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3 years ago

GUYS NEED HELP ASAP THE WHOLE PAGE

Mathematics

1 answer:

sasho [114]3 years ago

4 0

Answer:

Step-by-step explanation:

For the first one it looks like you are just going to have to measure sides and angles and then draw shapes that have the same angle measures, but however longer or shorter it tells you. So for the right triangle A it says a scale factor of 2 so each side length is going to be double what the original is, shape B will be redrawn with half the lengths and shape C will be redrawn with the lengths multiplied by 3/2, or 1.5. Again though, angle measures stay the same.

2 thankfully doesn't involve measuring. it's important to know that if you scale a shape it doesn't change the relationship of the sides. So the longest will be the longest after being scaled, the shortest will be the shortest and even the leftmost side will always be the leftmost side unless other transformations are carried out, like rotations or something. Though even with rotations, shortest will always be the shortest and so on.

Anyway, perimeter is the sum of the side lengths. Of shape A that is 6+9+9+12 = 36. Now we want the perimeter for shape B. It doesn't directly give us the measures, but it does tell us it s scaled so the shortest side from shape A is now 2. Well what side was the shortest on shape A? 6 was, so we know that the scaling factor is 1/3 since 6*1/3 = 2. That means all the other sides get the same scaling factor. so 9*1/3 and 12/3 which are 3 and 4 respectively. Now we know the side lengths are 2.3,3 and 4 and the perimeter is 12. Also, I want to point out the relationship between the two perimeters. what do you multiply 36 by to get to 12? 1/3, so the same thinking applies to sides as it does perimeter. So if you know the scaling factor you can just multiply the perimeter by it to find the new perimeter. Which is going to come in handy for the next question.

3 we can find the scaling factor y seeing what we multiply the original perimeter by to get 30, then we can just apply that to the different sides. Well, the side lengths of the original shape are 3, 1, 2, 1, and 2. So that makes the perimeter 9. Now, what do we multiply 9 by to get 30? It's not a nice number but if you solve an algebraic expression 9x=30 you get 30/9 or 10/3, or if you'd rather a mixed number it's 3 and 1/3. I am going to stick with 10/3. Now, if you multiply the sides we started with by 10/3 you get 3*(10/3)=10, 1*(10/3)=10/3 and 2*(10/3)=20/3. So the sides as I listed them before are 10, 10/3, 20/3, 10/3 and 20/3. If you add them up you get 10+ 10/3 + 20/3 + 10/3 + 10/3. Adding up the fractions is easy since they share a denominator, it becomes 60/3 or 20. Then it's just 20+10 which is 30, so it does give us the perimeter we want.

If there was anything you didn't understand let me know.

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3 years ago

In AWXY, mW Find mZX (2x – 12), m_X = (2x + 17), and m_Y = (9x-7) Find m

sladkih [1.3K]

Answer:

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180

2x - 12 + 2x + 17 + 9x - 7 = 180 add like terms

13x - 2 = 180 add 2 to both sides

13x = 182 divide both side by 13

x = 14

m<X = 2x + 17 replace x with 14

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2 years ago

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbar, is found

joja [24]

Answer:

(a) 80% confidence interval for the population mean is [109.24 , 116.76].

(b) 80% confidence interval for the population mean is [109.86 , 116.14].

(c) 98% confidence interval for the population mean is [105.56 , 120.44].

(d) No, we could not have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed.

Step-by-step explanation:

We are given that a simple random sample of size n is drawn from a population that is normally distributed.

The sample mean is found to be 113 and the sample standard deviation is found to be 10.

(a) The sample size given is n = 13.

Firstly, the pivotal quantity for 80% 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 mean = 113

s = sample standard deviation = 10

n = sample size = 13

$\mu$ = population mean

Here for constructing 80% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 80% confidence interval for the population mean, $\mu$ is ;

P(-1.356 < $t_1_2$ < 1.356) = 0.80 {As the critical value of t at 12 degree

of freedom are -1.356 & 1.356 with P = 10%}

P(-1.356 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.356) = 0.80

P( $-1.356 \times }{\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.356 \times }{\frac{s}{\sqrt{n} } }$ ) = 0.80

P( $\bar X-1.356 \times }{\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.356 \times }{\frac{s}{\sqrt{n} } }$ ) = 0.80

80% confidence interval for $\mu$ = [ $\bar X-1.356 \times }{\frac{s}{\sqrt{n} } }$ , $\bar X+1.356 \times }{\frac{s}{\sqrt{n} } }$ ]

= [ $113-1.356 \times }{\frac{10}{\sqrt{13} } }$ , $113+1.356 \times }{\frac{10}{\sqrt{13} } }$ ]

= [109.24 , 116.76]

Therefore, 80% confidence interval for the population mean is [109.24 , 116.76].

(b) Now, the sample size has been changed to 18, i.e; n = 18.

So, the critical values of t at 17 degree of freedom would now be -1.333 & 1.333 with P = 10%.

80% confidence interval for $\mu$ = [ $\bar X-1.333 \times }{\frac{s}{\sqrt{n} } }$ , $\bar X+1.333 \times }{\frac{s}{\sqrt{n} } }$ ]

= [ $113-1.333 \times }{\frac{10}{\sqrt{18} } }$ , $113+1.333 \times }{\frac{10}{\sqrt{18} } }$ ]

= [109.86 , 116.14]

Therefore, 80% confidence interval for the population mean is [109.86 , 116.14].

(c) Now, we have to construct 98% confidence interval with sample size, n = 13.

So, the critical values of t at 12 degree of freedom would now be -2.681 & 2.681 with P = 1%.

98% confidence interval for $\mu$ = [ $\bar X-2.681 \times }{\frac{s}{\sqrt{n} } }$ , $\bar X+2.681 \times }{\frac{s}{\sqrt{n} } }$ ]

= [ $113-2.681 \times }{\frac{10}{\sqrt{13} } }$ , $113+2.681 \times }{\frac{10}{\sqrt{13} } }$ ]

= [105.56 , 120.44]

Therefore, 98% confidence interval for the population mean is [105.56 , 120.44].

(d) No, we could not have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed because t test statistics is used only when the data follows normal distribution.

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3 years ago

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bekas [8.4K]

It’s 1 hope it helps

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3 years ago

Read 2 more answers

Find the measure of the exterior angle.

Illusion [34]

Answer:

108 degrees

Step-by-step explanation:

From the diagram we are given

Interior angles are 2x + 1 and 63 degrees

Exterior angle = 5x -2

The sum of interior angles is equal to the exterior angle

2x + 1 + 63 = 5x - 2

2x + 64 = 5x - 2

2x - 5x = -2-64

-3x = -66

x = -66/-3

x = 22

Get the exterior angle:

Exterior angle = 5x-2

Exterior angle = 5(22) - 2

Exterior angle = 110-2

Exterior angle = 108 degrees

Hence the measure of the exterior angle is 108 degrees

5 0

3 years ago