1
1.
A random variable X has expected value
and probability distribution as
12
follows:
X
-3
-2
-1
0
1
N
3
f(x)
a
2a
1
1
1
b
сле
b b
2
5
10
5
(a)
(b)
Find the values of a and b.
Find E[X2 + 1].
(8 marks)

Answer:

Take the absolute value of -17.5

Step-by-step explanation:

Answer:

2. Take the absolute value of ' - 17. 5 '

Step by Step Explanation:

The distance/length is always positive, so make sure to take the absolute value of -17.5

The vertices of the feasible region of the constraints is (0,2.5)

The constraints are given as:

x + 3y ≤ 6

4x + 6y ≥ 9

x ≥ 0,  y ≥ 0

Express the inequalities as equations

x + 3y = 6

4x + 6y = 9

Make x the subject in x + 3y = 6

x = 6 - 3y

Substitute x = 6 - 3y in 4x + 6y = 9

4(6 - 3y) + 6y = 9

Expand

24 - 12y + 6y = 9

Evaluate the like terms

-6y = -15

Divide by 6

y = 2.5

Substitute y = 2.5 in x = 6 - 3y

x = 6 - 3 * 2.5

Evaluate

x = -1.5

So, we have:

(x,y) = (-1.5, 2.5)

Recall that: x ≥ 0,  y ≥ 0

This means that the feasible region must have positive coordinates or zero

So, we set x = 0

(x,y) = (0, 2.5)

Hence, the vertices of the feasible region of the constraints is (0,2.5)

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Answer:

rise over run

Step-by-step explanation:

you look at the distance between the 2 points by looking at how many points its goes up or down, and you look at how points it goes from the left to the right or vice versa. but if you don't have a graph to look at, you will want to use the slope formula. look up the slope formula and plug it in.

Answer:

Step-by-step explanation:

From the point one on the graph, you go up (rise) making loops each time you go up (shown in red) then, once you've reached the same hight of point two, you go over (run), making loops once again (shown in blue). Then, you take the rise and put it over the run, so in the image attached it would be 4/3.

Step-by-step explanation:

→ 8 + 4 = 2(x -1)

→ 12 = 2x - 2

→ 2x - 2 = 12

→ 2x = 12 + 2 = 14

→ x = 14/2 = 7

→ x = 7

hence, option D (7) is correct.

Hope this answer helps you dear ! take care

Answer:

x = 9

Step-by-step explanation:

i took the quiz

[tex]\mathfrak{-2(x-6)=6} [/tex]

[tex]\mathfrak{-2x+12=6} [/tex]

[tex]\mathfrak{-2x=6-12} [/tex]

[tex]\mathfrak{-2x=-6} [/tex]

[tex]\boxed{\mathfrak{x=3} }[/tex]

Answer:

7

Step-by-step explanation:

Let's say the customer has x items. For each item, we add 2 seconds. For 3 items, we need 2 + 2 + 2 = 2*3 seconds. For x items, we need 2 * x seconds. Then, we add the processing payment time of 30 seconds, so for x items, the total amount of time = 30 + 2 * x

Here, the total amount of time is 44, so we have

44 = 30 + 2x

subtract 30 from both sides to isolate the variable and its coefficient

14 = 2x

divide both sides by 2 to isolate x

x = 7

[tex]\text{Given that,}\\\\(x_1,y_1) = (1,-2)~~ \text{and}~~ (x_2,y_2) = (3,-4)\\\\\text{Slope,}~ m= \dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{-4+2}{3-1} = -\dfrac 22 = -1\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y +2 = -1(x-1)\\\\\implies y = -x+1 -2\\\\\implies y = -x-1\\\\\text{This is the slope-intercept form(y =mx+b).}[/tex]

Answer:

y=-x-1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-4-(-2))/(3-1)

m=(-4+2)/2

m=-2/2

m=-1

y-y1=m(x-x1)

y-(-2)=-1(x-1)

y+2=-x+1

y=-x+1-2

y=-x-1

Answer:

x = √7km

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

You take a right triangle and find the lengths of the two sides that are vertical and horizontal. Then, using the formula a^2 + b^2 = c^2, find the length of C

(aka: Hypotenuse)

hope this helps!

Based on the information given, it can be deduced that the initial cost will be $187 and the hourly rate is $72 per hour.

From the information given, the initial cost is $187. The cost for 2 hours is $259 and the cost for 3 hours is $331.

Therefore, the rate per hour will be:

= $259 - $187 = $72

The equation will then be:

= 187 + 72h

Lastly, the difference in the costs is $72.

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Answer:

It's attached

Step-by-step explanation:

y=4/3x-4

is the equation for the line

So you just plot the line.

The equation for the given slope and point is y = 4x/3 - 4

The slope of a line is a number that describes both the direction and the steepness of the line.

Given that, a line that has a slope of 4/3 and contains the point (0,-4)

The slope intercept of a line is y = mx+c, where m is slope,

Here, m = 4/3, x = 0 and y = -4

Finding for c,

-4 = 4/3x0+c

c = -4

Establishing the equation,

y = 4x/3-4

Now plotting the graph,

(Attached)

Hence, the graph will pass through the points (3,0) and (0,-4)

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Answer:

b

Step-by-step explanation:

took the test a bit ago

I'll help.

The answer to your question is True!!

.........................

Answer:

y=log_2 (x)

Step-by-step explanation:

We see that the graph passes though the point (2,1). So we can write:

log_a (2) = 1  => a = 2

So it's a log in base 2.

Answer:

Step-by-step explanation:

Answer:

LQ = 54

Median = 69

UQ = 94

Step-by-step explanation:

This list is already sorted for you, so you don't need to worry about that, otherwise you would need to sort the numbers in ascending order. To find the median, we do [tex]\frac{n+1}{2}[/tex], where n is the amount of numbers. This gives us 4, so the median is at position 4, so the median is 69. The lower quartile is simply [tex]\frac{n+1}{4}[/tex], so 2, so the lower quartile is 54. The upper quartile is [tex]\frac{n+1}{2} X 3[/tex], so 6, so the upper quartile is 94.

Answer: pretty sure -7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

(-80) - (-10) is -79

-70 / (+10) = -7

Answer:

Step-by-step explanation:

S

(4,-5)

(5,-)

(9,-18)

(6,-19)

(6;-20)

(8,-20)

(6.-17)

(6.-8)

(3,-1)

(6, 1)

F2, -3)

(8,4).

(9, 7)

(10, 4)

(9, 2)

(8, 2)

LINEENDS

(-2, 5)

(-2. 12)

(2, 14)

(2, 15)

(0, 10)

(-1, 19)

(-1, 20)

(-5, 20)

(-5, 19)

(-6, 10)

(-8, 15)

(-9, 14)

(-10, 14)

(-10, 16)

(-6, 19)

(-7, 20)

(-11, 20)

(-11, 24)

(-10, 21)

(-9, 21)

(-9, 23)

(-8, 21)

(-6, 21)

(-5, 20)

LINEENDS

(-3, 15)

(-3, 16)

(-4, 17)

(-4, 19)

(-5, 18)

(-1, 18)

(-2, 19)

(-2, 17)

(-3, 16)

LINEENDS

(-i, 16)

(0, 16)

(-1, 15)

(-5, 15)

(-6, 16)

(-5, 16)

LINEENDS

(0,-7)

(2,-7)

(3,-8)

(3,-17)

W, 3)

(5, 4)

(3, 4)

(1, 3)

(0, 3)

(-1, 20)

(0, 21)

(2, 21)

(3, 23)

(3, 21)

Mystery Media

Answer:

y = 1/2x + 3

Step-by-step explanation:

Y= mx+b is slope-intercept form, m is for slope, and b is for my y-intercept. Also remember the pitch is the rise over the run or the y-direction over the x-direction.

In our case, they highlight 2 points to calculate the slope; looking at the graph, we can see it rises one and runs two to get to the second highlighted point at (2,4). And my slope is rise over run, so here it 1/2.

My b or y-intercept is simply three because that is where the line passes over or intercepts the Y-axis

Answer: y = 1/2 x + 3

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

7 Sizes * 3 Lengths * 4 Colors = 84

Answer:

LCM = 2^4 x 5^1 x 7^1 = 560

Step-by-step explanation:

Answer:

75%, or 7

Step-by-step explanation:

100-25=75

75% of 9 is 6.75 (because 9x0.75)

so we can round to 7, unless there's a decapitated reindeer involved

Answer: 6.75

Step-by-step explanation:

for this math problem we need to find the percentage and subtract that from the original number ( 9 ) . . .

what is 25% if 9 ? 2.25

what is 9 - 2.25 ? 6.75

Answer:

they are the same

Step-by-step explanation:

6x - 2x + 4 ← collect like terms

= 4x + 4

and

4(x + 1) ← distribute parenthesis by 4

= 4x + 4

The 2 expressions are equivalent to 4x + 4

Answer:

No, Jamie is incorrect

Step-by-step explanation:

No, because in the expression 4(x+1)  you will first need to multiply 4 by x, your result is 4x, and then you multiply 4 by 1, you get 4, so the answer will be 4x+4.

Also in the expression 6x-2x+4  ,you will first need to subtract 2x from  6x, your result is 4x ,and then you add 4 , so the answer will be 4x + 4

Our final answer is:

6x-2x+4 = 4x + 4 and 4(x+1) = 4x + 4

Answer:

Let’s take a point each on the x, y, and z-axis as follows:

A (1, 0, 0) on x-axis

B (0, 1, 0) on y-axis and

C (0, 0, 1) on z-axis

unit vector

So, we have

|OA→| = 1 , |OB→| = 1, and |OC→| = 1

These vectors OA→, OB→, and OC→, each having magnitude 1 are Unit Vectors along the axes OX, OY, and OZ respectively. They are denoted by i⃗ , j⃗ , and k⃗  as shown in Fig. 1 above.

Step-by-step explanation:

Answer:

Let x be the number of dimes and y the number of quarters

x +y = 100

a dime is $0.10 and a quarter is $0.25

0.1x + 0.25y = 21.40 multiply by 100 to remove the decimals

10x + 25y = 2140, From the first equation y = 100 - x and plug it in to the second equation.

10x + 25(100 -x) = 2140

10x + 2500 - 25x =2140

2500 - 15x = 2140

360 = 15x x = 24 and y = 76

There are 24 dimes and 76 quarters

Answer:

76 Quarters = $19.00

24 Dimes = $2.40

$19.00 + $2.40 = $21.40

Step-by-step explanation:

Yaga

Answer:

D. -2x^3 - 14x^2 + 22x

Step-by-step explanation:

1) Remove parentheses.

3x³ - 10x² + 13x - 5x³ - 4x² + 9x

2) Collect like terms.

(3x³ - 5x³) + (-10x² - 4x²) + (13x + 9x)

3) Simplify.

-2x³ - 14x² + 22x

If f(n) = f(n - 1) + 4, then

f(n - 1) = f(n - 2) + 4

and substituting this into the first equation gives

f(n) = f(n - 2) + 2•4

Similarly,

f(n - 2) = f(n - 3) + 4

so that

f(n) = f(n - 3) + 3•4

and so on.

Note the pattern:

f(n) = f(n - k) + k•4

so that when k = n - 1, we have

f(n) = f(n - (n - 1)) + (n - 1)•4

or

f(n) = f(1) + 4 (n - 1)

so that

[D] f(n) = -2 + 4 (n - 1)

Similar triangles may or may not have congruent sides, but the ratio of the corresponding sides will always be congruent.

(3) Corresponding sides of △MNP and △RST

Given that △MNP ∼△RST.

This means that, the corresponding sides are:

(4) The equal measures

Given that △ABC ∼△TUV

This means that, the corresponding angles are equal, but corresponding sides are not.

So, the equal measures are:

The unequal measure is:

(c) Scale mapping

The scale mapping is given as:

[tex]Ratio = 1\ in : 100\ mi[/tex]

The above scale means that 1 inches on the scale represents 100 miles of the actual distance.

Take for instance, 5 inches would represent 500 miles.

500 is 5 times 100

Hence, the actual distance between two towns 100 times the map distance between the two towns

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