Aisha runs a tutoring business. With Plan 1, students may choose to pay $15 per hour. With Plan 2, they may follow the plan shown on the graph.

Answer:

instead of X, we replace 9.

So we have: f(9)=4*9^2-2*9+4.

Again, f(9)= 4*81-18+4=324-14=310.

The types of variation and their constants are;

1) Direct variation with constant of variation as -1/4

2) Direct variation with constant of variation as ³/₂

A variation is defined as a relation that exists between a set of values of one variable and then a set of values of other variables.

In variation, if the variables change proportionately that is they either increase together or decrease together, then they are said to vary directly.

1) We are given the equation;

4y = -x

Now, y is the output while x is the input and so we make y the subject to get; y = -¹/₄x

Now, writing the relationship between y and x as a variation, we will have; y ∝ x

For this to be equal, there has to be a constant of proportionality which means; y = kx

Comparing with our equation tells us that;

This is a direct variation with constant of variation as -1/4

2) We are given the equation;

3x = 2y - 7

Rearranging gives;

2y = 3x + 7

y = ³/₂x + 7

Now, the greater the value of x, the greater the value of y and as such this is also a direct variation with the constant of variation being 3/2.

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Answer:

4 1/6 = 25/6

Why?:

Multiply the denominator with the mixed number 4.

Add the numerator 1 and get 25.

Then, you keep the denominator (Which is 6) on the bottom.

And finally, you get

25/6

Answer:

25/6

Step-by-step explanation:

first start by multiplying 6 and 4, which leads you to 24

then add the 1 from the numerator and you get 25 as your numerator.

for the denominator, leave six as it is so it becomes 25/6

The value of the larger number and the smaller number are 25 and 8 respectively.

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.

They are called simultaneous equations because the equations are solved at the same time.

If the bigger value is represented by x and the smaller value is represented by then

x+y= 33 equation 1

3x+ 4y= 107 equation 2

using Elimination method,

we multiply the coefficients of x by opposite equation

3x+3y=99 equation 3

3x+4y= 107 equation4

subtracting equation 3 from 4

y=107- 99

y= 8

substituting 8 for y in equation 1

x+8= 33

x= 33-8=25

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on dividing 100 by 200 we get answer as 0.5 or we can also write it as 1/2 in fraction.

What is division?

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

The fundamental goal of division is to produce equal groups or to ascertain how many individuals are in each category following a fair distribution.

To divide 12 donuts into three similar groups in the aforementioned case, you would need to put four doughnuts in each group. Consequently, 12 divided by 3 will equal 4.

We need to find 100/200,

on solving this division problem we get answer as 1/2 (in fraction) or 0.5 (in decimal).

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The quotient of 5 divided by 3/10 is equal to 50/3

When we want to divide by a fraction, we just need to replace that division by the product with the inverse of the fraction.

So, if we want to divide A by the fraction (b/c), then we can write:

A÷(b/c)

That will be equal to A*(c/b), so:

A÷(b/c) =  A*(c/b)

Here we want to divide 5 by 3/10, then we need to solve:

5÷(3/10)

Using the above rule we will get:

5÷(3/10) = 5*(10/3) = 50/3

That is the quotient.

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The probability that exactly two of the four live in elderly care facilities is; 0.244

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The general formula of binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

Px = the probability of exactly x events occurring.

x = the number of expected successful outcomes.

p is probability of success

n is sample size

We are given;

p = 72% = 0.72

n = 4

Thus;

P(X = 2) = 4C2 * (0.72)^(2) * (1 - 0.72)^(4 - 2)

P(X = 2) = 0.244

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Step-by-step explanation:

r - 535 = 175

r = 175 + 535 = 710

Answer:

take - 535 to the other side (over equal to side)

which makes it +535

r = 175 + 535

r = 710

The maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long is 3.33.

G = C×(w×h²/l)

Where,

C = constant

C = G×l/(w²h²)

Weight (w) = 6 in

Height (h) = 2 in

Length (l)= 10 ft

Maximum ton (G) = 8 t

C = 8×10/(6×2²)

C = 80/24

C = 10/3

G = (10/3)×(w×h²/l)

So, Maximum weight

G = (10/3)×(6×2²/24)

G = 10/3 t

G = 3.33 tones

The maximum weight is 3.33 tones.

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The coordinates of F' when reflected in the line y=x is F'(1,-7)

Given:

When point F is reflected in the line y = x, the image is located at F"(-7, 1).

The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x (the signs are changed). The point is on the line y = x. (y, x).

so the point  F"(-7, 1) after reflection changes to:

F'(1,-7)

Hence we get the value of F' as (1,-7).

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Answer:

(4)

Step-by-step explanation:

Let's make the smaller number equal to x. Since they are consecutive odd numbers, the larger number is x+2.

Twice the smaller number is 2x. Three times the larger number is 3(x+2). If twice the smaller is subtracted from three times the larger, then the expression should be: 3(x+2) - 2x

Then, since the result of this is four more than the smaller, this expression is x+4.

Finally, we put it all together, so we get: 3(x+2) - 2x = x + 4. Option 4 is our correct answer.

Hence, the option (4) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller.

Let us assume the smaller number is [tex]x[/tex].

The larger number is  [tex](x+2)[/tex].

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger than it is

[tex]3(x+2)-2x[/tex]

So, the result is four more than the smaller.

i.e., [tex]3(x+2)-2x=x+4[/tex]

Hence, the option (4) is correct.

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Answer:

16

Step-by-step explanation:

(8+2) + (6 − 4) × 3

= 10+6

=16

In actuality, "absolute value" refers to thinking of all numbers as positive and removing all negative signs from front of them (or zero). Symbol for absolute value. -71<181<|9|<1-10| set of absolute values

Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0.

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.

The exact distance of an integer or number from zero on a number line is its absolute value. As a result, the absolute value is never negative and is always positive.

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Answer:

The cost would be $99 with each artist if the job took Eva 1 hour

Step-by-step explanation:

99=10x+89

subtract 89 from both sides

10=10x

1=x

Answer:

y=-1/4x+4

Step-by-step explanation:

The graph starts on 4 so that is your y-intercept

Use slope formula to get the slop (y2-y1 over x2-x1)

Use 2 coordinates for formuls (In your case (0,4) and (4,3))

3-4=-1 4-0=4

slope is -1/4

y= -1/4x+4

After solving the value of x is -1/6.

Given:

[tex]25^3^x^+^2[/tex] = 125

[tex]5^{2(3x+2)}[/tex] = [tex]5^3[/tex]

2(3x+2) = 3

6x + 4 = 3

6x = 3-4

6x = -1

divide by 6 on both sides

6x/6 = -1/6

x = -1/6.

Therefore after solving the value of x is -1/6.

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The measurements 15, 17, 22 do not form a right triangle.

In this question, we have the measurements 15, 17, 22

We check whether the measurements 15, 17, 22 is Pythagorean triple.

22^2 = 484

15^2 = 225

17^2 = 289

15^ + 17^2 = 225 + 289

                = 514

                ≠ 484

i.e., 15^ + 17^2 ≠ 22^2

This means, these measurements do not form a right triangle.  

Therefore, the measurements 15, 17, 22 do not form a right triangle.

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The measures of the remaining three angles of the decagon are 40, 50 and 130 degrees.

A decagon is a polygon with 10 sides. In a regular decagon, the interior angles add up to 1440 degrees, and the exterior angles add up to 360 degrees.

Therefore, seven of the angles of a decagon have measures whose sum is 1220. Of the remaining 3 angles, exactly two are complementary and exactly two are supplementary.

Complementary angles sum up to 90 degrees while supplementary angles sum up to 180 degrees.

Therefore,

1440 - 1220 = 220

Let the angles be a, b and c.

Therefore,

a + b + c  =220

a + b = 90

b + c = 180

Hence,

a = 220 - 180

a = 40°

b = 90 - 40

b = 50°

c = 180 - 50

c = 130°

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The integer in the set S:{−24, 2, 20, 35} that will make the inequality five-sixths m minus five is less than one-half m plus 3 false is 35

Inequalities are created through the connection of two expressions. It should be noted that the expressions in inequality aren't always equal. Inequalities imply that the expressions are not equal. They are denoted by the symbols ≥  <  >   ≤.

In this case, based on the information we will replace m with 35. This will be illustrated thus:

= 5/6(35 - 5) < 1/2(35 + 3)

= 5/6(30) < 1/2(38)

= 25 < 19

In this case, 25 isn't less than 19. Therefore, 35 is the correct integer.

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If three of the patients are randomly selected, then the probability that none of the patients reacted favorable is 21/506.

In the given question,

A medical research study on a new medicine for multiple sclerosis is being conducted with 24 patients.

After the study was concluded, it was concluded it was determined that 15 patients reacted favorably to the medicine, 7 reacted unfavorably, and 2 were unaffected.

If three of the patients are randomly selected, then we have to determine the probability that none of the patients reacted favorable.

Total patient are 24.

The patients reacted favorably to the medicine is 15.

The patients reacted unfavorably to the medicine is 7.

The patients unaffected to the medicine is 2.

Randomly selected patients are 3.

So the probability that none of the patients reacted favorable

P(E) = 9/24 × 8/23 × 7/22

Simplifying

P(E) = 9/3 × 1/23 × 7/22

P(E) = 3 × 1/23 × 7/22

P(E) = 21/506

Hence, if three of the patients are randomly selected, then the probability that none of the patients reacted favorable is 21/506.

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The right question is

"A medical research study on a new medicine for multiple sclerosis is being conducted with 24 patients. After the study was concluded, it was concluded it was determined that 15 patients reacted favorably to the medicine, 7 reacted unfavorably, and 2 were unaffected. If three of the patients are randomly selected, then we have to determine the probability that none of the patients reacted favorable."

The point slope equation and slope of some lines are given below

1) For y - 6 = 3(x - 5), slope = 3

2) For  y - 4 = -9(x + 8), slope = -9

3) y - 2 = 5x, slope = 5

4) Point slope equation of line whose slope = -10 and passing through   (1, 4)

   y - 4 = -10(x - 1)

5) Point slope equation of line whose slope = 2 and passing through    (5, -3)

      y  + 3 = 2(x - 5)

6) Point slope equation of line whose slope = [tex]\frac{1}{2}[/tex] and passing through    (-7, -7)

   [tex]y +7 = \frac{1}{2}(x +7)\\[/tex]

What is equation of line in point slope form?

The most general form of equation of line in point slope form is given by [tex]y - y_1 = m(x - x_1)[/tex] , [tex](x_1, y_1)[/tex] is a point on the line

Where m is the slope of the line

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

1) y - 6 = 3(x - 5)

  y - 6 = 3x - 15

  y = 3x - 15 + 6

  y = 3x - 9

  Slope = 3

  If x = 0,

  [tex]y = 3 \times 0 -9\\y = -9[/tex]

  (0, -9) is a point on the line

2) y - 4 = -9(x + 8)

   y - 4 = -9x - 72

   y = -9x - 72 + 4

   y = -9x - 68

   Slope  = -9

   If x = 0

   [tex]y = -9 \times 0 -68\\y = -68[/tex]

   (0, -68) is a point on the line

3) y - 2 = 5x

   y = 5x + 2

  Slope = 5

    Putting x = 0

    [tex]y = 5 \times 0 + 2\\y = 2[/tex]

    (0, 2) is a point on the line

4) Slope = - 10

    The line passes through (1, 4)

    Point slope equation

      y - 4 = -10(x - 1)

5) Slope = 2

    The line passes through (5, -3)

     Point slope equation

      y - (-3) = 2(x - 5)

      y + 3 = 2(x - 5)

6) Slope = [tex]\frac{1}{2}[/tex]

      The line passes through (5, -3)

     Point slope equation

       [tex]y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\[/tex]

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The value of the translated function g(x) will be x²+1.

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.

Given that the function is f(x) = x². The function g(x) in the form of  a(x–h)²+k will be written as below,

The function is translated to the 1 unit up which means that the value of k will be equal to the positive 1.

The function is,

g(x) = a(x–h)²+k

g(x) = 1(x-0)² + 1

g(x) = x² + 1

Therefore, the value of the translated function g(x) will be x²+1.

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When a person from this group is selected at random, the probability that this person has type AB blood is 3/40

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

It should be noted that in this case, the number of people with AB blood is 15 and there are 200 people. The probability will be:

= Number of AB blood type / Total number of people

= 15 / 200

= 3/40

The probability is 3/40.

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Answer:

$208

Step-by-step explanation:

$79.50 x 24 = 1908

$1908 + 400 = 2308

$2100/2308 = 9%

Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.

Interest is a financial concept that represents the cost of borrowing money or the return on invested capital. It is a fee charged for the use of borrowed funds or the compensation received for lending money or investing in assets.

Total number of monthly payments

= 12 months/year x 2 years

= 24 months

and, Monthly payment amount = $79.50

Total amount paid in monthly installments

= Monthly payment amount x Total number of monthly payments

= $79.50 x 24

= $1,908

Next, we can subtract the initial down payment from the total amount paid to find the interest paid:

Total interest paid = Total amount paid - Down payment

= $1,908 - $400

= $1,508

Therefore, Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.

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Answer:

Step-by-step explanation:

domain: 1,2,3,4

Range: 8,6,4,2

D=-2

[tex]a_{n}=a_{1}+(n-1)-2[/tex] formula

The value of the function f(a+4) is  [tex]\frac{7}{a^{2} +8a+11}[/tex]

function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable called the dependent variable.

if f(x) = [tex]\frac{7}{x^{2} - 5}[/tex], which means this equation is a function of x,

To find another equation whose function is f(a + 4)

We substitute x for a + 4 in the above equation

f(a+4) = [tex]\frac{7}{(a+4) ^{2} - 5 }[/tex]

expanding [tex](a + 4)^{2}[/tex], and simplifying the denominator, we have

[tex]a^{2}[/tex] +8a + 16 - 5 = [tex]a^{2}[/tex] + 8a + 11

so the simplified form of the new function would be  [tex]\frac{7}{a^{2} +8a+11}[/tex]

In conclusion, the function f(a +4) =  [tex]\frac{7}{a^{2} +8a+11}[/tex]

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Answer:

9. 4/5

10. 3/4

11. 1/4

12. 1/8

13. 1/11

14. 1/9

15. 9/10

16. 1/10

Step-by-step explanation:

ur welcome

Answer:  The correct answer is $15.06 is remaining after 71 minutes

Step-by-step explanation:

What we need to find out:

What we know:

If we convert the minutes (m) and remaining credits (c) to (x,y) data sets, they would look like the following:

  x       y

 41    19.26       (41, 19.26)

 57   17.02       (57, 17.02)

Plugging the x, y values into a linear equation, we get:

y - 19.26 = (17.02 - 19.26) / (57 - 41) * (x-41)

Solve the equation for y by adding 19.26 to both sides:

y − 19.26 + 19.26 = −0.14x + 5.74 + 19.26

y = −0.14x + 25

Resulting standard slope-intercept format:

y = −0.14x + 25

Now plug in 71 for the x value (minutes):

y = (-0.14*71) + 25

y = 15.06

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