Which of the following formulas shows how to calculate the ending balance of an account with a beginning balance of $600 that earns 3.5% compound interest over 8 years?

Answer:

1) P(258.5-cm < M < 259-cm) = 8.71%.

2) P17 = 125.57cm

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question 1:

Mean of 258.5-cm and a standard deviation of 2.3-cm, which means that [tex]\mu = 258.5, \sigma = 2.3[/tex]

Find the probability that the average length of a randomly selected bundle of steel rods is between 258.5-cm and 259-cm.

This is the pvalue of Z when X = 259 subtracted by the pvalue of Z when X = 258.5.

X = 259

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{259 - 258.5}{2.3}[/tex]

[tex]Z = 0.22[/tex]

[tex]Z = 0.22[/tex] has a pvalue of 0.5871

X = 258.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{258.5 - 258.5}{2.3}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

0.5871 - 0.5 = 0.0871

0.0871*100% = 8.71%. So

P(258.5-cm < M < 259-cm) = 8.71%.

Question 2:

Mean of 127.1-cm and a standard deviation of 1.6-cm, which means that [tex]\mu = 127.1, \sigma = 1.6[/tex]

Find P17, which is the average length separating the smallest 17% bundles from the largest 83% bundles.

This is the 17th percentile, which is X when Z has a pvalue of 0.17. So X when Z = -0.954.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.954 = \frac{X - 127.1}{1.6}[/tex]

[tex]X - 127.1 = -0.954*1.6[/tex]

[tex]X = 125.57[/tex]

P17 = 125.57cm

9514 1404 393

Answer:

  36π mm²

Step-by-step explanation:

You know that (ab)² = a²b². This tells you that ...

  πr² = π(6 mm)² = π(6² mm²) = 36π mm²

The units of area are square millimeters (mm²).

_____

Additional comment

For a variety of reasons, I find it is often helpful to keep units of measure with the associated number. It serves as a check on the arithmetic, among other things. If the units don't make sense, chances are good that the math doesn't make any sense.

It should be fairly obvious that if linear dimensions are in millimeters, then the corresponding area dimensions will be square millimeters. (Volume will be cubic millimeters.)

In the math, the units can be treated in the same way as any other variable. This tells you, for example, that you can only add (or subtract) measures with the same units (like terms). Division can be used to cancel same units, or to get from volume to area, for example (mm³/mm = mm²).

Answer: exponential decay

Step-by-step explanation:

Exponential decay means that it's getting smaller and you can see that the numbers are getting smaller on the y axis.

Hope this helps :)

Answer:

Step-by-step explanation:

first thing you didn't give any quadratic equation and also didn't allude which method you indeed however I'll give you two methods

to get elaborately factoring method

see this question which is answered by me

quadratic formula:

by using this formula we can solve quadratic very early

we just need to substitute the value of a,b and c and simply to get x

Example 1 – Solve: Example 1

Step 1: Identify a, b, and c and plug them into the quadratic formula. In this case a = 1, b = –8, and c = 14.  

Step 1

Step 2: Use the order of operations to simplify the quadratic formula.  

Step 2

Step 3: Simplify the radical, if you can. In this case you can simply the radical into:  

Step 3

Step 4: Reduce the problem, if you can. In this case you can reduce the entire problem by 2.  

For the shower multiply the amount of water per minute by number of minutes:

10.6 x 7 = 74.2 liters.

Calculate volume of the tube and the amount of water in it:

35 x 40 x 120 = 168,000 cubic cm.

Convert to liters:

168,000/ 1000 = 168 liters.

Savings = 168 - 74.2 = 93.8 liters

[tex]{ :{ \implies { \tt{ \blue{ \frac{1}{4} x + 3 - \frac{1}{3} x + ( - 2)}}} }}\\ \\ \\ { : { \implies{ \blue{ \tt{ \frac{1}{4} x - \frac{1}{3} x + 3 - 2}}}}}[/tex]

[tex]{ : { \implies{ \tt{ \blue{ \frac{1}{4} x - \frac{1}{3} x + 1}}}}} \\ \\ \\ { : { \implies{ \tt{ \blue{ \frac{3x - 4x + 12}{12}}}}}} [/tex]

[tex]{ :{ \implies{ \blue{ \tt{ \frac{12 - x}{12}}}}}} \\ \\ \\ { : { \implies{ \blue{ \tt{1 - \frac{x}{12}}}}}} [/tex]

option ( D ) is correct

Answer:

-1

-1

5

-1,3

7fufuviiviviv8h

Answer:

Use photo math, it will explain all the steps

Answer:

x = 6 , y = 8 ( 6 , 8 )

Step-by-step explanation:

If we solve the linear system that you gave us,

y = 5x – 22

3x +2y=34

We get that x is 6 and y is 8.

In other words, since it's a point, it should be, ( 6 , 8 )

Answer:

w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]

(Anyone can correct me if I'm wrong)

Step-by-step explanation:

Before we start the solving, we can make the following statements:

Area = l x w

Area = 5x + 25

therefore,

l x w = 5x + 25

Since the question states that the length is x more than the width, so we can make the following statement:

w = l + x

With this, we can substitute it to the first statement we made, l x w = 5x + 25,

l x (l + x) = 5x + 25

[tex]l^{2}[/tex] + lx = 5x + 25

lx - 5x = 25 - [tex]l^{2}[/tex]

x(l - 5) = 25 - [tex]l^{2}[/tex]

x = [tex]\frac{25 - l^{2}}{l - 5}[/tex]

From this, we can find w by substituting it in the statement we made earlier, w = l + x,

w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]

Answer:

144in square

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Fifth grade has 80 students and sixth grade has 80 students. so if you get 90% of both then you have 72 and 72. Add and divide by 8 and you have the answer of 18 parent volunteers going.

Answer:

18 pls give brainliest i never get them :(

Step-by-step explanation:

1. 12 (i think)

i don't know about question 2

Answer: -8 > -6

Step-by-step explanation:

Answer:

132

Step-by-step explanation:

First divide the number of lampreys by the ratio.

162/27=6

Then multiply the result (6) by the oarfish part of the ratio

22*6=132

Answer:

Step-by-step explanation:

The area of a trapezoid is the average of the parallel bases times the height or distance between the two bases

A=h(b1+b2)/2

Here we have h=8cm, b1=6cm, and b2=11cm so

A=8(6+11)/2

A=8(17)/2

A=4(17)

A=68 cm^2

Answer:

so answer is b.42

Step-by-step explanation:

3 7

6 14

9 21

every time width increase by 3 length increase by 7 so:

12 28

15  35

18    42

Answer:

S = 2(5.5) + 4.1

Answer: s= 2(5.5) + 4.1

Answer:

314

Step-by-step explanation:

Does the line cuts through the diameter of the circle?

If so just apply π * 10^2 = 314.15 radius is just 20/2  = 10

Answer:

30 cm

Step-by-step explanation:

To find the perimeter you will have to use the formula L2 + W2 = A

1. Multiply the length (let's say 10 cm) by 2

       a. 20

2. Do the same for width (5 cm)

      a. 10

3. Add together

     a. 20 + 10 = 30 cm

(There is another way to do it but this is easier)

Hope this helps :)

Answer:

170

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

Do 36/0.18

200

Answer:

D. 32 inches 65-33=32 so its 32 inches

Step-by-step explanation:

Answer:

13.6 units (to 3 significant figures)

Step-by-step explanation:

C ( -4,6) and D (-4,-5)

the formula for distance is : √(x2 - x1)² + (y2-y1)²

in this case x1= -4 , x2= -4 and y1 =6 , y2 = -5

so substitute the values and you will get the answers

Answer:

8/3

Step-by-step explanation:

Answer:

C. 2/3

Step-by-step explanation:

this is the correct answer

Answer:

z-y/x

Step-by-step explanation:

then z

then z-y

z-y/x

Answer:

3/2 or 1.5

Step-by-step explanation:

have a good day

Answer:

-7

Step-by-step explanation:

I am sorry if I got it wrong.

Answer:

72 passengers

Step-by-step explanation:

What we know:

To find how many passengers are travelling alone, multiply 150 by 48%.

48% ⇒ 0.48 as a decimal

150 × 0.48 = 72

Therefore, 72 passengers are travelling alone.

I hope this helps!

Answer:

72

Step-by-step explanation: