Write the prime factorization of 36. Use Exponents when appropriate and order the factors from least to greatest

Liono4ka [1.6K]

You can solve for sides of a triangle using the following equation.

A = arccos (b^2 + c^2 - a^2/2bc)

And likewise for other variables by moving the letters.

Ultimately, in this problem you get the following angle measures:

15.87
23.97
140.16

8 0

2 years ago

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3p -3= 8p+5 need help please

lys-0071 [83]

Answer:

$\frac{8}{5} -= p$

Step-by-step explanation: 3p -3 =8p + 5 3 +5 =8p -3p 8=5p $\frac {8}{5}- = p$

6 0

2 years ago

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The level of nitrogen oxides (NOX) in a exhaust of cars of a particular model varies normally with mean 0.25 grams per miles and

antoniya [11.8K]

Answer:

a) 15.87% probability that a single car of this model fails to meet the NOX requirement.

b) 2.28% probability that the average NOX level of these cars are above 0.3 g/mi limit

Step-by-step explanation:

We use the normal probability distribution and the central limit theorem to solve this question.

Normal probability distribution:

Problems of normally distributed samples are 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 0.25, \sigma = 0.05$

a. What is the probability that a single car of this model fails to meet the NOX requirement?

Emissions higher than 0.3, which is 1 subtracted by the pvalue of Z when X = 0.3. So

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

$Z = \frac{0.3 - 0.25}{0.05}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8417.

1 - 0.8413 = 0.1587.

15.87% probability that a single car of this model fails to meet the NOX requirement.

b. A company has 4 cars of this model in its fleet. What is the probability that the average NOX level of these cars are above 0.3 g/mi limit?

Now we have $n = 4, s = \frac{0.05}{\sqrt{4}} = 0.025$

The probability is 1 subtracted by the pvalue of Z when X = 0.3. So

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

By the Central Limit Theorem

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

$Z = \frac{0.3 - 0.25}{0.025}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% probability that the average NOX level of these cars are above 0.3 g/mi limit

4 0

3 years ago

-20= -4x -6x + 2(10x)

ki77a [65]

Answer:

x = -2

Step-by-step explanation:

-20 = -4x - 6x + 2(10x)

Simplify both sides:

-20 = -4x - 6x + 20x

Combine like terms:

-20 = 10x

Isolate the variable:

x = -2

4 0

3 years ago

When planning space exploration, scientists face many

Inga [223]

Answer:

A

Step-by-step explanation:

Metal is stronger than plastic, but it is also much heavier.

The key idea in this paragraph is to highlight how to transport the required materials while reducing the weight as much as possible so orbital velocity can be achieved while breaking through the resistance of the atmosphere.

This statement is the key one because it gives engineers the problem they need to find the answer to make the space exploration a reality.

6 0

2 years ago

Write the prime factorization of 36. Use Exponents when appropriate and order the factors from least to greatest​

Write the prime factorization of 36. Use Exponents when appropriate and order the factors from least to greatest