Simplify the expression. −10−3

2 r squared + 3s cubed minus r squared + 40 squared minus r squared if R equals -2 s equals -3 and T equals 5

Flura [38]

$2r^2+3s^2-r^2+4t^2-r^2\\\\\text{simplify}\\\\(2r^2-r^2-r^2)+3s^2+4t^2=3s^2+4t^2\\\\s=-3;\ t=5\\\\3(-3)^2+4(5)^2=3(9)+4(25)=27+100=127$

6 0

3 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

Solve for p: -9 + p < 15 A. p > 24 B. -p > 6 C. p < 24 D. -p < -6

Soloha48 [4]

Answer:

C. In the given expression -9 + p < 15 , the value of p < 24.

Step-by-step explanation:

Here, the given expression is :

-9 + p < 15

Now, solving for the value of p.

If equals are added to both sides of inequality, the inequality remains unchanged.

Now, -9 + p < 15

⇒ -9 + p + 9 < 15 + 9 (adding +9 on both sides)

or, p < 24

Hence, in the given expression -9 + p < 15 the value of p < 24.

5 0

3 years ago

In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 8, and the ratio of flour to baking soda is 10 to 1

olasank [31]

Answer:

1,500

Step-by-step explanation:

Ratio of Sugar to Flour: 5:8 -> 25:40

Ratio of Flour to Baking Soda: 10:1 -> 40:4

Sugar to Flour to Soda: 25x:40x:4x

$\frac{40x}{(4x+60)}$ = $\frac{8}{1}$ -> x = 60

Sugar = 25x = 1,500

Hope this helps :)

7 0

3 years ago

Select the type of equations A.) Consistent B.) Equivalent C.) Inconsistent

qwelly [4]

Answer:

c

Step-by-step explanation:

the graph is inconsistent

5 0

3 years ago

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