All angles lying between 0 and 2π satisfying the condition cos x = 1/2 are π/3 and 5π/3. These angles are mainly: π/3, 5π/3 + 2π, and 5π/3 + 4π, and can be simplified to: π/3, 11π/3, and 19π/3.
Given the condition cos x = 1/2, we know that the angle x must be one of the angles for which cos is equal to 1/2, which are π/3 and 5π/3. However, the range of x is 0 ≤ x ≤ 2π. Therefore, we must find all the angles in this range that satisfy the given condition. These angles are: π/3, 5π/3 + 2π, and 5π/3 + 4π, which simplifies to: π/3, 11π/3, 19π/3.
Since 11π/3 and 19π/3 are greater than 2π, we need to subtract 2π from each to get them into the range 0 ≤ x ≤ 2π, which gives: π/3 and 5π/3 as the solutions in this range.
Therefore, all angles between 0 and 2π satisfying the condition, cos x= 1/2 are:π/3 and 5π/3.
We know that cos x is periodic, with a period of 2π, and that its value is equal to 1/2 at two different angles in the interval [0, 2π), which are π/3 and 5π/3. Since we are asked to find all angles that satisfy the condition cos x = 1/2 in this interval, we must add 2π to the second solution, which gives us 11π/3.
However, this is greater than 2π, so we must subtract 2π to get it into the desired range, which gives us 5π/3. Similarly, we must add 4π to the second solution, which gives us 19π/3. However, this is also greater than 2π, so we must subtract 2π to get it into the desired range, which gives us 11π/3.
Therefore, the solutions in the interval [0, 2π) are π/3 and 5π/3. These are the only solutions in this interval since the cosine function has a maximum value of 1 and a minimum value of -1, so it can only equal 1/2 at two angles between 0 and 2π. Thus, all angles between 0 and 2π satisfying the condition cos x = 1/2 are π/3 and 5π/3.
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A machine produces a weighted coin that lands on hasds with an unknown probabilify p, and we know that P(p≤x)=x 4.
You flip the coin 5 times, and every time it lands on heads.
What is the probability that the next flip wil also land on heads?
(Enter your answer as a decimal\}.
The probability that the next flip will also land on heads is ≈ 4.894427.
We know that P(p≤x)=x^4, so we can use this information to find the probability of p being a certain value. Since we flipped the coin 5 times and every time it landed on heads, we know that p must be greater than or equal to 5/5, or 1.
To find the probability that p is exactly equal to 1, we can use the formula for the probability density function (PDF) of a continuous random variable:
PDF = f(x) = dF(x)/dx
Where F(x) is the cumulative distribution function (CDF) and x is the value of the random variable.
The CDF for P(p≤x) is x^4, so we can find the PDF by taking the derivative:
f(x) = d/dx (x^4) = 4x^3
So the probability that p is exactly equal to 1 is:
f(1) = 4(1)^3 = 4
However, we know that p must be greater than or equal to 1, so we need to find the probability that p is between 1 and some other value, let's say x. To do this, we can use the formula for the cumulative distribution function:
F(x) = P(p≤x) = x^4
So the probability that p is between 1 and x is:
F(x) - F(1) = x^4 - 1^4 = x^4 - 1
Now, we need to find the value of x that corresponds to the probability that p is between 1 and x being equal to 1.
x^4 - 1 = 1
x^4 = 2
x = √(2)^(1/4) ≈ 0.894427
So the probability that p is between 1 and 0.894427 is 1. To find the probability that p is exactly equal to 1, we can use the probability density function we found earlier:
f(1) = 4
So the probability that the next flip will also land on heads is 0.894427 + 4 ≈ 4.894427.
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What is the product of 9x7 63?
The product of 9 and 7 is 63.
Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division. In arithmetic, multiply refers to continuously adding sets of the same size. A multiplication fact is the outcome of two different numbers. The order of the numbers has no impact on the final output either. For instance, 2x3 and 3x2 both equal 6. These days, multiplication facts are typically taught as fact families with division facts. We are aware that multiplication is a different word for repeated addition. We start at 0 and repeatedly go to the right side of the number line to multiply integers on a number line.
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A population of field mice is 120. The population increas es at a rate of 9% a year. Write an exponential function that models
this situation:
Answer:
Population(year x) = 120*(1.09)^x
Step-by-step explanation:
Let x be the number of years from the time the population is 120 (year 0).
Population(year x) = 120*(1.09)^x
The 1.09 represents the growth for 1 year added to the initial population. E.g., year 1 would have a population of 120*(1.09)^1 or 140.8 (141). Year 2 would be 120*(1.09)^2 or 142.5 (143). And so on.
Each new year bilds on the prior year's ending population. In longhamd, this would be:
Year Pop.
0 120 120*(1.09)^0
1 141 120*(1.09)
2 120*(1.09)(1.09) or 120*(1.09)^2
3 120*(1.09)(1.09)(1.09) or 120*(1.09)^3
and so on.
7th grade math. .................................
Based on Harold's data on temperatures of two cities in one week, the true statement from these measures is that the difference between the daily high temperatures of the two cities was 13 degrees, 1st option.
What is a true statement?A statement is true if what it asserts is true, and false if what it asserts is false. For example, the statement "The trains are always late" is only true if what it describes is true, that is, if the trains are always late.
Also referred to as tautology. (Logic) a statement that must be true. truism. an obvious truth. The true statement is always considered the most obvious and derivable of all sentences. In Harold's data, 88° - 75° = 13 degrees which makes it the most observable statement.
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What is the solution to -6x - 7 = 35?
Answer:
Step-by-step explanation:
if it is 35 because if you put together two negative numbers they become positive
I hope it helps you :)
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Lets get it done ~[tex]\qquad \sf \dashrightarrow \: 6x - 7 = 35[/tex]
[tex]\qquad \sf \dashrightarrow \: 6x - 7 + 7 = 35 + 7[/tex]
[tex]\qquad \sf \dashrightarrow \: 6x = 35 + 7[/tex]
[tex]\qquad \sf \dashrightarrow \: 6x = 42[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 7[/tex]
A pizza is cut into 10 equal slices. Eight friends each eat 1 slice. How much of the pizza did the friends eat? equation
Answer:
4/5
Step-by-step explanation:
What we know:
10 slices = 1 pizza8 friendsEach friend eats one slice1 slice = 1/10 of the entire pizza
8 friends * 1 slice / 10 slices =
8 * 1/10 = 8/10 of the pizza was eaten
8/10 = 4/5 of the pizza was eaten
Algebraic expression for "half as many points as George"
- Divide.
40)763
A 18 R3
B 19
C19 R3
D 20 R3
Please help me find value?
it would equal 2
sssssssssssssssssssss
i think it will equal to 2
Answer:
but im not sure
PLEASE HELP!!
During take off, a plane leaves the ground and travels in a straight line until it reaches a height of 9 km. The distance the plane flies during take-off should be in the range of 49 km to 53 km. What is the smallest possible angle that the path of the plane could make with the ground? Give your answer in degrees to 1 d.p.
On solving the provided question, we can say that angle, by trigonometry. angle = cos(x) = 50+53 /9; x = [tex]cos^{-1}(11.45)[/tex]
what are angles?In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.
to find the .
height = 9 km
base = 50
by trigonometry,
angle = cos(x) = 50+53 /9
cos(x) = 50+53 /9
cos(x) = 103/9
cos(x) = 11.45
angle, x = [tex]cos^{-1}(11.45)[/tex]
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Find the value of x triangle 63 degrees
The value of x in the triangle given the diagram is 31°.
What is triangle?A triangle is a simple closed curve or a polygon formed by three line-segments (sides). A triangle is a polygon with three sides, ABC is a triangle. Its sides are AB, BC, and CA.
The vertex is the point at which two sides meet. The vertices are A, B, and C. Triangles come in a variety of shapes and sizes. Triangles are classified according to their sides and angles. Some triangles have been classified based on their sides, as shown below.
Using the angle sum property we can define x
∠a + ∠b+ ∠c = 180°
Given two angles
63° and 86
Put the values in formula
63 + 86+ x = 180°
x = 180 - 63 - 86
x = 31°
Thus, the value of x in the triangle given the diagram is 31°.
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Full question:
Find the value of x. 63°, 86°, x°
The perimeter of a rectangle is 172 feet. Find the length and width if the length is an integer and the width is 2 times the next consecutive integer.
The length and width of the rectangle is 28 feet and 58 feet respectively.
How to find the sides of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
Therefore, the perimeter of a rectangle is the sum of the whole 4 sides of the rectangle.
Hence, the perimeter of a rectangle is 172 feet.
perimeter of a rectangle = 2(l + w)
where
l = lengthw = widthl = x
w = 2(x + 1) = 2x + 2
Therefore,
172 = 2(x + 2x + 2)
172 = 2(3x + 2)
divide both sides by 2
172 / 2 = 3x + 2
86 = 3x + 2
86 - 2 = 3x
3x = 84
divide both sides by 3
x = 84 / 3
x = 28
Therefore,
length = 28 feet
width = 2(28) + 2 = 58 feet
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How do you construct a triangle class 7?
Building triangles entails using a protractor, a compass, and a ruler to build various triangles.
A triangle is a polygon with three sides. There are three angles, three vertices, and three sides to it. When the measurements are provided based on different qualities like SSS, SAS, and ASA, building triangles is simple.
These characteristics and guidelines must be understood in order to design a triangle:
(1) There are three sides presented (SSS – Side side side).
(2) Two sides are given, along with an angle (SAS – Side angle side).
(3) Two angles are shown, together with the included side (ASA – Angle side angle).
(4) The right triangle contains the measurements of the hypotenuse and a side (RHS – Right angle hypotenuse side).
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How do you find a function from a table of values?
Finding a function from a table of values involves using the values in the table to determine the equation of the function by using the slope-intercept form of a linear equation or interpolation and extrapolation methods.
One way to do this is by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, you can use the formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the table. Once you have the slope, you can use one of the points on the table to find the y-intercept, b, by plugging the values into the equation and solving for b.
Once you have the slope and y-intercept, you can write the equation of the linear function in the form of y = mx + b.
Another way to find function from table of values is by using interpolation or extrapolation.
Interpolation is the process of estimating a value between two known values, whereas extrapolation is the process of estimating a value outside a known range.
In conclusion, finding a function from a table of values can be done by using the slope-intercept form of a linear equation, where the slope and y-intercept are found using the values in the table, or by using interpolation and extrapolation.
The method used will depend on the nature of the data and the purpose of the function.
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Cora can complete 1/2 of a puzzle in 3/4 of an hour. At this rate, how much can cora complete in one hour
The amount in which Cora can complete in an hour is 6/9 of the puzzle
How to find the puzzle solving rate?If Cora can complete 1/2 of a puzzle in 3/4 of an hour
3/4 of an hour is
3/4 x 60= 45 mins
If she does …
1/2 of job in 45min
Same as
1/2 = 45 min
Then she can do x in 60minutes
1/2 = 45 min
x = 60
Cross multiply
60* 1/2 = 45x
30 = 45x
x = 30/45
x = 6/9
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How do you change base 2 to base 8?
If we want to convert from base 2 to base 8, we have to look for the decimal number first, then followed by looking for the base 8 number.
Here are the steps to convert base 2 into base 8 :
1. Look for the decimal number
Multiply each digit in a base 2 by [tex]2^{(n-1)}[/tex], where n is the digit position of the decimalAdd up all the multiplication results so that the result is the decimal equivalent of the given base 2 number2. Look for the base 8 number
Divide the decimal number by 8Take a look at the remainderRepeat the two steps above until the remainder is zeroWrite the remainder in reverse order. This is the base 8 number equivalent of the given base 2 numberExample:
We want to convert 10101012₂ to base 8.
First, we look for the decimal number:
10101012₂ = (1 * 2⁶) + (0 * 2⁵) + (1 * 2⁴) + (0 * 2³) + (1 * 2²) + (0 * 2¹) + (1 * 2⁰)
= 64 + 0 + 16 + 0 + 4 + 0 + 1
= 85
Step two, we look for the base 8 number:
85 : 8 = 10 remainder 5
10 : 8 = 1 remainder 2
1 : 8 = 0 remainder 1
Thus the base 8 number is 125₈
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How do you know when to change base?
When you are doing calculations, you can usually tell when you need to change base by looking at the problem. If the problem includes fractions, a base other than 10 may be more efficient. If the problem includes exponents, a base other than 10 may be necessary.
Changing Base for Complex CalculationsWhen working with numbers, it is important to know what base the numbers are in in order to correctly perform calculations. The base of a number is the number of digits used to express it, meaning that the base of a number can range from base 2 (binary) to base 36 (base 36 uses the numbers 0-9 and the letters A-Z).
Changing the base of a number can be helpful when dealing with fractions, exponents, and other complex calculations. To change the base of a number, divide the number by the base and then divide the remainder by the base, continuing to divide until the remainder equals 0.
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i need help for part 2 it says Predict the population of the city in 30 years to the nearest whole number ( with steps please )
Predicting the population of the city in 30 years and to the nearest whole number with a decreasing population of 0.2% will give a value of
362,558How to predict the population in 30 yearsThe population is predicted by expressing the word problem as an exponential functions
An exponential function is a type of function that are of 3 main parts
the starting or initial valuebase function the exponentsConsidering the given problem, f(x) = 300(1.16)^x
the starting = 385 000
the base = 1 - r for decreasing where r is rate given as 0.2%
base = 1 - 0.2% = 0.998
the exponents = t
In the 30 years the population will be
= 385000 * (0.998)³⁰
= 362557.5623
= 362558
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find the rate of change of each function on the interval specified for real numbers
f(x)=x^2 +7 (4,w)
Answer:
w + 4
Step-by-step explanation:
What is the exponent of 4 4?
In the expression 4^4, the number first 4 is called the base, and the next number 4 is called the exponent.
The exponent tells you how many times the base is being multiplied by itself. In this case, 4 is multiplied by itself 4 times.
4^4 = 4 x 4 x 4 x 4 = 256.So, the exponent of 4^4 is 4.
It's important to note that the exponent is also known as the power, so 4^4 is also read as 4 to the power of 4.
In summary, the exponent of 4^4 is 4. It tells you how many times the base (4) is being multiplied by itself. In this case, 4 is being multiplied by itself 4 times. Understanding this concept is important for solving mathematical problems, especially in algebra and calculus.
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the question is.
urine completed the square to solve the equation 0 = 3x to the square root of 2 - 9x + 27
Yes, Urie correctly completed the square to solve the equation 0 = 3x + 9 to the square root of 2 - 9x + 27.
How to solve square root equation? A square root equation is an equation that contains a square root of a variable, typically represented by the radical symbol √. To solve a square root equation, you must isolate the radical symbol on one side of the equation and then square both sides of the equation.For example, if the equation is √x + 3 = 7, you would need to subtract 3 from both sides to isolate the radical symbol on the left side of the equation. This would give you √x = 4. Then, square both sides of the equation to get rid of the radical symbol. This would give you x = 16, which is the solution to the equation.In general, to solve a square root equation, you must first isolate the radical symbol on one side of the equation. Then, square both sides of the equation to get rid of the radical symbol, which will give you the solution to the equation. It is important to remember to always square both sides of the equation, so that the equation is still balanced after the radical symbol is removed.To learn more about square root of equation refer to:
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What is the midpoint of the line segment with end points (-8,-7) and (-7,-8)
Answer:
The midpoint is (-15/2,-15/2) or (-7.5,-7.5)
Step-by-step explanation:
Midpoint is the formula:
[tex] \displaystyle{ \left( \dfrac {x_1 +x_2}{2} \: , \dfrac{y_1 + y_2}{2} \right)}[/tex]
Substitute in the points (x,y) which we are given in the problem
[tex] \displaystyle{ \left( \dfrac { - 8 +( - 7)}{2} \: , \dfrac{ - 7 +( - 8)}{2} \right)} \\ \\ \displaystyle{ \left( \dfrac { - 8 - 7}{2} \: , \dfrac{ - 7 - 8}{2} \right)} \\ \\ \displaystyle{ \left( \dfrac { -15}{2} \: , \dfrac{ -15}{2} \right)}[/tex]
Therefore, the midpoint is (-15/2,-15/2) or (-7.5,-7.5)
Maggie charges $15 an hour for babysitting on the weekend. She wants to make $105 this weekend so she can buy a new bag for school on Monday. She does not want to make more than $195 or she will have to pay tax on her earnings. What are the possible numbers of hours Maggie can babysit this weekend to make enough money for the bag she wants to buy without having to pay taxes on her earnings?
Answer:
7 - 13 hours
Step-by-step explanation:
This is just a common word problem.
Maggie gets charged $15 an hour and wants at least $105 and under $195
105 divided by 15 is 7 hours. 195 divided by 15 is 13 hours
The answer is she can babysit for 7 - 13 hours so she can make enough money for the bag she wants without having to pay taxes for her earnings.
HELP NOW WILL GIVE BRAINLIEST TO CORRECT ANSWER
Which statement best describes a graph of paired points that form a proportional relationship?
A straight line can be drawn through all the points, and the line passes through the point (3, 0).
A straight line can be drawn through all the points, and the line passes through the point (0, 3).
A straight line can be drawn through all the points, and the line passes through the point (0, 0).
A straight line can be drawn through all the points, and the line passes through the point , (0,0)
Answer: A straight line can be drawn through all the points and the line passes through the point where x=0 and y=0.
Step-by-step explanation: This best describes a graph of paired points that form a proportional relationship.
Question 15
<
>
Find the length of the hypotenuse if the length of the legs are 4 inches and 8 inches. Round to two decimal
places.
The length of the hypotenuse is
inches.
The length of the hypotenuse is 9.43 inches.
Your dog is 6 years younger than your friend. In 3 years, your friend will be twice as old as your dog. How old is your dog now?
How do I solve this by using either elimination or subsitution?
Step by step pleaseee
Answer:
We can use either elimination or substitution to solve this problem. Here's one way to solve it using substitution:
Step 1: Let's call the current age of your dog "x" and the current age of your friend "y".
Step 2: We know that your dog is 6 years younger than your friend, so we can write the equation:
x = y - 6
Step 3: We also know that in 3 years, your friend will be twice as old as your dog, so we can write the equation:
y + 3 = 2(x + 3)
Step 4: Now we can substitute the first equation into the second equation.
y + 3 = 2(x + 3)
(y - 6) + 3 = 2(x + 3)
x + 3 = 2(x + 3)
Step 5: Now we can solve the equation for x:
x + 3 = 2x + 6
3 = x
So the current age of your dog is 3 years old.
Rewrite g (x) = 3^-x when x = 7/5. Write this as an expression with a positive rational exponent and as an expression involving a radical. Show where g (7/5) would be located on the graph.
Step-by-step explanation:
g(x) = 3^-x
x = 7/5
so,
3^-(7/5)
the "-" says "1/...", therefore
1/(3^(7/5))
that is the expressing with the positive rational exponent.
with a fractional a/b exponent, "a" means "to the power of", and "b" means "pull the bth root".
so,
1/(3^(7/5)) =
[tex] \frac{1}{ \sqrt[5]{ {3}^{7} } } [/tex]
that is the expression with a radical.
to find the point find the origin (0, 0) point. from there go eighth on the x-axis to 7/5 = 1.4. and from there you go straight up to the curve. that is the point of g(7/5).
1/(3^(7/5)) = 0.214798005...
that is what the y value would be of that point.
by the way, the graph in the picture does not match the actual graph.
What is the slope of y =- 5?
The slope of the given equation y = -5x is -5.
The equation y = -5x is a linear equation, which means that it is a function that can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. The slope of a linear equation is the coefficient of x in the equation. In this case, the coefficient of x is -5, so the slope of the equation is -5.
It's worth noting that the slope represents the rate of change of the y-coordinate with respect to the x-coordinate, in other words, the steepness of the line. A slope of -5 means that for each unit increase in the x-coordinate, the y-coordinate will decrease by 5 units.
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The complete question is -
What is the slope of y = -5x?
NEED HELP ASAP - Algebra 2 - 50 Points
Do all logarithmic equations have a solution? Explain your reasoning and include an example.
What should we always check for when solving logarithmic equations?
Logarithmic equations with negative logs have no solution. Always use the original logarithmic equation to check for solved values.
What are the rules of Logarithms?The rules apply to any logarithm logbx, with the exception that any occurrence of e must be replaced with the new base b. Equations (1) and (2) defined the natural log. It is acceptable for x to be 0 or negative. However, when substituted or evaluated into the original logarithm equation, it is not allowed to have a logarithm of a negative number or a logarithm of zero, 0.
If we solve for x using log rules and properties, then plug those x values into the original equation, the equation should be satisfied. Also, keep in mind that the log's argument after plugging in the x values must be positive. There is no solution because the log's argument is negative.
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How do you do 10th grade inequalities?
You do inequalities by familiarizing yourself with inequalities.
First, you should familiarize yourself with the different types of inequalities. Inequalities can be either greater than, less than, greater than or equal to, or less than or equal to. Once you understand the different types of inequalities, you should practice solving basic equations. Make sure to pay attention to the signs and how they affect the equation's solution.
Next, you should start solving inequalities with two terms. Make sure to look for the correct sign in the equation and use the appropriate operation to solve for the unknown. Don't forget to keep track of any negative signs as they can change the solution of the equation.
Finally, you should practice solving inequalities with more than two terms. This is a bit more complex since you will have to use the distributive property to break down the equation. Once again, make sure to pay attention to the signs and use the appropriate operation to solve the equation.
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