29. A horse ran around this rectangular paddock, 60m by 100m wide. What total distance was covered by the horse? A. 3.2km B. 6.4km C. 5km D. 20km.​

Just 1 (one) scoop of ice cream can melt in the cone and not overflow.

To decide the number of scoops of ice cream that may melt within the cone without flooding, we got to calculate the accessible space interior of the cone.

The volume of a cone can be calculated utilizing the equation V = (1/3)πr^2h, where r is the sweep and h is the stature. In this case, the sweep is half of the breadth, so r = 4.5 cm and h = 15 cm.

V = (1/3)π(4.5 cm)^2(15 cm) = 95.04 cm^3 (balanced to two decimal places)

The volume of each scoop of ice cream can be calculated utilizing the condition for the volume of a circle, V = (4/3)πr^3, where r is the span. In this case, the span is half of the breadth, so r = 2.5 cm.

V_scoop = (4/3)π(2.5 cm)^3 ≈ 65.45 cm^3 (adjusted to two decimal places)

To discover the number of scoops that may dissolve within the cone without flooding, we isolate the volume of the cone by the volume of each scoop:

Number of scoops = V_cone / V_scoop ≈ 95.04 cm^3 / 65.45 cm^3 ≈ 1.45

Since we cannot have a division of a scoop, the most extreme number of scoops that may liquefy within the cone without flooding is 1. In this manner, as it were one scoop of ice cream can be suited within the cone without spilling over.

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The sum of expected marks is given as follows:

9375.

Each question has four choices, hence the probability of choosing the correct choice is given as follows:

p = 1/4 = 0.25.

Then the expected number of correct answers is given as follows:

E(X) = 0.25 x 150

E(X) = 37.5.

Then the expected grade for a single student is given as follows:

37.5 - 0.25(150 - 37.5) = 9.375.

The expected sum for the 1000 students is then given as follows:

1000 x 9.375 = 9375.

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The Watkins family should install a chlorine pool to be more cost-efficient.

In order to compare the two graphs we take a value on the x-axis and then measure the output of the two graphs. This can be done with the help of the graph or by substituting the value of x in the function to measure the output y.

As in the given graph, the x-axis denotes the year while the y-axis denotes the cost of maintaining the pool in that year.

If we compare the two of the given graph we will find the cost of maintaining a chlorine pool is less as compared to a salt water pool at x=10, therefore, after 10 years.

Hence, the Watkins family should install a chlorine pool to be more cost-efficient.

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Let "x" be the number of years it takes for the two plants to be the same height.The first plant has an initial height of 7 inches and grows at a constant rate of 3 inches each year. So, the two plants will be the same height after 5 years.

Therefore, after "x" years, its height will be:7 + 3xThe second plant also grows at a constant rate and has an initial height of 2 inches. After 3 years, its height is 14 inches.

Therefore, its rate is: Rate = (Final height - Initial height) / TimeRate = (14 - 2) / 3Rate = 12 / 3Rate = 4So, after "x" years, the second plant's height will be:2 + 4x.

To find when the plants are the same height, we can set the expressions for their heights equal to each other:7 + 3x = 2 + 4xSolving for "x":3x - 4x = 2 - 73x = -5x = -5/(-1). Therefore, x = 5, the two plants will be the same height after 5 years.

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Answer:

76890000000 to 7.689 ×10^10

Step-by-step explanation:

Answer:

Because the P-value < α = 0.05, the correct decision is to reject H0.

Step-by-step explanation:

When the p-value is less than our given significance level, it's outside the rejection region, so there is strong evidence that suggest the null hypothesis is not true and that the alternate hypothesis is favored instead.

The rule used to determine the time value from its position in the sequence ​is discussed below.

In general, the rule could involve arithmetic progression (adding or subtracting a constant value at each step), geometric progression (multiplying or dividing by a constant value at each step), or a more complex pattern involving mathematical operations, functions, or other mathematical relationships.

To determine the time value, you would need to analyze the given sequence, identify the pattern or rule being followed, and then apply that rule to find the time value corresponding to a particular position in the sequence.

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To find the value of x, we can use the fact that the sum of the lengths of the line segments in a triangle is equal to the total length of the triangle.

In this case, we have:

AC = 8x - 9

AB = 3x + 1

BC = 4x - 5

The sum of the lengths of the line segments AB, BC, and AC should be equal to the total length of the triangle ABC. Therefore, we can set up the equation:

AB + BC + AC = total length of triangle ABC

(3x + 1) + (4x - 5) + (8x - 9) = total length of triangle ABC

Simplifying the equation, we get:

15x - 13 = total length of triangle ABC

Since we don't have any additional information about the triangle, we can't determine the exact length of the total triangle. Therefore, we cannot find the exact value of x using the given figure.

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Answer: 267.95 units^3 or 85.3333[tex]\pi[/tex]

Step-by-step explanation:

Formula: V = (4/3)*3.14*(4^3) = 267.95 units^3

(4/3)*[tex]\pi[/tex]*(4^3)=85.333[tex]\pi[/tex]

The total number of cars sold by two dealerships is 294.

Let x be the number of cars and y be the number of trucks.

As, there are total 164 cars then

x+ y= 164   ........(1)

The second dealership sells twice as many cars and half as many trucks as the first dealership and sold a total of 229 cars and trucks.

so, 2x+ y/2 = 229.....(2)

Solving the equation as

y= 164- x

and, 2x + (164-x)/2 = 229

4x + 164 -x = 458

3x= 458 - 164

3x = 294

x= 294/3

x = 98

Thus, the total number of cars sold by two dealerships is 294.

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The matrix corresponding to the vertices of the triangle after the rotation is given as follows:

[0 -1 -2]

[0 -3 1]

The five more known rotation rules are given as follows:

The vertices of the original triangle are given as follows:

(0,0), (-3,1) and (1,2).

The rotation rule is given as follows:

(x,y) -> (-y, x).

Hence the vertices of the rotated figure are given as follows:

(0,0), (-1, -3) and (-2, 1).

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The coordinates of P' after rotating triangle PQR counterclockwise by 270 degrees about the origin are P'(-3, 1).

To rotate a point counterclockwise about the origin, you can use the following rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

In this case, we want to rotate the triangle PQR 270 degrees counterclockwise. We can calculate the coordinates of each point after the rotation.

For point P(-1, -3):

x' = (-1) * cos(270°) - (-3) * sin(270°)

y' = (-1) * sin(270°) + (-3) * cos(270°)

We can simplify these equations using the values of cosine and sine for 270 degrees:

x' = (-1) * 0 - (-3) * (-1)

y' = (-1) * (-1) + (-3) * 0

Simplifying further:

x' = 0 - 3

y' = 1 + 0

x' = -3

y' = 1

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The rule for the translation is a horizontal shift of 6 units to the left (negative) and a vertical shift of 2 units up (positive).The correct answer is option D.

To find the rule for the translation from the original triangle ABC to the translated triangle A'B'C', we can compare the coordinates of corresponding points.

The translation rule can be determined by finding the horizontal and vertical shifts between the original points and the translated points.

Let's calculate the horizontal and vertical shifts for each point:

For point A:

Horizontal shift = x-coordinate of A' - x-coordinate of A

Vertical shift = y-coordinate of A' - y-coordinate of A

Horizontal shift = -3 - 3 = -6

Vertical shift = 3 - 1 = 2

For point B:

Horizontal shift = x-coordinate of B' - x-coordinate of B

Vertical shift = y-coordinate of B' - y-coordinate of B

Horizontal shift = 0 - 6 = -6

Vertical shift = 3 - 1 = 2

For point C:

Horizontal shift = x-coordinate of C' - x-coordinate of C

Vertical shift = y-coordinate of C' - y-coordinate of C

Horizontal shift = -5 - 1 = -6

Vertical shift = 5 - 3 = 2

Now, let's analyze the shifts:

- The horizontal shift is consistent for all three points and is -6 units.

- The vertical shift is consistent for all three points and is 2 units.

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We transformed 630 square yards to square inches, resulting in a value of 816,480 square inches.

To convert 630 square yards to square inches, we can utilize the following unit multipliers:

1 yard = 3 feet (since there are 3 feet in a yard)

1 foot = 12 inches (since there are 12 inches in a foot)

1 square yard = 1 yard × 1 yard = 3 feet × 3 feet = 9 square feet

1 square foot = 12 inches × 12 inches = 144 square inches

Now, we can set up the conversion using the unit multipliers:

630 square yards × (9 square feet / 1 square yard) × (144 square inches / 1 square foot) = 630 × 9 × 144 square inches

Simplifying the calculation:

630 × 9 × 144 square inches = 816,480 square inches

Therefore, 630 square yards is equal to 816,480 square inches.

By using the four unit multipliers and converting yards to feet and then to inches, we successfully transformed 630 square yards to square inches, resulting in a final value of 816,480 square inches.

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The required answer is: it is not possible to determine Alvin's average paddling rate based on the given information.

Given that table of terms Distance, Rate and  Time

Against the current d r - 2 km/hr 8 hours

With the current d r + 2 km/hr 3 hours

To set up an equation to solve for Alvin's average paddling rate, we can use the formula: rate = distance/time.

For the first row : (r - 2 km/hr) = d/8.

For the second row: (r + 2 km/hr) = d/3.

To solve for r, we can equate the rates against the current and solve for r.

(r - 2 km/hr) = (r + 2 km/hr)

Simplifying the equation, we get: r - 2 = r + 2.

By solving this equation, we find that the "r" terms cancel out, resulting in -2 = 2, which is not a true statement. This indicates that there is no solution for Alvin's average paddling rate in this scenario.

Therefore, it is not possible to determine Alvin's average paddling rate based on the given information.

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Answer:

I think answer is D but it could be wrong not sure

The value of x to the nearest hundredth of a foot as required to be determined in the task content is; Choice A; 7.51.

It follows from the task content that the value of x as indicated is to be determined.

As the given triangle is a right triangle whose hypothenuse and side x is opposite the angle whose measure is 28°.

It follows from trigonometric ratios that;

sin 28° = x / 16

x = 16 sin 28°

x = 7.51.

Ultimately, the value of x to the nearest hundredth is; Choice A; 7.51.

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Dolma will receive Rs.153,486.69 at the beginning of BS 2080 as detailed below

What is effective after-tax rate of return?

The effective after-tax rate of return in this case is determined as the 9% deposit return rate multiplied by 1 minus the tax rate as stated below:

effective after-tax rate of return= gross rate of return*(1-tax rate)

The gross rate of return is the return on the deposit before considering the tax rate.

gross rate of return=9%

tax rate=5%

effective after-tax rate of return=9%*(1-5%)

effective after-tax rate of return=8.55%

The future value of the deposit after three years(beginning of 2077-2080=3years), is determined using the future value formula of a single cash flow below:

FV=PV*(1+r)^N

FV=future value after 3 years=unknown

PV=Rs.120,000

r=8.55%

N=3

FV=120000*(1+8.55%)^3

FV=120000*(1,0855)^3

FV=120,000*1.279055776375

FV=Rs.153,486.69

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The percentage of age-groups has more male customers than female customers is approximately 50%.

The given graph depicts a company's customer analysis based on gender and age group.

Male percentage is more between the age 30-34, 45-49, 50-54 and 55-59.

Here, percentage = 20/41 ×100

= 0.487×100

= 48.7%

≈ 50%

Therefore, option B is the correct answer.

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The value of f(3) is 0.688.

To find the value of f(3), we need to determine the pattern of decrease and apply it to the given information.

Given that f(0) = 86, we know the starting value of the function. We are also told that for each increase in x by 1, the value of f(x) decreases by 80%. This means that for every unit increase in x, the value of f(x) becomes 80% of its previous value.

Let's calculate the values step by step:

f(0) = 86 (given)

f(1) = 86 - 0.8 * 86 = 17.2

f(2) = 17.2 - 0.8 * 17.2 = 3.44

Now, let's find f(3) by applying the same decrease:

f(3) = 3.44 - 0.8 * 3.44 = 0.688

In summary, starting with f(0) = 86, we applied an 80% decrease for each unit increase in x to calculate the values of f(1) = 17.2, f(2) = 3.44, and f(3) = 0.688. The pattern suggests that the function approaches zero rapidly as x increases.

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The sum of the first 33 terms of the following series, to the nearest integer is 4818.

The sum of the first 33 terms of the following series, to the nearest integer is calculated as follows;

n = (n/2)(2a + (n-1)d)

where;

From the given parameters, we have;

n = 33

a = 2

d = 9

The sum of the first 33 terms is calculated as;

S(33) = (33/2)(2x2 + (33-1)(9))

S(33) = (33/2)(4 + 32(9))

= (33/2)( 4 + 288)

= (33/2)(292)

= 33(146)

= 4818

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Answer:

2.5 days

Step-by-step explanation:

To solve this problem, we can use the concept of work rate. The work rate is defined as the amount of work done per unit of time.

Given:

15 people working 5 hours per day can make 30 units of the product in 10 days.

From this information, we can calculate the work rate of these 15 people:

Work rate = Total units of the product / (Number of people × Number of hours × Number of days)

Work rate = 30 units / (15 people × 5 hours × 10 days)

Work rate = 0.04 units per person per hour

Now, we need to find how many days it will take for 10 people, working 10 hours per day, to make 10 units of the product.

Using the work rate formula:

Number of days = Total units of the product / (Number of people × Number of hours × Work rate)

Number of days = 10 units / (10 people × 10 hours × 0.04 units per person per hour)

Number of days = 2.5 days

Therefore, 10 people, working 10 hours per day, can make 10 units of the product in 2.5 days.

The correct answer is:

2.5 days

This example demonstrates a two-step inequality where we first express the savings equation and then solve for the variable 'w' to determine the number of weeks needed to reach the savings goal.

Liam is saving money to buy a new video game console. He has already saved $50 and is saving $10 per week from his allowance. He wants to determine how many weeks it will take for his savings to reach at least $150.

Let:

number of weeks Liam saves = w

total amount of money he saves = S

Step 1: Express the first step of the problem as an inequality.

Liam saves $10 per week, so the amount of money he saves after w-weeks is 10w. We can write the first step of the inequality as:

10w + 50 ≥ 150

Step 2: Solve the inequality.

To isolate 'w', we can subtract 50 from both sides of the inequality:

10w ≥ 150 - 50

10w ≥ 100

Finally, divide both sides of the inequality by 10 to solve for 'w':

w ≥ 10

Therefore, it will take Liam at least 10 weeks to save enough money to reach $150 for the video game console.

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The measure of arc MN include the following: B. 45°.

In Mathematics and Geometry, the theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, the value of arc MN can be calculated as follows:

37= 1/2(arc MN + 29)

37(2) = arc MN + 29

74 = arc MN + 29

arc MN = 74 - 29

arc MN = 45 degrees.

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Answer:

y=x/3+2

Step-by-step explanation:

y=x/3+2 would be (-6,0) and (0,2)

An inequality that represents the state's hourly wage requirement include the following: C. m ≥ $9.25 per hour.

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Assuming the variable m represent the state's hourly wage requirement. Additionally, each interval on the number line represent 0.25 per hour.

Since the shaded circle (dot) is located at point 9.25 and the arrows points or increases to the right, an inequality that represents the state's hourly wage requirement is m ≥ $9.25 per hour.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

As per the given equation, when a = 3 and b = -2, the value of the expression [tex]b^2[/tex] - 4ab is 28.

When a = 3 and b = -2, we replace the given values into the formula and make the necessary calculations to evaluate the expression b² - 4ab.

Now,

[tex](-2)^2 - 4 * 3 * (-2)[/tex]

4 - 4 * 3 * (-2)

Multiplying -4 and 3 gives us -12, so the expression becomes:

4 - (-12) * (-2)

Multiplying -12 and -2 gives us 24, so the expression further simplifies to:

4 + 24

Adding 4 and 24 together yields:

28

Therefore, when a = 3 and b = -2, the value of the expression b² - 4ab is 28

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Your question seems incomplete, the probable complete question is:

Using quadratic formula, Evaluate b²-4ab when a= 3, b = -2

Answer:

Step-by-step explanation:

speed= distance/time taken

45=300/t

t=300/45

t=6.7

from 18:00 to 12:00, it's 6hours

so mark won't be on time

Since we do not know the value of u, we cannot find the time taken by the basketball to travel a distance of 8.5 meters. We cannot find the height of the basketball at its highest point.

Given that n(x) = 3 for 8 < x < 8.5.It is impossible to determine whether the shot will be made or not based solely on this information. Winning the playoffs depends on various factors, such as the score, time remaining, and the overall performance of the team.

Therefore, additional information is required to determine the outcome of the playoffs.However, to find the height of the basketball at its highest point, we need to know the equation of the trajectory of the basketball.

Assuming that the basketball follows a parabolic path, we can use the formula:

y = ax² + bx + c,

where y is the height of the basketball, and x is the horizontal distance traveled by the basketball.

To find the values of a, b, and c, we need to know three points on the trajectory of the basketball. Let's assume that the basketball is thrown from a height of 1.5 meters and lands on the floor after traveling a horizontal distance of 8.5 meters.

Therefore, the points on the trajectory of the basketball are:

(0, 1.5), (8.5/2, h), and (8.5, 0),

where h is the height of the basketball at its highest point.Substituting these values in the equation of the trajectory,

we get:

1.5 = a(0)² + b(0) + c...(1)0 = a(8.5)² + b(8.5) + c...(2)h = a(8.5/2)² + b(8.5/2) + c...(3)

Simplifying equations (1) and (2),

we get:

c = 1.5...(4)b = -a(8.5)²/8.5...(5)

Substituting equation (4) in equation (3), we get:

h = a(8.5/2)² + b(8.5/2) + 1.5h = a(8.5/2)² - a(8.5)²/8.5 + 1.5h = -29.375a + 1.5

Substituting the value of a from equation (5) in the above equation,

we get:

h = -29.375(-a(8.5)²/8.5) + 1.5h = 0.5a(8.5)² + 1.5

Therefore, to find the height of the basketball at its highest point, we need to find the value of a. Since we know that the basketball lands on the floor after traveling a horizontal distance of 8.5 meters,

we can use the formula:

x = ut + 0.5at²,

where u is the initial horizontal velocity of the basketball, and t is the time taken by the basketball to travel a distance of 8.5 meters.

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