Which Relations are functions?

Check the picture below.

\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)

Make sure your calculator is in Degree mode.

Answer:

the markup percentage is 66.67%

Step-by-step explanation:

The computation of the percent of markup based on cost is shown below:

= (Selling price - paid price) ÷ (paid price)

= ($15 - $9) ÷ ($9)

= 66.67%

By taking the difference of the selling price & paid price and then divided it by paid price we can get the percentage of markup

Hence, the markup percentage is 66.67%

Answer:

190

Step-by-step explanation:

i don't know the explantion

Answer:

\(\sf x = -\dfrac{5}{4} \qquad or \qquad -1\dfrac{1}{4}\)

Step-by-step explanation:

Given expression:

\(\sf \dfrac{12x-3}{12} = \dfrac{12x+3}{8}\)

Cross multiply:

\(\sf 8(12x-3)= 12(12x+3)\)

Distribute inside parenthesis:

\(\sf 96x-24= 144x+36\)

Collect like terms in one side:

\(\sf 96x-144x= 36+24\)

Simplify following:

\(\sf -48x= 60\)

Divide both sides by -48:

\(\sf \dfrac{-48x}{-48} = \dfrac{60}{-48}\)

Simplify following:

\(\sf x = -\dfrac{5}{4} \:\ (improper\ fraction) \qquad or \qquad -1\dfrac{1}{4} \ (mixed \:\ fraction)\)

Answer:

cs.a,C|"< dl\vds

Step-by-step explanation:

Answer:

Step-by-step explanation:

To construct a square with one side on the line l, we need to find the equation of a line perpendicular to l that passes through P. The slope of the line l is 3/4, so the slope of any line perpendicular to l is -4/3. Thus, the equation of the line through P with slope -4/3 is

y - 1 = (-4/3)(x + 6)

Simplifying, we get

y = (-4/3)x - 7

To find the intersection of this line with l, we can substitute y = (-4/3)x - 7 into the equation for l:

3x - 4((-4/3)x - 7) = 18

Solving for x, we get x = -24/5. Substituting back, we get y = -13/5.

So the intersection point of the two lines is (-24/5, -13/5), which we'll call Q.

To construct a square with side PQ, we need to find the midpoint M of PQ, and then find the points R and S that are equidistant from M and P.

The midpoint of PQ is

(((-24/5) + (-6))/2, ((-13/5) + 1)/2) = (-15/5, -6/5) = (-3, -1/5)

The distance between P and M is

sqrt((-3 - (-6))^2 + (-1/5 - 1)^2) = sqrt(45.04) ≈ 6.71

So the distance between M and R (or S) is also 6.71.

Since P has coordinates (-6, 1), and the distance from M to P is 6.71, we know that R and S must have coordinates (-6 ± 6.71, 1 ± 6.71), which simplifies to (-12.71, 7.71) and (0.71, -5.71), respectively.

So one possible set of vertices for the square is PQRSA, where P = (-6, 1), Q = (-24/5, -13/5), R = (-12.71, 7.71), S = (0.71, -5.71).

Answer:

x = 18

Step-by-step explanation:

The sum of interior angles in a triangle = 180 degrees

The given is a right triangle which means one of the angle is = 90

so the sum of 3x + 2x = 90

5x = 90 divide both sides by 5

x = 18 to find the measure of angles replace x with 18

Answer:This statement is not necessarily true

Step-by-step explanation:In general, the rate at which thermal energy is transferred depends on several factors, including the temperature difference between the material and its surroundings, the type of material, and its thermal conductivity. Some materials, such as air and glass, are poor conductors of heat and are therefore considered insulators. However, other materials, such as metal, are good conductors of heat and are not considered insulators.

9514 1404 393

Answer:

  414.5 cm³

Step-by-step explanation:

The lateral area of a cylinder is given by the formula ...

  LA = 2πrh

Then the radius is ...

  r = LA/(2πh)

The volume of the cylinder is given by ...

  V = πr²h

Using the above expression for r, this becomes ...

  V = π(LA/(2πh))²h = LA²/(4πh)

  V = (250 cm²)²/(4π·12 cm) ≈ 414.47 cm³

The volume of the cylinder is about 414.5 cm³.

The answer is:

Work/explanation:

Bear in mind that the sum of all the angles in a triangle is 180°.

Given two angles, we can easily find the third one.

Let's call it x.

Next, we set up an equation:

\(\sf{54+87+x=180}\)

\(\sf{141+x=180}\)

Subtract 141 on each side.

\(\sf{x=180-141}\)

\(\sf{x=39}\)

Answer:

2x+8x-3x= 7x

Step-by-step explanation:

simply just sum the number

1) probability that Ed will answer all 6 questions correctly is approximately 0.00024.

2) probability that Ed will answer exactly 2 questions correctly is approximately 0.29663.

3) probability that Ed will answer at least 2 questions correctly is approximately 0.46606.

What is Probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

1) Probability of answering 6 questions correctly:

Since there are 4 choices for each question, the probability of guessing the correct answer for a single question is 1/4.

P(6 correct) = \((1/4)^{6}\) = 0.00024414 ≈ 0.00024

So the probability that Ed will answer all 6 questions correctly is approximately 0.00024.

2) Probability of answering exactly 2 questions correctly:

The probability of guessing exactly 2 questions correctly can be calculated using the binomial probability formula:

P(exactly 2 correct) = (6 choose 2) * (1/4)² * \((3/4)^{4}\)

P(exactly 2 correct) ≈ 0.29663

So the probability that Ed will answer exactly 2 questions correctly is approximately 0.29663.

3) Probability of answering at least 2 questions correctly:

P(at least 2 correct) = P(2 correct) + P(3 correct) + P(4 correct) + P(5 correct) + P(6 correct)

P(k correct) = (6 choose k) * \((1/4)^{k}\) * \((3/4)^{(6-k)}\)

where k can be 3, 4, or 5.

P(at least 2 correct) ≈ 0.46606

So the probability that Ed will answer at least 2 questions correctly is approximately 0.46606.

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Answer:

103

Step-by-step explanation:

first you would need to plug in the 5 to the equation, this would get you 4(5)^2+3 and then you would simplify the exponent which would get you 4(25)+3 then you would multiply 4x25 which would give you 100 finally you would add the 3 giving you the final produt of 103.

Answer:

103

Step-by-step explanation:

You would sub in 5 for w

4(5) ^2 + 3

you square the 5 and get 25 then multiply by 4 which gets your 100 and then add the 3 which gets the Final Answer as 103

Answer:

does not have a solution because √-0.75 ≠ R

Step-by-step explanation:

x^2 - 5x + (5/2)^2 = -7

x^2 - 5x + 6.25 = -7 + 6.25

(x - 2.5)^2 = -0.75

(x - 2.5) = √-0.75

does not have a solution because √-0.75 ≠ R

Answer:

x = (1/2)(5 ± i√3)

Step-by-step explanation:

x² - 5x + 7 = 0

subtract 7 from both sides

x² - 5x = -7

Use half the x coefficent, -5/2, as the complete the square term

(x - 5/2)² = -7 + (-5/2)²

(x - 5/2)² = -7 + 25/4

(x - 5/2)² = -3/4

Take the square root of both sides

x - 5/2 = ±(√-3) / 2

x - 5/2 = ±(i√3) / 2

Add 5/2 to both sides

x = 5/2 ± (i√3) / 2

factor out 1/2

x = (1/2)(5 ± i√3)

a. For the supermarket manager, the mode is one that  is the right tool as the appropriate form of the measure of central tendency as it would tell them which type of lettuce that was bought most often.

b. For the students, the mean is one that will be the right measure of central tendency as it would give them the idea of the average of all their test scores.

c. For the real estate agent, the median is one that is be the right measure of central tendency as it would tell them the selling price that is in the middle of all the given comparable houses.

Lastly, The student that is known to be is reporting the mean as the average. , this is one that tends to misrepresents their course performance due to the fact that the mean is affected by outliers for example as the 75%, 70%, and 55% scores. The median is one that can give a better representation of their performance.

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See text below



1. Here are three examples where the mean, median, and mode can be used to describe a situation. Which measure of central tendency would you use for each one? Why? (Don't forget the why.)

a. A supermarket manager wants to know how many types of lettuce customers purchase most often.

b. Students want to know the average of all their test scores in a certain grading period.

c. A real estate agent wants to set the selling price of a three-bedroom house so that there are as many comparable houses above as below the price. 2. A student's parents promise to pay for next semester's tuition if an A average is earned in chemistry. With examination grades of 97%, 97%, 75%, 70%, and 55%, the student reports that an A average has been earned. Which measure of central tendency is the student reporting as the average? How is this student misrepresenting the course performance with statistics?

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4) D

Graph these twο pοints (0, -2) & (4/3, 0) and yοu have yοur slοpe graphed fοr the equatiοn y = 3/2x -2.

What is an equatiοn?  

An equatiοn is a mathematical statement containing two algebraic expressiοns flanked by equal signs (=) on either side.

It shows that the relationship between the left and right printed expressiοns is equal.

All fοrmulas have LHS = RHS (left side = right side).

Yοu can sοlve equatiοns tο determine the values οf unknοwn variables that represent unknοwn quantities.

If a statement does not have an equals sign, it is not an equatiοn. A mathematical statement called an equatiοn cοntains the symbοl "equal tο" between twο expressiοns οf equal value.

Tο find the x-intercept, substitute y = 0 and sοlve fοr x. Tο find the y-intercept, substitute x = 0 and sοlve fοr y.

y = 3/2(0) -2

y = -2

⇒ (0, -2)

And for x

0 = 3/2x -2

2 = 3/2x

x = 4/3

(4/3, 0)

Now graph these two points and you have your slope graphed

Hence, The graph of the equation is given below.

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9. The regression line is given as follows: y = 8.5x + 3.7.

10. The estimate for 2022 is given as follows: 71.7 million dollars.

The regression line is obtained inserting the points of the table into a linear regression calculator.

From the table, the points are given as follows:

(1, 13), (2, 19), (3, 31), (4, 36), (5, 47).

(considering x as the number of years since 2014).

Inserting these points into a calculator, the equation is given as follows:

y = 8.5x + 3.7.

2022 is 8 years after 2014, hence the estimate is given as follows:

y = 8.5(8) + 3.7 = 71.7 million dollars.

(numeric value at x = 8, replace the lone instance of x by 8).

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Answer: Tenias 1 3/8 de litros.

Step-by-step explanation:

Necesitas de sumar lo que quedo y lo que uso Gerardo, pero el 8 y el 4 necesitan de ser iguales. Si multiplicas 4x2 te da 8 y serían iguales. As lo mismo con el tres: 3x2 y te da 6. Suma el 6 por 5 y te da 11/8. Simplifica y te dará 1 litro y 3/8.

ANSWER

$166.67

EXPLANATION

We have that the equation that Luis has used to represent the given situation is:

4(t + 25) = 4(t + 50) - 4(0.15t)

where t = price per ticket for which the two airlines have the same total cost

From the question, we have to find the ticket price, t.

We do that by simplifying the equation given.

That is:

4(t + 25) = 4(t + 50) - 4(0.15t)

Expand the bracket:

4t + 100 = 4t + 200 - 0.6t

Collect like terms:

4t - 4t + 0.6t = 200 - 100

0.6t = 100

t = 100 / 0.6

t = $166.67

That is the ticket price that satisfies the situation.

The probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched:

No-hitters    probability

     0             0.5944

     1             0.3093

     2             0.0804

     3             0.0139

In this question, we have been given  the probability that a major league pitcher pitches a no-hitter in a game is about 1/1300.

We need to determine the probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched.

Here, p = 1/1300

            = 0.0008

q = 1 - p

  = 1 - 1/1300

  = 1299/1300

  = 0.9992

And n = 650

We know that the binomial distribution formula.

P(x) = nCx * p^(x) * q^(n - x)

Using binomial distribution we find required probability.

For x = 0,

P(x = 0) = 650C0 * (1/1300)^0 * (1299/1300)^(650 - 0)

P(x = 0) = 1 * 1 * (0.9992)^650

P(x = 0) = 0.5944

For x = 1,

P(x = 1) = 650C1 * (1/1300)^1 * (1299/1300)^(650 - 1)

P(x = 1) = 650 * (0.0008) * (0.9992)^649

P(x = 1) = 0.52  * 0.5948

P(x = 1) = 0.3093

For x = 2,

P(x = 2) = 650C2 * (1/1300)^2 * (1299/1300)^(650 - 2)

P(x = 2) = 210925 * (0.0008)^2 * (0.9992)^648

P(x = 2) = 0.0804

For x = 3,

P(x = 3) = 650C3 * (1/1300)^3 * (1299/1300)^(650 - 3)

P(x = 3) = 45559800 * (0.0008)^3 * (0.9992)^647

P(x = 3) = 0.0139

Therefore, the probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched are 0.5944, 0.3093, 0.0804, and 0.0139 respectively.

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The cost of students ticket is $37.5and the cost of general admission is $187.5.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Assume s be the students tickets cost and g be the general admission cost.

From the given information,

⇒  s + g = 225             ..(1)

 5s + 7g = 1500         ..(2)

From equation (1),

s = 225 - g

Plug the value of s in equation (2)

5(225 - g) + 7g = 1500

1125 - 5g + 7g = 1500

                  2g = 1500 - 1125

                  2g = 375

                    g = 187.5

Plug g = 125 in equation (1),

s + 187.5= 225

        s = 225 - 187.5

        s = 37.5

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Answer:

10000

Step-by-step explanation:

100 hugs x 100 hugs

= 10,000 hugs.

The equation of the perpendicular line in slope-intercept form is y = 4x + 25

The equation of line p given as

y = –4x + 1

Also, from the question

The point on line q is given as

Point = (-6, 1)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = -4

This means that the slope of y = –4x + 1 is -4

So, we have

m = 4

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the line q is 1/4

The equation of the perpendicular lines is then calculated as

y = m(x - x₁) +y₁

Where

m = 4

(x₁, y₁) = (-6, 1)

Substitute the known values in the above equation

So, we have the following equation

y = 4(x + 6) + 1

Evaluate

y = 4x + 24 + 1

Evaluate the sum

y = 4x + 25

Hence, the perpendicular line has an equation of y = 4x + 25

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Answer: 30

Step-by-step explanation:

Yvette- 100-7

Isandro- 0+3

1.) I'm going to speed up the process and multiply by 5.

Yvette: 100-7

7  × 5 = 35

100-35= 65

65-35= 30

Isandro: 0+3

3 × 5 = 15

0+15= 15

15+15= 30

2.) If they keep going on this pattern they will have the same number on the 10 round.

1. The monthly payments for 2 of these options are:

2. The total payments for 2 of these options are:

3. The percentage of the total amounts to be paid back as interest is:

4. The percentages above represent the aggregated interest portion of the total payments, while the APR (annual percentage interest) represents the yearly financing cost charged by the financing institution for extending credit.

5. Ramona should choose the Online Construction Business to remodel her kitchen because the total cost she will incur is less than the total cost for the Local Small Business Home Improvement Company.

Home improvement cost = $13,200

Financing:

Year 1 0% monthly payment of $100 = $1,200

Balance after Year 1 = $12,000

APR 16.99%

Remaining payment period = 3 years

N (# of periods) = 36 months

I/Y (Interest per year) = 16.99%

PV (Present Value) = $12,000

FV (Future Value) = $0

Results:

PMT = $427.77

Sum of all periodic payments = $15,399.83

Total Interest = $3,399.83

Total costs = $16,599.83 ($15,399.83 + $1,200)

Home improvement cost = $11,800

Financing:

3% origination fee = $354 ($11,800 x 3%)

APR = 7.5%

Payment period = 5 years

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 7.5%

PV (Present Value) = $11,800

FV (Future Value) = $0

Results:

PMT = $236.45

Sum of all periodic payments = $14,186.87

Total Interest = $2,386.87

Total costs = $14,540.87 ($14,186.87 + $354)

Interest as a percentage of the total payment = 16.41% ($2,386.87/$14,540.87 x 100)

Home improvement cost = $10,200

Additional applied amount = $1,000

Total = $11,200

APR = 11.9%

Payment period = 4 years

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 11.9%

PV (Present Value) = $11,200

FV (Future Value) = $0

Results:

PMT = $294.39

Sum of all periodic payments = $14,130.69

Total Interest = $2,930.69

Total cost = $14,130.69

Interest as a percentage of the total payment = 20.74% ($2,930.69/$14,130.69 x 100)

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Answer:

ok so first we have to find out how much each one increaces so llets just subtract the terms

3/4-2/5=0.35 so each time they add 0.35 so the nth term would be

2/5+0.35(n-1)

Hope This Helps!!!

Answer: A) 2 and a half B) 5 pints

Step-by-step explanation:

in 1 cup there are 16 table spoons.

a) 4tbsp (2 servings) times 10 (to reach 20 servings) =40 tbsp

40/16 =2.5

ANSWER A= 2 and a half cups of lemon juice.

in 1 pint there are 2 cups.

b)

1 cup = 1/2 a pint,

1/2 pint (2 servings) times 10 (to reach 20 servings) = 5 pints

ANSWER B= 5 pints of olive oil

9514 1404 393

Answer:

  5 years

Step-by-step explanation:

We want to find x such that ...

  2(5 +x) = 15 +x . . . . . after x years, Joyce will be 2 times as old

  10 +2x = 15 +x . . . . . eliminate parentheses

  x = 5 . . . . . . . . . . .  subtract x+10

Joyce will be twice as old as Mensah in 5 years.

Answer:

Joyce will be twice as old as Mensah in 5 years.

Step-by-step explanation:

Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3

The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.

In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;

Taking two points from the table;

m = y₂ - y₁ / x₂ - x₁

m = 0 - (-3) / -9 - (-11)

m = 3 / 20

Using the slope and one point on the table;

y = mx + x

-3 = 3/20(-11) + c

-3 = -1.65 + c

c = -3 + 1.65

c = -1.35

Putting the slope and y - intercept together;

y = 3/20x - 1.35

y = 3/20x - 27/20

f(x) = 3/20x - 27/20

Taking the inverse of the function;

f⁻¹(x) = (20x + 27)/3

To find the value of f⁻¹(4), we just need to substituting the value of x in the function;

f⁻¹(4) = (20(4) + 27)/3

f⁻¹(4) = 107/3

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