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Alborosie
2 years ago
6

Suppose that we don't have a formula for g(x) but we know that g(3) = −1 and g'(x) = x2 + 7 for all x.

Mathematics
1 answer:
Sliva [168]2 years ago
4 0

Answer:

  • g(2.95) ≈ -1.8; g(3.05) ≈ -0.2
  • A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.

Step-by-step explanation:

(a) The linear approximation of g(x) at x=b will be ...

  g(x) ≈ g'(b)(x -b) +g(b)

Using the given relations, this is ...

  g'(3) = 3² +7 = 16

  g(x) ≈ 16(x -3) -1

Then the points of interest are ...

  g(2.95) ≈ 16(2.95 -3) -1 = -1.8

  g(3.05) ≈ 16(3.05 -3) -1 = -0.2

__

(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)

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A tailor has 13 1/2 yards of fabric to use for making costumes. For each costume, he needs 1 1/2 yards of fabric for the top and
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Answer:

6 complete costumes

Step-by-step explanation:

he has 27/2 total fabric

1 costume requires 1 2/4 + 3/4 of fabric, which is 2 1/4

we divide 27/2 by 9/4

27/2 x 4/9 = 6

3 0
2 years ago
The triangles in the picture are congruent by which method
Kryger [21]
The second answer choice.
6 0
2 years ago
A plant cell has a lenght of 0.000085 meters. which is this length written in scientific notation ?
Leno4ka [110]

Answer:

8.5x10^-5

Step-by-step explanation:

Move the decimal over between the 8 and the 5, it "hops" 5 times. Since it moved over right, make it negative

8 0
3 years ago
Solve the problem. Use the Central Limit Theorem.The annual precipitation amounts in a certain mountain range are normally distr
bazaltina [42]

Answer:

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

Step-by-step explanation:

To solve this question, we use 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 establishes 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 109.0 inches, and a standard deviation of 12 inches.

This means that \mu = 109, \sigma = 12

Sample of 25.

This means that n = 25, s = \frac{12}{\sqrt{25}} = 2.4

What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches?

This is the p-value of Z when X = 112. So

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

By the Central Limit Theorem

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

Z = \frac{112 - 109}{2.4}

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

7 0
3 years ago
6 - 8a + 5a - 35
Fittoniya [83]
Ok, so after you do -8a+5a, you also have to do 6 -35, getting the equation
-29-3a
7 0
2 years ago
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