How do function models help us to understand the world?

Answer:

  (B)  $200,000

Step-by-step explanation:

The value of the simple interest account can be found using the formula ...

  A = P(1 +rt) . . . . . where P is the principal invested at rate r for t years

__

Using the given values, we find the value of the account to be ...

  A = $125,000(1 +0.04×15) = $125,000(1.6)

  A = $200,000

Katie's savings will be worth $200,000 after 15 years.

Answer 84.500

Step-by-step explanation: you have to multiply 1,300x65 then 300x 40

and  then 12,000

Answer: Division Property of equality

Step-by-step explanation:

5d= 75

1. Isolate the variable and remember, if the number is next to the letter, it means to multiply.

2. Reverse PEMDAS so instead of multiplying, divide instead.

3. 75/ 5 equals 15.

d=15

Answer: d=. 15

Step-by-step explanation:

Answer:

1) 14.137 2)10

Step-by-step explanation:

area of sector is central angle / 360 times (pi)(r^2)

45/360 x pi (6^2)

1/8 x 36pi

14.137

3-4-5- right triangle. Or Pythagorean Theorem.

6^2 + 8^2 = c^2

c= 10

Answer:

x = 35.20735

Step-by-step explanation:

Use tanФ = opposite/adjacent

tan58 = x/22

x = 35.20735

The residual points include the difference between the value in Irwin's dataset and the predicted values

The residual is calculated using:

Residual = Actual points - Predicted points

The actual points are:

(1,43), (3, 36), (5,22), (6, 25), (8,14)

The predicted points are:

(1,44), (3, 35), (5,26), (6, 22), (8,13)

Using the residual formula above, we have the residuals to be:

(x,y) = (1,-1), (3, 1), (5,-4), (6, 3), (8,1)

See attachment for the residual plot

Read more about residuals at:

https://brainly.com/question/1447173

Answer:

50 + 20 = 70
70 + 25 = 95
150 + 95 = 245

In conclusion, 150 + 20 + 25 equals to a total amount of 215.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

hemo

150 + 20 + 25

= 100 +50+20+20+5

= 100+90+5

=195

Answer:

Obviously Boston, since -27 is much less than 37

Using the Empirical Rule, it is found that the lifespans, in months, are given by:

1. 24 and 32.

2. 20 and 36.

3. 16 and 40.

It states that, for a normally distributed random variable:

Hence, considering the mean of 28 months and the standard deviation of 4 months, the life spans are given by:

1. 24 and 32.

2. 20 and 36.

3. 16 and 40.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

Approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.

Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.

A 15-meter by 23-meter garden is divided into two sections. In this rectangle,

Here, a vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. The length of the left side of the square will be 15 long. Thus, the lenght of its diagonal is,

[tex]d_1=15\sqrt{2}\\d_1=21.213\rm\; m[/tex]

The length of the sidewalk in smaller rectangle in the right side of figure is,

[tex]d_2=\sqrt{15^2+8^2}\\d_2=17\rm\; m[/tex]

Sum of the lengths of the two sidewalks using the pythagoras theorem is,

[tex]S=21.2+17\\S=38.2\rm\;m[/tex]

Thus, approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.

Learn more about the Pythagoras theorem here;

https://brainly.com/question/343682

Answer:

D 38.2

Step-by-step explanation:

E2020

Answer: x<-1

Step-by-step explanation:

The answer is A!

Answer:

See below.

Step-by-step explanation:

Solving the inequality :-

Graph A shows the solution to the inequality correctly

Answer:

42 yards.

Step-by-step explanation:

3 x 6 is 18. 18 x 84 is 1512. 1512 divided by 12 is 126. 126 divided by 3 is 42.

Answer:

9

41/4

23/2

51/4

14

Step-by-step explanation:

The first term is the first term that is given. Just copy it.

Each next term is the previous term plus the common difference.

First term: a_1 = 9

Second term: a_2 = 9 + 5/4 = 36/4 + 5/4 = 41/4

Third term: a_3 = 41/4 + 5/4 = 46/4 = 23/2

Fourth term: a_4 = 46/4 + 5/4 = 51/4

Fifth term: a_5 = 51/4 + 5/4 = 56/4 = 14

Answer:

[tex]y=0x+2[/tex]

Step-by-step explanation:

Given the following question:

Point A = (3, 2) = (x1, y1)
Point B = (-6, 2) = (x2, y2)

To write the following points in slope intercept form we first need to calculate the slope by using the formula for slope or rise over run.

[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{2-2}{-6-3} =\frac{0}{-9}[/tex]
[tex]0\div-9=0[/tex]
[tex]m=0[/tex]

Now that we have to slope, we can now write the points in slope intercept form by using the formula y = mx + b and solve for b.

[tex]y=mx+b[/tex]
[tex]y=2[/tex]
[tex]m=0[/tex]
[tex]x=3[/tex]
[tex]2=0(3)+b[/tex]
[tex]0\times3=0[/tex]
[tex]2=0+b[/tex]
[tex]2+0=2[/tex]
[tex]2=b[/tex]
[tex]b=2[/tex]
[tex]y=0x+2[/tex]

Your answer in slope intercept form is "y = 0x + 2."

Hope this helps.

Answer:

59

Step-by-step explanation:

[tex](-6)^2-5(-6)-7[/tex]

[tex]36+30-7[/tex]

[tex]59[/tex]

Answer:

⠀

Step-by-step explanation:

⠀

So,

[tex]{\longrightarrow \it\qquad { \ { (6n - 4) {}^{ \circ} = {(5n + 7)}^{ \circ} }}}[/tex]

⠀

Removing the brackets,

[tex]{\longrightarrow \it\qquad { \ { 6n - 4{}^{ \circ} = {5n + 7 \: }^{ \circ} }}}[/tex]

[tex]{\longrightarrow \it\qquad { \ { 6n - 5n = { 7 \: }^{ \circ} +4{}^{ \circ} }}}[/tex]

[tex]{\longrightarrow \it\qquad { \pmb{ n = { 11 \: }^{ \circ} }}}[/tex]

⠀

Therefore,

We will use the concept of Vertically Opposite angle here, i.e at the point of Intersection of two straight lines, the VOA (Vertically Opposite Angles) are equal

By using this property we will be having ;

[tex]{:\implies \quad \sf (6n-4)^{\circ}=(5n+7)^{\circ}}[/tex]

[tex]{:\implies \quad \sf 6n-5n=7+4}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{n=11}}}[/tex]

This is the required answer

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\stackrel{\textit{"z" inversely proportional to "t"}}{z=\cfrac{k}{t}}\qquad \textit{we also know that} \begin{cases} t=9\\ z=28 \end{cases} \\\\\\ 28=\cfrac{k}{9}\implies 252=k~\hfill \boxed{z=\cfrac{252}{t}} \\\\\\ \textit{when t = 12, what is "z"?}\qquad z=\cfrac{252}{12}\implies z=21 \\\\\\ \textit{when z = 36, what is "t"?}\qquad 36=\cfrac{252}{t}\implies t=\cfrac{252}{36}\implies t=7[/tex]

Answer:

x² + y² - 12x - 6y + 29 = 0

Step-by-step explanation:

Simplifying the equation using (a + b)² = a² + 2ab + b²:

(x - 6)² + (y - 3)² = 16

⇒ [x² - 2(x)(6) + 6²] + [y² - 2(y)(3) + 3²] = 16

⇒ [x² - 12x + 36] + [y² - 6y + 9] = 16

⇒ x² - 12x + 36 + y² - 6y + 9 = 16

General form of a circle = x² + y² + Cx + Dy + E = 0

Before we reorganize the equation in general form, we need to have the R.H.S as 0. For that, we need to subtract 16 both sides.

Subtract 16 both sides:

⇒ x² - 12x + 36 + y² - 6y + 9 = 16

⇒ x² - 12x + 36 + y² - 6y + 9 - 16 = 16 - 16

⇒ x² - 12x + 20 + y² - 6y + 9 = 0

Reorganizing the equation in general form:

x² - 12x + 20 + y² - 6y + 9 = 0

⇒ x² - 12x + 20 + y² - 6y + 9 = 0

⇒ x² + y² - 12x + 20 - 6y + 9 = 0

⇒ x² + y² - 12x + 20 - 6y + 9 = 0

⇒ x² + y² - 12x - 6y + 20 + 9 = 0

⇒ x² + y² - 12x - 6y + 29 = 0

Thus, the equation in general form is x² + y² - 12x - 6y + 29 = 0.

Step-by-step explanation:

The answer is in the picture

Answer:

Her solution is incorrect. The correct solution for the equation is x=7

Step-by-step explanation:

Sasha solved the equation incorrectly.

The correct way to solve this equation would be:

8x = 56

Divide both sides by 8.

[tex]\frac{8x}{8}= \frac{56}{8}[/tex]

You would get x=7.

This equation has 1 solution.

Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!

Stay Brainy!

−Kallmekrish

The average rates of change of a function f(x) and g(x) are their slopes

The average rate of change of the function f(x) is always less than the average rate of change of the function g(x)

The average rate of change of a function f(x) over the interval [a,b] is calculated as:

[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]

The average rates of change of the functions over the intervals are:

A. 0 ≤ x ≤ 3

[tex]m_1 = \frac{f(3) - f(0)}{3 - 0} = \frac{5 * 3 - 5 *0}{3 - 0} = 5[/tex] ---- f(x)

[tex]m_2 = \frac{g(3) - g(0)}{3 - 0} = \frac{25 * 3 - 25 *0}{3 - 0} = 25[/tex] --- g(x)

B. 0 ≤ x ≤ 2

[tex]m_1 = \frac{f(2) - f(0)}{2 - 0} = \frac{5 * 2 - 5 *0}{2 - 0} = 5[/tex] ---- f(x)

[tex]m_2 = \frac{g(2) - g(0)}{2 - 0} = \frac{25 * 2 - 25 *0}{2 - 0} = 25[/tex] --- g(x)

C. 3 ≤ x ≤ 6

[tex]m_1 = \frac{f(6) - f(3)}{6 - 3} = \frac{5 * 6 - 5 *3}{6 - 3} = 5[/tex] ---- f(x)

[tex]m_2 = \frac{g(6) - g(3)}{6 - 3} = \frac{25 * 6 - 25 *3}{6 - 3} = 25[/tex] --- g(x)

D. 1 ≤ x ≤ 2

[tex]m_1 = \frac{f(2) - f(1)}{2 - 1} = \frac{5 * 2 - 5 *1}{2 - 1} = 5[/tex] ---- f(x)

[tex]m_2 = \frac{g(2) - g(1)}{2 - 1} = \frac{25 * 2 - 25 *1}{2 - 1} = 25[/tex] --- g(x)

From the above computation, we can see that:

The average rate of change of the function f(x) = 5x is always less than the average rate of change of the function g(x) = 25x

Read more about average rates of change at:

https://brainly.com/question/8728504

Using the two given solutions and the general absolute value function we will get:

|x + 9|  = 27

The two solutions are:

x = 0 and x = -18.

Remember that the absolute value equation is something like:

|x - a| = b

If we want to have these solutions, then:

|0 - a| = b

|-18 -a| = b

From the first one, we have:

|-a| = b

Replacing that on the second equation we get:

|-18 -a| = |-a|

Notice that if we take a = -9, then we have:

|-18 + 9| = |+9|

|-9| = |+9|

This is true, so a = -9.

Then we find the value of b:

|18 + 9| = b = 27

Then the absolute value equation is:

|x + 9|  = 27

If you want to learn more about absolute value equations, you can read.

https://brainly.com/question/3381225

Step-by-step explanation:

What is 40% of 400?

Answer:

It would be,

The people who volunteer usually have a motive to do so and will be the only ones represented.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

[tex]5x^2 +3x +2 = 0\\\\\text{Apply the quadratic formula,}~ x=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\\text{In this case,}~a= 5, ~ b = 3~ \text{and}~ c = 2\\\\ \\x=\dfrac{-3\pm \sqrt{3^2 -4\cdot 5 \cdot 2}}{2\cdot 5}\\\\~~~=\dfrac{-3 \pm \sqrt{9-40}}{10}\\\\~~~=\dfrac{-3 \pm \sqrt{-31}}{10}\\\\~~~=\dfrac{-3 \pm i\sqrt{31}}{10}\\\\\text{So, there are 2 solutions,}~ x=\dfrac{-3 + i\sqrt{31}}{10}~ \text{and} ~x=\dfrac{-3 -i\sqrt{31}}{10}[/tex]

Another  way to find the number of solutions is by looking at the highest exponent(Degree), which indicates the number of solutions.  

[tex]\\ \rm\rightarrowtail 5x^2+3x+2=0[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm \sqrt{9-40}}{10}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm\sqrt{-31}}{10}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm\sqrt{31}i}{10}[/tex]

Answer:

4

Step-by-step explanation:

To calculate the mean or average, add all the data point up and whatever the amount of data point there are is supposed to be divided by the sum of the data points. So in this case, 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. This is the sum of the data points. Now we have to divide by the amount of data points which is 7 (0 obviously has no value whatsoever).  28 divided by 7 is 4. The average/mean of the number of post made is therefore 4.

Hope this helps,

IShowSpeed's Right Hand Enthusiast

Area of parallelogram is Base×height

10×18=15× x

x= 12

hope it helps

Answer:

x = 12

Step-by-step explanation:

So, area of a parallelogram is base times height.

In this picture, one of the base, height pair is 18 and 10.

18 * 10 = 180

The other base, height pair is 15 and x.

So, 15 and x should equal to 18 * 10.

Then, 15x = 180.

Divide both sides by 15, and you get 15x/15 = x and 180/15 = 12.

So, x = 12