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3 years ago

Which equation represents y= -x^2 + 6x + 7 in vertex form ?

Mathematics

1 answer:

Drupady [299]3 years ago

7 0

we are given

$y= -x^2 + 6x + 7$

we can use vertex form parabola formula

$y= a(x-h)^2+k$

so, we can complete x square

$y= -(x^2 - 6x - 7)$

$y= -(x^2 - 6x - 7+3^2-3^2)$

$y= -(x^2 - 6x +3^2-16)$

$y= -(x-3)^2+16$

so, option-A........................Answer

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If a pen and a pencil cost 1.10$ but the pen cost is 1$ more than pencil

Stella [2.4K]

Answer:

The pencil cost $0.05 and the pen cost $1.05.

Step-by-step explanation:

Let, the price of the pencil is $ .

Given that the pen costs a dollar more than the pencil,

So, the price of the pen=$+1.

Therefore, ++1=1.10

, 2+1=1.10

, 2=1.10–1

, 2=0.10

, =0.10/2

, =0.05

The pencil cost $0.05 and the pen cost $1.05.

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2 years ago

Florence looked at her school lunch account and realized it was –$10.83. Which statement accurately explains the value in her ac

Rudik [331]

Answer:

Step-by-step explanation:

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3 years ago

I’m haveing a hard time explaining why D is the right answer please help

Anon25 [30]

Because d actually collects data about what the people want.

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3 years ago

The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

hence,

$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

<em>Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection. </em>

This means that,

<em>Probability that at least one of them needs replacement at the first inspection = </em>

$\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021$

5 0

3 years ago

What is 2 x 9 x 18 x 28 x 46 x 58, its a hard question

Yuliya22 [10]

2x9 is 18x18 is 324 x28 is 9072 x 46 is 417,312 so the x 58 the answer is 24,204,096

8 0

3 years ago

Read 2 more answers