The sum of two numbers is 5 and their difference is 2. which of the following could be the difference of their squares

I will mark whoever solve it correct as Brainlist

Answer:

the step-by-step explanation for height first :

[tex]h=\sqrt{h^{2} } +r^{2} =26[/tex]

[tex]h=\sqrt{h^{2} } +10^{2} =676[/tex]

[tex]h=\sqrt{h^{2} } + 100 = 676[/tex]

[tex]100-100 = 0[/tex]

[tex]676-100=576[/tex]

[tex]\sqrt{576}[/tex]

[tex]height =[/tex] 24 m

________________

step-by-step explanation for the problem :

FORMULA :  [tex]v = \frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]

v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]10^{2}[/tex] · [tex]24[/tex] = [tex]800\pi[/tex] = [tex]2513.27412[/tex] = 2513

Answer:

c. The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

A variable is said to be continuous if it can take on any value in an interval. Examples are lengths, temperature, etc

A discrete variable, on the other hand, can only take on specific values. Examples of discrete variables are the number of students and age.

The exact lengths (in kilometers) of the ocean coastlines of different countries is a continuous variable because it can take on any value in an interval.

A stated earlier, Lengths are in general, continuous variables.

Answer:

Step-by-step explanation:

1) divide equilateral tri from the middle you will get two 30-60-90 triangles

2) by using pythagorean law & trigimintory, you will get two unknowns (height and side length) and two functions

Answer: the answer is 1 in the numerator and r to the 8th power times s to the 5th power in the denominator.

Step-by-step explanation:

Answer:

Step-by-step explanation:

its B

Answer:

the answer is B

Step-by-step explanation:

Answer:

D. No, because the differential equation does not have constant coefficients.

Step-by-step explanation:

The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.

Answer:

[tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex]

B.

B.

[tex]y = \frac{17}{8}e^4^x - \frac{1}{8}e^-^4^x[/tex]

Step-by-step explanation:

Question 1:

- We are given a homogeneous second order linear ODE as follows:

                                [tex]y'' + 49y = 0[/tex]

- A pair of independent functions are given as ( y1 ) and ( y2 ):

                               [tex]y_1 = cos ( 7x )\\\\y_2 = sin ( 7x )[/tex]

- The given ODE is subjected to following initial conditions as follows:

                               [tex]y ( 0 ) = 10\\\\y ' ( 0 ) = -4[/tex]

- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:

                               [tex]y = c_1y_1 + c_2y_2[/tex]

Solution:-

- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.

- Formulate the second derivatives of both functions y1 and y2 as follows:

                           [tex]y'_1 = -7sin(7x) , y''_1 = -49cos(7x)\\\\y'_2 = -7cos(7x) , y''_2 = -49sin(7x)\[/tex]

- Now plug the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.

                           [tex]y''_1 + 49y_1 = 0\\\\-49cos(7x) + 49cos ( 7x ) = 0\\0 = 0\\\\y''_2 + 49y_2 = 0\\\\-49sin(7x) + 49sin ( 7x ) = 0\\0 = 0\\\\[/tex]

- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.

- The complete solution to a homogeneous ODE is given in the form as follows:

                            [tex]y = c_1y_1 + c_2y_2\\\\y = c_1*cos(7x) + c_2*sin(7x)\\[/tex]

- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,

                           [tex]y (0) = c_1cos ( 0 ) + c_2sin ( 0 ) = 10\\\\y'(0) = -7c_1*sin(0) + 7c_2*cos(0) = -4\\\\c_1 ( 1 ) + c_2 ( 0 ) = 10, c_1 = 10\\\\-7c_1(0) + 7c_2( 1 ) = -4 , c_2 = -\frac{4}{7}[/tex]

- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:

                           [tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex]    .... Answer

Question 2

- We are given a homogeneous second order linear ODE as follows:

                               [tex]y'' -16y =0[/tex]

- A pair of independent functions are given as ( y1 ) and ( y2 ):

                               [tex]y_1 = e^4^x\\\\y_2 = e^-^4^x[/tex]

- The given ODE is subjected to following initial conditions as follows:

                               [tex]y( 0 ) = 2\\y'( 0 ) = 9[/tex]

- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:

                               [tex]y = c_1y_1 + c_2y_2[/tex]

Solution:-

- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.

- Formulate the second derivatives of both functions y1 and y2 as follows:

                         [tex]y'_1 = 4e^4^x , y''_1 = 16e^4^x\\\\y'_2 = -4e^-^4^x , y''_2 = 16e^-^4^x[/tex]  

- Now substitute the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.

                           [tex]y''_1 - 16y_1 = 0\\\\16e^4^x - 16e^4^x = 0\\\\0 = 0\\\\y''_2 - 16y_2 = 0\\\\16e^-^4^x - 16e^-^4^x = 0\\\\0 = 0[/tex]

- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.

- The complete solution to a homogeneous ODE is given in the form as follows:

                            [tex]y = c_1y_1 + c_2y_2\\\\y = c_1*e^4^x + c_2*e^-^4^x[/tex]

- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,

                           [tex]y ( 0 ) = c_1 * e^0 + c_2 * e^0 = 2\\\\y' ( 0 ) = 4 c_1 * e^0 - 4c_2 * e^0 = 9\\\\c_1 + c_2 = 2 , 4c_1 - 4c_2 = 9\\\\c_1 = \frac{17}{8} , c_2 = -\frac{1}{8}[/tex]

- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:

                           [tex]y = \frac{17}{8} e^4^x - \frac{1}{8}e^-^4^x[/tex]   .... Answer

Answer:

(x-1)(x-4)

Step-by-step explanation:

I used long division with polynomials to help me find the other factor to this problem.  Divide x cubed -5x squared -6x+8 by x+2 to get x squared -5x+4.

Hope this helps!

Answer:  (x + 2) (x - 4) (x - 1)

Step-by-step explanation:

Use synthetic division. If the remainder (last digit) is zero, then it is a factor. The other digits represent the coefficients of the reduced polynomial.

x³ - 3x² - 6 + 8   ; x + 2 = 0  --> x = -2

-2  |  1   -3    -6    8

    |  ↓   -2   10   -8  

       1    -5    4    0    → remainder is 0

Reduced polynomial: x² -5x + 4

                                = (x - 4) (x - 1)

Factored form: (x + 2) (x - 4) (x - 1)

Answer:

c)

The probability of a player weighing more than 238

P( X > 238) = 0.0174

Step-by-step explanation:

Step(i):-

Given mean of the normally distribution = 195 pounds

Given standard deviation of  the normally distribution

                                                              =  20 pounds.

Let 'x' be the random variable of  the normally distribution

Let   X = 238

[tex]Z = \frac{x-mean}{S.D} = \frac{238-195}{20} = 2.15[/tex]

Step(ii):-

The probability of a player weighing more than 238

P( X > 238) = P( Z> 2.15)

                  = 1 - P( Z < 2.15)

                 =  1 - ( 0.5 + A(2.15)

                =   1 - 0.5 - A(2.15)

               = 0.5 - 0.4821    ( from normal table)

               = 0.0174

The probability of a player weighing more than 238

P( X > 238) = 0.0174

Answer:

$23.64

Step-by-step explanation:

12 * $1.97 = $23.64

Answer:

Step-by-step explanation:

There are obviously two different sequence the first difference is (-4) while the other one is (+4)which makes the next numbers 13,-15.

Answer:

c- the right triangle altitude theorem

Step-by-step explanation:

i did it on edge! ; )

The missing statement in Step 6 is ,c- The right triangle altitude theorem.

We have given that,

In △ABC, AD ⊥ BC

Prove: StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction.

Triangle A B C is shown.

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse

Therefore we have,

A perpendicular bisector is drawn from point A to point D on side C B forming a right angle.

The length of A D is h, the length of C B is a, the length of C A is b, and the length of A B is c.

So the missing statement in Step 6

b = c

c=The right triangle altitude theorem.

To learn more about the right triangle altitude theorem visit:

https://brainly.com/question/723406

Answer:

50

Step-by-step explanation:

The probability of it landing on yellow or blue is 5 out of 7 total possibilities.

5/7

Multiply by 70.

5/7 × 70

350/7

= 50

Answer:

50 times

Step-by-step explanation:

Yellow or blue is 5/7 of the spinner

Multiply 70 by 5/7 to find the prediction of the number of times it will land there

70(5/7) = 50

Answer:

The theoretical probability is smaller than the relative frequency

Step-by-step explanation:

6-sided cube rolled 200 times

Probability of an even number is 1/2= 0.5

200*1/2= 100- theoretical probability

Experimental frequency= 115

Relative frequency= 115/200= 0.575

0.575 > 0.5

The theoretical probability is smaller than the relative frequency

Answer:

The theoretical probability is smaller than the relative frequency.

Step-by-step explanation:

Answer:

800

Step-by-step explanation:

10,000 x 64 = 640,000

Square Root It Makes It

800

Answer:

6,400

Step-by-step explanation:

The square root of 10,000 times 64 is simplified to 6,400

Answer:

0.0013

Step-by-step explanation:

The probability of selling a property is 40%, so the probability of not selling it is 60%.

To find the probability of selling at least 11 properties, we can calculate the following cases:

Selling 11:

P(11) = C(13,11) * P(sell)^11 * P(not sell)^2

P(11) = (13! / (11! * 2!)) * 0.4^11 * 0.6^2

P(11) = 13*12/2 * 0.4^11 * 0.6^2 = 0.001178

Selling 12:

P(12) = C(13,12) * P(sell)^12 * P(not sell)^1

P(11) = (13! / (12! * 1!)) * 0.4^12 * 0.6^1

P(11) = 13 * 0.4^12 * 0.6 = 0.000131

Selling 13:

P(13) = C(13,13) * P(sell)^13 * P(not sell)^0

P(11) = 1 * 0.4^13 * 0.6^0

P(11) = 1 * 0.4^13 * 1 = 0.000007

Final probability:

P(at least 11) = P(11) + P(12) + P(13)

P(at least 11) = 0.001178 + 0.000131 + 0.000007 = 0.001316

P(at least 11) = 0.0013

Answer:

-0.28

Step-by-step explanation:

(1/5) : (-5/7)=(1*5)/(5*(-5))=-(7/25)=-0.28

Answer:

[tex]-7/25[/tex]

Step-by-step explanation:

[tex]1/5 \div -5/7[/tex]

Do the reciprocal of the second fraction.

[tex]1/5 \times 7/-5[/tex]

Multiply the first fraction by the reciprocal of the second fraction.

[tex]7/-25=-0.28[/tex]

The answer in decimal form is -0.28.

Answer:

[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]

Step-by-step explanation:

You have the following differential equation:

[tex]3y''+12y=0[/tex]     (1)

In order to find the solution to the equation, you can use the method of the characteristic polynomial.

The characteristic polynomial of the given differential equation is:

[tex]3m^2+12=0\\\\m^2=-\frac{12}{3}=-4\\\\m_{1,2}=\pm2\sqrt{-1}=\pm2i[/tex]

The solution of the differential equation is:

[tex]y(x)=c_1e^{m_1x}+c_2e^{m_2x}[/tex]   (2)

where m1 and m2 are the roots of the characteristic polynomial.

You replace the values obtained for m1 and m2 in the equation (2). Then, the solution to the differential equation is:

[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]

Answer:

The sequence can be represented by the formula of its nth term:

[tex]a_n=\frac{(-1)^n}{n}[/tex]

Step-by-step explanation:

Notice that we are in the presence of an alternate sequence (the values alternate from negative to positive. Therefore we need to take into account that there should be a factor "-1" raised to the "n" value for the sequence. Also, given that the sequence looks in absolute value like the harmonic sequence, we conclude upon the following general form for the "nth" term of the sequence:

[tex]a_n=\frac{(-1)^n}{n}[/tex]

Answer:

25%

Step-by-step explanation:

less than 30 is from minimum to lower quartile. so, 25%

Answer:

20.43% probability that a randomly chosen graduate from these 300 graduated with honors given that neither parent graduated from college.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Graduated with honors:

98 students graduated with honors. Of those, 79 had at least one parent graduating from college. So 98 - 79 = 19 did not.

Of 300 students, 207 had one or both parents graduate from college. So 300 - 207 = 93 did not have at least one parent graduating.

Find the probability that a randomly chosen graduate from these 300 graduated with honors given that neither parent graduated from college.

Of the 93 with no graduated parent, 19 earned honors

19/93 = 0.2043

20.43% probability that a randomly chosen graduate from these 300 graduated with honors given that neither parent graduated from college.

Answer:

–0.029 to 0.229.

Step-by-step explanation:

So, we are given the following data or information or values/parameters which are going to help us in solving this particular equation:

=>" A class of entering freshmen = 6000 or more students) respectively"

=> "The class of entering freshmen graduated in the bottom third of their high school class."

=>" 99% confidence interval for p1 – p2"

Let p1 = k1 and p2 = k2

Here, we can deduce that p1 > p2; k1 > k2. Hence,

a = (1 - 0.99)/2 = 0.005.

b = 513 × 0.005 = 2.6.

c = standard deviation = ✓ [ k1 (1 - k1) / j1 + k2 (1 - k2) / j2] = 0.05.

99% confidence interval for p1 – p2 =

k1 - k2 - b × c = –0.029

Also, k1 - k2 + b × c = 0.029.

Which are the lower and upper boundaries respectively.

Answer:

  1.896

Step-by-step explanation:

You can answer this just using your number sense.

  [tex]\log_7{(40)}\approx 1.896[/tex]

You know that 49 = 7², so log₇(49) = 2. The log function has a fairly small slope, so log₇(40) will not be far from 2.

_____

If you want to use your calculator, you can use the "change of base formula".

  log₇(49) = log(49)/log(7) ≈ 1.602060/0.845098 ≈ 1.896

Answer:

8 L

Step-by-step explanation:

If x is the volume of 90% alcohol, then:

(0.90)(x) + (0)(2) = 0.72(x + 2)

0.90x = 0.72x + 1.44

0.18x = 1.44

x = 8

Answer/Step-by-step explanation:

==>Given:

=>Rectangular Pyramid:

L = 5mm

W = 3mm

H = 4mm

=>Rectangular prism:

L = 5mm

W = 3mm

H = 4mm

==>Required:

a. Volume of pyramid:

Formula for calculating volume of a rectangular pyramid us given as L*W*H

V = 5*3*4

V = 60 mm³

b. Volume of prism = ⅓*L*W*H

thus,

Volume of rectangular prism given = ⅓*5*3*4

= ⅓*60

= 20mm³

c. Volume of the prism = ⅓ x volume of the pyramid

Thus, 20 = ⅓ × 60

As we can observe from our calculation of the solid shapes given, the equation written above is true for all rectangular prism and rectangular pyramid of the same length, width and height.

Answer:

C.6x³-33x² + 45x-6

Step-by-step explanation:

(3x-6)(2x^2-7x+1)

= 3x(2x² - 21x +1) -6(2x² - 7x+1)

= (6x³ - 21x² + 3x) - (12x² - 42x+6)

= 6x³ - 21x² + 3x -12x² + 42x -6

= 6x³-33x² + 45x-6

Answer:

a) Probability that a team will win the match given that it has won the first game = 0.66

b) Probability that a team will win the match given that it has won the first two games= 0.81

c) Probability that a team will win the match, given that it has won two out of the first three games = 0.69

Step-by-step explanation:

There are a total of seven games to be played. Therefore, W and L consists of 2⁷ equi-probable sample points

a) Since one game has already been won by the team, there are 2⁶ = 64 sample points left. If the team wins three or more matches, it has won.

Number of ways of winning the three or more matches left = [tex]6C3 + 6C4 + 6C5 + 6C6[/tex]

= 20 + 15 + 6 + 1 = 42

P( a team will win the match given that it has won the first game) = 42/64 = 0.66

b)  Since two games have already been won by the team, there are 2⁵ = 32 sample points left. If the team wins two or more matches, it has won.

Number of ways of winning the three or more matches left = [tex]5C2 + 5C3 + 5C4 + 5C5[/tex] = 10 + 10 + 5 +1 = 26

P( a team will win the match given that it has won the first two games) = 26/32 = 0.81

c) Probability that a team will win the match, given that it has won two out of the first three games

They have played 3 games out of 7, this means that there are 4 more games to play. The sample points remain 2⁴ = 16

They have won 2 games already, it means they have two or more games to win.

Number of ways of winning the three or more matches left = [tex]4C2 + 4C3 + 4C4[/tex] = 6 + 4 + 1 = 11

Probability that a team will win the match, given that it has won two out of the first three games = 11/16

Probability that a team will win the match, given that it has won two out of the first three games = 0.69

Answer:

20gallons

Step-by-step explanation:

Answer:

It may look simple to the owner because he is not the one losing a job. For the three machinists it represents a major event with major consequences

Answer : The correct statements are,

AC = 5 cm

BA = 4 cm

The perimeter of triangle ABC is 12 cm.

Step-by-step explanation :

As we know that a, b, and c are midpoints of the sides of right triangle that means midpoint divide the side in equal parts.

Now we have to calculate the sides of triangle ABC by using Pythagoras theorem.

Using Pythagoras theorem in ΔACF :

[tex](AC)^2=(FA)^2+(CF)^2[/tex]

Now put all the values in the above expression, we get the value of side AC.

[tex](AC)^2=(3)^2+(4)^2[/tex]

[tex]AC=\sqrt{(9)^2+(16)^2}[/tex]

[tex]AC=5cm[/tex]

Using Pythagoras theorem in ΔDAB :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BD)^2=(AD)^2+(BA)^2[/tex]

Now put all the values in the above expression, we get the value of side BA.

[tex](5)^2=(3)^2+(BA)^2[/tex]

[tex]BA=\sqrt{(5)^2-(3)^2}[/tex]

[tex]BA=4cm[/tex]

Using Pythagoras theorem in ΔBEC :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BE)^2=(CE)^2+(CB)^2[/tex]

Now put all the values in the above expression, we get the value of side CB.

[tex](5)^2=(4)^2+(CB)^2[/tex]

[tex]CB=\sqrt{(5)^2-(4)^2}[/tex]

[tex]CB=3cm[/tex]

Now we have to calculate the perimeter of ΔABC.

Perimeter of ΔABC = Side AB + Side CB+ Side AC

Perimeter of ΔABC = 4 + 3 + 5

Perimeter of ΔABC = 12 cm

Now we have to calculate the area of ΔABC.

Area of ΔABC = [tex]\frac{1}{2}\times 4\times 3=6cm^2[/tex]

Now we have to calculate the area of ΔDEF.

Area of ΔDEF = [tex]\frac{1}{2}\times 8\times 6=24cm^2[/tex]

Area of ΔABC = [tex]\frac{6}{24}\times[/tex] Area of ΔDEF

Area of ΔABC = [tex]\frac{1}{4}[/tex] Area of ΔDEF