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3 years ago

Find the sum of the constants a, h, and k such that

Mathematics

1 answer:

ra1l [238]3 years ago

6 0

Answer:

Step-by-step explanation:

The value of "a" is the coefficient of x^2, so we know that is 2.

<u>Solve for h</u>

Now, we have ...

2x^2 -8x +7 = 2(x -h)^2 +k

Expanding the right side gives us ...

= 2(x^2 -2hx +h^2) +k

= 2x^2 -4hx +2h^2 +k

Comparing x-terms, we see ...

-4hx = -8x

h = (-8x)/(-4x) = 2

<u>Solve for k</u>

Now, we're left with ...

2h^2 +k = 7 = 2(2^2) +k = 8 +k

Subtracting 8 we find k to be ...

k = 7 -8 = -1

And the sum of constants a, h, and k is ...

a +h +k = 2 +2 -1 = 3

The sum of the constants is 3.

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Simplify 4x + 3(5x) + 4y - x =

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2 years ago

Read 2 more answers

Assume that a procedure yields a binomial distribution with a trial repeated n = 5 times. Use some form of technology to find th

Digiron [165]

Answer:

$P(X = 0) = 0.0263$

$P(X = 1) = 0.1407$

$P(X = 2) = 0.3012$

$P(X = 3) = 0.3224$

$P(X = 4) = 0.1725$

$P(X = 5) = 0.0369$

Step-by-step explanation:

Binomial probability distribution

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

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

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

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

And p is the probability of X happening.

In this problem we have that:

$n = 5, p = 0.517$

Distribution

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

$P(X = 0) = C_{5,0}.(0.517)^{0}.(0.483)^{5} = 0.0263$

$P(X = 1) = C_{5,1}.(0.517)^{1}.(0.483)^{4} = 0.1407$

$P(X = 2) = C_{5,2}.(0.517)^{2}.(0.483)^{3} = 0.3012$

$P(X = 3) = C_{5,3}.(0.517)^{3}.(0.483)^{2} = 0.3224$

$P(X = 4) = C_{5,4}.(0.517)^{4}.(0.483)^{1} = 0.1725$

$P(X = 5) = C_{5,5}.(0.517)^{5}.(0.483)^{0} = 0.0369$

6 0

3 years ago

The number 68 is increased to 73. What is the percentage by which the number was

Murljashka [212]

Answer: 1.1%

Step-by-step explanation:

To get a percentage you want to divide the ending number by the base number

73 / 68 = 1.07

It says to round to the neartest tenth, when rounding if the number is 5 or above you round up, if under 5 your number stays the same

7 is higher than 5 so we round up

1.1%

3 0

3 years ago

Bacteria colonies increase by 37% every 2 days. If you start with 55 microorganisms, how large would the colony be after 10 days

ahrayia [7]

The number of microorganisms that I will have after 10 days would be: 245.41 microoganisms.

<h3>How to calculate the number of microorganisms that I will have after 10 days?</h3>

To calculate the number of microorganisms that I will have after 10 days, I must perform the following operations:

We need to find 37% of 55 as shown below:

55 ÷ 100 = 0.55
0.55 x 37% = 20.35
55 + 20.35 = 75.35

So after 2 days I will have 75.35 microorganisms.

75.35 ÷ 100 = 0.75
0.7535 x 37% = 27.87
75.35 + 27.87 = 103.22

On the fourth day I will have: 103.22 microorganisms.

103.22 ÷ 100 = 1.0322
1.0322 x 37% = 38.19
103.22 + 38.19 = 141.41

On the sixth day I will have 141.41 microorganisms.

141.41 ÷ 100 = 1.4141
1.4141 x 37% = 52.32
141.41 + 52.32 = 193,73

On the eighth day I will have 193.73 microorganisms.

193.73 ÷ 100 = 1.9373
1.9373 x 37% = 71.68
193.73 + 71.68 = 265.41

On the tenth day I will have 245.41 microoganisms.

Learn more about percentages in: brainly.com/question/13450942

#SPJ1

3 0

1 year ago