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2 years ago

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the function of y= x^2 - 4x + 8 approximates the height y, of a bird and its horizontal distance, x as it flies from one fence p

ost to another all distances are in feet complete the square to find and interpret the extreme value vertex

2 answers:

Vika [28.1K]2 years ago

7 0

Rewrite the given equation as
$y=x^2-4x+8=x^2-4x+4+4=(x-2)^2+4$ .
Since $(x-2)^2\ge 0$ , you can conclude that the imimum value of y will be gained for the minimum value of $(x-2)^2$ . The minimum value of $(x-2)^2$ is 0 for x=2.
So, y(2)=0+4=4.
Answer: minimum value of y is 4, when x=2.

kogti [31]2 years ago

5 0

Answer:

Minimum at (2,4)

Step-by-step explanation:

Apex Verified,

I think the interpretation is straightforward from there.

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In a network of 40 computers, 5 hold a copy of a particular file. Suppose that 7 computers at random fail. Let F denote the numb

anzhelika [568]

Answer:

a. E(F)=0.875

b. 99.9976%

c. P(X=2)=0.1683

Step-by-step explanation:

a. We notice that this is a binomial distribution with the probability of success;

$p=\frac{5}{40}=0.125$

#We are given the sample size, n=7. The Expected value is calculated as:

$E(X)=np\\\\E(F)=np , n=7, p=0.125\\\\E(F)=7\times 0.125\\\\=0.875$

Hence the expectation, E(F)=0.875

b. To calculate the probability of the range of F, we need to calculate all possible outcomes of F in the given sample;

$P(X\leq 5)=1-P(X=6)-P(X=7)\\\\=1-{7\choose 6}(0.125)^6(1-0.125)^1-{7\choose 7}(0.125)^7(1-0.125)^0\\\\=1-0.000023365-0.000000476\\\\=0.999976158\\\\=99.9976\%$

Hence, the range of F is 99.9976%

c. The probability that F=2 is calculated using the binomial distribution function as:

$P(X=2)={7\choose 2}(0.125)^2(1-0.125)^5\\\\=0.1683$

Hence, the probability of F=2 is 0.1683

3 0

2 years ago

Cones A and B both have volume cubic 48π units, but have different dimensions. Cone A has radius 6 units and height 4 units. Fin

kogti [31]

Answer:

r = 2 units

h= 36 units

Step-by-step explanation:

Given That:

Cones A and B both have volume cubic 48π units

The volume of a cone = $\frac{1}{3} \pi r^2h$

So for cone A

$V_A = \frac{1}{3} \pi r_A^2 h_A$

Volume for cone B

$V_B = \frac{1}{3} \pi r_B^2 h_B$

Due to different dimensions;

Cone A has

radius = 6 units

height = 4 units

To determine the one possible radius and height for cone B;

we have

$\frac{1}{3} \pi r_A^2 h_A =\frac{1}{3} \pi r_B^2 h_B$

$\frac{1}{3} \pi (6)^2 (4) =\frac{1}{3} \pi r_B^2 h_B$

$150.9=\frac{1}{3} \pi r_B^2 h_B$

$150.9=1.047r_B^2 h_B$

$r_B^2 h_B=144.12$

$r_B^2 h_B=144$

Therefore; the only possible way for this equation is :

$r_B = (2)\\h_B = 36$

If we are to check: we will realize that;

$r_B^2h_B = (2)^2*36 =144$

Therefore, the possible radius for the cone B = 2 units and height = 36 units. Hence from the question, we are told they both have the same volume of 48 π units.

7 0

2 years ago

Read 2 more answers

The product of five rational numbers is positive. At most, of these rational numbers can be negative

Ivanshal [37]

Answer: A. 1

Step-by-step explanation:

sorry if im wrong

5 0

2 years ago

Which is the graph of linear inequality x – 2y ≥ –12?

Softa [21]

Answer: On a coordinate plane, a solid straight line with positive slope goes through (negative 8, 2) and (0, 6). Everything to the right of the line is shaded.

Step-by-step explanation:

4 0

2 years ago

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The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard d

Bezzdna [24]

Answer:

0% probability that it would take exactly 3.7 hours to construct a soapbox derby car

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Also, the probability of finding an exact value in the normal probability distribution is 0.

So

0% probability that it would take exactly 3.7 hours to construct a soapbox derby car

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2 years ago