The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points ​(4​,80​) and ​(7​,140​) to find the number of soda bottles the machine can make each minute.

Answer:

Diameter=35

Step-by-step explanation:

If your circumstance is 35pi then the formula would be C=35pi and to find that it would have been C=2 pi r. To find the diameter it would be d=c/pi. So it would be d=35pi/pi. The pi's would cancel out and you have 35 as the diameter and 17.5 as the radius

Check:

C=2 pi r

C= 2 pi 17.5

C=35pi ✅

D=2r

D=2(17.5)

D=35✅

I hoped this helped, I am not sure but this is what I think

Answer:

21700

Step-by-step explanation:

23400 - 1700 = 21700

Walter's salary last year can be found by subtracting the increase from his current salary. After calculating, we find that Walter's salary last year was $21,700.

To calculate Walter's salary last year, we need to subtract the amount his salary increased this year from his current salary. Walter's current salary is $23,400, and it has increased by $1,700 from last year. Thus, his salary last year was:

$23,400 (current salary) - $1,700 (increase) = $21,700

Therefore, Walter's salary last year was $21,700.

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Answer:

$16.74

Step-by-step explanation:

so for every pound is 2.79 so just so

6 times 2.79

Answer:

a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

EDGE 2021

Answer:

The labor cost per shirt of the American factory is 0.36 times the labor cost per shirt of the foreign company.

Step-by-step explanation:

A textile factory in the United States plays 300 workers a total of $9 million each year to produce 4.5 million shirts.

Therefore, the labor cost per shirt will be

[tex]\frac{9 \times 10^{6}}{300 \times 4.5 \times 10^{6}} = 0.0067[/tex]

Again, a foreign factory employs 225 workers at a total cost of $1,050,000 to produce 2,500,00 shirts.

Therefore, the labor cost per shirt will be

[tex]\frac{1050000}{250000 \times 225} = 0.01867[/tex]

Therefore, the labor cost per shirt of the American factory is 0.36 times (Approximate) the labor cost per shirt of the foreign company. (Answer)

Answer:

Step-by-step explanation:

        First alloy contains 34% copper and the second alloy contains 48% alloy.

We wish to make 46 pounds of a third alloy containing 37% copper.

       Let the weight of first alloy used be [tex]x[/tex] in pounds and the weight of second alloy used be [tex]y[/tex] in pounds.

       Total weight = [tex]46\text{ }pounds=x+y[/tex]        [tex]-(i)[/tex]

      Total weight of copper = [tex]37\%\text{ of 46 pounds = }34\%\text{ of }x\text{ pounds + }48\%\text{ of }y\text{ pounds }[/tex]

       [tex]\dfrac{37\times 46}{100}=\dfrac{34x}{100}+\dfrac{48y}{100}\\\\ 34x+48y=1702[/tex]        [tex]-(ii)[/tex]

       Subtracting 34 times first equation from second equation,

[tex]34x+48y-34x-34y=1702-34\times46\\14y=138\\y=9.857\text{ }pounds \\x=36.143\text{ }pounds[/tex]

∴ 36.14 pounds of first alloy and 9.86 pounds of second alloy were used.

Final answer:

The metallurgist must use around 36.14 pounds of the 34% copper alloy and approximately 9.86 pounds of the 48% copper alloy to make 46 pounds of a 37% copper alloy.

Explanation:

To solve the problem involving an alloy containing copper, we can use a system of equations based on the percentages provided and the total weight required for the new alloy.

Let's denote x as the number of pounds of the 34% copper alloy, and y as the number of pounds of the 48% copper alloy. We are aiming to create 46 pounds of a 37% copper alloy.

The first equation represents the total weight of the mixture:

x + y = 46

The second equation represents the total amount of copper in the new alloy:

0.34x + 0.48y = 0.37 * 46

Solving this system of equations, we get:

Multiply the second equation by 100 to remove decimals: 34x + 48y = 37 * 46

Substitute y from the first equation into the second: 34x + 48(46 - x) = 37 * 46

Simplify and solve for x: 34x + 2208 - 48x = 1702

This yields -14x = -506, so x = 506 / 14 = 36.14

Using x to solve for y gives us y = 46 - 36.14 = 9.86

Therefore, the metallurgist must use around 36.14 pounds of the 34% copper alloy and approximately 9.86 pounds of the 48% copper alloy to make 46 pounds of the third alloy containing 37% copper.

Answer:

12 756.2 kilometers

Step-by-step explanation:

12 756.2 kilometers

Answer:

The answer is 384.

Step-by-step explanation:

It starts at 3 going up by three to 6 then from there it adds 6 equaling 12 then so forth so it would be 3, 6, 12, 24, 48, 96, 192, 384

Answer:

y = 0.25x - 5

Step-by-step explanation:

Given line is 4x + y = 3

or y = -4x + 3

Comparing this with slope-intercept form y = mx + c :

slope of this line is -4

Product of slopes of perpendicular lines = -1

⇒ slope of a line perpendicular to this is [tex]\frac{-1}{-4}[/tex] = [tex]\frac{1}{4}[/tex] = 0.25

This line also passes through the point (-4,-6)

The equation of a line having slope m and passing through a point (h,k) is

y - k = m(x - h)

⇒ equation of line perpendicular to given line is y - (-6) = 0.25×{x - (-4)}

⇒ y + 6 = 0.25×(x + 4)

⇒ y + 6 = 0.25x + 1

⇒ y = 0.25x - 5

This is in the slope-intercept form y = mx + c with slope m = 0.25 and y-intercept (0,-5)

I think it's false.... 5/6 is 83.33% as a percent so I don't think it's true.

6/6 ......... 100%

5/6 ..............x%

x = 5/6*100/6/6 = 500/6 = 83,(3)%

Answer:

8<74 square root<9

Step-by-step explanation:

The first thing we have to do is to find the lowest number that can be squared to 74. 1,4,9,16,25,36,49,64,81,100.

As we see, 64 is the lowest closest number to 74 and the square root of 64 is 8. So right now, is 8<square root of 74<___.

Now, we have to find the highest number closest to 74. As we look back at our square roots, 81 is the closest number to 74 in the square roots and the square root is 9 and voila. 8<sqrt74<9

The inequality is -

8 < √74  < 9.

We have the following inequality -

_____<√74 <____.

We have to fill in the blanks with two consecutive integers to complete the above inequality.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

According to the question -

Let A = √74

Then -   A² = 74

The nearest integers, square of between which A² lies is between 8 and 9. So -

8² < A² < 9²

Therefore, the two consecutive integers will be - 8 and 9.

Hence, the inequality is -

8 < √74  < 9

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Answer:

8189.11

Step-by-step explanation:

If 8900 is 100% and we need to find 15%  we would multiply 8900 and 15 then divide by 100 and that equal 1335 so we would then subtract 1335 from 8900 because it is 15% off, which equals 7565, so now 7565 is 100% and we need to add the 8.25% tax, so we multiply 7565 and 8.25 then divide by 100 which equals 625.11 then we add 7565 and 625.11 which equals 8189.11

The sale price of the car is $8,188.36.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.

We have,

A car originally priced at $8,900 is on sale at 15% off.

If the sales tax rate is 8.25%.

So, Discount

= 15% of $8,900

= 0.15 x $8,900

= $1,335

Now, Price after discount

= $8,900 - $1,335

= $7,565

and, Sales tax

= 8.25% of $7,565

= 0.0825 x $7,565

= $623.36

So, Sale price of the car

= $7,565 + $623.36

= $8,188.36

Therefore, the sale price of the car is $8,188.36.

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Answer:

The area is 12.56, and the circumference is 12.56.

Step-by-step explanation:

For the area,

We need to use the formula A=3.14*radius*radius

So we plug it in, and we get 3.14*2*2, which is 12.56 centimeters squared.

For circumference, we need to do,

C = 3.14*diameter

To find the diameter we need to do 2 (radius) x 2 which is 4

Plugging it in that would be 3.14 * 4 which is 12.56

So, in this case, the area is 12.56, and the circumference is also 12.56.

The area of a circle with a radius of 2 cm is 12.56 cm², and the circumference is 12.56 cm, using 3.14 for pi.

To find the area and circumference of a circle with a radius of 2 cm, we can use the formulas A = πr² for the area and C = 2πr for the circumference, where π (pi) is approximately 3.14.

Area of the Circle

The area of the circle is calculated using the formula A = πr². Plugging in the radius:

A = 3.14 × (2 cm)²

A = 3.14 × 4 cm²

A = 12.56 cm²

Circumference of the Circle

The circumference of the circle is calculated using the formula C = 2πr. Plugging in the radius:

C = 2 × 3.14 × 2 cm

C = 12.56 cm

Answer:

He would score 154 points because he averages 14 points per game and 11 times 14 is 154

Data scored 42 points in 3 games, then points scored in 11 games will be equal to 154 points.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per information obtained from the question,

Let x points will be obtained in 11 games.

Data scored,

42 points = 3 games

Points earned in 1 game = 42/3 = 14

Then,

Points obtained in 11 games = 14 × 11

x = 154 points.

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Answer:

Step-by-step explanation:

2/10+6/100 is the same as 2/10*10/10+6/100

2/10*10/10=20/100

20/100+6/100

26/100

Answer: 26/100

Step-by-step explanation: Find the common denominator, which is 100 multiply both numerator and denominator by 10 which is 20/100 and then add on 6/100 which equals 26/100

The new copier can create 2000 copies in 20 minutes.

Step-by-step explanation:

Given,

It takes 60 minutes to make 2000 copies by old printer and 15 minutes to made x number of copies, therefore, using proportion

[tex]60:2000::15:x[/tex]

Product of mean = Product of extreme

[tex]2000*15=60*x\\30000=60x\\60x=30000[/tex]

Dividing both sides by 60

[tex]\frac{60x}{60}=\frac{30000}{60}\\x=500[/tex]

As the new copier is working with old copier, therefore,

Copies made by new printer = 2000 - 500 = 1500

New copier can make 1500 copies in 15 minutes and 2000 copies in x minutes, using proportion

[tex]1500:15::2000:x\\1500*x=15*2000\\1500x=30000[/tex]

Dividing both sides by 1500;

[tex]\frac{1500x}{1500}=\frac{30000}{1500}\\x=20[/tex]

The new copier can create 2000 copies in 20 minutes.

Keywords: ratio, proportion

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Answer:

1104 miles

Step-by-step explanation:

Given

Let x be the miles he drove in the United States

⇒

The total distance traveled by him= distance traveled in mexico + distance traveled in US

1851=747+x

x=1104 miles

⇒distance traveled in US= 1104 miles

Answer:

The reason for statement #7.

C) Converse of the same side consecutive angles theorem.

Step-by-step explanation:

For  Parallel Lines:

Same side consecutive angles theorem

When the lines are parallel, the interior angles on the same side of the transversal are supplementary.

Here,

It is Converse Of above Statement

∠ 6 and ∠ 13 are supplementary

i.e

∠ 6 + ∠ 13 = 180°

Therefore the Reason  is

C) Converse of the same side consecutive angles theorem.

That is If ∠ 6 and ∠ 13 are supplementary then the Lines are Parallel

i.e        t₁ || t₂

Answer:

C) Converse of the same side consecutive angles theorem.

Step-by-step explanation:

Step-by-step explanation:

I think it 1,180 yeah I think it is

Step-by-step explanation:

PART A

a=total amount

c=cans of oil

g=gasoline

a=2.85g+3.15c

PART B

a=2.85(8.4)+3.15(6)

a=23.94+18.90

a=42.84

Answer:

Step-by-step explanation:

12/4=3 and 16/8=2

The amount deposited in CD is $660

Given that , To save for the purchase of a new car, a deposit was made into an account that earns 8% annual simple interest.  

Let the amount deposited in new car be $ n

Another deposit, $1700 less than the first deposit, was placed in a certificate of deposit (CD) earning 12% annual simple interest.  

Then, amount deposited in CD will be $ (n – 1700)

The total interest earned on both accounts for 1 year was $676

The simple interest is given as:

[tex]\text { Simple interest }=\frac{\text { principal } \times \text {rate} \times \text {time}}{100}[/tex]

Simple interest for purchase of new car:

[tex]\text { S. } \mathrm{I}=\frac{n \times 8 \times 1}{100}=\frac{8 n}{100}[/tex]

Simple interest for CD:

[tex]\text { S.I } =\frac{(n-1700) \times 12 \times 1}{100}=\frac{12(n-1700)}{100}[/tex]

Now, given that S.I for new car + S.I for CD = 676

[tex]\begin{array}{l}{\frac{8 n}{100}+\frac{12(n-1700)}{100}=676} \\\\ {\frac{8 n+12 n-12 \times 1700}{100}=676}\end{array}[/tex]

20n = 67600 – 20400

n = 2360

So money deposited in CD = n - 1700 = 2360 – 1700 = 660

Hence, the CD deposit amount is $660

To find the amount deposited in the CD, set up an equation using the given information. Solve for x to find the amount of the first deposit. Subtract $1700 from the first deposit to find the amount deposited in the CD.

To find the amount of money deposited in the CD, we can set up an equation using the given information.

Let the amount of the first deposit be x.

The second deposit is $1700 less than the first deposit, so it is x - $1700.

Using the formula for simple interest, the interest earned on the first deposit is x * 0.08.

The interest earned on the second deposit is (x - $1700) * 0.12.

According to the given information, the total interest earned is $676. Therefore, we can set up the equation: x * 0.08 + (x - $1700) * 0.12 = $676.

Simplifying and solving for x:

0.08x + 0.12x - $204 = $676

0.20x - $204 = $676

0.20x = $880

x = $4400

Therefore, the amount of money deposited in the CD is $4400 - $1700 = $2700.

Answer:

I believe they made $4,550 each week.

Step-by-step explanation:

If they sold 74 puppies in a week, and there are 7 days in a week, You would divide 74 by 7 to get an estimate of 10. So that means that 10 puppies were sold each day. Then, because the puppies cost $65, you would multiple 65 by 10 to get $650. $650 is the amount of money they make in a day. Than multiple 650 by 7 to get $4,550. $4,550 is the amount of money they would have made.

74÷7 = about 10

65×10 = 650

650×7 = 4550

Answer:812/1000

Step-by-step explanation:

Answer:

Multiply the length by the width to find the area in square metres and then multiply that figure by 0.03 Kg to find out how much seed you'll need.

Step-by-step explanation:

Answer:

20 bags of seed is needed for the new lawn

Step-by-step explanation:

To answer this question, first find the area of the lawn and divide the area calculated by the number of square feet per bag of seed.

A  lawn is assumed to have a rectangular shape, the area (A) of the lawn  therefore is

               A = L x W

Where:    A = Area of lawn

                L = Length of lawn

               W =  Width of lawn

                A = L x W

                 L = ?

                W = 60 ft

To find the length, use the formula for the perimeter of a rectangle since the lawn is assumed to a rectangular shape

Perimeter (P) = 2(L+W)

                  P = 300 ft

            300  = 2(L + 60) ft

            300  = 2L + 120

Subtract 120 from both sides

   300 - 120  = 2L + 120 - 120

              180 = 2L

Divide both sides of the equation by the coefficient of L which is 2

         180/2 = 2L/2

             90 = L

              L  =  90 ft

That is, the length of the lawn is 90 ft

To calculate the area of the lawn

              A  = L x W

              L   =  90 ft

              W  = 60 ft

               A  = 90 ft x 60 ft

               A  = 5400 square feet

This means that the area of the lawn is 5,400 square feet

To get the number of bags of seed that will cover the lawn, divide the area of the lawn by the number square feet that a bag will cover.

Number of bags of seed  = Total Area of lawn/Number square feet per bag.

Total Area                          = 5400 square feet

Number square

feet per bag                      = 270

Number of bags               = 5400/270

                                          = 20 bags of grass seed

20 bags of seed is needed for the new lawn

Answer:

Step-by-step explanation:

       Meghan is soon going to have to spend $78.99 on a dress, $32.50 on shoes, $25 for the ticket and $50 for dinner.

       Meghan already has $52 from her savings to spend. She earns money from babysitting at $12 each hour.

       Let the number of hours Meghan babysits be denoted by [tex]x[/tex].

From [tex]x[/tex] hours of babysitting, Meghan earns $([tex]x\times12[/tex]).

So, her total earnings sum up to [tex]12x+52[/tex]. This should be greater than total spendings.

       [tex]12x+52\geq 78.99+32.50+25+50\\12x\geq 134.49\\x\geq 11.208[/tex]

So, Meghan must work for 12 hours so she has something left after spendings.

∴ Meghan must babysit for 12 hours.

2/5= 12/30

The road is 12/30 miles long, they pave 1/30 each hour.

60x12= 720 minutes= 12 hours

To repave the road that is 2/5 miles long, it will take the road crew 12 hours.

To find out how long it will take the road crew to repave the road, we need to divide the length of the road by the rate at which they can repave. The road is 2/5 miles long and the crew can repave 1/30 miles per hour. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, (2/5) ÷ (1/30) = (2/5) x (30/1) = 60/5 = 12. Therefore, it will take the crew 12 hours to repave the road.

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Answer:

Step-by-step explanation:

Let's find the volume of the room in ft³ and that will give

14×22×9=2772ft³

There are deductions. Hence we subtract them from this value

3×5=15, but there are two, hence 15×2=30ft²

And 4×7=28ft²

Hence 2772-(30+28)=2714

Dividing this value by 320 gives

8.4(to 2s.f)

Answer:

The coordinates of the lines when both lines meets at point is ( 0, 0 )

Step-by-step explanation:

Given as :

The two lines are

[tex]\frac{2}{3}[/tex]x + [tex]\frac{1}{6}[/tex]y = [tex]\frac{2}{3}[/tex]

And 4 x + y = 4

The coordinate of the lines are obtained when the two lines intersect

Let the coordinate of intersection points are ( x , y )

Now , The first lines as

[tex]\frac{2}{3}[/tex]x + [tex]\frac{1}{6}[/tex]y = [tex]\frac{2}{3}[/tex]

Or, Taking LCM we get ,

[tex]\frac{4x + y}{6}[/tex] = [tex]\frac{2}{3}[/tex]

Cross multiplication both sides

Or, 3 × ( 4 x + y ) = 2 × 6

Or,  3 × 4 x +  3 × y = 12

Or, 12 x + 3 y = 12          ...........A

Other line is 4 x + y = 4

i.e 3 × ( 4 x + y ) = 3 × 4

or, 12 x + 3 y = 12          .........B

Solving both the line equations

(12 x + 3 y ) - ( 12 x + 3 y ) = 12 - 12

I.e x = 0  and  y = 0

So coordinates are ( x , y )  =  ( 0 , 0 )

Hence The coordinates of the lines when both lines meets at point is ( 0, 0 ) Answer

Answer:

The Value of x is 40.

Step-by-step explanation:

Given:

∠SRT ≅ ∠STR

∠SRT = 20

m∠SRT = 4x

To find: Value of x

Solution:

From the given data,

m ∠SRT = 20

Also ∠SRT ≅ ∠STR

Hence from congruence and equality property we can say that;

m∠STR= 20

m∠STU= 4x

Now by straight angle property which states that sum of two angles which are created by a straight line is always 180.

Hence,

∠STR +∠STU =180

Now Substituting the given values we get;

[tex]20+4x=180\\4x=180-20\\4x=160\\\\x=\frac{160}{4} =40[/tex]

Hence m∠STU = 4x =4 ×40 = 160°

Hence the value of x = 40.