The Yoga class you wish to take is offering two price quotes: $108 for 5 weeks as (15 classes) or $125 for 8 weeks (24 classes). How much per class would you save by taking the 8 week class?
A $2.10
B $2.05
C $1.99
D $1.89

Ques 1)

                   [tex]g(x)=-12x+48[/tex]

Ques 2)

                 [tex]g(x)=|3x|+4[/tex]

Ques 1)

We know that if a graph is stretched by a factor of a then the transformation if given by:

    f(x) → a f(x)

Also, we know that the translation of a function k units to the right or to the left is given by:

  f(x) →  f(x+k)

where if k>0 then the shift is k units to the left

and if k<0 then the shift is k units to the right.

Here the graph of f(x) ​is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.

This means that the function g(x) is given by:

[tex]g(x)=4f(x-4)\\\\i.e.\\\\g(x)=4(-3(x-4))\\\\i.e.\\\\g(x)=-12(x-4)\\\\i.e.\\\\g(x)=-12x+48[/tex]

Ques 2)

We know that the transformation of the type:

  f(x) → f(x)+k

is a shift or translation of the function k units up or down depending on k.

If k>0 then the shift is k units up.

and if k<0 then the shift is k units down.

Here, The graph of the function f(x)=|3x| is translated 4 units up.

This means that the transformed function g(x) is given by:

                 [tex]g(x)=|3x|+4[/tex]

Answer:

-12(x-4)

Step-by-step explanation:

I just took the test this is the answer!! Basically you take -3 and 4 and times it which would be -12. You then have x and another 4 left over. Since you are translating to the right you will be negative therefore giving us the answer -12(x-4).

The probability that the kicker makes his first two kicks is 0.63, or 63%.

Let's denote the events:

A: The kicker makes his first kick

B: The kicker makes his second kick

Given:

P(A) = 0.7 (probability that the kicker makes his first kick)

P(B|A) = 0.9 (probability that the kicker makes his second kick given that he made his first kick)

To find the probability of both events A and B occurring (the kicker making his first two kicks), we can use the multiplication rule of probability:

P(A and B) = P(A) * P(B|A)

Substituting the given probabilities, we have:

P(A and B) = 0.7 * 0.9 = 0.63

Therefore, the probability that the kicker makes his first two kicks is 0.63, or 63%.

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The probability that the kicker makes his first two kicks is 0.63, or 63%.

To find the probability that the kicker makes his first two kicks, we need to multiply the probabilities of each individual kick.

The kicker has a 70% chance of making his first kick, which means he has a 30% chance of missing it.

If the first kick is made, his success rate rises to 90%. So, the probability of making the second kick, given that he made the first kick, is 90%.

To find the probability of both kicks being made, we multiply the probability of making the first kick (0.7) with the probability of making the second kick given that the first kick was made (0.9).

0.7 * 0.9 = 0.63

Therefore, the probability that the kicker makes his first two kicks is 0.63, or 63%.

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Answer:

The value of the index at the end of the day is $45392.6.

Step-by-step explanation:

Given : A simple index of three stocks opens the day with these values:

[name]  [number of shares] [price per share]

stock x      5000 shares            $4.10

stock Y      2000 shares           $4.50

stock z      4000 shares            $3.60

The index rises 3.4% over the course of the day.

To find : What is the value of the index at the end of the day? Round your answer to the nearest hundred ?

Solution :

Stock values of x,y and z is given by,

Stock x,

[tex]5000\times 4.10=\$20500[/tex]

Stock y,

[tex]2000\times 4.50=\$9000[/tex]

Stock z,

[tex]4000\times 3.60=\$14400[/tex]

The total amount will be

[tex]A=20500+9000+14400[/tex]

[tex]A=\$43900[/tex]

The index rises 3.4% over the course of the day.

The value of the index at the end of the day is

[tex]V=43900 \times (1+3.4\%)\\V=43900 \times (1+0.034)\\V=43900 \times 1.034\\V= 45392.6[/tex]

Therefore, the value of the index at the end of the day is $45392.6.

the measure of angle ABC (m∠ABC) is 130 degrees. it's essential to recognize that the sum of the angles along a straight line is always 180 degrees.

In this case, we have two angles, 2x and 5x+5, forming a straight line with an unknown angle (m∠ABC). So, we set up the equation:

2x + 5x + 5 = 180

Next, combine the like terms on the left side:

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 175/7

x = 25

Therefore, the measure of angle ABC = 5x + 5

= 5(25) + 5

=130 degree

So, the measure of angle ABC (m∠ABC) is 130 degrees.

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Answer:

Option C) is correct

Step-by-step explanation:

Given :  y is the daily production cost at a canning company such that [tex]y=650-15x+0.45x^2[/tex] wherex is the number of canned items .

To find : Minimum daily production cost

Solution :

[tex]y=650-15x+0.45x^2[/tex]

On differentiating both sides with respect to x, we get

[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=-15+0.9x[/tex]

On putting [tex]\frac{\mathrm{d} y}{\mathrm{d} x}=0[/tex] , we get [tex]-15+0.9x=0\Rightarrow 15=0.9x\Rightarrow x=\frac{15}{0.9}=\frac{150}{9}=\frac{50}{3}[/tex]

We get intervals as \left ( -\infty , \frac{50}{3}\right )\,,\,\left ( \frac{50}{3},\infty  \right )[tex]\left ( -\infty , \frac{50}{3}\right )\,,\,\left ( \frac{50}{3},\infty  \right )[/tex]

For [tex]x=0\epsilon \left ( -\infty ,\frac{50}{3} \right )[/tex] , [tex]f'(0)=-15< 0[/tex]

For [tex]x=16\epsilon \left ( \frac{50}{3},\infty  \right )[/tex] , [tex]f'(18)=-15+0.9(18)=-15+16.2=1.2> 0[/tex]

Therefore, [tex]y=\frac{50}{3}[/tex] is a point of minima.

So, minimum cost is equal to [tex]y\left ( \frac{50}{3} \right )[/tex]

[tex]y\left ( \frac{50}{3} \right )=650-15\left ( \frac{50}{3} \right )+0.45\left ( \frac{50}{3} \right )^2=650-250+125=\$ 525[/tex]

So, option C) is correct .

Answer:  The co-ordinates of the image H' are (-7, 6).

Step-by-step explanation:  Given that the rectangle EFGH is translated according to the following rule :

[tex]T_{-5,9}(x,y).[/tex]

We are to find the co-ordinates of the image H' if the co-ordinates of the pre-image H are (-2, -3).

We know that

[tex]T_{h,k}(x,y)=(x+h,y+k).[/tex]

For the given information, we have

(h, k) = (-5, 9)      ⇒ h = -5  and  k = 9.

Therefore, we get

[tex]T_{-5,9}(-2,-3)=(-2-5,-3+9)=(-7,6).[/tex]

Thus, the co-ordinates of the image H' are (-7, 6).

Answer:

[tex]2.99x+12.99y=43.92[/tex]

Step-by-step explanation:

Hanna shops for socks that cost $2.99 for each pair.

And blouses that cost $12.99 each.

Let x represent the number of pairs of socks purchased.

Let y represent the number of blouses purchased.

So, the cost for x socks will be [tex]2.99x[/tex]

And cost of y blouses will be [tex]12.99y[/tex]

Total amount spent by Hanna = $43.92

So, the equation that will model this situation will be:

[tex]2.99x+12.99y=43.92[/tex]

Answer:

not 480, answer is 453 according to K12.

Step-by-step explanation:

took the k12 test, the answer is in fact, 453.

The population of the bacteria after 30 hours will be 400.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the population of bacteria doubles every 12 hours initially the population of bacteria is 80 what is the population of bacteria after 30 hours?

The population will be calculated as,

12 hours = 2 times of 80

1 hour = 2 / 12 times of 80

30 hours = ( 30 x 2 x 80 ) / 12

30 hours = 400 bacterias

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Answer:  The required slope-intercept form is [tex]y\leq 3x+21.[/tex].

Step-by-step explanation:  We are given to write the following inequality in slope-intercept form :

[tex]-6x+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the slope-intercept form of an inequality of the given form is as follows :

[tex]y\leq mx+c,[/tex] where m is the slope and c is the y-intercept.

From inequality (i), we have

[tex]-6x+2y\leq 42\\\\\Rightarrow 2y\leq6x+42\\\\\Rightarrow y\leq\dfrac{6}{2}x+\dfrac{42}{2}\\\\\Rightarrow y\leq 3x+21.[/tex]

Thus, the required slope-intercept form is [tex]y\leq 3x+21.[/tex].

Answer:

About 7 hours per person

Step-by-step explanation:

412 divided by 60 because there are 60 minutes in an hour.

6.8667 which is about 7 hours.

The each member will take 7 hours.

The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value

Given:

total member = 6 member

Each flower take = 412 minutes

we know

1 hour= 60 minutes

So, each member will have

=412/60

=6.866

=7 hours

Hence, each member will work for 7 hours

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To solve for x in 5x² - 34x = -24, set the equation to equal 0, factor the equation, and find the possible values for x. In this case, the solutions are x = 6/5 and x = 4.

This is a problem in algebra, more specifically quadratic equations. To solve for x in the equation 5x² - 34x = -24, you first need to set the equation to equal zero: 5x² – 34x + 24 = 0.

Next you can factor the equation to find the possible values for x. In this case, the factored form is 5x² - 20x - 14x + 24 = 0 which further simplifies to 5x(x - 4) - 6(x - 4) = 0, and then (5x - 6)(x - 4) = 0.

When you set each factor equal to zero, you find the possible solutions for x. From 5x - 6 = 0, x = 6/5; and from x - 4 = 0, x = 4. Therefore the solutions are x = 6/5 and x = 4.

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volume = l x w x h

1568 /8 = 196

sqrt(196) = 14

 each side is 14 feet

Answer with Step-by-step explanation:

A fish tank is in the shape of cuboid.

It's height is 8 feet

and volume=1568 cubic feet

we know that volume of cuboid=lbh

where l is the length, b is the width and h is the height

The base of the tank is square

i.e. l=b

Volume=l²h

⇒ 1568=l²×8

⇒ l²=196

⇒ l=14

Hence, The length of base of tank=14 feet

width of tank=14 feet

and height=8 feet

In two column proof the right column states your reasons is true statement.

In a two-column proof, the right column typically contains the statements of reasons or justifications for each step taken in the left column.

The left column contains a sequence of statements that represent the logical progression of the proof, while the right column provides the reasoning or logical basis for each step to show that it follows from the previous statements.

This format is commonly used in geometry to provide a clear and organized presentation of the proof's logical structure.

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The ratio of men to class is 0.41.

We have a class of 10 men and 14 women.

We have to find out what is the ratio of men to the class.

Yes, a : b is same as [tex]\frac{a}{b}[/tex]. Here, ' a ' is called Antecedent and ' b ' is called Consequent.

In the question given -

Total number of men in the class , n(m) = 10

Total number of students in class, n(c) = 24

Ratio of men to class = [tex]\frac{n(m)}{n(c)}[/tex] = [tex]\frac{10}{24}[/tex] = 0.41

Hence, the ratio of men to class is 0.41.

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Final answer:

The ratio of men to the entire class of 10 men and 14 women is 5:12, simplified by dividing the numbers of men and total students by the greatest common divisor.

Explanation:

The question asks to find the ratio of men to the entire class. The class has a total of 10 men and 14 women, which means the class size is 10 (men) + 14 (women) = 24 students.

To calculate the ratio of men to the entire class, divide the number of men by the total number of students: Ratio = 10 (men) / 24 (students). This can be simplified by dividing both numbers by the greatest common divisor, which is 2, giving us a simplified ratio of 5 (men) to 12 (students).

The ratio of men to the class is therefore 5:12.

Answer:

the answer is C. -5/7

The ratio of 1 foot 4 inches to 1 yard is 16:36 or 4:9.

To find the ratio of 1 foot 4 inches to 1 yard, we first need to convert both measurements to the same unit. Since there are 3 feet in a yard and 12 inches in a foot, we can express both measurements in inches.

1 foot is equivalent to 12 inches.

Therefore, 1 foot 4 inches is:

1 [tex]\times[/tex] 12 + 4 = 12 + 4 = 16 inches

Now, since there are 3 feet in a yard, and each foot has 12 inches, 1 yard is equivalent to:

3 [tex]\times[/tex] 12 = 36 inches

Now we have both measurements in inches, and we can set up the ratio:

16 inches: 36 inches

Therefore, the simplified ratio is:

16:36.

We can further simplify this ratio by dividing both numbers by 4:

(16/4):(36/4) = 4:9.