Find the area of a parallelogram.

Compared to Monday, Gordon ran for an additional 15 minutes on Wednesday.

Let x be the number of additional minutes Gordon ran on Wednesday compared to Monday. Then, we can write an equation based on the given information:

43 minutes (Wednesday) = 28 minutes (Monday) + x minutes (additional time on Wednesday)

To solve for x, we can isolate it on one side of the equation:

43 minutes - 28 minutes = x minutes

15 minutes = x

Therefore, Gordon ran 15 more minutes on Wednesday compared to Monday.

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Answer:

We can use the proportion method to solve this problem.

Let's define the rate of dough preparation as the amount of dough Lia can prepare per hour. We can write:

rate = amount of dough / time

We are given that Lia prepared 35 kg of dough in 7 hours. We can use this information to find her rate of dough preparation:

rate = 35 kg / 7 hours = 5 kg/hour

Now we can use this rate to find how much dough Lia will prepare if she works for 9 hours:

amount of dough = rate x time

amount of dough = 5 kg/hour x 9 hours = 45 kg

Therefore, if Lia works for 9 hours, she will prepare 45 kilograms of dough.

The mean temperature of orange juice is 5 degrees greater than the mean temperature of water.

The mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in the dataset and then dividing by the total number of values.

According to the graph, the different temperatures of water and orange juice on different time can be taken into consideration.

Sum of Temperature of Water at different time

= 55 + 62 + 69 + 71 + 79 + 75

= 441 degrees

Mean Temperature of Water

= 441/6

= 68.5 degrees

Sum of Temperature of Orange juice at different time

= 59 + 65 + 72 + 79 + 85 + 81

= 441 degrees

Mean Temperature of Orang juice

= 441/6

= 73.5 degrees

Difference = 73.5 - 68.5 = 5 degrees

Hence, the mean temperature of orange juice is 5 degrees greater than the mean temperature of water.

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The mass of 50 quarters is 283.5 grams.

A quarter could be a unit of currency utilized in a few nations, including the United States and Canada. 

Mass could be a fundamental physical quantity that measures the sum of matter in an object. It is as a rule measured in kilograms (kg) or grams (g). 

In the given question,

One quarter has a mass of [tex]5.67[/tex] grams.

Mass of 50 quarters =?

To find out the mass of 50 quarters we have to multiply by the mass of one quarter.

Mass of 50 Quarter = [tex]5.67[/tex] ×[tex]50[/tex]

Mass of 50 Quarter = [tex]283.5 grams[/tex]

Therefore, the mass of 50 quarters is 283.5 grams.

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The requried, 120 ft³ of water was needed to fill the pool during the summer.

The volume of the child's pool is given by multiplying its length, width, and height.

The volume of the pool = Length x Width x Height
                                       = 5 ft x 4 ft x 2 ft
                                       = 40 cubic feet

Since the pool was filled 3 times during the summer, the total amount of water needed is:

The total volume of water = Volume of pool x Number of times filled
                                           = 40 ft³ x 3
                                           = 120 ft³

Therefore, 120 ft³ of water was needed to fill the pool during the summer.

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Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: [tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;

f(x) = √x

g(x) = -√9(x - 1) + 2

[tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]

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The exponential function model is y = (0.85[tex])^{t/12[/tex].

We know, The form of the function should be

y= a bˣ

Where, A should be the initial amount and b decrease rate.

Now, y = [tex]b^{t/12}[/tex]

So, the value of base be

= (100 - 15) / 100

= 0.85

Then, the function should be y = (0.85[tex])^{t/12[/tex]

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The value of the angle a is 38⁰

The value of the angle b is 52⁰

The value of the angle c is 104⁰

The value of the angle d is 90⁰

The value of the angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

a = ¹/₂ x arc 76⁰

a = 38⁰

Since the chord passed through the center, arc c is calculated as;

arc c = 180 - 76 (sum of angles of a semicircle)

arc c = 104⁰

b = ¹/₂ x 104⁰

b = 52⁰

d = 180 - (a + b) (sum of angles in a triangle)

d = 180 - (38 + 52)

d = 90⁰

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The Average Daily Balance is 6106.77

The interest to be paid on 1st April April is 152.67

Balance Due on April 1 is 6412.67

Average Daily Balance = Total of (Number of days * Balance) / 31 days

= 189310 / 31

= 6106.77

(b.) The Interest to be paid on 1st April April = Average Daily Balance * 2.5%

= 6106.77 * 2.5%

= 152.67

(c.) Balance Due on April 1 = 6260 + Interest for April

= 6260 + 152.67

= 6412.67

(d.) In case of Minimum Due = 6412.64 / 36 = 178.13

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The equation of line is,

⇒ y = 1/2x + 2

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 4, 0) and (0, 2).

Now,

Since, The equation of line passes through the points (- 4, 0) and (0, 2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 0) / (0 + 4)

m = 2 / 4

m = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - 0 = 1/2 (x + 4)

⇒ y = 1/2x + 2

Therefore, The equation of line is,

⇒ y = 1/2x + 2

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Comparing all the numbers, we can see that (d) 21/2500 is not equal to the other numbers, since it is a fraction and all the other numbers are decimals. Therefore, (d) is the answer.

To determine which of the numbers is not equal to the other, we can convert all the numbers to the same form and compare them.

a) 0.84% can be written as 0.0084 in decimal form.

b) (0.21)(0.04) equals 0.0084.

c) 8.4 x 10⁻² can be written as 0.084 in decimal form.

d) 21/2500 can be simplified by dividing both the numerator and denominator by 21 to give 1/119.

e) 21/2500 x 10⁻² can be simplified by dividing both the numerator and denominator by 21 and multiplying by 100 to give 0.084.

In conclusion, to determine which number is not equal to the other, we need to convert all the numbers to the same form and compare them. In this case, we converted all the numbers to decimal form except for (d), which is a fraction. By comparing the numbers, we found that (d) is not equal to the other numbers.

Therefore, (d) is the answer.

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Answer: The relationship between the area of rectangle and area of parallelogram is that they both are equal in area.

Step-by-step explanation:

parallelogram is formed when two parallel lines intersects other two parallel lines and rectangle is a type of parallelogram in which the intersecting lines intersects at right angle.

rectangle and parallelogram shares the same property and If we consider same base and same parallel lines then the area of parallelograms formed is always equal and as I mentioned above rectangle is also a parallelogram.

hence area of rectangle is equal to the area of parallelogram in same base and same parallel lines.

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The inverse function of the function f(x) is [tex]g(y) = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]

To find the inverse of the given function f(x) = -(1/2) - log₃√(9-x)

we need to solve for x in terms of y, where y = f(x).

Replace f(x) with y

Function y = -(1/2) - log₃√(9-x)

Solve for x

First, isolate the logarithmic term on one side of the equation.

y + (1/2) = -log₃√(9-x)

[tex]3^-^(^y^ +^ 1^/^2^) = 9-x[/tex]

[tex]x = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]

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It is the sum of rational numbers.

Any given number which can be expressed in form of fraction where its denominator is not zero, is said to be a rational number. Examples are: 2, 10, 3.14 etc.

While irrational numbers are numbers that can not be expressed as a fraction. Examples are: π, [tex]\sqrt{10}[/tex] etc.

To determine if the given number are rational or irrational numbers, then;

3.14 = 314/ 100

and

24 = 24/ 1

Therefore, both numbers are rational.

So that;

3.14 + 24 = 27.14

Then,

27.14 = 2714/ 100

Thus we can conclude that the sum is rational.

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Answer:(1,−7π/4)

Step-by-step explanation:

Note that the point is on the circle whose radius is labeled 1, so r=1 or −1. Of the choices available, only an angle of −7π4, drawn from the positive x axis plots at the point A. So θ=−7π4, and r must be positive, as the angle is measured from the positive x axis. Thus, the polar coordinates are (1,−7π4).

Step-by-step explanation:

so, the 1 yard is split into 6 equal parts.

each small square has therefore an area of 1/6 × 1/6 yard² = 1/36 yard²

the shaded area is 4×3 = 12 small squares large.

is area is therefore

12 × 1/36 = 1/3 yard²

since 1 yard = 3 ft, 1 × 1 = 1 yard² = 3 × 3 ft² = 9 ft².

and 1/3 yard² = 1/3 × 9 ft² = 3 ft²

so, whatever dimension you need.

the area is

1/3 yard² = 3 ft²

All values of n must be smaller than 11 in order to meet the inequality. The answer may be expressed as follows in interval notation: n (-∞, 10)

To solve the inequality 3n - 7 < 26, you can follow these steps:

Add 7 to both sides of the inequality to isolate the n variable on one side:

3n - 7 + 7 < 26 + 7

3n < 33

Divide both sides of the inequality by 3 to get n by itself:

3n/3 < 33/3

n < 11

Therefore, the values of n that satisfy the inequality are all values less than 11. In interval notation, you can write the solution as:

n ∈ (-∞, 10)

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The total surface area of the cylinder is 2260.8 cm².

The height of the cylinder is 18 centimetres and the diameter of the cylinder is 24 centimetres.

Therefore, the total surface area of the cylinder can be calculated as follows:

total surface area = 2πr(r + h)

where

Therefore,

r = 24 / 2 = 12 cm

h = 18 cm

total surface area = 2 × 3.14 × 12(12 + 18)

total surface area = 75.36(30)

total surface area = 2260.8 cm²

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Direct Materials Purchases Budget  is given by,

Rubber Steel

Expected production 3,718,000 lb. 590,000 lb.

Desired ending inventory 62,000 lb. 13,000 lb.

Total required 3,780,000 lb. 603,000 lb.

Less: Beginning inventory (73,000 lb.) (11,000 lb.)

Total to be purchased 3,707,000 lb. 592,000 lb.

Unit price $2.90/lb. $3.80/lb.

Total cost $10,749,300 $2,249,600

To prepare a direct materials purchases budget for Solid Grip Company,

The amount of rubber and steel belts needed for the production of 66,000 passenger car tires and 20,000 truck tires.

The desired ending inventories and estimated beginning inventories for each material.

First, let us calculate the amount of rubber and steel belts required for the production of passenger car and truck tires.

Passenger car tires,

Rubber,

66,000 tires x 33 lb. per unit = 2,178,000 lb.

Steel belts,

66,000 tires x 5 lb. per unit = 330,000 lb.

Truck tires,

Rubber,

20,000 tires x 77 lb. per unit = 1,540,000 lb.

Steel belts,

20,000 tires x 13 lb. per unit = 260,000 lb.

Next, let us calculate the total amount of rubber and steel belts needed for production.

Rubber,

2,178,000 lb. + 1,540,000 lb. = 3,718,000 lb.

Steel belts,

330,000 lb. + 260,000 lb. = 590,000 lb.

To calculate the total amount of rubber and steel belts required for purchase,

Add the desired ending inventories and subtract the estimated beginning inventories,

Rubber,

3,718,000 lb. + 62,000 lb. - 73,000 lb. = 3,707,000 lb.

Steel belts,

590,000 lb. + 13,000 lb. - 11,000 lb. = 592,000 lb.

Finally, calculate the total cost of rubber and steel belt purchases.

Rubber,

3,707,000 lb. x $2.90 per pound = $10,749,300

Steel belts,

592,000 lb. x $3.80 per pound = $2,249,600

Therefore, the direct materials purchases budget for Solid Grip Company for the year ended December 31, 20Y8 is as follows,

Direct Materials Purchases Budget

Rubber Steel

Expected production 3,718,000 lb. 590,000 lb.

Desired ending inventory 62,000 lb. 13,000 lb.

Total required 3,780,000 lb. 603,000 lb.

Less: Beginning inventory (73,000 lb.) (11,000 lb.)

Total to be purchased 3,707,000 lb. 592,000 lb.

Unit price $2.90/lb. $3.80/lb.

Total cost $10,749,300 $2,249,600

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Robert can make a maximum of 8 milkshakes with the remaining chocolate syrup.

Converting the mixed number 2 2/5 to an improper fraction: 2 2/5 = 12/5

Subtracting the amount of chocolate syrup used per milkshake from the total amount of chocolate syrup:

12/5 - 1/4 = (48 - 5) / 20 = 43/20

Therefore, Robert has 43/20 cups of chocolate syrup left, which is the maximum amount he can use to make milkshakes.

For maximum number of milkshakes:

(43/20) / (1/4) = (43/20) x (4/1) = 172/20 = 8.6

Since Robert cannot make a fraction of a milkshake, he can make a maximum of 8 milkshakes with the remaining chocolate syrup.

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The value that would help Charlie find out how long it takes his basketball to reach the highest point is "x at the vertex". The correct option is A.

When the basketball reaches the highest point, its vertical velocity is zero. The time taken to reach this point can be found using the equation:

t = -b / (2a)

where a is the acceleration due to gravity (-9.8 m/s²) and b is the initial vertical velocity of the basketball.

The vertex of the parabolic path that the basketball follows is the point where the basketball reaches its maximum height. This point occurs at the halfway point of the ball's total flight time. The horizontal distance the basketball travels during this time is called "Ox at the vertex".

Therefore, by finding the "x at the vertex", Charlie can calculate the total flight time of the basketball, and then use the equation above to find the time it takes to reach the highest point.

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The surface area of the triangular prism is  184 metres².

The surface area of the triangular base prism can be found as follows:

surface area of the prism = (s₁ + s₂ + s₃)l + bh

where

b =base

h = height

l = height of the prism

s₁, s₂ and s₃ are side length of the prism.

Therefore,

b = 6 units

h = 4 units

s₁ = 5 units

s₂ = 5 units

s₃ = 6 units

l = 10 units

Hence,

surface area of the prism = (5 + 5 + 6)10 + 6(4)

surface area of the prism = 160 + 24

Therefore,

surface area of the prism = 184 metres²

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Answer:

(2,0)

Step-by-step explanation:

Vertex is the top or bottom of the graph, depending on if the graph is upside down or not.

In this case, the graph is upside down, so the vertex will be at the top. We see that the vertex is located at (2,0) in this graph. So, the vertex is (2,0).

Answer:

65000 metres

Step-by-step explanation:

65*1000=65000

Answer: 4m^5-3m^2+2m+21

Step-by-step explanation: you just have to put the exponents int he right order which we always put the highest first so you put 4m^5-3m^2+2m+21 which is the answer

The rectangle's circumference is 27+ (3/2) fee and one of its sides is a semicircle.

We can start by finding the perimeter of the rectangle, which is simply the sum of the lengths of all four sides:

Perimeter of rectangle = 2(length + width) = 2(12 + 3) = 30 feet

Next, we need to find the perimeter of the semicircle.

The diameter of the semicircle is equal to the width of the rectangle, which is 3 feet. The formula for the perimeter of a semicircle is:

Perimeter of semicircle = (π/2) x diameter + diameter

Plugging in the values, we get:

Perimeter of semicircle = (π/2) x 3 + 3 = (3/2)π + 3

Now, we can add the perimeter of the semicircle to the perimeter of the rectangle to get the total perimeter:

Total perimeter = Perimeter of rectangle + Perimeter of the semicircle- 2*diameter of the semicircle

= 30 + (3/2)π + 3 - 3*2

= 27+ (3/2)π

Therefore, the perimeter of the rectangle with a semicircle on one side is 27+ (3/2)π feet, or approximately 31.71 feet (rounded to two decimal places).

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Answer:

Step-by-step explanation:

To differentiate y = 3x cos(x) + sin(x), we can use the product rule and the chain rule.

Let's start by differentiating the first term, 3x cos(x), using the product rule:

d/dx (3x cos(x)) = 3 cos(x) - 3x sin(x)

Next, we can differentiate the second term, sin(x), using the chain rule:

d/dx (sin(x)) = cos(x)

Putting it all together, we get:

dy/dx = 3 cos(x) - 3x sin(x) + cos(x)

Simplifying the expression, we get:

dy/dx = (4cos(x)) - (3xsin(x))

Therefore, the derivative of y = 3x cos(x) + sin(x) is dy/dx = 4cos(x) - 3xsin(x).

Answer:

So the smaller number is x = 1 and the larger number is y = 8.

Step-by-step explanation:

substitute y = 3x + 5 into the first equation and solve for x.

y = 2(x + 3) 3x + 5 = 2(x + 3) Expand the parentheses 3x + 5 = 2x + 6 Subtract 2x from both sides x + 5 = 6 Subtract 5 from both sides x = 1

Now we can plug x = 1 into either equation to find y.

y = 2(x + 3) y = 2(1 + 3) y = 2(4) y = 8