An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 6.
Event B: The sum is not divisible by 4.
Write your answers as fractions.

Answer: 39

Step-by-step explanation:

Answer:

um i think  about 39 foot it has been a little scenes i have done this

Step-by-step explanation:

Calvin's investment need to be increased by a factor of 115.9% to equal Marquez's investment at any time after Calvin's investment is made.

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Let v represent the value of the account after y years. Hence:

For Juana:

\(v=1500(1.03)^y\)

Marquez invests three years before Juana,  Hence:

\(v'=1500(1.03)^{y+3}=1500(1.03)^y(1.03)^3=(1.03)^3*v=1.092727v\)

Calvin invests two years after Juana. Hence:

\(v"=1500(1.03)^{y-2}=1500(1.03)^y*(1.03)^{-2}=(1.03)^{-2}v\)

v' / v" = ((1.03)³ * v) / ((1.02⁻²) * v) = 1.159 = 115.9%

Calvin's investment need to be increased by a factor of 115.9% to equal Marquez's investment at any time after Calvin's investment is made.

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Answer:

360 square inches

Step-by-step explanation:

12*15 = 360

Answer:

360 square inches^^^^^^

Step-by-step explanation:

the person above is correct

Depending on whether the movement is along the x-axis or the y-axis, the ordered pair would be either (0.25, 0) or (0, 0.25).

To plot an ordered pair starting from the origin and moving 0.25, we need both an x-coordinate and a y-coordinate.

We are starting from the origin (0, 0), we can apply the movement of 0.25 to either the x-axis or the y-axis.

If we move 0.25 units on the x-axis, the x-coordinate of the ordered pair would be 0.25, and the y-coordinate would remain 0 since there is no movement on the y-axis. Therefore, the ordered pair would be (0.25, 0).

Similarly, if we move 0.25 units on the y-axis, the x-coordinate would remain 0 since there is no movement on the x-axis, and the y-coordinate of the ordered pair would be 0.25. In this case, the ordered pair would be (0, 0.25).

So, depending on whether the movement is along the x-axis or the y-axis, the ordered pair would be either (0.25, 0) or (0, 0.25).

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Answer:3*10^4

Step-by-step explanation:

3 multiply 10 to the 4 power (positive)

Answer:

60%

Step-by-step explanation:

Let (xn) be a sequence of positive real numbers that converges to a positive number. We aim to show that the set {x_n : n ∈ N} is bounded below by a positive number. Since the sequence converges to a positive number, we can choose an ε > 0 such that for all sufficiently large n, |x_n - L| < ε, where L is the limit of the sequence. By considering the inequality x_n > L - ε, we can see that all terms of the sequence are greater than or equal to a positive number, thereby establishing the boundedness from below.

Since the sequence (xn) converges to L, for any ε > 0, there exists a positive integer N such that for all n ≥ N, |x_n - L| < ε. This means that eventually, all terms of the sequence will be arbitrarily close to L.

Now, consider the inequality x_n > L - ε. For all n ≥ N, we have |x_n - L| < ε, which implies L - ε < x_n. Since L and ε are positive, we can rearrange the inequality to get x_n > L - ε.

Therefore, for all n ≥ N, we have x_n > L - ε, and since ε can be chosen to be any positive number, we can conclude that all terms of the sequence (xn) are greater than or equal to L - ε, which is a positive number.

Hence, the set {x_n : n ∈ N} is bounded below by a positive number, as desired.

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Answer:

If a number is a multiple of 2, it may NOT be a multiple of 4. An example would be the number 6.

\(6\div2=3\), but \(6\div4=1.5\).

However, if a number is multiple of 4, it is guaranteed to be a multiple of 2, since 4 itself is a multiple of 2.

Example:

\(8\div4=2\)

This is simply

\(8\div2\div2=2\).

It is a multiple of 2 twice.

Answer:

A store sells six-packs of soda for $3.00 a six pack. If this relationship is graphed with the number of cans of soda on the x-axis and the cost on the y-axis, what is the slope of the graph in dollars per can?

Step-by-step explanation:

3/6 = 1/2 fph = .5fph

Answer:

Perimeter = 90

Step-by-step explanation:

We're going to start with HI and go around the circle (and triangle, clockwise) see image. HI is 11. From H to G, then also has to be 11.

Subtract 26 - 11 to find LG. LG is 15.

If LG is 15, then LK is also 15. Subtract 34 - 15 to find JK.

JK is 19, so JI is also 19.

Two sides of the triangle are 34 and 26. The other side is 19+11=30.

Perimeter = 34+26+30

= 90

Answer:

Steve got 32 points

Step-by-step explanation:

Take the total score and multiply by the percentage received

40 * 80%

Change to decimal form

40 * .80

32

Steve got 32 points

Lisa's percentile rank is approximately 7.857%.

To calculate Lisa's percentile rank, you can use the formula:

Percentile Rank = (Number of scores less than Lisa's score / Total number of scores) * 100

In this case, Lisa's score is 86, and it is the 23rd score from the top in a class of 280 scores. Therefore, the number of scores less than Lisa's score is 23 - 1 = 22 (excluding Lisa's score itself).

Substituting the values into the formula:

Percentile Rank = (22 / 280) * 100 ≈ 7.857%

Lisa's percentile rank is approximately 7.857%.

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Answer:

Step-by-step explanation:

(x - 3)(x + 2) (x + 4) =

x^3+3x^2-10x-24

Answer:

x^3+3x^2-10x-24

Step-by-step explanation:

(x - 3)(x + 2) (x + 4)

multiply the first two together first

(x^2+2x-3x-6)(x+4) add like terms first

(x^2-x-6)(x+4)

then multiply

x^3+4x^2-x^2-4x-6x-24

add like terms

x^3+3x^2-10x-24

The probability of the team advancing to third round is 0.55.

Let A be the event that a team advances to the second round

Let B be the event that the same team advances to the third round.

We want to find P(B|A) which is the probability of B given A.

Using Bayes' theorem, we have:

P(B|A) = P(A|B) * P(B) / P(A)

P(A) = 0.6 since 60% of teams advance

P(B) = 0.33 since 33% of teams advance.

To get P(A|B), we can use the fact that:

P(A|B) = P(A and B) / P(B)

Assume: P(A and B) = P(B) = 0.33.

P(A|B) = 0.33 / 0.33

P(A|B) = 1

Substituting the values, we get:

P(B|A) = 1 * 0.33 / 0.6

P(B|A) = 0.55.

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Answer:

X=11

b. 30

c. 30

Step-by-step explanation:

The process of simplifying square roots involves finding an equivalent expression for the square root that has smaller or more manageable numbers inside the root sign.

This can be achieved by using prime factorization, the properties of square roots, and rationalizing the denominator. The final result should be in the simplest form possible, without any radicals in the denominator, or any perfect square factors in the numerator.

A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9. The symbol for square root is √. For example, √9 = 3.

The square root of a number can be either positive or negative, but for most purposes, the positive square root is used.

Additionally, there are also square roots of expressions, not just numbers, which can be simplified using similar methods

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Answer:

C - x < -6 and x < 2

Step-by-step explanation:

2x ">" -12 and 7x < 14. with negative numbers, the bigger the number the less it is. -12 < -6 because negative numbers work the opposite way that positive numbers do. I hope this helps you!!!!

The indeterminant form to which the L'Hopital's Rule can be applied are 0/0 and ∞/∞ , the correct options are (d) and (f) .

L'Hopital's Rule in calculus is used to evaluate weird limits that result in indeterminate forms that are 0/0, ∞/∞ .  These types of limits

(a) cannot be calculated by direct substitution of limit and/or

(b) can be evaluated but using a very long procedure .

that means if \(\lim_{x \to a} \frac{f(x)}{g(x)}\) = 0/0  or ∞/∞ ,

then \(\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}\)

In the question ,

there are several indeterminant forms given which are  0.∞ ,  \(0^{0}\) , \(1^{\infty}\) , 0/0 ,  ∞ - ∞ , ∞/∞ ,  ∞⁰  .

By the definition of L'Hopital's Rule , the option that matches with the definition is 0/0 and ∞/∞ ,

So , the correct option is (d) 0/0 and (f) ∞/∞   .

Therefore , The indeterminant form to which the L'Hopital's Rule can be applied are 0/0 and ∞/∞ , the correct options are (d) and (f) .

The given question is incomplete , the complete question is

Select EVERY indeterminate form to which L'Hopital's Rule can be directly applied to (there may be more than one).

(a) 0.∞

(b) \(0^{0}\)

(c) \(1^{\infty}\)

(d) 0/0

(e) ∞ - ∞

(f) ∞/∞

(g) ∞⁰

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A study conducted in 2004 examined the usage of cable television and radio among 10 individuals to determine if there was a significant difference in the average hours spent on each medium. Using a significance level of 0.05, statistical analysis was performed to test for a disparity between the population mean usage of cable television and radio.

The researchers collected data on the number of hours per week spent watching cable television and listening to the radio from a sample of 10 individuals. The objective was to determine if there was a significant difference in the average usage between cable television and radio, considering the increasing competition among various entertainment options.

To test for a difference between the population mean usage for cable television and radio, a statistical hypothesis test was conducted. The significance level (α) of 0.05 was chosen, which means that the results would be considered statistically significant if the probability of obtaining such extreme results by chance alone was less than 5%.

The test compared the means of the two samples, namely the average hours spent watching cable television and listening to the radio. By analyzing the data using appropriate statistical techniques, such as a two-sample t-test, the researchers determined whether the observed difference in means was statistically significant or could be attributed to random variation.

After conducting the hypothesis test, if the p-value associated with the test statistic was less than 0.05, it would indicate that there was a significant difference between the population mean usage of cable television and radio. Conversely, if the p-value was greater than 0.05, there would be insufficient evidence to conclude a significant disparity.

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Answer:

Step-by-step explanation:

Hope that will help you with

it depends what the number is

Answer:

50

Step-by-step explanation:

20 divided by the percent value as a decimal 0.4 is 50

Answer:

"I hope your pillow is hot on both sides"

Step-by-step explanation:

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Answer:

57 is your answer......

The volume of the solids is given by

1. 2π (12 - sin(12))

2. π/7 * (4^{7/2} - 0)

3. 18π

To find the volume of the solid obtained by rotating the region about the given axis, we can use the method of cylindrical shells.

For the first problem:

The region is enclosed by the equations:

y = cos(θ), y = 0, θ = 0, θ = 12

To rotate the region about the line y = 1, we need to consider the distance between the line y = 1 and the function y = cos(θ).

The distance between y = 1 and y = cos(θ) is given by:

d(θ) = 1 - cos(θ)

To find the volume, we integrate the formula for the circumference of a cylindrical shell multiplied by the height:

V = ∫(2π * r * h) dθ

= ∫(2π * (1 - cos(θ)) * 1) dθ

= 2π ∫(1 - cos(θ)) dθ

= 2π (θ - sin(θ)) | from 0 to 12

= 2π (12 - sin(12) - (0 - sin(0)))

= 2π (12 - sin(12))

For the second problem:

The region is enclosed by the equations:

y = 2√(x), y = 4, x = 0

To rotate the region about the y-axis, we need to consider the distance between the y-axis and the function \(x = y^2/4\).

The distance between the y-axis and \(x = y^2/4\) is given by:

\(d(y) = y^2/4\)

To find the volume, we integrate the formula for the circumference of a cylindrical shell multiplied by the height:

V = ∫(2π * r * h) dy

= ∫(2π * \((y^2/4)\) * (2√(y))) dy

= π/2 ∫\((y^(5/2))\) dy

= π/2 * (2/7) * \(y^(7/2)\) | from 0 to 4

= π/7 * \((4^(7/2) - 0)\)

For the third problem:

The region is enclosed by the equations:

y = 1, x = 0, x = 9

To rotate the region about the line y = 1, we need to consider the distance between y = 1 and the x-axis.

The distance between y = 1 and the x-axis is given by:

d(x) = 1

To find the volume, we integrate the formula for the circumference of a cylindrical shell multiplied by the height:

V = ∫(2π * r * h) dx

= ∫(2π * 1 * (9 - 0)) dx

= 2π * 9 * x | from 0 to 1

= 18π

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Answer: 96 miles cubed.

Step-by-step explanation: First, are you sure that the unit of measure is miles? But, anyway, you probably know how to calculate the area of a rectangle or square: length × width. With a 3D shape you do length × width × height. So we have 3 × 4 × 8 = 96.

Answer:

radian

Step-by-step explanation:

A radian is a unit of angle that is equal to the angle created at the center of a circle whose arc is equal in length to the radius.

The measure of an angle at the center is 1 radian.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

Radius is equal to arc length.

To find the measure of the angle at the center:

We have the formula,

Angle in radian = arc length / radius

Let a be the arc length,

then a be the radius.

Substituting the values,

Angle in radian = a/a

Angle in radian = 1 radian

Therefore, 1 is the measure of an angle at the center.

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Answer:

C . x/12

Step-by-step explanation:

Answer:

0.14285714285

Step-by-step explanation:

This is what I got from the calculator.

Answer:

1/7 (1 over 7)

Step-by-step explanation:

The negative reciprocal of –7 is 1/7 (1 over 7)

Answer:

The answer would be 80.

Step-by-step explanation:

First you want to add 16 and 24.

Next you want to multiply that answer by 2.

Then you have your answer and I hope this helps

-21, -13. the pattern is adding 8 . example: -37+8=-29