A person invests 4000 dollars in a bank. The bank pays 6.25% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 9600 dollars?

Answer:

B. 3/4 cup of water

Step-by-step explanation:

1 1/3 + 1 1/2 + 1 2/3 + 3/4 = 5 1/4

6 - 5 1/4 = 3/4

Answer: B or 3/4

Step-by-step explanation:

ok first add all the amounts he drank together

1 1/3 + 1 1/2 + 1 2/3 + 3/4

because the denominators are all different, you have to change them to a common denominator, which is 12. i've also changed them to improper fractions.

1 1/3 = 4/3 = 16/12    1 1/2 = 3/2= 18/12    1 2/3 = 5/3= 20/12   3/4 = 9/12

now add them all together

16/12 + 18/12 + 20/12 + 9/12 = 63/12

now convert the original 6 cups to an improper fraction with the denominator of 12

6 = 72/12

now subtract 63/12 (the amount he drank) from 72/12 (the amount he started with)

72/12 - 63/12 = 9/12

9/12 is able to be simplified to 3/4

so the correct answer is B, or 3/4

Answer:

Step-by-step explanation:

6.3 x10^-5 -7.200 x10^-3= - 0.007137=7.137x10-3

Answer:-7.137 x 10^-3

Step-by-step explanation:

Answer:

[tex]y = 320x +2080[/tex]

Step-by-step explanation:

Given

Population in 1995 = 2400

Population in 2000 = 4000

Required

Determine the linear equation

Let the years be represented with x.

In 1995, x = 1 i.e. the first year

In 2000, x = 6

Let y represents the population

When x = 1; y = 2400

When x = 6; y = 4000

First, we calculate the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{4000 - 2400}{6 - 1}[/tex]

[tex]m = \frac{1600}{5}[/tex]

[tex]m = 320[/tex]

Next, we calculate the line equation as follows:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex]y - 2400 = 320(x - 1)[/tex]

[tex]y - 2400 = 320x - 320[/tex]

[tex]y = 320x - 320 + 2400[/tex]

[tex]y = 320x +2080[/tex]

Answer:

1) 0.99348

2) 0.55668

Step-by-step explanation:

Assume that men’s weights are normally distributed with a mean given by  = 172lb and a standard deviation given by  =29lb. Using the Central Limit Theorem to solve the following exercises

When given a random number of samples, we use the z score formula:

z-score is z = (x-μ)/σ/√n where

x is the raw score

μ is the population mean

σ is the population standard deviation.

(1) If 36 men are randomly selected, find the probability that they have a mean weight greater than 160lb.

For x > 160 lb

z = 160 - 172/29/√36

z = 160 - 172/29/6

z = -2.48276

Probability value from Z-Table:

P(x<160) = 0.0065185

P(x>160) = 1 - P(x<160) = 0.99348

(2) If 81 men randomly selected, find the probability that they have a mean weight between 170lb and 175lb.

For x = 170 lb

z = 170 - 172/29/√81

z = 170 - 172/29/9

z = -0.62069

Probability value from Z-Table:

P(x = 170) = 0.2674

For x = 175 lb

z = 175 - 172/29/√36

z = 175- 172/29/6

z = 0.93103

Probability value from Z-Table:

P(x = 175) = 0.82408

The probability that they have a mean weight between 170lb and 175lb is calculated as:

P(x = 175) - P(x = 170)

0.82408 - 0.2674

= 0.55668

Answer:  Approximately 1.9 atm

============================================

Work Shown:

[tex]P_1*V_1 = P_2*V_2 \ \text{ ... Boyle's Law}\\\\4.5*1.5 = P_2*3.5\\\\6.75 = P_2*3.5\\\\P_2*3.5 = 6.75\\\\P_2 = \frac{6.75}{3.5}\\\\P_2 \approx 1.92857142857142\\\\P_2 \approx 1.9\\\\[/tex]

If the volume is 3.5 liters, then the pressure is approximately 1.9 atm.

Note the increase in volume leads to the reduction of pressure, and vice versa. The two variables have an inverse relationship.

-----------

As a check,

[tex]P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.9*3.5\\\\6.75 \approx 6.65\\\\[/tex]

We don't get the exact thing on both sides, but the two sides are close enough. We have rounding error due to P2 being not exact.

A more accurate check could be

[tex]P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.92857*3.5\\\\6.75 \approx 6.749995\\\\[/tex]

which has the two sides much closer to one another. This helps us verify the answer.

Answer:

sure easy man the carrot is blue and green and orange there naswer soled

Answer:

x = 26

Step-by-step explanation:

m<B = m<E = (x + 17)°

180 - (25 + 112) = (x + 17) (sum of ∆)

180 - 137 = x + 17

43 = x + 17

Subtract both sides by 17

43 - 17 = x

x = 26

Answer:

A, 2 5/8 cups

Step-by-step explanation:

Since six dozen brownies is three times as much as two dozen, we can multiply 7/8 cups by 3. 3 x 7/8 = 21/8 If we simplify this fraction, it is 2 5/8. Therefore the answer is A, 2 5/8 cups.

Answer:

yes 40

Step-by-step explanation:

she got it correct

Answer:

the best interest rate would be a minimum of 3.5% annual interest

Step-by-step explanation:

An inflation rate of 3.5% would mean that the buying power of Lydia's money would decrease by 3.5% every single year. Therefore, the best interest rate would be a minimum of 3.5% annual interest. That way she would at least maintain the same buying power with her money as the day that she first placed it in the account. Any interest rate higher than 3.5% would be even better as Lydia will begin to make a profit from her savings.

$8.75 because 26.25 divided by 3 equals $8.75.

hope this helps

um kevin bought 31.50 of what? food?

Answer:

c is the correct answer

Step-by-step explanation:

Let's write this question as a systems of equations to solve.

x-y=7 (the difference)

x+y=23 (the sum)

Through the process of elimination we get

2x=30

x=15.

With that value of x, we can plug it back into any of the previous equations to get the value of y.

(15)-y=7 (Solve for y)

y=8.

The two numbers are 15 and 8.

Answer:

81 9^2

Step-by-step explanation:

3•3= 9

3•3=9

9•9=81

and 9•9=81

Answer:

0.88

Step-by-step explanation:

-5.37 + 8.14 - 1.89

-5.37 + 6.25

= 0.88

Step-by-step explanation:

please i worked on paper worksheet

please see it

Answer:

30

Step-by-step explanation:

Perimeter of rectangle = 5y - 1 + 4y + 2 + 5y - 1 + 4y + 2

                                      = 18y + 2

18y + 2 = 128

18y = 128 - 2

     = 126

y = 126 ÷ 18

y = 7

Length of AD = 4y + 2

                      = 4(7) + 2

                      = 28 + 2

                      = 30

Answer:

See below for Part A.

Part B)

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

Step-by-step explanation:

Part A)

The parabola given by the equation:

[tex]y^2=4ax[/tex]

From 0 to h is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

[tex]y=f(x)=\sqrt{4ax}[/tex]

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]

Where r(x) is the distance between f and the axis of revolution.

From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:

[tex]r(x)=y(x)=\sqrt{4ax}[/tex]

Now, we will need to find f’(x). We know that:

[tex]f(x)=\sqrt{4ax}[/tex]

Then by the chain rule, f’(x) is:

[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]

For our limits of integration, we are going from 0 to h.

Hence, our integral becomes:

[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]

Combine roots;

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]

Integrate. We can consider using u-substitution. We will let:

[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]

We also need to change our limits of integration. So:

[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]

Hence, our new integral is:

[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]

Simplify and integrate:

[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

FTC:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]

Simplify each term. For the first term, we have:

[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]

We can factor out the 4a:

[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

For the second term, we have:

[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =(2a)^3[/tex]

Hence:

[tex]\displaystyle =8a^3[/tex]

Thus, our equation becomes:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]

We can factor out an 8a^(3/2). Hence:

[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Hence, we have verified the surface area generated by the function.

Part B)

We have:

[tex]y^2=36x[/tex]

We can rewrite this as:

[tex]y^2=4(9)x[/tex]

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

We can write:

[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]

Solve for h. Simplify:

[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]

Divide both sides by 8π:

[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]

Isolate term:

[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]

Raise both sides to 2/3:

[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]

Hence, the value of h is:

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

You seem to have left out that 0 ≤ x ≤ h.

From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is

[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]

We have

y(x) = 2√(ax)   →   y'(x) = 2 • a/(2√(ax)) = √(a/x)

so the integral is

[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]

[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]

[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]

[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]

Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :

[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]

[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]

[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]

[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]

[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]

Answer:

30.5 + 1.5s

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

[tex] \huge\purple{TRUE}[/tex]

Step-by-step explanation:

The absolute value of any number is always positive.

Answer:

pfft no lol

Step-by-step explanation:

yeah no

have a good day!  :)

plz give me brainliest

Answer:

yes

Step-by-step explanation:

i think,because it goes past the center it all

Answer:

both are linear

a) 6x - y = 7

b) 2x - y = -5

Step-by-step explanation:

Answer:

2, 4, and 6 (b, d, f)

Step-by-step explanation:

dont  really know how to explain

Answer:

f(3)=g(3)

Step-by-step explanation:

the only one i see is that

f(3)=g(3)

because the two functions intersect there

that means the two values are the same

Answer:

The answer is translation :)

Answer:

C.  G' (4,-7), R' (2,-3), T'(6,-4)

Step-by-step explanation:

Get a piece of paper and draw 2 intersecting lines, like how a graph looks like. Then get another paper that's transparent enough, and place a dot roughly where R would be. Rotate it 270* clockwise (3 times around 90 degrees), and R would be in the bottom right area. That means the figure would be around that area and you can base the coordinates from that.

Step-by-step explanation:

what is this answer

(3x + 40) + (5x - 52) = 180°

8x - 12 = 180°

8x = 180 + 12

8x = 192

8x = 24

x = 3