1. If the domain of a function f(x) is the set {10, 20, 30}. What does the information tell you about f-1(x)?


2. If the graph of a function f(x) includes the point (3, 0), what point must the graph of f-1(x) include? Explain.


3.The first term in an arithmetic sequence is 2. The twelfth term is 211. Find the value of n so that an = 135.

Answer:

  4)  No, because over the long run your expected value is less than the cost to play

Step-by-step explanation:

The expected value is ...

  0.51×0.99 + 0.49×1.01 = 0.5049 +0.4949 = 0.9998

This expected value is less than the cost to play, so you will lose money in the long run. You should not play.

Answer:

Inter-quartile range =  3 .

Step-by-step explanation:

Given : diagram with data.

To find : What is the inter-quartile range of the given data set.

Solution : We have given data .

We can see from the given data lowest value of data is  15 .

highest value of data  = 21.

First quartile ( Q1) = 17

Second quartile (Q2) =18

Third quartile (Q3) = 20.

Inter-quartile range = Third quartile (Q3) - First quartile ( Q1) .

Inter-quartile range =  20 -  17

Inter-quartile range =  3 .

Therefore, Inter-quartile range =  3 .

For this case we expand the series for each value of "n":

[tex]125 (\frac {1} {5}) ^ {1-1} +125 (\frac {1} {5}) ^ {2-1} +125 (\frac {1} {5}) ^ {3 -1} +125 (\frac {1} {5}) ^ {4-1} =[/tex]

[tex]125+ \frac {125} {5 ^ 1} + \frac {125} {5 ^ 2} + \frac {125} {5 ^ 3} =\\125+ \frac {125} {5} + \frac {125} {25} + \frac {125} {125} =\\125 + 25 + 5 + 1[/tex]

So, the correct option is: A

Answer:

Option A

Answer:

It’s A

Step-by-step explanation:

Answer:

n is the fixed number of trials. x is the specified number of sucesses. N - X is the number of failures. P is the probablity of success on any given trail. 1 - P is the probabilty of failure on any given trial.

These probabilities hold for any value of X between 0 (lowest number of possible successes in n trials) and n (highest number of possible successes).

Hope this helps

Step-by-step explanation:

Answer:

A) 8x + 9y = −3

B) 6x + 7y = 1

We multiply A) by -(6/8)

A) -6x -6.75y = 2.25  then we add this to equation B

B) 6x + 7y = 1

.25y = 3.25

y = 13

and x = -15

Step-by-step explanation:

The value of x= -15 and the value of y= 13 for the given system of equations: 8x+9y=−3  and 6x+7y=1.

Let’s solve the system of equations:

8x+9y=−3

6x+7y=1

We can solve the system of equations using elimination.

Steps to solve:

1. Solve the second equation for y:

y= 1/7

​2. Substitute this value of y into the first equation:

8x+9(1/7)=−3

8x+9/7 =−3

8x=−120

x=−15

3. Substitute x=-15 back into the second equation to solve for y:

6(−15)+7y=1

−90+7y=1

7y=91

y=13

Therefore, the value of x= -15 and the value of y= 13 for the given system of equations: 8x+9y=−3  and 6x+7y=1.

Answer:

C.  two chords

Step-by-step explanation:

If the sides of an angle are inscribed in a circle that means that the endpoints of the sides of said angle lie on the circle.  That makes both of them chords.  

A diameter has to go through the center

A tangent is outside the circle

A radius comes from the center of the circle and meets the outside of the circle

The sides of an angle inscribed in a circle are two radii. These two radii connect from a single point on the circumference of the circle to two different points on the circumference.

In the field of Geometry, particularly in relation to circles, the sides of an angle that is inscribed in a circle constitute two radii. An inscribed angle is an angle formed by two lines (in this case, two radii) drawn from a single point on the circumference of a circle to two different points on the circumference. Therefore, the correct answer to the given problem would be option D, which states that the sides of an inscribed angle in a circle are two radii.

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Answer:

  29°

Step-by-step explanation:

Angles 1 and 8 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.

  m∠1 = m∠8

  3x+25 = 4x-17

  42 = m . . . . . . . . add 17-3x

Then the measure of ∠1 is 3·42 +25 = 151 (degrees), and the measure of its supplement, ∠2 is ...

  m∠2 = 180° -151° = 29°

Answer:

  B.)  24(y² -1)

Step-by-step explanation:

The denominator of the first fraction is 2³(y +1).

The denominator of the second fraction is 2·3(y +1)(y -1).

The LCD is the product of the unique factors to their highest powers:

  2³·3·(y +1)(y -1) = 24(y² -1)

Answer:

B

Step-by-step explanation:

Your answer should be C because the slope line is negative so you're answer should be negative

We are given y = ax + b.

Here, [a] represents the slope.

Which graph shows NEGATIVE SLOPE?

The graph starting at the upper left going to the bottom right is CHOICE C.

CHOICE C is the answer because the slope [a] must be negative.

Answer:

  1

Step-by-step explanation:

When you take the log of ...

  b = b^1

you get ...

[tex]\log_{b}{b}=1[/tex]

Answer:

If the semicircle rotated around the line, it would become a sphere. So, A. sphere.

Step-by-step explanation:

A sphere is generated when a semicircle is rotated about the line.

A solid of revolution is a solid figure obtained by rotating a plane curve around some straight line.

Sphere is the set of all points in three-dimensional space lying the same distance  from a given point  or the result of rotating a semicircle about one of its diameters.

According to the given question.

A semicircle is rotated about the line.

Now,

From the definition of sphere we can say that, when a semicircle is rotated about a line a sphere will generate.

Therefore, a sphere is generated when a semicircle is rotated about the line.

Find out more information about solid revolution and sphere here:

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Answer:

-12 is the correct answer

Answer:

The equation for the circle is (x-0)^2+(y+3)^2=25

Step-by-step explanation:

The radius is half the diameter.  To find the length of the diameter we need to calculate the distance that (3,1) is to (-3,-7) which is sqrt(6^2+8^2)=10 .

The radius is therefore 10/2=5.

We also need the center of the circle (the midpoint of a diameter is the center of a circle).  So we just need to average the x's and y's to find the midpoint between (3,1) and (-3,-7) which is (0,-3).

The equation for the circle is (x-0)^2+(y+3)^2=25

I just plugged my info into (x-h)^2+(y-k)^2=r^2

where (h,k) is center and r is radius

Answer:

  missing value: 7

Step-by-step explanation:

Put 2 where x is in the function and do the arithmetic.

  y = 5·2 -3 = 10 -3 = 7

The value corresponding to x=2 is y=7.

To complete the table of values for the function y = 5x - 3, you substitute the given x-value into the equation. The missing y-value for x=2 is 7.

The function provided is y = 5x - 3. This is a linear function. To get the y values, you need to substitute the x values from the table into this equation. For the last row where x = 2, substitute 2 into the equation:

y = 5(2) - 3 = 10 - 3 = 7

So, the y-value corresponding to x=2 is 7.

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Answer:

a red graph

Step-by-step explanation:

slope is 5 and the y intercept is negative 2(the y intercept is where the line crosses the y axis) then you rise over run

Answer:

D.Area of sector=88.31 square feet.

Step-by-step explanation:

We are given that a circle A and its radius is 15 feet.

The central angle is equal to 45 degrees.

Radius of circlle=15 feet

Angle at center=[tex]\theta=45^{\circ}[/tex]

We know that the area of sector

Area of sector=[tex]\frac{\theta}{360}\times \pi r^2[/tex].

We take value of [tex]\pi=3.14[/tex]

Substituting all given values in the given formula

Area of sector=[tex]\frac{45}{360}\times 3.14\times 15\times 15[/tex]

Area of sector=[tex]\frac{31792.5}{360}[/tex]

Area of sector= 88.3125 square feet

Hence, area of sector=88.31 square feet.Therefore, option D is correct answer.

Answer:

5 is the width and 7 is the length

Answer:

x=5 in (Width)

x+2=5+2=7 in (Length)

Step-by-step explanation:

You are given the equation 2x+2(x+2)=24 to solve for x where x is the width.

First step, use distributive property 2x+2x+4=24

Second step, subtract 4 on both sides  and combine the like terms on the left hand side: 4x=20

Divide both sides by 4:  x=20/4

So x=5 in

And since length is 2 more than the width so the length is 2+5=7 in

Answer:2.20

Step-by-step explanation:

[tex]\bf \textit{sum of all interior angles in a polygon}\\\\ n\theta =180(n-2)~~ \begin{cases} n=sides'~number\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =140 \end{cases}\implies n140=180(n-2) \\\\\\ 140n=180n-360\implies 140n+360=180n\implies 360=40n \\\\\\ \cfrac{360}{40}=n\implies 9=n[/tex]

Answer:

The area of the brick border is [tex](24x+144)\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of the brick border is equal to

[tex]A=(x+12)(x+12)-(x)(x)\\ \\A=(x+12)^{2} -x^{2}\\ \\A=x^{2}+24x+144-x^{2}\\ \\A=(24x+144)\ ft^{2}[/tex]

Answer:

B:  No

Step-by-step explanation:

P = 2L + 2W.  If L = 20 and W = 11, then P = 2(20) + 2(11), or 62.  This matches Answer B.

Answer:  The correct option is

(B) No. If the length is 20 and the width is 11, the perimeter is P = 40 + 22 = 62, not 64.

Step-by-step explanation:  Given that the perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle.

We are to check whether the perimeter of the rectangle can be 64 units when its width is 11 units and its length is 20 units.

According to the given information, we have

Length, L = 20 units,  width, W = 11 units  and  Perimeter, P = 64 units.

We have

[tex]P\\\\=2L+2W\\\\=2\times20+2\times11\\\\=40+22\\\\=62\neq64.[/tex]

Therefore, if length is 20 units and width is 11 units, then perimeter P = 40 + 22 = 62 units, not 64.

Thus, the answer is NO.

Thus, option (B) is CORRECT.

Answer:

B

Step-by-step explanation:

Assume the radius is r so the diameter is 2r

Height=2*d=2(2r)=4r since the diameter is twice the radius

Volume of cone=1/3 * pi*r^2*h

                         = 1/3 * pi*r^2*(4r)

                         =4/3 *pi *r^3

So B

Answer: B

h=2d

r=d/2

so h in terms of r is;

h=4r

V=pi*r^2*h/3

V=pi*r^2*4r/3=pi*4r^3/3=4/3(pi)(r^3)

Answer: perpendicular

Step-by-step explanation:

Lines with opposite and negated slopes are perpendicular, you can use desmos to graph and check

Answer:

Step-by-step explanation:

The product of the slopes (5/6), (-6/5) is -1, so the lines described by these functions are perpendicular.

Answer:

Step-by-step explanation:

a:  70°

Reason:  a is supplementary to the angle that measures 110°, so 180° - 110° = 70°

b:  55°

Reason:  b is vertical to the angle between 100° and 25° (which add up to 125°) and since all of those angles added together have to equal 180°, then the unidentified angle between 100° and 25° = 55°.  b is vertical to that angle so b = 55°

c:  25°

Reason:  c is vertical the angle measuring 25° so c = 25° also.

Answer:

The limitations on y-values changed from non-negative multiples of one-half to whole numbers, since Ezra cannot walk a fractional number of dogs.

The limitations on x-values did not change and must be non-negative multiples of one-half, since Ezra cannot work negative hours and charges by the half-hour.

The inequality x + y >= 1100 represents Ezra's earnings from his two jobs. If he changes his dog-walking fee to a per dog amount, the inequality changes to x + z >= 1100, shifting the solution set. This impacts the number of lawn mowing and dog walking jobs Ezra must do to earn at least $1100.

The question involves understanding of inequalities and how the solution set changes when the conditions change. Suppose Ezra earns x dollars for every lawnmowing job and y dollars for every dog-walking job. Then, his earnings would be represented by the inequality: x + y >= 1100.

Now, if he changes his dog-walking charges to be per dog instead of per hour, say z dollars per dog, we can modify our inequality to: x + z >= 1100.

The solution set for the new inequality would include all values of x and z that makes the inequality true - essentially how many lawn mowing and dogs walking jobs he needs to do to earn at least $1100. One thing to bear in mind is that both x and z must hold positive value since one cannot earn negative money from a job.

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Check the picture below.

[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=25\\ b=15 \end{cases}\implies \cfrac{(x-0)^2}{25^2}+\cfrac{(y-0)^2}{15^2}=1\implies \cfrac{x^2}{625}+\cfrac{y^2}{225}=1[/tex]

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =135\\ r=11.4 \end{cases}\implies s=\cfrac{\pi (135)(11.4)}{180}\implies s=8.55\pi \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill s\approx 26.86~\hfill[/tex]

Answer:

[tex]\boxed{\textbf{26.9 m}}[/tex]

Step-by-step explanation:

The formula for the arc (s) of a circle is

[tex]s = r\theta \times \dfrac{\pi  }{180^{^{\circ}}}[/tex]

where θ is measured in degrees.

Data:

r = 11.4 m

θ = 135°

Calculation:

[tex]s = \text{11.4 m} \times 135^{^{\circ}}\times\dfrac{\pi}{180^{^{\circ}}} = \textbf{26.9 m}\\\\\text{The length of the arc is }\boxed{\textbf{26.9 m}}[/tex]

Answer:

  f(w) = 3w + 2,000,000/w

Step-by-step explanation:

We know that the area of a rectangle is the product of its length and width:

  A = LW

Filling in the given values lets us write an expression for the length of the field.

  1,000,000 = Lw

  L = 1,000,000/w

Since there are 3 fences of length w and two of length L, the total perimeter fence length is the sum ...

  f(w) = 3w + 2(1,000,000)/w

Combining the constants, we have a function for the perimeter fence length in terms of the width of the field:

  f(w) = 3w +2,000,000/w

Final answer:

The function that models the amount of fencing required for a 1,000,000 square foot rectangular field divided in half by a fence is F(w) = 3w + 2,000,000 / w. This represents the total length of fencing as a function of the width w.

Explanation:

The student is asking for a function that models the amount of fencing required for a rectangular field with an area of 1,000,000 square feet, which is then divided in half by a fence parallel to the width, w. To begin, let's denote the length of the field as L and the width as w. Since the area of the rectangle is given by L multiplied by w, and we know that the area is 1,000,000 square feet, we can express the length L in terms of w as L = 1,000,000 / w.

Now, total fencing required would be the perimeter of the rectangle plus the additional fence dividing it in half. The perimeter is calculated as 2w + 2L. Therefore, the total fencing F in feet would be F(w) = 2w + 2L + w.

Substituting L with 1,000,000 / w, the function becomes F(w) = 2w + 2(1,000,000 / w) + w = 3w + 2,000,000 / w. This function represents the total length of fencing needed in terms of the width w of the field.

Answer:

x ≈ 46°

Step-by-step explanation:

Since the triangle is right use the sine ratio to solve for x

sinx = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{10}{14}[/tex], hence

x = [tex]sin^{-1}[/tex] ( [tex]\frac{10}{14}[/tex] ) ≈ 46°

Answer:

The last choice is the one you want.

Step-by-step explanation:

Simply take the x coordinate and subtract 4, then do the same with the y coordinate since the vector movement is <-4, -4>.  The first coordinate F is <4,0>.  Subtract 4 from both of those coordinates and end up at <0, -4>.  The second coordinate G is <1, 3>.  Subtract 4 from both of those and end up at <-3, -1>.  The third coordinate H is <2, 6>.  Subtract 4 from both of those and end up at <-2, 2>.  The last coordinate I is <4, 2>.  Subtract 4 from both of those and end up at <0, -2>.