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mel-nik [20]
3 years ago
10

Mary mixes white paint and blue paint in the ratio 2:3 . She makes a total of 20 litres of paint. How much more blue paint does

she need to add to the mixture so that the ratio of white paint and blue paint becomes 1:7 ?
Mathematics
1 answer:
lianna [129]3 years ago
6 0

Answer:

An additional amount of blue is: 44 liters

Step-by-step explanation:

We can solve this problem in the two steps:

First we will make proportion

w : b = 2 : 3  =>  w = 2 c  and b = 3 c  where c is coefficient of proportion

We know that we have a total of 20 l of paint, which mean>

w + b = 20 => 2 c + 3 c = 20 => 5 c = 20 => c = 20/5 = 4 => c = 4

w = 2 c = 2 · 4 = 8 liters

b = 3 · 4 = 12 liters

Now we will make second proportion:

w : (b + x) = 8 : (12 + x) = 1 : 7  

When we multiply external and internal members we get:

12 + x = 8 · 7 => 12 + x = 56  =>  x = 56 - 12 = 44 liters

x = 44 liters

God with you!!!

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Answer:

$22.50

Step-by-step explanation:

First, you subtract 30 from 300 which is 270, then you divide 270 by 12 because there is 12 months in a year, and then you get 22.50 per month.

7 0
3 years ago
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3 years ago
1) If the alpha level is changed from α = .05 to α = .01, what happens to boundaries for the critical region?
Alexxandr [17]

Answer:

1) a. Move farther into the tails

2) a. Decreases

Step-by-step explanation:

Hello!

1)

Let's say for example that you are making a confidence interval for the mean, using the Z-distribution:

X[bar] ± Z_{1-\alpha /2} * \frac{Sigma}{\sqrt{n} }

Leaving all other terms constant, this are the Z-values for three different confidence levels:

90% Z_{0.95}= 1.648

95% Z_{0.975}= 1.965

99% Z_{0.995}= 2.586

Semiamplitude of the interval is

d= Z_{1-\alpha /2} * \frac{Sigma}{\sqrt{n} }

Then if you increase the confidence level, the value of Z increases and so does the semiamplitude and amplitude of the interval:

↑d= ↑Z_{1-\alpha /2} * \frac{Sigma}{\sqrt{n} }

They have a direct relationship.

So if you change α: 0.05 to α: 0.01, then the confidence level 1-α increases from 0.95 to 0.99, and the boundaries move farther into the tails.

2)

The significance level of a hypothesis test is the probability of committing a Type I error.

If you decrease the level from 5% to 1%, then logically, the probability decreases.

I hope this helps!

5 0
3 years ago
The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which
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Answer: All the real values except x ≠ 7 and the x for which f(x)≠-3

Step-by-step explanation:

Since, For function f , the domain is R - {7}

That is, If x is any element of the domain of the function f,

Then,  x ≠ 7

(gof)(x) = g(f(x))

Since, For the function g, the domain is R - {-3}

Thus,  If f(x) is any element of the domain of the function g,

Then f(x)≠ -3

Hence, Fourth Option is correct.

8 0
3 years ago
Help 8th grade math need answers quick
stepladder [879]

Answer:

A few examples:

0. 0

1. Undefined

2. -3/5

3. Undefined

...

7. 493

8. 5/2

....

Learn how to find the slope below for the other problems.

Step-by-step explanation:

Slope is the rate of change for a linear function. It is found by subtracting the y values of two point on the line and dividing that difference by the difference of the x values of the points.

It can also be found using the formula y=mx+b known as the slope intercept form.

Here are a few examples:

0. This is a horizontal line which always has slope 0.

1. This is a vertical line which always has slope undefined.

2. Find two points that cross through a grid line intersection The line appears to cross them at (5,3) and (0,6). Count the unit squares between the two by counting up 3 and over to the left 5. Because it is left it is negative. The slope is -3/5

3. To find the slope, use the slope formula:

\frac{y_2-y_1}{x_2-x_1}=\frac{6--4}{-2--2}=\frac{6+4}{-2+2}=\frac{10}{0}=undefined

Since we can't divide by 0, it is undefined.

7. y=493x-257 follows the formula y=mx+b where m is the slope. m=493. The slope is 493.

8. Covert the equation into y=mx+b by rearranging the terms using y=mx+b.

5x-2y=48

-2y=48-5x

y=5/2 x -24

So the slope is 5/2.

8 0
4 years ago
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