Round to 1 significant figure:

Answer:

The formula for calculating the future value of an investment with compound interest is:

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

where A is the future value, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period in years.

In this case, P = $2500, r = 0.0125 (1.25% as a decimal), n = 12 (since the interest is compounded monthly), and t = 4.

Plugging these values into the formula, we get:

A = 2500(1 + 0.0125/12)^(12*4) ≈ $2,628.11

Therefore, the answer is $2628.11.

Answer: $ 2628.11

Step-by-step explanation:

Compound interest is nasty.

the formula (which you need to memorize) is:

[tex]A = P(1+\frac{r}{n} )^t^n[/tex]

A is the final amount, P is the principle, (original amount of money invested), r is the rate of return (as a decimal NOT percent), n is the number of times compounded annually, and t is the time, (in years), invested.

With all this information, our formula becomes:

[tex]A = 2500(1+\frac{0.0125}{12} )^4^8[/tex]

solving, we get A ≅ 2628.11

This corresponds to answer choice C

Answer:

x < 1.175

Step-by-step explanation:

-0.4x + 1.27 > 0.8

-0.4x > -0.47

x < 1.175

In order to find the upper and lower bounds of a rounded number:

The upper and lower bounds can be found by dividing the degrees of accuracy by 2 and then subtracting and adding with the value to give the lower and upper bounds respectively.

Kindly check the above explanation inorder to know how to calculate the value as your information is incomplete

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How does one find the upper and lower bound of a variable

The perimeter of the triangle is 23.623 units.

What is perimeter of triangle?

Finding the distance around a triangle entails determining its perimeter. The distance formula can be used to calculate the side lengths if you don't already know all of them. The simplest way to find a triangle's perimeter is to add up all of its sides' lengths.

The distance between two points (x1,y1) and (x2,y2) can be determined using the following formula: √(x₂-x₁)² + (y₂ - y₁)²

Let the given vertices are (-7, -2), (-2, -5) , and (2, 3).

Distance formula for two points is = √(x₂-x₁)² + (y₂ - y₁)²

Using the formula,

AB = √((-2)-(-7))² +((-5)-(-2))²

= √(-2+7)² + (-5+2)²

= √5² + (-3)²

= √25 + 9

= √31

Similarly, BC = √(2 - (-2))² + (3-(-5))²

= √(2+2)² + (3+5)²

= √4² + 8²

= √16+64

= √80

CA = √((-7)-2)² + (-2 + 3)²

= √(-9²) + 1

= √81+1

=√82

Perimeter of triangle = AB + BC + CA

= √31 +√81 +√82

= 5.5677 + 9 + 9.0553

= 23.623

Therefore, the perimeter of the triangle is 23.623 units.

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The given piecewise function has a range of:

Range = {46, 48, 50, 52, 54, 56}.

The range of a function is the set of all possible output values, or the set of all y-coordinates that correspond to the x-coordinates in the domain of the function.

It is, in other words, the entire set of values that the function is capable of returning as its result.

From the given piecewise function, we can see that the y-coordinates of the function are limited to the values 46, 48, 50, 52, 54, and 56.

These values correspond to the y-intercepts of each of the line segments in the graph.

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Answer:

Each student will have passed 17 tests; It will take 3 weeks.

Step-by-step explanation:

The explanation is in the picture.

The  probability that this particular fuel pump system  when put into the required condition would not remain functional  for the full 50 hours is 0.0199.

Therefore, the probability of a fuel pump failing in a mission can be evaluated using the formula designed for probability of failure in a system with two pumps in series connection

P(failure) = P(pump 1 fails) + P(pump 2 fails) - P(both pumps fail)

Here  
P(pump 1 fails) = P(pump 2 fails) = 0.01
P(both pumps fail) = (0.01)² = 0.0001.

Now,

P(failure) = 0.01 + 0.01 - 0.0001 = 0.0199

The  probability that this particular fuel pump system  when put into the required condition would not remain functional  for the full 50 hours is 0.0199.

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Answer:3

Step-by-step explanation:

1+2=3

Answer:

To find out how many gallons of paint are needed to cover the walls, we need to first find the total area of the walls.

The four walls are rectangles with a length of 20 feet and a height of 12 feet. So, the area of one wall is:

20 feet x 12 feet = 240 square feet

Since there are four walls, the total area of the walls is:

4 x 240 square feet = 960 square feet

We know that one gallon of paint can cover approximately 320 square feet. To find how many gallons of paint are needed, we can divide the total area of the walls by the area covered by one gallon of paint:

960 square feet ÷ 320 square feet per gallon = 3 gallons of paint

Therefore, you need approximately 3 gallons of paint to cover the walls.

The Toy Train Collectors' Club has 140 members who are 42 years of age or younger.

To find the number of members who are 42 years of age or younger, we need to look at the bars in the histogram that represent these age groups. Specifically, we need to add up the heights of the bars that represent members aged 0-42 years old.

The histogram shows that there are 30 members in the age group 0-10,

50 members in the age group 11-20,

40 members in the age group 21-30,

20 members in the age group 31-40, and

15 members in the age group 41-50.

To find the number of members who are 42 years of age or younger, we need to add up the heights of the bars that represent members aged 0-42 years old, which is 30+50+40+20 = 140.

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Answer:

1.5

Step-by-step explanation:

Move the decimal point two places to the left to go from a percentage to a decimal.

The error in the proportion is the second line should be 2x + 18 = 3x making the final answer 18 = x

The error in the solution of the proportion shown can be calculated as follows:

Therefore, let's solve the equation to know the error made.

2 / 3 = x / x + 9

cross multiply

2(x + 9) = 3x

open the brackets

2x + 18 = 3x

subtract 2x from both sides of the equation

2x + 18 = 3x

2x - 2x + 18 = 3x - 2x

x = 18

Therefore, he made mistake in the second line, it should be  2x + 18 = 3x making the final answer 18 = x

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Answer:

3×4-8=b

Step-by-step explanation:

The total number of batteries fatima has is :

3×4= 12

She has 12 batteries but she gave her brother 8

12-8=4

And batteries represent b

So the equation is

3×4-8=b

The side length of the square that has the given area would be = 1/4

To calculate the side length of a given square the formula for the area of a square should be used. That is;

Area of a square = a²

where;

a = length = ?

area = 1/16

That is = 1/16 = a²

a = √1/16

= 1/4

Therefore the side of the square whose area is given should have the length of 1/4

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The two quantities needed to determine the total amount of money Monte paid his employees this month are:

A. the hourly salary of each employee

C. the number of hours each employee worked this month.

With four employees at the Monte Bakery, who earn a different hourly wages, to work out the total salary for the month, Monte needs to multiply the hourly wage of each employee by the total number of hours each worked.

Thus, in this mathematical operation, we first use multiplication and then add each individual employee's total salary to sum the total salary for the month.

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The closest answer among the given options is B) 2,100.

To estimate the number of people in the town who would name chocolate as their favorite ice-cream flavor, we can use proportions. We know that 7 out of 50 people in the sample named chocolate as their favorite. To find the proportion of chocolate lovers in the sample, we can divide the number of chocolate lovers by the total number of people surveyed:

7 chocolate lovers / 50 people surveyed = 0.14

Now, we can apply this proportion to the total population of the town to estimate the number of chocolate lovers:

0.14 * 14,878 (total population) ≈ 2,082.92

Since we can't have a fraction of a person, we can round this number to the nearest whole number:

Approximately 2,083 people in the town would be expected to name chocolate as their favorite ice-cream flavor.

The closest answer among the given options is B) 2,100.

the first thing that you're supposed to do is multiply all the given measurements as we know that volume is equal to length times with times height so you have to multiply all the three given measurements the answer that you get after multiplying those three given measurements you have to round your answer to the nearest two decimal places therefore after they'll call my they need to be two numbers just after the coma

The function after each transformation is given as follows:

1. Reflected across the x-axis: f(x) = -|x + 3| + 7.

2. Translated left 4 units: f(x) = |x + 7| - 7.

3. Translated down 3 units: f(x) = |x + 3| - 10

The function for this problem is defined as follows:

f(x) = |x + 3| - 7.

When the function is reflected across the x-axis, we have that the entire function is multiplied by -1, hence:

f(x) = -(|x + 3| - 7)

f(x) = -|x + 3| + 7.

When the function is translated left 4 units, we have that x -> x + 4, hence:

f(x) = |x + 4 + 3| - 7

f(x) = |x + 7| - 7.

When the function is translated down 3 units, we have that f(x) -> f(x) - 3, hence:

f(x) = |x + 3| - 7 - 3

f(x) = |x + 3| - 10

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Answer:

840 feet

Step-by-step explanation:

1 yard = 3 feet

280 yards = x

x = 280 × 3

x = 840 feet

The expression[tex](2x^3y)(3x^4y^2)[/tex] simplifies to [tex]6x^7y^3[/tex]. The coefficients are multiplied, and the variables are combined by adding their exponents. Option C.

To simplify the expression [tex](2x^3y)(3x^4y^2),[/tex] we can multiply the coefficients and combine the variables with the same base by adding their exponents.

Multiplying the coefficients, we have:

2 * 3 = 6

For the variables, we multiply the x terms by adding their exponents (3 + 4 = 7), and the y terms by adding their exponents (1 + 2 = 3).

Therefore, simplifying the expression [tex](2x^3y)(3x^4y^2)[/tex] gives us:

[tex]6x^7y^3[/tex]

Hence, the simplified form of[tex](2x^3y)(3x^4y^2)[/tex] is[tex]6x^7y^3[/tex]. Option c is correct.

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Answer:

C:6x7y3

Step-by-step explanation:

i took the test and got it right

The exponential growth function for the given initial population of the city is y = 315,000 × (1 + 0.02)ⁿ .

And the population increase in the year 2020 is equal to 468000.

Population in the year 2000 = 315,000

Increase in population growth by 2%

The population is increasing by 2% annually, which means the growth rate is 0.02 per year.

The initial population in the year 2000 is 315,000.

An exponential growth function as follows,

y = a ( 1 + r )ⁿ

Where 'a' represents the initial population of the city.

And 'r' represents the rate of the growth of the population.

y = 315,000 × (1 + 0.02)ⁿ

where n is the number of years after 2000 .

And y is the population at that time.

To find the population in the year 2020,

Substitute n = 20 into the equation to get the population in 2020 and solve for y,

y = 315,000 × (1 + 0.02)²⁰

⇒ y = 315,000 × (1.02)²⁰

⇒ y = 315,000 × 1.4860

y ≈ 468073.4

Rounding to the nearest thousand, the population in 2020 will be about 468000.

Therefore, the exponential growth function is y = 315,000 × (1 + 0.02)ⁿ and the population in 2020 is 468000.

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The above question is incomplete, the complete question is:

The population of a city has been increasing by 2% annually. The sign shown is from the year 2000.

City limit

Brookfield

Population. 315,000

Write an exponential growth function that represents the population t

years after 2000?

y=

What will the population be in 2020? Round your answer to the nearest thousand.

The population will be about

The percentage of students at the school who describe their parents or guardians as "strict" is the key statistic. 2. A sample survey is the ideal research design for this project.

Since it would be impractical to poll all 1000 kids at the school, the students intend to collect data from a sample of students in order to concentrate on the strict guardians, which is a population parameter.

The sample proportion could be used by the students as a statistic to determine this population proportion. They can ask a sample of pupils drawn at random from the school whether they think their parents or guardians are "strict". The percentage of sample kids who respond "yes" can be used to approximate the percentage of school-wide students who view their parents or guardians as "strict". A statistic that offers an estimate of the population parameter of interest is the sample proportion.

Random sampling would be a suitable technique for generating a sample of 100 pupils. Each kid in the school might be given a number, and the pupils could then use a random number generator to choose 100 numbers from the list. The chosen students might then be contacted and asked to take part in the study. This technique lessens the possibility of bias in the sample selection process and aids in ensuring that the sample is representative of the population.

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Answer:

A

Step-by-step explanation:

it cant be 9 per hour cuz it is a smaller amount and A is the only one that makes sens

The perimeter of the rectangle is 72 cm.

Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all sides or edges of the shape.

The perimeter is usually measured in units such as centimeters (cm), meters (m), feet (ft), or inches (in), depending on the unit of measurement used for the sides or edges.

Let's start by assigning variables to the length and width of the rectangle.

Let x be the width of the rectangle in cm.

Then, the length of the rectangle is double the width, which is 2x cm.

We know that the area of the rectangle is 288 cm², so we can set up an equation:

Area = Length x Width

288 = 2x * x

Simplifying the equation, we get:

288 = 2x²

Dividing both sides by 2, we get:

144 = x²

Taking the square root of both sides, we get:

x = ± 12

Since x cannot be negative (as it represents a length), we take x = 12 cm as the width of the rectangle.

The length of the rectangle is 2x, which is 24 cm.

Now we can find the perimeter of the rectangle, which is given by the formula:

Perimeter = 2(Length + Width)

Substituting the values we found, we get:

Perimeter = 2(24 + 12) = 72 cm

Therefore, the perimeter of the rectangle is 72 cm.

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Mrs. Dundee will make more from the second publisher than from the first if she sells more than $25,000 worth of books.

In mathematics, rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.

Let's represent the number of books sold as "x". Then, the total amount of money that Mrs. Dundee will make from the first publisher is:

Total from first publisher = $80,000 + ($3 x x) = $3x + $80,000

Similarly, the total amount of money that she will make from the second publisher is:

Total from second publisher = $30,000 + ($5 x x) = $5x + $30,000

We want to find the range of values of x for which the total amount from the second publisher is greater than the total amount from the first publisher. In other words, we want to find the range of values of x for which,

$5x + $30,000 > $3x + $80,000

Simplifying this inequality, we get:

$2x > $50,000

x > $25,000

Therefore, Mrs. Dundee will make more from the second publisher than from the first if she sells more than $25,000 worth of books.

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Answer: 2:4

Step-by-step explanation:

The length of the diagonal of the door is approximately 14.308 feet. Rounding to the nearest whole number, the answer is 14 feet.

The lengths of the trim pieces that make an X on the door form the legs of a right triangle, and the diagonal of the door forms the hypotenuse of the right triangle. Using the Pythagorean theorem, we can find the length of the hypotenuse:

a^2 + b^2 = c^2

where a and b are the lengths of the trim pieces and c is the length of the hypotenuse.

Each trim piece forms a right triangle with the height of the door (7 feet) and one half of the width of the door (1.5 feet). Using the Pythagorean theorem, we can find the length of each trim piece:

a^2 + b^2 = c^2

where a = 7 feet and b = 1.5 feet

c = sqrt(a^2 + b^2) = sqrt((7 feet)^2 + (1.5 feet)^2) = sqrt(49 + 2.25) = sqrt(51.25) ≈ 7.154 feet

The length of each trim piece is approximately 7.154 feet. Since there are two trim pieces that intersect at the center of the door, the length of the hypotenuse is twice this length:

2 * 7.154 feet ≈ 14.308 feet

Therefore, the length of the diagonal of the door is approximately 14.308 feet. Rounding to the nearest whole number, the answer is 14 feet.

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You would use a Chi-square test to determine if sample data provide evidence that hypothesized proportions are not correct for a single categorical value from a single population.

You would use a hypothesis test to determine if sample data provide evidence that hypothesized proportions are not correct for a single categorical value from a single population. This type of hypothesis test is commonly used in statistics to evaluate the significance of differences between observed and expected frequencies.

The test involves selecting a sample from the population of interest, calculating the sample proportions, and comparing them to the hypothesized proportions using statistical methods. If the observed proportions are significantly different from the hypothesized proportions, then there is evidence to suggest that the hypothesized values are not correct.

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You would use a one-sample proportion test to determine if sample data provide evidence that hypothesized proportions are not correct for a single categorical value from a single population.

In this test, we compare the observed proportion (based on the sample data) to a hypothesized proportion (based on the null hypothesis) using a test statistic and a p-value. If the p-value is less than the chosen significance level (e.g., 0.05), we reject the null hypothesis and conclude that the observed proportion is significantly different from the hypothesized proportion.

This test is often used in quality control, market research, and public opinion polling to test whether a particular proportion (such as the proportion of defective products or the proportion of people who support a particular policy) is consistent with a hypothesized value.

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To cover the entire area of pyramid, Serena would need approximately 63.36 square inches of paper.

The area of the square base is

4.8 in x 4.8 in = 23.04 sq in

The area of each triangular face is

(1/2) x base x height = (1/2) x 4.8 in x 4.2 in = 10.08 sq in

Since there are four triangular faces, the total area of the triangular faces is

4 x 10.08 sq in = 40.32 sq in

Therefore, the total surface area of the pyramid is

23.04 sq in + 40.32 sq in = 63.36 sq in

So, it would take 63.36 square inches of paper to cover the entire pyramid.

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