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Triss [41]
2 years ago
12

Find the value of Y .....

Mathematics
1 answer:
vekshin12 years ago
4 0

Answer:

y = 6 \sqrt{3}  \: units

Step-by-step explanation:

In order to find the value of y, first we need to find the length of the perpendicular dropped from one of the vertices of the triangle to its opposite side.

By geometric mean theorem:

Length of the perpendicular

=\sqrt{9\times 3}

=\sqrt{27}\: units

Next, by Pythagoras theorem:

{y}^{2}  =  {9}^{2}  +  {( \sqrt{27} )}^{2}  \\  \\  {y}^{2}  = 81 + 27 \\  \\  {y}^{2}  = 108 \\  \\ y =  \sqrt{108}  \\  \\ y =  \sqrt{36 \times 3}  \\  \\ y =  \sqrt{ {6}^{2}  \times 3}  \\  \\ y = 6 \sqrt{3}  \: units

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One stats class consists of 52 women and 28 men. Assume the average exam score on Exam 1 was 74 (σ = 10.43; assume the whole cla
Svetllana [295]

Answer:

(A) What is the z- score of the sample mean?

The z- score of the sample mean is 0.0959

(B) Is this sample significantly different from the population?

No; at 0.05 alpha level (95% confidence) and (n-1 =79) degrees of freedom, the sample mean is NOT significantly different from the population mean.

Step -by- step explanation:

(A) To find the z- score of the sample mean,

X = 75 which is the raw score

¶ = 74 which is the population mean

S. D. = 10.43 which is the population standard deviation of/from the mean

Z = [X-¶] ÷ S. D.

Z = [75-74] ÷ 10.43 = 0.0959

Hence, the sample raw score of 75 is only 0.0959 standard deviations from the population mean. [This is close to the population mean value].

(B) To test for whether this sample is significantly different from the population, use the One Sample T- test. This parametric test compares the sample mean to the given population mean.

The estimated standard error of the mean is s/√n

S. E. = 16/√80 = 16/8.94 = 1.789

The Absolute (Calculated) t value is now: [75-74] ÷ 1.789 = 1 ÷ 1.789 = 0.559

Setting up the hypotheses,

Null hypothesis: Sample is not significantly different from population

Alternative hypothesis: Sample is significantly different from population

Having gotten T- cal, T- tab is found thus:

The Critical (Table) t value is found using

- a specific alpha or confidence level

- (n - 1) degrees of freedom; where n is the total number of observations or items in the population

- the standard t- distribution table

Alpha level = 0.05

1 - (0.05 ÷ 2) = 0.975

Checking the column of 0.975 on the t table and tracing it down to the row with 79 degrees of freedom;

The critical t value is 1.990

Since T- cal < T- tab (0.559 < 1.990), refute the alternative hypothesis and accept the null hypothesis.

Hence, with 95% confidence, it is derived that the sample is not significantly different from the population.

6 0
3 years ago
FOCUS ON HIGHER ORDER THINKING Work Area Katie said, "Negative numbers are integers." What was Explain the Error her error?
Sav [38]

Step-by-step explanation:

Consider the provided information.

Integers: Integers are the set of whole number and the negatives of the natural numbers, i.e, … ,-2, -1, 0, 1, 2,...

Rational number: A number   is said to be rational, if it is in the form   of p/q. Where p and q are integer and   denominator is not equal to 0.The decimal expansion of rational numbers may terminate or become periodic.

Irrational   number: A number is irrational if it cannot   be expressed be expressed by dividing two   integers. The decimal expansion of   Irrational numbers are neither terminate nor   periodic.

Now consider the provided statement "Negative numbers are integers."

The statement is incorrect as all negative numbers are not integers they might be rational number or irrational numbers.

For example: -2.5 is a negative number but it is not an integer. The number is a rational number.

Hence, her statement is incorrect.

She can say that all negative whole numbers are integers.

6 0
2 years ago
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