x = ㏑₂8 in the logarithmic function.
What is a logarithmic function?A logarithmic function is the inverse of an exponential function.
Given function if f(x) = [tex]2^{x}[/tex],
When strength is equal to 8 pascals, f(x) = 8
Therefore, 8 = [tex]2^{x}[/tex]
Taking log on both sides:
ln8 = ln[tex]2^{x}[/tex]
ln8 = xln2
or x = ln8/ln2
x = ㏑₂8
Hence, the required function is x = ㏑₂8.
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Find the 3 smallest positive x-intercepts of the graph of
y = cos(12x) + cos(16x) and list them in increasing order.
Submit your answer as a list of x-coordinates from least to greatest.
To find the 3 smallest positive x-intercepts of the graph of y = cos(12x) + cos(16x), you can use the following steps:
Set y equal to 0 and solve for x to find the x-intercepts of the graph.
Since the graph of y = cos(12x) + cos(16x) is periodic with period 2π/12 = π/6 and 2π/16 = π/8, respectively, you only need to consider x-intercepts in the interval [0,π/6).
Use the identity cos(a+b) = cos(a)cos(b) - sin(a)sin(b) to rewrite the equation y = cos(12x) + cos(16x) as:
y = 2cos(4x)cos(8x) - sin(4x)sin(8x)
Set y equal to 0 and solve for x to find the x-intercepts. This will give you the x-coordinates of all the x-intercepts of the graph.
Sort the x-coordinates in increasing order and take the first three smallest positive values to find the 3 smallest positive x-intercepts.
For example, if you set y equal to 0 and solve for x, you get:
0 = 2cos(4x)cos(8x) - sin(4x)sin(8x)
This equation can be rewritten as:
cos(4x)cos(8x) = sin(4x)sin(8x)
Using the identity cos(a) = sin(π/2 - a) and substituting this into the equation above, we get:
sin(4x)sin(8x) = sin(4x + π/2)sin(8x)
This equation simplifies to:
sin(4x)sin(8x) = sin(4x)cos(8x)
Dividing both sides by sin(4x) and rearranging, we get:
sin(8x) = cos(8x)
This equation holds for all values of x that satisfy sin(8x) = cos(8x), so we can find the x-intercepts by setting these two functions equal to each other and solving for x:
sin(8x) = cos(8x)
sin^2(8x) = cos^2(8x)
sin^2(8x) - cos^2(8x) = 0
1 - cos(16x) = 0
cos(16x) = 1
Thus, the x-intercepts of the graph are at x = 0, x = π/16, x = π/8, x = 3π/16, and so on. Since we are only interested in the 3 smallest positive x-intercepts, we can take the first three values in this list: x = 0, x = π/16, and x = π/8.
Therefore, the 3 smallest positive x-intercepts of the graph of y = cos(12x) + cos(16x) are [0, π/16, π/8].
A laptop computer i purchaed for. Each year, it value i $1500 of it value 75% the year before. After how many year will the laptop computer be worth $200 or le
After 7 years the laptop computer will be worth $200 or less.
In this question, we have been given a laptop computer is purchased for $1500 . Each year, its value is 75% of its value the year before.
We need to find the number of years when laptop computer be worth $200 or less.
We can see that given situation represents exponential decay function with initial value 1500, decay rate = 0.75 and the final value = 200
We need to find period t.
For given situation we get an exponential function as,
1500 * (0.75)^t ≤ 200
(0.75)^t ≤ 2/15
t * ln(0.75) ≤ ln(2/15)
t * (-0.2877) ≤ -2.0149
t ≥ (-2.0149)/(-0.2877)
t ≥ 7
Therefore, the laptop computer will be worth $200 or less after 7 years.
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calculate the diameter of a circle with an area of 56
Answer:8.44
Step-by-step explanation:
Area of the circle is 56.
Divide 56 by 3.14(Pi)
56/3.14=17.8343949
Square root it
Square root of 17.8343949=4.223078841
4.22 is the radius so to find the diameter you just multiple by 2.
4.223078841x2=8.446157683
A. How many cube with an edge length of b. What i the volume, in cubic inche, of inch are needed to build a cube with one cube with an edge length of inch? an edge length of 1 inch?
In order to build a cube with an edge length of b inches, b3 cubes with 1-inch edges are required.
What are cubes?A cube is a three-dimensional object with six square faces that are all the same size and form in mathematics. A cube has perpendicular sides and is symmetrical along all three axes. Finding the area of one of a cube's faces and increasing it to the third power yields the volume of the object. V=s3, where s denotes one of the cube's sides, is the formula for calculating a cube's volume. Cubes are frequently used in geometry and algebra, and they have a wide range of real-world uses, including volume measurement and the solution of mathematical equations.
How to solve?
The volume of a cube with an edge length of b inches is b3 cubic inches. For instance, if b=3, we would require 33=27 cubes with 1 inch-long edges, and the volume of a cube with a three inches edge would be 33=27 cubic inches.
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Find each percentage of 75. Explain your reasoning.
1. What is 10% of 75?
2. What is 1% of 75?
3. What is 0.1% of 75?
4. What is 0.5% of 75?
Answer:
1. 7.5
2. 0.75
3. 0.075
4. 0.375
Step-by-step explanation:
Yw, and have a good day to everyone who reads this <3 :)
in older adults, a higher level of social support is related to question 20 options: lower levels of physical activity. a higher probability of being institutionalized. an early cognitive decline. a lower probability of depression.
In older adults, a higher level of social support is related to question is D. a lower probability of depression.
What is depression?Depression is a prevalent mental illness. According to estimates, the disorder affects 5% of adults worldwide. Consistent sadness and a lack of interest in previously fulfilling or enjoyable activities are its defining traits. Additionally, it may impair appetite and sleep. Concentration problems and fatigue are frequent.
A severe mental illness called major depressive disorder has an impact on how people feel, think, and carry out their daily activities. The condition may also affect a person's ability to enjoy life, appetite, and sleep patterns. When there's social support, people are happier and this reduce depression.
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Workers install 480 chairs at a constant rate. After 3 days, the workers still have to install 120 chairs. How much time does it take to install the chairs from start to finish?
The 480 chairs were all finished by the employees in 4 days while maintaining a steady pace.
What is time and work?Time and work deals with the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the work done by each of them.
Work Done = Time Taken × Rate of Work.
Rate of Work = 1 / Time Taken.
Time Taken = 1 / Rate of Work.
If a piece of work is done in x number of days, then the work done in one day = 1/x.
Total Work Done = Number of Days × Efficiency.
Here,
Total number of chairs=480
Chairs left to work on=120
It took them 3 days to install 360 chairs which means if they were working at a constant rate they got 120 chairs installed daily.
With 120 chairs left that means in 1 days they will finish.
So overall, it took the workers 4 days to finish.
The workers took 4 days to complete all the 480 chairs from start to finish at a constant rate.
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Cameron has papayas and bananas in a ratio of 6:19. How many bananas does he have if he has 36 papayas?
Answer: 113 bananas
Step-by-step explanation:
The ratio is 6:19, with 6 papayas for every 19 bananas.
We have 36 papayas, which is 6 times, so we just need to get 19 times 6 = 113 bananas
what is the distance between -5, -3 and -5, -6
To calculate the distance between the points -5, -3 and -5, -6. We apply the following formula:
(x₁, y₁) and (x₂, y₂) d = √(x₂ - x₁)² + (y₂ - y₁)²
The points are:
(x₁ = -5, y₁ = -3) and (x₂= -5, y₂= -6)
We apply the above formula and solve.
d = √(x₂ - x₁)² + (y₂ - y₁)²d = √ (-5 - (-5))² + (-6 - (-3))²d = √ 02 + (-3)² = √ 0 + 9d = √9 = 3The distance between the points -5, -3 and -5, -6 is 3.
Calculate the distance between the points N=(-5, 7) and P=(-1, 3) in the coordinate plane.
Round your answer to the nearest hundredth.
: 0
Distance:
Answer:
distance ≈ 5.66 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = N (- 5, 7 ) and (x₂, y₂ ) = P (- 1, 3 )
d = [tex]\sqrt{(-1-(-5))^2+(3-7)^2}[/tex]
= [tex]\sqrt{(-1+5)^2+(-4)^2}[/tex]
= [tex]\sqrt{4^2+16}[/tex]
= [tex]\sqrt{16+16}[/tex]
= [tex]\sqrt{32}[/tex]
≈ 5.66 units ( to the nearest hundredth )
What types of values of the test statistic for the kruskal wallace test support the alternative hypothesis?.
Answer:
that at least one of the distributions function is not equal.statistical measures that communicate the most information should be used with scales that contain the most information. true false
True , statistical measures that communicate the most information should be used with scales that contain the most information.
Given :
statistical measures that communicate the most information should be used with scales that contain the most information. true or false .
we know that ,
What is statistical measures ?
The mean, median, mode, percentiles, range, variance, and standard deviation are the most commonly used numerical measures for quantitative data.
So the statistical measures that must communicate the most information should be used with scales that contain the most information for knowing the details of the given data .
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for both anorexia and bulimia, the rate of occurrence in females compared to in males is about: group of answer choices equal 10 to 1 5 to 1 2 to 1
Both Anorexia and Bulimia the rate of occurrence is high in females as compare to males so the choice is female to male ratio is 12 to 1.
Eating disorder of Anorexia nervosa and Bulimia nervosa is more common in women as compare to men due to dieting habits.Patient suffering from Bulimia nervosa eat in such a way that it implies to lose weight and prevent him ' her from weight gain.Anorexia nervosa patients used to follow restrictive diets and apply lots of restrictions in consumption of their food. Males are more into muscles making so they consume food in good quantity very less percent of males are into diet restriction .Rate of occurrence in both the case anorexia and bulimia in females sufferer is more compare to males.Correct option is ratio female to male is 12 to 1.Therefore, the rate of occurrence in females is much more than the males. Correct option is 12 to 1.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The three (3) statements which are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² ....equation 1.
Where:
h and k represents the coordinates at the center of a circle.
r represents the radius of a circle.
From the information provided, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
Comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius, r = 3
Additionally, this line and the circle's center lies on the x-axis because the y-value is equal to zero (0).
(x – 0)² + (y - 0)² = 3²
x² + y² = 9.
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plssss help me out thank you if you do
Answer: y = -2x + 5
Step-by-step explanation: I think it's the same one...
It takes one machine 25 minutes to pick a bale of cotton, and another machine takes 30 minutes to compete the same job. If both machines are used, how long will it take them to pick a bale of cotton?
Answer:
Hi i'm wondering how to find the answer the answer is 3 over 2 (2k-8) > 1 over 3(k-9)
A line passes through (−1, 5) and (1, 3).
Which answer is the equation of the line? PLEASE HELP
The parabola y=x^2 i reflected acro the x-axi and then caled vertically by a factor of 1/8. What i the equation of the new parabola?
The equation of the parabola will be y = -1/8[tex]x^{2}[/tex].
What is parabola?A right circular cone and a plane perpendicular to one of the cone's elements cross to form a parabola, also known as an open curve.
Y = a(x - h)2 + k or x = a(y - k)2 + h is the general equation of a parabola. The vertex is shown here as (h, k).
The parabola's y= value is provided to us.
When we mirror this parabola along the x-axis, we scale the resulting image vertically by a factor of 1/8.
Then we get y = -1/8[tex]x^{2}[/tex]
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help pretty please :)
Answer: B
Step-by-step explanation:
Sam had 1 whole 1/2 m 5/8 m used it for a project. how much rope does San have left.
Sam has 7/8 m of rope left.
What is fraction ?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
To derive a solution, you have to subtract the meter of rope that Sam has from the meter of rope he cut for a project.
Therefore,
1½ - 5/8,
Since the meter of rope Sam had is represent with a mixed fraction, we have to convert it to an improper fraction, and therefore 1½ can also be written as 3/2
Therefore, we have
3/2 – 5/8
To solve this fraction, you need to find the smallest number that can divide the denominator (2 and 8), which is 8.
Now divide the denominators with 8 and multiply the answers you get by the numerators.
Therefore, we have
3/2 -5/8
= 12/8 – 5/8
= 7/8 m.
Therefore, Sam has 7/8 m of rope left.
The smallest number used to divide the denominators is also known as the lowest common denominator (LCD).
A fraction has 2 parts, which are numerator and denominator. The numerator is the number at the top in a fraction while the denominator is the number below in a fraction.
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Which statements are not true and true?
statement 1: the sum of two negative integers is positive
Statement 2: the product of two negative integers is positive
Statement 3: the difference of two negative integers is positive
Statement 4: the quotient of two negative integers is positive
For both statements that are not true at all, provide one counter example for each statement that proves the statement can be false.
Answer: Statements 1, 3, and 4 are not true. The sum, difference, and quotient of two negative integers can be positive, negative, or zero, depending on the values of the two integers. For example, the sum of -5 and -7 is -12, which is a negative number. The difference of -5 and -7 is 2, which is a positive number. The quotient of -5 and -7 is -0.7142857142857143, which is a negative number.
Only statement 2 is true. The product of two negative integers is always a positive number. For example, the product of -5 and -7 is 35, which is a positive number. This is because the two negative signs "cancel out" when multiplying two numbers, resulting in a positive product.
Translate this phrase into an algebraic expression.
60 decreased by twice Jenny's score
Use the variable to represent Jenny's score. please help.
The expression for 60 decreased by twice Jenny's score 60 - 2x.
What is an algebraic expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Let Jenny's score be x.
Twice Jenny's score will be 2x.
Therefore, the expression will be:
= 60 - 2x
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A company has 30 employees 20 female 10 male, the board of directors decides to ask a group of 10 people, half of which are male, about expanding the company. Determine how many possible groups are there?
Answer:
M=960
F=480
Step-by-step explanation:
look at the work I did
Sarah pent 30 minute practicing her pelling word. She pent 3 time a much time reading. How many minute did Sarah pend reading?
Sarah completed reading for x = 18 minutes.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question
The number of pages Sarah will read in an hour is x. (this is "pages per hour" rate).
(10 minutes) / (3 pages) = (x pages) / (60 minutes)
cross-multiply:
10x = 3*60
x = 18
Hence, Sarah completed reading for x = 18 minutes.
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The sum of two consecutive odd integers is at least 16. Which of the following inequalities would model this statement
The sum of two successive odd integers must be at least 16, hence the inequality will be x+1≥4 and the solution will be x≥3.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here,
Sum of 2 consecutive odd integer=16
Let them be 2x+1 and 2x+3,
2x+1+2x+3≥16
4x+4≥16
x+1≥4
x≥3
The inequality will be x+1≥4 and solution to the inequality will be x≥3 as sum of two consecutive odd integers is at least 16.
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x+10=y, then 45 is equal to
im kinda confused of a question right now, i have to find the median and there are 2 numbers in the middle, and i think you add the 2 numbers in the middle and turn it into a fraction right? but do you always put the denominator as 2?
Answer:
Yes, you take the average value of the two numbers in the middle.
Step-by-step explanation:
Since there are TWO middle values, you always put 2 as a denominator.
the triangles are simialr solve for the question mark
you need to show the problem
Tom has a total of $220 and he spent $35 on a baseball ticket. What percent of his money did he have left
Answer:
He has $185 left
Step-by-step explanation:
Subtract $220 from how much he spent
2. (6) The probability distribution below is for the random variable X = number of mice
caught in traps during a single night in small apartment building.
a. Find P(X = 2)
0
X
P(X) 0.12
1
0.20
2
h
3
4
0.14 0.16
b. Describe P(X ≥ 2)in words and find its value.
5
0.07
c. Find μx and ox. Show work. You may use your calculator to check solutions.
The probabilities are P(X = 2) = 0.14 and P(X ≥ 2) = 0.30
The mean and the standard deviation are 0.96 and 0.90
How to determine the probabilitiesP(x = 2)
From the question, we have the following parameters that can be used in our computation:
X 0 1 2 3
P(X) 0.12 0.20 0.14 0.16
From the above table, we have
P(X = 2) = 0.14
P(x ≥ 2)
From the question, we have the following parameters that can be used in our computation:
X 0 1 2 3
P(X) 0.12 0.20 0.14 0.16
From the above table, we have
P(X ≥ 2) = P(2) + P(3)
Substitute the known values in the above equation, so, we have the following representation
P(X ≥ 2) = 0.14 + 0.16
Evaluate the sum
P(X ≥ 2) = 0.30
The mean and the standard deviationThe mean is calculated as
μx = sum of the products of x and P(x)
So, we have
μx = 0 * 0.12 + 1 *0.20 + 2 * 0.14 + 3 * 0.16
Evaluate
μx = 0.96
The standard deviation is calculated as
ox = the square root of sum of the products of x and P(x) * (1 - P(x)
So, we have
ox = √[(0 * 0.12 * 0.88) + (1 * 0.20 * 0.80) + (2 * 0.14 * 0.86) + (3 * 0.16 * 0.84)]
Evaluate
ox = 0.90
Hence, the standard deviation is 0.90
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