A path is 2.5 kilometers long. Joseph's estimate of the length of the path has an 8% error. His estimate is greater than the actual length of the path. What is his estimate?​

The area of the region enclosed by one loop of the curve r = sin(10θ) is π/40.

We have to find the area of the region enclosed by one loop of the curve.

The given curve is:

r = sin(10θ)

Consider the region r = sin(10θ)

The area of region bounded by the curve r = f(θ) in the sector a ≤ θ ≤ b is

A = \(\int^{b}_{a}\frac{1}{2}r^2d\theta\)

Now to find the area of the region enclosed by one loop of the curve, we have to find the limit by setting r=0.

sin(10θ) = 0

sin(10θ) = sin0   or    sin(10θ) = sinπ

So θ = 0             or      θ = π/10

Hence, the limit of θ is 0 ≤ θ ≤ π/10.

Now the area of the required region is

A = \(\int^{\pi/10}_{0}\frac{1}{2}(\sin10\theta)^2d\theta\)

A = \(\frac{1}{2}\int^{\pi/10}_{0}\sin^{2}10\theta d\theta\)

A = \(\frac{1}{2}\int^{\pi/10}_{0}\frac{(1-\cos20\theta)}{2}d\theta\)

A = \(\frac{1}{4}\int^{\pi/10}_{0}(1-\cos20\theta)d\theta\)

A = \(\frac{1}{4}\left[(\theta-\frac{1}{20}\sin20\theta)\right]^{\pi/10}_{0}\)

A = \(\frac{1}{4}\left[(\frac{\pi}{10}-\frac{1}{20}\sin20\frac{\pi}{10})-(0-\frac{1}{20}\sin20\cdot0)\right]\)

A = \(\frac{1}{4}\left[(\frac{\pi}{10}-\frac{1}{20}\sin2\pi)-(0-\sin0)\right]\)

A = 1/4[(π/10-0)-(0-0)]

A = 1/4(π/10)

A = π/40

Hence, the area of the region enclosed by one loop of the curve r = sin(10θ) is π/40.

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Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.

To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.

Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.

Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:

Total distance = 8t + 6t

We want to find the time when this total distance equals 21 km:

8t + 6t = 21

Combining like terms, we have:

14t = 21

To solve for t, we divide both sides of the equation by 14:

t = 21 / 14

Simplifying, we find:

t = 3 / 2

So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.

Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.

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a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

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The answer to the given question is option c) The blocks in this design are the four different litters.

In a block design, the experimental units are grouped into homogeneous sets or blocks based on one or more characteristics that are expected to affect the response variable. The purpose of blocking is to reduce the variability of the response variable by reducing the differences between the experimental units within each block. In this experiment, the four different litters are the blocks. The pigs within each litter are expected to be more similar to each other than to pigs from other litters, so the blocks will reduce the variability of the response variable (e.g. weight gain, feed consumption) by accounting for the differences between the litters. The three different dietary supplements are the treatments that are being compared, and the 24 identical pens are the locations where the treatments are applied.

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Answer:

- is the answers for the question

Step-by-step explanation:

please mark me as brainlest

By making and solving equations we know that the children's ticket costs $72.91 each and adult tickets cost $110.8 each.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

So, solve as follows:

31c + 28a = 842 ...(1)

26c + 28a = 792 ...(2)

Now,

31c  = 842 - 28a

c = 842 - 28a/31

Then,

26c + 28a = 792

26(842 - 28a/31) + 28a = 792

26(842 - 28a) + 28a = 24,552

21,892 - 52a + 28a = 24,552

21,892 - 24a = 24,552

24a = 24,552 - 21,892

24a = 2,660

a = 110.8

Now,

31c + 28a = 842

31c + 28(110.8) = 842

31c + 3,102.4 = 842

31c = 842 - 3,102.4

31c = 2,260.4

c = 72.91

Therefore, by making and solving equations we know that the children's ticket costs $72.91 each and adult tickets cost $110.8 each.

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

Tewanda reads 162 words per minute

Step-by-step explanation:

To find the unit rate of how fast Tewanda reads:

1458/9 = 162

Tewanda reads 162 words per minute

Referring to Table 3.1, if the government imposes a price of $3, a shortage will result.

To determine the outcome when the government imposes a price of $3, we need to compare the quantity demanded and quantity supplied at this price level.
According to Table 3.1, at a price of $3, the quantity demanded is 30 units, while the quantity supplied is 40 units. The quantity demanded (30 units) is less than the quantity supplied (40 units), resulting in a situation known as a shortage.
A shortage occurs when the quantity demanded exceeds the quantity supplied at a given price. In this case, a shortage of 10 units occurs because consumers are willing to buy more than what producers are offering at the price of $3.
To summarize, if the government imposes a price of $3 based on Table 3.1, a shortage will result. This means that the quantity demanded exceeds the quantity supplied at the given price, indicating that consumers are unable to purchase all the units they desire.

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 the complete question is:

Table 3.1
Quantity Demanded.
Price per Unit
Quantity supplied
10
$5
50
20
30
$4
$3
40
30
40
50
$2
$1
20
10
Refer to Table 3.1. If the government imposes a price of $3.
a shortage will result.
Market is in equilibrium.
the price will fall to $1 because producers will be forced to incur losses.
a surplus will result.

well, the decrease is 2 bucks, hmmm if we take 20 to be the 100%, how much is 2 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 20 & 100\\ 2& x \end{array} \implies \cfrac{20}{2}=\cfrac{100}{x} \\\\\\ 10=\cfrac{100}{x}\implies 10x=100\implies x=\cfrac{100}{10}\implies x=10\)

A z-score of -2.5 means that a score is located 2.5 standard deviations to the left of the mean.

A z-score is a measure of how many standard deviations a data point is away from the mean of a distribution. It helps in understanding the relative position of a particular value within a dataset. When a z-score is negative, it indicates that the data point is located to the left of the mean.

In the case of a z-score of -2.5, it means that the score is located 2.5 standard deviations to the left of the mean. This implies that the value is significantly lower than the mean. Since the z-score is negative, it indicates that the data point falls below the mean value in the distribution.

In a standard normal distribution, where the mean is 0 and the standard deviation is 1, a z-score of -2.5 indicates that the data point is located 2.5 standard deviations below the mean. This implies that the score is relatively low compared to the average value in the distribution. The negative sign signifies that the data point is to the left, or below, the mean.

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Answer:

x = 10.8

y = 11.2

Step-by-step explanation:

AB : AP = AC : AQ

5 :(5+9) = 6 : (6+x)

5: 14 = 6 :(6+x)

5(6+x) = 14*6

30 + 5x = 84

5x = 54

x = 10.8

AB : AP = BC :PQ

5 :14 = 4 : y

5y = 14*4

y = 11.2

Jeremy have the fastest speed of 10.16 m/s while Tim and Martin had a speed of 7.62 m/s and 5.83 m/s respectively

An equation is an expression that shows the relationship between two or more numbers and variables.

Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.

1 yard = 0.9144 m, hence 100 yard = 91.44 m

1 ft = 0.3048 m, hence 400 ft = 121.92 m

Tim speed = 91.44 m / 12 s = 7.62 m/s

Jeremy speed = 121.92 m / 12 s = 10.16 m/s

Martin speed = 70 m / 12 s = 5.83 m/s

Jeremy have the fastest speed of 10.16 m/s while Tim and Martin had a speed of 7.62 m/s and 5.83 m/s respectively

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Answer:

x = 2.25

Step-by-step explanation:

     Let us turn these diagram pictures into mathematical expressions so we can solve easier.

           On the left side,

                 -3x + 10

           On the right side,

                  5x - 8

     Now we see, in the middle, they are equal to each other. We will set the two expressions equal and solve for x.

-3x + 10 = 5x - 8

10 = 8x - 8

18 = 8x

2.25 = x

x = 2.25

Answer:

3.3

Step-by-step explanation:

hope this help

Answer:

There's no picture attached

Step-by-step explanation:

The number of pounds of cotton candy are consumed by a 12 year old is 120,000Ib

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious.

In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

Multiplication Formula

The multiplication formula is given by:

Multiplier × Multiplicand = Product

From the given information, 10,000 pounds of cotton candy are consumed each year.

Then, the number of pounds of cotton candy are consumed by a 12 year old is 10,000*12=120,000.

Thus, the correct option is e 120000 Ib

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The  volume of the largest right circular cone that can be inscribed in a sphere of radius r is  8/27 (volume of sphere)

Let r serve as the foundation. the volume of the area, and radius x is the separation between the base and the sphere's center. Height h of the cone = R + x

∴    V= 1/3πr² h= π/ 3 (R² −x²)(R + x)

       = π/3​ (R² + R² x − Rx² −x² )

∴   dV/ dx​ = π​ /3 [R²−2Rx−3x² ]

  d²V/ dx²​ = π/3​ [−2R−6x]

For max or min V dV/dx​ =0

∴   R² −2Rx−3x² =0

⇒(R + x)(x−3x)=0    

2) x=−R, x​/3 but x = −R

When x= R/3 d² V/dx² <0  V is max only when x= R/3

​∴   Max V= 1/3π(R² − R²/9 )(R+ R/3 )

= 32πR³/81

= 8/27 ( 4/3 πR³)

= 8/27 (volume of sphere)

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The dimensions of the largest wall area needed would be: sqrt(11 + x) by sqrt(11 + x)

If we were to use 11 of the 1 ft-by-1 ft units, the total area covered would be 11 square feet. To determine the largest wall area needed, we would need to know the dimensions of the remaining units. Assuming that the other units are also 1 ft-by-1 ft, we can calculate the total area of the wall by adding the areas of all the units. This would be 11 square feet (for the 11 units) plus the area of the remain+ing units. If we assume that there are x number of remaining units, then the total wall area needed would be:

11 + x square feet

To find the largest wall area needed, we would need to find the largest possible value for x. If we assume that the wall is rectangular in shape, then we can use the formula for the area of a rectangle:

A = l x w

where A is the area, l is the length, and w is the width. We know that the area needed is 11 + x, so we can set this equal to the formula for the area of a rectangle:

11 + x = l x w

We can then solve for x by rearranging the equation:

x = l x w - 11

Since we want to find the largest possible value for x, we want to maximize the product l x w. This can be done by setting l and w equal to each other (i.e. making the rectangle a square). Therefore, the dimensions of the largest wall area needed would be:

sqrt(11 + x) by sqrt(11 + x)

where x is the largest possible value that satisfies the equation:

x = l x w - 11

In summary, the dimensions of the largest wall area needed would be a square with side length equal to the square root of 11 plus the largest possible value for the area of the remaining units.

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Answer:

Shop B has a better value for their baked beans.

Step-by-step explanation:

Shop A:

5 kg = 5.65

1 kg = 5.65 / 5

= 1.13 pence

Shop B:

2 kg = 2.02

1 kg = 2.02 / 2

= 1.01 pence

Answer:

7, 5, 1, 3

Step-by-step explanation:

Hope this Helps!

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Answer:

oof u alone kid

Step-by-step explanation:

The Normal probability distribution function is left-skewed, right-skewed, or symmetric depending on the values of the variance and the standard deviation might the mean of a probability distribution for a discrete random variable be less than (or greater than) the average of possible values.

A probability distribution is a mathematical function that describes the probabilities of different possible values ​​of a variable. Probability distributions are often represented using graphs or probability tables.

Probability distributions are called discrete probability distributions, and the set of outcomes is inherently discrete. For example, if you roll a die, all possible outcomes are discrete and you get a large number of outcomes. Also called probability mass function.

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There are 30 ways to seat six people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors.

To solve this problem, we need to use the formula for circular permutations, which is (n-1)! where n is the number of objects to be arranged in a circle. In this case, there are 6 people to be seated around a circular table, so the formula becomes (6-1)! = 5!.

However, we need to adjust this formula to account for the fact that two seatings are considered the same when everyone has the same two neighbors, regardless of whether they are right or left neighbors. To do this, we divide the result of the circular permutation by 2, since each seating has two possible orientations.

So the final answer is (5!)/2 = 60/2 = 30. There are 30 ways to seat six people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors.

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The points will  meet x when it is folded are C or E

A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.

Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.

Given that,

A green colored Net,

After folding x point will  meet the points = ?

When we start folding,

First step,

Side ABCD and DEFG will be folded,

C and E will meet with each other

Second Step,

Side ABCD and AGHI will be folded,

B and I will meet with each other

Third step,

Side DEFG and AGHI will be folded,

F and H will meet each other

Fourth step,

Upper portion AHI will cover the upper portion BCF of the box

X will at position of C or E

Hence, the X will meet C or E

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Answer:

$11, $13, $14

Step-by-step explanation:

all of those answers are greater than $9 but less than or equal to $14.

The number of late insurance claim payouts per 100 should be measured with a p-chart. Therefore, the correct option is (e) p-chart.

A p-chart is a type of control chart used to monitor the proportion of nonconforming items in a sample, where nonconforming items are those that do not meet a certain quality standard or specification. In this case, the proportion of late insurance claim payouts would be the proportion of nonconforming items.

A p-chart is appropriate when the sample size is constant and the number of nonconforming items per sample can be either small or large. It is used to monitor the stability of a process and to detect any changes or shifts in the proportion of nonconforming items over time.

An X-bar chart and R-chart are used to monitor the mean and variability of a continuous variable, respectively, and would not be appropriate for measuring the number of nonconforming items.

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Answer:

------------------------------

Answer:

x = 39

Step-by-step explanation:

The equation is,

→ (x - 4)/5 - (x + 1)/6 = 1/3

Now the value of x will be,

→ (x - 4)/5 - (x + 1)/6 = 1/3

→ 6(x - 4)/30 - 5(x + 1)/30 = 1/3

→ (6x - 24)/30 - (5x + 5)/30 = 1/3

→ (6x - 24 - 5x - 5)/30 = 1/3

→ x - 29 = (1/3) × 30

→ x - 29 = 30/3

→ x = 10 + 29

→ [ x = 39 ]

Hence, the value of x is 39.

Answer:

26 red marbles

Step-by-step explanation:

52 marbles x 50% = 26

Answer:

26

Step-by-step explanation:

50/100=1/2

1/2*52 = 1*52=52

52/2=26