When Birchwood Elementary School opened for the first year, there were 240 students. During each of the following 10 years, the number of students increased exponentially. To determine the number of years (n) that had passed when the number of students reached 365, use the following equation.

240(1.15)n=365

After how many years did the number of students reach 365?

Responses

1 year


2 years

3 years


4 years

The population in thousands of a town in the year 2007 is 16.56 thousand.

In an exponential function, the base value controls how quickly the function increases or decreases. The function expands exponentially if the base value is more than 1, whereas it degrades exponentially if the base value is between 0 and 1. Faster growth or decay is indicated by a bigger base value.

Given that,

y = 8.5(1.1)ˣ

The value of x is calculated as:

x = 2007 - 2000 = 7 years.

Substitute the value of x in the given function:

y = 8.5(1.1)⁷

y = 16.56

Hence, the population in thousands of a town in the year 2007 is 16.56 thousand.

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The number of problems assigned initially to each student by Lin’s teacher is 4.

Equations are mathematical statements that have two algebraic expressions on either side of equals (=) sign. The phrases written on the left and right sides are equal, as shown by this example.

Equations can be resolved in order to ascertain the value of a variable that represents an unknowable quantity. In the absence of the "equal to" symbol, a statement is not an equation. That will be taken into consideration as a phrase.

Lin’s teacher assigned each of them the same number of problems to complete.

Total number of problems assigned by Lin's teacher  to students = 30

Let the  total number of problems assigned  to each student initially  be x

So, the number of problems assigned   to  all the  students  initially = 5x

Also it is given that  Lin's teacher assigns 2 more problems to each student

which means he gives 10 more problems to solve

5x+10 = 30

5x = 20

x = 4

Hence, The number of problems assigned initially to each student by Lin’s teacher is 4.

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Answer:

b,c,e

Step-by-step explanation: a: 5+0=5

b:15x0 =0

c: 1.4+2.7=4.1

d:2/3 x 5/9

e:4& 2/3 =5-1/3

Answer:

the answer is A

hope it helps u

mark brainlist

Answer: D

As x Values-Decrease, the function increases toward positive infinity.

As the x values decreases, the function decreases towards y=-2

Step-by-step explanation:

It's a basic function that follows within the 2^x format. Where x-> infinity would mean that y-> infinity as well. However, since there was a translation within the y unit (hence the -2) the asymptote decreased by two.

So as the x unit increases, so does the y.

However, as the x unit decreases, the y decreases to -2.

Answer:

Step-by-step explanation:

sorry I don’t know

The surface area of the figure is 549.5 square ft

Given that

The composite figure comprises of a cone and a cylinder of the following dimensions

Cone: Radius = 5 ft and Height = 12 ft

Cylinder: Radius = 5 ft and Height = 6 ft

The surface area of the figure is calculated as

Surface area = Cone + Cylinder -  Circle

So, we have

Surface area = πr(r + √[h² + r²]) + 2πr(r + h) - πr²

Substitute the known values in the above equation, so, we have the following representation

Surface area = 3.14 * 5 * (5 + √[12² + 5²]) + 2 * 3.14 * 5 * (5 + 6) - 3.14 * 5²

Evaluate

Surface area = 549.5

Hence, the surface area is 549.5

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The amount of work done is Option A) 12 N/m

Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.

It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.

Work done on a body is equivalent  to the increase in the energy of the body, because it transfers energy to the body.

The formula for work done is;

W = fd

Where, 'f' is the applied force and d is the distance

Substitute the values

Work done = 6(2)

Work done = 12 N/m

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Answer:

origin

Step-by-step explanation:

the point (0,0) is called the origin

Answer:

The center of a coordinate plane, which is point (0,0) is called "the origin."

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

4x - 9 + 3x = 8x - 1

7x - 9 = 8x - 1

7x = 8x + 8

x = -8

Therefore, the solution to the equation 4x - (9 - 3x) = 8x - 1 is x = -8.

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

The distance between the twο y-intercepts is 7 - 19 = -12.

Value is the impοrtance, wοrth, οr usefulness οf sοmething. It is a measure οf the relative wοrth οf sοmething and can be expressed in variοus ways, such as mοnetary, sοcial, οr practical. Value can be determined by cοnsidering factοrs such as quality, utility, and scarcity. Values are subjective and can be influenced by persοnal, cultural, and sοcietal factοrs. They οften reflect a persοn's beliefs, attitudes, οr preferences. Value is an impοrtant cοncept in ecοnοmics, finance, and sοcial science.

The y-intercept οf f(x) is 7, while the y-intercept οf g(x) is calculated by subtracting the x-value οf the first rοw frοm the g(x) value, which is 20 - 1 = 19.

Therefοre, the distance between the twο y-intercepts is 7 - 19 = -12.

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Answer:

(-4,-3,7,8)

Step-by-step explanation:

the inputs are the X values , the X values are the first number on the parenthesis (X , Y) , the outputs are the Y values

The area of the triangle is 3 cm^2.

Area is the measure of the amount of space inside a two-dimensional shape, such as a square, rectangle, triangle, or circle. It is usually measured in square units, such as square centimeters, square inches, or square meters.

Two-dimensional shapes are flat shapes that exist in only two dimensions - length and width. They are also known as 2D shapes. Some common examples of two-dimensional shapes include:

In the given question,

To find the area of a triangle, we need the length of two sides and the angle between them. We are given that the length of two sides of the triangle are 3 cm and 4 cm, and the angle between them is 30°.

We can use the formula for the area of a triangle, which is:

Area = (1/2) x base x height

We can take the side of length 3 cm as the base of the triangle, and the side of length 4 cm as the height, as it forms a right angle with the base. To find the height, we can use trigonometry.

sin(30°) = opposite/hypotenuse

sin(30°) = height/4

height = 4 x sin(30°)

height = 2 cm

Now, we can substitute the values in the formula for the area of the triangle:

Area = (1/2) x base x height

Area = (1/2) x 3 x 2

Area = 3 cm^2

Therefore, the area of the triangle is 3 cm^2.

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The end result of this equation is the value of the collection after 5 years. In this case, the total value would be V = 320(1.02)⁵ = 413.25.

Exponential growth is a pattern of growth that occurs when a base number is multiplied by a consistent number over a period of time. This type of growth is often seen in population growth, inflation, the money supply and other areas of mathematics. The growth rate of an exponential function increases over time, making it an important concept in mathematics, economics, and other fields.

This equation utilizes the concept of exponential growth, which is when a quantity increases at a rate which is proportional to its current value. In this case, the quantity is the value of the collection, and the rate of growth is 2% per year.

The equation can be broken down into its components in order to better understand what it is saying. The base value of the collection, 320, is represented by the first part of the equation, V = 320. The second part, (1.02)^5, represents the growth rate over 5 years. The 1.02 is the growth rate of 2% per year, and the 5 indicates that the growth rate will be compounded for 5 years. In other words, the rate of growth is applied to the original value, and then the resulting value is used as the new base for the growth rate to be applied again, and so on for 5 years.

The end result of this equation is the value of the collection after 5 years. In this case, the total value would be V = 320(1.02)⁵ = 413.25. This means that in 5 years, the collection would have appreciated to a total value of 413.25.

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Answer:

24.6063 ft

Step-by-step explanation:

The area of the compound figure is 41 square meters.

We can subdivide the compound figure into smaller shapes and add the areas of each to determine its area.

The figure can first be divided into two rectangles:

The first rectangle has a surface area of 18 m2 with measurements of 2 m by 9 m.

The second rectangle is 3 m by 7 m in size, which equals a surface area of 21 m2.

Next, we can calculate the two triangles' areas:

The area of the first triangle is 1/2 x 2 m x 2 m, or 2 m2, because its base is 2 m and its height is 2 m.

The area of the second triangle is 1/2 x 3 m x 2 m = 3 m2, with a base of 3 m and a height of 2 m.

The overlap between the two rectangles can then be subtracted:

The overlap measures 2 m by 3 m, making it a rectangle whose size is 2 m by 3 m, or 6 m2.

We sum the areas of the two rectangles, the two triangles, then subtract the overlap between the rectangles to determine the total area of the compound figure:

(18 m2 + 21 m2) + (2 m2 + 3 m2) - 6 m2 = total area

Area total: 41 m2.

Hence, the compound's area is 41 square metres.

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Complete question:

Area of compound figures.

2 m

2 m

3 m

9 m

2 m

3 m

7 m

14 m

What is the area of this figure?

The amount of time it would take the water to cool to 150°F is: C. About 8 min.

In this scenario, the time would be plotted on the x-axis of the scatter plot while the temperature would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the time and temperature, an exponential equation for the line of best fit is given by:

[tex]y = 192e^{-0.028x}[/tex]

When temperature y = 150°F, the value of x (in minutes) can be calculated as follows:

[tex]150 = 192e^{-0.028x}[/tex]

ln(150/192) = -0.028x

x = -0.24686007793/0.028

x = 8 mins.

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The best option to find a reasonable estimate for the amount of time it takes to run the obstacle course among 200 contestants is to option D: Time 20 contestants and average their times.

A reasonable estimate is an approximation that is based on logical reasoning and information available, and it is within a reasonable margin of error. It is not expected to be precise, but it is expected to provide a fair idea of the value being estimated.

For example, estimating the cost of a renovation project within 5% of the actual cost would be considered a reasonable estimate.

By timing only one contestant, the time might not be representative of the entire group since individual performances can vary significantly. Timing the race official himself also won't give an accurate estimate since the official might not be a typical contestant in terms of speed and agility.

On the other hand, timing 2 contestants and averaging their times might not provide a big enough sample size to get a good estimate.By timing 20 contestants, there is a higher chance that the sample size will be representative of the entire group, and the average time will provide a more accurate estimate of the typical performance on the obstacle course.

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Accordingly, if Britta only paid the interest during her two years of education, she would accrue about $33,782 in interest over the course of her loan.

The sum of money that a borrower must give a lender as interest is compensation for the use of borrowed funds. It is typically computed as a percentage of the principal, which is the amount borrowed, and is repaid alongside the principal over a predetermined amount of time. The cost of the lender, the likelihood of a default, and the desire for credit in the economy are just a few of the variables that affect the interest rate, or the percentage charged for borrowing the money.

given

We can use the following method to determine the total interest paid:

Principal x Interest Rate x Duration equals total interest.

where Principal denotes the sum borrowed, Interest Rate denotes the annual interest rate (in decimal form), and Time denotes the number of years over which interest will accrue.

Assume Britta took out a $50,000 loan to pay for her schooling.

Therefore, the amount of her loan at the conclusion of that time frame would be:

$50,000 x 1.06^2 = $56,420

The interest that will be charged on this balance for the remaining 10 years and 6 months of the loan period needs to be calculated now. Using the above method, we obtain:

$56,420 multiplied by 0.06 times 10.5 equals the total interest, or $33,782.

Accordingly, if Britta only paid the interest during her two years of education, she would accrue about $33,782 in interest over the course of her loan.

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The value of function f(x) at x =1 will be 4.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given a function f(x) = -3x + 7

To calculate the value of the function at x = 1,

We need to substitute the value of x = 1 in the function,

thus,

f(1) = -3 * 1 + 7

f(1) = -3+ 7

f(1) = 4

This represents the point (1, 4) on function f(x) = -3x +7.

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a. The x-intercepts are 1/4 and 4. b. The vertex of the graph of f(x) is (1.875, 56), and it represents a maximum point on the graph.

The object's form is symmetrical because of the axis of symmetry, which is a straight line. On each of its sides, the axis of symmetry produces a perfect reflection. It could be lateral, vertical, or horizontal. The two sides of an object are the same if we fold and unfold it along the axis of symmetry. Various forms have various symmetry lines. There are four lines of symmetry in a square, two lines in a rectangle, infinite lines in a circle, and no lines of symmetry in a parallelogram. There are n axes of symmetry in a regular polygon with n sides.

We know that,

To find the x-intercepts, we set f(x) equal to 0 and solve for x:

-16x² + 60x + 16 = 0

4x² - 15x - 4 = 0

4x² - 16x + x - 4 = 0

4x (x - 4) - 1(x - 4) = 0

(4x - 1) (x - 4) = 0

x = 1/4

x = 4

The x-intercepts are 1/4 and 4.

The vertex of the graph of f(x) can be found using the formula x = -b/2a

x = -60 / (2(-16)) = 1.875

To establish whether the vertex is a maximum or minimum, we examine the shape of the coefficient of the x square term, which is negative (-16). This signifies that the graph expands down and the vertex is a maximum.

Hence, the vertex of the graph of f(x) is (1.875, 56), and it represents a maximum point on the graph.

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Answer:

The statement that is sometimes true is C: A rectangle is a parallelogram.

Step-by-step explanation:

A parallelogram is a four-sided shape with opposite sides parallel. A rectangle is a specific type of parallelogram where all angles are right angles, and opposite sides have equal lengths. Therefore, a rectangle is considered a parallelogram. However, not all parallelograms are rectangles because other parallelograms may have angles that are not right angles.

Answer:

t ≤ -3

Step-by-step explanation:

4t + 5 ≤ -7

4t ≤ -12

t ≤ -3

Answer:

B

Step-by-step explanation:

The answer is 21 because the pattern is multiplying by 3!

Answer:

23

Step-by-step explanation:

(16-12)×4+7

(4)×4+7

16+7

=23 I think

Answer:

35$ - 17% gives you 29.05$

while 32$ - 12% gives you 28.16$

so 35$ - 17% would be your answer

Answer:

40?

Step-by-step explanation:

The future value of a 10-year investment of $1200 at an APR of 7% compounded monthly is $2366.84

what is compound interest ?

Compound interest is the interest earned on an initial deposit or investment, plus all the interest that has accumulated on it over time. It is interest calculated on both the principal amount and any interest earned from previous periods, which is added to the principal amount at the end of each compounding period.
[tex]FV = P * (1 + r/n)^{n*t}[/tex]

Where:

FV = Future Value

P = Principal or initial investment

r = Annual interest rate

n = Number of times interest is compounded per year

t = Time in years

According to the question:
In this case:

P = $1200

r = 7% = 0.07

n = 12 (compounded monthly)

t = 10

Plugging these values into the formula, we get:

[tex]FV = P * (1 + r/n)^{n*t}[/tex]

[tex]FV = 1200 * (1 + 0.07/12)^{12*10}[/tex]

[tex]FV = 1200 * (1.00583333)^{120}[/tex]

[tex]FV = 1200 * 1.97236812[/tex]

[tex]FV = 2366.84[/tex]

Therefore, the future value of a 10-year investment of $1200 at an APR of 7% compounded monthly is $2366.84 (rounded to the nearest cent).

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Answer:

The correct answer here is B

Step-by-step explanation:

You already did the first 2 rows and it got a COP of 3. The last few rows do not.

Answer:

Answer is C

Step-by-step explanation:

Yes, the person who said B is half correct but tables CAN show proportions, however this one doesn't since you aren't multiplying by 3 in every row. Only the top 3 rows do the rest don't. That's why C is correct not B.

The number that was added to complete the square is (7/2)²

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is x²+7x+27=0

Add and subtract (7/2)² = 49/4

x² + 7x + 27

= ( x² + 7x + 49/4) - 49/4 + 27=0

= (x + 7/2)² - 59/4

Now we can rewrite the original equation as:

(x + 7/2)² - 59/4 = 0

Adding 59/4 to both sides, we get:

(x + 7/2)² = 59/4

Taking the square root of both sides, we get:

x + 7/2 = ±√59/2

Solving for x, we get:

x = -7/2 ±√59/2

Therefore, the number that was added to complete the square is (7/2)²

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Lisa and her brothers share a mutual appreciation for the car, albeit for different reasons.

After finishing working on the car, Lisa's brothers are surprised by the changes she made to the car. They may compliment her on her work or express their appreciation for her efforts. On the other hand, Lisa is proud of her work and takes pride in the changes she made to the car. She may feel a sense of accomplishment and satisfaction in seeing the final result of her hard work. While her brothers may appreciate the car, Lisa feels a personal connection to it as she knows the effort and dedication she put into making it look and function better.

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Answer:

I have the answer

Step-by-step explanation:

1. Suprised by

2. Proud of

3.  unique

Hope it helps, Have a good day!