what is Probability?​

The total amount that would be found in the account after 4 years, would be $ 641. 69

The total amount after 4 years in Arik's account can be found by the formula :

= A = Amount invested x ( 1 + r /n )ⁿ

The variables are:

Amount invested = $ 500

r = 6.25% = 0. 0625

n = 12

t = 4 years

The total amount is then :

A = 500 x ( 1 + 0. 0625 / 12 ) ^ ⁽¹² ˣ ⁴ ⁾

A = $ 641. 69

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Step-by-step explanation:

grab two points from the line then subtract x with x and y with y and you will get a fraction which will be mx and -7 will be your b

y=(the answer you got)*mx*-7

this is how you sub then

1-1

2-3  and it will look like a fraction

i explained it better for you but you have to do the work so you can better understand it

(you can always find b by looking for the point on the y-axis the line crosses)

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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The value of x is equivalent to k in the equations x + y = k and x-k = y.

How do equations work?

A set of variables called an equation is one in which two mathematical expressions are equivalent to one another.

the equations provided are,

x + y = k (1) (1)

thus, x-k = y (2)

Substitute the value of y in equation (2) for equation (1)

2x=2k

⇒x=k

As a result, x has the value k.

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A multiplying polynomials calculator is a tool used to multiply two or more polynomials together.

A multiplying polynomials calculator is a tool used to multiply two or more polynomials together. It can be helpful for simplifying algebraic expressions, solving equations, and performing various calculations in mathematics and engineering.

The calculator takes the coefficients of each polynomial as input and uses the distributive property to multiply the terms of each polynomial together. It then combines like terms and arranges the result in descending order of degrees. Multiplying polynomials can be a tedious and error-prone process, especially for large polynomials, so using a calculator can save time and reduce the chances of errors. The multiplying polynomials calculator is commonly used by students, teachers, engineers, and anyone working with algebraic expressions.

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In a RAID-5 configuration with 7 SSDs, the system can tolerate the failure of one SSD without losing any data. The probability that any given SSD fails is 1x10^(-8).

To calculate the probability of data loss due to SSD failures, we need to consider the probability of multiple SSD failures that would result in data loss. Since RAID-5 can tolerate the failure of one SSD, we need to calculate the probability of two or more SSDs failing.

The probability of two or more SSDs failing can be calculated using the binomial distribution. The probability of k failures in a system of n SSDs, each with a failure probability p, is given by the formula:

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

In this case, we want to calculate the probability of k >= 2 failures out of 7 SSDs. Therefore, we need to sum up the probabilities for k = 2, 3, 4, ..., 7.

P(loss) = P(2) + P(3) + P(4) + P(5) + P(6) + P(7)

Using this formula and plugging in the values, we can calculate the probability of data loss due to SSD failures.

P(loss) = C(7, 2) * (1x10^(-8))^2 * (1 - 1x10^(-8))^(7 - 2) + C(7, 3) * (1x10^(-8))^3 * (1 - 1x10^(-8))^(7 - 3) + ... + C(7, 7) * (1x10^(-8))^7 * (1 - 1x10^(-8))^(7 - 7)

Calculating this sum will give us the probability of data loss due to SSD failures in the RAID-5 configuration.

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x = 1

Hi there !

3 + 3x - x + 2 = 3x + 4 | -3x

3 - x + 2 = 4

3 + 2 - 4 = x

x = 1

Good luck !

Answer:

45°

Step-by-step explanation:

sin∠U = 5√2 / 10 = √2/2

m∠U = sin⁻¹(√2/2) = 45°

Answer:

My best guess would probably be B because a point on the graph is negative. Math isnt't my strongest subject

Step-by-step explanation:

Answer: x=-3

Step-by-step explanation:

2(x)-39=5(x+2x)

2x-39=5(3x)

2x-39=15x

-39=13x

-39/13=-3

Answer: 31, 35, 39

Step-by-step explanation:

Answer:

Just add 4 to each number and do it how ever long it says

Step-by-step explanation:

Answer:54 is the54 d

Step-by-step explanation:

no sorry

Answer:

\(\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta} = \frac{1}{\sin\theta} = \csc\theta\)

Step-by-step explanation:

We have the expression:

\(\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta}\)

And we want to write the expression in terms of sine and cosine and simplify.

Thus, let tanθ = sinθ / cosθ and secθ = 1 / cosθ. Substitute:

\(=\displaystyle \frac{\dfrac{\sin\theta}{\cos\theta}}{\dfrac{1}{\cos\theta}-\cos\theta}\)

Multiply both layers by cosθ:

\(=\displaystyle \frac{\left(\dfrac{\sin\theta}{\cos\theta}\right)\cdot \cos\theta}{\left(\dfrac{1}{\cos\theta}-\cos\theta\right)\cdot \cos\theta}\)

Distribute:

\(\displaystyle =\frac{\sin\theta}{1-\cos^2\theta}\)

Recall from the Pythagorean Theorem that sin²θ + cos²θ = 1. Hence, 1 - cos²θ = sin²θ. Substitute and simplify:

\(\displaystyle =\frac{\sin\theta}{\sin^2\theta} \\ \\ =\frac{1}{\sin\theta}\)

We can convert this to cosecant if we wish.

The probability that the sample mean will be between 295 and 305 can be determined using the Central Limit Theorem and the properties of the normal distribution.

According to the Central Limit Theorem, for a large sample size (n ≥ 30), the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. In this case, since the sample size is 64, we can assume that the sample mean will follow a normal distribution.

To find the probability that the sample mean will be between 295 and 305, we need to standardize the sample mean using the formula z = (x - μ) / (σ / sqrt(n)), where x is the given range (295 to 305), μ is the population mean (300), σ is the population standard deviation (12), and n is the sample size (64).

By calculating the z-scores for the lower and upper limits of the range and referring to the standard normal distribution table, we can find the corresponding probabilities. The probability can be calculated by subtracting the cumulative probability corresponding to the lower limit from the cumulative probability corresponding to the upper limit.

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The mean fluoride concentration in the sample is approximately 0.6024 mg/l, and the 90% confidence interval for the average fluoride concentration is (0.5498, 0.6549) mg/l.

To determine the mean and 90% confidence interval for the average fluoride concentration in the sample, we can calculate the sample mean and the margin of error.

First, calculate the sample mean:

Mean = (0.611 + 0.591 + 0.611 + 0.589 + 0.611) / 5 = 0.6024 mg/l

Next, calculate the standard deviation of the sample:

Standard Deviation = sqrt(((0.611-0.6024)^2 + (0.591-0.6024)^2 + (0.611-0.6024)^2 + (0.589-0.6024)^2 + (0.611-0.6024)^2) / (5-1))

= sqrt(0.0002744 + 0.0006272 + 0.0002744 + 0.0007928 + 0.0002744)

= sqrt(0.0022432)

= 0.0473 mg/l (approximately)

Next, calculate the margin of error using the formula:

Margin of Error = (Critical Value) * (Standard Deviation / sqrt(n))

Since we want a 90% confidence interval, the critical value can be obtained from the t-distribution table for n-1 degrees of freedom. For a sample size of 5 and a 90% confidence level, the critical value is approximately 2.776.

Margin of Error = 2.776 * (0.0473 / sqrt(5))

= 0.0526 mg/l (approximately)

Finally, calculate the confidence interval:

Confidence Interval = (Mean - Margin of Error, Mean + Margin of Error)

= (0.6024 - 0.0526, 0.6024 + 0.0526)

= (0.5498, 0.6549)

Therefore, the mean fluoride concentration in the sample is approximately 0.6024 mg/l, and the 90% confidence interval for the average fluoride concentration is (0.5498, 0.6549) mg/l.

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Answer:

The velocity v(t) of the robot at time t can be determined by taking the derivative of the position function s(t). Therefore, v(t) = 18t - 90.

To find the total distance traveled by the robot between t = 0 and t = 9, we need to calculate the definite integral of the absolute value of the velocity function from t = 0 to t = 9. This is because the absolute value of velocity gives us the speed, and integrating the speed over the given time interval gives us the total distance traveled.

Integrating the velocity function v(t) = 18t - 90 from t = 0 to t = 9, we get:

∫(0 to 9) |18t - 90| dt

To solve this integral, we split it into two parts based on the regions where the integrand changes sign:

∫(0 to 9) (90 - 18t) dt + ∫(0 to 9) (18t - 90) dt

Evaluating the integrals, we get:

[90t - 9t^2/2] from 0 to 9 + [9t^2/2 - 90t] from 0 to 9

Plugging in the limits, we have:

[90(9) - 9(9^2)/2] + [9(9^2)/2 - 90(9)] = 405

Therefore, the total distance traveled by the robot between t = 0 and t = 9 is 405 units.

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The velocity function v(t) is found by taking the derivative of the position function s(t), resulting in v(t)=18t-90. To find the total distance traveled by the robot from t=0 to t=9, calculate the definite integral of the absolute value of the velocity function over this interval.

The position, s(t), of a robot moving along a track at time t is given by . To find the velocity of the robot at any time t, we need to derive the position function with respect to t, giving us

which represents the velocity function. Now, to find the total distance travelled by the robot between t=0 to t=9, we have to find the definite integral of the absolute value of the velocity function from 0 to 9. The absolute value is considered because we want total distance covered, not just displacement. This is an example of applying derivative and integral principles in a real-life scenario.

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Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

Here,

Given: Total number of freshman =500

mean =75 and standard deviation =7

a) the percentage of scores that fell between 68 and 82

340 is the number of freshman whose  scores that fell between 68 and 82

thus,

percentage = 340 /500 * 100

=> percentage = 68%

b)the percentage of scores that fell between 61 and 75

237 is the number of freshman whose  scores that fell between 61 and 75

thus,

percentage = 237/500 * 100

=> percentage = 47.4%

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

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Answer: 2+2

Step-by-step explanation: easy math

Answer:

Neither of the statements are true.

i. A large p-value indicates weak evidence against the null hypothesis. A small p-value (typically less than 0.05) is strong evidence against the null hypothesis.

ii. We cannot set a higher standard of proof by choosing a lower significance level (alpha) because doing so would increase the likelihood of making a Type II error, which is failing to reject a false null hypothesis. The level of significance should be chosen based on the goals of the study and the consequences of making a Type I or Type II error.

Answer: Three terms

Step-by-step explanation:

This is a trinomial, since there are three numbers. Since it is a trinomial, there are three terms.

Answer:

The correct answer is 4.

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Answer:

Step-by-step explanation:

36=4*9=2*2*3*3=2^2*3^2

72=8*9=4*2**3*3=2*2*2*3*3=2^3*3^2

60=4*15=2*2*3*5=2^2*3*5

If the  temperature was measured with a degree of accuracy to the nearest 1°C, and recorded as 45°C then the percentage of error is 1.11%.

To calculate the percentage of error, we need to compare the measured value to the actual or expected value.

if we assume that the recorded value of 45°C is close to the actual value, we can calculate the percentage of error relative to this recorded value.

To calculate the percentage of error, we use the formula:

Percentage of Error = (Error / Recorded Value) × 100%

Since the temperature was measured to the nearest 1°C, the possible error can be up to ±0.5°C.

Therefore, the error would be 0.5°C in this case.

Using the recorded value of 45°C, the percentage of error can be calculated as:

Percentage of Error = (0.5°C / 45°C) × 100%

Percentage of Error = 1.11%

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Answer:

x= 4/3 ; x= -2

Step-by-step explanation:

Your quadratic equation: 3x^2+2x-8 = 0

This is in ax^2+bx+c form which requires you to solve by many methods.

**BEST WAY to solve this is the Quadratic formula. You can factor, but it will take longer.**

Values of r + s and rs are -2/3 and -8/9, respectively.

To find the values of r and s, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

For our equation 3x² + 2x - 8 = 0, we have a = 3, b = 2, and c = -8.

Puting values into the formula, we get:

r, s = (-2 ± √(2² - 4(3)(-8))) / 2(3)
r, s = (-2 ± √100) / 6
r, s = (-2 ± 10) / 6
r = 2/3 or s = -4/3
r + s = (2/3) + (-4/3) = -2/3
rs = (2/3)(-4/3) = -8/9

Therefore, the values of r + s and rs are -2/3 and -8/9, respectively.

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When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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The population of zombies at each level in the game increases by 5% from the previous level's population, starting with an initial population of 50,000.

Let's calculate the population of zombies at each level based on the given information.

At level one, the population of zombies is 50,000.

To find the population at level two, we'll apply the growth rate of 5% to the previous level's population:

Population at level two = 50,000 + (50,000 * 0.05)

= 50,000 + 2,500

= 52,500

At level three:

Population at level three = 52,500 + (52,500 * 0.05)

= 52,500 + 2,625

= 55,125

Continuing this pattern, we can calculate the population at each subsequent level:

Level four: 55,125 + (55,125 * 0.05) = 57,881.25

Level five: 57,881.25 + (57,881.25 * 0.05) = 60,775.31

Level six: 60,775.31 + (60,775.31 * 0.05) = 63,814.07

Therefore,The population of zombies at each level in the game increases by 5% from the previous level's population, starting with an initial population of 50,000.

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I'm not 100% sure but I think it's the last two choices

sorry if its wrong

Answer:

a(45) =-209

Step-by-step explanation:

a(n) = a +(n-1)d

d=-6

we have to get a1

By using:

a(10) = a1 +(10-1)-6=1

a(10) = a1 +(9)-6 =1

          a1  =1+54=55

So:a(45) = 55 +(45-1)-6=-209

hope this helps

Answer:

x=10, y=-3

Step-by-step explanation:

3x+y=27

-3x+4y=-42

Add the two equations together:

5y=-15

Divide both sides by 5:

y=-3

Plug this back into one of the original equations to solve for x:

3x-3=27

3x=30

x=10

Hope this helps!

R_n is a normal subgroup of D_n, known as the subgroup of rotations.

To prove that the subgroup R_n = {I, r, r^2, r^3, ..., r^(n-1)} generated by r is a normal subgroup of D_n, the dihedral group of order 2n, we need to show that for any g in D_n and r^k in R_n, the conjugate g(r^k)g^(-1) is also in R_n.

Let's consider an arbitrary element g in D_n and an arbitrary power of r, r^k in R_n. We can express g as a product of a reflection s and a rotation r^j, where j is an integer and 0 ≤ j ≤ n-1.

Then, we have:

\(g(r^k)g^(-1) = (s r^j) (r^k) (s r^j)^(-1)\)

Expanding this expression, we get:

\(= (s r^j) (r^k) (r^(-j) s)\)

Using the fact that r and s commute with each other, we can rearrange the terms:

\(= s (r^j r^k r^(-j)) s\)

Since r is a rotation and r^k is a power of r, we have:

\(r^j r^k r^(-j) = r^(j+k-j) = r^k\)

Therefore, we obtain:

\(g(r^k)g^(-1) = s (r^k) s\)

We know that s^2 = I, so s is its own inverse. Therefore:

\(s (r^k) s = r^k\)

Hence, we have shown that for any g in D_n and r^k in R_n, the conjugate g(r^k)g^(-1) is also in R_n.

Since R_n satisfies the condition for normality, we conclude that R_n is a normal subgroup of D_n, known as the subgroup of rotations.

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