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poizon [28]
3 years ago
6

1.) A carpenter has boards of lengths 24, 36, and 42 inches that must be cut into smaller boards of equal length, with no scrap

wood left over.
What is the longest length of boards he can cut?

2 inches
4 inches
12 inches
6 inches

2.) Solve -2t + 5 ≥ -7.

t ≤ -6
t ≤ 6
t ≥ -6
t ≥ 6

3.) Luis needs to run at least 150 miles in order to go with the cross country team to a summer training camp. He has forty days to pre-train for the camp.

Which inequality can be used to find how many miles Luis must run each day to meet this goal?

40 m ≥ 150
40 m ≤ 150
40 m > 150
40 m < 150

Questions four and five is the screenshots. Please help me! BRAINLEST, 5 STARS AND A THANKS!

Mathematics
1 answer:
AlekseyPX3 years ago
6 0

Answer:

1) 12

2) t ≤ 6

3) 40 m ≥ 150

4) The second option

5) -1 < x

Step-by-step explanation:

1) Since he wants to seperrate the boards equally, you just have to find a common mulitple of all the boards that equate to the same number

2) First subtract 5 from both sides, (-2t ≥ -12), and then divide both sides by -2, when you divide both sides by a negative number in an equality, you always swith the sign so the answer is t ≤ 6.

3) I think its supposed to be at least 4 miles a day or more, but 40 miles a day or more each day is good enough

4) You can automaticly delete the first and last options and it's the second option because it shows that 'n' is a number that is bigger than the number -3

5) You can eliminate anything that has equal to line under the sign, and it's -1 < x because the line graph shows that something (x) is greater than -1

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In a study of 799 randomly selected medical malpractice​ lawsuits, it was found that 499 of them were dropped or dismissed. Use
Mademuasel [1]

Answer:

Claim is true that most medical malpractice lawsuits are dropped or dismissed.

Step-by-step explanation:

Given :In a study of 799 randomly selected medical malpractice​ lawsuits, it was found that 499 of them were dropped or dismissed.

To Find : Use a 0.05 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed.

Solution:

n =  799

x = 499

We will use one sample proportion test  

\widehat{p}=\frac{x}{n}\\\widehat{p}=\frac{499 }{ 799}\\\widehat{p}=0.6245

We are given that the claim is most medical malpractice lawsuits are dropped or dismissed.

Probability of dropped or dismissed is 1/2

 H_0:p=0.5\\H_a:p>0.5

Formula of test statistic = \frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}

                                        =\frac{0.6245-0.5}{\sqrt{\frac{0.5(1-0.5)}{799}}}

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p value (z>7.038) is 0

α =0.05

So, p value < α

So, we reject the null hypothesis

So,claim is true

Hence most medical malpractice lawsuits are dropped or dismissed.

6 0
3 years ago
Given: cosθ= -4/5 , sin x = -12/13 , θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan 1/2 θ
mrs_skeptik [129]

Answer:

Step-by-step explanation:

If you're looking for what the half angle of the tangent of theta is, I'm a bit confused as to why you think the angle in the 4th quadrant, x, is relevant.  But maybe you don't know it isn't and it's a "trick" to throw you off.  Hmm...

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tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{1+(-\frac{4}{5}) } which simplifies a bit to

tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{\frac{5}{5} -\frac{4}{5} }  and a bit more to

tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{\frac{1}{5} }

Bring up the lower fraction and flip it to divide to get

tan(\frac{\theta}{2})=-\frac{3}{5}*\frac{5}{1} which of course simplifies to

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