All categories

2 years ago

Line t passes through points (10, 4) and (7, 9). Line u is parallel to line t. What is the slope of line u?

Mathematics

1 answer:

Margarita [4]2 years ago

7 0

Answer: 3/5

Step-by-step explanation:

concept to know: the slope of perpendicular line is always opposite reciprocal

----------------------

Step 1. Find the slope of line t

(y2-y1)/(x2-x1)

=(4-9)/(10-7)

=-5/3

-------------------

Step 2. Apply the concept

Opposite reciprocal of (-5/3)=3/5

Hope this helps!! :)

Please let me know if you have any question

You might be interested in

The scatter plot suggests a relationship between time and the distance from the destination. The equation of the line of best fi

viva [34]

Answer:

Strong Negative

Step-by-step explanation:

We already know that the answer is between c and d because the correlation coefficient negative.

We just have to figure out whether it is strong or weak.

In general, anything between -.7 and -1 is considered to have a strong correlation. -.8 is in between -.7 and -1 therefore the correlation is best described as strong negative.

4 0

2 years ago

the original price of a winter jacket is $125 is on sale for $81.25 cents what is the percent discount

Hoochie [10]

81.25 / 125 = 0.65
so 65 %

to check 65% * 125 = 81.25
hope this helps ;)

5 0

3 years ago

10. Consider the diagrams below. Find the values of x and y that make the triangles congruent.

Natali5045456 [20]

Answer: where is the picture?

Step-by-step explanation:

6 0

1 year ago

How would I graph this on the paper? Thanks SO MUCH.

guajiro [1.7K]

I don't know
Math needs to answer its own problems

5 0

2 years ago

Hypothesis Testing

Yuri [45]

Answer:

Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2: We conclude that the volume of Google stock has changed.

Step-by-step explanation:

Problem 1:

We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.

Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement

So, Null Hypothesis, $H_0$ : p $\leq$ 50% {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}

Alternate Hypothesis, $H_A$ : p > 50% {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}

This is a right-tailed test.

The test statistics that would be used here is One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adult Americans who were worried about having enough saved for retirement = $\frac{156}{295}$ = 0.53

n = sample of adult Americans = 295

So, the test statistics = $\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }$

= 1.03

The value of z-test statistics is 1.03.

Also, the P-value of the test statistics is given by;

P-value = P(Z > 1.03) = 1 - P(Z $\leq$ 1.03)

= 1 - 0.8485 = 0.1515

Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2:

We are given that a random sample of 35 trading days in 2014 resulted in a sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.

Let $\mu$ = mean daily volume in Google stock

So, Null Hypothesis, $H_0$ : $\mu$ = 5.44 million shares {means that the volume of Google stock has not changed}

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ 5.44 million shares {means that the volume of Google stock has changed}

This is a two-tailed test.

The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean volume in Google stock = 3.28 million shares

s = sample standard deviation = 1.68 million shares

n = sample of trading days = 35

So, the test statistics = $\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }$ ~ $t_3_4$

= -7.606

The value of t-test statistics is -7.606.

Also, the P-value of the test statistics is given by;

P-value = P( $t_3_4$ < -7.606) = Less than 0.05%

Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.

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

Therefore, we conclude that the volume of Google stock has changed.

8 0

2 years ago