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4 years ago

F(x) = 2x^2+ 5x + 20 Find f(-9)

Mathematics

1 answer:

8_murik_8 [283]3 years ago

8 0

Answer:

137

Step-by-step explanation:

2(-9)^2+5(-9)+20

2(81)-45+20

162-45+20

117+20

137

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Will a 11.5-inch x 18-inch rectangular tray fit in<br> the box shown? Explain.

pychu [463]

Answer:

Option D

Step-by-step explanation:

From the picture attached,

In the parallelogram ABCD,

Length of diagonals AC and BD are equal.

By the property,

"If the lengths of the diagonals of a parallelogram are equal, parallelogram will be a rectangle".

Therefore ABCD is a rectangle.

That means all interior angles of the given rectangle will be 90°.

Now we apply Pythagoras theorem in right triangle ΔABC,

AC² = AB² + BC²

(22)² = (12)² + (BC)²

484 - 144 = (BC)²

BC = √340

BC = 18.44 inches

Dimensions of the given box are 12 inches by 18.44 inches.

Dimensions of the rectangular tray is 11.5 inches by 18 inches.

Since, dimensions of the box are larger than the dimensions of the tray, tray can be adjusted in the box.

Therefore, Option D will be the answer.

3 0

3 years ago

Order the numbers from least to greatest.<br> 23% , 1/4 , 0.225 .

Alla [95]

0.225, 23%, 1/4

Step my step

23% = 0.23
1/4 = 0.25

3 0

3 years ago

One recipe makes 8 1/2 cups of potato salad. If one serving is 1/2 cup, how many servings does the recipe make?

Aleonysh [2.5K]

Answer:

Step-by-step explanation:

8.5 / 0.5

7 0

3 years ago

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean

Dovator [93]

Answer:

B) 0.0069

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.

In this question, we have that:

$\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846$

Find the probability that their mean rebuild time exceeds 9.1 hours.

This is 1 subtracted by the pvalue of Z when X = 9.1. So

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

By the Central Limit Theorem

$Z = \frac{9.1 - 8.4}{0.2846}$

$Z = 2.46$

$Z = 2.46$ has a pvalue of 0.9931

1 - 0.9931 = 0.0069

So the answer is B.

6 0

3 years ago

Which statements prove that a quadrilateral is a parallelogram?

Arte-miy333 [17]

Answer:

It is the Quadrilateral DEFG has only one set of opposite angles that are congruent and Quadrilateral DEFG has one diagonal that bisects the other diagonal.

Step-by-step explanation:

4 0

2 years ago

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