Which equation uses the Pythagorean Theorem to determine whether the side lengths 12, 24, and 26 form a right triangle?

Drey makes $10 an hour plus $15 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week

blsea [12.9K]

490=10·40+15x

490=400+15x

90=15x

x=6

he worked a total of 46 hours

7 0

4 years ago

A manufacturer of a new medication on the market for Alzheimer's disease makes a claim that the medication is effective in 65% o

NeX [460]

Answer:

$z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309$

$p_v =P(z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65

Step-by-step explanation:

Data given and notation

n=180 represent the random sample taken

X=115 represent the adults with the medication was effective

$\hat p=\frac{115}{180}=0.639$ estimated proportion of adults with the medication was effective

$p_o=0.65$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that true proportion is less than 0.65.:

Null hypothesis: $p \geq 0.65$

Alternative hypothesis: $p < 0.65$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65

3 0

3 years ago

Find x show ur work !!!!

Luda [366]

Answer:

Step-by-step explanation:

x + 67 = 3x - 53 ( exterior angle of a triangle is equal to the sum of two opposite interior angles )

3x - x = 67 + 53

2x =120

x = 120 /2

x = 60

HOPE IT WILL HELP :)

3 0

3 years ago

Kamila has a rectangular lawn that measures 80 by 150 feet. She wants to lay gravel made from colored rock in a border, 6 feet w

Zarrin [17]

Part 1) Create a diagram that shows Kamila’s rectangular lawn and the gravel border. Assign variables to any unknown sides and label the diagram

see the attached figure

Part 2)Use your diagram to determine how many square feet of the gravel border will surround the lawn

area of the border=[162*92]-[150*80]----> 14904-12000-----> 2904 ft²

Part 3) Kamila decided that the depth of the gravel needs to be 2 inches. What is the total volume of gravel needed for the border?

we know that
1 ft-------> 12 in
x--------> 2 in
x=2/12------> x=0.17 ft

volume of gravel needed=area of the border*deep of the gravel
volume of gravel needed=2904*0.17----> 493.68 ft³

Part 4)A large bag of colored rock contains a cubic yard and costs $30. What is the total cost of the rocks needed for the border?

1 yd³--------> 27 ft³
x---------> 493.68 ft³
x=493.68/27-----> 18.28 yd³

if 1 yd³----------> cost $30
18.28 yd³------> x
x=18.28*30------> x=$548.53

the answer Part 4) is
$548.53

6 0

4 years ago

How do I write the interval(s) for which f(x) is greater than or equal to 0 (interval notation)

hram777 [196]

We are looking for the set of values for which y is greater than 0. This would be negative infinity to -2, but not including
-2. This could be expressed as (-infinity, -2). Also, all x values greater than 0 also lead to a y-value greater than 0. Thus, another interval would be (0, infinity). Thus, the answer is (-infinity, -2) and (0, infinity).

6 0

3 years ago