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Ksenya-84 [330]
4 years ago
8

Write an equation that represents the following problem.

Mathematics
1 answer:
pogonyaev4 years ago
5 0
35 + 0.05m = 50 + 0.01m <== ur equation
0.05m - 0.01m = 50 - 35
0.04m = 15
m = 15/0.04
m = 375.....u need to send 375 text messages for the plans to be equal
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4 years ago
Out of 2,000 random but normally distributed numbers with a mean of 45 and a standard deviation of x, approximately 1,360 number
Lilit [14]
Let Y denote the random variable representing a given number in the total set of numbers. We're told that \dfrac{1360}{2000}=0.68 of the numbers fall within a given range, so we know

\mathbb P(40\le Y\le50)=0.68

where Y is normally distributed with mean 45 and an unknown variance x^2.

Let's make the transformation to a random variable with a standard normal distribution:

\mathbb P\left(\dfrac{40-45}x\le\dfrac{Y-45}x\le\dfrac{50-45}x\right)=\mathbb P\left(-\dfrac5x\le Z\le\dfrac5x\right)

Since Z is symmetric, we have

\mathbb P(-\dfrac5x\le Z\le\dfrac5x\right)=2\mathbb P\left(0\le Z\le\dfrac5x\right)=2\bigg(\mathbb P\left(Z\le\dfrac5x\right)-\mathbb P(Z\le0)\bigg)

The mean of Z is 0, and by symmetry we know that exactly half of the distribution falls to the left of Z=0, so \mathbb P(Z\le0)=0.5. We're left with

0.68=2\mathbb P\left(Z\le\dfrac5x\right)-2\cdot0.5
\implies\mathbb P\left(Z\le\dfrac5x\right)=0.84

This probability corresponds to a value of Z\approx0.9945, which means

\dfrac5x\approx0.9945\implies x\approx5.0277
7 0
3 years ago
Find the term that must be added to the equation x2−6x=7 to make it into a perfect square.
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x²-6x =7

First we have get rid of that 7 from the right side and move it to the left side. To move 7 to the left side, we have to subtract 7 from both sides.

x²-6x-7= 7-7

x²-6x-7 = 0

To make this equation a perfect square, first we have to check the x term. Here -6x given. We have to divide the co-efficient of x by 2, and then we have to add the square of it.

The co-efficient of x is -6 here. Dividing it by 2, we will get -6/2 = -3.

We will have to add (-3)² here. (-3)² is 9. So in the place of -7, we have to make 9, to make the equation a perfect square.

9-(-7) = 9+7 = 16

So by adding 16 to the left side, we can make the equation a perfect square.

x²-6x-7+16 =0

x²-6x+9 =0

x²-6x+(-3)² =0

(x-3)² =0

5 0
3 years ago
Scientists found the wreck of the titanic 3797 m below sea level. How many km below sea level is the wreck?
WINSTONCH [101]

We are given that the titanic is found 3,797 m below sea level. This is simply equivalent to 3.797 km or 3.8 km when rounded off to one decimal.

We should take note that the letter k in km means kilo and a kilo is equivalent to 1000. So this means that for 1 km there is exactly 1000 m. So to convert, simply multiply a value with unit m with this conversion factor. Conversion factor = 1 km / 1000 m

Depth of titanic = 3,797 m (1 km / 1000 m)

Depth of titanic = 3.797 km = 3.8 km

4 0
3 years ago
Read 2 more answers
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