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2 years ago

6

Determine the function which corresponds to the given graph. (3 points) a natural logarithmic function crossing the x axis at ne

gative two and y axis at one. The asymptote is x = -3

1 answer:

Mekhanik [1.2K]2 years ago

5 0

Answer:

$y=\log_3{(x+3)}$

Step-by-step explanation:

The parent log function has a vertical asymptote at x=0, so the asymptote at x=-3 indicates a left shift of 3 units.

The parent log function crosses the x-axis 1 unit to the right of the vertical asymptote, which this one does, indicating there is no vertical shift.

The parent log function has an x-value equal to its base when it has a y-value of 1. Here, the y-value of 1 corresponds to an x-value 3 units to the right of the vertical asymptote, so the base of this logarithm is 3.

The function is ...

$\boxed{y=\log_3{(x+3)}}$

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At a gas station, suppose that 45% of the customers purchase premium grade gas. Assume that these customers decide independently

valkas [14]

Answer:

The answer to the question is

The probability that at least one of the next three customers purchases premium gas is the complement of the probability that none of the next three customers purchase premium gas = 1 - (1-P(A))³ = 0.834

Step-by-step explanation:

The probability that a customer would purchase premium grade = 45 %

That is P(A) = 0.45 and

The probability that the customer would purchase another grade = P(B) = 0.55

Therefore the probability of at least one of the next three customers purchase premium gas is

P(k=0) = (1 - P)ⁿ and the probability of at least one customer purchases premium gas is the compliment of the probability that the next three customers purchase another gas brand

that is (1 - P(A))×(1 - P(A))×(1 - P(A)) = P(B)×P(B)×P(B) = 0.55³ and the complement is 1 - 0.55³ = 0.834

8 0

1 year ago

Read 2 more answers

Leena walked 2/3 of a mile What is 2/3 written as a sum of unit fractions with the denominator of nine

aliya0001 [1]

Bear in mind that multiplying anything, and anything whatsoever by 1, has a product of the anything itself.

so, let's multiply 2/3 by 1 then and check about,

$\bf \cfrac{same}{same}=1\qquad thus\cfrac{2}{3}\cdot 1\implies \cfrac{2}{3}\cdot \cfrac{3}{3}\implies \cfrac{6}{9}
\\\\\\
\textit{now, we can split that and write it as a sum}\implies \cfrac{1+5}{9}\implies \cfrac{1}{9}+\cfrac{5}{9}$

3 0

2 years ago

Jason is designing the packaging for a new brand of snack crackers. To fit on shelves, the package must not be more than 8 1/2 i

drek231 [11]

Answer:

Step-by-step explanation:

8 1/2 inches = $\frac{17}{2}$ inches

To fit on shelves, the package must not be more than 8 1/2 inches tall, it means the height of the package can be at $\frac{17}{2}$ inches

The box must be able to hold 100 cubic units of crackers. it means the volume of the box is 100 cubic units.

The base of the package to be squared

And we have the formula:

V = h*S (Area of the base)

=> S = V/h = 100 : $\frac{17}{2}$ = $\frac{200}{17}$

=> the side of square: $\sqrt{\frac{200}{17} }$

The dimensions for Jason's design are:

The height: $\frac{17}{2}$ inches

The length and width: $\sqrt{\frac{200}{17} }$

6 0

2 years ago

Suppose that the researchers wanted to estimate the mean reaction time to within 6 msec with 95% confidence. Using the sample st

Lisa [10]

Answer:

a) The 95% confidence interval would be given by (509.592;550.308)

b) n=523 rounded up to the nearest integer

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=530$ represent the sample mean for the sample

$\mu$ population mean

s=70 represent the sample standard deviation

n=48 represent the sample size (variable of interest)

Confidence =95% or 0.995

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are df=n-1=48-1=47

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,47)".And we see that $z_{\alpha/2}=2.01$

Now we have everything in order to replace into formula (1):

$530-2.01\frac{70}{\sqrt{48}}=509.692$

$530+2.01\frac{70}{\sqrt{48}}=550.308$

So on this case the 95% confidence interval would be given by (509.592;550.308)

Part b

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

Assuming that $\hat \sigma =s$

And on this case we have that ME =6msec, and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval is provided, $z_{\alpha/2}=1.96$ , replacing into formula (b) we got:

$n=(\frac{1.96(70)}{6})^2 =522.88 \approx 523$

So the answer for this case would be n=523 rounded up to the nearest integer

3 0

1 year ago

Question 10 Multiple Choice Worth 1 points)

zheka24 [161]

Answer:

Linearly, because the table shows that the sunflowers increased by the same amount each month

Step-by-step explanation:

Given the table

$\begin{array}{lcccc}\text{Month}&1&2&3&4\\ \\\text{Sunflowers}&15&17.2&19.4&21.6\end{array}$

Note that months change one-by-one (21-1, 3-2=1, 4-3=1).

Also

$17.2-15=2.2\ [\text{from month 1 to month 2}]\\ \\19.4-17.2=2.2\ [\text{from month 2 to month 3}]\\ \\21.6-19.4=2.2\ [\text{from month 3 to month 4}]$

This means the number of sunflowers increases linearly, because the table shows that the sunflowers increased by the same amount each month

3 0

1 year ago