Using the graph, determine the coordinates of the y-intercept of the parabola.

The solution to the IVP given by y''+y=t, y(0)=1, y'(0)=-2 is y(t) = cos(t) - (3/2) sin(t) + (1/2) t.

To solve the Initial Value Problem, we can use the method of undetermined coefficients, which involves assuming a particular form for the solution to the non-homogeneous equation y'' + y = t, and then finding the coefficients of the terms in that form by substituting it back into the equation.

First, we find the general solution to the homogeneous equation y'' + y = 0

The characteristic equation is r² + 1 = 0, which has solutions r = ±i. Therefore, the general solution to the homogeneous equation is

y_h(t) = c₁ cos(t) + c₂ sin(t),

where c₁ and c₂ are constants determined by the initial conditions.

Next, we assume a particular form for the non-homogeneous solution, based on the form of the right-hand side t. Since t is a linear function, we assume that the particular solution has the form

y_p(t) = a t + b.

Substituting this into the differential equation, we get

y''_p + y_p = t

2a + (at+b) = t.

Equating coefficients, we get

a = 1/2, b = 0.

Therefore, the particular solution is

y_p(t) = (1/2) t.

The general solution to the non-homogeneous equation is then the sum of the homogeneous and particular solutions

y(t) = y_h(t) + y_p(t)

= c₁ cos(t) + c₂ sin(t) + (1/2) t.

To determine the constants c₁ and c₂, we use the initial conditions:

y(0) = c₁ cos(0) + c₂ sin(0) + (1/2) (0) = c₁ = 1,

y'(0) = -c₁ sin(0) + c₂ cos(0) + (1/2) (1) = c₂ - (1/2) = -2,

so c₂ = -3/2.

Therefore, the solution to the IVP is

y(t) = cos(t) - (3/2) sin(t) + (1/2) t.

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Answer:

Step-by-step explanation:

Find the area of the circle with a circumference of

. Write your solution in terms of

.

Area in terms of

: ______

Thus, the correct Percent response is B) 79%.

Percentage refers to a portion of every hundred. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, it is frequently shown using the percent sign, "%".

If you have 100 apples and distribute 10 of them, for instance, you have distributed 10% of your total apple supply.

We deduct Ms. Yamato's deductions from her gross income to determine her take-home pay:

$2644 - $548.30 = $2095.702.

By dividing her take-home pay by her gross pay and multiplying the result by 100%, we can determine what proportion of her gross pay is taken home:

($2095.70 / $2644) * 100% = 79%

Thus, the correct response is B) 79%.

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Sue works 5 out of 7 days a week, which implies that she has two days off. We need to discover how numerous conceivable plans there are for her to work on Tuesday or Friday or both.

There are two cases to consider:

1. Sue works on Tuesday as it were, Friday as it were, or both Tuesday and Friday.

2. Sue does not work on Tuesday or Friday.

For the primary case, there are three conceivable outcomes:

1. Sue works on Tuesday as it were and has Friday off.

2. Sue works on Friday as it were and has Tuesday off.

3. Sue works on both Tuesdays and Fridays.

For the moment case, there are two conceivable outcomes:

1. Sue works on one of the other 5 days of the week and has both Tuesday and Friday off.

2. Sue has Tuesday and Friday off.

In this manner, there are added up to 3 + 2 = 5 conceivable plans for Sue to work on Tuesday or Friday or both. 

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The volume of water in the tank won't be enough for the fish.

A cuboid is a solid shape or a three-dimensional shape. The volume of a cuboid is expressed as;

V = l×w× h

where l is the length, w is the width and h is the height.

The volume of water needed by the fish is 700,000× 1litre = 700,000 litres.

The volume of water the tank can occupy is

V = l× b× h

V = 80× 1200× 70

V = 6,720,000cm³

in litres ;

V = 6,720,000/1000

V = 6720litres

therefore the volume water in the tank is not enough for the fish

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The Probability that a student will complete the exam 0.2676.

The probability of completing the exam in one hour or less is:

[tex]P (x < 60)[/tex]

= [tex]P (z < (60-83)/13)[/tex]

=[tex]P (z < -1.77)[/tex]

= 0.0384.

The probability that a student will complete the exam in more than 60 minutes, but less than 75 minutes is.

[tex]P (60 < x < 75)[/tex]

= [tex]P (x < 75)-P (x < 60)[/tex]

Now,

[tex]P (x < 75)[/tex]

=[tex]P (z < (75-83)/13)[/tex]

= [tex]P (z < -0.62)[/tex]

=0.2676.

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The theorem is shown in a pythagoras theorem is c² = a² + b²

The theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.

The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Mathematically, we can express this as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.

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The equation with the new substitutions and conversion factor is a'B'T' = (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2)*a^6/6 where k is (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2) The intercept value of the log-log graph would have been -1.108.

Starting with Equation 4: T = ka^6/6, we can substitute a = (d/k)^(1/6) and b = (2/3)^(1/2) * (d/k)^(1/3) to get

T = k[(d/k)^(1/6)]^6/6

T = k(d/k)^(1/2)/6

T = (k^(1/2)/6) * d^(1/2)

Now we can rearrange the equation so that a, b, and t are on the left side

a'B'T' = ka^6/6

(a/d)^(1/6) * b^(2/3) * T' = k[(a/d)^(1/6)]^6/6 * T'

(a/d)^(1/6) * (2/3)^(1/2) * (d/k)^(1/3) * T' = (k^(1/2)/6) * d^(1/2) * T'

(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3) * T' = (k^(1/2)/6) * d^(1/2) * T'

(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3) = k^(1/2)/6

k = [(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3)]^2/6

k = (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2)

With this new conversion factor, the intercept of the log-log graph would have changed. The intercept represents the value of T when a = 1 (since log(1) = 0). Using the new conversion factor, we have

T = (1/6) * (2/3)^(1/3) * d^(1/2) * a^(1/3)

T = (1/6) * (2/3)^(1/3) * d^(1/2)

log(T) = log[(1/6) * (2/3)^(1/3) * d^(1/2)]

log(T) = log(1/6) + log[(2/3)^(1/3)] + log(d^(1/2))

log(T) = log(1/6) + (1/3) * log(2/3) + (1/2) * log(d)

So the intercept of the log-log graph would be log(1/6) + (1/3) * log(2/3) = -1.108, assuming that d is held constant. This intercept represents the value of log(T) when log(a) = 0, or when a = 1. In other words, when a = 1, the predicted value of T would be 0.162 (or 16.2% of its maximum value).

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--The given question is incomplete, the complete question is given

" Plug the two substitutions into Equation 4 (T = ka^6/6)). Rearrange the equation so that a, b,t are on the left side of the equation and d remains on the right side, e.g. a'B'T' = ka^6/6 you will figure out what the "k" if you used this version of the equation (including your new conversion factor, how would this have changed the intercept of your log-log graph? what would its value have been?"--

Answer:

Yo wassup bro, at this computer factory, they be making two types of computers, laptops and desktops. They churn out 70 laptops a day and 55 desktops a day. They got a total of 14 machines to make these computers. And they make a total of 905 computers a day. We gotta figure out how many machines are making laptops and how many are making desktops, ya know?

Alright, let's set up a system of equations to solve this. Let's call the number of machines making laptops "x" and the number of machines making desktops "y".

So, we got two equations here:

The total number of computers they make in a day is 905, so we can write: x laptops + y desktops = 905.

They got a total of 14 machines, so we can write: x + y = 14.

Now, let's solve this system of equations to find the values of x and y, man. Once we got those, we'll know how many machines are making laptops and how many are making desktops at this computer factory, yo!

The most appropriate response to the claim would be: "At the 95% confidence level, the mean exercise time of all students might not be 10 hours per week based on the sample data."

Based on the given data, we can see that the sample mean exercise time is 7.8133 hours per week. The standard deviation of the exercise time is 5.8032, indicating that there is some variability in the data.

To determine whether the claim that the mean exercise time of all students is 10 hours per week is reasonable, we can conduct a hypothesis test.

Our null hypothesis would be that the mean exercise time of all students is equal to 10 hours per week, and the alternative hypothesis would be that the mean exercise time is different from 10 hours per week.

We can then calculate a test statistic and compare it to a critical value based on a t-distribution with n-1 degrees of freedom, where n is the sample size.

Alternatively, we can use the confidence interval provided in the table to make a statement about the claim.

We can see that the 95% confidence interval for the mean exercise time is [7.0769, 8.5497]. Since 10 is outside of this interval, we can say that at the 95% confidence level, the claim that the mean exercise time of all students is 10 hours per week is not supported by the data.

Therefore, the most appropriate response to the claim would be: "At the 95% confidence level, the mean exercise time of all students might not be 10 hours per week based on the sample data."

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Scenic Cinemas should offer discounted weekday matinee showings for seniors and continue to focus on weekend showings for their broader audience.

Based on the survey results, it would be wise for Scenic Cinemas to tailor their offerings to accommodate both preferences.

One option would be to offer discounted weekday matinee showings targeted toward seniors. This could incentivize them to visit on weekdays while also offering them a more affordable option. At the same time, Scenic Cinemas could continue to focus on weekend showings to cater to their broader audience.

Another approach would be to offer more diverse programming during the weekdays, such as classic films or independent movies that may appeal more to seniors. This could create a niche for Scenic Cinemas and attract a more loyal customer base.

Ultimately, it's important for Scenic Cinemas to balance the needs of their different audience segments to maximize revenue and customer satisfaction. By offering targeted promotions and programming, they can ensure that both seniors and other moviegoers feel valued and have a reason to visit the theatre.

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The scale factor of the dilation must be greater than 1. if the image A'B'C' is bigger than the preimage ABC

If the image A'B'C' is bigger than the preimage ABC, then the scale factor of the dilation must be greater than 1.

In other words, the length of any segment in the image is larger than the corresponding segment in the preimage by the same factor.

Since D is the center of the dilation, we can use the ratio of the corresponding side lengths of the image and preimage triangles to find the scale factor.

For example, if we want to find the scale factor for A', we can use:

scale factor = B'C'/BC

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I'm sorry, but I cannot provide a definitive answer to your question as I do not have access to the table you are referring to.

However, in general, to find the price per spool of each kind of thread, you would need to know the total price of the package and the number of spools in the package.

To calculate the price per spool, you would divide the total price of the package by the number of spools in the package. For example, if a package costs $10 and contains 50 spools of thread, the price per spool would be $0.20 ($10 ÷ 50 = $0.20).

You can use this method to find the price per spool for each type of thread in the table you are looking at.

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The cardholder will pay an additional $1,471.66 in interest by making monthly payments of $200 until the balance is paid off instead of paying off the current balance in full.

First, we need to calculate the total interest that will accrue on the current balance of $4,528.34. We can do this using the formula

Interest = Balance x (APR/12)

where APR is the annual percentage rate and is divided by 12 to get the monthly interest rate. Plugging in the values, we get:

credit card Interest = $4,528.34 x (22.99%/12) = $87.80

So the total interest that will accrue on the current balance is $87.80.

Next, we need to calculate how long it will take to pay off the balance by making monthly payments of $200. We can use a credit card repayment calculator to do this, but we'll use a simplified formula here

Months = -log(1 - (Balance x (APR/12))/Payment) / log(1 + (APR/12))

where Payment is the monthly payment amount. Plugging in the values, we get

Months = -log(1 - ($4,528.34 x (22.99%/12))/$200) / log(1 + (22.99%/12)) = 29.6 months

So it will take about 30 months (or 2.5 years) to pay off the balance by making monthly payments of $200.

Finally, we can calculate how much more the cardholder will pay in total by subtracting the current balance from the total amount paid over 30 months

Total amount paid = $200 x 30 = $6,000

Total interest paid = $6,000 - $4,528.34 = $1,471.66

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The answer is B

The internal angles of a triangle have to be 180

IN ΔABC, m∠A=70° and m∠B=35°.

70°+35°+x=180°

105°+x=180°

x=180°-105°

x=75°

Answer B meets the requirements because in ΔPQR m∠P=70° and m∠R=75°

70°+75°+x=180°

145°+x=180°

x=180°-145°

x=35°

The angles of both triangles measure the same

∠A = ∠C in trapezoid ABCD with arcAB = arcCD, can be proven with the property of isosceles triangles.

Since arcAB = arcCD, the lengths of the two arcs are equal. This implies that the lengths of the segments subtended by these arcs, AB and CD, are also equal.

Let E and F be the midpoints of the non-parallel sides AD and BC, respectively. Connect E and F with a line segment EF.

Since E and F are midpoints, DE = EA and BF = FC. In addition, since AB = CD = L, we can say that:

DE + EA = BF + FC

EA = FC

So, by the Hypotenuse-Leg (HL) theorem of congruence, triangles AEF and CFE are congruent:

ΔAEF ≅ ΔCFE

Now, since the triangles are congruent, their corresponding angles are equal:

∠A = ∠C

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Answer:

To find the greatest possible value of x + y, we need to maximize the values of x and y such that they are still positive integers and satisfy the given equation 18x + 11y = 2020.

We can start by rearranging the equation to solve for y:

11y = 2020 - 18x

y = (2020 - 18x)/11

For y to be a positive integer, 2020 - 18x must be divisible by 11. We can test values of x starting from x = 1 and increasing by 1 until we find the largest possible value of x that satisfies this condition.

When x = 1, 2020 - 18x = 2002, which is divisible by 11. This gives us a value of y = 182/11, which is not a positive integer.

When x = 2, 2020 - 18x = 1984, which is divisible by 11. This gives us a value of y = 180/11, which is not a positive integer.

When x = 3, 2020 - 18x = 1966, which is divisible by 11. This gives us a value of y = 178/11, which is not a positive integer.

When x = 4, 2020 - 18x = 1948, which is divisible by 11. This gives us a value of y = 176/11, which is not a positive integer.

When x = 5, 2020 - 18x = 1930, which is divisible by 11. This gives us a value of y = 174/11, which is not a positive integer.

When x = 6, 2020 - 18x = 1912, which is divisible by 11. This gives us a value of y = 172/11, which is not a positive integer.

When x = 7, 2020 - 18x = 1894, which is divisible by 11. This gives us a value of y = 170/11, which is not a positive integer.

When x = 8, 2020 - 18x = 1876, which is divisible by 11. This gives us a value of y = 168/11, which is not a positive integer.

When x = 9, 2020 - 18x = 1858, which is divisible by 11. This gives us a value of y = 166/11, which is not a positive integer.

When x = 10, 2020 - 18x = 1840, which is divisible by 11. This gives us a value of y = 164/11, which is not a positive integer.

When x = 11, 2020 - 18x = 1822, which is divisible by 11. This gives us a value of y = 162/11, which is not a positive integer.

When x = 12, 2020 - 18x = 1804, which is divisible by 11. This gives us a value of y = 160/11, which is not a positive integer.

When x = 13, 2020 - 18x = 1786, which is divisible by 11. This gives us a value of y = 158/11, which is not a positive integer.

When x = 14, 2020 - 18x = 1768, which is divisible by 11. This gives us a value of y = 156/11, which is not a positive integer.

When x = 15, 2020 - 18x = 1750, which is divisible by 11. This gives us a value of y = 154/11, which is not a positive integer.

When x = 16, 2020 - 18x = 1732, which is divisible by 11. This gives us a value of y = 152/11, which is not a positive integer.

When x = 17, 2020 - 18x = 1714, which is divisible by 11. This gives us a value of y = 150/11, which is not a positive integer.

When x = 18, 2020 - 18x = 1696, which is divisible by 11. This gives us a value of y = 148/11, which is not a positive integer.

When x = 19, 2020 - 18x = 1678, which is divisible by 11. This gives us a value of y = 146/11, which is not a positive integer.

When x = 20, 2020 - 18x = 1660, which is divisible by 11. This gives us a value of y = 144

Answer:

Harry can buy 5 gallons of lemonade and 5 gallons of iced tea and still have $1.50 left over from his original $24 dollar budget

Step-by-step explanation:

Answer:

Step-by-step explanation:

Graph #          Matching equation

1                             |-3x|

2                            |-x|

3                           -|2x|

You can tell which one matches by finding the slope and whether the V points up or down

Step-by-step explanation:

4^-3   =   1/4^3   =   1/64

Answer:

  $9.50

Step-by-step explanation:

You want Suzie's hourly rate on Saturday if she babysat for 3.5 hours on Friday, earning 8.50 per hour, and for 4.5 hours on Saturday, earning a total of 72.50 from both jobs.

For (hours, rates) of (h1, r1) and (h2, r2), Suzie's total earnings for the two jobs are ...

  earnings = h1·r1 +h2·r2

Filling in the known values, we can find r2:

  72.50 = 3.5·8.50 +4.5·r2

  72.50 = 29.75 +4.5·r2 . . . . . . . simplify

  42.75 = 4.5·r2 . . . . . . . . . . . subtract 29.75

  9.50 = r2 . . . . . . . . . . . . divide by 4.5

Suzie earned $9.50 per hour on Saturday.

__

Additional comment

The steps of the "multistep" problem are ...

Effectively, these are the steps to solving the equation we wrote.

Thus, the appropriate measure of variability found for the given data is 10.

The difference here between maximum and smallest values in a data set is known as the range. Utilizing the exact same units as the data, it measures variability. More variability is shown by larger values.

Given length of ribbons:

3, 6, 9, 11, 12, 13

Minimum value = 3

Maximum value = 13

Actually, the range, which is determined by deducting the lowest value from the greatest value in the dataset, would be the proper measure of variability for this data.

Range = Maximum value - Minimum value

Range = 13 - 3

Range = 10

Thus, the appropriate measure of variability found for the given data is 10.

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The number of bacteria after 5 hours is approximately 1013.8.

We can use the formula for exponential growth to solve this problem. If a population grows at a rate proportional to its size, then we can writ

N(t) = N₀ × e^(rt),

where N(t) is the size of the population at time t, N₀ is the initial size of the population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.

We know that the culture starts with 40 bacteria, so N₀ = 40. We also know that after 2 hours, the size of the population is 180. We can use this information to solve for r:

180 = 40 × e^(2r)

180/40 = e^(2r)

ln(180/40) = 2r

r = ln(180/40)/2

r ≈ 0.6931

Now we can use the formula to find the size of the population after 5 hours:

N(5) = 40 × e^(0.6931×5)

N(5) ≈ 1013.8

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The volume of this sphere is equal to 4,000 cm³.

In Mathematics and Geometry, the volume of a sphere can be calculated by using this mathematical equation (formula):

Volume of a sphere = 4/3 × πr³

Where:

r represents the radius.

Note: Radius = diameter/2 = 20/2 = 10 cm.

By substituting the given parameters into the formula for the volume of a sphere, we have the following;

Volume of a sphere = 4/3 × 3 × (10)³

Volume of a sphere = 4 × 1000

Volume of a sphere = 4,000 cm³

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The sample space are:

{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}

The favorable outcomes care:

{RS, RT, SR, ST, TR, TS}

The probability is  0.3 or 30%

Part A:

The sample space represents all possible outcomes that can occur when two cards are randomly selected without replacement from the given pile of cards.

The sample space can be represented as follows:

{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}

Part B:

The favorable outcomes are those outcomes in which both cards are consonants. In this case, the consonants are R, S, and T.

The favorable outcomes can be represented as follows:

{RS, RT, SR, ST, TR, TS}

Part C:

To calculate the probability of selecting 2 cards that are consonants, we need to find the ratio of favorable outcomes to the sample space.

The number of favorable outcomes is 6, and the size of the sample space is 20.

Therefore, the probability of selecting 2 cards that are consonants is:

P(consonants) = favorable outcomes / sample space

P(consonants) = 6 / 20

P(consonants) = 0.3 or 30%

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More people that rode the roller coaster are between the ages of 11 and 30, than people that are between the ages of 41 and 60 is the best description of the data which is obtained by using the arithmetic operations.

What are arithmetic operations?

Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." Operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference in mathematics.

We are given a chart. From the chart we get the following data:

Number of people aged 11 - 20 riding roller coaster = 20

Number of people aged 21 - 30 riding roller coaster = 15

Number of people aged 31 - 40 riding roller coaster = 10

Number of people aged 41 - 50 riding roller coaster = 5

Number of people aged 51 - 60 riding roller coaster = 0

Using addition operation, we get

Total people = 20 + 15 + 10 + 5 + 0

Total people = 40

Now,

Total riders between 11 - 30 = 20 + 15

Total riders between 11 - 30 = 35

Similarly,

Total riders between 41 - 60 = 5 + 0

Total riders between 41 - 60 = 5

Hence, the fourth option is the correct answer.

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Answer: Circumference = 18 π cm

Step-by-step explanation:

We can use this formula to find the circumference of a circle:

➜ r is equal to the radius, also known as half the width of a circle.

      C = 2πr

We will substitute our known values and solve for C by multiplying. Since the answer option includes π in our units, we do not multiply this into the 18.

      C = 2πr

      C = 2π(9)

      C = 18 π cm

Answer: 18π

Step-by-step explanation:

The circumference of a circle is equal to 2πr, with r being equal to the radius. The radius of a circle is defined as the length from any point on the circle to its middlemost point. In this case, we are given the value of the radius as defined by the line. The radius equals 9, which we can plug into the equation.

C= 2πr

C = 2π(9)

C = 18π = 56.55

Hope this helps!

The results of the balls in Phillip's bag are:

The mean = 8.

The median = 7.

The mode = blue

The range = 12

The mean (or the average) is the sum of all the values divided by the total number of values. Let's calculate the mean for the given data:

Total number of balls = 8 + 3 + 6 + 3 + 13 + 15 = 48

Mean = (8 + 3 + 6 + 3 + 13 + 15) / 6 = 48 / 6 = 8

Mean = 8.

The median is the middle value when a set of values is arranged in ascending or descending order.

Let's arrange the given data in ascending:

3, 3, 6, 8, 13, 15

As the total number of values is even, the median will be the average of the two middle values, which are 6 and 8.

Median = (6 + 8) / 2 = 7

The median = 7.

The mode is the value that appears most frequently in a set of values. Let's find the mode of the given data:

Red balls: 8

Green balls: 3

Yellow balls: 6

Orange balls: 3

Black balls: 13

Blue balls: 15

Blue balls have the highest frequency (i.e., 15) among all the colors.

The range is the difference between the highest and lowest values in a set of values. Let's find the range of the given data:

Highest value = 15 (blue balls)

Lowest value = 3 (green balls and orange balls)

Range = Highest value - Lowest value = 15 - 3 = 12

Range = 12.

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9. The volume of the triangular pyramid is given by:

V = (1/3)Bh

Here, B is the base area.

The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:

h = sqrt(26.7² - 11.7²) = 23.274 km

The area if the base is:

B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km

Now, the volume is:

V = (1/3)(136.89)(15) = 2053.35 cubic km

Hence, the volume of the triangular pyramid is 2053.35 cubic km.

9. The volume of the triangular pyramid is 2053.35 cubic km. 11. The area of the shaded portion is 348.19 cubic in 13. The slant height of the cone is 8.53 meters.

A fundamental conclusion in geometry relating to the lengths of a right triangle's sides is known as Pythagoras' theorem. According to the theorem, the square of the length of the hypotenuse, the side that faces the right angle, in any right triangle, equals the sum of the squares of the lengths of the other two sides, known as the legs.

9. The volume of the triangular pyramid is given by:

V = (1/3)Bh

Here, B is the base area.

The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:

h = √(26.7² - 11.7²) = 23.274 km

The area if the base is:

B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km

Now, the volume is:

V = (1/3)(136.89)(15) = 2053.35 cubic km

Hence, the volume of the triangular pyramid is 2053.35 cubic km.

11. The volume of a cone is given by:

V = (1/3)πr²h

The dimension of the bigger cone is radius is 9 in, and height 15 in:

V1 = (1/3)π(9 in)²(15 in) = 381.7 cubic in

The dimension of the smaller cone is radius is 4 in, and height 10 in:

V2 = (1/3)π(4 in)²(10 in) = 33.51 cubic in

Now, the area of the shaded portion is:

V1 - V2 = 381.7 - 33.51  = 348.19

13. The volume of a cone is given by:

V = (1/3)πr²h

Substituting the values we have:

542.87 = (1/3)π(6 m)²h

h = 542.87 / [(1/3)π(6 m)²] = 6.05 m

Now, using the Pythagoras Theorem for the slant height we have:

s² = r² + h²

s² = (6 m)² + (6.05 m)²

s² = 72.9

s = √(72.9) = 8.53 m

The slant height of the cone is 8.53 meters.

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