Abe purchased a second candle that is shorter with a wider diameter than the first candle. It is 8 inches in length, and this candle burns down at the rate of 2/5 inches per hour. How long can this candle burn before its length is zero inches?

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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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 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 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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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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35 16 oz jars and 47 28 oz jars of peanut butter were donated to the food bank by solving equation

Let x be the number of 16 oz jars of peanut butter collected, and y be the number of 28 oz jars of peanut butter collected.

The system of equations that represents the constraints in this situation is:

x + y = 82 (total number of jars collected)

16x + 28y = 1876 (total amount of peanut butter collected in ounces)

b. To solve for the number of 16 oz jars and 28 oz jars of peanut butter donated to the food bank

we need to solve the system of equations from part (a). One way to do this is to use elimination:

Multiplying the first equation by 16, we get:

16x + 16y = 1312

Subtracting this equation from the second equation, we get:

12y = 564

Dividing both sides by 12, we get:

y = 47

Substituting this value of y into the first equation, we get:

x + 47 = 82

Subtracting 47 from both sides, we get:

x = 35

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The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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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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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).

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).

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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Answer:D

Step-by-step explanation:

got it right

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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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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6a7

Step-by-step explanation:

To simplify the expression (2a³) (3a4), you can use the laws of exponents. First, you can multiply the coefficients 2 and 3 to get 6. Then, you can add the exponents of 'a' which gives you a total of 3+4=7. Therefore, the simplified expression is 6a7. It does not have any negative exponents, and it represents the product of two expressions with the same base 'a' and coefficient multiplication.

Answer: 6a7

Step-by-step explanation: Got this right b4.

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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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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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:

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.

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: 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

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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10 times will the smaller gear turn.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Since the smaller gear has 10 teeth and the bigger gear 20, the smaller gear will turn twice for every rotation of the larger gear (20/10=2).

Therefore, if the larger gear rotates five times, the smaller gear will rotate two times five times, or ten times. The smaller gear will thus rotate 10 times.

So, if the bigger gear turns around 5 times, the smaller gear will turn around 5 x 2 = 10 times.

Therefore, the smaller gear will turn 10 times.

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Answer:

65000 metres

Step-by-step explanation:

65*1000=65000

Answer:

y = 2

Step-by-step explanation:

substitute x = [tex]\frac{4}{5}[/tex] ( = 0.8) into the formula

y = [tex]\frac{4}{0.8}[/tex] + [tex]\sqrt{0.8+0.2}[/tex] - 5(0.8)

 = 5 + [tex]\sqrt{1}[/tex] - 4

 = 5 + 1 - 4

 = 6 - 4

 = 2

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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Answer:

142ft^2

Step-by-step explanation:

I hope this picture helps, but if you have any questions about the steps let me know