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3 years ago

If ∠BAC = 17° and ∠CED = 17° are the two triangles, ΔBAC and ΔCED similar? If so, by what criterion?

1 answer:

7 0

Yes, they are similar. The definition of similar triangles is two triangles that have congruent angles. All angles of a triangle must add up to 180. So, if you take the angles that you already have and add them up (17 plus 17 = 34), Then there is only one option of what the last angle is. To find the last angle you take 180 and subtract 34 which would give you 146.

You might be interested in

Convert 150 g/L to the unit g/mL. .

Alekssandra [29.7K]

G/L=1000*g/mL, since 1 mL = 1/1000 of a litre.
Therefore, 150g/L=150 000 g/mL.

7 0

3 years ago

Assume that we want to construct a confidence interval. Do one of the following, as appropriate:_________.

andreyandreev [35.5K]

Answer:

B. z Subscript alpha divided by 2 zα/2 = 1.96.

Step-by-step explanation:

We are given that we want to construct a confidence interval. For this, the summary statistics for randomly selected weights of newborn girls:

n = 236, $\bar x$ = 30.3 hg, s = 7.2 hg. The confidence level is 95%.

As we can clearly see here that the population standard deviation is unknown and the sample size is also very large.

It has been stated that when the population standard deviation is unknown, we should use t-distribution but since the sample size is very large so we can use z distribution also as it is stated that at very large samples; the t-distribution corresponds to the z-distribution.

Here, $\alpha$ = level of significance = 1 - 0.95 = 0.05 or 5%

$\frac{\alpha}{2}=\frac{0.05}{2}$ = 0.025 or 2.5%

So, the value of $Z_(_\frac{\alpha}{2} _)$ in the z table is given as 1.96 with a 2.5% level of significance.

3 0

3 years ago

Single-sample t test and paid days off: The number of paid days off (e.g., vacation, sick leave) taken by eight employees at a s

SVEN [57.7K]

Answer:

A. µ is the population average number of paid days off taken by employees that the company.

Null Hypothesis: µ=15 days

Alternate Hypothesis: µ≠15 days

B. one-sample t-test

C. We are unsure if it meets the conditions for a one-sample t-test

D. t=-0.79178; df=7

Step-by-step explanation:

For the null and alternate hypotheses, you want to first define what µ represents. Next, you state them, the null hypothesis being equal to the previously known average, and the alternate hypothesis being greater than, less than, or not equal to the previous average, selecting one depends on the context in the problem.

A one-mean t-test would be used as we are looking to compare the mean of a data set, as well as the fact that we do not know the population standard deviation.

When conducting these tests, we need to ensure that three conditions are being met. The first is random, which means that the data set is randomly gathered, or not, the data here does not seem to be random, which may be concerning. Next is independence, this is done when we survey less than 10% of the overall population, in this case it is a small company, so we do not know if it is less than 10% of the population. Last is normality, the data set is not sufficiently large (greater than 30 people surveyed) so we cannot use the central limit theorem to justify that the data is normal. We can use a normality plot, but when the data is placed on a normality plot most of the data appears to be linear, but the 27 day data point does not seem to be normal, so we cannot fully ensure that it is normal. Based on the data not following these conditions, we have concerns about proceeding with the test, we will therefore have to proceed with caution.

For the last part, use that T-test function on a calculator with statistics functions. Remember to include the degrees of freedom in the answer. (The degrees of freedom is one less than the sample size).

6 0

3 years ago

a stone is thrown downward with an intitial velocity of 29.5 m/sec will travel a distance of a meters, where s(t) = 4.9t^2 + 29.

Alenkinab [10]

Answer:

t = 9 s

Step-by-step explanation:

A stone is thrown downward with an intitial velocity of 29.5 m/sec will travel a distance of a meters, where

$s(t) = -4.9t^2 + 29.4+132.3$

We need to find when the stone will hit the ground. It means when s(t) = 0. So,

$-4.9t^2 + 29.4t+132.3=0\\\\t=-3\ and\ t=9$

So, the stone will take 9 seconds to hit the ground. Hence, this is the required solution.

5 0

3 years ago

What is the solution to the system of equations?

Tatiana [17]

If you would like to know the solution to the system of equations, you can do this using the following steps:

y = –5x + 3
y = 1
_______________
1 = –5x + 3
5x = 3 - 1
5x = 2 /5
x = 2/5 = 0.4

(x, y) = (0.4, 1)

The correct result would be (0.4, 1).

3 0

3 years ago

Read 2 more answers