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2 years ago

There are a total of 66 students in the

Mathematics

1 answer:

attashe74 [19]2 years ago

7 0

Answer:

A = 26

Step-by-step explanation:

sum of students = classA + classB + classC

let's say classA = A, classB = B, and classC = C

A + B + C = 66

class A has five more students than class B, so A = 5 more than B so A = 5+B

class C has 2 less students than class B, so C = 2 less than class B = B -2, so C = B-2

A + B + C = 66

A = 5+B

C = B-2

substitute 5+B for A and B-2 for C in the first equation to limit this to one variable (B)

(5+B) + B + (B-2) = 66

3B + 3 = 66

subtract 3 from both sides to isolate the variable and its coefficient

3B = 63

divide both sides by 3 to solve for B
B = 21

A = 5 + B = 5 + 21 = 26

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the area of ava rectangular back yard is 325 square yards.if the length of the yards is 13 yards,what is the width of the yard

Viktor [21]

It is given in the question that, The area of ava rectangular back yard is 325 square yards and the length of the yards is 13 yards.

Let the width be w yard .

And area of rectangle is the product of length and width .

So we have

$325 = 13 w$

Dividing both sides by w

$\frac{325}{13} = \frac{13w}{13} => w = 25 yards .$

So the width is 25 yards .

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3 years ago

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The angles of a triangle are equal to x, x+4 and 20x. What is the measure of the largest angle of the triangle?

Ipatiy [6.2K]

Answer:

160°

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°. The sum of angles in the given triangle is ...

x + (x +4) + 20x = 180

22x +4 = 180 . . . . . . . . . . collect terms

22x = 176 . . . . . . . . . . subtract 4

x = 8 . . . . . . . . . . . divide by 22

20x = 160 . . . . find the largest angle

The measure of the largest angle is 160°.

3 0

2 years ago

A college student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal,

eduard

Answer:

a) Sample size = 822

b) Margin of error = 0.03407

Step-by-step explanation:

We are given the following in the question:

p = 74% = 0.74

a) Sample size is required to obtain margin of error of 0.03

Formula:

$\text{Margin of error} = z_{\text{statistic}}\times \sqrt{\dfrac{p(1-p)}{n}}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get,

$0.03 = 1.96\times \sqrt{\dfrac{0.74(1-0.74)}{n}}\\\\n = (\dfrac{1.96}{0.03})^2(0.74)(1-0.74)\\\\n = 821.24 \approx 822$

Thus, the sample size must be approximately 822 to obtain a 95% confidence interval with an approximate margin of error of 0.03

b) Margin of error for the 95% confidence interval

p = 54% = 0.54

Formula:

$\text{Margin of error} = z_{\text{statistic}}\times \sqrt{\dfrac{p(1-p)}{n}}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get,

$\text{Margin of error} = 1.96\times \sqrt{\dfrac{0.54(1-0.54)}{822}}\\\\=0.03407$

The margin of error now will be 0.03407.

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3 years ago

PLEASE HELP!! I HAVE TO TURN THIS IN IN 10 MINUTES

grin007 [14]

Answer:

0.8

Step-by-step explanation:

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6 0

3 years ago

Is it ever possible that cos (A−B)=cos ⁡A−cos ⁡B? Why or why not?

Nookie1986 [14]

Answer:

The given equation is never possible i.e cos ( A - B ) ≠ cos A - cos B

Step-by-step explanation:

Given as :

Is cos ( A - B ) = cos A - cos B

To check this possibility , Let us put the value of angle A and B on both side of equation

Now, Let A = 60° and B = 30°

From Left hand side equation

cos ( A - B ) = cos ( 60° - 30° )

Or, cos ( A - B ) = cos 30°

∴ cos ( A - B ) = $\frac{\sqrt{3} }{2}$

or, cos ( A - B ) = 0.866

From Right hand side equation

cos A - cos B = cos 60° - cos 30°

Or, cos A - cos B = $\frac{1}{2}$ - $\frac{\sqrt{3} }{2}$

∴, cos A - cos B = 0.5 - 0.866

I.e cos A - cos B = - 0.366

So, Left hand side ≠ Right hand side

Since while equating the values of angle A and b in the given equation on both sides, we get that the value of both sides are not equal , Thus we can say that the given equation is not equal to each other .

Hence given equation is never possible i.e cos ( A - B ) ≠ cos A - cos B Answer

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3 years ago