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3 years ago

Mrs. White graded 85% of her class papers. If there are 60 papers in all, how

Mathematics

2 answers:

rusak2 [61]3 years ago

7 0

She has graded 51 papers!

eimsori [14]3 years ago

3 0

Answer:

MRS. White graded 51 papers.

Step-by-step explanation:

85/100= 0.85

0.85 x 60 = 51

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12 out of 15 people in the US like to eat out. if 400 people selected eating out how many people took the survey?

butalik [34]

12/15 = 400/500

500 people took the survey.

3 0

3 years ago

Which account has the highest effective annual interest rate? Account 1: Interest is compounded quarterly at an annual rate of 4

LenKa [72]

Answer:

Account 1 has the highest effective annual interest rate (0.042666142)

Step-by-step explanation:

Hi, to answer this question we have to apply the Effective Annual Interest Rate formula:

EAIR = [(1+r/n)^n ]-1

Where:

r = nominal interest rate

n = number of periods

If interest is compounded annually, then n = 1; if semi-annually, then n = 2; quarterly, then n = 4; monthly, then n = 12

SO:

Account 1: Interest is compounded quarterly at an annual rate of 4.20%.

EAIR = [(1+r/n)^n ]-1 = [(1+(4.20/100)/4)^4 ]-1 = 0.042666142

Account 2: Interest is compounded monthly at an annual rate of 4.15%.

EAIR = [(1+r/n)^n ]-1 = [(1+(4.15/100)/12)^12 ]-1 =0.042298535

Account 3: Interest is compounded semiannually at an annual rate of 4.10%

EAIR = [(1+r/n)^n ]-1 = [(1+(4.10/100)/2)^2]-1 = 0.04142025

Account 4: Interest is compounded annually at a rate of 4.25%.

EAIR = [(1+r/n)^n ]-1 = [(1+(4.25/100)/1)^1 ]-1 = 0.0425

Since:

0.042666142 (1) < 0.0425 (4) < 0.042298535(2) <0.041420258(3)

Account 1 has the highest effective annual interest rate 0.042666142

7 0

4 years ago

\sqrt{53+20\sqrt{7}} can be written in the form a+b\sqrt{c}, where a, b, and c are integers and c has no factors which is a perf

choli [55]

<h3>Answer: 14</h3>

=====================================================

Explanation:

Since the range of $y = \sqrt{x}$ is $y \ge 0$ , this means that $\sqrt{53+20\sqrt{7}}$ cannot be negative.

-----------------------------------

Let's set the given nested radical expression equal to the form a+b*sqrt(c), and then square both sides to see what happens

$\sqrt{53+20\sqrt{7}} = a+b\sqrt{c}\\\\\left(\sqrt{53+20\sqrt{7}}\right)^2 = \left(a+b\sqrt{c}\right)^2\\\\53+20\sqrt{7} = a^2+2ab\sqrt{c}+b^2c\\\\53+20\sqrt{7} = (a^2+b^2c)+2ab\sqrt{c}\\\\$

Equating the corresponding parts shows that

$53=a^2+b^2c \text{ and } 20\sqrt{7} = 2ab\sqrt{c}\\\\$

Therefore c = 7 must be the case to allow the radicands to match up.

-----------------------------------

Since c = 7, we can update the first equation like so

$53=a^2+b^2c\\\\53=a^2+b^2*7\\\\53=a^2+7b^2\\\\$

We'll come back to this later.

-----------------------------------

Focus on $20 = 2ab\sqrt{7}$

Note how 20 and 2ab are coefficients outside the root. So 20 = 2ab leads to ab = 10.

Here are all the ways to multiply to 10 where a,b are integers

1*10 = 10
-1*(-10) = 10
2*5 = 10
-2*(-5) = 10

So we could have these possibilities.

a = 1, b = 10
a = 10, b = 1
a = -10, b = -1
a = -1, b = -10
a = 2, b = 5
a = 5, b = 2
a = -5, b = -2
a = -2, b = -5

If you try all of those a,b combinations with $53 = a^2 + 7b^2$ , then you should find that a = 5 and b = 2 works. I'm skipping a bunch of steps here. All you basically do is plug and chug.

Due to symmetry, we could have a = -5 and b = -2 as another solution to $53 = a^2 + 7b^2$ . However, if a < 0 and b < 0, then $a+b\sqrt{c}$ would be negative which contradicts the fact that $\sqrt{53+20\sqrt{7}}$ is positive. So we'll ignore any case where a,b are negative.

Therefore, the only combination that works is a = 5 and b = 2

-----------------------------------

Overall, we found that

a = 5
b = 2
c = 7

And therefore,

$\sqrt{53+20\sqrt{7}} = a+b\sqrt{c}\\\\\sqrt{53+20\sqrt{7}} = 5+2\sqrt{7}\\\\$

You can confirm this with your calculator by taking advantage of the idea "If x = y, then x-y = 0". In other words, if you subtract the left and right sides, you should get 0 as a result (the order of subtraction doesn't matter in this case). Don't forget to use parenthesis correctly, or you may not get 0. It might help to think of it as the form (x) - (y) = 0.

After we confirmed we have the correct a,b,c values, we simply add them up to get a+b+c = 5+2+7 = 14.

7 0

3 years ago

A bag contains 19 red marbles, 27 green marbles, and 20 blue marbles. You choose a marble at random from the bag. What color mar

Andrej [43]

Answer:

Green

Step-by-step explanation:

As the majority of marbles are green, It will be most likely that you will get a green marble from the bag.

6 0

2 years ago

Read 2 more answers