What is the explicit rule for the arithmetic sequence shown in the graph?

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)?

The car gets 214.3 miles per gallon of gasoline in the city and 27.8 miles per gallon of gasoline on the highway.

Let the number of miles per gallon that the car gets in the city be x. Hence, the number of miles per gallon that the car gets on the highway would be 3x.

A salesperson purchased a car that is advertised as getting 3 times as many miles per gallon of gasoline on the highway than it does in the city. On a recent sales trip that covered 1500 miles in total, the car used up 18 gallons on the highway and 7 gallons in the city.

Calculation of miles per gallon of gasoline in the city:7 gallons of gasoline cover city distance: x miles is covered by 1 gallon of gasoline.

Thus, 7 gallons will cover 7x miles. Hence, we can equate: 7x = 1500 ....(1)

Calculation of miles per gallon of gasoline on the highway:18 gallons of gasoline cover the highway distance.3x miles is covered by 1 gallon of gasoline.

Thus, 18 gallons will cover 54x miles.

Hence, we can equate: 54x = 1500 ....(2)

Dividing equation (1) by 7:7x/7 = 1500/7x

= 214.3 miles per gallon of gasoline in the city.

Dividing equation (2) by 54:54x/54

= 1500/54x

= 27.8 miles per gallon of gasoline on the highway.

Therefore, the car gets 214.3 miles per gallon of gasoline in the city and 27.8 miles per gallon of gasoline on the highway.

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Answer:

.5 or 1/2

hope this helps!!!

Answer:

Step-by-step explanation:

2 would have a greater b value because its x.  Also the other answer is 2.

Hence proved ,the series for j 0(x) converges for all x .

A series in mathematics is the process of adding an unbounded number of quantities, after the one  other, to a specified initial amount. A significant component of calculus and its generalization, mathematical analysis, is the study of series.

Then we call that the series has converged and  in that case we define the total of the series as the limit of the partial sums,When the sequence of partial sums in a series are converges.

J 0(x) is called the Bessel function of the first kind of order zero,

we know that , \(J0(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ...\)is called JO(x) series,

We use the ratio test to determine that this series converges for all values of x.

According to the ratio test, the series of the form \(\frac{a_(n+1)}{a_n}\) also converges if the series JO(x) converges. The series converges if it is less than 1.  and diverges if the limit of the ratio test is greater than 1,

Let a use the ratio test for the J0(x) series:

let a consider term  is  R=\(((a_(n+1))/a_n) = (x^2_(n+2)) / [(2n+2)(2n+1)] / (x^2n) / [(2n)(2n-1)] | = | x^2 / [(2n+2)(2n+1)] |\)

Considering the limit as n tends to infinity:

\(\lim_{n \to \infty} |a_(n+1) / a_n) |=\lim_{n \to \infty} | x^2 / [(2n+2)(2n+1)] = 0\)

For all values of x, the series converges  since the limit is less than 1.

therefore the J 0(x) series converges for all x.

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 Recursive formula of an arithmetic sequence is given by the expression,

                          \(T_n=a+(n-1)d\)

                 Where, \(T_n=\) nth term

                              \(a=\) First term of the sequence

                              \(n=\) Number of term

                              \(d=\) Common difference

Therefore, number of sticks in the 6th pattern are 32.

                   And number of sticks in the nth pattern are \(T_n=5n+2\)

From the picture attached,

Number of sticks in 1st pattern = 7

Number of sticks in 2nd pattern = 12

Number of sticks in 3rd pattern = 17

Sequence formed is 7, 12, 17..... nth term

This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.

Therefore, nth term of the sequence will be,

       \(T_n=a+(n-1)d\)

       \(T_n=7+(n-1)5\)

       \(T_n=5n+2\)

If \(n=6,\)

       \(T_n=7+(6-1)5\)

       \(T_n=7+25\)

       \(T_n=32\)

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Answer:

13/16 = 0.813

Step-by-step explanation:

The inequality that could be used to determine the mean number of miles, m. Abbie would need to drive her car each day is; 20 + 6m > 100.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Given that Abbie wants to drive her car more than 100 miles this week. And she has already driven her car 20 miles.

Let the number of miles represented by m.

The inequality could be used to determine the mean number of miles, m, will be:

20 + 6m > 100

Hence, Abbie would need to drive her car each day is; 20 + 6m > 100.

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Answer:

Step-by-step explanation: A 4-column table with 4 rows. Column 1 is labeled Service with entries Restaurant, Florist, Cab Fare, Dog Groomer. Column 2 is labeled Cost with entries 40 dollars, 94 dollars, 32 dollars, 62 dollars. Column 3 is labeled Gratuity with entries 18 percent, 12 percent, 20 percent, 26 percent. Column 4 is labeled Tax with entries 8.5 percent, 12 percent, 0 percent, 5.75 percent.About how much should the gratuity for the restaurant server be? Round the percent of gratuity to the nearest benchmark percent to find the answer.$

Answer:8 percent

Step-by-step explanation:

The probability that a voter is either female or Democrat is 0.64 or 64%.

To calculate the probability, we need to determine the number of individuals who are either female or Democrat and divide it by the total number of voters.

From the table, we can see that there are 405 females and 253 Democrats. However, we need to be careful not to double-count the individuals who fall into both categories.

To find the number of individuals who are either female or Democrat, we add the number of females (405) and the number of Democrats (253), and then subtract the number of individuals who are both female and Democrat (150).

So, the number of individuals who are either female or Democrat is 405 + 253 - 150 = 508.

Now, we divide this number by the total number of voters, which is 802, to get the probability: 508 / 802 ≈ 0.64 or 64%.

Therefore, the probability that a voter is either female or Democrat is approximately 0.64 or 64%.

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Answer:

1) The image of the line has the same slope as the pre-image but a different y-intercept.

hope this helps ;)

Answer: True

Step-by-step explanation: Because Im A Top G

A condition that is impossible to satisfy has no solution.

Mathematics can be a powerful tool for solving many problems, but there are some issues that can't be solved.

In particular, any condition that is impossible to satisfy, such as the logical statement ‘this statement is false’, has no solution in mathematics. This is because the statement can’t be proven true or false, and so it can’t be solved.

An unsolvable condition is one that cannot be solved using any combination of logical and mathematical steps.

This means that no matter how much time and effort is put in, a solution to the problem cannot be discovered.

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We need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

What is ASA congruence of triangle?

The two triangles are considered to be congruent according to the ASA rule if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.

We are given the following:

1. ∠A ≅ ∠X

2. ∠C ≅ ∠Z

Now, in order to show the triangles as congruent by ASA congruence of triangle, we need the side which is in between both the angles.

The sides in between both the angles are AC and XZ.

Hence, we need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

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Answer:

x = 69

Step-by-step explanation:

Knowns:

y = 69

Problem Workout

180 - z = 2y

180 - z = 2 (69)

180 - z = 138

-z = -42

z = 42

Since there is no picture, I am guessing x is the third angle.

x = 180 - (y + z)

x = 180 - (69 + 42)

x = 180 - 111

x = 69

The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.

The mean absolute deviation (MAD) measures the average distance between each data point and the mean of the dataset. To find the MAD, you need to follow these steps:

1. Calculate the mean of the dataset by adding up all the numbers and dividing the sum by the total number of data points. In this case, the dataset consists of the following numbers: 3, 6, 3.8, 3.2, and 3.4. Adding them up gives us a sum of 19.4. Dividing this sum by 5 (since there are 5 data points) gives us a mean of 3.88.

2. Find the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value. For example, for the first data point, 3, the absolute deviation would be |3 - 3.88| = 0.88. Repeat this step for all the data points.

3. Calculate the mean of the absolute deviations by adding up all the absolute deviations and dividing the sum by the total number of data points. In this case, the absolute deviations are: 0.88, 2.12, 0.72, 0.68, and 0.58. Adding them up gives us a sum of 4.98. Dividing this sum by 5 gives us a mean of 0.996.

So, the mean absolute deviation for the given dataset is approximately 0.996.


The mean absolute deviation helps us understand how much each data point varies from the mean of the dataset. By calculating the absolute deviation for each data point and finding the average, we can determine the typical amount of variation in the dataset.


The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.

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Answer:

70 + 4 + .3

Step-by-step explanation:

Effortless!

Answer:

1st. 1/4

2nd. Not proportional

Step-by-step explanation:

Answer:

both are not proportional

Step-by-step explanation:

16 : 4 = 16/4 = 4

20 : 5 = 20/5 = 4

9 : 36 = 9/36 = 1/4

not the same so NOT proportional

4 : 12 = 4/12 = 1/3

5 : 20 = 5/20 = 1/4

9 : 45 = 9/45 = 1/5

not the same so NOT proportional

Answer:

1/2

Step-by-step explanation:

8(1/2)^4

= 8 * 1 / 2^4

= 8/(2*2*2*2)

= 8/16

= (8*1) / (8*2)

= 1/2

Answer:

this is not a rational number

Step-by-step explanation:

cause you cant put it as a fraction

Answer:

Yes.

Step-by-step explanation:

Because it can be written as a fraction:

5 .97 = 5 97/100  or   597/100.

Answer:

0.9 as a fraction is 9/10

Step-by-step explanation:

Answer:

9/10

Step-by-step explanation:

Based on the information given and the figure provided, we can determine the following:

- Since the support at B is a roller, it can only provide a vertical reaction force. Therefore, the horizontal component of the reaction force at B is zero. This means that the shear force at point C is equal to the applied load F = 12 kips.
- To determine the internal normal force at point C, we need to draw a free body diagram of the section of the beam to the left or to the right of point C (it doesn't matter which side we choose). Let's assume we choose the left side, as shown in Figure 2.

(Figure 2)

- The internal normal force N is perpendicular to the cross-section of the beam, and it points away from the section we are considering. Since there are no external vertical forces acting on this section, the internal normal force must be equal in magnitude and opposite in direction to the sum of the vertical components of the applied load and the reaction force at B. Therefore, we have:

N = - (F + VB)

where VB is the vertical reaction force at B. To find VB, we can use the equation of equilibrium of forces in the vertical direction:

VB = F

since there are no other vertical forces acting on the beam. Substituting this into the equation above, we get:

N = - 2F = - 24 kips

Therefore, the internal normal force at point C is equal to -24 kips, and it points away from the section to the left of point C.
- To determine the bending moment in the beam at point C, we need to use the equation of equilibrium of moments about point C:

M = 0 = - (F)(8 ft) + (VB)(6 ft) + (N)(0 ft)

where the signs of the terms are based on the right-hand rule (clockwise moments are negative, counterclockwise moments are positive). Solving for M, we get:

M = - 48 kip-ft

Therefore, the bending moment in the beam at point C is equal to -48 kip-ft, which means that the beam is experiencing a clockwise bending moment at this location.
To determine the internal normal force, shear force, and bending moment at point C, we need to first analyze the beam with the given load and support conditions. Since we don't have a visual representation of the problem, I will assume a simply supported beam with the roller support at B, and point C is located just to the right of the F = 12 kip load.

1. Internal normal force at point C:
In a simply supported beam, the internal normal force is typically zero, as there are no axial loads acting on the beam. Therefore, the internal normal force at point C is 0 kip.

2. Shear force at point C:
To find the shear force at point C, we need to calculate the reactions at the supports. Let's assume the reaction at support A is R_A and at support B is R_B. Since the beam is in equilibrium, the sum of the vertical forces must be equal to zero:
R_A + R_B = 12 kip
Now, considering the moment equilibrium around point A, we get:
R_B * L = 12 kip * (L/2)
R_B = 6 kip
Since R_A + R_B = 12 kip, we find R_A = 6 kip as well.

The shear force at point C, just to the right of the 12 kip load, is equal to the reaction at support A, as there are no other loads between point A and point C:
Shear force at point C = R_A = 6 kip

3. Bending moment at point C:
To determine the bending moment at point C, we can use the moment equilibrium equation considering the section just to the right of point C:
M_C = R_A * x - F * (x - a), where x is the distance from support A to point C, and a is the distance from support A to the 12 kip load.

Since point C is just to the right of the 12-kip load, x = a. Therefore, the bending moment equation simplifies to:
M_C = R_A * x - F * 0
M_C = 6 kip * x

To find the exact value of the bending moment at point C, we need the value of x.

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Answer:

74 in²

Step-by-step explanation:

The easiest way to find the area is to imagine the rectangle as a whole rectangle, then subtract the area of the empty space.

The area of the whole rectangle can be found with:

A = b · h

A = 9 in · 11 in

A = 99 in²

So the area of the entire rectangle (with the empty space included) is 99 in².

In order to find the area of the composite figure, you need to subtract the area of the empty space, which can be found with:

A = b · h

A = 5 in · h

In order to find the height of the empty space, we can take the whole side (11 in) and subtract the values already there (4 in and 2 in).

11 in - (4 in + 2 in) = 5 in

So the height is 5 in:

A = 5 in · 5 in

A = 25 in²

The area of the composite figure is:

A = 99 in² - 25 in²

A = 74 in²

Answer:

Step-by-step explanation:

My in-head skip solutioning method...:

the 4, 5__2,9___4,4,2__=10in.___5,4__=9in.

......__74

Answer:

66.42°

Step-by-step explanation:

Given

cos ? = \(\frac{2}{5}\) , then

? = \(cos^{-1}\) (\(\frac{2}{5}\) ) ≈ 66.42° ( to the nearest hundredth )

Answer:

Height of the cereal box = 18 in.

Step-by-step explanation:

A cereal box is in the shape of a cuboid.

And volume of a cuboid is represented by the expression,

Volume = Length × Width × Height

It's  given that volume of the box = 432 in³

Length of the base = 2 in.

Width of the base = 12 in

By substituting these values in the expression,

432 = 2 × 12 × h

h = \(\frac{432}{24}\)

h = 18 in.

Therefore, height of the cereal box is 18 in.

Answer:

Step-by-step explanation:

1

8

−

3

6

+

4

0