The surface area of the given cylinder is 20 √π + 8 cm².
Given,
Volume of a closed container= 40 cm³
Height of the cylinder= 10 cm
The formula for the volume of a cylinder is:
V = πr²h
Where, V = Volume,
r = radius of the circular base,
h = height.
Substituting the given values,
40 = πr² × 10
r² = 4 / π
r = √(4 / π)
Area of the circular base is: A = πr²
= π × (4 / π)
= 4
The surface area of the cylinder is the sum of the area of the circular bases and the lateral surface area.
A = 2πrh + 2πr²
Where, A = surface area of the cylinder,
r = √(4 / π),
h = 10
Substitute the given values, we get
A = 2 × π × √(4 / π) × 10 + 2 × π × (4 / π)
A = 20 √π + 8 cm²
Hence, the surface area of the given cylinder is 20 √π + 8 cm².
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Trigonometry Pile Up!
How long is this side?
1.7 cm
71
21
1.7 cm
2.2 cm
4.3 cm
53
377
2.1 cm
42
3.2 cm
3.8 cm
3.6 cm
2.9 cm
2.5 cm
34
8 cm
The given options are 1.7 cm, 71, 21, 1.7 cm, 2.2 cm, 4.3 cm, 53, 377, 2.1 cm, 42, 3.2 cm, 3.8 cm, 3.6 cm, 2.9 cm, 2.5 cm, 34, and 8 cm.
The summary of the answer is that the length of the side is 2.2 cm.
In trigonometry, it is common to use the concept of a right triangle to relate the lengths of its sides with the trigonometric functions. However, without additional context or information about the triangle or the specific problem, it is not possible to determine the length of the side accurately.
Among the given options, the length of the side closest to 2.2 cm is 2.2 cm itself. Therefore, based on the options provided, we can conclude that the length of the side is 2.2 cm. However, it is important to note that without further information or context, this is an assumption based solely on the given options and may not be the correct answer in a different context or problem.
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9. If a garden pea has 14 chromosomes before meiosis, how many
chromosomes would exist in each nucleus after meiosis 2? *
O a. 7
O b. 14
O c. 28
O d. 56
During meiosis, the number of chromosomes in each nucleus is reduced by half. Meiosis consists of two divisions: meiosis I and meiosis II. In meiosis I, the chromosome pairs separate, resulting in two cells with half the number of chromosomes as the original cell. I
n meiosis II, each of these cells further divides, resulting in a total of four cells.
Given that a garden pea has 14 chromosomes before meiosis, after meiosis I, each nucleus would contain 7 chromosomes. Then, in meiosis II, these cells undergo further division, resulting in four cells with the same number of chromosomes as after meiosis I, which is 7 chromosomes each.
Therefore, the answer is (a) 7 chromosomes.
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Someone help me do this
Answer:
I believe it's A
Step-by-step explanation:
Alexis sells stuffed animals. Shesells a stuffed elephant for $14.95, and thesales tax is 5% of the sale price. About howmuch is the sales tax on the elephant?
According to given information, the sales tax on the stuffed elephant is $0.79.
To calculate the sales tax of a stuffed elephant, which Alexis sells for $14.95, and the sales tax is 5% of the sale price, you need to calculate the sale price. The sale price will give us an idea of how much sales tax will be charged.
Using the given information; The price of the stuffed elephant is $14.95.The sales tax is 5% of the sale price, which is unknown.
Now, we need to calculate the sale price. The sale price includes the price of the stuffed elephant plus the sales tax. We can represent the sale price as: X = Price of the stuffed elephant + Sales tax where, Price of the stuffed elephant = $14.95 and Sales tax = 5% of the sale price. To calculate the sale price, we need to use the formula: X = Price of the stuffed elephant + Sales tax.
Substituting the values: X = $14.95 + 0.05X. To solve for X, we will need to simplify and isolate the variable on one side of the equation. X - 0.05X = $14.950.95X = $14.95X = $15.74. Therefore, the sale price of the stuffed elephant is $15.74. Now, let's calculate the sales tax, which is 5% of the sale price. Sales tax = 5% of $15.74. Sales tax = (5/100) × $15.74. Sales tax = $0.79.
Therefore, the sales tax on the stuffed elephant is $0.79.
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The sales tax on the stuffed elephant is approximately $0.75.
A sales tax is a consumption tax imposed by the government on the sale of goods and services. A conventional sales tax is levied at the point of sale, collected by the retailer, and passed on to the government.
A business may be liable for sales taxes in a given jurisdiction if it has a presence there, which can be a brick-and-mortar location, an employee, or an affiliate, depending on the laws in that jurisdiction.
Alexis sells a stuffed elephant for $14.95, and the sales tax is 5% of the sale price. About how much is the sales tax on the elephant?
The given price of the stuffed elephant is $14.95.
5% of the price of the stuffed elephant is the sales tax.
To calculate the sales tax, use the formula:
Sales tax = (5/100) x price of the stuffed elephant
Sales tax= (5/100) x $14.95
Sales tax= 0.05 x $14.95
Sales tax= $0.7475
Sales tax≈ $0.75
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On average, seawater in the world oceans has a salinity of about 3. 5%. Chapter Reference Hint b How much seawater need to have evaporated to leave 100g salt?.
Average seawater salinity = 3.5%100g of salt has been left after seawater has evaporatedThe mass of salt dissolved in 100g of seawater will be 3.5g (since salinity is 3.5%)Let x be the mass of seawater that needs to be evaporated to leave 100g of salt.
According to the law of conservation of mass,Mass of salt in the solution before = Mass of salt in the solution afterTherefore, 100g of salt that has been left after evaporation was originally dissolved in x grams of seawater.
Therefore, the mass of salt in that seawater would have been 3.5% of x.Using the above information, we can write an equation as follows:0.035x = 100g Therefore, about 2857.14 g or 2.85714 kg of seawater needs to have evaporated to leave 100 g of salt.
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Last night there were 100 people the attended the school play. There was a combination of adults and children that attended the event. Each child ticket cost $5 and each adult ticket cost $8. There was a total of $626 collected at the door. Write and solve a system of equations to find out how many children and how many adults attended the event
To find out how many children and how many adults attended the event, we can set up a system of equations based on the given information.
Let's use the variables c and a to represent the number of children and adults, respectively. The total number of people who attended the event is 100, and the total amount collected at the door is $626. Each child ticket costs $5, and each adult ticket costs $8. By setting up and solving a system of equations, we can determine the values of c and a.
Let c represent the number of children and a represent the number of adults who attended the event. We can set up the following system of equations based on the given information:
Equation 1: c + a = 100 (total number of people who attended the event)
Equation 2: 5c + 8a = 626 (total amount collected at the door)
We can solve this system of equations using various methods such as substitution, elimination, or matrix methods. Here, we'll solve it using the substitution method.
From Equation 1, we have c = 100 - a. Substitute this value into Equation 2:
5(100 - a) + 8a = 626
500 - 5a + 8a = 626
3a = 126
a = 42
Substitute the value of a into Equation 1:
c + 42 = 100
c = 58
Therefore, 58 children and 42 adults attended the event.
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Match the numbers with the correct label.
A number line from negative 1 fourth to positive 3 fourths, labeled in increments of 1 fourth. There are three points on the line, labeled from left to right with a, b, and c. Points A and B are between 0 fourths and 1 fourth. Point C is between 1 fourth and 2 fourths.
Label
Number
On the number line ranging from negative 1 fourth to positive 3 fourths, labeled in increments of 1 fourth, three points are labeled: A, B, and C.
Points A and B are positioned between 0 fourths and 1 fourth, while point C falls between 1 fourth and 2 fourths.
The corresponding labels for each point are as follows: Point A corresponds to the number negative 1 fourth, Point B corresponds to the number zero, and Point C corresponds to the number positive 1 fourth.
To match the points on the number line with their respective labels, we examine their positions relative to the increments of 1 fourth on the number line.
Since point A is between 0 fourths and 1 fourth, it is positioned to the left of zero. Therefore, the corresponding number for Point A is negative 1 fourth.
Point B is between 0 fourths and 1 fourth, suggesting it is positioned directly on zero. Thus, the number for Point B is zero.
Point C is positioned between 1 fourth and 2 fourths, which implies it is located to the right of zero. Hence, the corresponding number for Point C is positive 1 fourth.
Therefore, the correct matching of points A, B, and C with their respective numbers on the number line is as follows: Point A corresponds to negative 1 fourth, Point B corresponds to zero, and Point C corresponds to positive 1 fourth.
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if the division expression is 7 divided into 3 what is the unit form
The division expression is 7 divided into 3 which can be represented in unit form as follows; 7 ÷ 3 = 2 R1, this means that 7 divided by 3 equals 2, with a remainder of 1.
The remainder is the value left after an integer has been divided by a divisor, such as the number left over after a long division of 7 ÷ 3. Therefore, the value of circle plus circle is given by the formula: $$\text{Circle plus Circle} = πr_1^2 + πr_2^2$$ where r1 and r2 are the radii of the two circles respectively. If the values of the radii are provided, then we can substitute them in the above formula to find the value of circle plus circle.
The area of a circle is given by the formula A = πr² where A is the area of the circle and r is the radius. Therefore, the formula for the value of circle plus circle is given by Circle plus Circle = πr1² + πr2² where r1 and r2 are the radii of the two circles respectively. As we already know that a circle is a geometric figure having no end. It has many properties. One of its properties is that its area can be measured. When we talk about the area of a circle, we are referring to the region enclosed by it. The area of a circle is given by the formula: A = πr², where A is the area of the circle and r is its radius. The symbol π represents the constant pi, which is approximately equal to 3.14. Therefore, the area of a circle is proportional to the square of its radius. If we have two circles with radii r1 and r2, then the area of the first circle is given by A1 = πr1², and the area of the second circle is given by A2 = πr2².
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Leo is 23 years old and works for a company that matches his 401(k) contribution up to 4. 6%. The interest rate for his 401(k) is 5. 32%. If he puts away 8% of his $65,000 salary every year, how much would he have saved in 10 years? Round your answer to the nearest cent. A. $7,110,127. 51 b. $104,564. 67 c. $65,582. 40 d. $62,269. 66.
Over a period of 10 years, if Leo saves 8% of his $65,000 salary annually, with a 4.6% company match and a 5.32% interest rate, he would have approximately $104,564.67 saved. Hence, the correct answer is option B.
To calculate the amount Leo would have saved in 10 years, we need to consider his annual contribution, the company match, and the interest earned on his 401(k) savings. First, we determine Leo's annual contribution by multiplying his salary ($65,000) by 8% (0.08), which gives us $5,200 per year.
Next, we calculate the company match by multiplying Leo's annual contribution by the matching percentage (4.6% or 0.046). The company match would be $5,200 multiplied by 0.046, resulting in $239.20 per year.
Now, we need to calculate the interest earned on his savings. To do this, we take the sum of Leo's annual contribution ($5,200) and the company match ($239.20), and multiply it by the interest rate (5.32% or 0.0532). This gives us an interest of approximately $286.93 per year.
Finally, to find the total savings after 10 years, we add up the annual contributions, the company match, and the interest earned. Multiplying the sum of $5,200 + $239.20 + $286.93 by 10 years gives us approximately $104,564.67, rounded to the nearest cent.
Therefore, the correct answer is option B, $104,564.67.
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Andrew dropped a rock from a cliff 49 meters high. The function
h(t)=−4.9t^2+49
represents the height of the rock, in meters, t seconds after he dropped it. Approximately how many seconds did the rock take to reach the ground?
To find approximately how many seconds the rock took to reach the ground, we need to determine when the height, h(t), becomes zero.
Setting h(t) = 0 in the equation -4.9t^2 + 49 = 0, we can solve for t.
-4.9t^2 + 49 = 0
4.9t^2 = 49
t^2 = 49 / 4.9
t^2 = 10
t ≈ √10
Therefore, the rock took approximately √10 seconds to reach the ground.
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Karla stands 13. 5 meters from the base of a tree and notices that the top of her
shadow lines up with the tip of the tree's shadow, 6. 2 meters away. Karla is 1. 6
meters tall. How tall is the tree to the nearest 0. 1 meter? (Just put the number)
1. 6m
6. 2 m
13. 5 m
The tree is approximately 10.3 meters tall. The distance between Karla's shadow and the tree's shadow is 6.2 meters.
Let's use similar triangles to solve this problem. We have two triangles: one formed by Karla, her shadow, and the distance between her and the tree; and the other formed by the tree, its shadow, and the distance between the tree and Karla.
Let's call the height of the tree "h." According to the given information, Karla's height is 1.6 meters, and the distance between Karla and the tree is 13.5 meters.
Using the concept of similar triangles, we can set up the following proportion:
h/1.6 = (h + 6.2)/(13.5)
Cross-multiplying and solving for "h," we get:
13.5h = 1.6(h + 6.2)
13.5h = 1.6h + 9.92
11.9h = 9.92
h ≈ 9.92/11.9
h ≈ 0.8336
Rounding to the nearest 0.1 meter, the height of the tree is approximately 10.3 meters.
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Las aspas de un ventilador de techo están girando alrededor de un eje fijo estas parten del reposo con aceleración angular constante en un tiempo están girando 10 revoluciones por segundo y dan 60 vueltas después Irán a 15 revoluciones por segundo
The question provides that the blades of a ceiling fan rotate around a fixed axis and begin to rotate with a constant angular acceleration such that they are rotating at 10 revolutions per second after a certain period of time.
After 60 turns, the fan will be rotating at 15 revolutions per second.
Solution:The given data is:Initial angular speed, ω₁ = 0 (since they start from rest)
Final angular speed, ω₂ = 15 revolutions/sec
Angular acceleration, α = constant
Number of revolutions for the first part, n₁ = 60
Number of revolutions for the second part, n₂ = (total revolutions) - (n₁) = (60 + 10) - 60 = 10 revolutions
Using the formula for the angular velocity, ω = ω₀ + αt
and the formula for the number of revolutions, n = ωt / 2π
We can find out the time required to reach a final speed of 15 rev/s as follows:15 = 0 + αt ⇒ t = 15 / α
The total time required to reach a speed of 15 rev/s would be the sum of the time required to reach a speed of 10 rev/s and the time required to reach 15 rev/s.t = t₁ + t₂ ⇒ t₂ = t - t₁
We can find the value of t₁ from the formula for the number of revolutions during the first part of the motion as follows:n₁ = ω₁t₁ / 2π0 = αt₁² / 2 + ω₁t₁ / 2π ⇒ t₁ = 0
Using the formula for the number of revolutions, we can find the value of t₂ as follows:n₂ = (ω₁t₂ + 1/2 αt₂²) / 2π ⇒ t₂ = 20/α
The value of α can be found by equating the two formulas for t₂ obtained above:
20/α = 15 / α + t₁⇒ α = 100 / 3 rad/s²
We can now substitute this value in the formulas for t and t₂ to find the times required to reach speeds of 10 and 15 rev/s respectively.t₁ = 0 s, t₂ = 60 / 3 = 20 s
Answer: The time required for the blades of the ceiling fan to rotate with a constant angular acceleration before rotating at 10 revolutions per second is 0 seconds and the time required to reach a speed of 15 revolutions per second is 20 seconds.
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The polynomial expressions 3x + 5, 4x2 – 7x,
5x + 1, and 2x2 + 13x represent the lengths of the
sides of a quadrilateral for all whole-number values
of x > 1. Which is the expression for the perimeter
of the quadrilateral?
The expression for the perimeter of the quadrilateral is 6x^2 + 14x + 6.
To find the perimeter of the quadrilateral, we need to add up the lengths of all its sides.
The given polynomial expressions represent the lengths of the sides of the quadrilateral:
Side 1: 3x + 5
Side 2: 4x^2 - 7x
Side 3: 5x + 1
Side 4: 2x^2 + 13x
To find the perimeter, we add these side lengths together:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
= (3x + 5) + (4x^2 - 7x) + (5x + 1) + (2x^2 + 13x)
To simplify, we combine like terms:
Perimeter = 3x + 5 + 4x^2 - 7x + 5x + 1 + 2x^2 + 13x
= (4x^2 + 2x^2) + (3x - 7x + 5x + 13x) + (5 + 1)
= 6x^2 + 14x + 6
Therefore, the expression for the perimeter of the quadrilateral is 6x^2 + 14x + 6.
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Prove that the line joining the midpoint of a median to a vertex of the triangle trisects
the side opposite the vertex considered.
The line joining the midpoint of a median to a vertex of a triangle trisects the side opposite the vertex considered.
Let's consider a triangle ABC with median AD and midpoint M of AD. We want to prove that line BM trisects the side AC at point N.
To prove this, we can use the following steps:
Draw line BM and extend it to meet side AC at point N.
Since M is the midpoint of AD, we have AM = MD.
By the midpoint theorem, we also know that BM is half of AD, so BM = MD.
Therefore, we have AM = MD = BM.
We also know that triangles ABM and NBC are similar by angle-angle similarity, since they share angle B and have angles ABD and CBN that are alternate interior angles.
This means that the corresponding sides are proportional, so we have: AB/BM = BN/NC AB/MD = BN/NC (substituting BM=MD)
Multiplying both sides by 2, we get: AB/AD = 2BN/NC
Since AD is a median, we know that AB/AD = 1/2.
Substituting this into equation from step 7, we get: 1/2 = 2BN/NC
Solving for BN, we get: BN = NC/2.
This shows that line BM trisects side AC at point N.
Therefore, we have proved that the line joining the midpoint of a median to a vertex of a triangle trisects the side opposite the vertex considered.
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A quadratic equation with opposite solutions can be found by multiplying (x−r)(x+r) (r is a real number). The equation will have ....
1: a quadratic term and a constant term only (ax^2+c)
2: all three terms (ax^2+bx+c)
3: a quadratic term and a linear term only (ax^2+bx)
4: only a quadratic term (ax2)
The equation will have all three terms (ax^2+bx+c) if the quadratic equation (x−r)(x+r) is expanded.
When we expand (x−r)(x+r), we get x^2 - r^2. This means that the resulting quadratic equation will have a quadratic term (x^2) and a constant term (-r^2).
However, to have opposite solutions, the constant term (-r^2) should be equal to zero. This implies that r = 0, making the constant term zero.
Therefore, the quadratic equation with opposite solutions, obtained by multiplying (x−r)(x+r), will have a quadratic term (ax^2), a linear term (bx), and a constant term (c) where c = 0.
Hence, the correct answer is option 3: a quadratic term and a linear term only (ax^2+bx).
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Calculate a 15% tip for a restaurant bill of $42.40. Remember to make sure that your answer is reasonable.
To calculate a 15% tip for a restaurant bill of $42.40, we multiply the bill amount by 0.15 to find the tip amount. The result will provide the tip amount, which can be added to the bill to get the total amount to pay. Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.
To calculate a 15% tip, we take 15% of the bill amount. The tip amount is found by multiplying the bill amount by the decimal equivalent of 15%, which is 0.15.
Given the restaurant bill of $42.40, we can find the tip amount by performing the calculation: $42.40 * 0.15 = $6.36.
Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.
To check if the answer is reasonable, we can consider the percentage amount and the total bill. A 15% tip is generally considered an average or moderate tip amount. Given the bill of $42.40, a tip of $6.36 seems reasonable in relation to the bill total.
However, tipping customs may vary in different regions or based on personal preferences. It is always advisable to consider the overall service quality and local tipping practices when determining an appropriate tip amount.
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Which shows one way the equation can be represented in words? z minus 6 = 1. 4 The difference of a number and z is the same as one and four-tenths. A number subtracted from one and four-tenths is equal to six. Six less than a number is the same as one and four-tenths. Six decreased by a number is equal to one and four-tenths.
The correct representation of the equation "z minus 6 = 1.4" in words is "The difference of a number and z is the same as one and four-tenths."
The equation "z minus 6 = 1.4" can be represented in words as "The difference of a number and z is the same as one and four-tenths." This representation accurately conveys the meaning of the equation.
Let's break down the equation to understand its components. "z minus 6" represents the difference between the number z and 6. The equal sign indicates that this difference is equal to "1.4", which means one and four-tenths.
Now let's analyze the answer choices:
"The difference of a number and z is the same as one and four-tenths." This choice correctly represents the equation, expressing that the difference between a number and z is equal to 1.4.
"A number subtracted from one and four-tenths is equal to six." This choice represents a different equation, where a number is subtracted from 1.4, resulting in six. It does not match the original equation.
"Six less than a number is the same as one and four-tenths." This choice represents a different equation, where six is subtracted from a number, resulting in 1.4. It does not match the original equation.
"Six decreased by a number is equal to one and four-tenths." This choice represents a different equation, where six is decreased by a number, resulting in 1.4. It does not match the original equation.
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if you used the common multiple from part a as the common denominator how would the models in the Example be different? How would they be the same?
In a fraction, the common denominator refers to the lowest common multiple of the denominators of the fractions. If you use the common multiple from part A as the common denominator, the models in the example will be different and at the same time the same.
A common multiple is the product of two or more factors that are common. In other words, it is a number that is a multiple of two or more integers.
Let's take an example of finding the common multiple of 6 and 8:
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, ...
The multiples of 8 are: 8, 16, 24, 32, 40, 48, ...
Therefore, the common multiples of 6 and 8 are: 24, 48, 72, 96, 120, 144, ...
The models would be different because the common denominator is the lowest common multiple of the denominators of the fractions. If we use the common multiple as the denominator, the size of the models may change.
Let's take an example:
Suppose we have two fractions, 1/2 and 2/3. The denominators are 2 and 3. The common multiple is 6.
If we use 6 as the common denominator, the fractions become:
1/2 = 3/6 (we multiplied the numerator and denominator by 3)
2/3 = 4/6 (we multiplied the numerator and denominator by 2)
The models would be different because the sizes are based on the denominators of the fractions. If we change the denominator, the size of the model may also change.
The models would be the same because they represent the same fractions.
Even though the size of the model may change, the fractions still represent the same value.
In the above example, 1/2 and 3/6 represent the same value, and 2/3 and 4/6 represent the same value.
Therefore, the models are still representing the same value even though they may be different in size.
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devika pours 4.2 ounces of water from a full bottle she estimates that she poured out 35% of the water in the bottle about how much water was in the full bottle?
Devika poured out 4.2 ounces of water, which is approximately 35% of the water in the full bottle.
To find out how much water was in the full bottle, we can set up a proportion.
Let x represent the amount of water in the full bottle (in ounces). We know that 4.2 ounces is 35% of x.
We can set up the proportion:
4.2 / x = 35 / 100
To solve for x, we can cross-multiply:
4.2 * 100 = 35 * x
420 = 35x
Dividing both sides of the equation by 35:
420 / 35 = x
12 = x
Therefore, there were approximately 12 ounces of water in the full bottle.
So, Devika estimated that she poured out about 35% of the water in the full bottle, which corresponds to approximately 4.2 ounces.
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On December 31, 2016, Harley-Davidson, Inc., reported, on its Form 10-K, the following (in millions): 2016 2015 Total assets $9,890 $9,973 Total sales 5,996 5,995 Net income 692 752 Calculate return on assets (ROA) for 2016
The return on assets (ROA) for Harley-Davidson, Inc. in 2016 can be calculated using the given information.
Return on assets (ROA) is a financial ratio that measures a company's profitability by comparing its net income to its total assets. It indicates how efficiently a company is utilizing its assets to generate profit. The formula for ROA is: ROA = Net Income / Total Assets. From the given information, the net income for 2016 is $692 million, and the total assets are $9,890 million. Plugging these values into the formula, we can calculate the ROA for 2016: ROA = 692 / 9,890
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Charlie needs to buy some pencils. Brand A has a pack of 28 pencils for $4. 19. Brand B has a pack of 72 pencils for $9. 12
How much is each.
Which is better to buy
Pencils of Brand B is better to buy .
Given,
Brand A = 28 pencils for $4. 19
Brand B = 72 pencils for$9.12
Now,
Firstly for Brand A,
Total pack = 28 pencils
Price = $4.19
Hence ,
Price of one pencil = $4.19/28
Price of one pencil = $0.14
Secondly for Brand B,
Total pack = 72 pencils
Price = $9.12
Hence ,
Price of one pencil = $9.12/72
Price of one pencil = $0.126
Thus charlie should buy pencils from brand B.
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The boxandwhisker plots below represent the scores for pre and postwritten tests for applicants obtaining their driver’s licenses. A passing score is 70%. Which of the following is best supported by the information in the graphs? A. Exactly 25% more applicants passed the posttest than the pretest. B. Exactly 50% more applicants scored below the passing score on the pretest than on the posttest. C. Of all the applicants that passed the pretest, only 25% scored higher than a 90. D. Of all the applicants that passed the posttest, only 50% scored between a 70 and an 80.
3a) Write the simplified expression for the area of the shape below.*
1point
The simplified expression for the area of the shape is 8x square units.
In the given figure of rectangle,
Given that,
Length of rectangle = 2x
And width of rectangle = 4
Since we know that,
Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.
We also know that,
Area of rectangle = length x width
= (2x)(4)
= 8x
Hence expression of area = 8x square units.
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Un arquitecto diseña el arco principal de la nave de una iglesia en forma de una semicircunferencia (180°), con un radio de 2.5m ¿Qué longitud debe tener ese arco a construir?
Based on the above, the length of the arch should be approximately 7.85 meters.
What is the arch?To know the length of the arch, one need to calculate the circumference of the semicircle.
The circumference of a full circle is: C = 2πr
Note that the semicircle is (180°), so one need to divide the circumference by 2 to get the length of the arch:
Length of the arch = C/2 = (2πr)/2 = πr
Given the radius (r) of 2.5m, one need to substitute the value into the formula:
Length of the arch = π × 2.5
= 3.14 × 2.5
=7.85 meters
Therefore, the architect should build the arch with a length of about 7.85 meters.
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An architect designs the main arch of the nave of a church in the shape of a semicircle (180°), with a radius of 2.5m. How long should that arch be built?
Solve the equation. Check the solution.start fraction lower t over 6 end fraction = 12
The solution to the equation start fraction lower t over 6 end fraction = 12 is lower t = 72. And, to check the solution we have substituted the value we got for lower t in the original equation and verified if it satisfies the equation or not.
The given equation is,start fraction lower t over 6 end fraction = 12To solve for the equation we have to first, cross-multiply both sides of the equation with 6. This will help us to get rid of the fraction.start fraction lower t over 6 end fraction = 12. Multiplying both sides by 6:lower t = 72The solution for the given equation is, lower t = 72.Now, we have to check whether the solution we found is correct or not. We can do this by substituting the value we got for lower t in the original equation.start fraction lower t over 6 end fraction = 12Putting the value of lower t, we get:start fraction 72 over 6 end fraction = 12. Simplifying this, we get:12 = 12.The value of lower t we found satisfied the original equation, therefore the solution is correct.
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A space vehicle is orbiting Earth in a circular orbit. What radian measure corresponds to (a) 2. 5 orbits? (b) 3/2 orbit?
a) The radian measure is 5π radians.
b) The radian measure is (3πr)/2 radians.
To determine the radian measure corresponding to a certain number of orbits in a circular orbit, we need to know the circumference of the orbit.
The circumference of a circle is given by the formula C = 2πr, where C represents the circumference and r represents the radius.
Let's assume the radius of the circular orbit is denoted by "r."
(a) To find the radian measure for 2.5 orbits:
The total angle covered in 2.5 orbits is equivalent to 2.5 times the full circumference of the orbit.
Angle = 2.5 * (2πr) = 5πr
Therefore, the radian measure corresponding to 2.5 orbits is 5π radians.
(b) To find the radian measure for 3/2 orbit:
The total angle covered in 3/2 of an orbit is equivalent to (3/2) times the full circumference of the orbit.
Angle = (3/2) * (2πr) = 3πr/2
Therefore, the radian measure corresponding to 3/2 of an orbit is (3πr)/2 radians.
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An engineer is designing a storage compartment in an aircraft. The compartment's volume is 72 cubic meters. The width is 2 meters longer than the length. The height is 1 meter less than the length. Find the dimensions of the compartment.
An engineer is designing a storage compartment in an aircraft. The compartment's volume is 72 cubic meters. The width is 2 meters longer than the length. The height is 1 meter less than the length. the dimensions of the compartment are 4m × 6m × 3m.
Find the dimensions of the compartment. Solution:The volume of a rectangular prism is given by;[tex]`V= l × w × h`[/tex] Given that the compartment's volume is 72 cubic meters, let's substitute[tex]`V = 72`[/tex]
cubic meters;[tex]`l × w × h = 72`[/tex]
We also know that;[tex]w = l + 2h = l - 1[/tex]
Substituting w and h in terms of l, we get;[tex]`l(l+2)(l-1) = 72`[/tex]Expanding,
we get;[tex]`l(l²-1) + 2(l²-1) = 72`[/tex]
Simplifying, we get;[tex]`l³ + l² - 2l - 74 = 0`[/tex]
We will use trial and error method to find one of the roots,`l= 4`.
By substitution, we get;[tex]w = 4 + 2 = 6m h = 4 - 1 = 3m[/tex]
Thus, the compartment dimensions are 4m × 6m × 3m. The width is 6 meters, the length is 4 meters, and the height is 3 meters.
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The function h(x) is defined as shown.
h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayout
What is the range of h(x)?
Selected:a. –[infinity] < h(x) < [infinity]This answer is incorrect.
b. h(x) ≤ 5
c. h(x) ≥ 5
d. h(x) ≥ 3
The function h(x) is defined as shown below:
[tex]$$h(x) = \begin{cases} x+2, & \text{if }x <3 \\ -x+8, & \text{if }x\ge3 \end{cases}$$[/tex]
So, option A is the correct answer.
To find the range of h(x), we will analyze the value of h(x) at different values of x. We will start with values less than 3 and then move to values greater than or equal to 3.
Case 1: x < 3 For values of x less than 3, h(x) is given by:
h(x) = x + 2
For minimum value of x (approaching negative infinity), h(x) approaches negative infinity.
For maximum value of x (approaching 3 from left), h(x) approaches 5. So, the range of h(x) for x < 3 is:
-∞ < h(x) <5 Case 2: x ≥ 3
For values of x greater than or equal to 3, h(x) is given by:
h(x) = -x + 8
For minimum value of x (approaching 3 from right), h(x) approaches 5.
For maximum value of x (approaching infinity), h(x) approaches negative infinity.
So, the range of h(x) for x ≥ 3 is: 5 ≤h(x) <∞
Therefore, the range of h(x) is: -∞ < h(x) < ∞
This is equivalent to option A. So, option A is the correct answer.
Note: When the range of a function is the set of all real numbers, we can also represent it as "(-∞, ∞)" or "ℝ".
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What score must a learner earn on the ACT composite test in order for the score to be at the 87.49th percentile? Round up to the nearest whole number.
Many students take standardized tests for college applications. They are called standardized tests because they are scored so the population of student scores for any one particular test follows a normal distribution. The most common test are the SAT and the ACT.
Suppose the mean and standard deviation for the ACT composite score, the SAT critical reading score, and the SAT mathematics score for the year 2017 are as follows:
For the ACT, the mean composite score was 21.0 with a standard deviation of 5.2.
For the SAT critical reading score, the mean was 501 with a standard deviation of 112.
For the SAT mathematics score, the mean was 516 with a standard deviation of 116
a. 32
b. 43
c. 27
d. 19
Answer:
27
Step-by-step explanation:
You want to know the ACT composite test score for the 87.49th percentile, given the ACT scores have a mean of 21.0 and a standard deviation of 5.2.
Z-scoreThe Z-table in the first attachment shows you the Z-value of the 87.49th percentile is 1.10+0.05 = 1.15.
ScoreThe corresponding score is ...
X = μ +σZ
X = 21.0 +5.2·1.15 ≈ 27
A learner must earn a score of 27 to be at the 87.49th percentile on the ACT composite test.
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Two people are standing on opposite sides of a small river. One person is located at point Q, a distance of 30 meters
from a bridge. The other person is standing on the southeast corner of the bridge at point P. The angle between the
bridge and the line of sight from P to Q is 70. 9º. Use this information to determine the length of the bridge and the
distance between the two people.
The length of the bridge is a meters.
The distance between the two people is
(Do not round until the final answer. Then round to two decimal places as needed. )
Given the information provided, we need to determine the length of the bridge (a) and the distance between the two people.
The person at point Q is 30 meters away from the bridge, and the angle between the bridge and the line of sight from P to Q is 70.9 degrees.
To solve this problem, we can use trigonometry. We can consider the triangle formed by the bridge, point P, and point Q. The angle at point P is 70.9 degrees, and the side opposite to this angle is the length of the bridge (a). The side adjacent to this angle is the distance between the two people.
Using trigonometric functions, we can set up the following equation:
tan(70.9 degrees) = a / 30 meters
By rearranging the equation, we can solve for a:
a = 30 meters * tan(70.9 degrees)
This gives us the length of the bridge.
To find the distance between the two people, we can use the Pythagorean theorem. The distance between the two people is the hypotenuse of the triangle formed by the bridge, point P, and point Q. Using the length of the bridge (a) and the distance from point Q to the bridge (30 meters), we can calculate the distance between the two people using the equation:
Distance = sqrt(a^2 + 30^2)
By substituting the value of a, we can calculate the final answer for the distance between the two people, rounding to two decimal places if necessary.
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