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2 years ago

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A container contains 13 almonds, 8 walnuts, and 19 peanuts. You randomly choose one nut and eat it. Then you randomly choose ano

ther nut. Find the probability that you choose a walnut on your first pick and an almond on your second pick.

1 answer:

Fantom [35]2 years ago

6 0

Answer: 8/40 and 13/40

Step-by-step explanation:

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The area of a rectangular painting is given by the trinomial x2 + 4x - 21. What are the possible dimensions of the painting? Use

zloy xaker [14]

To find the dimensions you can just factor the equation...

x^2+4x-21

x^2-3x+7x-21

x(x-3)+7(x-3)

(x+7)(x-3) and this is equal to LW or WL

And note that x>3 for any possible solution.

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If f Superscript negative 1 Baseline (x) = negative one-fifth x, what is f Superscript negative 1 Baseline (x) = one-fifth x?

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Answer:

a different inverse function

Step-by-step explanation:

If $f^{-1}(x)=-\frac{1}{5}x$ then $f^{-1}(x)=\frac{1}{5}x$ is a different inverse function.

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The second (inverse) function is the first reflected over the y-axis.

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The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

Step-by-step explanation:

Previous concepts

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".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

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

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

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: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

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

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

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2 years ago

A cereal company fills boxes with 16 ounces of cereal. The acceptable percent error in filling a box is 2.5%. Find the least and

Ket [755]

If the acceptable percent error is 2.5%, then the amount it can be over or under 16 oz is 0.4oz.
16 + 0.4
16 - 0.4
16.4 is the greatest, 15.6 is the least

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Which is the graph of the linear inequality 2x – 3y < 12? On a coordinate plane, a solid straight line has a positive slope a

RoseWind [281]

Answer:

A dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.

Step-by-step explanation:

To graph the solution set of the inequality 2x - 3y < 12, first plot the dashed line 2x - 3y = 12 (dashed because the inequality has sign < without notion "or equal to"). This line passes through the points (0,-4) and (3,-2) (their coordinates satisfy the equation of the line). this line has positive slope because

$3y=2x-12\\ \\y=\dfrac{2}{3}x-4$

and the slope of the line is 2/3.

Now, identify where the origin is (in the region or outside the region). Substitute (0,0) into the inequality:

$2\cdot 0-3\cdot 0=0$

This means coordinates of the origin satisfy the inequality, so origin belongs to the shaded region. Thus, shade that part which contains origin.

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