This right rectangular prism is filled with 1/3-foot unit cubes.



What are the actual dimensions of the prism?
How many unit cubes are in this prism?
What is the total volume of the prism, in cubic fee

Answer:

y=4/3x-3

Step-by-step explanation:

+4x-(-3y)=1-1/3

The match can be scheduled in 900 different ways.

Here, the number of players from each school = 3.

Let us assue that the players of the first school be A, B, and C.

And the players of the second school be X, Y, and Z.

Here, each player from the first school has to play twice with each player from the second school.

We can organize the schedule into six different rounds, i.e.,

R1 : AX BY CZ

R2 : AX BZ CY

R3 : AY BX CZ

R4 : AY BZ CX

R5 : AZ BX CY

R6 : AZ BY CX

So, the number of possible ways to do this would be : 6! = 720 ways.

Now, three rounds are played simultaneously in each round.

R1 : AX BZ CY

R2 : AX BZ CY

R3 : AY BX CZ

R4 : AY BX CZ

R5 : AZ BY CX

R6 : AZ BY CX

And R1 : AX BY CZ

R2 : AX BY CZ

R3 : AY BZ CX

R4 : AY BZ CX

R5 : AZ BX CY

R6 : AZ BX CY

The total number of possible ways for the second case would be twice of  6! / (2! 2! 2!), which is equal to 90+ 90 = 180.

Therefore, the total number of ways in which the match can be scheduled is 720 + 180 = 900.

Learn more about the permutation here:

https://brainly.com/question/28720645

#SPJ4

The complete question is:

central high school is competing against northern high school in a backgammon match. each school has three players, and the contest rules require that each player play two games against each of the other school's players. the match takes place in six rounds, with three games played simultaneously in each round. in how many different ways can the match be scheduled?

Answer:

Step-by-step explaintation

a2 + 10a = 24

10a + a2 = 24

10a + a2 = 24

Solving for variable 'a'.

Reorder the terms:

-24 + 10a + a2 = 24 + -24

Combine like terms: 24 + -24 = 0

-24 + 10a + a2 = 0

Factor a trinomial.

(-12 + -1a)(2 + -1a) = 0

Set the factor '(-12 + -1a)' equal to zero and attempt to solve:

Simplifying

-12 + -1a = 0

Solving

-12 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '12' to each side of the equation.

-12 + 12 + -1a = 0 + 12

Combine like terms: -12 + 12 = 0

0 + -1a = 0 + 12

-1a = 0 + 12

Combine like terms: 0 + 12 = 12

-1a = 12

Divide each side by '-1'.

a = -12

Simplifying

a = -12

The (f + g)(x) = 15x - 2 is represent the total round trip time.

According to the statement

we have given that the f(x) represents the time it takes a boat to travel upstream and g(x) represents the time it takes a boat to travel downstream.

And we have to find the total round trip time.

So, For this purpose, the given information is:

f(x) = 3x − 10 and g(x) = 12x + 8

And

The total round trip time is represented by the term (f + g)(x)

We know that the

(f + g)(x) = f(x) + g(x)

Substitute the given values in it

So, (f + g)(x) = f(x) + g(x)

(f + g)(x) = (3x - 10) + (12x + 8)

(f + g)(x) = 15x - 2

Hence, The (f + g)(x) = 15x - 2 is represent the total round trip time.

Learn more about Upstream and downstream here

https://brainly.com/question/2108925

#SPJ1

Answer:

4,16,32,320,240

Step-by-step explanation:

Answer:

he got it super wrong itś v/4,v/16,v/32,v/320,v/240

Step-by-step explanation:

Answer:

The median is greater.

Step-by-step explanation:

Median = (2+3) ÷ 2

             = 2.5

Mean = (0+1+2+3+3+5) ÷ 6

          = \(2\frac{1}{3}\)

The probability that this event will happen is 0.295 on the basis of the four predictions. This means that there is a 29.5% chance that the event will happen, according to the forecasters' combined predictions.

1. First, list out all the probabilities assigned by the forecasters: 1/4, 1/5, 2/5, and 1/3.

2. Convert these fractions to decimals to make them easier to work with: 0.25, 0.20, 0.40, and 0.33 (rounded to two decimal places).

3. Add all the decimal probabilities together: 0.25 + 0.20 + 0.40 + 0.33 = 1.18.

4. Divide the sum by the total number of forecasters (4 in this case) to find the average probability: 1.18 ÷ 4 = 0.295.

5. Convert the average probability back to a fraction (optional): 0.295 is approximately equal to 59/200 (rounded to the nearest whole number).

So, based on the average of the four forecasters' predictions, the probability that it will rain tomorrow is 0.295, or 59/200 as a fraction.

Know more about probability here:

https://brainly.com/question/14210034

#SPJ11

The Distance that Ellie ran each evening is 16.5 miles for a entirety week.

We can use the following equation to find how many miles, x, Ellie ran each afternoon:

x + 2.5(3) = 24

Here, x represents the number of miles Ellie ran each afternoon, 2.5 represents the number of miles she ran each morning, and 3 represents the number of days she trained. The total number of miles she ran, 24, is on the right side of the equation.

To solve for x, we can start by simplifying the left side of the equation:

x + 7.5 = 24

Then, we can subtract 7.5 from both sides:

x = 16.5

So, Ellie ran 16.5 miles each afternoon.

To know more on equation at:

brainly.com/question/2972832

#SPJ4

Let's start with the two consecutive numbers. We don't know what are the two numbers that are side by side (consecutive), so we'll use variables but with a twist...instead of x and y, we'll use x for the first number and x+1 for the other number because the other number is 1 more than the value of x. So part of the problem looks like this: (x)+(x+1).

The problem says "the sum of one-third of the first and one-fourth of the second equal 9." One-third of the first would be 1/3(x) and one-fourth of the second would be 1/4(x+1) so if the sum is 9, then the problem is:

1/3(x)+1/4(x+1)=9.

Since we need to solve for x, we must remove the fractions. Right now they have different denominators so we need to make them the same. The least common denominator is 12 so that's the denominator to use, thus...

1/3x becomes 4/12(x) and 1/4(x+1) becomes 3/12(x+1).

Now the equation is 4/12(x)+3/12(x+1)=9

Multiply both sides by 12 so the denominators are gone:

[12•]4/12x+3/12(x+1)=9•12

4x+3(x+1)=108

Using distribution, it's now 4x+3x+3=108. Continuing on with the math...

7x+3=108

7x=105

x=15

We found x! If x=15 the the next number must be 16. Let's check the math: Does 1/3(15)+1/4(16)=9?

5+4=9 and 9=9 so YES! The numbers are 15 and 16

Answer: 227

Step-by-step explanation:

To find the 46th term of the sequence, we need to first determine the pattern of the sequence. We can see that the sequence increases by 5 between each consecutive term. Therefore, the common difference of the sequence is 5.

Using this information, we can find the \(n\)th term of the sequence using the formula:

\(\Large \boxed{an = a1 + d(n-1)}\)

where

Using the given terms, we have:

To find the 46th term, we substitute \(n = 46\) into the formula:

Therefore, the 46th term of the sequence is 227.

________________________________________________________

To find the pattern in the sequence, we can observe that each term is obtained by adding 5 to the previous term. Therefore, we can write the recursive formula for the sequence as:

\(\large a_1 = 2\)

\(\large a_n = a_{n-1} + 5\)

To find the 46th term, we can use the recursive formula to generate each term until we reach the desired term:

\(\large a_1 = 2\)

\(\large a_2 = a_1 + 5 = 2 + 5 = 7\)

\(\large a_3 = a_2 + 5 = 7 + 5 = 12\)

\(\large a_4 = a_3 + 5 = 12 + 5 = 17\)

\(\vdots\)

\(\large a_{46} = a_{45} + 5 \approx \boxed{227}\)

\(\therefore\) The 46th term of the sequence is approximately 227.

We can also write the explicit formula for the sequence as:

\(\large a_n = 5n - 3\)

To verify that this formula generates the same sequence as the recursive formula, we can substitute the value of n = 1, 2, 3, etc. and compare the results.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

The contribution margin ratio for The Halpert Group is approximately 0.63. Therefore, option B. is correct.

To find the contribution margin ratio for The Halpert Group, we'll use the formula:

Contribution Margin Ratio = (Selling Price - Variable Cost) / Selling Price.

Identify the selling price and variable cost per unit.
Selling Price = $20
Variable Cost = $7

Calculate the contribution margin per unit.
Contribution Margin = Selling Price - Variable Cost

Contribution Margin = $20 - $7

Contribution Margin = $13

Calculate the contribution margin ratio.
Contribution Margin Ratio = Contribution Margin / Selling Price

Contribution Margin Ratio = $13 / $20

Contribution Margin Ratio = 0.65

The closest answer to 0.65 is option B. 0.63. Therefore, the contribution margin ratio for The Halpert Group is approximately 0.63.

So, option B. is correct.

Learn more about contribution margin:

https://brainly.com/question/24881206

#SPJ11

With the help of probability we can conclude our answer.

acc to our question-

learn more about probability click here:

brainly.com/question/13604758

#SPJ4

Answer:

800

Step-by-step explanation:

Area of square:

Area of triangle:

Combine the areas:

I hope this helps!

Answer:

0.085

Step-by-step explanation:

We know that 1/2=0.5. And to convert from percent to decimal you have to divide by 100.

Given equation g = x-1/k in terms of x would be x = 1 + gk

for given question,

we have been given an equation g = x-1/k

Dyani began solving the equation g = x-1/k for x by using the addition property of equality.

We solve given equation for x.

⇒ g = x-1/k                      ..........(Given)

⇒ gk = (x - 1/k)k               .........(Multiply both the sides by k)

⇒ gk = x - 1

⇒ gk + 1 = x - 1 + 1           .........(Add 1 to each side)

⇒ gk + 1 = x

⇒ x = 1 + gk

Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

Answer: ↓↓

Step-by-step explanation:

10 ÷ -5

The answer's -2 btw

Hope this was what you were asking

Answer:

B

Step-by-step explanation:

Answer:

Just took the test the answer is 85%

Answer:

options (a), (b), (c), and (e) have the same solution as the solution of  3/5 x + 2/3 + x = 1/2 -1/5x.

Step-by-step explanation:

The given equation is

3/5 x + 2/3 + x = 1/2 -1/5x

First, rearrange the equation to have constant terms and the terms having variable on the separate side.

3/5 x + x +1/5x= 1/2 - 2/3

9/5 x = -1/6

x= -1/6 ÷ 9/5

x= -1/6 x 5/9

x= -5/54 ...(i)

Now, find the solution of all the options in the similar way:

(a) 8/5 x +2/3 = 1/2 -1/5 x

8/5 x + 1/5 x = 1/2 - 2/3

9/5 x = -1/6

x= -1/6 ÷ 9/5

x= -1/6 x 5/9

x= -5/54 which is same as the solution of the mentioned equation. [ from equation (i)]

(b) 18x + 20 + 30x = 15 – 6x

18x+30x+6x = 15 -20

54x=-5

x= -5/54 which is same as the solution of the mentioned equation. [from equation (i)]

(c) 18x + 20 + x = 15 – 6x

18x+x+6x = 15 -20

25x=-5

x= -5/25 which is not the same as the solution of the mentioned equation. [ from equation (i)]

(d) 24x + 30x = –5

54x = -5

54x=-5

x= -5/54 which is same as the solution of the mentioned equation. [ from equation (i)]

(e) 12x + 30x = –5

42x = -5

42x=-5

x= -5/42 which not is same as the solution of the mentioned equation. [ from equation (i)].

Hence, options (a), (b), (c), and (e) have the same solution as the solutions of the given equation.

The solution for the x for the inequality ||3x −1|+5| <1 is x<7/3

In the given problem basically, ||3x −1|+5| <1, we are dealing with the absolute value, which for real numbers is referred to as the non-negative value of that number without regard for consideration to its sign. Denoted by the symbol "| |', it is also known as the modulus of the number, and also with the inequality, which is a non-equal comparison between two numbers, additional mathematical expressions.

the inequality equation we got is ||3x-1|+5|<1

now we are taking the absolute value of it, we get

=>3x + 1 + 5 < 1

subtracting 1, and 5 from both sides, we get

=>3x < 1 + 5 + 1

=>3x < 7

=>x < 7/ 3

To know more about inequality, refer to the link brainly.com/question/20383699

#SPJ1

Answer:

78

Correct term:60

Step-by-step explanation:

We are given that

\(\frac{4x^4-6x^3+6x+3}{x-3}\)

The quotient of this expression is given by

\(4x^3+6x^2+18x+78+\frac{183}{x-3}\)

We have to find the term in this expression  which contains an error.

\(\frac{4x^4-6x^3+6x+3}{x-3}\)

The quotient of this expression is given by

\(=4x^3+6x^2+18x+60\)

\(Dividend=Divisor\times quotient+ remainder\)

Using the formula

\(4x^4-6x^3+6x+3=(x-3)(4x^3+6x^2+18x+60)+\frac{183}{x-3}\)

We can see that in the given expression there is 60 in place of 78.

The error in the expression of quotient is 78.

Correct term is 60.

Answer:

10. 3.75 cm

Step-by-step explanation:

10. (5x-5)/56=(3x-5)/32

                 x=1.75

AC=5x-5

    =5*1.75-5

    =3.75 cm

Mark me as brainliest

If the intended margin of error equals 4 less than with a 0.95 probability, the sample size is 126.

The \(\alpha\) level is calculated by subtracting 1 from the confidence interval and dividing by 2.

\(\alpha\) = (1 - 0.95) ÷ 2

\(\alpha\) = 0.025

Find z inside the Z-table because it has a p-value of 1 - \(\alpha\).

So, z = 1.96 with a p-value = 1 - 0.025 = 0.975.

Now, consider that margin of error M.

M = z × (σ ÷ √n)

The standard deviation is determined as the square root of variance.

σ = √522 = 22.84

With a 0.95 probability, the sample size that requires to be accepted if the expected margin of error is 4 or less is,

The sample size of at least n, in which n is encountered when M = 4. So,

M = z × (σ ÷ √n)

4 = 1.96 × (22.84 ÷ √n)

4√n = 1.96 × 22.84

√n = (1.96 × 22.84) ÷ 4

√n = 11.1916

n = (11.1916)²

n = 125.25 ≈ 126

A sample size of at minimum 126 people is required.

Learn more about the probability at

https://brainly.com/question/15121653?referrer=searchResults

#SPJ4

Answer:

c

Step-by-step explanation:

sorry if it is wrong

The distribution of X is uniform distribution (U(5, 12)). The probability that it takes Lizzie at least 13 minutes is 0, the probability that it takes less than 9.5 minutes is 0.5833,

The probability that it takes between 5.3 and 9.7 minutes is 0.7333, and the probability that it takes fewer than 5.3 minutes or more than 9.7 minutes is 0.2667.

a. The distribution of X, the time it takes Lizzie to eat an apple, is a uniform distribution. We can denote it as X ~ U(5, 12), where U represents the uniform distribution and (5, 12) indicates the interval from 5 to 12 minutes.

b. To find the probability that it takes Lizzie at least 13 minutes to finish the next apple, we calculate the probability of X being greater than or equal to 13. Since the distribution is uniform, the probability is zero because the interval only goes up to 12 minutes.

P(X ≥ 13) = 0

c. To find the probability that it takes Lizzie less than 9.5 minutes to finish the next apple, we calculate the cumulative probability up to 9.5 minutes.

P(X < 9.5) = (9.5 - 5) / (12 - 5) = 0.5833

d. To find the probability that it takes Lizzie between 5.3 minutes and 9.7 minutes to finish the next apple, we calculate the difference between the cumulative probabilities at 9.7 minutes and 5.3 minutes.

P(5.3 ≤ X ≤ 9.7) = (9.7 - 5.3) / (12 - 5) = 0.7333

e. To find the probability that it takes Lizzie fewer than 5.3 minutes or more than 9.7 minutes to finish the next apple, we subtract the probability of the interval (5.3, 9.7) from 1.

P(X < 5.3 or X > 9.7) = 1 - P(5.3 ≤ X ≤ 9.7) = 1 - 0.7333 = 0.2667

In summary, the distribution of X is uniform (U(5, 12)). The probability that it takes Lizzie at least 13 minutes is 0, the probability that it takes less than 9.5 minutes is 0.5833, the probability that it takes between 5.3 and 9.7 minutes is 0.7333, and the probability that it takes fewer than 5.3 minutes or more than 9.7 minutes is 0.2667.

Learn more about Uniform Distribution here:

brainly.com/question/30639872

#SPJ11

Answer:

5/6

Step-by-step explanation:

The correct answer is B. quotient. In the context of sequences, the term "common difference" refers to the constant value by which each term in an arithmetic sequence increases or decreases.

On the other hand, the term "common ratio" is used in geometric sequences to represent the constant value by which each term is multiplied or divided to obtain the next term.

Given this information, let's examine the options:

A. Ratio: A ratio is a comparison of two quantities. While ratios can be used in various mathematical contexts, it is not directly associated with the idea of a common difference in an arithmetic sequence or a common ratio in a geometric sequence. Therefore, option A is not the correct choice.

B. Quotient: A quotient is the result of dividing one quantity by another. Although quotients can be calculated in both arithmetic and geometric sequences, it does not directly capture the concept of a common difference or a common ratio. Therefore, option B is not the correct choice.

C. Proportion: A proportion is an equation that states two ratios are equal. While proportions are applicable in certain situations involving sequences, it is not specifically related to the concept of a common difference or a common ratio. Therefore, option C is not the correct choice.

D. Denominator: The denominator is the bottom part of a fraction, representing the total number of equal parts into which a whole is divided. The denominator is not directly related to the concept of a common difference or a common ratio in sequences. Therefore, option D is not the correct choice.

In conclusion, the correct answer is none of the given options. The term "common ratio" is used to describe the constant value by which each term is multiplied or divided in a geometric sequence.

Learn more about arithmetic sequence here;

https://brainly.com/question/28882428

#SPJ11