You deposit $150 each month into an account earning 3% interest compounded monthly.
a. How much will you have in the account in 30 years?
b. How much total money will you put into the account?
c. How much total interest will you earn?

Answer:

.2 dollars and 17 cents

Step-by-step explanation:

Carlos has 8dollars and 48 cents --->8+0.48=8.48

Alissa has 4dollars and 14 cents--->4+0.14=4.14 let

x--->amount of money that Carlos needs to give Alissa

The linear equation that represents this situation is 8.48-x=4.14+x

2x=8.48-4.14

2x=4.34

x=2.17

the amount of money is 2 dollars and 17 cents.

thank you

by Angel osei

Answer:

22x + 155

Step-by-step explanation:

9(x-3)+ 13(x+14)    use distributive law

9x - 27   + 13x + `182    gather 'like' terms

(9x+13x)  + ( -27+ 182)  simplify

22x + 155

Answer:

3x-10=65

Step-by-step explanation:

So, since he used the coupon, you can do 65+10=75.

The cost before the coupon is 75.

The cost of each shirt is 75/3, but that doesn't solve the question.

You can do (assume each shirt's cost is x)

3x-10=65

I could give more in depth but I can't see the options, sorry!

Answer:

(65+10) / 3= x

x would equal what each shirt costs

Step-by-step explanation:

answer:

[tex]\frac{4}{9}[/tex]

explanation:

the area of the larger square is 36 (6*6), and the area of the smaller square is 16 (4*4). to find the ratio of the area, simply just put 16 over 36 and simplify.

[tex]\frac{16}{36} = \frac{4}{9}[/tex]

--

if this helped, please consider giving brainliest !

Step-by-step explanation:

to calculate circumference:

[tex]2\pi \: r[/tex]

if the diameter is 16 then the radius would be 8.

[tex]2\pi \:r \\ = 2\pi(8) \\ = 16\pi \\ =Rationalize(50.26548245744) \\circumference = 50.27[/tex]

to calculate the area of a circle:

[tex]\pi {r}^{2} \\ = \pi( {8})^{2} \\ = Rationalize(201.06192982975) \\ area = 201.06 \: ^{2} [/tex]

The surface area of the rectangular prism is 94 in² and the surface area of the two triangular prisms is 142 in².

The total surface area of the rectangular prism is the space occupied by each of the face of it. It is the sum of area of all the faces of the prism.

Total surface area of the rectangular prism is calculated with the following formula.

[tex]A=2(lb+bh+lh)[/tex]

Here, (b) is the breath of the base (l) is the length and (h) is the height of the rectangular prism.

A rectangular prism is cut along a diagonal on each face to create two triangular prisms. The distance between A​ and B​ is 5​ inches.

The length, width, and height of the prism is 5in, 3 in and 4 in long. Put these value in the above formula as,

[tex]A=2(5\times3+3\times4+5\times4)\\A=2(15+12+20)\\A=2(47)\\A=94\rm\; in^2[/tex]

The formula for surface area of one triangle prism is,

[tex]A_t=(a+b+c)l+bh[/tex]

Here, (a,b,c) are the sides of a triangle. The sides of the triangular face are 3 in, 4in and 5 in long. Thus, the surface area of it is,

[tex]A_t=(4+3 +5)5+3\times4\\A_t=(12)5+12\\A_t=72\rm\;in^2[/tex]

For the two triangular prism,

[tex]A_t=2\times72\\A_t=142\rm\; in^2[/tex]

Hence, the surface area of the rectangular prism is 94 in² and the surface area of the two triangular prisms is 142 in².

Learn more about the total surface area of a rectangular prism here;

https://brainly.com/question/15456870

#SPJ1

Answer:

Exact form would be 1/8

and the decimal form is 0.125

Answer:

2^-3=1/8=0.125

Step-by-step explanation:

We have a negative exponent (-3) in order to make an exponent positive write the reciprocal of the number

We get 2^-3 = 1/(2^3)

and 2^3=8

so we get 2^-3= 1/8 =0.125

A number less than 5

⇒ x < 5

When all the numbers in the spinner are substituted in the inequality, we can see that only three numbers are less than 5.

⇒ 2, 3, and 4

[tex]\dfrac{\text{Total numbers less than 5}}{\text{Total numbers in the spinner}} = \text{Probabilty of getting less than 5}[/tex]

[tex]\dfrac{\text{Total numbers less than 5}}{\text{Total numbers in the spinner}} = \text{Probabilty of getting less than 5}[/tex]

     [tex]\bullet \ \text{Total numbers less than five: 3}[/tex]

     [tex]\bullet\ \text{Total numbers in the spinner} = 4[/tex]

[tex]\implies \boxed{\dfrac{3}{\text{4}} = \text{Probabilty of getting less than 5}}[/tex]

Option B is correct.

Answer:

To find the mean absolute deviation take each number in the data set, subtract the mean, and take the absolute value. Then take the sum of the absolute values. Now compute the mean absolute deviation by dividing the sum above by the total number of values in the data set.

6,6,3,4,4 - Mean Absolute Deviation: 1.12

Answer
[tex]\sqrt29[/tex]

Step-by-step explanation:

1. Write the distance formula:

[tex]\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}[/tex]

2. Substitute

Substitue (6, -4) and (1, -6) into

[tex]\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}[/tex]

[tex]\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}[/tex]

3. Calculate

[tex]\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}[/tex]

[tex]\sqrt(-5) ^{2} + (-2)^{2}[/tex]

[tex]\sqrt5 ^{2} + 2^{2}[/tex]

[tex]\sqrt25 + 4[/tex]

[tex]\sqrt29[/tex]

Answer:

~181 containers filled completely, 6 eggs left over

Step-by-step explanation:

2178 ÷ 12 (a dozen, the number of eggs per container) = 181.5 containers

181 × 12 = 2,172 eggs

2,178 eggs - 2,172 = 6 eggs left over

Applying the Pythagorean theorem, the amount of inches of wood required = Perimeter of triangle = 15 + 13 + 9 = 37 inches.

The Pythagorean theorem is used to find a side of a right triangle, and it states that if c is the hypotenuse and a and b are the other legs, therefore: c² = a² + b².

Find the altitude/height of the triangle using the Pythagorean theorem:

height = √(13² - 5²)

height = 12

Also, use the Pythagorean theorem to find the missing side (part of the longest side of the main triangle):

missing side = √(15² - 12²) = 9

Amount of inches of wood required = Perimeter of triangle = 15 + 13 + 9 = 37 inches.

Learn more about the Pythagorean theorem on:

https://brainly.com/question/16176867

[tex]a~~\pm~~bi\implies r[\cos(\theta ) \pm i\sin(\theta )] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt{3}~~ + ~~i\implies \stackrel{x}{\sqrt{3}}~~ + ~~\stackrel{y}{1} i\qquad \qquad \begin{cases} r=\sqrt{x^2+y^2}\\\\ \theta =\tan^{-1}\left( \frac{y}{x} \right) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]r=\sqrt{(\sqrt{3})^2+(1)^2}\implies r=\sqrt{3+1}\implies r=2 \\\\\\ \theta =\tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies \theta =\cfrac{\pi }{6} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 2\left[\cos\left( \frac{\pi }{6} \right)~~ + ~~i\sin\left( \frac{\pi }{6} \right) \right]~\hfill[/tex]

Check the picture below.

Answer:

no solution

Step-by-step explanation:

6x + 4x - 1 = 2(5x + 4) ← distribute parenthesis

10x - 1 = 10x + 8 ( add 1 to both sides )

10x = 10x + 9 ( subtract 10x from both sides )

0 = 9 ← not possible

this indicates the equation has no solution

Answer:

[tex]m=\frac{6}{7}[/tex]

Step-by-step explanation:

[tex]m=\frac{10-4}{9-2}=\frac{6}{7}[/tex]

Answer:  [tex]\frac{6}{7}[/tex]

Explanation:

In the numerator we have [tex]y_2 - y_1 = 10-4 = 6[/tex] to represent the change in y, aka the rise. This is the vertical change. It's how much we go up.

The denominator has [tex]x_2 - x_1 = 9-2 = 7[/tex] to represent the run. It is the horizontal change, or how much we go to the right.

We go up 6 and to the right 7 to have a slope of [tex]m = \frac{\text{rise}}{\tex{run}} = \frac{6}{7}[/tex]

Here's how you can show the steps

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{10-4}{9-2}\\\\m = \frac{6}{7}\\\\[/tex]

Note: To write [tex]\frac{6}{7}[/tex] on the keyboard, you can type 6/7

Answer:

y = -2/3x + 4

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

These two are similar triangles. 3 corresponds to 9, and x corresponds to 6. Since 3 is being multiplied by 3 to get 9, x*3 should equal 6. Therefore, x is 2.

like salsa              hate salsa               total

like ballet                       32                         42                          74  

hate ballet                      22                           4                          26

total                                54                         46                         100

if a student does not like ballet (there is 26 that do not like ballet)..what is the probability that the student does not like salsa..of those 26 that do not like ballet, 4 do not like salsa...

4/26 = 0.1538 = 15.38% rounds to 15.4% <=

Answer:

-5 and 9

Step-by-step explanation:

To find the solutions we will factor the equation.

First we take out a 2:

[tex]2(x^2-4x-45)[/tex]

Then we can factor again:

[tex]2(x+5)(x-9)[/tex]

This provides us with the answer of:

[tex]x+5=0[/tex]

and

[tex]x-9=0[/tex]

Hence the solutions of -5 and 9.

The two vertices (-5, 8) and (-5, -6) of the rectangle have the same x-coordinates

The distance between the two vertices is 14 units

The vertices are given as:

(-5, 8) and (-5, -6)

The distance between the two vertices is calculated using:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

So, we have:

d = √[(-5 + 5)^2 + (8 + 6)^2]

Evaluate the sum

d = √196

Evaluate the square root

d = 14

Hence, the distance between the two vertices is 14 units

Read more about distance at:

https://brainly.com/question/7243416

Answer: 14

Step-by-step explanation:

Answer:

Biased

Step-by-step explanation:

Answer:

3cm

Step-by-step explanation:

the radius is half the diameter

If the diameter = 6, the radius must = 3.

Hope this helps!

- profparis

There's sufficient evidence to reject the null hypothesis between the treatment group and placebo group.

From the complete information, the value of the test statistic is -1.76 and the p-value is 0.085.

In this case, there's sufficient evidence to reject the null hypothesis. Therefore, there's evidence to warrant the rejection of the claim that the two samples are from population with same mean.

Learn more about hypothesis on:

https://brainly.com/question/15980593

Answer:

  7.2224

Step-by-step explanation:

The value of the summation is given by the formula ...

  Sn = (a1)(1 -r^n)/(1 -r) . . . . . where a1 is the first of n terms, and r is the common ratio.

Your sum has first term and ratio ...

  a1 = 2(0.6) . . . . . summation term for n=1

  r = 0.6

So the sum is ...

  [tex]\displaystyle \sum_{n=1}^4{2(0.6^n)}=2(0.6)\dfrac{1-0.6^4}{1-0.6}=\dfrac{1.2}{0.4}(0.8704) = 2.6112[/tex]

Then the value of the entire given expression is ...

  [tex]\displaystyle 2+2\sum_{n=1}^4{}2(0.6^n)=2+2(2.6112)=\boxed{7.2224}[/tex]

_____

A calculator can help you find the value.

Answer:

3

Step-by-step explanation:

3/10 = .3

Answer:

Step-by-step explanation:

m∠ABC + m∠BAC + m∠ACB = 180°

a + 2a + 6a = 180°

9a = 180°

a = 20°

m∠ABC = 20°

m∠BAC = 2 × 20° = 40°

m∠ACB = 6 × 20° = 120°

Answer:

2.5*10^-8 for sea water, 3.16*10^-11 for milk of magnesium, and 790 times greater

Step-by-step explanation:

We're trying to find the concentration of H+ in the solution using the pH, so

let's define pH first.
pH=-log(H+)

This equation can be re-written as
H+ = 10^(-pH), or H+ = 1/(10^pH)

The pH of sea water is 7.6, so the concentration of H+ in sea water is 10^(-7.6), which is about 2.5*10^-8

The pH of milk of magnesium is 10.5, so the concentration of H+ in milk of magnesium is 10^(-10.5), which is about 3.16*10^-11

To compare how much more the concentration of the hydrogen ion is, we just divide

(2.5*10^-8)/(3.16*10^-11) = 791, or 790 with sig figs.

Answer:

Step-by-step explanation:

You are correct that the relationship is inverse, and that the product of x and y is a constant, 25.

__

The equation should be written so that y is a function of x:

  [tex]\boxed{y=\dfrac{25}{x}}[/tex]

The x in the denominator clearly shows that y is proportional to the inverse of x.

Answer:

Linear relationship: increasing or decreasing one variable will cause a corresponding increase or decrease in the other variable.

Inverse relationship:  the value of one variable decreases as the value of the other variable increases.

Exponential relationship: a constant change in the independent variable (x) gives the same proportional change in the dependent variable (y)

Question 5

As the x-value increases (by one unit), the y-value decreases.

Therefore, this is an inverse relationship.

The y-values can be calculated by dividing 25 by the x-value.

[tex]\sf y=\dfrac{25}{x}[/tex]