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3 years ago

4. For which of the following probability assignments are events A and B independent?

Mathematics

1 answer:

Aleksandr [31]3 years ago

3 0

Answer:

Step-by-step explanation:

formatting is so bad lol

but yeah its the first one because for independent events, the probably of a and b is the product of both probabilities, just like how 0.3*0.4=0.12

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Brainliest will be given to the correct answer!

IrinaK [193]

Answer:

A) The height of the trapezoid is 6.5 centimeters.

B) We used an algebraic approach to to solve the formula for $b_{1}$ . $b_{1} = \frac{2\cdot A}{h}-b_{2}$

C) The length of the other base of the trapezoid is 20 centimeters.

D) We can find their lengths as both have the same length and number of variable is reduced to one, from $b_{1}$ and $b_{2}$ to $b$ . $b = \frac{A}{h}$

Step-by-step explanation:

A) The formula for the area of a trapezoid is:

$A = \frac{1}{2}\cdot h \cdot (b_{1}+b_{2})$ (Eq. 1)

Where:

$h$ - Height of the trapezoid, measured in centimeters.

$b_{1}$ , $b_{2}$ - Lengths fo the bases, measured in centimeters.

$A$ - Area of the trapezoid, measured in square centimeters.

We proceed to clear the height of the trapezoid:

1) $A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})$ Given.

2) $A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})$ Definition of division.

3) $2\cdot A\cdot (b_{1}+b_{2})^{-1} = (2\cdot 2^{-1})\cdot h\cdot [(b_{1}+b_{2})\cdot (b_{1}+b_{2})^{-1}]$ Compatibility with multiplication/Commutative and associative properties.

4) $h = \frac{2\cdot A}{b_{1}+b_{2}}$ Existence of multiplicative inverse/Modulative property/Definition of division/Result

If we know that $A = 91\,cm^{2}$ , $b_{1} = 16\,cm$ and $b_{2} = 12\,cm$ , then height of the trapezoid is:

$h = \frac{2\cdot (91\,cm^{2})}{16\,cm+12\,cm}$

$h = 6.5\,cm$

The height of the trapezoid is 6.5 centimeters.

B) We should follow this procedure to solve the formula for $b_{1}$ :

1) $A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})$ Given.

2) $A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})$ Definition of division.

3) $2\cdot A \cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot (b_{1}+b_{2})$ Compatibility with multiplication/Commutative and associative properties.

4) $2\cdot A \cdot h^{-1} = b_{1}+b_{2}$ Existence of multiplicative inverse/Modulative property

5) $\frac{2\cdot A}{h} +(-b_{2}) = [b_{2}+(-b_{2})] +b_{1}$ Definition of division/Compatibility with addition/Commutative and associative properties

6) $b_{1} = \frac{2\cdot A}{h}-b_{2}$ Existence of additive inverse/Definition of subtraction/Modulative property/Result.

We used an algebraic approach to to solve the formula for $b_{1}$ .

C) We can use the result found in B) to determine the length of the remaining base of the trapezoid: ( $A= 215\,cm^{2}$ , $h = 8.6\,cm$ and $b_{2} = 30\,cm$ )

$b_{1} = \frac{2\cdot (215\,cm^{2})}{8.6\,cm} - 30\,cm$

$b_{1} = 20\,cm$

The length of the other base of the trapezoid is 20 centimeters.

D) Yes, we can find their lengths as both have the same length and number of variable is reduced to one, from $b_{1}$ and $b_{2}$ to $b$ . Now we present the procedure to clear $b$ below:

1) $A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})$ Given.

2) $b_{1} = b_{2}$ Given.

3) $A = \frac{1}{2}\cdot h \cdot (2\cdot b)$ 2) in 1)

4) $A = 2^{-1}\cdot h\cdot (2\cdot b)$ Definition of division.

5) $A\cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot b$ Commutative and associative properties/Compatibility with multiplication.

6) $b = A \cdot h^{-1}$ Existence of multiplicative inverse/Modulative property.

7) $b = \frac{A}{h}$ Definition of division/Result.

8 0

4 years ago

the smiths spend 11% of their budget on entertainment. their total budget this year is $1,000 more than last year, and this year

Nadusha1986 [10]

Answer: $41000 Was the Smiths family budget last year.

Step-by-step explanation:

First you take $4620 and DIVIDE it by .11 you will get $42000 and since last year had $1000 less to spend you subtract $1000 from $42000 to get $41000 for the budget last year.

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2 years ago

5 8 7 Find the area of the parallelogram. HELP PLSSS ITS DUE TMRW

Yuri [45]

Are of a parallelogram is base (height)
since the height of this parallelogram is 7(that’s it’s altitude) and the base is 5
the area of this parallelogram is 35 unites sq