If the sinø=7/12, what is cosø?

Answer:

8 18 16 27

Step-by-step explanation:

The answer and explanation to the hint is given below.

A word problem is a topic in mathematics which requires expressing a given statement or situation with a mathematical equation. The mathematical equation derived would be solved further so as to determine the unknown value of a variable.

In the given question, let the age of Marcus' little brother be represented by x. Thus since Marcus is 10 years older than his little brother, then we have to add 10 to his little brother's current age.

Thus,

Marcus age = his little brother's age+10

                    = x+10

So that, Marcus's age is expressed as; x+10.

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The recurrence interval for the second largest flood on the Bow River in 1932 is approximately 1.0106 years. The probability of a flood with a discharge of 1,520 m3/s occurring next year is roughly 98.95%. When examining the 100-year trend of peak discharges, excluding major floods, there is likely a general pattern of fluctuations but with overall stability in typical peak discharge values.

Using the provided data on the highest discharge per year on the Bow River at Calgary, Canada, we can calculate the recurrence interval (R) for specific flood magnitudes and determine the probability of such floods occurring in the future. Additionally, we can examine the 100-year trend for floods on the Bow River, excluding major floods, to identify the general trend of peak discharges over time.

1) Calculating the Recurrence Interval for the Second Largest Flood (1,520 m3/s in 1932):

To calculate the recurrence interval (R) for the second largest flood, we need to determine the rank of that flood. Since there are 95 data points in total, the rank of the second largest flood would be 94 (as the largest flood, in 2013, is excluded). Applying the formula R = (n + 1) / r, we have:

R = (95 + 1) / 94 = 1.0106 years

Therefore, the recurrence interval for the second largest flood (1,520 m3/s in 1932) is approximately 1.0106 years.

2) Probability of a Flood of 1,520 m3/s Occurring Next Year:

The probability of a flood of 1,520 m3/s happening next year can be calculated by taking the reciprocal of the recurrence interval for that flood. Using the previously calculated recurrence interval of 1.0106 years, we can determine the probability:

Probability = 1 / R = 1 / 1.0106 = 0.9895 or 98.95%

Thus, the probability of a flood of 1,520 m3/s occurring next year is approximately 98.95%.

3) Examination of the 100-Year Trend for Floods on the Bow River:

To analyze the 100-year trend for floods on the Bow River while excluding major floods, we focus on the peak discharges over time. Without considering the labeled major floods, we can observe the general trend of peak discharges.

Unfortunately, without specific data on the peak discharges for each year, we cannot provide a detailed analysis of the 100-year trend. However, by excluding major floods, it is likely that the general trend of peak discharges over time would show fluctuations and variations but with a relatively stable pattern. This implies that while individual flood events may vary, there might be an underlying consistency in terms of typical peak discharges over the 100-year period.

In summary, the recurrence interval for the second largest flood on the Bow River in 1932 is approximately 1.0106 years. The probability of a flood with a discharge of 1,520 m3/s occurring next year is roughly 98.95%. When examining the 100-year trend of peak discharges, excluding major floods, there is likely a general pattern of fluctuations but with overall stability in typical peak discharge values.

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The  difference between addition and subtraction of polynomials is that addition involves like terms  and subtraction  involves taking one polynomial away from another.

A polynomial is characterized as an expression that is composed of variables, exponents, and constants, that are combined utilizing numerical operations such as addition, subtraction, multiplication, and division (No division operation by a variable).In addition to polynomials, the like terms are included whereas, in subtraction, the like terms are subtracted. The addition of polynomials involves combining like terms to form a single expression, while subtraction involves taking one polynomial away from another. In addition, when subtracting polynomials, the sign of each term in the second polynomial needs to be changed (from positive to negative, or from negative to positive).

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Answer:

0.238

Step-by-step explanation:

Answer:

58.6 miles per hour

Step-by-step explanation:

205.1 miles /3.5 hours= 58.6 mph

Answer:

-5, -3

Step-by-step explanation:

True

In a symmetrically shaped distribution of scores, regardless of whether it has one mode or two modes, the mean value tends to be similar to the median value.

When a distribution is symmetric, it means that the data is evenly distributed around the central point, resulting in a bell-shaped curve. In such cases, the mean, median, and mode are typically close to each other.

The mean is the arithmetic average of all the scores in a distribution, while the median represents the middle value when the scores are arranged in ascending or descending order. In a symmetric distribution, the mean and median are located at the exact center of the distribution.

If the distribution has only one mode, it means that there is one prominent peak or high point in the data. In this case, the mean and median will coincide with the mode and will be similar.

If the distribution has two modes, it means that there are two prominent peaks in the data, but they are symmetrical around the center. Even though there are multiple modes, the mean and median will still be similar and tend to be located between the two modes.

In summary, in symmetrically shaped distributions, regardless of the presence of one or two modes, the mean and median values are expected to be close to each other.

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Answer:

4.5

Step-by-step explanation:

→ Set up the direct proportion equation

z = kx

→ Substitute in the values

12 = 3k

→ Divide both sides by 3 to isolate k

4 = k

→ Substitute the value of k back into the original direct proportion equation

z = 4x

→ Substitute the value of z in

18 = 4x

→ Divide both sides by 4 to isolate x

4.5 = x

Answer:

4.5

Step-by-step explanation:

The bank you should open a savings account with is Bank A and the bank, should you apply for your vehicle loan is Bank B. Thus the correct option is C.

What is Bank?

A bank is referred to as a financial institution that allows an individual to deposit and withdraw cash and allow them to borrow funds with a fixed interest rate for the purpose of investment.

In the given case, it is explained that Both opening a savings account and getting a car are decisions you have made. You want to borrow money for a car at a cheap interest rate and have the greatest interest rate savings account.

In order to avoid any burden you should make decisions with Bank B for the car loan and Bank A for the savings account and enjoy the assets for a lifetime with appropriate benefits.

Therefore, option C is appropriate.

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Critical angle for the total internal reflection icrit, β =  78.28⁰

Critical angle for the total internal reflection crit, α = 17,22⁰

We have the refractive index of core, \(n_c_o_r_e\) = 1.46

We have the refractive index of clad , \(n_c_l_a_d\) = 1.4

Critical angle can be defined as the incidence angle which results in the refraction angle being equal to  at that angle of incidence.

For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.

We know that the critical angle, θ is given by:

sinθ = \(\frac{n_c_l_a_d}{n_c_o_r_e}\)

sinθ = \(\frac{1.4}{1.46}\)

sinθ = 0.959 = sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

\(\frac{sin(90-\alpha )}{sin\alpha } = \frac{1}{n_c_o_r_e}\)

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17,22⁰

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Critical angle for total internal reflection icrit β = 78.28⁰

Critical angle for total internal reflection crit, α = 17.22⁰

The refractive index of the core is ncore = 1.46.

The refractive index of clad is nclad = 1.4.

We know that the critical angle, θ is given by:

sinθ = nclad/ ncore

sinθ = 1.4/1.46

sinθ = 0.959

sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

sin(90- α) / sin α = 1 / ncore

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17.22⁰

Critical angle for icrit β = 78.28⁰

Critical angle for crit α = 17.22⁰

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In statistical experiments, each time the experiment is repeated, a different outcome may occur. The correct answer is C.

Statistical experiments involve random processes, such as the random selection of individuals from a population, the random assignment of subjects to groups, or the random measurement of a variable.

The outcome of a statistical experiment is influenced by chance and is inherently uncertain, so it is not possible to guarantee that the same outcome will occur every time the experiment is repeated. Different outcomes may occur, even if the experimental conditions are kept constant, due to the random nature of the processes involved.

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Answer:

Can u put a pic 9f the question

If you are putting a quadratic function in the form of \(ax^2 + bx + c\) into the quadratic formula \(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\) and the b value in the function is negative, then you still write it as negative in the quadratic formula.

The reason is that the b term in the quadratic formula is being added or subtracted, depending on whether it is positive or negative.The quadratic formula is used to solve quadratic equations that are difficult to solve using factoring or other methods. The formula gives the values of x that are the roots of the quadratic equation.

The quadratic formula \(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\) can be used for any quadratic equation in the form of \(ax^2 + bx + c = 0\).

In the formula, a, b, and c are coefficients of the quadratic equation. The value of a cannot be zero, otherwise, the equation would not be quadratic.

The discriminant \(b^2-4ac\) determines the nature of the roots of the quadratic equation. If the discriminant is positive, then there are two real roots, if it is zero, then there is one real root, and if it is negative, then there are two complex roots.

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Answer:

C

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image P to original N

scale factor = \(\frac{10}{4}\) = \(\frac{5}{2}\)

-Answer: The scale factor that takes polygon N to polygon P is 2.5.

There are black, blue, and white marbles in a bag. The probability of choosing a black marble is 0.75.

Let's assume that there are 100 marbles in the bag. If the probability of choosing a black marble is 0.36, there are 36 black marbles in the bag. Therefore, there are 64 marbles of other colors (white and blue) in the bag.

Using the same method, we can say that the probability of choosing a white marble after drawing a black one is \(\frac{0.27}{0.36}= 0.75\)  (rounded to the nearest hundredth). It means that there are 75 white marbles for every 100 black marbles in the bag.

Therefore, the probability of the second marble being white if the first marble chosen is black is

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The -3 is not in the exponent

Explanation:

The parent function is \(f(x) = 2^x\). Plugging in x = 0 leads to y = 1. So the point (0,1) is on the f(x) curve. Going from (0,1) to (0,-2) is a vertical shift of 3 units downward. To represent this shift, we tack on a "-3" at the end of the f(x) function.

\(g(x) = f(x) - 3\\\\g(x) = 2^x - 3\)

You could look at other points as well, but I find working with x = 0 is easiest.

As a check, plugging x = 0 into g(x) leads to...

\(g(x) = 2^x - 3\\\\g(0) = 2^0 - 3\\\\g(0) = 1 - 3\\\\g(0) = -2\)

This confirms our answer.

The first expression  X (Y + Z) = X.Y + X.Z is distributive property of multiplication and the second expression X(Y.Z) = (X.Y)Z = X.Y.Z is associative property of multiplication.

According to the question,

We have the following two expressions:

X (Y + Z) = X.Y + X.Z

X(Y.Z) = (X.Y)Z = X.Y.Z

Now, the distributive property of multiplication states that the number outside the bracket is multiplied into each number within the bracket and the sign remains the same.

For example, 2(5+7) is 2*5+2*7.

The associative property of multiplication states that the result of the multiplication of numbers is same even when the bracket is changed from one number to another.

Hence, the first expression  X (Y + Z) = X.Y + X.Z is distributive property of multiplication and the second expression X(Y.Z) = (X.Y)Z = X.Y.Z is associative property of multiplication.

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According to the Boolean algebra, the first expression  X (Y + Z) = X.Y + X.Z uses distributive property of multiplication and

The second expression X(Y.Z) = (X.Y)Z = X.Y.Z uses the associative property of multiplication.

Boolean Algebra:

Basically, Boolean algebra is a branch of mathematics that deals with operations on logical values with binary variables.

And there are three properties in Boolean algebra.

They are, Commutative, associative, and distributive properties.

Given,

Sam’s teacher wrote two Boolean expressions on the whiteboard. Identify the names of the laws of these expressions.

Expression 1: X (Y + Z) = X.Y + X.Z

Expression 2: X(Y.Z) = (X.Y)Z = X.Y.Z

Here we need to find the name of the property used by the teacher on those two expression.

While we looking into the question,

We have the give the two expressions:

They are

=> X (Y + Z) = X.Y + X.Z

=> X(Y.Z) = (X.Y)Z = X.Y.Z

When we take the first expression,

X (Y + Z) = X.Y + X.Z

That states that the distributive property of multiplication is used here and the process of the distribution property is the number outside the bracket is multiplied into each number within the bracket and the sign remains the same.

Similarly, when we take the second expression

X(Y.Z) = (X.Y)Z = X.Y.Z

That uses the associative property of multiplication which is the result of the multiplication of numbers is same even when the bracket is changed from one number to another.

Therefore, the first expression  X (Y + Z) = X.Y + X.Z uses the distributive property of multiplication and the second expression X(Y.Z) = (X.Y)Z = X.Y.Z uses the associative property of multiplication.

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The correct process for finding 9'(9) involves using the chain rule of differentiation. Thus  the closest is probably (9) ,f + (8) ,f (g ') (9) 9(g '(9)) = 9'(3) &nd 9'(3) = f' (3) + 2f" (6).

We know that g(9) = f(8), and therefore we can write 9'(9) = f'(8) * g'(9). To find g'(9), we can use the values given in the table and the definition of an increasing function. Since g is increasing, we know that g(1) = f(3) and g(3) = f(9). Therefore, we can write:

g'(9) = (g(3) - g(1))/(3-1) = (f(9) - f(3))/2

To find f'(8), we can use the value given in the table. We know that f'(6) = 4, and therefore we can use the mean value theorem to find f'(8). Specifically, since f is differentiable and increasing, there exists some c between 6 and 8 such that:

f'(c) = (f(8) - f(6))/(8-6) = (g(1) - g(8))/2

Now we can use the given equation to find 9'(3):

9'(3) = f'(3) + f'(6) = 2f'(6)

And we can use the values we just found to find 9'(9):

9'(9) = f'(8) * g'(9) = (g(1) - g(8))/2 * (f(9) - f(3))/2

Note that none of the answer choices given match this process exactly, but the closest is probably (9) ,f + (8) ,f (g ') (9) 9(g '(9)) = 9'(3) &nd 9'(3) = f' (3) + 2f" (6).

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Answer:

EGQ ERKNG BQEG'QERJ

Step-by-step explanation:

Answer:

most I know I don't know and I don't want to know

The degrees of freedom used in the calculation of this confidence interval is 51.

Given that,

Confidence interval is (4, 10).

Population standard deviation, σ = 17.638

Sample size, n = 52

Degrees of freedom can be calculated using the formula,

Df = n - 1

Here, n = 52

So, Df = 52 - 1 = 51

Hence the degrees of freedom associated with the given situation is 51.

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Answer:

6 times

Step-by-step explanation:

\( \frac{1}{6} \times 36 = 6\)

Answer:B

Step-by-step explanation:

The expression 0.3d = 0.95 could be used to find the number of dimes he has.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have joe who has dime and nickels in his piggy bank totaling $1.45 the number of nickels. He has is 5 more than twice the number of dimes [d].

We can write the the number of nickels as -

[n] = 2d + 5

0.1d + 0.1(2d + 5) = 1.45

0.1d + 0.2d + 0.5 = 1.45

0.3d = 0.95

Therefore, the expression 0.3d = 0.95 could be used to find the number of dimes he has.

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Answer:

x=6,25

Step-by-step explanation:

8x=50

8÷8 which we will be only left with x and then 50÷8 will give us 6,25

An example is y = ax + b. yay

A sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%

To estimate the sample size, we can use the following formula:

n = (Z^2 * p * (1-p)) / E^2

where:

n = sample size

Z = the Z-score for a given confidence level (for 97% confidence, Z = 2.33)

p = the proportion in the pilot sample (0.641)

E = the maximum allowed error of estimation (0.047)

Plugging in the values, we get:

n = (2.33^2 * 0.641 * (1 - 0.641)) / 0.047^2

n = (5.3929 * 0.359) / 0.00222009

n = 1.928 / 0.00222009

n = 869.75

Since the sample size must be a whole number, we round up to the nearest whole number.

n = 870

Therefore, a sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%

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The specific number within the range of 33 to 40 would depend on my assessment of the situation and my intuition at the time of playing the game

In this guessing game, the goal is to choose a number that is closest to 2/3 of the average of the guesses. To determine the optimal strategy, we need to consider the likely approach of the inexperienced player.

Given that the inexperienced player may not be aware of the optimal strategy, they might choose their number based on a random guess or by focusing on their intuition rather than employing any specific mathematical reasoning.

To maximize my chances of winning, I would consider the average behavior of inexperienced players and make an educated guess. Based on statistical analysis, inexperienced players often tend to choose numbers towards the middle of the given range, such as around 50. To counter this, I would choose a number that is slightly below the midpoint, but still close enough to benefit from the averaging process.

Considering these factors, I would choose a number around 33 to 40. This range is likely to be below the average of the inexperienced player's guess, but still close enough to the 2/3 threshold to increase my chances of winning. By strategically positioning my guess in this manner, I aim to take advantage of the likely choices made by the inexperienced player.

Ultimately, the specific number within the range of 33 to 40 would depend on my assessment of the situation and my intuition at the time of playing the game.

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