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3 years ago

The function g is a transformation of f. If g has a y-intercept at 4, which of the following functions could represent g?

Mathematics

1 answer:

guajiro [1.7K]3 years ago

8 0

Answer:

g(x) = f(x) - 2

g(x) = f(x + 2)

Step-by-step explanation:

y-intercept of a function:

The y-intercept of a function is the value of y when x = 0.

Function f:

Graph given in this question

When $x = 0, y = 6$ , so the y-intercept is 6.

Additionally, when $x = -2, y = 4$

If g has a y-intercept at 4, which of the following functions could represent g?

Either we subtract 2 from f, that is:

$g(x) = f(x) - 2$

Or we can also add 2 on the domain, that is, moving 2 units to the right, so:

$g(x) = f(x+2)$

So the first two options are correct.

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Is 4/5 greater or less than 7/12

Paha777 [63]

I would belive its great because if you have 4/5 of a pie compared to 7/12 of a pie having 4/5 would be more of the pie , I hope that helped that's how I have to think about fractions

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3 years ago

In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A

Marina86 [1]

Answer:

(a) 0.94

(b) 0.20

Step-by-step explanation:

From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let $p_1$ be the probability that a bearing meets the specification.

So, $p_1=0.9$

Sample size, $n_1=500$ , is large.

Let X represent the number of acceptable bearing.

Convert this to a normal distribution,

Mean: $\mu_1=n_1p_1=500\times0.9=450$

Variance: $\sigma_1^2=n_1p_1(1-p_1)=500\times0.9\times0.1=45$

$\Rightarrow \sigma_1 =\sqrt{45}=6.71$

(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.

So, $X\geq 440.$

Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56$ .

So, the probability that a given shipment is acceptable is

$P(z\geq-1.56)=\int_{-1.56}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}}=0.94062$

Hence, the probability that a given shipment is acceptable is 0.94.

(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.

Denote the probability od acceptance of a shipment by $p_2$ .

$p_2=0.94$

The total number of shipment, i.e sample size, $n_2= 300$

Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, $\mu_2$ , and variance, $\sigma_2^2$ .

Mean: $\mu_2=n_2p_2=300\times0.94=282$

Variance: $\sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92$

$\Rightarrow \sigma_2=\sqrt(16.92}=4.11$ .

In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85$ .

So, the probability that a given shipment is acceptable is

$P(z\geq0.85)=\int_{0.85}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}=0.1977$

Hence, the probability that a given shipment is acceptable is 0.20.

(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).

The area right to the z-score=0.99

and the area left to the z-score is 1-0.99=0.001.

For this value, the value of z-score is -3.09 (from the z-score table)

Let, $\alpha$ be the required probability of acceptance of one shipment.

So,

$-3.09=\frac{285.5-300\alpha}{\sqrt{300 \alpha(1-\alpha)}}$

On solving

$\alpha= 0.977896$

Again, the probability of acceptance of one shipment, $\alpha$ , depends on the probability of meeting the thickness specification of one bearing.

For this case,

The area right to the z-score=0.97790

and the area left to the z-score is 1-0.97790=0.0221.

The value of z-score is -2.01 (from the z-score table)

Let $p$ be the probability that one bearing meets the specification. So

$-2.01=\frac{439.5-500 p}{\sqrt{500 p(1-p)}}$

On solving

$p=0.9053$

Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.

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3 years ago

What is the solution of this equqtion? 1w= -17

devlian [24]

Answer:

-17

Step-by-step explanation:

1w= -17

(1)(-17)=

-17

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3 years ago

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Which property is shown below?

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Answer:

Step-by-step explanation:

The identity property for addition tells us that zero added to any number is the number itself.

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3 years ago

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Y= <br> Help me please thanks

MArishka [77]

The value of y will be equal to 4.61.

<h3>What is trigonometry?</h3>

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

The value of y will be calculated by using the Pythagorean theorem:-

a² + a² = (9√2)²

a = 9

Applying angle property in the triangle:-

$tan26 = \dfrac{MK}{9}$

9tan26 = MK

LM = 9 - 9tan26

LM = 9 - 4.38

LM = 4.62

Therefore the value of y will be equal to 4.61.

To know more about Trigonometry follow

brainly.com/question/24349828

#SPJ1

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2 years ago