A product sells at a regular price of $150 which is on sale for 60% off the regular price. Find the sale price.

By using the concept of complex number, it can be calculated that

There is only one complex number which satisfies  |z – 1| = |z + 1| = |z – i|  

What is a complex number?

Any number of the form a+ib where, a and b are real numbers and           i = [tex]\sqrt{-1}[/tex] are called complex number.

Let z = x + iy

[tex]|z - 1|^2 = |z + 1|^2 = |z - i|^2[/tex]

[tex]|x + iy - 1|^2 = |x+iy + 1|^2 = |x+iy - i|^2\\(x-1)^2+y^2 = (x+1)^2+y^2 = x^2+(y -1)^2[/tex]

So the point (x, y) is equidistant from (1, 0), (-1, 0) and (0, 1)

(0, 0) is the only point which is equidistant from (1, 0), (-1, 0) and (0, 1)

z = 0 is the only complex number which satisfies  |z – 1| = |z + 1| = |z – i|

There is only one complex number which satisfies  |z – 1| = |z + 1| = |z – i|  

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Answer:$17.50 remaining

Step-by-step explanation: 0.25 x 30 = 7.50

7.50 - 25.00 = $17.50 remaining

Answer:

$17.5

Step-by-step explanation:

B = 25 -0.25(30)

B = 25 - 7.5

B = 25.0 - 7.5

B = $17.5

The value of v in the triangle is 15 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

The exterior angle theorem is used to find the value of v.

Therefore,

31 + 4v + 44 = 9v

31 + 44 = 9v - 4v

75 = 5v

divide both sides by 5

v = 75 / 5

v = 15

Therefore,

v = 15

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The value of ''- X'' will be;

⇒ - X = 19

What is Number line?

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

X is 19 units to the left of 0.

Now,

Since, X is 19 units to the left of 0.

Hence, The value of X = - 19

So, We get;

The value of - X = - (- 19)

                         = 19

Thus, The value of ''- X'' will be;

⇒ - X = 19

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Answer:

The slope is -0.5, which indicates a negative correlation.

Step-by-step explanation:

y = mx + b

Is a slope-intercept form of the equation.

The y represents the distance of the line from the y-axis. (if u were to graph the problem)

M represents the slope of the line.

An the value of b is equal to y when x = 0

The equation that was given is y = 4.0 - 0.5x, which wasn't written the normal way, like  y = mx + b, they just switched the spots from y = mx + b, to y = b + mx.

So the slope is the 0.5. (which is also -0.5)

Trust me, I took a test and it had this answer, and I got it right.

Answer:

B- -0.5

Step-by-step explanation:

-.05 is a negative correlation

Negative Correlation definition- Is a  situation or an event where two variables move in the opposite direction

(Plus I also Took the test and got it right)

Answer:

y = 5x

Step-by-step explanation:

the equation of variation in which y varies directly as x is

y = kx ← k is the constant of variation

to find k use the given y = 21.25 when x = 4.25

21.25 = 4.25k ( divide both sides by 4.25 )

5 = k

y = 5x ← equation of variation

the f-test statistic to test the claim that the population variances are equal is F test = 2.54

We are given two samples

Standard deviation of the first sample = 2.1971

Standard deviation of the second sample = 7.32

F test statistic = Variance of the Larger sample/ Variance of the smaller sample

Variance = (Standard deviation)²

Variance for the first sample = 2.1971²

= 4.8272

Variance for the second sample = 7.32² = 53.5824

F test = 53.5824/4.8272

= 11.100

Therefore, the F test approximately = 11.100

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As describes in geometry the area of the rectangle = 288cm

what is geometry ?

The area of mathematics known as geometry is concerned with the characteristics of the surrounding space as well as the shapes of individual objects and their spatial relationships.

solution

radius of semicircle = 12

diameter will be = 24 and this is the length of rectangle s given in the question

area of the rectangle  = l*b

                                     = 24*12

area of the rectangle = 288cm

Hence the area of the rectangle = 288cm

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

sus

There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.

From the graph,

x axis represents the arm length of the catapult and the y axis represents the distance.

The point at which the catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance is the intersecting point of the both line

The coordinates of the intersecting point = (-30, 90)

Here arm length represents -30, but the arm length cannot be a negative value

Therefore, there is no arm length that gives equal distance

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Answer:

There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.

Step-by-step explanation:

hana is 4 year older than her brother. 2 years ago, her brother’s age was ¾ of her age then brother age will be 19 years

The concept of age describes how old a person is at a particular point in time. It is defined as the measure of the time elapsed from date of live birth to a specific point in time, usually the date of collection of the data

Hana is 4 years older then her brother

let x be brother present age

and x+4 be the hana present age

2 year ago

hana was x+2

and brother was x-2

according to the question

x-2= 3/4 * ( x+2)

x= 14

after 5 years he will be 19 years

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

15/8 quart of grape juice is needed for 15/4 quart of sparkling water.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The recipe for sparkling grape juice calls for 1(1/2) quart of sparkling water and 3/4 quart of grape juice,

This means,

1(1/2) quart of sparkling water = 3/4 quart of grape juice

3/2 quart of sparkling water = 3/4 quart of grape juice

Multiply 15/6 on both sides.

15/6 x 3/2 quart of sparkling water = 15/6 x 3/4 quart of grape juice

15/4 quart of sparkling water = 15/8 quart of grape juice

Thus,

15/8 quart of grape juice is needed for 15/4 quart of sparkling water.

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The time when Anita finished making the cookies is 12.05 pm.

From the information illustrated, Anita started making sugar cookies for her friends at 9:55 A.M, it took her 1 hour and 15 minutes to make the dough and 40 minutes to bake all of the cookies and then, Anita spent 15 minutes decorating the cookies with icing and sprinkle.

It should be noted that the time that she finishes will be the addition of the time given. This will be:

9.55 + 1.15 + 40 + 15

= 9.55 + 1.15 + 55

= 9.55 + 2.10

= 12.05

The time is 12.05 pm

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Answer:

0.40

Step-by-step explanation:

.04 x 10 = .40

Answer: $0.40

Step-by-step explanation: The sales tax will be 4% of the selling price

The end price will be 10.40

The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.

The maximum volume of  right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.

How to find volume of Right Circular Cylinder?

Right cylinders are cylinders with axes that are perpendicular to the bases.

Volume of a Right Circular Cylinder= πr²h  

where,

r = radius of the base

h = height of right circular cylinder

Maximum volume of right circular cylinder that can be inscribed in a sphere will be,    

                  [tex]\pi r^{2} h-\frac{\pi }{4} h^{3}\\\\= \frac{4\pi r^{3} }{3\sqrt{3} }[/tex]

given that, radius=70cm=0.0.7 m

so,

       [tex]Maximum\ volume=\frac{4\pi r^{3} }{3\sqrt{3} } \\\\= \frac{4\pi (70)^{3} }{3\sqrt{3} }\\\\=2640.4\pi \ m^{3}[/tex]

Using volume of right circular cylinder,

                [tex]h=\frac{2r}{\sqrt{3} }\\\\ h = \frac{2(0.07)}{\sqrt{3} }\\\\h= 0.08\ m[/tex]

Hence, The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.

The maximum volume of  right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.

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Answer:X+(X+10)+(2X)

Step-by-step explanation:

Lets say X is the amount of children tickets sold.

So she sold some kid tickets and we get an X

So X

and then she sold ten more than X tickets to adults

So now we have

X+(X+10)

And then she sold twice as many senior tickets than kids tickets

so now we have

X+(X+10)+(2X)

hope that helped at all!

Answer:

Step-by-step explanation:

You want to identify the true statements about the function f(x) = |x+3|.

A graph of the function is attached. It shows the function is decreasing to the left of x = -3, increasing to the right of that point, and has an x-intercept at x = -3. The function is positive everywhere.

The true descriptions are ...

Answer:

The Tiger has the better record, because the Leo won 5 games out of 8 and the Tiger won 7 games out of 11. When we change both denominator to the same number, the Leo's is 55/88 and the Tiger is 56/88, so the Tiger has the better record

Total number of straight lines are 45 and it can be found out using combination.

What is combination?

A combination could be a choice of things from a collection that has distinct members, such the order of choice doesn't matter.

Main body:

Total points = 10

we need to find no three lie on the same straight line.

so , to find we can select 2 lines out of 10 and assume packing them together so  no 3 points lie on a line .

selection of 2 points out of 10.

C(10,2) = ¹⁰C₂

           = 10!/2!8!

           = 10*9/2

           = 45 lines.

Hence ,Total number of straight lines are 45 .

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The equation (y = mx + b) of this graph is equal to the equation for this arithmetic sequence aₙ =  a₁ + (n - 1)d

Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:

aₙ =  a₁ + (n - 1)d

Where:

For the 10th term, the equation for the arithmetic sequence is given by;

a₁₀ =  a₁ + (n - 1)d

15 =  a₁ + (10 - 1)d

15 =  a₁ + 9d

For the 14th term, the equation for the arithmetic sequence is given by;

a₁₄ =  a₁ + (n - 1)d

35 =  a₁ + (14 - 1)d

35 =  a₁ + 13d

Next, we would determine the common difference as follows;

a + 9d = 15

a + 13d = 35

-4d = -20

Common difference, d = -20/-4

Common difference, d = 5.

For the first term of this arithmetic sequence, we have;

a + 9d = 15

a + 9(5) = 15

a = 15 - 45

First term, a = -30

Finally, we would write an equation for the nth term of an arithmetic sequence as follows;

aₙ =  a₁ + (n - 1)d

aₙ =  -30 + (n - 1)5

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When the car is acquired for $22600 and depreciates at an 11.5% rate, it will take 6.7 years for its worth to reach $5200.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Here,

Cost of car=$22600

Rate of depreciation=11.5%

After n years, value of car=$5200

Annual depreciation expense=22600*11.5%

=$2599

Value of the Car = Purchase cost - (Annual depreciation expenses * n)

5200=22600-(2599*n)

2599n=22600-5200

2599n=17400

n=6.695

n=6.7 years

The number of years until the value of the car is 5200 dollars at depreciation rate of 11.5% when purchased at 22600 dollars will be 6.7 years.

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Answer:

  yes

Step-by-step explanation:

You want to know if the sides are congruent in a triangle with congruent angles.

The Law of Sines tells us the sides of a triangle are proportional in length to the sines of the opposite angles.

If the angles are congruent, their sines are equal, and the sides are congruent.

A triangle with congruent angles has all angles 60°. Such a triangle is called an equilateral triangle. The name "equilateral" refers to the fact that the sides are the same length.

Answer:

900

Step-by-step explanation:

l = 2w + 5

2(2w + 5) + 2w = 130

4w + 10 + 2w = 130

6w + 10 = 130

6w = 120

w = 20

l = 2(20) + 5

l = 40 + 5

l = 45

130 = 2(45) + 2(20)

130 = 90 + 40

130 = 130

A = l × w

A = 45 × 20

A = 900

Could you please give me brainliest for this? Thank you!

Answer:

215.1x

Step-by-step explanation:

2.151x(102)

=2.151*x*100

=215.1*x

=215.1x

Answer:

The answer would be 215.1x

Step-by-step explanation:

2.151 x 10^2 = 215.1x

10^2 = 100

Then multiply 100 and 2.151x

100 x 2.151x = 215.1x

The standard deviation of the number of days absent is found as 1.1616.

For the stated question-

Number of Days Absent/Probability

Thus, the mean is found as;

Mean = (0x0.60) + (1x0.20) + (2x0.12) + (3x0.04) + (4x0.04)

Mean = 0.72

Standard deviation σ = (0-0.72)² x 0.60 + (1-0.72)² × 0.20 + (2-0.72)² × 0.12 + (3-0.72)²  × 0.04 + (4-0.72)² × 0.04

Standard deviation  = 1.1616

Thus, the standard deviation of the number of days absent is found as 1.1616.

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The complete question is-

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.

Number of Days Absent/Probability

0 0.60

1 0.20

2 0.12

3 0.04

4 0.04

5 0.00

What is the standard deviation of the number of days absent?

The co-ordinates of the point P that divides the line segment AB in the ratio 3:2 are (3,0)

What is Line Geometry?

A line is an endlessly long object with no breadth, depth, or curve in geometry. Lines are thus one-dimensional objects, even if they can exist in two, three, or higher dimensions. In ordinary language, the term line can also refer to a line segment with two points denoting its endpoints.

Solution:

To find the co-ordinates of point P we wil use section formula

(x,y) = (m*x2 + n*x1 / m+n), (m*y2 + n*y1 / m+n)

(x,y) = (3*3 + 2*3)/5 , (3*2 + 2*(-3))/5

(x,y) = 15/5 , 0/5

(x,y) = 3,0

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