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2 years ago

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In a random sample of 250 students, 150 were in favor of longer hours at the school library. At 98% level of confidence, what is

the margin of error?
Select one:

0.051

0.080

0.065

0.072

0.078

0.061

1 answer:

Wewaii [24]2 years ago

3 0

0.072 is the margin of error.

<h3>What is standard error?</h3>

The standard error (SE) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation.

According to the question,

In a random sample of 250 students,

p= 0.98 (or 98%) were in favor of longer hours at the school library.

The standard error of p(the sample proportion) is (approximately)

The standard error of p = $\sqrt{\frac{p(1-p)}{n} }$

p = 0.98

1 - p = 1 - 0.98 = 0.02

Here,

n = 250

The standard error of p = $\sqrt{ \frac{0.98 (0.02) }{250}$

The standard error of p ≈ 0.072

Therefore,

The margin of error is 0.072.

Learn more about is standard error here:

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Answers are needed urgently..ty

SIZIF [17.4K]

Angle <QAB is =15° because the opposite angles of an isosceles triangle are equal.

The length of the straight line AB = 80cm

<h3>Calculation of angle of a triangle</h3>

The angle at a point = 360°

Angle AQB= 360 - 210° = 150

But the angle that makes up a triangle= 180°

180-150= 30°

But <QAB = <QBA because triangle AQB is an isosceles triangle.

30/2 = 15°

To calculate the length of the straight line the following is carried out using the sine laws.

a/ sina, = b sinb

a= 8cm, sin a { sin 15)

b= ? , sin B = 150

make b the subject formula;

8/sin15= b/sin 150

b= 8 × sin 150/sin 15

b= 80cm

Learn more about isosceles triangle here:

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7 0

2 years ago

Prove the divisibility:<br><br>45^45·15^15 by 75^30

garri49 [273]

Answer:

$3^{75}$ .

Step-by-step explanation:

We have been an division problem: $\frac{45^{45}*15^{15}}{75^{30}}$ .

We will simplify our division problem using rules of exponents.

Using product rule of exponents $(a*b)^n=a^n*b^n$ we can write:

$45^{45}=(9*5)^{45}=9^{45}*5^{45}$

$15^{15}=(3*5)^{15}=3^{15}*5^{15}$

$75^{30}=(15*5)^{30}=15^{30}*5^{30}$

Substituting these values in our division problem we will get,

$\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}$

$\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}$

Using product rule of exponents $(a*b)^n=a^n*b^n$ we will get,

$\frac{(3*3)^{45}*5^{60}*3^{15}}{(3*5)^{30}*5^{30}}$

$\frac{3^{45}*3^{45}*5^{60}*3^{15}}{3^{30}*5^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{3^{(45+45+15)}*5^{60}}{3^{30}*5^{(30+30)}}$

$\frac{3^{105}*5^{60}}{3^{30}*5^{60}}$

$\frac{3^{105}}{3^{30}}$

Using quotient rule of exponent $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{3^{105}}{3^{30}}=3^{105-30}$

$3^{105-30}=3^{75}$

Therefore, our resulting quotient will be $3^{75}$ .

7 0

3 years ago

The sum of two numbers is 21 the second number is 6 times the first number of

romanna [79]

the numbers are 3 and 18

let the first number be n then the second number = 6n and the sum

sum = n + 6n = 21 thus

7n = 21

divide both sides of the equation by 7

n = $\frac{21}{7}$ = 3

the numbers are 3 and 6 × 3 = 18 → (3 + 18 = 21)

8 0

2 years ago

Read 2 more answers

Need help ASAP Will mark u brainlyest

balandron [24]

Step 2 is wrong: 4x - x = 5x
X = -11 is the actual answer, pretty sure.
Hope this helps and please mark as brainliest. If you have any other doubts, feel free to ask.

4 0

2 years ago

When the sun's angle of elevation is 76°, a tree casts an 18-foot shadow on the ground. Find the length of the tree to the neare

Yanka [14]

Answer:

<u>56.5 ft</u>

Step-by-step explanation:

See the attached figure which represents the explanation of the problem.

We need to find the length of the tree to which is the length of AD

From the graph ∠BAC = 90° and ∠ABD = 76°, AB = 18 ft

At ΔABD:

∠BAD = ∠BAC - ∠DAC = 90° - 4° = 86°

∠ADB = 180° - ( ∠BAD + ∠ABD) = 180 - (86+76) = 180 - 162 = 18°

Apply the sine rule at ΔABD

∴ $\frac{AB}{SinD} =\frac{AD}{sinB}$

∴ 18/sin 18 = AD/sin 76

∴ AD = 18 * (sin 76)/(sin 18) ≈ 56.5 (to the nearest tenth of a foot)

So, The length of the tree = 56.5 ft.

<u>The answer is 56.5 ft</u>

3 0

2 years ago