Caden Carpenter is a college student applying for a student loan to complete the final year of his degree program. During the application process, Caden decided that he will pay off the student loan in 5 years. A private loan company approves Caden for a $15,000 student loan that has an interest rate of 3.5% compounded monthly over 5 years. Find the total amount Caden will pay over the course of the loan. Round to the nearest cent as needed.

Answer:(-1/2^x)(50000)

Step-by-step explanation:

Answer:

A - B = 11x² -9x + 14

A - B = 11x² -9x + 14

The perimeter of the deck area to the right of the beam of light (ABDC) is  64.6 feet.

The trigonometric ratio of 30° is sin30°=1/2, cos30°=√3/2, tan30°=1/√3. Similarly, the trigonometric ratio of 60° is sin60°=√3/2, cos60°=1/2, tan60°=√3.

It is the sum of the lengths of all the sides of a given shape. It is a measure of the distance around the outside of a two-dimensional object.

The perimeter of the deck area to the right of the beam of light (ABDC) can be found using the trigonometric ratios.

Since, AB = 10 feet

BD and BE trisect LABC,

then BD = 5 feet

and BE = 5 feet.

Therefore, the perimeter of the deck area to the right of the beam of light (ABDC)

= AB + BD + DC + AD, or 10 + 5 + 5 + 10

= 30 feet.

To calculate DC and AD, we can use trigonometric ratios.

Using the law of cosines, we can find that

DC = 10√3 or 17.3 feet,

and AD = 10√3 or 17.3 feet.

Therefore, perimeter=30 + 17.3 + 17.3=64.6feet.

In a triangle BDC, if the side of BC is given then using the ratios of 30° and 60°, the remaining sides of the triangle can be identified.

The trigonometric ratio of 30° is sin30°=1/2, cos30°=√3/2, tan30°=1/√3. Similarly, the trigonometric ratio of 60° is sin60°=√3/2, cos60°=1/2, tan60°=√3.

Using these ratios, the sides of the triangle can be found.

If the side BC = 6 cm,

BD= 3 cm and

CD=3√3 cm.

Thus, using the trigonometric ratios of 30° and 60°, the sides of the triangle can be calculated and labelled.

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The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

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Answer:

47 inches

Step-by-step explanation:

45 + 48 + 49 + 40 + 53 = 235

235/5 = 47

\(\displaystyle\int~4t(5t^2-1)^6 dt \\\\[-0.35em] ~\dotfill\\\\ u=5t^2-1\implies \cfrac{du}{dt}=10t~\hspace{10em} \cfrac{du}{10t}=dt \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~4t~u^6\cdot \cfrac{du}{10t}\implies \int~\cfrac{4t~u^6}{10t}\cdot du\implies \int~\cfrac{2~u^6}{5}du\implies \cfrac{2}{5}\int~u^6\cdot du \\\\\\ \cfrac{2}{5}\cdot \cfrac{u^7}{7}\implies \cfrac{2(5t^2-1)^7}{35}\)

Answer:2,440,000,000

Step-by-step explanation:

Answer:

x = 35

Step-by-step explanation:

since the figures are similar then the ratios of corresponding parts are in proportion, that is

\(\frac{x}{10}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) ( cross- multiply )

2x = 7 × 10 = 70 ( divide both sides by 2 )

x = 35

Calista's grade on her last assignment is 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

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Answer:

x=25

Step-by-step explanation:

2x-14=36

2x=50

x=25

Answer:

1:

26

24

57

47

59

61

16

23

2:

58.5

56.556

49.75

93.75

62.2857142857

98.667

28.223

57.5

56.5714285714

19.28

57.75

Answer:

100r1

Step-by-step explanation:

Answer/Step-by-step explanation:

1. Given:

m<ABC = 4x°,

m<BCD = 3x°,

m<CDA = 2x°,

m<DAB = 3x°

Sum of quadrilateral = (n - 2)180

Quadrilateral has 4 sides, therefore, n = 4.

Sum of quadrilateral = (4 - 2)180 = 2*180 = 360°

Equation to solve for x would be:

m<ABC + m<BCD + m<CDA + m<DAB = 360

Substituting the given expression for each angle, we have:

4x + 3x + 2x + 3x = 360

12x = 360

Use the above equation to solve for x by dividing both sides by 12

x = 30

Find the measures of all the interior angles by substituting the value of x in each given expression for each angle as follows:

m<ABC = 4x = 4*30 = 120°

m<BCD = 3x = 3*30 = 90°

m<CDA = 2x = 2*30 = 60°

m<DAB = 3x = 3*30 = 90°

[Check: 120 + 90 + 60 + 90 = 360°]

2. <CDA and <ADE form a linear pair. They are supplementary angles.

Since supplementary angles sum up to equal 180°, and <ADE is a supplement of <CDA (60°), therefore:

m<ADE = 180° - 60° = 120°

We need to use the following property of radicals to solve this question:

The expression given is:

If we want to simplify, we need to rewrite the second term in terms of sqrt(3). We know that 108 is divisible by 3 because the sum of its digits is also divisible by 3.

Then:

We can rewrite:

Using the property above:

Now, we can simplify:

Thus, the answer is:

Answer:

All real numbers greater than -3

Step-by-step explanation:

The domain of a log is the baseline is greater than 0.

Set x + 3 greater than zero and solve

x + 3 > 0

x > -3

The value of x in 7-3(2x-1)= 2x+26 is -4

Linear equation is is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true. In the case of one variable, there is only one solution. For example, the equation x + 3= 0 has only one solution as x = -3.

To find x in 7-3(2x-1)= 2x+26 ,we solve the parentheses first which will give

7- 6x+3= 2x+26

collect the like terms

-6x-2x=26-3-7

-8x= 16

divide both side by -8

-8x/-8= 16/-8

therefore x= -2

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Answer:

Um.....there isnt enough information for anybody to really figure this out.

Step-by-step explanation:

Answer:

3x+2=26

3x=24

x=8

Step-by-step explanation:

Answer:

The answer is 8.

Step-by-step explanation:

you need to undo.

to get the 2 out of the bottom you need to multiply both sides of the equation by 2.

now you have  3x+2= 13(2)

3x+2=26.

Now you need to subtract 2 from both sides to get rid of the 2.

Now you have 3x=26-2

3x=24.

The final step in solving for x is to divide both sides by 3.

Now you have x=24/3

which give you your final answer of x=8

Hope this helps!

Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)

then

\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)

= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression

= \(3^{\frac{2}{9} }\) ← third expression

The balance over the acceptable debt ratio is $1089.90.

A debt ratio calculates a company's leverage by comparing its total debt to its total assets.

Although this ratio varies greatly between industries, capital-intensive enterprises typically have significantly larger debt ratios than other types of businesses.

Divide total debt by total assets to find a company's debt ratio.

A debt ratio of less than 100% signifies a corporation has more assets than debt, and a debt ratio of larger than 1.0 or 100% means the opposite.

According to some sources, the debt ratio is calculated by dividing all obligations by all assets.

Given that, credit card balance = $3,589.90

credit limit = $5,000

Debt Ratio percentage = 50% = 0.50

The balance over is given as

balance = Current Balance - (Credit Limit × 0.50 )

balance = 3589.90 - (5000 × 0.5)

balance = 3589.9 - 2500

balance = 1089.9

Hence, the balance over the acceptable debt ratio is $1089.90.

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The distance between the points (-1, 5) and (-7, -3) is 10 units.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Point 1 (-1,5)

Point 2 (-7,-3)​

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √[(-7 - (-1))² + (-3 - 5)²]

D = √[(-7 + 1)² + (-3 - 5)²]

D = √[-6² + (-8)²]

D = √[36 + 64]

D = √100

D = 10

Therefore, the distance is 10 units.

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The growth rate in US exports over the last five years was 6.3%.

1. Gather the data for US exports over the last five years

2. Calculate the difference between each year to determine the rate of growth

3. Calculate the average annual growth rate

4. Round the average growth rate to the nearest tenth

5. The growth rate in US exports over the last five years was 6.3%.

Gather the US export data over the last five years. Calculate the difference between each year to find the growth rate. Calculate the average annual growth rate, then round to the nearest tenth. The growth rate in US exports over the last five years was 6.3%.

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If we consider the ordered pair (0,0) then only the graph still represents a function.

In a function, there can not be two different values of x corresponding to the same value of y.

Here, the points on the graph are (0,0), (-3,1), (1,3) and (3, 1).

If we consider point (-3,1) then there will be two points corresponding to the same y value i.e. (-3,1) and (3, 1).

The values of x for a single value of y.

i.e. y = 1.

So, if we consider the ordered pair (0,0) then only the graph still represents a function. Therefore, the correct answer is option (a) (0,0).

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I suppose the curve is \(r(\theta)=e^\theta\).

Tangent lines to the curve have slope \(\frac{dy}{dx}\); use the chain rule to get this in polar coordinates.

\(\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}\)

We have

\(y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta\)

\(x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta\)

\(r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta\)

\(\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}\)

The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:

\(\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1\)

\(\implies\theta=\boxed{-\dfrac\pi4+n\pi}\)

(where \(n\) is any integer)

The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:

\(\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1\)

\(\implies\theta=\boxed{\dfrac\pi4+n\pi}\)

Answer:

câu này là 500 nhen

The probability of rolling a sum of 7 when rolling a pair of six-sided number cubes is 1/6

It is a branch of mathematics that deals with the occurrence of a random event.

We need to count the number of ways in which the cubes will have a sum of 7

There are six possible ways to roll a sum of 7

(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).

Since each cube has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes when rolling two number cubes.

The probability of rolling a sum of 7 is the number of ways to roll a sum of 7 divided by the total number of possible outcomes:

Probability of rolling a sum of 7 = number of ways to roll a sum of 7 / total number of possible outcomes

Probability of rolling a sum of 7 = 6 / 36

Probability of rolling a sum of 7 = 1 / 6

Therefore, the probability of rolling a sum of 7 when rolling a pair of six-sided number cubes is 1/6

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Answer:

\(\cos(11x)\)

Step-by-step explanation:

Given

\(\cos 5x\ \cos 6x- \sin\ 5x \sin 6x\)

Required

Express as a single function

In trigonometry, we have:

\(\cos(A + B) = \cos A\cos B - \sin A \sin B\)

By comparison, we have

\(\cos(5x + 6x) = \cos 5x\cos 6x - \sin 5x \sin 6x\)

\(\cos(11x) = \cos 5x\cos 6x - \sin 5x \sin 6x\)

Answer:

i.She needs 96 bags of beads

ii.She will spend $56.64 on the beads

Step-by-step explanation:

i.19×24=456

12÷456=96

96 bags

ii.96×0.59

=56.64

$56.64

The domain of this function is all the real numbers except - 7 / 3 and 23 / 3.

In accordance with function theory, the domain of a function is a set of x-values such that y-values exist. Herein we find that the given function is a rational function whose denominator includes an absolute value function. The numerator is a linear equation.

Therefore, the domain of the function is all real numbers except those x-values such that denominator is equal to zero. We need to solve the following expression in two cases:

|3 · x - 15| = 8

For x ≥ 5:

3 · x - 15 = 8

3 · x = 23

x = 23 / 3

For x < 5:

- 3 · x + 15 = 8

- 3 · x = - 7

x = - 7 / 3

Then, the domain of this function is all the real numbers except - 7 / 3 and 23 / 3.

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Answer:

i got the answer i put a picture below

Step-by-step explanation: