How long will it take 5 machines to complete a task, given that it takes 10 days for 8 machines to complete the same task?

A source of laser light sends rays AB and AC toward two opposite walls of a hall. The light rays strike the walls at points B an

11Alexandr11 [23.1K]

Well there is a lot of trigonometry in this. I will try my best.

Finding: Distance between Wall A and Wall B.

1. Trig and phythagorean properties for left triangle.
30m

2. Trig and Pythagorean properties for right triangle.
40m (approx)

30 + 40 = 70.

Therefore the distance is APPROXIMATELY 70 meters. I haven't learned trig yet so sorry if I am wrong.

5 0

3 years ago

Which statement is true about the equation (x – 4)(x 2) = 16?

n200080 [17]

The roots of the given quadratic equation are 6 and -4.

The given quadratic equation is:

$(x-4)(x+2)=16$

<h3>What is a quadratic equation?</h3>

Any equation of the form $ax^{2} +bx+c=0$ is called a quadratic equation where $a\neq 0$ .

$x^{2} -2x-8=16$

$x^2-2x-24=0$

$x^{2} -6x+4x-24=0$

$x(x-6)+4(x-6)=0$

$(x-6)(x+4)=0$

$x=6$

$x=-4$

Hence, the roots of the given quadratic equation are 6 and -4.

To get more about quadratic equations visit:

brainly.com/question/1214333

3 0

2 years ago

Define what a prime factor decomposition

nadya68 [22]

It means to factorise a number, and divide it by the first possible prime number.

5 0

3 years ago

Yoko evaulates 7÷1/6 by using a related multiplaction expression. Which multiplication expression should she use?

Minchanka [31]

So u have to do how many times 7 goes into 6 an see what u get and then u just just have to keep the 1 on the top

8 0

3 years ago

Suppose a researcher believes that college students vote at a lower rate than college faculty. She collects data from 200 colleg

Paladinen [302]

Answer:

We conclude that college students vote at a lower rate than college faculty which means researcher’s claim was correct.

Step-by-step explanation:

We are given that a researcher believes that college students vote at a lower rate than college faculty.

She collects data from 200 college faculty and 200 college students using simple random sampling. If 138 of the students and 167 of the faculty voted in the 2008 Presidential election

Let $p_1$ = proportion of college students who voted in the 2008 Presidential election.

$p_2$ = proportion of college faculty who voted in the 2008 Presidential election.

So, Null Hypothesis, $H_0$ : $p_1-p_2\geq$ 0 or $p_1\geq p_2$ {means that college students vote at a equal or higher rate than college faculty}

Alternate Hypothesis, $H_A$ : $p_1-p_2$ < 0 or $p_1$ {means that college students vote at a lower rate than college faculty}

The test statistics that would be used here Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of college students who voted in the 2008 Presidential election = $\frac{138}{200}$ = 0.69

$\hat p_2$ = sample proportion of college faculty who voted in the 2008 Presidential election = $\frac{167}{200}$ = 0.835

$n_1$ = sample of college students = 200

$n_2$ = sample of college faculty = 200

So, test statistics = $\frac{(0.69-0.835)-(0)}{\sqrt{\frac{0.69(1-0.69)}{200}+\frac{0.835(1-0.835)}{200} } }$

= -3.458

The value of z test statistics is -3.458.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that college students vote at a lower rate than college faculty which means researcher’s claim was correct.

8 0

3 years ago