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telo118 [61]
3 years ago
6

If a number is increased by 20% the result is 24. find the number

Mathematics
1 answer:
marin [14]3 years ago
3 0

Answer:

20

Step-by-step explanation:

  • x+20%=24
  • x+x*20/100=24
  • x+0.2x=24
  • 1.2x=24
  • x=24/1.2
  • x=20
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Marcus hikes at a rate of 2 miles per hour if he hikes for 6 1/3 hours how many will he hike
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Trevor thinks that left-handed pitchers in a baseball league are more likely to strike out batters than right-handed pitchers ar
Scilla [17]

Answer:

C. H0: PL - PR = 0

Ha: PL - PR > 0

The null hypothesis for this case is that left-handed pitchers in a baseball league are not more likely to strike out batters than right-handed pitchers are. That is the proportion of at-bats resulting in a strikeout is significantly equal for both left-handed and right-handed pitchers.

H0: PL - PR = 0

The alternative hypothesis is that the proportion of at-bats resulting in a strikeout is significantly higher for left-handed pitchers

Ha: PL - PR > 0

PL - proportion of at-bats resulting in a strikeout for left-handed pitchers

PR - proportion of at-bats resulting in a strikeout for right-handed pitchers

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

The null hypothesis for this case is that left-handed pitchers in a baseball league are not more likely to strike out batters than right-handed pitchers are. That is the proportion of at-bats resulting in a strikeout is significantly equal for both left-handed and right-handed pitchers.

H0: PL - PR = 0

The alternative hypothesis is that the proportion of at-bats resulting in a strikeout is significantly higher for left-handed pitchers

Ha: PL - PR > 0

PL - proportion of at-bats resulting in a strikeout for left-handed pitchers

PR - proportion of at-bats resulting in a strikeout for right-handed pitchers

8 0
3 years ago
What is the area of a regular 16-gon with a radius of 15 feet? Round your answer to the nearest tenth.
Sedbober [7]

Split up the 16-gon into 16 congruent isosceles triangles. Cut each of these isosceles triangles in half to get a right triangle.

The radius of the 16-gon corresponds to the hypotenuse of any of these 32 right triangles. As you probably know, the area of a triangle is half the product of its base and height. For a right triangle, the base and height can be taken to be the two legs. So you need to find their lengths.

Recall that the exterior angles of any convex polygon sum to 360º in measure. For a regular polygon, these angles are all congruent. There are 16 of them in this case, so they each have measure (360/16)º = 22.5º.

Interior angles are supplementary to exterior angles, which means each interior angle of the 16-gon has measure (180 - 22.5)º = 157.5º.

When we split up the 16-gon into isosceles triangles, the "base angles" are equal in measure to half the measure of the interior angles, since each hypotenuse bisects the interior angle. So each base angle has measure 78.75º.

In each right triangle, we then have base <em>b</em> and height <em>h</em> such that

sin(78.75º) = <em>h</em>/15

cos(78.75º) = <em>b</em>/15

Solve for <em>h</em> and <em>b</em> to get

<em>b</em> = 15 cos(78.75º)

<em>h</em> = 15 sin(78.75º)

Then the area of each right triangle is

1/2 <em>b h</em> = 225/2 sin(78.75º) cos(78.75º) = 225/4 sin(157.5º)

and so the area of the 16-gon is

32(1/2 <em>b h</em>) = 1800 sin(157.5º) ≈ 688.8 sq. ft.

4 0
3 years ago
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