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kondaur [170]
3 years ago
6

What are the new vertices of triangle ABC if the triangle is translated three units to the right and then three units downward?

Mathematics
1 answer:
DerKrebs [107]3 years ago
4 0

Answer:

A=(0,-1), B=(5,0) and C=(-2,-6)

Step-by-step explanation:

If the translation is 3 units to the right then to every x coordinate we add three and to the y coordinate we subtract 3.

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uppose that an automobile manufacturer advertises that its new hybrid car has a mean gas mileage of 50 miles per gallon. You tak
Harlamova29_29 [7]

Answer:

t=\frac{47-50}{\frac{5.5}{\sqrt{30}}}=-2.988    

p_v =2*P(t_{(29)}  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the true mean is significantly different from 50 mpg at 5% of signficance.  

Step-by-step explanation:

Data given and notation  

\bar X=47 represent the sample  mean  

s=5.5 represent the sample standard deviation

n=30 sample size  

\mu_o =50 represent the value that we want to test

\alpha=0.01 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is 50 or no, the system of hypothesis would be:  

Null hypothesis:\mu = 50  

Alternative hypothesis:\mu \neq 50  

If we analyze the size for the sample is = 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{47-50}{\frac{5.5}{\sqrt{30}}}=-2.988    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=30-1=29  

Since is a two tailed test the p value would be:  

p_v =2*P(t_{(29)}  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the true mean is significantly different from 50 mpg at 5% of signficance.  

4 0
3 years ago
Solving Rational equations. LCD method. Show work. Image attached.
Ugo [173]

Answer:

k=\frac{1}{2}

Step-by-step explanation:

The given rational equation is

\frac{5k}{k+2}+\frac{2}{k}=5

The Least Common Denominator is

k(k+2)

Multiply each term by the LCD.

k(k+2)\times \frac{5k}{k+2}+k(k+2)\times \frac{2}{k}=5k(k+2)

Simplify;

k\times \frac{5k}{1}+(k+2)\times \frac{2}{1}=5k(k+2)

\Rightarrow k(5k)+2(k+2)=5k(k+2)

Expand;

\Rightarrow 5k^2+2k+4=5k^2+10k

Group similar terms;

\Rightarrow 5k^2-5k^2+2k-10k=-4

\Rightarrow -8k=-4

Divide by -8.

k=\frac{1}{2}

5 0
3 years ago
(1 x 106) - (8 x 109)<br> How do I solve it
choli [55]
First of all 1 x 106= 106, secondly 8 x 109= 872. Therefore you would subtract 872 from 106 and that’s your answer
5 0
3 years ago
Read 2 more answers
Which line will have no solution with the parabola y – x 2 = x2?
Klio2033 [76]

Step-by-step explanation:

y = –3x –3

y = –2x –3

y = 2x –3

y = 3x –3

3 0
2 years ago
Find all solutions for a triangle with a = 14, b= 12, and B = 90°.
ziro4ka [17]

Answer:

No solution.

Step-by-step explanation:

Given

a = 14; b= 12; B = 90^\circ

Required

Find all possible solutions

If B = 90^\circ, then the triangle is right-angled and the hypotenuse is at b

Given that a = 14; b= 12;

This implies that a > b

In a right-angled triangle, the hypotenuse (side b) is the longest.

Since this is not true for the given sides, then the triangle has no solution.

5 0
3 years ago
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