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3 years ago

A random sample of n = 64 observations has a mean x = 29.9 and a standard deviation s = 3.7.

Mathematics

1 answer:

Elis [28]3 years ago

4 0

Answer:

(29.128,30.672)

Step-by-step explanation:

Given that a random sample of n = 64 observations has a mean x = 29.9 and a standard deviation s = 3.7.

a) the point estimate of the population mean μ.

= Sample mean = 29.9

For 90% we use t critical value since population standard deviation is not known.

T critical for 90% is 1.669

Margin of error = ± $1.669*\sqrt{\frac{3.7}{\sqrt{64} } } \\=0.7719$

b) Confidence interval 90%

= Mean±Marginof error

= $(29.128,30.672)$

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Write this number in standard form.

zzz [600]

Answer:

10,014,070

Step-by-step explanation:

6 0

3 years ago

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse B A is 9.8 inches, the length of C B is 6.3 inch

german

Answer:

$\angle B=\cos^{-1}\left(\dfrac{6.3}{9.8}\right)\\ \\\angle B=\sin^{-1}\left(\dfrac{7.5}{9.8}\right)$

Step-by-step explanation:

Consider right triangle ABC with right angle C.

In this triangle,

BA = 9.8 in
CB = 6.3 in
CA = 7.5 in

Write trigonometric functions:

$\cos \angle B=\dfrac{BC}{AB}=\dfrac{6.3}{9.8}\\ \\\sin \angle B=\dfrac{AC}{AB}=\dfrac{7.5}{9.8}$

Hence,

$\angle B=\cos^{-1}\left(\dfrac{6.3}{9.8}\right)\\ \\\angle B=\sin^{-1}\left(\dfrac{7.5}{9.8}\right)$

7 0

2 years ago

Read 2 more answers

A trout lurking 32 cm below the surface of a lake spies an insect flying 17cm above the lake. How many centimeters would the tro

Bumek [7]

Answer:

The Trout will have to jump 49 cm in order to catch the insect

Step-by-step explanation:

Here, we want to calculate the distance the Trout has to jump in order to catch the Insect

To calculate this, we need to know the difference in the distances

From what we have, the Trout is 32 cm below the surface while the Insect is 17 cm above the surface of the lake

The difference in height which will represent the distance that the Trout has to jump to catch the insect will be ;

17 + 32 = 49 cm

3 0

2 years ago

Find the value of cos 0 , If sec 0 = 3/2 0 < 90

UNO [17]

Answer:

Step-by-step explanation:

cos theta is 2/3 because cos means reciprocal of sec

7 0

2 years ago

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I just need no. a please help me to prove this.

OleMash [197]

Answer: see proof below

<u>Step-by-step explanation:</u>

Given: A + B + C = π and cos A = cos B · cos C

scratchwork:

A + B + C = π

A = π - (B + C)

cos A = cos [π - (B + C)] Apply cos

= - cos (B + C) Simplify

= -(cos B · cos C - sin B · sin C) Sum Identity

= sin B · sin C - cos B · cos C Simplify

cos B · cos C = sin B · sin C - cos B · cos C Substitution

2cos B · cos C = sin B · sin C Addition

$2=\dfrac{\sin B\cdot \sin C}{\cos B \cdot \cos C}$ Division

2 = tan B · tan C

$\text{Use the Sum Identity:}\quad \tan(B+C)=\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}$

<u>Proof LHS → RHS</u>

Given: A + B + C = π

Subtraction: A = π - (B + C)

Apply tan: tan A = tan(π - (B + C))

Simplify: = - tan (B + C)

$\text{Sum Identity:}\qquad \qquad \qquad =-\bigg(\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}\bigg)$

Substitution: = -(tan B + tan C)/(1 - 2)

Simplify: = -(tan B + tan C)/-1

= tan B + tan C

LHS = RHS: tan B + tan C = tan B + tan C $\checkmark$

5 0

2 years ago