Which linear system of equations does the matrix represent?<br><br> -3 5 | 15<br> 2 3

95 - 3/4 what is the value of the expression

natulia [17]

Answer:377 /4 = 94 and 1 / 4 =94.25

Step-by-step explanation:

Subtract

95 − 3 /4

= 377 / 4

Convert integer to fraction

95 = 95 / 1

Find common denominator

95 over 1

− 3 over 4

= ( 95 × 4 ) over ( 1 × 4 )

− ( 3 × 1 ) over ( 4 × 1 )

= 380 over 4

− 3 over 4

4 is the least common multiple of denominators 1 and 4. Use it to convert to equivalent fractions with this common denominator.

Subtract

380 over 4

− 3 / 4

= ( 380 − 3 ) / 4

= 377 /4

Simplify

377 / 4

= 94 and 1 /494

Reduce fraction to lowest terms

1 is the greatest common divisor of 377 and 4. The result can't be further reduced.

Step 2 of 2: Simplify, sub-step b: Convert improper fraction to mixed number.

Convert improper fraction to mixed number

377 /4

= 94 1 /4

377 ÷ 4 = 94 remainder 1

6 0

3 years ago

Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that ar

Colt1911 [192]

Answer:

$z=\frac{0.0211-0.0132}{\sqrt{0.0141(1-0.0141)(\frac{1}{18440}+\frac{1}{2123})}}=24.827$

$p_v =P(Z>24.827)\approx 0$

So the p value is a very low value and using any significance level for example $\alpha=0.05, 0,1,0.15$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of children with ASD in Utah is significantly higher than the proportion of children with ASD in Pennsylvania

Step-by-step explanation:

Data given and notation

$X_{P}=245$ represent the number of children with ASD in Pennsylvania

$X_{U}=45$ represent the number of children with ASD in Utah

$n_{P}=18440$ sample for Pennsylvania

$n_{U}=2123$ sample for Utah

$p_{P}=\frac{245}{18440}=0.0133$ represent the proportion of children with ASD in Pennsylvania

$p_{U}=\frac{45}{2123}=0.0212$ represent the proportion of children with ASD in Utah

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion for Utah is higher than the proportion for Penssylvania , the system of hypothesis would be:

Null hypothesis: $p_{U} \leq p_{P}$

Alternative hypothesis: $p_{U} > \mu_{p}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{U}-p_{P}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{U}}+\frac{1}{n_{P}})}}$ (1)

Where $\hat p=\frac{X_{U}+X_{P}}{n_{U}+n_{P}}=\frac{245+45}{18440+2123}=0.0141$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.0211-0.0132}{\sqrt{0.0141(1-0.0141)(\frac{1}{18440}+\frac{1}{2123})}}=24.827$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a one right tailed test the p value would be:

$p_v =P(Z>24.827)\approx 0$

So the p value is a very low value and using any significance level for example $\alpha=0.05, 0,1,0.15$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of children with ASD in Utah is significantly higher than the proportion of children with ASD in Pennsylvania

6 0

3 years ago

Which of the following is NOT true about the tails in a distribution?

Alla [95]

Answer:

The answer is D: The inequality symbol in the alternative hypothesis points away from the critical region.

Step-by-step explanation:

We usually have a one-tailed and two-tailed tests. Examples of a one-tailed test are the left-tailed and the right tailed test. These tests are referred to as one-tailed tests because the critical region or rejection region is located in only one tail. The critical region of a left or right tailed test is that region that correlate with the rejection region and is usually located in extreme left or right tail. Furthermore, tails in a distribution are usually the extreme critical regions also known as the rejection regions which are bound by critical values. However there is nothing that suggests the statement in Option D when talking about tails in a distribution.

6 0

4 years ago

Wendy’s family lost the power at their house when there was a bad storm. The power was out for 3 days! Wendy’s neighbors lost po

Nikolay [14]

Wendy’s family lost power for the longer time than the neighborhood, 68 hours to days would be 2.83 which would be 2.8.

4 0

3 years ago

which of these expressions is the same as 6 × (a 2)? a 6 × a 6 × 2 b 6 (a × 2) c (6 × a) 2 d a × (6 2)

Thepotemich [5.8K]

B. 6 (a x 2)
is your answer

4 0

3 years ago

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Which linear system of equations does the matrix represent? -3 5 | 15 2 3 | -10