MATHEMATICS COLLEGE

Find the midpoint of the segment with these endpoint (4,6),(9,3)​

Answers

Answer 1
Answer:

Answer:

The midpoint of the segment is (6, 4.5).

Step-by-step explanation:

Midpoint of a segment:

The midpoint of a segment is given by the mean of the coordinates of their endpoints.

Segment with coordinates (3,6) and (9,3).

Mean x-coordinate: (3+9)/2 = 12/2 = 6

Mean y-coordinate: (6+3)/2 = 9/2 = 4.5

The midpoint of the segment is (6, 4.5).

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Use the order of operations to simplify: 9 ÷ 3 + 4 × 6

Answers

Answer:

27

Step-by-step explanation:

First is 9 / 3 which is 3 and then 4 x 6 which is 24 then 24 + 3  = 27

Answer:

PEMDAS

4 × 6 is 24

9 ÷ 3 is 3

24  + 3 = 27

Step-by-step explanation:

-1-3=
A. -5
B. 2
C. -4
D. 4

Answers

Answer:

-4

Step-by-step explanation:

subtracting form a negative will result in a negative number

Answer:

c)-4

Step-by-step explanation:

-1 minis 3 is 3 less that -1

What is the answer to a10/a3 ?

Answers

Answer:

a^7

Step-by-step explanation:

(a^(10))/(a^3)\n\n\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=x^(a-b)\n(a^(10))/(a^3)=a^(10-3)\n\n=a^7

What is the length of the hypotenuse of the right angle defined by the points (-3,-1),(1,-1),and (1,2)?A)square root of 3
B)square root of 3
C) 2 timessquare root of 3
D)5

Answers

To find the length of the triangle first find the two coordinates with a common x coordinate, (1,-1) and (1,2). Now find the difference between their y coordinates, -1 and 2. This means that the length of the triangle is 3.
To find the width of the triangle first find the two coordinates with a common y coordinate, (-3,-1) and (1,-1). Now find the difference between their x coordinates, -3 and 1. This means that the width of the triangle is 4. 
By Pythagoras' theorem, we know that hypotenuse = \sqrt{ width^(2) + length^(2) }. Inserting our newfound values into this equation, we an find thelength of the hypotenuse:
hypotenuse = \sqrt{ 4^(2) +3^(2)} hypotenuse = √(16+9) hypotenuse = √(x) 25hypotenuse = 5
Therefore, your answer is D0 5. To visualise this question better, you can plot the points on a graph. 

. In a study of air-bag effectiveness it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashes resulted in hospitalization of the drivers (based on data from the highway Loss Data Institute). Using a 0.01 significance level, you need to test the claim that the air-bag hospitalization rate is lower than the 7.8% rate for crashes of mid-size cars equipped with automatic safety belts. What conclusion should you make

Answers

Answer:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

0.00885... < 0.01

The test statistic of 46 is significant

There is sufficient evidence to reject H₀ and accept H₁

Air bags are more effective as protection than safety belts

Step-by-step explanation:

821 crashes

46 hospitalisations where car has air bags

7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts

α = 0.01 or 1% ← level of significance

One-tailed test

We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;

The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;

So we are testing if hospitalisations in cars with air bags is less than 0.078;

So, firstly:

Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags

X~B(821, 0.078)

Null hypothesis (H₀): p = 0.078

Alternative hypothesis (H₁): p < 0.078

According to the information, we reject H₀ if:

P(X ≤ 46 | X~B(821, 0.078)) < 0.01

To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;

If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:

P(X = r) = nCr * p^(r) * (1 - p)^(n - r)

You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

Now, we need to consider if the condition for rejecting H₀ is met and recognise that:

0.00885... < 0.01

There is sufficient evidence to reject H₀ and accept H₁.

To explain what this means:

The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;

In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.

Kurt's truck uses 10 gallons of gas to travel 140miles. He has 5 gallons in the tank. How much more gas will he need to drive 322 miles

Answers

Answer:

18 gallons

Step-by-step explanation:

Step 1:

140 : 10 = x : 5      Equation / Ratio

Step 2:

10x = 700     Multiply

Step 3:

x = 70     Divide

Step 4:

322 miles - 70 miles     To find how many miles are needed to get to 322

Step 5:

252 miles ÷ 14        To find the amount of gas  / Divide

Answer:

18 gallons more

Hope This Helps :)
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