Classify each number below as a rational number or an irrational number.

Answer:

1/√2

Approximate numerical value

1/√2 = 0.707106781186548

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

Rationalize the denominator

(1/√2) * (√2 / √2) = √2 / 2

The sailboat traveled an average of 18,000 meters per hour based on the given information that it traveled 9000 meters in 30 minutes.

Given that a sailboat traveled 9000 meters in 30 minutes, we can find the average meters traveled by the sailboat. The average meters traveled by a sailboat can be calculated by dividing the total distance covered by the sailboat with the total time taken.

This can be done as follows:

Average meters traveled = Total distance / Total time

Total distance traveled by the sailboat = 9000 meters

Total time taken by the sailboat to travel this distance = 30 minutes = 0.5 hours

Average meters traveled = 9000 / 0.5 = 18,000 meters per hour

Therefore, on average, the sailboat traveled 18,000 meters per hour.

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The value of x is 9 when f(x) = - 10.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -x - 1 _____(1)

f(x) = -10 ____(2)

Now,

From (1) and (2),

-x - 1 = -10

10 - 1 = x

x = 10 - 1

x = 9

Thus,

x is 9.

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Answer:

One solution, 8x + 9

Step-by-step explanation:

3x + 9 + 4x + x

Add the x's

8x + 9

good luck, hope this helps :)

Answer:

See below

Step-by-step explanation:

a) The vertex is (0,2) so the standard form equation is (x-0)^2=4p(y-2). Since p=1/(4a) and a=1/8, then p=1/(4(1/8))=1/(1/2)=2. This makes the equation now x^2=8(y-2). Given the focus point for a vertical parabola is (h,k+p) then the focus point is (0,2+2) which is (0,4)

b) They are both 4 units away

c) I can't solve

d) I can't solve

Answer:

$60

Step-by-step explanation:

x-0.32x=40.8

0.68x=40.8

x=60

Answer: The original cost of the sweatshirt would be $60 because

x-0.32x=40.8

0.68x=40.8

x=60

Hope this helps :) please mark Brainliest

Answer:

1. 24%

2. 30%

3. 30%

Step-by-step explanation:

1. 100%/25= 4%   4%*6=24%

2. 100%/50= 2% 2%*15=30%

3.  100%/40=2.5% 2.5%*12= 30%

Answer:

30$ is 15% of 200$

Step-by-step explanation:

To find how much percent Jennie spent let's first find how much one percent of $200 is.

∴200/100=2

so one percent of 200 is 2

now let's find how much percent 30$ is of 200$

∴30/2=15

meaning that 30$ is 15% of 200$

Answer:

19.72

Step-by-step explanation:

Answer:

x=15

Step-by-step explanation:

2/3x = 10

To find x divide both sides by 2/3.

2/3x÷2/3 = 10÷2/3

x=15

Easy!! :3

x = 15

(2/3)*x = 10 // - 10

(2/3)*x-10 = 0

2/3*x-10 = 0 // + 10

2/3*x = 10 // : 2/3

x = 10/2/3

x = 15

Hope i helped!!

Have a great day!!

( `w`)``

The  probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.

Using the binomial probability formula, the probability of x successes in n independent trials with a probability of success p can be calculated as:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where "n choose x" represents the number of ways to choose x items from a set of n items, and is calculated as:

(n choose x) = n! / (x! * (n-x)!)

So, for the given parameters nequals=7, pequals=0.65, xequals=6, we have:

P(6) = (7 choose 6) * 0.65^6 * (1-0.65)^(7-6)
     = 7 * 0.65^6 * 0.35^1
     = 0.3052

Therefore, the probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.

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Both Sheila and Bob together can wash the car in 10 minutes

Calculating work :

The formulas to find work and time is given by

Time Taken = 1 / Rate of Work

Rate of Work = 1 / Time Taken

If a work can be done in x number of days, then the work can be done in one day = 1/x

Total Work done = Number of Days × Efficiency ( of the person or machine )

Given that,    

Sheila can wash her car in 15 minutes

Let us consider washing the car is 1 unit of work

Then the work can done by Sheila in 1 minute = 1/15  

Bob take twice as long as Sheila to wash the same

Bob can wash the same car in 30 minutes

Then the work can done by Bob  in 1 minute = 1/30  

From above calculation,

The work can be done by Sheila and Bob = (1/15 + 1/30)

= (2+1) /30 = 3/30 = 1/10  

So the efficiency of Both Sheila and Bob per minute = 1/10

Let Both can complete the work in x minutes

As we know Total Work done = time × Efficiency

⇒ 1 = x × 1/10

⇒ x = 1 × 10

⇒ x = 10 minutes

Therefore,

Both Sheila and Bob together can wash the car in 10 minutes

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Answer:

The slope is -1/8 and the y intercept is 7/6

Step-by-step explanation:

This equation is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = -1/8 x + 7/6

The slope is -1/8 and the y intercept is 7/6

Answer:

\(X = \sqrt{39}\)

Step-by-step explanation:

\(1)\ X^2 + 5^2 = Y^2\ (Y\ is\ the\ hypotenuse\ of\ the\ smaller\ triangle)\)

\(2)\ Y^2 + 6^2 = 10^2\)

\(3)\ X^2 + 25 + 36 = 100\)

\(4)\ X^2 = 39\)

\(5)\ X = \sqrt{39}\)

Answer:

X = \(\sqrt{39}\)

Step-by-step explanation:

Answer: 18

Step-by-step explanation:

Answer: 18.04347826086957

Step-by-step explanation: you could use a calculator too-

The approximate distance from Town A to Town C is 12.5 miles.

What is the midpoint?

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

To find the midpoint of Town A and Town B, you need to find the average of the x-coordinates and the average of the y-coordinates.

The x-coordinate of Town A is -8 and the x-coordinate of Town B is 10, so the average is (10 - (-8))/2 = 9/2 = 4.5.

The y-coordinate of Town A is 2 and the y-coordinate of Town B is 8, so the average is (8 - 2)/2 = 6/2 = 3.

Therefore, Town C is located at (4.5, 3).

To find the distance from Town A to Town C, you can use the distance formula, which is the square root of the difference in x-coordinates squared plus the difference in y-coordinates squared.

The distance from Town A to Town C = √((4.5 - (-8))^2 + (3 - 2)^2) = √(12.5^2 + 1^2) = √(156.25 + 1) = √(157.25) = 12.5 miles

Hence, the approximate distance from Town A to Town C is 12.5 miles.

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Answer:

the constant is 4 because you always add 4 and it stays 4 no matter what you do to the equation

Step-by-step explanation:

Answer:

It is 4

Step-by-step explanation:

The numerical limits for a D grade: 59 to 64

In this question we have been given that the scores on the test are normally distributed with a mean of 70 and a standard deviation of 7.3

μ = 70, σ = 7.3

We need to find the numerical limits for a D grade

D: Scores below the top 79% and above the bottom 6%

So between the 6th and the 21st percentile.

6th percentile:

X when Z has a pvalue of 0.06. So X when Z = -1.555

Z = X - μ/σ

-1.555 = (X - 70)/7.3

X - 70 = -11.35

X = 58.65

X ≈ 59

21st percentile:

X when Z has a pvalue of 0.21. So X when Z = -0.81

Z = X - μ/σ

-0.81 = (X - 70)/7.3

X - 70 = -5.91

X = 64.09

X ≈ 64

Therefore, you get a D if you have a grade between 59 and 64

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In order to prove that the system has an unlimited number of solutions, h must be equal to the product of the matrix's number of columns and rows.

The number of columns in the matrix less the number of rows in the matrix must equal h for the matrix to be an augmented matrix of a system with infinitely many solutions. This is thus because a matrix with more columns than rows is known as an augmented matrix in a system with infinitely many solutions. Since the equations are linearly dependent in this situation, which means that one equation can be solved by more than one, the system of equations has an infinite number of solutions

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Answer:

x = -2

y = 3

Step-by-step explanation:

You are given a system of two linear equations:

-2x + 3y = 13

3x + 4y = 6

One of the good ways to solve this system is trying to eliminate one variable (x or y), calculate the remaining variable and substitute the calculated variable back into system to solve for eliminated variable.

Here, we will manipulate the original system, so that we can easily eliminate x.

Let's multiply both sides of the first equation by 3 and the second equation by 2 (this manipulating step does not change the original system of equations).

3*(-2)x + 3*3y = 3*13

2*3(x) + 2*4y = 2*6

<=>

-6x + 9y = 39

6x + 8y = 12

Now, we add up two equations, left side + left side, right side + right side, we obtain:

-6x + 9y + 6x + 8y = 39 + 12

or

17y = 51

We divide both sides of equation by 17, to get y.

=> y = 51/17 = 3

Substitute y = 3 back into the first equation of system (or the second equation, it doesn't matter, here we choose the first one).

=> -2x + 3*3 = 13

=> -2x + 9 = 13

=> -2x = 4

=> x = -2

=> The solution of this system is (x, y) = (-2, 3)

Hope this helps!

:)

Answer:

1440

Step-by-step explanation:

60x24 = 1440

hope this helps

Answer:

\(60*24=1440\)

Step-by-Step Explanation:

~Kandy~
Hope this helped!

Brainliest Please!

Answer:

71.092

Step-by-step explanation:

The number in the standard form i.e. seventy-one and ninety-two thousandths should be considered as the 71.092.

Since the numbers are mentioned in alphabets like

seventy-one and ninety-two thousandths

We have to write in standard form

So, it should be like 71.092.

Hence, The number in the standard form i.e. seventy-one and ninety-two thousandths should be considered as the 71.092.

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Answer:

90 hours.

Step-by-step explanation:

As we know there are 30 days in a month 3 hours a day there fore we say 30 x 3 = 90 :D

Numbers which are co- prime number which have greatest common factor one are 1, 7, 13, 17, 19, 23, 29, 31

Two integers a and b are coprime, comparatively prime, or mutually prime in mathematics if and only if the single positive integer that divides both of them is 1. As a result, every prime integer that divides a does not divide b, and the opposite is also true. This translates to having a greatest common divisor of 1 for them. Co-prime numbers are collections of numbers with just one common factor between them. Their highest common factor (HCF) is 1, which signifies. For Co-Primes to exist, there must be at least two Numbers. Relatively Prime Numbers is another name for co-prime numbers.

Given,

A date is called weird if the number of its month and the number of its day have greatest common factor 1.

Numbers which are co- prime which have greatest common factor one are:

1, 7, 13, 17, 19, 23, 29, 31

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Answer:the 2nd

Step-by-step explanation:

The quotient in the simplest form are:

Each person will run 1/8 mile in the relay race.

To divide a fraction by a whole number, we can multiply the fraction by the reciprocal of the whole number. For example, to find 4/5 ÷ 5, we can write it as 4/5 x 1/5, which simplifies to 4/25.

Similarly, to find 3/7 ÷ 2, we can write it as 3/7 x 1/2, which simplifies to 3/14.

To find 2/5 ÷ 4, we can write it as 2/5 x 1/4, which simplifies to 1/10.

To find 8/9 ÷ 5, we can write it as 8/9 x 1/5, which simplifies to 8/45.

To find 6/7 ÷ 3, we can write it as 6/7 x 1/3, which simplifies to 2/7.

For the relay race, the total distance is 1/2 mile, which will be divided equally among four runners. To find the distance each person will run, we can divide 1/2 by 4, which gives us 1/8 mile for each person.

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2.18 is the right z-value to utilize for a level of confidence of 98.54%.

Assuming a two-sided confidence interval,

(100-98.54)/2 = 1.46

Lower percentile = 1.46%

In terms of the information that is provided, we have that the percentile is the 3-th percentile.

We need to find the z-score associated to this percentile. How do you we do so? We need to find the

value z* that solves the equation below.

P(Z < z*) = 0.0146

The value of z" that solves the equation above cannot be made directly, it solved either by looking at

a standard normal distribution table or by approximation (the way Excel or this calculator does)

Then, it is found that that the solution is z* = -2.18

Therefore, it is concluded that the corresponding z-score associated to the given 2nd percentile is

Z =-2.18

The results found above are depicted graphically as follows:

The Z-score z = -2.18 is associated to the 2nd percentile

Hence, lower interval Z-score =-2.18

Since the standard normal distribution is symmetric around 0,

Therefore, upper interval Z-score = 2.18

Appropriate z-value =2.18

Hence, the appropriate z-value to use for a 98.54% level of confidence is 2.18

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Answer:

76.4 m

Step-by-step explanation:

The race track has two straights and two semi circles.

Each straight is 80m

total perimeter for the straights is 80 * 2 = 160m

two semi circles which creates a full circle

perimeter of a full circle = \(\pi\) d

NB : (d) is the diameter

therefore we can find the value of the diameter

400 = 160 + \(\pi\) d

400- 160 = \(\pi\)d

240 = \(\pi\)d

d = 240/\(\pi\)

d = 76.394.....

d = 76.4 m

The pseudo-inverse of A is:

A+ =

⎡ cosφ/σ1 -sinφ/σ2 ⎤

⎢ sinφ/σ1 cosφ/σ2 ⎥

⎣ 0 0 ⎦

The pseudo-inverse of a 2x3 matrix A, we first need to compute the singular value decomposition (SVD) of A.

The SVD of A can be written as A = \(U\Sigma V^T\), where U and V are orthogonal matrices and Σ is a diagonal matrix with non-negative diagonal elements in decreasing order.

Since A is a 2x3 matrix, we can assume that the rank of A is either 2 or 1. If the rank of A is 2, then Σ will have two non-zero diagonal elements, and we can compute the pseudo-inverse as A+ = \(V\Sigma ^{-1}U^T\).

If the rank of A is 1, then Σ will have only one non-zero diagonal element, and we can compute the pseudo-inverse as A+ = \(V\Sigma^{-1}U^T\), where \(\Sigma^{-1\) has the reciprocal of the non-zero diagonal element.

Let's assume that the rank of A is 2, so we need to compute the SVD of A.

Since A is a 2x3 matrix, we can use the formula for SVD to write:

A = \(U\Sigma V^T\) =

⎡ cosθ sinθ ⎤

⎣-sinθ cosθ ⎦

⎡ σ1 0 0 ⎤

⎢ 0 σ2 0 ⎥

⎣ 0 0 0 ⎦

⎡ cosφ sinφ 0 ⎤

⎢-sinφ cosφ 0 ⎥

⎣ 0 0 1 ⎦

where θ and φ are angles that satisfy 0 ≤ θ, φ ≤ π, and σ1 and σ2 are the singular values of A.

The diagonal matrix Σ contains the singular values σ1 and σ2 in decreasing order, with σ1 ≥ σ2.

The pseudo-inverse of A, we first compute the inverse of Σ.

Since Σ is a diagonal matrix, its inverse is easy to compute:

\(\Sigma^{-1\)=

⎡ 1/σ1 0 0 ⎤

⎢ 0 1/σ2 0 ⎥

⎣ 0 0 0 ⎦

Next, we compute \(V\Sigma^{-1}U^T\):

A+ = VΣ^-1U^T =

⎡ cosφ -sinφ ⎤

⎣ sinφ cosφ ⎦

⎡ 1/σ1 0 ⎤

⎢ 0 1/σ2 ⎥

⎡ cosθ -sinθ ⎤

⎣ sinθ cosθ ⎦

The pseudo-inverse is not unique, and there may be different ways to compute it depending on the choice of angles θ and φ.

Any valid choice of angles will yield the same result for the pseudo-inverse.

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The pseudo-inverse A+ of a 2x3 matrix A does not exist.

The pseudo-inverse of a matrix is a generalization of the matrix inverse for non-square matrices. However, not all matrices have a pseudo-inverse.

In this case, we have a 2x3 matrix A, which means it has more columns than rows. For a matrix to have a pseudo-inverse, it needs to have full column rank, meaning the columns are linearly independent. If a matrix does not have full column rank, its pseudo-inverse does not exist.

Since the given matrix A has more columns than rows (2 < 3), it is not possible for A to have full column rank, and thus, its pseudo-inverse does not exist.

Therefore, the pseudo-inverse A+ of the 2x3 matrix A is undefined.

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