Its phase is 60 degrees and π/3 radian
From the question, we have
Each complete cycle measures 360 degrees.
So, 1/6 cycle = 1/6 × 360° = 60°
Each complete cycle measures 2π radian.
So, 1/6 cycle = 1/6 × 2π = π/3 radian
Multiplication:
In mathematics, multiplying two or more numbers yields the product of the numbers. One of the basic mathematical operations is one that we commonly perform. The most obvious example is using multiplication tables. Mathematicians multiply two integers to illustrate the process of repeatedly adding one number to another. The types of numbers that can be included include natural numbers, fractions, integers, whole numbers, and others. When M is multiplied by n, it either adds or subtracts from itself 'n' times.
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each roll of black ribbon has 3 2/3ths yards of ribbon if amanda has 4 1/2th rolls of black robbin how many yards does amanda have
Amanda have roll of black ribbon [tex]= 3_3^2th[/tex]
If Amanda has rolls of black ribbon [tex]= 4_2^1th[/tex]
total rolls of black ribbon amanda have [tex]= 3_3^2th+4_2^1th[/tex][tex]= 8_6^1 th[/tex]
What is Fraction?
A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
What is mixed fraction?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
Consider the expression;
[tex]= 3_3^2th+4_2^1th[/tex]
Rewriting our equation with parts separated
[tex]= 3+\frac{2}{3}+4+\frac{1}{2}[/tex]
Solving the whole number parts
3 + 4 = 7
Find the LCD of 2/3 and 1/2 and rewrite to solve with the equivalent fractions.
LCD = 6
[tex]\frac{4}{6}+\frac{3}{6} = \frac{7}{6}[/tex]
Combining the whole and fractional parts
[tex]7+1+\frac{1}{6} = 8_6^1[/tex]
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You can choose a prize of either a $25,000 car or one penny on
the first day, triple that (3 cents) on the second day, and so on for a month. On what
day would you receive more than the value of the car?
If you can choose a prize of either a $25,000 car or one penny on the first day. The number of days you receive more than the value of the car is 15 days.
How to find the number of days?Let x represent the number of days
Convert $25,000 to cents by multiplying it by 100
$25,000 × 100 = 2,500,000 cents
Hence:
3^x-1 > 2,500,000
(x-1) log3/log 3 > log 2500000/log 3
x-1 > 13.409
x = 13.409+1
x =14.409
x = 15 days (Approximately)
Therefore the number of days is 15.
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An airplane
30,000 feet above the
ground begins descending at a rate of
2,000 feet per minute. Write an
equation to model the situation. Find
the altitude of the plane after 5
minutes.
An equation to model the situation: h = 30000 - 2000t
the altitude of the plane after 5 minutes is 20000 feet
In this question, an airplane 30,000 feet above the ground.
It begins descending at a rate of 2,000 feet per minute.
We need to write an equation to model the situation. Also, we need to find
the altitude of the plane after 5 minutes.
Let h be the altitude of plane after t hours.
So, we get an equation,
h = 30000 - 2000t
For t = 5 minutes,
h = 30000 - 2000(5)
h = 30000 - 10000
h = 20000 feet
Therefore, an equation to model the situation: h = 30000 - 2000t
the altitude of the plane after 5 minutes is 20000 feet
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The points A(0,5), B(4,2), and C(0,2) form the vertices of a right triangle in the coordinate plane. What is the equation of the line that forms the hypotenuse
Answer:
y = - [tex]\frac{3}{4}[/tex] x + 5
Step-by-step explanation:
the hypotenuse is the line AB
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A (0, 5 ) and (x₂, y₂ ) = B (4, 2 )
m = [tex]\frac{2-5}{4-0}[/tex] = [tex]\frac{-3}{4}[/tex] = - [tex]\frac{3}{4}[/tex]
the line AB crosses the y- axis at A (0, 5 ) ⇒ c = 5
y = - [tex]\frac{3}{4}[/tex] x + 5 ← equation of hypotenuse
18.9x{2x2.7}-4.6} - to the second power
The equivalent value to the expression 18.9 x [(2 x 2.7) - 4.6] - 2² is given by the following option:
C. 11.12.
How to obtain the equivalent value to the expression?The equivalent value to an expression is given by the solution to the expression.
The expression in this problem is given as follows:
18.9 x [(2 x 2.7) - 4.6] - 2²
The brackets take precedence, hence the first operation to be solved is of:
(2 x 2.7) - 4.6
The parenthesis take precedence relative to the subtraction, hence:
(2 x 2.7) - 4.6 = 5.4 - 4.6 = 0.8.
Then the expression is given by:
18.9 x [(2 x 2.7) - 4.6] - 2² = 18.9 x 0.8 - 2².
The square takes precedence, hence:
18.9 x 0.8 - 4.
Then the multiplication takes precedence, which means that the equivalent result is of:
18.9 x 0.8 - 4 = 15.12 - 4 = 11.12.
Given by option C.
Missing InformationThe problem is given by the image shown at the end of the answer.
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A sign company is building a sign with the dimensions shown. What is the area, in square feet, of the sign.
A.) 65ft^2
B.) 60ft^2
C.) 130ft^2
The area of the triangle will be 60ft².
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
Now using the Pythagoras theorem we can find out the length of the other wall
b²+p²=h²
So here h=13ft and b=5ft
p²= h²-b²
= 13²-5²
=169-25
p = √144 = 12ft
So the area of the trinagle is = 1/2*b*p
1/2(10*12)= 60ft²
Hence the area of the triangle will be 60ft².
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A square has an area of 36 squares centimetres what is the perimeter of the square
Answer:
24 centimeters
Step-by-step explanation:
we find a side by finding the square root of the area
Square root of 36 is 6
Now we find the perimeter by multiplying 6 by 4
6x4=24
Hopes this helps please mark brainliest
If a board of directors consists of 18 people, how many ways can a chief executive officer, a director, a treasurer, and a secretary be selected?.
There are 204 possible methods to choose a chief executive officer, a director, a treasurer, and a secretary, if there are 18 members on the board of directors.
What is combination?Combinations are mathematical procedures that count how many different ways a collection of items might be arranged when the order in which they are chosen is immaterial. Regardless of the order in which the things are chosen, a combination is the choice of all or part of a collection of objects. A combination is "an arrangement of items where the order of the components is unimportant," according to the definition. When these two terms are combined, "Selection of things" is meant, where the order of the items is not important.
Here,
If the order doesn't matter then we have a combination, if the order do matter then we have a permutation.
18C4=18!/(18-4)!(4)!
=18!/14!4!
=18*17*16*15/4*3*2*1
=3*17*4
=204 ways
A chief executive officer, a director, a treasurer, and a secretary be can be selected in 204 ways If a board of directors consists of 18 people.
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What is the next term in the sequence 4, 11, 18, 25, ...?
Answer: 32
Step-by-step explanation: you have to count by 7 everytime
Pete,Joe, and Blake shared a large pizza. The pizza was cut into eight pieces. Pete ate two pieces, Joe ate two piece, and Blake ate one piece. Which fraction is equivalent to the amount of pizza that was eaten by all the boys.
Answer:
Pete ate 2, Joe ate two, and Blake ate 1
2 + 2 + 1 = 5
They ate 5 out of 8 slices. The boys ate 5/8 of the pizza
the overall speedup of a system that spends 40% of its time in calculations with a processor upgrade that provides for 100% greater throughput is
The overall speedup of such a system that spends 40% of its time performing calculations is 1.25 when a processor upgrade results in 100% more throughput.
What is defied as the processor upgrade?One of the most efficient and affordable changes you can do to a more aged system is swapping the processor with a speedier one. In some circumstances, you can significantly increase CPU performance at a little cost. Not every system is a good candidate for a processor upgrade, which is unfortunate.The overall speedup of a machine that spends 40% of its time processing data with a processor upgrade that offers 100% more throughput answers the issue.
Thus, with a CPU upgrade that results in 100% more throughput, a system that spends 40% of its time performing calculations sees an overall speedup of 1.25.
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A car rental charges an initial fee of $42 and a daily fee of $12. A costumer pays a total of $138. How many days did the customer rent the car?
Answer: 8 days
Step-by-step explanation: 138-42 = 96 then you divide that by daily fee of 12 to get 8 days
10. Suppose the length and width of the rectangle are doubled. What effect would this have on the area? 15 points!!!!
Answer:
area increases by a factor of 4
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = lw ( l is length and w is width )
doubling the length and width , that is
l = 2l and w = 2w , then
A = 2l × 2w = 4lw
that is the area is increased by a factor of 4
2 step equations
3y+4=22
Answer:
3y+4=22
3y+4-4=22-4
3y=18
(3y)/3=18/3
y=6
Step-by-step explanation:
pls mark brainliest
7) Find the discriminant to determine the number of roots, then solve the quadratic equation
using the quadratic formula.
2x² + 7x-4 = 0
The Determinant of the equation is 17
What is the determinant of the equation?
The determinant is a scalar variable in mathematics that is a function of the elements of a square matrix. It enables the characterization of some characteristics of the matrix as well as the linear map expressed by the array. The determinant is nonzero, in particular, if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a matrices product is the product of their determinants (the preceding property is a corollary of this one). The determinant is a scalar variable in mathematics that is a function of the elements of a square matrix. It enables the characterization of some attributes of the matrix as well as the vertical map presented by that of the array.
Given equation is 2x² + 7x - 4 = 0
Therefore, determinant = (7)² - 4x2x(-4)
= 49 - 32
= 17
Hence, the determinant of the given equation is 17
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A family wants to build a pen for their new puppy. They
want the area of the pen to be more than 225 square feet.
If the width of the pen is 25 feet, what is the set of possi-
ble lengths for the pen?
The value of length of pen should always be greater than 5 feet.
Rectangle:
Rectangle is a special kind of parallelogram in which opposite sides are equal and adjacent sides are perpendicular to each other.It contains of length and breadth,The area of rectangle is given by,
Area = length x breadth
Now as per question,
A family wants to build a pen for their new puppy.
They want's the area of the pen to be more than 225 square feet.
width of the pen is = 25 feet
let,
The length of the pen is [tex]x[/tex] feet.
Area of pen = length * width
= [tex]x[/tex] * 25
= 25x
According to the question,
Area of pen > 225 square feet
25x > 225
x >225/25
x > 5 feet
Thus,
The value of length should always be greater than 5 feet.
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Which reason should you use to prove the following triangles are congruent?
A. SAS
B. AAS
C. Not enough information (Not Congruent)
D. ASA
E. HL
Answer:
A A S
Step-by-step explanation:
Angle - Angle- side: they have two consecutive equal angles and a non-included side that is equal
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, what is the total weight in tons of all the wheat that will be placed on the first 59 squares? (Assume that each grain of wheat weighs 1/7000 pound. Remember that 1 ton2000 lbs.)
The number of grains on square 59 will be 5.7646075230342 x 10^17grains.
How to calculate the number of grain?No. of grains on the first square = 1 = 2^0
No. of grains on the second square = 2 = 1*2 = 2¹
No. of grains on the third square = 4 = 2*2 = 2²
No. of grains on the fourth square = 8 = 2*4 = 2³
From the pattern it could be seen that amount of wheat is doubled for every next square
So, the number of grains in the nth square = 2^n-1
Therefore, No. of grains on 59th square
= 2^59 -1 =
= 5.7646075230342 x 10^17
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in a certain chemical the of zinc to copper is 4 to 15 if a jar contains 600 grams of copper how much zinc is there
The amount of zinc in the jar is 160 grams.
According to the question,
We have the following information:
In a certain chemical the of zinc to copper is 4 to 15 and a jar contains 600 grams of copper.
Let's take the amount of zinc in a chemical to be 4x and that of copper to be 15x.
So, we have the following expression:
15x = 600
Dividing both the sides by 15 will give us the value of x:
x = 600/15
x = 40 grams
Now, we will put this value of x in the amount of zinc:
4x grams
4*40
160 grams
Hence, the amount of zinc in the given jar is 160 grams.
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1. in 2009, 33% of americans felt that one parent should stay home to raise the children instead of using day care. in a poll conducted in 2011, 416 out of 1015 americans believed that one parent should stay home. at a 99% level of confidence, is there sufficient evidence to conclude that the percentage has increased from its 2009 value?
Answer: Yes
Step-by-step explanation: To show that the percentage has increased we would need to prove that 416/1015 with a 99% level of confidence or a 1% margin of error to do this we divide 416 by 1015
This equals 0.40985221674
Which can be rounded to 0.41 or 41% since there is a one percent margin of error we can assume that this is enough evidence, because if 1% of the poll's recipients mistakenly voted for a option they did not really think was true it would not be enough to change 41% to 33%
Hope this helps!
The figure below was made with a scale of 1 unit = 3 ft.
Draw the figure with a new scale of 1 unit = 6 ft.
You can place your figure anywhere on the grid on the right
The second side will therefore be 12 feet long if one side is 6 feet long. We just need to calculate two sides because each comparable side is equal.
Define scaling.A linear transformation known as uniform scaling in affine geometry enlarges or reduces objects in all directions by the same scale factor. The final product of uniform scaling resembles the initial. Normal practize allows for a scale factor of 1, which allows for the classification of congruent shapes as similar.
Given,
The process for scaling a rectangle is as follows:
Let's say one of the sides is two units long, and you count the number of units on that side.
1 unit = 6 feet.
12 feet = 2 units
We only need to double the rectangle's size to rescale. The second side will therefore be 12 feet long if one side is 6 feet long. You just need to calculate two sides because each comparable side is equal.
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please help thank you
9. The perimeter and the ratio of the
length to the width of a rectangle are
given. Find the length and width of the
rectangle.
Perimeter: 132 cm 1:w = 7:4
Answer:
Length: 42, width: 24
Step-by-step explanation:
Perimeter: 132
L: W = 7:4
7u+7u+4u+4u= 22u (Length + length + width + width)
132/22= 6 (1u)
6x4= 24 (Width/ 4u)
6x7=42 (length/7u)
recheck:
42+42+24+24= 132cm
perimeter= 132
Find the perimeter of the figure below. Use 3.14 for pi
10 m
16 m
I hope this is the last on I need help with!-
I need an answer immediately and i will give a lot of points
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╚╗╔╝
╔╝ (¯`v´¯)
╚══`.¸.*when you answer*
Answer:
72.52
Step-by-step explanation:
circumference of a circle formula = [tex]2\pi r[/tex]
where r is the radius
the radius is half of diameter, and the diameters for all semicircles are given.
so the radius for the smaller semicircles is 10/2 which is 5
so [tex]2\pi 5[/tex] = 2(3.14)(5) = 31.4
31.4 is the circumference of the whole circle, since we have 2 semicircles with the same radius, we don't need to divide this by 2, we will simply use 31.4 for instead of doing this exact calculation again for the other small semicircle.
for the larger cemicircle, the diameter is 16 so the radius will be 16/2 which is 8
[tex]2\pi 8[/tex] = 2(3.14)(8) = 50.24
since 50.24 is the circumference of an entire circle, we will have to divide this by 2 to d=find the circumference of the semicircle.
50.24/2 = 25.12
Now we will simply add up the lengths of the borders,
31.4 + 25.12 + 16 = 72.52
Answer:
57.7 meters total perimeter for the object.
Step-by-step explanation:
See the attached worksheet. Break up the object into three circles and one rectangle. Label them to keep track of the work. The object's perimeter is coprised of:
- One side of rectangle R (16 m)
- 1/2 the circumference of circles b and c, each with a radius of 5 m
- 1/2 the circumference of circle a, with a circumference of 8 m.
The perimeter of a circle is 2πr. The perimeter of circles b and c is 31.4 meters in total, which is reduced to (1/2) or 15.7 m total. Circle a contributes 26 meters to the object's perimeter.
The sum of these measurements is (16m) + (15.7m) + (26m) = 57.7 meters total perimeter for the object.
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The values of the function are 1/9, 1/3, 1, 3 and 9.
What is a function?A function is defined as a relation between a set of inputs having one output each.
Given a function, f(x) = [tex]3^{x}[/tex]
When x = -2
y = [tex]3^{-2}[/tex] = 1/3² = 1/9
When x = -1
y = [tex]3^{-1}[/tex]
y = 1/3
When x = 0
y = [tex]3^{0}[/tex]
y = 1
When x = 1
y = 3
When x = 2
y = 3² = 9
Hence, The values of the function are 1/9, 1/3, 1, 3 and 9.
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can anybody help please?
A box is a cuboid with dimensions 26 cm by 15 cm by 20 cm all measured to the nearest centimetre. Disc cases are cuboids which measure 1.6 cm by 14.2 cm by 19.3 cm all measured to the nearest millimetre. 20 cm If the disc cases are stacked as shown, show that it may not be possible for 16 cases to fit in the box. box measurements: 26 cm 15 cm 20cm disc measurements: 1.6 cm 19.3 cm 14.2 cm
The number of discs that can be filled in the box is 17.
length of box , l =26 cm , breadth , b =15 cm , height = 20 cm
So,the volume of the box = l × b × h
= 26 × 15 ×20 cm³
= 7800 cm³
Now length of a disc case, l= 1.6 cm
breadth ,b =14.2 cm
height, h =19.3 cm
So the volume of a disc case = 1.6×14.2×19.3 cm³
= 438.496 cm³
No of disc cases can be stacked inside the box
= 7800 ÷ 438.496
=7800000÷438.496
= 17.8
Hence 17 disc cases can be fitted into the box.
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What is the value for x and y? and how do you use the systems to figure them out?
The value of x is 22.37 and y is 20
What is Interior angle?
An angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon.
What is Exterior angle?
An exterior angle (also called an external angle or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.
We know, the sum of interior angle is 180 degree
The given interior angles is ,
3y + 5 and 5y + 15
So, equate to 180°
3y + 5 + 5y + 15 = 180°
Solve for 'y'
8y + 20 = 180
4(2y + 5) = 180
2y + 5 = 45
2y = 45 - 5
2y = 40
y = 20
Now, we know the sum of exterior angle is 360 degree
The given exterior angle is,
17x - 70 and 2x + 5
So, equate to 360°
17x - 70 + 2x + 5 = 360°
Now, solve for 'x'
19x - 65 = 360
19x = 360 + 65
19x = 425
x = 22.368 or 22.37
Hence, the value of x is 22.37 and y is 20
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Primo car rental agency charges $25 per day plus $0.30 per mile. Ultimo car rental agency charges $30 per day plus $0.95 per mile. Find the daily mileage for which the Ultimo charge is three times the Primo charge.
The mileage is
Answer:
[tex]28\frac{4}{7}[/tex] miles
Step-by-step explanation:
mileage = m
Primo: cost = 0.3m + 20
Ultimo: cost = 0.95m + 30
Ultimo = twice Primo
0.95m + 30 = 0.6m + 40
subtract 0.60m and 30 from each side and simplify to get
0.35m = 10
divide by 0.35 into both sides to get
m = [tex]28\frac{4}{7}[/tex]
therefore, the daily mileage would be [tex]28\frac{4}{7}[/tex] miles
wall-to-wall carpeting is installed in a room that is ft long and ft wide. the edges of the carpet are held down by tack strips. how many feet of tack-strip material are needed?
If wall-to-wall carpeting is installed in a room 21 ft long and 17 ft wide and the edges of the carpet are held down by tack strips, the feet of tack-strip material needed are 76 ft calculated by determining the perimeter of the rectangle room.
Tack strips are thin pieces of wood studded with nails or tacks in the installation of carpets. These thin strips are placed along all the edges of the carpet. In order to determine the length of the tack strips needed to hold the wall to wall carpeting installed in a rectangular room of 21 ft by 17 ft. The formula of the perimeter of a rectangle is:
P = 2 (length + width)
P = 2 (21 + 17)
P = 2 (38)
P = 76 ft
Hence, the feet of tack-strip material needed are 76 ft.
Note: The question is incomplete. The complete question is Wall-to-wall carpeting is to be installed in a rectangular room that is 21 ft long and 17 ft wide. The edges of the carpet are to be held down by tack strips. How many feet of tack-strip material is needed?
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The comprehensive graph of a polynomial function y=f(x) is shown
how many real zeros does the function f have?
There is only 1 real zero of the function.
What are Zeros of a Function?
The zeros of a function are the values of the function's variables that fulfil the equation and yield the function's value of 0. The zeros of a function can be represented graphically as the x-coordinates (x-intercepts) where the graph intersects the x-axis.
Solution:
As mentioned above,
The zeros of a function can be represented graphically as the x-coordinates (x-intercepts) where the graph intersects the x-axis.
So,
We can see that there is only one point where the graph intersects the x-axis.
Therefore, it can be said that there is only 1 real zero of the function.
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