prove that every prime number greater than 3 is either one or more or one less than a multiple of 6

The volume of the solid is 4/5π.

The volume of a solid generated by revolving a region around a line is given by V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region, respectively, and y is a function of x.

In this case, the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Therefore, the volume of the solid generated when the region is revolved about the y-axis is given by

V = ∫0 1 π(y)2dy

= ∫0 1 πx6dx

= π/7

= 4/5π

The volume of the solid is calculated using the formula V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region and y is a function of x. In this case, the lower limit is a=0 and the upper limit is b=1, since the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Integrating from a=0 to b=1 gives the volume of the solid as V = ∫0 1 πx6dx = π/7 = 4/5π.

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The proportion of candy bars with fewer than 200 calories cannot be determined without additional information.

To calculate the proportion of candy bars with fewer than 200 calories, we need to know the total number of candy bars and the number of candy bars that have fewer than 200 calories.

Without this information, we cannot determine the proportion. The number of candy bars with fewer than 200 calories could vary greatly depending on the specific dataset or context.

The proportion of candy bars with fewer than 200 calories cannot be determined without additional information regarding the total number of candy bars and the number of candy bars that fall into that category.

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Answer:

C) 6

Step-by-step explanation:

I converted the equation into slope-intercept form and then identified the y-intercept.

\(4x+2y=12\\\\4x-4x+2y=12-4x\\\\2y=12-4x\\\\\frac{2y=12-4x}{2}\\\\ y=6-2x\\\\y=-2x+6\\\\y=-2x+\boxed{6}\)

C should be the correct answer.

Hope this helps.

Answer: 6

Step-by-step explanation: The y-intercept is a point where a line

crosses the y-axis and all y-intercepts have an x-coordinate of zero.

So to find the y-intercept of this line, we can plug a 0 in for x.

So we have 4(0) + 2y = 12.

So 2y = 12 which means that y = 6.

So the y-intercept of this line is 6.

the only possible resulting function after dilation is y = 5x. Option D is correct

Given a coordinate point (x, y), if the coordinate is dilated by a factor of "k", the resulting coordinate point will be at (kx, ky).

Note that both coordinates were multiplied by the factor "k"

Given the expression y = x, for this expression to show a dilation, we can multiply the input variable by an integer.

From the given option, we can see that the only possible resulting function after dilation is y = 5x

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Answer:

none

Step-by-step explanation:

all the numbers are relatively close to each other, so there is no significant gap between each.

Answer:

(0,1)

Step-by-step explanation:

moving right 2 units makes it (0,-3)

moving up 4 units makes it (0,1)

Molly gave the least to charity. To determine who gave the least to charity, we need to calculate how much each person gave.

Amber gave 30% of £50, which is (30/100) x £50 = £15.

Molly gave 0.25 of £50, which is 0.25 x £50 = £12.50.

Liam gave 15 of £50, which is (15/100) x £50 = £7.50.

Therefore, Molly gave the least amount to charity with £12.50, while Amber gave the most with £15. Liam gave an amount in between £7.50.

In general, when comparing percentages, it is important to also consider the absolute values of the amounts being compared. While Molly gave the smallest percentage of her money to charity, the amount she gave was larger than what Liam gave as Liam chose to give only a small percentage of his money to charity. This is a reminder that percentages can be misleading if we do not also consider the actual amounts involved.

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Answer:

$58.50

Step-by-step explanation:

1.2 kg = 1200g

To get from 200 to 1200, we time 6, so we take $9.75 times 6 to get the price.

$9.75 times 6 = $58.50

So, the cost of 1.2kg cheese is $58.50

The answer is $58.50

I have attached the explanation! :)

Answer:

y - 2 = 36(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 36 and (a, b ) = (4, 2 ) , then

y - 2 = 36(x - 4) ← equation of line

Answer:

Could u help me with my question

Step-by-step explanation:

Answer:

Step-by-step explanation:

Finding final velocity.

\(\boxed{v_{f}=v_{i} + at}\\\\v_{f} -- > final \ velocity\\\\v_{i} -- > Initial velocity\)

a -> accelaration

t ---> time

\(v_{i} = 7 \ m/s\)

a = 2 m/s²

t = 5 s

\(v_{f}= 7 + 2*5\)

     = 7 + 10

     = 17 m/s

10) h = 5 m

g = -10m/s²

\(t =\sqrt{\dfrac{2*h}{g}}\\\\ =\sqrt{\dfrac{2*5}{10}}\\\\= \sqrt{\dfrac{10}{10}}\\\\= 1\)

t = 1 sec

The statement is True. Since $n^2(1+\sqrt{n})$ is neither $o(n^2 \log n)$ nor $\omega(n^2 \log n)$, we can conclude that $n^2(1+\sqrt{n}) \neq O(n^2 \log n)$.

Problem 5: The statement $\sqrt{n} = O(\log n)$ is False.

To determine whether $\sqrt{n}$ is big-O of $\log n$, we need to consider the growth rates of both functions.

As $n$ approaches infinity, the growth rate of $\sqrt{n}$ is slower than the growth rate of $\log n$. This is because $\sqrt{n}$ increases as the square root of $n$, while $\log n$ increases at a much slower rate.

In big-O notation, we are looking for a constant $c$ and a value $n_0$ such that for all $n \geq n_0$, $\sqrt{n} \leq c \cdot \log n$. However, no matter what constant $c$ we choose, there will always be a value $n$ where $\sqrt{n}$ surpasses $c \cdot \log n$ in terms of growth rate. Therefore, $\sqrt{n}$ is not big-O of $\log n$, and the statement is False.

Problem 6: The statement $n^2(1+\sqrt{n}) \neq O(n^2 \log n)$ is True.

To prove this, we can make use of the fact that if $f(n) = o(g(n))$, then $f(n) \neq \Omega(g(n))$, and if $f(n) = \omega(g(n))$, then $f(n) \neq O(g(n))$.

First, let's simplify $n^2(1+\sqrt{n})$:

$$

n^2(1+\sqrt{n}) = n^2 + n^{5/2}

$$

Now, let's compare it with $n^2 \log n$. We can see that the term $n^{5/2}$ grows faster than $n^2 \log n$ as $n$ approaches infinity. This implies that $n^2(1+\sqrt{n})$ is not big-O of $n^2 \log n$.

Since $n^2(1+\sqrt{n})$ is neither $o(n^2 \log n)$ nor $\omega(n^2 \log n)$, we can conclude that $n^2(1+\sqrt{n}) \neq O(n^2 \log n)$.

Therefore, the statement is True.

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(a) There can be a maximum of 18 teams.

(b) The largest possible number of teams is 18, and there will be a total of 19 players on each team.

Given information:

In a local, recreational soccer league there are 252 men and 90 women signed up to play. The organizers need to make sure that everyone is on a team, the teams are the same size, each team has the same number of males; and each team has the same number of females.

(a) To find the largest possible number of teams, we need to divide the players (252 men and 90 women) into teams, where each team has the same number of males and females. Let's find the GCD (greatest common divisor) of 252 and 90:

GCD of 252 and 90 = GCD (252,90) = 18.

Therefore, there can be a maximum of 18 teams.

(b) Since the number of teams is 18, and we have 252 men and 90 women, there will be a total of 342 players.

Now, we need to divide these 342 players into 18 teams. Each team must have an equal number of males and females. Number of males = 252, Number of females = 90.

To divide the players equally into teams, we need to find the number of males and females that can be in one team.

Number of males in one team = 252/18 = 14

Number of females in one team = 90/18 = 5

Therefore, each team will have 14 males and 5 females, and there will be a total of 19 players on each team (14 + 5).

Thus, the largest possible number of teams is 18, and there will be a total of 19 players on each team.

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Let's call the amount of lugagge the first men had as x, and the amount of lugagge the second men had as y.

Since both had to pay for excess of luggage, both had the permitted amount of luggage plus an extra amount. Let's call the permitted amount as a, the extra the first men had as z, and the extra the second man had as w. Then, our total amounts of luggage can be rewritten as

Since their total amount of luggage added together was 135 kg, this gives to us the following equation

The charge for the extra luggage is a flat rate, let's call it r, then, the price you pay for the extra luggage is given by the product between this rate and the amount of extar luggage. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage, therefore

If we divide one equation by the other, we can write the excess of luggage of one as a function of the other.

If all of the luggage belonged to one person, this person would have to pay $8.10 for the excess. If we call the excess of this person as p, the amount of luggage this person had would be

Using the "rate formula" we created before, we can also write p as a function of z.

Rewritting all the total amounts, we have

If we add the equations for x and y together, we have

From the first equation, we know that the sum between both total amounts of luggage is equal to 135.

Now, we have two equations for our two variables.

If we multiply the first equation by 2, and subtract the second equation, we're going to get a new equation only for a(the amount in kilograms of permitted luggage).

The amount of luggage permitted to bring onto the plane for free is 45 kilograms.

Answer: D. 16/25

Step-by-step explanation:

Answer: $9.26

Step-by-step explanation:

The total cost for each of their smoothies was:

= 4.95 * 2

= $9.90

Including taxes it will rise to:

= 9.90 * (1 + tax)

= 9.90 * (1 + 8.5%)

= $‭10.74

Change she will receive is:

= 20 - 10.74

= $9.26

Step-by-step explanation:

S.P. = $483

Gain = 15%

C.P. = ?

Profit =

$483 × 15/100

$72.45

Then,

C.P. = S.P. - Profit

= $483 - $72.45

= $410.55

Hence,

Cost price of the bed sheet is $410.55

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the engineer's claim. Hence, the engineer's claim is false.

To answer this question, we need to conduct a hypothesis test with a significance level of α = 0.05. The null hypothesis (H0) is that the true mean commute time is equal to or greater than 25 minutes, while the alternative hypothesis (Ha) is that the true mean commute time is less than 25 minutes. We can use a one-sample t-test to test this hypothesis, where the test statistic is calculated as:
t = (sample mean - hypothesized mean) / (standard deviation/sqrt (sample size))
t = (24.6 - 25) / (13 / sqrt(1923))
t = -1.53

Using a t-distribution table with degrees of freedom (df) equal to the sample size minus 1 (df = 1922), we find that the p-value for this test is 0.064. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the engineer's claim that the mean commute time is less than 25 minutes. The deviation from the hypothesized mean is -0.4 which is less than 1 standard deviation, hence we cannot say with confidence that the mean commute time is less than 25 minutes.

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Answer:

C

Step-by-step explanation:

Domain is what x values are allowed in a function

The relative frequency is solved and the table of values is plotted

Given data ,

The lunch order is given by the 2 sets of dishes as

A = { Sandwich , Pastas }

Now , the sports activities are given by 2 sets as

B = { Volleyball , Swimming }

From the table of values , we get

The relative frequency is solved as

Relative Frequency = Subgroup frequency / Total frequency

The percentage of Swimming ( sandwich ) = 26/36

Swimming ( sandwich ) = 72 %

And , the percentage of Swimming ( pasta ) = 10/36

Swimming ( pasta ) = 28 %

Now , the percentage of total sandwich = 45/70 = 64 %

And , the percentage of total pasta = 25/70 = 36 %

Hence , the relative frequency is solved

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The probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.

Assuming that each die is fair and that the outcome of rolling one die does not affect the outcome of rolling the others, the probability of rolling a 6 with the red die is 1/6, the probability of rolling a 5 with the green die is also 1/6, and the probability of rolling a 4 with the blue die is 1/6.

Since the three events of rolling each die are independent of each other, we can multiply their probabilities to get the probability of all three events happening at the same time, i.e., rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die:

Probability of rolling 6 with the red die = 1/6

Probability of rolling 5 with the green die = 1/6

Probability of rolling 4 with the blue die = 1/6

Probability of rolling 6 (R), 5 (G), 4 (B) at the same time = Probability of rolling R and G and B together = Probability of R × Probability of G × Probability of B

= 1/6 × 1/6 × 1/6 = 1/216

Therefore, the probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.

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You have three dice: one red (R), one green (G), and one blue (B). When all three dice are rolled at the same time, calculate the probability of the following outcome: 6 (R), 5 (G), 4 (B)?

Answer: 2/3

Step-by-step explanation:

Eloise has a mat that has a length of 8/9 meter and a width of 3/4meter. The area of Eloise's mat will be gotten by multiplying the length by the width. This will be:

= 8/9 × 3/4

= 24/36

= 2/3

Answer:

40% more.

Step-by-step explanation:

40% of 40 is 16. 40+16 is 56

Answer: 71%

Step-by-step explanation: 40/56*100

A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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The approximate length of a side of the rhombus is 10.67 cm.

A rhombus is a quadrilateral with all sides of equal length.

The diagonals of a rhombus bisect each other at right angles.

Let's label the length of one diagonal as d1 and the other diagonal as d2.

In the given rugby-shaped figure, the length of d1 is 14 cm, and the length of d2 is 12 cm.

Since the diagonals of a rhombus bisect each other at right angles, we can divide the figure into four right-angled triangles.

Using the Pythagorean theorem, we can find the length of the sides of these triangles.

In one of the triangles, the hypotenuse is d1/2 (half of the diagonal) and one of the legs is x (the length of a side of the rhombus).

Applying the Pythagorean theorem, we have \((x/2)^2 + (x/2)^2 = (d1/2)^2\).

Simplifying the equation, we get \(x^{2/4} + x^{2/4} = 14^{2/4\).

Combining like terms, we have \(2x^{2/4} = 14^{2/4\).

Further simplifying, we get \(x^2 = (14^{2/4)\) * 4/2.

\(x^2 = 14^2\).

Taking the square root of both sides, we have x = √(\(14^2\)).

Evaluating the square root, we find x ≈ 10.67 cm.

Therefore, the approximate length of a side of the rhombus is 10.67 cm.

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Answer:

D. 120

Step-by-step explanation:

42 miles = 35%

84 miles = 70%

120 miles = 100%

Because 120 divided by 0.35 is equal to 42.

Answer:

2x^2 + x + 9 + (18/(x+2))

Step-by-step explanation:

To find the result when 2x^3 - 5x^2 - 9x + 18 is divided by x + 2 using the long division method, you can follow these steps:

Divide the first term of the dividend (2x^3) by the first term of the divisor (x). The result is 2x^2.

Multiply the divisor (x + 2) by 2x^2. The result is 2x^3 + 4x^2.

Subtract this result from the dividend (2x^3 - 5x^2 - 9x + 18). The result is -x^2 - 9x + 18

Bring down the next term of the dividend (-5x^2) and add it to the result from step 3. The result is -6x^2 - 9x + 18

Divide -6x^2 by -6x and the result is x.

Multiply the divisor by x. The result is x^2 + 2x

Subtract this result from the result of step 4. The result is -9x + 18

Bring down the next term of the dividend (-9x) and add it to the result from step 7. The result is -18x + 18

Divide -18x by -18 and the result is x

Multiply the divisor by x. The result is x^2 + 2x

Subtract this result from the result of step 8. The result is 18

Therefore, the quotient is 2x^2 + x + 9 and the remainder is 18

So the result when 2x^3 - 5x^2 - 9x + 18 is divided by x + 2 is 2x^2 + x + 9 + (18/(x+2))

Answer:

Step-by-step explanation:

pattern by pattern

Answer:

5 x^2  + 2y^2  + 12x + 5y

Step-by-step explanation:

6x + 2y +y^2 + 6x + 2y + y^2 + 4x^2 + x^2 + y

12x +y^2 + 4y + y^2 + 4x^2 + x^2 + y

12x + 2y^2 + 4x^2 + x^2 + 5y

2y^2 + 5x^2 + 12x + 5y

5 x^2  + 2y^2  + 12x + 5y