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(a) D(c) = f + cx    

(b) Delivery fee is $5.

(c) The cost per calendar is $19.

Step-by-step explanation:

Let,

Delivery fee = f

Cost of calendar = x

No. of calendars = c

Total cost with delivery fee = D

Therefore,

The cost of 2 calendars plus delivery fee is $43.

D(c)= f + cx

43 = f + 2x Eqn 1

The cost of 4 calendars plus delivery is $81.

D(c) = f + cx

81 = f +4x    Eqn 2

(a)Write an equation that gives the  total cost as a function of calendars bought.

D(c) = f + cx      

(b)What is the delivery fee?

Multiplying Eqn 1 by 2;

[tex]2(43 = f + 2x)\\86=2f+4x\ \ \ Eqn\ 3[/tex]  

Subtracting Eqn 2 from Eqn 3;

[tex](2f+4x)-(f+4x)=86-81\\2f+4x-f-4x=5\\f=5[/tex]

Delivery fee is $5.

(C)What is  the cost per calendar?

Putting f=5 in Eqn 1;

[tex]43=5+2c\\43-5=2c\\2c=38\\[/tex]

Dividing both sides by 2

[tex]\frac{2c}{2}=\frac{38}{2}\\c=19[/tex]

The cost per calendar is $19.

Keywords: function, linear equation

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Answer:

3 7/12

Step-by-step explanation:

first you have to make both denominators the same through multiplication but remember if you do that you have to multiply the numerator by the same number as the denominator. then after you do that you can add them and if it comes out improper then you need to simplify your fraction and you have the answer.

Answer: 3⁷/₁₂

Explanation:

Numerator- number on top of fraction

Denominator- number on bottom of fraction

First find a common denominator. A number that both denominators can go into. In this case we'll use 12. Because both of the denominators, 6 and 4, fit into 12.

6 goes into 12 twice. And 4 goes into 12 three times.

To convert to a common denominator, multiply both the numerator and the denominator by the same number. Do not multiply the whole number.

So because 6 goes into 12 twice, we multiply by 2.

⁵/₆ x 2 = ¹⁰/₁₂

And because 4 goes into 12 three times, we multiply by 3.

2³/₄ × 3 = 2⁹/₁₂

Okay so now that both numbers have a common denominator, we can add.

¹⁰/₁₂ + 2⁹/₁₂ = 2 ¹⁹/₁₂

Simplified as 3 ⁷/₁₂

Answer:

[tex]111\ grams\ of\ zinc[/tex]

Step-by-step explanation:

Let

x -----> grams of zinc

y ----> grams of copper

we know that

[tex]\frac{x}{y}=\frac{3}{17}[/tex] -----> equation A

For y=629 grams of copper

substitute in the equation A and solve for x

[tex]\frac{x}{629}=\frac{3}{17}[/tex]

[tex]x=\frac{3}{17}(629)[/tex]

[tex]x=111\ grams\ of\ zinc[/tex]

Answer:

18 (3) + 18 (X) = 18 (3+X)

Step-by-step explanation:

AB + AC = A ( B + B )

A is the common factor

Factor to find common factor

54 = 2 * 3 * 3 * 3

18 = 2 * 3 * 3 * x

greatest common factor (GCF) = 2 * 3 * 3 = 18

18 (3) + 18 (X) = 18 (3+X)

hope it helps! <3

Answer:

4

2

3

1

Step-by-step explanation:

1) [tex](p^6.q^{{\frac{3}{2}}})^{{\frac{1}{3}}}[/tex]

Therefore, [tex]$ p^{\frac{6}{3}}.q^{\frac{3}{2}.\frac{1}{3}} $[/tex]

[tex]$ \implies p^2.q^{\frac{1}{2}} $[/tex]

2) [tex]$ \frac{p^5}{p^{-3}q^{-4}} $[/tex]

[tex]$ = p^5.p^3.q^4 = p^8.q^4 $[/tex]

Now, [tex]$ (p^8q^4)^{\frac{1}{4}} $[/tex]

[tex]$ \implies p^{\frac{8}{4}}.q^{\frac{4}{4}} $[/tex]

[tex]$ = p^2. q $[/tex]

3) [tex]$ (\frac{p^2.q^7}{q^4} )^{\frac{1}{2} $[/tex]

[tex]$ \implies p^{{\frac{2}{2}}}.q^{\frac{3}{2}} $[/tex]

[tex]$ \implies pq^{\frac{3}{2}} $[/tex]

4) [tex]$ \frac{(pq^3)^{{\frac{1}{2}}}}{(pq)^{{\frac{-1}{2}}}} $[/tex]

[tex]$ \implies p^{{\frac{1}{2}}}q^{{\frac{3}{2}}}. p^{{\frac{1}{2}}}.q^{{\frac{1}{2}}}} $[/tex]

[tex]$ = pq^2 $[/tex]

Hence, the answers.

Answer:

2 and 2/5 candy bars

Step-by-step explanation:

To figure this out, simply add the fractions together 6 times or multiply 2/5 by 6.

(2/5)(6/1)

Multiply the numerator

2*6=12

Multiply the denominator

5*1=5

so the answer is 12/5 or 2 and 2/5 candy bars.

Answer:

The rational zero of the polynomial are [tex]\pm \frac{7}{4}, \pm \frac{1}{4},\pm \frac{7}{2},\pm \frac{1}{2},\pm 7,\pm 1[/tex]  .  

Step-by-step explanation:

Given polynomial as :

f(x) = 4 x³ - 8 x² - 19 x - 7

Now the ration zero can be find as

[tex]\dfrac{\textrm factor of P}{\textrm factor Q}[/tex] ,

where P is the constant term

And Q is the coefficient of the highest polynomial

So, From given polynomial ,  P = -7 , Q = 4

Now , [tex]\dfrac{\textrm factor of \pm P}{\textrm factor of \pm Q}[/tex]

I.e  [tex]\dfrac{\textrm factor of \pm P}{\textrm factor of \pm Q}[/tex] = [tex]\frac{\pm 7 , \pm 1}{\pm 4 ,\pm 2,\pm 1 }[/tex]

Or, The rational zero are [tex]\pm \frac{7}{4}, \pm \frac{1}{4},\pm \frac{7}{2},\pm \frac{1}{2},\pm 7,\pm 1[/tex]

Hence The rational zero of the polynomial are [tex]\pm \frac{7}{4}, \pm \frac{1}{4},\pm \frac{7}{2},\pm \frac{1}{2},\pm 7,\pm 1[/tex]  .  Answer

Answer:

8.75 minutes

Step-by-step explanation:

This is a simple linear relation between two variables, time and depth

We can solve it by simple inspection like this.

If the diver is 5 feet deep and plans to go 75 feet deep, he must move 70 feet deeper.

At a rate of 8 feet/minute, it will take him/her

70/8= 8.75 minutes

It is 8 minutes and 45 seconds

Answer:

We can conclude that Δ XYZ ≅ Δ RST by ASA postulate.

Step-by-step explanation:

Δ XYZ and Δ RST are congruents by ASA postulate because:  

1. Their included sides XZ  and RT are equal.  

2. Their angles ∠Z and ∠T are equal (92° = 92°)

3. Their angles ∠X and ∠R are equal.  

4. Their non-included sides XY and RS are equal.

Now, we can conclude that Δ XYZ ≅ Δ RST by ASA postulate.

Answer:

22m²

Step-by-step explanation:

Area of parallelogram is simply the base length x height.

In this case, base length = 4m and height = 5.5m

hence,

Area = 4 x 5.5 = 22m²

Answer:

22 m^2

Step-by-step explanation:

A = (base)(height), so:

A = (4 m)(5.5 m) = 22 m^2

Answer:

730.36

Step-by-step explanation:

.24 × 589= 141.36

141.36+589=730.36

so the original price would be 730.36

Answer:

20 cups

Step-by-step explanation:

15 / 6 = 5/2

8 * 5/2 = 20

20 cups of milk would be required by Brian to prepare 15 dozen brownies. By utilizing ratios and proportions, this conclusion has been obtained.

To solve this problem, we can use both proportions and ratio. Brian uses 8 cups of milk for every 6 dozen (or 72) brownies. This can be written as the ratio 8:72 or the proportion 8/72 = x/180. From the proportion, we know the cross products are equal, so 8*180 = 72*x. Solving for x gives us x = (8*180)/72. Therefore, Brian would need 20 cups of milk to make 15 dozen brownies.

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Answer:

12:45 pm and 7:30 pm

Step-by-step explanation:

In a 24 hour clock, we don't use pm or am to identify time. But in a 12 hour clock , am or pm is used. Given time is in 24 hour clock.

So, for 12:45, in 12 hour clock it will be 12:45 pm because, when the time crosses 11:59, it becomes pm.

For, 19:30, it will 19:30-12:00= 7:30 pm.

Final answer:

To convert 12:45 from the 24-hour clock to the 12-hour clock, it remains 12:45 AM. To convert 19:30, you subtract 12 hours, making it 7:30 PM because it is after noon.

Explanation:

To convert times from the 24-hour clock to the 12-hour clock, you need to remember that the 24-hour clock runs from 0:00 (midnight) to 23:59, while the 12-hour clock repeats the cycle of AM and PM hours from 1 to 12.

Solution to (a):

12:45 in the 24-hour clock is straightforward. Since it's already in the AM range, it's the same in the 12-hour clock - 12:45 AM.

Solution to (b):

To convert 19:30 from the 24-hour clock to 12-hour clock format, subtract 12 hours from the 24-hour time if it is greater than 12. Thus, 19:30 becomes 7:30 PM because 19 - 12 = 7, and any time past noon is in the PM.

Answer:

Yes.

Step-by-step explanation:

A rational number is any number that can be expressed as a ratio of two integers. 1 and 3 are integers, and 1/3 is a ratio of them, so 1/3 is a rational number.

Answer: Yes it is

Step-by-step explanation: A rational number is a number that can be written in the form of a fraction, so yes it is a rational number.

Answer:

97.5 sq. ft.

Step-by-step explanation:

Im presuming the question asks to find area of the shaded region.

First of all, the total figure is a rectangle. We can write an expression(in words) for the shaded area.

Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)

Now, we find respective areas.

Area of rectangle:

length * width = (5+10) * (12) = 15 * 12 = 180

Area of Small Triangle (white):

A = (1/2) * base * height = (1/2) * 5 * (12-3) = (1/2) * 5 * 9 = 22.5

Area of Large Triangle (white):

A = (1/2) * base * height = (1/2) * 10 * (12) = 60

Now, we find area of shaded region:

Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)

Shaded Area = 180 - 22.5 - 60 = 97.5 sq. ft.

Answer:

97.5 sq. ft.

Step-by-step explanation:

See the given diagram with given measurements.

The area of the shaded portion is to be determined.

Now, we have to first find the area of the two right triangles formed at the left and right sides.

We know that the area of a right triangle = [tex]\frac{1}{2} \times (\textrm {Base})\times (\textrm {Height})[/tex]

Then the area of the left side triangle = [tex]\frac{1}{2} \times 5 \times (12 - 3) = 22.5[/tex] sq. ft.

Now, the are of the right side triangle = [tex]\frac{1}{2} \times 10 \times 12 = 60[/tex] sq. ft.

Now, the area of non-shaded region = Total are of the two right triangles  

= (60 + 22.5) = 82.5 sq. ft.

Therefore, the area of the shaded region is = (Area of the total rectangle - Area of the non-shaded region)

= [(10 + 5) × 12] - 82.5

= 97.5 sq. ft. (Answer)

Answer:

10. 7n - 1 < -8

Isolate the variable, n. Do the opposite of PEMDAS. Treat the < as equal sign, what you do to one side, you do to the other. First, add 1 to both sides:

7n - 1 (+1) < - 8 (+1)

7n < - 8 + 1

7n < - 7

Isolate the variable, n. Divide 7 from both sides:

(7n)/7 < (-7)/7

n < -7/7

n < -1

n < -1 is your answer.

11. 3 > -7v + 4v

Combine like terms, then isolate the variable, v. First, add -7v and 4v together.

3 > (-7v + 4v)

3 > (4v - 7v)

3 > (-3v)

Isolate the variable, v. Divide -3 from both sides. Note that since you are dividing a negative number, you must flip the sign:

(3)/-3 > (-3v)/-3

3/-3 > v

-1 < v

v > -1 is your answer.

~

Answer:

53 degrees

Step-by-step explanation:

Since we don't know the measure of the radius

UZ =127

UX=127

ZX =154

 360-154=  106

106/2=53

XY=53

YZ=53

Answer:

1/12

Step-by-step explanation:

You want to find the compatible numbers with the common denominator so you want to multiply by ones until you get something with the same denominator. In this case it's 12, 1/3 x 4 = 4/12 and 1/4 x 3 = 3/12, Then subtract. Therefore you get your answer 1/12

George ate 1/12 of the pan of brownies.

There are 1/3 pan of brownies. George eats 1/4 of this pan.

In order to find out the fraction of the brownie pan that George ate, you need to multiply the proportion of the pan that still has brownies with the proportion that George ate.

The total fraction of the pan he ate is:

= Amount of pie George has x Amount of brownies he eats

= 1/3 x 1/4

= 1/12 of the pan

This means that out of the whole pan of brownies, George ate 1/12.

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Answer:

C

Step-by-step explanation:

Two pyramids are similar. It means that their side lengths are proportional.

So, let's see the proportionality constant from SMALL PYRAMID to LARGE PYRAMID.

The corresponding length of 8 in small pyramid is 24 in large pyramid. We ask ourself:  "8 times WHAT gives us 24?"

This is the proportionality constant (aka "k").

So, 8 times "3" is 24. So the proportionality constant is "3".

k = 3

Now, the height of small pyramid is 6 and height of large pyramid is "x". These sides will be same way proportional. So, we can say:

6 times the proportionality constant (3) would give us x

So,

6 * 3 = x

x = 18

Correct answer is C

Answer:

It's in standard form.

Answer:

Standard Form

Step-by-step explanation:

Answer:

605100

Step-by-step explanation:

6.051*10^5=605100

Answer:

5 centimeters of snow per hour.

Step-by-step explanation:

We are given an equation d = 5h, where d = depth of snow and h = hours of the snowstorm.

We need to find the number of centimeters of snow that accumulate in 1 hour.

In order to find the number of hours that accumulate the  snow to 1 centimeter, we need to plug d=1 in the given equation.

On plugging d=1, we get

1= 5h.

Dividing both sides by 5, we get

1/5 = h.

Therefore, it would take 1 hour for 5 centimeters of snow to accumulate in Harper's yard.

The amount of snow accumulation per hour varies, ranging from 0.5 cm in light snow to up to 5 cm in heavy snowfall. However, actual snow accumulation can be influenced by various factors such as temperature, wind speed, and humidity.

The amount of snow accumulation per hour can vary greatly depending on the intensity of the snowfall. For example, a light snowfall might result in as little as 0.5 cm of snow per hour while a heavy snowfall could accumulate up to 5 cm of snow per hour. However, it's important to note that these are just average estimates and actual snow accumulation can be influenced by various factors such as temperature, wind speed, and humidity.

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Answer:

Step-by-step explanation:

[tex]\bold{STEP\ 1:}\\\\\dfrac{6}{7}\ of\ 28=\dfrac{6}{7\!\!\!\!\diagup_1}\cdot28\!\!\!\!\!\diagup^4=(6)(4)=24\\\\\bold{STEP\ 2:}\\\\_{\bold{METHOD\ 1}}\\\\p\%=\dfrac{p}{100}\to30\%=\dfrac{30}{100}=0.3\\\\x-\text{a number}\\\\0.3x=24\qquad\text{divide both isdes by 0.3}\\\\\dfrac{0.3x}{0.3}=\dfrac{24}{0.3}\\\\x=80[/tex]

[tex]_{\bold{METHOD\ 2}}\\\\\begin{array}{ccc}30\%&-&24\\\\100\%&-&x\end{array}\qquad\text{cross multiply}\\\\\\(30)(x)=(100)(24)\\\\30x=2400\qquad\text{divide both sides by 30}\\\\\dfrac{30x}{30}=\dfrac{2400}{30}\\\\x=80[/tex]

[tex]_{\bold{METHOD\ 3}}\\\\\begin{array}{cccc}30\%&-&24&\text{divide both sides by 3}\\\\\dfrac{30\%}{3}&-&\dfrac{24}{3}\\\\10\%&-&8&\text{multiply both sides by 10}\\\\(10\%)(10)&-&(8)(10)\\\\100\%&-&80\end{array}[/tex]

The value of the number will be;

⇒ x = 80

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The algebraic expression is,

''If 6/7 of 28 is equal to 30% of that number''

Now,

Let the number = x

So, We can formulate;

⇒ 6/7 × 28 = 30% of x

Solve for x as;

⇒ 6 × 4 = 30/100 × x

⇒ 24 = 3/10 × x

⇒ 24 × 10 = 3x

⇒ 240 = 3x

⇒ x = 240/3

⇒ x = 80

Thus, The value of the number will be;

⇒ x = 80

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Answer:

Julie worked 18 hours at Job A and 17 hours at Job B.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Rate per hour at Job A = US$ 6.10

Rate per hour at Job B = US$$ 7.40

Hours at Job A = x

Hours at Job B = 35 - x

Total of hours worked by Julie = 35 hours

Total weekly earnings = US$ 235.60

2. How many hours did she work at each job the week that she made $235.60?

For finding the result, we will use the following formula:

6.10x + 7.4 (35 - x) = 235.60

6.10x + 259 - 7.4x = 235.60

-1.3x = 235.60 - 259 (Subtracting 259 to both sides)

-1.3x = - 23.40

x = -23.4/-1.3 (Dividing by -1.3)

x = 18

Julie worked 18 hours at Job A, so she worked 17 (35 - 18) hours at Job B.

3. Proof that x = 18 is correct.

6.10x + 7.4 (35 - x) = 235.60

6.10 (18) + 7.4 (35 - 18) = 235.60

109.80 + 125.80 = 235.60

235.60 = 235.60

It's proven that x = 18 is correct.

Answer:

Step-by-step explanation:

Let x represent the number of hours worked at Job A and 35-x represent the number of hours worked at Job B.

($6.10 × x) +$7.40 × (35-x) =$235.60

Solving for x

$6.10x + $259 - $7.40x = $235.60

Collect like terms and solve for x

$6.10x-$7.40x=$235.60-$259

-$1.3x=-$23.4

x=18hours for Job A while 35-x=17hours for Job B

Answer:

160

Step-by-step explanation:

2+2=4

4 x 40= 160

The mile symbol 'm' was commonly used before the widespread adoption of the metric system. The total miles taken by Ashlynn to ride her bike to school and home in 40 days is 160.

A mile is defined as the unit of length which is exactly equal to 5280 feet or 1760 yards and it is standardized as exactly 1609.344 meters. It is the largest unit which is commonly used to measure the distance between places that are far from each other.

Here the total miles covered by the bike is 2 + 2 = 4

The total miles covered by Ashlynn = 4 × 40 = 160

A mile is a customary unit of distance. It is commonly used to express the distance between cities, roads and the lengths of the rivers. The symbol of mile is denoted as 'mi'.

Thus the total miles is 160.

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[tex](-22)^{\frac{1}{2}}[/tex] and [tex](-10)^{\frac{1}{4}}[/tex] are not real numbers

A real number is any positive or negative number. This includes all integers and all rational and irrational numbers

They are called "Real Numbers" because they are not Imaginary Numbers.

When you take an even root of a negative number, there is no real answer. (2 is an even number)

In the real number set, you can't take an even-indexed root of a negative number.

Given options are:

[tex]\begin{array}{l}{\text { A) }(-22)^{\frac{1}{2}}} \\\\ {\text { B) }(-16)^{\frac{1}{3}}} \\\\ {\text { C) }(-16)^{\frac{1}{5}}} \\\\ {\text { D) }(-10)^{\frac{1}{4}}}\end{array}[/tex]

Looking at the answer choices here, we can see that A and D use even roots, so they will give non-real answers.

Thus [tex](-22)^{\frac{1}{2}}[/tex] and [tex](-10)^{\frac{1}{4}}[/tex] are not real numbers

Answer:

(-16)^1/3 and (-6)^1/5

Step-by-step explanation:

Answer:

In 68229 ways can the quiz be selected such that there is atleast three multiple choice questions

Step-by-step explanation:

Given:

Number of True or false questions= 10

Number of multiple choice questions= 20

To Find:

How many ways can 5 questions can be selected if there must be at least three multiple choice questions =?

Solution:

Combination

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.  

The question States there sholud be ATLEAST 3 multiple choice question,

So, we may have

(3 Multiple choice question and 2 true or false question) or

(4 Multiple choice question and 1 true or false question) or

(5 Multiple choice question and 0 true or false question)

Required Number of ways = (20C3 X10C2) +(20C4 X10C1) + (20C5 X10C0)

Required Number of ways [tex]=(\frac{20!}{20!(20-3)!}\times\frac{10!}{10!(10-2)!})+(\frac{20!}{20!(20-4)!} \times \frac{10!}{10!(10-1)!}) +(\frac{20!}{20!(20-4)!} \times \frac{10!}{10!(10-0)!})[/tex]

Required Number of ways = ( 1140 x 42) + (4845 x 10) +(15504 x 1)

Required Number of ways = 47880+48450+15504

Required Number of ways = 68229

Answer:

Mrs. Dryson made 3 groups with 17 glasses of bears each or she made 17 groups with 3 glasses of bears each.

Step-by-step explanation:

Let the number of groups is x and each group gets y number of bears.

Now, Mrs. Dryson distributed 52 glass bears equally in groups and there was 1 bear left over.

Therefore, xy = 52 - 1 = 51

Now, x and y both must be whole numbers.

Now, we have 51 = 3 × 17, which is the only possible factorization of 51.

So, if x = 3 then y = 17 and if x = 17, then y = 3.

Therefore, Mrs. Dryson made 3 groups with 17 glasses of bears each or she made 17 groups with 3 glasses of bears each. (Answer)

Answer:

262

Step-by-step explanation:

If x is the first integer, then x+1 is the second, x+2 is the third, and so on.  Meaning the 7th term in the list is x+6.

x + x + 6 = 518

2x = 512

x = 256

The first integer is 256, so the last integer is 262.

Answer:

1 movie ticket costs $9. I hope this helps!

Step-by-step explanation:

Are you wondering how much the tickets would cost seperatly? If that's the case then you would divide $45 by 5 which would be $9 for each ticket.