Similar polygons have corresponding sides that are proportional and corresponding angles that are -

A new dental bondlng agent. When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive(called "Smartbon

Gemiola [76]

Answer:

(a) H₀: μ ≥ 5.70 vs. Hₐ:μ < 5.70

(b) The rejection region is (t₀.₀₁,₉ ≤ -2.821).

(c) The value of the test statistic is -4.33.

(d) The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

Step-by-step explanation:

A hypothesis test should be conducted to determine that the if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(a)

The hypothesis is:

H₀: The true mean breaking strength of the new bonding adhesive is not less than 5.70 Mpa, i.e. μ ≥ 5.70.

Hₐ: The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, i.e. μ < 5.70.

(b)

The alternate hypothesis indicates that the hypothesis test is left-tailed.

The rejection region for the left tailed test will be towards the lower tail of the t-distribution curve.

The significance level of the test is: α = 0.01.

The critical value is:

$t_{\alpha ,(n-1)}=t_{0.01,(10-1)}=t_{0.01,9}$

Use the t-table for the critical value.

$t_{\alpha ,(n-1)}=t_{0.01,9}=-2.821$

Since rejection region is in the lower tail the critical value will be negative.

Thus, the rejection region is (t₀.₀₁,₉ ≤ -2.821).

(c)

The test statistic value is:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}$

Given:

$\bar x=5.07\\s=0.46\\n=10\\\mu=5.70$

Compute the value of the t-statistic as follows:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{5.07-5.70}{0.46/\sqrt{10}} =-4.33$

The value of the test statistic is -4.33.

(d)

The value of the test is less than the critical value.

$t=-4.33$

This implies that the test statistic lies in the rejection region.

Hence the null hypothesis will be rejected at 1% significance level.

Conclusion:

As the null hypothesis is rejected it can be concluded that the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(e)

The conditions required for the t-test for single mean to be valid is:

The data should be continuous.
The parent population should be normally distributed.
The sample should be randomly selected.

5 0

3 years ago

What is 20/8 in the lowest mixed form?

Kisachek [45]

20/8 = 10/4 = 5/2

So, it's mixed form would be 2 1/2

8 0

3 years ago

Your sister is considering two different shapes for her garden. One is a square with side lengths of 3.5 meter, and the other is

Bess [88]

Hello! I can help you with this!

A. Okay. So, to find the area of the square all you have to do is the number square, or multiply the number by itself, in this case. 3.5. 3.5^2 is 12.25. The area of the square is 12.25 square meters large.

B. To find the area of the circle, you do pi*r^2. Radius is half the the diameter. Half of 4 is 2. 2^2 is 4. To multiply by pi, we can just do it as 3.14. 4 * 3.14 is 12.56. The circle is 12.56 square meters large.

C. The circle garden would give her the most space to plant, because 12.56 is larger than 12.25 by 0.31. The circle garden 0.31 square meters larger than the square garden.

3 0

3 years ago

Which statement is true about the sum of (5y/y^2)+(y-4/5y) ? A: The denominator of the simplified sum is y2 + 5y. B: The denomin

lora16 [44]

Answer:

Dude the answer is B

Step-by-step explanation:

7 0

3 years ago

Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with

Stels [109]

Answer:

P(X > 25) = 0.69

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 thousand dollars and 2 thousand dollars, respectively.

This means that $\mu = 26, \sigma = 2$