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2 years ago

The graph of h is a translation 4 units right and 1 unit down of the graph of f(x) = x².

Mathematics

1 answer:

maxonik [38]2 years ago

6 0

9514 1404 393

Answer:

B. h(x) = (x -4)² -1

Step-by-step explanation:

The translation moved the vertex from (0, 0) to (4, -1). The vertex form equation is ...

h(x) = (x -h)² +k . . . . . quadratic with vertex (h, k)

Filling in the values of the vertex, we get ...

h(x) = (x -4)² -1

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Brook makes this conjecture: Because the angles are equal, the proportion of area of each sector relative to the area of the giv

AnnZ [28]

Answer:

The Brooks conjecture is true as the proportion of the area of a sector to the area of a circle is only dependent on the angle.

Step-by-step explanation:

The area of a sector for a radius r and an angle θ is given as

$\Delta Sector=\dfrac{1}{2}r^2\theta$

Whereas the area of a circle for a radius r is given as

$\Delta Circle=\pi r^2$

Now the ratio is given as

$\dfrac{\Delta Sector}{\Delta Circle}=\dfrac{\dfrac{1}{2}r^2\theta}{\pi r^2}$

Here as r is the radius of the circle and it is the same therefore the above ratio is simplified to

$\dfrac{\Delta Sector}{\Delta Circle}=\dfrac{\theta}{2\pi }$

Here as π is constant the only variable here is θ. Thus according to Brooks conjecture when the angles are equal, the proportion of area of each sector relative to the area of the given circle is also equal is true.

6 0

2 years ago

olice response time to an emergency call is the difference between the time the call is first received by the dispatcher and the

yan [13]

Answer:

0.7823 = 78.23% probability that the response time is between 3 and 9 minutes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 7.2 minutes and a standard deviation of 2.1 minutes.

This means that $\mu = 7.2, \sigma = 2.1$

For a randomly received emergency call, find the probability that the response time is between 3 and 9 minutes.

This is the pvalue of Z when X = 9 subtracted by the pvalue of Z when X = 3.

X = 9

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

$Z = \frac{9 - 7.2}{2.1}$

$Z = 0.86$

$Z = 0.86$ has a pvalue of 0.8051

X = 3

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

$Z = \frac{3 - 7.2}{2.1}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228

0.8051 - 0.0228 = 0.7823

0.7823 = 78.23% probability that the response time is between 3 and 9 minutes.

4 0

2 years ago

A circle has a diameter of 6 meters. Which statement about the circumference and area is true?

My name is Ann [436]

Answer:

The numerical value of the circumference is greater than the numerical value of the area.

6 0

2 years ago

Mr. and Mrs. Parker's bed is 2 1/3 yards wide. That also have 2 nightstands that are 22 inches wide. The bedroom wall is 12 1/2

vampirchik [111]

Conversions: to smallest (inches)
n= 22 inches
b= 2 1/3 yard = 84 inches
t= 12 1/2 feet = 150 inches

total space = t
night stand = n (2n for two nightstands)
bed=b

b+2n has to be < or = to t

84+2(22)=x
84+44=128
128 is < 150

therefore the answer is yes they will fit with 22 inches left over.

3 0

2 years ago

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Mr. Ramirez informs the students that some of the trees they plant will not survive their first year, so the class will take pre

Anni [7]

The percentage of trees that will survive are 26%

4 0

2 years ago

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