The sum of 3 consecutive even numbers is 408. What is the largest of the numbers

Answer: Neither

Step-by-step explanation:

Answer:

a) [tex]y=m+6.75[/tex] where [tex]m[/tex] is the number of comic books

b) Case B has better deal  

Step-by-step explanation:

a)

Thus, this is in the form of :

[tex]y=m*x+b[/tex]

Given :

subtracting both ,

The cost of one comic book is $1;

substituting in the first equation ,

[tex]12.75=6+b\\b=6.75;[/tex]

The equation is :

[tex]y=m+6.75[/tex]

b)

Since the shop sells poster with a comic book , initial value is the cost of one comic book plus one poster.

[tex]7.99=x+b\\x=1;[/tex] --since its similar.

In case of a. , The cost of one book plus poster = $1+6.75=$7.75

which is lesser than $7.99 .

Thus case B has the best deal.  

Answer:

Should be used 28 pounds of pecans and 32 pounds of chocolate candies

Let

x -----> pounds of pecans used

y ----> pounds of chocolate candies used

we know that

-----> equation A

----->  -----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

Using a graphing tool

The solution is the point (28,32)

see the attached figure

therefore

Should be used 28 pounds of pecans and 32 pounds of chocolate candies

Answer:

18 miles in 1.5 hours

Step-by-step explanation:

2 miles = 10 minutes

90 minutes (1.5 hours) / 10 minutes = 9

Multiply

2 miles (9) = 10 minutes (9)

18 miles = 90 minutes

18 miles in 1.5 hours

Hope this helps :)

Answer:

Total Cost of Week = 81.20 Euros

Total Cost of Week (in dollars) = $102.31

Step-by-step explanation:

117 km per day

You drive 7 days

So,

Total miles driven = 117 * 7 = 819 km

Mileage is 42 miles per gallon. So how many gallons would it require to drive 819 km?

819/42 = 19.5 gallons

We know 1 gallons = 3.78 liters

So,

19.5 gallons would be:

19.5 * 3.78 = 73.82 liters

1.10 Euro PER LITER, so the total cost:

Total Cost of Week = 73.82 * 1.10 = 81.20 Euros

In dollars (1 euro = 1.26 dollars):

Total Cost of Week (in dollars) = 81.20 * 1.26 = $102.31

The cost on gas is approximately 7.2 euros

Data given;

If 1mi = 1.609km

And we cover 117km daily, let's convert this into miles

[tex]1mi=1.62km\\ x mi = 117km\\ x = 117/1.62\\ x = 72.2mi[/tex]

This shows that we cover a distance of 72.2 miles daily.

But the car consumes 1 gallon in 42 miles, let's calculate the gas required to cover 72.2 miles

[tex]42mi = 1g\\ 72.2mi =x\\ x = 72.2/42\\ x = 1.719[/tex]

The total gas consumed daily is approximately 1.72 gallons.

The cost of gas daily can be calculated from the data given but we have to convert the volume from gallon to liter

1L = 0.26 gallon

xL = 1.72 gallons

cross multiply this and solve for x

[tex]x = \frac{1*1.72}{0.26}\\ x = 6.6[/tex]

This shows that we consume 6.6L daily.

But we were given that the cost of 1 liter of gas is equal to 1.10 euros

1L = 1.10 euros

6.6L = x euros

[tex]x = \frac{1.1*6.6}{1}\\ x = 7.26[/tex]

The cost of gas daily is 7.26 euros or approximately 7.2 euros.

learn more about rate here;

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Answer:

The answers are- 4x-5: 5 less than the product of 4 and a number.

4(x-5): The product of 4 and the difference of a number and 5.

4(x+5): The product of 4 and the sum of a number and 5.

Step-by-step explanation:

I took the test on k12 and when I reviewed it, it said were the correct answers:)

Hope this helped!!

Hope you have a wonderful day!!:)

Answer:

Step-by-step explanation:

Given:

TU ≅ WU

∠T ≅ ∠W

To Prove:

[tex]\overline{TS} \cong \overline{WV}[/tex]

Proof:

In  Δ TUS and Δ  WUV

STATEMENT                                                 REASON

1. TU ≅ WU                                     1. Given

2. ∠T ≅ ∠W                                    2. Given

3.∠TUS ≅ ∠WUV                           3. Vertically Opposite Angles are equal

4. ΔTUS  ≅ ΔWUV                         4. Angle-Side-Angle congruence test.

5. ∴ TS ≅  WV                                 5. Corresponding parts of congruent triangles.

[tex]\overline{TS} \cong \overline{WV}[/tex].......Proved

Answer:

11/147

Step-by-step explanation:

11 + 7 + 3 = 21

chances of red = 11/21

and chances of yellow = 3/21

3/21 = 1/7

11/21 x 1/7 = 11/147

Answer:

14:30

Step-by-step explanation:

Okay so your looking for the probability of red or yellow roses so you would combine the numbers of red and yellow roses then add all the roses up together, all the red and yellow are 14 and there are 30 roses in the shop so the answer would be 14:30

Answer:

6.7√2 in ≈ 9.48 in

Step-by-step explanation:

First, use the area of the square to find the side length.

A = s²

44.89 in² = s²

s = 6.7 in

The diagonal of a square divides it into 45-45-90 triangles.  You can use Pythagorean theorem to find the length of the diagonal.

c² = a² + b²

c² = (6.7 in)² + (6.7 in)²

c = 6.7√2 in

c ≈ 9.48 in

Answer: 6.7√2

Step-by-step explanation: Let's start this problem by drawing a picture of a square with a diagonal of length x.

Now to find the length of the diagonal, let's first find the length of a side of the square. To find the length of a side, remember that the formula for the area of a square is S² and since we know that the area of the given square is 44.89 inches, we can set up the equation 44.89 = S².

Square rooting both sides, we have 6.7 = S so we can give the side of our square a length of 6.7. Now to find the value of x, it's important to understand that the diagonal of a square creates 45° 45° 90° triangles and in a 45° 45° 90° triangle, the hypotenuse = √2 × leg.

So we have x = 6.7√2.

So the length of the diagonal of the square is 6.7√2 inches.

Image provided.

Answer:

160/x = 4/3

x = (160/4)(3) = 40(3) = 120

Apples: 160 pounds

Grapes: 120 pounds

Blackberries: 160 pounds

The total weight of this truckload of fruit is 160 + 120 + 160 = 440 pounds.

To find the total weight of the truckload of fruit with apples weighing 160 pounds in a ratio of 4:3:4, calculate the total ratio parts and apply it to the weight of apples. The total weight of the fruit is 440 pounds.

The truck carries apples, grapes, and blackberries in the ratio of 4:3:4.

To find the total weight, you need to calculate the total ratio parts, which is 4 + 3 + 4 = 11 parts. Then, for apples alone, 4 parts represent 160 pounds, so each part is 160/4 = 40 pounds. The total weight of the truckload of fruit would be 11 parts * 40 pounds = 440 pounds.

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Answer:

x = 5

Step-by-step explanation:

7x is a secant- secant angle and has measure equal to half the difference of the intercepted arcs, that is

7x = 0.5(22x + 10 - 50)

7x = 0.5(22x - 40) ← distribute

7x = 11x - 20 ( subtract 11x from both sides )

- 4x = - 20 ( divide both sides by - 4 )

x = 5

Answer:

The correct answer is B. $310 at $2 per kilogram

Step-by-step explanation:

1. Let's find out the maximum profit Ms. Ortiz can make with a loaf of tomatoes:

function p(x)=–80x² + 320x – 10

For x = 1, price per kilogram of tomatoes would be: 4 - x = 3

–80x² + 320x – 10, replacing with x = 1

-80 * 1² + 320 * 1 - 10 = -80 + 320 - 10 = 230

For x = 2 price per kilogram of tomatoes would be: 4 - x = 2

–80x² + 320x – 10, replacing with x = 2

-80 * 2² + 320 * 2 - 10 = -320 + 640 - 10 = 310

For x = 3, price per kilogram of tomatoes would be: 4 - x = 1

–80x² + 320x – 10, replacing with x = 3

-80 * 3² + 320 * 3 - 10 = -720 + 960 - 10 = 230

The correct answer is B. $310 at $2 per kilogram

Answer:The correct answer is B.) $310 at $2 per kilogram

Hope this helps :D

Answer:

Infinitely many solutions.

Step-by-step explanation:

-t=9(t-10)-t=9(t-10)

-t=9t-90-t=9t-90

-t=8t-90=9t-90

8t-(-t)-90=9t-90

8t+t-90=9t-90

9t-90=9t-90

Answer:

If you mean −t=9(t−10), then the answer is 9, if you mean −t=9(t−10)−t=9(t−10) then infinite solutions.

Step-by-step explanation:

Here is the answer if you mean −t=9(t−10):

−t = 9 (t−10)

Simplify the equation.

-t = (9)(t) + (9)(-10)

-t = 9t + -90 (Add the opposite)

-t = 9t - 90

Subtract -9t

-t -9t = 9t - 90 - 9t

-10t = - 90

Divide -10 on both sides to make sure the equation is balanced on both sides. And to isolate t to get the final answer.

-10t  =  -90

-10t  =  -10

Therefore,

Is the final answer.

I Hope this helps! Have a great rest of your morning, afternoon, or evening! :D

Average speed is 12.6 miles per hour

Solution:

Given that team tool bella canoed [tex]15\frac{3}{4}[/tex] miles in [tex]\frac{5}{4}[/tex] hours

To find: average rate of speed in miles per hour

From given information,

[tex]distance = 15\frac{3}{4} \text{ miles } = \frac{15 \times 4+3}{4} = \frac{63}{4} \text{ miles}[/tex]

[tex]time = \frac{5}{4} \text{ hours}[/tex]

To find the speed we use the below formula,

[tex]speed = \frac{distance}{time}[/tex]

Substituting the given values we get,

[tex]speed = \frac{\frac{63}{4}}{\frac{5}{4}}\\\\speed = \frac{63}{4} \times \frac{4}{5} = \frac{63}{5} = 12.6[/tex]

Thus average speed is 12.6 miles per hour

Answer:

Brook is faster.

Step-by-step explanation:

1 hour=60 minutes

2 hours=2*60=120 minutes

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

7 miles in 30 minutes vs 25 miles in 120 minutes

7/30=0.233...mile per minute

25/120=0.20833...mile per minute

Brook is faster than Joshua.

To determine which person is faster, we can compare their average speeds.

Average speed is calculated by dividing the total distance traveled by the total time taken.

For Brook, she traveled 7 miles in 30 minutes, so her average speed is:

7 miles ÷ 30 minutes = 0.2333 miles per minute.

For Joshua, he traveled 25 miles in 2 hours, which is equivalent to 120 minutes. So his average speed is:

25 miles ÷ 120 minutes = 0.2083 miles per minute.

Therefore, Brook is faster than Joshua as her average speed is higher.

Answer:

From left to right:

3, 30, 20

Step-by-step explanation:

Start by determining the ratio of yellow to red paint. Use the column where both amounts are given:

yellow to red = 2 to 6 = 1 to 3

2 to 6 the same as 1 to 3 when reduced, by dividing both sides by 2.

This means yellow paint is a third of red paint. Backwards, red paint is three times yellow paint.

To go from yellow to red, do yellow X 3.

To go from red to yellow, do red ÷ 3.

Column 1:

1 X 3 = 3

Column 3:

10 X 3 = 30

Column 4:

60 ÷ 3 = 20

The ratios are:

1 to 3

2 to 6

10 to 30

20 to 60

The solution is price of 1 slice of pizza is $ 1.542 and price of 1 bottle of water is $ 2.083

Solution:

Let "p" be the price of 1 slice of pizza

Let "b" be the price of 1 bottle of water

Given that Abby bought two slices of pizza and two bottles of water for $7.25

So we can frame a equation as:

two slices of pizza x price of 1 slice of pizza + two bottles of water x price of 1 bottle of water = $ 7.25

[tex]2 \times p + 2 \times b = 7.25[/tex]

2p + 2b = 7.25 ---- eqn 1

Also given that Cameron bought four slices of pizza and one bottle of water for $8.25

So we can frame a equation as:

four slices of pizza x price of 1 slice of pizza + one bottles of water x price of 1 bottle of water = $ 8.25

[tex]4 \times p + 1 \times b = 8.25[/tex]

4p + b = 8.25 ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "p" and "b"

Multiply eqn 2 by 2

8p + 2b = 16.5 --- eqn 3

Subtract eqn 1 from eqn 3

8p + 2b = 16.5

2p + 2b = 7.25

(-) ----------------------

6p = 9.25

From eqn 1,

2p + 2b = 7.25

2(1.542) + 2b = 7.25

2b = 4.166

Thus price of 1 slice of pizza is $ 1.542 and price of 1 bottle of water is $ 2.083

Answer:

B

Step-by-step explanation:

B. Each year development expenses increase by $60,000.

Answer:

B. Each year development expenses increase by $60,000.

Step-by-step explanation:

Answer:

C. there is no solution since 4=7 is a false statement

Linear equations are equations with a leading degree of 1. This shows that there is no solution since 4 =7 is a false statement

Linear equations are equations with a leading degree of 1. Given the linear equation

Given

13+4x-9=7x+7-3x

Simplify

4 + 4x = 4x + 7

Collect the like terms

4x - 4x = 7 - 4
0x = 3

This shows that there is no solution since 4 =7 is a false statement

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Number of hamburgers bought is 23 and number of bags of fries bought is 14

Let "h" be the number of hamburgers bought

Let "f" be the number of bags of fries bought

Cost of one hamburger = $ 1.49

Cost of one bag of fries = $ 1.19

Given that Ben spent a total of 50.93

Thus we can frame a equation as:

number of hamburgers bought x Cost of one hamburger + number of bags of fries bought x Cost of one bag of fries = $ 50.93

[tex]h \times 1.49 + f \times 1.19 = 50.93[/tex]

1.49h + 1.19f = 50.93 ------ eqn 1

Also given that the number of hamburgers was five less than twice the amount of fries

number of hamburgers bought = 2(number of fries) - 5

h = 2f - 5  ---------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "h" and "f"

Substitute eqn 2 in eqn 1

1.49(2f - 5) + 1.19f = 50.93

2.98f - 7.45 + 1.19f = 50.93

4.17f = 50.93 + 7.45

4.17f = 58.38

[tex]f = \frac{58.38}{4.17}[/tex]

Substitute f = 14 in eqn 2

h = 2(14) - 5

h = 28 - 5 = 23

Summarizing the results:

number of hamburgers bought = h = 23

number of bags of fries bought = f = 14

Answer:

Step-by-step explanation:

4x - 2y = -5

-2y = -4x - 5

y = 2x + 5/2.....slope here is 2

-2x + 3y = -3

3y = 2x - 3

y = 2/3x - 1.....slope here is 2/3

NONE OF THE ABOVE.....they are not the same line....they are not parallel because they dont have the same slope....they are not perpendicular because they do not have negative reciprocal slopes

Answer:

this would be none of the above.

Step-by-step explanation:

its not equal because when solving, x and y isnt the same for both equations.

i cant explain the rest, my apologies but if u use a website called *desmos* you can put up equations and itll graph them for you. :3

Solving for m...

-7/8≤m-13/8

6/8≤m

m≥3/4

answer: m≥3/4

Answer: m≥3/4

Step-by-step explanation:

Solving for m:

Step 1: -7/8≤m-13/8

Step 2: 6/8≤m

Step 3: m≥3/4

answer: m≥3/4

Answer:

20

-

3

Step-by-step explanation:

Final answer:

To raise the fraction 1/5 to 15ths, multiply both the numerator and the denominator by 3 to get the equivalent fraction 3/15.

Explanation:

To raise the fraction 1/5 to 15ths, we need to find an equivalent fraction that has a denominator of 15. To do this, we need to find a number that we can multiply both the numerator and the denominator of 1/5 by to get a new fraction with a denominator of 15. Since 5 multiplied by 3 equals 15, we multiply both the numerator and the denominator of 1/5 by 3.

Thus, we have:

1/5 × 3/3 = 3/15

To raise the fraction 1/5 to 15ths, multiply both the numerator and the denominator by 3 to get the equivalent fraction 3/15.

The fraction 1/5 is equivalent to 3/15 when raised to 15ths.

Answer:

Step-by-step explanation:

Just do the long division and you'll find out.

Answer:

Step-by-step explanation:

Total earnings = f(x) = 6x

Total expenses =g(x) = 0.5x + 50

Profit p(x) = f(x)  - g(x)

               = 6x - ( 0.5x + 50)

               = 6x - 0.5x - 50 = 5.5x - 50

Answer:

22/35

Step-by-step explanation:

-12/14=-6/7

-6/7*-11/15=66/105=22/35

Step-by-step explanation:

[tex]12:36=\dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}[/tex]

Answer: 1/3

Step-by-step explanation: The ratio 12:36 can be written as the fraction 12/36. So, we simply put the 12 as the numerator of our fraction and put the 36 as the denominator of our fraction.

12/36 can be simplified by dividing the numerator and the denominator by the greatest common factor of 12 and 36 which is 12 and we get the fraction 1/3.

The fraction 1/3 still represents the ratio 1/3 even though we have written it in the form of a/b or fraction form.

The question doesn't require any specific probabilities, but I'm adding my own calculations to make it easier for you to solve your own problem

Answer:

Questions added and answered below

Step-by-step explanation:

Venn Diagram

When we have different sets, some of them belong only to one set, some belong to more than one, some don't belong to any of them. This situation can be graphically represented by the Venn Diagrams.

Let's analyze the data presented in the problem and fill up the numbers into our Venn Diagram. First, we must use the most relevant data: there are 60 people in both the choir and the band. This number must be in the common space between both sets in the diagram (center zone, purple).

We know there are 110 people in the choir, 60 of which were already placed in the intersection zone, so we must place 110-60=50 people into the blue zone, belonging to C but not to B.

We are also told that 240 people are in a band, 60 of which were already placed in the intersection zone, so we must place 240-60=180 people into the red zone, belonging to B but not to C.

Finally, we add the elements in all three zones to get all the people who are in the choir or in the band, and we get 50+60+180=290. Since we have 450 people in the school, there are 450-290=160 people who are not in the choir nor in the band.

The question doesn't ask for a particular probability, so I'm filling up that gap with some interesting probability calculations like

a) What is the probability of selecting at random one person who is in the band but not in the choir?

The answer is calculated as

[tex]\displaystyle P(A)=\frac{180}{450}=0.4[/tex]

b) What is the probability of randomly selecting one person who belongs only to one group?

We look for people who are in only one of the sets, they are 50+180=230 people, so the probability is

[tex]\displaystyle P(B)=\frac{230}{450}=0.51[/tex]

b) What is the probability of selecting at random one person who doesn't belong to the choir?

We must add the number of people outside of the set C, that is 180+160=340

[tex]\displaystyle P(C)=\frac{340}{450}=0.76[/tex]