In 1983, a pair of jeans cost $66.35. If a pair of jeans costs $118.10 today, what is the CPI? a. 152 b. 156 c. 178 d. 184

Answer:

First question

a = 1 , h = 0 , k = 6 ⇒ third answer

Second question

y = 2x² + 4 ⇒ second answer

Third question

No of the choices correct ⇒ fourth answer

Step-by-step explanation:

First question

∵ f(x) = x² + 6

- It is a quadratic function with general form ax² + bx + c

- Its vertex is (h , k), where h = -b/2a and k = f(h)

∵ a = 1 , b = 0 , c = 6

∴ h = 0/2(1) = 0

∴ f(0) = 0² + 6 = 6

∴ a = 1 , h = 0 , k = 6 ⇒ third answer

Second question

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

∵ y = 2x²

∵ y is shifted 4 units up

∴ k = 4

∴ y + 4 = 2x² + 4

∴ y = 2x² + 4 ⇒ second answer

Third question

∵ y = -2x² + 3

- It is a quadratic equation with general form ax² + bx + c

- It represented graphically by parabola

- If a is positive the parabola opens upward

- If a is negative the parabola opens downward

∵ a = -2

∴ The parabola opens downward

∴ No of the choices correct ⇒ fourth answer

The question is a binomial distribution problem in mathematics. You can use the binomial probability formula to calculate the probability that exactly 4 out of 8 treated dolphins are cured.

This mathematics problem involves understanding probability and the binomial distribution. The word 'exactly' is a clue that this is a binomial problem.

The general formula for a binomial probability is: P(X = k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where:

So, if we substitute the values into the formula, we have:

P(X = 4) = C(8, 4) * (0.94^4) * ((1-0.94)^(8-4))

Therefore, Use this formula to find the probability that exactly 4 out of 8 dolphins are cured.

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Basically, the question is asking for 18% of $23.

The answer is $4.14.

The tip was $4.14, because you take 18% of $23 and then you end up with $4.14

Answer:

A=13+B

Step-by-step explanation:

Linda earns $13  each hour working part-time at a bookstore.

Linda earns $1 for each book she sells.

Let

A be the amount (in dollars) that Linda earns in an hour;

B be the number of books Linda sells in an hour.

So,

[tex]A=13+B\cdot 1\\ \\A=13+B[/tex]

The graph is shown in attached diagram

Answer:

t+m=20--------> t=20-m

3t+11m=100

Substitute

3(20-m)+m=100

60m-3m+11m=100

Get rid of 60

-3m+11m=40

8m=40

Divide by 8

m=5

This tells us that there are 5 Multiple Choice questions. So the remaining 15 question on the test must be True/False questions.

If we got all 5 Multiple Choice questions correct we would score 11 points for each of the five questions and this would give us 55 points. Then if we got all 15 True/False questions correct at 3 points each, we would score 15 times 3 or 45 points. So the total number of points on the test would be 55 + 45 = 100.

Step-by-step explanation:

The answer is:

There are 15 true/false questions while there are 5 multiple choice questions.

To solve the problem, we need to write two equations using the given information.

We know that there are twenty (20) questions consisting of true/false and multiple choice questions, so, writing the first equation we have:

Let be the true/false questions "x" and the multichoice questions "y".

First equation,

[tex]x+y=20[/tex]

Also, we know that the true/false questions worth 3 points while the  multichoice questions worth 11 points making a total of 100 points for the total examen, so, writing the second equation, we have:

Second equation,

[tex]3x+11y=100[/tex]

Now, we have to isolate one of the variables in function of the other variable, so, from the first equation, we have:

[tex]x+y=20[/tex]

[tex]x=20-y[/tex]

Then, substituting "x" into the second equation, we have:

[tex]3x+11y=100[/tex]

[tex]3(20-y)+11y=100[/tex]

[tex]60-3y+11y=100[/tex]

[tex]60+8y=100[/tex]

[tex]8y=100-60=40[/tex]

[tex]y=\frac{40}{8}=5[/tex]

Then, substituting "y" into the first equation, we have:

[tex]x+y=20[/tex]

[tex]x+5=20[/tex]

[tex]x=20-5=15[/tex]

Hence, we have that there are 15 true/false questions while there are 5 multiple choice questions.

Let's prove that we are right by substituting the obtained answers into the both equations, if the equations are satisfied, the answers are ok.

Substituting into the first and the second equation, we have:

First equation,

[tex]x+y=20\\5questions+15questions=20questions\[/tex]

Second equation,

[tex]3x+11y=100points\\3*(15)+11*(5)=100points\\45points+55points=100points[/tex]

We can see that both equations are satisfied, so, the answers are ok.

Have a nice day!

Answer:

Step-by-step explanation:

1. First, put together the information we have. Total = 121. Emily has 40% more than Carl, and Carl has 60% more than Antony.

2. Next, set each person as a variable. Antony = x. Carl = 1.6x. Emily = 1.4 times 1.6x.

3. Next, form an equation using these variables.

    x + 1.6x + (1.4 x 1.6x) = 121

    x + 1.6x + 2.24x = 121

    4.84x = 121

    x = 25

4. Finally, plug in x to our previous variables in step #2 to find the number of stamps Emily and Carl have.

Antony: x = 25 stamps

Carl: 1.6x = 40 stamps

Emily: 1.4 times 1.6x = 56 stamps

By the way, is this for RSM? If so, I am working on that problem right now and I searched up the solution but couldn't find it, so I stumbled upon this. I hope this helped!

Answer: x= 8

Step-by-step explanation:

x^2 = 64

sqrt{x^2} = sqrt64}

x = 8

The volume of the gigantic fridge is 2.5 times grater than the volume of the regular fridge.

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic m.

The volume is found as the product of the area and the length;

Volume  = Area ×length

V=A×L

Volume of the regular fridge;

V=  1 m²× 2 m

V=2 m³

Volume of the large fridge;

V=  2 m²× 5/2 m

V=5 m³

The ratio of the volume of the gigantic fridge as the volume of the regular fridge is;

[tex]\rm n = \frac{5}{2} \\\\ n= 2.5[/tex]

Hence, volume of the gigantic fridge is 2.5 times grater than the volume of the regular fridge

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Answer: -x^2+12x+3

Step-by-step explanation:

Answer:

[tex](\frac{6}{n})-8[/tex] .

Step-by-step explanation:

Given  : "8 less than the quotient of 6 and a number".

To find : expression represents the following word phrase.

Solution : We have given 8 less than the quotient of 6 and a number.

According to question :

Quotient of 6 and n = [tex](\frac{6}{n})[/tex]  .

For less than we will use negative sign.

8 less than the quotient of 6 and a number.

[tex](\frac{6}{n})-8[/tex] .

Therefore,  [tex](\frac{6}{n})-8[/tex]  .

Answer:

2 square root 15, or the second one down

ANSWER

[tex]2 \sqrt{15} [/tex]

EXPLANATION

We want to simplify

[tex] \sqrt{60} [/tex]

There is a perfect square under the radical sign:

[tex] \sqrt{4 \times 15} [/tex] Split the radical sign for both factors:

[tex] \sqrt{4} \times \sqrt{15} [/tex]

Simplify the first factor

[tex]2 \sqrt{15} [/tex]

The second option is correct.

Find the exact value of each one:

5^2 = 25

2^4 = 16

3^3 = 27

1^8 = 1

Now you can list them in order from smallest to largest:

1^8, 2^4, 5^2, 3^3

Answer:

Step-by-step explanation:

5²=25

2^4=16

3^3=27

1^8=1

1<16<25<27

so 1^8<2^4<5^2<3^3

Answer:

f(x) ⇒ Graph C

g(x) ⇒ Graph D

h(x) ⇒ Graph A

j(x) ⇒ Graph E

Step-by-step explanation:

* Lets revise the quadratic function and its inverse

- The quadratic function if f(x) = x², its vertex is the origin

- To find its inverse, switch x and y and solve for y

∵ y = x² ⇒ switch x and y

∴ x = y² ⇒ solve for y

∴ y = ± √x

- If y = √x , then the graph is up the x-axis

- If y = -√x , the graph is down the x-axis

∴ The inverse function is y = √x

* Now lets solve the problem

- All the figure are the inverses of the quadratic function y = x²

∵ f(x) = √(x - 1)

# x - 1 means the graph move to the right 1 unit

∴ Its vertex is (1 , 0)

* The graph of f(x) = √(x - 1) is graph C

∵ g(x) = -√x

# The sign (-) means the graph reflected about the x-axis

∴ Its vertex is (0 , 0) but the graph under the x-axis

* The graph of g(x) = -√x is graph D

∵ h(x) = √x

∴ Its vertex is (0 , 0)

- It is the inverse of y = x² , the graph up to the x-axis

* The graph of h(x) = √x is graph A

∵ j(x) = -√(x - 1)

# x - 1 means the graph move to the right 1 unit

# The sign (-) means the graph reflected about the x-axis

∴ Its vertex is (1 , 0) , the graph down the x-axis

* The graph of j(x) = -√(x - 1) is graph E

Answer:

Oxygen and Silicon

Step-by-step explanation:

Oxygen and Silicon make up 75% of the weight of the Earth's crust.

Answer = oxygen and silicone.

Answer:a

aStep-by-step explanation:    ive done it

The area of a triangle with a base of 6 cm and height of 8 cm, is 24 cm²

Area is the amount of space occupied by a two dimensional shape or object.

The area of a triangle is given by:

Area of triangle = (1/2) * base * height

Assume the triangle has a base of 6 cm and height of 8 cm, hence:

Area of triangle = (1/2) * 6 * 8 = 24 cm²

The area of a triangle with a base of 6 cm and height of 8 cm, is 24 cm²

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Hello There!

The "Inter-Quartile Range" is 9

Answer:

The interquartile range is 9

Step-by-step explanation:

13. y > 2

14. x - 13 < 9;; x < 22

15. x + 86 < 263;; at most 177 pounds

Answer:

g(b)=4b+5

Step-by-step explanation:

because this is how you write it as a function

Answer:2 > -6 or -6 < 2

Step-by-step explanation:

Answer:  2>-6 is correct

Step-by-step explanation:

We know that 2 is a grater number than -6 so what we can do is put this > but make sure that its facing the 2 and there its simple  hope I helped! :p plz rate me

Answer:

A)3,9

Step-by-step explanation:

lets take the length as "x"

since the width is 3 times the length we can use 3x to represent the width

formula for perimeter: 2(l)+2(w)

2(x)+2(3x)=24

2x+6x=24

8x=24

8x/8=24/8

x=3

if x is 3, the length is 3

if x is 3, the width, 3x is 9, (3*3)

The dimensions of the rectangle are a length of 9 inches and a width of 3 inches, with the width being one-third of the length. This corresponds to option D (9, 3) in the list of given choices.

The length and width of the rectangle when the perimeter is 24 inches and the length l is 3 times the width w, we can set up equations based on the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Given that l = 3w, we substitute this into the perimeter formula to get:
24 = 2(3w) + 2w24 = 6w + 2w24 = 8w
Dividing both sides by 8 to solve for w:
w = 3

Now that we know the width is 3 inches, we can find the length by multiplying the width by 3:
l = 3w = 3(3) = 9

So, the length is 9 inches, and the width is 3 inches, which corresponds to option D. Therefore, the dimensions of the rectangle are a length of 9 inches and a width of 3 inches.

The answer is C. Compass.

Compass isn't used in the geometric constructions.

Among pencil, protractor, compass, ruler protractor is not used in the geometric constructions.

Geometric construction refers to the process of drawing lines, angles and other geometric shapes and figures using only a compass and a ruler.

There are four things pencil, protractor, compass, ruler.

For any drawing we need a pencil, To draw straight lines we need a ruler and to draw circles we need to use compass.

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Answer:

192 cups is equal to 12 gallons

Step-by-step explanation:

we know that

1 cup=0.0625 gal

or

1 gal=16 cups

Method 1

192 cups=192*0.0625=12 gal

Method 2

192 cups=192/16=12 gal

Answer:

Step-by-step explanation:

Convert 192 cups to gallons. Enter your answers in the boxes.

For the blanks answer it like this

There are   16 cups in 1 gallon. Therefore, 192 cups is equal to  

12  gallons.

it’s the last option

The  correct application of the quadratic formula is:

               [tex]x=\dfrac{9\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex]

The quadratic equation is given by:

[tex]y=6x^2-9x+22[/tex]

We know that the solution of the quadratic equation:

[tex]y=ax^2+bx+c[/tex]

is given by:

[tex]y=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here we have:

[tex]a=6[/tex]

[tex]b=-9[/tex]

and

[tex]c=22[/tex]

Hence, the quadratic formula is given by:

[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4\cdot (6)\cdot (22)}}{2\cdot (6)}[/tex]

i.e.

[tex]x=\dfrac{9\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex]

Answer:

Step-by-step explanation:

Surface area of a cylinder = 2 x 3.14 x rh + 2 x 3.14 x r^2

S.A. = (2 x 3.14 x 3 x 18.2) + (2 x 3.14 x 3^2)

S.A. = 399.4cm^2

Answer:

x = 2.

y =  6.

Step-by-step explanation:

Consider the triangle on the left.

Because there are 2 equal angles at the vertex on the bottom right:

3/9 = x/(8 - x)

1/3 = x / (8 - x)

3x = 8 - x

4x = 8

x = 2  (answer).

Similarly, for the second triangle:

3/y = 2/4

3/y = 1/2

y = 6

(answer).

Answer:

-51, -41, -38, 13, 41, 50

Step-by-step explanation:

The integers ordered from least to greatest are: -51, -41, -38, 13, 41, 50.

To order the integers from least to greatest, one must start by identifying the negative integers and then the positive integers. Among negative integers, the larger the absolute value, the smaller the number. Conversely, for positive integers, the larger the number, the greater it is.

Starting with the negative integers:

-51 is the smallest because it has the largest absolute value among the negative numbers.

-41 is the next smallest negative number.

-38 is the smallest negative number because it has the smallest absolute value among the negatives.

Now, moving on to the positive integers:

13 is the smallest positive number.

41 is the next smallest positive number.

50 is the largest positive number.

Putting it all together:

-51, -41, -38, 13, 41, 50.

ANSWER

[tex]x = - \frac{2\pi}{3} [/tex]

EXPLANATION

The given function has equation

[tex]y = \tan( \frac{3}{4}x) [/tex]

This can be rewritten as

[tex]y = \frac{ \sin( \frac{3}{4}x ) } { \cos(\frac{3}{4}x )}[/tex]

The asymptote occurs at:

[tex]\cos(\frac{3}{4}x ) = 0[/tex]

This implies that,

[tex] \frac{3}{4} x = \frac{ \pi}{2} [/tex]

[tex]x = \frac{ \pi}{2} \times \frac{4}{3} [/tex]

[tex]x = \frac{2\pi}{3} [/tex]

Or

[tex]\frac{3}{4} x = - \frac{ \pi}{2} [/tex]

[tex]x = \frac{ - \pi}{2} \times \frac{4}{3} [/tex]

[tex]x = - \frac{2\pi}{3} [/tex]

The second choice is correct.

Answer:

B) [tex]x = \frac{2\pi }{3}[/tex]

Step-by-step explanation:

this is the correct answer on ed-genuity, hope this helps! :)

[tex]\text{Hey there!}[/tex]

[tex]\text{Both numbers are divisible to 4, so divide the numerator and denominator from 4}[/tex]

[tex]\frac{7,848\div4}{4\div4}[/tex]

[tex]\text{7,848}\div4=1,962[/tex]

[tex]\text{4}\div4=1[/tex]

[tex]\text{1,962}\div1=1,962[/tex]

[tex]\boxed{\boxed{\text{Answer: 1,962}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

The explicit formula is:

[tex]a_n = 200 +5(n-1)[/tex]

Step-by-step explanation:

Freya increases 5 yards daily to the number of yards she runs.

Note that the increase factor is constant, so this problem can be modeled using an arithmetic sequence.

The explicit formula for an arithmetic sequence is:

[tex]a_n = n_1 + d(n-1)[/tex]

Where:

[tex]a_n[/tex] is the number of yards that Freya runs on the day

[tex]a_1[/tex] is the number of yards that he runs on day 1

d is the increase factor. [tex]d = 5[/tex] yards

n is the number of days

Then as [tex]a_1 = 200[/tex] and [tex]d = 5[/tex], the explicit formula is:

[tex]a_n = 200 +5(n-1)[/tex]

Answer:

a_n = 200 (n-1)5

Step-by-step explanation:

just to simplify from those over achievers who confuse the living  h e l l out of everyone

Answer:

(−1, –1.25), (5, –2.75)

Step-by-step explanation:

If "slope-intercept form" is mentioned, then we already know that the function rule is that of a straight line with slope m and y-intercept b.

As we go from (−1, –1.25) to (5, –2.75), x increases by 6 and y decreases by 1.50.  Thus, the slope, m, is m = rise / run = -1.50 / 6, or m = -0.25 or -1/4.

Choosing one of the given points at random:  (8, -3.5), we start with the slope-intercept form y = mx + b and substitute -1/4 for m, 8 for x and -3.5 for y:    y = mx + b  becomes  -3.5 = (-1/4)(8) + b.  Then -3.5 + 2 = b, or b = -1.5.

The desired equation is y = (-1/4)x - 3/2, or y = -0.25x - 1.5

To write a function rule in slope-intercept form for the given ordered pairs, we need to calculate the slope and find the y-intercept. The slope can be calculated using the formula (Y2 - Y1) / (X2 - X1), and the y-intercept can be found by using the point-slope form and substituting one of the ordered pairs. The function rule in slope-intercept form for the given ordered pairs is y = -0.25x - 1.5.

To write a function rule in slope-intercept form, we need to find the slope (m) and the y-intercept (b). Given the ordered pairs (–12, 1.5), (−1, –1.25), (5, –2.75), (8, −3.5), we can calculate the slope using the formula m = (Y2 - Y1) / (X2 - X1). Let's choose two ordered pairs to calculate the slope:

Using (–12, 1.5) and (−1, –1.25):

m = (-1.25 - 1.5) / (-1 - (-12)) = (-2.75) / (11) = -0.25

Now, we can use the point-slope form y - y1 = m(x - x1), where (x1, y1) is one of the ordered pairs and substitute the slope and one of the points to find the y-intercept:

Using the ordered pair (–12, 1.5):

y - 1.5 = -0.25(x - (-12))

y - 1.5 = -0.25(x + 12)

y - 1.5 = -0.25x - 3

y = -0.25x - 3 + 1.5

y = -0.25x - 1.5

Therefore, the function rule in slope-intercept form (fraction form) is y = -0.25x - 1.5.

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