MATLAB DATA CREATION Create a 120-by-5 matrix of elements for 120 student exam grades for 5 units to be stores as matrix grades. This part is random data generation. So, you are expected to be innovat

Answer:

261 ft²

Explanation:

This entire shape can be divided into one square and four triangles.

Area of square:

Side² = 9² = 81 ft²

Area of four triangles:

4 × 1/2 × base × height

2 × 9 × 10

180 ft²

Total Area:

180 + 81 = 261 ft²

Answer:

4

Step-by-step explanation:

Volume of cylinder = 2πrh = 2π(4)(6) = 48π

Volume of cone = πr²h/3

Height of cone = √(5² - 3²) = 4

Volume of cone = π(3²)(4)/3 = 12π

Cones to fill cylinder = 48π ÷ 12π = 4

Answer:

For part 1:

-2x^6 + 7x^4 + 3x^3 - 3x^2 + 11x + 20

For part 2:

Based on the foiling of both, they are equal.

Step-by-step explanation:

(-2x^3 +x -5)( x^3 -3x-4)

What we need to do is foil one by one.

I’ve attached a picture of this.

Once you foil, you add like terms.

Now for part 2, x^3 -3x-4 and -2x^3 +x -5, we do the same process.

Answer:

B is the answer because 28 + the product is n so it is B.

Step-by-step explanation:

Answer:

4 3/5

Step-by-step explanation:

Answer:

4 3/5

Step-by-step explanation:

How many 5s are in 23?

4 whole 5s and 3 left over.

23/5 = 4 3/5

Answer:

6 weeks.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The scale factor is 5.3 repeating. So I divided 24 by 5.33333333333333333 and got 4.5. I don't know if it's accurate since it's a reapeating decimal but it's close enough. Then I multiplied 2 by 5.3333333333333333333333 and got 10.6666667.

Answer:

80+ 0.3x = 60 + 0.4x

20 = 0.1x

x = 200

Therefore, at 150 miles, the best deal changes companies

Step-by-step explanation:

Answer:

$3.80, Three dollars and eighty cents

Step-by-step explanation:

:) yw

Answer:

$3.25

Step-by-step explanation:

There are 3 dollar bills, 1 dime (worth 10 cents), and 3 nickles (worth 5 cents each). Just add it all together; and therefore, the value of the money shown is $3.25

Hope this helps :)

She could make her approximation in the multiples of 1/6.

Probability is the chance of happening a certain event of all the possible events that can occur.

Statistics is a branch of mathematics where organising and interpretation of data analysing is needed.

A fair 6 sided dice has 6 sides having numbers from 1 to 6 and for a fair dice each side has a probability of 1/6. So she could make her approximation in the multiples of 1/6 for example 6/36 and the numerator she can vary by ±10 % for approximation.

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1. It can be piecewise linear; from x = 1 to x = 4, the y-value increases by the same amount each time. From x = 0 to x = 1, the y-value stays the same.

However, if it is supposed to be a single function, it would be non-linear because it changes slope.

2. It is discrete because there is no data between the points.

From the information provided in this question, it is not possible to accurately determine the proportion of winning actresses who were between 30 and 40 years old when they won the Oscar or the shape of the distribution.

The histogram only provides the frequencies (proportions) of actresses at different age ranges (e.g. 0.39, 0.40, 0.41, 0.45), but it does not provide information about the actual ages or the number of actresses.

In order to determine the proportion of winning actresses within a specific age range, additional information such as the number of actresses in each age group or a plot of the actual ages would be necessary. Similarly, the shape of the distribution cannot be determined accurately based on the information provided, as the histogram only provides the frequencies.

Therefore, the information provided is not sufficient to answer the questions asked.

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The gamma distribution with parameters $\alpha$ and $\beta$ is a probability distribution that can be derived using the transformation $x = \beta y$.

The probability density function of the gamma distribution is:

f(x; α, β) = \frac{(\beta x)^{\alpha - 1} e^{-\beta x}}{\Gamma(\alpha)}

where $\alpha$ is the shape parameter and $\beta$ is the rate parameter.

The derivation is as follows:

* The gamma function is defined as:

Γ(α) = \int_0^{\infty} x^{\alpha - 1} e^{-x} dx

* Using the transformation $x = \beta y$, we get:

Γ(α) = \int_0^{\infty} (\beta y)^{\alpha - 1} e^{-\beta y} \beta dy

* We can then write the probability density function of the gamma distribution as:

f(x; α, β) = \frac{1}{\Gamma(\alpha)} \int_0^{\infty} (\beta y)^{\alpha - 1} e^{-\beta y} \beta dy

* This is the same as the probability density function of the gamma distribution with parameters $\alpha$ and $\beta$.

The mean and variance of the gamma distribution can be found using the following formulas:

E(X) = \alpha \beta

Var(X) = \alpha \beta^2

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The Converse of the Pythagorean Theorem states that if the sum of the squares of the lengths of two sides of a triangle is equal to the square of the measure of its third side, then the triangle is a right triangle.

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation: a² + b² = c²

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proved numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.

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All the values are,

a)  lim x → 3 [ 2 f (x) - g (x)] = 18

b)  lim x → 3 [ 2 g (x) ]² = 16

c)  lim x → 3 [ ∛ f (x) / g (x) ] +  lim x → 3 [ 4 h (x) / x + 7 ] = - 1

We have to given that;

Limits are,

lim x → 3 f (x) = 8

lim x → 3 g (x) = - 2

lim x → 3 h (x) = 0

Now, We can simplify all the limits as;

1) lim x → 3 [ 2 f (x) - g (x)]

⇒  lim x → 3 [ 2 f (x)] -  lim x → 3 [ g (x) ]

⇒ 2  lim x → 3 [  f (x) ] - (- 2)

⇒ 2 × 8 + 2

⇒ 16 + 2

⇒ 18

2)  lim x → 3 [ 2 g (x) ]²

⇒ 4 [ lim x → 3  g (x) ]²

⇒ 4 × (- 2)²

⇒ 4 × 4

⇒ 16

3)  lim x → 3 [ ∛ f (x) / g (x) ] +  lim x → 3 [ 4 h (x) / x + 7 ]

⇒ ∛8 / (- 2) + 4 × 0 / (3 + 7)

⇒ - 2/2 + 0

⇒ - 1

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Answer:

total cup = 32

1 student = 1/2 cup

find remaining cup = y

*we don't know how many students are there, so we just let it be x .

remaining cup = total cup - cup drank by students

y = 32 - 1/2x

y = -1/2x + 32 ( option c )

why 1/2x ? because we don't know how many students drank the juice, so we just let it be x .

Step-by-step explanation:

To find out how much she spent:

30 - 27.15 = 2.85

Change it to cents:

2.85 x 100 = 285 cents

Calculate how many yards of ribbon she bought:

285 / 19 = 15

Therefore, she bought 15 yard of ribbon.

Answer:

117,649

Step-by-step explanation:

Good luck! <3

Answer:

7 to the 6th power is conventionally written as 76, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 7^6.

76 stands for the mathematical operation exponentiation of seven by the power of six.

As the exponent is a positive integer, exponentiation means a repeated multiplication:

The exponent of the number 7, 6, also called index or power, denotes how many times to multiply the base (7).

Thus, we can answer what is 7 to the 6th power as

7 to the power of 6 = 76 = 117649.

Answer:

x = 60.6

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan x = 3.9/ 2.2

Taking the inverse tan of each side

tan ^-1 (tan x )=  tan ^-1(3.9/ 2.2)

x=60.57254

To the nearest tenth

x = 60.6

Numbering starts from the leftmost figure.

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1) Opposite sides are equal $\implies$ quadrilateral is a parallelogram. (Can be proven using basic congruency theorems)

2)

Opposite sides are parallel $\implies$ trapezium.

But the other pair of sides are not parallel, hence in the general case this is not a parallelogram but is a trapezium with two equal sides.

3) One pair of opposite sides are congruent and parallel $\implies$ this is a parallelogram.

Proof: Join two vertices and you get that the two triangles formed are congruent.

4)

Diagonals are bisected at their intersections $\implies$ Quadrilateral is a parallelogram.

Show that the two opposite little triangles are congruent by using SAS test (or whatever you call it)

So the figure which is not a parallelogram is 2.

This matrix is not symmetric, skew-symmetric, or orthogonal and the eigenvalues of the matrix are: λ = (1 + √65) / 2 and λ = (1 - √65) / 2

Symmetric matrices are defined as matrices that are equal to their transpose, meaning that each element in the matrix is equal to the element in the corresponding position of the transpose.

A skew-symmetric matrix is a matrix whose transpose is the negative of itself. Orthogonal matrices are matrices whose inverse is equal to its transpose, meaning that the product of the matrix and its transpose is equal to the identity matrix.

To determine if it is orthogonal, we can check if it satisfies the condition for orthogonality, which is that its transpose is equal to its inverse.

The transpose of the matrix [1 4 -4 1] is:

[1 -4 4 1]

To find the inverse, we need to calculate the determinant of the matrix and the adjugate of the matrix. The determinant is:

(1)(1) - (4)(-4) = 1 + 16 = 17

The adjugate is:

[1 -4 -4 1]

So, the inverse of the matrix is:

[1/17 -4/17 -4/17 1/17]

The transpose of the matrix is not equal to its inverse, so this matrix is not orthogonal.

The spectrum of this matrix can be found by finding its eigenvalues. To do this, we solve for the values of λ that satisfy the characteristic equation:

det (A - λI) = 0

where A is the matrix [1 4 -4 1] and I is the identity matrix.

The determinant of A - λI is:

[1-λ 4 -4 1-λ]

[(1-λ)(1-λ) - (4)(-4) = (1-λ)^2 + 16]

So, we need to find the values of λ that satisfy:

(1-λ)^2 + 16 = 0

This equation can be solved using the quadratic formula:

λ = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -1, and c = -16.

So, λ = (-(-1) ± √((-1)^2 - 4(1)(-16))) / 2(1)

λ = (1 ± √(1 + 64)) / 2

λ = (1 ± √65) / 2

So, the eigenvalues of the matrix are:

λ = (1 + √65) / 2 and λ = (1 - √65) / 2

These are the eigenvalues of the matrix and make up its spectrum.

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The two vectors [2x + 4y; 6x + 8y] and [2x; 2y], we can see that they are not equal. Therefore, lambda = 2 is not an eigenvalue of matrix A. To determine if lambda is an eigenvalue of the matrix A, we need to find if there exists a non-zero vector v such that Av = lambda * v.

1. Let's start by computing the matrix-vector product Av.
2. Multiply each element of the first row of matrix A by the corresponding element of vector v, then sum the results. Repeat this for the other rows of A.
3. Next, multiply each element of the resulting vector by lambda.
4. If the resulting vector is equal to lambda times the original vector v, then lambda is an eigenvalue of matrix A. Otherwise, it is not.

For example, consider the matrix A = [1 2; 3 4] and lambda = 2.
Let's find if lambda is an eigenvalue of A by solving the equation Av = lambda * v.

1. Assume v = [x; y] is a non-zero vector.
2. Compute Av: [1 2; 3 4] * [x; y] = [x + 2y; 3x + 4y].
3. Multiply the resulting vector by lambda: 2 * [x + 2y; 3x + 4y] = [2x + 4y; 6x + 8y].
4. We need to check if this result is equal to lambda times the original vector v = 2 * [x; y] = [2x; 2y].

Comparing the two vectors [2x + 4y; 6x + 8y] and [2x; 2y], we can see that they are not equal. Therefore, lambda = 2 is not an eigenvalue of matrix A.

In summary, to determine if lambda is an eigenvalue of matrix A, we need to find if Av = lambda * v, where v is a non-zero vector. If the equation holds true, then lambda is an eigenvalue; otherwise, it is not.

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Answer:

m= -84

Step-by-step explanation:

Step 1- Multiply both sides by 7

42-m= 126

Step 2- Move constant to the right hand side and change its sign

-m= 126-42

Step 3- Subtract the numbers

-m= 84

Step 4- Change the signs on both sides of the equation

m= -84

The number of possible combinations of three coins from the bag of 16 coins with different dates can be calculated using the formula for combinations, which is nCr = n! / r!(n-r)!, where n is the total number of objects, r is the number of objects to be chosen, and ! denotes factorial (the product of all positive integers up to the given number).

In this case, we have n = 16 (the total number of coins in the bag) and r = 3 (the number of coins to be chosen for each combination). Using the formula for combinations, we can calculate the number of possible combinations as follows:

nCr = 16! / 3!(16-3)!
nCr = (16 x 15 x 14) / (3 x 2 x 1)
nCr = 560

Therefore, 560 possible combinations of three coins can be chosen from the bag of 16 coins with different dates. These combinations could represent different historical events, significant dates, or other symbolic meanings depending on the dates inscribed on the coins. The calculation of combinations is an important concept in combinatorics and probability theory, and it has many real-world applications in fields such as statistics, economics, and computer science.

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Answer:

Domain: {-3, -1, 0, 3}

Step-by-step explanation:

{(-3, 4), (-1,3), (0, 4), (3, 6)}

Domain is just the x values so:

Domain: {-3, -1, 0, 3}

Answer:

1: 0.80

2: 1.30

Step-by-step explanation:

Hope this helps

Answer:

0.80 and 1.30

Step-by-step explanation:

0.80, 1.05, 1.30, 1.55, 1.80, 2.05

... + 0.25 = 1.05

= 1.05 - 0.25

= 0.80

0.80 + 0.25 = 1.05

1.05 + 0.25 = 1.30

1.30 + 0.25 = 1.55

1.55 + 0.25 = 1.80

1.80 + 0.25 = 2.05

As per the 95% confidence interval, the true average age of all students in the university is approximately 23 to 24.

Confidence interval

Confidence interval means the interval calculation, obtained from the observed data that holds the actual value of the unknown parameter.

Given,

A random sample of 64 students at a university showed an average age of 23 years and a sample standard deviation of 3 years.

And we need to find the 95% confidence interval for the true average age of all students in the university.

While we looking through the given question we have identified the following,

Number of samples = 64

Average age = 23

Standard deviation = 3

Confidence interval = 95%

Based on this confidence interval, the z score is 1.96

According to the formula,

u = 23 ± 1.96 x 3/√64

u = 23  ± 1.96 x (3/8)

u = 23  ± 1.96 x 0.375

u = 23  ± 0.735

u = 23.735, 22.635

Therefore, the average age of the student is approximately 23 to 24.

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Answer:

He should use the negative 1 unit tile.

Step-by-step explanation:

He should do this because in this equation you wish to isolate the variable on one side, and it would be better to first take away any constants. Afterwards, the variable would be next.

Answer:  It does not matter which he does first. Either way, zero pairs will be created on both sides, which will isolate the variable to determine x. Adding the x-tiles and then the unit tile, or visa versa, will give the same solution.\

Explanation: that's what i put and i got it right

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