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lord [1]
3 years ago
14

Suppose that scores on the mathematics part of a test for eighth-grade students follow a Normal distribution with standard devia

tion σ = 150. You want to estimate the mean score within ±20 with 90% confidence. How large an SRS of scores must you choose? (Round your answer up to the next whole number.)
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
8 0

Answer:

We need an SRS of scores of at least 153.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

How large an SRS of scores must you choose?

This is at least n, in which n is found when M = 20, \sigma = 150. So

M = z*\frac{\sigma}{\sqrt{n}}

20 = 1.645*\frac{150}{\sqrt{n}}

20\sqrt{n} = 1.645*150

\sqrt{n} = \frac{1.645*150}{20}

\sqrt{n} = 12.3375

(\sqrt{n})^{2} = (12.3375)^{2}

n = 152.2

Rounding to the next whole number, 153

We need an SRS of scores of at least 153.

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39.2 is what percent p of 112
madam [21]
39.2 is what percent p of 112

39.2/112

39.2 ÷ 112 = 0.35

Convert to percent:-

0.35 × 100 = 35
35%

3.92 is 35% of 112.
3 0
3 years ago
5 1/2 qt -_= 4 cups plreaseeeee help
nignag [31]

Answer: 5.5 quarts = 22 cups

Step-by-step explanation:

1 cup = 4 cups

to convert cups to quart, just multiply by 4

5.5 x 4 = 22

7 0
2 years ago
Need help pls help me will mark first
Xelga [282]

Answer:

angles 5,6 are supplementary

angles 7 and 4 are vertical angles

(one solution of many)

Step-by-step explanation:

Lets start with supplementary angles. those are two angles that add up to 180 degrees or make a straight angle. Two angles that fulfill this statement are 5 and 6 because 5 and 6 make a straight angle.

Now lets do vertical angles. Vertical angles are angles that are opposite of each. They are made by intersecting diagonals. One pair of angles that fulfill this are angles 7 and 4. if you can tell, they are opposite of each other.

supplementary= 5 and 6

vertical= 7 and 4

have a wonderful day!

4 0
2 years ago
Read 2 more answers
Segments
Kazeer [188]

Given

AB  and  CD  intersect

AC,  CB,  BD  and  AD  are congruent.

Prove that AB  is the bisector of ∠CAD and ray  CD  is the bisector of ∠ACB.

and AB  and  CD  are perpendicular.

To proof

Bisector

<em>A bisector is that which cut an angle in two equal parts.</em>

In ΔACB and ΔADB

AD = AC  ( Given )

AB = AB   ( common )

BC = DB  ( Given )

by SSS congurence property

we have

ΔACB ≅ΔADB

∠CAB =∠ DAB

∠CBA = ∠DBA

( By corresponding sides of the congurent triangle )

Thus AB is the bisector of the ∠CAD.

InΔ DAC and ΔDBC

AD = DB (Given)

AC = CB  ( Given )

CD = CD (common)

By SSS congurence property

ΔDAC≅ Δ DBC

∠  ACD =∠ BCD

∠ADC =∠BDC

( By corresponding sides of the congurent triangle )

Therefore CD is the bisector of the CAD.

In ΔBOC andΔ BOD

BO = BO ( Common )

∠BCO = ∠BDO

( As prove above ΔACB ≅ΔADB

Thus ∠ACB = ∠ADB by corresponding sides of the congurent triangle , CD is a bisector

∠BCO = ∠BDO )

 CB = DB ( given )

by SAS congurence property

ΔBOC ≅ ΔBOD

∠BOC =∠ BOD

∠BOC +∠ BOD = 180 °( Linear pair )

2∠ BOC = 180°

∠BOC = 90°

∠BOC =∠ BOD = 90°

also

In ΔCOA and ΔAOD

AO = AO ( Common )

∠ACO =∠ ADO

(  As prove above ΔACB ≅ΔADB Thus ACB = ADB by corresponding sides of congurent triangle ,CD is a bisector

thus  ∠ACO = ∠ADO )

AC =AD ( given )

by SAS congurence property

Δ COA ≅ ΔAOD

∠AOC = ∠AOD

( By corresponding angle of corresponding sides )

∠AOC + ∠AOD = 180°

2∠ AOC = 180°   ( Linear pair )

∠AOC = 90°

∠AOC = ∠AOD = 90 °

Thus AB  and  CD  are perpendicular.

Hence proved









   


 



6 0
3 years ago
Rewrite the following polynomial in standard form.<br> 1 + 10x3 + x2
boyakko [2]

Answer:

31 + x

Step-by-step explanation:

1) 1 + 10 × 3 + x

2) 1 + 30 + x

3) 31 + x

4 0
2 years ago
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