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balandron [24]
3 years ago
15

Given g(x) = 3x + 3, find g(-6).

Mathematics
1 answer:
Strike441 [17]3 years ago
6 0

Answer:

-15

Step-by-step explanation:

g(x) = 3x + 3

Let x = -6

g(-6) = 3*-6 + 3

           = -18 +3

            = -15

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When graphing the inequality y ≤ 2x − 4, the boundary line needs to be graphed first. Which graph correctly shows the boundary l
Volgvan

Answer:

See Below

Step-by-step explanation:

The boundary line follows the graph of y = 2x - 4 because it represents the line of maximum or minimum values the graph could take. y = 2x - 4 has a y-intercept of -4 because it is in slope-intercept form. It also has a slope of 2, so to find another point on the line, you can go up two and right one. Also, this inequality has a solid line because it is "less than or equal to" and a solid line represents the values that equal.

6 0
2 years ago
Given h(x)=-3x-2,solve for x when h(x)=1​
lora16 [44]

Answer:

-5

Step-by-step explanation:

6 0
2 years ago
Life Expectancies In a study of the life expectancy of people in a certain geographic region, the mean age at death was years an
Sphinxa [80]

Answer:

The probability that the mean life expectancy of the sample is less than X years is the p-value of Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}, in which \mu is the mean life expectancy, \sigma is the standard deviation and n is the size of the sample.

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 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.

We have:

Mean \mu, standard deviation \sigma.

Sample of size n:

This means that the z-score is now, by the Central Limit Theorem:

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

Find the probability that the mean life expectancy will be less than years.

The probability that the mean life expectancy of the sample is less than X years is the p-value of Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}, in which \mu is the mean life expectancy, \sigma is the standard deviation and n is the size of the sample.

8 0
2 years ago
Quick answers please!​
MakcuM [25]

Answer:

27.44

Step-by-step explanation:

area of the half sircle = 12.56

area of the rectangle = 40

area of the shaded protion = 40 -12.56

=27.44 square yards

7 0
3 years ago
Use calculus to find the first order conditions. Use solver then to solve the first order conditions. Show your work for the fir
DaniilM [7]

The values of x and y are 70/22 and 30/22 respectively by using the first-order condition of differential calculus.

<h3>What is the first-order condition in differential calculus?</h3>

A first-order differential equation is represented by the equation \mathbf{ \dfrac{dy}{dx} =f (x,y) }with 2 variables x & y, including its function f(x,y) specified on a xy-plane.

Given that:

\mathbf{f(x,y) =-22x^2+22xy-11y^2+110x-40y-23}

Let us first differentiate the above equation with respect to x, we have:

\mathbf{\dfrac{\partial f(x,y) }{\partial x}  = -44x +22y -0+110-0-0=0}

\mathbf{\implies  -44x +22y+110=0}        (multiply by -1)

44x - 22y = 110    ------ (equation 1)

Now, differentiating with respect to y, we have:

\mathbf{\dfrac{\partial f(x,y) }{\partial y}  =0 +22x-22y +0-40-0=0}

\mathbf{\implies 22x-22y -40=0}

22x - 22y = 40      ----- (equation 2)

Now, we have a system of equations:

44x - 22y = 110

-                      ---- ( subtracting equation 2 from 1; elimination method)

<u> 22x - 22y = 40  </u>

<u>22x    + 0  = 70    </u>

<u />

x = 70/22

Replacing the value of x into equation (1), we have:

44x - 22y = 110

44(70/22) - 22y = 110

140 - 22y = 110

140 - 110 = 22y

30 = 22y

y = 30/22

Learn more about the first-order conditions in differential calculus here;

brainly.com/question/14528981

#SPJ1

4 0
1 year ago
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