what are the values of each variable

Using compound interest, it is found that:

a) A(8) = 2389.66

b) t = 31.15

c) P = 1870.85

Compound interest:

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

In this problem:

Item a:

[tex]P = 2000[/tex], hence:

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

[tex]A(8) = 2000\left(1 + \frac{0.0225}{1}\right)^{8}[/tex]

[tex]A(8) = 2389.66[/tex]

Item b:

[tex]A(t) = 4000[/tex], hence:

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

[tex]4000 = 2000\left(1 + \frac{0.0225}{1}\right)^{t}[/tex]

[tex](1.0225)^t = 2[/tex]

[tex]\log{(1.0225)^t} = \log{2}[/tex]

[tex]t\log{1.0225} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.0225}}[/tex]

[tex]t = 31.15[/tex]

Item c:

[tex]A(3) = 2000[/tex], hence:

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

[tex]2000 = P\left(1 + \frac{0.0225}{1}\right)^{3}[/tex]

[tex]P = \frac{2000}{(1.0225)^3}[/tex]

[tex]P = 1870.85[/tex]

A similar problem is given at https://brainly.com/question/24850750

Answer:

Another way to calculate the correlation coefficient (r) is to multiply the slope of the regression line by the standard deviation of X and then divide by the standard deviation of Y.

The function that gives the surface area has the radius as a denominator.

Reasons:

The given parameter are;

The expression Clare finds is the surface area for a fixed volume in terms of the radius, r, is S(r)

The function is used to plot the graph

The values r are allowed to take (obtained from a similar question are) = -1, 2, and 3

The graph of a similar function representing the surface area is attached;

[tex]\displaystyle S(r) = \mathbf{2 \cdot \pi \cdot r^2 + \frac{2 \cdot \pi }{r}}[/tex]

From the graph, it is observed that there is a vertical asymptote at x = 0 (infinite discontinuity)

Therefore, Claire should use the a domain that gives a continuous graph,

given that r is a denominator of the function, by allowing the radius, r to

take on only natural number values (values larger than 0)

The domain is therefore; 0 < r < ∞

The values r can take should therefore be 0.1, 1, 2, and 3

Learn more about asymptotes here:

https://brainly.com/question/17257427

Answer:

12 R20

Step-by-step explanation:

changed 41 to 40 and 533 to 500. work is in file above.

Answer:

x = -2, y = -6

Step-by-step explanation:

(8x - 3y) + (-8x - 5y) = 2 + 46

-8y = 48

y = -6

8x - 3y = 2

8x - 3(6) = 2

8x + 18 = 2

8x = -16

x = -2

Answer:

[tex]\boxed { \sf (-2, -6) }}[/tex]

Step-by-step explanation:

We are asked to find the solution of the system of equations.

[tex]8x-3y=2\\-8x-5y=46[/tex]

When we solve systems of equations, we have to do 2 steps. The first step eliminates one variable so we can solve for the other. The next step helps us find the variable we canceled.

The first equation has the term 8x and the second equation has the term -8x. If these are added, they cancel, so we are left with the variable y. Add the equations together.

[tex](8x-3y=2) \\+ (-8x-5y=46)[/tex]

8x and -8x cancel, then add.

[tex](-3y=2)\\+ (-5y=46)[/tex]

___________

[tex]-8y= 48[/tex]

We are solving for y, so we must isolate the variable. It is being multiplied by -8. The inverse operation of multiplication is division. Divide both sides by -8.

[tex]-8y/-8=48/-8 \\y= 48/-8 \\y=-6[/tex]

Now we know what y is equal to, so we can plug it back into one of the original equations and solve for x.

I chose the first equation.

[tex]8x-3y=2[/tex]

[tex]8x-3(-6)=2[/tex]

[tex]8x+18=2[/tex]

Subtract 18 from both sides to isolate 8x.

[tex]8x+18-18=2-18\\8x=2-18\\8x=-16[/tex]

Divide both sides by 8.

[tex]8x/8=-16/8 \\x=-16/8 \\x= -2[/tex]

Coordinate points are written as (x,y) so our solution is (-2, -6)

The graph that models the relationship between the factory production and the time is the graph in option D

The number of bolts produced within four hours is 3200

The rate of production is the ratio of the change in the number of bolts produced to the the change in time

Change in the number of bolts produced, ∆y = 3200 bolts

Change in time, ∆t  =  4 hours

Rate of change = ∆y / ∆t

Rate of change = 3200/4

Rate of change = 800 bolts per hour

The only graph that models this relationship is the graph in option D because it also have a rate of change of 800 bolts per hour

Learn more here: https://brainly.com/question/25553795

Answer:

In the case of a decimal number, we round down to find the actual number of guesses. Therefore, for a 1000-element array, binary search would require at most 10 guesses. (which is 2,097,152), so we would need at most 22 guesses.

Step-by-step explanation:

Answer:

Same line I think

Step-by-step explanation:

Both go through -2 in x axis

Answer:

Neither

Step-by-step explanation:

To find the slope of the line using the points, we use the equation:

y2 - y1 / x2 - x1

Which would make the lines as follows:

y = 4/3x - 1/3

y = 10/9x + 2/9

And since these lines intersect at point (2.5 , 3), that would make them Neither because the slopes are not mirrored or the same.

Answer:

1580÷100×60

=948

60%=948

60-20

=40

1580÷100×40

=632

948-632

=316

Explanation:

First add up the scores: 75+70+80+80+85+90 = 480

Then divide by n = 6 because there are 6 scores. We get 480/n = 480/6 = 80 as the mean.

Answer:

To multiply square roots, we multiply the numbers inside the radical. Any numbers outside the radical are also multiplied.

Step-by-step explanation:

Answer:

D. 62 1/4 inches

Step-by-step explanation:

Convert 3 1/2 to 3 2/4 so the denominator is 4. Then add that to 58 3/4 inches and you get 62 1/4.

Hope this helps!

Answer:

c - 7.3 < 6

Step-by-step explanation:

c - 7.3 is less than 6

less than is the same as <

So c - 7.3 < 6

-Chetan K

Answer:

c - 7.3 < 6

Step-by-step explanation:

Answer:

In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. ... Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers

Step-by-step explanation:

Answer:

parallel, perpendicular are opposite

Answer:

PARALLEL PERPENDICULAR

Step-by-step explanation:

Difference = 60 - 48 = 12

Percentage = [tex] \frac{12}{60} \times 100 = \frac{12}{3} \times 5 = 4 \times 5 = 20\% \\ [/tex]

Answer:

$26.40

Step-by-step explanation:

Answer:

$26.40

Step-by-step explanation:

1 paper flower=$0.55

Therefore,48 paper flowers=?

cross multiplying,we have 0.55×48=$26.40

[tex]-2(-4)\cdot 8 (-1)\\\\=8 \cdot (-8)\\\\=-64\\\\\text{This one is negative.}[/tex]

Hello! :)

The slope of this line is 0.

Remember, to find the slope, we divide the rise by the run. The rise is how many units we move up; the run is how many units we move right or left.

Here, we move 0 units up, so the rise is 0.

No matter what the run is, the slope is 0 anyway.

Hope it helps you!

If you have any questions, feel free to ask! (:

~An excited gal

[tex]SparklingFlower :)[/tex]

Answer:

its 0 sowe

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

To change a fraction into a percentage, multiply by 100% , then

[tex]\frac{10}{25}[/tex]

= [tex]\frac{10}{25}[/tex]  × 100%

= 0.4 × 100%

= 40%

Answer:

Triangle

Area-9 units

Perimeter-9 units

Rectangle

Area- 18

Perimeter- 18

Step-by-step explanation

For the triangle, you first plot the points. Then you find two of the side lengths and multiply them together. After that you divide the result by two. You get the area. You add the sides together for the perimeter. For the rectangle, you have 3 and 6. Multiply to get 18. 3+3+6+6 is also 18.

Answer:-6- x = 24

Step-by-step explanation:

Answer:

3s = 6q + 9

Step-by-step explanation:

Remember y = mx + b? The function you provided is exactly that but with different letters. As written, the dependent variable is 6q since that is what is isolated. To make it the independent variable, isolate something else so that it becomes the dependent variable. In other words, solve for s by moving the 9 to the other side of the equation.

6q = 3s - 9

3s = 6q + 9

Answer:

10

Step-by-step explanation:

200-65= 135

135/13.5=10

Answer: 234

Step-by-step explanation:

Answer:

v=12

Step-by-step explanation:

1/2v-12+20=14

Add.

1/2v+8=14

Subtract 8 from both sides of the equation.

1/2v=6

Divide 1/2 from both sides of the equation.

v=12

Hope this helps :)