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3 years ago

What is the range of the function f(x)=(x-4)^2-5

Mathematics

2 answers:

Ksivusya [100]3 years ago

5 0

The answer to this question is a

uranmaximum [27]3 years ago

4 0

f(x) = (x - 4)^2 - 5

Vertex (4 , -5)

This function opens upward and has min. value = -5

So range y >= - 5

So answer is A. -5 <= f(x) < ∞

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Note angles not necessarily drawn to scale

kondaur [170]

Answer:

Step-by-step explanation:

Angles CGE and 30° are vertical angles.

Thus, Angle CGE is thus 30°.

Angle CGE and Angle x are complementary, so x = 90° - 30° = 60°

7 0

3 years ago

Read 2 more answers

Plz help me plz I really need help

Zolol [24]

Step 1: 198 × $\frac{1}{3}$ = 66, the number of men who left the party

Step 2: 256× $\frac{1}{4}$ = 64, the number of women who left the party

66+64=130

Since 130 is the number of people that left, you would subtract it from the total number of people at the party originally.

198+256=454

454-130=325

So, 325 people are left at the party

3 0

3 years ago

A foreign student club lists as its members 2 Canadians, 3 Japanese, 5 Italians, and 2 Germans. If a committee of 4 is selected

Fittoniya [83]

Answer:

(a) The probability that the members of the committee are chosen from all nationalities $=\frac{4}{33}$ =0.1212.

(b)The probability that all nationalities except Italian are represent is 0.04848.

Step-by-step explanation:

Hypergeometric Distribution:

Let $x_1$ , $x_2$ , $x_3$ and $x_4$ be four given positive integers and let $x_1+x_2+x_3+x_4= N$ .

A random variable X is said to have hypergeometric distribution with parameter $x_1$ , $x_2$ , $x_3$ , $x_4$ and n.

The probability mass function

$f(x_1,x_2.x_3,x_4;a_1,a_2,a_3,a_4;N,n)=\frac{\left(\begin{array}{c}x_1\\a_1\end{array}\right)\left(\begin{array}{c}x_2\\a_2\end{array}\right) \left(\begin{array}{c}x_3\\a_3\end{array}\right) \left(\begin{array}{c}x_4\\a_4\end{array}\right) }{\left(\begin{array}{c}N\\n\end{array}\right) }$

Here $a_1+a_2+a_3+a_4=n$

${\left(\begin{array}{c}x_1\\a_1\end{array}\right)=^{x_1}C_{a_1}= \frac{x_1!}{a_1!(x_1-a_1)!}$

Given that, a foreign club is made of 2 Canadian members, 3 Japanese members, 5 Italian members and 2 Germans members.

$x_1$ =2, $x_2$ =3, $x_3$ =5 and $x_4$ =2.

A committee is made of 4 member.

N=4

(a)

We need to find out the probability that the members of the committee are chosen from all nationalities.

$a_1$ =1, $a_2$ =1, $a_3$ =1 , $a_4$ =1, n=4

The required probability is

$=\frac{\left(\begin{array}{c}2\\1\end{array}\right)\left(\begin{array}{c}3\\1\end{array}\right) \left(\begin{array}{c}5\\1\end{array}\right) \left(\begin{array}{c}2\\1\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }$

$=\frac{2\times 3\times 5\times 2}{495}$

$=\frac{4}{33}$

=0.1212

(b)

Now we find out the probability that all nationalities except Italian.

So, we need to find out,

$P(a_1=2,a_2=1,a_3=0,a_4=1)+P(a_1=1,a_2=2,a_3=0,a_4=1)+P(a_1=1,a_2=1,a_3=0,a_4=2)$

$=\frac{\left(\begin{array}{c}2\\2\end{array}\right)\left(\begin{array}{c}3\\1\end{array}\right) \left(\begin{array}{c}5\\0\end{array}\right) \left(\begin{array}{c}2\\1\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }+\frac{\left(\begin{array}{c}2\\1\end{array}\right)\left(\begin{array}{c}3\\2\end{array}\right) \left(\begin{array}{c}5\\0\end{array}\right) \left(\begin{array}{c}2\\1\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }$ $+\frac{\left(\begin{array}{c}2\\1\end{array}\right)\left(\begin{array}{c}3\\1\end{array}\right) \left(\begin{array}{c}5\\0\end{array}\right) \left(\begin{array}{c}2\\2\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }$

$=\frac{1\times 3\times 1\times 2}{495}+\frac{2\times 3\times 1\times 2}{495}+\frac{2\times 3\times 1\times 1}{495}$

$=\frac{6+12+6}{495}$

$=\frac{8}{165}$

=0.04848

The probability that all nationalities except Italian are represent is 0.04848.

6 0

3 years ago

A circular swimming pool has diameter 60 feet and is centered in a fenced-in square region measuring 80 feet by 80 feet. a concr

borishaifa [10]

If I read the question correctly, the information about the 80x80 fencing and the grass region are all irrelevant information.

In order to find the area of the side walk we are going to use the formula A=pi(r^2) where r = the radius. The diameter of the pool is 60 feet and the the sidewalk is 5 feet bigger all around meaning we had 5 feet to both sides of this 60 feet giving you an overall diameter of 70 feet (or 60 + 5*2). To find the radius take half of the diameter. 70/2 = 35.

Now we plug in 35 to the equation. A = Pi(35^2) = 1225pi. Leave your answer like this as we are not finished and will need to round at the end for an accurate answer. This is NOT the end, that number is the area of the sidewalk AND the pool.

The sidewalk is not a full circle, just a border so we now have to find the area of the actual pool and subtract it from this 1225pi for the sidewalk's area. Same formula, Area = pi(r^2). The diameter of the pool is 60 meaning the radius is 30 (or 60/2). Plug into the equation, pi(30^2) = 900pi.

Now do 1225pi - 900pi to get 325pi. Break out your calculator and hit the approximation button. 325pi is approximately 1021.018 if rounded to 3 decimal places.

The area of the 5-foot wide sidewalk encircling the pool is approximately 1021.018 square feet.

5 0

3 years ago

When a river flows, the strength or force of the river depends on how far the river falls vertically compared to how far it flo

strojnjashka [21]

The figure is missing. There are several problems with same wording but different numbers

Here, we can use:

Horizontal distance: 258 feet

Vertical fall: 56.0 feet

Answer:

Slope = 56.0 ft / 258 ft ≈ 0.217

Explanation:

The <em>slope</em> measures how the rate of change of the vertical distance (vertical fall) with respect to the horizontal distance.

There are several forms to express this with words, which represent the same formula. Here are some of them:

Slope = rise / run
Slope = vertical change / horizontal change
Slope = change in y / change in x
Slope = Δy / Δx
Slope = (y₂ - y₁) / (x₂ - x₁)

As said, all those forms mean the same; they are equivalent.

Here, we have vertical fall = 56.0 feet, and horizontal distance = 258 feet, and by specifications of the problem (in the hint) the slope must be positive. Thus, you get:

Slope = vertical fall / horizontal distance = 56.0 feet / 258 feet ≈ 0.217

8 0

3 years ago