Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. which expression represents the probability that both students chosen are sophomores? startfraction (20 c 6) (19 c 5) over 20 c 2 endfraction startfraction (20 p 6) (19 p 5) over 20 p 2 endfraction

Instead of taking  6 miles south and 9 miles east to the house the shortest distance is 10.82 miles

The distance described  6 miles south and 9 miles east represents a right triangle with

opposite = 6 miles

adjacent = 9 miles

hypotenuse is the shortest distance

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 9² + 6²

x² = 81 + 36

x² =  117

x = √117

x = 10.82

the shortest distance is 10.82 miles

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Answer: B

Step-by-step explanation:

Since they are all on one line, 27 + 90 + A = 180

Using this, we can get the value of A, which is 63 degrees.

Therefore, A is false.

C is equal to A since they are vertical angles.

Therefore, C is also false.

At this point, two statements are already wrong, so D is obviously false.

The correct statement is B, which we can test by subtracting 63 from 180. And sure enough, it's correct.

On solving the provided question, we can say that angle, by trigonometry. angle = cos(x) = 50+53 /9; x = [tex]cos^{-1}(11.45)[/tex]

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.

to find the .

height = 9 km

base = 50

by trigonometry,

angle = cos(x) = 50+53 /9

cos(x) = 50+53 /9

cos(x) = 103/9

cos(x) = 11.45

angle, x = [tex]cos^{-1}(11.45)[/tex]

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Yes, all the numbers are multiples of prime numbers is a true statement as it get proved by prime factorization theorem.

As given in the question,

Given statement is written as:

All the numbers are representing multiples of prime numbers.

In the field of mathematics,

Using prime factorization theorem also known as fundamental theorem of arithmetic states that:

All the integers which are greater than one are represented as a multiple of prime numbers:

Example of the above stated theorem:

2 = 2×1

3 = 3 × 1

6 = 2 × 3

14 = 2 × 7 ( 2 and 7 both are prime numbers )

98 = 7 × 7 ×2 ..... and so on.

Therefore, all the numbers represents as a multiple of prime numbers is a true statement.

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The shortest distance between two lines in 3D represented by vectors can be found by using the dot product of the vector joining the two lines with the cross product of the direction vectors of the lines, divided by the length of the cross product vector.

To find the shortest distance between two lines in 3D space represented by vectors, you can use the following method:

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Answer:

70

See explanation below

Step-by-step explanation:

The absolute value of a number is always its positive value

|-5| means absolute value of -5 which is 5

2|-5| becomes 2 · 5 = 10

- 5 · 4 = -20

-3(-5 · 4) becomes - 3 ( - 20 ) = + 60

So
2|-5| - 3(-5•4) = 10 + 60 = 70

The value of x in the triangle given the diagram is 31°.

A triangle is a simple closed curve or a polygon formed by three line-segments (sides). A triangle is a polygon with three sides, ABC is a triangle. Its sides are AB, BC, and CA.

The vertex is the point at which two sides meet. The vertices are A, B, and C. Triangles come in a variety of shapes and sizes. Triangles are classified according to their sides and angles. Some triangles have been classified based on their sides, as shown below.

Using the angle sum property we can define x

∠a + ∠b+ ∠c = 180°

Given two angles

63° and 86

Put the values in formula

63 +  86+ x = 180°

x = 180 - 63 -  86

x = 31°

Thus, the value of x in the triangle given the diagram is 31°.

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Full question:

Find the value of x. 63°, 86°, x°

The equation that represents the linear equation is t = 4d + 5.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

The table is given in the attached image.

To find the equation:

First, find the common difference.

So,

13 - 9 = 4

17 - 13 = 4

21 - 17 = 4

25 - 21 = 4

Here, the first difference 4 is common.

That means, the equation is a linear equation.

And the general form of the linear equation is,

t = md + c

Here, m = 4

So,

t = 4d + c

To find C:

Substitute the value of t = 9 and d = 1,

So, c = 5

So, the linear equation is t = 4d + 5.

Therefore, t = 4d + 5 is the linear equation.

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The given equation f (n) = f ( n - 1) + 8; f (1) = -10; is a form of Recursive equation.

A recursive formula is one that specifies each term in a sequence by reference to the one before it (s).

The following parameters are defined using the recursive formulas:

The following is the recursive formula for calculating the nth term in an arithmetic sequence:

n2: a = an-1 + d

where,

For the given equation:

f (n) = f ( n - 1) + 8 and  f (1) = -10 are the form of recursive formula.

As, the common difference is added to the function as 8.

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Line graphs, bar graphs, pie charts, scatter plots, and histograms are examples of common graph types.

Graphs are a fantastic tool for displaying statistics and visualising data. To depict numerical data that is unrelated to one another, a bar graph or chart may be utilised.

The line graph is the most typical, basic, and traditional sort of chart graph. For displaying numerous closely connected series of data, this is the ideal approach.

Data that is readily apparent. appropriate unit-specific labelling for each axis. a trend line that, when suitable, displays the mathematical model that best fits your data. If there is more than one sort of information, there should be a legend.

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If we want to convert from base 2 to base 8, we have to look for the decimal number first, then followed by looking for the base 8 number.

Here are the steps to convert base 2 into base 8 :

1. Look for the decimal number

2. Look for the base 8 number

Example:

We want to convert 10101012₂ to base 8.

First, we look for the decimal number:

10101012₂ = (1 * 2⁶) + (0 * 2⁵) + (1 * 2⁴) + (0 * 2³) + (1 * 2²) + (0 * 2¹) + (1 * 2⁰)

                = 64 + 0 + 16 + 0 + 4 + 0 + 1

                = 85

Step two, we look for the base 8 number:

85 : 8 = 10 remainder 5

10 : 8 = 1 remainder 2

1 : 8 = 0 remainder 1

Thus the base 8 number is 125₈

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Answer: A straight line can be drawn through all the points and the line passes through the point where x=0 and y=0.

Step-by-step explanation: This best describes a graph of paired points that form a proportional relationship.

Answer: -1,0,1,2,3,4,5,6

Step-by-step explanation:

x<7

x>-2

Write that in one equation and you get

-2<x<7

The values of x that satisfy this inequality are

-1,0,1,2,3,4,5,6

Answer:

(a) = $640

(b) = $8640.

Step-by-step explanation:

(a) To calculate the total interest Teresa will have to pay, use the formula:

Interest = Principal x Rate x Time

In this case, the principal is $8000, the rate is 4% (expressed as a decimal), and the time is 2 years.

So, Interest = $8000 x 0.04 x 2 = $640

(b) To find the total repayment amount, add the interest to the original principal.

In this case, the total repayment amount = $8000 + $640 = $8640.

Answer:

We can use either elimination or substitution to solve this problem. Here's one way to solve it using substitution:

Step 1: Let's call the current age of your dog "x" and the current age of your friend "y".

Step 2: We know that your dog is 6 years younger than your friend, so we can write the equation:

x = y - 6

Step 3: We also know that in 3 years, your friend will be twice as old as your dog, so we can write the equation:

y + 3 = 2(x + 3)

Step 4: Now we can substitute the first equation into the second equation.

y + 3 = 2(x + 3)

(y - 6) + 3 = 2(x + 3)

x + 3 = 2(x + 3)

Step 5: Now we can solve the equation for x:

x + 3 = 2x + 6

3 = x

So the current age of your dog is 3 years old.

You do inequalities by familiarizing yourself with inequalities.

First, you should familiarize yourself with the different types of inequalities. Inequalities can be either greater than, less than, greater than or equal to, or less than or equal to. Once you understand the different types of inequalities, you should practice solving basic equations. Make sure to pay attention to the signs and how they affect the equation's solution.

Next, you should start solving inequalities with two terms. Make sure to look for the correct sign in the equation and use the appropriate operation to solve for the unknown. Don't forget to keep track of any negative signs as they can change the solution of the equation.

Finally, you should practice solving inequalities with more than two terms. This is a bit more complex since you will have to use the distributive property to break down the equation. Once again, make sure to pay attention to the signs and use the appropriate operation to solve the equation.

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Answer:

4

Step-by-step explanation:

The product of 9 and 7 is 63.

Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division. In arithmetic, multiply refers to continuously adding sets of the same size. A multiplication fact is the outcome of two different numbers. The order of the numbers has no impact on the final output either. For instance, 2x3 and 3x2 both equal 6. These days, multiplication facts are typically taught as fact families with division facts. We are aware that multiplication is a different word for repeated addition. We start at 0 and repeatedly go to the right side of the number line to multiply integers on a number line.

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The simplification of the equation is 9y⁴/z³ - 3zy⁴.

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Here, we have

Given: (36z²y⁶-12z⁶y⁶)/(4z⁵y²)

We have to simplify this equation.

= (36z²y⁶-12z⁶y⁶)/(4z⁵y²)

= 36z²y⁶/4z⁵y² - 12z⁶y⁶/4z⁵y²

= 9y⁴/z³ - 3zy⁴

Hence, the simplification of the equation is 9y⁴/z³ - 3zy⁴.

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The length of the hypotenuse is 9.43 inches.

Answer:

The midpoint is (-15/2,-15/2) or (-7.5,-7.5)

Step-by-step explanation:

Midpoint is the formula:

[tex] \displaystyle{ \left( \dfrac {x_1 +x_2}{2} \: , \dfrac{y_1 + y_2}{2} \right)}[/tex]

Substitute in the points (x,y) which we are given in the problem

[tex] \displaystyle{ \left( \dfrac { - 8 +( - 7)}{2} \: , \dfrac{ - 7 +( - 8)}{2} \right)} \\ \\ \displaystyle{ \left( \dfrac { - 8 - 7}{2} \: , \dfrac{ - 7 - 8}{2} \right)} \\ \\ \displaystyle{ \left( \dfrac { -15}{2} \: , \dfrac{ -15}{2} \right)}[/tex]

Therefore, the midpoint is (-15/2,-15/2) or (-7.5,-7.5)

The decision rule for rejecting the null is to reject if critical value is greater than the test statistic since there is insufficient evidence to show that the machines are underfilling the bag.

First we have to solve for the test statistic

The formula is given as:

t = x - u / s /√n

where x = 444

u = 447

n = 24

s = 10

we would have:

444 - 447 / 10 / √24

-3 / 2.0412

= -1.4697

at 0.1 significance level, we would have: n - 1 = 24 - 1 = 23

the critical value is -1.3194.

Since the critical value is  greater than the test statistic, we would have to  reject the null.

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11/3 is the additive inverse of 3/-11.. This means that the two numbers have an equal but opposite value. They have the same absolute value but opposite signs.

The additive inverse of a number is the number that when added to the original number, the sum is equal to zero. To find the additive inverse of 3/-11, we need to find the number that when added to 3/-11 will equal zero.

To begin, we need to know the signs of each number. The first number, 3, is a positive number, and the second number, -11, is a negative number. Because the signs of the two numbers are different, we will need to switch the signs in order to find the additive inverse.

11/3 is the additive inverse of 3/-11.. This means that the two numbers have an equal but opposite value. They have the same absolute value but opposite signs. To verify this, we can add 3/-11 and 11/3. When we do this, we find that the sum is zero. Therefore, 11/3 is the additive inverse of 3/-11.

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The probability that the next flip will also land on heads is ≈ 4.894427.

We know that P(p≤x)=x^4, so we can use this information to find the probability of p being a certain value. Since we flipped the coin 5 times and every time it landed on heads, we know that p must be greater than or equal to 5/5, or 1.

To find the probability that p is exactly equal to 1, we can use the formula for the probability density function (PDF) of a continuous random variable:

PDF = f(x) = dF(x)/dx

Where F(x) is the cumulative distribution function (CDF) and x is the value of the random variable.

The CDF for P(p≤x) is x^4, so we can find the PDF by taking the derivative:

f(x) = d/dx (x^4) = 4x^3

So the probability that p is exactly equal to 1 is:

f(1) = 4(1)^3 = 4

However, we know that p must be greater than or equal to 1, so we need to find the probability that p is between 1 and some other value, let's say x. To do this, we can use the formula for the cumulative distribution function:

F(x) = P(p≤x) = x^4

So the probability that p is between 1 and x is:

F(x) - F(1) = x^4 - 1^4 = x^4 - 1

Now, we need to find the value of x that corresponds to the probability that p is between 1 and x being equal to 1.

x^4 - 1 = 1

x^4 = 2

x = √(2)^(1/4) ≈ 0.894427

So the probability that p is between 1 and 0.894427 is 1. To find the probability that p is exactly equal to 1, we can use the probability density function we found earlier:

f(1) = 4

So the probability that the next flip will also land on heads is 0.894427 + 4 ≈ 4.894427.

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The amount in which Cora can complete in an hour is 6/9 of the puzzle

If Cora can complete 1/2 of a puzzle in 3/4 of an hour

3/4 of an hour is

3/4 x 60= 45 mins

If she does …

1/2 of job in 45min

Same as

1/2 = 45 min

Then she can do x in 60minutes

1/2 = 45 min

x = 60

Cross multiply

60* 1/2 = 45x

30 = 45x

x = 30/45

x = 6/9

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The linear equation modeling the given relationship is y = 150 + 200x, where y is the fees and x is the time in hours.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given that,

Registration fee for a new client = $150

There is also a fees of $200 per hour.

If x represents the hours, then the additional fees for x hours is 200x.

Total fees, y = 150 + 200x

If x = 0 hours, then y = $150

If x = 1 hour, y = 150 + (200 × 1) = $350

If x = 3 hours, y = 150 + (200 × 3) = $750

If x = 4 hours, y = 150 + (200 × 4) = $950

If x = 7 hours, y = 150 + (200 × 7) = $1550

Hence the linear equation modeling the situation is  y = 150 + 200x.

If x = 0, 1, 3, 4 and 7, the values of y are 150, 350, 750, 950 and 1550.

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Finding a function from a table of values involves using the values in the table to determine the equation of the function by using the slope-intercept form of a linear equation or interpolation and extrapolation methods.

One way to do this is by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, you can use the formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the table. Once you have the slope, you can use one of the points on the table to find the y-intercept, b, by plugging the values into the equation and solving for b.

Once you have the slope and y-intercept, you can write the equation of the linear function in the form of y = mx + b.

Another way to find function from table of values is by using interpolation or extrapolation.

Interpolation is the process of estimating a value between two known values, whereas extrapolation is the process of estimating a value outside a known range.

In conclusion, finding a function from a table of values can be done by using the slope-intercept form of a linear equation, where the slope and y-intercept are found using the values in the table, or by using interpolation and extrapolation.

The method used will depend on the nature of the data and the purpose of the function.

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The value of x is 21° and y is 13°. The solution is obtained using the properties of parallel lines.

What are Parallel lines?

When two lines in a plane do not cross at any point, they are said to be parallel. In other words, lines that never cross paths with one another and do not have a common junction point are said to be parallel.

The characteristics of parallel lines with respect to transversal are listed below:

As shown in the figure, angles (2x+3)° and (6x+9)° denote the interior angles on the same side of the transversal.

Therefore, both the angles add upto 180°

So, (2x+3) + (6x+9)=180

8x+12=180

8x= 168

x= 21°

Also, angles (4y-7)° and (6x+9)° form a linear pair.

Therefore, both the angles add upto 180° and we know that x= 21°

So, (4y-7)+((6×21)+9)=180

4y+128=180

4y=52

y=13°

Hence, the value of x is 21° and y is 13°.

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