The amount of interest accrued on
a $7,000 loan with 6% interest after t years.

Answer:

tan theta = 8/15

Step-by-step explanation:

Sin is equal to opposite over hypotenuse. So it means that the side opposite from theta is 8, and the hypotenuse is 17.

To find the value of the adjacent side from theta, use the Pythagorean Theorem.

a^2 + b^2 = c^2

8^2 + b^2 = 17^2

64 + b^2 = 289

Subtract 64.

b^2 = 225

Take the square root.

b = 15.

So that means:

the side opposite from theta is 8,

the side adjacent from theta is 15,

the hypotenuse is 17.

Now we take tan, opposite over adjacent, and use the values from the triangle.

tan = opposite / adjacent

tan = 8/15.

Answer:144

Step-by-step explanation:

Use a calculator

or 1/2 x 288 =  288/2 = 144

Answer: 144

Step-by-step explanation:

I'm assuming that the "x" in this statement is a multiplication symbol.

Multiplying any number by 1/2 or 0.5 is the same thing as dividing it by 2.

Therfore the answer is 288/2 which is 144.

Answer:

Step-by-step explanation:

Answer:

Ha: μ < 24

The test statistic is z = -1.75.

The pvalue of the test is 0.0401 > 0.02, which means that we do not reject the null hypothesis, as there is insufficient evidence.

Step-by-step explanation:

A recent survey reported that small businesses spend 24 hours a week marketing their business.

This means that the null hypothesis is:

[tex]H_0: \mu = 24[/tex]

A local chamber of commerce claims that small businesses in their area are not growing because these businesses are spending less than 24 hours a week on marketing.

This means that the alternate hypothesis is:

[tex]H_a: \mu < 24[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

24 is tested at the null hypothesis:

This means that [tex]\mu = 24[/tex]

The chamber conducts a survey of 93 small businesses within their state and finds that the average amount of time spent on marketing is 23.0 hours a week.

This means that [tex]n = 93, X = 23[/tex]

The population standard deviation is 5.5 hours

This means that [tex]\sigma = 5.5[/tex]

Value of the test-statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{23 - 24}{\frac{5.5}{\sqrt{93}}}[/tex]

[tex]z = -1.75[/tex]

The test statistic is z = -1.75.

Do we reject the null hypothesis? Is there sufficient or insufficient evidence?

The pvalue of the test is the probability of finding a sample mean below 23, which is the pvalue of z = -1.75.

Looking at the z table, z = -1.75 has a pvalue of 0.0401

The pvalue of the test is 0.0401 > 0.02, which means that we do not reject the null hypothesis, as there is insufficient evidence.

Answer:

186.66

Step-by-step explanation:

9514 1404 393

Answer:

  y = 11.2 in

Step-by-step explanation:

The product of segment lengths to the near and far intersection points of the secant with the circle are the same for all secants from the same external point. Here, there are three, so we have the relations ...

  9×9 = 5(5+y) = x(x+19)

Then the value of y can be found as ...

  81/5 = 5+y

  16.2 -5 = y = 11.2

__

The value of x is a little trickier, as a quadratic is involved.

  81 = x² +19x

  81 + 90.25 = x² +19x +90.25 . . . . complete the square

  171.25 = (x +9.5)²

  x = √171.25 - 9.5 ≈ 3.58625...

__

Additional comment

For the purpose here, the tangent can be considered to be a degenerate case of a secant in which the two points of intersection with the circle are the same point. For the purpose of this calculation, the length of the tangent is squared. (The distance to the points of intersection is the same.)

I find it easier to remember one rule, rather than a separate rule for tangents. With some imagination, the same rule can be applied when the "secants" meet inside the circle. In that case, they are called "chords".

We have shown the value for x because we suspect some versions of this question may ask for x instead of y. (Rounding may be required in that case.)

Answer:

A

Step-by-step explanation:

How you find x is you do 27-8. You get 19. If you do 19+8 and think of 19 as x, you get 27. This is why A is correct

Answer:

456.9

Step-by-step explanation:

[tex](1 + \sqrt{2^{4} }) = 5[/tex]

[tex](1 - \sqrt{2^{4} } ) = - 3[/tex]5--3=8

Answer:

Sorry for the wait.

Step-by-step explanation:

5. the two bottom angles are the same btw

[tex]2x+2x+x-15=180\\5x-15=180\\5x-15+15=180+15\\5x=195\\5x/5=195/5\\x=39[/tex]

6. straight lines are 180

[tex]3x+17+x-9=180\\4x+8=180\\4x+8-8=180-8\\4x=172\\4x/4=172/4\\x=43[/tex]

7. another 180

[tex]2x-4+3x+5+2x+11=180\\7x-10=180\\7x-10+10=180+10\\7x=190\\7x/7=190/7\\x=27.14\\[/tex]

8. 90 degree angle

[tex]x+x+4+3x-9=90\\5x-5=90\\5x-5+5=90+5\\5x=95\\5x/5=95/5\\x=19[/tex]

Answer:

$900

Step-by-step explanation:

The formula for simple interest is I = PRT where I is the interest earned, P is the principal/amount deposited or borrowed, R = rate as a decimal, and T = time in years

I = PRT

I = (500)(0.04)(20)

I = 400

Add the interest to the principal, and she will have $900 in 20 years.

Please let me know if you have questions about this.

Answer:

Step-by-step explanation:

When you are taking off percentages from numbers, you first want to make the percent a number. This step is super simple. Just divide the 18 by 100

This gets you 0.18

Now multiply

84 * 0.18 = 15.12

So 15.12 is the discount

Then take 84 and subtract 15.12

84 - 15.12 = 68.88

So 68.88 is the sell price

Answer:

T₂ = 1.2 s

Step-by-step explanation:

The time period of a simple pendulum is given by :

[tex]T=2\pi \sqrt{\dfrac{L}{g}}[/tex]

Where

L is length of the pendulum

g is acceleration due to gravity

We have,

T₁ = 1.4 s, L₁ = 0.49 m, L₂ = 0.36 m, T₂= ?

[tex]\dfrac{T_1}{T_2}=\sqrt{\dfrac{L_1}{L_2}} \\\\T_2=\dfrac{T_1}{\sqrt{\dfrac{L_1}{L_2}}}\\\\T_2=\dfrac{1.4}{\sqrt{\dfrac{0.49}{0.36}}}\\\\T_2=1.2\ s[/tex]

So, the new time period is equal to 1.2 seconds.

Answer:

D

Step-by-step explanation:

The other graphs are functions.

Graph A is a linear function, and C is an Absolute Value Function.

Graph B also seems to be a function.

However- I can only narrow it down to B or C.  I apologize if my answer is not correct.

Answer:

[tex]A=\frac{215*x}{2}-x^2)[/tex]

Step-by-step explanation:

From the question we are told that:

Total length of building side [tex]x=25feet[/tex]

Perimeter of  fence in [tex]P=190feet[/tex]

Generally the perimeter of the display area is given as mathematically given by

[tex]2L+2B=P+x\\2L+2B=190+25[/tex]

Therefore

[tex]2L+2B=215[/tex]

[tex]L+B=\frac{215}{2}[/tex]

[tex]B=\frac{215}{2}-L[/tex]

Generally the Area of the display area A is given as mathematically given by

[tex]Area A=L*B[/tex]

[tex]Area A=L*(\frac{215}{2}-L)[/tex]

[tex]Area A=\frac{215*L}{2}-L^2)[/tex]

Length L in terms of x

[tex]Area A=\frac{215*x}{2}-x^2)[/tex]

Answer:

Bug0

Step-by-step explanation:

tangá Bubv haha yaanka amp

Answer:

Your answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

A looks good

Answer:

D

Step-by-step explanation:

225 is the closest to point (200, 200)

Answer:

c

Step-by-step explanation:

trust

Answer:

63

Step-by-step explanation:

Mode is the number that is repeated the most, in this case its 63

Answer:

24

Step-by-step explanation:

i did it

Answer:

182

Step-by-step explanation:

Add 178 + 209 + 159 = 546

Then divide 546 by 3 = 182

Answer: 7/17

add all the marbles to get the total

6 + 7 + 4 = 17

there are 7 blue marbles so

7/17

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

i belive it is correct.

Answer:

x=4 is a solution

Answer:

11,143.3

Step-by-step explanation:

Density measures the number of people per unit area

Density = population / area

1,579,000 / 141.7  = 11,143.30

Answer:

Step-by-step explanation:

==