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andriy [413]
2 years ago
6

Y = A system of equations. Y equals StartFraction one-half EndFraction x minus 6. X equals negative 4.X – 6 x = –4 What is the s

olution to the system of equations?
Mathematics
1 answer:
MrRa [10]2 years ago
3 0

Answer:

x = -4, y =-8 is the solution to the system of equations.

Step-by-step explanation:

Given the system of equations as:

y= \dfrac{1}{2}x-6

and

x =-4

To find:

The solution to the system of equations = ?

Solution:

Here, we are given two equations and two variables i.e. x and y.

So, we can solve the system of equations for the values of x and y.

Let us first consider the 2nd equation.

x =-4 we already have the value of x.

Now, let us put the value of x in the 1st equation to find the value of y.

y= \dfrac{1}{2}x-6

\Rightarrow y= \dfrac{1}{2}\times (-4)-6\\\Rightarrow y= -\dfrac{1}{2}\times 4-6\\\Rightarrow y= -2-6\\\Rightarrow \bold{y =-8}

So,  the solution to the system of equations is:

x = -4, y =-8

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Step-by-step explanation:

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2 years ago
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According to a Pew Research survey, about 27% of American adults are pessimistic about the future of marriage and the family. Th
IgorLugansk [536]

Answer:

P(X≤5)=0.5357

Step-by-step explanation:

Using the binomial model, the probability that x adults from the sample, are pessimistic about the future is calculated as:

P(x)=\frac{n!}{x!(n-x)!} *p^{x}*(1-p)^{n-x}

Where n is the size of the sample and p is the probability that an adult is pessimistic about the future of marriage and family. So, replacing n by 20 and p by 0.27, we get:

P(x)=\frac{20!}{x!(20-x)!}*0.27^{x}*(1-0.27)^{20-x}

Now, 25% of 20 people is equal to 5 people, so the probability that, in a sample of 20 American adults, 25% or fewer of the people are pessimistic about the future of marriage and family is equal to calculated the probability that in the sample of 20 adults, 5 people of fewer are pessimistic about the future of marriage and family.

Then, that probability is calculated as:

P(X≤5)= P(1) + P(2) + P(3) + P(4) + P(5)

Where:

P(0)=\frac{20!}{0!(20-0)!}*0.27^{0}*(1-0.27)^{20-0}=0.0018

P(1)=\frac{20!}{1!(20-1)!}*0.27^{1}*(1-0.27)^{20-1}=0.0137

P(2)=\frac{20!}{2!(20-2)!}*0.27^{2}*(1-0.27)^{20-2}=0.0480\\P(3)=\frac{20!}{3!(20-3)!}*0.27^{3}*(1-0.27)^{20-3}=0.1065\\P(4)=\frac{20!}{4!(20-4)!}*0.27^{4}*(1-0.27)^{20-4}=0.1675\\P(5)=\frac{20!}{5!(20-5)!}*0.27^{5}*(1-0.27)^{20-5}=0.1982

Finally, P(X≤5) is equal to:

P(X≤5) = 0.0018+0.0137 + 0.0480 + 0.1065 + 0.1675 + 0.1982

P(X≤5) = 0.5357

3 0
2 years ago
In 2003, the owl population P in a park was measured to be 340. By 2007, the population was measured again to be 285. The popula
Anon25 [30]

Answer:

y = -13.75x + 340

120 owls in 2019

Step-by-step explanation:

To find the population in a future year, use the formula y=mx+b since it changes linearly.

So over 4 years the owl population changed from 285-340=-55. Divide by 4 and this is a yearly change of -13.75. This is m.

The y-intercept is the starting point known as b in the equation. Here it is 340.

So the equation is y=-13.75x+340.

In 2019, t=16 so y=-13.75(16)+340 = 120.


3 0
2 years ago
Find an equation for the contour of f(x,y)=2x2y+7x+20f(x,y)=2x2y+7x+20 that goes through the point (3,−2)(3,−2).
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That equation will be
.. f(x, y) = f(3, -2)
.. 2x^2y +7x +20 = 2*3^2*(-2) +7*3 +20

2x^2*y +7x +20 = 5

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2 years ago
Of the following people in the concentration camp , who behaves kindly to wiesel and his father
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