Complex number :
[tex]i^{99}[/tex]= - i.
Why is it called a complex number?A complex number is one that has the notation a + b I a + bi a+bi, where a and b are real numbers and I is the imaginary unit denoted by the expressions I 2 = 1 I 2 = -1 I 2 = 1. Real numbers (R) and pure imaginary numbers (I) are both included in the set of complex numbers, represented by the letter C.In the 19th century, the phrase "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complicated number that is not real or, more commonly, a number whose real portion is zero (a.k.a "pure imaginary").here,
i = [tex]\sqrt{-1}[/tex]
If the power is
even then the value could be -1 or 1odd then the value could be -i or i99 is odd so now is
-i if (99+1)/2 is even or is
i is (99+1)/2 is odd
Now check (99+1)/2= 100/2= 50,
50 is even so
i^99 = -i
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If a biker travels 380 meters in 20 seconds at that rate how far could he travel in 3 seconds
I think its 57 meters.
Answer the questions below to find the total surface area of the can..
The total surface area of the cylinder is equal to 117.8 in^2
Total Surface Area of Cylinder
The total surface area of a cylinder can be calculated using the formula
[tex]TSA = 2\pi rh + 2\pi r^2[/tex]
h = height of cylinderr = radius of cylinderLet's substitute the values and proceed to solve.
[tex]TSA = 2\pi rh + 2\pi r^2\\TSA = 2\pi * 2.5 * 5 + 2\pi * 2.5^2\\TSA = 117.8in^2[/tex]
The total surface area of the cylinder is 117.8 squared inch.
The area of each circle is
[tex]A = \pi r^2 \\A = 19.6in^2[/tex]
And there are two identical circle in the diagram and this will have a total area of
[tex]A = 2 * 19.6\\A = 39.2in^2[/tex]
The area of the sum of the two circles is 39.2in^2 and the total surface area of the cylinder is 117.8in^2
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An empty swimming pool is shaped like a rectangular prism with a length of 18 feet and a width of 9 feet. once water begins to be pumped into the pool, the depth of the water increases at a rate of 0.5 foot per hour.
Answer:
volume=length×width×depth
Step-by-step explanation:
solve. 2-6: MathXL for School: Practice & Problem Solving (Grade 8 Pre-Algebra)
The area of the rectangle is [tex]b^2[/tex] +9b square feet
The rectangle is the quadrilateral whose opposite sides are parallel and equal. The rectangle is a four sided shape that all the angles are 90 degrees
The area is defined as the total space occupied by the two dimensional shape like rectangle, triangle, circle etc..
The length of the rectangle = (5/3)b+15 feet
The width of the rectangle = (3/5)b feet
The area of the rectangle = The length of the rectangle × The width of the rectangle
Substitute the values in the equation
The area of the rectangle = [(5/3)b+15] ×(3/5)b
Apply the distributive property in the equation
[(5/3)b+15] ×(3/5)b = [tex]b^2[/tex] +9b square feet
Hence, the area of the rectangle is [tex]b^2[/tex] +9b square feet
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Find x 109° x 31° 35°
No need to help anymore. I figured out the answer.
The value of x is 43.
As per the property of exterior angles, the exterior angle is equal to sum of opposite interior angles. Also, the rightmost interior angle of triangle will be 35°. This will be according to the property that opposite angles are equal. Now, forming the equation for sum of exterior angles.
109 = x + 31 + 35
Performing addition on Right Hand Side of the equation
109 = x + 66
Rearranging the equation
x = 109 - 66
Performing subtraction on Right Hand Side of the equation
x = 43
Therefore, as per the angles of triangle, the value of x is 43.
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12. Triangle ABC has vertices A(-4, 0), B(-4, 5) and C(1, 5) along line AC. Which are the
coordinates of another slope triangle along the same line?
A. D(-2,-2), E(-2, 1) F(-1,0)
B₁6
B. D(-3, 0), E(-3, 1) F(-2, 1)
C. D(-5, -1), E(-5, 0) F(-4, -1)
D. D(-6, -2), E(-6, -1) F(-5, -1)
Please help will mark brainliest
Considering the given triangle ABC that has vertices A(-4, 0), B(-4, 5) and C(1, 5). The option that has same slope with similar interval is B. D(-3, 0), E(-3, 1) F(-2, 1)
What is slope?Slope refers to the gradient and is the ratio of the difference in the ordinate to the difference in the abscissa of in a given coordinate plane.
How to calculate slopeThe given information from the question include
A(-4, 0), B(-4, 5) and C(1, 5)
The slope of the given triangle is calculated as follows
slope = ( 0 - 5 ) / ( -4 - 1 )
slope = -5 / -5
slope = 1
The domain of the line is -4 ≤ x ≤ 1
The range of the line is 0 ≤ y ≤ 5
options C and D values do not satisfy the domain and range conditions
Options B and A satisfies the the domain and range conditions however the slope of option B is what is equal to the slope of the sloping part of the given triangle and hence the correct option.
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Is it possible to have a series of true conditional statements that lead to a false
conclusion? Explain.
It is possible to have a series of true conditional statements that lead to a false conclusion.
How to illustrate the information?Making decisions based on particular situations is made easier with conditional statements.
A conditional statement's truth value can be either true or false. Simply demonstrate that the conclusion is true whenever the hypothesis is true to establish the truth of a conditional.
Simply demonstrating that the conclusion is wrong each time the hypothesis is true suffices to demonstrate that a conditional is untrue.
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the table show the total cost to be a member of the gym for different numbers of months.number of months. total costs3. $53.976. $77.9412. $125.88create a function that gives the total cost C,in dollars to be a member of the gym given the number of months M of member ship.
The table shows the total cost to be a member of the gym for different numbers of months.
Number of months. total costs
3. $53.97
6. $77.94
12. $125.88
Create a function that gives the total cost C, in dollars to be a member of the gym given the number of months M of membership.
_____________________________________
Total cost = M* (factor per month ) + b
_____________________________________
The expression for a linear equation is
*The slope-intercept form.
y = mx + b
m= (y2-y1)/ (x2-x1) (I)
y-intercept is (0, b)
*and the point-slope form
y- y1 = m(x-x1) (II)
________________________
Point 1 (3, 53.97)
Point 2 (12, 125.88)
Replacing in (II)
The slope m = (y2- y1)/ (x2-x1) = (125.88- 53.97)/(12-3) = 7.99
y - 53.97 = 7.99* (x- 3)
y = 7.99 x - 7.99* 3 + 53.97
y = 7.99x + 30
____________________
Verifying
y = 7.99x + 30
x= 3
y = 7.99*3 + 30
y= 53.97
x= 6
y = 7.99*6 + 30
y= 77.94
x= 12
y = 7.99*12 + 30
y= 125.88
_________________________
Answer
The linear function is y = 7.99x + 30
About 30% of people age 50 to 60 suffer from mild depression. A researcher is interested in determining if a vitamin d supplement will increase or decrease the proportion of people that have mild depression. The researcher randomly selects 500 people between the ages of 50 and 60 and ask them to take a vitamin d supplement for 6 months. At the end of the six months, the participants are asked to complete a survey. A psychologist then classifies each participant as either depressed or not. The psychologist classifies 158 people as depressed. Is the proportion of people that are classified as depressed different from 0. 30? what is the null and alternative hypothesis?.
The null and alternative hypothesis is H₀ : p = 0.30 and Hₐ : p ≠ 0.30 respectively.
A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis.
Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance.
One of the ideas put out in the hypothesis test is the alternate hypothesis.
Mild depression affects about 30% of adults in the 50 to 60 age range.
500 people between the ages of 50 and 60 are chosen at random by the researcher, and they are instructed to take a vitamin D pill for six months.
The psychologist classifies 158 people as depressed.
The null hypothesis will be:
H₀ : p = 0.30 and;
The alternative hypothesis is,
Hₐ : p ≠ 0.30
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PLEASE HELP ME THANK YOU
The area of half circle is 14.13 sq.unit
The total area of the figure is 86.13 sq.unit
Given,
The figure is combined by a triangle, rectangle and a half circle.
The area of triangle = 18 sq.units
The area of rectangle = 54 sq.units
We have to find the area of half circle to get the total area of the figure;
Here,
Area of circle = π r²
Then,
Area of half circle = π r² / 2
Here,
r = 6/2 = 3 units
Now,
Area = π r² / 2 = π × 3² / 2 = 28.27/2 = 14.13 sq.units
That is,
The area of half circle is 14.13 sq.unit
Then,
The total area of figure = Area of [triangle + rectangle + half circle]
The total area of figure = 18 + 54 + 14.13 = 86.13 sq.units
Therefore,
The total area of the figure is 86.13 sq.unit
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ANSWER FAST I WILL GIVE BRAINLIEST
Which graph represents the solution to one seventhm ≤ −1 over 22? number line with closed circle on point negative 14 over 11 and arrow shaded to the right number line with closed circle on point negative 7 over 22 and arrow shaded to the right number line with closed circle on point negative 14 over 11 and arrow shaded to the left number line with closed circle on point negative 7 over 22 and arrow shaded to the left
Answer: arrow shaded to the left number line with closed circle on point negative 7 over 22 and arrow shaded to the left
Step-by-step explanation:
Answer:
for easier explanation.... it's D
Step-by-step explanation:
Elena received a $25 gift card to a fun center. She drives a race car which costs $4.75. She also wants to use the gift card to play video games. Each game costs $0.75 which of these inequalities describe this situation, where n is the number of games Elena wants to play.
A. 4.75 + 0.75. ≤ 25
B. 4.75 + 0.75. ≥ 25
C. 4.75 - 0.75. ≥ 25
D. 4.75 - 0.75. ≤ 25
Answer: B - 4.75 + 0.75 is greater than 25
Step-by-step explanation:
so, first you have 4.75 and she want to play video games that cost 0.75 each but we don't know how many video games she played.
so, n = how many video games played4.75 + 0.75n =? which is greater than 25divide 4.75 + 0.75n 0.75 0.75after dividing you will get 4,100 + 1n = which equals 4.101 is greater than 25Antonio draws a spuare that has 13 centimeters what the perimeter of his spuare
Answer:
52 centimeters
Step-by-step explanation:
A square has 4 sides
Side of square = 13 cm
Perimeter of square = sum of all sides of square
Perimeter of square = 4 x 13 = 52 cm
Samuel was preparing for the triathlon. He did 3 activities every morning: ran for 30 minutes, covering 4.5 miles swam for 20 minutes, covering 2 3 mi biked for 45 minutes, covering 9 miles What was Samuel's average speed during his morning training?
Samuel's average speed during his morning training is 0.41 miles/minute.
Here we have to find the average speed of Samuel. We can solve this problem by following a few steps.
According to the problem, Samuel was preparing for the triathlon. He did 3 activities every morning; ran for 30 minutes, covered 4.5 miles; swam for 20 minutes, covered 2.3 miles biked for 45 minutes, and covered 9 miles.
We have to recall the formula of average speed as,
average speed = total covered distance/ total time
The total distance which has been covered is,
4.5 miles by running,2.3 miles by swimming,9 miles by biking.The total covered distance is, ( 4.5 + 2.3 + 9 ) = 36.5 miles.
The total time which has been spent is,
30 minutes for running,20 minutes for swimming,45 minutes for biking.The total spent time is, (30+ 20+ 40) = 90 minutes.
Now, we can easily calculate the average speed. Which is (36.5/90) = .41 miles/minute.
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Orlando makes a trail mix for his hiking trip. He uses 1 \frac{5}{6}1 6 5 pounds of cashews, 1.6 pounds of sunflower seeds, 1 \frac{1}{8}1 8 1 pounds of raisins, and 1.625 pounds of pecans. Which answer choice shows these weights in order from least to greatest ? DUE TODAY NEED NOW WILL GIVE BRAINLIEST PART OF TEST REALLY NEED
An answer choice shows these weights in order from least to greatest is:
1 1/8 pounds of raisins.1.6 pounds of sunflower seeds.1.625 pounds of pecans.1 5/6 pounds of cashews.What is a numerical data?A numerical data can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.
In order to arrange the given numerical data (weights) in order from least to greatest, we would convert the fractions into a decimal number as follows:
1 5/6 pounds of cashews = 11/6 = 1.8333 pounds.1.6 pounds of sunflower seeds = 1.6 pounds.1 1/8 pounds of raisins = 9/8 = 1.125 pounds.1.625 pounds of pecans = 1.625 pounds.Now, we can arrange the numerical data in order from least to greatest based on the weight of each item:
1.125 pounds = 1 1/8 pounds of raisins.1.6 pounds = 1.6 pounds of sunflower seeds.1.625 pounds = 1.625 pounds of pecans.1.8333 pounds = 1 5/6 pounds of cashews.Read more on greatest numbers here: brainly.com/question/24654699
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the number of messages that arrive at a web site is a possion distirbuted random variable with a mean of 5 messages per hour. round your asnwers to four decimal places. what is the probaiblity taht 5 messages are received in 1 hour
17.54% is the probability that 5 messages are received in 1 hour.
The chance that X reflects the number of successes of a random variable in a Poisson distribution is provided by the following formula:
P(X = x) = ([tex]e^{-u}[/tex] × [tex]u^{x}[/tex]) ÷ x!
In where x is the number of successes, e is the Euler number, and u is the mean in the specified time frame.
In this case, the average message rate is 5 messages per hour.
The probability of receiving 5 texts in one hour.
Determine the value of P for x = 5 and u = 6.
P(X = x) = ([tex]e^{-5}[/tex] × [tex](5)^{5}[/tex]) ÷ 5!
P(X = x) = 21.0560 ÷ 5!
P(X = x) = 0.1754
There is a 17.54% chance that 5 messages will be received in 1 hour.
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How many solutions does this equation have?
–4k − 13 = 19 − 8k + 20
Answer: k = 13
Step-by-step explanation:
which of these expressions are equal to 3/5×6?Explain why the others aren't equal to this expression.3×(6÷5)3÷(5×6)(3×6)÷53×6/5
Answer:
(3×6)÷5
Step-by-step explanation:
We are given the following expression:
(3/5)*6
The 6 can also be written as a fraction(6/1).
So we have a multiplication of fractions, is which we multiply the numerators and denominators.
So
(3*6)/5
The fraction sign means division
So the answer is:
(3×6)÷5
Please help. See picture attached.
The trapezoid's area can be understood as triangle a + triangle b. So, we write these triangles as an expression, and, since we cannot solve with no values, we simplify to prove the area of the trapezoid.
A triangle's area is 1/2bh. In their case, b is represented as b or a depending on the triangle.
t = 1/2ah + 1/2bh
Now, since both expressions use the terms 1/2 and h, distributed onto a second variable, it can be rewritten as a single expression where both are distributed onto both variables at the same time. This is because both terms being multiplied by something separately is the same as combining both terms and multiplying them both at the same time.
t = 1/2(a)h + 1/2(b)h
t = 1/2(a + b)h
Characterize the slope of the line in the graph,
A. Positive
B. Negative
C. Zero
D. Undefined
Answer:
D. Undefined
Step-by-step explanation:
[tex]m=[/tex] ∞
Hope this helps
Ben's monthly housing costs for his new home will be $2100 per month. What
must his monthly net income be to keep housing as 30% of his budget?
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
The monthly net income to keep housing a 30% of his budget is $7000.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Cost of monthly housing per month = $2100
$2100 = 30%
Monthly income = 100%
30% = 2100
Multiply 100/30 on both sides.
100/30 x 30% = 100/30 x 2100
100% = 7000
Thus,
The monthly net income to keep housing a 30% of his budget is $7000.
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50 POINTS
What system of linear inequalities is shown in the graph? Enter your answers in the boxes.
enter your answers in the boxes
□
□
Answer:
[tex]\begin{cases}y \geq -\dfrac{1}{2}x+2\\\\y > 2x-3\end{cases}[/tex]
Step-by-step explanation:
Find the equations of the two lines by substituting two points on each line into the slope formula to find the slope, then substituting the found slope and one of the points into the point-slope formula.
Equation of Line 1
Points on the line: (0, 2) and (2, 1).
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{2-0}=-\dfrac{1}{2}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]
[tex]\implies y=-\dfrac{1}{2}x+2[/tex]
Equation of Line 2
Points on the line: (0, -3) and (2, 1).
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-(-3)}{2-0}=-\dfrac{4}{2}=2[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-3)=2(x-0)[/tex]
[tex]\implies y=2x-3[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.As the line for equation 1 is solid and there is shading above the line, the line is represented by the inequality:
[tex]\boxed{y \geq -\dfrac{1}{2}x+2}[/tex]
As the line for equation 2 is dashed and there is shading above the line, the line is represented by the inequality:
[tex]\boxed{y > 2x-3}[/tex]
Therefore, the system of linear inequalities shown in the graph is:
[tex]\begin{cases}y \geq -\dfrac{1}{2}x+2\\\\y > 2x-3\end{cases}[/tex]
a triangle with a base of 6cm has an area of 30cm squared. What is its perpendicular height?
The area of a triangle is 1/2bh. We know the area, a, the base, b, and we are attempting to find the height, h. So, we simplify the area formula with the value of b and solve for h, given a.
1/2(6)h = 30
3h = 30
Isolate h.
3h/3 = 30/3
h = 10
Don’t ignore help pls I think i know it but I’m not sure
Answer:
The y intercept is 0
Step-by-step explanation:
Where the line crosses the y axis that is your y intercept
Check the picture below.
Name a pair or vertical angles.
Answer:
There are two pairs:
1 and 3
2 and 4
Step-by-step explanation:
Verticle angles are angles opposite to each other when two lines intersect.
a) How much time do people in Bhutan spend watching TV each night?
Answer:
about 2 hours
Step-by-step explanation:
it is the reported average
6. What is the constant of proportionality of the linear function?
Time, x 12 3 4
Cost ($), y 25 50 75 100
F. 2 G. 12 H. 25 I. 50
Pls help!!
The table has a constant of proportionality of 25
How to determine what is the constant of proportionality?The table represents the given parameter
On the table, we have the following points
(x, y) = (1, 25)
The constant of proportionality of the points is then calculated as
k = y/x
Substitute the known values in the above equation
So, we have
k = 25/1
Evaluate the quotient
So, we have
k = 25
Hence, the constant of proportionality of the table is 25
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7. A crate of soft drinks contains 9 bottles of coke, 6 bottles of pepsi and 4 bottles of limca. Ademola picks one bottle of soft drink and thereafter Adedeji picks another bottle. Find the probability that: (a) They both. picked limca (b) Ademola only picked pepsi (c) They both picked the same brand (d) They picked different brands.
The probability that the events (a) they both picked Limca = 0.04, (b) Ademola only picked Pepsi = 0.32, (c) They both picked the same brand = 0.33 (d) They picked different brand=0.67.
What is probability?Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.
Total possible outcome of the event of picking drinks contained in the crate = 19
Hence, we can compute the following as follows;
(a) The probability they both picked Limca = (4/19)×(3/18)
Limca = 12/342
Limca = 0.04
(b) The probability Ademola only picked pepsi = 6/19
pepsi = 0.32
(c) The probability they both picked the same brand = (9/19)×(8/18)+(6/19)×(5/18)+(4/19)×(3/18)
=(72+29+12)/342
= 114/342
= 0.33
(d) The probability they picked different brand = (9/19)×(6/18)+(9/19)×(4/18)+(6/19)×(9/18)+(6/19)×(4/18)+(4/19)×(9/18)+(4/19)×(6/18)
The probability they picked different brand = (54+36+54+24+36+24)/342
The probability they picked different brand = 228/332
The probability they picked different brand = 0.67
Therefore, the probability for events (a) is 0.04, (b) is 0.32, (c) is 0.33 and (d) is 0.67.
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Write (9m) to the power of 4 without exponents.
6561m⁴ is the value of the expression (9m)⁴ without applying the exponent property.
What is an exponent?
The type of mathematical shorthand known as exponential notation enables us to write complex expressions more concisely. The base, which can be either a number or letter, is an exponent. It implies that the base is to be raised to a specific level of power. While n is the power, X is the base.
The expression is (9m)⁴.
The value of the expression (9m)⁴ without applying the property of the exponent will be
→ 9m × 9m × 9m × 9m
(we've simply expanded (9m)⁴ )
which on further simplifying gives,
→ 6561m⁴
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Jennie drew a scale drawing of her family's game room. The pool table is 4 feet wide in real life. Using a scale of 1 inch: 2 feet, how wide is the pool table in her drawing?
Please answer ASAP.
(Will give brainliest)
When Jennie drew a scale drawing of her family's game room. If the pool table is 4 feet wide in real life and using a scale of 1 inches: 2 feet, then the width of the pool table in her drawing is 2 inches
The width of the pool table in real life = 4 feet
The scale of width in drawing to real life = 1 inch : 2 feet
Therefore the equivalent ratio is
1 inch : 2 feet :: x inches : 4 feet
1 / 2 = x / 4
x = (1/2) × 4
= 2 inches
Hence, when Jennie drew a scale drawing of her family's game room. If the pool table is 4 feet wide in real life and using a scale of 1 inches: 2 feet, then the width of the pool table in her drawing is 2 inches
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