Using the given graph of the function​ f, find the following.
​(a) the​ intercepts, if any
​(b) its domain and range
​(c) the intervals on which it is​ increasing, decreasing, or constant
​(d) whether it is​ even, odd, or neither

Answer:

[tex]x=(x-3)^{\frac{9}{5}}[/tex]

Step-by-step explanation:

The first thing we are going to do is change both sides of the equation to be base (x-3):

[tex](x-3)^{log_{(x-3)}(x)}=(x-3)^{\frac{9}{5}}[/tex].

Now, since the log is in base (x-3), the base (x-3) and the log cancel out:

[tex]x = (x-3)^\frac{9}{5}[/tex]

This is the final answer.

Answer:

Step-by-step explanation:

The equation to solve the problem is:

x + 550 = 750

Explanation:

The manager has already distributed $550, and the remaining amount to distribute is represented by the variable x. Adding the distributed amount to the remaining amount should equal the total amount of tips the manager has, which is $750. Therefore, the correct equation is x + 550 = 750.

This question involves using the binomial distribution.

Let X be the number of male high school lacrosse players who will play at the college level out of the 20 selected players . We can model X as a binomial random variable with parameters n=20 and p=0.128, where p is the probability of success (i.e., a player going on to play at the college level).

The probability of exactly 4 players playing at the college level is given by the formula:

P(X=4) = (20 choose 4) * (0.128)^4 * (1-0.128)^(20-4)

Using a calculator, we can evaluate this expression to find:

P(X=4) = 0.155

Therefore, the probability that exactly four of the 20 male high school lacrosse players selected at random will end up playing at the college level is 0.155, or between C and 1 (inclusive).

Note that we rounded to three decimal places as requested .

Answer:

L'' = (6, - 5 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 3, y - 3 ) means

add 3 to the original x- coordinate and

subtract 3 from the original y- coordinate

then

L (3, - 2 ) → L'' (3 + 3, - 2 - 3 ) → L'' (6, - 5 )

Please upload an image or give a question.

Answer:

please see explanation and attachment

Step-by-step explanation:

√16 = 4.

√14 = ?

how do we get from 16 to 14? we subtract 2. r = remainder. denominator is twice √16, ie 8.

so we have 4 r -2 r 8

= 4 r -1 r 4

= 3 r 3 r 4

= 3.75

= 3.8 to nearest tenth

Amount of ice cream can the cone hold is, 9.8 inches³

We have to given that;

An ice cream cone has a height of 6 inches and a diameter of 2.5 inches.

Hence, We get;

Radius of cone = 2.5 / 2 = 1.25 inches

Since, We know that;

Volume of cone is,

V = πr²h/3

v = 3.14 × 1.25² × 6 / 3

V = 9.8 inches³

Hence, Amount of ice cream can the cone hold is, 9.8 inches³

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Answer:

972 square feet

Step-by-step explanation:

length, a, of rectangle with  width, b, will have area a X b (simplified to just ab).

so area = 36 (feet) X 27 (feet) = 972 (square feet)  

Answer:

Q6.  x = 8.1 ***

Q7   x = 27.87

***For question 6:  Your picture of question 6 is so blurred I could not really make out the angle; I took it as 36° . If it is something else, use the formula given below with the correct angle and compute **

Step-by-step explanation:

In right triangle, with one of the angles = θ , the following relationships hold

[tex]\cos \theta = \dfrac{adjacent}{hypotenuse}\\\\\sin\theta = \dfrac{opposite}{hypotenuse}\\\\\tan\theta = \dfrac{opposite}{adjacent}\\[/tex]

where

adjacent means side adjacent to θ
opposite means side opposite to θ

In the given figure in Q6,

θ = 36°  (I had difficulty making out the picture)

adjacent = x

hypotenuse = 10

so

[tex]\cos 36^\circ = \dfrac{x}{10}\\\\x = 10 \cdot \cos 36^\circ\\\\x = 10 \cdot 0.809\\\\x = 809\\\\\text{x = 8.1 rounded to the nearest tenth}[/tex]

I have answered question 7 also since it is very similar:

[tex]\sin 35^\circ = \dfrac{16}{x}\\\\x = \dfrac{16}{\sin 35^\circ}\\\\\\= \dfrac{16}{0.574}\\\\\\= 27.8745\\\\= 27.87 \text{ to the nearest hundredth\\}[/tex]

The area of the Japanese garden around the koi pond is 195.74 square feet.

To find the area of the Japanese garden around the koi pond, we need to subtract the area of the circular pond from the area of the rectangular garden. Let's use the given terms and follow these steps:
1. Calculate the area of the rectangular garden.
Area = Length × Width
Area = 16 feet × 14 feet
Area = 224 square feet
2. Calculate the area of the circular koi pond.
Area = π × (radius)^2
Area = 3.14 × (3 feet)^2
Area = 3.14 × 9 square feet
Area = 28.26 square feet
3. Subtract the area of the koi pond from the area of the garden.
Garden area around the koi pond = Area of the rectangle - Area of the circle
Garden area = 224 square feet - 28.26 square feet
Garden area = 195.74 square feet
Your answer: The area of the Japanese garden around the koi pond is 195.74 square feet.

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10.8

.......................................

Part 1a) An exponential function is a better model to represent the data because the rate of change is not constant instead of using a linear function, whose rate of change (slope) is constant.

Part 1b) The slope between each points are different.  So, the data is best represented by an exponential function.

Part 2a) The estimated number of college degrees earned in the United States in 2050 is about 2 million.

Part 2b) The estimated number is more likely to be an under-estimation.

Exponential equations increase by a constant exponent or power, written in the form of $$f(x) = ab{x}$$.

Linear equations or functions increase by a constant slope, written in the form of y = mx + b, where m is the slope.

Year    College degrees

            (  thousands)

1910                37

1930             122

1950            432

1970            792

1990          1,051

2010          1,650

Using exponential smoothing in Excel, the result of the prediction shows that 2,237,000 college degrees will be earned in 2050.

The number of college degrees earned in the United States in 2050 = 2,237,000 ≈ 2 million.

Learn more about exponential and linear functions at https://brainly.com/question/7296377.

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