Simplify the following expression: 8x − 8y + 5z − 3x − 14y + 3z

Please help me with this question please

zheka24 [161]

*im sorry but I cant see the bottom number but I'll consider it as x

tan 45° = 3/x

x = 3/tan45

x is 3

hope this helps :)

5 0

3 years ago

Find the missing side or angle.

bonufazy [111]

Answer:

c = 6.1

Step-by-step explanation:

Given that: B = 18° , C = 152°, and b = 4.

The missing side, c, can be determined by applying the sine rule which states that:

$\frac{b}{Sin B}$ = $\frac{c}{Sin C}$

$\frac{4}{Sin 18^{o} }$ = $\frac{c}{Sin 152^{o} }$

c = $\frac{4* Sin 152^{o} }{Sin 18^{o} }$

= $\frac{1.8779}{0.3090}$

= 6.0773

c = 6.1

Therefore, the value of the missing side, c, is 6.1

3 0

3 years ago

Joe is saving money for his

tatyana61 [14]

Answer:

He will need to save $295

Step-by-step explanation:

he needs 450 and he has 155, so all you would do is subtract 155 from 450 and you get the rest he needs which is 295

6 0

2 years ago

Suppose a continuous probability distribution has an average of μ=35 and a standard deviation of σ=16. Draw 100 times at random

yulyashka [42]

Answer:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

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 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 normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

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

For sums, we have that the mean is $\mu*n$ and the standard deviation is $s = \sigma \sqrt{n}$

In this problem, we have that:

$\mu = 100*35 = 3500, \sigma = \sqrt{100}*16 = 160$

This probability is the pvalue of Z when X = 4000 subtracted by the pvalue of Z when X = 3000.

X = 4000

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

By the Central Limit Theorem

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

$Z = \frac{4000 - 3500}{160}$

$Z = 3.13$

$Z = 3.13$ has a pvalue of 0.9991

X = 3000

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

$Z = \frac{3000 - 3500}{160}$

$Z = -3.13$

$Z = -3.13$ has a pvalue of 0.0009

0.9991 - 0.0009 = 0.9982

So the correct answer is:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

5 0

3 years ago

Evaluate and answer in standard form:<br><br>4^2/3^2

Semenov [28]

the answer is : 1.7777

6 0

2 years ago