Factorise fully 6x² - 15x

The experimental probability of correctly guessing at random exactly zero correct answers is (4/5)⁵

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, total multiple choice quiz = 5 questions

          Each question contains 5 choices in which 1 choice is correct and remaining 4 are incorrect.

Possibility of first wrong choice = 4/5

Possibility of second wrong choice = 4/5

Possibility of third wrong choice = 4/5

Possibility of fourth wrong choice = 4/5

Possibility of fifth wrong choice = 4/5

Overall probability for Zero correct answer=(4X4X4X4X4)/(5X5X5X5X5)

                                                                        = (4/5)⁵

Thus, the experimental probability of correctly guessing at random exactly zero correct answers is (4/5)⁵

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Answer:

24/(2/3)=(24*3)/2=16

Step-by-step explanation:

Hope this helps

Pepe's balance will be greater as it is increasing exponentially while Leo's is increasing linearly

(see graph, where red is Pepe and blue is Leo)

Pepe's balance will be greater because Pepe's balance is growing exponentially option (A) is correct.

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent \(y = a^x\)

where a is a constant and a>1

We have:

Pepe and Leo deposit money into their savings accounts at the end of each month.

From the table, we can plot a graph on a coordinate plane.

As we can see in the graph:

Because Pepe's balance is growing exponentially and Leo's is growing linearly, it will be bigger.

Thus, Pepe's balance will be greater because Pepe's balance is growing exponentially option (A) is correct.

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Explanation:

The positions of Drea and Bryan are locked in as last, and 2nd to last respectively. This means the 15 slots drops to 15-2 = 13 slots.

There are 13 other people and 13 slots to fill.

That gives 13*12*11*10*9*8*7*6*5*4*3*2*1 = 6,227,020,800 different permutations where Drea is last and Bryan is 2nd to last. Order matters in a permutation.

This is out of 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 = 1,307,674,368,000 different ways to arrange the 15 people. This larger count will have Drea and Bryan move to other slots.

If you divide the smaller number over the larger, then the block "13*12*11*10*9*8*7*6*5*4*3*2*1" cancels out.

We'll be left with 1/(15*14) = 1/210 as the final answer

Answer:

876/7

Step-by-step explanation:

Just plug the number 5 into the equation and solve. Remember your Order of Operations (PEMDAS).

Answer:

if im correct, it 9.81 or 9.8

The equilibrium of this game is {s1 = 1/2, s2 = 1/4} and Player 2 plays A if sA2 = 3/4 and plays B if sB2 = 1/2.

Consider the following two-player game. Si = [0, 1], for i = 1, 2. Player 2 is equally likely to be type A or type B, and the realization of her type is private information to her.

Payoffs are as follows:

u1(s1,s2)=1−[s1 −(1/2)s2]^4

uA2(s1,sA2)=100−[sA2 −s1−1/4]^2

uB2 (s1,sB2 )=100−[sB2 −s1]^2.

To find a Bayes-Nash equilibrium of this game, we need to solve this problem by backwards induction.

The equilibrium of this game is {s1 = 1/2, s2 = 1/4} and Player 2 plays A if sA2 = 3/4 and plays B if Subs = 1/2.

A Bayes-Nash equilibrium is a pair of strategies, one for each player, such that each player's strategy is optimal given the other player's strategy and her private information about the game.

This is a refinement of the Nash equilibrium that takes into account the players' information about the game.

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Answer.

Use the sum-product pattern. (a*2 − 9  + 20)

                                                   (a*2 −4a-5a + 20)

Common factor from the two pairs. (a*2 − 4a − 5a + 20)

                                                             ( a − 4 ) − 5 ( a − 4 )

Rewrite in factored form. a( a − 4 ) − 5 ( a − 4 )

                                              ( a − 5 ) ( a − 4 )

Answer:

c = 5cm

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

do the square root of 25 and c to solve for c

the square root of c^2 is c

therefore, c= 5cm

Answer:

Step-by-step explanation:

Here you go mate

step 1

k^2+8k+22=6​  equation

step 2

k2+8k+22(-6)=6(-6)  subtract -6

k2+8k+16=0

step 3

k2+8k+16=0  factor

(k+4)(k+4)=0

step 4

(k+4)(k+4)=0  set the numbers equal to zero

answer

k=-4

Answer:

5050

Step-by-step explanation:

we can use the formula n(n+1)/2

Answer:

5050

Step-by-step explanation:

because n(n+1)/2 is compatible here, which is (100x101)/2, and that gives us 5050.

A sinusoidal function with a frequency of 16π, a maximum value of 12, a minimum value of -6, and a y-intercept of 3 can be modeled using the general equation of a sinusoidal function, which is:y = A sin (Bx - C) + D, where A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.

The given frequency is 16π. The value of B is equal to 2π divided by the period. Therefore, the period of the function is 1/16.π.

The amplitude is equal to the difference between the maximum and minimum values divided by 2. Therefore, the amplitude is 9.

The vertical shift is equal to the y-intercept, which is 3. The general equation for the sinusoidal function is:y = 9 sin (16πx) + 3

Hence, the function that could be described as the one described in the problem is:y = 9 sin (16πx) + 3, and it is the function that models the given sinusoidal function in general form with the characteristics provided.

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The sinusoidal function described is y = 9 sin(16πx) + 3. This is derived by identifying the amplitude, frequency and vertical shift.

The sinusoidal function described could be written as:

y = A sin(Bx) + D

In this case, the amplitude A is half the difference between the maximum and minimum, so A = (12 - -6) / 2 = 9. The frequency B is 16π. The vertical shift D is the average of the maximum value and the minimum value, so D = (12 + -6) / 2 = 3. Thus, we get:

y = 9 sin(16πx) + 3

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Step-by-step explanation:

CH4 + 2O2 →2H2O + CO2

the answer

Answer:

The balanced chemical equation of the given reaction are;

b.CH4 + 202-> 2H20 + CO2

Step-by-step explanation:

C=C

H4=2H2

2O2=O2+2O(2O2)

I Think it helps you.

a. the probability of getting exactly 3 drivers involved in a car accident is approximately 0.2111. b. the probability of getting 3 or fewer drivers involved in a car accident is approximately 0.8866. c.The probability of getting at least one driver involved in a car accident is approximately 0.6833. d. the mean number of drivers involved in a car accident is 1.32, and the standard deviation is approximately 1.043.

To solve these problems, we can use the binomial distribution formula:

P(x) = C(n, x) * p^x * (1 - p)^(n - x)

where P(x) is the probability of getting exactly x successes, n is the number of trials, p is the probability of success in a single trial, and C(n, x) represents the binomial coefficient.

In this case:

n = 12 (number of drivers)

p = 0.11 (probability of a driver being involved in an accident)

q = 1 - p = 0.89 (probability of a driver not being involved in an accident)

a) To find the probability of getting exactly 3 drivers involved in a car accident:

P(x=3) = C(12, 3) * (0.11)^3 * (0.89)^(12 - 3)

Using a binomial coefficient calculator or software, we find that C(12, 3) = 220.

P(x=3) = 220 * (0.11)^3 * (0.89)^9 ≈ 0.2111

Therefore, the probability of getting exactly 3 drivers involved in a car accident is approximately 0.2111.

b) To find the probability of getting 3 or fewer drivers involved in a car accident:

P(x≤3) = P(x=0) + P(x=1) + P(x=2) + P(x=3)

Using the binomial distribution formula for each value of x and summing them up:

P(x≤3) = C(12, 0) * (0.11)^0 * (0.89)^12 + C(12, 1) * (0.11)^1 * (0.89)^11 + C(12, 2) * (0.11)^2 * (0.89)^10 + C(12, 3) * (0.11)^3 * (0.89)^9

Calculating this expression, we find that P(x≤3) ≈ 0.8866

Therefore, the probability of getting 3 or fewer drivers involved in a car accident is approximately 0.8866.

c) To find the probability of getting at least one driver involved in a car accident:

P(x≥1) = 1 - P(x=0)

Using the binomial distribution formula for x=0:

P(x=0) = C(12, 0) * (0.11)^0 * (0.89)^12

Calculating this expression, we find that P(x=0) ≈ 0.3167

Therefore, P(x≥1) = 1 - 0.3167 ≈ 0.6833

The probability of getting at least one driver involved in a car accident is approximately 0.6833.

d) The mean and standard deviation for the number of drivers involved in a car accident can be calculated using the formulas:

Mean (μ) = n * p

Standard Deviation (σ) = √(n * p * q)

Mean (μ) = 12 * 0.11 = 1.32

Standard Deviation (σ) = √(12 * 0.11 * 0.89) ≈ 1.043

Therefore, the mean number of drivers involved in a car accident is 1.32, and the standard deviation is approximately 1.043.

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The abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent is not provided in the given information.

The given information states that ∠c and ∠f are right angles (rt. ∠'s), and ∠b is not explicitly mentioned. In order to determine the abbreviation of the postulate or theorem that supports the conclusion of triangle congruence, we would need additional information regarding the sides or angles of the triangles.

Triangle congruence can be established using various postulates and theorems, such as the Side-Angle-Side (SAS) postulate, Angle-Side-Angle (ASA) theorem, Side-Side-Side (SSS) postulate, and others. These criteria establish specific conditions that need to be met in order to prove that two triangles are congruent.

Without knowing the specific side or angle relationships between the triangles in the given information, it is not possible to determine the appropriate postulate or theorem that supports the conclusion of triangle congruence.

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The fourth vertex's coordinates are as follows: ( 2.1, -3.6)

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

So, let the missing coordinates be (a,b).

Let's now utilize the midpoint formula to locate the erroneous coordinate.

Let the reference point be (-2.3, 3.6) A.

Let point B be (2.3, 2.2).

(2.1, 2.2) Let C be the point.

The center of AC should be at BD.

Step 1: Locating the AC's midpoint

Middle pint of AC:

(-2.3 + 2.1/2), (-3.6 + 2.2/2)

(0.2/2), (1.4/2)

(-0.1, -0.7)

Let's equate the midpoints in step two.

The BD mid-point:

(a + -2.3/2), (b + 2.2/2) =  (-0.1, -0.7)

(a + -2.3/2) = -0.1

(a -2.3/2) = -0.1*2

a = -0.2+2.3

a = 2.1

(b + 2.2/2) = -0.7

b + 2.2 = -0.7*2

b + 2.2 = -1.4

b = -1.4 -2.2

b = -3.6

Therefore, the fourth vertex's coordinates are as follows: ( 2.1, -3.6)

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Complete question:

Freddy drew a plan for a rectangular piece of material that hehe will use for a blanket. Three of the vertices are ​( -2.3 and −3.6​), ​(−2.3​, and 2.2​), and ​(2.1​, and 2.2​). What are the coordinates of the fourth​ vertex?

Answer:

2  171717/100000

The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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Based on the calculation below, the rate at which the weeds grow each day is 0.7%.

Given:

f(x) = 3(1.05)x = 3(1 + 0.05)x ................... (1)

Since there are 7 days in a week, the rate at which the weeds grow each day can be calculated from equation (1) by dividing 0.05 (i.e. 5% weekly growth rate) as follows:

f(x) = 3(1 + (0.05 / 7))x

f(x) = 3(1 + 0.007)x

f(x) = 3(1.007)x

Since 0.007 is the same as 0.7%, this implies that the rate at which the weeds grow each day is 0.7%.

The correct option is "f(x) = 3(1.007)7x; spreads at a rate of approximately 0.7% daily".

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Answer: Option 1

Step-by-step explanation: Correct for my test.

Based on the given data, The shape's whole surface area is about 252 mm².

Based on the image, the shape appears to be a set of rectangles with different lengths and widths.

To find the area of this shape, we can break it down into smaller rectangles and add up their areas.

Starting from the bottom, we can see that the first rectangle has a length of 6 mm and a width of 4 mm. Its area is:

Area1

= 6 mm × 4 mm

= 24 mm²

Moving up to the second rectangle, we see that it has a length of 6 mm and a width of 3 mm. Its area is:

Area2

= 6 mm × 3 mm

= 18 mm²

The third rectangle has a length of 6 mm and a width of 5 mm. Its area is:

Area3

= 6 mm × 5 mm

= 30 mm²

The fourth rectangle has a length of 6 mm and a width of 3 mm. Its area is:

Area4

= 6 mm × 3 mm

= 18 mm²

The fifth rectangle has a length of 6 mm and a width of 15 mm. Its area is:

Area5

= 6 mm × 15 mm

= 90 mm²

The sixth rectangle has a length of 3 mm and a width of 9 mm. Its area is:

Area6

= 3 mm × 9 mm

= 27 mm²

Finally, the seventh rectangle has a length of 5 mm and a width of 9 mm. Its area is:

Area7

= 5 mm × 9 mm

= 45 mm²

To find the total area of the shape, we can add up the areas of all seven rectangles:

Total Area

= Area1 + Area2 + Area3 + Area4 + Area5 + Area6 + Area7

= 24 mm² + 18 mm² + 30 mm² + 18 mm² + 90 mm² + 27 mm² + 45 mm²

= 252 mm²

Therefore, the total area of the shape is approximately 252 mm².

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..............answer..

Safety net policies like food assistance, housing assistance, and family tax credits keep millions of Americans from poverty each year and reduce hardship for millions more.

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The equation to represent the situation is given as $2h -$10 = 0

We have been given that

    Money earned by Shane for babysitting =  $8 per hour

    Money earned by Shane for walking dogs = $6 per hour

Let the number of hours spent by Shane be h hours

Tips she received for babysitting = $12

Tip she received for walking dogs = $10

Total amount earned by Shane for babysitting = $8*h + $12

Also Shane worked two more hours for walking dogs then the amount will be = 2*$6 = $12

Total amount earned by Shane for walking dogs = $6*h + $12 + $10

                                                                                  = $6h + $22

As she earned the same total amount of job the equation will be given as

  $8h + $12 = $6h + $22

  $2h -$10 = 0

Which is the required equation

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Answer:

x = 8 or x = -8

Step-by-step explanation:

Answer:

absolute value will always be positive

the answer is x=8

Answer:

the answer is B because 3(x-2) is the same as 3x -2

Probability of chosen the acre of land as per given conditions are as follow:

a. Probability of chosen the acre of land not forested is 0.62.

b. Probability of chosen the acre of land either forest or agriculture is 0.45.

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

As given in the question,

Given probability are:

Probability of chosen the acre of land is forest is equal to 0.38.

Probability of chosen the acre of land is agriculture is equal to 0.07.

Probability of chosen the acre of land as per given conditions are as follow:

a. Let P(A) represents the probability of chosen the acre of land is forest.

Then P(A') is the probability of not forested.

P(A) + P(A') = 1

⇒0.38 + P(A') = 1

⇒ P(A') = 1 - 0.38

⇒ P(A') = 0.62

b. Let P(G) is the probability of chosen acre of land agricultural.

No common land given for forest or agriculture, they are independent events.

P(A∩G) = 0

Probability of chosen the acre of land either forest or agriculture

= P( A or G)

= P(A) + P(G) - P(A∩G)

= 0.38 + 0.07 -0

= 0.45

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

Therefore, probability of chosen the acre of land as per given conditions are as follow:

a. Probability of chosen the acre of land not forested is 0.62.

b. Probability of chosen the acre of land either forest or agriculture is 0.45.

c. Probability of chosen the acre of land other than forest or agriculture is non-forested which is equal to 0.62.

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Answer:

-12 and 14

Step-by-step explanation:

let the be x and y

x+y=2

x-y=26

add it down

2x=28

x=14

x-y=26

14-y=26

y=-12

give me branlist answer

Answer:

0, 1, 1.5, 1.8, 1.3

Step-by-step explanation:

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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