Ted invests $6,082 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 13 years?

Answer:

28.26

Step-by-step explanation:

A = pie x radius*2

The radius is 3, and pie is 3.14. This means the equation is

A = 3.14 x 3*2

3*2 is just 3 x 3, which is 9.

9 x 3.14 = 28.26

Answer:

x = 28

Step-by-step explanation:

given,  x/2 + 49 = 21/4

x/2 + 49 = 9x/4

2x +196 = 9x

7x = 196

x = 28

I hope this helps a little bit.

Answer:

There is enough statistical evidence to suggest that there is no difference between the mean number of households picking either service

Step-by-step explanation:

The parameters of the music streaming service are;

The average number of households using Apple Music, [tex]\overline {X}_1[/tex] = 1.73 million

The standard deviation, σ₁² = 0.46 million

The average number of households using Spotify, [tex]\overline {X}_2[/tex] = 2.17 million

The standard deviation, σ₂² = 0.33 million

The significance level = 0.01

Hypothesis testing with different population standard deviation

[tex]Z = \dfrac{\overline {X}_1 - \overline {X}_2}{\sqrt{\dfrac{\sigma_1^2}{n_1} +\dfrac{\sigma_2^2}{n_2}} }[/tex]

H₀: [tex]\overline {X}_1[/tex] ≠ [tex]\overline {X}_2[/tex]

H₁:  [tex]\overline {X}_1[/tex] = [tex]\overline {X}_2[/tex]

[tex]Z = \dfrac{1.73- 2.17}{\sqrt{\dfrac{0.46^2}{12} +\dfrac{0.33^2}{12}} } = -2.6923[/tex]

p-value for the test statistic = 2 × P(Z <-2.6923) = 2 × 0.00357 = 0.00714

Therefore, the p-value is less than the significance level, and it is therefore unlikely that the result will be observed under the null hypothesis

We therefore reject the null hypothesis and there is enough statistical evidence to suggest that there is no difference between the mean number of households picking either service

Answer:

7 square inches hope this helps brainlest plzzz

Step-by-step explanation:

Answer:

a. Expected frequency of losses per semester = 0*0.08 + 5*0.16 + 10*0.28 + 15*0.32 + 20*0.14 + 25*0.02

Expected frequency of losses per semester = 11.7 losses per semester

b. Variance = (0-11.7)²*0.08 + (5-11.7)²*016 + (10-11.7)²*0.28 + (15-11.7)²*0.32 + (20-11.7)²*0.14 + (15-11.7)²*0.02

Variance = 10.9512 + 7.1824 + 0.8092 + 3.7848 + 9.6446 + 3.5378

Variance = 35.61

c. As losses equal $60, expected losses per semester = 11.7*$60 = $702

d. Expected losses of all textbooks per semester = 250*11.7*$60 = $175,500

Answer:

8.2m

Step-by-step explanation:

Formula : Area = base x height

rearrange : Base = area ÷ height

37.72÷4.6=8.2m

Answer:

8.2

Step-by-step explanation:

Answer:

5 feet = 60 inches

Step-by-step explanation:

Every foot is 12 inches, so.. this problem can be turned into simple multiplication..

12 x 5= 60

So, Jim is 60 inches tall.

Hope this helps! :)

Have a nice day!♥

Answer:

2. c. 1/2

3. d. 13/16

5. d. 5/12

1. b. simplified

4. b. Nicholas did not divide the numerator and..............

Answer:

i know it’s been months since you posted this question but...

Step-by-step explanation:

2. c) 1/2, 9/18 / 9 = 1/2

3. d) 13/16, 26/32 / 2 = 13/16

5. d) 5/12, 10/24 / 2 = 5/12

1. b) simplified, you can’t simplify 8/9, it’s already smaller.

4. b) Nicholas did not divide the numerator and denominator by the same number, the GCF [greatest common factor]. 4/5 is not equivalent to 20/30. He should have divided by 10. 20/30 = 2/3.

why does that say 20/24 tho?- i think it meant 20/30.

i hope this helped! also, a definition of gcf:

GCF - A set of numbers' greatest common factor (GCF) is the largest factor that all of the numbers share. Twelve, twenty, and twenty-four, for example, all have two common factors: two and four. The GCF of 12, 20, and 24 is 4 since the highest is 4. The GCF method is often used to identify common denominators.

Answer:

3072

Step-by-step explanation:

double the number until the 11th time which would be -3072 so C

Answer:

A' = (1, 2)

B' = (2, 3)

C' = (2, 4)

Step-by-step explanation:

Ok so you are given the scale factor of 1/3. You will basically multiply 1/3 to all of the values of point A, B, and C in order to find the values of point A', B', and C'.

A = (3, 6) ---> 3 × 1/3 = 1 and 6 × 1/3 = 2

A' = (1, 2)

B = (6, 9) ---> 6 × 1/3 = 2 and 9 × 1/3 = 3

B' = (2, 3)

C = (6, 12) ---> 6 × 1/3 = 2 and 12 × 1/3 = 4

C' = (2, 4)

Hope this helps and stay safe, happy, and healthy, thank you :) !!

Answer:

Step-by-step explanation:

Pythagorean theorem,

Hypotenuse² = base² + altitude²

Substitute the known values and you can find the missing length

Answer:

• A change from 54 to 81 represents a positive change (increase) of 50%

Answer:

[tex]11a[/tex]

Step-by-step explanation:

[tex]4a + 7a = 11a[/tex]

Hope this helps you

Can I have the brainliest please?

Answer:

157.92 + d =t

Step-by-step explanation:

Answer:

one is 2 inches bigger that the other.

Step-by-step explanation:

becuase if one of the pizza is 20in ans the other is 22 the 20 on is only 2in away frof the XXL pizza .

Answer: 16 times 20 is 320

Step-by-step explanation: 1 floor is 16 feet. Because of 32/2 to find the rate

Answer:

X= 6.2 + 68 ???

Step-by-step explanation:

I'm not sure that's what I would write in an exam

Given:

A figure of a right triangle.

To find:

The missing side by using the trigonometric ratios.

Solution:

In a right angle triangle,

[tex]\cos \theta=\dfrac{Adjacent}{Hypotenuse}[/tex]

In triangle ABC,

[tex]\cos A=\dfrac{AC}{AB}[/tex]

[tex]\cos (31^\circ)=\dfrac{b}{270}[/tex]

[tex]0.857=\dfrac{b}{270}[/tex]

Multiply both sides by 270.

[tex]0.857\times 270=b[/tex]

[tex]231.39=b[/tex]

[tex]b\approx 231.4[/tex]

Therefore, the missing side length is b=231.4 inches.

Answer:

200

Step-by-step explanation:

pi · radius · height

3.14 · 8 · 25 = 200

Answer:

Well, how many people are there?

Step-by-step explanation:

We can't solve this without the number of people.

Answer:

13

Step-by-step explanation:

Answer:

[tex]Height = 2.5[/tex]

Step-by-step explanation:

Given

[tex]Volume = 35[/tex]

[tex]Length =7[/tex]

[tex]Base=4 cm[/tex]

Required

Determine the height

The volume is calculated as:

[tex]Volume = Height * Base\ Area[/tex]

Since, it has a triangular cross-section, the expression becomes:

[tex]Volume = Height * \frac{1}{2} * Base * Length[/tex]

So, we have:

[tex]35 = Height * \frac{1}{2} * 4 * 7[/tex]

[tex]35 = Height * 14[/tex]

[tex]Height = 35/14[/tex]

[tex]Height = 2.5[/tex]

Answer:

First, realize that angle ABC is the sum of the two other angles. Hence, form an equation in which you subtract the measure of one of the angles from angle ABC to get the measure of the other angle -- the one you are solving for.

Step-by-step explanation:

Mark me brainly please hop this helps.

Answer: After Nancy bought the sandwich, the cashier handed back $2.36

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The formula for any geometric sequence is:

[tex]a_n=a_1\cdot r^{n-1}[/tex]

Where aₙ is the value of the nth term, a₁ is the value of the first term, r represents the common ratio, and n represents the term number.

We want the formula for the geometric sequence:

-3, -6, -12, -24, ...

Note that our first term is -3. Hence, a₁ = -3.

Next, each subsequent term is twice the previous term. Hence, our common ratio r = 2.

Therefore, by substitution, we acquire:

[tex]a_n=-3\cdot (2)^{n-1}[/tex]

Our answer is C.

Answer:

Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

Answer:

She has to invest $5,160 for the value of the account to reach $7,600 in 7 years.

Step-by-step explanation:

Continuous compounding:

The amount of money earned, after t years, in continuous compounding, is given by:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which A(0) is the value of the initial investment and r is the interest rate, as a decimal.

Lillian is going to invest in an account paying an interest rate of 5.7% compounded continuously.

This means that [tex]r = 0.057[/tex]

How much would Lillian need to invest, to the nearest ten dollars, for the value of the account to reach $7,600 in 7 years?

We have to find A(0) when [tex]A(t) = 7600, t = 7[/tex]

So

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]7600 = A(0)(1+0.057)^7[/tex]

[tex]A(0) = \frac{7600}{(1.057)^7}[/tex]

[tex]A(0) = 5156[/tex]

To the nearest ten dollars, she has to invest $5,160 for the value of the account to reach $7,600 in 7 years.