Alvin incorrectly simplified 4 x 42 and got an answer of 166.
What did Alvin do wrong? Explain and then solve the
problem correctly.

Answer:

x - 5y

Step-by-step explanation:

6x - 8y - 5x + 3y =

= 6x - 5x - 8y + 3y

= x - 5y

Answer:

1x + 11y

Step-by-step explanation:

The area of the sector with a central angle of 60 degree and radius of 8 units is approximately 33.5 sqaure units.

A sector of a circle is simply part of a circle made up of an arc and two radii.

The area of a sector of a circle can be expressed as:

Area = (θ/360º) × πr²

Where θ is the sector angle in degrees, and r is the radius of the circle.

From the image:

Measure of central angle θ = 60 degrees

Radius r = 8 units

Plug these values into the above formula and solve for the area:

Area = (θ/360º) × πr²

Area = (60°/360°) × π × 8²

Area = 1/6 × π × 64

Area = 1/6 × π × 64

Area = 33.5 sqaure units.

Therefore, the area is approximately 33.5 sqaure units.

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The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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The circumference around the flower bed in yards is D) 8×π.

The circumference of a circle is defined as the linear distance around it.

The formula for the circumference of a circle is \(2\pi r\). Where r is the radius of the circle.

It is given that the radius of the flower bed is 4 yards.

The flower bed is in the shape of a circle.

The circumference of the flower bed is 2×π×r.

Substitute the value of r in the equation.

Therefore the circumference around the flower bed is 8×π.

The correct option is D) 8×π.

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Answer:

16

Step-by-step explanation:

U is the midpoint of TV ⇒ TV = TU + UV

TU and UV equals each others since U is the midpoint of TV

                          add -x to both sides

                           \(x + 8 -x = 2x - x \\8 = x \\x = 8\)

Answer:

\(y = \frac{1}{8}(x + 4)^2 + 4\)

Step-by-step explanation:

Given:

Focus of parabola: (-4, 6)

Directrix: y = 2

Required:

Equation for the parabola

Using the formula, \( y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) \) , the equation for the parabola can be derived.

Where,

a = -4

b = 6

k = 2

Plug these values into the equation formula

\( y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) \)

\(y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)\)

\(y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}\)

\(y = \frac{1}{8}(x + 4)^2 + 4\)

The equation that represents the given graph is

f(x) = 1/(x - 1) - 2

The graph of a rational function

A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational

function if, it can be represented as f (x) = p (x)/q (x), where p (x) and q (x) are polynomials such that q (x) ≠ 0.

To write the equation that represents this function, we need to identify the key features of the graph.

The graph is a hyperbola with the vertical asymptote x = 1 and the horizontal asymptote y = -2.

The graph passes through the point (0, -1).

Therefore, the general form of the equation that represents the given graph isf(x) = A/(x - 1) - 2

Since the horizontal asymptote is y = -2, A = -2.

Therefore, the equation that represents the given graph is f(x) = 1/(x - 1) - 2.

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Answer:

5x+1

Step-by-step explanation:

the perimeter is the outside values of the shape, and we know all the values, so we just have to add them all up.

(x+4) + (2x-1) + (3x-2) = perimeter

since it's all subtraction and addition we can remove the parentheses

x+4+2x-1+3x-2 = perimeter

now let's put all the x's on one side and the numbers on the other side to make it easier

x+2x+3x+4-1-2= perimeter

5x+1

Answer:

Perimeter of the triangle is :---

\((x + 4) + (3x - 2) + (2x + 1) \\ = x + 4 + 3x - 2 + 2x + 1 \\ = \boxed{(6x + 3 )\: ft }\)

Answer:

-4x^3+12x^2-1

Step-by-step explanation:

The government agency that does not regulate banking or financial market is the The FCC. option C

The term FCC stands federal Communication Commission.  We should know that the duty of the federal communication Commission not to regulate finance in the society or regulate banking activities rather than to regulate Communication

It is the duty of the Commission to report on chain broadcasting, assign television stations to private and government individuals in the state.

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Answer:

0.738 km/h

Step-by-step explanation:

It took 42 minutes from takeoff to get to its destination, so when you divide 31/ 42 (42 representing the time and 31 km representing the distance), you get 0.738 km/h

The maximum clearance of the underpass ahead is 12 feet and 6 inches.

Based on the information provided, the sign indicates that there is an underpass ahead with a clearance of 12 feet and 6 inches. The sign further mentions that the train in question is also 12 feet and 6 inches long, and it highlights the presence of a narrow median, which is only 6-12 inches wide.

In this context, the sign serves as a warning to drivers approaching the underpass. The clearance measurement of 12 feet and 6 inches informs drivers of the maximum height of vehicles that can safely pass through the underpass without any risk of collision. Since the train length matches the clearance, it implies that vehicles longer than the underpass clearance may not be able to pass through safely if the train is present.

The mention of a narrow median emphasizes the limited space available between the opposing lanes of traffic. With a width of only 6-12 inches, the median may not provide sufficient room for larger vehicles to maneuver, particularly when encountering oncoming traffic or passing through the underpass while the train is present.

Overall, the sign conveys important information regarding the underpass clearance, the train length, and the narrow median, all of which should be considered by drivers to ensure safe passage through the upcoming area.

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The sign indicates the clearance height of an underpass, warns of a narrow median, and mentions the length of a train.

The sign in question is indicating that there is an underpass ahead with a clearance of 12 feet and 6 inches. This means that any vehicle taller than that would not be able to pass through without hitting the underpass ceiling. Additionally, the sign mentions that the train itself is also 12 feet and 6 inches long, so it is important for drivers to be cautious and aware of the height restrictions. The narrow median mentioned refers to the strip of land or barrier between lanes, which in this case is only 6-12 inches wide.

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Using the information provided, it appears that your neighbor will not save money by picking up the soil himself as its total cost is $103.86 as opposed to cost of delivery $30.

Here is a detailed breakdown of the calculations and assumptions made:

The area of the yard is estimated to be around 7,200 sq.ft. Assuming a 4 inch layer of topsoil, this requires 4 cubic yards (1 cubic yard = 27 cubic feet).

The cost of the soil delivery is $30 per truckload (up to 18 cubic yards). So the delivery cost for 4 cubic yards of soil would be $30.

The cost of topsoil per cubic yard is $18. Thus, the total cost of the topsoil is $72.

The weight of topsoil is 2000 pounds per cubic yard, so the total weight of the soil is 8,000 pounds (4 cubic yards x 2000 pounds).

The pickup truck's payload capacity is 1800 pounds, so the truck can only transport 1/4 of the total weight of the soil (1800/8000 = 0.225). Thus, it would require 4 trips to transport the soil, and the total trip distance is 36 miles (9 miles x 4 trips).

The truck gets 17 miles per gallon, so it would require 2.1 gallons of gas for each trip (36 miles/17 mpg = 2.12). The total amount of gas needed for the 4 trips is 8.4 gallons (2.1 gallons x 4 trips). The cost of gas per gallon is assumed to be $3.79, so the total cost of gas for the 4 trips is $31.86.

Thus, the total cost of picking up the soil himself is $31.86 + $72 = $103.86. This is higher than the cost of delivery which is only $30, so it would be better to pay for delivery.

To conclude, your neighbor will not save money by picking up the soil himself, and it is recommended that he pays for delivery.

Note: The question is incomplete. The complete question probably is: He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this. Here is (most of) the information you asked for:

Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery? Detail all your assumptions and calculations, and clearly write out your final conclusions.

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Answer:

11.86824cm

Step-by-step explanation:

Answer:

11.86824cm

Step-by-step explanation:

For this problem, let's pick (2x - 4) and (3x + 7) as the two binomial factors.

To multiply two binomials, we use the FOIL method, which stands for First, Outer, Inner, Last.

First: Multiply the first term of each binomial together, which gives 2x × 3x = 6x²

Outer: Multiply the outer terms of each binomial together, which gives 2x × 7 = 14x

Inner: Multiply the inner terms of each binomial together, which gives -4 × 3x = -12x

Last: Multiply the last term of each binomial together, which gives -4 × 7 = -28

Then, we combine the like terms to get the final result:

(2x - 4)(3x + 7) = 6x² + 14x - 12x - 28 = 6x² + 2x - 28

To factor by grouping, we first group the terms in pairs:

(2x - 4)(3x + 7) = (2x + ?)(3x + ?)

We want to fill in the question marks with two numbers that multiply to give 6x² and add up to 2x. The numbers are 6x and 1x:

(2x - 4)(3x + 7) = (2x + 6x)(3x + 1) - 4(3x + 1) = (2x + 6x - 4)(3x + 1) = 2( x + 3 )( 3x + 1 )

The expressions in 2) and 3) are the same because they are both equivalent forms of the same polynomial. The FOIL method in step 2) expands the polynomial, while the factor by grouping method in step 3) breaks it down into its factors. Since multiplication is distributive over addition, the product of the factors in step 3) can be expanded using the distributive property to give the polynomial obtained in step 2).

The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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To determine the number of hours it took to service your mower when the charge was $90, we need to subtract the fixed service call fee ($50) from the total charge and then divide the remaining amount by the hourly rate of $80.

Let's denote the number of hours it took to service the mower as 'h'. The total charge for the service is given as $90.

To find the number of hours, we first subtract the fixed service call fee of $50 from the total charge: $90 - $50 = $40.

Next, we divide the remaining amount ($40) by the hourly rate of $80: $40 / $80 = 0.5 hours.

Therefore, it took 0.5 hours (or 30 minutes) to service your mower when the charge was $90.

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The true population mean is (222.52, 227.48) with a 95% confidence interval.

The critical factor for a 90% confidence interval for the true population mean is given by;

Critical factor = (x-μ)/(s/√n)

where, x = sample mean repair cost

s =  standard deviation of a sample

n = sample of stereos

μ  = critical value

⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95

⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95

⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95

95% confidence interval for

⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))

Here, x = 225, s  = 8.5, and n = 45

⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))

⇒ μ = (222.52, 227.48)

Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.

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The question seems to be incomplete the correct question would be

Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.

The number of people are 72.

Highest Common Factor is the full name for HCF in mathematics.

According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.

Least Common Multiple is the full name for LCM in mathematics.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.

We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.

Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.

We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:

288 / x² = (16*18) / x² = 288 / x²

Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.

As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.

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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.

The total area of the cake is:

16 inches x 18 inches = 288 square inches

To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:

√(288 square inches) ≈ 16.97 inches

Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:

Each piece of cake will be approximately 16 inches by 16 inches.

To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:

288 square inches ÷ (16 inches x 16 inches) = 18

Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

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Answer:

B

Step-by-step explanation:

Multiply each side of the equation by ax-2 and use FOIL to finish up the process.

Answer:

B

Step-by-step explanation:

The probability of drawing three cards with replacement from a standard deck of 52 cards is 1/416.

The probability of drawing three cards with replacement from a standard deck of 52 cards is to be found when the first card is a club, the second card is a red card, and the third card is the six of hearts.

Here, the Probability of the first card being a club = P(C) = 13/52 = 1/4 [Since there are 13 clubs in the deck of 52 cards]

Probability of the second card being a red card = P(Red) = 26/52 = 1/2 [Since there are 26 red cards in the deck of 52 cards]

Probability of the third card being six of hearts = P(6 of hearts) = 1/52 [Since there is only one six of hearts in the deck of 52 cards]

Therefore, the Probability of drawing three cards with replacement from a standard deck of 52 cards is

= P(C) × P(Red) × P(6 of hearts)= 1/4 × 1/2 × 1/52= 1/416

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Answer:

11 inches

Step-by-step explanation:

7^2+8^2=c^2

49+64=c^2

113=c^2

square root both side

c=10.63014581

round up and get c=11

hope this helped :)

Answer:equal and parallel opposite sides

Step-by-step explanation:

equal sides

parallel opposite sides

It is found that ABCD and ABEC are parallelograms because a parallelogram can be divided into congruent triangles of different orientations.

The pre-image of the rotations are given as: Triangle ABC

Triangle ABC

The image of the rotations are given as: Triangle CDA

Triangle ECB

Notice that the triangles ABC and CDA have a common line segment AC, while the triangles ABC and ECB have a common line segment CB because the triangle is rotated by 180 degrees through its own midpoint

ΔCAD = ΔABC but of different orientations, then ABCD is a parallelogram.

Also,

ΔABC = ΔECB, so that ABEC is a parallelogram.

So then:

ΔCAD = ΔABC = ΔECB

Therefore, ABCD and ABEC are parallelograms.

It is found that ABCD and ABEC are parallelograms because a parallelogram can be divided into congruent triangles of different orientations.

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By increasing the sample size to 248, the researcher can be more confident in their estimate of the mean drying time for the type of cement being studied.

To determine the sample size required to estimate the mean drying time for a certain type of cement, the following formula can be used:

\(n = ((Zα/2 \times σ) / E)^2\) where: Zα/2 is the critical value of the standard normal distribution for the desired confidence level (99% in this case), which is 2.576 σ is the standard deviation of the population (68 minutes)E is the maximum margin of error that can be tolerated (7 minutes).

Substituting these values into the formula, we get:

\(n = ((2.576 \times 68) / 7)^2\) = 247.36. Rounding up to the nearest whole number, the sample size required is 248.

This means that if the researcher takes a random sample of 248 drying times and calculates the mean drying time, with 99% confidence we can say that the true population mean drying time is within plus or minus 7 minutes of the sample mean.

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Answer:

C.

Step-by-step explanation:

-6 4/5 and 64/5 are opposites or a zero pair so when you add them you get zero.

Answer:

The squirrel could burrow 6 holes in 9 minutes.

Step-by-step explanation:

Answer:

sorry di ko alam

Step-by-step explanation:

A) A translation involves shifting the entire triangle horizontally or vertically.

B) A rotation involves rotating the triangle about a fixed point.

C) A reflection involves flipping the triangle over a line, resulting in a mirror image.

Comparing the x-coordinates:

A (-2) and A' (2) are not mirror images.

B (-1) and B' (-1) are mirror images.

C (3) and C' (-2) are not mirror images.

To determine which transformation produces an image with the given vertices A' (2, -2), B' (-1, -1), and C' (-2, 3) from the original triangle with vertices A (-2, -2), B (-1, 1), and C (3, 2), we need to analyze the transformations.

1. Translation:

A translation involves shifting the entire triangle horizontally or vertically. In this case, the vertices A' (2, -2), B' (-1, -1), and C' (-2, 3) are not simply shifted horizontally or vertically from the original triangle's vertices. Therefore, a translation is not the correct transformation.

2. Rotation:

A rotation involves rotating the triangle about a fixed point. Since the given vertices A' (2, -2), B' (-1, -1), and C' (-2, 3) do not appear to be rotated versions of the original triangle's vertices, a rotation is also not the correct transformation.

3. Reflection:

A reflection involves flipping the triangle over a line, resulting in a mirror image. To determine if a reflection is the correct transformation, we can compare the coordinates of the original and transformed vertices.

Comparing the x-coordinates:

A (-2) and A' (2) are not mirror images.

B (-1) and B' (-1) are mirror images.

C (3) and C' (-2) are not mirror images.

Since not all the x-coordinates match, a reflection is not the correct transformation.

4. Dilation:

A dilation involves either expanding or shrinking the triangle from a fixed center point. Since the given vertices A' (2, -2), B' (-1, -1), and C' (-2, 3) do not appear to be scaled versions of the original triangle's vertices, a dilation is not the correct transformation.

Based on the analysis above, none of the provided transformations (translation, rotation, reflection, dilation) produce an image with the given vertices A' (2, -2), B' (-1, -1), and C' (-2, 3) from the original triangle.

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Answer:

2 mins= 8 gallons 3 mins= 12 gallons 4 mins= 16 gallons 5 mins= 20 gallons 6 mins= 24 gallons

Step-by-step explanation:

12 divided by 3 equals 4 so just multiply 4 by each minute