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3 years ago

How do you know that (-3/4) (-8a) + (-3/4) (-12) is equivalent to both -3/4(-8a - 12) and 6a + 9?

Mathematics

2 answers:

Mademuasel [1]3 years ago

6 0

Answer:

Step-by-step explanation:

We know these outcomes by applying Order of Operations rules.

(-3/4) (-8a) + (-3/4) (-12) after performing the two indicated multiplications is

6a + 9.

The original (-3/4) (-8a) + (-3/4) (-12) can be factored as follows:

(-3/4) (-8a) + (-3/4) (-8a - 12) = (-3/4)(-8a - 12)

Marta_Voda [28]3 years ago

5 0

Answer:

Step-by-step explanation:

$\frac{-3}{4}*(-8a) + (\frac{-3}{4})* (-12) = (-3)*(-2a) + (-3) * 3\\ = 6a + 9$

Here, we simplified the expression.

$\frac{-3}{4}*(-8a) + (\frac{-3}{4})(-12) = (\frac{-3}{4})(-8a - 12)$

Here, (-3/4), the common factor for two terms is taken outside.

You might be interested in

What are the solutions to the following system?

Dima020 [189]

The answer is
2x+(3x+4)=6

4 0

1 year ago

What is the solution of the system ? <br> 2x+3y=4 <br> x-y=-3

fgiga [73]

Change the equation, x - y = -3, to isolate x or y and plug that new equation into the equation 2x + 3y = 4

I changed it to: x = y - 3
so
2(y - 3) + 3y = 4
2y - 6 + 3y = 4
5y - 6 = 4
5y = 4 + 6
5y = 10
y = 10/5
y = 2

then you plug that 2 into the equation x = y - 3 to get the value of x

x = (2) - 3
x = -1

you can check this by plugging the x and y values into the equation 2x + 3y = 4

2(-1) + 3(2) = 4
-2 + 6 = 4
4 = 4

hope this helps :)

6 0

3 years ago

A research study uses 800 men under the age of 55. Suppose that 30% carry a marker on the male chromosome that indicates an incr

ss7ja [257]

Answer:

a) There is a 12.11% probability that exactly 1 man has the marker.

b) There is a 85.07% probability that more than 1 has the marker.

Step-by-step explanation:

There are only two possible outcomes: Either the men has the chromosome, or he hasn't. So we use the binomial probability distribution.

Binomial probability

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

In this problem, we have that:

30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure, so $\pi = 0.30$

(a) If 10 men are selected randomly and tested for the marker, what is the probability that exactly 1 man has the marker?

10 men, so $n = 10$

We want to find P(X = 1). So:

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{10,1}.(0.30)^{1}.(0.7)^{9} = 0.1211$

There is a 12.11% probability that exactly 1 man has the marker.

(b) If 10 men are selected randomly and tested for the marker, what is the probability that more than 1 has the marker?

That is $P(X > 1)$

We have that:

$P(X \leq 1) + P(X > 1) = 1$

$P(X > 1) = 1 - P(X \leq 1)$

We also have that:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = 0) = C_{10,0}.(0.30)^{0}.(0.7)^{10} = 0.0282$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0282 + 0.1211 = 0.1493$

Finally

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1493 = 0.8507$

There is a 85.07% probability that more than 1 has the marker.

3 0

3 years ago

Write the equation of the line passing through the point (3,5) with a slope of 2

Nady [450]

Y - y1 = m(x - x1)
y - 5 = 2(x - 3)
y - 5 = 2x - 6
y = 2x - 1

answer: equation y = 2x - 1

7 0

3 years ago

Write an equation of the line that passes through please (2, -2) and is parallel to line y=3x+9

gayaneshka [121]

Answer: y=3x-8

Step-by-step explanation:

To find the parallel line, you know that the slope must stay the same. If the slope is different, the graphs will touch at one point. This goes against parallel lines as they NEVER touch or cross.

y=3x+b

We can use the given point to find the y-intercept.

-2=3(2)+b [multiply]

-2=6+b [subtract both sides by 6]

b=-8

Now that we have found the y-intercept, we can finish our equation.

y=3x-8

5 0

3 years ago