How many ways can the train be made up?

How Many Ways Can The Train Be Made Up?

Answers

Answer 1

Answer:

16c9

Step-by-step explanation:

First, we will add up the number of different car possibilities. This is:

6 + 7 + 3 = 16.

Then, we need to take 9 of these 16 cars, giving us 16c9.

Hope this helped!

Answer 2

Answer:

4,151,347,200

Step-by-step explanation:


Related Questions

Evan completed his math homework in 23 minutes. It took Troy 2 times as long
to complete his math homework. How long did it take Troy to complete his
homework?
minutes

Answers

Answer:

46

Step-by-step explanation:

You multiply 23×2 and that is how I got my answer.

What are the factors of the expression x² 4x 3?

Answers

The factors of the expression x² 4x 3 are (x + 3)(x − 3).

What is factor?

Factor is a number that can be multiplied to produce another number. Factors are used to find the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers. Factors are also used in equations to find solutions and in algebra to solve polynomials. Factors are also important in computing, since they are used to identify prime numbers and prime factorisation.

This is determined by using the factoring technique called factoring by grouping.

First, the expression is written in two groups: x2 and 4x 3. Then, each group must be factored. For the first group, the factors are x and x, since any number multiplied by itself results in the number itself. For the second group, the factors are 4 and 3, since 4 multiplied by 3 equals 12.

Next, the two factors of each group must be multiplied together. The product of x and 4 is 4x, and the product of x and 3 is 3x. The product of 4 and 3 is 12.

Finally, the two groups of factors are combined to form the final expression: (x + 3)(x − 3).

To know more about factor click-
https://brainly.com/question/2826496
#SPJ4

The Measures of two sides of a triangle are 12 and 13. Use an inequality to express the range of the measure of the third side, m.

A. 1 < m < 15
B. 1 < m < 25
C. 12 < m < 25
D. 0 < m < 11

Answers

The required inequality expression for the third side is 1 < m < 25. The correct option is (B).

What is linear inequality?

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The sides of the triangle are given as 12 and 13 units respectively.

As per the rule for sides of a triangle, the third side is always less than the sum and greater than the difference of two sides.

Then, the inequality can be written as,

13 - 12 < m < 13 + 12

⇒ 1 < m < 25

Hence, the measure of third side can be written in inequality as 1 < m < 25.

To know more about linear inequality click on,

https://brainly.com/question/11897796

#SPJ1

What is a 2 step equation example?

Answers

The general two steps to solve the two-step equations are:

Step 1: Addition and subtraction to isolate the variable.

Step 2: Multiplication or division to determine the value of the variable.

Now, According to the question:

Solving Two Step Equations:

Two step equations are very easy to solve. It includes just one extra step as compared to one-step equations to solve. We can solve a two-step equation by isolating the variable (usually represented by an alphabet or letter) on one side of the equation and all other values on the other side. The general two steps to solve the two-step equations are:

Step 1: Addition and subtraction to isolate the variable.

Step 2: Multiplication or division to determine the value of the variable.

Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are:

2x + 3 = 70.3y + 5 = 1(2/3)z - 12 = 10

Learn more about Two-Step equation at:

https://brainly.com/question/26119747

#SPJ4

margin of error of 1 percentage and use a confidence level of ​90%.

Answers

The sample size needed for a margin of error of 1%, for a confidence level of 90%, is of:

6,766.

What is a confidence interval of proportions?

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.

The margin of error of the interval is defined as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.

We have no prior estimate, hence the proportion is given as follows:

[tex]\pi = 0.5[/tex]

For a margin of error of M = 0.01, the needed sample size n is obtained as follows:

[tex]0.01 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.645 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{1.645 \times 0.5}{0.01}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 0.5}{0.01}\right)^2[/tex]

n = 6,766.

(rounding up, as for a sample size of 6,765 the margin of error would be slightly above 0.01).

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

A football team consists of 20 each freshmen and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that

Answers

On solving the provided question, we can say that Probability ( At least one of the students is a senior) = 0.4632 approx

What is probability?

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

P(All four players are senior) = 0.00033 approx

P(There is one each: freshman, sophomore, junior and senior) = 0.0944 approx.

P(There are 2 sophomores and 2 freshman) = 0.0568  approx

P( At least one of the students is a senior) = 0.4632 approx

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ4

150% ×_____ = $6.75 ​find the unknown

Answers

Answer:

The answer is $4.50.

Step-by-step explanation:

To solve this problem, divide the result ($6.75) by the percentage (150%). This gives you the original number which was multiplied by the percentage. So,

$6.75 / 150% = $4.50.

Answer:

$4.50

Step-by-step explanation:

150% × □ = $6.75

First, we can rewrite 150% as the fraction 3/2.

[tex]\dfrac{3}{2} \times \square = \$ 6.75[/tex]

Then, we can also rewrite 6.75 as the fraction 27/4.

[tex]\dfrac{3}{2} \times \square = \$ \, \dfrac{27}{4}[/tex]

Next, we can isolate the unknown by multiplying both sides by 2/3 (the reciprocal of 3/2).

[tex]\left(\dfrac{2}{3} \right)\left(\dfrac{3}{2} \times \square \right) = \left(\$ \, \dfrac{27}{4}\right)\left(\dfrac{2}{3} \right)[/tex]

After that, simplify by multiplying out the numerators and denominators on the right side of the equation.

[tex]\square = \$ \, \dfrac{27 \times 2}{4 \times 3}[/tex]

[tex]\square = \$ \, \dfrac{54}{12}[/tex]

Finally, simplify the expression on the right side to a decimal form.

[tex]\square = \$ \, \dfrac{54 \div 2}{12 \div 2}[/tex]

[tex]\square = \$ \, \dfrac{27 \div 3}{6 \div 3}[/tex]

[tex]\square = \$ \, \dfrac{9}{2}[/tex]

[tex]\square = \$ 4.50[/tex]

Determine the prices for which quantity demanded is greater than quantity supplied.

Answers

The prices where the quantity demanded is greater than quantity supplied are :

$ 2$ 1$ 0

When is quantity demanded greater than quantity supplied ?

Quantity demanded refers to the amount of goods and services that people and businesses in an economy demand.

This amount of goods and services demanded will be more than the quantity supplied when the price of the good or service is less than the equilibrium price.

The equilibrium price here is $ 3 and so the prices less than $ 3 are $2, $1, and $ 0.

Find out more on quantity demanded at https://brainly.com/question/1692392

#SPJ1

Explain if the ordered pairs represent a function or not.
(1,2)(1,3)(2,4)(3,6)(0,0)(-1,4)

Answers

Not a function, the x values have different y values. In order for it to be a function, all the x values must have specific y values

Makea is making smoothies. For every 4 cups of orange juice, she uses 3 tablespoons of yogurt. Which ratio of orange juice to yogurt is NOT equivalent to the ratio she wants to use in the recipe?
A-40:30
B-19:9
C-15:20
D-8:6

Answers

Answer: A ratio is a comparison of two or more values. To compare the ratios of orange juice to yogurt, we want to ensure that the proportion of orange juice to yogurt is the same in each ratio.

Option A is 40:30. To compare this ratio to the original ratio, we can convert the amounts in cups to tablespoons. 40 cups is equal to 320 tablespoons and 30 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 320 is not equivalent to 3.

Option B is 19:9. To compare this ratio, we convert the amount in cups to tablespoons. 19 cups is equal to 152 tablespoons of orange juice and 9 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 4 cups of orange juice is not equal to 19 cups.

Option C is 15:20. To compare this ratio, we convert the amount in cups to tablespoons. 15 cups is equal to 120 tablespoons of orange juice and 20 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 4 cups of orange juice is not equal to 15 cups.

Option D is 8:6. To compare this ratio, we convert the amount in cups to tablespoons. 8 cups is equal to 64

Step-by-step explanation:

Which equation has 3 as a solution set *?

Answers

The equation 3x - 9 = 0 has 3 as a solution out of all the given equations in the options.

Check the solution of equation 3x - 9 = 0

3x - 9 = 0

3x = 9

x = 3

Check the solution of equation 4x - 3 = 0

4x - 3 = 0

4x = 3

x = 3/4

Check the solution of equation 5x - 10 = 0

5x - 10 = 0

5x = 10

x = 10/5

x = 2

Check the solution of equation 7x - 49 = 0

7x - 49 = 0

7x = 49

x = 49/7

x = 7

Thus, only 3x - 9 = 0 satisfy the solution x = 3.

Hence, the correct option is A.

--The given question is incomplete, the complete question is

''Which equation has 3 as a solution set?

A. 3x - 9 = 0

B. 4x - 3 = 0

C. 5x - 10 = 0

D. 7x - 49 = 0''--

To know more about equation, here

https://brainly.com/question/14686792

#SPJ4

I got this from Khan Academy.

Answers

The function which has greater slope is Function 2.

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Function 1:

y = -2x + 10

and Function 2:

Slope = (5-10)/( 2-0) = -5/2

So, the Equation of line

(y - 10) = -5/2 (x -0)

y - 10 = -5/2x

y = -5/2x + 10

y= -2.5x +10

So, the slope of Function 1 is greater than slope of function 2.

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ1

One angle of a triangle measures 45°. The other two angles are in a ratio of 7:20. What are the measures of those two angles?

Answers

Answer:

35° and 100°

Step-by-step explanation:

The total angle of a triangle = 180°
The total angle of two angles = 180° - 45° = 135°
One part of the ratio = 135° : (20 + 7) = 5°
The smaller angle = 5° x 7  = 35°
The bigger angle = 5° x 20 = 100°

Answer:

35° and 100°

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180°

the ratio of 2 angles is 7 : 20 = 7x : 20x ( x is a multiplier )

equate the sum to the 3 angles to 180 and solve for x

45 + 7x + 20x = 180

45 + 27x = 180 ( subtract 45 from both sides )

27x = 135 ( divide both sides by 27 )

x = 5

Then

7x = 7 × 5 = 35

20x = 20 × 5 = 100

the measure of the 2 angles is 35° and 100°

What is .15 written as a rational number

Answers

Answer:

it is a rational number already

Step-by-step explanation:

How do I solve for the fourth line

Answers

Answer:

y = -8/3x + 73/4

Step-by-step explanation:

A line perpendicular to the 3rd equation has a slope that is the negative inverse of the other line. It also has the same y-intercept (b) because it is forming a square.

Therefore, the equation of the 4th line is:

y = -8/3x + 73/4

Name the property that i hown by each equation. A. 6a 4 = 4 6a
B. 30 60 = 15(2 4)
C. 3(8x 4) = 3(4 8x)
D. 4(6a) = (4 · 6)a

Answers

A. Commutative property of addition

B. Distributive property

C. Commutative property of addition

D. Associative property of multiplication

Commutative property of addition: The commutative property of addition says that a change in the order of the numbers being added does not affect the sum. We define a commutative property of addition as adding the numbers in any order that will give the same answer.  

                                    a + b =b + a

        Here, a and b is whole numbers, integers or decimals, or even fractions.

Distributive property: According to this property, multiplying the summation of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. In other words, according to the distributive property, an expression of form A (B + C) can be solved as A (B+ C) = AB + AC.Associative property of multiplication:  The associative property of multiplication is defined as that while multiplying three numbers, regardless of the way the numbers are grouped, the end result will always be the same.

Read more about the distributive property:

https://brainly.com/question/2807928

#SPJ4

The complete question is:

Name the property that is shown by each equation.

A. 6a + 4 = 4 + 6a

B. 30 + 60 = 15(2 + 4)

C. 3(8x + 4) = 3(4 + 8x)

D. 4(6a) = (4 · 6)a

What is the value of aaa when we rewrite 6^{x}6 x 6, start superscript, x, end superscript as ax4 ?

Answers

The equation can be rewritten as: [tex]ax^4 = (log(6))(2^4)[/tex]

Therefore, [tex]a = log(6) \ and\ x=2[/tex]

What is logarithm?

A logarithm is a mathematical function that describes the relationship between a number and its exponent. It is the inverse operation of exponentiation. Logarithms are typically written as log base b, where b is the base of the logarithm and is a positive number.

The logarithm of a number x to base b is denoted as [tex]logb(x)[/tex] and it is the exponent to which we need to raise the base b in order to get the number x.

For example, if we are given [tex]log10(100) = 2[/tex], this means that [tex]10^2 = 100[/tex].

The equation [tex]6^x * 6 * 6[/tex] can be rewritten as [tex]6^x * 6^2[/tex].

To convert 6^x to ax form, we need to take the logarithm of both sides of the equation:

[tex]log(6^x) = log(6^2)[/tex]

And we can simplify the equation as:

[tex]xlog(6) = 2log(6)[/tex]

So, the value of a is log(6) and the value of x is 2.

Therefore, the equation can be rewritten as:

[tex]ax^4 = (log(6))(2^4)[/tex]

Therefore, [tex]a = log(6)\ and\ x=2[/tex]

To know more about Logarithms visit:

https://brainly.com/question/28346542

#SPJ4

The scatter plot shows a hikers elevation above sea level overtime. The equation of the trend line is shown y equals 8.77x plus 686. To the nearest whole number predicted hikers elevation will be at 145 minutes

Answers

The predicted elevation of hikers at 145 minutes, based on the trend line equation, y = 8.77x + 686 is 1,958.

What is a trend line equation?

A trend line equation is the equation of a linear relationship, represented as y = mx + b.

In this linear equation, y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.

Equation:

y = 8.77x + 686, where x = 145 minutes

Therefore,

y = 8.77(145) + 686

y = 1,271.65 + 686

y = 1,957.65

y = 1,958

Thus, after 145 minutes of hiking, hikers' elevation will be 1,958 units.

Learn more about trend line equations at https://brainly.com/question/8241509

#SPJ1

Which is 536,900 in scientific notation

Answers

Answer:

5.369 x 105

Step-by-step explanation:

Answer:

5.369 x 105

Cause in scientific notation, the decimal point is always after the first number from the left.

Jason made a model stop sign for his model train
set. An actual stop sign measures 12 inches on
each side. Jason's model stop sign measures
1 inch on each side.

Answers

actual measures : model measures = 12 : 1 .

What is Ratio?

In mathematics, a ratio shows how many times one number contains another. The comparison or simplified form of two quantities of the same kind is referred to as a ratio. This relation gives us how many times one quantity is equal to the other quantity. In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones.

The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things. The sign used to denote a ratio is ‘:’.

A ratio can be written as a fraction, say 2/5. We happen to see various comparisons or say ratios in our daily life.

Given,

Actual sign measures 12 inches on each side

Jason's model sign measures 1 inch on each side.

Ration between actual to model sign measurement=

Measurement of actual sign / Measurement of model sign

= 12/1

Ratio = 12:1

Hence, the ratio between actual to model sign measurement is 12:1.

Learn more about ratio here:

https://brainly.com/question/13419413

#SPJ1

What is an unsolvable problem?

Answers

As a result, it may be shown that the answer to the algorithm problem at hand is a halting problem, which is indecidable and thus impossible to solve.

Algorithm : what is it ?

No matter the circumstance, algorithms are fundamentally problem solvers of expression ; they exist to identify, resolve, and frequently automate of solution to a specific problem. Algorithms are frequently introduced in area introductory textbooks by characterizing them as "a series of steps to complete a problem."

Here,

one of the most common problems that hasn't been solved is the stopping problem. It asks the following question:

Does M come to a standstill when given the input w for any Turing machine with the parameters alphabet = a, b, and any string w over

It can be shown that the halting problem cannot be resolved since it is indecisive.

As a result, it may be shown that the answer to the algorithmic problem at hand is a halting problem, which is indecidable and thus impossible to solve.

To know more about algorithm , visit:

brainly.com/question/29289479

#SPJ4

Two cars start from the same intersection with one traveling southbound while the other travels eastbound going 10 mph faster. If after 2 hours they are 10sqrt(34) apart, how fast was each car traveling?

Answers

The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.

What is meant by intersection ?

They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.

Let speed of Car 1 = x mph

Speed of car 2 = (x + 10) mph

Hence,

OA = Distance travelled by car2 in 2 hours

⇒ OA = (x + 10) × 2 = 2x + 20

And, OB = Distance travelled by Car 1 in 2 hours

⇒ OB = x × 2 = 2 x

Now, In ΔOAB, OA² + OB² = AB²

substitute the values in the above equation

⇒  (2 x+20)² + (2 x)² = [tex](10 \sqrt{34})^2 \\[/tex]

⇒  4x² + 400 + 80x + 4x² = 3400

simplifying the equation

⇒ 8x² + 20x - 3000 = 0

⇒ x² + 10x - 375 = 0

⇒ x² + 25x - 15x - 375 = 0

simplifying the above equation, we get

⇒ x(x + 25) - 15(x + 25) = 0

⇒ (x + 25)(x - 15) = 0

⇒ x + 25 = 0, x - 15 = 0

⇒ x = -25, x = 15

Since speed can not be negative.

Hence, x = 15 mph

⇒ x + 10 = 15 + 10 = 25 mph.

Hence, speed of car moving towards south =15 mph.

And, speed of (as moving towards East = 25 mph.

To learn more about speed refer to:

https://brainly.com/question/13943409

#SPJ4

The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.

What is meant by intersection ?

When two or more lines in a plane cross one another, they are referred to as intersecting lines. The common point shared by all intersecting lines is the point of intersection, which can be found on all of them.

What do you mean by Speed?

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Let speed of Car 1 = x mph

Speed of car 2 = (x + 10) mph

Hence,

OA = Distance travelled by car2 in 2 hours

⇒ OA = (x + 10) × 2 = 2x + 20

And, OB = Distance travelled by Car 1 in 2 hours

⇒ OB = x × 2 = 2 x

Now, In ΔOAB, OA² + OB² = AB²

substitute the values in the above equation

⇒  (2 x+20)² + (2 x)² =

⇒  4x² + 400 + 80x + 4x² = 3400

simplifying the equation

⇒ 8x² + 20x - 3000 = 0

⇒ x² + 10x - 375 = 0

⇒ x² + 25x - 15x - 375 = 0

simplifying the above equation, we get

⇒ x(x + 25) - 15(x + 25) = 0

⇒ (x + 25)(x - 15) = 0

⇒ x + 25 = 0, x - 15 = 0

⇒ x = -25, x = 15

Since speed can not be negative.

Hence, x = 15 mph

⇒ x + 10 = 15 + 10 = 25 mph.

Hence, speed of car moving towards south =15 mph.

And, speed of (as moving towards East = 25 mph.

To learn more about speed refer to:

brainly.com/question/13943409

#SPJ4

State the rule. Then write the next two terms. 240,120,60,

Answers

Answer:

The numbers are being divided by 2 each time.

240/2 = 120

120/2 = 60

So the next set of numbers would be:

30, 15 because

60/2 = 30

30/2 = 15

Step-by-step explanation:

Hope it helps!

Match each power of a power expression with its simplified expression.
(4-3)-3
(46)-3
(49)-9
(-49)²


1
418
49
(-4)18
40
need to know which one goes to which

Answers

Answer:

(4^6)^-3 = 1/4^18(4^0)^-9 = 4^0(4^-3)^-3 = 4^9(-4^9)^2= (-4)^18Step-by-step explanation:(4^6)^-3 = 1/4^18(4^6)^-3= 4^(6*-3)(4^6)^-3= 1/4^18(4^0)^-9 = 4^0(4^0)^-9 = 4^(0*-9)(4^0)^-9= 4^0(4^-3)^-3 = 4^9(4^-3)^-3= 4 ^ (-3*-3)(4^-3)^-3 = 4^(9)(-4^9)^2= (-4)^18(-4^9)^2= -4^(9*2)(-4^9)^2=(-4)^18

Step-by-step explanation:

Answer:

[tex](4^{-3})^{-3}=4^9[/tex]

[tex](4^6)^{-3}=\dfrac{1}{4^{18}}[/tex]

[tex](4^0)^{-9}=4^0[/tex]

[tex](-4^9)^2=(-4)^{18}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{3 cm}\underline{Exponent Rules}\\\\$(a^b)^c=a^{bc}$\\\\$a^{-n}=\dfrac{1}{a^n}$\\\end{minipage}}[/tex]

Apply the above exponent rules to simplify each expression.

[tex]\begin{aligned}\implies (4^{-3})^{-3}&=4^{-3 \times -3}\\&=4^9\end{aligned}[/tex]

[tex]\begin{aligned}\implies (4^6)^{-3}&=4^{6 \times -3}\\&=4^{-18}\\&=\dfrac{1}{4^{18}}\end{aligned}[/tex]

[tex]\begin{aligned}\implies (4^0)^{-9}&=4^{0 \times -9}\\&=4^0\end{aligned}[/tex]

[tex]\begin{aligned}\implies (-4^9)^2&=(-4)^{9 \times 2}\\&=(-4)^{18}\end{aligned}[/tex]

What is the area when the diameter is 16?

Answers

201.06 square units (rounded to 2 decimal places) is the area of the given circle.

The formula for the area A of a circle is A = πr², where r is the radius of the circle and π is the famous, well-known irrational number pi equal to 3.14159 (rounded to 5 decimal places).

Given that the circle's diameter is 16, and that a circle's radius is equal to half its diameter, the following conclusions can be drawn:

r = d/2

= 16/2

= 8

A=πr2

AND HALF THE DIAMETER IS THE RADIUS (r)

r=8

A= πr2 = π (8) squared = 64 * π = 200.96

or,

Now, substituting the values of r and π into the formula for the area of a circle, we get

A = πr²

= (3.14159)(8²)

= (3.14159)(64)

= 201.06 square units (rounded to 2 decimal places) is the area of the given circle.

Learn more about the area of a circle at:

https://brainly.com/question/14068861

#SPJ4

what value of x would prove that the following triangle is a right angle? Answers x=7 x=2 x= 14 x= 10​

Answers

Step-by-step explanation:

Pythagoras' Theorem

For Pythagoras' Theorem to be valid, the triangle must be a right-angled one.

The formula is:

c^2 = a^2 + b^2

Where c is the longest side. While a,b are the side lengths.

Solution

Using the above formula and the measurements given in the question, we can find the value of x.

By Pythagoras' Theorem,

26^2 = (5x)^2 + (12x)^2

676 = 25x^2 + 144x^2

169x^2 = 676

x^2 = 676 ÷ 169

x^2 = 4

x = 2

The casino game of chuck-a-luck seems quite simple and that it would be a pretty good bet. In this game, three dice are rolled (usually inside a wire cage). You can bet a set amount, let's say $5, on a specific number 1-6. You win the amount of your bet for each appearance of your number on the dice. If the number does not appear, you lose your bet. For example, let's say you bet $5 on the number 3. If it appears on exactly one die, you win $5 (and keep your bet) with probability 75/216. If it appears on exactly two dice, you win $10 (and keep your bet) with probability 15/216. If it appears on all three dice, you win $15 (and keep your bet) with probability 1/216. If it appears on none of the dice, you lose your original $5 bet. Construct the probability distribution for chuck-a-luck and determine your expected winnings on a $5 bet.

Answers

The expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.

Therefore, the game is not a good bet, as you are expected to lose money in the long run.

What is the probability distribution?

A probability distribution is a mathematical function that describes the probability of different possible values of a variable.

The probability of winning on a $5 bet on a specific number in chuck-a-luck is determined by the number of ways that the number can appear on the three dice and the total number of possible outcomes.

If the number appears on exactly one die, there are 3 ways that this can happen out of a total of 6^3 = 216 possible outcomes, giving a probability of 3/216 or 1/72.

If the number appears on exactly two dice, there are 3 ways to choose the two dice on which it appears, and 3 ways to choose the third die, giving a total of 33 = 9 ways out of 216 possible outcomes, giving a probability of 9/216 or 1/24.

If the number appears on all three dice, there is only 1 way this can happen out of 216 possible outcomes, giving a probability of 1/216.

If it appears on none of the dice, there are (543) ways this can happen, giving a probability of (54*3)/216 = 20/216.

We can use this information to construct the probability distribution for chuck-a-luck:

x P(x)

-5 (losing the bet) 20/216

5 (winning the bet for one appearance) 1/72

10 (winning the bet for two appearances) 1/24

15 (winning the bet for three appearances) 1/216

To find the expected winnings on a $5 bet, we can multiply the value of each outcome by its corresponding probability, and sum the results:

E(X) = (-5)(20/216) + (5)(1/72) + (10)(1/24) + (15)(1/216)

E(X) = -5/43.2 + 5/72 + 5/12 + 15/216

E(X) = -0.1157

Hence, the expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.

Therefore, the game is not a good bet, as you are expected to lose money in the long run.

To learn more about the probability distribution visit,

https://brainly.com/question/28021875

#SPJ4

A falcon was recorded travelling 100 metres in 0. 93 seconds.


What was its average speed


a in m/s to 3 significant figures

Answers

The average speed of the falcon to 3 significant figures will be 107.526 m/s

Distance travelled by falcon = 100 meters

Time taken by falcon to travel the distance = 0.93 seconds

As we have the formula for finding the average speed:

Average speed is a pace defined as a quantity divided by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t is used to compute average speed, where S is the average speed, d is total distance, and t is total time.

Average speed can be find by simply dividing the total distance covered by falcon by the total time taken by him to cover the distance.

So, the value of the average speed will be = (100 m/0.93 sec) =107.526 m/s

For more questions on Average speed

https://brainly.com/question/24739297

#SPJ4

Graph the system on equation . Y-2x+5=0 and y+ 4x-1=0

Answers

The graph of the system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0 intersect at (0.667, - 3.667)

What is a graph?

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0.

Let's write the terms in the order x, y therefore,

y - 2x + 5 = 0

- 2x + y = - 5.

2x - y = 5.

And

y + 4x + 1 = 0.

4x + y = - 1.

The graph of the system of equations is attached in the image.

learn more about graphs here :

https://brainly.com/question/2288321

#SPJ1

7{-7+8[5-3(4+6)]-9(9-4)}​

Answers

Answer:

-1764

Step-by-step explanation:

use BODMAS rule

⇒7{-7+8[5-3(4+6)]-9(9-4)}

solve round brackets

⇒7{-7+8[5-3(10)]-9()}

multiply 3 by 10 within the square bracket

⇒7{-7+8[5-30]-9(5)}

solve square bracket

⇒7{-7+8[-25]-9(5)}

move to curly brackets and multiply first

⇒{-7-200-45}

subtract

⇒7{-252}

multiply

⇒-1764 Answer

hope that helps...

Other Questions
Why are some producers forced to sell their products at the prevailing market price?A. price takers find market analysis is too costlyB. they are very small players in the overall marketC. high degree of similarity to competitor's productsD. they can increase output without affecting quality How do you find f inverse? the set {...,-2,-1,0,1,2...} is called what? What is the central idea of the Trujillo? What is the difference of the two polynomials 9x2 8x 2x2 3x? Select the correct answer from the drop-down menu. Look at the underlined details in paragraphs 12 and 13. [12] I must have been in a deep sleep for a long time, but all of a sudden I was awakened with a start by the fall of a heavy body tumbling right on top of my own, and, at the same time, I received on my face, on my neck, and on my chest a burning liquid which made me utter a howl of pain. And a dreadful noise, as if a sideboard laden with plates and dishes had fallen down, almost deafened me. [13] I was smothering beneath the weight that was crushing me and preventing me from moving. I stretched out my hand to find out what was the nature of this object. I felt a face, a nose, and whiskers. Then, with all my strength, I launched out a blow at this face. But I immediately received a hail of cuffings which made me jump straight out of the soaked sheets, and rush in my nightshirt into the corridor, the door of which I found open. How do the underlined details create tension in the story? These details create tension by 1. making it seem as if the narrator is losing his sense of reality 2. confirming that the main characters friends were planning to trick him 3. appealing to the readers sense of touch and hearing 4. withholding information about who is attacking the narrator What is the difference between Explicit and implicit bias and how do you identify if you have a bias What is the value of 2 by 7 and 3 by 7? If the cell's external environment becomes very WATERY (dilute) then the outside of the cell will have a higher water concentration. We say the cell environment is HYPOTONIC. Water will diffuse in this case.Which way is the water going to diffuse? Spanish help ACT.5 in spanish book Is this statement true or false?There was a lack of Native American unity in fighting Europeans because the natives were descended from different peoples that came in different waves of immigration.A:TrueB:False Walt Whitman called his most famous poem 'Song of Myself'. What does he actually say about who he is, and what do we learn about him Write a procedure ConvertToBinary that takes an input as a number from 0 to 16 (including 0 but not 16) and converts it to a binary number. The binary number should be returned as a list. A year in the modern Gregorian Calendar consists of 365 days. In reality, the earth takes longer to rotate around the sun. To account for the difference in time, every 4 years, a leap year takes place. A leap year is when a year has 366 days: An extra day, February 29th. The requirements for a given year to be a leap year are: 1) The year must be divisible by 4 2) If the year is a century year (1700, 1800, etc.), the year must be evenly divisible by 400 Some example leap years are 1600, 1712, and 2016. Define a function called OutputLeapYear that takes an integer as a parameter, representing a year, and output whether the year is a leap year or not. Then, write a main program that reads a year from a user, calls function OutputLeapYear() with the input as argument to determines whether that year is a leap year. coral code 30 PTS: Please help meYou can earn money by shoveling your neighbors' driveways in the winter and get paid $10 per hour. What is a function that would define this situation? Define the domain and range of this function and describe reasonable values for each. What is one of the main differences between a 401(k) and a Roth 401(k)? O A. A Roth 401(k) is offered by banks, while a 401(k) is offered by an employer. B. The amount you can contribute depends on your age. C. Contributions are taxed differently. D. You have to be different ages in order to withdraw money. The stomach is the only part of the alimentary canal with three muscular layers. Why does the stomach need three layers of muscle How does smoking weaken damage the respiratory system? The number cube with sides labeled 1 through 6 is rolled. Which events are likely to occur? Select all that apply. Multiple select question. A) rolling a 1 or a 2 B) rolling an odd number C) rolling an even number D) rolling a a number less than 6 E) rolling a number greater than 2 LMNP is a rectangle. Find the value of x and the length of each diagonal.