A rectangular exercise mat has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the length, in feet, of the mat. Then find the area, in square feet, of the mat.

Answer:

So, the rational number is [tex]\frac{52}{12}[/tex] .

Step-by-step explanation:

Let x be the other number.

We know ,

[tex]\frac{7}{36}[/tex] + x = [tex]\frac{5}{6}[/tex]

To find x, we need to convert both to have a common denominator.

So, if we multiply [tex]\frac{7}{36}[/tex] by [tex]\frac{10}{36}[/tex]  ,

[tex]\frac{10}{1}[/tex] × [tex]\frac{7}{36}[/tex] + x = [tex]\frac{56}{10}[/tex]

After multiplication the fraction  [tex]\frac{7}{36}[/tex] becomes [tex]\frac{70}{360}[/tex]  .

[tex]\frac{70}{360}[/tex]+ x =  [tex]\frac{56}{10}[/tex]

Now we have common denominator of 360in both fraction,

Now,

we can simplify the equation ,

[tex]\frac{70}{360}[/tex]  + x = [tex]\frac{56}{10}[/tex]

70 + 360x = 56 × 36

2520 + 360x = 2016

504 + 360x = 2016

360x = 1512

x = [tex]\frac{1512}{360}[/tex]

   =[tex]\frac{52}{12}[/tex]

So, the rational number is [tex]\frac{52}{12}[/tex] .

Approximately one full tablespoon of coffee powder is required for each 200 ml cup of coffee. We advise using seven teaspoons of ground coffee to produce a full litre of filter coffee at once.

To create coffee, coffee beans must first be roasted. Coffee is a dark-colored, bitter, and slightly acidic beverage that stimulates individuals due to its high caffeine content. In terms of sales, hot beverages have the largest market worldwide. The roasted beans are ground into tiny particles, frequently steeped in hot water, and then filtered to create a cup of coffee. Despite the fact that coffee is typically served hot, it is frequently served cold or iced. Unroasted green coffee beans are made by separating the seeds from the fruits of the Coffea plant. To produce a cup of coffee, the roasted beans are ground into tiny particles, regularly soaked in hot water, and then filtered. Coffee is commonly served cold or iced even though it is traditionally served hot.

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Answer:

1/237.12.

Step-by-step explanation:

The probability of winning the minimum award can be calculated by multiplying the probability of picking 4 numbers correctly from 1 to 51 and then multiplying by the probability of picking 1 number correctly from 1 to 42.

The probability of picking 4 numbers correctly from 1 to 51 is given by the formula:

(number of combinations of 4 numbers from 51) / (number of combinations of 5 numbers from 51)

= (51 choose 4) / (51 choose 5)

= 51! / (4! * 47!) / (51! / (5! * 46!))

= (51 * 50 * 49 * 48) / (5 * 4 * 47 * 46)

= 19600 / 10,946

= 1/5.6 approximately

The probability of picking 1 number correctly from 1 to 42 is given by the formula:

1/42

The final probability of winning the minimum award is given by multiplying the above two probabilities:

1/5.6 * 1/42 = 1/237.12

So, the probability of winning the minimum award is approximately 1/237.12.

Answer:

so im a little confused  3,5203,5203, is not a proper number and there is not enought yards to make a full mile could you reword it?

Step-by-step explanation:

Answer:

To solve it, you need to use compound interest. Let me show you how.

Let P be the initial amount that Terry invested. Then after 4 years, the amount in the account is:

P × (1 + 0.037)^4

After withdrawing $2000, the remaining amount is:

P × (1 + 0.037)^4 - 2000

This amount is then moved to another account earning 4.5% p.a. compounded annually. After 3 more years, the amount in the account is:

(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3

We are given that this amount is equal to $5635.66. So we can write an equation:

(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3 = 5635.66

Simplifying the equation, we get:

P × 1.1597 - 2000 = 5635.66 / 1.1406

Adding 2000 to both sides, we get:

P × 1.1597 = 5635.66 / 1.1406 + 2000

Dividing both sides by 1.1597, we get:

P = (5635.66 / 1.1406 + 2000) / 1.1597

Using a calculator, we get:

P ≈ 5000.01

Therefore, Terry initially invested about $5000.01.

Step-by-step explanation:

Answer:

C. m4/n2    :))))

The addition and subtraction of the fractions by finding the LCD gives:

NUMBER 1: (8y-49) /(y²-49)

NUMBER 2: (x+10) /(2x+8)

NUMBER 3: (7a-2)/10b

NUMBER 4: 1

Least Common Denominator (LCD) refers to the smallest multiple that two or more denominators have in common, and is used in operations involving fractions.

NUMBER 1

y/(y²-49) - 7(y+7) = y/[(y+7)(y-7)] - 7(y+7)

LCD of (y+7)(y-7) and (y+7) is (y+7)(y-7):

                          = [y + 7(y-7)] / [(y+7)(y-7)]

                          = [y + 7y-49)] / [(y+7)(y-7)]

                          = (8y-49) / (y+7)(y-7)

                          = (8y-49) /(y²-49)

NUMBER 2

1/2 + 3/(x + 4) = [1(x+4) + 3*2] /[2(x+4)]

                      = [x+4 + 6] /[2(x+4)]

                      = (x+10) /(2x+8)

NUMBER 3

(a+2)/4b + (a-1)/10b + (a-3)/5b = [5(a+2) + 2(a-1) + 4(a-3)]/20b

                                                 = [5a+10 + 2a-2 + 4a-12]/20b

                                                 = (14a-4)/20b

                                                 = 2(7a-2)/20b

                                                 = (7a-2)/10b

NUMBER 4

x/(x+1) - 1/(x-1) + 2x/(x²-1) = [x(x-1) - 1(x+1) + 2x]/(x²-1)

                                         = [x²-x -x-1 + 2x]/(x²-1)

                                         = (x²-1)/(x²-1)

                                         = 1

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Answer

Step-by-step explanation:

The cups of milk required for the  ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee is given by 2.4 cups.

Here,

( 2 / 5 ) of a gallons is equal to 0.4 gallons.

( 1 / 4 ) of gallons used for coffee that is equal to 0.25 gallons.

Total gallons left after coffee is equal to

= ( 0.4 ) - ( 0.25 )

= ( 0.15 )gallons

Conversion of gallons to cups is given by :

1 gallon = 16 cups

⇒  ( 0.15 )gallons = 0.15 × 16 cups

⇒  ( 0.15 )gallons = 2.4 cups of milk used.

Therefore, the 2.4 cups of milk is used when  ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee.

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The reference angle would be 155 degrees.

An angle's reference angle is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the horizontal axis.

The positive reference angles have terminal sides that lie in the first quadrant and can be used as models for angles in other quadrants.

The reference angle is acute angle, it must be < 90°.

The terminal side lies in Quadrant II.

The positive measure is:

=180-25

=155°.

And the negative measure is:

= 155-360

= -205°.

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As per the discount, the customer will only need to pay P4,950 on May 12.

Discounts are a common practice in business transactions, where the seller offers a reduction in the price of goods or services as an incentive for the buyer to make a purchase.

The terms of the sale are as follows: 2/10, 1/15, n/30. This means that the customer is entitled to a 2% discount if they pay within 10 days, or a 1% discount if they pay within 15 days. Otherwise, the full amount is due within 30 days.

The customer makes a partial payment of P1,000, which means that they still owe P5,000. However, since the discount is only given upon full payment, the customer is not eligible for any discounts at this point.

Assuming that the customer pays the balance on May 12, they will have taken 11 days to make the payment. Since this is within the 15-day discount period, they are entitled to a 1% discount.

The calculation of the discount is as follows: P5,000 x 1% = P50. Therefore, the customer will only need to pay is calculated as,

=> P5,000 - P50 = P4,950

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Complete Question:

On May 1, RVQ Company sold goods for P6,000 on terms of 2/10, 1/15, n/30. Customer made a partial payment of P1,000 discounts are given only upon full payment of an account. The customer pays the balance on May 12, RVQ will receive on May 12 the amount of

He earns $184 in commission yesterday on sold 5 watches for $60 each and 4 watches for $40 each.

A sales commission is a sum of money paid to an employee upon completion of a task, usually selling a certain amount of goods or services. Employers sometimes use sales commissions as incentives to increase worker productivity. A commission may be paid in addition to a salary or instead of a salary.

A salesman earns a commission 40%

He sold yesterday 5 watches for $60 each

and, 4 watches for $40 each.

We have to find the how much he earn commission?

Now, According to the question:

Price of 5 watches = 60.00 × 5 = $300

4 watches = $40.00 each

Price of 4 watches = 40.00 × 4 = $160

Total sales made = 300 + 160 = $460

His commission is 40% of the sales = 40% × 460

                                                       = 0.40 × 460 = $184

Hence, He earns $184 in commission.

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Answer:

34 bricks is the greatest amount Mary could have used

Step-by-step explanation:

A quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. The value "59%" is a statistic.

In this scenario, a sample of the quarterback's passes was taken during the championship football game, and the completion percentage was calculated based on that sample. Since the percentage was calculated based on a sample, it is a statistic. A parameter, on the other hand, is a value that describes a characteristic of an entire population. For example, if we were to consider the completion percentage of all quarterbacks in the league, then the mean or median completion percentage would be a parameter because it would describe a characteristic of the entire population of quarterbacks. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.

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Complete Question

Determine whether the underlined value is a parameter or a statistic. In a championship football game, a quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. Is the value a parameter or a statistic?

The ratio of cups of flour to water for 6 batches is 18:6

18:6 = 3:1

The ratio is maintained.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Two batches:

The ratio of cups of flour to water.

= 6: 2

= 3:1

Now,

For 1 batch.

The ratio of cups of flour to water.

= 3 : 1

Now,

For m batches.

The ratio of cups of flour to water.

= 3m : 1m

So,

For m = 6

The ratio of cups of flour to water.

= 18 : 6

Thus,

The ratio of cups of flour to water for 6 batches is 18:6.

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The complete question.

For two batches the ratio is 6 cups of flour to 2 cups of water,

This means for every 3 cups of flour, you need 1 cup of water.

The ratio 3:1 is maintained.

Find the ratio for 6 batches

Answer:

Step-by-step explanation:d = 14t + 21t = 35t

So, after 3 hours, the distance between the boats will be:

d = 35 * 3 = 105 miles

Therefore, the Serenity and the Mystic will be 105 miles apart after traveling for 3 hours.

Answer: y = x(x+1)(x-4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,y=x^3-3x^2-4x

taking x commonly

y=x(x^2-3x-4)

y=x(x^2+x-4x-4)

y=x[x(x+1)-4(x+1)]

y=x(x+1)(x-4)

Distributive property is expressed as:

Apply this to the given expression and simplify

Equation of line DC is y = -1/2 x - 8

Equation of line AD is y = 2x + 2

Equation of line BC is y = 2x - 8

The equation of the line 2y + x = 4 is arranged in slope intercept form to have

y = -x/2 + 2

The slope is -1/2

with a slope of -/2 and points (0, -8) line DC is written as

y - -8 = -1/2 (x - 0)

y + 8 = -1/2 x

y = -1/2 x - 8

Equation of line AD

line AD is a perpendicular line  to line DC hence the slope is negative reciprocal of the slope of line DC

slope = 2

point A(0, 2) line AD is written as

y - 2 = 2 (x - 0)

y - 2 = 2x

y = 2x + 2

Equation of line BC

line BC is a parallel to line AD hence the slopes are equal

slope = 2

point C (0, -8) line AD is written as

y - - 8 = 2 (x - 0)

y + 8 = 2x

y = 2x - 8

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The point estimator for the proportion of registered voters expressed concern about a loosening of restrictions is 0.58. The margin of error for this poll is 3.6%.

The point estimator for the proportion of registered voters expressing concern about a loosening of restrictions is:

58/100 = 0.58 or 58%

To determine the margin of error for this poll assuming a confidence level of 95%, we can use the following formula:

margin of error = zsqrt(p(1-p)/n)

where z is the z-score for the desired confidence level (1.96 for 95%), p is the point estimator for the proportion (0.58), and n is the sample size (900).

So, the margin of error is:

1.96sqrt(0.58(1-0.58)/900) ≈ 0.036 or 3.6%

Therefore, the margin of error for this poll is 3.6%.

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____The given question is incomplete, the complete question is given below:

Read the following news article and then answer the two questions at the end According to an NBC News/Wall Street Journal poll released Sunday, 58 percent of registered voters expressed concern about a loosening of restrictions compared with 32 percent who worried that the restrictions would stay in place for too long 3 percent said they were concerned about both scenarios. A mere 3 percent said the pandemic had no impact on their lives, compared with 77 percent who said it had affected them either in a very major way" or "fairly major way The sample size was 900 registered voters a What is the point estimator for the proportion of registered voters expressed concern about a loosening of restrictions b. Determine the margin of error for this poll assuming a confidence level of 95%.

There are 12 trapezoids needed to create two hexagons with pattern blocks.

1. To create two hexagons with pattern blocks, you will need 12 trapezoids.

2. Each hexagon consists of six trapezoids.

3. Since you need two hexagons, you will need 12 trapezoids in total.

In order to create two hexagons with pattern blocks, you will need to use 12 trapezoids in total. Each hexagon consists of six trapezoids, so you will need two hexagons to use all twelve trapezoids. The two hexagons can be formed by arranging the trapezoids in a pattern of two triangles, two parallelograms, two rhombuses, and two trapezoids. With these 12 trapezoids, you will be able to create two complete hexagons.

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Answer:

Step-by-step explanation:

how many pattern blocks triangles would create 1 hexagon

The perimeter of the rectangle in the given diagram is: D. 42 units.

In order to determine the perimeter of this rectangle, we would have to find the length of the third side of the right-angled triangle by using Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

9² + b² = 15²

81 + b² = 225

b² = 225 - 81

b = √144

b = 12 units.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

P = 2(9 + 12)

P = 42 units.

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Answer:

74.90d + 0.13m = Total cost of the car rental

Step-by-step explanation:

Hmmm you didn't give enough information but....

let d represent the number of days

let m represent the number of miles driven

74.90d + 0.13m = Total cost of the car rental

For example Tyee rents the car for 2 days and drives 100 miles

149.8 + 13 = Total cost of the car rental.

$162.8 is the Total cost of the car rental.

Ten pounds of chopped walnuts would total cost $30.00. That is because 3/4 pound of chopped walnuts costs $3.75, and 10 pounds would be 13.33 times as much.

1. 3/4 pound of chopped walnuts costs $3.75

2. 1 pound of chopped walnuts costs $5.00 (3.75 x 1.33)

3. 10 pounds of chopped walnuts costs $50.00 (5.00 x 10)

To calculate the cost of 10 pounds of chopped walnuts, we need to first calculate the cost of 1 pound of chopped walnuts. We know that 3/4 of a pound of chopped walnuts costs $3.75. To calculate the cost of 1 pound, we can multiply 3.75 by 1.33, which gives us the result of $5.00. We then multiply $5.00 by 10, which gives us the result of $50.00. Therefore, 10 pounds of chopped walnuts would cost $50.00. This is because 3/4 pound of chopped walnuts costs $3.75, and 10 pounds would be 13.33 times as much.

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The shortest distance is 5.83 miles as we calculate this by distance formula.

A distance formula is a formula used to find the distance between any two points only if the coordinates are known. These coordinates can be on the x-axis, y-axis, or both. Suppose we have two points, P and Q, in the XY plane. Point P has coordinates (x1,y1) and Q has coordinates (x2,y2). Then the formula for the distance PQ between two points is:

PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])

The school is located 5 miles west of your home the co ordinate is (-5,0)

The playground is 3 miles south of the school so co - ordinate is (0,-3)

shortest distance  = PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])

√([tex]5^{2} +3^{2}[/tex]) = √34

=5.830 miles

And this Question also can be do by right angle triangle method

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