the monthly salaries (in thousands of dollars) for a sample of 7 employees of a firm are: 9, 7, 8, 7, 10, 11 and 11. which of the following statements is true about the mean, median and mode?

The a) equation for the vertical nullcline is y = -4x + 4 and horizontal nullcline is x = -3y + 1. The b) equilibrium points are (0,0) , (0 , 0.8) , (0.75 , 0), and (0.375,0.5)

We have

dx/dt = x(1 - x/3 - y)

dy/dt = y(1 - y/4 - x)

a) To get the equation for vertical nullcline, not on the coordinate axis we take

dy/dt = 0

or, y(1 - y/4 - x) = 0

or, 1 - y/4 - x = 0

or, y/4 = 1 - x

or, y = -4x + 4

Similar;y for horizontal nullcline not on coordinate axis we take

dx/dt = 0

or, (1 - x/3 - y) = 0

or, x/3 = 1 - y

or, x = -3y + 1

b)

To get the equilibrium points of the nullcline system we simply take

Here the x nullcline will intersect y nullcline at

x = 0 and x = 1 - x/3 - y

y = 0 and y = 1 - y/4 - x

therefore we have equilibrium points

for x = 0 and y = 0  at(0,0)

x = 0 and y = 1 - y/4 - x at (0, 4/5)

x =  1 - x/3 - y and y = 0 at (3/4 , 0)

x = 1 - x/3 - y and y = 1 - y/4 - x  at (3/8 , 1/2)

Hence the equilibrium points are (0,0) , (0 , 0.8) , (0.75 , 0), and (0.375,0.5)

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Complete Question

(Image Attached)

Answer:

10 [tex]\frac{5}{28}[/tex] days

Step-by-step explanation:

There are a lot of places to make mistakes, but I think that I am good.

Make a proportion:

[tex]\frac{Days}{Inches}[/tex] = [tex]\frac{Days}{Inches}[/tex]  Put in the three number that you know and solve for the number of days.

[tex]\frac{7\frac{13}{21} }{10\frac{2}{3} }[/tex] = [tex]\frac{x}{14\frac{1}{4} }[/tex]  Cross multiply and solve for x

10 [tex]\frac{2}{3}[/tex] x = [tex]7\frac{13}{21}[/tex]([tex]14\frac{1}{4}[/tex])  Change everything into improper fractions

[tex]\frac{32}{3}[/tex]x = ([tex]\frac{160}{21}[/tex])[tex]\frac{57}{4}[/tex]  I am going to cross cancel the 160 and 4  They both can be divided by 4 and I am going to cross cancel the 21 and 57.  They are both divisible by 3

[tex]\frac{32}{3}[/tex] x =( [tex]\frac{40}{7}[/tex])[tex]\frac{19}{1}[/tex]

[tex]\frac{32}{3}[/tex] x = [tex]\frac{760}{7}[/tex]  Multiply both sides by [tex]\frac{3}{32}[/tex]

([tex]\frac{3}{32}[/tex])[tex]\frac{32}{3}[/tex]x =([tex]\frac{3}{32}[/tex])[tex]\frac{760}{7}[/tex]  I can cross cancel 32 and 760.  They both can be divided by 8

x = ([tex]\frac{3}{4}[/tex])[tex]\frac{95}{7}[/tex]

x = [tex]\frac{285}{28}[/tex]

x = 10 [tex]\frac{5}{28}[/tex] Days

Answer:

This statement is false

Step-by-step explanation:

This statement is false. The volume of a cylinder with a given height and diameter will always be greater than that of a cone with the same height and diameter if the base of the cone is smaller than the base of the cylinder. However, if the base of the cone is the same size as the base of the cylinder, then the volume of the cone will be equal to that of the cylinder.

Answer:

$18

Step-by-step explanation:

15 : 100 = x : 15

x =  15 · 15 / 100

x = 225 / 100

x = $ 2.25 (tips)

5 : 100 = x : 15

x = 15 · 5 / 100

x = 75 / 100

x = $ 0.75 (tax)

15 + 0.75 + 2.25 = $18

The probability of both people being Democrats is 0.243, and the probability of one person being a Republican and one person being a Democrat is 0.486.

To find the probability of each of the following, we can use the formula for the probability of selecting a group of items from a larger group with replacement:

P(A and B) = P(A) * P(B)

Where P(A) is the probability of selecting the first item, and P(B) is the probability of selecting the second item.

Both people are Democrats:

There are 16 Democrats and 31 total people, so the probability of selecting a Democrat is 16/31. Therefore, the probability of selecting two Democrats is (16/31) * (16/31) = 0.243.

One person is a Republican and one person is a Democrat:

There are 15 Republicans and 31 total people, so the probability of selecting a Republican is 15/31. There are 16 Democrats and 31 total people, so the probability of selecting a Democrat is 16/31. Therefore, the probability of selecting one Republican and one Democrat is (15/31) * (16/31) = 0.486.

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Answer: x =2, -1

Step-by-step explanation:

Answer: A

Step-by-step explanation:

D is wrong because its saying 3 times of the flat fee of 52.5 per month.

B is wrong because it is saying 52.5$ per gigabyte

C is wrong because the total amount is not 64.2

The remaining roots of p(x) is x =  -5 , 4 + 5i , 4 - 5i and the factored form of p(x) =  ( x + 5 ) ( x - ( 4 +  5i ) ( x - ( 4 - 5i )

Given :

The polynomial function p(x)=x³-3 x²+x+205 has x=-5 as a root.

using synthetic division :

x = -5

5     1    -3    1    205

     0     5    10    55

  1     2    11   260

on solving using the quadratic formula or calculator the roots are :

x = -5 , 4 + 5i , 4 - 5i

so quadratic form of p ( x ) = ( x + 5 ) ( x - ( 4 +  5i ) ( x - ( 4 - 5i )

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The expression for the sequence of operations is  3s - u - t .

In the question ,

it is given that ,

the sequence of operation is given as " triple s, subtract u from the result, then subtract t from what you have" .

we have to write an expression for the above operation ,

So ,

first step is : triple s ,

that means the expression is  3s .

next subtract u from the result , that means ⇒ 3s - u .

next we have to subtract t from what we have ,

that means ⇒ 3s - u - t .

Therefore , the final expression is 3s - u - t .

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Answer:

The total driving distance from Austin, TX to Seattle, WA is 2,128 miles

Step-by-step explanation:

Answer:

i believe it is a 2,116.4 mile drive.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Firstly, I presume that the question talks about a rectangle and there is consistency in units i.e.Area is in units^2 and perimeter is in units (else there is no possible solution).

Now, perimeter = 2(L+B) = 40

OR (L+B) = 20.

Also, area = LxB = 100.

Now, LxB = 100 will give you the following values for LxB (Note in a rectangle, L>B or L=B):- (100×1),(50×20),(25x4),(20×5),(10×10).

Only one value gives L+B = 20 viz.L=10 & B=10.

Hope this helps! :)

(This was by another user you can search it up and see.)

Answer:

y = [tex]\frac{1}{2}[/tex] x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

- 2x + 4y = 12 ( add 2x to both sides )

4y = 2x + 12 ( divide through by 4 )

y = [tex]\frac{2}{4}[/tex] x + [tex]\frac{12}{4}[/tex] , that is

y = [tex]\frac{1}{2}[/tex] x + 3

For the given circle the value of cotθ is -√30/√19.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The terminal side of an angle θ.  

The standard position intersects the unit circle at (√30/7, -√19/7).

We need to find the value of cotθ.

Suppose that θ is an angle in standard position whose terminal side intersects the unit circle at (√30/7, -√19/7)

cotθ=x/y

=-√30/7/√19/7

=-√30/7×7/√19

=-√30/√19

Hence, the value of cotθ is -√30/√19 for the given circle.

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Answer:

Step-by-step explanation:

that normally means we want to add our subtract a certain of the 2 equations, so that we are led with one summary equation with only one variable.

the easiest way here is possibly to multiply the second equation by 5 (to get also 10y) and then subtract it from the first equation :

3x + 10y = -4

- 10x + 10y = 10

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

-7x + 0 = -14

7x = 14

x = 2

2x + 2y = 2

gives us then

2×2 + 2y = 2

4 + 2y = 2

2y = -2

y = -1

x = 2

y = -1

Answer:

x = 2

y = -1

Step-by-step explanation:

3x + 10y = -4

- 10x + 10y = 10

7x + 0 = -14

7x = 14

x = 2

2x + 2y = 2

2×2 + 2y = 2

4 + 2y = 2

2y = -2

y = -1

The Subtraction of the given fraction using the number line is 5/6.

The correct answer option is option A

Fraction refers to a number which consists of a numerator and a denominator.

A numerator is the upper value of a fraction while a denominator is the lower value or bottom value of a fraction.

1 2/3 - 5/6

= 5/3 - 5/6

Find the lowest common multiple of the denominators and divide

= (10-5) / 6

= 5/6

In conclusion, 5/6 is the answer to the subtraction of fraction.

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x= 6;

y= 4.

[tex](1)7x-8y=10\\\\ (2)x-8y=-26\\[/tex]

[tex](1)7x-8y=10\\-\\ (2)x-8y=-26\\--------\\\\6x+0y=36\\ \\6x=36[/tex]

[tex]\frac{6x}{6} =\frac{36}{6} \\ \\x=6[/tex]

For this solution, we are going to use equation 2 to get the value of "y".

[tex](6)-8y=-26\\\\-8y=-26-6\\ \\-8y=-32\\ \\\frac{-8y}{-8} =\frac{-32}{-8} \\ \\y=4[/tex]

If the answers are correct, both equations should return the same value in both sides of the equal (=) sign.

[tex]7(6)-8(4)=10\\ \\42-32=10\\ \\10=10[/tex]

That's correct.

[tex](6)-8(4)=-26\\ \\6-32=-26\\ \\-26=-26[/tex]

That's correct.

Hence, the answers are correct.

42) The functions  F and G  are G(x) = (2x - 1)/ (3x + 4) and F(x) = √x

43) The functions  F and G  are G(x) = 3x² - 4 and F(x) = 1/x⁻³.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given composite function is

H(x) =  (fog)(x).

42)

H(x) =√[(2x - 1)/ (3x + 4)]

Rewrite the above equation

H(x) =√[G(x)] where G(x) = (2x - 1)/ (3x + 4)

H(x) = F(G(x)) where F(x) = √x

42)

H(x) =1/(3x² - 4)⁻³

Rewrite the above function

H(x) =1/[G(x)]⁻³ where G(x) = 1/(3x² - 4)

H(x) = F(G(x)) where F(x) = 1/x⁻³

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After changing  the denominators to rename these fractions  the sum is 5/6 .

Given :

If necessary, use / for the fraction bar(s).

We still need to find a way to add these fractions. Now you try.

Change the denominators to rename these fractions and find their sum.

To find sum we need to find LCM of denominators .

Least common multiple :

Least Common Multiple ( LCM ) is a method to find the smallest common multiple between any two or more numbers.

so = 1 / 2 + 1 / 3

LCM of 2 and 3 is 6

= 1 * 3 + 1 * 2 / 6

= 3 + 1 * 2 / 6

= 3 + 2 / 6

= 5 / 6

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Done :) Refer to the photo taken. Let me know if this is what you where looking for. Sorry for the sideways image.

The length of the side DE, that is parallel to the side AC is 6.3 units

Here the line DE is parallel to the side AC of the triangle

In the given triangle

The length of the side BD = The length of the side AD

The length of the side BE = The length of the side EC

That mean the parallel line AC is equally dividing the two side of the triangle

Therefore, the length of the line DE will be be exactly half of the line AC

The length of the side AC = 12.6 units

The length of the side DE = The length of the side AC / 2

Substitute the values in the equation

= 12.6 / 2

= 6.3 unit

Therefore, the length of DE is 6.3 units

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a) The number of seventh graders that participated in the competition was of 223.

b) The number of eight graders that participated in the competition was of 208.

c) The total number of students that participated in the competition is of 431.

The amounts in this problem are obtained applying the proportions given by the fractions.

For item a, we have that the amount is 5/8 of 3/5 of 595, hence the total amount is obtained as follows:

5/8 x 3/5 x 595 = 223 students.(rounding to the nearest integer).

For eight graders in item b, we have that 7/8 of 2/5 of 595 students participated, hence the number of students that participated in the competition is given as follows:

7/8 x 2/5 x 595 = 208 students. (rounding to the nearest integer).

Then the total number of students that participated in the competition is given by the sum of these amounts as follows:

223 + 208 = 431 students.

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According to the profit point of view, compared to smaller firms that export larger companies tend to systematically scan foreign markets to see where export opportunities lie.

What does profit mean?

In math, profit means the excess of returns over expenditure in a transaction or series of transactions.

Here we have given that, compared to smaller firms that export, larger companies tend to to be what.

And for the reason more firms are not proactive is that they are unfamiliar with foreign market opportunities; they simply do not know how big the opportunities actually are or where they might lie. Simple ignorance of the potential opportunities is a huge barrier to exporting

Here we know that, smaller firms, are often intimidated by the complexities and mechanics of exporting to countries where business practices, language, culture, legal systems, and currency are very different from the home market

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Answer:

14772

Step-by-step explanation:

The total expected waiting time including the morning and the evening time is 41/3

given that your waiting time for a bus in the morning is uniformly distributed on [0, 8], whereas waiting time in the evening is uniformly distributed on [0, 10] independent of morning waiting time.

Sum of both waiting times = X+Y

Where X = morning wait time is U(0.8) and

Y = evening wait time is U(0,10)

Since X and Y are independent

Var(x+y) = Var(x)+Var(y)

Var(x) = (8^2 - 0^2)/12 = 16/3

Var(Y) = (10^2 - 0^2)/12 = 25/3

Var(x+y) = 16/3 + 25/3

= (16 + 25)/3

= 41/3

Therefore, the total expected value of waiting time including the morning and the evening time is 41/3.

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The Florida health insurance company can use a variety of predictive methods to predict the annual claims for the sample of 50 customers. These methods include machine learning algorithms such as linear regression and decision trees, as well as statistical methods such as regression analysis and logistic regression.

The company can also use qualitative methods such as interviews and surveys to gain insight into customer needs and preferences. By combining quantitative and qualitative methods, the company can create a more accurate prediction of the annual claims for its sample of 50 customers.The company can calculate its predictions by first gathering data on each of the 50 customers, such as age, gender, health history, lifestyle, and other factors. It can then use this data to create a predictive model that can be used to estimate the annual claims of each customer. These methods include machine learning algorithms such as linear regression and decision trees, as well as statistical methods such as regression analysis and logistic regression. The model can be tested and refined as necessary to ensure it is accurate and reliable. Finally, the company can use the model to make its predictions for the 50 customers.

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Answer:

-4 im pretty sure

Step-by-step explanation:

= -4

= -4

Let X and Y be IID Unif(0, 1). the distance between X and Y.Expected value: 0 and Standard deviation: [tex]$\sqrt{\frac{1}{3}}$[/tex]

Expected value:

E(X-Y)

= E(X) - E(Y)

= 0 - 0

= 0

Standard deviation:

Var(X-Y) = Var(X) + Var(Y) = 1 + 1 = 2

SD(X-Y) = [tex]$\sqrt{2}$[/tex]

= [tex]$\sqrt{\frac{1}{3}}$[/tex]

The expected value of X-Y is the difference of the expected values of X and Y, which are both 0 since they are both IID Unif(0, 1). The variance of X-Y is the sum of the variances of X and Y, which are both 1. Since the standard deviation is the square root of the variance, the standard deviation of X-Y is the square root of 2.

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Answer: D & C

Step-by-step explanation:

The net Income of the business is represented as

Net profits or income = Net sales revenue (gross income) – Cost of goods and services sold – Administration, operating, marketing, and advertising costs, taxes, interests, and other expenses.

Here C is an option because we need to take operating expenses into consideration but if you consider cost of goods brought into store as operating then option changes to D.

D represents the sales which helps us determine the net income of the business.

Answer:

Step-by-step explanation: Raúl should put a turn of -30° in the walkway after the tree in order to continue in the same direction as before. This is because the negative angle will cancel out the positive angle and the walkway will continue in the same direction as before.

(a) The probability mass function of X will be P(X=n) = 5/(6n)

(b) E[X] =1.2

(c) Probability [ Alice win] will be =0.5

(d) The value of expected winnings will be 4.25

(a) Let 'p' represent the probability of getting the same number on both the dices on a roll of pair of die

And (1-p) = probability of not getting the same number on both the dices on a roll of pair of die

Sample space for the same number appearing on both the dices on a roll of pair of die = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

As there are a total of 36 outcomes on a roll of pair of dice,

p = 6/36 = 1/6

Let the events be defined as:

Dn : Both Alice and Bob roll the same number on the nth roll

Wn : The game is finished in the nth roll (i.e. Alice and Bob roll different numbers (as the numbers are different, one will be larger))

Then,P(W) = P(W) , n = 1,2,3,4....infinity

Wn takes place when event D takes place in the first (n-1) rolls and Event W takes place in the nth roll

[tex]$\mathrm{P}(\mathrm{W})=\sum P\left(W_n\right), \mathrm{n}=1,2,3,4 \ldots .$[/tex]. infinity

And, W_n takes place when

Event D takes place in the first (n-1) rolls and event W takes place in the [tex]$n^{\text {th }}$[/tex] roll

[tex]P\left(W_n\right)=P\left(D_1\right)^* P\left(D_2\right)^* P\left(D_3\right) \ldots . .{ }^* P\left(D_{n-1}\right) P\left(W_n\right)P\left(D_n\right)\\=(p)P\left(W_n\right)\\=(1-p)[/tex]

Implies

[tex]$$\begin{aligned}& \left.P\left(W_n\right)=(p)^{n-1}\right)^*(1-p) \\& =\left((1 / 6)^{n-1}\right)^*(1-(1 / 6)) \\& =\left((1 / 6)^{n-1}\right)^*(5 / 6) \\& =5 /\left(6^n\right)\end{aligned}$$[/tex]

(b)

[tex]$$\begin{aligned}& \mathrm{E}[\mathrm{X}]=\sum n * P(X=n), \mathrm{n}=1,2,3,4 \ldots . . \text { infinity } \\& =\sum n * \frac{5}{6^n} \\& =5 * \sum n * \frac{1}{6^n}\end{aligned}$$[/tex]

If [tex]$\mathrm{S}=\sum n * \frac{1}{6^n}$[/tex]

Then S is a sum of infinite aritho-geometric series of the form

[tex]$$\sum_{k=1}^{\mathrm{inf}} k * r^k \text {, }$$[/tex]

The sum of which is given as [tex]$S=\frac{r}{(1-r)^2}$[/tex] for 0 < r < 1

Here, r=(1 / 6)

[tex]\Rightarrow & S=\frac{\frac{1}{6}}{\left(\frac{5}{6}\right)^2} \\& =\frac{6}{25}[/tex]

E[X] = (5) x (6/25) = (6/5)= 1.2

(c) Since the dies are fair, and the outcomes are independent, the probability of each player winning is equal

Therefore,

P(Alice WIn) = P(Bob WIn) = 0.5

(d) If X represent the round in which the game ends, then the probability of us winning in that round

P(W|X=n) = 0.5*P(X=n)

= (0.5)*(5/(6n))

P(W|X=1) = (0.5)*(5/(61)) = (5/12)

P(W|X=2,3,4...) = 0.5 - P(W|X=1) = (1/2) - (5/12) = (1/12)

Leth the variable W represent the winnings

(W|X=1) = 10

(W|X=2,3,4...) = 1

E[W] = P(W|X=1)*(W|X=1) + P(W|X=2,3,4...)*(W|X=2,3,4...)

= (10 x (5/12)) + (1 x (1/12))

= (50/12) + (1/12)= (51/12)= 4.25

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