(a) Since cosθ = 7/12 and sinθ < 0, we can find the other four trigonometric functions as follows:
sinθ = √(1 - cos²θ) = √(1 - (7/12)²) = √(1 - 49/144) = -√(95/144)
tanθ = sinθ / cosθ = (-√(95/144)) / (7/12) = -4√(5/18)
cotθ = 1 / tanθ = -1 / (-4√(5/18)) = 1/(4√(5/18))
secθ = 1 / cosθ = 1 / (7/12) = 12/7
cscθ = 1 / sinθ = -1 / (-√(95/144)) = √(95/144)
(b) Since tanθ = 4/3 and θ is in Quadrant III, we can find the other five trigonometric functions as follows:
cosθ = √(1 / (tan²θ + 1)) = √(1 / (16/9 + 1)) = √(9 / 25) = 3/5
sinθ = cosθ * tanθ = (3/5) * (4/3) = 4/5
cotθ = 1 / tanθ = 1 / (4/3) = 3/4
secθ = 1 / cosθ = 1 / (3/5) = 5/3
cscθ = 1 / sinθ = 1 / (4/5) = 5/4
What is trigonometric functions?Trigonometric functions are a set of functions that relate the angles of a right triangle to the ratios of the sides of the triangle. The six most commonly used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
The sine function, represented by sin, gives the ratio of the side opposite the angle to the hypotenuse. The cosine function, represented by cos, gives the ratio of the adjacent side to the hypotenuse. The tangent function, represented by tan, gives the ratio of the opposite side to the adjacent side.
The cotangent function, represented by cot, gives the ratio of the adjacent side to the opposite side. The secant function, represented by sec, gives the ratio of the hypotenuse to the adjacent side, and the cosecant function, represented by csc, gives the ratio of the hypotenuse to the opposite side.
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A population of bacteria grows according to function p (t) = p. 1. 42', where t is measured in hours. If the initial population size was 1,000 cells, approximately
how long will it take the population to exceed 10,000 cells? Round your answer to the nearest tenth
The time duration for the population to exceed 10,000 is approximately 6.6 hours
What is time ?
In mathematics, time is described as a continuing and continuous series of events that take place in chronological order from the past through the present and into the future. The duration of events, the gaps between them, or even the sequencing of occurrences can all be quantified, measured, or compared using time.
the time frame that an activity, process, or state lasts or continues to exist: duration is a non-spatial continuum that is measured in terms of subsequent occurrences from the past, present, and future.
The mathematical symbol used to represent the multiplication process and its subsequent product is the multiplication sign, sometimes referred to as the times sign or the dimension sign.
t = The time duration in hours
The initial population of the cells = 1,000
Therefore, at t = 0, P(0) = 1,000 = P₀ × 1.42^0
∴ P(0) = 1,000 = P₀ × 1 = P₀
P₀ = 1,000
When the population is 10,000, we have;
P(t) = 10,000 = 1,000 × 1.42^t
∴ 1.42^t = 10,000/1,000 = 10
㏒(1.42^t) = ㏒(10) = 1
∴ t × ㏒(1.42) = 1
t = 1/㏒(1.42) = 6.56649071898
∴ The time duration for the population to exceed 10,000, t ≈ 6.6 hours.
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Complete the table with values for x or y that make this equation true : 3x+y=15.
Answer:
Step-by-step explanation:
So first, with the given table you need to "plug-in" the numbers that are there for x and y.
Ok, for example 2 is listed in the "x" row. So plug it 2 for "x":
3x+y=15
3(2)+y=15
6+y=15
-6 -6
y=9
So do this for all of them...the same goes with all of the values...just plug in one, complete the steps then you'll get the answer for the other variable.
Hope this helps!
A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events. The probabilities assigned were , , and a. If an individual recalls seeing the advertisement, what is the probability that the individual purchased the product (to 1 decimals)
0.30 is the probability that the individual purchased the product
What is probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.
Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.
Let, B = individual purchased the product
S = individuals recalls seeing the advertisement.
Here, P(B) = 0.20
P(S) = 0.40
P(B ∩ S) = 0.12
Thus, P(B | S) = P(B ∩ S) / P(S)
= 0.12/0.40
= 0.30
P(B) = 0.20 < P(B | S) =0.30
Yes, thus the probability that an individual will purchase the product will increase if the individual sees the advertisement first.
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The complete question is as follows:
There are 8 employees on The Game Shop's sales team.
Last month, they sold a total of g games. One of the
sales team members, Chris, sold 17 fewer games than
what the team averaged per employee.
How many games did Chris sell?
Write your answer as
an expression.
games
According to the solving the team average is g/17 and Chris sold (g/8) - 17 games.
What do you mean by average?The term "Average" refers to a value that should be used to describe the sample as a whole. The average is determined by dividing the total number of values in a set by the total number of values. also known as the arithmetic mean.
How do you calculate the mean?Average A collection of integers are added, their count is divided, and the sum is used to determine the arithmetic mean.
According to the given information:average game sold = g/8
since Chris sold 17 games less than average
hence, Chris sold games
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A forest covers 78,000 acres. A survey finds that 0. 4% of the forest is old-growth trees. How many
acres of old-growth trees are there?
There are
acres of old-growth trees.
Answer:
There would be 312 acres of old tree growth for 0.4% of the forest. There would be 31.2 acres of old tree growth for 0.04%. I wasn't sure if you meant 0.4 or 0.04.
Is Infinity a interval?
To represent "infinity" or the notion that an interval lacks an ending, we use the symbol.
Is infinity an open interval?The endpoints of infinity and negative infinity can be seen in two different ways. One the one hand, we can never get to infinity because it is a concept and not a real quantity.
In this sense, the interval is said to be open because it excludes the endpoints infinity and negative infinity. The infinity symbol is placed on the right side since there is no higher endpoint (all values must be larger than or equal to -3). An interval is closed if its boxed end is on -3. Because there is no endpoint on that side, infinity always has a curved end.
To represent "infinity" or the notion that an interval lacks an ending, we use the symbol. The symbol shouldn't be used with a square bracket because it's not a number. Visit this tutorial on set-builder and interval notation for a more thorough discussion of set notation and interval notation.
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Refer to the equation a-6 equals b if a equals 45 what is the value of b?
Answer:
Step-by-step explanation: a=4, b=2.
Answer:
b = 39
Step-by-step explanation:
[tex]a-6=b[/tex]
if a = 45:
[tex]45-6=b\\39=b[/tex]
Hope this helps
To find the distance from the edge of a lake to the tree on the island in the lake, Lisa sets up a
triangular configuration as show in the diagram. The distance from Location A to Location B is 97
meters. The measures of the angles at A and B are 46 and 103 °. What is the distance from the
edge of the lake at B to the tree on the island at C? Round the distance to the nearest tenth of a
meter.
A
B
C
Answer:
135.5 m
Step-by-step explanation:
Given a triangle with angles A=46°, B=103°, and side c=97 m, you want to find the length of side 'a'.
Law of SinesGiven one side and two angles we can solve the triangle using the Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
In order to do that, we need to have a (side, angle) pair, so we need to find the measure of angle C.
A + B + C = 180°
46° +103° +C = 180° . . . use the given measures
C = 31° . . . . . . . . . . . . . subtract 149°
Now, we can find 'a' from ...
a/sin(A) = c/sin(C)
a = c·sin(A)/sin(C) = (97 m)·sin(46°)/sin(31°) ≈ 135.477286 m
The distance from B to the tree at C is about 135.5 meters.
How do you write 10000000 in words?
Flow chart to find the biggest of 3 numbers
The flowchart to find the biggest of 3 numbers is mentioned below:
Define Flowchart.A flowchart is a type of diagram that represents an algorithm, process, or workflow. It is a visual representation of the steps and decisions involved in a problem-solving or decision-making process. Flowcharts use a variety of symbols and shapes to represent different types of steps and decisions, such as inputs, outputs, process steps, and decision points. They are used to communicate the logic of a program or process to different stakeholders, such as developers, managers, and users.
Define Algorithm.An algorithm is a set of instructions or a step-by-step procedure for solving a problem or completing a task. It is a well-defined sequence of operations or actions that are taken in order to achieve a specific goal or outcome. Algorithms can be expressed using natural language, pseudocode, or programming languages. The steps in an algorithm must be unambiguous and have a clear stopping point.
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Match the following factored-form quadratics with their equivalent standard form
The factored quadratic functions with their equivalent standard form are given as follows:
1. e -> x² - 3x - 10 = (x - 5)(x + 2)
2. a -> x² + 7x - 10 = (x + 5)(x + 2).
3. c -> x² - 7x + 10 = (x - 5)(x - 2).
4. d -> x² - 2x - 63 = (x - 9)(x + 7)
5. f -> x² + 2x - 63 = (x + 9)(x - 7).
6. b -> x² + 16x + 63 = (x + 7)(x + 9).
How to factor a quadratic function?A quadratic function is defined as follows:
y = ax² + bx + c.
A quadratic function can be factored as a function of it's roots x* and x**, as follows:
y = a(x - x*)(x - x**).
For item a, the function is given as follows:
y = x² + 7x + 10.
The coefficients are given as follows:
a = 1, b = 7, c = +10.
The discriminant is of:
D = 7² - 4(1)(10)
D = 49 - 40
D = 9.
Hence the first root is of:
x = (-7 - square root of 9)/2
x = -5.
The second root is of:
x = (-7 + square root of 9)/2
x = -2.
Meaning that the factored expression is given as follows:
y = (x + 5)(x - 2).
Matched with the second expression of column A.
The same procedure is followed for the remaining quadratic functions.
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In a math question, Magda correctly answered a question that asked for a typical measure of orange juice in a full family-size jug. Which was her answer
Magda said the typical measure of orange juice in a full family-size jug is 1 gal in value.
What is meant by mathematical expression?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.
The collection of mathematical symbols that emerges from the right arrangement of numbers is known as a mathematical expression and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
The three different types of algebraic expressions are monomial, binomial, and polynomial.
The complete question is : In a math question, Magda correctly answered a question that asked for a typical measure of orange juice in a full family-size jug. Which was her answer?
a. 2 cups
b. 1 gal
c. 10 gal
d. 10 fl oz
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What is the answer of 7 to the power of 2?
The answer to 7 to the power of 2 is 49.
This is because when a number is raised to a power, it means that it is multiplied by itself that number of times. 7 to the power of 2 is 7 multiplied by itself 2 times, which is 7 x 7, which equals 49.
An expression known as "power" denotes the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.
As an illustration, the power 63 demonstrates how three times the number 6 is multiplied.
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A rescue boat just picked up some sailors in a lifeboat. Now the rescue boat is heading north at 14 miles per hour. The lifeboat, which they abandoned, is drifting south at a speed of 3 miles per hour. How long will it be before the rescued sailors are 57 miles from their lifeboat?
The time it will take for the rescued sailors to be 57 miles from their life boat is given as follows:
3.35 hours.
What is relative velocity?Relative velocity is obtained considering the direction in which the objects are traveling, as follows:
Opposite direction: the relative velocity is given by the sum of the velocities of each object.Same direction: the relative velocity is given by the subtraction of the velocities of each object.For this problem, the sailors and the lifeboat are traveling in opposite directions, hence the relative velocity, considering each of their velocities is given as follows:
v = 14 + 3 = 17 miles.
(meaning that they get 17 miles farther each hour).
Velocity is distance divided by time, hence the time it will take for them to be 57 miles apart is given as follows:
17 = 57/t
17t = 57
t = 57/17
t = 3.35 hours.
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Use the graph of the function to find the domain and range of f (Enter your answers using interval notation)
In the given graph the domain and range of function y=f(x) is
Domain: (-2,2]
Range : [-4, 5)
What is domain and range?A function's domain is the set of all possible inputs to the function. This means it can be any number that can be entered into a function. For the majority of functions, this will be any number that can be substituted for the letter x. Except for a few exceptions such as square root functions and rational numbers, your domain will almost always be all real numbers.
The set of all possible outputs of a function is referred to as its range. This is usually represented by the letters y or f(x). The range is any number obtained by substituting any number for x.
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( r - 8 ) - ( r + 15 )
Find the Sum or Difference! :)
Answer:
-23
Step-by-step explanation:
Open up the parenthesis
R - 8 - R - 15
R - R - 8 - 15
-23
Answer:-23 ITS SUPER EASY:0
Step-by-step explanation:
Open up the parenthesis
R - 8 - R - 15
R - R - 8 - 15
-23
I GIVE THANKS AND MARK BRAINLIEST
What is the correct answer?
Please help.
Answer:if the siblings are less and the child are more u should remove the percent from the difference and put it to the another one the one from down there so the difference is 70% so try the same from down there is 18 so it got to be 20
Answer:20
F18) if y varies jointly as x and the inverse of z, and y = -5 and z = 6, find y when x = 5 and z = -8
Answer:
gfifhdrtjttt9668ztjt*
The scores on the last math quiz are summarized in the following frequency table:
Score
10 9
8
7
6
4 3 2 1 0
7
5
3 2
1
0
0
10
0
Frequency 6
The information is then put into the following histogram:
Frequency
5
4
3
210
1 2 3 4 5 6 7 8 9 10
5
1
Score
Therefore , the answer to the above problem is 5.75 for the mean and 9 for the median.
What is mean?Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the amount of values present in the dataset by its total number of values in the data. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the integers in a data set and dividing the total by the total number of numbers. For example, in the data below
Here,
Spread it all out here first:
4, 5, 6, 7, 7, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10
The mean is calculated by dividing total total by the total number of scores. Add up each number.
There are 16 numbers total, and they add up to 92. 92 / 16 = 5.75
To get the median, identify the middle number among all the other numbers.
Sadly, there is no "center number" given that there are 16.
Add the ninth and eighth numbers together, then divide by to find the middle.
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OPEN ENDED NOT MULTIPLE CHOICE
Some recent studies suggest that a teenager sends an average of 60 texts per day. For each of
the following scenarios, find the linear function that describes the relationship between the input
value and the output value. Then, determine whether the graph of the function is increasing,
decreasing, or constant.
a. The total number of texts a teen sends is considered a function of time in days. The input is
the number of days, and output is the total number of texts sent.
b. A teen has a limit of 500 texts per month in his or her data plan. The input is the number of
days, and output is the total number of texts remaining for the month.
c. A teen has an unlimited number of texts in his or her data plan for a cost of $50 per month.
The input is the number of days, and output is the total cost of texting each month
150 people went to see "Ode to Algebra" performed in the school auditorium. If the number of children that attended the performance was c, how many adults attended?
Answer:
150-c
Step-by-step explanation:
150= total
c= children
adults=x
x=150-c
Write the equation of the line, that passes through the points (- 6, 1) and (10, 0)
Equation:
Now, write an equation of a line that is parallel to the above line and passes through point (-7, 2) in all three forms below.
Point-Slope Form
Slope-Intercept Form
Standard Form
The equation of the line, that passes through the points (- 6, 1) and (10, 0) is y = - (1/16)x + (5/8) and the equation of a line that is parallel to the above line and passes through point (-7, 2) is y = - (1/16)x + (25/16).
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that the line passes through the points (- 6, 1) and (10, 0).
The slope of the line will be -
{m} = (0 - 1)/(10 + 6) = -1/16
{m} = -1/16
We can write the equation as -
y = - (1/16)x + c
For the point (10, 0), we can write -
0 = - (1/16) x 10 + c
0 = - (10/16) + c
c = 10/16
c = 5/8
So, we can write the equation as -
y = - (1/16)x + (5/8)
The equation of a line that is parallel to the above line and passes through point (-7, 2) is as follows -
y = - (1/16)x + c
2 = - (1/16) x - 7 + c
c = 2 - 7/16
c = 25/16
y = - (1/16)x + (25/16)
Therefore, the equation of the line, that passes through the points (- 6, 1) and (10, 0) is y = - (1/16)x + (5/8) and the equation of a line that is parallel to the above line and passes through point (-7, 2) is y = - (1/16)x + (25/16).
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I need help with this, please
expand this expression using the distributive property. 4(-2g+4-3t)
Answer:
-8g+16-12t is the answer
Step-by-step explanation:
multiply everything by 4
Write an equation of the line that passes through the given point and is perpendicular to the given line.
(2, 5); x = -6
well, since the given line is a horizontal line, a perpendicular line to that will just be, yeap, you guessed it, a vertical line, Check the picture below.
Dominique decorates a round cake with fruits. The cake has a diameter of 16 inches. She frosts just the top if the cale. How many square inches of the cake are covered with icing?Use 3. 14 for π
The amount of square inches of the cake that are covered with icing is 201.06, calculated by using the formula (π * radius2), with π equal to 3.14 and the radius equal to 8 inches.
1. Use the formula (π * radius2), with π equal to 3.14
2. The radius is half of the diameter, divide the diameter (16 inches) by 2
3. Radius = 16 inches / 2 = 8 inches
4. Calculate π * radius2: 3.14 * (8 inches)2 = 201.06 square inches
π * (8 inches)2
= 3.14 * (64 inches2)
= 201.06 square inches
Dominique is decorating a round cake with fruits and has frosted just the top of the cake. To determine the area of the cake that is covered with icing, we can use the formula (π * radius2). Since the cake is round, we can determine the radius of the cake by dividing the diameter of the cake (16 inches) by 2, resulting in the radius being 8 inches. We can then calculate the area of the cake covered with icing by multiplying π by the radius squared. Using the number 3.14 for π, the calculation is 3.14 * (8 inches)2, which equals 201.06 square inches. Therefore, 201.06 square inches of the cake are covered with icing.
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Find the product of the factors 8.075*0.08
Annie bought a brand new car for $32,000. The car is now worth $21,000.
(This is percent over change!!)
Using percentages we know that the value of a car decreases by 34% on average.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
So, we know that:
Annie brought a car at: $32000
Current price of the car: $21000
The decline in car percentage:
21000/32000 * 100
65.625%
⇒ 100 - 65.625 = 34.375%
Rounding off: 34%
Therefore, using percentages we know that the value of a car decreases by 34% on average.
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Complete question:
Annie bought a brand-new car for $32,000. The car is now worth $21,000.
By what percentage does the car's worth decrease?
3x + 2y = 5
x = 2y + 7
Answer:
I hope this helps you...
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What is a power of 3 equation called?
A power of 3 equation is called as cubic equation.
The term equation in math is known as a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Here we need to find the term that has been used for power of 3 equation.
Here we have to know that the power of 3 equation is known as cubic equation.
in other terms the polynomial equation which has a degree of three is called a cubic polynomial equation or trinomial polynomial equation.
As we all know that the power of the variable is the maximum up to 3, therefore, we get three values for a variable, say x.
The general form of the power of 3 equation is written as
=> ax³ + bx² + cx + d = 0
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