Question 1 of 5
Which expression is equivalent to?x1/3

Answer:

124

Step-by-step explanation:

You'll need a calculator for this one

Answer:

Step-by-step explanation:

There are two ways to write 4/15 as a decimal.

**Method 1: Using long division**

1. Divide 4 by 15.

2. The quotient is 0.26.

3. The remainder is 6.

4. Since the remainder is not zero, we need to bring down a zero and continue dividing.

5. We get 0.266666...

**Method 2: Using a calculator**

1. Enter 4/15 into the calculator.

2. Press the "equals" button.

3. The answer is 0.266666...

The decimal representation of 4/15 is 0.266666..., which is a repeating decimal. This means that the 6 repeats indefinitely.

Answer:

The answer is 0.2666

Step-by-step explanation:

4/15

=0.2666

The calculated value of the volume of the solid is (d) V = ∫[0,2] (x² + 1) - (2x + 1) dx

To find the volume of the solid when the region R is rotated about the horizontal line y = -1, we can use the method of cylindrical shells.

The height of each cylindrical shell will be the difference between the function y = 2x and the horizontal line y = -1, which is (2x + 1).

The radius of each cylindrical shell will be the distance from the axis of rotation (y = -1) to the function y = x².

This distance is given by (x² + 1).

The thickness of each cylindrical shell will be dx.

Thus, the volume of the solid can be expressed as:

V = ∫[0,2] (x² + 1) - (2x + 1) dx

Hence, the expression is (d) V = ∫[0,2] (x² + 1) - (2x + 1) dx

Read more about volume at

https://brainly.com/question/11942113

#SPJ1

Answer:

K = √-6k

i did the math and got this answer and it was right

Answer:

The answer is Zack garden

The vector 6v is -24j - 126.

What is vector?

In mathematics, a vector is a mathematical object that represents a quantity that has both magnitude (size) and direction. Vectors are used to describe physical quantities that have both magnitude and direction, such as velocity, force, and displacement.

Given the vector v = -4j - 21, we can find the vector 6v by multiplying each component of v by 6:

6v = 6(-4j - 21)

Distributing the 6:

6v = -24j - 126

So the vector 6v is -24j - 126.

To learn more about vector visit the link:

https://brainly.com/question/15519257

#SPJ1

Complete question: Let v = - 4j- 21 Find the vector 6v.

Answer:

x = 7

Step-by-step explanation:

if A and B are parallel , then

4x + 14 and 3x + 21 are alternate angles and are congruent , that is

4x + 14 = 3x + 21 ( subtract 3x from both sides )

x + 14 = 21 ( subtract 14 from both sides )

x = 7

For A and B to be parallel then x = 7

The value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions can be used to represent mathematical relationships and patterns in a variety of contexts.

Algebraic expressions can include one or more variables, which are letters or symbols that represent unknown values or values that can vary. For example, in the expression 3x + 5, "x" is the variable.

To evaluate the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)), we first need to determine the value of cos(2) and cos(-π/2).

cos(2) cannot be evaluated directly since the range of cosine function is -1 to 1, and 2 is outside this range. Therefore, we can conclude that sin⁻¹(cos(2)) does not exist.

Next, we can evaluate cos(-π/2) using the unit circle, which is a circle of radius 1 centered at the origin of the coordinate plane. The angle -π/2 is located on the negative y-axis, where the cosine function is 0. Therefore, cos(-π/2) = 0.

Substituting this value into the expression, we get:

sin⁻¹(0) = 0

Therefore, the value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.

To know more about function visit:

https://brainly.com/question/30954499

#SPJ1

Answer: Without the options for the vector matrices resulting from rotation, I cannot provide a specific matching. However, I can provide the general formula for rotating a vector by an angle of θ degrees counterclockwise as follows:

To rotate a vector with coordinates (x, y) counterclockwise about the origin by an angle of θ degrees, we use the following formula to find the new coordinates (x', y'):

x' = xcos(θ) - ysin(θ)

y' = xsin(θ) + ycos(θ)

Therefore, to obtain the vector matrix resulting from rotating the vector (-6, -3) by a certain angle of rotation, we plug in the values of x = -6 and y = -3 into the above formulas, and use the corresponding angle of rotation in degrees for θ.

Step-by-step explanation:

According to the question the volume formula to find the height of the pyramid is 9 units.

Formula is a mathematical rule or equation expressed symbolically, that describes the relationship between different variables. It is a set of symbols or terms that expresses a relationship between different entities, such as numbers, objects, ideas, or concepts. Formulas are used to calculate, analyze, and predict data, and are essential in many scientific and mathematical fields.

The volume of a pyramid is given by the formula V = (1/3) × b × h, where b is the area of the base and h is the height of the pyramid.
Since the base of the pyramid is a right triangle, we can use the formula to find the area of a right triangle, A = (1/2) × b × h, to find the base of the pyramid.
A = (1/2) × 8 × 9 = 36
Now we can use the volume formula to find the height of the pyramid:
V = (1/3) × 36 × h

108 = (1/3) × 36 × h

108 = 12 × h

h = 9 units

To learn more about volume of a pyramid
https://brainly.com/question/17615619
#SPJ1

a) The system of equations can be written in the matrix form AV-B as: | -3 3 | | V2 | | -10 |

b) V1 = 369/22 volts and V2 = -51/22 volts.

A matrix is a rectangular array of numbers or symbols, arranged in rows and columns. Matrices are often used in mathematics, science, engineering, and other fields to represent and manipulate data, perform operations, and solve equations. The size of a matrix is determined by the number of rows and columns it contains, and is usually written in the form "m x n", where "m" is the number of rows and "n" is the number of columns. Matrices can be added, subtracted, multiplied, transposed, and inverted, and can be used to represent a wide range of mathematical objects, including systems of linear equations, transformations, and graphs.

a) The system of equations can be written in the matrix form AV-B as:

| 15 -7 | | V1 | | 60 |

| | x | | = | |

| -3 3 | | V2 | | -10 |

b) To solve for V1 and V2 using matrix algebra, we can use the inverse of matrix A as follows:

AV = B

V = A⁻¹B

First, let's find the inverse of matrix A:

A = | 15 -7 |

| -3 3 |

To find the inverse of A, we need to calculate the determinant of A:

det(A) = (15)(3) - (-7)(-3) = 66

Then, we can find the inverse of A as follows:

A⁻¹ = (1/det(A)) x | 3 7 |

| 3 15 |

Now, we can solve for V by multiplying A⁻¹ and B:

| V1 | | 3 7 | | 60 | | 369/22 |

| | = | | x | | = | |

| V2 | | 3 15 | |-10 | | -51/22 |

Therefore, V1 = 369/22 volts and V2 = -51/22 volts.

To know  more about matrix visit:

https://brainly.com/question/27929071

#SPJ1

Let's say you're trying to decide whether or not to invest in a certain stock. You've analyzed the company's financial reports and economic indicators, but you're still uncertain about the stock's future performance. Based on your intuition and experience with the stock market, you estimate that there is a 70% chance that the stock's value will rise in the next six months.

You decide to invest based on that probability, and six months later the stock has actually gone up in value. Your decision turned out to be a good one, but that doesn't necessarily mean your probability estimate was accurate. The stock could have gone down in value just as easily, despite your assessment of its likelihood of going up.

Therefore, even when we make decisions based on probability, there is always a level of uncertainty involved and the outcome may not always line up with our initial estimates. However, taking the time to consider the likelihood of different outcomes can help us make more informed decisions and better manage risk.

Find out more about probability at:

https://brainly.com/question/24756209

#SPJ1

The volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

In general, volume refers to the amount of space occupied by a three-dimensional object. In physics, volume is a measure of the amount of space an object takes up, typically measured in cubic meters (m³) or cubic centimeters (cm³).

In mathematics, volume is often used to refer to the measure of the size of a solid object or region in three-dimensional space. This measure can be calculated using various methods depending on the shape of the object or region, such as integration, formulae, or counting.

For example, the volume of a cube can be calculated by multiplying its length, width, and height together. The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius of the sphere.

In finance, volume can also refer to the number of shares or contracts traded in a particular market or stock exchange over a given period of time. High trading volume often indicates a more active market, while low trading volume may indicate less interest or activity in a particular security or market.

The formula for calculating the volume of air passing through a filter is:

Volume = Filter Area x Airflow Velocity

Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:

Filter Area = Length x Width

Filter Area = 4 ft x 2 ft

Filter Area = 8 square feet

Now we can substitute the values into the formula:

Volume = Filter Area x Airflow Velocity

Volume = 8 sq ft x 100 ft/min

Volume = 800 cubic feet per minute (CFM)

Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

To know more about area visit:

https://brainly.com/question/7624796

#SPJ1

The pre-image ABCD was translated into the picture A'B'C'D' by moving 7 units to the right. answer is option (a).

A translation transformation is one in which the pre-image's size and orientation are maintained while the position of the points on the pre-image changes.

The polygon ABCD's vertices are located at these coordinates (1, 5), (3, 1), (7, 1), (5, 5)

The polygon's vertices are located at these coordinates: (8, 5), (10, 1), (14, 1), (12, 5)

where the preimage's and image's vertices are;

A(1, 5), B(3, 1), C(7, 1), D(5, 5), and A'(8, 5), B'(10, 1), C'(14, 1), D'(12, 5),

the x and y values disagree, which shows;

A' - A = (8 - 1, 5 - 5) = (7, 0)

B' - B = (10 - 3, 1 - 1) = (7, 0)

C' - C = (14 - 7, 1 - 1) = (7, 0)

D' - D = (12 - 5, 5 - 5) = (7, 0)

In view of this, the transformation employed to produce the image A'B'C'D' from the pre-image, ABCD, is a translation, 7 units to the right.

To know more about vertices, visit:

https://brainly.com/question/1217219

#SPJ1

Answer:

7 units to the right

Step-by-step explanation:

Answer:

Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.

On Thursday, she practiced for 5 minutes according to the table.

On Friday, she practiced for 9 minutes according to the table.

Adding these two times together, we get:

5 minutes + 9 minutes = 14 minutes

Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.

Answer:

Road:

Distance to Greg's house = 3.2 + 1.7 =

4.9 miles

Time to get to Greg's house =

(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)

Shortcut:

Distance to Greg's house:

[tex] \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 [/tex]

Time to get to Greg's house:

(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)

The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)

The probability of the card is as stated at 7/52, which simplifies it to 1/8.

Probability is the study of the possibility that an event or phenomenon will occur. It can be expressed numerically as a number between 0 and 1, where 1 implies a certain outcome of an event and 0 denotes an inconceivable chance of occurrence.

There are four cards that are under a 3 (the 2, the Ace, the King, and the Queen) and four cards that are above an 8 (the 9, the 10, the Jack, and the Queen). However, the Queen is both above an 8 and under a 3, so we need to subtract one from the total count.

Therefore, the number of cards that are either under a 3 or above an 8 is 4 + 4 - 1 = 7.

Therefore, the probability that the card is as stated is 7/52, which simplifies it to 1/8.

Learn more about probability, here:

https://brainly.com/question/29862517

#SPJ1

Answer:

[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]

A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.

Answer:

3n+15

Step-by-step explanation:

18, 21, 24

+3. +3

3n

18-3=15

3n+15

Answer:

1/4 of the pot is left.

Step-by-step explanation:

Let x be the total amount of pasta in the pot.

Then the amount of pasta her mother got= 1x/12

The amount of pasta her brother got=  1x/6

The total amount of pasta he serve= 1x/12 + 1x/6

First, convert them into like fractions, then

The total amount of pasta he serve= 1x/12 + 2x/12 = (x+2x)/12 = 3x/12 = 1x/4

Hence, 1/4 of the pot is left over.

Step-by-step explanation:

Mom: 1/12

Brother: 1/6

1/6 × 2/2 = 2/12

2/12 + 1/12 = 3/12

12/12 (= 1 whole) - 3/12 = 9/12 of pasta is left

The set 2Z is associative under the operation *, has an identity element of 2, and every element (except for 0) has an inverse element.

The set 2Z is defined as follows:

2Z = {2n | n ∈ Z, a * b = a + b}

Associative element:

There exists an associative element in 2Z if, for all a, b, and c in 2Z, the equation a*(bc) = (ab)*c holds.

Let a, b, and c be arbitrary elements of 2Z:

a = 2n₁

b = 2n₂

c = 2n₃

Then we have:

a*(bc) = a(2n₂2n₃) = a(4n₂n₃) = 2n₁ + 4n₂n₃ = 2(n₁ + 2n₂n₃)

(a*b)c = (2n₁2n₂)*2n₃ = (4n₁n₂)*2n₃ = 8n₁n₂n₃ = 2(2n₁n₂n₃)

Therefore, a*(bc) = (ab)*c, and 2Z is associative under the operation *.

Identity element:

There exists an identity element in 2Z if there exists an element e in 2Z such that, for all a in 2Z, the equation ae = ea = a holds.

Let e be an arbitrary element of 2Z:

e = 2n

Then we have:

ae = a2n = a + 2n = 2m, where m = n + (a/2) ∈ Z

ea = 2na = a + 2n = 2m', where m' = n + (a/2) ∈ Z

Therefore, e = 2n is an identity element in 2Z.

Inverse element:

There exists an inverse element in 2Z if, for all a in 2Z, there exists an element b in 2Z such that ab = ba = e, where e is the identity element.

Let a be an arbitrary element of 2Z:

a = 2n

Then we need to find an element b in 2Z such that ab = ba = e = 2.

We have:

ab = ba = 2n*b = 2

Therefore, b = 1/(2n) is the inverse of a in 2Z if n ≠ 0.

Read more about set at

https://brainly.com/question/24462379

#SPJ1

The linear regression model from a set of data is y =5.2956+4.0946*X.

A statistical tool for examining the relationship between two quantitative variables is a linear regression model. Finding the best linear relationship between the dependent variable (Y) and one or more independent variables (X) in order to forecast the value of the dependent variable based on the value of the independent variable is the objective of a linear regression study.

The regression line is determined using the formula:

y = bo + b1 X

Now, using the table we have:

sum of (x) = ∑x = 103

sum of (y) = ∑y = 480

Calculating the squares we have:

sum of (x^2)= ∑x² = 1073

sum of (y^2)= ∑y² = 22868

Multiplying the variables we have:

sum of (x*y)= ∑x*y = 4939

mean(x)= ∑x/n = 9.3636

mean(y)= ∑y/n = 43.6364

Now, the intercept is given as:

intercept (bo) = (∑y)(∑x²) - (∑x)(∑xy) / n(∑x²) - (∑x)²

Substituting the values we have:

intercept (bo) = (480)(1073) - (103)(4939) / 11(1073)-(103)^2

intercept (bo) = (515040-508717) / (11803-10609)

intercept (bo) = 5.2956

The slope is given as:

slope (b1) = n(∑xy) - (∑x)(∑y) /n(∑x²) - (∑x)²

Substituting the values we have:

slope (b1) = (11(4939) -(103)(480))/(11(1073) - (103)^2

slope (b1) = (54329-49440)/(11803-10609)

slope (b1) = 4.0946

regression equation is, y = bo + b1 X

Substituting the values we have:

y =5.2956+4.0946*X

Hence, the linear regression model from a set of data is y =5.2956+4.0946*X.

Learn more about linear regression model here:

https://brainly.com/question/29855836

#SPJ1

The complete question is:

91.3 pounds of fruit are left

Jason bought = 91.5 pounds

class ate = 0.2 pounds

You subtract the amount the class ate from the amount Jason bought to get the amount of fruit left.

91.5 - 0.2 = 91.3 pounds

The scalar projection and projection vector of vector (5,3) onto vector (7,-2) can be calculated by using the appropriate formulas and then interpreted graphically.

The scalar projection of (5,3) onto (7,-2) was found to be 29/53, and the projection vector was found to be (203/53, -58/53). This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).

Graph is a data structure that consists of nodes and edges, which are used to represent relationships between different objects. A graph is often used to represent the real-world relationships between objects such as cities, towns, and roads. Graphs can also represent abstract relationships such as between two people or mathematical formulas. Graphs are widely used in computer science, networking, and mathematics.

(a) Scalar Projection:
The scalar projection of vector A onto vector B can be calculated by using the following formula:

Projection = (A⋅B)/|B|

In this case, the scalar projection of (5,3) onto (7,-2) is:

Projection = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2))
           = (35 - 6)/53
           = 29/53

Projection Vector:
The projection vector of vector A onto vector B can be calculated by using the following formula:

Projection Vector = (A⋅B/|B|²)B

In this case, the projection vector of (5,3) onto (7,-2) is:

Projection Vector = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2)) ⋅ (7,-2)
                 = (35 - 6)/53 ⋅ (7,-2)
                 = (29/53)⋅(7,-2)
                 = (203/53, -58/53)

(b) Interpretation Graphically:
The projection of vector (5,3) onto vector (7,-2) can be interpreted graphically as follows:

First, draw the two vectors (5,3) and (7,-2) on a graph. Then draw a line from the origin to the tip of vector (7,-2). This line will represent vector (7,-2). Next, draw a line from the origin to the tip of vector (5,3). This line will represent vector (5,3).

Finally, draw a line from the tip of vector (7,-2) to the tip of vector (5,3). This line will represent the projection vector of (5,3) onto (7,-2). The length of this line will be the scalar projection of (5,3) onto (7,-2).

This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).

To know more about graph click-
http://brainly.com/question/19040584
#SPJ1

Answer:

s/3

Step-by-step explanation:

since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.