Could a quadrilateral have 4 obtuse angles? Why?

Mathematics

2 answers:

Otrada [13]3 years ago

6 0

No! Because the angles have to add up to 360.

worty [1.4K]3 years ago

3 0

No it cant... Because the angles have to add up to 360

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A study claims that college students spend an average of 4 hours or less studying per day. A researcher wants to check if this c

kirill115 [55]

<h2>Answer with explanation:</h2>

Let $\mu$ be the population mean.

By observing the given information, we have :-

$H_0:\mu\leq4\\\\H_a:\mu>4$

Since the alternative hypotheses is left tailed so the test is a right-tailed test.

We assume that the time spend by students per day is normally distributed.

Given : Sample size : n=121 , since n>30 so we use z-test.

Sample mean : $\overline{x}=3.15$

Standard deviation : $\sigma=1.2$

Test statistic for population mean :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$\Rightarrow\ z=\dfrac{3.15-4}{\dfrac{1.2}{\sqrt{121}}}\\\\\Rightarrow\ z=-7.79166666667\approx-7.79$

Critical value (one-tailed) corresponds to the given significance level :-

$z_{\alpha}=z_{0.1}=1.2816$

Since the observed value of z (-7.79) is less than the critical value (1.2816) , so we do not reject the null hypothesis.

Hence, we conclude that we have enough evidence to accept that the college students spend an average of 4 hours or less studying per day.

4 0

3 years ago

Suppose a friend is having difficulty solving -2(q-5) > -3(q+1). Explain how to solve the inequality, showing all the necessa

IgorC [24]

Firstly, use the distributive property of multiplication (A(B + C) = A×B + A×C) on -2(q - 5) and -3(q + 1): $-2q+10>-3q-3$

Next, apply the addition property of equality (whatever you add to one side you have to add the same quantity to the other), and add 3q on both sides: $q+10>-3$

Lastly, apply the subtraction property of equality (whatever you subtract on one side you have to subtract the same amount on the other side), and subtract 10 on both sides. <u>Your final answer will be $q>-13$ </u>