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3 years ago

7

The annual expenditure of the US federal government is approximately 444 trillion dollars. If a one dollar bill is 0.00010.00010

, point, 0001 meters thick, how many meters tall would a stack of 444 trillion one dollar bills be? Write your answer in scientific notation. For reference: 111 trillion =10^{12}=10 12

1 answer:

Vsevolod [243]3 years ago

7 0

Answer:

$4*10^{7}$ meters.

Step-by-step explanation:

This question can be solved using a rule of three.

If a one dollar bill is 0.0001 meters thick.

So 1 dollar is $10^{-5}$ m tall.

How tall is 4 trillion one dollar bills?

1 trillion = $10^{12}$

So 4 trillion = $4*10^{12}$

Then

1 dollar - $10^{-5}$ m

$4*10^{12}$ - xm

$x = 4*10^{12}*10^{-5} = 4*10^{7}$

The answer is $4*10^{7}$ meters.

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grigory [225]

Answer:

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Step-by-step explanation:

It has clusters from 1 to 5 because that is where all the dots are that are not seperated.

8 0

3 years ago

14(0.89)^x+4.5 =162

lisabon 2012 [21]

$14(0.89)^{x + 4.5} = 162$
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$ln(0.89^{x + 4.5}) = ln(11\frac{4}{7})$
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3 0

3 years ago

The Town of Hertfordshire clerk knows that 23% of dogs in the town have completed emotional support training. Hertfordshire plan

Nataly_w [17]

Answer:

95.64% probability that under 30% of the dogs are emotional support trained

Step-by-step explanation:

For each dog, there are only two possible outcomes. Either they have completed emotional support training, or they have not. So we use the binomial probability distribution to solve this problem.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$\mu = E(X) = np = 100*0.23 = 23$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.23*0.77} = 4.21$

What is the probability that under 30% of the dogs are emotional support trained?

30% of 100 is 0.3*100 = 30

So this is the pvalue of Z when X = 30.

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3 years ago

Help with 4 and 5 please!!

Ghella [55]

Question 4
The magnitude;
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= 566.5 mi
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Tan θ = opposite/adjacent
= 200/530
= 0.3774
θ = tan^-1 (0.3774)
= 20.67
≈ 21°
The direction from the Cartesian plane is south of west.
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To get the resultant of two vectors we just add the two vectors given.
This involves adding the corresponding values.
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Resultant vector = <(-6+6),(5+-5>
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3 years ago

For a sequence defined by f(1)=13 and 2f(n-1)+(n-2), which of the following is the value of f(4)

densk [106]

Given that:
f(1)=13 and 2f(n-1)+(n-2)
then:
f(4) will be found as follows:
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f(3)=2f(3-1)+(3-2)=2f(2)+1=2*26+1=53
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Thus:
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3 years ago