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Rama09 [41]
4 years ago
10

If the base of a triangle is shortened by 60 percent, by what percent must the height be increased if the area is to remain the

same?
Mathematics
1 answer:
Ahat [919]4 years ago
8 0

Answer:

150%

Step-by-step explanation:

The area is half base times height.  We want the product to be the same, so if we scale one factor by f, we have to scale the other factor by 1/f to compensate.

Reducing by 60% is multiplication by f=1-60/100 = 0.4

So we have to multiply the height by 1/0.4=2.5 to compensate.

A factor of 2.5 is an increase of 150%

Check:

(1-60/100)(1+150/100) = 1, good

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The state highway department is studying traffic patterns on one of the busiest highways in the state. As part of the study, the
larisa86 [58]

Answer:

The need to sample 76 days.

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{1-0.99}{2} = 0.005

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

So it is z with a pvalue of 1-0.005 = 0.995, so z = 2.575

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.

How many days do they need to sample

We need to sample n days.

n is found when M = 300.

We have that \sigma = 1010

So

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

300 = 2.575*\frac{1010}{\sqrt{n}}

300\sqrt{n} = 2.575*1010

\sqrt{n} = \frac{2.575*1010}{300}

(\sqrt{n})^{2} = (\frac{2.575*1010}{300})^{2}

n = 75.1

Rounding up

The need to sample 76 days.

3 0
3 years ago
Can you solve 2x^2 = 200 in the method Completing the Square
Elanso [62]
Hello there ^ _ ^

2x² = 200
We need to start by dividing both sides by 2
2x²/2 = 200/2
x² = 100
Now we can take square root.
x = +/-√100
x = 10 or x = -10

I hope this help!
7 0
3 years ago
Read 2 more answers
Can someone pls help me I'm stuck o these two questions
jeka57 [31]

Problem 1

<h3>Answers:</h3><h3>arc AB = 122 degrees</h3><h3>angle ADB = 61 degrees</h3>

--------------------

Explanation:

Arc BC is 58 degrees. The arc AB combines with it to form semicircle ABC, which is basically arc ABC with measure 180

This must mean arc AB is 180-58 = 122 degrees

When in doubt, chances are the number 180 might be involved (in some way) when it comes to geometry problems. Of course, this isn't always a guarantee. The number does show up a lot though.

Once we determine what arc AB is equal to, we cut it in half to get the inscribed angle ADB. Refer to the inscribed angle theorem. Notice how angle ADB subtends the arc AB.

==========================================================

Problem 2

<h3>Answer:  9</h3>

--------------------

Explanation:

x = length of AE

Since AC = 13, this makes EC = 13-x

We'll use the intersecting chords theorem to find x.

(AE)*(EC) = (BE)*(DE)

x*(13-x) = 6*6

13x-x^2 = 36

-x^2 + 13x - 36 = 0

x^2 - 13x + 36 = 0

(x-9)(x-4) = 0

x-9 = 0 or x-4 = 0

x = 9 or x = 4

This means AE could be 9 units long or 4 units long.

Usually the diagram isn't drawn to scale so we don't really use it all too much (other than initial set up). However, if the diagram was drawn to scale, then notice that AE is over the halfway point of AC. This means we would be able to rule out x = 4 since 4 is not over the halfway point of 13. I have a feeling this is what your teacher might be going for.

In short, only AE = 9 is possible.

4 0
2 years ago
How many faces does the solid made from the net below have?
Rasek [7]

Check the picture below.

4 0
4 years ago
Read 2 more answers
1
Lubov Fominskaja [6]

Answer:

A

Step-by-step explanation:

8.5 x 8.5= 72.25

so basically it's the closest answer

7 0
3 years ago
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