The ratio of pens to pencils that Katy has on his desk is 6:5. If Katy has 15 pencils on his desk then how many pens does he have?

The dimension of V is 2, and it is spanned by the basis vectors (1, 0, -1), (3, 1, 2).

The dimension of a vector space is the number of vectors in a basis for the space. To find a basis for a subspace of R³, we need to find a set of linearly independent vectors that span the subspace.

First, let's consider U. The subspace U is defined by the equations x + y = 2z and x - y = 0.

Solving these equations for x and y, we can express them in terms of z: x = 2z and y = -2z. Therefore, every vector in U can be written as (x, y, z) = (2z, -2z, z) = z(2, -2, 1).

Since z is a scalar, the vector (2, -2, 1) is the only vector needed to span the subspace U, which means that it is a basis for U.

Therefore, the dimension of U is 1, and it is spanned by the basis vector (2, -2, 1).

Now let's consider V. The subspace V is defined by the set of vectors that can be written as a linear combination of the vectors (1, 0, -1) and (3, 1, 2). We can start by showing that these vectors are linearly independent. Suppose that there are scalars a and b such that a(1, 0, -1) + b(3, 1, 2) = (0, 0, 0). Then we have:

a + 3b = 0

b = 0

-a = 0

Since a and b are real numbers, the above equation only holds if a = 0 and b = 0. This shows that (1, 0, -1) and (3, 1, 2) are linearly independent, and a basis of V.

Therefore, the size of V is 2, and it is traversed by the basis vectors (1, 0, -1), (3, 1, 2).

Learn more about the vectors here :

https://brainly.com/question/17254148

#SPJ1

The profits last year were $2041.66

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here, profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, then let the profit last year be x then we have 2.4x=4900

                            x=4900/2.4

                            x=2041.66

Hence, The profits last year were $2041.66

Learn more about percentages here:

https://brainly.com/question/29306119

#SPJ1

Answer:

Sample

Population

Step-by-step explanation:

Explain regent? its a term I've never heard of

Answer:

the equation with the slope m=1/5 that passes through point (-10,-15) is: y = -1/5x+15

Answer:

¹31.5

Step-by-step explanation:

Area of trapezium= 1/2 ×h×(b1+b2)

A=1/2×3×(12+21)

A=31.5

Answer:

-0.80, is a large effect

Step-by-step explanation:

From the given information:

The mean of the sample = [tex]\dfrac{10+ 11+ 8+ 14+ 13+ 12+12+11+13}{9}[/tex]

= 11.556

Using Excel Formula:

The standard deviation = 11.8105

We are told that the population mean = 13

Thus, the effect size can be determined by using the formula:

[tex]Effect \ size = \dfrac{sample\ mean \ ( \bar x) - population \ mean \ \mu }{standard deviation (\sigma)}[/tex]

[tex]Effect \ size = \dfrac{11.5556 -13 }{1.8105}[/tex]

Effect size = -0.80

Thus, -0.80, is a large effect

Answer:

far   t more far     t

Step-by-step explanation:

The angles add up to 180° so the angles are supplementary.

The value of x is 31.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

From the figure,

Two angles:

3x + 25  and 2x

These two angles form a straight angle.

Now,

3x + 25 + 2x = 180

5x = 180 - 25

5x = 155

x = 31

When the sum of two angles is 90°, then the angles are known as complementary angles.

When the sum of two angles is 180°, then the angles are known as supplementary angles.

Now,

3x + 25

= 3 x 31 + 25

= 93 + 25

= 118

2x

=2 x 31

= 62

Now,

118 + 62 = 180

Thus,

The angles are supplementary.

The value of x is 31.

Learn more about corresponding angles here:

https://brainly.com/question/1597341

#SPJ1

Answer:

He take 5 months in Brazil and 9 months in Portugal.

Step-by-step explanation:

Let us assume the number of months in Portugal be P

And, the number of months in Brazil be B

  So, the following equations are made

P + B = 14 ..............(1)

130P + 150B = 1920 .........(2)

We can easily write as  

P = 14 - B

Now put the value of P in the second equation

So,  

130(14 - B) + 150B = 1920

20B = 100

B = 100 ÷ 20 = 5

P = 14 - 5 = 9

 Hence, He take 5 months in Brazil and 9 months in Portugal.

Answer:

Simple! She earned $280

Step-by-step explanation:

3500 x 2 x 4 = 28000/100 = 280

In 10yrs operating on the same frequency of rate, she's gonna earn;

3500 x 10 x 4 = 140000/100 = $1,400.

Therefore, $1400 dollars is what she's gonna earn in 10 years time.

Answer:

I can’t tell if both number are positive, ones negative ect but here’s the answer if both are negativ, let me know if the numbers are negative or positive and I can come back and give ya the right answer! Xoxo

Step-by-step explanation:

Answer:

1.75%

Step-by-step explanation:

Answer:

x=4 and y=2

Step-by-step explanation:

You should use graph, point of intersection(for example point M(4,2) ) is solution

And we can conclude that x=4 and y=2

Rewriting 6-6-6-6 in exponential notation is -1.2×10¹

Exponential notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form.

When writing in exponential notation, it must be in standard l i.e writing in this format 3.577× 10⁴ not 35.77× 10³.

Though both of the expression are literally correct but 3.577× 10⁴ is the acceptable way of writing a scientific notation.

similarly 6-6-6-6 will give -12

writing -12 in exponential notation is -1.2×10¹

Therefore the exponential notation of 6-6-6-6 is -1.2×10¹.

learn more about exponential notation from

https://brainly.com/question/5756316

#SPJ1

Answer:

72yd^2

Step-by-step explanation:

Answer:

87

Step-by-step explanation:

14*3 + 9*5

Answer:

Step-by-step explanation:

2/9 = 0.222....

Basically, the two's repeat forever - that's why C would be the correct answer

Hope that helps! :)

-Aphrodite

Gavin is incorrect. To find how much cake each person gets, divide 1/3 by 4 or multiply 1/3 by one-fourth. Therefore, each of the friends gets one-twelfth of the cake.

Good Luck!

Answer:

7

Step-by-step explanation:

A coefficient is the front number. A term is separated by the operators such as +, -, etc.

Answer:

[tex]b \leqslant - 16[/tex]

Only x = -3 is less than -2.

We have the following statement -

"A number b is at least -16"

Given is the following statement -

"a number b is at least -16".

We can write the given inequality as -

b ≥ - 16

Therefore, we can write the given statement as -

b ≥ - 16

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ2

Answer:

A

Step-by-step explanation:

sheeeeesh

Answer:(7.-10))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

The angle of elevation of a 20-foot railroad crossing arm is fixed at 35 degrees. As necessary, round up to the next tenth. 20 ft, 35 ft, x -11.5 feet, y- 16.4 feet .

Between the horizontal line and the line of sight, an angle called the angle of elevation is created. The angle of elevation formula tan =QR/PR can be used to calculate the building's height (QR). Therefore, the building has 8 units of height. When it lies between the line of sight and the horizontal line, the angle of elevation is generated. The angle created, known as the angle of elevation, occurs when the line of sight is above the horizontal line. However, in the depression angle, the line of sight is downward and parallel to the ground.

When we multiply in algebra, we come before a variable with a number. In the same way, xy means to multiply variable x by variable y, while 7xy means to multiply variable x by variable y and then to multiply the entire expression by seven. Due to the complexity of how train-based questions are frequently presented, it is always advisable to read the question thoroughly before responding. After reading the question, try to use a formula in it; this may lead to a direct solution and save you time.

To learn more about angle of elevation refer to :

https://brainly.com/question/21137209

#SPJ1

Answer: I don't remember how to solve, but, I figured out the lengths of each side in the shaded region:

11, 11, 7, 7, 4, 4

Step-by-step explanation:

Hope this helps!! :D

Answer:

ummmmmmmmmmmmmmmmmmmm i forgot srry sugar

Step-by-step explanation:

Answer:

1 comes 4 numbers before 6

Step-by-step explanation:

1,2,3,4,5,6

/ / / /

Answer:

18 feet

Step-by-step explanation:

Perimeter=2(l+b)

80=2(w+w+4)

80=2(2w+4)

80=4w+8

80-8=4w

72/4=w

W=18 feet

Step-by-step explanation:

{x : x < 100}

means all numbers smaller than 100. but that includes all negative numbers. so, NO.

{y|y > -0.1}

while this includes all positive numbers, it also includes all numbers between -0.1 and 0. e.g. -0.001

so, NO

{x|x in N}

N is the set of all natural numbers. that is the set of all positive integers.

so, YES

{y : 0 < y < 1}

that is all numbers between 0 and 1. that's are only positive numbers between 0 and 1.

so, YES

{x|x in Z}

Z is the set of all integer numbers (including the negative ones). so, NO

{y : 3 <= y < 22}

ask numbers between 3 and 22, including 3. there are only positive numbers, as there cannot be suddenly a negative number between 2 positive numbers.

so, YES.

Part A

g(x) = 9.25x

g(8) = 9.25*8

g(8) = 74

He would make $74 before taxes if he worked 8 hours.

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

Part B

g(x) = 9.25x

g(14) = 9.25*14

g(14) = 129.50

He would make $129.50 before taxes if he worked 14 hours.

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

Part C

g(x) = 9.25x

g(27.5) = 9.25*27.5

g(27.5) = 254.375

g(27.5) = 254.38

He would make $254.38 before taxes if he worked 27.5 hours.

Answer:

Solution below.

Step-by-step explanation:

This question is basically asking you to substitute corresponding x values to find g(x).

Given the function from the question:

g(x) = 9.25x where x is the work hours and g(x) is the wages.

Given x = 8,

g(8) = 9.25 * 8 = $74.00

Given x = 14,

g(14) = 9.25 * 14 = $129.50

Given x = 27.5,

g(27.5) = 9.25 * 27.5 = $254.38 (rounded off to nearest cent)

Answer:

5x+3

Hope this helps!

9514 1404 393

Answer:

  68.6 m/s

Step-by-step explanation:

The speed at a given time is the derivative of the height at that time.

  dh/dt = -9.8t

At t=7, the speed is ...

  -9.8(7) = -68.6 . . . . . meters per second (downward)

The speed is 68.6 meters per second.

_____

Additional comment

Height is considered to be positive in the up direction, so velocity and acceleration are also positive in the up direction. The derivative of height will be the velocity. Its negative sign in this case indicates the object is moving in the downward direction. The speed is the magnitude (absolute value) of the velocity.