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1 year ago

Which of the following could represent the graph of f(x) = y3 – x2 - 6x?

Mathematics

1 answer:

professor190 [17]1 year ago

6 0

Answer: A

Step-by-step explanation:

$x^{3}-x^{2}-6x=0 \\ \\ x(x^{2}-x-6)=0 \\ \\ x(x-3)(x+2)=0 \\ \\ x=-2, 0, 3$

So there needs to be roots at x=-2, 0, and 3.

Also, the end behavior needs to approach infinity as x approaches infinity and negative infinity as x approaches negative infinity (since the leading coefficient is positive). This rules out the last option.

Now, we can also use the fact that the maximum number of turning points is one less than the degree, for a maximum of 2 turning points. This rules out the middle option as well.

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Cloud [144]

Answer and Step-by-step explanation:

6(2x + 3y - 10) is the answer.

This is because 6 can be taken out from all 3 numbers, and will create these two factors, the factors being 6 and (2x + 3y - 10).

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Sam has two coupons for a bicycle. coupon A: $20 rebate on a $95 bicycle. coupon B: 25% off a $95 bicycle. choose the coupon tha

ANTONII [103]

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Step-by-step explanation:

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2 years ago

Give brainlest on time limit pls help

inysia [295]

Answer:

336 sq un

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The area of a rhombus is pq/2 where p and q are the diagonals.

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2 years ago

A laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighings. Scale readings in repeated we

weqwewe [10]

Answer:

99% confidence interval for the given specimen is [3.4125 , 3.4155].

Step-by-step explanation:

We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.

Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.

Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean weighing of specimen = $\frac{3.412+3.416+3.414}{3}$ = 3.414 g

$\sigma$ = population standard deviation = 0.001 g

n = sample of specimen = 3

$\mu$ = population mean

<em>Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).</em>

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

<u>99% confidence interval for</u> $\mu$ = [ $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $3.414-2.5758 \times {\frac{0.001}{\sqrt{3} } }$ , $3.414+2.5758 \times {\frac{0.001}{\sqrt{3} } }$ ]

= [3.4125 , 3.4155]

Therefore, 99% confidence interval for this specimen is [3.4125 , 3.4155].

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2 years ago