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Aloiza [94]
3 years ago
14

Distributive property/collecting like terms. 4n -2 - 2n

Mathematics
1 answer:
marusya05 [52]3 years ago
7 0

Distributive property: a(b + c) = ab + ac

4n - 2 - 2n = 2(2n - 1 - n)

4n - 2 - 2n = 2n - 2 = 2(n - 1)

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Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 5 million dollars
GuDViN [60]

Answer:

Probability that a randomly selected firm will earn less than 100 million dollars is 0.8413.

Step-by-step explanation:

We are given that the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 5 million dollars. Also, incomes for the industry are distributed normally.

<em>Let X = incomes for the industry</em>

So, X ~ N(\mu=95,\sigma^{2}=5^{2})

Now, the z score probability distribution is given by;

         Z = \frac{X-\mu}{\sigma} ~ N(0,1)

where, \mu = mean income of firms in the industry = 95 million dollars

            \sigma = standard deviation = 5 million dollars

So, probability that a randomly selected firm will earn less than 100 million dollars is given by = P(X < 100 million dollars)

    P(X < 100) = P( \frac{X-\mu}{\sigma} < \frac{100-95}{5} ) = P(Z < 1) = 0.8413   {using z table]

                                                     

Therefore, probability that a randomly selected firm will earn less than 100 million dollars is 0.8413.

5 0
3 years ago
Find the values of x and y
Grace [21]

Answer:

C

Step-by-step explanation:

8 0
3 years ago
Lins father is paying for a $20 meal. He has a%15 off coupon for the meal. After the discount, a 7% sales tax is applied. What d
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he pays $18.19 hope this helps have a nice day please give me brainliest

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Inequality to x2 &lt; 64
Anarel [89]
              NOT MY WORDS TAKEN FROM A SOURCE!

(x^2) <64  => (x^2) -64 < 64-64 => (x^2) - 64 < 0 64= 8^2    so    (x^2) - (8^2) < 0  To solve the inequality we first find the roots (values of x that make (x^2) - (8^2) = 0 ) Note that if we can express (x^2) - (y^2) as (x-y)* (x+y)  You can work backwards and verify this is true. so let's set (x^2) - (8^2)  equal to zero to find the roots: (x^2) - (8^2) = 0   => (x-8)*(x+8) = 0       if x-8 = 0 => x=8      and if x+8 = 0 => x=-8 So x= +/-8 are the roots of x^2) - (8^2)Now you need to pick any x values less than -8 (the smaller root) , one x value between -8 and +8 (the two roots), and one x value greater than 8 (the greater root) and see if the sign is positive or negative. 1) Let's pick -10 (which is smaller than -8). If x=-10, then (x^2) - (8^2) = 100-64 = 36>0  so it is positive
2) Let's pick 0 (which is greater than -8, larger than 8). If x=0, then (x^2) - (8^2) = 0-64 = -64 <0  so it is negative3) Let's pick +10 (which is greater than 10). If x=-10, then (x^2) - (8^2) = 100-64 = 36>0  so it is positive Since we are interested in (x^2) - 64 < 0, then x should be between -8 and positive 8. So  -8<x<8 Note: If you choose any number outside this range for x, and square it it will be greater than 64 and so it is not valid.

Hope this helped!

:)
7 0
3 years ago
NEED ANSWER ASPA.... PLS HURRY
a_sh-v [17]
We have that
y=- x^{2} +36

we know that
Is the equation of a vertical parabola open down
so
the vertex is a maximum

step 1
convert the equation of the parabola in the vertex form
y=- x^{2} +36 \\ y-36=- x^{2}

the vertex (h,k) is the point (0,36)

Part a) The point on the graph where the height of the tunnel is a maximum is (0,36)

Part b) The points on the graph where the height of the tunnel is zero feet is when y=0
so
for y=0
- x^{2} +36=0 \\ x^{2} =36 \\ x= (+/-) 6

the points are (-6,0)  and (6,0)

see the attached figure 

5 0
3 years ago
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