Expanding Expressions: Expand the following expressions.
5 (r +2)
6b (b-2a)
8cd (c-2 +40)

The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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Answer:

30 eggs

Step-by-step explanation:

1 egg makes 3 pancakes so 30 eggs would make 90 pancakes becaue the ratio is 1:3.

To find your answer you could have done 90÷3

An interval variable is one that has numerical values and still makes sense when you average the data values. This type of variable is used in statistics and data analysis to measure continuous data, such as temperature, time, or weight.

Interval variables are based on a scale that has equal distances between each value, meaning that the difference between any two values is consistent throughout the scale.

Interval variables can be used to create meaningful averages or means. The arithmetic mean is a common method used to calculate the average of interval variables. For example, if a researcher is studying the temperature of a city over a month, they can use interval variables to represent the temperature readings. By averaging the temperature readings, the researcher can calculate the mean temperature for the month.

In summary, interval variables are essential in statistics and data analysis because they can be used to measure continuous data and create meaningful averages. They are based on a scale with equal distances between each value and are commonly used in research studies.

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Answer:

1.25 hours  (1 and 1/4 hours)

Step-by-step explanation:

Kiran;s aunt bikes at an average rate of 8 miles/hr.  Assuming it is an average day, we can determine the time it will take her to bike 10 miles by dividng the miles by her average speed:

  (10 miles)/(8 miles/hr)

The miles cancel and the hr comes to the top:

 (10/8) hours or 1.25 hours  1 and 1/4 hours

Kiran's aunt takes 1.25 hours to cover the distance of 10 miles at the average speed of 8 miles per hour.

In unit time, the distance covered by any object is called speed.

In mathematical term, Speed is express as S = D/T,

where S=speed, D=distance, T= time.

Given that,

Distance that Kiran's aunt plans to bike = 10 miles.

The average speed of bike = 8 miles per hour.

To find the time taken by Kiran' aunt to cover 10 miles distance,

Use Formula

Time = Distance / speed

Time = 10 / 8

Time = 1.25

The time taken by Kiran's aunt to cover 10 miles distance is 1.25 hours.

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153 is the smallest integer greater than 1 with the property that it is equal to the sum of the cubes of its digits.

We can approach this problem by testing small integers to see if they satisfy the given property. We know that any integer greater than 1 can be written as a sum of powers of 10. For example, 123 can be written as:

\(1 \times 10^2 + 2 \times10^1 + 3 \times 10^0\)

We can then cube each digit and add them together to see if we get the original number. For example:

\(1^3 + 2^3 + 3^3 = 1 + 8 + 27 = 36\)

So 123 is not the number we're looking for. We can repeat this process for other integers until we find the smallest one that satisfies the property.

After testing a few small integers, we can see that the smallest integer greater than 1 that satisfies the property is 153. We can check this as follows:

\(1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153\)

Therefore, the answer is 153.

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The taylor polynomial of degree n=4 for x near the point a=π for the function cos(x) is P4(x) = −1 + (x−π) − (x−π)^2/2 + (x−π)^3/6 − (x−π)^4/24.

To find the Taylor polynomial of degree 4 for cos(x) near the point a = π, we need to use the Taylor series formula:

cos(x) = ∑(−1)^k/k! (x−π)^k

where we have used the fact that cos(π) = −1 and the Maclaurin series for cos(x):

cos(x) = ∑(−1)^k/(2k)! x^2k.

We can then simplify the formula by only taking the first four terms of the series, as we want the Taylor polynomial of degree 4:

cos(x) ≈ ∑(−1)^k/k! (x−π)^k ≈ −1 + (x−π) − (x−π)^2/2 + (x−π)^3/6 − (x−π)^4/24.

Therefore, the Taylor polynomial of degree 4 for cos(x) near the point a=π is:

P4(x) = −1 + (x−π) − (x−π)^2/2 + (x−π)^3/6 − (x−π)^4/24.

Note that this polynomial is an approximation of cos(x) near x=π and becomes more accurate as x approaches π.

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Answer:

-3x, where x is the number of yards lost on the first play.

Step-by-step explanation:

The percentage of the data that is less than 76.4 will be 50% if scores of an exam follow an approximately bell-shaped distribution with a mean of 76.4 and a standard deviation of 6.1.

To determine by how many standard deviations the raw score is above or below the mean z score used.

z = (x - μ)/σ

x: raw score, σ: standard deviation, μ: mean

For x = 76.4 points:

z = (76.4 - 76.4)/6.1 = 0

Now, the percentage of data is less than 76.4:

P(x < 76.4) = P(z < 0)

We know that the area is equally distributed around the y-axis.

So, P(z<0) = 50 %

Therefore, the percentage of the data is less than 76.4 will be 50%.

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Answer:

Step 1

Step-by-step explanation:

The problem distributed 2 into x and -4 which resulted in 2x - 8

The equation of the line which is perpendicular to this line would be 3x - 2y = 13.

The equation of a parallel line to the line would be 2x + 3y = 0

The slope of the line perpendicular to this would be the negative reciprocal of -2/3, which is 3/2.

So the equation of the perpendicular line is:

y - ( -2 ) = 3/2 (x - 3)

y + 2 = 3/2x - 9/2

2y + 4 = 3x - 9

3x - 2y = 13

The slope of the line parallel to the given line would be equal to the slope of the given line, which is -2/3.

So the equation of the parallel line is:

y - (-2) = -2/3 (x - 3)

y + 2 = -2/3x + 2

y = -2/3x

2x + 3y = 0

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Answer

root 354

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(√19 -√7)(√19 +√7)

( a +b)( a -b) = a²-b²

(√19)² -(√7)² = 19 -7 = 12

The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

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Answer: See below

Step-by-step explanation:

1) For the first question, we have to multiply the width by the length to find the area of the whole rectangle:

(4x-4)(x+1)= 4x^2 -4

2) For the second question, we have to multiply the width by the length to find the area of the shaded area in the rectangle:

(2x+2)(x-1)= 2x^2-2

3) The total area of the unshaded part of the whole triangle equals the area of the whole rectangle minus the shaded area:

4x^2-4 - 2x^2 -2 = 2x^2 - 6

Answer/Step-By-Step Explanation:

A). 4/52 —> 1/13

B). 1/52 (there’s only one Queen of Hearts)

C). 4/52 —> 1/13

D). 8/52 —> 2/13 (cards less than 4 are 2 and 3).

E). 13/52 —> 1/4

F). 8/52 —> 2/13 (probability of choosing a queen is 4/52, probability of a 3 is 4/52).

G). 12/52 —> 3/13

Answer:

Step-by-step explanation:

Whichever one has the greatest area for the cost would be the best value. The area of the first pizza is

\(A =\pi (5)^2\) so

A = 25(3.14) and

A = 78.5 inches squared

Let's find the cost per square inch:

\(\frac{8}{78.5}=.102\) which is just over ten cents per square inch.

For the other pizza:

\(A=\pi (7.5)^2\) so

A = 56.25(3.14) and

A = 176.625 inches squared. Let's find the cost per square inch of this one:

\(\frac{16}{176.625}=.090\) This one costs 9 cents per square inch, so it's the better deal. Not by a whole lot, but a better deal nonetheless.

The 15-inch pizza is a better deal because the unit cost is one costs 9 cents per square inch.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

It is given that:

A 10-inch diameter pizza for $8 or a 15-inch diameter pizza for $16

The area of the pizza with a 10-inch diameter

A = π(10/2)²

A = 25π square inch

A = 78.5 square inch

The cost per square inch = 8/78.5= $0.102 per square inch

(ten cents per square inch)

Similarly for 15-inch pizza:

A = 56.25(3.14)

A = 176.6 square inch

The cost per square inch = 16/176.6 = $0.090 per square inch

(one costs 9 cents per square inch)

Thus, the 15-inch pizza is a better deal because the unit cost is one costs 9 cents per square inch.

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Control limits are based on multiples of the sample statistic's standard deviation, hence the assertion is false that "control limits are based on multiples of the process standard deviation".

A control chart is made up of many different parts. There are two control limitations. The top dashed line represents the upper control limit (UCL), and the bottom dashed line represents the lower control limit (LCL).The solid middle line denotes the statistic's average for the plot.

The horizontal lines known as control limits in a control chart show the upper and lower limits of the acceptable range of results for a process. When plotted data goes over a control limit, a process is out of control and requires management action. The control limits are defined as three standard deviations on either side of the mean.

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Answer:

35

Step-by-step explanation:

i got it  on khan

Answer: 18

Step-by-step explanation: I got it on the Khan test don't trust the first one. ,,ԾㅂԾ,,

The radian measure of angle A is (16/9)π.

To convert degrees to radians, we use the conversion factor:

\(1\ degree = \pi /180\ radians\)

Given that angle A is 320 degrees, we can calculate its radian measure as follows:

Angle A in radians = (320 degrees) * (π/180 radians/degree)

                    = (320π)/180 radians

                    = (16/9)π radians

Therefore, the radian measure of angle A is (16/9)π.

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The graph will show a linear relationship, where the distance increases steadily as time increases.

To complete the table and graph, we need to determine the relationship between distance and time based on the given information.

Given:

Time taken = 5 minutes

Distance travelled = 13 kilometers

Since the distance is proportional to the time taken, we can set up a proportion to find the constant of proportionality:

Distance / Time = Constant

Let's calculate the constant of proportionality:

13 kilometers / 5 minutes = 2.6 kilometers/minute

Now, we can complete the table and graph:

| Time (minutes) | Distance (kilometers) |

|---------------|----------------------|

| 5              | 13                     |

| 10             | 26                    |

| 15             | 39                    |

| 20            | 52                    |

| 25            | 65                    |

To graph the data, we can plot the points (5, 13), (10, 26), (15, 39), (20, 52), and (25, 65) on a coordinate plane with time on the x-axis and distance on the y-axis. Connect the points with a straight line to represent the constant speed of the train.

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Answer:

Your answer is 40√3.

The value of n is 30.33. The thirty-fourth term can be found by solving for the common difference (d) and the number of terms (n) in the arithmetic sequence and then using the formula for the nth term of an arithmetic sequence.

Let's assume that the common ratio of the geometric sequence is r. Then, the terms of the geometric sequence are given by:

\(a_2 = a_1 * ra_{10} = a_1 * r^8a_{34} = a_1 * r^{32}\)

Since these terms also appear in the arithmetic sequence, we can write:

\(a_2 = a_1 + da_{10} = a_1 + 9da_{34} = a_1 + 33d\)

Substituting the expressions for a_2 and a_{10} from the geometric sequence into the arithmetic sequence, we have:

\(a_1 * r = a_1 + da_1 * r^8 = a_1 + 9d\)

Solving for d, we get:

\(d = a_1 * (r - 1)d = a_1 * (r^8 - 1) / 9\)

Next, we use the expression for a_{34} from the arithmetic sequence and substitute the expression for d to obtain:

\(a_{34} = a_1 + 33d = a_1 + 33a_1 * (r^8 - 1) / 9\)

Since the first term of the arithmetic sequence is 1, we have:

\(a_{34} = 1 + 33 * 1 * (r^8 - 1) / 9\)

The value of n can be found by using the formula for the nth term of an arithmetic sequence:

\(a_n = a_1 + (n-1)d\)

Setting n = 34 and substituting the expression for d, we have:

\(a_{34} = 1 + (33) * (a_1 * (r^8 - 1) / 9)\)

So the thirty-fourth term of the arithmetic sequence is:

\(a_{34} = 1 + 33 * (1 * (r^8 - 1) / 9) = 34 - 33/9.\)

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Complete Question:

An arithmetic sequence with first term 1 and common difference not equal to 0 has second, tenth, and thirty-fourth terms that form a geometric sequence.

What is the thirty-fourth term of the arithmetic sequence?

The fourth term in the geometric sequence above appears as the nth term in the arithmetic sequence. Find the value of n.

Answer:

107 is the answers for the question

Step-by-step explanation:

please give me brainlest

The number obtained 9/4 is the reciprocal of the number 4/9.

For the given number.

Divide 1 by 4/9

This can be written as;

= 1/(4/9)

= 9/4

Then, the number obtained 9/4 is the reciprocal of the number 4/9.

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Probability that the first person has an injection-site reaction, but the next two do not is 0.0871 (option C)

The probability that the first person has an injection-site reaction is 11%, or 0.11. The probability that the next two people do not have an injection-site reaction is (89%)^(2), or 0.7921.

The probability that the first person has an injection-site reaction and the next two do not is the product of these probabilities. Therefore, the probability that the first person has an injection-site reaction, but the next two do not is 0.11 * 0.7921 = 0.0871.

Therefore, Probability that the first person has an injection-site reaction, but the next two do not is 0.0871 (option C)

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Answer:

297cm^3π

Step-by-step explanation:

R is a radius of the base of a cone, and r of top surface radius.

V=(1/3)×π×depth×(r^2+r×R+R^2)

V=(1/3)×π×3cm×(3^2+3×4.5×4.5^2)

V=(1/3)×π×3cm×(9cm^2+3cm×4.5cm×20.25cm^2)

V=(1/3)×π×3cm×(12cm^2×24.75cm^2)

V=(1/3)×π×3cm×(297cm^4)

V=(1/3)×π×891cm^3

V=(891cm^3/3)π

V=297cm^3π

hope it help yuh

plz mark brianliest if its correct

The computation shows that the number of years ruled is 41 years.

From the information, Octavian became the emperor of Rome in 27 B.C and he ruled until his death in A.D. 14.

Therefore, the number of years that he rules will be:

= 14 - (-27)

= 14 + 27

= 41

Therefore, the number of years will be 41.

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Answer: 365 days five hours 40 minutes 45 seconds

Step-by-step explanation:

The median is the exact middle number in a sequence or set of numbers.

Steps to find the median is given below:

Finding the Median in an Odd Set of Numbers:

Step 1: Sort your set of numbers from least to greatest. If they're scrambled, line them up, starting with the lowest number and ending with the highest number.

Step 2: Find the number that is exactly in the middle. This means that the median number has the same amount of numbers in front of it as it does behind it.

Finding the Median in an Even Set of Numbers

Step 1: Sort out your set of numbers from least to greatest. An even set of numbers is going to have two numbers exactly in the middle.

Step 2: Find the average of the two numbers in the middle. If 2 and 3 are both in the middle, so you need to add 2 and 3, then divide the sum by 2. The formula for finding the average of two numbers is (the sum of the two middle numbers) ÷ 2.

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The balloons reached the same altitude after 30 seconds.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. 

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

Purple balloon altitude = 2.5 t+0 m = 2.5 t

Starting at a height of 15 meters above sea level, the gold balloon rose 2 meters every second.

Altitude of the gold balloon: 2 t + 15 m

Hence , The balloons reached the same altitude after 30 seconds.

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If there were 132 crayons in John's backpack, the number of blue crayons is equal to blue crayons.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying direct proportion to the given information, we have the following mathematical expression:

3 crayons = 8 blue crayons

132 crayons = X blue crayons

By cross-multiplying, we have the following:

3x = 132 × 8

3x = 1,056

x = 1,056/3

x = 352 blue crayons.

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