. if seven balanced dice are rolled, what is the probability that each of the six different numbers will appear at least once?

Answer:

Example 1:

Given that y varies proportionally with x , with a constant of proportionality k=1/3 , find y when x=12 .

Write the equation of the proportional relationship.

The variable x varies proportionally with y with a constant of proportionality equal to 1/3

So, y=1/3x

Substitute the given x value.

y=1/3×12

y=4

Step-by-step explanation:

hope it helps

Table is a way to represent the data of the two or more variable.

The correct order for the ranks of the waves from the lowest energy wave to the highest energy wave of the given table is 1-4-3-2. Thus the option 1 is the correct option.

Table is a way to represent the data of the two or more variable.

To read the data from the table look for the value of one variable, and get the resultant value of other variable from the corresponding block.

Given information-

The first column labeled Wave has entries 1, 2, 3, 4.

The table given in the problem is,

First column                         Second column

  1                          This wave has 3 centimetre amplitude

  2                         The distance from the midpoint to the crest is 6 cm,

  3                         The distance from the midpoint to the trough is 12 cm,

  4                         This wave has a 4 centimetre amplitude.

The ranks of the waves from the lowest energy wave to the highest energy wave of the given table has to find out.

As the energy of a wave is related to the amplitude of the wave, as the how much amount of energy it is carrying with it.

The distance from the midpoint to the crest is called the amplitude.

Thus the more value of the amplitude gives the more energy.

Therefore,

Hence, the correct order for the ranks of the waves from the lowest energy wave to the highest energy wave of the given table is 1-4-3-2. Thus the option 1 is the correct option.

Learn more about the data table here;

https://brainly.com/question/15602982

Answer:

A

Step-by-step explanation:

Answer:

x = 93.7ft or x = 94ft

Step-by-step explanation:

Hope that helps :)

Sample Mean: 3.25

Standard Deviation: 2.29

CI: 1.36 to 5.14

To compute the sample mean, add up all the values and divide the sum by the number of values in the data set. In this case, the data set is 3, 4, 6, 8, 2, 1, 0, 2.

Summing up the values: 3 + 4 + 6 + 8 + 2 + 1 + 0 + 2 = 26.

There are 8 values in the data set, so divide the sum by 8: 26 / 8 = 3.25.

Therefore, the sample mean is 3.25 cups of coffee per day.

To compute the sample standard deviation, we need to find the square root of the variance. The variance is the average of the squared differences from the mean.

First, calculate the squared differences from the mean for each value:
(3 - 3.25)^2 = 0.0625
(4 - 3.25)^2 = 0.5625
(6 - 3.25)^2 = 7.5625
(8 - 3.25)^2 = 20.0625
(2 - 3.25)^2 = 1.5625
(1 - 3.25)^2 = 5.0625
(0 - 3.25)^2 = 10.5625
(2 - 3.25)^2 = 1.5625

Next, find the average of these squared differences:
(0.0625 + 0.5625 + 7.5625 + 20.0625 + 1.5625 + 5.0625 + 10.5625 + 1.5625) / 8 = 5.25.

Finally, take the square root of the variance to find the sample standard deviation:
sqrt(5.25) ≈ 2.29.

Therefore, the sample standard deviation is approximately 2.29 cups.

To construct a 95% confidence interval for the mean number of cups of coffee consumed among all undergraduates, we can use the formula:

CI = sample mean ± (t * (sample standard deviation / sqrt(n))),

where t is the t-value for the desired confidence level, sample standard deviation is the calculated standard deviation, sqrt(n) is the square root of the sample size, and the sample mean is the calculated mean.

For a 95% confidence level, with a sample size of 8, we can find the t-value from a t-table. The t-value for a 95% confidence level with 8 degrees of freedom is approximately 2.306.

Plugging in the values, the confidence interval is:

CI = 3.25 ± (2.306 * (2.29 / sqrt(8))).

Calculating the lower limit:
3.25 - (2.306 * (2.29 / sqrt(8))) ≈ 1.36.

Calculating the upper limit:
3.25 + (2.306 * (2.29 / sqrt(8))) ≈ 5.14.

Therefore, the 95% confidence interval for the mean number of cups of coffee consumed among all undergraduates is approximately 1.36 to 5.14 cups per day.

Learn more about Confidence Intervals: https://brainly.com/question/20309162

#SPJ11

The note Micah made for the test on right triangles is correct by the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

so by Pythagoras rule we can write:

For the first right triangle;

(x/√2)² + (x/√2)² = x²...(1)

from the left hand side of equation (1): (x/√2)² + (x/√2)²

x²/2 + x²/2

2(x²)/2 = x² {the right hand side of equation (1)}

and for the second right triangle;

(x√3/2)² + (x/2)² = x²...(2)

from the left hand side of equation (2): (x√3/2)² + (x/2)²

x²(3)/4 + x²/4

3x²/4 + x²/4

(3x² + x²)/4

4x²/4 = x² {the right hand side of equation (2)}

Therefore by Pythagoras rule the note Micah made for the test on right triangles is correct

Know more about Pythagoras here:https://brainly.com/question/343682

#SPJ1

Answer:

2

+

8

+

6Step-by-step explanation:

Answer:

Step-by-step explanation:

\(x^2+8x+6 =\\\\=\underline{x^2+2\cdot x\cdot 4+4^2}-4^2+6=\\\\=(x+4)^2-16+6=\\\\=(x+4)^2-10\)

To estimate the chance of getting 12 heads and 13 tails when a coin is tossed 25 times, we can use the binomial probability formula.

The binomial probability formula is given by:

P(x) = (nCx) * p^x * q^(n-x)

Where:

P(x) is the probability of getting x successes,

n is the total number of trials,

x is the number of desired successes,

p is the probability of success on a single trial,

q is the probability of failure on a single trial, which is equal to 1 - p,

and (nCx) is the number of combinations of n items taken x at a time.

In this case, n = 25, x = 12 (number of heads), p = 0.5 (since the coin is fair), and q = 1 - p = 0.5.

Using the binomial probability formula, we can calculate the probability of getting 12 heads and 13 tails as:

P(12 heads) = (25C12) * (0.5^12) * (0.5^13)

Calculating this expression will give us the estimated chance of getting 12 heads and 13 tails when a coin is tossed 25 times.

To learn more about probability : brainly.com/question/31828911

#SPJ11

Given:

The arithmetic sequence is:

\(1, 6, 11, 16, 21,...\)

To find:

1. The rule for the nth term of the given arithmetic sequence.

2. The 10th term of the given arithmetic sequence.

Solution:

1. We have,

\(1, 6, 11, 16, 21,...\)

Here, the first term is 1 and the common difference is:

\(d=a_2-a_1\)

\(d=6-1\)

\(d=5\)

The nth term of an arithmetic sequence is:

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

Where, a is the first term and d is the common difference.

Putting \(a=1,\ d=5\), we get

\(a_n=1+(n-1)5\)

\(a_n=1+5n-5\)

\(a_n=5n-4\)

Therefore, the nth term of the given sequence is \(a_n=5n-4\).

2. We need to find the 10th term of the given arithmetic sequence.

From part 1 it is clear that the nth term of the given arithmetic sequence is:

\(a_n=5n-4\)

Putting \(n=10\), we get

\(a_{10}=5(10)-4\)

\(a_{10}=50-4\)

\(a_{10}=46\)

Therefore, the 10th term of the given arithmetic sequence is 46.

Answer:

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. We know that 1 yard is 36 inches, therefore, 50 yards expressed in inches is:

(50)(36)=1800in

2. If he is 50 yards from school and the map shows that the school is 34 inches from his current location, when it shows 3 inches the real distance is:

(1800)(3in)/24in=158.82

3. If you can to express it in yards:

158.82/36=4.41yd

Therefore, the answer is: 158.82 inches or 4.41 yards.

Answer:

Step-by-step explanation:

Solving for x,

This way, we can conlcude that:

Answer:

Difficult to infer an answer with such little information but I would assume it's "Definition of Midpoint" if you're writing a proof.

Hey there!

Answer: \( \Rightarrow \sf{\frac{x+3}{x -2}}\)

\( \rightarrow \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } }\)

\( \rightarrow{ \rm{factorise} \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } } = \frac{(x + 2)(x + 3)}{ {x}^{2} - 4} = \frac{(x + 2)(x + 3)}{(x + 2)(x - 2)} = \Rightarrow \sf{\frac{x+3}{x -2}}}\)

Answer:

0, 3 , 8

Step-by-step explanation:

substitute n = 1, 2, 3 into the pattern rule

T₁ = 1² - 1 = 1 - 1 = 0

T₂ = 2² - 1 = 4 - 1 = 3

T₃ = 3² - 1 = 9 - 1 = 8

Answer:

P(t) = 10t - 400

Step-by-step explanation:

Selling price of each ticket = $10

Cost of setting up the dance= $400

Profit = Revenue - cost

Revenue = price × quantity

Revenue that will maximize profit = 10t

where t= quantity of tickets that maximises profits

Cost = $400

Profit(t) = Revenue - cost

P(t)= 10t - 400

We want to find the equation that represents the school's profit. We will get:

P(x) = $10*x - $400

We know that the tickets to the school dance are sold for $10 each, then the revenue, if they sell x tickets, is just:

r(x) = $10*x

And we know that they spent a total of $400.

Remember that profit is defined as the difference between revenue and costs, so the profit equation is just:

P(x) = $10*x - $400

If you want to learn more, you can read:

https://brainly.com/question/15379502

3q+30q+12q = 45q

Hope that helped :)

Answer:

35q+8qq

Step-by-step explanation:

i know is ryt

but y did u separate de first 4's other q like dat?

Answer:

3²

Step-by-step explanation:

We have to use BPEMDAS Order of Operations:

B - Brackets

P - Parenthesis

E - Exponents

M - Multiply

D - Divide

A - Addition

S - Subtraction

We use this order left to right. Since we have parenthesis, we look at that first. Inside, we have division and exponents. Since exponents come first, we have to evaluate 3² first.

Answer:

square the 3

Step-by-step explanation:

In the order of operations, you must do the exponent inside the parentheses first, so the first step is:

4(27 ÷ 3²) =

= 4(27 ÷ 9)

Answer: square the 3

Answer:

A). 15

B). -1.2

Step-by-step explanation:

A). [10(x+3)]-20 = 160

10x+30-20 = 160

10x+10 = 160

10x = 160-10

10x = 150

x = 150/10

x = 15

B). 5{[4(8+(5x))]-9} = 85

5(32+20x+9) = 85

5(32+9+20x) = 85

5(41+20x) = 85

205+100x = 85

100x = 85-205

100x = -120

100x/100 = -120/100

x = -1.2

----------------------------------------------------------------------

HOPE THIS HELPS!!!

The three computations covered by the reliability factor table are sample size, index of reliability, and index of precision. Sample size deals with the size of the sample being used in order to achieve a desirable level of reliability.

Index of reliability is used to measure the consistency of results achieved over multiple trials. It does this by calculating the total number of items that contribute significantly to the final result. Finally, the index of precision measures the effect size of the sample, which is determined by comparing the results from the sample with the expected results.

The sample size computation gives the researcher an idea of the number of items that should be included in a sample in order to get the most reliable results. This is done by taking into account a number of factors including the variability of the population, the type of measurements used, and the desired level of accuracy.

The index of reliability is commonly calculated by finding the ratio of the number of items contributing significantly to the total result to the total number of items in the sample. This ratio is then multiplied by 100 in order to get a final score.

know more about reliability here

https://brainly.com/question/32178729#

#SPJ11

When the problem asks to evaluate an expression often means to test certain variable with a specific value. However, in this case, evaluating this equation refers to solving it to see if the equation is true or false. So, let's solve it

The first step is to solve products:

Then, we solve the difference:

As you can observe, 17 isn't equal to 12, which means the initial expression is completely false.

Therefore, according to the evaluation, the expression is false.

To accumulate $2,176,097.00 in his retirement account by age 65, Derek needs to make annual deposits of $5,000.00 starting on his 27th birthday and ending on his 65th birthday, assuming an 8.00% interest rate.

To determine the annual deposits Derek needs to make, we can use the future value of an ordinary annuity formula. First, we calculate the number of years between Derek's 25th and 65th birthdays, which is 65 - 25 = 40 years. Next, we calculate the future value of the retirement account using the given interest rate of 8.00%. Using the formula:

Future Value = Present Value * (1 + interest rate)^number of periods

In this case, the future value is $2,176,097.00, the interest rate is 8.00%, and the number of periods is 40. We can rearrange the formula to solve for the present value:Present Value = Future Value / (1 + interest rate)^number of periods

Substituting the values:Present Value = $2,176,097.00 / (1 + 0.08)^40 = $123,529.31 (rounded to 2 decimal places)

Now, we need to find the annual deposit amount. Since Derek starts making deposits on his 27th birthday and ends on his 65th birthday, he makes deposits for 65 - 27 = 38 years.Annual Deposit = Present Value / ((1 + interest rate)^number of periods - 1)Substituting the values:

Annual Deposit = $123,529.31 / ((1 + 0.08)^38 - 1) = $5,000.00 (rounded to 2 decimal places)Therefore, Derek must make annual deposits of $5,000.00 into his retirement account starting on his 27th birthday and ending on his 65th birthday to accumulate $2,176,097.00 by the time he turns 65.

To learn more about interest rate click here

brainly.com/question/32615546

#SPJ11

==============================================

Further Explanation:

Whenever you are doing a proof, always start with the given info. It may seem silly to literally repeat (word-for-word) what your teacher has given you, but this is how all proofs start out. It helps place an anchor point in which you can connect to what you want to prove.

So this is why the first line is literally a repeat of what your teacher has stated. The reason you'll state is "given".

------------------

For reason 2, we use the vertical angle theorem. Vertical angles are always congruent.

Vertical angles form whenever we have an X shape like this of two segments crossing. The angles are opposite one another (almost like mirror images of sorts).

-----------------

Lastly, reason 3 uses the SAS (side angle side) similarity theorem.

This is the theorem which says that if you have two pairs of sides in proportion and a pair of congruent angles between those sides, then we can prove the triangles similar.

Statement 1 handles the sides being in proportion. Statement 2 handles the congruent angles.

As you can see, everything in this proof builds step by step toward the final goal of saying triangle ABC is similar to triangle EBD.

Answer:

well 1 plus 1 is 2 so i dont know

Step-by-step explanation:

:)

The peak of the graph represents option B: the number of larvae in the water is greatest at 5 degrees Celsius.

The peak of a graph represents the highest point of the graph. In this case, it represents the temperature at which the number of insect larvae in the water is greatest. So, if you look at the graph created by the biologist, you can see that the number of larvae in the water is greatest at 5 degrees Celsius.

The graph is a quadratic function graph because it is a parabola and opens downward; as a result, it has a negative leading coefficient, or a negative coefficient of x².

The function's graph demonstrates that,

The parabola's peak, or highest point, is (450).

In other words, if x=5, then the value of y=450.

That is, when the temperature of the water is 5°, then the number of larvae in water is 450. Therefore, at 5 degrees Celsius, the number of larvae in the water is at its peak.

To know more about the peak of the graph, refer:

https://brainly.com/question/10278809

#SPJ4

Complete question is:

A biologist created the following graph to show the relationship between the temperature of water (x), in degrees Celsius, and the number of insect larvae (y) in the water: what does the peak of the graph represent?

the number of larvae in the water is greatest at 450 degrees celsius.

the number of larvae in the water is greatest at 5 degrees celsius.

the least number of larvae in the water is 450.

the least number of larvae in the water is 5.

Answer:

to get x look at that triangle that it is in I know the angles in a triangle add up to 180° so it will be 180 - 63 degrees plus 36 degrees then to get z it will be 36 + 63 because interior angles add up to one exterior angle then to get y addz + 13 degrees then subtract it from 180°

In order to find the values of the sides of the triangle you take into account the relation between sides and hypotenuse.

h: hypotenuse

c1: shorter leg

c2: longer leg

Longer leg c2 is 3 inches longer than c1:

c2 = c1 + 3

hypotenuse h is 6 inches longer than c1:

h = c1 + 6

The formula for the calculation of the hypotenuse is:

h² = c1² + c2²

you replace for h and c2 in terms of c1:

(c1 + 6)² = c1² + (c1 + 3)²

You solve the previous equation for c1:

c1² + 12c1 + 36 = c1² + c1² + 6c1 + 9

c1² - 6c1 - 27 = 0

the roots of the previous equation are:

(c1 - 9 )(c1 + 3) = 0

c1 = 9

c1 = -3

You take the positive number because there is no length of sides with negative values.

Then, c2 and h are:

c2 = c1 + 3 = 9 + 3 = 12

h = c1 + 6 = 9 + 6 = 15

Hence, shorter leg is 9 inches, longer leg 12 inches and hypotenuse 15 inches

A matrix structure is an adaptation of the divisional structure whereby various divisions or parts of divisions are grouped together based on some common strategic elements, usually linked to distinct product/market differences.

In a matrix structure, organizations create a dual reporting system where employees report to both functional managers and project or product managers. This structure allows for greater flexibility and collaboration across departments, as individuals from different functional areas come together to work on specific projects or initiatives. The matrix structure is often employed in complex organizations that operate in multiple markets or industries, as it enables efficient resource allocation and coordination. By grouping divisions or parts of divisions based on common strategic elements, organizations can streamline decision-making processes and enhance cross-functional communication and cooperation.

To learn more about matrix structure : brainly.com/question/30403441

#SPJ11

The value of x is 5 from the diagram.

The sum of interior angle of a triangle is 180 degrees. Hence:

From the information given,;

73 = 8y - 7 (base angles are equal)

8y = 80

y = 10

Take the sum of the angles:

73  + 6x + 4 + 73 = 180

6x + 150 = 180

6x = 30

x= 5

Hence the value of x is 5 from the diagram.

Learn more on triangles here: https://brainly.com/question/2938476

The value of x is 5.

Since triangle ABC is an isoceles triangle, angle A = Angle C(base angles of an isoceles triangle are equal)

Since angle A = 73° and angle C = (8y - 7)°

angle A = angle C

⇒ 73 = 8y - 7

Adding 7 to both sides, we have

73 + 7 = 8y - 7 + 7

80 = 8y

Dividing both sides by 8, we have

y = 80/8

y = 10

Also, angle A + angle B + angle C = 180° (sum of angles in a triangle)

73 + 6x + 4 + 8y - 7 = 180

Collecting like terms, we have

73 + 4 - 7 + 6x + 8y = 180

6x + 8y + 70 = 180

Subtracting 70 from both sides, we have

6x + 8y + 70 - 70 = 180 - 70

6x + 8y = 110

Making x subject of the formula, we have

6x = 110 - 8y

x = (110 - 8y)/6

Substituting the value of y into the equation, we have

x = (110 - 8y)/6

x = (110 - 8 × 10)/6

x = (110 - 80)/6

x = 30/6

x = 5

So, the value of x is 5.

Learn more about angles in a triangles here:

https://brainly.com/question/7888180