Ms. Ironperson and Mr. Thoro are making Avenger posters to give children when they visit Avenger Academy. Ms. Ironperson has completed 12 posters and will complete 6 more per day. Mr. Thoro has not started yet but can make 12 per day. At some point Mr. Thoro will catch up and both will have finished the same number of posters. When this does happen, how many posters will each Avenger have completed? If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?

Answer:

64000

Step-by-step explanation:

Answer:

64000

Step-by-step explanation:

Answer:

The algebraic equation describing the above

X+y= x-30

Step-by-step explanation:

The initial temperature of the environment= x degrees

Temperature of the front= y degrees

the environment dropped 30 degrees, means loosed 30 degrees.

The final temperature f the environment= x-30

The algebraic equation describing the above

X+y= x-30

Answer:

0

Step-by-step explanation:

To find the slope of two points, here is the formula (y2-y1)/(x2-x1)

So we have (1,2) and (4,2),

We let y2 = 2 and y1 = 2 and we let x2 = 4 and x1 = 1

So, (2-2)/(4-1) = 0/3

Our slope is 0.

Answer:

10.9361

Step-by-step explanation:

The lower control limit for xbar chart is

xdoublebar-A2(Rbar)

We are given that A2=0.308.

xdoublebar=sumxbar/k

Rbar=sumR/k

xbar      R

5.8        0.42

6.1         0.38

16.02    0.08

15.95    0.15

16.12     0.42

6.18      0.23

5.87     0.36

16.2      0.4

Xdoublebar=(5.8+6.1+16.02+15.95+16.12+6.18+5.87+16.2)/8

Xdoublebar=88.24/8

Xdoublebar=11.03

Rbar=(0.42+0.38+0.08+0.15+0.42+0.23+0.36+0.4)/8

Rbar=2.44/8

Rbar=0.305

The lower control limit for the x-bar chart is

LCL=xdoublebar-A2(Rbar)

LCL=11.03-0.308*0.305

LCL=11.03-0.0939

LCL=10.9361

Answer:

y=-1/4x-1/2

Step-by-step explanation:

When two lines are parallel, they have the same slope.

So for this line, we already know that the slope (m) has to equal -1/4x.

Slope intercept form is y=mx+b, where m is the slope and b is the y intercept.

in order to find the equation, we must plug in x and y to solve for b, the y intercept (the value of y when x=0).

Now, let's plug in 2 for x and -1 for y and solve for b:

-1=-1/4(2)+b=-1=-1/2+b=-1+1/2=b

b=-1/2

Hence, the answer is y=-1/4x-1/2

Answer:

The answer is -1/4x - 1/2

Step-by-step explanation:

Just took the Unit Session

False.

Slope is the "rise over run" (y/x) in a linear equation. Because the denominators are the same in both fractions, it means you can just focus on the numerator with the larger number as that one will be the steeper line.

Answer:

2/11 or approx. 18%

Step-by-step explanation:

There are 2 blue marbles out of 11 total marbles, so the probability will be 2/11.

2/11 = 0.18, or 18%

So, the odds are 2/11 or approx. 18%

Answer:

9:2

Step-by-step explanation:

9 red  and  2 blue

ways that an outcome cannot occur : how many ways it can occur

9 : 2  are the odds against a blue marble

Answer:

8i+8j

Step-by-step explanation:

3i+4j+5i+4j

i(3+5) + j(4+4)

Therefore 8i +8j

HAPPY TO HELP YOU

Answer:

Step-by-step explanation:

we have :

a=3i+4j

b=5i+4i

so that : a+b=3i+4j+5i+4j

=(3i+5i)+(4j+4j)

so    a+b=8i+8j=8(i+j)

Answer:

56 degrees

Step-by-step explanation:

They are supplementary, so they add to 180. 180 - 124 = 56.

Answer:

56 degrees

Step-by-step explanation:

They are supplementary, so they add to 180. 180 - 124 = 56.

Answer:

$1500

6 hours

Step-by-step explanation:

There is no one off fee, therefore we got (0,0) a starting point.

(1,125) is representing the first hour of rent, so 1 hour rent costs $125.

There is a direct relationship between the time and rental fee.

As a function is will be:

For x= 12, we get:

So, if f(x) = 750, then:

Step-by-step explanation:

If (5) = 3

Then (10) = 6

Because 5 x 2 = 10 so 3 x 2 = 6

Answer:

(a) The cumulative frequency curve for the data is attached below.

(b) (i) The inter-quartile range is 10.08.

(b) (ii) The 70th percentile class scores is 0.

(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.

Step-by-step explanation:

(a)

To make a cumulative frequency curve for the data first convert the class interval into continuous.

The cumulative frequencies are computed by summing the previous frequencies.

The cumulative frequency curve for the data is attached below.

(b)

(i)

The inter-quartile range is the difference between the third and the first quartile.

Compute the values of Q₁ and Q₃ as follows:

Q₁ is at the position:

[tex]\frac{\sum f}{4}=\frac{100}{4}=25[/tex]

The class interval is: 34.5 - 39.5.

The formula of first quartile is:

[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

Here,

l = lower limit of the class consisting value 25 = 34.5

(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 24

f = frequency of the class interval = 20

h = width = 39.5 - 34.5 = 5

Then the value of first quartile is:

[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

     [tex]=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75[/tex]

The value of first quartile is 34.75.

Q₃ is at the position:

[tex]\frac{3\sum f}{4}=\frac{3\times100}{4}=75[/tex]

The class interval is: 44.5 - 49.5.

The formula of third quartile is:

[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

Here,

l = lower limit of the class consisting value 75 = 44.5

(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 74

f = frequency of the class interval = 15

h = width = 49.5 - 44.5 = 5

Then the value of third quartile is:

[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

     [tex]=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83[/tex]

The value of third quartile is 44.83.

Then the inter-quartile range is:

[tex]IQR = Q_{3}-Q_{1}[/tex]

        [tex]=44.83-34.75\\=10.08[/tex]

Thus, the inter-quartile range is 10.08.

(ii)

The maximum upper limit of the class intervals is 69.5.

That is the maximum percentile class score is 69.5th percentile.

So, the 70th percentile class scores is 0.

(iii)

Compute the probability that a student scored at most 50 on the examination as follows:

[tex]P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}[/tex]

                                 [tex]=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89[/tex]

Thus, the probability that a student scored at most 50 on the examination is 0.89.

That means our price markup is $67.00-$50.00=$17.00

The markup price  is 34%.

It is given that cost price of the products is $ 50 and selling price of the product is  $ 67.

To find the markup price.

The profit and loss statement is a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period.

Thus, the markup in the price = [tex]\frac{S.P-C.P}{C.P} *100[/tex]

=[tex]\frac{67-50}{50} *100[/tex]

= 34[tex]%[/tex]%

So, the markup price  is 34%.

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Answer:

11.68ft or 11.68 feet

Step-by-step explanation:

From the above question, we are told that:

Area of the square and the Area semicircle is to be 190 ft squared.

We are also told in the question that:

The window has the shape of a square with a semicircle mounted on it.

Hence, the Diameter of the semicircle = Width of the Square

Let the Width of the square = x

Area of a square = Width²

= x²

Let the Diameter of the semi circle = x

Radius of the semi circle = Diameter of the semi circle/2 = x/2

Area of a semicircle = πr²/2

Area of a the semi Circle = π ×(x/2)² /2

= (πx²/4)/2

= πx²/8

Therefore,

Area of a square + Area of a semicircle = 190ft²

= x² + πx²/8 = 190

Cross Multiply

x² + πx² = 190

= x² ( 1 + π/8) = 190

x² = (190)/(1 + π/8)

x² = 136.42573798

x = √136.42573798

x = 11.680142892ft

Approximately x ≈ 11.68ft

Therefore, the width of the window = 11.68ft

Answer:

C. [tex] \sqrt {149} [/tex]

Step-by-step explanation:

Coordinates of the endpoints of the segment are (4, 4) & (-6, - 3)

By distance formula

Length of segment

[tex] = \sqrt {(4+3)^2 +(4+6)^2} [/tex]

[tex] = \sqrt {(7)^2 +(10)^2} [/tex]

[tex] = \sqrt {49 +100} [/tex]

[tex] = \sqrt {149} [/tex]

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

Work Shown:

LCM = least common denominator

List out the prime factorization of each denominator

So we have the list of primes 2,3, and 11 that help form the denominators when we multiply some of them together.

The prime 2 shows up at most twice, so 2*2 = 4 is a factor of the LCM

The prime 3 shows up at most one time, meaning 3 is also a factor

The prime 11 shows up at most one time, so 11 is another factor

Multiply these factors to get 4*3*11 = 12*11 = 132

The LCM is 132

---------------------

Another Approach:

Focus on 1/6 and 10/11 for now. The LCM is 66 because 6*11 = 66. We simply multiply the denominators together. Then we divide over the GCF 1 to get 66/1 = 66.

The LCM of 1/6 and 10/11 is 66

The fractions 1/6 and 10/11 are equivalent to 11/66 and 60/66 respectively

The original list of fractions updates to 11/66, 60/66, 5/12

We've gone from 3 different denominators to now 2 different denominators.

Repeat the steps of multiplying the denominators and dividing by the GCF

66*12 = 792

792/(gcf of 66 and 12) = 792/6 = 132

So the LCM of all the fractions is 132.

Answer:

To score good marks because 1 marks can give us good life in future

-12 is the answer

Step-by-step explanation:

[tex] \frac{3x}{4} = - 9[/tex]

Firstly we have to take 4 to the R.H.S and multiply -9 with 4

[tex]3x = - 9 \times 4 [/tex]

[tex]3x = - 36[/tex]

Now, take 3 to R.H.S and divide 3 by -36

[tex]x = \frac{ - 36}{ \: \: 3} [/tex]

so after solving this we get our answer,

[tex]x = - 12[/tex]

Hope it helps u

Answer:

3 / 13

Step-by-step explanation:

Hello!

There are 52 cards in a deck with half being red and half being black. The question ask for when a black card is drawn so we divide the total by 2

52/ 2 = 26

There are 6 black face cards in a deck so to get the probability one will be drawn we put how many there are over the total amount

6/26 we can simplify this

3 / 13

The answer is 3 / 13

Hope this helps!

Answer:

3/13

Step-by-step explanation:

In a standard 52-card deck, there are 26 black cards and 26 red cards. Of the 26 black cards, 13 are spades and 13 are clubs. Each suit has 3 face cards, Jack, Queen, and King. Therefore, there are 6 black face cards out of a total of 26 black cards.

p(face given black) = 6/26 = 3/13

Answer: a = [tex]\frac{u+2}{2}[/tex]

We want to isolate a. Add both sides by 2. Then we get u + 2 = 2a. To get just a, we can divide by 2 to get (u+2)/2.

Hope that helped,

-sirswagger21

Hey there! I'm happy to help!

We want to get a on one side of the equation all on its own.

Let's flip the equation around so a ends up on the left. Usually variables are supposed to be on the left.

2a-2=u

We add 2 to both sides.

2a=u+2

We divide both sides by 2.

a=(u+2)/2

We divide both u and 2 by 2 so our answer is completely simplified.

a=1/2u+1.

I hope that this helps! Have a wonderful day! :D

Answer: t = 4.87s

Step-by-step explanation: The vertical position y is given by

[tex]y = -16t^{2}+380[/tex]

If y at the base of the cliff equals 0, then equation is

[tex]-16t^{2}+380=0[/tex]

[tex]-16t^{2}=-380[/tex]

[tex]t^{2}=\frac{-380}{-16}[/tex]

[tex]t=\sqrt{\frac{380}{16}}[/tex]

[tex]t=\sqrt{23.75}[/tex]

t = 4.87

Since it is time we want, the negative value of the square root can be ignored. So, at the base of the cliff, the rock will hit the ground after 4.87 seconds.

Answer: He doesn't have any money left that period point blank

Step-by-step explanation

7-6=1

1-3= you cant do that

so he doesn't get soda at all.

The two number with the largest product would be the two numbers closest together.

Divide 23 in half:

23/2 = 11.5

Use the whole numbers on each side of 11.5, so you have 11 + 12 = 23

Multiply: 11x 12 = 132

Answer:

$43,350

Step-by-step explanation:

To find the increase in the salary we need to find the percentage.

2 percent of $42,500 = $850.

$42,500 + $850 =  $43,350.

New salary = $43,350.

Answer:

7/5

Step-by-step explanation:

rise over run

start at the bottom point and count up along y axis and then count over along x axis

The value of a in the function's equation is 3

A function is an equation that has only one answer for y for every x. A function assigns exactly one output to each input of a specified type

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions,

equation of  parabola is :

[tex]y= a (x-h)^{2} + k[/tex]

where ,

h= horizontal coordinate of graph

k = vertical coordinate of graph

a =  the value of the coefficient

According to the question

horizontal coordinate of graph  = -2

vertical coordinate of graph = 2

[tex]y= a (x-h)^{2} + k[/tex]

[tex]y= a (x+2)^{2} + 2[/tex]

now we will take one point from  x and y value from the graph  to take out value of  coefficient a  

from graph (x,y) = (-1,5)

[tex]5= a (-1+2)^{2} + 2[/tex]

[tex]\\3= a (-1+2)^{2}[/tex]

[tex]\\3= a (1)^{2}[/tex]

[tex]a = 3[/tex]

Hence, the value of a in the function's equation is 3

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Answer:

5 calories.

Step-by-step explanation:

We begin by calculating the rate at which Raquel burns calories while hiking.

This can be obtained as follow:

Calories burned = 225 calories

Time = 45 mins

Rate =?

In this case, the Rate is simply defined as calories per unit time. Mathematically, it is expressed as:

Rate = Calorie/time

With the above formula, we can obtain the rate at which Raquel burns calories as follow:

Calories burned = 225 calories

Time = 45 mins

Rate =?

Rate = Calorie/time

Rate = 225/45

Rate = 5 cal/min

Therefore, Raquel burns Calories at a rate of 5 cal/min.

Now, we shall determine the calories burned by Raquel in 1 minutes. This is illustrated below:

Rate = 5 cal/min

Time= 1 min

Calorie =.?

Rate = Calorie /time

5 = Calorie /1

Cross multiply

Calorie = 5 x 1

Calorie = 5

Therefore, Raquel burns 5 calories in 1 minute while hiking.

Answer:DC=7

Step-by-step explanation:

As it is written △ABC = △DBC.   So the corresonding legs (the legs which are equal ) are as follows:

AC=DC       AB=DB      BC= BC

So DC=7  the same like AC