Mary decides to take out a $4,000 student loan this year. If she will pay 10% interest compounded annually, how much will the total loan amount be in four years when she graduates?

Answer:

Anything 3 or more

Step-by-step explanation:

3 x 4 = 12.

12 > 10.

If you follow through with the next multiple of 4, 4, we get 16.

16 > 10.

This is true for any other multiple of 4, making any value 3 or me greater than 10.

Answer:

18.09

Step-by-step explanation:2.4x2.4, then x3.14  

Answer:

answers below

Step-by-step explanation:

If you are trying to find the area the answers are:

Earth= 289.52918

Saturn=6,532.5021

The formula for area for a sphere is:

4 x pie x r2

If you are trying to find the volume the answers are:

Earth=57.90584

Saturn=46,647.01596

The formula for volume for a sphere is:

4/3 x pie x r3

Also the radius (r) is half of the diameter, so you divide the diameter by 2.

Answer:

b

Step-by-step explanation:

Answer:

7^4

Step-by-step explanation:

7 power 4 equals to 7×7×7×7

To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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Answer:

Joel had 120 dimes and 80 quarters.

Step-by-step explanation:

Given that Joel had 200 coins, which were dimes and quarters, and the total value was $ 32, to determine how many coins of each type he had, the following calculation must be performed:

0.25 - 0.10 = 0.15

200 x 0.10 = 20

32 - 20 = 12

12 / 0.15 = 80

200 - 80 = 120

(80 x 0.25) + (120 x 0.1) = X

20 + 12 = X

32 = X

Thus, Joel had 120 dimes and 80 quarters.

Answer:

x = -1

Step-by-step explanation:

6+4 = 10

14-10 = 4

2x + 6 = 4

2x (-2) = -2

-2 + 6 = 4

The exponential function that can model the county population, y, x decades after Tiana was born, is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 in 6.6 decades after Tiana was born.

The definition of the exponential function is presented as follows:

\(y = a(b)^x\)

In which the parameters of the exponential function are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the function is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 when y = 600000, hence:

\(y = 641000(0.99)^x\)

\(600000 = 641000(0.99)^x\)

\((0.99)^x = \frac{600000}{641000}\)

\(\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}\)

\(x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}\)

\(x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}\)

x = 6.6 decades.

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We will rewrite the equation as follows:

So, the equation without fractions is:

After simplification we got the above expression in the form 3f + 16m -56

The word "simplify" implies to turn something in a simpler form.

In mathematics, simplify an expression means write an expression in such a way that is comparatively less complicated than before. The main purpose of simplify an expression is to make it easy to solve as well as calculation.

3f + 8(2m-7)

we rearrange the expression by removing the parenthesis.

we remove the parenthesis by multiplying the factors.

3f + 8 × 2m - 8 × 7

3f + 16m -56

the above expression has no like terms to add or subtract so it is kept in this form.

Hence, 3f + 16m -56 is the simpler form.

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Answer:

m = ½

y = ½x - 3

Step-by-step explanation:

m = (-12 + 14)/(‐18 + 22)

m = ½

y + 14 = ½(x + 22)

y = ½x + 11 - 14

y = ½x - 3

The equation of the line is y = x.

To find the equation of a line given its graph, you need to follow the steps below.

Step 1: Determine the slope of the line.The slope of the line can be determined using the formula: slope = rise/run or m = Δy/Δx. Rise is the change in the y-coordinates and run is the change in the x-coordinates.

Step 2: Determine the y-intercept of the line.The y-intercept is the point where the line intersects the y-axis. You can determine the y-intercept by looking at the point where the line crosses the y-axis on the graph. The y-intercept is denoted by the letter b.

Step 3: Write the equation of the lineThe equation of the line can be written in slope-intercept form, which is y = mx + b. The slope (m) and y-intercept (b) that were determined in steps 1 and 2 are used to substitute into this equation. Thus, the equation of the line becomes y = slope(x) + y-intercept.

Example:Let's say you are given the graph of a line below: .

Step 1: Determine the slope of the line.To determine the slope of the line, you need to choose two points on the line and calculate the rise and run. Let's choose the points (2, 1) and (4, 3). The rise is 2 (3 - 1) and the run is 2 (4 - 2). Therefore, the slope of the line is: m = 2/2 = 1.

Step 2: Determine the y-intercept of the lineThe line crosses the y-axis at the point (0, 0). Therefore, the y-intercept of the line is b = 0.

Step 3: Write the equation of the line.The equation of the line in slope-intercept form is y = mx + b. Substituting the slope and y-intercept into this equation gives: y = 1x + 0 or y = x.

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The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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Answer:

area is 173cm

Step-by-step explanation:

Answer:

25 feet

Step-by-step explanation:

Use the pythagorean theorem, where the width and length of the pool are the legs of the triangle.

Solve for c, the hypotenuse/diagonal

a² + b² = c²

15² + 20² = c²

225 + 400 = c²

625 = c²

25 = c

So, the length of the diagonal is 25 feet

sec(theta) = 1/cos(theta)

I believe that is your option D

Answer:(a) The relative rate of growth is given by the derivative of the population function:

Step-by-step explanation:n'(t) = 0.35 * 990e^0.35t

To find the relative rate of growth, we divide the derivative by the population and multiply by 100%:

n'(t)/n(t) * 100% = 0.35 * 990e^0.35t / (990e^0.35t) * 100%

= 0.35 * 100%

= 35%

Therefore, the relative rate of growth of the bacterium population is 35%.

(b) The initial population of the culture is given by the population function at t = 0:

n(0) = 990e^0.35(0)

= 990 * e^0

= 990 * 1

= 990

Therefore, the initial population of the culture is 990 bacteria.

(c) To find the number of bacteria at time t = 5, we plug in t = 5 into the population function:

n(5) = 990e^0.35(5)

= 990 * e^1.75

≈ 132426.28

Therefore, the culture will contain approximately 132426 bacteria at time t = 5 hours.

Answer:

False

Step-by-step explanation:

False, through any three points not on the same line, there is exactly one plane, but three points on the same line could be in separate planes.

Hope this helps :)

The midpoint of the line segment with endpoints at (1, 7) and (9, -3) is (5, 2)

An equation is an expression that shows the relationship between two or more numbers and variables.

The midpoint O(x, y) of the line segment with endpoint at A(x₁, y₁) and B(x₂, y₂) is:

x = (x₁ + x₂) / 2; y = (y₁ + y₂)/2

Given the line segment with endpoints at (1, 7) and (9, -3). Let O(x, y) be the midpoint, hence:

x = (1 + 9) / 2 = 5

y = (7 +  (-3)) / 2 = 2

The midpoint of the line segment with endpoints at (1, 7) and (9, -3) is (5, 2)

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Answer:

}

Step-by-step e.xplanati:kljkjk

petroleum formation happens When dinosaurs became extinct 65 million years ago, their bodies decayed to become petroleum.

Dead creatures are broken down into their basic chemicals through the process of decomposition by bacteria and fungus. The cycle can be completed by plants absorbing and using these substances once again. Because of how they decompose dead organic stuff, decomposing bacteria and fungus are referred to be saprophytic.

Oil and gas are created from organic material that has been decomposed and altered over millions of years, mostly as sediments on the seafloor.

Fuels known as petroleum products are created from crude oil and the hydrocarbons found in natural gas. Coal, natural gas, and biomass can also be used to make petroleum products.

Plant and animal remains are used to create petroleum. Animals and plants that pass away sink and land on the seafloor. These extinct animals and plants decayed millions of years ago and mingled with sand and silt.

Therefore, we can say Petroleum is produced. Dinosaurs became extinct 65 million years ago, and when their corpses decomposed, petroleum was created. Petroleum doesn't form until hundreds of millions of years. Oil was created in chilly climates.

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Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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7.5, 7.058, 8.508,

8.58

Step-by-step explanation:

Answer:

1. 8.58, 8.508, 7.5, 7.058

2. 439.612, 439.261, 439.216, 439.126

Step-by-step explanation:

Prioritize the numbers that have a higher digit at a higher position. Just for fun:

In[1]:= ReverseSort[{8.508, 8.58, 7.5, 7.058}]

Out[1]= {8.58, 8.508, 7.5, 7.058}

In[2]:= ReverseSort[{439.216, 439.126, 439.612, 439.261}]

Out[2]= {439.612, 439.261, 439.216, 439.126}

To solve the exponential equation 4^(3+x) = 25 for x, we need to use logarithms. We can use any base of the logarithm to solve this equation. However, some bases may be more convenient or easier to use than others. The possible bases of the logarithm that we can use to solve this equation are:

Log base 4: If we take the logarithm of both sides of the equation with base 4, we get:

log₄(4^(3+x)) = log₄(25)

(3+x)log₄(4) = log₄(25)

3+x = log₄(25)/log₄(4)

3+x = 2.3219

x ≈ -0.6781

Log base 25: If we take the logarithm of both sides of the equation with base 25, we get:

log₂₅(4^(3+x)) = log₂₅(25)

(3+x)log₂₅(4) = 1

3+x = 1/log₂₅(4)

3+x = 1/1.3219

x ≈ -1.6781

Log base x: If we take the logarithm of both sides of the equation with base x, we get:

logₓ(4^(3+x)) = logₓ(25)

(3+x)logₓ(4) = logₓ(25)

3+x = logₓ(25)/logₓ(4)

3+x = log₄(25)/log₄(x)

x = log₄(25)/log₄(x) - 3

Log base 10: If we take the logarithm of both sides of the equation with base 10, we get:

log₁₀(4^(3+x)) = log₁₀(25)

(3+x)log₁₀(4) = log₁₀(25)

3+x = log₁₀(25)/log₁₀(4)

3+x = 1.3979

x ≈ -1.6021

Therefore, we can use any of the above logarithm bases to solve for x in the given equation.

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Answer:8

Step-by-step explanation:

3 3 4 4 4 6 6 8 8 9

data in upper quartile section are 6 8 8 9

We therefore find the median of 6 8 8 9

The median is the upper quartile

Upper quartile=(8+8)/2

Upper quartile=16/2

Upper quartile=8

The triangle ∠ADC is a central angle, m∠ADC is 60 degrees, and m∠ABC is 30°.

The central angle is the angle that a circle's arc occupies in its centre. The arms of the central angle are formed by the radius vectors. In other terms, it is an angle whose vertex is the centre of a circle, with the two radii lines acting as its arms and intersecting the circle at two distinct places. These two points make an arc when they are coupled together. The angle that this arc at the circle's centre subtends is called the central angle.

Half of the central angle is the circumferential angle.

∠ABC is equal to 1/2 of ∠ABC.

∠ABC = \(\frac{1}{2}*60\)

∠ABC = 30°

Option b. 30° is the right response, so.

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Answer:

\(\frac{1}{7}\) probability that the next president of the United States was born on Monday

Step-by-step explanation:

A theoretical probability is given by the number of desired outcomes divided by the number of total outcomes.

The next president of the United States was born on Monday

Any person, including the next president of the United States, can be born on 7 possible days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday or Saturday, one of which is Monday.

So

\(\frac{1}{7}\) probability that the next president of the United States was born on Monday

Answer:

72

Step-by-step explanation:

Answer: mmm when I did it it going to be the same answer because There are no like terms. Here look at the picture

Step-by-step explanation: hope this help