SHEILA either walks or cycles to school.

if she walks, the probability that she is late is 0.4

if she cycles, the probability that she is late is 0.1


Work out the probability that on any one day sheila will not be late for school

Jen's average speed for the entire round trip, including the outbound and return trips, is 30 mph.

To determine Jen's average speed for the entire round trip, we need to calculate the total distance traveled and the total time taken.

Let's assume the distance between Boston and Cape Cod is "d" miles.

For the outbound trip from Boston to Cape Cod, Jen traveled at a speed of 60 mph. The time taken for this leg of the trip is given by:

Time = Distance / Speed

Time = d / 60

For the return trip, it took Jen 3 times longer due to heavy traffic. Therefore, the time taken for the return trip is 3 times the time taken for the outbound trip:

Time for return trip = 3 * (d / 60) = (3d) / 60

The total time for the round trip is the sum of the outbound and return trip times:

Total Time = d / 60 + (3d) / 60 = (d + 3d) / 60 = 4d / 60 = d / 15

The total distance for the round trip is twice the distance from Boston to Cape Cod:

Total Distance = 2d

Now, we can calculate Jen's average speed by dividing the total distance by the total time:

Average Speed = Total Distance / Total Time

Average Speed = 2d / (d / 15)

Average Speed = 2 * 15

Average Speed = 30 mph

Therefore, Jen's average speed for the entire round trip, including the outbound and return trips, is 30 mph.

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The expression (5x)² is equal to ___ x², where the twos are cubes.

To simplify the expression (5x)², we need to apply the exponent rules. Since the twos are cubes, we need to cube both the base and the exponent.

(5x)² can be rewritten as (5x)³³. Applying the exponent rule for a power of a product, we raise each factor inside the parentheses to the third power:

(5x)³³ = (5)³(x)³ = 125x³.

Therefore, the expression (5x)² is equal to 125x³, where the twos are cubes.

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Therefore, the value that needs to be added to (-5)/8 in order to get 5/9 is -5/72.

To get 5/9, what number should be added to (-5)/8?

We can begin the solution by adding "x" to (-5)/8. Then, we will have:((-5)/8) + x = 5/9

The next step is to isolate the variable x, which is accomplished by subtracting (-5)/8 from both sides. The equation becomes:(-5/8) + (5/9) = x

We'll need to find a common denominator for this expression:

((-45)/72) + (40/72) = xSimplifying, we get:

((-45) + 40)/72 = x(-5)/72 = x

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Given a quadrilateral ABCD, with the sides AB and DC parallel and equal in length. Let us denote angle BAD as ∠α and angle ADC as ∠β. Now, we have to find the values of the variables x and y such that ABCD is a parallelogram.

Parallelogram has a pair of parallel sides. So, we have AB ∥ CD. It is given that ∠α = ∠β and AB = CD. So, by angle-angle-side rule, the two triangles ABD and DCA are congruent.

In triangle ABD, we have:∠DAB = 180° - ∠α = 180° - ∠β (as ∠α = ∠β)⇒ ∠DAB + ∠CDA = 180° (linear pair of angles)⇒ ∠CDA = ∠β.In triangle DCA, we have:∠CDA = ∠β (as obtained above)⇒ ∠CAD = ∠α (as ∠α = ∠β)⇒ ∠BDC = 180° - ∠α = 180° - ∠β (linear pair of angles)⇒ ∠BDC = ∠DAB.In quadrilateral ABCD, the adjacent angles are supplementary. So, we have:∠BDC + ∠BCD = 180° (adjacent angles are supplementary)⇒ ∠DAB + ∠BCD = 180° (as ∠BDC = ∠DAB)⇒ ∠BCD = 180° - ∠DAB.In triangle ACD, we have:∠C = ∠C (common)⇒ ∠CAD + ∠BCD = 180° (angles of a triangle add up to 180°)⇒ ∠α + (180° - ∠DAB) = 180°⇒ ∠α + ∠β = 180°.

Now, we can solve for x and y.In triangle ABD, we have:AB = BD⇒ 3x = 21 - x⇒ 4x = 21⇒ x = 21/4.In triangle DCA, we have:CD = DA⇒ 3y = 22 - y⇒ 4y = 22⇒ y = 11/2. Therefore, the value of x is 21/4 and the value of y is 11/2.

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The coefficient is:

Work/explanation:

To find the coefficient of m, we will take a look at the number that comes in front of m.

That number is 9. Hence, that's the coefficient.

Extra info

Answer: To find 20% of 10, Karin can set up the equation as follows:

20% of 10 = (20/100) * 10

Now, let's calculate it:

20% of 10 = (20/100) * 10 = 0.20 * 10 = 2

Therefore, 20% of 10 is equal to 2.

The polynomial represented by the algebra tiles is: x - 4

Given algebra tile configuration:

3 large tiles, 5 tiles each half the size of a large tile, and 8 tiles each one-quarter the size of a large tile.

Two of the large tiles are labeled plus x squared and 1 is labeled negative x square. Two smaller tiles are labeled plus x and 3 are labeled negative x. Six of the smallest tiles are labeled + and 2 are labeled minus.

In order to find the polynomial represented by the algebra tiles, let us consider the number of positive and negative tiles.

Polynomials represented by the algebra tiles:

There are 2 large tiles labeled as x² and a single large tile labeled as -x²

Hence, the net contribution from these 3 large tiles is equal to

+ x² + (-x²) = 0

Now, let's look at the smaller tiles, there are two tiles labeled +x and three tiles labeled -x.

Therefore, the net contribution from these tiles is equal to

2x + (-3x) = -x

Similarly, six smallest tiles are labeled as positive and two are labeled as negative, thus the net contribution from the smallest tiles is equal to 6 - 2 = 4

Hence, the polynomial represented by the algebra tiles is:

x - 4

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my friend earned a total of $21 by mowing neighbors' lawns and hauling away bags of recyclables.

To calculate the total amount earned by my friend, we need to find the sum of the earnings from mowing lawns and hauling away recyclables.

Given:

Earnings per hour for mowing lawns: $7

Earnings for hauling away recyclables: $14

To calculate the total earnings, we can add the two amounts together:

Total earnings = Earnings from mowing lawns + Earnings from hauling recyclables

Total earnings = $7 + $14

Total earnings = $21

Therefore, my friend earned a total of $21 by mowing neighbors' lawns and hauling away bags of recyclables.

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Question: When mowing her neighbors' lawns, Sarah earns $7 per hour. Additionally, she earned $14 for hauling away bags of recyclables for her neighbors. Please provide the missing information to complete this question.

Answer choices:

a) Number of hours Sarah spent mowing

b) Total amount earned by Sarah for mowing

c) Number of bags of recyclables hauled by Sarah

d) Total amount earned by Sarah for both mowing and hauling recyclables

With a principal of $7000 earning a 7% annual interest rate compounded annually over 8 years, the total amount accumulated at the end of the period would be $11,595.76.

To calculate the total amount accumulated, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the principal (P) is $7000, the interest rate (r) is 7%, the interest is compounded annually (n = 1), and the number of years (t) is 8.

Using the formula, we have A = 7000(1 + 0.07/1)^(1*8) = 7000(1.07)^8 ≈ $11,595.76.

Therefore, at the end of 8 years, the total amount accumulated would be approximately $11,595.76.

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1: The number closest to zero is not always the least.

2: The number farthest from zero is not always the greatest.

3: The number farthest right is not always the least.

4: The number left is always the least.

The first statement, "The number closest to zero is always the least," is not necessarily true.

It depends on whether the numbers being compared are positive or negative.

For example, -2 is closer to zero than -4, but it is actually greater than -4.

The second statement, "The number farthest from zero is always the greatest," is also not necessarily true.

Just like the first statement, it depends on whether the numbers being compared are positive or negative.

For example, -5 is farther from zero than -3, but -3 is actually greater than -5.

The third statement, "The number farthest right is always the least," is definitely not true.

The direction of the number line (left or right) has nothing to do with whether a number is greater or lesser than another number.

That leaves us with the fourth statement, "The number left is always the least."

This statement is true! On a number line going from negative to positive numbers, the numbers to the left of zero (the negative numbers) are always less than the numbers to the right of zero (the positive numbers).

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In order to simplify 1/2/3 : 2/2/3 without the use of a calculator, follow these steps: Step 1:  Convert the mixed fractions into improper fractions.1/2/3 : 2/2/3 is same as 1/2 ÷ 2/3.

We know, 1/2 means that we have half of a whole. But the whole is divided into 2 parts, so the denominator is 2.

1/2 can be converted to 3/6, because 3 out of 6 parts make half of a whole. Similarly, 2/3 can be converted to 8/3. Thus, we can write the expression as follows:3/6 ÷ 8/3Step 2: Invert the second fraction and multiply.3/6 ÷ 8/3 = 3/6 x 3/8Step 3: Simplify the fraction.3/6 x 3/8 = 9/48 = 3/16Therefore, the simplified expression is 3/16. Hence, the final answer is 3/16,

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PS and PC are both equal to 16000 feet when SC is 24000 feet. These lengths are determined based on the relationship between the centroid and the midpoints of the sides in a triangle.

In a triangular park, with point P as the centroid, if SC (one of the sides) is equal to 24000 feet, the lengths of PS and PC can be determined.

To find the lengths of PS and PC, we need to consider the properties of a centroid in a triangle. The centroid divides each median into two segments, with the ratio of 2:1.

In other words, the distance from the centroid to the midpoint of a side is two-thirds of the length of the entire median.

In this case, since SC is equal to 24000 feet, PS and PC can be calculated as follows:

PS = (2/3) * SC = (2/3) * 24000 = 16000 feet.

PC = (2/3) * SC = (2/3) * 24000 = 16000 feet.

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The table that best shows the conditional relative-frequency of rows for the data is the fourth option for A school for learning foreign languages has 72 students who learn German, and 54 of those students also learn Russian. There are 12 students who do not learn German but learn Russian, and 10 students do not learn either German or Russian using data-handling.

Given data, 72 students learn German

54 students learn Russian and German

12 students learn Russian but not German

10 students learn neither Russian nor German.

Therefore, The total number of students in the school is 72 + 10 = 82.

Let's fill the table:Learn German Do not learn German Total Learn Russian 54     12      66

Do not learn Russian 18    10     28

Total 72    22     82

Now, we can find the conditional relative frequency of rows as follows:

For students who learn Russian:0.82 = 66/81.00 = 1For students who do not learn Russian:0.64 = 18/28 0.36 = 10/28 1For students who learn German:0.54 = 54/1.00 = 1For students who do not learn German:0.12 = 12/28 0.88 = 22/28 1Thus, the fourth option shows the conditional relative frequency of rows for the given data.

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Based on the information, the probability is 1/144, or approximately 0.0069.

Each number cube has 12 possible outcomes, as there are 12 faces labeled from 1 to 12.

The probability of rolling an 11 on one number cube is 1 out of 12, as there is only one face labeled 11 out of the 12 possible outcomes.

Since the two number cubes are rolled simultaneously, the total number of possible outcomes is the product of the possible outcomes for each cube, which is 12 * 12 = 144.

The number of favorable outcomes, in this case, is 1, as both number cubes need to show 11.

Therefore, the probability that both number cubes land with the number 11 facing up in one roll is:

Number of favorable outcomes / Total number of possible outcomes

= 1 / 144

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The function that represents the parent function vertically stretched by a factor of 3, reflected over the x-axis, and translated right 2 units and up 4 units is g(x) = 3∣x - 2∣ + 4.

This can be explained as follows:

In the parent function ∣x∣, the absolute value of x ensures that the graph is reflected over the x-axis, resulting in a V-shaped graph in the positive y-axis region. By replacing x with (x - 2), we achieve a horizontal translation of 2 units to the right. Next, multiplying the absolute value term by 3 vertically stretches the graph by a factor of 3, making the V-shape narrower and taller. Finally, adding 4 to the function translates the graph upward by 4 units.

Thus, the function g(x) = 3∣x - 2∣ + 4 combines the vertical stretching, reflection, and translations described above to match the given criteria.

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3 students have been in a choir but not on a radio show.

In order to determine how many students have been in a choir but not on a radio show, we can use the Principle of Inclusion-Exclusion (PIE) to solve the problem.

The PIE formula is: n(A or B) = n(A) + n(B) - n(A and B)

Here, A represents the set of students who have been on a radio show, B represents the set of students who have been in a choir, and A and B represents the intersection of the two sets.

Using the information provided, we know that:

n(A) = 3 (3 students have been on a radio show)n(B) = 3 (3 students have been in a choir)n(A and B) = 0 (0 students have been both on a radio show and in a choir)

Therefore, using the PIE formula:

n(A or B) = n(A) + n(B) - n(A and B)n(A or B) = 3 + 3 - 0n(A or B) = 6

So, 6 students have either been on a radio show or in a choir. However, we want to find the number of students who have been in a choir but not on a radio show. To do this, we can subtract the number of students who have been in both from the total number of students who have been in a choir:

n(B but not A)

= n(B) - n(A and B)n(B but not A)

= 3 - 0n(B but not A)

= 3

Therefore, 3 students have been in a choir but not on a radio show.

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It will take Laura 19 months to have a total of $6,775 in her deposit account.

To find the number of months it will take for Laura to have a total of $6,775 in her deposit account, we can set up an equation based on the given information.

Let's break down the steps:

1. Laura made an initial deposit of $2500.

2. She plans to contribute an additional $225 every month.

3. The account does not pay any interest.

4. We need to find the number of months it will take for her total balance to reach $6,775.

Let's denote the number of months as "n." In the first month, Laura's total balance is the initial deposit of $2500. For the following months, her total balance will increase by $225 each month.

We can set up the equation:

Total balance = Initial deposit + Monthly contributions

$6,775 = $2500 + ($225 * n)

Now, we can solve for "n" by rearranging the equation:

$6,775 - $2500 = $225n

$4,275 = $225n

Dividing both sides of the equation by $225:

n = $4,275 / $225

n = 19

Therefore, it will take Laura 19 months to have a total of $6,775 in her deposit account.

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The value of y in the pair of points (7, 4) and (3, y), lying on the same line with a slope of 1/4, is y = 5. This is obtained by setting up and solving an equation using the slope formula.

The value of y can be determined by using the slope formula. The slope between two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). In this case, we have the points (7, 4) and (3, y), with a slope of 1/4. Plugging in the values, we get (y - 4) / (3 - 7) = 1/4. Simplifying this equation, we have (y - 4) / (-4) = 1/4. Cross-multiplying, we get -4(y - 4) = 1(-4), which simplifies to -4y + 16 = -4. Solving for y, we subtract 16 from both sides, giving us -4y = -20. Dividing by -4, we find y = 5.

To summarize, the value of y in the pair of points (7, 4) and (3, y), lying on the same line with a slope of 1/4, is y = 5. This is obtained by setting up and solving an equation using the slope formula.

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The use of Arabic numerals in mathematical calculations provides a consistent, efficient, and universal framework for representing, manipulating, and communicating numerical information, contributing to the development and advancement of various fields of mathematics and sciences.

Arabic numerals, also known as Hindu-Arabic numerals, are the number system we commonly use today, consisting of the digits 0-9. They play a crucial role in performing mathematical calculations for several reasons:

1. Positional notation: Arabic numerals utilize a positional notation system, where the value of a digit depends on its position within the number. This allows for concise representation of numbers and makes arithmetic operations like addition, subtraction, multiplication, and division more efficient and intuitive.

2. Flexibility: Arabic numerals are versatile and can represent a wide range of numbers, from small integers to extremely large or small values. This makes them suitable for all types of mathematical calculations, including basic arithmetic, algebra, calculus, and more advanced mathematical concepts.

3. Universality: Arabic numerals are widely adopted and recognized across the world, making them a universal system for mathematical communication. This standardization enables mathematicians, scientists, engineers, and individuals from different cultures and languages to understand and collaborate on mathematical problems without language barriers.

4. Decimal system: Arabic numerals are based on a decimal system, meaning that they operate in multiples of 10. This aligns with our everyday experiences and facilitates easy comprehension and estimation of quantities. It also allows for efficient conversions between different units and simplifies complex calculations involving fractions and percentages.

Overall, the use of Arabic numerals in mathematical calculations provides a consistent, efficient, and universal framework for representing, manipulating, and communicating numerical information, contributing to the development and advancement of various fields of mathematics and sciences.

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The dimensions of the rectangle are 16 inches in width and 24 inches in length.

Let's assume the width of the rectangle is x inches. According to the problem, the length is 8 inches greater than the width, so the length can be represented as (x + 8) inches.

The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 384 square inches. So, we can set up the equation:

Length * Width = Area

(x + 8) * x = 384

Expanding the equation:

x^2 + 8x = 384

Rearranging the equation to solve for x:

x^2 + 8x - 384 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. Factoring it, we find:

(x - 16)(x + 24) = 0

So, x = 16 or x = -24.

Since dimensions cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 16 inches.

Substituting this value back into the equation for the length:

Length = x + 8 = 16 + 8 = 24 inches

Hence, the dimensions of the rectangle are 16 inches in width and 24 inches in length, which gives an area of 384 square inches.

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It would take 15/4 or 3.75 hours to paint one full room.

If it takes 3/2 of an hour to paint 2/5 of a room, we can use proportions to find how long it would take to paint one full room. Let's represent the time it takes to paint one full room as x.

Then we have the following proportion:

2/5 room : 3/2 hour = 1 room : x

To solve for x, we can cross-multiply: (2/5) * x = (3/2) * 1

Simplifying the right side gives:(2/5) * x = 3/2

Multiplying both sides by the reciprocal of 2/5 gives us:x = (3/2) / (2/5)

Multiplying by the reciprocal is the same as dividing, so we have:x = (3/2) * (5/2)

Simplifying gives:x = 15/4

Therefore, it would take 15/4 or 3.75 hours to paint one full room.

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The expression to determine the total cost in dollars to make and ship a photo book with x extra pages is: 25 + 1.65x.

To calculate the total cost of making and shipping a photo book with x extra pages, we need to consider the base cost, the cost of extra pages, and the shipping cost.

The base cost of making a photo book with 15 pages is $20.

Each additional page beyond the initial 15 pages incurs a cost of $1.65 per page.

Therefore, the cost of x extra pages would be 1.65x.

The shipping cost to ship the completed photo book is a fixed $5.

To calculate the total cost, we add the base cost, the cost of extra pages, and the shipping cost together:

Total Cost = Base Cost + Cost of Extra Pages + Shipping Cost

Total Cost = $20 + $1.65x + $5

Total Cost = $25 + $1.65x

Thus, the expression to determine the total cost in dollars to make and ship a photo book with x extra pages is 25 + 1.65x.

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The formula of height h = (3v) / (π * r^2)To find the height (h) of a cone given the volume (v) and the radius of the base (r), we can rearrange the equation v = (π * r^2 * h) / 3.

By multiplying both sides by 3 and dividing by π * r^2, we isolate the variable h and obtain the formula h = (3v) / (π * r^2). Substituting the appropriate values for volume and radius into this equation allows us to calculate the height of the cone.

To solve for the height (h) in the equation v = (π * r^2 * h) / 3, we first multiply both sides by 3 to eliminate the fraction. This results in the equation 3v = π * r^2 * h. Next, we isolate the variable h by dividing both sides of the equation by π * r^2, giving us the formula h = (3v) / (π * r^2). By substituting the known values for volume (v) and radius (r) into this equation, we can calculate the height (h) of the cone. It is important to ensure that the units for volume and radius are consistent and compatible to obtain the correct result.

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Let x be the number of regular bouquets and y be the number of mini bouquets the florist makes.so the florist makes 5 regular bouquets and 15 mini bouquets

Then we can write the following system of equations based on the given information:

6x + 2y = 60

(since each regular bouquet has 6 roses and 2 peonies)

2x + 2y = 40

(since each mini bouquet has 2 roses and 2 peonies)We can use any method to solve this system of equations, but we will use the substitution method. We will solve the first equation for y in terms of x:y = 30 - 3xSubstitute this expression for y into the second equation and solve for

x:2x + 2(30 - 3x) = 402x + 60 - 6x = 40-4x = -20x = 5Substitute x = 5 into the expression we found for y:y = 30 - 3(5) = 15

Therefore, the florist makes 5 regular bouquets and 15 mini bouquets. Another method to solve the system of equations is by graphing: Graph the two equations on the same set of axes and find the intersection point. The x-coordinate of the intersection point will give us the number of regular bouquets, and the y-coordinate will give us the number of mini bouquets. We can see that the intersection point is (5, 15), which agrees with the solution we found using the substitution method.

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According to the tangent-chord theorem, when a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency.  The measure of CD is 60 degrees.

In the given diagram, we can observe that AB is a tangent to the circle at point B. According to the tangent-chord theorem, when a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency. Therefore, angle BCD is a right angle, measuring 90 degrees.

Since BCD is a right angle and angle ACD is given as 30 degrees, we can determine the measure of angle BCA by subtracting the sum of angles ACD and BCD from 180 degrees.

Angle BCA = 180 degrees - (30 degrees + 90 degrees) = 180 degrees - 120 degrees = 60 degrees.

Therefore, the measure of CD is 60 degrees.

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Therefore, the total cost of the knives is $50.

Arithmetic is the fundamental of mathematics that includes the operations of numbers. These operations are addition, subtraction, multiplication and division. Arithmetic is one of the important branches of mathematics, that lays the foundation of the subject 'Maths', for students.

The total cost of the knives is $50.

What is being offered in the television ad?

A set of knives is being offered in the television ad. The knives are being sold for $20 down and $5 a month for six months.How to determine the total cost of the knives?To calculate the total cost of the knives, we will use the formula:

Total cost = Down payment + Monthly payment × Number of monthsTotal cost

= $20 + $5 × 6 = $20 + $30

= $50

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The work done is 400.0 Joules A force of 80 Newtons pushes a 50-kilogram object across a level floor for 8.0 meters.

To find the work done, we can use the formula:work = force x distance x cos(theta)where force is 80 N, distance is 8.0 m, and theta is the angle between the force and the displacement. Since the force is applied in the direction of motion, theta is 0° and cos(0°) is 1.

we can simplify the formula as:work = force x distance x cos(theta)work = 80 N x 8.0 m x cos(0°)work = 640.0 JHowever, we need to check the units of our answer to make sure they are in Joules (J). The units of force are Newtons (N), the units of distance are meters (m), and the units of cos(theta) are dimensionless. Therefore, our answer is in Joules (J).So, the work done is 640.0 Joules.

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The function f(x) = -4x^2 + 32x - 48 is a quadratic function.

To analyze the function algebraically, we can look at its key characteristics:

Quadratic term: The term -4x^2 indicates that the function is a quadratic function.

Coefficients: The coefficient of the quadratic term is -4, the coefficient of the linear term is 32, and the constant term is -48.

Vertex: The vertex of the quadratic function can be found using the formula x = -b/(2a). In this case, the vertex is located at x = -32/(2*(-4)) = 4. Substitute this value back into the function to find the y-coordinate of the vertex: f(4) = -4(4)^2 + 32(4) - 48 = 0. Hence, the vertex is (4, 0).

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You are driving and the maximum speed limit is 55, then the The inequality for this situation can be written as s ≤ 55.

An inequality is a mathematical expression that shows the difference between two values by stating that one value is higher, lower, or not equal to the other.

Let's write "s" for the speed you are travelling at. The inequality that describes a situation where the 55 mph speed restriction is in effect is as follows:

s ≤ 55

Thus, your speed "s" should be less than or equal to 55 mph, according to this discrepancy. It guarantees that you are travelling within the permitted speed limit and not going over it.

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Your question seems incomplete, the probable complete question is:

Write an inequality for this situation: You are driving, and

the maximum speed limit is 55

the value of n remains indeterminate in this case.To find the value of n in the expression (y^20)(y^-5)^2i equivalent to yn, we can simplify the expression first.

Starting with (y^20)(y^-5)^2i, we can simplify the exponent by multiplying the exponents of y:
(y^20)(y^-5)^2i = y^(20 + (-5 * 2))i = y^(20 + (-10))i = y^10i.

Now, we can equate this simplified expression to yn:
y^10i = yn.

To find the value of n, we can compare the exponents:
10i = n.

Since the imaginary unit i represents the square root of -1, and the exponent in this case is not purely real, we cannot find a specific value for n. Therefore, the value of n remains indeterminate in this case.

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