Which of the following inequalities has a solution x≥−3?

Hi It would mean everything if you could help me on this. Thanks!

True [87]

Answer:

False

Step-by-step explanation:

hope this helps!

5 0

3 years ago

Read 2 more answers

Find the length of a rectangle with a diagonal of 10 and a height of 8.

Dmitry_Shevchenko [17]

Answer:

The length of the rectangle is 6.

Step-by-step explanation:

Given: The diagonal of a rectangle is 10 and the height is 8.

Please understand, that a diagonal, divides the rectangle into two tringles.

To find the length of the rectangle, you can use Pythagoras on one of the right sided triangles, because the length of the triangle, is also the length of the rectangle!

EXTRA:

If you know the special 3 4 5 triangle, a so called Pythagorean Triple, then you can "see" the simularity between the numbers.

Instead of 5, a diagonal of 10 is given (factor of 2 bigger).

Instead of 4, the height of 8 is given (factor of 2 bigger). By scaling the Pythagorean Triple 3 4 5 by a factor of 2, you get the numbers 6 8 10. Could it be, that the number we need to find, is six?

Try to verify, by calculating the missing number (which is the length of the rectangle we are looking for).

a² + b² = c²

a = length (and is unknown)

b = height = 8

c = hypothenusa/diagonal = 10

Substitute the numbers given:

a² + 8² = 10²

Subtract 8² left and right of the = sign.

a² +8² -8² = 10² - 8²

a² + 0 = 100 - 64

a² = 36

a = + - √36

a = + - 6

EXTRA:

You can ignore the -√36 = -6 part of the solution, because a length of -6 has no meaning here.

a = 6

So, the length of the triangle is 6 and thus, the length of the rectangle is also 6.

8 0

3 years ago

In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and de

Naily [24]

Answer:

$z=\frac{0.0156-0.0114}{\sqrt{0.01554(1-0.01554)(\frac{1}{32601}+\frac{1}{88})}}=0.318$

$p_v =P(Z>0.318)=0.375$

So the p value is a very high value and using the significance level provided $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in arizona is not significantly higher than the national incident rate at 1% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=507$ represent the number of children diagnosed with Autism Spectrum Disorder (ASD) in Arizona

$n_{1}=32601$ sample elected from arizona

$\hat p_{1}=\frac{507}{32601} =0.0156$ represent the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in arizona

$p_{2}=\frac{1}{88}= 0.0114$ represent the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in the nation

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 that the incident of ASD is more in Arizona than nationally, the system of hypothesis are:

Null hypothesis: $p_{1} \leq p_{2}$

Alternative hypothesis: $p_{1} > p_{2}$

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

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{507+1}{32601 +88}=0.01554$

Calculate the statistic

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

$z=\frac{0.0156-0.0114}{\sqrt{0.01554(1-0.01554)(\frac{1}{32601}+\frac{1}{88})}}=0.318$

Statistical decision

The significance level provided is $\alpha=0.01$ , and we can calculate the p value for this test.

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

$p_v =P(Z>0.318)=0.375$

So the p value is a very high value and using the significance level provided $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in arizona is not significantly higher than the national incident rate at 1% of significance.

5 0

3 years ago

You make 12 per hour and work for 40 hours in week.3% of your paycheck is taken by taxes.After taxes how many of your salary wil

wariber [46]

Answer:

$478.56

Step-by-step explanation:

12*40=480

.003(.3%)*480=1.44

480-1.44=$478.56 after taxes.

4 0

3 years ago

A family of 7 are seated in their circular dining table . In how many ways can they be arranged?

ankoles [38]

Answer:

7

Step-by-step explanation:

the answer is 7 because if there is 7 people then there will be 7 different ways to arrange the chairs in the table

7 0

3 years ago