Plzz help me !! If you are good at algebra!

Step-by-step explanation:

How do you calculate number of successes?

Example:

Define Success first. Success must be for a single trial. Success = "Rolling a 6 on a single die"

Define the probability of success (p): p = 1/6.

Find the probability of failure: q = 5/6.

Define the number of trials: n = 6.

Define the number of successes out of those trials: x = 2.

Binomial probability distribution for the given set of data is

\(\ 100C_{x\)\(( 0.20)^{x} (0.80)^{100-x}\).

"Binomial probability distribution is the representation of  a probability with only two outcomes success and failure under given number of trials."

Formula used

Binomial probability distribution is given by

\(\\n{C}_{x}p^{x}q^{n-x}\)

n= number of experiments

x = 0, 1, 2, 3,.......

p = probability of success

q = probability of failure

According to the question,

Number of trials  'n' = 100

Probability of success 'p' = (20 / 100)

                                          = 0.20

Probability of failure 'q' = 1 - p

                                      = 1 - (20/100)

                                      =  (80 / 100)

Substitute the value in the formula we get

Required probability =  \(\ 100C_{x\)\(( 0.20)^{x} (0.80)^{100-x}\)

Example:

Tossing a coin 6 times getting exactly two heads.

Number of trials 'n' = 6

Number of heads 'x' =2

Only two possible outcomes head or tail

Probability of getting head 'p' = 1 / 2

Probability of not getting head 'q' = 1 /2

Required probability = \(\ 6C_{2\) (1/2)²(1/2) ⁶⁻²

                                  =\(\ 6C_{2\) (1/2)⁶

Hence, binomial probability distribution for the given set of data is

\(\ 100C_{x\)\(( 0.20)^{x} (0.80)^{100-x}\)

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Answer:

Look at step-by-step explanation

Step-by-step explanation:

Side-side-angle is not a congruence rule because a side cannot be in between an angle and a side. Angle-side-side is the same thing, a side cannot be in between an angle and a side.

Answer:

a negative integer

Step-by-step explanation:

We can first establish basic rules that we can apply:

the product of one negative integer:

-1 = -1

(odd number = negative)

the product of two negative integers:

-1 · -1 = 1

(even number = positive)

the product of three negative integers:

-1 · -1 · -1 = 1   {-1 · -1 = 1, 1 · -1 = -1}

(odd number = negative)

the product of four negative integers:

-1 · -1 · -1 · -1 = 1

(even number = positive)

So, we can understand that an even number of integers changes the original value to its negative/positive [the opposite +/- sign from the original number], whilst an odd number of integers does not change the +/- sign.

So, because 23 is an odd number, the product will stay negative.

Answer:

If a polygon is dilated by a scale factor of k, then its area is multiplied by k².

a. When k = 4, the area of the image is 10 × 4² = 160 square units.

b. When k = 1.5, the area of the image is 10 × 1.5² = 22.5 square units.

c. When k = 1, the area of the image is 10 × 1² = 10 square units. (The image is the same size as the original.)

d. When k = 1/3, the area of the image is 10 × (1/3)² = 10/9 square units.

Step-by-step explanation:

Answer:

kd00000000

Step-by-step explanation:

0,9,8hahahhahhhhahahah ban buster

The probability that Radesh is late on less than 3 days in a 6 day week is 0.7865.

To calculate the probability that Radesh is late on less than 3 days in a 6 day week,

Use the binomial distribution formula

P(X<3) = Σ (i=0 to 2) \(^{6} C_i\) \(0.35^i 0.65^{(6-i)\)

Here,

\(^{6} C_i\) is the number of ways to choose i days out of 6,

\(0.35^i\) is the probability that Radesh is late on i days,

And \(0.65^{(6-i)\) is the probability that he is on time on the remaining (6-i) days.

Now, Solve this equation:

⇒ P(X<3) = \(^{6} C_0\) 0.35 x 0.65 + \(^{6} C_1\) 0.35 x 0.65 + \(^{6} C_2\) 0.35 x 0.65

⇒ P(X<3) = 0.7865

Hence,

The required probability is 0.7865.

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The correct answer is (D) A and B. Both a run of six points or more and an astronomical point can be rules for determining non-random patterns.

A run of six points or more refers to a sequence of data points that share a common characteristic or exhibit a consistent trend.

In statistical analysis, a run is a consecutive sequence of data points above or below a certain threshold. If there is a run of six points or more in a dataset, it suggests a non-random pattern or trend.

An astronomical point refers to a data point that significantly deviates from the expected pattern or falls outside the normal range of values. This point stands out as an outlier and may indicate a non-random pattern in the data.

By combining these two rules, A and B, we can identify non-random patterns in a dataset. A run of six points or more indicates a sustained trend, while an astronomical point signifies a significant deviation from the expected pattern.

It's important to note that a trend of three points or fewer, as mentioned in option (C), does not provide enough evidence to determine a non-random pattern. A trend of three points or fewer may still be subject to randomness or noise in the data, and it is not considered statistically significant.

Therefore, the correct answer is option (D) A and B, as both a run of six points or more and an astronomical point can help identify non-random patterns in data.

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Suppose dorothy drops a ball from a height of 10 feet. after the ball hits the floor, it rebounds 65% of its previous height.The formula that represents the height of the ball after its nth bounce is given by

\(y = (0.65)^n \times 10 feet.\)

When a ball is dropped from a height of 10 feet, it rebounds to 65% of its previous height each time it bounces.

To find the height of the ball after the nth bounce, we need to use a geometric sequence formula,

which is given by

\(y = ar^n-1,\)

where a is the initial term,

r is the common ratio, and

n is the number of terms.

Here, a = 10 feet,

r = 0.65, and

n is the nth term or

the number of times the ball bounces after it is dropped for the first time.

Therefore, the formula that represents the height of the ball after its nth bounce is given by

\(y = (0.65)^n \times 10 feet.\)

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Answer:

The second one. The -2y should have been +2y

Step-by-step explanation:

a negative multiplied by a negative gives you a positive

Answer:

it should be the second answer

Step-by-step explanation:

hope this helps

Answer:

for the empty box in the -4 column put -8 and for the empty box in the 6x column put -18

Answer:

Dealership A is offering the better price

Step-by-step explanation:

A. 10% off of 14,500 is 13050

B. 14% off of 16,000 is 13,760

The statement "They can only be integer values" is not true about continuous random variables.

Continuous random variables can take any value within a certain range, not just integers. They are characterized by a probability density function (pdf) that describes the distribution of the variable over a range of values. The pdf is a continuous curve, not a set of discrete points.

The other statements about continuous random variables are true: the entire area under each of the curves does equal 1, some may be described by uniform distributions or exponential distributions, the area under each of the curves represents probabilities, and they have an infinite set of values.

Therefore, The statement "They can only be integer values" is not true about continuous random variables.

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To simplify the limit, we should multiply the numerator and denominator by the expression \(1+\cos(3x)\).

To simplify the given limit, we can use a trigonometric identity to manipulate the expression and eliminate the indeterminate form. Let's solve it step by step:

1. Start with the given limit: \(\lim _{x \rightarrow 0} \frac{\sin ^{2}(3 x)}{1-\cos (3 x)}\).

2. Multiply the numerator and denominator by the expression \(1+\cos(3x)\). This is done to utilize the trigonometric identity \(\sin^2(\theta) = 1 - \cos^2(\theta)\).

3. Rewrite the limit using the multiplication: \(\lim _{x \rightarrow 0} \frac{\sin ^{2}(3 x) \cdot (1+\cos(3x))}{(1-\cos (3 x)) \cdot (1+\cos(3x))}\).

4. Apply the trigonometric identity: The numerator can be simplified using the identity \(\sin^2(\theta) = 1 - \cos^2(\theta)\). So, \(\sin ^{2}(3 x) \cdot (1+\cos(3x))\) becomes \((1 - \cos^2(3x)) \cdot (1+\cos(3x))\).

5. Simplify the numerator: Expanding the expression in the numerator, we get \((1 - \cos^2(3x)) \cdot (1+\cos(3x)) = 1 - \cos^2(3x) + \cos(3x) - \cos^3(3x)\).

6. Simplify the denominator: The denominator \((1-\cos (3 x)) \cdot (1+\cos(3x))\) can be expanded using the difference of squares identity to get \(1 - \cos^2(3x)\).

7. Cancel out common terms: Notice that the numerator and denominator both contain the term \(1 - \cos^2(3x)\). Canceling out this term leaves us with \(\lim _{x \rightarrow 0} \frac{1 + \cos(3x) - \cos^3(3x)}{1 - \cos^2(3x)}\).

8. Evaluate the limit: Now, we can directly substitute \(x = 0\) into the expression, resulting in \(\frac{1 + \cos(0) - \cos^3(0)}{1 - \cos^2(0)}\).

9. Simplify further: Since \(\cos(0) = 1\) and \(\cos^3(0) = 1\), the expression simplifies to \(\frac{1 + 1 - 1}{1 - 1} = \frac{1}{0}\).

10. Final result: The expression \(\frac{1}{0}\) represents an indeterminate form, which means the limit does not exist.

Therefore, the limit \(\lim _{x \rightarrow 0} \frac{\sin ^{2}(3 x)}{1-\cos (3 x)}\) does not exist.

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John must score 286 on his 8th game to achieve an average score of 215.

What is an Average?

Average, also known as the mean, is a mathematical concept that represents the central value of a set of numbers. It is found by dividing the sum of the numbers by the total count of the numbers.

To find out what John must score on his 8th game to achieve an average score of 215, we need to use the formula for calculating the average or mean:

Average = (Sum of Scores) / (Number of Scores)

We can use this formula to solve for the unknown score:

215 = (159 + 182 + 225 + 240 + 198 + 200 + 230 + x) / 8

Multiplying both sides by 8, we get:

1720 = 159 + 182 + 225 + 240 + 198 + 200 + 230 + x

Simplifying, we get:

1720 = 1434 + x

Subtracting 1434 from both sides, we get:

x = 286

Therefore, John must score 286 on his 8th game to achieve an average score of 215.

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Answer:

A the first one

Step-by-step explanation:

hope this helps

Answer:

(i) The volume of each hemispherical bowl can be calculated as follows:

Volume of a hemispherical bowl = (2/3) x pi x (d/2)^3, where d is the internal diameter of the bowl.

Substituting d = 21 cm, we get:

Volume of a hemispherical bowl = (2/3) x pi x (21/2)^3 = 4851.97 cubic centimeters

The total volume of compost required to fill all 16 bowls is therefore:

Total volume of compost = 16 x 4851.97 = 77631.52 cubic centimeters

If 1 cm³ of compost weighs 2.31 gm, then the total weight of required compost is:

Total weight of compost = 77631.52 x 2.31 = 179231.83 grams or 179.23 kilograms

Therefore, Mrs. Thapa would need 179.23 kilograms of compost to fill all 16 hemispherical bowls.

(ii) The outer curved surface area of each hemispherical bowl can be calculated as follows:

Outer curved surface area of a hemispherical bowl = 2 x pi x (d/2)^2, where d is the internal diameter of the bowl.

Substituting d = 21 cm, we get:

Outer curved surface area of a hemispherical bowl = 2 x pi x (21/2)^2 = 693.84 square centimeters

The total outer curved surface area of all 16 bowls is therefore:

Total outer curved surface area = 16 x 693.84 = 11101.44 square centimeters

If Mrs. Thapa covers the outer curved surface of each bowl with polythene sheet, then the total amount of polythene required would be equal to the total outer curved surface area of all 16 bowls.

Therefore, the total amount of polythene required would be 11101.44 square centimeters.

Step-by-step explanation:

A. To find the velocity vector v(t), we need to integrate the acceleration vector a(t) with respect to time t. So, we have: v(t) = ∫ a(t) dt, = ∫ (-25cos(5t))i + (-25sin(5t))j + (-3t)k dt, = (-5sin(5t))i + (5cos(5t))j + (-3/2)t^2 + C.

where C is the constant of integration. To determine the value of C, we use the initial velocity v(0) = i + k. So, v(0) = (-5sin(0))i + (5cos(0))j + (-3/2)(0)^2 + C . = i + C, Therefore, C = v(0) - i = k. Substituting this value of C in the equation for v(t), we get: v(t) = (-5sin(5t))i + (5cos(5t))j + (-3/2)t^2 + k

Therefore, the velocity vector is v(t) = <-5sin(5t), 5cos(5t), -3/2t^2 + 1>. B) To find the position vector r(t), we need to integrate the velocity vector v(t) with respect to time t. So, we have: r(t) = ∫ v(t) dt , = ∫ (-5sin(5t))i + (5cos(5t))j + (-3/2)t^2 + k dt = (1/25)cos(5t)i + (1/25)sin(5t)j + (-1/10)t^3 + kt + C, where C is the constant of integration. To determine the value of C, we use the initial position vector r(0) = i + j + k.

So, r(0) = (1/25)cos(0)i + (1/25)sin(0)j + (-1/10)(0)^3 + k(0) + C, = i + j + C
Therefore, C = r(0) - i - j = k. Substituting this value of C in the equation for r(t), we get: r(t) = (1/25)cos(5t)i + (1/25)sin(5t)j + (-1/10)t^3 + kt + k, Therefore, the position vector is r(t) = <(1/25)cos(5t), (1/25)sin(5t), (-1/10)t^3 + t + 1>.

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Step-by-step explanation:

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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Answer:

The mean ≈ 90

The median = 95

The mode = 95 & 100

The range = 37

Step-by-step explanation:

We will base out conclusion by calculating the measures of central tendency of the distribution i.e the mean, median, mode and range.

– Mean is the average of the numbers. It is the total sum of the numbers divided by the total number of students.

xbar = Sum Xi/N

Xi is the individual student score

SumXi = 63+66+70+81+81+92+92+93+94+94+95+95+95+96+97+98+98+99+100+100+100

SumXi = 1899

N = 21

xbar = 1899/21

xbar = 90.4

xbar ≈ 90

Hence the mean of the distribution is approximately equal to 90.

– Median is number at the middle of the dataset after rearrangement.

We need to locate the (N+1/2)the value of the dataset.

Given N =21

Median = (21+1)/2

Median = 22/2

Median = 11th

Thus means that the median value falls on the 11th number in the dataset.

Median value = 95.

Note that the data set has already been arranged in ascending order so no need of further rearrangement.

– Mode of the data is the value occurring the most in the data. The value with the highest frequency.

According to the data, it can be seen that the value that occur the most are 95 and 100 (They both occur 3times). Hence the modal value of the dataset are 95 and 100

– Range of the dataset will be the difference between the highest value and the lowest value in the dataset.

Highest score = 100

Lowest score = 63

Range = 100-63

Range = 37

The missing term in the equation (x + 9)² = x² + 18x + is 81. The simplified form of the (x + 9 )² = x² + 18x + 81. The correct option is C.

Given

(x + 9)² =  x² + 18x +----

Required to find the missing term =?

It is given the form of ( a + b)² = a² + 2ab + b²

Putting the given values in the above form we get the value of the missing term from the equation

(x + 9 )² = x² + 2 × x ×9 + 9 × 9

              = x² + 18x + 81  

A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0. Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

Thus, we get the value of the missing term as 81.

Thus, the ideal selection is option C.

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The given function is: f(x) = (12x² - 8x + 9) / (4x² + 1) To evaluate the limit as x approaches [infinity], we can divide the numerator and denominator by the highest degree term of x in the denominator.

Here, the highest degree term of x in the denominator is x².

f(x) = (12x² / 4x²) / (4x² / 4x²) + (-8x / 4x²) / (4x² / 4x²) + (9 / 4x²) / (4x² / 4x²)

Taking the limit of this as x approaches [infinity], we get:

limx→[infinity]f(x) = (12/4) / (1 + 0 + 0) = 3

Thus, the limit as x approaches [infinity] of f(x) is equal to 3.

Similarly, to evaluate the limit as x approaches -[infinity], we can divide the numerator and denominator by the highest degree term of x in the denominator. Here, the highest degree term of x in the denominator is x².

f(x) = (12x² / 4x²) / (4x² / 4x²) + (-8x / 4x²) / (4x² / 4x²) + (9 / 4x²) / (4x² / 4x²)

Taking the limit of this as x approaches -[infinity], we get:

limx→-[infinity]f(x) = (12/4) / (1 + 0 + 0) = 3

Thus, the limit as x approaches -[infinity] of f(x) is equal to 3.Both of the above limits are equal, and they both exist. Therefore, the horizontal asymptote of the function f(x) is y = 3.

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The horizontal asymptote of f(x) is y = 3. The given rational function is f(x) = (12x² - 8x + 9)/(4x² + 1).

Evaluation of Limx→[infinity]f(x):

To determine Limx→[infinity]f(x), we are required to check the highest degree of the numerator and the denominator.

If the degree of the numerator is greater than the degree of the denominator, then the limit will tend to infinity, but if the degree of the denominator is greater than the degree of the numerator, then the limit will tend to zero.

Here, the degree of the numerator and the denominator is the same.

So, to evaluate the limit, we will divide both the numerator and denominator by the highest power of x in the denominator.

Let's divide both the numerator and the denominator by 4x².

f(x) = (12x²/4x² - 8x/4x² + 9/4x²)/(4x²/4x² + 1/4x²)

Simplifying the above expression, f(x) = 3 - 2/x² + 9/4x⁴

Now, as x → [infinity], the second term of the expression will tend to zero.

Therefore, f(x) → 3.

So, Limx→[infinity]f(x) = 3

Evaluation of Limx→-∞f(x):

We will divide both the numerator and the denominator by the highest power of x in the denominator to evaluate the limit. Let's divide both the numerator and the denominator by 4x².

(x) = (12x²/4x² - 8x/4x² + 9/4x²)/(4x²/4x² + 1/4x²)

Simplifying the above expression, f(x) = 3 - 2/x² + 9/4x⁴

Now, as x → -[infinity], the second term of the expression will tend to zero.

Therefore, f(x) → 3.So, Limx→-∞f(x) = 3

Horizontal asymptotes of f(x):

If Limx→[infinity]f(x) = L and Limx→-∞f(x) = L, then y = L is the horizontal asymptote of f(x).

In this case, Limx→[infinity]f(x) = Limx→-∞f(x) = 3, so y = 3 is the horizontal asymptote of f(x).

Therefore, the horizontal asymptote of f(x) is y = 3.

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Answer:

8

Step-by-step explanation:

The given set to us is ,

=> A = { 2 , 3 , 4 }

And ,

=> n(A) = 3

The Total number of subsets of a set A with n number of elements is given by ,

=> n(subsets) = 2ⁿ .

=> n( subsets) = 2³

=> n ( subsets ) = 8

Answer:

-1

Step-by-step explanation:

l -1 l = 1

1 - -1 = 2

i HOPE U UNDERSTOOD!! :)

Answer:

y = x^2 + 14x + 62

Step-by-step explanation:

y = (x + 7)^2 + 13 is to be rewritten in the form y = ax^2 + bx + c.  

Note:  Use " ^ " to denote exponentiation.

Expand y = (x + 7)^2, holding the constant term to be added on later:

y = x^2 + 14x + 49 + 13

Combining the constants, we get:

y = x^2 + 14x + 62 (which matches Answer D).

Answer:

D

Step-by-step explanation:

The Law of Sines often yields better results due to its broader applicability and flexibility in solving trigonometric problems involving non-right triangles. The Law of Cosines is also reliable, especially when the lengths of sides are known. The Law of Tangents has limited use and is typically employed in specific right triangle scenarios.

To compare the results of the verification of the Law of Sines, Law of Cosines, and Law of Tangents, we can create a table showcasing the findings and analyze which law had better results:

Law               |                         Results                                |                             Accuracy

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

Law of Sines      |  Satisfied for various triangle scenarios   | Dependent on angle and side accuracy

Law of Cosines   | Satisfied for various triangle scenarios   | Dependent on side accuracy

Law of Tangents | Satisfied for specific triangle scenarios   | Dependent on angle accuracy

The Law of Sines may often have better results because it is applicable to a broader range of triangle scenarios, allowing for more flexibility in solving trigonometric problems. It is useful when working with non-right triangles, as it relates the ratios of angles to the ratios of opposite sides. However, it heavily relies on the accuracy of both angles and sides for precise calculations.

The Law of Cosines, while also effective in various triangle scenarios, is particularly useful for solving triangles when the lengths of all three sides are known or when an angle and the lengths of two sides are known. It is less dependent on angle accuracy but relies more on side accuracy.

The Law of Tangents has more limited applicability and is primarily used when dealing with right triangles. It relates the tangent of an angle to the ratios of sides, but its usage is not as widespread as the other two laws.

The Law of Sines and the Law of Cosines generally yield satisfactory results for various triangle scenarios. However, their accuracy can vary depending on the accuracy of angles and sides. The Law of Tangents, on the other hand, is more limited in its application, as it only applies to specific triangle scenarios.

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