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2 years ago

Triangle ABC has the side lengths 6 in., 9 in., and 11 in.

Mathematics

1 answer:

andriy [413]2 years ago

4 0

Answer:

The BEST statement describes how the triangle could be altered in order to make it a right triangle

One inch could be removed from the 9 in. leg and a new hypotenuse could be drawn.

Step-by-step explanation:

Triangle ABC has the side lengths 6 in., 9 in., and 11 in.

The only condition is that satisfy to become Δ ABC a Right angle triangle is

Longer leg (one inch remove) = 9 - 1 = 8 inch

New hypotenuse = 10 inch

So that Pythagoras theorem must satisfy

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

So (Hypotenuse)² = 10² = 100

(Shorter leg)² = 6² = 36

(Longer leg)² = 8² = 64

So we have,

(Shorter leg)² + (Longer leg)² = 36 + 64

= 100

= (Hypotenuse)²

Therefore, Δ ABC is right Triangle By Converse of Pythagoras Theorem.

Therefore,

The BEST statement describes how the triangle could be altered in order to make it a right triangle

One inch could be removed from the 9 in. leg and a new hypotenuse could be drawn.

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The average score of all golfers for a particular course has a mean of 64 and a standard deviation of 3. Suppose 36 golfers play

kondaur [170]

Answer:

the probability that the exceeded 65 = 0.3707

The average score of the 36 golfers exceeded 65

= 36 X 0.3707 = 13.3452

Step-by-step explanation:

<u>Step 1</u>:-

The average score of all golfers for a particular course has a mean of 64 and a standard deviation of 3.

mean (μ) = 64

standard deviation (σ) =3

by using normal distribution

given (μ) = 64 and (σ) =3

i) when x =65

$z = \frac{x-mean}{S.D} = \frac{65-64}{3} = 0.33 >0$

P( X≥ 65) = P(z≥0.33)

= 0.5 - A(z₁)

= 0.5 - 0.1293 (see normal table)

= 0.3707

The average score of the 36 golfers exceeded 65

= 36 X 0.3707 = 13.3452

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2 years ago

The manager at Gabriela's Furniture Store is trying to figure out how much to charge for a book shelf that just arrived. The boo

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The shelf should sell for $235.20.

Marking the price up by 60% means taking 160% of the cost:
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Answer: the last one

Step-by-step explanation:

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2 years ago

A population has a standard deviation of 80. A random sample of 400 items from this population is selected. The sample mean is d

Helga [31]

Answer:

$ME= 1.8808 * \frac{80}{\sqrt{400}} =7.5232$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =80$ represent the population standard deviation

n=400 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.94 or 94%, the value of $\alpha=0.06$ and $\alpha/2 =0.03$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that $z_{\alpha/2}=1.8808$