Which of the following are irrational? Explain how you know?
a. √27
b. 5.0287
c. √49
d. _³√125

The product of 3√3 and 3√30 in simplest radical form is 27√10

It is important to note that surds are nth root of numbers.

Surds are also seen as the values in square root that cannot be further simplified to whole numbers or integers.

Surds are irrational numbers.

Given the expression;

3√3 and 3√30

To determine the value, multiply, we get;

9 √90

Find the pair factors of 90, we have;

9 √9 × 10

Find the square root

27√10

Hence, the value is 27√10

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That’s easyyyyy

Step-by-step explanation:

It’s 62...

:)

Answer:

62 :)

Step-by-step explanation:

His total earnings for a total sale of 7,000​ could be 1450sh

From the question, we have the following parameters that can be used in our computation:

Salary = 400

Commission = 15%

using the above as a guide, we have the following:

Total earnings = 400 + 15% * Total sales

So, we have

Total earnings = 400 + 15% * 7000

Evaluate

Total earnings = 1450

Hence, the total earnings is 1450

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Question

Simon earned 400sh weekly for goods sold and a commission of 15%

What could be his earnings for a total sale of 7,000​.

Answer:

65/100 that is the answer to this question

Answer:

y = 6x + 43

Step-by-step explanation:

Our unknown line is of the form

y = kx + m

Where k is the slope of the line.

Since our line is parallel to 6x+1, the slope of the two lines must be equal. In other words, the two must have the same value of k.

In our line 6x+1, the k value is 6.

Thus, our unknown line must look like this:

y = 6x + m

Now, we need to find out what m is. Our line passes through (-7, 1).

Thus, we know that when x is equal to -7, y is equal to 1,

We can put these two values:

x = -7

y = 1

...into our line to find m.

y = 6x + m

1 = 6 * (-7) + m

Since 6 * (-7) = -42

1 = - 42 + m

1 = m - 42

Now, we can add 42 to both sides:

1 + 42 = m - 42 + 42

43 = m

m = 43

Our line has the k-value of 6, and m-value of 43. As such, the equation will be the following:

y = kx + m

y = 6x + 43

Answer: y = 6x + 43

Some arithmetic sequences could be easier to write as functions. As long as I know what value "n" has, I can find out any term in a particular Sequence whenever I need to. You might choose the implicit term over the prior term of a Sequence if it is known.

The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Some arithmetic sequences could be easier to write as functions. You are aware of the prior term.

Consider that we only have the numbers (...,4,...) from an arithmetic sequence with a common difference of 5.

The complete question is:

You are given the first four terms of an arithmetic sequence. Under what conditions might a recursive formula be preferred over the explicit formula? Under what conditions might an explicit formula be preferred over the recursive formula?

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The correct match for each linear system with one of the phase plane direction fields will be:

1:B

2:C

3:D

4:A

What is plane?

In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true instances of geometric planes, despite the fact that it is difficult to envision a plane in real life.

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8489.6

We know that:

\(T=2\\ P=7580\\ R=6\ percent\)

Substitute into formula

\(T=2\\ P=7580\ into\ formula\\ R=6\ percent\\ F=P+prt\\ F=7580+7580rt\)

Calculate

\(7580\times(1+0.06\times2)\)

Calculate the product or quotient

\(7580\times(1+0.12)\)

Calculate the sum or difference

\(7580\times1.12\)

Calculate the product or quotient

\(8489.6\)

I hope this helps you

:)

(0.2)x = 2.

Taking log on both sides

log (0.2)x = log 2.

x log (0.2) = 0.3010, [since log 2 = 0.3010].

x log (2/10) = 0.3010.

x [log 2 - log 10] = 0.3010.

x [log 2 - 1] = 0.3010,[since log 10=1].

x[-0.699] = 0.3010.

x= 0.3010/-0.699.

x= = -0.4306….

x= = -0.4.

(0.2)x = 2.

Taking log on both sides

log (0.2)x = log 2.

x log (0.2) = 0.3010, [since log 2 = 0.3010].

x log (2/10) = 0.3010.

x [log 2 - log 10] = 0.3010.

x [log 2 - 1] = 0.3010,[since log 10=1].

x[-0.699] = 0.3010.

x = 0.3010/-0.699

x = -0.4306

x= -0.4 (nearest tenth)

The mode is 2.

The mode is the value that appears often in a set of data values.

The mode is a way of expressing, in a single number, important details about a random variable. The numerical value of the model is the alike as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions.

Given Data :

84, 87,84,88,85,90,91

First, arranging the data in ascending order :

84, 84, 85, 87, 88, 90,91

Now, we have to find how many times this number occurs :

⇒ 84 occurs 2 times

⇒ 85 occurs 1 time

⇒ 87 occurs 1 time

⇒ 88 occurs 1 time

⇒ 90 occurs 1 time

⇒ 91 occurs 1 time

So, the mode is 2.

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The baker needs 13/8 more ounces of green food color.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

The process of subtraction can also be termed as finding difference.

Given that,

A baker uses food coloring to color cake batter.

He needs 4 1/8 ounces of green food coloring.

Total amount of food color needed for the batter = 4 1/8 ounces

                                                                        = (4 × 8 + 1) / 8

                                                                        = 33/8 ounces

The baker only has 2 1/2 ounces.

Amount of food color he has = 2 1/2 ounces

                                               = (2 × 2 + 1) / 2

                                               = 5/2 ounces

Amount of color he need = 33/8 ounces - 5/2 ounces

                                         = 13/8 ounces

                                         = 13/8 ounces

Hence the baker needs 13/8 more ounces of color.

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The equation of a circle with a center at (4,−9) and a radius of 5 is

(x−4)^2+(y+9)^2=25. The correct Option C.

A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.

The equation of a circle with center (h, k) and radius r units is

(x−h)^2+(y−k)^2=r^2 .

where h = 4

k = -9

r = 5

The equation of the circle

(x−4)^2+(y−(-9))^2 = 5^2

The equation of the circle

(x−4)^2+(y+9)^2 = 25

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Answer:

2π/5  

Step-by-step explanation:

We are given a data set, and we are told that this can be represented as a linear equation. Let's remember the general form for the equation of a line:

Where "m" is the slope and "b" is the y-intercept. To find the slope we use the following formula:

where:

Are points through which the line passes. These two points can be found in the given data set. Let's take the following points:

We can find the slope using the previous formula, like this:

This is the daily rate for the pricing plan. Now we can find the y-intercept "b" using one of the points given, like this:

replacing the point (2,105), we get:

Solving the operation:

subtracting 90 on both sides:

Replacing the value of "b" in the equation:

This is the equation of the line that models the data set given.

Thus, the expression obtained after multiplying and removing all perfect squares from inside of square roots is: 6y²√2.

The opposite of squaring an integer is the square root procedure. In other words, an operation which undoes a 2 exponent is the square root.

Given data:

The word problem is:

square root 12 times square root y^3 times square root 6y

In which 'y' is the positive number.

The expression formed for the word problem is:

= √12 x √y³ x √6y

Taking Product of all.

= √(12 * y³ * 6y)

= √(6*2 * y⁴ * 6)

taking the square of the values outside the square root:

= 6y²√2

Thus, the expression obtained after multiplying and removing all perfect squares from inside of square roots is: 6y²√2.

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Answer:

The domain of the inverse is x >= -1

Step-by-step explanation:

Functions:

Domain: Values of input(usually x).

Range: Values of output(usually y)

Inverse function:

The domain of the inverse function is the range of the original function.

The range of the inverse function is the domain of the original function.

In this question:

Original function has range y >= -1.

So the domain of the inverse is x >= -1

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

9514 1404 393

Answer:

   $40,615.20

Step-by-step explanation:

The amortization formula will tell you Michelle's monthly payment.

  A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . . loan value P at interest rate r for t years

  A = $124,500(0.059/12)/(1 -(1 +0.059/12)^(-12·10)) ≈ $1375.96

__

The total of Michelle's 120 monthly payments is ...

  12 × $1375.96 = $165,115.20

This amount pays both principal and interest, so the amount of interest she pays is ...

  $165,115.20 -124,500 = $40,615.20

Michelle will pay $40,615.20 in interest over the course of the loan.

__

A calculator or spreadsheet can figure this quickly.

Answer:

(x + 5) and (x -1)

Step-by-step explanation:

Given

The attached graph

Required

The \(factors\) of the graph

The x \(values\) are where the \(curve\) \(touches\) the x-axis

The first is at:

\(x = -5\)

Add 5 to both sides

\(x +5= -5+5\)

\(x +5= 0\)

This implies that the first factor is: (x + 5)

The second is at:

\(x =1\)

Subtract 1 from both sides

\(x - 1 = 1 - 1\)

\(x - 1 = 0\)

This implies that the other factor is: (x - 1)

Answer:

The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.

Answer: B

Step-by-step explanation:

The percentage of players serves were between 115 mph and 145 mph is approximately 16%.

Given :

The statistician reported that the mean serve speed was 100 miles per hour

the standard deviation of the serve speeds was 15 mph

Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric

To find :

What percentage of the player's serves were between 115 mph and 145 mph?

Solution :

μ =100

σ = 15

P ( 115 < x <145)

= P ( \(\frac{115-100}{15}\) <  x-μ /6 <\(\frac{145-100}{15}\) )

= P ( \(\frac{15}{15}\) < z < \(\frac{15}{15}\) )

= p ( 1<z<3)

= p( z<3)-p(z-1)

=0.9987-0.8413

=0.1574

p ( 115<xx<145)= 15.74 %

p( 115<x<145)= approximately 16%

The percentage of players serves were between 115 mph and 145 mph is approximately 16%.

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Each package has 18 granola bars.

This problem can be solved through a system of linear equations.

Let "x" be the total number of granola bars that each pack of granola has. Let "y" be the total amount of granola bars that each cafeteria has.

For cafeteria A: \(7x+12=y\)

For cafeteria B: \(3x+84=y\)

Since both equations are solved for y, we may take the argument at the left of the equal sign from both equations and equal them.

\(7x+12=3x+84\).

\(7x+12=3x+84\)

\(7x-3x=84-12\) --> Substract 3x and 12 from both sides.

\(4x=72\) --> Simplify by solving the substraction.

\(\frac{4x}{4} =\frac{72}{4}\)--> Divide both sides by 4.

\(x= 18\)

\(y=7(18)+12\\ \\y=138.\)

If a system of linear equations was created, where 2 equations that gave the number of granola bars that each cafeteria has, then the x value obtained when the system was solved, indicates the amount of granola bars that each cafeteria has in each package. Each package has 18 granola bars.

Once we have this data, we can substitute the values into the formula to find the empirical probability that a person prefers apple pie given that they prefer whipped cream. Therefore, the missing probability is 1/12, and we know this because it is the value that makes the sum of all probabilities equal to 1.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur. For example, if the probability of winning a coin toss is 1/2, this means that there is an equal chance of the coin landing heads or tails. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability approach. Another approach is empirical probability, where probabilities are calculated based on observed data or experiments. Lastly, subjective probability involves making an informed guess or estimate about the likelihood of an event occurring based on subjective factors such as experience, intuition, or expert opinion. Probability is a fundamental concept in statistics and is used in many application

Here,

1. The formula needed to calculate the empirical probability that a person prefers apple pie given that they prefer whipped cream is:

P(Apple Pie | Whipped Cream) = P(Apple Pie and Whipped Cream) / P(Whipped Cream)

where P(Apple Pie and Whipped Cream) is the probability that a person prefers both apple pie and whipped cream, and P(Whipped Cream) is the probability that a person prefers whipped cream.

This formula is used because it is a conditional probability, which is a measure of the probability of an event occurring given that another event has occurred. In this case, we want to find the probability that a person prefers apple pie given that they already prefer whipped cream.

To calculate P(Apple Pie and Whipped Cream), we would need to gather data on the number of people who prefer both apple pie and whipped cream. Similarly, to calculate P(Whipped Cream), we would need to gather data on the number of people who prefer whipped cream.

2. To find the missing probability, we need to use the fact that the sum of all probabilities in a probability distribution must be equal to 1. Therefore, we can set up an equation to solve for the missing probability:

1/6 + 1/3 + x + 5/12 = 1

Simplifying the equation by finding a common denominator gives:

2/12 + 4/12 + x + 5/12 = 1

Combining like terms gives:

11/12 + x = 1

Subtracting 11/12 from both sides gives:

x = 1 - 11/12

x = 1/12

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Answer:

1/2, 5/8, 3/4, 7/16, 3/8, 5/16

Answer:

7/16, 5/16, 5/8, 3/8, 3/4, 1/2

Step-by-step explanation:

you see the biggest numbers mean the more times its been split so the smaller each peice would be so therefor the biggest number would be the smallest tool and vice versa

Answer:

5

Step-by-step explanation:

To find the slope we will use the slope formula:

\(slope = \frac{y2 - y1}{x2 - x1}\)

They give us the points of (0,1) and (-2,-9) in the equation. Let's label each thing to fit the equation:

y2 = -9

y1 = 1

x2 = -2

x1 = 0

Now, plug it all in to the equation:

\(\frac{-9-1}{-2-0} = \frac{-10}{-2} = 5\)

Therefore, the slope is 5.

I hope this helps!!

- Kay :)