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3 years ago

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Choose an equation that when paired with the equation below, will create a system of equations with infinitely many solutions, o

ne solution, or no solutions.

1 answer:

Alchen [17]3 years ago

4 0

Answer:

Infinitely many solutions: $-5x+9y=2$

One solution: $-10x+5y=4$

No solution: $-10x+18y=5$

Step-by-step explanation:

Solve for y from each equation to obtain the equation of the line in slope-intercept form:

$y=mx+b$

m: slope

b: y-intercept

<u>EQUATION ON THE TOP:</u>

$-10x+18y=4\\\\y=\frac{5}{9}x+\frac{2}{9}$

Equation 1:

$5y=10x+4\\\\y=2x+\frac{4}{5}$

The equation on top and the equation equation 1 has different slopes and different y-intercept, therefore the system will have one solution.

Equation 2:

$9y=5x+2\\\\y=\frac{5}{9}x+\frac{2}{9}$

The equation on top and the equation equation 2 are the same, therefore, the system will have infinitely many solutions.

Equation 3:

$18y=10x+5\\\\y=\frac{5}{9}x+\frac{5}{18}$

The slopes are equal, then both lines will be parallels, therefpre the system will have no solution.

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Suppose that the population mean for income is $50,000, while the population standard deviation is 25,000. If we select a random

Fudgin [204]

Answer:

Probability that the sample will have a mean that is greater than $52,000 is 0.0057.

Step-by-step explanation:

We are given that the population mean for income is $50,000, while the population standard deviation is 25,000.

We select a random sample of 1,000 people.

<em>Let </em> $\bar X$ <em> = sample mean</em>

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = $50,000

$\sigma$ = population standard deviation = $25,000

n = sample of people = 1,000

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, probability that the sample will have a mean that is greater than $52,000 is given by = P( $\bar X$ > $52,000)

P( $\bar X$ > $52,000) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{52,000-50,000}{\frac{25,000}{\sqrt{1,000} } }$ ) = P(Z > 2.53) = 1 - P(Z $\leq$ 2.53)

= 1 - 0.9943 = 0.0057

<em>Now, in the z table the P(Z </em> $\leq$ <em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.53 in the z table which has an area of 0.9943.</em>

Therefore, probability that the sample will have a mean that is greater than $52,000 is 0.0057.

5 0

3 years ago

I needddd heelpppp please

Nostrana [21]

Okay I am not 100% sure because that is an extremely confusing question. But here is what I got.

(A) 2c² = 2bc + ac/2 Given

(B) 4c² = 2bc + ac Multiplication and Distribution

(C) 4c = 4b + a Division and Distribution

(D) 4c - a + 4b Subtraction

(E) 4b = 4c - a Symmetric

6 0

4 years ago

Which function has a range of y>_4

nikklg [1K]

B
The answer is b. Because you x can be a negative, but you’re squaring it so it will equal a positive, and if you add 4, it is still 4 or greater

3 0

3 years ago

Read 2 more answers

Graph the following lines and write the equation in slope-intercept form. With y intercept of −3 and an x intercept of −4.5.

makvit [3.9K]

Answer:

$y=-\frac{2}{3}x-3$

Step-by-step explanation:

To write the equation of a line we need 2 points. We know:

If the y-intercept of the line is -3 then the point is (0,-3).

If the x-intercept of the line is -4.5 then the point is (-4.5,0).

Using these two point, we will find the slope and then substitute it into the point slope form $y-y_1=m(x-x_1)$ with a point.

Slope: $m=\frac{0--3}{-4.5-0}=\frac{0+3}{-4.5}=\frac{3}{-4.5}=-0.6667$

This decimal is -2/3. We will now substitute -2/3 and (0,-3) into the point slope form.

$y--3=-\frac{2}{3}(x-0)\\y+3=-\frac{2}{3}(x)\\y+3=-\frac{2}{3}x\\y=-\frac{2}{3}x-3$

6 0

3 years ago

City A is 25% less than population of city B so city A's population is what % of city B

omeli [17]

Answer:

75%

Step-by-step explanation:

we have

A ----> population of the city A

B ----> population of the city B

we know that

25% of B is equal to

$(25/100)B=0.25B$

so

$A=B-0.25B$

$A=0.75B$

$0.75*100=75\%$

That means ----> population of city A is 75% of population city B

7 0

3 years ago