what is the mean of the data set?301, 222, 287, 310, 346

The volume of the solid obtained by rotating the region about the y-axis is 2048π/5 cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves 2x = y^2, x = 0, and y = 4 about the y-axis, we can use the method of cylindrical shells.

We can see that the region is bounded below by the x-axis and above by the curve 2x = y^2. To use the method of cylindrical shells, we imagine slicing the region into thin vertical strips of width dx, and then revolving each strip about the y-axis to form a cylindrical shell.

The height of each shell is the difference between the y-coordinates of the upper and lower curves at the corresponding value of x, which is given by:

height = y - 0 = y

The radius of each shell is the distance from the y-axis to the corresponding value of x, which is given by:

radius = x

The volume of each cylindrical shell is therefore:

dV = 2πrh dx = 2πxy dx

To find the total volume, we integrate this expression over the range of x from 0 to 4, which gives:

V = ∫(0 to 4) 2πxy dx

= 2π ∫(0 to 4) x(y^2/2) dx

= π ∫(0 to 4) y^2 x dx

= π ∫(0 to 16) (y^2/2)(y^2/4) dy (using the equation 2x = y^2)

= π ∫(0 to 16) y^4/8 dy

= π [y^5/40] from 0 to 16

= π (16^5/40)

= 2048π/5.

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By Using Pythagorean Theorem, the value of x is 6.2 units.

Pythagorean Theorem:

In mathematics, the Pythagorean Theorem or Pythagorean Theorem is the fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that the area of ​​a square whose side is the hypotenuse (opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation for the lengths of sides a, b and hypotenuse c and is often called the Pythagorean equation.

                              a² +b² =c²

Now,

By using the Pythagorean theorem:

Hypotenuse² =  Perpendicular² + Base²

Now,

In the Δ ABD

As given

DB² = DA² + AB²

As given

DB = 13 units

AB = 9 units

Putting values in the above

13² = 9²+ DA²

169 - 81 = DA²

88 = DA²

Now,

In ΔABC

AB² = AC² + CB²

(As given AB = 9 units , CB = x)

9² = AC² + x²

AC ² = 81 - x²

Now in ΔADC.

AD² = AC² + DC ²

As

AC ² = 81 - x²

DC = 13 - x

AD = \(\sqrt{88}\)

(√88)² = 81 -x² +( 13 - x²)

By using the formula (a + b)² = a² + b² + 2ab

    88 = 81 - x² + 13²- 2 × 13 × x + ²

⇒ 88 = 81 - x² + 13² - 26x + x²

⇒ 88-81 - 169 = -26x

⇒ 88-250 =-26x

⇒ -162 = - 26x

x = 6.2 (Approx.)

Therefore the value of x is 6.2 units.

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Answer:

See below:

Step-by-step explanation:

\(p \: \therefore \: q \implies \: p \: therefore \: q \\ \\ p \: \iff \: q \implies \: p \: if \: and \: only \: if \: q \\ \\ p \: \land \: q \implies \: p \: and \: q \\ \\ p \: \lor \: q \implies \: p \: or \: q \\ \\ p \: \land \: \sim \: q \implies \: p \: and \: not \: q \\ \\ q \: \implies \: \sim \: p \implies \: if \: q \: then \: not \: p \\ \\ \sim \: p \implies \: q \implies \: if \: not \: p \: then \: q\)

Since cos 3α is positive, then its inverse trigonometric function, which is 3α, lies within the first quadrant of the unit circle, or in the interval [0, π/2]. We can rewrite this as 0 ≤3α < π/2 or 0 ≤ 3α < 3600.

This means that whenever 3α is positive, there must exist an acute angle β such that 3α does not equal 3β or 3(β + 900). In this case, the sets of numbers cos β, cos (β + 1200), cos (β + 2400), cos (β + 900), cos (β + 2100), and cos (β + 3300) are the same numbers with different angles. This phenomenon is called periodicity, and is seen in the periodicity of all angles of the unit circle.

To sum up, since cos 3α is positive, this implies that there is an acute angle β with 3α ≠ 3β or 3α = 3 (β + 900) and that the sets of numbers cos β, cos (β + 1200), cos (β + 2400), cos (β +900), cos (β + 2100), and cos (β + 3300) coincide.

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Answer:

24 Girls

Step-by-step explanation:

3/4 = 18/x

3*x = 18*4

3x=72

3x/3=72/3

x=24

Answer:

x = 13

Step-by-step explanation:

NM + ML + LK = x - 6 + 9 + 2x - 19

NK = 23

x - 6 + 9 + 2x - 19 = 23

3x - 16 = 23

3x = 39

x = 13

Answer:

21

Step-by-step explanation:

1+6=7

7+4=11

11+11=21

Answer:

m=7

Step-by-step explanation:

it's in the picture

the left got cut out but there's a bracket at the end of the first line

Answer:

4=4, in infinitely many solutions

Step-by-step explanation:

hope this helps

Answer:

9$

Step-by-step explanation:

Answer:

v = 21

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Geometry

Step-by-step explanation:

Step 1: Set Up Equation

2v + 3v + 75 = 180

Step 2: Solve for v

Answer:

21 degrees

Step-by-step explanation:

3v + 2v + 75 = 108

3v + 2v = 5v

5v + 75 = 108

-75 -75

÷5. 105

÷5 = 21

X=21

Answer:

C

Step-by-step explanation:

it’s the only one that is a line

Answer:

c because the line is straight

Step-by-step explanation:

in order for a line on a graph to be linear it must have the same rise over run so the line would have to be strait

The probability that the child spends less than 1 hour per day unsupervised is approximately 0.1335.

To find the probability that the child spends less than 1 hour per day unsupervised, we can use the normal distribution and the given mean and standard deviation.

Given:
Mean (μ) = 3 hours
Standard Deviation (σ) = 1.8 hours

We want to find the probability that the child spends less than 1 hour per day unsupervised, which is equivalent to finding the area under the normal distribution curve to the left of 1 hour.

Using the Z-score formula:
Z = (x - μ) / σ

Substituting the values:
Z = (1 - 3) / 1.8
Z = -1.11

Now, we can use a Z-table or a calculator to find the probability associated with the Z-score of -1.11. The probability can be found as the area to the left of the Z-score.

Looking up the Z-score of -1.11 in the Z-table, we find the corresponding probability to be 0.1335.

So, the probability that the child spends less than 1 hour per day unsupervised is approximately 0.1335.

The probability statement is: p(x < 1) = 0.1335.

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Answer:B or A is the answer

Step-by-step explanation:

Answer:

option A and B is a correct answer......

Answer:

99   (cm^2)

Step-by-step explanation:

Perpendicular to the AB segment at points D and C, the graph is divided into two triangles and a rectangle.

The area of the middle rectangle is equal to 8*9=72. The hypotenuse of the right triangle is 10cm, and one of the right sides is 9cm, so the other side is SQRT (10^2-9^2) = SQRT (19).

One side of the left triangle is 9cm long and the other side is 14-8-sqRT (19) = 6-sqRT (19) cm.

Then, add the area of the three parts.

72+9*sqrt（19）/2+9*（6-sqrt（19））/2=99    (cm^2)

Answer:

1049760

Step-by-step explanation:

Just multiple

This is the answer to this question

Answer:

1,049,760

Step-by-step explanation:

9 x 3 = 27

27 x 8 x 3 = 648

648 x 15 x 3 = 29,160

29,160 x 6 x 6 = 1,049,760

Therefore the answer is 1,049,760.

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

d = st, d = 100 x 3

Step-by-step explanation:

distance = speed x time

distance = 100 x 3, therefore, distance = 300, but if you just want the equation, it is d = 100 x 3 or d = st

Step-by-step explanation:

d = 100 x 3.

d= 100n

where n = time the journey took.

Answer :- Constant term

In p(x) = x - 12, 1 is the coefficient of x and -12 is the constant term.

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

Step 1

Rule for converting radians to degrees

Formula

Step 2

Final answer

126

Answer: 4.5 pounds

Explanation: To convert 72 ounces into pounds, we use the conversion factor for ounces and pounds which is 16 ounces = 1 pound.

Next, notice that we're going from a smaller unit, ounces, to a larger unit, pounds and when we go from a smaller unit to a larger unit, we divide. So here, we divide 72 by the conversion factor, 16, to get 4.5.

So 72 ounces equals 4.5 pounds.

Answer:

x>2

Step-by-step explanation:

9x+5>23

9x>23-5

when the five grosses the inequality sign it changes to a negative since it was initially a positive

9x>18

\( \frac{9x}{9} > \frac{18}{9} \)

x>2

The Annual Percentage Yield (APY) in this situation is approximately 2.454%.

To find the Annual Percentage Yield (APY) in this situation, use the formula:

\(APY = (1 + r/n)^n - 1\)

where:

- r is the annual interest rate (APR) expressed as a decimal,

- n is the number of compounding periods per year.

In this case, the APR is 2.42% or 0.0242 (expressed as a decimal), and the interest is compounded monthly, so there are 12 compounding periods per year (n = 12).

Substituting these values into the formula,

\(APY = (1 + 0.0242/12)^{12} - 1\)

Calculating this expression:

\(APY = (1 + 0.002017)^{12} - 1\)

  \(= (1.002017)^{12} - 1\)

   ≈ 0.02454 or 2.454%

Therefore, the Annual Percentage Yield (APY) in this situation is approximately 2.454%.

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Answer: 10.8 seconds

Step-by-step explanation:

\(-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)\)

The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.

The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:

(7/8)^10 = 0.362

This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:

P(at least one winner) = 1 - P(no winners)

P(at least one winner) = 1 - 0.362

P(at least one winner) = 0.638

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Answer:

n=3

Step-by-step explanation:

5n+3=18

subtract 3 from both sides

5n=15

divide by 5 on both sides

n=3

Answer:

n=3

Step-by-step explanation:

step 1- subtract 3 to both sides

+3-3=0    18-3=15

5n=15

step 2- divide both sides by 5

5÷5=1       15÷5=3

step 3- check answer by plugging in for n

5(3)+3=18

15+3=18

18=18

Hope this helps!

A statistic is a a) sample characteristic, so the correct option is a) a sample characteristic.

A statistic is a numerical value calculated from a sample of data that is used to describe or make inferences about a larger population from which the sample was drawn. It is different from a parameter, which is a numerical value that describes a characteristic of a population.

Statistics are used in various fields, including science, business, economics, social sciences, and government. They can help researchers to summarize and analyze data, test hypotheses, and make predictions about future events or outcomes.

It is important to note that statistics are subject to variability due to sampling error, which can be reduced by increasing the sample size. Additionally, the distribution of statistics depends on the underlying distribution of the population from which the sample was drawn, and it may not always be normally distributed.

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Answer: "Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality"."

Step-by-step explanation: I got this from a website. Hope it works!!!

Answer:

x=3/4

Step-by-step explanation:

3 ^2x+1=3x+5

6x+1 -3x-5=0

3x-4=0

3x=4

x=3/4

Answer:

3.5

Step-by-step explanation:

This is a 30-60-90 triangle so the hypotenuse is equal to 2 times \(\sqrt{3}\).

\(x = 2\sqrt{3}\) ≈ 3.5