15% of 500 is what number

Answer:

\(\frac{9\pm\sqrt{61}}{2}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(5)}}{2(1)}=\frac{9\pm\sqrt{81-20}}{2}\\\\=\frac{9\pm\sqrt{61}}{2}\)

Answer: 3

Step-by-step explanation:

Basically all you have to do is subtract 6 from both sides so you will get:

3 = v

Answer:

x =  \(\frac{9\sqrt{6} }{2}\)

Explanation:

using sohcahtoa method:

middle line: 9 ÷ sin(45) = 9√2

x = sin(60) * 9√2 = \(\frac{9\sqrt{6} }{2}\)

Answer:

a) 2.5^2+19\times2.5-16.75

Step-by-step explanation:

(2.5)² +(19× 2.5) - 16.75

= 6.25 + 47.5 - 16.75 = 37

Answer:

Step-by-step explanation:

Use perimeter formula

Find width:

Find length:

Find area:

Answer:

Step-by-step explanation:  It means a high level of quality, with 3.4 defects per million opportunities. It is this sigma level that leads to the term Six Sigma, which is a philosophy of delivering near perfect products or services by eliminating variabilities that lead to defects.

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

-1/4

Step-by-step explanation:

You just need to see what number is being divided from each term

Answer:

the sequence is the a geometric sequence because the terms has a common ratio. the common ratio = -80 / 200 = -2 / 5common ratio = 32 / -80 = -2 /5

so the next to term can be solve multiplying the last term with the common ratio

x = -12.8 ( -2 / 5)x = 5.12

y = 5.12 ( - 2 / 5)y = -2.048

Step-by-step explanation: HOPE THIS HELPS!!

A chord is a combination of three or more tones (notes) played together.

To determine the notes in a chord, we need to calculate the intervals between the notes. An interval is the distance between two notes. Intervals are measured in half steps (or semitones). A half step corresponds to the interval between two adjacent keys of a piano.

In a major chord, the formula for determining the intervals is 1-3-5. This means the root note (1st note) is a major third (4 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.

For example, if the root note is C, the 3rd note is E and the 5th note is G. The intervals in this chord are C to E (4 half steps) and C to G (7 half steps). Therefore, the chord is a C major chord.

In a minor chord, the formula for determining the intervals is 1-b3-5. This means the root note is a minor third (3 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.

For example, if the root note is F, the 3rd note is Ab and the 5th note is C. The intervals in this chord are F to Ab (3 half steps) and F to C (7 half steps). Therefore, the chord is a F minor chord.

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Answer:

-1.5

Step-by-step explanation:

Hope this helps .

Pls mark brainliest.

Thank if correct :)

The range of possibilities for the third side of the triangle, after using the triangle inequality theorem is 13 < n < 25.

According to the theorem of triangle inequality, the sum of any two of a triangle's sides must exceed the length of the third side. When we know the lengths of two sides, x and y, we can apply the triangle inequality theorem to estimate the length of the third side, which will be between x + y and x - y.

As a result,

x – y < n < x + y

19 – 6 < n < 19 + 6

13 ft < n < 25 ft

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Answer:

A= 4.5×10^11

B= 3.5×10^3

Step-by-step explanation:

A

(5×10^3)= 5000

(9×10^7)=90000000

multiply both of them

=450000000000 or 4.5×10^11

B

(7×10^5)=700000

(2×10^2)=200

700000÷200

3500 or 3.5×10^3

The product of (7.2×10¹¹) and (5×10⁶) in scientific notation, rounded to the appropriate number of significant digits, is 3.6 × 10¹⁸.

To write each product or quotient in scientific notation, we first need to multiply the numbers and then adjust the result to scientific notation. Let's start with the multiplication:

(7.2×10¹¹) (5×10⁶)

To multiply these numbers, we can simply multiply the coefficients (7.2 and 5) and add the exponents (10¹¹ and 10⁶):

(7.2 × 5) × (10¹¹ × 10⁶)

= 36 × 10¹⁷

Now, to express this result in scientific notation, we need to have a coefficient between 1 and 10. We can achieve this by moving the decimal point one place to the left:

3.6 × 10¹⁸

Therefore, the product of (7.2×10¹¹) and (5×10⁶) in scientific notation, rounded to the appropriate number of significant digits, is 3.6 × 10¹⁸.

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The equation in x and y representing the path of the particle is x² + 9y² = 1. This equation describes an ellipse centered at the origin. At t = 0, the particle's acceleration vector is -4i.

The given position vector of the particle in the xy-plane is r(t) = (cos(2t))i + (3sin(2t))j, where t represents time. We are also given t = 0. To find an equation in x and y that represents the path of the particle, we need to eliminate the parameter t.

We can express x and y in terms of t as follows:

x = cos(2t)

y = 3sin(2t)

To eliminate t, we can use the trigonometric identity cos²(θ) + sin²(θ) = 1. Rearranging this identity, we have:

sin²(θ) = 1 - cos²(θ)

Substituting x = cos(2t) and y = 3sin(2t) into the identity, we get:

sin²(2t) = 1 - cos²(2t)

(3sin(2t))² = 1 - (cos(2t))²

9y² = 1 - x²

Therefore, the equation in x and y representing the path of the particle is:

x² + 9y² = 1

Next, to find the particle's acceleration vector at t = 0, we need to differentiate the position vector twice with respect to time. Let's calculate it step by step:

r'(t) = (-2sin(2t))i + (6cos(2t))j

r''(t) = (-4cos(2t))i - (12sin(2t))j

Evaluating at t = 0, we get:

r'(0) = -2i + 6j

r''(0) = -4i

Therefore, the particle's acceleration vector at t = 0 is -4i.

To find an equation representing the path of the particle, we eliminated the parameter t by expressing x and y in terms of t and applying a trigonometric identity. This yielded the equation x² + 9y² = 1, which represents an ellipse centered at the origin with x and y as the variables.

Next, we found the particle's acceleration vector by differentiating the position vector twice with respect to time. Evaluating at t = 0, we obtained the acceleration vector as -4i. This indicates that the particle has constant acceleration along the x-axis, while its acceleration along the y-axis is zero.

These calculations provide insights into the motion of the particle. The equation of the path gives a geometric representation of the particle's trajectory, while the acceleration vector at t = 0 gives information about the particle's instantaneous acceleration at that specific time.

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Answer:

2√3

Step-by-step explanation:

√12 =

√4 * √3 =

√2^2 * √3 =

2 * √3 =

2√3

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Answer:

We can write 12 as 4 + 4 + 4, or 4 ∙ 3. So, create three squares that each have two columns and two rows.

a series of 3 squares, each composed of 4 smaller squares

so √12 =√4 x 3 = √4 x √3 = 2√3

Step-by-step explanation:

Answer:

216 cockroaches

Step-by-step explanation:

Let's establish that 125 cockroahes is Day 0, the start.  This means Day 1 is the next day.

Day 0 is 125 cockroaches.

They grow at 20% per day.  That is a factor of 120% for the second day.

(125)*(1.20) = 150 cockroaches on Day 1.

The second day would be (150)*(1.20) = 180 cockroaches on Day 2.

The third day is (180)*(1.20) = 216 cockroaches on Day 3.

Let C(x) be the number of cockroaches on the xth day.  The resulting formula for this would be:

The third day (x=3)

C(x) = 125*(1.20)^x

C(3) = (1.25)^(1.20)^3

The statement "correlation is measured on a scale from 0 to 1, where 0 indicates no linear relationship between two variables, and 1 indicates a perfect linear relationship" is true.

The correlation coefficient, typically denoted as r, is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 represents a perfect negative linear relationship, 1 represents a perfect positive linear relationship, and 0 indicates no linear relationship or correlation between the variables.

A correlation coefficient of 0 means that there is no linear association between the variables being analyzed. As the correlation coefficient moves closer to 1 or -1, it indicates a stronger linear relationship between the variables. Therefore, the scale from 0 to 1 is commonly used to represent the extent of correlation, where 0 signifies no linear relationship and 1 signifies a perfect linear relationship.

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Given the function f(x) = 0.25(2)x, where x represents time, we can determine the rate of growth or decay and the initial amount.

Rate of growth or decay: The general formula for exponential growth or decay is given by f(x) = a(b)x, where a is the initial amount, b is the growth or decay factor, and x is time. We can compare this with the given function f(x) = 0.25(2)x to determine the rate of growth or decay.

In the given function, b = 2, which is greater than 1. This indicates that the function represents exponential growth. Therefore, the rate of growth is 200% per unit of time.Initial amount:The initial amount, a, is the value of the function when x = 0. Substituting x = 0 in the given function f(x) = 0.25(2)x, we get:f(0) = 0.25(2)0= 0.25(1) = 0.25Therefore, the initial amount is 0.25.To summarize, the given function represents exponential growth with a rate of growth of 200% per unit of time and an initial amount of 0.25.

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To guarantee that the 3 team compositions (and team leads) are repeated, the professor would need to form groups a total of 3 times over the course of the semester. Each time the professor forms groups, there would be 3 possible team compositions (since the team lead can change within each group) and after 3 formations, all 3 compositions would have been used and repeated.

To determine the number of possible unique team compositions and team leads that can be formed.
1. First, we'll find the number of ways to choose team leads for each group:
There are 12 students and 3 team leads needed, so there are 12 choose 3 ways to pick the team leads, which is calculated as C(12,3) = 12! / (3! * (12-3)!) = 220.
2. Now, we'll calculate the number of ways to divide the remaining 9 students into 3 groups of 3 students each. We can use the multinomial coefficient formula, which is:
C(9,3,3,3) = 9! / (3! * 3! * 3!) = 1680
3. To find the total number of unique team compositions (including team leads), we multiply the results from steps 1 and 2 Total unique team compositions = 220 * 1680 = 369,600
4. The professor needs to form the groups 369,601 times in order to guarantee that the 3 team compositions (and team leads) will repeat.

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The equations are x² = y + 16 & 4y - 1 = 7x and the solution is (5, 9)

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

x = first number

y = second number

Given that

The square of the first number is 16 more than the second number

This means that

x² = y + 16

Also, we have the difference expression to be

4y - 1 = 7x

When these equations are solved graphicaly, we have

(x, y) = (5, 9)

Hence, the equations are x² = y + 16 & 4y - 1 = 7x and the solution is (5, 9)

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The equation of the tangent line to the curve f(x) = 6 + 5x − 5x² at x = 3 is y = -25x + 63.

The function given is f(x) = 6 + 5x − 5x². We need to find the equation of the tangent line to the curve at x = 3

.To find the equation of the tangent line at x = 3, we need to find the slope of the tangent at x = 3. The slope of the tangent at a point can be obtained by taking the derivative of the function at that point.

Thus, we first find the derivative of the given function at x = 3.f(x) = 6 + 5x − 5x²

Differentiating f(x) w.r.t x, we get:

f'(x) = 5 - 10x

At x = 3,f'(3) = 5 - 10(3) = -25

Thus, the slope of the tangent at x = 3 is -25.

We also know that the tangent line passes through the point (3, f(3)) = (3, 6 + 5(3) − 5(3)²) = (3, -12).

Using the point-slope form of the equation of a straight line, we can find the equation of the tangent line:

y - y₁ = m(x - x₁), where m is the slope of the line and (x₁, y₁) is a point on the line.

Substituting m = -25, x₁ = 3, and y₁ = -12 in the above equation, we get:y + 12 = -25(x - 3)

Simplifying the above equation, we get:

y = -25x + 63

Thus, the equation of the tangent line to the curve f(x) = 6 + 5x − 5x² at x = 3 is y = -25x + 63.

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Step-by-step explanation:

2x + 9° + 3x + 1° =180° (opposite angles of a cyclic quadrilateral are supplementary)

5x + 10° = 180°

5x = 180° - 10°

5x = 170°

x = 34°

Now

Angle A

= 2 * 34° + 9°

= 77°

Hope it will help :)❤

Answer:

yes that is correct

Step-by-step explanation:

negative times negative always positive

The gallons of gas required by Ryan to travel 286 miles is 13.2 gallons.

As the stated question;

Total gallon of gas used to drive the 260 miles = 12 gallons

Let 'x' be the gallon of gas used to drive the 286 miles.

Then, bu using the proportion

12 / 260 = x / 286

Thus,

x = 286 x 12 / 260

x = 13.2 gallons

Thus, the amount of gas required by Ryan to travel 286 miles is 13.2 gallons.

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Answer:

The answer is 2x² + 11x + 12.

Step-by-step explanation:

You have apply Distributive Law,

\(a(m + n) = am + an\)

So for this question :

\((2x + 3)(x + 4)\)

\( = 2x(x) + 2x(4) + 3(x) + 3(4)\)

\( = 2 {x}^{2} + 8x + 3x + 12\)

\( = 2 {x}^{2} + 11x + 12\)

\((2x + 3)(x + 4) \\ = 2x(x + 4) + 3(x + 4) \\ = 2x \times x + 2x \times 4 + 3 \times x + 3 \times 4 \\ = {2x}^{2} + 8x + 3x + 12 \\ = {2x}^{2} + 11x + 12 \\ hope \: it \: helps\)

Answer:

42/50 x2 =84%

Step-by-step explanation:

The total cost of raspberries and pears if she buys 2.5 pounds of raspberries and 2 pounds of pears is $16.5.

Total cost = (Cost of raspberries × pounds of raspberries) + (Cost of pears × pounds of pears)

= (4 × 2.5) + (3.25 × 2)

= 10 + 6.5

= $16.5

Total cost = (Cost of raspberries × pounds of raspberries) + (Cost of pears × pounds of pears)

= (4 × x) + (3.25 × y)

= 4x + 2y

Therefore, the equation that can be used to represent the total cost of raspberries and pears given the cost per pound of raspberries and pears is 4x + 2y.

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