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2 years ago

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Which graph shows the solution to the inequality –0.5x ≤ 7.5? A number line going from negative 18 to negative 8. A closed circl

e is at negative 15. Everything to the right of the circle is shaded. A number line going from negative 18 to negative 8. A closed circle is at negative 15. Everything to the left of the circle is shaded. A number line going from negative 5 to negative 2.5. A closed circle is at negative 4. Everything to the right of the circle is shaded. A number line going from negative 5 to negative 2.5. A closed circle is at negative 4. Everything to the left of the circle is shaded.

2 answers:

Dima020 [189]2 years ago

8 0

Answer:

A

Step-by-step explanation:

I just did it and because of the person above

kirill [66]2 years ago

3 0

Answer:

Answer = a

Step-by-step explanation:

i did it

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The answer should be $31.80.
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The sum of two numbers is 240. If one number is twice the other number, find the two numbers.

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The sum of two numbers is 240. The larger number is 6 less than twice the smaller. Find the numbers.

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Let the smaller be "x" ; Larger is "2x-6"

EQUATION:

x + 2x-6 = 240

3x= 246

x = 82 (smaller)

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Step-by-step explanation:

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Prove that the figure is a parallelogram. If so, classify the parallelogram. Be specific and justify your answer.

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Answer:

Step-by-step explanation:

If it is a parallelogram the opposite sides will a have the same slope.

Using the diagram we see from the coordinates of A and B:

Slope of AB = (5 - -1)/(-1 - -5)

= 6/4

= 3/2.

In the same way

slope of CD = (2 - -4) / (1 - -3)

= 3/2.

So AB and CD can be shown to be parallel.

Similarly the lines BC and AD are parallel.

So the figure is a parallelogram

Finding the perimeter (counting the units between the points):

Perimeter = 2AB + 2BC

By Pythagoras:

AB = sqrt (6^2 + 4^2) = sqrt 52

BC = sqrt (3^2 + 2^2) = sqrt 13

So Perimeter = 2sqrt52 + 2sqrt13

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or 21.63 unit^2 to 2 decimal places.

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2 years ago

There are three power plants [X, Y, Z] that at any given time each one either generates electricity or idles. Event A is that pl

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We're told that

$P(A\cap B)=0.15$

$P(A\cup B)^C=0.06\implies P(A\cup B)=0.94$

$P(B\mid A)=P(B^C\mid A)=0.5$

where the last fact is due to the law of total probability:

$P(A)=P(A\cap B)+P(A\cap B^C)$

$\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)$

$\implies 1=P(B\mid A)+P(B^C\mid A)$

so that $B\mid A$ and $B^C\mid A$ are complementary.

By definition of conditional probability, we have

$P(B\mid A)=P(B^C\mid A)$

$\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}$

$\implies P(A\cap B)=P(A\cap B^C)$

We make use of the addition rule and complementary probabilities to rewrite this as

$P(A\cap B)=P(A\cap B^C)$

$\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)$

$\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)$

$\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]$

$\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]$

$\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C$

$\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)$

By the law of total probability,

$P(B)=P(A\cap B)+P(A^C\cap B)$

$\implies P(A^C\cap B)=P(B)-P(A\cap B)$

and substituting this into $(*)$ gives

$2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]$

$\implies P(B)=P(A\cup B)-P(A\cap B)$

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Answer:

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