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3 years ago

Simplify (7t^2+9)+(6t^2+8)

Mathematics

2 answers:

Alborosie3 years ago

8 0

Answer:

13t^2 +17

Step-by-step explanation:

It helps to regroup the terms so like terms are together. Then you can more easily see how to combine them.

(7t^2 +9) + (6t^2 +8) = 7t^2 + 9 + 6t^2 + 8

= 7t^2 + 6t^2 + 9 + 8

= t^2·(7 + 6) + (9 +8)

= 13t^2 +17

Svetradugi [14.3K]3 years ago

3 0

Assignment: $\bold{Simplify \ Equation: \ \left(7t^2+9\right)+\left(6t^2+8\right)}$

<><><><><><><>

Answer: ➣ $\boxed{\bold{13t^2+17}}$

<><><><><><><>

Explanation: $\downarrow\downarrow\downarrow$

<><><><><><><>

➤ [ Step One ] Remove Parenthesis: (a) = a

$\bold{7t^2+9+6t^2+8}$

➤ [ Step Two ] Group Like Terms

$\bold{7t^2+6t^2+9+8}$

➤ [ Step Three ] Combine Similar Elements: $\bold{7t^2+6t^2=13t^2}$

$\bold{13t^2+9+8}$

➤ [ Step Four ] Add Numbers: $\bold{9+8=17}$

$\bold{13t^2+17}$

$\bold{\rightarrow Mordancy \leftarrow}$

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Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

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 $\mu$ and standard deviation $\sigma$ , the z-score 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 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 $\mu$ 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.

Mean of 20 hours, standard deviation of 6:

This means that $\mu = 20, \sigma = 6$

Sample of 150:

This means that $n = 150, s = \frac{6}{\sqrt{150}}$

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

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

By the Central Limit Theorem

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

$Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}$

$Z = 2.04$

$Z = 2.04$ has a p-value of 0.9793

X = 19.5

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

$Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}$

$Z = -1.02$

$Z = -1.02$ has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

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3 years ago

Choose all the number sentences that have a sum less than 345,195: A) 189,753 + 155,655 B) 324,675 + 19,285 C) 185,476 + 155,923

fgiga [73]

Answer:

C, D

Step-by-step explanation:

Calculate the sum of all.

C and D have less then 345,195.

That is the answer.

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3 years ago

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So the answer is D. 25 children and 75 adults
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3 years ago

Simplify (7t^2+9)+(6t^2+8)​

Simplify (7t^2+9)+(6t^2+8)