one of euler's conjectures was disproved in the 1960s by three american mathematicians when they showed that there is a positive integer such that find the value of .

The simplified expression for (0.2a²b³)(-5a³b)² is given as follows:

5a^8b^5.

The expression for this problem is given as follows:

(0.2a²b³)(-5a³b)²

First we apply the power of power simplification, in which the square of each term inside the parenthesis is calculated as follows:

Now the expression is:

(0.2a²b³)(25a^6b²).

Then:

Hence the simplified expression is:

5a^8b^5.

More can be learned about simplification of expressions at https://brainly.com/question/723406

#SPJ1

1/6  is the probability that in seven rolls of a six-sided die, the result of 2 appears exactly 4 times

Define Probability

Probability can be defined as the likelihood or chance of an event occurring.

Probability is a branch of Mathematics that deals with the calculation on the chances of happening of a particular event.

The probability of getting some number in a cube corresponds to 1/6, the cube has six sides.

P(1) =1/6

P(2) =1/6

P(3)=1/6

P(4)= 1/6

P(5)=1/6

P(6)= 1/6

learn more about of probability here

https://brainly.com/question/16383548

#SPJ4

Answer:

I belive c

Step-by-step explanation:

Alex, Stephen and Bridget have 77 sweets altogether.

According to the question,

We have the following information:

Alex, Stephen and Bridget share some sweets in the ratio 5:4:2. Bridget gets 21 more sweets than Alex. (This is the correct statement otherwise the answer will be in negative which is not possible.)

Now, let's take the number of sweets Alex has to be 5x, that of Stephen to be 4x and that of Bridget to be 2x.

Now, we have the following expression:

2x+21 = 5x

Subtracting 2x from both sides:

21 = 5x-2x

3x = 21

x = 21/3

x = 7

Now, we have the following number of sweets:

Alex = 5*7 = 35

Stephen = 4*7 = 28

Bridget = 2*7 = 14

Now, total number of sweets:

35+28+14

77

Hence, Alex, Stephen and Bridget have 77 sweets altogether.

To know more about sweets altogether here

https://brainly.com/question/16768615

#SPJ1

Answer:

b is the answer

Step-by-step explanation:

hi hope it helps

Answer:

Step-by-step explanation:

there would be 18 muffins.

if you multiply each number by 3 then add them it will end up at 48.

6x3=18

10x3=30

30+18=48

30:18

The value of the discriminant is -71. The roots of the equation are imaginary and two in number.

We are given a quadratic equation. The equation is given below.

2x² + 10x + 9 = 9x

We will simplify this equation.

2x² + x + 9 = 0

We need to find the discriminant of the equation. If the general quadratic equation is represented by ax² + bx + c = 0, then the discriminant is given below.

D = b² - 4*a*c

D = 1² - 4(2)(9)

D = 1 - 72

D = -71

The discriminant is negative, so no real roots exist for the given quadratic equation. Thus, there exist two imaginary roots for the given quadratic equation.

To learn more about discriminant, visit :

https://brainly.com/question/15884086

#SPJ1

The solution is

The distance between the point A and C is greater than the distance between the points B and C

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the first point be = A

The value of A = A ( 5 , 6 )

Let the second point be = B

The value of B = B ( 5 , 3 )

Let the reference point be C = C ( -3 , 2 )

Now , the distance between the points A and C = P

The distance between the points B and C = Q

Now , the value of P is calculated from the distance formula

Distance Q = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Substituting the values in the equation , we get

P = √ ( 5 - ( - 3 ) )² - ( 6 - 2 )²

P = √ ( 8 )² + ( 4 )²

P = √ ( 64 + 16 )

P = √80 units

Now , the value of Q is calculated from the distance formula

Substituting the values in the equation , we get

Distance Q = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Q = √ ( 8 )² + ( 1 )²

Q = √ ( 64 + 1 )

Q = √65 units

So , the value of Q is less than value of P

Therefore , the distance of point B to C is lesser than point A to C

Hence , The point B ( 5 ,3 ) is closer to the point C ( -3 , 2 )

To learn more about distance between 2 points click :

https://brainly.com/question/18234495

#SPJ1

The expression that represents the perimeter is 8.6b  and the expression that represents the area of the exercise mat is  3.3b²  .

In the question ,

it is given that ,

the exercise mat is is 3.3 times as long as it is wide .

let the width of the exercise mat be = "b" .

So , the length of the exercise mat will be = 3.3b

The Perimeter of the exercise mat = 2( length + width)

= 2(3.3b + b)

= 2(4.3b)

= 8.6b

the perimeter is = 8.6b

The Area of the exercise mat = length × width

= 3.3b × b

= 3.3b²

the area is = 3.3b²

Therefore , The expression that represents the perimeter is 8.6b  and the expression that represents the area of the exercise mat is  3.3b²  .

Learn more about Algebraic Expression here

https://brainly.com/question/1276736

#SPJ1

Answer:

[tex]8 \sqrt{2} [/tex]

Step-by-step explanation:

This is a special right triangle with angle measures 45°-45°-90°

and side lengths represented with a-a-a√2 respectively

a is given as 8 here so a√2 would be 8√2 the answer is c.

The solutions of the quadratic equation are:

A general quadratic equation:

a*x^2 + b*x + c = 0

Has solutions of the form:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4a} }{2a}[/tex]

In this case, the quadratic is:

2*x^2 + x + 2 = 0

a = 2

b = 1

c = 2

Then using above formula we get the two solutions:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*2*2} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-8} }{4}[/tex]

So the solutions are:

x = (-1 +√8*i)/4

x = (-1 -√8*i)/4

Learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

Jennifer had 25 percent increase in number of hours worked

Percentage increase describes the eventual increase in the quantity in percent form. The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time. Mathematically, this formula is represented as the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.

Data;

Percentage Increase = [(15 - 12) / 12] * 100

Percentage Increase = 3/12 * 100

Percentage Increase = 0.25 * 100

Percentage Increase = 25%

The increase is 25%

Learn more on percentage increase here;

https://brainly.com/question/11360390

#SPJ1

A hot-air balloon is at a height of 2,250 feet. It begins to descend at a rate of 150 feet per minute.

In context, after 6 minutes the balloon is at 1,350 ft, after 8 minutes the balloon is at 1,050 ft, and after 10 minutes the balloon is at 750 ft.

So for this, since the rate is linear we will be using the slope-intercept form, which is y = mx+b (m = slope/rate of change, b = y-intercept)

Since the rate of change "descends 150 ft per min", the m variable is -150.

The y-intercept is, in this case, the height of the balloon at 0 mins, or the starting height. Since the balloon "is at a height of 2250 ft", the b variable is 2250.

Putting our equation together, its y = -150x + 2250.

Since time is our independent variable, plug in 6, 8, and 10 mins into the x variable to solve for their heights:

y = -150(6)+2250

y = -900+2250

y = 1350

y = -150(8)+2250

y = -1200+2250

y = 1050

y = -150(10)+2250

y = -1500+2250

y = 750

Hence the answer, In context, after 6 minutes the balloon is at 1,350 ft, after 8 minutes the balloon is at 1,050 ft, and after 10 minutes the balloon is at 750 ft.

To learn more about expressions click here https://brainly.com/question/22048677

#SPJ9

The occupations that fits her plan is Private detective

How would you define statistics?

Statistics is the study of data gathering, analysis, presentation, and interpretation. Early government demands for census data and knowledge of various economic operations were a major source of inspiration for the study of statistics.

What three sorts of statistics are there?

They are (i) the mean, (ii) the median, and (iii) the mode. The study of statistics involves gathering, analyzing, interpreting, presenting, and organizing data in a particular way.

According to the table, the private detective and mathematical activities are the professions that have an average pay over $ 33,500, desired by Jasmine. She must attend college, which she does not want to do, in order to become a math teacher. She can therefore choose to work as a private investigator.

Learn more about statistics:

https://brainly.com/question/15525560
#SPJ1

For n as 5,7,8 and 9 the relation will become function

A relation is a function if it has only One y-value for each x-value.

The given relation is two comma eight comma six comma zero comma four comma two comma two times of n comma n.

{(2,8), (6,0), (4,2), (2n,n)}

We need to make it  function for which n should not be 2,6, or 4.

When n is 1, it is not function

n is 3, it is not function

n is 5, it is function

n is 7, it is  function

n is 8, it is function

n is 9, it is function

Hence for n as 5,7,8 and 9 the relation will become function

To learn more on Functions click:

https://brainly.com/question/21145944

#SPJ1

Answer:

x-intercepts:  -4, -2, 1 and 3

y-intercept:  24

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x&-5&-3&0&2&4\\\cline{1-6}y&144&-24&24&-24&144\\\cline{1-6}\end{array}[/tex]

Step-by-step explanation:

Given polynomial:

[tex]y=(x+4)(x+2)(x-1)(x-3)[/tex]

The x-intercepts are the points at which the curve intersects the x-axis, so when the function equals zero.

Zero Product Property

If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Therefore, to find the x-intercepts, set each factor of the given polynomial equal to zero and solve for x:

Therefore:

[tex]\implies (x+4)=0 \implies x=-4[/tex]

[tex]\implies (x+2)=0 \implies x=-2[/tex]

[tex]\implies (x-1)=0 \implies x=1[/tex]

[tex]\implies (x-3)=0 \implies x=3[/tex]

Therefore, the x-intercepts are -4, -2, 1 and 3.

The y-intercept is the point at which the curve intersects the y-axis, so when x is zero.  

To find the the y-intercept, substitute x = 0 into the given polynomial:

[tex]\implies y=(0+4)(0+2)(0-1)(0-3)[/tex]

[tex]\implies y=(4)(2)(-1)(-3)[/tex]

[tex]\implies y=(8)(-1)(-3)[/tex]

[tex]\implies y=(-8)(-3)[/tex]

[tex]\implies y=24[/tex]

Therefore, the y-intercept is 24.

To find the other points on the graph, substitute each value of x into the polynomial and solve for y:

[tex]\begin{aligned}x=-5 \implies y&=(-5+4)(-5+2)(-5-1)(-5-3)\\&=(-1)(-3)(-6)(-8)\\&=(3)(-6)(-8)\\&=(-18)(-8)\\&=144\end{aligned}[/tex]

[tex]\begin{aligned}x=-3 \implies y&=(-3+4)(-3+2)(-3-1)(-3-3)\\&=(1)(-1)(-4)(-6)\\&=(-1)(-4)(-6)\\&=(4)(-6)\\&=-24\end{aligned}[/tex]

[tex]\begin{aligned}x=2 \implies y&=(2+4)(2+2)(2-1)(2-3)\\&=(6)(4)(1)(-1)\\&=(24)(1)(-1)\\&=(24)(-1)\\&=-24\end{aligned}[/tex]

[tex]\begin{aligned}x=4 \implies y&=(4+4)(4+2)(4-1)(4-3)\\&=(8)(6)(3)(1)\\&=(48)(3)(1)\\&=(144)(1)\\&=144\end{aligned}[/tex]

Therefore:

[tex]\large\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x&-5&-3&0&2&4\\\cline{1-6}y&144&-24&24&-24&144\\\cline{1-6}\end{array}[/tex]

Answer:

8505

Step-by-step explanation:

Step 1

Firstly, work out 5 × 243. The smaller figures in green are the tens figures carried over. Working from right to left:

5 × 3 = 15

Put the 5 in the appropriate column and carry the 1.

5 × 4 + 1(carried) = 21

Put the 1 in the appropriate column and carry the 2.

5 × 2 + 2(carried) = 12

Put the 2 in the appropriate column and carry the 1.

Step 2

Lastly, work out 30 × 243.

This can be written as 3 × 243 × 10.

Because we are multiplying by 10, we place 1 zero to the right and then work out 3 × 243.

3 × 3 = 9

3 × 4 = 12

Put the 2 in the appropriate column and carry the 1.

3 × 2 + 1(carried) = 7

Step 3

Finally, the 2 rows are added together starting at the right. The smaller figures in green are the tens figures carried over.

0 + 5 = 5

9 + 1 = 10

Put the 0 in the appropriate column and carry the 1.

2 + 2 + 1(carried) = 5

7 + 1 = 8

So: 243 × 35 = 8505

Answer:

Step-by-step explanation:

black wombat in the dessert jungle

i know its wrong but its right

trust it

the process

Using the formula of equation of perpendicular line, the new equation is y = 2/3x - 5

A perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes. Coordinates and line equation is the prerequisite to finding out the perpendicular line.

The equation of perpendicular line is given as

(y - y₁) = m(x - x₁)

m = slope of the line.

But the slope of a perpendicular line is given as

m₁m₂ = -1

-3/2m₂ = -1

m₂ = 2/3

The slope of the new equation is 2/3

Using equation of a perpendicular line;

(y - y₁) = m(x - x₁)

y - (-9) = 2/3(x -(-6))

y + 9 = 2/3(x + 6)

y + 9 = 2/3x + 4

y = 2/3x - 5

The equation of perpendicular line is y = 2/3x - 5

Learn more on equation of perpendicular line here;

https://brainly.com/question/6691986

#SPJ1

Answer:

79?

Step-by-step explanation:

The moment-generating function for y is given as eⁿᵇ - eⁿᵃ / n(b-a) and derivation of  moment-generating function of y is e-1/t

Given that,

The interval (0, 1) is covered by a uniform distribution of y, and a > 0 is a constant.

The moment generating function is eⁿᵇ - eⁿᵃ / n(b-a)

The given interval is (0,1)

Here a =0;

         b=1;

Now substitute the values of a and b in the above moment generating function we get,

y=eⁿᵇ - eⁿᵃ / n(b-a)

y=e^1-e^0/t(1-0)

y= e-1/t

Therefore, the derivation of the moment generating function is e-1/t

Learn more about moment-generating function here:

brainly.com/question/15061360

#SPJ4

The radius of the cone if the volume of a right cone is 448 π cube units and if its height is 21 units is 8 units.

First, let us understand the cone:

It is a solid or hollow item with a round or approximately circular base that tapers to a point.

The volume of the cone is given by;

Volume = 1/3 π r^2 h

where r = radius of the base of the cone

and h = height of the cone

We are given;

The volume of a right cone is 448 π cube units.

Height is 21 units.

Put the values in the volume formula;

448 π = 1/3 π r^2 * 21

448 π = 7 π r^2

r^2 = 448 π / 7 π

r^2 = 64

r = 8 units

So, the radius of the base is 8 units.

Thus, the radius of the cone if the volume of a right cone is 448 π cube units and if its height is 21 units is 8 units.

To learn more about cone visit:

https://brainly.com/question/15936918

#SPJ1

Answer:

8

Step-by-step explanation:

don't know how to explain it but I had he same problem and I got 8 and it was right.

The conditional probability that a Philadelphian who got the flu got a flu shot is of:

0.4375 = 43.75%.

Conditional probability is the probability of one event happening, considering the outcome of a previous event.

The formula is presented as follows:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which each probability in the formula is described as follows:

In the context of this problem, the events are described as follows:

The probability of people who got the flu is obtained as follows:

Hence:

P(A) = 0.02 x 0.7 + 0.06 x 0.3 = 0.032.

The probability of both getting the flu and the shot is:

P(A and B) = 0.02 x 0.7 = 0.014.

Hence the conditional probability that a Philadelphian who got the flu got a flu shot is calculated applying the conditional probability formula as follows:

P(B|A) = P(A and B)/P(A) = 0.014/0.032 = 0.4375 = 43.75%.

More can be learned about conditional probability at https://brainly.com/question/14398287

#SPJ1

Total triangles on all the quilt are 672.

What is quilt?

Quilts are often made of two or more layers of cloth or fibre and are multi-layered textiles. Three layers and a filler substance are frequently employed. These layers are often made up of a woven top, a batting or wadding layer, and a woven back that are all connected using quilting techniques.

Main Body:

Number of triangles on 1 quilt = 32

Total number of quilt = 21

So total triangles can be calculated by simply multiplying the two values,

Total triangles = 32*21

                        = 672 quilts

Hence total number of triangles = 672

To learn more about quilt click on the link below

https://brainly.com/question/28036274

#SPJ4

The correct conclusion is:

"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."

Given,

At a huge institution, a doctor is determining the typical height of the male students.

Inches are used to measure the heights of a sample of 40 male baseball team players.

The doctor computes the 95% confidence interval using this information (63.5, 74.4).

The following conclusions is valid:

"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."

We can guarantee that the target variable will be within the confidence interval for a given confidence level since we know the confidence interval reflects an interval.

The true mean of heights for male students at the college where the doctor measured heights is represented by the provided case's confidence level of 95% and confidence interval of (63.5, 74.4).

The doctor is therefore 95% certain that the range of the mean height of male students at the college is valid (63.5, 74.4).

Learn more about conclusions here;

https://brainly.com/question/16519901

#SPJ4