Find the sum of the multiples of 9 from 1 to 300

Answer:

The roots are real and distinct.

Step-by-step explanation:

Given the following equation:

\(x^{2} + kx - k -2 =0\)

In this problem, a = 1, b = k and c = -k - 2

The discriminant is b² - 4ac, and for the roots to be real and distinct, it must be at least or greater than 0.

We get,

(k)²- 4(1)(-k - 2) = 1 - 4(-k - 2)

= k² + 4k + 8

Let's check:

At k = -2,

\((-2)^{2} + 4(-2) + 8 = 4 - 8 + 8 = 4 \)

At k = 0,

\((0)^2 + 4(0) + 8 = 8 \)

At k = -100,

\((-100)^2 + 4(-100) + 8 = 10,000 - 400 + 8 = 9608\)

Therefore, we can conclude that for all values of k, the roots are real and distinct.

This has been a long way in answering this question, so it would be great if you could mark me as brainliest

Therefore, the given planes are neither parallel nor perpendicular.

Given planes are 9x+36y−27z=1 and −12x+24y+28z=0.

Let's compare the coefficients of x,y, and z in both planes to check whether the planes are parallel, perpendicular or neither.

We know that, two planes are parallel if and only if the normal vectors are parallel.

Two planes are perpendicular if the dot product of their normal vectors is zero.

Let's write the given planes in the vector form by equating the coefficients of x, y, and z.9x+36y−27z=1 => (9, 36, -27) . (x, y, z) = 1−12x+24y+28z=0 => (-12, 24, 28) . (x, y, z) = 0

Now let's find the dot product of the normal vectors in both planes to determine whether the planes are parallel or perpendicular(9, 36, -27) . (-12, 24, 28) = -432 - 648 + (-756) = -1836

The dot product is not zero, so the planes are not perpendicular.

Since the normal vectors are not parallel (one is not a scalar multiple of the other), the planes are not parallel.

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Answer:

umm where is the answer?

Step-by-step explanation:

i just need the answers bro

Answer: stated down below

Step-by-step explanation:

To determine the print sizes that Naomi can order without needing to crop the pictures or leave any extra space, we need to consider the aspect ratio of the pictures and the aspect ratios of the available print sizes.

The aspect ratio of the pictures is given as 3:2, which means that the width of the picture is 3/2 times the height. Let's denote the width as 3x and the height as 2x, where x is a positive constant.

Now, let's consider the available print sizes. Suppose the aspect ratio of a print size is given as a:b, where a represents the width and b represents the height. For the print size to accommodate the picture without any cropping or extra space, the aspect ratio of the print size must be equal to the aspect ratio of the picture.

We can set up a proportion using the aspect ratios of the picture and the print size:

(Width of Picture) / (Height of Picture) = (Width of Print Size) / (Height of Print Size)

Using the values we determined earlier:

(3x) / (2x) = a / b

Simplifying the equation:

3/2 = a / b

Cross-multiplying:

3b = 2a

This equation tells us that for the print size to match the aspect ratio of the picture without cropping or leaving extra space, the width of the print size (a) must be a multiple of 3, and the height of the print size (b) must be a multiple of 2.

Therefore, the print sizes that Naomi can order without needing to crop the pictures or leave any extra space are those that have aspect ratios that are multiples of the original aspect ratio of 3:2. For example, print sizes with aspect ratios of 6:4, 9:6, 12:8, and so on, would all be suitable without requiring any cropping or extra space.

By considering the properties of similar figures and setting up the proportion using the aspect ratios, we can determine which print sizes will preserve the entire picture without any cropping or additional space on the sides.

The probability that the athlete has actually been using the prohibited drug given that they tested positive is approximately 0.5789 or 57.89%.

To solve this problem, we can use Bayes' theorem, which relates the conditional probabilities of two events.

Let A be the event that the athlete has been using the prohibited drug, and let B be the event that the athlete tests positive.

We want to find the probability of A given B, which we can write as P(A | B).

Using Bayes' theorem, we have:

P(A | B) = P(B | A) * \(\frac{P(A) }{P(B)}\)

where P(B | A) is the probability of testing positive given that the athlete has been using the prohibited drug, P(A) is the prior probability of the athlete using the prohibited drug, and P(B) is the overall probability of testing positive, which can be calculated using the law of total probability:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

where P(B | not A) is the probability of testing positive given that the athlete has not been using the prohibited drug, and P(not A) is the complement of P(A), i.e., the probability that the athlete has not been using the prohibited drug.

Using the given information, we can plug in the values:

P(B | A) = 1 - 0.12 = 0.88 (probability of testing positive given the athlete is using the drug)

P(A) = 0.05 (prior probability of the athlete using the drug)

P(B | not A) = 0.04 (probability of testing positive given the athlete is not using the drug)

P(not A) = 1 - P(A) = 0.95 (probability that the athlete is not using the drug)

Then, we can calculate P(B) as:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

= 0.88 * 0.05 + 0.04 * 0.95

= 0.076

Finally, we can calculate P(A | B) as:

P(A | B) = P(B | A) * \(\frac{P(A) }{ P(B)}\)

= 0.88 * \(\frac{0.05 }{ 0.076}\)

= 0.5789

Therefore, the probability that the athlete has actually been using the prohibited drug given that they tested positive is approximately 0.5789 or 57.89%.

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Answer:

3,975.16 United States Dollar

Step-by-step explanation:

Answer:

8.8 hours

Step-by-step explanation:

happy paws charges $21 in addition to $2.5 per hour -- we can write this as

21 + 2.5 per hour -- since the number of hours is x, this is equal to

21 + 2.5 (x)

similarly, woof watchers is

10 + 3.75 (x)

we must find when the services are equal --

21 + 2.5x = 10+3.75x

subtract 10 from both sides

11 + 2.5x = 3.75x

subtract 2.5x from both sides

11 = 1.25

divide both sides by 1.25

x = 8.8

The reading on the y-axis when the time x =0 is 10

The definition of the function is given as

f(x) = 10 . (2)*

Rewrite the function properly

So, we have the following representation

f(x) = 10(2)ˣ

From the question, we understand that:

Time, x = 0

So, we substitute 0 for x in the equation f(x) = 10(2)ˣ

So, we have

f(0) = 10(2)⁰

Evaluate the exponent

f(0) = 10 * 1

So, we have

f(0) = 10

Hence, the value of the y-axis is 10

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We want to solve the proportion:

For doing so, we remember that solving a proportion equivals to find the variable x. We will multiply means and extremes:

This means that the value of x is 8, which is the solution of the proportion.

Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

Answer:

19,855

Step-by-step explanation:

(-19)5*(-19)11

-95*-209= 19,855

can i get brainliest please?

Answer:

$125

Step-by-step explanation:

Given the following :

Number of desks sold = 3

Amount of rent paid = $4

Amount paid to carpenter = 1/2 of revenue

Amount left = $185.50

At what price did Ryan sell each desk?

If Rayee gave half of his revenue to the carpenter and then had $185.50 left,

The his revenue before paying the carpenter will be twice what he has left ($185.50 * 2) = $371

Hence, total revenue from the sale of 3 desk= ($371 + rent) = (371 + 4) = $375

Then each desk cost :

$375 / 3 = 125

$125

The intersection of plane TUYX and plane VUYZ is found as UY.

For the stated question-

According to the supplied figure, TUYX is one side of both the rectangular prism while UVYZ is its opposite side.

One edge, which is represented by the line segment UY, has both sides intersecting perpendicularly.

It is depicted in the figure.

Thus, UY is the line that intersects as a result.

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The correct question is attached.

Answer:

? You didn't send the whole question

Step-by-step explanation:

The formula for calculating the area of a trapezoid is given by;

where a and b are the base and h is the height

From the question,

a = 5

b= 13

h = 3

substitute the vakues into the formula

Answer:

D) 8x - 1

Step-by-step explanation:

Let's say that x = 5.  That would mean Amelia put 15(5) - 4 gallons of gas in her car, which equals 71 gallons.  She used 7(5) - 3 gallons driving to work, which is 32 gallons used.  71 - 32 = 39 gallons left.  

What else equals 39, you might ask?

8(5) - 1

40 - 1

39.

Answer:

D is the answer

Step-by-step explanation:

The probability of being able to form a triangle with three sticks of random length is 1/2 or 50%.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The probability of being able to form a triangle with three sticks of random length can be found using geometric probability.

First, we can assume that the length of the first stick is x, where 0 ≤ x ≤ 1. The second stick can be any length y such that 0 ≤ y ≤ 1. The third stick can be any length z such that 0 ≤ z ≤ 1.

For the three sticks to form a triangle, they must satisfy the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we have three cases to consider:

x + y > z

x + z > y

y + z > x

We can graph these three inequalities on a coordinate plane, where x and y are the lengths of two sides of the triangle, and the third side is represented by the area below the line.

The area of the triangle formed by the inequalities is 1/2, and the total area of the square representing the possible lengths of the sticks is 1.

Therefore, the probability of the three sticks forming a triangle is the ratio of the area of the triangle to the area of the square:

P(triangle) = area of triangle / area of square = (1/2) / 1 = 1/2

Hence, the probability of being able to form a triangle with three sticks of random length is 1/2 or 50%.

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Answer:

2

Step-by-step explanation:

\(\frac{5}{9}\) ÷ \(\frac{5}{18}\)

• leave first fraction , change ÷ to × , turn second fraction upside down

= \(\frac{5}{9}\) × \(\frac{18}{5}\) ( cancel the 5's and 9 and 18 by 9 )

= \(\frac{1}{1}\) × \(\frac{2}{1}\)

= 1 × 2

= 2

The type of armored cable listed under UL 4 with permitted conductor sizes of 14 AWG through 1 AWG only is Type AC Cable.

Type AC Cable is also known as armored cable or BX cable, and it is a type of electrical wiring that consists of two or more insulated conductors that are wrapped in a flexible metal sheath. The metal sheath provides protection against physical damage and also serves as a grounding conductor.

UL 4 is a standard for Armored Cable and it covers various types of armored cables, including Type AC cable. UL 4 specifies the construction, performance, and testing requirements for armored cables. It also includes requirements for the thickness and composition of the metal sheath, as well as the thickness and type of insulation on the conductors.

In summary, Type AC Cable is the type of armored cable that is listed under UL 4 and has permitted conductor sizes of 14 AWG through 1 AWG only.

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Answer:Look at explanation

Step-by-step explanation: Let X be the number of liters of the 20% alcohol solution to be added.

To find the resulting concentration when X liters of 20% alcohol solution are added to 40 liters of 50% alcohol solution, we can set up the following equation:

0.2X + 0.5(40) = 0.3(X + 40)

Simplifying and solving for X, we get:

0.2X + 20 = 0.3X + 12

0.1X = 8

X = 80

Therefore, 80 liters of the 20% alcohol solution should be added.

To check this answer, we can verify that the resulting solution will be 30% alcohol:

0.2(80) + 0.5(40) = 0.3(80 + 40)

16 + 20 = 36

So the resulting solution is indeed 30% alcohol.

Therefore, X = 80 liters and Y = 40 liters (the original amount of the 50% alcohol solution).

The distance between the park and Ezequiel's house is 20 meters. It takes Ezequiel 2.5 minutes to get home from the park.

(1) To determine the distance between the park and Ezequiel's house, we can calculate the difference between the two distances at which Ezequiel is from his house.

Ezequiel is 100 meters away from his house after a few minutes, and 80 meters away from his house after 10 minutes. The difference between these two distances is 100 - 80 = 20 meters.

Therefore, the distance between the park and Ezequiel's house is 20 meters.

(2) To determine how long it takes Ezequiel to get home from the park, we can use the concept of speed.

We have the information that Ezequiel is walking at a constant speed. Since the distance from the house is 80 meters after 10 minutes, we can calculate the speed by dividing the distance by the time: Speed = 80 meters / 10 minutes = 8 meters/minute.

Since we know the distance between the park and Ezequiel's house is 20 meters, we can calculate the time by dividing the distance by the speed: Time = 20 meters / 8 meters/minute = 2.5 minutes.

Therefore, it takes Ezequiel 2.5 minutes to get home from the park.

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The number of randomly selected Americans that must be surveyed is equal to 38 if the confidence interval is 97.5% with a 0.16 margin of error.

First, we calculate the critical value as follows;

a = (1 - 0.975) = 0.025 = 0.025 / 2 = 0.0125 = (1 - 0.0125) = 0.9875

Z - Critical value = NORM.S.INV (0.9875) = 1.96

As margin of error(ME) = 0.16

Therefore;

n = pq(Z²) / ME²

n = 0.5 × 0.5 (1.96)² / (0.16)²

n = 0.25 × 3.8416 / 0.0256

n = 0.9604 / 0.0256

n = 37.515

Rounding it to the nearest whole number;

n = 37.515 = 38

Hence 38 randomly selected Americans must be surveyed if the estimated confidence interval is 97.5% and the margin of error is 0.16.

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Answer:

plz give me brainly but the answer is

Step-by-step explanation:

In a two-variable problem rewrite the equations so that when the equations are added, one of the variables is eliminated, and then solve for the remaining variable. Step 1: Multiply equation (1) by -5 and add it to equation (2) to form equation (3) with just one variable.

We can see that the first component of the vector equation is always zero, so the parabola lies in the xz-plane.

Moreover, the second component is a quadratic function of t, which gives us a vertical parabola when plotted in the yz-plane. The third component is a linear function of t, so the curve extends infinitely in both directions. Therefore, we have a vertical parabola in the xz-plane.

This statement is referring to a specific vector-valued function, which we can write as:

f(t) = (0, t^2, ct)

where c is a constant.

The second component of this vector function is t^2, which is a quadratic function of t. When we plot this function in the yz-plane (i.e., we plot y = t^2 and z = 0), we get a vertical parabola that opens upward. This is because as t increases, the value of t^2 increases more and more quickly, causing the curve to curve upward.

The third component of the vector function is ct, which is a linear function of t. When we plot this function in the xz-plane (i.e., we plot x = 0 and z = ct), we get a straight line that extends infinitely in both directions. This is because as t increases or decreases, the value of ct increases or decreases proportionally, causing the line to extend infinitely in both directions.

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Answer: The answer is the second equation (y = 3x-4 and y = -1/3x - 2)

Step-by-step explanation:

This is because two lines are perpendicular when the slopes of the equations are negative reciprocals from each other.

Answer:

The solution to the recurrence relation is given by an = 2^(n+1) - 1.

Step-by-step explanation:

(a) To solve the recurrence relation an = an-2 + 4, with initial conditions a1 = 3 and a2 = 5, we'll consider two cases: one for when n is even and one for when n is odd.

For n even:

Substituting n = 2k (where k is a positive integer) into the recurrence relation, we get:

a2k = a2k-2 + 4

Now let's write out a few terms to observe the pattern:

a2 = a0 + 4

a4 = a2 + 4

a6 = a4 + 4

...

We notice that a2k = a0 + 4k for even values of k.

Using the initial condition a2 = 5, we can find a0:

a2 = a0 + 4(1)

5 = a0 + 4

a0 = 1

Therefore, for even values of n, the solution is given by an = 1 + 4k.

For n odd:

Substituting n = 2k + 1 (where k is a non-negative integer) into the recurrence relation, we get:

a2k+1 = a2k-1 + 4

Again, let's write out a few terms to observe the pattern:

a3 = a1 + 4

a5 = a3 + 4

a7 = a5 + 4

...

We see that a2k+1 = a1 + 4k for odd values of k.

Using the initial condition a1 = 3, we find:

a3 = a1 + 4(1)

a3 = 3 + 4

a3 = 7

Therefore, for odd values of n, the solution is given by an = 3 + 4k.

(b) To solve the recurrence relation an = 2an-1 + 1, with initial condition a1 = 1, we'll find a general expression for an.

Let's write out a few terms to observe the pattern:

a2 = 2a1 + 1

a3 = 2a2 + 1

a4 = 2a3 + 1

...

We can see that each term is one more than twice the previous term.

By substituting repeatedly, we can express an in terms of a1:

an = 2(2(2(...2(a1) + 1)...)) + 1

= 2^n * a1 + (2^n - 1)

Using the initial condition a1 = 1, we have:

an = 2^n * 1 + (2^n - 1)

= 2^n + 2^n - 1

= 2 * 2^n - 1

Therefore, the solution to the recurrence relation is given by an = 2^(n+1) - 1.

Answer:

w(15)=112.5

Step-by-step explanation:

All you have to do is put the number in the parentheses in the place of the variable, which in this case is h, and perform the prescribed operation.

In this case, you make the equation w(15)=7.5(15) which you can rewrite as

                                                                                  w(15)= 7.5×15, which gives                        .                                                                                  you 112.5 as the product.