To find the arc length, we use the formula L = rθ, where r is the radius of the circle, θ is the central angle of the arc in radians, and L is the arc length.
Arc length refers to the distance covered along the curved portion of a circle or any other curved shape. It is an important concept in geometry and trigonometry and is used to measure the size of circular arcs, the size of angles, and in many other mathematical applications.
To find the arc length, we need to use the formula for the circumference of a circle and the central angle of the arc.
The circumference of a circle is given by the formula 2πr, where r is the radius of the circle.
The central angle of the arc is given in radians and is defined as the angle between two radii that meet at the endpoints of the arc.
To find the arc length, we use the formula
=> L = rθ,
where L is the arc length, r is the radius of the circle, and θ is the central angle of the arc in radians.
To convert the central angle from degrees to radians, we use the formula θ = (π/180) x degrees, where degrees are the central angle in degrees.
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Are the domain and range of function F? F(x)=x-6\x^2-3x-18
Answer:
domain: all x except -3, 6range: all y except 0, 1/9Step-by-step explanation:
You want the domain and range of the function ...
F(x) = (x -6)/(x² -3x -18)
DomainWe can simplify the function to ...
[tex]F(x) = \dfrac{x-6}{x^2-3x-18}=\dfrac{x-6}{(x-6)(x+3)}\\\\F(x)=\dfrac{1}{x+3}\quad x\notin\{-3,6\}[/tex]
The domain is the set of x-values for which the function is defined. It is undefined where the denominator is zero. So, x=-3 and x=6 are excluded from the domain, which would otherwise be all real numbers.
RangeThe range is the set of values that the function may have. Here, the function can have any y-value except 0 (the value of the horizontal asymptote), and 1/9, the location of the "hole" at x=6.
The range is all real numbers except 0 and 1/9.
solve
ax+b=dx-1
please help me
Answer:x=\frac{b-1}{a-d}
Step-by-step explanation:
18. Pilihan ganda30 detik1 ptQ. Year Consumption (million barrels per day)1986 621987 631988 651989 661990 661991 671992 671993 671994 681995 701996 721997 74What was the approximate percent increase in consumption from 1986 to 1997?Pilihan jawaban10%20%30%50%80%
The approximate percent increase in consumption from 1986 to 1997 is:
B. 20%
What is the percentage increase in consumption?The initial consumption level for the year, 1986 is 62 million barrels per day and by 1997, the percent increase in consumption shot up to 74 million barrels per day.
When we subtract the latter consumption levels from the former, we will have a total of 12 million barrels per day. So, the percentage increase will be:
12 million barrels per day/ 62 million barrels per day × 100
= 19.35 %
Thus, we can arrive at the conclusion that the total consumption levels per day increased by 19.35%, which is approximately 20%.
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Antonia visits the park every 6 days and goes to the library every 7 days. If Antonia does both of these today, how many days will pass before Antonia gets to do them both on the same day again?
Antonia will have to wait 42 days before she gets to do both activities on the same day again.
The smallest positive integer that is a multiple of both 6 and 7 is the least common multiple (LCM) of 6 and 7. This is the number of days that will pass before Antonia does both of these activities on the same day again.
We can find the LCM of 6 and 7 using the formula as follows -
LCM(6, 7) = 6 * 7 / GCD(6, 7)
where GCD is the greatest common divisor.
The GCD of 6 and 7 is 1, so we can write -
LCM(6, 7) = 6 * 7 / 1 = 42
Therefore, Antonia will have to wait 42 days before she gets to do both activities on the same day again.
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3. you want to determine whether the race of the defendant has an impact on jury verdicts. you assign participants to watch a trial with either a hispanic or caucasian defendant, and you measure on a 1 (not at all) to 7 (very) scale how guilty the defendant is. what is the best dv scale of measurement?
The best discrete variable of measurement for the situation is an interval.
What is the Scale of Measurement?Finding the scale of measurement for the variables is the next step in selecting a statistical test after identifying the independent and dependent variables. The dependent variable must be measured using an interval or ratio scale for each of the parametric tests that we have covered so far. Many psychologists also subject variables with roughly interval scales of measurement to parametric tests. You must decide whether to use "scale" or "interval" scores when performing parametric tests of means.
Given the condition about whether the race of the defendant has an impact on jury verdicts,
and measure on a 1 (not at all) to 7 (very) scale how guilty the defendant,
The best scale of measurement for the condition is an interval.
Although the interval scale has characteristics of nominal and ordered data, it also allows for the quantification of data point differences. The variables' actual positions in the order as well as their differences are both displayed by this form of data. They can be combined or split, but not added to or subtracted from.
The fact that zero is an existing variable adds another characteristic to this scale. Zero in the ordinal scale indicates that there is no data.
Hence the scale of measurement is an interval.
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Given: number of free throws made by a basketball player varies directly with
number of attempts the player has. If she makes 12 out of 40 attempts, how
many would she make during the season if she had 135 total attempts?
If she makes 135 attempts, the number of throws will be 40.5 .
How to find the number she makes?Number of free throws made by a basketball player varies directly with number of attempts the player has. If she makes 12 out of 40 attempts, the amount of throws she will make during the season if she made 135 total attempts can be calculated as follows:
Therefore,
y ∝ x
y = kx
where
k = number of free throwsx = number of attemptsTherefore,
12 = 40k
k = 12 / 40
k = 6 / 20 = 3 / 10
Hence,
y = 3 / 10 × 135
y = 405 / 10
y = 40.5
Therefore, the number of throws will be 40.5.
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adam is standing next tot he palmetto building in columbia, south carolina. he is 6 feet tall and the length of his shadow is 9 feet. if the length of the shadow of the building is 322.5 feet, how tallis the building?
He stands 6 feet tall, and his shadow extends 9 feet. if the building's shadow extends for 322.5 feet.
Now 6/9 = X/322.5
9X = 1935
X = 215ft
The Height of the building = 215ft
Consider an object AB of height h such that its shadow of length s is formed and angle of elevation is θ.
The object AB depicts a right triangle in which ∠ABO = 90o.
Now we know that in trigonometry, the tangent ratio for an angle is equal to the opposite side to that angle divided by its adjacent side.
So, for the angle of elevation θ, we have
=> tan θ = AB/OB
Putting AB = h and OB = s, we get
=> tan θ = h/s
=> s/h = 1/tan θ
=> s = h/tan θ
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checking whether such a variable is 1or 0 is typically done without explicit comparison to 1 or 0, and is instead done as
The answer is Relational operators, they are binary operators that evaluate the truthhood or falsehood of a relationship between any two arguments, and that produce value of true (1) or false (0) as a result.
This is usually done by checking whether a variable is true or false. True values are true values. For example Non-zero numbers, strings, and objects. Incorrect values are the values that correspond incorrectly. lets take 0, empty strings and undefined. By testing whether a variable is true or false, we can also determine whether it equals 1 or 0 without explicitly comparing it to 1 or 0.
This is a useful way to determine the value of a variable without having to write a comparison statement and useful way for determining the value of any variable without being written any comparison statement.
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Solve two step equations s/-2+10=13
[tex]\frac{s}{-2 + 10} = 13[/tex]
To solve this, we first remove any fraction. So we have to multiply "-2 + 10" on each sides:
[tex]s = 13(-2+10)\\s = 13(8)\\s = 104[/tex]
If any step didn't make sense, tell me and I will help you :)
Compare using
>
,
<
,
>,<,is greater than, comma, is less than, comma or
=
=equals.
72
×
3
7
72×
7
3
72, times, start fraction, 3, divided by, 7, end fraction, space
72
72space, 72
How do you know your answer is correct?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Because we are multiplying
72
7272 by a fraction that is less than
1
11.
(Choice B)
B
Because we are multiplying
72
7272 by a fraction that is equal to
1
11.
(Choice C)
C
Because we are multiplying
72
7272 by a fraction that is greater than
1
11.
The examination of the results of the two numerical articulations, 72 × 3 and 72 × 7, can be resolved utilizing the duplication administrator (×). 72 × 3 = 216 and 72 × 7 = 504.
While contrasting the results of these two expressions, we can see that 504 is more prominent than 216. This can be addressed as 504 > 216.
This implies that when 72 is duplicated by 7, the outcome is more prominent than when 72 is increased by 3.
This is on the grounds that 7 is a bigger number than 3, and thus, when it is increased by 72, the outcome will be bigger. All in all, the expression 72 × 7 delivers a more noteworthy worth than the expression 72 × 3.
All in all, the examination between 72 × 3 and 72 × 7 outcomes in 72 × 7 being more prominent than 72 × 3, or 504 > 216.
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D) If fx)=-x-11; find the following
1) 4f(-2) +5f(1) =
3) -5f12)-2f-9) =
2) 3f(5) x (2)
4)f(9)/f(-6)=
Pls I need help quick
To find 4f(-2) + 5f(1), we need to first find the values of f(-2) and f(1). Using the given equation, we have:
An easy definition of a function
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
f(-2) = -(-2) - 11 = 9
f(1) = -1 - 11 = -12
So, 4f(-2) + 5f(1) = 4 * 9 + 5 * -12 = 36 - 60 = -24.
To find 3f(5) * 2, we need to first find the value of f(5). Using the given equation, we have:
f(5) = -5 - 11 = -16
So, 3f(5) * 2 = 3 * -16 * 2 = -96
To find -5f(12) - 2f(-9), we need to first find the values of f(12) and f(-9). Using the given equation, we have:
f(12) = -12 - 11 = -23
f(-9) = -(-9) - 11 = 2
So, -5f(12) - 2f(-9) = -5 * -23 - 2 * 2 = 115 + 4 = 119
To find f(9)/f(-6), we need to first find the values of f(9) and f(-6). Using the given equation, we have:
f(9) = -9 - 11 = -20
f(-6) = -(-6) - 11 = 5
So, f(9)/f(-6) = -20 / 5 = -4.
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Travelling to America, Jenny received 88 cents American for each Australian dollar. When she returned from America, she had n American dollars. What is this amount equivalent to in Australian dollars?
Answer:
Australian dollar = n * 100 / 88
Step-by-step explanation:
n = American dollars
1 Australian dollar = 88 cents American
HELP
The mean daily pocket money of 35 pupils in another class is m cents. Given that the mean daily pocket money of the 80 pupils from these two classes is 72.25 cents, calculate the value of m.
Answer:-0.696
Step-by-step explanation:Let the total daily pocket money of the 35 pupils in the other class "A" and the total daily pocket money of all 80 pupils "B".
The mean daily pocket money of the 35 pupils in the other class is m cents, so:
A = 35 * m
The mean daily pocket money of all 80 pupils is 72.25 cents, so:
B = 80 * 72.25
Since we know the total pocket money of both classes, we can use this information to solve for m:
A + B = 115 * m
35 * m + 80 * 72.25 = 115 * m
35 * m = 115 * m - 80 * 72.25
35 * m = 115 * m - 5780
5780 = 115 * m - 35 * m
5780=80 * m
Finally, we can solve for m:
m = 5780/80
m = 72.25
Is 20 - 5x = 50- 10x true ?
Answer:
Step-by-step explanation:
that is incorrect.
if it were to be equal, one side should equal each other when multiplied to make the ratio equal.
20-5x=40-10x (when multiplied by 2 on each side)
It CANNOT equal 50, if it were there would not be -10x
20-5x=100-25x
DIVIDE BY 2 to get 50 WOULD GIVE:
20-5x=50-17.5x
Answer:
Yes
Step-by-step explanation:
solve the equation for x , then evaluate and compare both sides
20 - 5x = 50 - 10x ( add 10x to both sides )
20 + 5x = 50 ( subtract 20 from both sides )
5x = 30 ( divide both sides by 5 )
x = 6
then
left side = 20 - 5x = 20 - 5(6) = 20 - 30 = - 10
right side = 50 - 10x = 50 - 10(6) = 50 - 60 = - 10
since both sides are equal then
20 - 5x = 50 - 10x is true
Q.5. The sum of distances of point P(- 3, 4) from both the axes is
Answer:
7 units
Step-by-step explanation:
The point is 4 units from the x axis and 3 units from the y axis.
4 + 3 = 7
A system of linear equations is shown in the graph. How many solutions does the system have? a coordinate plane with one line that passes through the points 0 comma 3 and 3 comma 2 and another line that passes through the points 0 comma negative 2 and 3 comma negative 3 One solution at (0, 3) One solution at (−6, 0) Infinitely many solutions No solution
The system of linear equations shown in the graph has no solution.
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given the coordinates of two lines,
line 1: line passes from (0, 3) and (3, 2)
and slope of the line is given by,
m = (y₂ - y₁)/(x₂ - x₁)
m = (2 - 3)/(3 - 0)
m = -1/3
Line 2: line passes from (0, -2) and (3, -3)
slope = (y₂ - y₁)/(x₂ - x₁)
m = (-3 - (-2))/(3 - 0)
m = -1/3
since both, the lines have the same slope so both lines will be parallel,
If two lines are parallel, they will never intersect and so there is no solution to the given system of equations.
Hence lines will have no solution.
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• On Dec. 9, Rick worked from half past seven o'clock a.m. to half past four o'clock p.m. He took a half-hour lunch break.
On Dec. 10, Rick worked from seven o'clock a.m. to half past four o'clock p.m. He took a half-hour lunch break.
On Dec. 11, Rick worked from half past eleven o'clock a.m. to five o'clock p.m. He did not take a lunch break.
•
On Dec. 12, Rick worked from half past seven o'clock a.m. to half past five o'clock p.m. He took a one-hour lunch break.
• On Dec. 13, Rick worked from half past seven o'clock a.m. to seven o'clock p.m. He took a one and a half-hour lunch break.
On Dec. 14, Rick worked from eight o'clock a.m. to five o'clock p.m. He took a one and a half-hour lunch break.
On Dec. 15, Rick did not work.
The timesheet of Rick's working hours is given below.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
From the given data points of Rick's working hours:
Date Start Time End Time Time away Regular hours
Dec. 9, 7:30 am 4:30 pm 30 minutes 8.5
Dec. 10, 7:00 am 4:30 pm 30 minutes 8.5
Dec. 11, 11:30 am 5:00 pm - 5.5
Dec. 12, 7:30 am 5:30 pm 60 minutes 9
Dec. 13, 7:30 am 7:00 pm 90 minutes 10
Dec. 14, 8:00 am 5:00 pm 90 minutes 4.9
Dec. 15, - - - -
Therefore, the timesheet is given.
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The complete question:
Make a timesheet for the following dates and times: Dec. 9, Rick...
Make a timesheet for the following dates and times:
Dec. 9, Rick worked from 7:30am to 4:30 p.m. He took a 30 min lunch break
Dec. 10, Rick worked from 7 am to 4:30 p.m. He took a 30 min lunch break
Dec. 11, Rick worked from 11:30 am to 5:00 p.m. He didn't take a lunch break
Dec. 12, Rick worked from 7:30 am to 5:30 p.m. He took an hour lunch break
Dec. 13, Rick worked from 7:30 am to 7:00 p.m. He took an hour and a half lunch break
Dec. 14, Rick worked from 8 am to 5 p.m. He took an hour and a half lunch break
Dec. 15, Rick did not work.
The ratio of children to adults at a party is 2:3. A busload of 30 more children
arrives at the party, and now the ratio of children to adults is 3:2. How many
people were at the party before the bus arrived?
Answer:
60 people
Step-by-step explanation:
Before
C:A
2:3
After
C:A
3:2
We know that the number of adults never change.
Before
C:A
4:6
After
C:A
9:6
difference in units of children= 9-4
= 5
5 units= 30
1 unit= 30÷5
= 6
total units [before]= 4+6
= 10
10 units= 6×10
=60
is 9/10 simplify or not to simplify?
Answer:Not to simplify
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
9/10 is already in its simplest form. It cannot be further simplified as it is a fraction with two prime numbers in its numerator and denominator.
In a circle with radius 8, an angle intercepts an arc of length 16pi/3. Find the angle in radians in simplest form.
The angle in radians in simplest form is 2π/3 radians.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.
Given the radius of the circle = 8
and length of arc = 16π/3
the relation between angle and arc is given by,
s = rθ
where r = radius, s = arc length and θ = angle in radians,
so, θ = s/r
θ = (16π/3)/8
θ = 2π/3 radians
Hence the angle is 2π/3 radians.
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Explain in your own words the definition of hypotenuse
there are 8 women and 10 men. how many are there ways to form a committee of 11 with more women than men?
Answer:
Below
Step-by-step explanation:
If the men are indistinguishable and the women are too, then
6 w 5 m
7 w 4 m
8 w 3 m
3 ways
IF they ARE distinguishable it becomes a much larger, complex calculation:
8 C 6 * 10 C 5 + 8 C 7 * 10 C 4 + 8 * 10 C 3
( is THIS what you are studying ? )
General Sherman, a tree located in Sequoia National Park, stands 275
feet tall. To see the top of the tree, Carlos looks up at a 15° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the nearest foot? There are 4 options A.1004 B.1020 C.1026 D.1049
Answer:
Step-by-step explanation:
If Carlos is 6ft tall and looks up at the tree that is 275 ft tall, subtract those two.
275 - 6 = 269
Use tangent with the given angle and the new height. The distance is x.
tan15 = 269/x
x = 269/tan15
x = 1004ft
The distance from Carlos to the tree, given he is 6 feet tall and looks up at a 15° angle of elevation to see the top of a 275-foot tall tree located in Sequoia National Park, is 1026.
Hence option C is correct.
According to the information given,
We can set up a right triangle with Carlos's eye level, the top of the tree, And the base of the tree as the three points of the triangle.
Carlos's height of 6 feet can be used as one side of the triangle,
And we can use the tangent function to find the length of the adjacent side.
A tangent of 15 degrees is equal to the opposite side (height of the tree) divided by the adjacent side (distance from Carlos to the tree).
So, we can solve for the adjacent side by multiplying the height of the tree by the tangent of 15 degrees:
tan(15) = height of the tree / distance from Carlos to the tree
Distance from Carlos to the tree = height of the tree / tan(15)
Plugging in the values given:
Distance from Carlos to the tree = 275 / tan(15)
≈ 1026
Therefore,
The nearest foot to the distance from Carlos to the tree is option C. 1026.
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Which of the following is a line through the point (-3, 1) with a slope of 3/5? Please hurry
The equation of the line is y = (3/5)x + 14/5.
This graph is option D.
Option D is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Slope = 3/5
Passes through the point = (-3, 1)
Now,
The equation of the line.
y = mx + c
m = 3/5
(-3, 1) = (x, y)
1 = (3/5)(-3) + c
1 = -9/5 + c
c = 1 + 9/5
c = 14/5
Now,
y = mx + c
y = (3/5)x + 14/5
This graph is option D.
Thus,
The equation of the line is y = (3/5)x + 14/5.
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Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠A1 is smaller than ∠A2.)
b = 121, c = 162, ∠B = 48°
The values of triangle ABC are
< A = 47.8 < C = 84.2a = 120.6How to find the angels in triangle ABCThe angles in triangle ABC is calculated using the sine rule which sates that the ratio of a side and the opposite angles are equal to each other
This represented by the formula
Sine A / a = Sine B / b = Sine C / c
applying the formula for the problem
Sine B / b = Sine C / c
Sine 48 / 121 = Sine C / 162
cross multiplying
Sine C = 162 * Sine 48 / 121
Sine C = 0.99495
C = arc sine (0.99495)
C = 84.2
Applying sum of angles in a triangle
< A + < B + < C = 180
< A + 48 + 84.2 = 180
< A = 180 - 48 - 84.2
< A = 47.8 degrees
side a
Sine A / a = Sine B / b
Sine 47.8 / a = Sine 48 / 121
121 * sine 47.8 / Sine 48 = a
a = 120.6
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according to the u.s. census bureau, 5% of americans age 25 or older had completed a bachelor's degree or higher in 1940. write this percent as a ratio and do not simplify.
5% as a ratio not in simplified form is 5/100 or 5:100.
To write a percent as a ratio, we can divide it by 100 and express the result as a fraction. For example, 5% can be written as 5/100.
So, according to the U.S. Census Bureau, 5% of Americans age 25 or older had completed a bachelor's degree or higher in 1940 can be written as a ratio as:
= 5/100
This fraction represents the ratio of Americans age 25 or older who had completed a bachelor's degree or higher in 1940 to the total number of Americans age 25 or older.
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What is the rate of change
The rate of change of the table is 3
How to calculate the rqte of change of the table?From the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have the following ordered pairs
(9, -6) and (11, -12)
The rate of the table is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (9, -6) and (11, -12)
Substitute the known values in the above equation
So, we have the following equation
Slope = (-12 + 6)/(11 - 9)
Evaluate
Slope = -3
Hence, the rate of the table is -3
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Find the domain of f(x) below
√(x-7) / x³ + 1
Domain of function is in Set Builder Notation is, {x | x ≥ 7 }.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = √(x-7) / (x³ + 1)
Now, We can find the domain of function as;
⇒ f (x) ≥ 0
⇒ √(x-7) / x³ + 1 ≥ 0
⇒ √ (x - 7) ≥ 0
⇒ x - 7 ≥ 0
⇒ x ≥ 7
Thus, Domain of function is in Set Builder Notation is, {x | x ≥ 7 }.
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Adwoa travelled 12 km due north and 5 km due east. How far was she from her starting point?
Arun walked 5 km to east and then 12km to north. By joining the starting point and the end point by straight line we will get a right angled triangle, hypotenuse of which will tell how far is he from his starting point.
What is Pythagoras theorem?The square on the hypotenuse's area is equal to the sum of the two squares on the legs (a and b) (c). Pythagoras, a Greek philosopher who was born in 570 BC, is honored by having his theorem named after him. The theorem has already been shown more than once through various techniques, possibly greater than any other mathematical theorem. The hypotenuse side of a right-angled triangle's square is equal to the total of its other two sides, according to Pythagoras' Theorem. These right triangle three sides are known as the Perpendicular, Base, and Hypotenuse.
So Pythagoras theorem,
H²= 5² + 12²
H²= 25 + 144
H² = 169
H = 13
So, he will be 13 km far away from his starting point.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
3 cm
Step-by-step explanation:
Given
Triangle ABC and Triangle DEF are similar
BC=4cm
EF = 16cm
FD = 12cm
ED = 10cm
Since we know that the triangles are similar,
AB/DE = BC/EF = CA/FD as they are the corresponding sides of the similar triangles
or
BC/EF = AC/FD
or
4/16 = AC/12
1/4 = AC/12
12/4 = AC
3 = AC
Therefore the value of AC is 3 cm