Which function has an inverse that is also a function?
A. {(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)}
B. {(-4, 6), (-2, 2), 6-1, 6), (4, 2), (11, 2)}
C. {(-4,5), (-2, 9), (–1, 8), (4, 8), (11,4)}
D. {(-4, 4), (-2, -1), (–1, 0). (4.1), (11, 1)}

Answer:

R 237.67  monthly

Step-by-step explanation:

Ordinary annuity  

PV = C [  1 - (1+i)^-n] / i

PV = 11000 - .08 (11000) = 10120

i= .06/12=.005       n = 4 yrs x 12months =48

Plug in the numbers and calculate 'C'  = 237.67

The measure of the angle indicated is 104 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

There are intersecting chords on the circle

Using teh equation of intersecting chords, we have

? = 1/2 * Sum of the intersecting arcs

substitute the known values in the above equation, so, we have the following representation

? = 1/2 * (130 + 78)

Evaluate

? = 104 degrees

Hence, the measure of the angle indicated is 104 degrees

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The probability distribution of y is:

y = 0: 0.16

y = 1: 0.24

y = 2: 0.14

y = 3: 0.10

To determine the probability distribution of the random variable y, which represents the number of days beyond Wednesday it takes for both magazines to arrive, we can construct a tree diagram to visualize the different combinations of arrival days for the two magazines.

In the tree diagram, the first generation of branches represents the possible arrival days for Magazine 1 (M1), and the second generation represents the possible arrival days for Magazine 2 (M2).

The numbers in parentheses represent the value of y, the number of days beyond Wednesday. For example, (1) indicates y = 1, which means both magazines arrive on Thursday.

To determine the probability associated with each outcome, we multiply the probabilities of the individual branches along the corresponding paths.

Using the provided probabilities:

P(W) = 0.40, P(T) = 0.30, P(F) = 0.20, P(S) = 0.10

The probability distribution of y is as follows:

y = 0: P(M1 = W and M2 = W) = P(W) * P(W) = 0.40 * 0.40 = 0.16

y = 1: P(M1 = W and M2 = T) + P(M1 = T and M2 = W) = P(W) * P(T) + P(T) * P(W) = 0.40 * 0.30 + 0.30 * 0.40 = 0.24

y = 2: P(M1 = W and M2 = F) + P(M1 = T and M2 = T) + P(M1 = F and M2 = W) = P(W) * P(F) + P(T) * P(T) + P(F) * P(W) = 0.40 * 0.20 + 0.30 * 0.30 + 0.20 * 0.40 = 0.14

y = 3: P(M1 = W and M2 = S) + P(M1 = T and M2 = F) + P(M1 = F and M2 = T) + P(M1 = S and M2 = W) = P(W) * P(S) + P(T) * P(F) + P(F) * P(T) + P(S) * P(W) = 0.40 * 0.10 + 0.30 * 0.20 + 0.20 * 0.30 + 0.10 * 0.40 = 0.10

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The verdict which is true about the radius of all three arcs when constructing an angle bisector is; - No; the second two arcs must have the same radius but it can be different from the first.

The correct answer option is option C.

Recall that an angle at point, O is formed by the intersection of two lines; say lines A and B.

Hence, in a bid to draw the Angie bisector of the angle; AOB, three arcs are needed.

The first arc is an arc drawn by placing the pivot of the compass at the point, O and drawing an arc which intersects lines A and B. The radius of this first arc in discuss can be any value.

Subsequently, the other two arcs are propagated using the points of intersection of the first arc with both lines such that the two arcs intersect.

It is however noteworthy to know that these two arcs must have the same radius.

Ultimately, the second two arcs must have the same radius but it can be different from the first.

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a) The length of p is 21.4 cm

b) The measure of angle P is 45.6°

From the question, we are to determine the length of p

From the Pythagorean theorem, we can write that

30² = 21² + p²

p² = 30² - 21²

p² = 900 - 441

p² = 459

p = √459

p = 21.4 cm

∴ The length of p is 21.4 cm

b)

Measure of angle P

Using SOH CAH TOA

\(cos P= \frac{21}{30}\)

cos P = 0.7

P = cos⁻¹(0.7)

P = 45.6°

Hence, the measure of angle P is 45.6°

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Answer:

d = 1 + 3p  

Step-by-step explanation:

Leon already ran 1 miles on his own and he is expected to cover a distance d of 3 miles during each practice. The number of practices is expressed as p and the distance covered is expressed as d.

For every track practice he is expected to cover a distance of 3 miles. Recall he has already cover 1 mile on his own.

Therefore, the relationship between the practices p and the distance d can be expressed as follows.

number of track practice = p

distance covered = d

The distance covered  d in miles is 1 miles plus the number of track practice p multiply by 3

d = 1 + 3p  

Answer:

They are the same equations. (I don't know what you mean by "true.")

Step-by-step explanation:

If you divide 2x + 2y = 6 by 2, it turns into x + y = 3. This means that the graphs of the lines are the same, or there are infinite solutions.

I am really sorry if this is wrong because I am not really sure what you meant by "Which statement is true?"

Therefore, the probability of landing on a blue and a number greater than 3 is 1/24 or approximately 0.042.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there is one favorable outcome (heads) out of two possible outcomes (heads or tails). Probability is used in many fields, including mathematics, statistics, physics, engineering, and finance. It is used to make predictions and to estimate the likelihood of various outcomes. In addition, probability theory provides a framework for analyzing and understanding random processes, which occur in many real-world situations.

Here,

To find the probability of landing on a blue and a number greater than 3, we need to first identify all the possible outcomes when spinning both spinners.

The first spinner has four equally likely outcomes (red, blue, green, and yellow), and the second spinner has six equally likely outcomes (1, 2, 3, 4, 5, and 6). Therefore, there are a total of 4 x 6 = 24 possible outcomes.

We need to find the number of outcomes where we spin a blue on the first spinner and a number greater than 3 on the second spinner. There is only one blue section on the first spinner, and there are three sections with numbers greater than 3 on the second spinner (4, 5, and 6). Therefore, there is only one possible outcome that satisfies both conditions, which is landing on blue and a number greater than 3.

So the probability of landing on a blue and a number greater than 3 is 1 out of 24 possible outcomes:

P(blue and number > 3) = 1/24

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The decision-maker is willing to pay a risk premium of $250 to eliminate the risk of lottery p', and a risk premium of $500 to eliminate the risk of lottery p?. Therefore, the decision-maker prefers lottery p?.

The decision-maker's utility function suggests that they have a logarithmic utility index, v(r) = In(2). To calculate the risk premia, we compare the expected utilities of the lotteries. For lottery p', the expected utility is E[v(p')] = (1/2) * v(-1000) + (1/2) * v(0) = (1/2) * In(2) + (1/2) * In(2) = In(2). For lottery p?, the expected utility is E[v(p?)] = v(-500) = In(2). Since both lotteries have the same expected utility, the decision-maker is indifferent between them in terms of expected utility.

However, the decision-maker is risk-averse, which means they prefer to eliminate risk when possible. To eliminate the risk of lottery p', the decision-maker is willing to pay a risk premium of $250 (which is half the difference between the potential losses of $1000 and $0). On the other hand, to eliminate the risk of lottery p?, the decision-maker is willing to pay a risk premium of $500 (the full potential loss amount).

Therefore, the decision-maker prefers lottery p? as they are willing to pay a higher risk premium to eliminate its risk.

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The roller coaster track, shaped like a parabola, has a maximum height of 90 feet. The equation of the track is y = (-1/10)x^2 + 90.



To find the equation of the parabolic portion of the roller coaster track, we can use the vertex form of a parabola equation, which is given by:

y = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola.

Given that the maximum height is 90 feet, the vertex will be the highest point on the track. The y-coordinate of the vertex will be 90, and since the x-coordinate is not provided, we can assume it to be 0.

So, we have:

y = a(x - 0)^2 + 90

y = ax^2 + 90

To determine the value of 'a', we need another point on the parabola. Let's assume that the track is symmetrical, meaning that it descends symmetrically from the vertex. In that case, we can assume another point (x, y) on the parabola to be (-x, y).

For this point, we have:

y = a(-x)^2 + 90

y = ax^2 + 90

Now, let's substitute the coordinates (x, y) = (-x, y) = (-30, 0) into the equation:

0 = a(-30)^2 + 90

900a = -90

a = -1/10

Therefore, the equation of the parabolic portion of the roller coaster track is:

y = (-1/10)x^2 + 90

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\(\Large\underline{\rm Solution :- }\)

According to the Question ,

\(\implies Volume = \pi r^2 h \)

And ,

Therefore ,

\(\implies Volume = \pi r^2h \\\\\implies Volume = \pi \times (2x + 4)^2 \times (-3x ) \\\\\implies Volume = \pi ( 4x^2 + 16x + 16 ) (-3x) \\\\\implies \underline{\boxed{Volume = \pi ( -12x^3 - 48x - 48 ) }}\)

Answer: S and T.

Step-by-step explanation:

I watched a video on how to do this just to answer, so it might not be right LOL. But since the angles are the same if you draw them from each other they both show the angles are equal which means the lines are parallel.

Answer:

uhm chile sooooo anywayzz

Step-by-step explanation:

The given two-way Frequency table, there are 33 left-handed students who are not in the music program.

The number of left-handed students who are not in the music program, we need to examine the data presented in the two-way frequency table.

From the table, we can see that the number of left-handed students in the music program is 15, and the total number of left-handed students is 48.

the number of left-handed students not in the music program, we subtract the number of left-handed students in the music program from the total number of left-handed students.

Number of left-handed students not in the music program = Total number of left-handed students - Number of left-handed students in the music program

Number of left-handed students not in the music program = 48 - 15

Calculating this, we find that the number of left-handed students not in the music program is 33.

Therefore, there are 33 left-handed students who are not in the music program, based on the data provided in the two-way frequency table.

In conclusion, based on the given two-way frequency table, there are 33 left-handed students who are not in the music program.

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List pairs of corresponding parts of congruent triangles by determining congruent sides, angles, and vertices from the triangle congruence statement.

What is congruent triangles ?

Congruent triangles are triangles that have the same size and shape. They can be matched up exactly, side-by-side, with no gaps or overlaps.

To list the six pairs of corresponding parts of congruent triangles using the triangle congruence statement, we can use the following steps ,

Begin by stating that the two triangles are congruent, using the triangle congruence statement such as "Triangles ABC and DEF are congruent by ASA, SAS, or SSS."

From the statement, we can determine the pairs of corresponding sides by noting which sides are congruent. For example, if the statement is "Triangles ABC and DEF are congruent by ASA," we know that angle A in triangle ABC is congruent to angle D in triangle DEF, angle B in triangle ABC is congruent to angle E in triangle DEF and side AC in triangle ABC is congruent to side DE in triangle DEF

Next, we can determine the pairs of corresponding angles by noting which angles are congruent. For example, if the statement is "Triangles ABC and DEF are congruent by SAS," we know that side AB in triangle ABC is congruent to side DE in triangle DEF, side BC in triangle ABC is congruent to side EF in triangle DEF, and angle A in triangle ABC is congruent to angle D in triangle DEF.

List pairs of corresponding parts of congruent triangles by determining congruent sides, angles, and vertices from the triangle congruence statement.

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Answer:

42.50

Step-by-step explanation:

bill + tip = total bill

The tip is based on the bill

tip = bill * 20%

tip = bill * .20

Replace in the original equation

bill + .20 bill = total bill

Combine like terms

1.20 bill = total bill

The total bill was 51 dollars

1.20 bill = 51

Divide each side by 1.20

1.20 bill / 1.2 = 51/ 1.2

bill =42.50

Answer:

$42.50

Step-by-step explanation:

If the total was $51 with the tip, and you know the tip was 20%, you can set up an equation and solve:

0.2x+x=51

1.2x=51

x=42.5

Therefore, the bill (w/o tip) was $42.50

p.s.Please give me brainliest. Thank you! :)

One solution and it is (-1,-2)

==========================================

Explanation:

I used GeoGebra to graph the two equations. See below. The two lines cross at (-1,-2) which is the solution to the system.

We can check this point by plugging the coordinates into x and y of each equation. You should get the same number on both sides after simplifying.

Side note: Desmos is another free graphing tool you could use.

Answer:

29:21

Step-by-step explanation:

The ratio of the diagonal to the base of the rectangle is 58:42

The ratio can be simplified further.

The simplified ratio is 29:21.

The table of values which represent the equation y = 7x - 3 is: table D.

In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

In order to determine the true ordered pair that is a solution for the given linear equation, we would have to test the ordered pair contained in each table by substituting it into the linear equation as follows;

For ordered pair (-2, -1), we have:

y = 7x - 3

-1 = 7(-2) - 3

-1 = -14 - 3

-1 = -17 (False).

For ordered pair (-2, -19), we have:

y = 7x - 3

-19 = 7(-2) - 3

-19 = -14 - 3

-19 = -17 (False).

For ordered pair (-2, -15), we have:

y = 7x - 3

-15 = 7(-2) - 3

-15 = -14 - 3

-15 = -17 (False).

For ordered pair (-2, -17), we have:

y = 7x - 3

-17 = 7(-2) - 3

-17 = -14 - 3

-17 = -17 (True).

In this context, we can logically deduce that all of the coordinates in table D represents the equation y = 7x - 3.

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The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.

The maximum volume of  right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.

How to find volume of Right Circular Cylinder?

Right cylinders are cylinders with axes that are perpendicular to the bases.

Volume of a Right Circular Cylinder= πr²h  

where,

r = radius of the base

h = height of right circular cylinder

Maximum volume of right circular cylinder that can be inscribed in a sphere will be,    

                  \(\pi r^{2} h-\frac{\pi }{4} h^{3}\\\\= \frac{4\pi r^{3} }{3\sqrt{3} }\)

given that, radius=70cm=0.0.7 m

so,

       \(Maximum\ volume=\frac{4\pi r^{3} }{3\sqrt{3} } \\\\= \frac{4\pi (70)^{3} }{3\sqrt{3} }\\\\=2640.4\pi \ m^{3}\)

Using volume of right circular cylinder,

                \(h=\frac{2r}{\sqrt{3} }\\\\ h = \frac{2(0.07)}{\sqrt{3} }\\\\h= 0.08\ m\)

Hence, The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.

The maximum volume of  right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.

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Answer:

6 square units

Step-by-step explanation:

Given shape is of a trapezoid:

\(area \: of \: trapezoid \\ = \frac{1}{2} \times (4 + 2) \times 2 \\ \\ = 6 \: {units}^{2} \)

Area of shape = area of square + area of triangle

\( = 2^2 + \frac{1}{2} \times 2\times 2\\

= 4 + 2\\

= 6\: units^2 \\\)

A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

Bean advertised footwear on 29 of its 192 catalog pages.

we randomly survey 20 pages

the random variable X is

X = The number of pages that advertise footwear

It is given that 20 pages have been surveyed

so, X = 1, 2, 3.....20

The average value for binomial distribution can be calculated as follows

μ = np

= 20 (29/192)

= 580/192

=3.02

On average 3.02 pages expect to advertise footwear on them

Therefore, A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

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The length side AB is 64 ft , Option D is the correct answer.

A triangle that has one angle 90 degree is called Right angled Triangle.

From the figure it can be seen that

The triangle CDE is a right Triangle

Applying Pythagoras theorem to find the length of CE

CE² = 12² + 16²

CE = 20 ft

As both the triangles are similar therefore the ratio of the sides will be equal

BC : CD = AC : CE

48 / 12 = AC / 20

AC = 80ft

As Triangle ABC is also a right angled triangle

Applying Pythagoras theorem to find the length of AB

AC² = BC² +AB²

6400 = 48² +AB²

AB² = 4096

AB = 64 ft

Therefore Option D is the correct answer.

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Answer:

64 ft.

Step-by-step explanation:

Keep it simple, just givin' the answer :)

Answer:

3 = 6

Step-by-step explanation:

Answer:

C. p > -3

Step-by-step explanation:

We observe the characteristics of the shaded ray on the number line.

It goes to the right, so the inequality must be either greater than or greater than or equal to.

The circle where it starts on is open, so the inequality must not be less than or equal to or greater than or equal to.

Now, without even looking at the numbers themselves, we can find our answer.

There are four different types of inequalities, and we eliminated three of them (<, <=, >=). This leaves only one left (>). The only answer choice that uses the greater than symbol is C, so it must be our answer.

a) Two equivalent expressions to model the purchase made by Mrs. Singh, who bought 9 folders and 9 notebooks at the cost of each folder $2.50 and each notebook $4.00 respectively, are:

b) The total cost of the purchase by Mrs. Singh is $58.50.

Algebraic expressions involve the combination of variables, numbers, constants, and values using mathematical operands (addition, subtraction, division, and multiplication).

The unit cost of folders = $2.50

The unit cost of notebooks = $4.00

The number of folders bought = 9

The number of notebooks bought = 9

Let the number of folders bought = x

Let the number of notebooks bought = y

Folders: 2.50x

Notebooks: 4.00y

Folders: 2.50x = $22.50 ($2.50 x 9)

Notebooks: 4.00y = $36.00 ($4 x 9)

Total costs = $58.50

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The value of 6x is 102.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x=51/3

For 6x put x= 51/3 we get

6x = 6 x 51/3

6x = 2 x 51

6x = 102

Or, \(x^6\) = \((51/3)^6\)

\(x^6\) = 17,596,287,801 / 531,441

Hence, the value of 6x = 102.

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Answer:

6

Step-by-step explanation:

This is a 6th-degree polynomial because the leading term contains the exponent 6.

The values of x and y are 23.3 and 106 as per given diagram.

What is Alternate Interior Angles?

Hence, (3x + 4)° = 74°

3x = 74° - 4°°

x = 70° / 3

x = 23.3

What is Interior Angles on the Same Side of the Transversal?

Hence, (3x+4)° + y° = 180°

74° + y° = 180°

y = 106°

Hence, the values of x and y are 23.3 and 106 as per given diagram.

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