Which representation has a constant of variation of –2.5?


A
x
–2
–3
–4
–5
y
–5
–7.5
–10
–12.5


B
5 x + 2 y = 0


C
y = negative 2.5 x + 1


D
On a coordinate plane, a line goes through points (negative 1, 0) and (0, negative 2).

A
B
C
D

Answer:

The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].

Step-by-step explanation:

Let [tex]\vec u[/tex] and [tex]\vec a[/tex], from Linear Algebra we get that component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] by using this formula:

[tex]\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a[/tex] (Eq. 1)

Where [tex]\|\vec a\|[/tex] is the norm of [tex]\vec a[/tex], which is equal to [tex]\|\vec a\| = \sqrt{\vec a\bullet \vec a}[/tex]. (Eq. 2)

If we know that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec a=(4,-4,2,-2)[/tex], then we get that vector component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] is:

[tex]\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)[/tex]

[tex]\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)[/tex]

[tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]

Lastly, we find the vector component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] by applying this vector sum identity:

[tex]\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}[/tex] (Eq. 3)

If we get that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex], the vector component of [tex]\vec u[/tex] is:

[tex]\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]

[tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex]

The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].

Answer:

7.y-side by side

8.n-lines don't cross, not vertical

9.n-don't equal 90 degrees

10.n-don't equal 180 degrees

11.AOB

12.COE

13.EOD

14.DOC

15.DOC, BOA

Step-by-step explanation:

Answer:

In the simplest of words, $1,000 at 1% interest per year would yield $1,010 at the end of the year. But that is simple interest, paid only on the principal. Money in savings accounts will earn compound interest, where the interest is calculated based on the principal and all accumulated interest.

Step-by-step explanation:

Answer:

x = 150

Step-by-step explanation:

We know a circle is 360°, so the angles must add up to 60°.

Step 1: Set up equation

x - 120 + x - 120 = 60

Step 2: Solve for x

Step 3: Check

Plug in x to verify it is correct.

150 - 120 = 30°

150 - 120 = 30°

30° + 30° = 60°

60° + 300° = 360°

Answer:

2000 dollars

Step-by-step explanation:

Answer:

p = -4.33636363636

Step-by-step explanation:

subtract 2.2 from -4.001 which equals -4.001-2.2=-6.201 and divide -6.201 by 1.43p and that equals -4.33636363636 so p = -4.33636363636

Answer:

B. "at the mall"

Step-by-step explanation:

EDU 2020

Answer:b

Step-by-step explanation:

Answer:

He has had a quarter of the red one

Step-by-step explanation:

3/12 is 1/4 when simplified

Answer:

1)0.2502

2)0.475

3)0.003505

Step-by-step explanation:

Total No. of question n= 10

There are four choices in each question

So, Probability of success [tex]p = \frac{1}{4}[/tex]

Probability of failure q  = [tex]1- \frac{1}{4}=\frac{3}{4}[/tex]

We will use binomial over here

[tex]P(X=x)=^nC_r p^r q^{n-r}[/tex]

1)

[tex]P(X = 3)=^{10}C_3 (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=\frac{10!}{3!7!} (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=0.2502[/tex]

2)  [tex]P(X > 2)=1-P(X\leq 2)[/tex]

P(X>2)=1-(P(X=0)+P(X=1)+P(X=2))

[tex]P(X>2)=1-(^{10}C_0 (\frac{1}{4})^0 (\frac{3}{4})^{10}+(^{10}C_1 (\frac{1}{4})^1 (\frac{3}{4})^9+^{10}C_2 (\frac{1}{4})^2 (\frac{3}{4})^8)[/tex]

[tex]P(X>2)=1-((\frac{1}{4})^0 (\frac{3}{4})^{10}+(\frac{10!}{1!9!} (\frac{1}{4})^1 (\frac{3}{4})^9+\frac{10!}{2!8!} (\frac{1}{4})^2 (\frac{3}{4})^8)[/tex]

P(X>2)=0.475

3)

[tex]P(X\geq 7)=P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\P(X\geq 7)=^{10}C_7 (\frac{1}{4})^7 (\frac{3}{4})^{3}+(^{10}C_8 (\frac{1}{4})^8 (\frac{3}{4})^2+^{10}C_9 (\frac{1}{4})^9 (\frac{3}{4})^1+^{10}C_{10} (\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=\frac{10!}{7!3!} (\frac{1}{4})^7 (\frac{3}{4})^{3}+\frac{10!}{8!2!} (\frac{1}{4})^8 (\frac{3}{4})^2+\frac{10!}{9!1!} (\frac{1}{4})^9 (\frac{3}{4})^1+\frac{10!}{10!0!}(\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=0.003505[/tex]

Answer:

A and D.  

Step-by-step explanation:

A sequence is a set of the objects or numbers in a specific order. It is a function whose domain is a set of natural numbers or non-negative integers i.e. {1, 2, 3,..}

(A)

"An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers."  

The general form an arithmetic sequence is:

[tex]a_{n}=a_{1}+(n-1)d[/tex]

The function is linear. The sequence consists of either numbers that are increasing or decreasing based on the value of d, the common difference.

So, the statement provided is True.

(D)

"A geometric sequence is an exponential function whose domain is restricted to the set of non-negative integers."

The general form an geometric sequence is:

[tex]a_{n}=a_{1}\cdot r^{n-1}[/tex]

The function is exponential. The sequence consists of either numbers that are exponentially increasing or decreasing by the factor r, the common ratio.

So, the statement provided is True.

Answer:

48

Step-by-step explanation:

If 12 is one-fourth of a number, just multiply 12 by four to find the whole number.

12 x 4 = 48

You could have also set this up as an equation

12 = 1/4x

And then divide 12 by one-fourth

12/(1/4) = 48

Answer:

Divergent

Step-by-step explanation:

an = 3 sin(2/n)

Choose bn = 3 (2/n).

Using Limit Comparison Test:

lim(n→∞) an / bn

= lim(n→∞) [3 sin(2/n)] / [3 (2/n)]

= lim(n→∞) [sin(2/n)] / (2/n)

= 1

The limit is greater than 0, and bn diverges, so an also diverges.

Answer:

Diverges

Step-by-step explanation:

an = 7 / n^(1 + 1/n)

As n approaches infinity, an approaches 7 / n.

bn = 7 / n

Apply Limit Comparison Test.

lim(n→∞) an / bn

= lim(n→∞) [7 / n^(1 + 1/n)] / (7 / n)

= lim(n→∞) n / n^(1 + 1/n)

= lim(n→∞) 1 / n^(1/n)

= lim(n→∞) 1 / n⁰

= 1

The limit is greater than 0, and bn diverges, so an also diverges.

Answer:

45.7941176471

Step-by-step explanation:

Answer: graph b

Step-by-step explanation:

Answer:

(3,3)

Step-by-step explanation:

Use the midpoint formula to find your answer. The formula is [tex](x_{1} +x_{2} /2; y_{1} +y_{2} /2)[/tex].

If that equation looks funny then let me explain. You need to add 10 and -4 together, then divide it by 2. You also need to add -3 and -9, then divide that by 2.

Answer:

The individual in the data set is the cars sold

There are 4 variables but 3 are numerical or quantitative

Step-by-step explanation:

See Attachment for proper format of question.

Required

The individuals in this data set are:

This data set contains:

Solving (a):

From the attachment, we have the following columns:

Cars Sold; Retail Price; Miles Per Gallon; Seats; Navigation

From the list of columns, the individual in the data set is the cars sold because it represent what is being referenced in the table

Solving (b):

In (a) above, we established the individual to be cars sold.

The other 4 elements are what the data set contains i.e. variables.

From the attachment, we have that

retail price, miles per gallon and seats are numerical data while navigation isn't.

So, we can conclude that.

There are 4 variables but 3 are numerical or quantitative

Answer:

B

D

Step-by-step explanation:

I got it right on khan. Please send thanks

Answer:

2.25

Step-by-step explanation:

let x be cost of a hotdog

let y be cost of hamburger

so,

5x + 4y = 17.75                    eq. 1

4x + 5y = 18.25                    eq. 2

manipulate eq. 1 so solve for x:

5x = 17.75 - 4y

x = 17.75/5 - (4/5)y

x = 3.55 - (4/5)y                  eq. 3

substitute eq. 3 to eq. 2:

4(3.55 - (4/5)y) + 5y = 18.25

14.2 - (16/5)y + 5y = 18.25

14.2 + (9/5)y = 18.25

(9/5)y = 18.25 - 14.2

4.05= (9/5)y

y = 2.25

x = 3.55 - (4/5)(2.25)

x = 1.75

hotdog costs $1.75

hamburger costs $2.25

Answer:

The correct answer is k = 5.

Step-by-step explanation:

The Chi-square goodness of fit test would be used to determine whether the frequency of insect heads in batches follows a distribution called a Poisson distribution.

The hypothesis for the test can be defined as follows:

H₀: The frequency of insect heads in batches does not follows a Poisson distribution.

Hₐ: The frequency of insect heads in batches follows a Poisson distribution.

Assume that the significance level of the test is, α = 0.05.

The Chi-square test statistic is given by:

[tex]\chi^{2}=\sum\limits^{k}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]

It is provided that the 500 batches included at least 5 batches having 0, 1, 2, 3, or 4 insect heads. No batches had more than four heads.

So, the number of classes or categories are, k = 5.

Thus, the correct answer is k = 5.

Answer: the answer is 7 dollars for 1 guest

Step-by-step explanation:

Answer:

6rad2

Step-by-step explanation:

Answer:

8.845 units

Step-by-step explanation:

First start by plotting the points on a graph. Doing so will give you two points that you can connect and then turn into a triangle. Find the length and height of the triangle by counting how many units long each is. The length should be 6 units, while the height should also be 6 units. You can then use the pythagorean theorum to find the length of b to c:

A^2 + B^2 = C^2

6^2  + 6^2 = C^2

36 + 36 = C^2

72 = C^2

C = 8.845 units

9514 1404 393

Answer:

  31

Step-by-step explanation:

The relationship between sides and the sum of angles is ...

  sum of angles = (sides - 2)·180°

Filling in the given value and solving for "sides", we get ...

  5220 = (sides -2)180

  29 = sides -2 . . . . . . . . . divide by 180

  31 = sides . . . . . . . . . . . . add 2

The polygon has 31 sides.

Answer:

31

Step-by-step explanation:

5220/180=29+2=31

Answer:

x = -3

Step-by-step explanation:

The line just passes through x = -3 so, it's parallel to the Y-vector.

Answer:

dilation

Step-by-step explanation:

dilation will make the shape larger or smaller which will change the shape.

Answer:

the answer is 7.1 inches tall

Answer:

x = 5

Step-by-step explanation:

1. Combine like terms

2. Multiply by 1

3. Distribute

4. Subtract  3

5  from both sides of the equation

5. Simplify

6. Divide both sides of the equation by the same term

7. Simplify

im only in 6th grade

Step-by-step explanation: