What is the sum of the third and
ninth square numbers?

Answer:

12%

Step-by-step explanation:

Simple Interest Formula

\(\large \boxed{ \sf I = Prt}\)

where:

Given:

Substitute the given values into the formula and solve for r:

\(\implies \sf 104=1300r \left(\dfrac{8}{12}\right)\)

\(\implies \sf \dfrac{104}{1300}=\left(\dfrac{8}{12}\right)r\)

\(\implies \sf r=\dfrac{104 \cdot 12}{1300 \cdot 8}\)

\(\implies \sf r=\dfrac{1248}{10400}\)

\(\implies \sf r=0.12\)

Convert into a percentage by multiplying by 100:

\(\implies \sf r=0.12 \times 100=12 \%\)

Therefore, the interest rate is 12%.

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The coordinates of the unit vector, having positive first coordinate and orthogonal to the plane through a given point P(3, -4, 4) = \((\frac{\sqrt{2} }{2}, \frac{-\sqrt{2} }{2},0)\)

Let the coordinates of Q be (6 , -1 , 7) and R be (6, -1 ,9).

Then coordinates of vector(PQ) = < 6 - 3, -1 - (-4), 7 - 4 > = (3, 3, 3)

And coordinates of vector(PR) = < 6 - 3, -1 - (-4), 9 - 4 > = (3, 3, 5)

Thus, vector (n) = vector (PQ) x vector (PR)

=> vector (n) =  \(\left[\begin{array}{ccc}3&3&3\\3&3&5\end{array}\right]\)

Solving for the determinant, we get the coordinates of vector (n)

= (6, -6, 0).

Magnitude of vector (n) = \(\sqrt{6^{2}+{(-6)^{2}+{0^{2} }\) = \(6\sqrt{2}\)

Thus, the unit vector (n) = \(\frac{Coordinates Of Vector (n)}{Magnitude Of Vector(n)}\)

=> Unit vector (n) = \(\frac{(6,-6,0)}{6\sqrt{2} }\) = \((\frac{\sqrt{2} }{2},\frac{-\sqrt{2} }{2},0)\)

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COMPLETE QUESTION:

Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P (3,-4,4).

Its b, because only 13 and 14 work

Kenny had 1/3 of a candy bar. He shared 3/4 of his part of the candy bar with his sister.

To find out how much of a candy bar Kenny shared with his sister, you can follow these steps:

Step 1: Find\(3/4 of 1/3.3/4 * 1/3 = 1/4\) Step 2: Convert the answer to a mixed number.1/4 = 0.25, which can be written as 1/4 as a fraction. Therefore, Kenny shared 1/4 of a candy bar with his sister.

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Answer:

hi

Step-by-step explanation:

how are you

Answer:  A: L: W: H = 10: 5: 8

Step-by-step explanation:  The height of the tank is 18 feet longer than the width

H = 8 parts, W = 5 parts => 8 – 5 parts = 18 feet i.e. 3 parts = 18, 1 part = 6 feet

Hence, L = 10 * 6 = 60 feet

W = 5 * 6 = 30 feet

H = 8 * 6 = 48 feet

Volume = 60 * 30 * 48 = 86400 ft³

Surface Area = 2 * (30 * 60 + 48 * 60 + 30 * 48) =12240 ft²

Answer:

2 & 13

Step-by-step explanation:

The square of 2 plus the prime number 13 add up to 17

\(2^{2}+13=4+13 =17\)

Hope this helps

Answer:

Square number = 4

Primer number = 13

Step-by-step explanation:

A square number is the result when a number has been multiplied by itself.

A prime number is a whole number greater than 1 that only has two factors, itself and 1.

List all the square numbers and prime numbers below 17:

Square numbers: 1, 4, 9, 16, ...

Prime numbers: 2, 3, 5, 7, 11, 13, ...

Therefore, the only combination of square number and prime number that sums to 17 is:  4 + 13 = 17

Solution

Square number = 4

Primer number = 13

Answer:

64

Step-by-step explanation:

140/56=2.5

160/2.5=64

Answer:

24

Step-by-step explanation:

Hello!

it's 21.9 for me

Answer: I dont know if that is an "I" or a "1" but if it is an "I" the answer is "16-3i" but if is a "1" its 7

Step-by-step explanation:

3x^2 + 1 = 5x

3x^2 - 5x + 1 = 0

quadratic formula

where ax^2 + bx + c = 0

so

You can see that the 25 - 12 = 13 so the answers are A and B

The amount A of a substance can be expressed as A = A₀ * e^(kt), where A₀ is the initial amount, t is time, k is the decay constant, and e is the base of the natural logarithm. The half-life of the substance is used to determine the decay constant. In this case, the half-life is 20 days, which means k = ln(0.5) / 20. To find the amount of the substance at a specific time, we substitute the values into the equation. In part (b), we set A = 2.9 grams and solve for t using logarithmic methods.

(a) The equation expressing the amount A of the substance as a function of time is A = 158.999999999997 * e^(kt), where k = ln(0.5) / 20. The value of k is calculated by taking the natural logarithm of 0.5 (representing half-life) divided by the half-life of 20 days. The coefficient of t in the exponent should have at least five decimal places for accuracy.

(b) To find when the substance will be reduced to 2.9 grams, we set A = 2.9 grams in the equation A = 158.999999999997 * e^(kt). Then we solve for t. Taking the natural logarithm of both sides, we have ln(2.9) = ln(158.999999999997) + kt. Rearranging the equation and solving for t gives t = (ln(2.9) - ln(158.999999999997)) / k. Substituting the value of k calculated earlier, we can find the value of t in days.

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Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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Option B is correct, 40/3 is the slope of the line that represents the function.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Beth has 380 pages left to read in her literature book.

She has decided to read 40 pages every three days

y be the total number of pages that Beth has left to read, and let x be the number of days that have passed.

Beth is reading 40 pages every 3 days, so her rate can be expressed as 40/3 pages per day.

Since slope is defined as change in y (pages) over change in x (days), the slope of the line is 40/3.

Hence, Option B is correct, 40/3 is the slope of the line that represents the function.

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Answer:

-28,000

and also that goat is soooo cute

After set s1.addAll(s2), s1 is [1, 2, 5, 2, 3, 6].

After performing the operation s1.addAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become[1, 2, 5, 2, 3, 6].

To determine the value of s1, the following steps has to be taken:

1. Start with sets s1 [1, 2, 5] and s2 [2, 3, 6].

2. Apply the addAll operation with set s2: [2, 3, 6]

3. Add each element from set s2 to set s1, while avoiding duplicates (since sets cannot have duplicate elements).

4. Therefore, suppose if set s1 is [1, 2, 5] and set s2 is [2, 3, 6] then, after s1.addAll(s2), the set s1 becomes [1, 2, 5, 2, 3, 6].

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We can use the formula for inverse variation, which states that the product of the time and the speed is constant:

time × speed = constant

Let's use t to represent the time needed to travel the distance at 54 miles per hour. We know that the time is 10 hours when the speed is 24 miles per hour. So we can set up the equation:

10 × 24 = t × 54

Simplifying, we get:

240 = 54t

Dividing both sides by 54, we get:

t = 240/54

Simplifying this fraction, we get:

t = 40/9

So it will take approximately 4.44 hours, or 4 hours and 26 minutes, to travel the same distance at 54 miles per hour.

Answer:

steps below

Step-by-step explanation:

This is not a fresh game, you can find it everywhere on the web. The basic trick to fill 3x3 square with consecutive numbers is put the middle number at the middle box and all the row, column or diagonal sum should be 3 x that number. Here is 3 x 7 = 21.

So 3,4,5,6, 7 ,8,9,10,11

The curvature κ(t) of the vector r(t) = 11cos(3t)i + 11sin(3t)j + 7tk is given by (\(1138^{3/2}\)) / 3267.

To find κ(t) using the given formula, we need to find the first and second derivatives of the vector r(t) = 11cos(3t)i + 11sin(3t)j + 7tk.

First, let's find the first derivative of r(t)

r'(t) = (-33sin(3t)i + 33cos(3t)j + 7k).

Next, let's find the second derivative of r(t)

r''(t) = (-99cos(3t)i - 99sin(3t)j).

Now, we can calculate the values needed to find κ(t):

||r'(t)|| = ||-33sin(3t)i + 33cos(3t)j + 7k|| = √((-33sin(3t))² + (33cos(3t))² + 7²) = √(1089sin²(3t) + 1089cos²(3t) + 49) = √(1089 + 49) = √1138.

||r'(t) × r''(t)|| = ||(-33sin(3t)i + 33cos(3t)j + 7k) × (-99cos(3t)i - 99sin(3t)j)|| = ||(-33)(-99)(-1)k|| = 3267.

Now, we can calculate κ(t)

κ(t) = (||r'(t)||³) / (||r'(t) × r''(t)||) = (\(1138^{3/2}\)) / 3267.

Therefore, κ(t) = (\(1138^{3/2}\)) / 3267.

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Answer:

120

Step-by-step explanation:

75-15=60. (Edit) Just realized that she spent her allowance that week, so it would be 120 because you need to multiply.

Answer:

The answer is 120$

Step-by-step explanation:

75-15=60

60x2=120

You multiply it by 2 because she spent half of her allowance on cyberpunk 2077

To express the quadratic function f(x) = x^2 - 18x + 63 in standard form, we need to complete the square.

First, we can factor out the coefficient of x^2, which is 1: f(x) = 1(x^2 - 18x + 63), Next, we want to find the value that completes the square for the expression inside the parentheses,

which is (-18x + 63). To do this, we take half of the coefficient of x, which is -9, square it, and add it to both sides: f(x) = 1(x^2 - 18x + 81 - 81 + 63).

Notice that we added and subtracted 81 inside the parentheses, which is the value we got from (-9)^2. This allows us to write the expression as a perfect square trinomial, which can be factored as: f(x) = 1[(x - 9)^2 - 18].

Finally, we can simplify this expression by distributing the 1 and adding 63 outside the brackets: f(x) = (x - 9)^2 - 18 + 63, So the quadratic function f(x) in standard form is: f(x) = (x - 9)^2 + 45.

Note that standard form for a quadratic function is usually written as ax^2 + bx + c, where a, b, and c are constants. In this case, we factored out the coefficient of x^2, which is why our standard form expression doesn't have an "a" term.

A quadratic function in standard form is written as f(x) = a(x - h)^2 + k, where a, h, and k are constants. Our goal is to rewrite the given function in this format. So, the standard form of the given quadratic function is: f(x) = (x - 9)^2 - 18

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The work to empty a parabolic tank filled with water which can be seen as the rotation about the y-axis of the function is -ρgπ(a³ - b²(3a - 2b))/6.

The equation of parabola is y = x². Therefore x = √y. Let us assume the parabolic tank is of height (a-b) where a is the y-coordinate of the top of the tank and b is the y-coordinate of bottom of the tank.

The work done to empty the parabolic tank filled with water is the integral (summation) of the work done to remove a circular area strips of height dy from height y to b.

Work done = ∫dW

= ∫FΔy

= ∫ρgdVΔy

= ∫ρg(y - a)dV  

Volume of the circular area strip ,dV = πr²dy  

= πx²dy

= π(√y)²dy

= πydy

Total work done to empty the tank = ₐ∫ᵇρg(y - a)dV

= ₐ∫ᵇρgπy(y - a)dy

= ρgπ[y³/3 - ay²/2]ₐᵇ

= ρgπ(b³/3 - a³/3 - ab²/2 + a³/2)

= -ρgπ(a³ - b²(3a - 2b))/6

The work done is negative when emptying the tank.

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===========================================================

Explanation:

We have four values to pick from {1,3,5,9} and we want to form a three-digit number.

Kick one of those values out, let's say we kick out "9" at the end to get the subset {1,3,5}.

The sum of these remaining values is 1+3+5 = 9 which is a multiple of 3. Therefore three-digit numbers that have any order of 1,3,and 5 will be a multiple of 3.

Eg: 135/3 = 45 exactly.

There are 3*2*1 = 6 such numbers as shown at the very bottom of this solution post.

This is a permutation since the order matters.

Let A = 6 so we can use it later.

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

Go back to {1,3,5,9}

Now let's say we kicked "5" out this time.

We go from {1,3,5,9} to {1,3,9}

The digits sum to 1+3+9 = 13 which is not a multiple of 3

No matter how we arrange these digits, we won't get a multiple of 3.

Eg: 139/3 = 46.33 approximately

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

Let's go back to {1,3,5,9}. This time we'll kick out "3" from the group.

{1,3,5,9} shrinks to {1,5,9}

Add the values: 1+5+9 = 15 which is a multiple of 3.

Therefore, we get 6 more permutations (refer to the first section for similar steps). Let B = 6 so we can use it later.

Example: 159/3 = 53 exactly

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

Return back to {1,3,5,9} once more. We have one final value to kick out.

Let's remove the "1" to end up with {3,5,9}

Add the values: 3+5+9 = 17 which isn't a multiple of 3, so we ignore this sub-case. It's similar to the 2nd section shown above.

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

Each previous section had us remove exactly one value to have 3 digits leftover. This is a methodical way to guarantee we have looked through all possible cases.

The first case had us kick out 9 so that a permutation of {1,3,5} led to some multiple of 3. There were A = 6 cases for that section.

The third section had {1,5,9} which led to B = 6 more cases.

In total, there are A+B = 6+6 = 12 different three-digit numbers possible if we are only allowed to use {1,3,5,9} without repeats allowed. In other words, all three digits must be different.

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

Check:

Here are the first 6 cases involving 1,3,5

Here are the other 6 cases involving 1,5,9

Since the interest rate is 5%. She needs to express the percentage as a decimal.

In order to do it, she needs to divide 5 by 100, so:

Answer:

r = 0.05

Score-based generative modeling through SDEs is an active area of research, and there are many variations and extensions of the method that are being developed to improve its performance and scalability.

In this method, the goal is to learn a set of SDEs that can generate samples that are similar to the true data distribution. The SDEs are typically specified as a system of coupled differential equations that describe the evolution of the system over time. The parameters of the SDEs are learned by maximizing the likelihood of the data under the model, which can be achieved by minimizing a loss function that is derived from the score function.

One advantage of this approach is that it can be used to model complex, high-dimensional data distributions, such as images or videos, that are difficult to model using traditional parametric methods. Another advantage is that it can handle missing data or irregularly sampled data, which can be common in many real-world datasets.

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The probability that we did not see all three colors is \($\frac{13}{16}\)

Consider the event,

A: Did not see all 3 colors

Complement of the event A is A’ where

A' : All colors were seen

Since 3 balls are drawn and all colors should be seen, it implies that there is 1 ball of each color

It is required to find P(A) = P(did not see all colors)

By the probability rule for complement:

P(A)  =1-P(A')

P(A') & =P(all colors were seen )

=P(1 White AND 1 Green AND 1 Red )

Total number of balls = 4

Number of combinations of 3 balls possible = 64

Since drawing a ball is with replacement, we have the following number of combinations with each color represented where R1 and R2 are the two red balls.

The table attached at end of the solution

Total number of combinations with each color represented = 12

Thus the probability of A’ is:

\($P\left(A^{\prime}\right) & =\frac{12}{64} \\\)

\($P(A) & =1-\frac{12}{64} \\\)

\($=\frac{52}{64} \\\)

\($=\frac{13}{16}\)

Hence, the required probability P(did not see all 3 colors) is \($\frac{13}{16}$\)

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Answer:

The answer is -3.71666

Step-by-step explanation:

Answer:

d = 47°

Step-by-step explanation:

Image is attached

Sum of angles drawn along a straight line = 180°:

The angle drawn in pink : 180° - 112° = 68°

The angle drawn in green: 180° - 66° = 114°

The angle drawn in yellowish orange: 180° - 23° = 157°

The angle marked in purple: 180° - 102° = 78°

The figure drawn in the center is a 5-sided irregular pentagon

∴ Sum of interior angles in a 5-sided polygon = (n - 2) ×180°

                                                                            = (5 - 2) × 180°

                                                                            = 540°

The four angles calculated above will assist in calculating the fifth remaining angle of the pentagon (which is marked in light blue):

   68° + 114° + 78° + 157° + angle in light blue = 540°

Angle in light blue = 540° - 68° - 114° - 78° - 157°

                               = 123°

Sum of angles drawn along a straight line = 180°:

Angle marked in dark blue = 180° - 123°

                                                = 57°

Now focus on the angles present inside the triangle

Sum of interior angles of a triangle = 180°

= d + 76° + 57° = 180°

d has to be isolated and made the subject of the equation:

d = 180° - 76° - 57°

d = 47°