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Burka
1 month ago
10

Which sample size will produce the widest 95% confidence interval, given a sample proportion of 0.5?

Mathematics
1 answer:
babunello [11.8K]1 month ago
3 0
D. 50. The width of the interval is calculated as 2z × sqrt(var/n). The interval expands under these conditions: z is larger and n is lesser. Among the given choices, the smallest n is 50.
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Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL
Leona [12618]

Answer:

KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47

Step-by-step explanation:

Given:

KL ║ NM,

LM = 45

m∠M = 50°

KN ⊥ NM  

NL ⊥ LM

To determine: KN and KL

1. Analyzing triangle NLM, we see it is a right triangle due to NL ⊥ LM. In this context,

LM = 45

m∠M = 50°

Consequently,

\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}

It is also true that

(angles LNM and M are complementary).m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}

2. Now considering triangle NKL, it also forms a right triangle as KN ⊥ NM. Within this triangle,

NL=45\tan 50^{\circ}

m\angle KLN=m\angle LNM=40^{\circ} (alternate interior angles)

m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ} (angles KNL and KLN are complementary).

Thus,

\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08

and

\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47

3 0
2 months ago
Read 2 more answers
You and your friends Jose and Sarah all live on the same street. You know that Jose lives five blocks from away from you. Jose s
Svet_ta [12734]

Answer:

Please refer to the explanation

Step-by-step explanation:

Given that:

Sarah, Jose, and you all reside on the same street:

The distance between you and Jose is 5 blocks

The distance between Jose and Sarah is 2 blocks

Calculating the distance (b) between you and Sarah:

Since it is not specified if Sarah is closer to you or to Jose;

Thus;

Distance b from you to Sarah will be:

(The distance to Jose ± the distance to Sarah)

b = (5 ± 2)

b = (5 + 2) or (5 - 2)

b = 7 blocks or 3 blocks

4 0
1 month ago
A Candlestick burns at a rate of 0.2 inches per hour. After 8 straight hours of burning , the candlestick is 13.4 inches tall. W
lawyer [12517]
The initial height of the candle is 14.8 inches.
8 0
2 months ago
Colton has 16 blue marbles and 8 white ones.if he wants to place them in identical groups without any marbles left over what is
Svet_ta [12734]
For the blue marbles:
16 = 8 * 2 (8 sets containing 2 marbles each)
For the white marbles:
8 = 4 * 2 (4 sets with 2 in each)
8 + 4 = 12
Answer:
The maximum number of groups that Colton can form is 12.
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Takuya's parents gave him $100dollar as a birthday gift. Since he loves board games, he spent $20dollar out of his present on bo
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To create a recursive formula, start by identifying if the sequence is geometric (for example, if the same number is being multiplied or divided for one term or more). After that, determine the common ratio (the specific number used for multiplication or division).
3 0
2 months ago
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