A whole number is one from the set containing zero and all of the positive numbers. A negative number, therefore, is not a whole number, but it is an integer. So the answer is false.

3 0

4 years ago

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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

Am I correct?? If not please correct me

pickupchik [31]

The answer would actually be A
F(x)=3x^2+4x
G(x)=2x^2-x+1
The two x^2 items are both positive and are added together to be 5x^2
The two x items would be added together to get 3x cause of the -x
Then +1 is just +1
Making the equation 5x^2+3x+1
If we were subtracting you would be absolutely correct, but since we are adding would go the opposite direction.
I hope this helps!

3 0

3 years ago

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the coordinates of a quadrilateral are (5,8), (7,10), (9,12) and (11,14). after a transformation, the sign of the x-coordinate a

BartSMP [9]

Answer:

The quadrilateral is rotated 180° about the origin

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

∴ Its image is (-y , -x)

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or

anti-clockwise around the origin

* In our problem:

- The sign of the x-coordinate and the sign of the y- coordinate

for each ordered pair have changed

- The image of each point is (-5 , -8) , (-7 , -10) , (-9 , -12) , (-11 , -14)

∴ The quadrilateral is rotated 180° about the origin

7 0

3 years ago