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wlad13 [49]
3 years ago
11

You make 72 cookies for a bake sale.this is 20%of the cookies at the bake sale.how many cookies are at the bake sale?

Mathematics
2 answers:
ASHA 777 [7]3 years ago
5 0
Hey there! 

<span>Here is how you solve the question:

1. Write the question out as a fraction.

</span>\frac{72}{20} 
<span>
2. Since percent means, 'Out of 100', get 100 as the denominator. 

</span>\frac{72}{20} = \frac{360}{100}
<span>
So, the answer is 360 cookies.

(If you feel that my answer has helped you, please consider rating it and giving it a thank you! Also, feel free to choose the best answer, the brainliest answer!)
</span>
Thank you for being part of the brainly community! :D
snow_tiger [21]3 years ago
3 0
360 cookies total:D

72*5
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Find the exact value of the expression.<br> tan( sin−1 (2/3)− cos−1(1/7))
Sonja [21]

Answer:

\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}

Step-by-step explanation:

I'm going to use the following identity to help with the difference inside the tangent function there:

\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}

Let a=\sin^{-1}(\frac{2}{3}).

With some restriction on a this means:

\sin(a)=\frac{2}{3}

We need to find \tan(a).

\sin^2(a)+\cos^2(a)=1 is a Pythagorean Identity I will use to find the cosine value and then I will use that the tangent function is the ratio of sine to cosine.

(\frac{2}{3})^2+\cos^2(a)=1

\frac{4}{9}+\cos^2(a)=1

Subtract 4/9 on both sides:

\cos^2(a)=\frac{5}{9}

Take the square root of both sides:

\cos(a)=\pm \sqrt{\frac{5}{9}}

\cos(a)=\pm \frac{\sqrt{5}}{3}

The cosine value is positive because a is a number between -\frac{\pi}{2} and \frac{\pi}{2} because that is the restriction on sine inverse.

So we have \cos(a)=\frac{\sqrt{5}}{3}.

This means that \tan(a)=\frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}}.

Multiplying numerator and denominator by 3 gives us:

\tan(a)=\frac{2}{\sqrt{5}}

Rationalizing the denominator by multiplying top and bottom by square root of 5 gives us:

\tan(a)=\frac{2\sqrt{5}}{5}

Let's continue on to letting b=\cos^{-1}(\frac{1}{7}).

Let's go ahead and say what the restrictions on b are.

b is a number in between 0 and \pi.

So anyways b=\cos^{-1}(\frac{1}{7}) implies \cos(b)=\frac{1}{7}.

Let's use the Pythagorean Identity again I mentioned from before to find the sine value of b.

\cos^2(b)+\sin^2(b)=1

(\frac{1}{7})^2+\sin^2(b)=1

\frac{1}{49}+\sin^2(b)=1

Subtract 1/49 on both sides:

\sin^2(b)=\frac{48}{49}

Take the square root of both sides:

\sin(b)=\pm \sqrt{\frac{48}{49}

\sin(b)=\pm \frac{\sqrt{48}}{7}

\sin(b)=\pm \frac{\sqrt{16}\sqrt{3}}{7}

\sin(b)=\pm \frac{4\sqrt{3}}{7}

So since b is a number between 0 and \pi, then sine of this value is positive.

This implies:

\sin(b)=\frac{4\sqrt{3}}{7}

So \tan(b)=\frac{\sin(b)}{\cos(b)}=\frac{\frac{4\sqrt{3}}{7}}{\frac{1}{7}}.

Multiplying both top and bottom by 7 gives:

\frac{4\sqrt{3}}{1}= 4\sqrt{3}.

Let's put everything back into the first mentioned identity.

\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}

\tan(a-b)=\frac{\frac{2\sqrt{5}}{5}-4\sqrt{3}}{1+\frac{2\sqrt{5}}{5}\cdot 4\sqrt{3}}

Let's clear the mini-fractions by multiply top and bottom by the least common multiple of the denominators of these mini-fractions. That is, we are multiplying top and bottom by 5:

\tan(a-b)=\frac{2 \sqrt{5}-20\sqrt{3}}{5+2\sqrt{5}\cdot 4\sqrt{3}}

\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}

4 0
3 years ago
PLESEEE HELP I WILL GIVE THE BRAINLIEST TO THE BEST ANWSERS
miss Akunina [59]
The answer to the first question is D.)

The 6 in front of the parentheses modifies both 'x' and 3

The answer to the second question is D.)

When you plug 4 into the equation, you get 14

3(4) + 2 = 14
12 + 2 = 14
14=14

Hope this helps!
6 0
2 years ago
Read 2 more answers
(05.05)On the coordinate plane below, what is the length of AB?
JulsSmile [24]

the lenght of the picture is 14

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Mr. Coffman asked his students to write an example of a square root with a value greater than 11 but less than 11.5. Select the
Leto [7]

Answer:

Dean and Candace

Step-by-step explanation:

4 0
2 years ago
The question is in the photo/image
Lina20 [59]
The answer is <span>π8^2 or about 201.06</span>
3 0
3 years ago
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