Mark earns $440 per week. He receives a 20% raise. What is Mark's weekly pay rate?

Answer:

(4.5, 8) and (8, 4.5)

Step-by-step explanation:

Given the equations

(x+y)=12.5 ... 1

X ×Y=36 .... 2

From 2, Y = 36/X

Substitute into 1

x+ 36/x = 12.5

x^2 + 36 = 12.5x

x^2 - 12.5x + 36 = 0

10x^2 - 125x + 360 = 0

2x^2 - 25x + 72 = 0

Factorize

2x^2 - 16x - 9x + 72 = 0

2x(x-8)-9(x-8) = 0

2x-9 = 0 and x-8 = 0

x = 9/2 and x = 8

when x = 9/2

Y = 36/(9/2)

Y = 36 * 2/9

Y = 8

When x = 8

Y = 36/X

Y = 36/8

Y =  4.5

Hence the solutions are (4.5, 8) and (8, 4.5)

Answer: Yes

You still need to simplify 3/12 because it is not in its MOST simplified form.

3/12 can be simplified to 1/4 by dividing 3.

Answer:

16

Step-by-step explanation:

use the acroname sohcahtoa

sin 60=8√3/h

sin60=0.8660 while 8√3=13.8564

divide both side by 0.8660

0.8660/0.8660=13.8564/0.8660

h=16.0

Answer:

I think the answer would be X= 7.9999999999 .

Y= 15.9999999999

Step-by-step explanation:

Tan 60 = Rad 192 / X

X= 7.9999999999

Y = 15.9999999999

Hope it was helpful ^^ Good luck .

Answer:

[tex]16\sqrt{17}[/tex]

Step-by-step explanation:

The perimeter is two times width plus two times length:

[tex]2\sqrt{17} + 2\cdot 7\sqrt{17} = 2\sqrt{17} + 14\sqrt{17} = 16\sqrt{17}[/tex]

There is no way to simplify further.

Answer:

226 inches cube

Step-by-step explanation:

The volume of the cylinder is the area of the base X height therefore it would be 3^2 * 3.14 * 8 = 72 * 3.14 = 226.08.

Answer:

151 in^3

Step-by-step explanation:

pi x 3^2 x 5.5 (the approximate water level)

= 155

151 is the closest answer

Answer:

Step-by-step explanation:

B two pairs of sides have the same slope.

I've done this before.

Answer:

1. We want to write an equation in the form:

Ix - bI ≤ c

Such that the solutions are the range  −1 ≤ x ≤ 3

First, the extremes of the range are: - 1 and 3

Half of the difference between these values is:

m = (3 - (-1))/2 = (3 + 1)/2 = 4/2 = 2

Now let's go to the lower extreme, and add this value, we get:

-1 + m = -1 + 2 = 1

(if we go to the upper value and we subtract m, we get the same)

This is the mid-value of the solution interval, and we will define it as M

We now can write the absolute value inequality as:

I x - MI ≤ m

In our case, we get:

Ix - 1I ≤ 2

2.

Now we want to have the solution set given by:

x ≤ -9

x ≥ -5

In this case, we will have an equation of the form:

Ix - MI ≥ m

(before we used the symbol ≤, which means that the solutions are inside the interval, now we use the symbol ≥, which means that the solutions are outside of the interval (-9, -5) in this case).

So let's do the same than in the above case:

m = (-5) - (-9) = (-5 + 9)/2 = 4/2 = 2

M = -9 + 2 = -7

Replacing these in the absolute value inequality we got:

Ix - (-7)I ≥ 2

Ix + 7I ≥ 2

Answer:

49.41

Fine the lengths of the top, bottom, and left side first. the do bottom - top and you get 6. To get the length of the right side, do left side squared + 6 squared and you get the length of the right side squared. The answer is top + bottom +   left side + square root of right side squared.

Answer:

Y=0.5X+5

Step-by-step explanation:

Hope this helps ;)

Answer:

168

Step-by-step explanation:

24x7=168

Answer:

In total, the amount of milk every kid combined drank is 672 ounces.

Step-by-step explanation:

If four kids drank 24 ounces of milk for seven days, you would solve it as follows:

First, the amount all the kids drink in one day combined is 96 ounces.

If they drink 96 per day, and they do so for a week (7 days), then that is 96 × 7 because its 96 seven times.

7 × 96 = 672

Answer:

75.51%

Step-by-step explanation:

hopefully this helps

x/100 = 74/98

98x = 7,400

x = 7,400/98

× = 75.51 % of 98

Answer:

Hi! The answer is in the pictures!!

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

Answer:

the correct answer is

229/479 = 0.48

The probability that a randomly chosen person from this group is male is 0.48.

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

The probability of choosing a male = number of males / total number of males and females

229/479 = 0.48

To learn more about frequency tables, please check: https://brainly.com/question/26577861

Answer:

231.59 years

Step-by-step explanation:

To model this situation we are going to use the exponential decay function:

f(t)= a (1-b)^t

where f(t) is the final amount remaining after t years of decay

a is the final amount

b is the decay rate in decimal form

t is the time in years

For Substance A:

Since  we have 300 grams of the substance, a=300. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r = 0.15/100 = 0.0015. Replacing the values in our function:

f(t) = a (1-b)^t

f(t) = 300 (1-0.0015)^t

f(t) = 300 (0.9985)^t equation (1)

For Substance B:

Since we have 500 grams of the substance, a= 500. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r=0.37/100= 0.0037. Replacing the values in our function:

f(t) = a (1-b)^t

f(t)= 500 (1-0.0037)^t

f(t)=500(0.9963)^t equation (2)

Since they are trying to determine how many years it will be before the substances have an equal mass M, we can replace f(t) with M in both equations:

M=300(0.9985)^t equation (1)

M=500(0.9963)^t equation (2)

We can conclude that the system of equations that can be used to determine how long it will be before the substances have an equal mass, M, is :

{M=300(0.9985)^t

{M=500(0.9963)^t

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{4 centigrams = [blank] milligrams}[/tex]

[tex]\mathsf{4 \times \dfrac{10}{1}}[/tex]

[tex]\mathsf{= \dfrac{4}{1}\times\dfrac{10}{1}}[/tex]

[tex]\mathsf{=\dfrac{4\times10}{1\times1}}[/tex]

[tex]\mathsf{4\times10=\bf 40}\leftarrow\large\textsf{NUMERATOR}[/tex]

[tex]\mathsf{1\times1 = \bf 1}\leftarrow\large\textsf{DENOMINATOR}[/tex]

[tex]\mathsf{= \dfrac{40}{1}}[/tex]

[tex]\mathsf{\dfrac{40}{1}=40\div1=\bf 40}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: 4 centigrams = \huge\bf{40 milligrams}}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

A “Towel”

Step-by-step explanation:

x = 5/2 or x = 1/3

C is the answer.

Answer:

x = 5/2 or x = 1/3

Step-by-step explanation:

Simplify  

( 2 x − 5 )( 3 x − 1 ) .

6 x 2 − 17 x + 5 = 0

Use the quadratic formula to find the solutions.

[tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] or [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Substitute the values  a = 6 ,  b = − 17 , and  c = 5  into the quadratic formula and solve for  x .

17 ±sqrt(-17)^2-4*(6*5)

_________________

2*6

Simplify.

x = 17 ± 13 /12

The final answer is the combination of both solutions.

x = 5 /2 ,  1 /3

Answer:

[tex]x = ln(2 - 1) [/tex]

Answer:

63°

Step-by-step explanation:

First, by looking at the angle we see that the overall angle is a right angle. This means that the total will add up to 90°.

Knowing this we can then subtract

90° - 27° = 63°

Answer:

63

Step-by-step explanation:

The measure of a right angle is always 90 so

90-27=63

Answer:

14. 44.8 feet

cos48=30/x

x=30/cos48

x=44.8

15. 2352 feet

tan12=500/x

x=500/tan12

=500/0.2126

x=2352

Answer:

75

Step-by-step explanation:

Answer:

3x(x-1) = 0

x= 1

Step-by-step explanation:

is 3x2 supposed to mean 3x^2 i dont know

Answer:

-3/4

Step-by-step explanation:

The slope is -3/4

The line goes down three and four left.  

Answer:

The second one

Step-by-step explanation:

A visual for law of sines can be found below

Sin (an angles) over its opposite side length is equal to sin ( a different angle) over its opposite side length

In the given triangle we are given side length BC and side length AB

we are also given AB's opposite angle  (40)

And we need to find side length BC's opposite angle (A)

That being said we are given enough information to set up an equation using the law of sines

Remember angle A's opposite side length is 16 and the angle that has a measure of 40 degrees' opposite side length is 12

so the equation would look like...

[tex]\frac{sin(40)}{12} =\frac{sin(A)}{16}[/tex]

Answer: B. The procedure for constructing the confidence interval is robust. The larger the sample​ size, the more resistant the mean.​ Therefore, the confidence interval is more robust.

Step-by-step explanation:

Large sized data samples usually have more stability than data with small samples, they yield a mean value which edges closer to the value of the population data. This means that large size data samples will have a mean which is more resistant to change than samples with a lower sample size. The confidence interval gives robustness while constructing a model by giving te leverage for a range of values based in a certain level of confidence upon which a statistical vale can be tested for validity.

Answer:

y=40x-30

Step-by-step explanation:

Answer:

A. is correct

Step-by-step explanation:

Divide both sides by 11