a person invested $330 in an account growing at a rate allowing the money to double every 8 years. Write a function showing the amount of money in the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year, to the nearest hundredth of a percent.

Answer:

Part A) The distance between Whitney's house and Anh's house is 6.5 miles.

Part B) The total distance traveled by Whitney during the trip was 9.5 miles.

Step-by-step explanation:

Part A)

Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.

So, instead, we can calculate Whitney's total displacement. Total displacement is given by:

[tex]\displaystyle \text{Displacement}=\int_a^bv(t)\, dt[/tex]

Where v(t) is the velocity function.

So, the displacement of Whitney when she traveled from her house to Anh's house will be:

[tex]\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt[/tex]

To calculate the integral, we can split it off at t = 11, t = 16, and t = 24.

The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:

[tex]\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt[/tex]

Now, we can calculate the area of each figure.

The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:

[tex]\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}[/tex]

The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:

[tex]\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}[/tex]

Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:

[tex]\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}[/tex]

However, notice that the second figure is below the x-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.

Then the displacement will be:

[tex]\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}[/tex]

So, the distance between Whitney's house and Anh's house is 6.5 miles.

Part B)

The total distance differs from displacement in that it includes all the distances in both directions. It is given by:

[tex]\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt[/tex]

In other words, all of our values are now positive. We will utilize the same strategy:

[tex]\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt[/tex]

Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:

[tex]\displaystyle \text{Distance} =5.6+1.5+2.4=9.5[/tex]

Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.

Answer:

true

Step-by-step explanation:

Answer:

true?

Step-by-step explanation:

Answer:

6) 5(1/3)

7) 5(1/3)

8) 3(3/5) or 18/5

because answer were cut off

Answer:

7) 5 [tex]\frac{1}{3} \\[/tex]

8) 5 [tex]\frac{1}{3}[/tex]

9) 3 [tex]\frac{3}{5}[/tex]

hope it is right, just use your calculator

Answer:

1/8 = 0.125

1/9 = 0.1

2/3 = 0.6

4/7 = 0. 571428

3/10 = 0.3

5/3 = 1.6

9/5 = 1.8

5/6 = 0.83

Answer:

x=5

Step-by-step explanation:

The pythagorean theorem stats a^2+b^2=c^2. We are already given the values of the two legs of the triangle so we need to solve for the length of the hypotenuse (the longest part of the triangle). To do so, you put in 3 and 4 as a and b so you get 3^2+4^2=c^2. After squaring both numbers you get 16+9=c^2. Then you add 16 and 9 to get 25=c^2. To get rid of the power of 2, we square root both sides to get rid of the exponent. Since 25 is a perfect square, you get c=5 which means that the x value eqals 5.

Step-by-step explanation:

Answer:

15×3+7(4+1)-52

15×3+7(5)-52

15×3+35-52

45+35-52

80-52

=28

Answer:

44

Step-by-step explanation:

ieubedhjdidieuehehbebeheiduudueuehhehehe

Answer:

Slope, m = -12

Step-by-step explanation:

Given the following data;

Points on the x-axis (x1, x2) = (-2, -1)

Points on the y-axis (y1, y2) = (17, 5)

To find the slope, m;

Mathematically, slope is given by the formula;

[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]

[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

Substituting into the equation, we have;

[tex] Slope, m = \frac {5 - 17}{-1 - (-2)} [/tex]

[tex] Slope, m = \frac {-12}{-1 + 2} [/tex]

[tex] Slope, m = \frac {-12}{1} [/tex]

Slope, m = -12

Answer:

B

Step-by-step explanation:

minimum = 1

first quartile = 12

median = 6

third quartile = 16

maximum = 19

The inner circle circumference is 18 and the outer is 4

Answer:

the big one has a circumstance of 2*pi*9=56.52

the small one 2*pi*7=43.96

difference = 12.56= 4pi

Answer:

3?

Step-by-step explanation:

Solution :

Given :

[tex]$n_1=388$[/tex] , [tex]$x_1 = 294, \ n_2 = 566, \ x_2 = 38$[/tex]

Sample proportion, [tex]$(\hat p_1)=\frac{x_1}{n_1}$[/tex]

                                        [tex]$=\frac{294}{388}$[/tex]

                                       = 0.7577

Sample proportion, [tex]$(\hat p_2)=\frac{x_2}{n_2}$[/tex]

                                        [tex]$=\frac{38}{566}$[/tex]

                                       = 0.0671

For 95 % CI, z = 1.96

The confidence interval for the population proportion,

[tex]$p_1-p_2=(\hat p_1-\hat p_2)\pm z \left\{\sqrt{\frac{\hat p_1 \times (1- \hat p_1)}{n_1}+\frac{\hat p_2 \times (1- \hat p_2)}{n_2}}\right\}$[/tex]

           [tex]$=(0.7577-0.0671)\pm 1.96 \left\{\sqrt{\frac{0.7577 \times (1- 0.7577)}{388}+\frac{0.0671 \times (1- 0.0671)}{566}}\right\}$[/tex]

[tex]$=0.6906 \pm 1.96 \times \left 0.0241$[/tex]

= [tex]$0.6906 \pm 0.0472 $[/tex]

Lower limit : 0.6906 - 0.0472 = 0.6434

Upper limit : 0.6906 + 0.0472 = 0.7378

Answer:

[tex]\frac{28}{3}=t[/tex]

Step-by-step explanation:

[tex]\frac{4}{3}=\frac{t}{7}[/tex]

Use cross products to simplify the equation. Multiply the denominator of the second fraction by the numerator of the first fraction, and the denominator of the first fraction by the numerator of the second,

[tex](4)(7) = (3)(t)[/tex]

Simplify,

[tex]28=3t[/tex]

Inverse operations,

[tex]\frac{28}{3}=t[/tex]

Answer:

what are the statements

Step-by-step explanation:

Answer:

10/6 or 5/3

Step-by-step explanation:

1/2 ---> 3/6

1/3 ---> 2/6

5/6 ---> 5/6

Add those new fractions together:

(3/6) + (2/6) + (5/6) = 10/6 or 5/3

Answer:

10/6 or 5/3

Step-by-step explanation:

Hope it help's :)

Answer:

Smaller part = $33 and total amount = $77

Step-by-step explanation:

Let the numbers be 4x and 3x.

The larger number is $44

ATQ,

44x = 44

x = 11

(1) Smaller number = 3x

= 3(11)

= 33

(2) Total amount

T = 33+44

T = 77

Hence, this is the required solution.

Answer:

you did not send the graph-_-

Step-by-step explanation:

Answer:

dont know im sorry

Step-by-step explanation:

Answer:

3.67

Step-by-step explanation:

Because, 9% is literally just 9/100

and when you multiply that by 245 then you get 3.67

Answer:

(g0f)= (2x0+6 x 0x3)= 8x3= 24

Step-by-step explanation:

I'm not sure

:) sorry

Answer:

14 unit I think hope it helps

Answer:

D. y = –2x + 10  

Step-by-step explanation:

1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].  

Since [tex]m[/tex] represents the slope, substitute -2 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (5,0) into the formula as well. This gives the following equation:

[tex]y - 0 = -2(x-5)\\y = -2(x-5)[/tex]

2) Expand the right side of the equation to find the answer:

[tex]y = -2(x-5)\\y = -2x+10[/tex]

So, option D is correct.

Answer:

He had origanlly had 68 altogether

Step-by-step explanation:

Because if u count the scrateched ones which was 6 is now 62 then add the other six because there was 12 and his brother scrateched half which is basically 12 / 2 = 6 so if u add the six is 68

What Im basically saying is 56 + 12 = 68

Answer:

theyre correct

Step-by-step explanation: