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4 years ago

What is the measure of angle A if angle A and angle B are supplementary and the measure of angle B is 20?

Mathematics

1 answer:

Volgvan4 years ago

5 0

Answer:

A. 160

Step-by-step explanation:

Supplementary angles add to be 180. Subtract 20 from 180 and you get 160.

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A factory is discharging pollution into a lake at the rate of r(t) tons per year given below, where t is the number of years tha

alexandr402 [8]

Answer:

The total amount of pollution discharged during the first 7 years of operation is 1.955 tons

Step-by-step explanation:

Given

$r(t) = \frac{t}{t^2 + 1}$

Required

The total amount in the first 7 years

This implies that:

$r(t) = \frac{t}{t^2 + 1}; [0,7]$

The total amount is calculated by integrating r(t) i.e.

$v = \int\limits^a_b {r(t)} \, dt$

So:

$v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt$

--------------------------------------------------------------

We have:

$t^2 + 1$

Differentiate

$d(t^2 + 1) = 2t$

Rewrite as:

$2t = d(t^2 + 1)$

Solve for t

$t = \frac{1}{2}d(t^2 + 1)$

---------------------------------------------------------------------------

So:

Make t the subject

$v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt$

$v = \int\limits^7_0\frac{1}{2}* {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt$

$v = \frac{1}{2}\int\limits^7_0 {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt$

Integrate

$v = \frac{1}{2}\ln(t^2 +1)|\limits^7_0$

Expand

$v = \frac{1}{2}[\ln(7^2 +1) - \ln(0^2 +1)]$

$v = \frac{1}{2}[\ln(50) - \ln(1)]$

$v = \frac{1}{2}[3.91 - 0]$

$v = \frac{1}{2}[3.91]$

$v = 1.955$

7 0

3 years ago

Help this one pplss

erik [133]

Answer:

x = 10, y = $\frac{4}{3}$

Step-by-step explanation:

The opposite sides of a parallelogram are congruent.

For LMNO to be a parallelogram then

ON = LM and OL = NM, that is

ON = LM

7x - 6 = 6x + 4 ( subtract 6x from both sides )

x - 6 = 4 ( add 6 to both sides )

x = 10 , then

NM = x - 9 = 10 - 9 = 1 and

OL = NM , that is

3y - 3 = 1 ( add 3 to both sides )

3y = 4 ( divide both sides by 3 )

y = $\frac{4}{3}$

3 0

3 years ago

Read 2 more answers

Determine mu Subscript x overbar and sigma Subscript x overbar from the given parameters of the population and sample size. mu e

Mademuasel [1]

Answer:

$\bar x \sim N(\mu_{\bar x}=86, \sigma_{\bar x}=3)$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

Let X the random variable who represents the variable of interest. We know from the problem that the distribution for the random variable X is given by:

$X\sim N(\mu =86,\sigma =24)$

We select a sample of size n=64. That represent the sample size.

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

The mean for the sample distirbution would be given by:

$\mu_{\bar x}=86$

And the deviation given by:

$\sigma_{\bar x} =\frac{24}{\sqrt{64}}=3$

And then the distribution for the sample mean is:

$\bar x \sim N(\mu_{\bar x}=86, \sigma_{\bar x}=3)$

7 0

3 years ago

I don’t know this please help

Tom [10]

Answer:

Slope- is up 8 over 5

y-intercept- is 0,-3

Step-by-step explanation:

count up till you get to where the second dot and then count over.

8 0

3 years ago

What numbers are a distance of 1/2 unit from 3/5 on a number line? Select the locations on the number line to plot the points.

Allushta [10]

<span>The numbers that are a distance of 1/2 unit from 3/5 on a number line are the numbers that are 1/2 units to the right and to the left of 3/5 on the number line.

The numbers are given by 3/5 - 1/2 and 3/5 + 1/2.

The numbers are 1/10 and 1 1/10
</span>

3 0

4 years ago

Read 2 more answers