Using the formula S = P(1 + r)t, where P is the original principal, r is the annual interest rate, and t is the number of years, what is the investment savings, S, if P = $14,500.00, r = 7.5%, and t = 5 years?

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]

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.

Answer: Angle 3 and Angle 2

Step-by-step explanation:

The angles form a linear pair, which means they are supplementary.

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:

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]

Answer:

18.85 years

Step-by-step explanation:

Using the [tex]A=P(1+\frac{r}{n} )^{nt}[/tex] we can manipulate it to give us time.

However, let's identify our variables:

A is our final amount which is given to us, $1400.

P is our principle which is $500.

r is our rate which is 5.5% which can be traducted into 0.055.

n is the # of time our money get compounded per year, in this case quarterly means 4 times a year therefore n = 4.

t is time and is what we are trying to solve for.

Now let's manipulate our equation to find t:

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

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

[tex]\frac{1400}{500} =(1+\frac{0.055}{4} )^{4t}[/tex]

[tex]2.8=1.01375^{4t}[/tex]

[tex]log_{1.01375}(2.8)=log_{1.01375}1.01375^{4t}[/tex]

[tex]log_{1.01375}(2.8)=4t[/tex]

[tex]\frac{log_{1.01375}(2.8)}{4} =t[/tex]

[tex]18.84876253=t[/tex]

It would take about 18.85 years in order for you to accumulate at least $1400.

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:

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Answer:

3cm

Step-by-step explanation:

the radius is half the diameter

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

Hope this helps!

- profparis

Answer:

y = -2/3x + 4

Step-by-step explanation:

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

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:

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Answer: 14

Step-by-step explanation:

Answer:

144 sq cm

Step-by-step explanation:

The base is a triangle. Area of a triangle is:

A = 1/2 b • h

A = 1/2(4)•3

A = 6

There are 2 of these bases.

Area of 2 bases= 12.

There are three rectangular sides. Area of a rectangle is:

A = l × w (or b•h)

A = 5 × 11 = 55

A = 3 × 11 = 33

A = 4 × 11 = 44

Add up three rectangular faces and two bases for Total Surface Area:

12 + 55 + 33 + 44

= 144 sq cm

Answer:

144 cm ²

Step-by-step explanation:

The surface area of a right triangular prism is made up of 2 congruent triangles (these are called the "bases") and 3 rectangles.

Surface area of a right triangular prism formula

Surface area = (S₁ + S₂ + S₃)L + bh

where:

⇒ Surface area = (3 + 4 + 5)11 + 4 × 3

                          = (12)11 + 12

                          = 132 + 12

                          = 144 cm²

[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:

Step-by-step explanation:

Owing represent a negative balance.

So the inequality for this case is:

The word owing is given which simply denotes to negative transaction

So here the inequality is

Or

In order to solve a proportion, you should cross-multiply:-

[tex]\bf{\displaystyle\frac{3x}{10} =\frac{3}{2}}[/tex]

Multiply 3x times 2 and 10 times 3:-

[tex]\bf{6x=30}[/tex]

Divide both sides by 6:-

[tex]\boxed{\bf{x=5}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

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:

3

Step-by-step explanation:

3/10 = .3

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]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:

[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]

--

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Answer:

Cylinder height = 10

Semi-circle height = 3

Cone height = 4

Step-by-step explanation:

The height of the cylinder is always going to be the long side. 6 is the diameter of its circle. Here is a list of variables:

Diameter, D = 6

Radius, r = 3

Slant height of cone, c = 5

To find the height of the cylinder, we will need to find the height's of the cone and semi-circle:

CONE (see image attached)

a² + b² = c²

3² + h² = 5²

h² = 25 - 9

h = √16

h = 4

SEMI-CIRCLE

h = radius

h = 3

CYLINDER

Cylinder height = total h - semi-circle h - cone h

h = 17 - 3 - 4

h = 10

I'm not sure if you're trying to solve for volume, so I'll end it here LOL. Hope this helps and have a great evening!

Answer:

Biased

Step-by-step explanation:

Although Alex and Lauren will both step into position 4,6, they will not do it at the same time, so they will not meet.

Lauren:

Alex:

Both will step in the position 4,6, However, Lauren will be in this positon in the second 4, while Alek will do it on the second 3.

Learn more about parametric equations in: https://brainly.com/question/12718642

#SPJ1

Answer:

multiple tasking them right

Answer:

results-driven

Step-by-step explanation:

Answer:

option A

Step-by-step explanation:

Answer os option a

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:

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