Suppose a certain trial has a 60% passing rate. We randomly sample 200 people that took the trial. What is the approximate probability that at least 65% of 200 randomly sampled people will pass the trial?

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

For more such questions on lengths

https://brainly.com/question/28322552

#SPJ8

Answer:

z = 6

Step-by-step explanation:

\(8z-36=2z\\6z-36=0\\6z=36\\z=6\)

The slope of the lines are:

12. -2.

13. 3/2

14. -1/4

15. 4/5

16. 8/7

17. -1.

The second points are:

18. (2, 7).

19. (4, 6)

20. (10, -5.6)

21. (8, 31/4)

The slope = m = change in y / change in x = \(\frac{y_2 - y_1}{x_2 - x_1}\).

12. Using any two points, (1, 11) and (2, 9):

Slope (m) = 11 - 9 / 1 - 2

= 2/-1

= -2.

13. Using any two points, (0, 11) and (2, 14):

Slope (m) = 14 - 11 / 2 - 0

= 3/2

14. Slope (m) = change in y / change in x = 3 - 2 / 0 - 4

= 1/-4

= -1/4

15. Slope (m) = change in y / change in x = 4 - 0 / 5 - 0

= 4/5

16. Slope (m) = change in y / change in x = 11 - 3 / 12 - 5

= 8/7

17. Slope (m) = change in y / change in x = -3 - 6 / 6 -(-3)

= -9/9

= -1.

18. We can use the point-slope form of the equation of a line to find the equation of the line passing through the given point and having the given slope. Then we can use this equation to find the other point.

The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the given slope.

In this case, the given point is (1, 3), and the given slope is m = 4. Substituting these values into the point-slope form, we get:

y - 3 = 4(x - 1)

Expanding the right side and simplifying, we get:

y - 3 = 4x - 4

y = 4x - 1

Now we have the equation of the line passing through the given point and having the given slope. To find the other point, we can choose any value of x and plug it into the equation to get the corresponding value of y.

For example, if we choose x = 2, then:

y = 4(2) - 1 = 7

So the other point is (2, 7). Therefore, the two points are (1, 3) and (2, 7).

Using the above method explained above, we have the following answers for the rest of the questions as:

19. (4, 6)

20. (10, -5.6)

21. (8, 31/4)

Learn more about the slope of a line on:

https://brainly.com/question/16949303

#SPJ1

(-3, 4) is the solution to the given system of simultaneous equation

Given the system of equation

y = -x + 1

y = -1/3x + 3​

When solving graphically, the point of intersection of both lines on an xy plane is the solution to the system of equation.

According to the graph attached, the solution to the system of equation is (-3, 4).

Learn more on graphical system of equation here https://brainly.com/question/7853772:

#SPJ1

Therefore, (a) Increasing intervals: [0,π/4), (5π/4,2π],  Decreasing interval: (π/4,5π/4). (b) Local max: 18 at π/4; Local min: 9 at 5π/4. (c) Inflection points: 3π/4, 7π/4, Concave up interval: (3π/4,7π/4), Concave down intervals: [0,3π/4), (7π/4,2π]

To find the intervals where f is increasing or decreasing, we need to take the first derivative of f, which is f'(x) = 9cos(x)-9sin(x). Setting f'(x) = 0 and solving for x, we get x = π/4, 5π/4. Thus, f is increasing on the intervals [0,π/4) and (5π/4,2π], and decreasing on the interval (π/4,5π/4). To find the local maxima and minima, we need to check the sign of f''(x) at x = π/4, 5π/4. We get f''(π/4) = -18, which means f has a local maximum of 18 at x = π/4, and f''(5π/4) = 18, which means f has a local minimum of 9 at x = 5π/4. To find the inflection points, we need to set f''(x) = 0 and solve for x. We get x = 3π/4, 7π/4. Thus, f is concave up on the intervals (3π/4,7π/4) and concave down on the intervals [0,3π/4) and (7π/4,2π].

Therefore, (a) Increasing intervals: [0,π/4), (5π/4,2π],  Decreasing interval: (π/4,5π/4). (b) Local max: 18 at π/4; Local min: 9 at 5π/4. (c) Inflection points: 3π/4, 7π/4, Concave up interval: (3π/4,7π/4), Concave down intervals: [0,3π/4), (7π/4,2π]

To know more about congruent visit :

https://brainly.com/question/11949261

#SPJ11

This is the solution to the given initial value problem (IVP).

y(t) ≈ 1.129 * e^(-5.343t) + 0.367 * e^(-0.816t) * cos(4.844t) + 0.467 * e^(-0.816t) * sin(4.844t)

To solve the given initial value problem (IVP) of the third-order linear homogeneous differential equation, we can use the method of characteristic equation.

The given differential equation is: y''' + 7y" + 33y' - 41y = 0

Characteristic Equation

We assume the solution in the form of y = e^(rt), where r is a constant to be determined.

Substituting y = e^(rt) into the differential equation, we get:

r^3 + 7r^2 + 33r - 41 = 0

Solving the Characteristic Equation

To solve the characteristic equation, we can factor it or use numerical methods. In this case, let's use numerical methods to find the roots.

Using numerical methods or a calculator, we find the roots of the characteristic equation as follows:

r ≈ -5.343, -0.816 ± 4.844i

General Solution

The general solution of the differential equation is given by:

y(t) = c1 * e^(-5.343t) + c2 * e^(-0.816t) * cos(4.844t) + c3 * e^(-0.816t) * sin(4.844t)

where c1, c2, and c3 are constants to be determined.

Solve for Constants Using Initial Conditions

Given initial conditions:

y(0) = 1, y'(0) = 2, y"(0) = 4

Substituting the initial conditions into the general solution, we get the following equations:

For t = 0:

c1 + c2 = 1

For t = 0:

-5.343c1 - 0.816c2 + 4.844c3 = 2

For t = 0:

28.482c1 + 0.667c2 + 3.949c3 = 4

Solving these equations simultaneously, we can find the values of c1, c2, and c3.

After solving the system of equations, we find:

c1 ≈ 1.129, c2 ≈ 0.367, c3 ≈ 0.467

Final Solution

Substituting the values of c1, c2, and c3 back into the general solution, we obtain the final solution to the IVP:

y(t) ≈ 1.129 * e^(-5.343t) + 0.367 * e^(-0.816t) * cos(4.844t) + 0.467 * e^(-0.816t) * sin(4.844t)

This is the solution to the given initial value problem (IVP).

for such more question on initial value problem

https://brainly.com/question/27746495

#SPJ8

To estimate the mean EPA combined city and highway mileage, the automaker conducted EPA mileage tests on a random sample of 35 midsize cars. The sample mean is 24, and the population standard deviation is 1.2. The task is to calculate the 70% confidence interval for the population mean.

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))

First, we need to determine the critical value associated with a 70% confidence level. The critical value can be found using a standard normal distribution or a t-distribution, depending on the sample size and whether the population standard deviation is known.

Since the sample size is relatively large (n = 35), we can use the standard normal distribution. The critical value for a 70% confidence level corresponds to a z-score of ±1.036.

Next, we calculate the margin of error:

Margin of Error = (Critical Value) * (Standard Deviation / √(Sample Size)) = 1.036 * (1.2 / √35) ≈ 0.380

Finally, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = Sample Mean - Margin of Error = 24 - 0.380 ≈ 23.62

Upper Bound = Sample Mean + Margin of Error = 24 + 0.380 ≈ 24.38

Therefore, the 70% confidence interval for the mean EPA combined city and highway mileage is approximately 23.62 to 24.38.

Learn more about standard deviation here: brainly.com/question/29808998

#SPJ11

solution

W=f×d×cos theta

=25N×16m×cos 45°

=400Nm×cos 45°

=282.84J

W=f×d×cos theta

=25N×7m×cos 10°

=175Nm×cos10°

=172.34J

Total workdone=282.84J+172.34J=455.18J

Quadratic Equations: 1. \(x^{2} -15x+56=0\), 2. \(x^{2} +x-12=0\), 3. \(x^{2} -11x+28=0\) Factored Polynomials:10. (r + 9)(r - 6), 12. (c - 7)(c + 7), 14. (4r + 13)(4r - 13), 11. 2(4a - 3)(ra + 1), 13. (x + 2)\((x^{2} -2x+4)\), 15. (b + 3)(b - 3)

The given problem asks to write the quadratic equation in standard form given the roots and then factor the polynomials.

A quadratic equation in standard form is written as \(ax^{2} +bx+c=0\), where a, b, and c are constants.

To write the equation in standard form, we can use the sum and product of the roots of the equation. The sum of the roots can be found by adding the given roots, and the product of the roots can be found by multiplying them. We then use these values in the equation \(ax^{2} +bx+c=0\) as follows:

Once we have the equation in standard form, we can factor it by finding two binomials whose product is equal to the equation.

For example, let's consider the equation \(x^{2} -11x+28=0\) with roots 7.2 and -5.8.

So, b = -(sum of roots) = -1.4 and c = product of roots = -41.76. Hence, the equation in standard form is \(x^{2} -11x-41.76=0\). To factor the polynomial, we look for two binomials that multiply to give the equation. We can find these by inspection or by using a formula. In this case, the factorization is (x - 7.2)(x + 5.8) = 0.

Learn more about polynomial here:

https://brainly.com/question/29146511

#SPJ4

Answer:  ∠1 = 52°, ∠4 = 40°, ∠7 = 100°, ∠10 = 49°, ∠13 = 65°

Step-by-step explanation:

There are three formulas you need to find the angles. Each formula is based on where the vertex lies.

On the circle: Measure of the angle = (1/2) the arc (Images 1-3)

∠4 = (1/2)°80             ∠10 = (1/2)(18° + 80°)           ∠13 = (1/2)130°

    = 40°                           = (1/2)98°                            = 65°

                                       = 49°

Inside the circle: (1/2) Sum of the Big arc and Little Arc (Image 4)

∠7 = (1/2) (130° + 70°)

    = (1/2)200°

   = 100°

Outside the circle: (1/2) Difference of Big arc and Little Arc (Image 5)

∠1 = (1/2)[(62° + 130°) - (70° + 18°)]

    = (1/2) (192° - 88°)

   = (1/2)104°

   = 52°

I can only add 5 attachments.  If you want to see image 6 (which contains the measures for all of the angles), you will need to ask the question again.  Sorry!

Answer:

The area will be:

\(A=18(1+\sqrt{3}) \: u^{2}\) or \(A=49.18 \: u^{2}\).

Step-by-step explanation:

Using the definition of tangent, we have:

\(tan(\alpha)=\frac{6}{\vec{AB}}\)

We know that tan(α) = 1, then we can find AB

\(1=\frac{6}{\vec{AB}}\)

\(\bar{AB}=6\: u\)

u means any unit.

Now, we need to find the distance BC. If the angle ∠D is 60°, then ∠C must be 30°. Using the tangent definition in the triangle BCD we have:

\(tan(30)=\frac{6}{\bar{BC}}\)

\(\bar{BC}=\frac{6}{tan(30)}\)

\(\bar{BC}=\frac{6}{1/\sqrt{3}}\)

\(\bar{BC}=6\sqrt{3} \: u\)

So, the base of the triangle will be:

\(b=\bar{AB}+\bar{BC}=6+6\sqrt{3}=6(1+\sqrt{3}) \: u\)

The area of a triangle is given by the following equation:

\(A=\frac{b*h}{2}\)

\(A=\frac{6(1+\sqrt{3})*6}{2}\)

\(A=18(1+\sqrt{3})\)

Therefore, the area will be \(A=49.18 \: u^{2}\).

I hope it helps you!

The measures of the angles of the parallelogram are

The measure of ∠A = 72°

The measure of ∠B = 108°

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , the measure of ∠A = ( 5y - 3 )°

The measure of ∠C = ( 3y + 27 )°

For a parallelogram , opposite angles are congruent

So , measure of ∠A = measure of ∠C

Substituting the values in the equation , we get

( 5y - 3 )° =  ( 3y + 27 )°

On simplifying the equation , we get

( 5y - 3 ) =  ( 3y + 27 )

Subtracting 3y on both sides of the equation , we get

2y - 3 = 27

Adding 3 on both sides of the equation , we get

2y = 30

Divide by 2 on both sides of the equation , we get

y = 15

So , the measure of ∠A = ( 5y - 3 )°

The measure of ∠A = ( 5 ( 15 ) - 3 ) )°

The measure of ∠A = ( 75 - 3 )°

The measure of ∠A = 72°

Now , for a parallelogram , same-side interior angles (consecutive angles) are supplementary

So , the measure of ∠A + the measure of ∠B = 180°

Substituting the values in the equation , we get

72° + the measure of ∠B = 180°

Subtracting 72° on both sides of the equation , we get

The measure of ∠B = 108°

Hence , the measures of angles of the parallelogram are 72° and 108° respectively

To learn more about parallelogram click :

https://brainly.com/question/23488153

#SPJ1

To reparametrize the curve with respect to arc length, we need to find the arc length function s(t) and then solve for t in terms of s.

The arc length function is given by:

s(t) = ∫√[r'(t)·r'(t)] dt

where r'(t) is the derivative of r(t) with respect to t.

We can calculate r'(t) as:

r'(t) = (2e^(2t)cos(2t) - 4e^(2t)sin(2t))i + (12e^(2t)sin(2t))j + (2e^(2t)sin(2t) + 6e^(2t)cos(2t))k

Now we can substitute this into the arc length formula and integrate:

s(t) = ∫√[(2e^(2t)cos(2t) - 4e^(2t)sin(2t))^2 + (12e^(2t)sin(2t))^2 + (2e^(2t)sin(2t) + 6e^(2t)cos(2t))^2] dt

This integral looks quite complicated, so we will use a numerical integration method to approximate s(t).

We can use the trapezoidal rule to numerically integrate s(t) between t = 0 and some value t = T:

s(T) ≈ ∑[s(iΔt) + s((i+1)Δt)]/2 * Δt

where Δt = T/n is the step size, and n is the number of intervals we use.

Once we have approximated s(t), we can solve for t in terms of s using numerical methods such as the bisection method or Newton's method.

For example, if we want to find the value of t that corresponds to s = 10, we can solve:

s(t) = 10

for t using numerical methods. Once we have t, we can plug it back into r(t) to get the reparametrized curve in terms of arc length s.

To know more about arc length refer to

https://brainly.com/question/2005046

#SPJ11

9514 1404 393

Answer:

  £336

Step-by-step explanation:

Work through the sequence of statements, converting them to numbers.

800 tickets at £2 each will raise 800×£2 = £1600 in gross revenue.

4% of the tickets are 800×4% = 32 tickets.

If the 32 prizes cost £20 each, their total cost is 32×£20 = £640.

Then the net profit is ...

  revenue - cost = profit

  £1600 -640 = £960

The amount that goes to Charity B is 35% of this (what's left over after 65% goes to Charity A).

  £960 × 35% = £336

Dorothy raises £336 for Charity B.

The  number corrected to 1 decimal place is 78.5

The number corrected to the nearest hundredth is 78.47

From the question, we are to estimate the given number to the nearest 1 decimal place

The given number is

78.4695

Correcting to 1 decimal place

In the given number, we can observe that the hundredth digit is greater than 5, thus we will add 1 to the tenth digit

Thus,

78.4695 corrected to 1 decimal place is 78.5

Correcting to the nearest hundredth

The thousand digit is greater than 5, thus we will add 1 to the hundredth  digit

Thus,

78.4695 corrected to the nearest hundredth is 78.47

Hence,

The  number corrected to 1 decimal place is 78.5

The number corrected to the nearest hundredth is 78.47

Learn more on Estimation here: https://brainly.com/question/886963

#SPJ1

Answer:

.0097

Step-by-step explanation:

Take the decimal and move it 3 (variable for any negative exponent) places to the left

Answer:

0.0097 is the answer.

Step-by-step explanation:

You start by counting from the decimal place. For negative exponents, you would count to the left. Three decimal places to the left of 9.7 is 0.0097.

No, 25 is not a prime number. It can be divided by 5 without a remainder, so it has factors other than 1 and itself.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and by itself. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.

The factors of 25 are 1, 5 and 25. Prime numbers are numbers that are divisible by only 1 and themselves. So 25 is not a prime number.

To know more on prime number

https://brainly.com/question/11799672

#SPJ4

Therefore, the order-reversed integral is:

∫ba∫dcsin(x^2) dydx, where a= 0, b= 3, c= √(3y), and d= √(9y).

We have:

∫30∫3ysin(x^2) dxdy

To reverse the order of integration, we need to express the limits of integration as inequalities of x and y:

3y ≤ x^2 ≤ 9y

√(3y) ≤ x ≤ √(9y)

0 ≤ y ≤ 1

So, we have:

∫30∫√(9y)√(3y)sin(x^2) dxdy

Integrating with respect to x first, we get:

∫√(9y)√(3y) [-cos(x^2)/2] |_0^(√(3y)) dy

= ∫30 [-cos(3y)/2 + cos(y)/2] dy

= [-sin(3y)/6 + sin(y)/2] |_0^3

= (-sin(9)/6 + sin(3)/2) - (0 - 0)

= (-sin(9)/6 + sin(3)/2)

Therefore, the order-reversed integral is:

∫ba∫dcsin(x^2) dydx, where a= 0, b= 3, c= √(3y), and d= √(9y).

Note: We can also check the answer by evaluating the original integral and comparing it with the answer obtained by reversing the order of integration.

To know more about integrals refer here:

https://brainly.com/question/18125359

#SPJ11

Answer:

The formula for calculating the compound amount is:

A = P( 1 + R ) ^ T

Put in the numbers and calculate:

A = 800( 1.09 ) ^ 2

A = 800 x 1.1881

A = 950.48

I = A - P

I = 950.48 - 800

I = 150.48

Answer:

Jay is 18

Step-by-step explanation:

Because if Nadia is 6 and Jay is 3 times her age, then he would be 18.

Also, you add 10 to both of their ages, there is an age gap of 12 years.

Answer:

1155

Step-by-step explanation:

165 × 7 = 1155

i hink this is the answert

An integer known as a binomial number is created by evaluating a homogeneous polynomial with two terms, also known as a binomial.

Polynomials are algebraic expressions that include constants and indeterminates. Polynomials are a type of mathematics. In almost every branch of mathematics, they are used to express numbers, and calculus is one of those branches where they play a particularly significant role.

Polynomials include formulas like 2x + 9 and x² + 3x + 11. You may have noticed that none of these examples include the "=" sign.

Each variable's exponent in an algebraic expression for a polynomial must be a whole number. Polynomial exponents have to be non-negative integers. A polynomial cannot be divided by a variable even though it contains both constants and variables.

Learn more about polynomials

https://brainly.com/question/11536910

#SPJ4

The complete inequality expressions are

-5/8 < 3/8, 4/5 > 0.71, 5/6 < 0.875, 1.2 < 1 2/9, 8/15 > 0.53 and -7/11 > -2/3

To do this, we solve the expressions one after the other.

So, we have:

-5/8 o 3/8

Negative numbers are less than positive numbers.

So, we have:

-5/8 < 3/8

4/5 o 0.71

Express 4/5 as decimal

0.8 o 0.71

0.8 is greater than 0.71

So, we have:

0.8 > 0.71

Rewrite as:

4/5 > 0.71

5/6 o 0.875

Express 5/6 as decimal

0.83 o 0.875

0.83 is less than 0.875

So, we have:

0.83 < 0.875

Rewrite as:

5/6 < 0.875

1.2 o 1 2/9

Express 1 2/9 as decimal

1.2 o 1.222

1.2 is less than 1.222

So, we have:

1.2 < 1.222

Rewrite as:

1.2 < 1 2/9

8/15 o 0.53

Express 8/15 as decimal

0.5333 o 0.53

0.5333 is greater than 0.53

So, we have:

0.5333 > 0.53

Rewrite as:

8/15 > 0.53

-7/11 o -2/3

Express as decimals

-0.637 o -0.67

-0.637 is greater than -0.67

So, we have:

-0.637 > -0.67

Rewrite as:

-7/11 > -2/3

Read more about inequality expressions at

https://brainly.com/question/25275758

#SPJ1

Answer:

Step-by-step explanation:

Tangent line is:

Perpendicular line to this has a slope of -3 and passes through  point (1, 2).

Its equation is:

Using the second line passing through the center, find the coordinates of the center:

Solve the system by elimination:

Then

The center is (0, 5) and radius is the distance from center to point (1, 2):

The equation of circle:

The person can see far upto 53.08 miles.

The Pythagorean Theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

In other words, for the triangle shown below, a² + b² = c².

The legs, a and b, are the perpendicular sides of the right triangle and the hypotenuse, c, is the side opposite the right angle.

This application is frequently used in construction projects and basically anything that involves right triangles life roofs to a house and so on

The length of the hypotenuse (4960 miles + 1500 feet) and you know the length of the base (4960 miles), you can readily find the height using the Pythagorean theorem (c² = a² + b²).

I converted the distances from miles to feet. The numbers are large but manageable.

Earth's radius = 4960 miles = 26,188,800 feet.

Earth's radius plus height of the skyscraper = 26,9188,800 + 1500 ft

= 26,190,300 feet.

c² = a² + b²

(26,190,300)² = (26,188,800)² + h²

Solve for h

h² = 6.85931814X10^14 - 6.85853245X10^14

h^2 = 78,569,000,000

h = 280,301.623 feet = 53.08 miles

Thus, the person can see far upto 53.08 miles.

To learn more about Pythagorean theorem, visit brainly.com/question/14930619

#SPJ4

The person can see far upto 53.08 miles.

The Pythagorean Theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

In other words, for the triangle shown below, a² + b² = c².

The legs, a and b, are the perpendicular sides of the right triangle and the hypotenuse, c, is the side opposite the right angle.

This application is frequently used in construction projects and basically anything that involves right triangles life roofs to a house and so on

The length of the hypotenuse (4960 miles + 1500 feet) and you know the length of the base (4960 miles), you can readily find the height using the Pythagorean theorem (c² = a² + b²).

I converted the distances from miles to feet. The numbers are large but manageable.

Earth's radius = 4960 miles = 26,188,800 feet.

Earth's radius plus height of the skyscraper = 26,9188,800 + 1500 ft

= 26,190,300 feet.

c² = a² + b²

(26,190,300)² = (26,188,800)² + h²

Solve for h

h² = 6.85931814X10^14 - 6.85853245X10^14

h² = 78,569,000,000

h = 280,301.623 feet = 53.08 miles

Thus, the person can see far upto 53.08 miles.

To learn more about Pythagorean theorem

brainly.com/question/14930619

#SPJ4

First of all, stop thinking on the number 1000 and turn your attention to the number 990 instead. If you solve the problem for 990 you just have to add 993,995,996 & 999 to it for the final answer. This sum is (a)=3983

Count all the #s divisible by 3: From 3... to 990 there are 330 terms. The sum is 330(990+3)/2, so (b)=163845

Count all the #s divisible by 5: From 5... to 990 there are 198 terms. The sum is 198(990+5)/2, so (c)=98505

Now, the GCD (greatest common divisor) of 3 & 5 is 1, so the LCM (least common multiple) should be 3×5=15.

This means every number that divides by 15 was counted twice, and it should be done only once. Because of this, you have an extra set of numbers started with 15 all the way to 990 that has to be removed from (b)&(c).

Then, from 15... to 990 there are 66 terms and their sum is 66(990+15)/2, so (d)=33165

The answer for the problem is: (a)+(b)+(c)−(d)=233168

Simple but very fun problem.

The additive inverse of the polynomial is:

7y^(2) - x^(2)y + 3xy + 7x^(2)

The additive inverse of a number A is a number B such that:

A + B = 0

B = -A

Similarly for polynomials, to find the additive inverse, you just need to multiply it by -1.

Here the polynomial is:

-7y^(2) + x^(2)y - 3xy - 7x^(2)

Then the additive inverse is:

-1*(-7y^(2) + x^(2)y - 3xy - 7x^(2))

7y^(2) - x^(2)y + 3xy + 7x^(2)

Learn more about polynomials at:

https://brainly.com/question/4142886

#SPJ1