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3 years ago

What is the approximate distance around the half circle with radius 12 centimeters?

1 answer:

4 0

You can find the perimeter of a circle by using the radius.
circumference = 2 $\pi r$
Circumference = 2 $\pi x 12$
circumference = 24 pi
Since you are only trying to find half of the circle you would divide your answer by 2

24pi / 2 = 12 pi

12 pi = 37.68

The answer is B. 37.7

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A laboratory tested n = 98 chicken eggs and found that the mean amount of cholesterol was LaTeX: \bar{x}x ¯ = 86 milligrams with

Harrizon [31]

Answer:

1.3859

Step-by-step explanation:

The formula for Margin of Error is given as:

Margin of Error = Critical value × Standard Error

Critical value = z score

In the question, we are given a confidence interval of 95%.

Z score for a 95% confidence level is given as: 1.96

Hence, critical value = 1.96

Standard Error = σ / √n

Where n = number of samples = 98 chicken eggs

σ = Standard deviation = 7 milligrams

Standard Error = 7/√98

Standard Error = 0.7071067812

Hence, Margin of Error = Critical value × Standard Error

Margin of Error = 1.96 × 0.7071067812

Margin of Error = 1.3859292911

Therefore, the margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is approximately 1.3859

8 0

3 years ago

If the distance on a Texas map from San Marcos to Austin is 3.8 centimeters, what is the actual distance between these two citie

Gnom [1K]

The answer is 285 miles

x = 3.8×150/2

x = 570/2

x = 285 miles

6 0

3 years ago

Find the whole if 2.5% of n is 0.01.

Lunna [17]

Answer:

$2.5\% \: of \: n = 0.01 \\ \frac{2.5}{100} \times n = 0.01 \\ 2.5n = 1 \\ n = 0.4$

5 0

2 years ago

Geometry, dont need explanation. Just those 3 questions.

Aloiza [94]

Answer:

1. B

2. A

3. C

Step-by-step explanation:

6 0

2 years ago

John, Sally, and Natalie would all like to save some money. John decides that it

brilliants [131]

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) $y=100x+300$

Part 3) $\$12,300$

Part 4) $\$2,700$

Part 5) Is a exponential growth function

Part 6) $A=6,000(1.07)^{t}$

Part 7) $\$11,802.91$

Part 8) $\$6,869.40$

Part 9) Is a exponential growth function

Part 10) $A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

Part 11) $\$13,591.41$

Part 12) $\$6,107.01$

Part 13) Natalie has the most money after 10 years

Part 14) Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

$m=\$100\ per\ month$

The y-intercept or initial value is

$b=\$300$

$y=100x+300$

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

$10\ years=10(12)=120 months$

For x=120 months

substitute in the linear equation

$y=100(120)+300=\$12,300$

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

$2\ years=2(12)=24\ months$

For x=24 months

substitute in the linear equation

$y=100(24)+300=\$2,700$

Part 5) What type of exponential model is Sally’s situation?

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$P=\$6,000\\ r=7\%=0.07\\n=1$

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}$

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{10}=\$11,802.91$

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{2}=\$6,869.40$

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$P=\$5,000\\r=10\%=0.10$

substitute in the formula above

$A=5,000(e)^{0.10t}$

Applying property of exponents

$A=5,000(1.1052)^{t}$

therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

$A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

$A=5,000(e)^{0.10*10}=\$13,591.41$

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

$A=5,000(e)^{0.10*2}=\$6,107.01$

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

3 0

3 years ago