Choose the system for the graph.
y 2 2x+2
y2-x
A.
B.
C.
D.
≤ 2x - 1
yz -x + 2
y≤-2x + 2
(y 2 x
ys 2x + 2
y >- 1x

The inverse of a function is given as √x - 1

To get the inverse of any function f(x) we need to ensure that it passes the horizontal line test.

Given the following function

f(x) = (x+1)^2

Let y= f(x) to have:

y = (x+1)^2

Replace y with x to have:

x = (y+1)^2

Make y the subject of the formula

√x =y + 1

Subtract 1 from both sides

√x - 1 = y

Swap

y = √x - 1

Hence the inverse of a function is given as √x - 1

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Answer:

[tex] - \frac{ \sqrt{2} }{2} [/tex]

Step-by-step explanation:

The sine of an angle is equal to the y coordinate point where the terminal side of the angle intersects the unit circle.

Answer:

y = 2x - 11.

Step-by-step explanation:

Use the point-slope form of the straight line.

y - y1 = m(x - x1)   where m = slope and (x1, y1) is the given point.

Here m = 2 and (x1, y1) = (7,3) so the equation is:

y - 3 = 2(x - 7)

y - 3 = 2x - 14

y = 2x - 11

The statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.

To determine which statement is true, we need to know the conditions for continuity and differentiablity of a function.

So, since f(x) = {x² - 1 if -1 ≤ x ≤ 3 and x²/3 if 3 < x ≤ 8}

From the equality on the first condition,we see that f(x) is exists at x = 3 but is not continuous since f(x) changes to another function when x > 3. So,left hand limit of f(x) and the right hand limit of f(x) as x → 3 are not equal.

That is [tex]\lim_{x \to 3^{-} } f(x) \neq \lim_{x \to 3^{+} } f(x)[/tex] . Thus, the function is discontinuous at x = 3.

For differentiability, both conditions must be met. Since only one condition is met, it is non-differentiable.

So, the function is discontinuous and non-differentiable at x = 3.

So, the statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.

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The required minimum sample size to construct a 95% confidence level for the population mean is 267.

In this question,

In the probability and statistics theory, the confidence interval of the population parameter is the estimated range of values we are sure with a certainty that our parameter will lie within, the range being calculated from the sample obtained. The smaller is the margin of error, the more confidence we have in our results.

The population standard deviation, σ = 25

Confidence level for the population mean = 95%

Margin of error = ±3

Let n be the sample size of the population

The z-score for the confidence level of 95% for the population mean is 1.96.

The formula of margin of error is

[tex]E=\frac{z \sigma}{\sqrt{n} }[/tex]

Now, the sample size of the population can be calculated as

[tex]n=(\frac{z\sigma}{E} )^{2}[/tex]

On substituting the above values,

⇒ [tex]n=(\frac{(1.96)(25)}{3} )^{2}[/tex]

⇒ [tex]n=(\frac{49}{3}) ^{2}[/tex]

⇒ [tex]n=(16.33)^{2}[/tex]

⇒ n = 266.77 ≈ 267

Hence we can conclude that the required minimum sample size to construct a 95% confidence level for the population mean is 267.

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The intervals which represents those in which case the function, f(x) is reducing are as follows; [–2.5, –2], [–2, –1.5], [1.5, 2], [2, 2.5].

It follows from the complete task content that the x-intervals between which the function value of f(x) is reducing are to be identified from the graph as attached.

On this note, by observation on the graph, it follows that from between the interval; [–2.5, –2], the function f(x) is decreasing.

Also, between the interval; [–2, –1.5], the function f(x) is decreasing.

Also, between the interval; [1.5, 2], the function f(x) is decreasing.

Also, between the interval; [2, 2.5], the function f(x) is decreasing.

Remark: The answer choices are as follows; [–2.5, –2] [–2, –1.5] [–1, 1] [1.5, 2] [2, 2.5) [2.5, 3]

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The time it was when Frank left the playground is; 6:10 PM.

We are given;

Time at which Frank went to the playground; 5:20 p.m

Amount of time that frank played on the slide = 45 minutes

Amount of time that frank swings on the play ground = 5 minutes

Now, we are told that after he played on the slide and swung on the playground, that he went home.

Thus, he spent a total time of 45 + 5 = 50 minutes on the playground before going home.

Thus, time he went home = 5:20 p.m + 50 minutes = 6:10 p.m

Thus, we can conclude that the time it was when Frank left the playground is; 6:10 PM.

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Applying properties of exponents, the quotient is given as follows:

[tex]2\sqrt[3]{3} - \sqrt[3]{18}[/tex]

The expression is given by:

[tex]\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}}[/tex]

The 3 can be inserted into the cube root, as follows:

[tex]\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}} = \frac{6 - \sqrt[3]{6 \times 3³}}{\sqrt[3]{9}}[/tex]

Applying the subtraction, we have that the expression is:

[tex]\frac{6}{\sqrt[3]{9}} - \frac{\sqrt[3]{162}}{\sqrt[3]{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{\frac{162}{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{18}[/tex]

The denominator can be simplified as follows:

[tex]\sqrt[3]{9} = \sqrt[3]{3^2} = 3^{\frac{2}{3}}[/tex]

Then:

[tex]\frac{6}{\sqrt[3]{9}} = \frac{2 \times 3}{3^{\frac{2}{3}}} = 2 \times 3^{1 - \frac{2}{3}} = 2 \times 3^{\frac{1}{3}} = 2\sqrt[3]{3}[/tex]

Hence the quotient is given by:

[tex]2\sqrt[3]{3} - \sqrt[3]{18}[/tex]

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The equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A).

The equation of the line is represented by a polynomial of the form y = m · x + b, where m is the slope of the line and b is the intercept of the line. The slope is equal to the change in the dependent variable (Δy) and in the independent variable (Δx) and the intercept is the vertical distance of the line with the origin when x = 0.

In accordance with the picture, we notice that the scatter plot indice that Δy < 0 and Δx > 0 and therefore, m < 0. Besides, the intercept of the equation of the line must be greater than zero. Thus, the equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A)

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Check the picture below.

to get the equation of any straight line, we simply need two points off of it, so let's use those in the picture

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{6 -1}{4 +2} \implies \cfrac{ 5 }{ 6 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{5}{6}}(x-\stackrel{x_1}{(-2)})\implies y-1=\cfrac{5}{6}(x+2) \\\\\\ y-1=\cfrac{5}{6}x+\cfrac{5}{3}\implies y=\cfrac{5}{6}x+\cfrac{5}{3}+1\implies y=\cfrac{5}{6}x+\cfrac{8}{3}[/tex]

Answer:

109°

Step-by-step explanation:

The sum of angles in all triangles is equal to 180. For this given triangle, we can solve for x.

48° + 23° + x° = 180°
180° - 71° = x°
x = 109°

The computation shows that the value of b will be 91.864.

From the information given, we are told to find the value of b (b - 4.21 = 87.654). This will be:

b - 4.21 = 87.654

b = 87.654 + 4.21

b = 91.864

Also. dividing 1.86 and 8.4 will be:

= 1.86/8.4

= 0.2213

Therefore, the values are 91.864 and 0.2213.

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688,747,536 ways in which the people can take the seats.

There is a 2 by 10 rectangular greed of seats with people. so there are 2 rows of 10 seats.

When the whistle blows, each person needs to change to an orthogonally adjacent seat.

(This means that the person can go to the seat in front, or the seats in the sides).

This means that, unless for the 4 ends that will have only two options, all the other people (the remaining 16) have 3 options to choose where to sit.

Now, if we take the options that each seat has, and we take the product, we will get:

P = (2)^4*(3)^16 = 688,747,536 ways in which the people can take the seats.

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The value of x in 6/7x + 1/2 = 7/8 is 7/16

The equation is given as:

6/7x + 1/2 = 7/8

Subtract 1/2 from both sides

6/7x + 1/2 -1/2 = 7/8 -1/2

Evaluate the difference

6/7x = 3/8

Multiply both sides by 7

6x = 21/8

Divides both sides by 6

[tex]x = \frac {7}{16}[/tex]

Hence, the value of x is 7/16

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The coefficient of determination is 1.

Given

Total Sum of squares (SST) = 90

Sum of squares due to error (SSE) = 0

We have to find coefficient of determination.

The correlation of determination is the ratio of the explained variation to the total variation.

The coefficient of determination is used to analyze how differences in one variable can be explained by a difference in a second variable.

The coefficient of determination is also called r-squared or r-square.

Its the percentage of variation in the y-variable(response) that can be explained by the least squares regression line of y on x.

Coefficient of determination can be found with the following formula:

Formula of coefficient of determination :

[tex]R^{2} = 1 - \frac{SSE}{SST}[/tex]

= 1 - [tex]\frac{0}{90}[/tex]

= 1 - 0

= 1

[tex]R^{2}[/tex] = 1

Therefore,

The coefficient of determination is 1.

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The expression that represent the given statement is p/q - m²

From the question, we are to write an expression for the word problem

We are to write an expression for the statement

"Subtract the square of m from the ratio of p and q"

Square of m = m²

Ratio of p and q = p/q

Thus,

subtract the square of m from the ratio of p and q, becomes

p/q - m²

Hence, the expression that represent the given statement is p/q - m²

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Answer:

3/10

Step-by-step explanation:

=4/7 + 9/70 - 4/10

=l.C.M of 7 , 70 and 10 =70

=4/7 .10/10 +9/70 -4/10 .7/7

=40/70 +9/70 -28/70

=40+9-28/70

=49-28/70

=21/70

=3/10

Answer:

22

I remember this question in school

Assuming there are at least 12 of each kind of cupcake, number of ways can you choose 12 cupcakes is; 1399358844975 ways

We are given the quantity of each type of cupcake as follows;

Number of types of cupcakes = 5

Number of Chocolate Cupcakes = 12

Number of Vanilla Cupcakes = 12

Number of Lemon cupcakes = 12

Number of Strawberry Cupcakes = 12

Number of coffee cupcakes = 12

Thus, total number of cupcakes will be gotten by adding all the quantities given above of the different types of cupcakes and we will get; Total number of cupcakes = 12 + 12 + 12 + 12 + 12

Total number of cupcakes = 60

Now, since there is no order of selection, then the number of ways that you can choose 12 cupcakes will be gotten by using the combination formula which is; nCr = n!/(n!(n - r)!)

Thus, number of ways that you can choose 12 cupcakes =

60C12 = 60!/(12! * (60 - 12)!) = 1399358844975 ways

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[tex] \rm9(a + 4b + 3c) \\ 9(a) + 9(4b) \rm+ 9(3c) \\ \rm 9a + 36b + 27c \\ \therefore \tt9(a + 4b + 3c) = 9a + 36b + 27c[/tex]

Step-by-step explanation:

Circumference = πd

= π × 12

= 37.6991

=38

Answer:38

Step-by-step explanation:

Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:

Polynomial functions are known to be a kind of an expressions that is made up of a set of variables of different extent or degrees, non-zero coefficients, positive exponents (of variables), and also it is made up of constants.

Note that the equation of the functions are stated as:

f(x) = 2x² + 7x + 6

g(x) = 2^x + 5

The right and next thing to do is to plot a graph of both functions (see image attached)

From the graph, we have the fact that Both f(x) and g(x) have the same y-intercept of (0,6)

Therefore, Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:

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Answer:

(2030)4

Step-by-step explanation:

Base 6 to decimal calculation:

(352)6 = (3 × 62) + (5 × 61) + (2 × 60) = (140)10

Decimal to base 4 calculation:

Divide by the base to get the digits from the remainders:

= (2030)4

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The answer is 2030.

First, convert from base 6 to base 10.

Now, convert from base 10 to base 4.

Connecting the digits, the answer is : 2030

Answer:

9/14.

Step-by-step explanation:

The probability is given as a fraction or percentage.

9:5 odds in favour of a horse winning  means the horse will win 9 races for every 5 it does not win.

So the probability that this horse will win is 9/(9+5)

= 9/14.

Answer:

B.  -x³ - 9x².

Step-by-step explanation:

- (3x³ + x²) +2 (x³ - 4x²)

= -3x³  + 2x³  - x² - 8x²

= -x³ - 9x²

Answer: [tex]\Large\boxed{-x^3-9x^2}[/tex]

Hi there! By my calculation, I got the answer above. However, it doesn't fit any one of the answer choices. I am not sure if I am totally correct, but I have been double-checking my answers. Please let me know whether it's the answer choices mistaken or I am wrong so that I could modify my answer if necessary.

Step-by-step explanation:

Given expression

- (3x³ + x²) +2 (x³ - 4x²)

Expand parenthesis by the distributive property

= -3x³ - x² + 2x³ - 8x²

Combine like terms

= -3x³ + 2x³ - x² - 8x²

[tex]\Large\boxed{=-x^3-9x^2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The value of x in the angles of Quadrilateral is 52 degree.

According to the statement

we have given a four angles and we have to  find the value of x in these give angles.

From given 4 angles it is clear that the these angles are of a quadrilateral.

And we know that the

A quadrilateral is a four-sided polygon, having four edges and four corners.

And the sum of all angles of a quadrilateral is 360 degree.

so,

50° + 3X + X + (X+110) = 360 degree

50° + 4X + (X+110) = 360 degree​

50° + 5X + 110 = 360 degree

160° + 5X  = 360

5X = 360-100

5X = 260

X = 52 degree.

So, The value of x in the angles of Quadrilateral is 52 degree.

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The general expression is 130 x - 600 and total points scored by the player is 1220

A) Let the number of correctly answered questions be x.

∴ Number of incorrectly answered questions will be 20 - x.

+ 100 points is awarded for each question answered correctly while -30 points is awarded for each question answered incorrectly.

Thus, the general equation becomes

= 100x - (20 - x)(-30)

= 100x +30x - 600

= 130x - 600

Thus the general expression becomes 130 x - 600

B)  The player answers 14 questions correctly, thus x = 14

Substituting the value of x =14 in the general equation we get,

= 130(14) - 600

= 1820 - 600

= 1220.

Thus the total points scored by the player will be 1220

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Answer:

Step-by-step explanation:

The reflection preserves the side lengths and angles of triangle ABC. The dilation preserves angles but not side lengths.