Solve for x.

Help me please

The statement "P(A or B) = P(A) + P(B)" is False.

The correct statement is "P(A or B) = P(A) + P(B) - P(A and B)," which is known as the general law of addition for probabilities. This law takes into account the possibility of events A and B overlapping or occurring together.

The general law of addition for probabilities states that the probability of either event A or event B occurring is equal to the sum of their individual probabilities minus the probability of both events occurring simultaneously. This adjustment is necessary to avoid double-counting the probability of the intersection.

Let's consider a simple example. Suppose we have two events: A represents the probability of flipping a coin and getting heads, and B represents the probability of rolling a die and getting a 6. The probability of getting heads on a fair coin is 0.5 (P(A) = 0.5), and the probability of rolling a 6 on a fair die is 1/6 (P(B) = 1/6). If we assume that these events are independent, meaning the outcome of one does not affect the outcome of the other, then the probability of getting heads or rolling a 6 would be P(A or B) = P(A) + P(B) - P(A and B) = 0.5 + 1/6 - 0 = 7/12.

In summary, the general law of addition for probabilities states that when calculating the probability of two events occurring together or separately, we must account for the possibility of both events happening simultaneously by subtracting the probability of their intersection from the sum of their individual probabilities.

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Answer:

They sold

20 Roses and 20 Carnations

Step-by-step explanation:

The total sales of 40 flowers is $100 not $10 as in the question

Roses=$3

Carnations=$2

Total flowers sold=40

Total sales=$10

Let Roses=r

Carnations=c

c+r=40. (1)

3r+2c=100 (2)

From (1)

c=40-r

Substitute c=40-r into (2)

3r+2c=100

3r+2(40-r)=100

3r+80-2r=10

r=100-80

r=20

Substitute r=20 into (1)

c+r=40

c+20=40

c=40-20

=20

c=20

r=20

Check:

3r+2c=100

3(20)+2(20)=100

60+40=100

100=100

Answer: 4 1/2

Step-by-step explanation: you put 4 times 2 subtracted by -3 time 2 divided by 2 times 2

Answer: 471.2

Step-by-step explanation:

Answer:

Answer = 471.24 square millimeters

Step-by-step explanation:

Answer:

(2x-5)(3x+1)

Step-by-step explanation:

make brackets:

(    )(    )

(    )(    )

we no that since there is two minuses in the trinomial there will be one - and one +

there are two beacause 6 is 6*1 and 2*3

(2x-   )(3x+  )

(6x+  )(1x-    )

now use some ingenuity to find where 5 and 1 should go to complete

(2x-5)(3x+1)

(2x+5)(3x-1)

(2x-1)(3x+5)

(2x+1)(3x-5)

the first binomial is the answer

2x*3x = 6x^2

-5*+1 = -5

2x*1 = 2x

3x*-5 = -15x

6x^2 +2x - 15x - 5

6x^2 - 13x - 5

Step-by-step explanation:

\( \underline{ \underline{ \text{Given}} }: \)

\( \underline{ \underline{ \text{To \: find}}} : \)

Let E ( -3 , 2 ) be ( x₁ , y₁ ) & H ( 1 , -1 ) be ( x₂ , y₂ )

\( \underline{ \underline{ \text{Solution}}} : \)

\( \sf{Midpoint = ( \frac{x_{1} + x_{2}}{2} \: , \frac{ y_{1} + y_{2}}{2} )}\)

⟶ \( \sf{( \frac{-3 + 1}{2} \: , \frac{2 + ( - 1)}{2} )}\)

⟶ \( \sf{( \frac{-2}{2} \:, \frac{2 - 1}{2} )}\)

⟶ \( \sf{( -1 \: ,\frac{1}{2} )}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt{(-1 \: , \: \frac{1}{2} )}}}}}}}\)

Hope I helped ! ♡

Have a wonderful day / night ! ツ

▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔

To find the minimum surface area of the container, we can follow these steps: Start with the given volume: The volume of the container is 80 in³.

Express the volume in terms of the variables: The volume can be expressed as V = s²h. Write the equation for the volume: Substitute the known values into the equation: 80 = s²h.

Express the height in terms of the side length: Rearrange the equation to solve for h: h = 80/s². Express the surface area in terms of the variables: The surface area of the container can be expressed as A = s² + 4sh.

Substitute the expression for h into the equation: Substitute h = 80/s² into the equation for surface area. Simplify the equation: Simplify the expression to get the equation for surface area in terms of s only.

Take the derivative: Differentiate the equation with respect to s.

Set the derivative equal to zero: Find the critical points by setting the derivative equal to zero. Solve for s: Solve the equation to find the value of s that minimizes the surface area.

Substitute the value of s into the equation for h: Substitute the value of s into the equation h = 80/s² to find the corresponding value of h. Calculate the minimum surface area: Substitute the values of s and h into the equation for surface area to find the minimum surface area. The correct order of steps for finding the minimum surface area (A) of the container is: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

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In a perfectly symmetrical distribution with a mean (µ) of 30, there is no specific mode because all values occur with equal frequency.

In a perfectly symmetrical distribution, such as a symmetric bell-shaped curve or a uniform distribution, each value occurs with the same frequency. This means that there is no value that occurs more frequently than others, resulting in multiple modes or no mode at all.

The mode is typically used to identify the most common value in a dataset, but in a perfectly symmetrical distribution, all values have equal frequency, and there is no single mode. Instead, the distribution is characterized by its symmetry around the mean (µ). The mean represents the central tendency of the distribution, indicating the balance point of the data. In this case, with a mean of 30, the distribution is centered around this value, with equal numbers of observations on either side.

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Answer:

0.5,5/8, 58.3

Step-by-step explanation:

0.5 is 1/2, and 5/8 is 1/8th larger than 1 half, and 58.3 is the only one with a whole number, so its the largest. Hope this helped, can i maybe get brainliest :D

The required ascending order is given as 0.5, 58.3%, and 5/8.

Given that,
To arrange the given number in ascending order,
5/8 , 0.5 , 58.3%

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
5 / 8 = 0.625
58.3% = 0.583

So,
0.5 < 58.3% < 5/8

Thus,the required ascending order is given as 0.5, 58.3%, and 5/8.

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Since all the properties hold, we conclude that (R - {1}, *) is an abelian group.

To show that (R - {1}, *) is an abelian group, we need to verify the following properties:

Closure: For any a, b ∈ R - {1}, we have a * b ∈ R - {1}. To see this, note that a + b - ab ≠ 1 since either a ≠ 1 or b ≠ 1 (or both), so a * b is well-defined and belongs to R - {1}.

Associativity: For any a, b, c ∈ R - {1}, we have (a * b) * c = a * (b * c). To see this, we compute:

(a * b) * c = (a + b - ab) * c = ac + bc - ab*c = a * (c + b - cb) = a * (b * c),

where we used the fact that multiplication is associative and distributive over addition in R.

Identity: There exists an element e ∈ R - {1} such that a * e = a = e * a for any a ∈ R - {1}. To find e, we solve the equation a + e - ae = a for any a ≠ 1, which gives e = 0. Thus, 0 is the identity element of (R - {1}, *).

Inverse: For any a ∈ R - {1}, there exists an element b ∈ R - {1} such that a * b = e = b * a. To find b, we solve the equation a + b - ab = 0, which gives b = (a-1)/a. Note that b ≠ 1 since a ≠ 1, and b is well-defined since a ≠ 0. Moreover, we have:

a * b = a + (a-1)/a - a(a-1)/a = (a-1) + (a-1)/a = e,

and similarly, b * a = e. Thus, b is the inverse of a in (R - {1}, *).

Commutativity: For any a, b ∈ R - {1}, we have a * b = b * a. To see this, we compute:

a * b = a + b - ab = b + a - ba = b * a,

where we used the commutativity of addition in R.

To show that (R - {1}, ) is isomorphic to (R, ·), we need to find a bijective function f : R - {1} → R* such that f(a * b) = f(a) · f(b) for all a, b ∈ R - {1}. Let's define f as:

f(a) = 1/(1-a) for all a ∈ R - {1}.

Note that f is well-defined and bijective since a ≠ 1 implies that 1-a ≠ 0, and we have:

f(a * b) = f(a + b - ab) = 1/(1 - (a+b-ab)) = 1/((1-a) * (1-b)) = f(a) · f(b)

for all a, b ∈ R - {1}, where we used the fact that multiplication is distributive over addition and the formula for the inverse of a product in R*. Thus, f is an isomorphism between (R - {1}, ) and (R, ·).

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The solution to the linear programming problem 0.3x₁ + 0.1x₂ ≤ 1.8 using the simplex method shows that the problem has optimal solutions.)

Convert the inequality into an equation by subtracting 1.8 from both sides:
0.3x₁ + 0.1x₂ - 1.8 ≤ 0

Introduce slack variables to convert the inequality into an equation:
0.3x₁ + 0.1x₂ + s₁ = 1.8

Set up the initial simplex tableau:

┌───┬───┬───┬───┬───┐
│   │ x₁ │ x₂ │ s₁ │  1│
├───┼───┼───┼───┼───┤
│  1│ 0.3│ 0.1│  1  │1.8│
└───┴───┴───┴───┴───┘
```

Select the pivot column. Choose the column with the most negative coefficient in the bottom row. In this case, it is the second column (x₂).

Select the pivot row. Divide the numbers in the rightmost column (1.8) by the corresponding numbers in the pivot column (0.1) and choose the smallest positive ratio. In this case, the smallest positive ratio is 1.8/0.1 = 18. So the pivot row is the first row.


The simplex method is an iterative procedure that systematically improves the solution to a linear programming problem. It starts with an initial feasible solution and continues to find a better feasible solution until an optimal solution is obtained. In each iteration, the simplex method selects a pivot column and a pivot row to perform row operations, which transform the current tableau into a new tableau with improved objective function values. The process continues until the objective function values cannot be further improved or the linear programming problem is unbounded.

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The correct answer is

0.3x1+0.1x2≤2.7→0.3x1+0.1x2≤1.8 Work Through The Simplex Method Step By Step. How The Solution Changes (I.E., LP Has Optimal

Answer:

the 2:The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate. 3

Step-by-step explanation:

40 to 8

Each pizza costs $8 and the delivery fee is $3.

Answer:

The equation y = -2x + 1 describes a line on a coordinate plane. To find two ordered pairs that work, you can pick any two x-values and plug them into the equation to get the corresponding y-values. For example, if you choose x = -1 and x = 4, then the corresponding y-values are y = -2(-1) + 1 = 1 and y = -2(4) + 1 = -7. This means that the two ordered pairs that work are (-1, 1) and (4, -7).

The number of different hands that can be dealt from a standard deck of 52 cards, where each player is dealt 7 cards, is given by the combination formula.

The number of different hands that can be dealt from a standard deck with 52 cards, where each player receives 7 cards, is calculated as follows:

a. The number of different hands can be determined using the combination formula. We need to choose 7 cards out of 52, without considering the order. Therefore, the number of different hands is given by the combination of 52 cards taken 7 at a time:

\(\[\binom{52}{7} = \frac{52!}{7!(52-7)!} = 133,784,560\]\)

So, there are 133,784,560 different hands that can be dealt.

b. To find the probability of being dealt a hand with 4 of a kind and the remaining 3 cards having different values, we need to determine the number of favorable outcomes (hands with 4 of a kind) and divide it by the total number of possible outcomes (all different hands).

The number of favorable outcomes can be calculated as follows: We need to choose one of the 13 different values for the 4 of a kind, and then choose 4 suits out of the 4 available for that value. The remaining 3 cards should have different values, which can be chosen from the remaining 12 values, and each of those values can be assigned any of the 4 suits. Therefore, the number of favorable outcomes is:

\(\[13 \times \binom{4}{4} \times 12 \times \binom{4}{1} \times \binom{4}{1} \times \binom{4}{1} = 3744\]\)

The probability is then given by:

\(\[\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3744}{133,784,560} \approx 0.0000280\]\)

So, the probability that a randomly dealt hand contains 4 of a kind is approximately 0.0000280 or 0.0028%.

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The product of the two matrices Q₁Q₂ is orthogonal

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. ... {\displaystyle Q^{\mathrm {T} }Q=QQ^{\mathrm {T} }=I,} where QT is the transpose of Q and I is the identity matrix.

It is said to be an orthogonal matrix if its transpose is equal to its inverse matrix, or when the product of a square matrix and its transpose gives an identity matrix of the same order.

If A is an n*n orthogonal matric, then A*A¹ = A¹*A

Therefore A*A¹ = A¹*A  = 1

This implies that the product Q₁O₂ is orthogonal.

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Answer: 1, 3, and 4

Step-by-step explanation:

Haha i had this math problem once.

So i assume the choices are:

1: 714,578

2: 704,988

3: 714,601

4: 714,099

so its 1, 3, and 4

Answer:

A and C

Step-by-step explanation:

ive seen this question before

Given the graph of the function f shown to the right as shown below: Graph of the function fIn order to find f(-7) and f(2) of the given function, we need to follow the given steps.(a) Find f(-7) and f(2)For f(-7):

We observe that the given graph passes through (-7,-39), hence to find f(-7), we need to substitute x = -7 in the equation of the given function f(x).f(-7) = -39. Therefore, f(-7) = -39For f(2):We observe that the given graph passes through (2,12), hence to find f(2), we need to substitute x = 2 in the equation of the given function f(x).f(2) = 12Therefore, f(2) = 12.

Thus, the required values are: f(-7) = -39 and f(2) = 12.

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Answer:

527 grams

Step-by-step explanation:

Use the density formula, d = m/v

Plug in the density and volume, then solve for m (mass):

d = m/v

0.85 = m/620

527 = m

So, the mass is 527 grams

The daily percent of increase in tourists from one month to the next is approximately 5.4% which is obtained through mathematical operations.

To calculate the daily percent of increase, we need to determine the difference in the number of tourists between the two months and divide it by the number of days in the second month. Then, we express this difference as a percentage.

In the given scenario, the increase in tourists from the first month to the second month is 6355 - 4500 = 1855. The number of days in the second month is 31. Dividing the increase by the number of days gives us

1855 / 31 = 59.8387.

To express this increase as a percentage, we multiply the result by 100, yielding 5983.87%. Rounding this to the nearest tenth of a percent gives us approximately 5983.9%.

Finally, to find the daily percent of increase, we divide the percentage by the number of days in the second month: 5983.9% / 31 = 5.4%.

Therefore, the daily percent of increase in tourists from one month to the next is approximately 5.4%.

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Rectangular coordinates use the x and y axes, while polar coordinates use the radius and angle. By converting between these coordinate systems, we can gain new insights into the same equation and solve problems using different methods.

When converting rectangular equations to polar form, we can use the following conversion equations:
1. r^2 = x^2 + y^2 (this is the equation for the radius in terms of x and y)
2. tanθ = y/x (this is the equation for the angle θ in terms of x and y)
Using these equations, we can convert any rectangular equation (in terms of x and y) to its equivalent polar form (in terms of r and θ).
On the other hand, when converting polar equations to rectangular form, we can use the following conversion equations:
1. x = r*cos(θ) (this is the equation for x in terms of r and θ)
2. y = r*sin(θ) (this is the equation for y in terms of r and θ)
Using these equations, we can convert any polar equation (in terms of r and θ) to its equivalent rectangular form (in terms of x and y).
It's important to note that when converting equations between rectangular and polar forms, we're essentially changing the coordinate system used to describe the equation.

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Answer:

sin I = 28 / 35

Step-by-step explanation:

sin I = opposite side / hypotenuse

hyp^2 = 28^2 + 21^2

= 784 + 441

= 1225

hyp = \(\sqrt{1225}\)

= 35

sin I = 28 / 35

Solomon's study on circadian rhythms in a sample of 45 pregnant women admitted to a hospital in the first 6 months of 2021 due to severe preeclampsia is an example of consecutive sampling.

Consecutive sampling, also known as continuous or complete sampling, is a non-probability sampling method.

In this approach, researchers collect data from every subject that meets the eligibility criteria within a specific time frame.

In Solomon's study, the eligibility criteria were pregnant women admitted to the hospital with severe preeclampsia during the first 6 months of 2021.

By including all eligible subjects during this period, Solomon ensured that the sample was representative of the population under study.

The consecutive sampling method has several advantages, including ease of implementation and the potential for a relatively large sample size.

Additionally, it can provide a comprehensive view of the population during the specified time frame.

However, it may be susceptible to biases if there is a change in the population over time, or if the subjects who meet the eligibility criteria within the given period are not representative of the overall population.

In summary, Solomon's study on circadian rhythms in pregnant women with severe preeclampsia used consecutive sampling, a non-probability sampling method that involves collecting data from every subject meeting the eligibility criteria within a specific time frame.

This method is straightforward to implement and can yield a large sample size, but it may be susceptible to biases if the sample is not representative of the overall population.

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Answer: 150 wpm

Step-by-step explanation:

if he reads 1,500 words in 10 minutes, then we simply divide 1500 by 10, in order to get how many words that he can read in one minute.

1500/10 = 150

The length of the apothem of the regular triangle with a perimeter of 96√3 units is 16 units.

To find the length of the apothem of a regular triangle, we need to know the length of one of its sides. We are given the perimeter of the triangle, which is 96√3 units. Since a regular triangle has three equal sides, we can divide the perimeter by 3 to get the length of one side:

96√3 ÷ 3 = 32√3 units

Now, we can use the formula for the apothem of a regular triangle:

apothem = (side length) / (2 * tan(π/3))

where π/3 is the angle between the apothem and one side of the triangle (which is 60 degrees for a regular triangle).

Plugging in the values we have:

apothem = (32√3) / (2 * tan(π/3))

apothem = (32√3) / (2 * √3)

apothem = 16 units

Therefore, the length of the apothem of the regular triangle with a perimeter of 96√3 units is 16 units.

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Answer:

27..

Step-by-step explanation:

w - 10 ≤ 16

w - 10 + 10 ≤ 16 + 10

w ≤ 26

all apply except 27.

Answer:

Substitute the given values of x into the given equation to find the values of y:

when x = -8

\(y=\dfrac54(-8)+1=-9\)

Point = (-8, -9)

when x = -4

\(y=\dfrac54(-4)+1=-4\)

Point = (-4, -4)

when x = 0

\(y=\dfrac54(0)+1=1\)

Point = (0, 1)

when x = 4

\(y=\dfrac54(4)+1=6\)

Point = (4, 6)

when x = 8

\(y=\dfrac54(8)+1=11\)

Point = (8, 11)

The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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Answer:

Orion reports a higher density than Guang.

Step-by-step explanation:

Khan said it was right.

Answer: Orion or number 2

Step-by-step explanation:

khan is always correct