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Reptile [31]
3 years ago
15

Mr. Patrick teaches math to 1515 students. He was grading tests and found that when he graded everyone's test except Payton's, t

he average grade for the class was 8080. After he graded Payton's test, the test average became 8181. What was Payton's score on the test?
Mathematics
1 answer:
julsineya [31]3 years ago
7 0
Given:
15 students
average grade: 80 for 14 students
average grade: 81 for 15 students

80 * 14 = 1120
81 * 15 = 1215

1215 - 1120 = 95

Payton's score on the test is 95.
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The following data represent the pH of rain for a random sample of 12 rain dates in Tucker County, West Virginia. A normal proba
Sphinxa [80]

Answer:

Step-by-step explanation:

n = 12

Mean = (4.58 + 5.72 + 4.77 + 4.76 + 5.19 + 5.05 + 4.80 + 4.77 + 4.75 + 5.02 + 4.74 + 4.56)/12 = 4.8925

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (4.58 - 4.8925)^2 + (5.72 - 4.8925)^2 + (4.77 - 4.8925)^2 + (4.76 - 4.8925)^2 + (5.19 - 4.8925)^2 + (5.05 - 4.8925)^2 + (4.80 - 4.8925)^2 + (4.77 - 4.8925)^2 + (4.75 - 4.8925)^2 + (5.02 - 4.8925)^2 + (4.74 - 4.8925)^2 + (4.56 - 4.8925)^2 = 1.122225

Standard deviation = √(1.122225/12

s = 0.31

a) Point estimate = sample mean = 4.8925

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

Margin of error = z × s/√n

Where

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 12 - 1 = 11

b) Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.201

Margin of error = 2.201 × 0.31/√12

= 0.197

95% confidence interval = 4.8925 ± 0.197

Upper limit = 4.8925 + 0.197 = 5.0895

Lower limit = 4.8925 - 0.197 = 4.6955

We are 95% confident that the population mean of the rain water ph lies between 4.6955 and 5.0895

c) For 99% confidence level, z = 3.106

Margin of error = 3.106 × 0.31/√12

= 0.278

99% confidence interval = 4.8925 ± 0.278

Upper limit = 4.8925 + 0.278 = 5.1705

Lower limit = 4.8925 - 0.278 = 4.6145

We are 99% confident that the population mean of the rain water ph lies between 4.6145 and 5.1705

d) The interval gets wider as the confidence level is increased. This is logical since the test score is higher for 99% and therefore, increases the range of values. Since we want to be more confident, the range of values must be extended.

3 0
3 years ago
Two ships leave the same port at the same time. Two hours later ship A has traveled 12 miles and ship B has traveled 8 miles.
MakcuM [25]

Answer:

the angle between their paths is <em>100.8°</em>

Step-by-step explanation:

From the given information, you can construct a triangle, just like the one in the figure.

We will use the <em>Cosine Rule</em> which is:

c² = b² + a² - 2 b c cos(θ)

where

  • c = 16 miles
  • b = 8 miles
  • a = 12 miles

Therefore,

2 b c cos(θ) = b² + a² - c²

cos(θ) = (b² + a² - c²) / 2 b c

θ = cos⁻¹( (b² + a² - c²) / (2 b c) )

θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )

<em>θ = 100.8°</em>

<em></em>

Therefore, the angle between their paths is <em>100.8°</em>

4 0
3 years ago
Draw a rhombus that is not a square. Label the lengths of its sides and its height so it represents a rhombus with an area of 20
Tcecarenko [31]

Answer:

          /\

\sqrt{20} /     \\sqrt{20}

     /         \

     \         /

\sqrt{20}  \     / \sqrt{20}

          \/

Step-by-step explanation:

i hope this is right it took me 30 min for the ascii

6 0
3 years ago
Please help -6(-5)+12
madreJ [45]
<span>-6(-5)+12
Multiply -6 by -5.
Note: Whenever you multiply or divide a negative number by another negative number, it automatically becomes a positive number.
30+12
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Final Answer: 42</span>
4 0
3 years ago
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d1i1m1o1n [39]
Both lines intersect at the point
(-0.5, 0.5)
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