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3 years ago

Find the distance between points P(3, -8) Q(7,4). Round to the nearest tenth if necessary

1 answer:

3 0

To calculate the distance between two points, we can use a formula that is a variation Pythagorean Theorem. Look:

$\mathsf{d=\sqrt{(x_Q-x_P)^2+(y_Q-y_P)^2}}$

"d" represents the distance and coordinates are expressed as follows: (x, y)

Let's go to the calculations.

$\mathsf{d=\sqrt{(x_Q-x_P)^2+(y_Q-y_P)^2}}\\\\ \mathsf{d=\sqrt{(7-3)^2+(4-(-8))^2}}\\\\ \mathsf{d=\sqrt{(4)^2+(4+8)^2}}\\\\ \mathsf{d=\sqrt{16+(12)^2}}\\\\ \mathsf{d=\sqrt{16+144}}\\\\ \mathsf{d=\sqrt{160}}\\\\ \mathsf{d=12,649110640673...}\\\\ \underline{\mathsf{d\approxeq12,6}}$

The answer is 12,6 u.c.

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In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AH=4 and HC=1, find BH.

Rudik [331]

Answer:

Length of BH is 2 units.

Step-by-step explanation:

We have, ΔABC with ∠ABC = 90° and an altitude BH.

Also, it is given that the length of sides AH is 4 units and HC is 1 units.

Since, the 'Altitude Rule' states that 'the length of the altitude is the geometric mean of the line segments it bisects'.

So, we get that,

$BH^{2}=AH\times HC$

i.e. $BH^{2}=4\times 1$

i.e. $BH^{2}=4$

i.e. $BH=\pm 2$

Since, the length of the side cannot be negative.

So, length of BH is 2 units.

3 0

4 years ago

What was the experimental probability of how many times an even number was actually rolled using the table? Put your answer in f

kumpel [21]

Answer:

5/12

Step-by-step explanation:

Just took quiz and got problem right.

5 0

3 years ago

Ne #3: When I take half of my number and add two, I get twenty-four. What is my number

irga5000 [103]

Answer:

My number will be 44.

Step-by-step explanation:

My number will be divided by 2.
I will get 22.
Then I'll 2 to my 22.
It will give me 24.

44 divided by 2 = 22
22 + 2 = 24

4 0

3 years ago

james cut three squares lasagnas so that each piece was 1/5 of the lasagnas. how many pieces did james cut the lasagna into?

uysha [10]

The answer is 15. Each one is 5 pieces and there are 3 of them. so 5 x 3 = 15

4 0

3 years ago

Read 2 more answers

A tire manufacturer wants to estimate the average number of miles that may be driven in a tire of a certain type before the tire

alexandr402 [8]

Answer:

97% confidence interval for the average number of miles that may be driven is [26.78 miles, 33.72 miles].

Step-by-step explanation:

We are given that a random sample of tires is chosen and are driven until they wear out and the number of thousands of miles is recorded;

32, 33, 28, 37, 29, 30, 22, 35, 23, 28, 30, 36.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

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

where, $\bar X$ = sample average number of miles = $\frac{\sum X}{n}$ = 30.25

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = 4.71

n = sample of tires = 12

$\mu$ = population average number of miles

Here for constructing a 97% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.

So, 97% confidence interval for the population mean, $\mu$ is ;

P(-2.55 < $t_1_1$ < 2.55) = 0.97 {As the critical value of t at 11 degrees of

freedom are -2.55 & 2.55 with P = 1.5%}

P(-2.55 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.55) = 0.97

P( $-2.55 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.55 \times {\frac{s}{\sqrt{n} } }$ ) = 0.97

P( $\bar X-2.55 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.55 \times {\frac{s}{\sqrt{n} } }$ ) = 0.97

97% confidence interval for $\mu$ = [ $\bar X-2.55 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.55 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $30.25-2.55 \times {\frac{4.71}{\sqrt{12} } }$ , $30.25+2.55 \times {\frac{4.71}{\sqrt{12} } }$ ]

= [26.78 miles, 33.72 miles]

Therefore, 97% confidence interval for the average number of miles that may be driven is [26.78 miles, 33.72 miles].

7 0

4 years ago