What is the range of the data? 2,8,7,8,6,15,6,3,8

Answer:

Step-by-step explanation:

Solution:

Given:

A word problem.

To solve the question, we develop the statements into mathematical equations.

Hence,

Let the two numbers be represented by x and y

where;

x is one number

y is another number

Solving both equations generated simultaneously, using the elimination method, we subtract equation (1) from equation (2).

That is equation (2) - equation (1);

Substituting the value of y gotten into equation (2) to solve for x,

Hence, the solution to the equations is;

Therefore, the numbers are 10 and 4.

The general solution of the differential equation d²y/dx² - 36y = cosh(3x) is: \(C_1e^(^6^x^) + C_2e^(^-^6^x^) - (1/27) cosh(3x)\)

We have the following information from the question is:

The differential equation is given as:

d²y/dx² - 36y = cosh(3x)

Now, we have to solve by using the method of undetermined coefficients, we assume a particular solution of the form:

yₙ = A cosh(3x) + B sinh(3x)

where A and B are constants to be determined.

We have to find the second order derivatives of \(y_p\) with respect to x:

yₙ' = 3A sinh(3x) + 3B cosh(3x) y_p'' = 9A cosh(3x) + 9B sinh(3x)

Substituting these derivatives into the original differential equation,

we get:

(9A cosh(3x) + 9B sinh(3x)) - 36(A cosh(3x) + B sinh(3x)) = cosh(3x)

Simplify the equation, we get :

(9A - 36A) cosh(3x) + (9B - 36B) sinh(3x) = cosh(3x)

This leads to the following system of equations:

-27A = 1

-27B = 0

When solving above two equation we get the value of A and B:

The value of A and B are -1/27 and 0 respectively

Therefore, the particular solution is

yₙ = (-1/27) cosh(3x)

To find the general solution, we need to find the complementary solution, he solution to the homogeneous equation is d²y/dx² - 36y = 0.

The characteristic equation is r² - 36 = 0, which has roots r = ±6.

Hence, the complementary solution is:

\(y_a = C_1e^(^6^x^) + C_2e^(^-^6^x^)\)

where C₁ and C₂ are arbitrary constants.

Therefore, the general solution of the given differential equation is

y = yₙ + yₐ = \(C_1e^(^6^x^) + C_2e^(^-^6^x^) - (1/27) cosh(3x)\)

Learn more about Differential equation at:

https://brainly.com/question/25731911

#SPJ4

The given question is incomplete, complete question is:

Find the general solution for the following differential equation using the method of undetermined coefficients d²y/dx - 36 y = cosh3x.

The number of solution in 2(x + 1) = 2x + 5 is (a) no solution

The equation is given as:

2(x + 1) = 2x + 5

Open the brackets

2x + 2 =2x + 5

Subtract 2x from both sides

2 = 5

The above equation is false

This means that the equation has no solution

Hence, the number of solution in 2(x + 1) = 2x + 5 is (a) no solution

Read more about equations at:

https://brainly.com/question/2972832

#SPJ1

Answer:

100 ft²

Step-by-step explanation:

There are 4 congruent sides in a square

Perimeter = 4x

40 = 4x

x = 10

Area = base x height or length x width

Since all sides are the same, 10 is base and height

10x10 = 100

units = ft²

Answer = 100 ft²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

100 feet (I forget area units so there might be an exponent or something)

Step-by-step explanation:

Basically, the formula for perimeter is the sum of all sides. With area, you are just multiplying length times width. With a square, all of the sides are equal, and there are four sides. 40/4=10. So, each side is 10 feet. With that, you can multiply 10*10 and get 100!

Answer:

Amount of frozen soup = 2500 mL

Step-by-step explanation:

We are told that tom made 5,000 mL of soup.

We are also told he packed 2.5 Litres into his kids' lunches.

Now, from conversions,

1 liter = 1000 mL

Thus,

2.5 litres = 2.5 × 1000 = 2500 mL

Now, we are told he froze the rest of the soup.

Thus;

Amount of frozen soup = total amount of soup made - amount given to kids' lunch pack.

Amount of frozen soup =

5000 - 2500 = 2500 ml

Answer:

-.8

Step-by-step explanation:

divide both sides by 2.8

3d-2=-4.4

add two to both sides

3d=-2.4

divide both sides by 3

d=-.8

Answer:

The numbers which have definite value is known as constant. The numbers which don't have a definite value is known as variables.

Answer:

question 1:  23.111.etc question 2: 7

Step-by-step explanation:

208/9=23.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111112

question 2: 21/7=3 answer:7

The solutions are given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Part A

the dotted line formes the thrid side of the triangle.

part B

The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.

part c

If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.

part D

You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.

part e

The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.

part f

Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters

To learn more on triangle click:

brainly.com/question/29126067

#SPJ1

The distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.

The distribution of X, representing the IQ of an individual from the ruling species on the faraway planet, is a normal distribution with a mean (μ) of 106 and a standard deviation (σ) of 18. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.

In this distribution, the majority of IQ values will cluster around the mean of 106. The standard deviation of 18 indicates the average amount of variation or dispersion from the mean. The normal distribution is symmetric, which means that the probabilities of IQ values being above or below the mean are equal.

The shape of the normal distribution is bell-shaped, with the highest point being at the mean. As we move away from the mean, the probability of observing extreme values decreases. The spread of the distribution is determined by the standard deviation, where a larger standard deviation indicates a wider spread of IQ values.

the distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet.

Learn more about standard deviation here:

https://brainly.com/question/13498201

#SPJ11

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual.  What is the distribution of X? X ~ N( 106 , 18 )  

Answer:

(-4,-11)

Step-by-step explanation:

-11<-4(-4)+11

-11<16+11

-11<27 which is true

Average There are 120 ways to choose the three positions so that at least one freshman and one sophomore is chosen.

There are a total of 4 possible combinations of freshman and sophomore for the three positions, with at least one of each:

1. Freshman President, Sophomore Vice-President, Sophomore Treasurer

2. Sophomore President, Freshman Vice-President, Sophomore Treasurer

3. Freshman President, Sophomore Vice-President, Freshman Treasurer

4. Sophomore President, Freshman Vice-President, Freshman Treasurer

For each of the four combinations, there are 10 possible ways to choose the specific freshmen and sophomores for the positions (5 freshmen and 5 sophomores). That means there are 40 possible ways to choose the three positions with at least one freshman and one sophomore. Multiplying this by the 3 possible orders of the positions (President-Vice-President-Treasurer, President-Treasurer-Vice-President, Vice-President-President-Treasurer) gives us a total of 120 possible ways to choose the three positions so that at least one freshman and one sophomore is chosen.

Learn more about average here

https://brainly.com/question/24057012

#SPJ4

Answer:

288 good ways

Step-by-step explanation:

:)

Equation of a line is \(x+3y =-3\).

A perpendicular bisector is a line that cuts a line segment connecting two points exactly in half at a 90 degree angle. To find the perpendicular bisector of two points, all you need to do is find their midpoint and negative reciprocal, and plug these answers into the equation for a line in slope-intercept form.

Given that,

Endpoints of the line segment are (\(x_{1},y_{1}\)) = (4, 1) and (\(x_{2},y_{2}\)) = (2, -5).

First find the midpoints of the given line segment.

M = \(\left(\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2}\Right)\)

    =  \(\left(\frac{4+2 }{2},\frac{1-5 }{2}\Right)\)

M   =  \((3,-2)\)

Now, Find the slope of the line :

It is perpendicular to the line with (4,1) and (2,-5)

Slope between (\(x_{1},y_{1}\)) and (\(x_{2},y_{2}\)) = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

so,

the slope between (4,1) and (2,-5)  =  \(\frac{-5-1 }{2-4 }\)

                                                         = 3

perpendicular lines have slopes the multiply to get -1

3 times m=-1

m= \(\frac{-1}{3}\)

The equation of a line that has a slope of m and passes through the midpoints M(3,-2)  is

\(y-y_{1} =m(x-x_{1} )\)

\(y-(-2) =\frac{-1}{3} (x-3 )\)

\((y+2) =\frac{-1}{3} (x-3 )\)

if we want slope intercept form

\((y+2) =\frac{-1}{3} x+1\)

\(y= \frac{-1}{3} x-1\)

If we want standard form

\(\frac{1}{3} x+y = -1\)

\(x+3y =-3\)

Hence, Equation of a line is \(x+3y =-3\).

To learn more about perpendicular bisector of the line segment from the given link:

https://brainly.com/question/4428422

#SPJ4

Answer:

35$

Step-by-step explanation:

25 x 1.40 = 35

Answer:

a

Step-by-step explanation:

Answer:

Im pretty sure its d its defenantly NOT A

Step-by-step explanation:

Answer:

used bedmas

Step-by-step explanation:

=(22)x49+6

= 1070+6

=1076

Answer:

59/9

Step-by-step explanation:

d=100. 12/4=3 min/lap

12mins 4 laps. 100/180= 59/9

R=50

2(pie)(50)=100(pie)

rate at which Peter moves in m/s :

= 100m / 12 s

= 8.33 m/s

rate at which John moves in m/s :

since it should be given in meters per second let's convert km to m and minutes to second

2.5 km = 2500m ( as 1km = 1000m)

4 minutes = 240s ( as 1 min = 60s )

so the rate in m/s :

= 2500m / 240 s

= 10.416 m/s

Answer:

3x:4x for some real number x

Step-by-step explanation:

Since answer choices weren't provided, I generalized my answer.

First, notice we can simplify 6:4 into 3:2 because we can write the ratio as a fraction and simplify (6 and 4 are both multiples of 2).

Since 3 and 2 are relatively prime and the ratio cannot simplify anymore, we can say that the ratio of 6:4 = 3:2 = 3x:2x for some real number x because we can see that 3x:2x = 3:2  by simplifying  (3x and 3 are both multiples of x).

As long as the answer choice you choose matches the format above, you should be correct! I hope this helps! :)

The mean of the given set of group numbers is 6.6

Given,

In the question:

The Group of numbers are as follows:

6.1, 5.9, 4.2, 5.9 and 10.7

To find the mean of the given set of group of numbers.

Now, According to the question:

Given is the following data:

6.1, 5.9, 4.2, 5.9 and 10.7

We can find the mean of the given set of data using the formula-

Mean (M) = Σ a[i]/n = (Sum of all the elements)/(total number of elements)

Now, n = 5

and Σ a[i] = 6.1 + 5.9 + 4.2+ 5.9 + 10.7 = 32.8

Putting the values in the formula, we get:

M = 32.8/5 = 6.56 = 6.6

Hence, The mean of the given set of group numbers is 6.6

Learn more about Mean at:

https://brainly.com/question/1537458

#SPJ4

Answer:

Sssss

Step-by-step explanation:

Answer:

you take a step than you take another

Step-by-step explanation:

Solution

We want to find the area of the triangle given te sides

b = 20

a = 29

c = 21

Note: Hero formula for calculating the Area of a Triangle

We will first find S

To find the Area

Therefore, the area is

The unbiased estimator

Point A is at (4,1).

Point B is at (1,5).

Imagine drawing that blue triangle with a point at (1,1).

The distance of that bottom side would be (4-1) = 3.

The distance of the left side would be (5-1) = 4.

You can just could these distances on the graph or subtract the coordinates.

Now use the pyth. Theorem to find the hypotenuse, which is the length of one of the edges of the square.

3^2 + 4^2 = c^2

9+16 = 25 = c^2, so c = 5.

All sides of a square are the same.

AB = 5

BC = 5

CD = 5

DA = 5

Perimeter = 5+5+5+5 = 20 units

Area = 5x5 = 25 sq units.

See screenshot attached.

Have a good afternoon.

There are \(18\) square units in the area of the shaded rectangle.

The Latin words "rect" (which means "right") and "angulus" (which means "angle") are the roots of the English word "rectangle." These two words together form the term "rectangle." A rectangle has 90° straight angles at each of its four corners. A rectangular also has two equal-length diagonals that meet in the centre.

In addition to rectangles, we also refer to them as geometric figures, quadrilaterals, and polygons. This is so that it is clear that a rectangle fulfils the specifications of all of these other forms.

width \(= 7\) units

length \(= 10\) units

We remove the frame, each measure will lose\(2*2\) units, or \(4\) units

\(width = 7 units - 4 units = 3 units\)

\(length = 10 units - 4 units = 6 units.\)

\(A = (3 units)*(6 units) = 18\) square units.

To know more about rectangle visit:

https://brainly.com/question/28637495

#SPJ1

The completed question is:

One rectangle is "framed" within another. Find the area of the shaded region if the

"frame" is 1 unit wide.

10

5

The probability that one green and one yellow is selected (without replacement) is 3/7.

What are examples and probability?

Probability that one green and one yellow is selected (without replacement).

Since the cellphone is not replaced, the probability is calculated as follows

Pr = \(\frac{G}{n} * \frac{Y}{n - 1 } + \frac{Y}{n} * \frac{G}{n- 1}\)  The subtraction means the cellphones are not replaced

This gives

\(Pr = \frac{6}{8} * \frac{2}{8 - 1} + \frac{2}{8} * \frac{6}{8 - 1}\)

\(Pr = \frac{3}{4} * \frac{2}{7} + \frac{1}{4} * \frac{6}{7}\)

\(Pr = \frac{3}{14} + \frac{3}{14}\)

take lcm

\(Pr = \frac{3}{7}\)

Hence, the probability that one green and one yellow is selected (without replacement) is 3/7.

Learn more about probability

brainly.com/question/11234923

#SPJ4

He has eaten \(\frac{5}{8}\) pizza altogether.The total pieces of pizza was 8.Marco ate 3 for lunch and 2 for dinner.So, he ate 5 pieces of pizza out of 8.

What is fraction?

A fraction is a numerical value that is a part of whole number.In this numerator divided by denominator .In simple term both are integers.The word fraction means to break.

there are many types of fraction.Proper fraction, improper fraction,mixed fraction,whole fraction, like fraction, unlike fraction and unit fraction.

Total pieces of pizza =8

Marco ate for lunch =3

He ate for dinner =2

Total he ate =3+2

                     =5

Now remaining pieces of pizza=8-5

                       =3

To learn more about fractions visit:

https://brainly.com/question/10354322

#SPJ4

Answer:

5/8

Step-by-step explanation: