Please help!
A card is selected at random from the set of cards below.

A sample space for the experiment is {F, G, H, J, K, L, M}. Let W represent the event “the card is white”, let S represent “the card is shaded”, and let E represent “the number is even”. Select all that apply.
A. The event S is {F, H, K, L, M}.
B. The event not E is {F, G, H, M}.
C. The event S or E is {F, H, J, K, L, M}.
D. The event S and E is {K, L, M}.
E. P(W or S) = 1
F. P(W and S) = 1

The sequence is recursively defined by

[tex]\begin{cases}a_1 = 1 \\ a_2 = 2 \\ a_n = a_{n-1} a_{n-2} & \text{for } n \ge 3\end{cases}[/tex]

By this definition,

[tex]a_{n-1} = a_{n-2} a_{n-3} \implies a_n = a_{n-2}^2 a_{n-3}[/tex]

[tex]a_{n-2} = a_{n-3} a_{n-4} \implies a_n = (a_{n-3} a_{n-4})^2 a_{n-3} = a_{n-3}^3 a_{n-4}^2[/tex]

[tex]a_{n-3} = a_{n-4} a_{n-5} \implies a_n = (a_{n-4} a_{n-5})^3 a_{n-4}^2 = a_{n-4}^5 a_{n-5}^3[/tex]

[tex]a_{n-4} = a_{n-5} a_{n-6} \implies a_n = (a_{n-5} a_{n-6})^5 a_{n-5}^3 = a_{n-5}^8 a_{n-6}^5[/tex]

and so on.

Recall the Fibonacci sequence, {1, 1, 2, 3, 5, 8, 13, 21, …}, where the next term in the sequence is the sum of the previous two terms. If [tex]F_n[/tex] is the n-th Fibonacci number, then continuing the pattern above we would arrive at

[tex]a_n = {a_2}^{F_{n-1}} {a_1}^{F_{n-2}} = 2^{F_{n-1}}[/tex]

Notice that the sequence of positive powers of 2 leaves a periodic sequence of residues mod 10 :

[tex]2 \equiv 2 \pmod{10}[/tex]

[tex]2^2 \equiv 4 \equiv 4 \pmod{10}[/tex]

[tex]2^3 \equiv 8 \equiv 8 \pmod{10}[/tex]

[tex]2^4 \equiv 16 \equiv 6 \pmod{10}[/tex]

[tex]2^5 \equiv 2 \times 2^4 \equiv 2 \times 6 \equiv 2 \pmod{10}[/tex]

[tex]2^6 \equiv 2^2 \times 2^4 \equiv 4 \times 6 \equiv 4 \pmod{10}[/tex]

and so on; the period of this sequence of residues is 4.

The period of [tex]F_n[/tex] taken mod 4 is 6 :

[tex]\{1, 1, 2, 3, 5, 8, \ldots\} \equiv \{1, 1, 2, 3, 1, 0, \ldots\} \pmod 4[/tex]

(This follows from the "properties" section in the link in comment. In this case, π(4) = 3/2 × 4 = 6.)

It follows that

[tex]34 \equiv 4 \pmod 6 \implies F_{34} \equiv 3 \pmod 4 \implies 2^{F_{34}} \equiv 2^3 \equiv 8 \pmod{10}[/tex]

which means the last digit of [tex]a_{35}[/tex] is 8.

Answer:

prob of being a red=1/2

prob of being an ace=1/13

Answer:

radius 4

center (3,6)

Step-by-step explanation:

(x - h)^2 + (y - k)^2 = r^2

coordinates of the center (h, k) and the radius is (r)

x² + y²- 6x - 12y +29=0

x² - 6x + y²- 12y +29=0

(x² - 6x) + (y²- 12y) +29=0

complete the square

(x² - 6x) + 9 + (y²- 12y) +36 +29=  + 9  +36

(x² - 6x + 9) + (y²- 12y + 36) = + 9  +36 -29

(x-3)^2 + (y-6)^2 = 16

(x - h)^2 + (y - k)^2 = r^2

coordinates of the center (h, k) and the radius is (r)

center (3,6)

radius 4

cuemathcom

varsitytutors

Answer: Center: (3,2)                Radius: 5

Step-by-step explanation:#x^2 - 6x +y^2 - 4y = 12

Then take 1/2 of the 'b' term for both quadratic expressions, square those values and add them to both sides.

#x^2 -6x + 9 + y^2 - 4y + 4 = 12 + 9 + 4

(x - 3)^2 + (y -2)^2 = 25

Circle centered at (3,2) with radius = 5

Answer:

little falls has more

Step-by-step explanation:

show your work: little falls total rainfall is 1 6/8 and riverside is 1 5/8

use that to explain :) your welcome

Answer:

  Riverside had the greatest rainfall total

Step-by-step explanation:

The total amount of rain in a city will be the sum of products of rain amount and days that got that amount. The city with the largest sum got the most rain. The difference in rainfall can be found by subtracting the lesser amount from the greater.

__

Total rainfall in Riverside was ...

  (1/8)×1 +(2/8)×3 +(3/8)×3 +(4/8)×1 +(5/8)×1

  = (1 +6 +9 +4 +5)/8 = 25/8 = 3 1/8 . . . . inches

__

Total rainfall in Little Falls was ...

  (1/8)×1 +(3/8)×1 +(4/8)×1 +(6/8)×2

  = (1 +3 +4 +12)/8 = 20/8 = 2 1/2 . . . . inches

__

Riverside had more rainfall, because 3 1/8 is more than 2 1/2.

__

You can "cancel" dots that are in the same place on each plot. Doing so leaves Riverside with 3 dots at 2/8, 2 dots at 3/8, and 1 dot at 5/8. The remaining dots on the Little Falls plot are the 2 dots at 6/8.

The 3 dots at 2/8 add up to 6/8, as do the 2 dots at 3/8 on the Riverside plot. These two 6/8 values cancel the two 6/8 dots on the Little Falls plot. That leaves one uncancelled dot at 5/8 on the Riverside plot, indicating more rain fell at Riverside.

Pull out a factor of 1/n from the summand and the result follows.

[tex]\displaystyle \lim_{n\to\infty} \sum_{i=1}^n \frac{i^4}{n^5} = \lim_{n\to\infty} \frac1n \sum_{i=1}^n \left(\frac in\right)^4 = \boxed{\int_0^1 x^4 \, dx}[/tex]

Answer:

Step-by-step explanation:

1. 150 * π/180

= 150π/180

= 5π/6

=2.62

2. π/2

π/2 * 180/π

= 90 degrees

Step-by-step explanation:

1)150° 's radian measure

[tex] \rm \implies150 \: Deg × π/180 = 2.618 \: Radians[/tex]

2)π/2 's degree measure

[tex] \rm \: \implies \: π/2 × 180/π= 180/2 = 90 \: degrees[/tex]

Basically,we need to use formulas to solve these type of sums.

Answer:

See below

Step-by-step explanation:

Use protractor to measure the UNmarked angle (approx 135 degrees)

    then subtract this value from 360 degrees to find the angle in question

Answer:

f(x) = 4x + 6

Step-by-step explanation:

Using f(x) = 4x + 6

lets find some answers

lets take x as (-2)

f(-2) = 4(-2) + 6

f(-2) = -8 + 6

= -2

Also, take x as (-1)

f(-1) = 4(-1) + 6

f(-1) = -4 + 6

= 2

If the significance level is about 5% then the result is not statistically significant; which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.

The term significance level has to do with the probability of rejecting the null hypothesis even though it is true.

The significance level tells us if a result is statistically significant. Thus, if the significance level is about 5% then the result is not statistically significant; which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.'

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A)The result is statistically significant, which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.

Did the project

Answer:

See below

Step-by-step explanation:

Basically, when you have a product to two factors set equal to 0, you can use the Zero Product Property and make two separate equations, both set equal to 0, to find the roots for each factor:

[tex]2x+10=0\\2x=-10\\x=-5[/tex]

[tex]x-7=0\\x=7[/tex]

Notice that by plugging these roots back into the equation, either factor will be 0, making the whole expression 0:

[tex](2x+10)(x-7)=0\\(2(7)+10)(7-7)=0\\(24)(0)=0\\0=0[/tex]

[tex](2x+10)(x-7)=0\\(2(-5)+10)(-5-7)=0\\(0)(-12)=0\\0=0[/tex]

Answer:

3.14×5(2)×6=471.24

Step-by-step explanation:

you have to take square of 5

Answer: On a coordinate plane, 2 solid straight lines are shown. The first line is vertical to the x-axis at x = 20. Everything to the right of the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the right of the line is shaded.

Step-by-step explanation:

x = # of stools = 20

y = # of recliners = 50-20 = 30

Answer:

On a coordinate plane, 2 solid straight lines are shown. The first line is vertical to the x-axis at x = 20. Everything to the right of the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the left of the line is shaded.

Answer: The answer is [tex]16[/tex], You need to reduce the expression, if possible, by canceling the common factors. Then its lateral area of 12 inches and the radius of 3/4 inches would be 16.

Therefore your answer would be [tex]16[/tex].

Based on the concrete of the lateral area and the content of the question, the right answer is 18π

The lateral area is the term that is used to describe the surface of an object as all of the sides of the object, excluding its base and top. Generally, the term lateral area is different from the surface area, which is the lateral surface area together with the areas of the base and top.

Hence, in this case, to calculate the lateral area of the paint roller, find the circumference of the roller and multiply it by its length.

The circumference of a circle can be found using the formula: C = 2πr where r is the radius.

Given that the roller has a radius of 3/4 inch let's substitute this value into the formula to find the circumference:

C = 2π(3/4)

C = 6π/4

C = 3π/2

Now we have the circumference of the roller.

To find the lateral area we multiply the circumference by the length of the roller which is 12 inches:

Lateral Area = Circumference x Length

Lateral Area = 3π/2 x 12

Lateral Area = 36π/2

Lateral Area = 18π

Therefore, in this case, it is concluded that the lateral area of the paint roller is 18π square inches.

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Answer:

- 95/18

Step-by-step explanation:

1st you have to convert the mixed number to an improper fraction so 2 ×6 = 12 +1 = 13 and that together equals 13/6 same goes for the next take away the parentheses 13/6 - 8/3 - 4 7/9

then you have to do the same thing with the 1st fraction convert it 4 × 9 = 36 + 7 = 43 that equals together 43/9

lastly you have to calculate the difference 13/6 - 8/3 - 43/9 and that equals negative 95/18

by the way the 95 isnt a negative the fraction itself is

6x4=24

24x1/2=12

12+3=15

15+2=17

17 is the answer

Answer:

126 cm^2 (please mark me brainliest)

Step-by-step explanation:

(14x16)/2+(2*14)/2=

112+14=126

Answer:

$70.76 or 70.7595

Step-by-step explanation:

Here’s the function:

67.39(1+0.05)^1

Hope this helps! ;-)

The probability that Dalia will pick two red pencils without replacement is  1/3.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability of picking two red pencils = 6/10 x 5/9 = 1/3

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Answer:

x = 6

Step-by-step explanation:

Taking the sides in proportion :

Step-by-step explanation:

If you have any question about the sollution, ask me

Answer:

Put all terms to the side of the equals side, and make sure there are none on the other side. That would be unbalanced if there were terms on the opposite side.

Factor out the problem.

Set each factor of the problem equal to zero.

Solve each new equation.

Check to see if it makes sense by putting your new equation into the original equation.

Associative property

Multiplication properties are different statements that are always true. These statements help prove that different operations can be performed on equations and still remain equal.

Associative Property

The associative property states that (a x b) x c = a x (b x c). This means that in any equation where only multiplication is present, the parentheses can be moved and the equation remains equal.

Other Examples

The associative property is always true; this means that we can create other examples.

Let's take the expression 4 x (2 x 9). As the property states, we can move the parentheses and create the new expression (4 x 2) x 9. Now we can set these expressions equal to each other.

Due to the property we know that this equation must be true.

We can prove this property by working out each side of the equation. If we multiple both sides out we are left with 72 = 72. Since this is true the equation above must also be true.

Answer:

Step-by-step explanation:

It's called The Associative Property of Multiplication

(a * b) * c = a * (b * c)

Answer:

Output: 3

Step-by-step explanation:

(x, y)

(Input, Output)

(2, 3)

The set of equation that models the point of intersection of the arrow

and the target is: y = -0.002x² +0.25x + 6 and y = 0.15x.

Given parameters:

Point of intersection of the line and the parabola=(85.21,12.78)

Hence:

First set

y = -0.002 × 48.67² + 0.25 × 85.21 + 6= 12.78

Linear function y ≠ x

Third set

y = -0.002 × 85.21² + 0.25 × 85.21+ 6= 12.78

y = C·x

12.78 = 85.21·x

C=12.78/85.21

C=0.149

C=0.15 (Approximately)

Hence:

y=0.15x

Therefore the set of equation that models the point of intersection of the arrow and the target is: y = -0.002x² +0.25x + 6 and y = 0.15x.

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Answer:

88 m^2

Step-by-step explanation:

We can split the parallelogram into three shapes. 1 square and 2 triangles.

To find the area of a square, multiply one side by another side that does not face it. To find the area of a triangle, divide the base by half OR multiply the base by 0.5, and then multiply by the height.

Since these shapes are all pieces of the parallelogram, add together their total areas to get the area of the parallelogram.

Square: 7 x 8

Triangle: 0.5 x 4 x 8 or 4/2 x 8

(7 x 8) + 2 x (0.5 x 4 x 8)

56 + 2 x (2 x 8)

56 + 2 x 16

56 + 32

56 + 32 = 88 m^2