what is the area of the rectangular piece of wood?

Answer:

0.2061 = 20.61% probability of having a sample mean of 115.8 or less for a random sample of this size

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 17.

This means that [tex]\mu = 118, \sigma = 17[/tex]

A randomly selected group of 40 members

This means that [tex]n = 40, s = \frac{17}{\sqrt{40}} = 2.6879[/tex]

What is the probability of having a sample mean of 115.8 or less for a random sample of this size?

This is the pvalue of Z when X = 115.8.

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

By the Central Limit Theorem

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

[tex]Z = \frac{115.8 - 118}{2.6879}[/tex]

[tex]Z = -0.82[/tex]

[tex]Z = -0.82[/tex] has a pvalue of 0.2061

0.2061 = 20.61% probability of having a sample mean of 115.8 or less for a random sample of this size

Answer:

its b have  a nice day

Step-by-step explanation:

Answer:

I think its D.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

1. x=34

2. c=8

3. x=9

4. m=32

That the answer for all 4.

Step-by-step explanation: Hope this help :D

Answer:

B

Step-by-step explanation:

Answer:

$8.32

Step-by-step explanation:

I found one percent of 46.25 ( which was 0.4625) by dividing it by 100 then i multiplied that number by 18 in order to get how much the 18% tip would be.  From that I got 8.325 but since this is in a currency the answer would be 8.32

thats just how I do it there's other ways

Answer:

p = 308

Step-by-step explanation:

Answer:

Z = 80 degrees and X = 8 degrees

Step-by-step explanation:

The reason Z = 80 degrees is because a flat line always has a measure of 180 degrees.

I forget the term, but we know that 6x + 52 is equal to 100 due to some angle theorem. (Once again, I do not remember the term.)

We then subtract 52 from 100 to get the equation 6x = 48. Divide them both by 6 and you get X = 8!

Hope this helped!

Answer:

Solution given:

<6+24=180[co- interior angle]

<6=180-24=156°

<6=156°

Answer:

The value of x is 7

Step-by-step explanation:

Complementary angles have a sum of 90°, therefore the equation to solve for x is:

∠1+∠2=90°

60°+5(x-1)°=90°

5(x-1)=30°

x-1=6

x=7

So the value of x is 7

Answer:

wdDW

Step-by-step explanation:

WDDwdWD

Answer:  

Step-by-step explanation:

The answer is m • (2m - 3) • (4m + 1)

Answer:

D. 7 1/2

Step-by-step explanation:

-3 divided by -2/5

-(-3(-5/2)

-(-3 x 5/2)

-15/2

7 1/2

Hope it helps

Answer:

in x>5 x is larger than 5

Step-by-step explanation:

x=5 means x is equal to 5

x>5 means x is greater than 5

Answer:

X=5 means that the unknown variable in the equation is equal to the number 5, while x > 5 means that the unknown variable is larger then the number 5.

Step-by-step explanation:

9514 1404 393

Answer:

  A

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

__

Using these rules, along with the distributive property, we can simplify the given expression.

  [tex]\displaystyle 9a^3b^6(3a^3b^2+7a^2b^2)-(5a^4b^4)^2\\\\=\displaystyle 9a^3b^6(3a^3b^2+7a^2b^2)-(5^2a^{4\cdot2}b^{4\cdot2})\\\\=(9)(3)a^{3+3}b^{6+2}+(9)(7)a^{3+2}b^{6+2}-25a^8b^8=27a^6b^8+63a^5b^8-25a^8b^8\\\\=\boxed{-25a^8b^8+27a^6b^8+63a^5b^8}\qquad\text{matches A}[/tex]

Answer:

-2

Step-by-step explanation:

I got it wrong and it told me negative 2 was the correct answer lol

Answer:

9 = x^2+y^2

Step-by-step explanation:

3^2 = (x-0)^2 + (y-0)^2

9 = x^2+y^2

Answer: D

Step-by-step explanation:

D

Answer:

5x<50

Step-by-step explanation:

Answer:

Step-by-step explanation:

5n < 50 <--- subtracts 4 from both sides

n < 10 <--- divides both sides by 5

Check: testing n=0, we have 4 + 5(0) = 4 + 0 = 4 < 54, so yes it works

testing n=10, 4 + 5(10) = 4 + 50 = 54.

testing n=11, 4 + 5(11) = 4 + 55 = 59 <--- fails as expected.

X < 10, proven, verified, correct

Answer:

4.2

Step-by-step explanation:

Answer:

Volume of the sphere is 2065.24

I have no idea how to calculate the slope of that.

Step-by-step explanation:

3·π·7.93≈2065.23693

Answer:

a) The exponential function is [tex]A(t) = 10083(1.068)^t[/tex]

b)

The balance after 1 year is of $10,768.644

The balance after 2 years is of $11,500.91

The balance after 5 years is of $14,010.25.

The balance after 10 years is of $19,467.15

c)

The doubling time is of 10.54 years.

Step-by-step explanation:

Continuously compounded interest:

The amount of money earning after t years, with interest compounded continuously, is given by:

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

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

a) Find the exponential function that describes the amount in the account after time t, in years.

Suppose that $10,083 is invested at an interest rate of 6.8% per year

This means, respectively, that [tex]A(0) = 10083, r = 0.068[/tex]

So

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

[tex]A(t) = 10083(1+0.068)^t[/tex]

[tex]A(t) = 10083(1.068)^t[/tex]

b) What is the balance after 1 year? 2 years? 5 years? 10 years?

After 1 year:

[tex]A(1) = 10083(1.068)^{1} = 10,768.644[/tex]

The balance after 1 year is of $10,768.644

After 2 years:

[tex]A(2) = 10083(1.068)^{2} = 11,500.91[/tex]

The balance after 2 years is of $11,500.91.

After 5 years:

[tex]A(5) = 10083(1.068)^{5} = 14,010.25[/tex]

The balance after 5 years is of $14,010.25.

After 10 years:

[tex]A(10) = 10083(1.068)^{10} = 19,467.15[/tex]

The balance after 10 years is of $19,467.15.

c) What is the doubling time?

This is t for which [tex]A(t) = 2A(0)[/tex]. So

[tex]A(t) = A(0)(1.068)^t[/tex]

[tex](1.068)^t = 2[/tex]

[tex]\log{(1.068)^t} = \log{2}[/tex]

[tex]t\log{1.068} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.068}}[/tex]

[tex]t = 10.54[/tex]

The doubling time is of 10.54 years.

Answer:

This relationship is a function because the plant can only be one height at a time.

Step-by-step explanation:

Functions occur when the recorded x-value is varied each time. Since the height of the plant (the x-value) varies each day, it is a function.

Answer:

3 hours

Step-by-step explanation:

15÷5=3 so that's ot