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2 years ago

Use part 1 of the fundamental theorem of calculus to find the derivative of the function. y = 5 u3 1 + u2 du 4 − 3x

1 answer:

3 0

Looks like

$y(x)=\displaystyle\int_5^{4-3x}u^3(1+u^2)\,\mathrm du$

in which case the FTC asserts that

$\dfrac{\mathrm dy}{\mathrm dx}=(4-3x)^3(1+(4-3x)^2)\cdot\dfrac{\mathrm d(4-3x)}{\mathrm dx}$

$\dfrac{\mathrm dy}{\mathrm dx}=-3(4-3x)^3(1+(4-3x)^2)$

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You operate a fresh fruit and vegetable market. For normal shipments, about 9.0% of the peaches are spoiled when they reached yo

Nastasia [14]

Given:

Spoilage rate of fruits = 9% = 0.09

To find:

Amount of fruits to be order to have 100 pounds of peaches and considering the spoilage rate.

Solution:

Let the required amount of fruits you should order be x.

So, spoiled fruits = 9% of x = 0.09x

He would like to have 100 pounds of peaches to sell.

$x-0.09x=100$

$0.91x=100$

Divide both sides by 0.91.

$x=\dfrac{100}{0.91}$

$x=109.89$

$x\approx 110$

The required amount of fruits to be order is 110 lbs. Therefore, the correct option is D.

6 0

2 years ago

Use the values on the number line to find the sampling error.

pantera1 [17]

Part 1:

Given a number line with the point $\bar{x}=3.8$ and the point $\mu=4.27$

The sampling error is given by:

$\bar{x}-\mu=3.8-4.27=-0.47$

Part 2:

Given a number line with the point $\bar{x}=26.43$ and the point $\mu=24.67$

The sampling error is given by:

$\bar{x}-\mu=26.43-24.67=1.76$

4 0

2 years ago

PLEASE HELP!! laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standa

Lunna [17]

Answer:

P = 0.0215 = 2.15%

Step-by-step explanation:

First we need to convert the values of 900 and 975 to standard scores using the equation:

$z = \frac{x - \mu}{\sigma}$

Where z is the standard value, x is the original value, $\mu$ is the mean and $\sigma$ is the standard deviation. So we have that:

standard value of 900: $z = \frac{900 - 750}{75} = 2$

standard value of 975: $z = \frac{975 - 750}{75} = 3$

Now, we just need to look at the standard distribution table (z-table) for the values of z = 2 and z = 3:

z = 2 -> p_2 = 0.9772

z = 3 -> p_3 = 0.9987

We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:

P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215

So the probability is 0.0215 = 2.15%

8 0

2 years ago

The 8th term of a GP is -7/32 find its common ratio if its first term is 28

Ugo [173]

<h2>Common ratio = -1/2</h2>

Step-by-step explanation:

$\text{8}^{th}$ term of a Geometric progression is given as $\dfrac{-7}{32}$ . The first term is given as $28$ .

Any general Geometric progression can be represented using the series $a,ar,ar^{2},ar^{3},ar^{4}...\text{ }ar^{n-1}$ .

The first term in such a GP is given by $a$ , common ratio by $r$ , and the $n^{th}$ term is given by $ar^{n-1}$ .

In the given GP, $a=28;t_{8}=ar^{7}=\dfrac{-7}{32}\\\\28r^{7}=\dfrac{-7}{32}\\\\r^{7}=\dfrac{-1}{128}\\\\r=\dfrac{-1}{2}$

∴ Common ratio is $\dfrac{-1}{2}$ .

5 0

2 years ago

You have filed your taxes more than 60 days late which means you are subject to a penalty of $135 or 100% of your unpaid tax, wh

forsale [732]

Answer: $135

Step-by-step explanation: 48% of $355 would be 170 so therefore the $135 would be the cheaper penalty

3 0

2 years ago

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