Carolyn, Julia, and Roberta share $77 in a ratio of 4:2:1, respectively. How many dollars did Carolyn recieve?

If ABCD is the rectangle, then AB and BC are perpendicular.

Let m₁ and m₂ - slopes of perpendicular lines. Therefore

m₁m₂ = -1 → m₂ = -1/m₁.

We have m₁ = 2/3 then m₂ = -1/(2/3) = -3/2.

The slope of BC is -3/2.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

We are given ABCD is the rectangle, then AB and BC are perpendicular.

Let m₁ and m₂ are slopes of perpendicular lines. Therefore.

m₁m₂ = -1

m₂ = -1/m₁.

We have m₁ = 2/3 then;

m₂ = -1/(2/3) = -3/2.

Hence, The slope of BC is -3/2.

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Answer:

C: 0.25  

Step-by-step explanation:

We will use conditional probability formula to solve our given problem.

[tex]P(B|A)=\frac{P(\text{A and B})}{P(A)}[/tex], where,

[tex]P(B|A)[/tex]= Probability of event B, given probability of event A.

[tex]P(\text{A and B})[/tex]= Probability of event A and event B.

[tex]P(A)[/tex]= Probability of event A.

Let us substitute our given values in conditional probability formula.

[tex]P(B|A)[/tex]= Probability that a student plays a sport given that student is a senior.

[tex]P(\text{A and B})[/tex]=The probability that a student is a senior and plays a sport = 0.05.

[tex]P(A)[/tex]= Probability that a student is a senior = 0.20.

[tex]P(B|A)=\frac{0.05}{0.20}[/tex]

[tex]P(B|A)=\frac{1}{4}[/tex]

[tex]P(B|A)=0.25[/tex]

Therefore, the probability that a randomly selected student plays a sport, given that the student is a senior will be 0.25 and option C is the correct choice.

Answer:

probability that a randomly selected student plays a sport, given that the student is a senior is 0.25

Step-by-step explanation:

Let, A be an event that a student is senior.

Probability can be given as , p(A) = 0.20

B be the event where student plays a sport

Probability can be given as , p(B) = 0.15

We have given that the probability of a student is a senior and plays a sport is 0.05.

i.e p(A∩B) =  0.05

We need to find the probability that a randomly selected student plays a sport, given that the student is a senior i.e p(B/A) .

Use the formula: p(B/A) = p(A∩B) / p(A)

Plug corresponding values to get p(B/A).

p(B/A) = p(A∩B) / p(A)  = 0.05 /0.20

p(B/A) = 0.25 , this is the answer

Answer:

D

Step-by-step explanation:

I have answers to whole packet:

1.D

2.A

3.C

4.D

5.C

6.D

7.A

8.C

9.A

10.B

11.A

12.A

13.A

14.B

15.A

16.B

17.A

18.A

19.B

20.C

21.A

22.A

23.D

24.B

Answer:

D) x = 14

Step-by-step explanation:

x/2 = 7

We want to isolate x

We can multiply by 2 on each side.

2 * x/2 = 7*2

x = 14

Answer:

14

Step-by-step explanation:

Well if you simplify or divide how ever you want to say it, it will be simplified to 7.

Answer:

Essence is 140 flyers per hour

Raizon is 80 flyers per hour

Step-by-step explanation:

In essence (if you see what I did there) a unit rate (strictly in this context) is how much work is done for 1 hour of time. To find this, we simply divide the number of flyers by the number of hours of worked.

So, for Essence:

[tex]\frac{420}{3} = 140[/tex]

The units for this problem will be flyers per hour. So, Essence has a unit rate of 140 flyers per hour.

For Raizon:

[tex]\frac{640}{8} = 80[/tex]

Raizon has a unit rate of 80 flyers per hour.

Answer:

13/30

Step-by-step explanation:

5/6 -2/5

We need to get a common denominator of 30

5/6 *5/5 = 25/30

2/5 * 6/6 = 12/30

5/6 - 2/5

25/30 - 12/30

13/30

Answer:

13/30

Step-by-step explanation:

First find their least common multiple. ( you can list it out)

6= 6,12,18,24,30

5=5,10,15,20,25,30

LCM= 30

5/6= 25/30

2/5=12/30

25/30 - 12/30= 13/30

Answer:

(1-2)3X/10

-1(3X)/10

-3X/10

Answer:

Income = 637

Step-by-step explanation:

Income = weekly salary + commission

commission = 6.5% * sales

commission = .065* 4800

                     = 312

Income = weekly salary + commission

Income = 325+312

Income = 637

Answer: j(kl) I hope I helped the reason this correct is because it the expression but then the parenthesis are in a different placement.

your question is incomplete. please read below to find the missing content.

A. (j + k)

B. l j(kl)

C. (2jk)l

D. (j + k)l

(jk)l is  equivalent to  l j(kl)

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Answer:

ITS 1/2

Step-by-step explanation:

Marble's mother requires 1/2 cup of flour .

Proportion is the number which is considered in comparative relation to a whole.

Fraction is  a number expressed as a quotient, in which a numerator is divided by a denominator

According to the problem,

∴ Number of cup of flour that Marble's mother require is 2/3 part of 3/4

                       = (2/3 x 3/4) = 1/2

∴ Marble's mother requires 1/2 cup of flour .

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Based on the information given, it can be concluded that 35% of the circle is shaded, which is equivalent to the fraction 7/20.

To understand what area of the circle is shaded, let's first calculate how much is not shaded:

First area: 1/4 = 0.25

Second area: 2/5 = 0.4

Total of the area that is not shaded: 0.65

The total area shaded: 1 -0.65 = 0.35

This means that the total shaded is 0.35. Now, let's convert 0.35 to a fraction:

[tex]\frac{35}{100} = \frac{7}{20}[/tex]

Based on this, the shaded area is 7/20

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Final answer:

The equation that best models the situation of the pizza delivery worker's scooter mileage is 50d = 12,900, where d represents the number of days worked.

Explanation:

The question asks us to find out which equation best models the situation where a pizza delivery worker drives a certain number of miles after d days of pizza delivery. To start, the worker bought a scooter with 12,100 miles on it. Each day of work he adds 50 miles to the total. After d days of delivery, the total miles driven on the scooter equals 25,000. We are looking for an equation that represents this scenario.

The total mileage on the motor scooter after d days can be calculated by the initial mileage plus the product of the number of days and the average miles driven per day. Mathematically, this is represented by:

12,100 miles + 50 miles/day × d days = 25,000 miles

To find the equation that models this situation, we subtract 12,100 from both sides to isolate the term with d on one side:

50d = 25,000 - 12,100

So, the equation that models this situation is:

50d = 12,900

Answer:

x is all real numbers

Step-by-step explanation:

6 + 5|2x -3| ≥ 4

The first step is to subtract 6 from each side

6 -6+ 5|2x -3| ≥ 4-6

5|2x -3| ≥ -2

Now divide each side by 5

5/5|2x -3| ≥ -2/5

|2x -3| ≥ -2/5

Absolute values are always positive.  Our absolute value is greater than a negative number.  It is always true.  X can be any number and our absolute value will still be greater than -2/5.

x is all real numbers

x            40

------ = --------

955    100

Cross multiply

955x40=38200

38200÷100=382

u get 382

955 -382= 573

$573

So here are the rules with change by percentage (m = percentage in decimal form, n = original, and r = new):

Since this is a price reduction, we will be following the second rule. In this case:

[tex]40\%=0.4\\\\(1-0.4)*955=r\\0.6*955=r\\573=r[/tex]

In short, the reduced price of the computer is $573.

Answer:

The correct answer is A.

Step-by-step explanation:

In order for a set to be a solution set, all of the numbers in the set must satisfy the equation. In this case, we are looking to satisfy the equation x < 14. So we must be able to tell that every number in the set is less than 14. In each of the sets (except for A), there is at least one number that is greater than 14. There are no numbers greater than 14 in A.

Answer:

For 46•.029

First you would show how you multiply 9 times six then 9 times 4 then you put it on the bottom

After that you would do 2 times six then 2 four then you put it one space down from the other aanswer and add them

Sorry ignore this if it’s complicated

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

evaluate the parenthesis before raising to power 66

3² = 9 and 2³ = 8, hence

(3² - 2³)= (9 - 8) = 1

[tex](3^2-2^3)^{66}[/tex] = [tex]1^{66}[/tex] = 1

Answer:

van : 12 miles per gallon

cabinets: 3 cabinets a day

retail job for $500

Step-by-step explanation:

van: 240 miles/20 gallons = 12 miles per gallon

cabinets: 24/8= 3

jobs: $500 for 40 hours and $12 times 40 hours gets you $480

first job pays $20 bucks more

Ques 1)

A van travels 240 miles on 20 gallons of gas.

This means that 20 gallons of gas is used to travel 240 miles.

This means that:

1 gallon of gas is used to travel  :

              [tex]\dfrac{240}{20}=12\ miles[/tex]

Hence, it travels 12 miles per gallon.

Ques 2)

Carlos installed 24 wooden cabinets in 8 days.

i.e. in 8 days he install 24 cabinets

This means in 1 day he will install

[tex]\dfrac{24}{8}=3\ cabinets[/tex]

On the average, he will  install 3 cabinets each day.

Ques 3)

100 sheets cost $ 2.50

This means that cost of 1 sheet is: $ 0.0250

( since,   [tex]\dfrac{2.50}{100}=0.0250[/tex] )

150 sheets at $3.50

This means that cost of 1 sheet is: $ 0.0233

( since,  [tex]\dfrac{3.50}{150}=0.02333[/tex] )

This means that the cost per sheet is cheaper in the buy:

    150 sheets at $3.50.

Ques 4)

Pack A has 36 cookies for $5.90.

This means that cost of 1 cookie is: $ 0.16388 )

(  since,  [tex]\dfrac{5.90}{36}=0.16388[/tex] )

and  Pack B has 24 cookies for $4.10.

This means that cost of 1 cookie is: $ 0.170833

( since, [tex]\dfrac{4.10}{24}=0.170833[/tex] )

The cost per cookie is cheaper in Pack A.

Hence, the pack which has cheaper cookies is: Pack A.

Ques 5)

One is in retail and pays $500 for a 40-hour work week.

This means that the payment for 1 hour is: $ 12.5

( since, [tex]\dfrac{500}{40}=12.5[/tex] )

The other job is at a restaurant and pays $12 an hour.

This means that the job which has a higher hourly rate is:

In retail which pays $500 for a 40-hour work week.      

( since 12.5>12  )        

Answer:

Option C.

Step-by-step explanation:

The given expression is

[tex]\sqrt{18}[/tex]

We need to find the most simplified form of the given expression.

The given expression can be rewritten as

[tex]\sqrt{2\times 3\times 3}[/tex]

[tex]\sqrt{2\times 3^2}[/tex]

Using the properties of radical expression, we get

[tex]\sqrt{2}\times \sqrt{3^2}[/tex]     [tex][\because \sqrt{mn}=\sqrt{m}\sqrt{n}][/tex]

[tex]\sqrt{2}\times 3[/tex]

[tex]3\sqrt{2}[/tex]

Therefore, the correct option  is C.

Answer:

1/4

Step-by-step explanation:

The probability of getting a heads is 1/2

The probability of getting an odd number

1,3,5

-----------   =   3/6  = 1/2

1,2,3,4,5,6  

Since they are independent events, we multiply the probabilities

1/2 * 1/2 = 1/4

Answer:

[tex]\frac{1}{4} (16-x)[/tex]

Step-by-step explanation:

Let the number be x

difference of 16 and a number =[tex]16-x[/tex]

one fourth the difference of 16 and a number =[tex]\frac{1}{4} (16-x)[/tex]

Answer:

The expression represents the phrase is  [tex]\frac{1}{4}[/tex] (16-x)

Step-by-step explanation:

Let the number is 'x'

The difference of 16 and a number is

16-x

The one fourth the difference of 16 and a number is

[tex]\frac{1}{4}[/tex] (16-x)

Hence, the expression which represent the phrase is

[tex]\frac{1}{4}[/tex] (16-x)

Answer:

300-124=176

I think this is corroct

Answer:

Everything should simplify down to -9a-3 (your answer)

Step-by-step explanation:

Distributive property is basically multiplying the outside number into the inside parenthesis ().  Basically #(a)--->#a        or   #(a+b)---> #a+#b

Since you're not ask to solve for anything but simplify, just multiply 3 to -3a and -1.....

so 3*-3a is -9a and 3*-1 is -3      and you have 3(-3a-1)= -9a-3

Final answer:

The distributive property is a mathematical property that allows us to distribute multiplication over addition or subtraction. It helps simplify expressions and perform calculations more efficiently in algebra and arithmetic.

Explanation:

The distributive property is a mathematical property that allows us to distribute multiplication over addition or subtraction. It states that for any numbers a, b, and c, the expression a * (b + c) is equal to a * b + a * c. This property helps us simplify expressions and perform calculations more efficiently.

For example, if we have the expression 3 * (2 + x), we can use the distributive property to simplify it to 3 * 2 + 3 * x, which becomes 6 + 3x. This allows us to break down the calculations into smaller steps and avoid errors.

The distributive property is one of the fundamental properties of multiplication and is widely used in algebra and arithmetic.

Answer: 81 in. (6.75 ft.) by 60 in. (5 ft.)

First, convert 27 ft. and 20 ft. to inches to make it easier to work with. This would convert like this:

27 ft. x 12 in. = 324 in.

20 ft. x 12 in. = 240 in.

This also means that the scale converts to 1/4 in. = 12 in.

Now, take your 324 in. and 240 in. and apply them to the scale.

For every 12 in. (1 ft.) in the non-scale room dimensions, there will be one 1/4 in. on the scale. That would apply like this:

324 in. (27 ft.) x

1/4 in. =81 in. [or 6.75 ft.]

240 in. (20 ft.) x

1/4 in. = 60 in. [or 5 ft.]

Step-by-step explanation: If incorrect sorry, Hope this helps!!

Answer:

Answer is explained down below.

Hope this helped, brainliest?

Step-by-step explanation:

Not exactly sure if there are other questions included, but to fill out the table im assuming you break up the hours and miles.

Jamal hiked 6 miles in 3 hours, first block would be 1.5miles in 45 minutes, 2nd block would be 3miles in 1hour 30minutes, 4.5miles in 2hours 15minutes, and last 6 miles in 3 hours.

For rubi it would be 2.5miles, 5miles, 7.5miles, 10miles. the time would be 1 hour, 2 hour, 3 hour, 4 hour.

If this isnt what it is asking please provide more info and i'll help

Answer:

1) Given

2) if lines are parallel, then corresponding angles are equal

3) Substitution

4) if altenate interior angles are equal, then the lines are parallel

ΔABC and ΔACD are similar. Therefore the sides are in proportion:

[tex]\dfrac{x}{4}=\dfrac{4}{2}[/tex]

[tex]\dfrac{x}{4}=2[/tex]      multiply both sides by 4

[tex]\boxed{x=8}[/tex]