3. Matt bought 12 packages of hot dogs and hamburgers for a barbecue. Let x represent the number of packages of hot dogs, which cost $2.75 each. Let y represent the number of packages of hamburgers, which cost $3.20 each. Matt spent a total of $35.25. Write and solve a system of equations that can be used to represent the amount of hot dogs and hamburger packages Matt bought. Are there any constraints on your variables? Is the solution viable or non-viable?

Answer: 13

Step-by-step explanation:

x = 5

-5 (5) + 12

-25 + 12

-13

abs(-13) = 13

To find absolute value, solve the equation as is and then make the answer positive.  

Answer:

190% I believe, I hope this helped!

Step-by-step explanation:

Answer:

Please see the answer below:

Step-by-step explanation:

1. Loss 5%

Cost = Rs.320

Loss % = 5% = 0.05

Sale Price = Rs.320 - (Rs.320 x 0.05) = Rs.320 - Rs.16 = Rs.304

2. Profit 20%

Cost = Rs.320

Profit % = 20% = 0.20

Sale Price = Rs.320 + (Rs.320 x 0.2) = Rs.320 + Rs.64 = Rs.384

3. Sold for Rs.360

Cost = Rs.320

Sale Price = Rs.360

Gain % = (Rs.360 - Rs.320) / Rs.320 = Rs.40 / Rs.320 = 0.125

or

Gain % = 12.5%

Answer:

If sold at a loss of 5%, the selling price would be Rupee 304

If sold at a Profit of 20% the selling price would be Rupee 384

Step-by-step explanation:

Cost of shoes                                  =   Rupees 320

Loss incurred  (5% x 320)               =   Rupees   16

Price of shoe                                   = (320 - 16)  = 304  

The selling price if sold at a loss of 5% would be Rupees 304

IF SOLD AT A PROFIT OF 20%

Cost of shoes                                  =   Rupees 320

Loss incurred  (20% x 320)               =   Rupees   64

Price of shoe                                   = (320 + 64)  = 384  

The selling price if sold at a loss of 5% would be Rupees 384

Answer:

x=18

Step-by-step explanation:

12-2/3x=x-18

12-2/3x-x=-18

12-2/3x-3/3x=-18

12-5/3x=-18

5/3x=12-(-18)

5/3x=12+18

5/3x=30

x=30/(5/3)

x=(30/1)(3/5)

x=90/5

x=18

Answer:

Step-by-step explanation:

[tex]12-\dfrac{2}{3}x=x-18\qquad\text{subtract 12 from both sides}\\\\12-12-\dfrac{2}{3}x=x-18-12\\\\-\dfrac{2}{3}x=x-30\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup\cdot\left(-\dfrac{2}{3\!\!\!\!\diagup_1}x\right)=3\cdot x-3\cdot30\\\\-2x=3x-90\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-2x-3x=3x-3x-90\\\\-5x=-90\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5x}{-5}=\dfrac{-90}{-5}\\\\x=18[/tex]

The percent markdown is 30%

Step-by-step explanation:

Given

Regular price of jeans = r = $129.99

Sale price = s = $90.99

The percent markdown can be given by the formula:

[tex]percent\ markdown = \frac{Markdown}{Regular\ price}*100[/tex]

Where markdown = Regular price - Sale price

So,

[tex]Markdown = r -s\\= 129.99 - 90.99\\=39[/tex]

Putting the values in the formula

[tex]Percent\ Markdown = \frac{39}{129.99} * 100\\=0.300 * 100\\=30\%[/tex]

Hence,

The percent markdown is 30%

Keywords: Percentage, markdown

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Final answer:

If everyone on Earth shared the largest sandwich ever made equally, each person would get approximately 0.00000069 pounds of the sandwich. This represents a fraction of 69/1,000,000,000 of a regular sandwich.

Explanation:

To find out how much each person would get if everyone on Earth shared the largest sandwich ever made equally, we can divide the weight of the sandwich by the population of the Earth. According to the most recent estimates, the population of the Earth is approximately 7.9 billion people.

So, if we divide the weight of the sandwich (5440 pounds) by the population of the Earth (7.9 billion), each person would get approximately 0.00000069 pounds or 0.00000031 kilograms of the sandwich.

To express this as a fraction of a regular sandwich, we need to compare it to the weight of a regular sandwich. Let's say a regular sandwich weighs 1 pound. In that case, the amount each person would get from the largest sandwich ever made represents a fraction of 0.00000069/1 or simply 69/1,000,000,000 of a regular sandwich.

Answer:

[tex](s+t+r)^7[/tex]

Step-by-step explanation:

Sequential Operations

Mathematical operations can be done in sequence or in batches if they are of the same type. For example, we can add many terms in one single operation, but we cannot add and multiply in one go, because there are priorities when dealing with products and sums. Same happens with powers.

In our problem we are required to perform a sequence of operations like follows

Add s to t:

[tex]s+t[/tex]

Add the result to r

[tex]s+t+r[/tex]

Raise what you have to the 7th power

[tex]\boxed{(s+t+r)^7}[/tex]

This is the final result

Answer:

Step-by-step explanation:

5/8*5/4=25/32

1/16*25/2=25/32

25/16*1/2=25/32

To find three different pairs of fractions that multiply to 25/32, start by factoring the numerator and denominator. Then pair up the factors to form fractions.

To find three different pairs of fractions that multiply to 25/32, we can start by factoring the numerator and denominator of 25/32. 25 can be factored as 5 * 5 and 32 can be factored as 2 * 2 * 2 * 2 * 2. We can then pair up the factors to form fractions:

So, three different pairs of fractions that multiply to 25/32 are 5/2 * 5/2 = 25/4, 5/2 * 5/32 = 25/64, and 5/2 * 1/4 = 5/8.

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Answer:

The closest option is C. 430, but of course this estimation depends of the size of the serving, specially for the chops and the potato.

Step-by-step explanation:

Let's calculate the number of calories of this meal:

A. 2 pork chops: We could assume 145 calories in a 3-ounce serving, so we have 145 * 2 = 290

B. 1 baked potato: We could assume 130 in a baked small potato (around 130 grams)

C. 1/2 cup of broccoli: We could assume 15 calories

Then the total estimation of calories is:

290 + 130 + 15 = 435

The closest option is C. 430, but of course this estimation depends of the size of the serving, specially for the chops and the potato.

Answer:

The answer is 430.

Step-by-step explanation:

On the chart given with the question (which was not posted),

2 pork chops = 260 (on the chart the individual pork chop is 130)

1/2 broccoli = 25

1 baked potato = 145

Now you simply add the numbers together!

Hope this helps!

Answer:

The ordered pairs of A and C are not functions

Step-by-step explanation:

To determine if the ordered pairs are a function you look at the x values to see if they repeat. You don't want one input(x values) to lead to two outputs(y values). This would mean that you are never sure which output you will get.

In the answer A the x value "2" repeats, in the answer C the x value "1" repeats thus not making them functions.

To find the speed of the motorboat and the current, two equations were set up based on the distances and times provided. The system of equations was solved to find the boat speed to be 36 km/h and the current speed to be 4 km/h.

The student is asking a question related to the mathematical concept of relative motion involving a motorboat and a current.

To solve this problem we can set up two equations based on the information given:

Using the distances and times provided:

We can solve this system of equations to find the values for Boat Speed and Current Speed.

Let the speed of the boat be b and the speed of the current be c. From equation (1), we can express c in terms of b:

c = 40 - b (1)

Substitute c from equation (1) into equation (2):

160 = (b - (40 - b)) * 5

160 = (2b - 40) * 5

160 = 10b - 200

360 = 10b

b = 36 km/h

So the speed of the boat is 36 km/h. Now we can find the speed of the current using equation (1):

c = 40 - b

c = 40 - 36

c = 4 km/h

The speed of the current is 4 km/h.

3 cups + the original 6 = 9 cups.

Answer:

The answer is 9 cups of water

Step-by-step explanation:

Answer:

P'(2, - 2 )

Step-by-step explanation:

The translation rule

(x, y ) → (x + 9, y - 3 )

Means add 9 to the original x- coordinate and subtract 3 from the original y- coordinate, thus

P(- 7, 1 ) → P'(- 7 + 9, 1 - 3 ) → P'(2, - 2 )

Answer:

2,-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

A cyclist moving at 10 kilometers per hour is traveling at a rate of 6.25 miles per hour. Over 4 hours, the cyclist will travel a total distance of 25 miles.

To convert kilometers per hour to miles per hour, you have to divide the kilometers value by 1.6 (because it's given that 1 mile = 1.6 kilometers). So, if the cyclist is cycling at 10 kilometers per hour, this translates to 10 / 1.6 = 6.25 miles per hour.

Next, to find out how many miles the cyclist will travel in 4 hours, we'll simply multiply this rate by the time. So, 6.25 (miles per hour) * 4 (hours) = 25 miles.

Therefore, the cyclist, if maintaining a speed of 10km per hour, will travel 25 miles in a 4 hour time span.

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A subtraction story problem for a total of 14 could be: Lucy has 17 cookies and she wants to share them with her friend Amanda. If Lucy gives Amanda some cookies and ends up with 14 cookies, how many cookies did Lucy give to Amanda?

A subtraction story problem for a total of 14 could be:

Lucy has 17 cookies and she wants to share them with her friend Amanda. If Lucy gives Amanda some cookies and ends up with 14 cookies, how many cookies did Lucy give to Amanda?

To solve this, subtract the cookies Lucy ends up with (14) from the cookies she initially had (17):

17 - 14 = 3

Therefore, Lucy gave Amanda 3 cookies.

Final answer:

The solution set for |h-3|>5 is h > 8 and h < -2, which on a number line is all values to the right of 8 and to the left of -2, with open circles at -2 and 8.

Explanation:

The question requires us to find the solution set for the inequality |h-3|>5 on a number line. To solve an absolute value inequality, we split the problem into two separate inequalities based on the definition of absolute value:

For h - 3 > 5, we add 3 to both sides to get h > 8.For h - 3 < -5, we again add 3 to both sides, which gives h < -2.

Therefore, the solution set on the number line includes all values to the right of 8 and all values to the left of -2. Remember, these are not included in the solution set because the inequality is strict (>). This means we use open circles or unshaded dots to represent -2 and 8, and shade the number line to the right of 8 and to the left of -2.

Answer:

3* 10⁵

Step-by-step explanation:

6* 10⁸ / 2 * 10³ = 3 * 10⁸⁻³ = 3* 10⁵

Answer:

[tex]AB=5\sqrt{15}\ units[/tex]

Step-by-step explanation:

we know that

In the right triangle ABC

we have

[tex]AC=20\ units[/tex] ----> is the hypotenuse

[tex]BC=5\ units[/tex] ----> is a leg

[tex]AB=?\ units[/tex] ----> is a leg

see the attached figure to better understand the problem

Applying the Pythagorean Theorem

[tex]AC^2=AB^2+BC^2[/tex]

substitute the given values

[tex]20^2=AB^2+5^2[/tex]

solve for AB

[tex]AB^2=20^2-5^2[/tex]

[tex]AB^2=375[/tex]

[tex]AB=\sqrt{375}\ units[/tex]

simplify

we know that

[tex]375=(25)(15)=5^2(15)[/tex]

substitute

[tex]AB=\sqrt{5^2(15)}\ units[/tex]

[tex]AB=5\sqrt{15}\ units[/tex]

We have 15 ways to chose 2 students for the position of president and Vice President

Solution:

Given that,

There are 6 students. 2 of them are chosen for the position of president and Vice President.

To find: number of ways we have to choose the students from the 6 students

So now we have 6 students, out of which we have to choose 2 students

As we just have to select the students. We can use combinations here.

In combinations, to pick "r" items from "n" items, there will be [tex]^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}[/tex] ways

[tex]^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\frac{n !}{(n-r) ! r !}[/tex]

Then, here we have to pick 2 out of 6:

Total students = n = 6

students to be selected = r = 2

[tex]\begin{aligned} 6 C_{2} &=\frac{6 !}{(6-2) ! 2 !} \\\\ 6 C_{2} &=\frac{6 !}{4 ! 2 !} \\\\ 6 C_{2} &=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1 \times 2 \times 1} \\\\ 6 C_{2} &=15 \end{aligned}[/tex]

Thus we have 15 ways to chose 2 students for the position of president and Vice President

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3 x 4 = 12

5 x 4 = 20

2 x 4 = 8

6 x 4 = 24

12 + 20 + 8 + 24 = 64

She has 64 marbles  

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Answer:

72

Step-by-step explanation:

If you move the decimal point 3 times, you get 72!

Answer:

72. the decimal point will move. (promise not copying) (the other person can get the credit though)

Step-by-step explanation:

[tex]\bf \begin{array}{|ll|ll} \cline{1-2} bridge&\stackrel{tons}{materials}\\ \cline{1-2} concrete&1,000\\ \textit{steel structure} & 400\\ \textit{glass and granite}&200\\ \cline{1-2} \end{array}\qquad \qquad \stackrel{~\hfill \textit{total weight}}{1000+400+200=1600} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{\stackrel{\textit{steel structure}}{400}}{\underset{\textit{total weight}}{1600}}\implies \stackrel{\textit{simplified}}{\cfrac{1}{4}}~\hfill \cfrac{\stackrel{\textit{glass and granite}}{200}}{\underset{\textit{total weight}}{1600}}\implies \stackrel{\textit{simplified}}{\cfrac{1}{8}}[/tex]

Answer:

The Inequality which shows Amount of time spent on other sports each day is [tex]x\leq \frac{4.25}{4}[/tex].

Nyasia spends approximately 1 hour each day on Other sports.

Step-by-step explanation:

Total number of hours spent on sports each week =7.5 hrs

Time spent on basket ball each week = 3.25 hours

Number of days spent on sports = 4 days.

We need to find amount of time spent on other sports each day.

Let amount of time spent on other sports each day be 'x'.

First we will find amount of time spent on other sports each week.

Amount of time spent on other sports each week can be calculated by Subtracting Total number of hour spent on sports each week minus Time spent on basket ball each week.

Amount of time spent on other sports each week = 7.5 -3.25 = 4.25 hrs.

Now we can say amount of time spent on other sports each day we will less than or equal to Amount of time spent on other sports each week divided by number of days.

Framing in equation form we get;

[tex]x\leq \frac{4.25}{4}[/tex]

Hence The Inequality which shows Amount of time spent on other sports each day is [tex]x\leq \frac{4.25}{4}[/tex].

ON solving the inequality we get;

[tex]x\leq \frac{4.25}{4}\\\\x\leq1.0625\ hrs[/tex].

Hence we can say Nyasia spends approximately 1 hour each day on Other sports.

The linear equation is y = -2 x + 198

Jeff’s weight after 12 weeks is 174 pounds

Step-by-step explanation:

Jeff is keeping Trace of his weight over several weeks

We need to write a linear equation represents the Jeff’s weight, and find his weight after 12 weeks

The form of the linear equation is y = mx + b, where m is the slope of the line, and b is the y-intercept

The formula of the slope of a line which passes through points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let y represents Jeff's weight in x weeks

∵ After 2 weeks, he weighs 194 pounds

∴ [tex](x_{1},y_{1})[/tex] = (2 , 194)

∵ After 6 weeks , he weighs 186 pounds

∴ [tex](x_{2},y_{2})[/tex] = (6 , 186)

- Use these two points to find m

∵ [tex]m=\frac{186-194}{6-2}=\frac{-8}{4}=-2[/tex]

∴ m = -2

- Substitute the value of m in the form of the equation

∴ y = -2 x + b

- To find b substitute x and y in the equation by the coordinates

   of any point on the line

∵ x = 2 and y = 194

∴ 194 = -2(2) + b

∴ 194 = -4 + b

- Add 4 to both sides

∴ 198 = b

∴ y = -2 x + 198

The linear equation is y = -2 x + 198

To find his weight after 12 weeks substitute x by 12 in the equation

∵ x = 12

∴ y = -2(12) + 198

∴ y = -24 + 198

∴ y = 174

Jeff’s weight after 12 weeks is 174 pounds

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Answer:

Step-by-step explanation:

The ratio is 12/8 or 3/2

So we can use proportions

3/2=x/15

x=22.5

Answer:

36 hours

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

GIven that the lightest is 1.4 and the heaviest is 1.6, this implies that ALL the fruit must weigh between 1.4 and 1.6.

This also implies that the average weight of the fruit must also be between 1.4 lb and 1.6 lb.

recall that : average weight = total weight / number of fruit

we are given than total weight = 25.29 lb, so

average weight = 25.29 / number of fruit

Just go down the choices and test which choice gives an average weight between 1.4 and 1.6 lbs.

Choice A: number of fruit = 19

average = 25.29 / 19 = 1.33  (outside of range, not the answer)

Choice B: number of fruit = 17

average = 25.29 / 17 =1.49   (within range , possible answer)

Choice C: number of fruit = 10

average = 25.29 / 10 = 2.529 (outside of range, not the answer)

Choice D: number of fruit = 50

average = 25.29 / 50 = 0.5058  (outside of range, not the answer)

From the above, we can see that only B gives an average between 1.4 and 1.6 lb.

Answer:

B

Step-by-step explanation:

GIven that the lightest is 1.4 and the heaviest is 1.6, this implies that ALL the fruit must weigh between 1.4 and 1.6.

This also implies that the average weight of the fruit must also be between 1.4 lb and 1.6 lb.

recall that : average weight = total weight / number of fruit

we are given than total weight = 25.29 lb, so

average weight = 25.29 / number of fruit

Just go down the choices and test which choice gives an average weight between 1.4 and 1.6 lbs.

Choice A: number of fruit = 19

average = 25.29 / 19 = 1.33 (outside of range, not the answer)

Choice B: number of fruit = 17

average = 25.29 / 17 =1.49 (within range , possible answer)

Choice C: number of fruit = 10

average = 25.29 / 10 = 2.529 (outside of range, not the answer)

Choice D: number of fruit = 50

average = 25.29 / 50 = 0.5058 (outside of range, not the answer)

From the above, we can see that only B gives an average between 1.4 and 1.6 lb.

Answer:

Step-by-step explanation:

If 1000 divided by 40 equals 25, then you would want to stay under that.

so your next best bet is 24

then we just input our variable and sign

[tex]x \leqslant 24[/tex]

Answer:

After 12 yrs the height of both trees type A and type B will be same.

Step-by-step explanation:

Given,

Height of Type A at the time of planting = [tex]9\ ft=9\times12=108\ in[/tex]

Height of Type B at the time of planting =  [tex]2\ ft=2\times12=24\ in[/tex]

Let the number of years be 'x'.

After 'x' years height of Type A = [tex]108+17x[/tex]

After 'x' years height of Type B = [tex]24+24x[/tex]

We have to find out the number of years will take for these trees to be the same height.

Now according to question, after 'x' years the height of plant type A and plant type B will be equal.

[tex]108+17x=24+24x[/tex]

Combining the like terms, we get;

[tex]24x-17x=108-24\\\\7x=84\\\\x=\frac{84}{7}=12\ yrs[/tex]

Hence After 12 yrs the height of both trees type A and type B will be same.