The water was pumped out of a backyard pond. What is the domain of this
graph?
Water Depth
110
100
90
80
70
50
40
30
20
10
1 2 3 4 5 6 7 8 9 10 11 12 13
Time (minutes)
Depth (inches)
0

Step-by-step explanation:

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The inverse of the graph is (b)

To determine the inverse of the graph, we have to swap the x and the y axes.

This means that we plot the y coordinates on the x coordinates and vice versa.

The interpretation of this on the given curve is that:

The vertical curve becomes an horizontal curve (as seen in graph b)

Hence, the inverse of the graph is (b)

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Yes all your used tiles are correct.

Let's solve the equation too

The value of variable x in the equation 2x+4=3x+(-1) is 5.

Equation is a relationship between two or more variables that are expressed in equal to form. Equation of twwo variable looks like ax+y=c. It cab be linear equation, quadratic equation and cubic equation. linear equation has a straight line curve.

We have been given equation 2x4=3x+(-1) and we have to solve the equation. Our equation has only one variable, so we have to solve for that variable only.

2x+4=3x+(-1)

2x+4=3x-1

5=x

Hence the value of x in the equation 2x+4=x+(-1) is 5.

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Answer:

Step-by-step explanation:

Refer to the attachment

Work Shown:

5x-6 = 44

5x-6+6 = 44+6 ... see note 1

5x = 50

5x/5 = 50/5 ... see note 2

x = 10

Answer:

This graph does not represent a function.

Step-by-step explanation:

The vertical line test describes how, in order to be a function, there must be only one output for every input. Remember, the input of a function is the "x" value and the output is the "y" value.

Because of the circular nature, this graph does not represent a function. As you can see, there are "x" values which could correspond with mutliple "y" values. For example, when x = 2, there are two "y" values:  y = -1 and y = -5.

The vertex form of all expressions is given below.

We have given that the expressions

We have to write the function in vertex form.

The vertex form of a quadratic function is given by f (x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Therefore the first equation

[tex]f(x)=(x-1)^2-7[/tex]

it can be written as

[tex]f(x)=1(x-1)^2+(-7)[/tex]

The second equation can be written as

[tex]f(x) = (x+1)^2 -7[/tex]

vertex for is,

[tex]f(x)=1(x-(-1))^2+(-7)[/tex]

The third equation is,

[tex]f(x) = (x -1)^2 - 5[/tex]

Vertex form is,

[tex]f(x)=1(x-1)^2+(-5)[/tex]

Forth equation is,

[tex]f(x) = (x +1)^2 +(- 5)[/tex]

Vertex form is,

[tex]f(x) =1 (x -(-1))^2 +(- 5)[/tex]

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The area of a regular hexagon with an apothem 18.5 inches long and a side 21 inches is 1, 165. 5 In²

The formula is given thus;

Area of hexagon = (1/2) × a × P

where a = the length of the apothem

P = perimeter of the hexagon

Given a = 18. 5 inches

Note that Perimeter, p = 6a with 'a' as side

p = 6 × 21 = 126 inches

Substitute values into the formula

Area, A = 1 ÷2 × 18. 5 × 126 = 1 ÷2 × 2331 = 1, 165. 5 In²

Thus, the area of the regular hexagon is 1, 165. 5 In²

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Using the hypergeometric distribution, it is found that there is a 0.1363 = 13.63% theoretical probability of 5 students from your school being selected as contestants out of 10 possible contestant​ spots.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

N = 130, k = 40, n = 10.

The theoretical probability of 5 students from your school being selected is P(X = 5), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,120,10,40) = \frac{C_{40,5}C_{80,5}}{C_{120,10}} = 0.1363[/tex]

0.1363 = 13.63% theoretical probability of 5 students from your school being selected as contestants out of 10 possible contestant​ spots.

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Kellie's original number given the analogy and corresponding equation is 13

let

(x × 2) × 3 = x + 65

2x × 3 = 65 + x

6x = 65 + x

6x - x = 65

5x = 65

x = 65/5

x = 13

check:

6x = 65 + x

6(13) = 65 + 13

78 = 78

Therefore, the unknown number, x is 13

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Answer:

x = z - m + y

Step-by-step explanation:

Given:

[tex]\displaystyle \large{z = m+x-y}[/tex]

To solve for x-term, we have to isolate it. We can do by subtracting m-term both sides and add y-term both sides.

[tex]\displaystyle \large{z-m+y=m+x-y-m+y}\\\\\displaystyle \large{z-m+y=x}\\\\\displaystyle \large{x=z-m+y}[/tex]

Therefore, the answer to this question is x = z - m + y

Please let me know if you have any questions regarding my answer or explanation!

Answer:

A.

Step-by-step explanation:

Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?

A.

2.8 pounds of apples and 4.8 pounds of grapes

B.

3.3 pounds of apples and 1.3 pounds of grapes

C.

3.8 pounds of apples and 1.8 pounds of grapes

D.

4.5 pounds of apples and 2.5 pounds of grapes

The transformation of a function may involve any change. The graph of g(x) is the graph of f(x) shifted 4 units to the right.

The transformation of a function may involve any change.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units, y=f(x+c) (same output, but c units earlier)

Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

As per the transformation of the function, if the function g(x) = f(x-4), then the graph of g(x) will be 4 units in the right of f(x).

Hence, the graph of g(x) is the graph of f(x) shifted 4 units to the right.

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Answer:

No solution

Step-by-step explanation:

[tex]3(5x - 4) < 15x \\ 15x - 12 < 15x \\ 15x - 15x < 12 \\ 0 < 12[/tex]

Answer:

just solve normally as if theres no x,

1. 26x

2. -7x

Answer:

Use given values of h and j, and find the value of k:

The equation is now:

Find the value of g when h is 2 and j is 3:

Correct choice is D

Answer:

D. 144

Step-by-step explanation:

Answer:

21 rounds

Step-by-step explanation:

[tex]1[/tex] [tex]round = 0.4km[/tex]

[tex]Total[/tex] [tex]distance = 8.4km[/tex]

[tex]8.4/0.4[/tex]

[tex]=21[/tex]

The number of rounds he makes, if he runs a total of 8.4 km distance.

[tex]\large\boxed{R=\frac{Total \: distance}{Distance \: covered \: in \: 1 \: round}}[/tex]

So, we'll have to divide the total distance covered by distance covered in 1 round.

Let's substitute according to the formula.

[tex]R= \frac{8.4}{0.4}[/tex]

= 21 rounds

Hence, the number of rounds he makes, if he runs a total of 8.4 km distance is 21

An absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean is; |x – 515| ≤ 114

A) We are told that;

Mean score = 515

Standard deviation = 114

We are now given that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean. Thus, the absolute value inequality is;

|x – 515| ≤ 114

B) The range of scores to within ±2 standard deviations of the mean is;

Range = 515 ± 2(114)

Range = 287 to 743

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Answer:

15 units

Step-by-step explanation:

15.0

Answer:

39 and 65

Step-by-step explanation:

the ratio of the two numbers is 3 : 5

sum the parts of the ratio, 3 + 5 = 8 parts

divide the sum by 8 to find the value of one part of the ratio

104 ÷ 8 = 13 ← value of 1 part of the ratio , then

3 parts = 3 × 13 = 39

5 parts = 5 × 13 = 65

the two numbers are 39 and 65

Answer:

8

Step-by-step explanation:

The median is the number right in the middle. Eight is in the middle of the number line making it the median.

The answer is A , for determining range look at Y-axis only from down to up .For this question we can also say

range: [1,7] , if both ends of the line are arrows it means the line goes from negative infinity to positive infinity (which means range is all real numbers) , but if the point is include just like this graph the points will be also include in range , but if the points are an empty circle the points won't be include for writing range

hope it helps

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Answer:

Step-by-step explanation:

Explanation

On a 6 sided die, there are three even numbers (2,4,6)

That's 1/2 the number on the die.

So getting 6 even numbers is

P(6) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.00781

Where did that extra 1/2 come from? Well one of the numbers thrown was an odd number, and it has to be counted.

P(7) = the same answer.                            0.00781

Total                                                           0.0156

Vowels = {a, e, i, o, u}

There are 5 vowels out of 26 letters in the English alphabet. This leaves 26-5 = 21 consonants.

The theoretical probability of getting a consonant is 21/26 = 0.8077 = 80.77% approximately

Wayne found the empirical probability of a consonant as 60% which is quite a distance away from the 80.77% mentioned. The discrepancy is likely because vowels are tended to be used quite often in many words.

Words that are composed of consonants only are quite rare, but they do happen. Example: "fly" is a word with only consonants. I'm considering y to be a consonant.

[tex]~~~~~~~~\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac 1{R_2}\\\\\\\implies \dfrac 1{R_2} = \dfrac{1}{R } - \dfrac 1{R_1}\\\\\\\implies \dfrac 1{R_2} = \dfrac{R_1 -R}{RR_1}\\\\\\\implies R_2 = \dfrac{RR_1}{R_1-R}\\\\\\\text{When}~ R= 24~ \Omega ~ \text{and}~ R_1 = 30~ \Omega,\\\\R_2 = \dfrac{24 \times 30}{30-24}~\Omega\\\\\\~~~~~=\dfrac{720}{6}~ \Omega\\\\\\~~~~= 120~ \Omega[/tex]

Answer:

Step-by-step explanation:

The profit = 150 000 - 120 000 = 30 000

………………………………………………………

The profit percentage is :

[tex]=\frac{30000}{120000} \times 100=0.25 \times 100 = 25 \%[/tex]

The area of the target which earns 30 points on a throw.

[tex]\huge\boxed{Formula: a= \pi{r}^{2}}[/tex]

[tex]4+3[/tex]

[tex]=7[/tex]

Let's solve

We have to find the answer in terms of π so, we'll just have to multiply the radius by itself.

[tex]a={7}^{2}[/tex]

[tex]\large\boxed{a= 49 \pi\: {in}^{2}}[/tex]

Hence, the area of the target which earns 30 points on a throw is 49π square inches.

Answer= Option B