If a = 5-2√6, then find the value of

:(i)√a−1/√a

(ii)a2+1/a2

Answer:

146⁰

Step-by-step explanation:

You simply add the measurements of the two angles together.

59⁰ + 87⁰ = 146⁰

The magnitude of the resultant force is 25.5 N, and the direction is approximately 49.4 degrees.

To find the magnitude and direction of the resultant force, we can use vector addition. We'll break down the given forces into their horizontal and vertical components.

Force 1:

Magnitude: 15 N

Angle: 30 degrees

Force 2:

Magnitude: 25 N

Angle: 60 degrees

First, let's calculate the horizontal and vertical components of each force using trigonometry:

Force 1 horizontal component: 15 N × cos(30 degrees)

Force 1 vertical component: 15 N × sin(30 degrees)

Force 2 horizontal component: 25 N × cos(60 degrees)

Force 2 vertical component: 25 N × sin(60 degrees)

Force 1 horizontal component = 15 N × √3/2 = 12.99 N

Force 1 vertical component = 15 N × 1/2 = 7.5 N

Force 2 horizontal component = 25 N × 1/2 = 12.5 N

Force 2 vertical component = 25 N × √3/2 = 21.65 N

Now, let's calculate the horizontal and vertical components of the resultant force by summing up the respective components:

Resultant horizontal component = Force 1 horizontal component + Force 2 horizontal component

= 12.99 N + 12.5 N

= 25.49 N

Resultant vertical component = Force 1 vertical component + Force 2 vertical component

= 7.5 N + 21.65 N

= 29.15 N

To find the magnitude of the resultant force, we can use the Pythagorean theorem:

Magnitude of the resultant force = √(Resultant horizontal component^2 + Resultant vertical component^2)

= √(\(25.49 N^2 + 29.15 N^2\))

= √(\(650.1406 N^2\))

= 25.5 N (rounded to one decimal place

The magnitude of the resultant force is approximately 25.5 N.

To find the direction of the resultant force, we can use trigonometry. The angle can be determined using the arctan function:

Direction of the resultant force = arctan(Resultant vertical component / Resultant horizontal component)

= arctan(29.15 N / 25.49 N)

= 49.4 degrees (rounded to one decimal place)

Therefore, the magnitude of the resultant force is 25.5 N, and the direction is approximately 49.4 degrees.

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Answer:

y = 1/2x + 2

Comparison: The black and blue line haver the same y-intercept, however they have different slopes. The slope of the black line is 2/3 and the slope of the blue line is 1/2.

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Answer:

241.9026

Step-by-step explanation:

2*pi*r

Answer:

241.9 cm

Step-by-step explanation:

circumference= \(\pi\)d

circumference= \(\pi\)(77)

circumference= 241.9 cm

Answer:

It was A 4/7

Step-by-step explanation:

Matrix factorization is a method that reduces the dimensionality of a rating matrix, revealing latent factors and enabling clustering in recommendation systems and data analysis.

Matrix factorization is a popular technique used in recommendation systems and data analysis. Its basic intuition lies in decomposing a large rating matrix into lower-dimensional matrices, allowing for better understanding and utilization of the underlying data.

One key intuition is that matrix factorization provides a way to represent users and items in a shared low-dimensional space. By factorizing the rating matrix, we can identify latent factors or features that capture the preferences and characteristics of both users and items. These factors can be computed from the rating matrix and enable a compact representation of the data.

Another insight is that matrix factorization allows for clustering of users and items. By factoring the user and item matrices, we can partition them into clusters based on similar characteristics. This clustering enables us to treat users or items within the same cluster identically, reducing computational complexity and making recommendations more efficient by retaining representative users or items in each cluster.

Furthermore, matrix factorization reveals that content filtering and collaborative filtering are two different factorizations of the same rating matrix. Content filtering focuses on the attributes of items, while collaborative filtering analyzes user-item interactions. By factorizing the matrix, we can bridge the gap between these two approaches and gain a more comprehensive understanding of the data.

Therefore, the basic intuition behind matrix factorization lies in finding a lower-dimensional representation of the rating matrix, identifying latent factors, enabling clustering of users and items, and providing a shared space to describe them. This technique proves valuable in recommendation systems, data analysis, and uncovering hidden patterns within complex datasets.

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Answer:

no

Step-by-step explanation:

2 points have the same "x"

Answer:

I would think 10,700

Step-by-step explanation:

21.25 + 17.50 + 41.50 + 26.75 = 107

107 x 100 = 10,700

(I'm so sorry if I'm wrong)

The height of the pole is approximately 64 feet when rounded to the nearest tenth.

To determine the height of the pole, we can use the concept of a right triangle formed by the pole and the two cables. Let's denote the height of the pole as 'h'.

In the given scenario, one cable is 48 feet long and the other is 63 feet long. The ground distance between them is 80 feet. We can visualize this as follows:

      A

     /|

    / |

 h /  | 63

  /   |

 /    |

/     |

/______C

  48    B

Here, A represents the top of the pole, B represents the point where the 48-foot cable touches the ground, and C represents the point where the 63-foot cable touches the ground.

Using the Pythagorean theorem, we can establish the following relationship:

\(AB^2 + BC^2 = AC^2\)

Substituting the given values, we get:

\(h^2 + 48^2 = 80^2\\h^2 + 2304 = 6400\\h^2 = 6400 - 2304\\h^2 = 4096\)

Taking the square root of both sides, we find:

h =\(\sqrt{4096}\)

h ≈ 64

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Answer:

Gary worked 41 and a half hours

Step-by-step explanation:

$310.42 divided by $7.48 per hour = 41.5 hours

The PMF of the random variables Y = max{0, X} is \(\frac{|a|+1}{b-a+1}\)

and W = min{0, X} is \(\frac{b+1}{b-a+1}\)

Assume that X be the discrete random variable with uniform distribution over the range [a, b].

There, the probability density of the random variable X is expressed as follows;

\(f_X(x) = \frac{1}{b-a} , a < x < b\\\)

The comulative distribution function of the random variable X is defined as,

\(f_X(x)=P(X\leq x)\\\\=\int\limits^x_a {\frac{1}{b-a} } \, dx =\frac{x}{b-a} -\frac{a}{b-a} =\frac{x-a}{b-a}\)

The probability mass function of the random variable

Max{0, X} is

Max{0, X } = \(\left \{ {{X, \\if X\geq 0} \atop {0, ifX\leq 0}} \right.\)

\(P(X\leq 0)=\frac{|a|+1}{b-a+1}\)

The probability mass function of the random variable

Max{0, X} is

\(P(X\geq 0)=\frac{b+1}{b-a+1}\)

Therefore, A probability mass function of the random variable \(\frac{|a|+1}{b-a+1}\)

and W = min{0, X} is \(\frac{b+1}{b-a+1}\).

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Incomplete Question:

Let X be a discrete random variable that is uniformly distributed over the set of integers in the range [a, b], where a and b are integers with a < 0 < b. Find the PMF of the random variables Y = max{0, X} and W = min{0, X}.

If the cost of one paperback book is less than $1, he would receive even more change.

To solve this problem, we need to know the cost of one paperback book. Unfortunately, that information is missing from the question. Without it, we cannot determine the total cost of the 5 paperback books and therefore cannot calculate Prakash's change.

However, we can make an educated guess based on the fact that the question mentions both paperback and hardcover books. Typically, hardcover books are more expensive than paperbacks, so we can assume that the cost of one paperback book is less than the cost of one hardcover book.

Assuming that each hardcover book costs $10, the total cost of 3 hardcover books would be $30. If Prakash gives the clerk $20 bills, he would pay $60 in total. If we subtract the cost of the 3 hardcover books ($30) from the total amount paid ($60), we are left with $30.

This is the maximum amount of change Prakash could receive if each paperback book costs $1.

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Answer:

The first group's success rate adheres to the Binomial law B(5, 0.5).

The second group comes after B(5, 0.6). We look in the table of binomial probabilities to discover:

k=0 k=1 k=2 k=3 k=4 k=5

p=0.5 0.0312 0.1562 0.3125 0.3125 0.1562 0.0312

p=0.6 0.0102 0.0768 0.2304 0.3456 0.2592 0.0778

Given is the likelihood that the first group will achieve at least as many successes as the second group,

0.03120 + 0.0102 + 0.1562 + (0.0102 + 0.0768) + ... + 0.0312 × 1.

The binomial distribution with parameters n and p in probability theory and statistics is the discrete probability distribution of the number of successes in a series of n independent experiments, each of which asks a yes-or-no question and has a unique Boolean value: success (with probability p) or failure. A single trial is also referred to as a Bernoulli experiment or trial, and a single trial's series of results is referred to as a Bernoulli process.

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The critical value z a/2 that corresponds to a 97% level of confidence is 1.96, and the critical value z a/2 that corresponds to an 80% level of confidence is 1.28.

In statistical hypothesis testing, the critical value is the point beyond which we reject the null hypothesis. To find the critical values, we need to use the standard normal distribution table or calculator.

For a 97% level of confidence, the significance level (α) is 0.03, and the critical value can be found by dividing α by 2 to get 0.015 (since it's a two-tailed test), and then finding the corresponding z-value using the standard normal distribution table or calculator. The z-value is 1.96.

Similarly, for an 80% level of confidence, the significance level (α) is 0.20, and the critical value can be found by dividing α by 2 to get 0.10 (since it's a two-tailed test), and then finding the corresponding z-value using the standard normal distribution table or calculator. The z-value is 1.28.

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ANSWER :

The answer is B. y = (x + 4)^2 + 9

EXPLANATION :

From the problem, we have :

Group the terms in which the constant term and the terms with variables are separated.

add and subtract a variable m to the parenthesis to maintain equivalency.

Calculate the value of m using b^2/4a^2 with a = 1 and b = 8

Then :

The first parenthesis will be a perfect square trinomial.

Factor and simplify :

the probability that at least 370 voted in their most recent local election is approximately 0.9636.

To find the probability that at least 370 voted in their most recent local election, find P(X ≥ 370). The normal approximation to the binomial distribution with parameters p and n is

P(X≥r)=1-Φ(r-µ/σ)P(X≥370)

=1-Φ(369.5-375/√93.75)P(X≥370)

=1-Φ(-5.5/3.063)P(X≥370)

=1-Φ(-1.795)

By standard normal distribution table,

Φ(-1.795) = 0.0364

Therefore, P(X≥370) = 1 - 0.0364= 0.9636

Hence, the probability that at least 370 voted in their most recent local election is approximately 0.9636.

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The critical values for the 95% confidence interval for the population standard deviation with n=15 and α=0.05 are 6.262 and 26.119

We must utilise the chi-square distribution with (n-1) degrees of freedom to establish the crucial values for the confidence interval for the population standard deviation.

With n=15 and α=0.05, we can find the critical values using a chi-square table or a calculator. For a 95% confidence interval (α=0.05), the critical values are:

Lower critical value = chi-square value at (n-1) degrees of freedom and

α/2 = chi-square value at 14 degrees of freedom and 0.025

= 6.262

Upper critical value = chi-square value at (n-1) degrees of freedom and

1-α/2 = chi-square value at 14 degrees of freedom and 0.975

= 26.119

Therefore, the critical values for the 95% confidence interval for the population standard deviation with n=15 and α=0.05 are 6.262 and 26.119 (rounded to three decimal places).

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Complete question is below

determine the critical values for the confidence interval for the population standard deviation from the given values. round your answers to three decimal places. n=15 and α=0.05.

The equation u × v = |u| |v| sinθ states that the cross product of u and v is equal to the area of the parallelogram formed by u and v, which is |u| |v| sinθ.

The equation u × v = |u| |v| sinθ represents the cross product of two vectors u and v, where θ is the angle between them. The cross product results in a vector that is perpendicular to both u and v, with a magnitude equal to the product of their magnitudes and the sine of the angle between them.

Geometrically, the magnitude of the cross product |u × v| represents the area of the parallelogram formed by u and v. The magnitudes of u and v, |u| and |v|, represent the lengths of the vectors. Therefore, the right-hand side of the equation |u| |v| sinθ represents the area of the parallelogram as well.

Hence, The equation u × v = |u| |v| sinθ states that the cross product of u and v is equal to the area of the parallelogram formed by u and v, which is |u| |v| sinθ.

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Only (d) 1 equation can you write to represent a single line using a point-slope equations

From the question, we have the following parameters that can be used in our computation:

Equation = Linear equation

A linear equation can only be represented with one equation

When it is represented with multiple equations, the equations are equivalent equations

This means that the equations can be converted to one another

Hence, the solution is (d) 1 equation

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Answer:

188

Step-by-step explanation:

\(\sqrt{188}*\sqrt{188}=\sqrt{188*188}=\sqrt{188^2}=188\)

Step-by-step explanation:

Hope it will help you a lot.

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

Answer

FALSE

Step-by-step explanation:

Answer:

(5, -7).

Step-by-step explanation:

Solution is the point of intersection.

(5, -7).

Answer:

Step-by-step explanation:

C the probability that a customer buys a hat given that the customer has bought a sweater.

Answer:

True

Step-by-step explanation:

2.5 times 2 = 5

So, the answer is true.

The probability that a given class period runs between 50.5 and 51.25 minutes is 15%.

Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make probability-based predictions, and also probability has extensive applications in this new area of artificial intelligence.

The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes. Also, the favorable number of outcomes cannot be negative.

\(P(50.5 < = X < = 51.25) =\frac{51.25-50.5}{54-49 } = \frac{0.75}{5} = 0.15\)

P = 0.15 means that the probability is 15%.

Thus, the probability that a given class period runs between 50.5 and 51.25 minutes is 15%.

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The area of a two-dimensional cross-section depends on the shape it represents, such as a square, rectangle, triangle, circle, or any other polygon. Each shape has its own formula for calculating its area.

In order to determine the area of the cross-section, we need additional information such as the shape of the cross-section, its dimensions, or any other relevant details. Without this information, it is not possible to calculate the area. Please provide more details or a specific shape or scenario so that an accurate answer can be generated. Once the shape is specified, the appropriate formula can be applied to calculate the area.

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