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yan [13]
2 years ago
11

What is the slope of the line given by the equation 2x+3y=6

Mathematics
1 answer:
expeople1 [14]2 years ago
6 0

Step-by-step explanation:

Rearrange the terms by writing

3y = -2x + 6 ---> y = (-2/3)x + 2

The slope of this equation is m = -2/3

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Karen is 6 yrs older than her sister Michelle and Michelle is two years younger than their brother David If the sum of their age
frosja888 [35]
You are told the ages of Karen and David in terms of Michelle's age.
Let m = Michelle's age.

Michelle's age = m
Karen's age = m + 6

Michelle is two years younger than David, so David is two years older than Michelle.

David's age = m + 2

Add the ages and get 62.

m + m + 6 + m + 2 = 62

3m + 8 = 62

3m = 54

m = 18

Michelle is 18 years old

Karen is 6 years older, so she is 24 years old.

David is 2 years older than Michelle, so he is 20 years old.
4 0
3 years ago
If the volume of a cone is 757 units and the height of the cone is uits, what is the radius of the cone?
Musya8 [376]

Answer:

The answer is going to be

B. 25units

4 0
3 years ago
Using the numbers (8,8,4and5) one time and any of the math operations (+,-,x,and division) create the numbers 0,10,and 24
horrorfan [7]

Answer:

8 - 8 = 0 , 8 * 5 / 4 = 10 , 8 * 4 - 8 = 24

Step-by-step explanation:

8 - 8 = 0

8 * 5 = 40 / 4 = 10

8 * 4 = 32 - 8 = 24

3 0
3 years ago
2. If you used the 23 cm basketball as your Moon sphere, how big
castortr0y [4]

Ok so I heard this question a few times already and couldn't remember how it went so I decided to put my brain to the test, I used my algebra to use and complete it.

If the Earth were shrunk down to the size of a basketball (radius:4.69 inches) the Moon would be a tennis ball (radius: 1.2768 inches, to be exact) 23.5 feet away.

The Sun would be a 42.6-foot sphere (source) located 1.7 miles away.

The closest star, Proxima Centauri, would still be 463,151 miles away – almost twice the distance of the actual moon."

6 0
3 years ago
The distribution of a sample of the outside diameters of PVC pipes approximates a normal distribution. The mean is 14.0 inches,
lakkis [162]

Answer:

A. 13.9 and 14.1 inches

See explanation below.

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 outside diameters of a population, and for this case we know the distribution for X is given by:

X \sim N(14,0.1)  

Where \mu=14 and \sigma=0.1

If we want the middle 68% of the data we need to have on the tails 16% on each one

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.84   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.16 of the area on the left and 0.84 of the area on the right it's z=-0.994. On this case P(Z<-0.994)=0.16 and P(z>-0.994)=0.84

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-0.994

And if we solve for a we got

a=14 -0.994*0.1=13.9

And since the distribution is symmetrical for the upper limit we can use z = 0.994 and we have:

z=0.994

And if we solve for a we got

a=14 +0.994*0.1=14.1

So the correct answer for this case would be:

A. 13.9 and 14.1 inches

3 0
3 years ago
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