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3 years ago

12

Choose the answer. 4. (1 pt) Which property justifies this statement? If x + y = z and z = x + 4, then x + y = x + 4. A. symmetr

ic B. associative C. distributive D. transitive

1 answer:

yuradex [85]3 years ago

5 0

The symmetric property of equality says that if a = b, then b = a.

The associative property for addition merely states that a+(b+c) = (a+b)+c.

The distributive property says that if a, b, and c are real numbers, then

a · (b + c) = (a · b) + (a · c).

The transitive property of equality says that if a = b and b = c, then a = c.

Consider statament: If x + y = z and z = x + 4, then x + y = x + 4. Denote a=x+y, b=z and c=x+4. Now you have if a=b and b=c, then a=c. This is exactly transitive property.

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If the mean of a normal distribution is 22, what is the median of the distribution?

DerKrebs [107]

Answer:

22

Step-by-step explanation:

Normal Distributions are the most important in statistics. They are also know as "bell curves".

There are special properties of Normal Distributions. I name 3 of them below:

1. Normal distributions are symmetric about their mean.

2. The area under the normal curve is 1

3. The mean, mode, and median of normal distribution are equal

This question can easily be solved using property #3 in the stated above properties.

The mean and median of normal distribution are equal. Since mean is given as 22, the median will also be 22.

8 0

4 years ago

25x^-4-99x^-2-4=0 <br> How do I solve for this?

OlgaM077 [116]

Given

$25x^{-4} - 99x^{-2} - 4 = 0$

consider substituting $y=x^{-2}$ to get a proper quadratic equation,

$25y^2 - 99y - 4 = 0$

Solve for $y$ ; we can factorize to get

$(25y + 1) (y - 4) = 0$

$25y+1 = 0 \text{ or } y - 4 = 0$

$y = -\dfrac1{25} \text{ or }y = 4$

Solve for $x$ :

$x^{-2} = -\dfrac1{25} \text{ or }x^{-2} = 4$

The first equation has no real solution, since $x^{-2} = \frac1{x^2} > 0$ for all non-zero $x$ . Proceeding with the second equation, we get

$x^{-2} = 4 \implies x^2 = \dfrac14 \implies x = \pm\sqrt{\dfrac14} = \boxed{\pm \dfrac12}$

If we want to find all complex solutions, we take $i=\sqrt{-1}$ so that the first equation above would have led us to

$x^{-2} = -\dfrac1{25} \implies x^2 = -25 \implies x = \pm\sqrt{-25} = \pm5i$

8 0

2 years ago

A 25-foot flag pole casts a shadow of 40 feet. What is the approximate height from the top of the flag pole to the top of the sh

Ann [662]

Answer:

The height from the top of the flag pole to the top of the shadow = 47 feet.

Step-by-step explanation:

Given:

Height of the flag pole = 25 ft

Length of the shadow cast by the flag pole = 40 ft

To find the approximate height from the top of the flag pole to the top of the shadow.

Solution:

On drawing the flagpole and the shadow, we get a right triangle of which the legs are given.

$Leg 1 =25\ ft$

$Leg 2 = 40\ ft$

We need to find the hypotenuse of the right triangle.

Applying Pythagorean theorem.

$Hypotenuse^2=Leg1^2+Leg2^2$

$Hypotenuse^2=25^2+40^2$

$Hypotenuse^2=625+1600$

$Hypotenuse^2=2225$

Taking square root both sides :

$\sqrt{Hypotenuse^2}=\sqrt{2225}$

$Hypotenuse=47.1\approx 47$

Thus, the height from the top of the flag pole to the top of the shadow = 47 feet.

8 0

3 years ago

n a Gallop poll of 1012 randomly selected adults, 9% said that cloning of humans should be allowed. We are going to use a .05 si

Vanyuwa [196]

Answer:0.1446

Step-by-step explanation:

Let p be the population proportion of adults say that cloning of humans should be allowed.

As per given , the appropriate set of hypothesis would be :-

$H_0: p\geq0.10\\\\ H_a: p$

Since $H_a$ is left-tailed and sample size is large(n=1012) , so we perform left-tailed z-test.

Given : The test statistic for this test is -1.06.

P-value for left tailed test,

P(z<-1.06)=1-P(z<1.06) [∵P(Z<-z)=1-P(Z<z]

= $1-0.8554=0.1446$ (Using z-value table.)

Hence, the p-value for this test statistic= 0.1446

4 0

3 years ago

If x+y=580 and x=3y then what are x and y?

sergejj [24]

Answer:

x=435 ,y=145

Step-by-step explanation:

You substitute x for 3y in this equation and get

3y+y=580

from here you simplify

4y=580

and divide 580 by 4 to get what y is

y=580/4

y=145

now since x=3y you mutiply y by 3

x=3(y)

x=3(145)

x=435

7 0

3 years ago

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