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Answer: Yes, 59 is a prime number

Step-by-step explanation: 59 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 59 are 1 and 59.

Yes, 59 is a prime number.

What is a prime number?

Any natural number greater than 1 that is not the sum of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than one that is not prime.

In other terms, prime numbers are positive integers greater than one that only has the number itself and 1 as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are just a few examples. Never forget that 1 is neither a prime number nor a composite. Apart from 1, the other numbers can all be categorised as prime and composite numbers. Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd.

The number in question, which is 59,  has only two factors: 1 and 59.

Therefore 59 is a prime number.

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Answer:

-3 > P

Step-by-step explanation:

1 > 3P + 10​

Subtract 10 from each side

1-10 > 3P + 10-10​

-9 > 3P

Divide each side by 3

-9/3 > 3P/3

-3 > P

Answer:

78 degrees

Step-by-step explanation:

All inner angles of a triangle make a sum of 180 degrees. Given 41 and 61 add up to 102, that leaves 78 degrees left to make 180

Answer: 8 + 2.25x = 35

Step-by-step explanation: When you bought the tree it was already 8 feet tall. each year you have it, which is what x represents after putting 2.25 in front of x. it would somehow equal 35. 1st year 2.25 2nd year 4.5 3rd year 6.75 4th year 9 so on and so forth.

Since the proposed side length of the square is between 6 and 7, we can assume that it is 6.5 hence, the lengths will be d = 6.5 and c = 9.19.

Here is what we were given:

Side length of square = 6 > x <7

A convenient assumption for this is 6.5

We also know that d and c and the base of two right triangles. where their hypotheses' are equal to the side lenght of the square = 6.5

we also know that the in between the line formed by D and C is a 90 degree angle.

Hence the sum of the other angle will be 45 degrees each.

This is  based on sum of angles in a triangle.

Hence,

c = b /sin(β)

= 6.5/sin (45)

= 6.5/0.70710678118

 c = 9.19

d = √c² - b²

 = √(9.19238815542512² - 6.52²)

= √42.25

d = 6.5

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Answer:

48x+8y

Step-by-step explanation:

Distribute the 8, 8 times 6x is 48x, and 8 times y is 8y

The measure of angle X is 96°, and its exterior angle measures 84° in triangle XYZ.

In triangle XYZ, the sum of the measures of the interior angles is always 180°. We are given that the measure of angle X is (7g 12)°. Let's denote the measure of angle X as α.

Since the exterior angle to angle X measures (2g 60)°, we know that the exterior angle and the interior angle are supplementary. Therefore, the exterior angle to angle X is (180° - α).

Setting up an equation, we have:

α + (180° - α) = (7g 12)° + (2g 60)°.

Simplifying the equation:

180° = 9g 72°.

Subtracting 72° from both sides:

108° = 9g.

Dividing both sides by 9:

g = 12°.

Now that we have determined the value of g, we can substitute it back into the expressions for angle X and its exterior angle to find their measures.

Angle X: (7g 12)° = (7 * 12 + 12)° = 96°.

Exterior angle to angle X: (2g 60)° = (2 * 12 + 60)° = 84°.

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Step-by-step explanation:

multiply and the both number and divide by bytwo

3/12, or 1/4 is the probability that it is blue.

What is probability?

Probability = number of successes / total number of outcomes

Total marbels in bag = 4+ 3 + 5 = 12  

A total of 12 marbles are in the bag.

3 blue marbles are in the bag.

Therefore, the probability of picking a blue is 3/12, or 1/4.

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The graph shown is a vertical compression and reflection of the graph of y = sin x with an amplitude of 3, period of 2π, phase shift of π/2 units to the right, and a vertical shift of 0. The equation of the graph shown is y = 3 sin (2x - π).

The graph shown appears to be a vertical compression and reflection of the graph of y = sin x. The point indicated on the graph is (π/2, 0), which is the point of maximum compression and reflection for the graph of y = sin x.

To write the equation of the graph shown, we need to determine the amplitude, period, phase shift, and vertical shift of the function.

Amplitude: The amplitude of the graph shown is 3.

Period: The period of the graph shown appears to be 2π.

Phase shift: The phase shift of the graph shown appears to be π/2 units to the right.

Vertical shift: The vertical shift of the graph shown is 0.

Therefore, the equation of the graph shown is:

y = 3 sin (2x - pi)

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--The given question is incomplete, the complete question is given below " 9. The graph shown is a transformation graph of y=sinx. The pointed indicated has coordinates (π/2,0). The equation of the graph shown is y= "--

The cross-sectional area of a sphere that passes through its center is a circle with a diameter equal to the diameter of the sphere. In this case, the diameter of the sphere is 6.69 meters * 2 = 13.38 meters.

The formula for the area of a circle is: A = π * r^2, where r is the radius.

Therefore, the cross-sectional area of the sphere that passes through its center is: A = π * (13.38/2)^2 = π * (6.69)^2 = 136.57 square meters.

A sphere is a three-dimensional shape that has a uniform, rounded surface that is symmetrical in all directions. When you cut a sphere through its center, you get a cross-sectional area that is a circle.

This is because a sphere can be thought of as a set of circular cross-sections that are concentric with each other and with the center of the sphere.

The cross-sectional area of the sphere that passes through its center is called the central cross-section of the sphere. It has the same diameter as the sphere itself and its area can be calculated using the formula for the area of a circle: A = π * r^2, where r is the radius of the circle.

In this case, the sphere has a radius of 6.69 meters, which means that its diameter is 6.69 * 2 = 13.38 meters.

The radius of the central cross-section of the sphere is half of the diameter, which is 6.69 meters. Therefore, the area of the central cross-section of the sphere is: A = π * (6.69)^2 = 136.57 square meters.

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Answer:

42

Step-by-step explanation:

42 i think

maybe 5

.....................

Answer:

They will flash together at 36 seconds after 8:00 p.M which can be written as 8:00:36 PM.

Step-by-step explanation:

This question can be solved using concept of LCM

LCM is the least number which is divisible by all the set of given number.

LCM is found by finding the prime factors of given set of numbers and then taking the each numbers highest power and then multiplying all.

for example

lets find LCM of 20 and 75

prime factor of 20 = 2*2*5

prime factor of 75 = 3*5*5

highest power of 2 is 2*2 = 4

highest power of 3 is 3 = 3

highest power of 5 is 5*5 = 25

thus LCM is 4*3*25 = 300

Thus, 300 is the least number which will be commonly divisible by 20 and 75.

Now in the problem given One light flashes every 18 seconds and another light flashes every 12 seconds.

Thus, they will will flast together at time when the time will be commonly divisible by both 12 and 18.

to find that time, lets find the LCM of 12 and 18

The number is 12 , 18

prime factor of 12 = 2*2*3

prime factor of 18 = 2*3*3

highest power of 2 is 2*2 = 4

highest power of 3 is 3*3 = 9

thus LCM is 9*4 = 36

Thus, the lights will flash together after 36 seconds.

Given that they flash together at 8:00 p.M

They will flash together at 36 seconds after 8:00 p.M which can be written as 8:00:36 PM.

Answer:

(-4,-9)

Step-by-step explanation:

vertex form: y=a(x-h)^2+k

hk=vertex of x and y

inside parentheses=horizontal (opposite signs)

that’s why it’s -4 instead of 4 for h (x) while -9 stays the same since it’s not inside the parentheses

The final amount of the compound interest after 6 years would be $ 294, 122, 500

The formula for the final amount is given as;

\(A = P( 1 + \frac{r}{n}) ^n^t\)

Where

A = final amount

P = principal interest

r = interest rate

n = number of times

t = time of periods

We have,

A = \(2500\) \(( 1 + \frac{6}{1}) ^1^*^6\)

A = \(2500 ( 7)^6\)

A = \(2500\) × \(117, 649\)

A =$ \(294, 122, 500\)

Thus, the final amount of the compound interest after 6 years would be $ 294, 122, 500

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Answer:

the answer is 2

Step-by-step explanation:

2 times 4 is 8. 8 times 8 is 64

4 times 8 is 32.

32 times 2 is 64

Answer:

B

Step-by-step explanation:

We can't see the answer choices?

Answer:

23/50

Step-by-step explanation:

46% is the same as 46/100 that can be simplified to 23/50

The percentage 46% as a fraction in its simplest form is 23/50.

The given fraction is 46%.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

The percentage can be written in fraction by dividing the number by 100.

Here, 46% = 46/100

= 23/50

Therefore, the percentage 46% as a fraction in its simplest form is 23/50.

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Among the given options, the correct statement is: C. Var (X + Y) = Var (X) + Var (Y).

This statement is known as the addition rule for variance and holds true for all random variables X and Y, regardless of their specific distributions.

To understand why this statement is true, let's briefly discuss the concept of variance. Variance measures the dispersion or spread of a random variable's values around its expected value (mean). Mathematically, variance is defined as the average of the squared deviations of the random variable from its mean.

Now, let's prove statement C:

Var (X + Y) = E[(X + Y - E[X + Y])^2] (definition of variance)

= E[(X + Y - E[X] - E[Y])^2] (linearity of expectation)

Expanding the square term:

mathematica

Copy code

       = E[(X - E[X])^2 + 2(X - E[X])(Y - E[Y]) + (Y - E[Y])^2]

By linearity of expectation, we can split this expression into three parts:

scss

Copy code

       = E[(X - E[X])^2] + 2E[(X - E[X])(Y - E[Y])] + E[(Y - E[Y])^2]

       = Var(X) + 2Cov(X, Y) + Var(Y)     (definition of variance and covariance)

Note that Cov(X, Y) represents the covariance between X and Y, which measures the extent to which X and Y vary together. However, the given options do not mention anything about the covariance between X and Y, so we cannot determine its value.

Therefore, statement C is correct because it expresses the addition rule for variance, which states that the variance of the sum of two random variables is equal to the sum of their individual variances.

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A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5. Also, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7. Therefore, it is clear that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, or hypotenuse. For example, the triple (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 5^2.

Now let's talk about triangular numbers. A triangular number is the sum of the first n positive integers, and it can be represented by the formula Tn = 1 + 2 + 3 + ... + n = (n(n+1))/2. The first few triangular numbers are 1, 3, 6, and 10.

Interestingly, in the list of the first few Pythagorean triples, we can observe a pattern where the value of b is four times a triangular number. For example, in the Pythagorean triple (3, 4, 5), we have b = 4T1. In (5, 12, 13), b = 4T2. In (7, 24, 25), b = 4T3. And in (9, 40, 41), b = 4T4.

So the question is: is this pattern true for all triangular numbers? Let's investigate further.

a) To find a primitive Pythagorean triple (a, b, c) with b = 4T5, we need to find a value of a and c such that a^2 + b^2 = c^2 and b = 4T5. Using the formula for T5, we get T5 = (5(5+1))/2 = 15. Therefore, b = 4T5 = 60. We can use the Euclid's formula for generating Pythagorean triples, which states that for any two positive integers m and n with m > n, a Pythagorean triple (a, b, c) can be generated by a = m^2 - n^2, b = 2mn, and c = m^2 + n^2.

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5.

Similarly, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7.

b) Now, the question is whether there is a primitive Pythagorean triple (a, b, c) with b = 4Tn for any triangular number Tn. Let's assume this is true and try to prove it.

Using the same Euclid's formula, we can generate a primitive Pythagorean triple (a, b, c) with b = 4Tn by setting m = 2Tn+1 and n = Tn. This gives us a = 4Tn^2 + 1 and c = 4Tn^2 + 2Tn + 1, and we can verify that b = 4Tn using the formula for Tn.

Therefore, we have proven that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

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The length of CD is \(15√(1 + 25x^2)\)

Describe length.

A measurement of length is the separation of two points or the size of an object. Units like centimeters, meters, and inches are frequently used to measure length. Time or the amount of space something occupies are other ways to measure length. Calculating area, volume, and other measurements can be done using length, a key idea in mathematics.

Let AB = 5+3x and BC = 20-2x.

To calculate the length of CD, we can use the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of\((x2 - x1)^2 + (y2 - y1)^2\)

Therefore, to calculate the length of CD, we can use this formula with the given values:

CD = \(√(20 - 5)^2 + (-2x - 3x)^2\)

CD = \(√(15)^2 + (-5x)^2\)

CD =\(15√(1 + 25x^2)\)

Therefore, the length of CD is \(15√(1 + 25x^2)\)

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I can't see what you posted it's blocked off but I could probably answer it if I knew what the questions were

The system has no solution, there is no particular solution x₀, and the general solution does not exist in this case.

The equation Ax = b, where A is a 3x3 matrix and b is a 3x1 column vector, represents a system of linear equations. To find all solutions of this system, we can either use Gaussian elimination or Cramer's rule.

In this case, A = [[2, -5, 3], [-2, 6, -5], [-4, 7, 0]] and b = [[-3], [4], [3]].

Using Gaussian elimination, we can transform the matrix A into its reduced row echelon form and then use back substitution to solve for the variables. The reduced row echelon form of A is:

[[1, 0, 1/2], [0, 1, -5/2], [0, 0, 0]]

Since the last row is all zeros except for the last entry, the system is inconsistent and has no solution.

Alternatively, we can use Cramer's rule to find the solution. The formula for Cramer's rule is:

x_i = det(A_i) / det(A), where A_i is the matrix A with the i th column replaced by the vector b.

In this case, det(A) = 0, so the system has no solution.

The general solution of this system of linear equations is the set of all linear combinations of the columns of A. If the system has a solution, the general solution can be expressed in the parametric vector form as:

x = x₀ + t₁ * v₁ + t₂ * v₂, where x₀ is a particular solution, v₁ and v₂ are the non-trivial solutions, and t₁ and t₂ are scalar parameters.

Since the system has no solution, there is no particular solution x_0, and the general solution does not exist in this case.

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Answer:

The answers are A, B, E

Step-by-step explanation:

C and D are less but not greater than-1.6

"meso-" and "medi-" both relate to the middle or intermediate position, but they may be used in different contexts and have distinct origins (Greek and Latin, respectively).

The prefixes "meso-" and "medi-" have different meanings:

Meso-: The prefix "meso-" generally means "middle" or "intermediate." It is derived from the Greek word "mesos," which carries the same meaning. In scientific and medical terminology, "meso-" is often used to indicate something that is located in the middle or intermediate position.

For example:

Mesoderm: The middle germ layer in the early development of an embryo.

Mesozoic: The era between the Paleozoic and Cenozoic eras, often referred to as the "Age of Reptiles."

Medi-: The prefix "medi-" typically means "middle" or "between." It is derived from the Latin word "medius," which conveys a similar sense. In various contexts, "medi-" is used to indicate something that is in the middle or intermediary position.

For example:

Median: Referring to the middle value in a set of numbers or the middle line or point dividing something into equal halves.

Mediastinum: The central area within the thoracic cavity, located between the lungs, which contains the heart, great vessels, and other structures.

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Answer:

a = 7

Step-by-step explanation:

Equation of line : y = mx + b

m = slope

Plug in coordinates:  

Slope = Change in y/Change in X

Slope = 13-4/5-2 = 9/3 = 3

Plug in coordinates:

y - intercept = b

13 = 5(3) + b

13 = 15 + b

b = -2

Equation: y = 3x - 2

Input 3 for x

y = 3x - 2

y = 9 - 2

y = 7

-Chetan K

The coordinate functions of the line parametrized by r(t) = 6t - 1, 9t^2 are x(t) = 2t - (1/3) and y(t) = -10t^2/3 + (10t/3) - (5/9).

To find the coordinate functions of the line parametrized by r(t) = 6t - 1, 9t^2, we need to use the vector form of the line and substitute in the given values of t.

First, let's recall the vector form of the line which is r(t) = a + tb where r(t) is the position vector of a point on the line, a is a point on the line, t is a scalar parameter, and b is the direction vector of the line. In this case, we are given the direction vector as (3,-5) and a point on the line as (2,0). So, the vector form of the line is r(t) = (2,0) + t(3,-5).

Now, we need to find the coordinate functions by replacing t with the given values in the parametrization r(t) = 6t - 1, 9t^2.

For the x-coordinate function, we have:

x(t) = 2 + 3t
x(t) = 2 + 3((6t - 1)/9)
x(t) = 2 + 2t - (1/3)

So, the x-coordinate function is x(t) = 2t - (1/3).

For the y-coordinate function, we have:

y(t) = 0 - 5t
y(t) = 0 - 5((6t - 1)/9)^2
y(t) = 0 - 10t^2/3 + (10t/3) - (5/9)

So, the y-coordinate function is y(t) = -10t^2/3 + (10t/3) - (5/9).

Therefore, the coordinate functions of the line parametrized by r(t) = 6t - 1, 9t^2 are x(t) = 2t - (1/3) and y(t) = -10t^2/3 + (10t/3) - (5/9).

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