Randy has 16 dimes more than triple the number of quarters he has. He has a total of $4.35. How many of each coin does he have?

Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x

Solnce55 [7]

Answer:

The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is $\mathbf{y=-\frac{2}{3}x+3 }$

Step-by-step explanation:

We need to Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x

The equation in slope-intercept form is: $y=mx+b$ where m is slope and b is y-intercept.

Finding Slope:

The both equations given are parallel. So, they have same slope.

Slope of given equation y= - 2/3x is m = -2/3

This equation is in slope-intercept form, comparing with general equation $y=mx+b$ where m is slope , we get the value of m= -2/3

So, slope of required line is: m = -2/3

Finding y-intercept

Using slope m = -2/3 and point (-3,5) we can find y-intercept

$y=mx+b\\5=-\frac{2}{3}(-3)+b\\5=2+b\\ b=5-2\\b=3$

So, we get b = 3

Now, the equation of required line:

having slope m = -2/3 and y-intercept b =3

$y=mx+b\\y=-\frac{2}{3}x+3$

The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is $\mathbf{y=-\frac{2}{3}x+3 }$

5 0

3 years ago

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(a) Suppose Y1(t) is a solution of an autonomous system dY/dt = F(Y). Show that Y2(t) = Y1(t +t0) is also a solution for any con

alexandr1967 [171]

Answer:

Step-by-step explanation: see attachment

6 0

3 years ago

Write the number in two orher forms 314,207

asambeis [7]

Word Form: Three hundred fourteen thousand two hundred seven

Expanded Form: 300,000 + 10,000 + 4,000 + 200 + 7

5 0

3 years ago

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A Starbucks coffee shop serves an average of 3500 customers per day, with a standard deviation of 250. What is the probability t

castortr0y [4]

Answer:

$P(3300$

And we can find this probability with this difference:

$P(-0.8$

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the amount of cofee shops of a population, and for this case we know the distribution for X is given by:

$X \sim N(3500,250)$