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2 years ago

Question 2

Mathematics

1 answer:

shutvik [7]2 years ago

5 0

9514 1404 393

Answer:

45°, 45°, 90°

Step-by-step explanation:

If the difference of two angles is 0°, then they are congruent, and the triangle is isosceles.

The angle measures of the isosceles right triangle are 45°, 45°, 90°.

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A road is 4 cm long on the map. Find the actual length of the road.

Usimov [2.4K]

The distance between two cities is

Explanation:

As a road of

on road map indicates a road of length equal to

Each

on map indicates

7.5

Hence a distance of

between two cities on the map indicates

7.5

7 0

2 years ago

The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

$y = 2-x \,\,\,\,\,, 1 \leq x \leq 2$ .

If you rotate the first region around the "y" axis you get that

$A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51$

And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

And the sum would be 2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

7 0

3 years ago

A toy manufacturer wants to know how many new toys children buy each year. A sample of 305 children was taken to study their pur

Harrizon [31]

Answer:

The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.8}{2} = 0.1$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.1 = 0.9$ , so Z = 1.28.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.28\frac{1.5}{\sqrt{305}} = 0.1$

The lower end of the interval is the sample mean subtracted by M. So it is 7.6 - 0.1 = 7.5

The upper end of the interval is the sample mean added to M. So it is 7.6 + 0.1 = 7.7

The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.

8 0

3 years ago

The bases of a trapezoid are 24 feet and 16 feet. The height of the trapezoid is 12 feet. What is the area of the trapezoid?

stepan [7]

The formula to use is A=(b1+b2)h if one base is 24 and the other one is 16 which equals to 40 when you add then you still have H which is 12 so you could either divide 12 by two to get half or multiply by 12 and then divide it
40•12=480
480 divided by 2= 240
Your final answer should be 240ft

4 0

2 years ago

Ms portillo cat weighs 6 kilograms her dog ways 22 more killergrams how much does the dog way

Alex Ar [27]

Answer:

28 kilograms

Step-by-step explanation:

All you have to do is 22+6

4 0

2 years ago