Each possible outcome of the number cube has the same theoretical probability. what is that probability?

You're answer would be 3.21.

↓ Rounding to a decimal...

[tex]3.2142857142857[/tex]

↓ Rounding to the nearest hundredth...

[tex]3.21[/tex]

Thus, your answer is 3.21.

Answer:

An equilateral triangle has all side lengths the same, and all angles are 60 degrees. Using this we can split the triangle along its altitude to get two right triangles with a hypotenuse of length 10 and a base of 1/2 of the original length, so 5. Now we can either use the Pythagorean theorem (a^2+b^2=c^2) or the fact that it is a 30 60 90 triangle (angles measure at 30 60 and 90 degrees) Pythagorean theorem is probably easier.

It stated that the squares of the two legs of a right triangle add to the square of the hypotenuse. So a(the altitude)^2+5(the base)^2=10(the hypotenuse)^2

A^2+5^2=10^2

A^2+25=100

A^2=75

A=sqrt(75)

A=5*sqrt(3)

Final answer:

The altitude of an equilateral triangle with side length 10 is 5sqrt(3), or about 8.66

Step-by-step explanation:

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In the equation y=kx  , y varies directly with x and k . The constant of variation, k, is 8 .

What is a constant?

A predetermined amount. In algebra, a constant is a number that stands alone or, occasionally, a letter like a, b, or c that denotes a fixed number. 5 and 9 are constants in the formula "x + 5 = 9," for instance.

Since the equation can be written in the form y=kx  , y varies directly with x and k . The constant of variation, k, is 8 .

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Using the concept of probability and the information given, it is determined that the probability of a randomly selected student receiving a GED is 0.0175 = 1.75%.

The specified percentages are:

7% of students drop out and 25% of them get  GED.

So 100 - 7 = 93% of students will not drop out. So 0% have a diploma so they doesn't need a GED.

as a result:

p =  0.07 (0.25) + 0.93 (0) =0.0175

A randomly selected student has a 0.0175 = 1.75% chance of receiving her GED.

your question is incomplete but most probably your full question was

In a certain high school, the probability that a student drops out is 0.07 , and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.25 . What is the probability that a randomly selected student gets a GED?

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Answer:

87 degrees

Step-by-step explanation:

since 37 degrees + angle 1 equals to 124 degrees,  in order to found the measurement of angle 1 you just have to do  124 - 37 which is equal to 87 degrees, so 87 degrees is your answer.

Answer:

No, it is not possible to create a triangle with these measurements.

Step-by-step explanation:

It must follow these rules:

a + b > c

a + c > b

b + c > a

It cannot be equal to it.

The angle 1 is proved congruent to the angle 2 in the triangle ABC and XYZ respectively.

Given, two triangles ABC and XYZ,

we have to prove that the angle A is congruent to the angle X.

Now, as AB = XY (Given)

BC = YZ (Given)

AC = XZ (Given)

By using the Side-Side-Side congruence rule, we get

Δ ABC ≅ ΔXYZ

Now, ∠A = ∠X (By CPCT)

So, the angle 1 is proved congruent to the angle 2 in the triangle ABC and XYZ respectively.

Hence, the angle 1 is proved congruent to the angle 2 in the triangle ABC and XYZ respectively.

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The graph of the linear equality will be a solid line with a y-intercept of negative four and a slope of seven. Description of the graph is The graph will be shaded above the line.

The inequality is expressed as y  ≥ 7x - 4

Now, just focusing on the equality sign

y = 7x - 4

y = 7x + (-4) --- (1)

Any linear equation in slope-intercept form has the following generic form:

y = mx + c --- (2)

so by equation 1 and 2

mx = 7x

m = 7

the equation  y  ≥ 7x - 4,

Put x = 0

y = 7(0) - 4

y = -4

As a result, the graph will look like a solid line with such a negative y-intercept of 4 and a seven slope. It will be shaded above the line on the graph.

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The Ratio Test says that the series converges absolutely it is convergent but not absolutely convergent every absolutely convergent series is also convergent the series is called absolutely convergent

What is the ratio test used for?

Ratio test is one of the tests used to determine the convergence or divergence of infinite series. You can even use the ratio test to find the radius and interval of convergence of power series! Many students have problems of which test to use when trying to find whether the series converges or diverges.

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The work required to pump the oil over the top of the tank is 1.5080 × 10⁶

Given:

We start as we often do: we partition an interval into sub intervals. We orient our tank vertically since this makes intuitive sense with the base of the tank at  y=0 . Hence the top of the oil is at  y=10 , meaning we are interested in subdividing the  y -interval  [0,10]  into  n  sub intervals as

0 = y₁ < y₂ < ..... <yₙ₊₁ = 15

Consider the work  Wi  of pumping only the oil residing in the  ith  sub interval. The force required to move this oil is equal to its weight which we calculate as volume  ×  density. The volume of oil in this sub interval is  Vi=5²πΔyi ; its density is  48  lb/ft ₃ . Thus the required force is  4800πΔyi  lb.

We approximate the distance the force is applied by using any  y -value contained in the  ith  sub interval; for simplicity, we arbitrarily use  yi  for now (it will not matter later on). The oil will be pumped to a point 5 feet above the top of the tank, that is, to the height of  y=15  ft. Thus the distance the oil at height  yi  travels is  15−yi  ft.

In all, the approximate work  Wi  performed in moving the water in the  ith  sub interval to a point 5 feet above the tank is

Wi≈4800πΔyi(15−yi).

To approximate the total work performed in pumping out all the oil from the tank, we sum all the work  Wi  performed in pumping the oil from each of the  n  sub intervals of  [0,10] :

W≈∑i=1nWi=∑i=1n4800πΔyi(15−yi).

This is a Riemann sum. Taking the limit as the sub interval length goes to 0 gives

W=∫3006240π(35−y)dy

=6240π(35y−12y2)∣∣10 0

=  48000π ≈ 1.5080 × 10⁶

Hence we get the required work done.

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Your question is incomplete. Please find the missing content below.

a cylindrical tank 5 feet in diameter and 10 feet high is filled with oil whose density is 48 lbs/ft3 . how much work is required to pump the oil  up to a point 5 feet above the top of the tank.

At cathode reduction occurs so, here Ag(s) will form because it has high reduction potential.

However, at anode oxidation occurs and , here the substance with high oxidation potential can oxidises easily so bromine will form.

Electrolysis:

Electrolysis, the process of passing an electric current through a substance to cause a chemical change. A chemical transformation is when a substance loses or gains electrons (oxidation or reduction).

Small silver ions or bromide ions or both.

Electrolysis of the remaining solution is dependent on concentration, pH, electrodes, current density, etc. Some bromine may be present at the anode if there is a significant amount of bromide ions in solution. Otherwise O₂ will occur. Some silver deposition may occur at the cathode if a significant concentration of silver ion solution is present. If not, the electrochemical reaction will be either oxygen reduction or hydrogen evolution.

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The cost per candle bought  by the Kayla is found as $2.

First off, Kayla purchases 5 candle holders despite the fact that 1 candle holder costs $3.50.

As a result of multiplying the cost with one candle holder with 5, which equals $3.50, we get $17.50.

After deducting 17.50 from 27.50,  10 is left.

Thus, if 5 candles cost $10.

Then, divide 10 by 5 = 2

Therefore, a candle was $2.

Thus, the cost per candle bought  by the Kayla is found as $2.

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The number of black hair pin Janice have is 30.

Given:

Janice ha a collection of 36 hairpin.

1/6 of them are red.

The rest of the pins are black.

we are asked to find the number of black pin Janice have = ?

first calculate the number of red pins:

⇒ 1/6 of 36

⇒ 1/6 × 36

⇒ 6

Janice have 6 red pins, and the remaining as black pins.

⇒ subtract the red pins from the total.

⇒ black pins = 36-6

⇒ black pins  = 30

Hence the number of black pins Janice have is 30.

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In give word problem June 25, 1987 fell on Thursday.

What is word problem?

  Math word problems are math problems consisting of one or more sentences that require children to apply their math knowledge to "real world" scenarios. This means that in order to understand word problems, children must be familiar with the vocabulary associated with familiar mathematical symbols. Students must develop models.

One year = 365 days except for leap years = 366 days

52 weeks in a year 7 days per week = 364 days

1982 25th a Friday, if we move 365 days in the next year we end up on the 25th, but the weekday will be Saturday since we have moved 52 weeks + 1 day into the future.

Hence,

1982 25th Friday

1983 25th Saturday (+1 day)

1984 25th Monday (+1 day and +1 extra day for leap year)

1985 25th Tuesday (+1 day)

1986 25th Wednesday (+1 day)

1987 25th = Thursday

If the system had been 364 days per year, every year we would have end up on the same day every year.

Therefore June 25 , 1987 fell on Thursday.

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The required probability that at least five spots will be showing up on the die is 1/6.

A probability is a number that mirrors the opportunity or probability that a specific occasion will happen. Probabilities can be communicated as extents that reach from 0 to 1, and they can likewise be communicated as rates going from 0% to 100 percent.

Since the quantity of decisions or results is six each "roll" of the die on falls on either 1,2,3,4,5 or 6. That is, each roll has a 1/sixth possibility of a solitary number coming up as a result.

So, the probability that at least five spots will be showing up on the die = 1/6.

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The expressions are solved below :

sinu = -3/5 3π/2 < u < 2π is [ 4th quadrant ]

Now we know that

By using trigonometric identities,

When there are trigonometric functions present in an expression or equation, trigonometric Identities come in handy. Every value of a variable appearing on both sides of an equation is valid in terms of trigonometric identities. These trigonometric functions of one or more angles, such sine, cosine, and tangent, are involved in these geometric identities.

sin²u + cos²u = 1

cos²u= 1-sin²u

cos²u = 1 -(-3/5)²

cos²u= 1 - 9/25

cosu = +4/5

:. u is in 4th quadrant

Now

1.  sin2u = 2 sinu cosu

= 2 (-3/5)(4/5) = -24/25

2. cos2u = 2cos²u- 1

       = 2(4/5)²- 1

       = 7/25

3. tan2u = sin2u /cos2u

              = -24/7

The exact values of the sine, cosine, and tangent of the angle are found.

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When making a joint probability table, the type of probabilities is contained in the cells except those cells on the margin of the table joint probabilities, while those on the margins are marginal probabilities.

A joint probability refers to the probability that two independent events will both occur. two or more random variables. It is a statistical measure that calculates the probability of two events occurring together and at the same point in time i.e., joint probability is the probability of event Y occurring at the same time that event X occurs. A joint probability table represents a joint probability distribution for two or more random variables illustrating the relationship between variables (it uses variables or conditions instead of events). In the joint probability table, the type of probabilities that are contained in the cells are joint probabilities, while those on the margins are marginal probabilities (probabilities of values of the variables in the subset without reference to the values of the other variables.).

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Using Cosine law,

the angle between two shortest sides of triangle is 85.1°..

We have provided that,

A garden has triangular shape.

let "AB" , "BC" , "CA" be sides of triangular shape garden and

we have the sides of triangle are 475 feet , 595 feet and 401 feet i.e AB = 475 , AC = 595 ,

BC= 401

we have to measure of angle between two shortest sides i.e angle between side AB and BC

let x degree be an angle between two shortest sides of triangle .

Using cosine rule ,

(AC)² = (BC)² + (AB )² - 2 AB×BC Cosx

=> (595)² = (401)² + ( 475)² - 2× 475 ×401 Cosx

=> 2(475×401) Cosx = (401)² + (475)² - (595 )²

=> 2 ( 475×401) Cosx = 32401

=> Cosx = 0.085

=> x = cos⁻¹(0.085) = 85.1°

Hence, the angle between two shortest sides of triangle is 85.1°

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The sprinter gene means having Alpha-actinin-3(ACTN3) gene.

In the given question we have to find what does having the sprinter gene mean.

The ACTN3 gene is the recently identified "sprinters gene."

A gene, as we already stated, codes for a protein. Alpha-actinin-3 is designated by ACTN3. This protein, which can only be found in fast twitch muscle fibres, gives muscles their explosive ability.

The fast twitch muscle fibres of sprinters like Usain Bolt and other Olympic athletes would create a lot of alpha-actinin-3.

In order to summarise the genetic component, an individual has the ACTN3 gene if alpha-actinin-3 is present in muscle cells. They are therefore better suited for quick movements.

However, if a person lacks alpha-actinin-3, they have a variant copy of the ACTN3 gene. In other words, they are appropriate for long-distance activities.

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Step-by-step explanation:

The factors divisible by 3 are:

3,6,9,12,15,18,21,24,27,30,33,36,...

Answer:

The pizza restaurant put 1/10 of the sauce on each pizza.

Step-by-step explanation:

Take the 3/5, and on a calculator divide the 3 by the 5:

0.6

Then, take the 0.6 and divide it by the 6 pizzas:

0.1, converted into a fraction equals 1/10.

The pizza restaurant put 1/10 of the sauce on each pizza.

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The continuity theorem, also known as the intermediate value theorem, asserts that if a function is continuous on a closed interval, then it takes on every value inside the interval between the function's minimum and maximum values.

a. Using the continuity theorem, we know that as n→∞, the distribution of Xn converges to a Poisson distribution if the probability mass function of Xn converges to the probability mass function of a Poisson distribution.

This is true because the probability mass function of Xn, which is bin(n, 1/n), converges to the probability mass function of a Poisson distribution as n→∞.

b. Similarly, using the continuity theorem, we know that as n→∞, the distribution of Yn converges to an exponential distribution if the probability mass function of Yn converges to the probability mass function of an exponential distribution.

This is true because the probability mass function of Yn, which is geometric with parameter p = a/n, converges to the probability mass function of an exponential distribution as n→∞.

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The correct answer is yes, because the p-value is 0.0145.

Null hypothesis is the car accidents are equally distributed through out the year

Alternate hypothesis is the car accidents are not equally distributed through out the year

Given that,

Observed Frequencies = O

Spring - 27

Summer - 39

Fall - 31

Winter - 53

Total number of car accidents = 150

Expected Frequencies = E

Spring - 150/4 = 37.5

Summer - 150/4 = 37.5

Fall - 150/4 = 37.5

Winter - 150/4 = 37.5

Test Statistic = 10.5333

Degrees of freedom = 4-1=3

For 3 degrees of freedom ,

p-value = 0.0145;

Given,  level of significance :

=0.05;

As p-value is 0.0145 < level of significance

0.05; Reject null hypothesis.

Hence, there is sufficient evidence to conclude that car accidents are not equally distributed through out the year because the p-value is 0.0145.

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If a team at a factory collected data on the number of nonconforming parts to construct an np-chart then the average fraction has been mentioned below.

The term "average" refers to the mean or centre tendency of a group of data. In other words, it serves as a gauge for the average or median value among a group of numbers. This may be computed by adding up all of the set's values and dividing the result by the total number of values. As an illustration, the average would be (1 + 2 + 3 + 4 + 5) / 5 = 3  if given numbers were 1, 2, 3, 4, and 5.

Average fraction may also be used to represent the expected value or usual outcome of a random variable. For example, if we flip a coin and assign a value of 1 to heads and a value of 0 to tails, the average of the potential outcomes.

How to solve?

= 0.2 and the standard deviation was s = 0.1.

Based on this information, the team can construct an np-chart to monitor the process and identify any potential issues.

The np-chart plots the number of nonconforming parts in each sample against the sample number.

The average fraction nonconforming (p) is indicated by a horizontal line on the chart, and any points that fall outside the upper and lower control limits, which are determined by the standard deviation (s), are considered to be out of control and require further investigation.

This allows the team to monitor the process and take corrective action if necessary to ensure that the number of nonconforming parts remains within acceptable limits.

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A) Probability = 0

B) Probability = 0.4059

C) Probability = 0.7647

D) Probability = 0.4118

A probability simple definition is what?

Probability is a metric used to express the possibility or chance that a particular event will occur. Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.

where a = 8 and b = 25 are the uniform distribution parameters.

A)

probability = P(X>25)= 1-P(X<25)= 1-(25-8)/(25-8)= 0.0000

B)

probability = P(X<14.9)= (14.9-8)/(25-8)=   0.4059

C)

probability = P(10<X<23)= (23-10)/(25-8)=   0.7647

D)

probability = P(18<X<27)= (25-18)/(25-8)=   0.4118

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Answer:

a/ 5

b/ 2

c/ 6

d/ 10

Step-by-step explanation:

For A you can see that 5 divided by 1 equal 5, and 10 divided by 2 = 5, so the scale factor is 5

for B you can see that 10 divided by 5 = 2, and 12 divided by 6 = 2, so the scale factor is 2.

Possible combinations of 2 seats table and 4 seat tables using linear relation is 2x+4y=120 are (0,30) and (60,0) etc.

Given:

The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4 . The total number of people that can be seated in the restaurant is 120.

Let x and y be the number of 2 seat and 4 seats tables.

2x+4y=120

consider x = 0

0+4y=120

4y=120

y = 30

so combination is (0,30)

if y = 0

2x+4*0=120

2x=120

x = 60

(60,0)

Using this equation we can make different type of combinations.

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The volume, in cubic inches, of a packing box is 24000 cubic inches

What is a cuboid?

A cuboid is a solid shape or a three-dimensional shape in geometry. A cuboid is a convex polyhedron that has eight vertices, twelve edges, and six rectangular faces. A rectangular prism is another name for a cuboid. A cube is an object with six square faces on a cuboid.

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

The box is a cuboid.

Volume = length*width*height

             = 40*30*20

             = 24000 cubic inches

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Answer:

9x² + 4x + 8

Step-by-step explanation:

(4x² - 5x + 3) - (-5x² - 9x - 5)

4x² - 5x + 3 + 5x² + 9x + 5

9x² + 4x + 8

I hope this helps!

The equation related to the number of hour and amount of water filled is

y=540x+10000.

What is equation?

 An equation is a mathematical formula containing an equal sign. Equations often involve algebra. Algebra is used in mathematics when we don't know the exact number in a calculation. In its simplest form in algebra, the definition of an equation is a mathematical statement that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign. There are three main forms of linear equations: point-slope form, standard form, and slope  intercept form.

Here given rate per hour = 540 and after 7 hours the pool contain 13780 gallon of water.

Here we need to write equation , then rate is equal to slope.

slope m = 540 .

The number of hours x and amount of water as y, Then,

=> [tex](x_1,y_1)=(7,13780)[/tex]

Now using equation formula,

=> [tex]y-y_1 = m(x-x_1)[/tex]

=> y-13780 = 540(x-7)

=> y-13780 = 540x-3780

=> y = 540x+13780-3780

=> y = 540+10000

Hence the equation is y=540x+10000.

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