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3 years ago

Write an equation to express the value of h+k

1 answer:

3 0

When written in "vertex form":
• (h, k) is the vertex of the parabola, and x = h is the axis of symmetry.

• the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0).

• the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0).

• notice that the h value is subtracted in this form, and that the k value is added.
If the equation is y = 2(x - 1)2 + 5, the value of h is 1, and k is 5.
If the equation is y = 3(x + 4)2 - 6, the value of h is -4, and k is -6.

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Find the value of x to the nearest tenth.

Sergeu [11.5K]

Answer:

A)7.5

Step-by-step explanation:

you divide 62 by 4 and you get A

6 0

3 years ago

I need some help, with my algebra

Viktor [21]

Answer:

Hey there!

Perimeter: 24

Area: 24

36+64=x^2

x=10

Perimeter: 10+6+8=24

Area: 1/2bh, 1/2(48)=24

Both the area and perimeter are 24.

Hope this helps :)

5 0

3 years ago

Read 2 more answers

I need help Whats the Domain and range

lukranit [14]

Domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

6 0

3 years ago

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.3 years, and standard deviation of

Zolol [24]

Answer:

probability of lasting longer = 1.7%

Step-by-step explanation:

We are given:

x' = 14 years

μ = 12.3 years

s = 0.8 years

Thus, let's use the formula for the Z-score value which is;

z = (x' - μ)/s

Thus;

z = (14 - 12.3)/0.8

z = 2.125

From the z-distribution table attached, the p-value is ;

P(x' > 2.125) = 1 - 0.983 = 0.017 = 1.7%

Thus,probability of lasting longer = 1.7%

5 0

3 years ago

According to Padgett Business Services, 20% of all small-business owners say the most important advice for starting a business i

elena-s [515]

Answer:

a) There is a 6.88% probability that none of the owners would say preparing for long hours and hard work is the most important advice.

b) There is a 1.93% probability that six or more owners would say preparing for long hours and hard work is the most important advice.

c) There is a 10.32% probability that exactly five owners would say having good financing ready is the most important advice.

d) The expected number of owners who would say having a good plan is the most important advice is 2.28

Step-by-step explanation:

Questions a), b), c) are all solved as binomial distribution problems.

Question d) is a simple calculation.

Binomial probability distribution

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

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

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.

For these problems

12 business owners were contacted, so $n = 12$ .

a. What is the probability that none of the owners would say preparing for long hours and hard work is the most important advice?

20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work, so $\pi = 0.2$ .

That is P(X=0) when $\pi = 0.2$ .

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

$P(X = 0) = C_{12,0}.(0.2)^{0}.(0.8)^{12} = 0.0688$

There is a 6.88% probability that none of the owners would say preparing for long hours and hard work is the most important advice.

b. What is the probability that six or more owners would say preparing for long hours and hard work is the most important advice?

20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work, so $\pi = 0.2$ .

This is:

$P = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

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

$P(X = 6) = C_{12,6}.(0.2)^{6}.(0.8)^{6} = 0.0155$

$P(X = 7) = C_{12,7}.(0.2)^{7}.(0.8)^{5} = 0.0033$

$P(X = 8) = C_{12,8}.(0.2)^{8}.(0.8)^{4} = 0.0005$

$P(X = 9) = C_{12,9}.(0.2)^{9}.(0.8)^{3} = 0.00006$

$P(X = 10) = C_{12,10}.(0.2)^{10}.(0.8)^{2} = 0.000004$

$P(X = 11) = C_{12,11}.(0.2)^{11}.(0.8)^{1} = 0.0000002$

$P(X = 12) = C_{12,12}.(0.2)^{12}.(0.8)^{0} = 0.000000004$

So:

$P = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.0155 + 0.0033 + 0.0005 + 0.000006 + 0.000004 + 0.0000002 + 0.000000004 = 0.0193$

There is a 1.93% probability that six or more owners would say preparing for long hours and hard work is the most important advice.

c. What is the probability that exactly five owners would say having good financing ready is the most important advice?

Twenty-five percent say the most important advice is to have good financing ready, so $\pi = 0.25$

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

$P(X = 5) = C_{12,5}.(0.25)^{5}.(0.75)^{7} = 0.1032$

There is a 10.32% probability that exactly five owners would say having good financing ready is the most important advice.

d. What is the expected number of owners who would say having a good plan is the most important advice?

Nineteen percent say having a good plan is the most important advice, so that is $0.19*12 = 2.28$

The expected number of owners who would say having a good plan is the most important advice is 2.28

4 0

3 years ago