Ask question

Ask question

All categories

3 years ago

15

Two sides of an obtuse triangle measure 9 inches and 14 inches. The length of longest side is unknown. What is the smallest poss

ible whole-number length of the unknown side? 16 inches 17 inches 24 inches 25 inches

1 answer:

Fofino [41]3 years ago

6 0

Answer:

126.

Step-by-step explanation:

also, Rounded to 17.

You might be interested in

A savings and loan association needs information concerning the checking account balances of its local customers. A random sampl

Marina86 [1]

Answer:

The 99% confidence interval for the true mean checking account balance for local customers is ($439.29, $888.99).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 13

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$ . So we have T = 3.0123

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 3.0123\frac{279.29}{\sqrt{14}} = 224.85$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 664.14 - 224.85 = $439.29

The upper end of the interval is the sample mean added to M. So it is 664.14 + 224.85 = $888.99.

The 99% confidence interval for the true mean checking account balance for local customers is ($439.29, $888.99).

4 0

3 years ago

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past

Vadim26 [7]

Answer:

We conclude that deluxe tire averages less than 50,000 miles before it needs to be replaced which means that the claim is not supported.

Step-by-step explanation:

We are given that a particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8000.

From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9800 miles.

<u><em>Let </em></u> $\mu$ <u><em> = average miles for deluxe tires</em></u>

So, Null Hypothesis, $H_0$ : $\mu \geq$ 50,000 miles {means that deluxe tire averages at least 50,000 miles before it needs to be replaced}

Alternate Hypothesis, $H_A$ : $\mu$ < 50,000 miles {means that deluxe tire averages less than 50,000 miles before it needs to be replaced}

The test statistics that will be used here is <u>One-sample z test statistics</u> as we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean lifespan = 46,500 miles

$\sigma$ = population standard deviation = 8000 miles

n = sample of tires = 28

So, <u><em>test statistics</em></u> = $\frac{46,500-50,000}{\frac{8000}{\sqrt{28} } }$

= -2.315

The value of the test statistics is -2.315.

Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is less than the critical value of z as -2.315 < -1.6449, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that deluxe tire averages less than 50,000 miles before it needs to be replaced which means that the claim is not supported.

4 0

3 years ago

Please help me, the attachment is below. (If you don't know the answer to the question please don't answer, thank you.)

Liono4ka [1.6K]

Answer:

See Below.

Step-by-step explanation:

Paragraph Proof:

We are given that ∠1 ≅ ∠4. ∠1 and ∠4 are alternate exterior angles. Since they are congruent, by the Alternate Exterior Angles Converse, the two lines being cut by the transversal must be parallel. Then by the Alternate Interior Angles Theorem, ∠3 ≅ ∠2.

2-Column Proof

Statements Reasons:

1) $\angle 1\cong \angle 4$ Given

2) $\text{The two lines are parallel}$ Alternate Exterior Angles Converse

3) $\angle 3\cong \angle 2$ Alternate Interior Angles Theorem

I would write a flowchart as well, but unfortunately, I never learned it that way.

8 0

3 years ago

What is the inverse of y= e^x+3 -4

ASHA 777 [7]

Answer:

log(x + 1)inverse function y(x) = e^x + 3 - 4

6 0

3 years ago

The sum of two numbers is 50. The first number is 43 less than twice the second number. Write and solve a system of equations to

Simora [160]

Answer: 19 and 31

Step-by-step explanation: Make the first number x, the second number y.

The sum of x and y is 50: x+y=50

x is 43 less than 2y: x=2y-43

replace x in equation x+y=50 with x=2y-43: 2y-43+y=50

combine like terms: 3y-43=50

add 43 to both sides: 3y=93

divide both sides by 3: y=31

replace y in equation x+y=50 with y=31: x+31=50

subtract 43 31 from both sides: x=19

the solution to the question is the first number is 19, the second number is 31

6 0

3 years ago