magnitude 5 m/s, direction angle 210˚

Learn more about vector on

https://brainly.com/question/12980270

#SPJ1

Since John cannot buy a fraction of a can, he needs to round up to the nearest whole number. So, John needs at least 5 cans of paint to cover the entire wall as per the height and length.

To calculate the area of the wall, we need to multiply the height and the length of the wall.

From the diagram, we can see that the height of the wall is 2 meters and the length is 5 meters.

So the total area of the wall is:

Area = height x length

Area = 2 meters x 5 meters

Area = 10 square meters

To convert this to square feet, we can use the conversion factor:

1 square meter = 10.764 square feet

So:

Area = 10 square meters x 10.764 square feet/square meter

Area = 107.64 square feet

Since 1 can of paint covers 24 square feet, John needs:

Number of cans = Area ÷ Coverage per can

Number of cans = 107.64 square feet ÷ 24 square feet/can

Number of cans = 4.485 cans

Thus, John needs at least 5 cans of paint to cover the entire wall.

For more details regarding area, visit:

https://brainly.com/question/27683633

#SPJ1

Your question seems incomplete, the probable complete question is:

John needs to paint one wall in his school. He knows that 1 can of paint covers an area of 24 square feet.

John uses a meter stick to measure the dimensions of the wall as shown.

[1 meter = approximately 39 inches]

What is the fewest number of cans of paint John can use to paint the wall?

Using the statistical tool, the following were arrived at:

It should be noted that when arranged from lowest to highest, the IQR represents the central 50% of values.

Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).

These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.

Learn more about statistic on

https://brainly.com/question/27829654

#SPJ1

1. The diagram below shows the net of a pyramid with all its labeled sides.

2. The surface area; S = L + B

3. The total surface area = 22.44 cm².

To calculate the total surface area, we use the formula to find Area = (1/2) x b x h.

After we've found the area, we say

Total surface area = 1/2 x 2.24 x (3 x 4) + (3)²

= 22.44 cm²

The above answers are based on the full questions below;

A pyramid with the sides of 2.24 cm and a height of 4 and the base of 3.

1. Draw a net for the pyramid. Label all sides with measurement?

2. Write an expression for the surface area of the pyramid and then find the total surface area

Find more exercises on solving total surface area of pyramids;

https://brainly.com/question/16493393

#SPJ1

Answer:

Step-by-step explanation: