The equation of the rational function with the given features is given as follows:
F(x) = [4(x² + 5x + 4)]/(x² - x - 6).
How to define the rational function?A rational function is a fraction, in which both the numerator and the denominator contain instances of the variable x.
Considering the x-intercepts, the numerator of the function is defined as follows:
y = a(x + 4)(x + 1)
y = a(x² + 5x + 4).
Considering the y-intercept at (0,4), the leading coefficient a is given as follows:
a = 4.
The vertical asymptotes determine the zeros of the denominator, which is given as follows:
(x + 2)(x - 3) = x² - x - 6.
Hence the function is defined as follows:
F(x) = [4(x² + 5x + 4)]/(x² - x - 6).
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A grocer bought 100 pounds of mushrooms at 79¢ per pound. Experience
indicates that, as a result of aging, 40% of the mushrooms are sold at cost and
another 20% are discarded. Find the original marked price that will produce a
25% markup on cost.
The original markup price that will lead to a markup on cost of 25 % would be $ 1. 68 per pound
How to find the marked price ?To find the marked up price, first, find the amount that is a 25 % markup on cost to be :
= ( 100 pounds x 79 cents per pound ) x ( 1 + 25 %)
= 79 x 1. 25
= $ 98. 75
The 40 % sold would bring in:
= 40 % x 100 x 0. 79
= $ 31. 60
The amount left to be raised is:
= 98. 75 - 31. 60
= $ 67. 15
The markup price on the rest of the mushrooms is:
= 67.15 / ( 100 - 40 % - 20 %)
= $ 1. 68 per pound
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find the unknown terms in the sequence: 1 3/4, 1 9/16, 1 3/8, 1 3/16, A, B, C, 7/16, 1/4
The 5th , 6th and 7th term of the arithmetic sequence is 1 , 13/16 and 10/16 respectively
What is Arithmetic Progression?An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the first term of the AP be a₁ = 1 3/4
Let the second term of the AP be a₂ = 1 9/16
So , the common difference of AP d = a₂ - a₁
On simplifying the equation , we get
The common difference d = 1 9/16 - 1 3/4 = ( 25/16 - 7/4 )
The common difference d = - ( 3/16 )
And , the nth term of the AP is a + (n - 1) d
So , the 5th term of the AP = ( 1 3/4 ) + ( 4 ) ( -3/16 )
On simplifying the equation , we get
The 5th term of the AP = ( 7/4 ) + ( -3/4 )
The 5th term of the AP = 4/4 = 1
Therefore , the value of A = 1
And , the 6th term of the AP = ( 1 3/4 ) + ( 5 ) ( -3/16 )
On simplifying the equation , we get
The 6th term of the AP = ( 7/4 ) + ( -15/16 )
The 6th term of the AP = 13/16
Therefore , the value of B = 13/16
And , the 7th term of the AP = ( 1 3/4 ) + ( 6 ) ( -3/16 )
On simplifying the equation , we get
The 7th term of the AP = ( 7/4 ) + ( -18/16 )
The 7th term of the AP = 10/16
Therefore , the value of C = 10/16
Hence , the arithmetic progression is solved
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4. The U.S. Census Bureau calculated the homeownership rate in the United States for the second quarter of 2019
(April, May, and June) at 64.1 percent.
A. What does that mean? Please describe what a rate is and what that specific figure tells us.
B. How would they have calculated that rate? Please explain how rates are calculated and how this specific rate
would have been calculated.
A) The homeownership rate in the United States calculated by the U.S. Census Bureau for the second quarter of 2019 as 64.1 percent means that about 64% of the U.S. homes are owner-occupied instead of renting.
B) The homeownership rate is the quotient of the number of owner-occupied homes and the total number of U.S. homes.
What is the homeownership rate?The homeownership rate describes the percentage or proportion of U.S. homes occupied by owners instead of renters.
The rate refers to the ratio, which is the relative size of one quantity compared to another.
To compute the homeownership rate, the number of owner-occupied homes is divided by the total number of U.S. homes and multiplied by 100.
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As part of a school project students will be randomly sampling from the students in the class. The assignment is to estimate the proportion of students who play on a sports team. Each student will randomly select 7 students. One student found out that 2 of the 7 play a sport. The teacher has collected data from all students and found that out of the 31 students in the class 20 of them played sports.
On solving the provided question, we can say that percentage terms is 41.93%
What is percentage?A percentage in mathematics is a figure or ratiο that is stated as a fraction of 100. The abbreviatiοns "pct.," "pct," and "pc" are also occasionally used. It is frequently denοted using the percent symbol "%," though. The amount of percentages has nο dimensions. With a denominator of 100, percentages are basically fractiοns.
To show that a number is a percentage, place a percent symbol (%) next tο it. For instance, if yοu correctly answer 75 out of 100 questions on a test (75/100), yοu receive a 75%. To cοmpute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.
total no. of students = 31
no. of students play sports = 13
percentage terms = 13/31 × 100= 41.93%
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Select the correct answer.
of a group of 500 people, 60 are fit enough to climb Mount Shasta in California. The group has 300 women and 200 men. 12% of the men are fit
to climb the mountain. What is the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta?
OA
OC
OD.
Answer as a fraction
Answer:
As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.
Step-by-step explanation:
Let the number of fit men is x.
Now,
we know
x = 12% of 200 men
x = [tex]\frac{12}{100}[/tex] ×200
x = 0.12 × 200
= 24 men.
Given,
The 60 people are fit to climb the Mount Shasta ,24 of them are men,
so there must be
60 - 24 = 36 women who are fit to climb the mountain.
The probability of a person picked at random from the group is a male or is fit to climb Mount Shasta is the sum total of the probability of picking a fit male and the probability of picking a fit female is,
P(male or fit) = P(male and fit) + P(female and fit)
P(male or fit) = P(male) × P(fit | male) + P(female) × P(fit | female)
P(male or fit) = ([tex]\frac{200}{500}[/tex]) ×([tex]\frac{24}{200}[/tex]) + ([tex]\frac{300}{500}[/tex]) × ([tex]\frac{36}{300}[/tex])
=.4 × .12 + .6 × .12
= 0.048 + 0.072
=.12
So,
P(male or fit) ≈ 0.12
As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.
another way to find 4x2x5
Another way to find 4x2x5 is to multiply two of the digits and multiply the last digit with the product of two.
What is multiplication?Multiplication is when you take one number and add it together a number of times. Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20. We took the number 5 and added it together 4 times. This is why multiplication is sometimes called "times".
Given are three numbers multiplied, 4x2x5, we need to find the another way to solve it,
So,
4x2x5 = 40
So, in another method,
Multiply 4 and 2, we get, 8 as product, now multiply the product 8 to the last number 5,
8x5 = 40
Hence, the another way to find 4x2x5 is to multiply two of the digits and multiply the last digit with the product of two.
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The question is incomplete solved for:
Find the another method to solve 4x2x5
Consider a lease for 120,000 square feet of space and specifies base rent of $5 psf. In addition, the lease provides for percentage rent of 3% of sales in excess of the natural breakpoint. a) Calculate the natural breakpoint for this lease.
Answer:
$20M
Step-by-step explanation:
You want the "natural breakpoint" for a lease that specifies rent is the maximum of $5 per square foot for 120,000 square feet, or 3% of sales.
Minimum rentThe minimum rent is ($5/ft²)×(120000 ft²) = $600,000.
BreakpointThe amount of sales that makes $600,000 equal to 3% of sales is ...
$600000 = 0.03s
s = $600000/0.03 = $20,000,000
The "natural breakpoint" is $20M in sales.
__
Additional comment
When sales exceeds $20M, 3% of sales is more than $5/ft², so the rent will be based on sales.
Martina has been given a list of 5 bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?
Answer:
Step-by-step explanation:
Martina has been given 5 bands and asked to place a vote for her favorite and second favorite bands. The number of different votes possible can be calculated using combinations.
A combination is a way of selecting items from a set, where order does not matter and repetition is not allowed. To find the number of combinations, we can use the formula:
C(n, k) = n! / (k! * (n - k)!)
where:
n is the number of items
k is the number of items being selected
! denotes factorial, which is the product of all positive integers up to that number
Step-by-step, the calculation is as follows:
Determine the number of items and the number of items being selected:
n = 5 (the number of bands)
k = 2 (the number of bands Martina is voting for)
Calculate the number of combinations using the formula:
C(n, k) = n! / (k! * (n - k)!)
C(5, 2) = 5! / (2! * (5 - 2)!)
C(5, 2) = 120 / (2 * 3!)
C(5, 2) = 120 / (2 * 6)
C(5, 2) = 120 / 12
C(5, 2) = 10
So, there are 10 different votes possible for Martina's favorite and second favorite bands from the list of 5 bands.
if seven less than three times a number is negative one. What is the number?
if seven less than three times a number is negative one then the number is 2.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let the number be x.
Seven less than three times a number is negative one.
We need to find the unknown number x from the given statement.
Less than we use when we use subtraction, times we use for multiplication.
seven less than three times a number is negative one.
3x-7=-1
Add 7 on both sides
3x=6
Divide both sides by 3
x=2
Hence, if seven less than three times a number is negative one then the number is 2.
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Would sorting the tiles with positive coefficients and tiles with negative coefficients together help to simplify an expression that involves all tiles? Explain.
Yes, sorting the tiles with positive coefficients and tiles with negative coefficients together can help simplify an expression that involves all tiles.
Would sorting the tiles with positive coefficients and tiles with negative coefficients together help to simplify an expression that involves all tiles?When sorting the tiles, the positive coefficients are grouped together and the negative coefficients are grouped together. This makes it easier to perform operations such as addition and subtraction on the tiles and simplify the expression.
For example, if you have two tiles with positive coefficients and one tile with a negative coefficient, it becomes easier to see that the expression can be simplified by subtracting the negative tile from the sum of the two positive tiles.
Additionally, grouping the positive and negative coefficients together makes it easier to see any patterns or relationships that may exist between the coefficients and terms in the expression, which can further aid in simplification.
In summary, sorting the tiles with positive coefficients and tiles with negative coefficients together can help simplify an expression by making it easier to perform operations on the tiles and identify patterns and relationships between the coefficients and terms.
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each expansion represents the total number of dots in a pattern where n represents the step number select all the expressions that represent a quadratic relationship between the step number and total number of dots
The number of dots will be in each pattern in 4th step:
1. In pattern A: 16 dost
2. In pattern B: 18 dots
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
two patterns,
Pattern A:
number of dots,
step 0: 0
step 1: 4
step 2: 8
step 3: 12
So here it can be seen that,
4 dots are more in each step in compare with previous step,
So generalized expression can be written as:
Number of dots in nth step = 0 + 4n
In 4th step, there will be- 16 dots
Similarly, in Pattern B:
Number of dots in nth step = 2 + n²
In 4th step, there will be- 18 dots
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Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $1000 deposit in an account with an APR of 3%. The balance in the account after 1 year is approximately
The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
What is meant by continuous compounding?
If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.
Given,
rate per period = 3%
Principal amount = $1000
Compounding is done after 1,5 and 20 years.
But we are asked to find the amount after continuous compounding after 1 year.
The formula of the amount after continuous compounding is:
[tex]A = Pe^{rt}[/tex]
where A = amount after continuous compounding
r = rate of period
t = time period
P = principal amount
[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45
Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]
n = times it compounds per year = 365
r = 0.03
AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]
= 3.04%
Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
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D) Linear Functions: Model from a Verbal Description - Quiz - Level H Rebecca is flying a drone at a constant height. She decides to make the drone rise vertically. It rises 18 m every 3 s. After 5 s, the drone is at a height of 40 m. The drone's height in meters, y, is a function of the time in seconds, x. How many meters does the drone rise each second? Find the rate of change. 6 meters per second What is the height of the drone before Rebecca makes it rise? Find the initial value. 10 meters ◄» Write an equation to represent the function. y = ? x + ?
The equation to represent the function is y = 6x + 10 where y is the height of the drone in meters and x is the time in seconds. so the drone rises 6 meters per second.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Let us find the rate of change, we can divide the total change in the height of the drone by the time taken for the change.
rate of change = (change in height) / (time taken)
(40 m - 10 m/ (5 s - 0 s)= 30 m/5 s=6m/s
The drone rises 18 m every 3 s
rise per second = 18 m / 3 s = 6 m/s
This means that the initial height of the drone is 10 meters, since it takes 3 seconds for the drone to rise to a height of 28 meters
Therefore, the equation to represent the function is:
y = 6x + 10
where y is the height of the drone in meters and x is the time in seconds.
Therefore, the drone rises 6 meters per second.
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Some researchers want to compare meditation and exercise to see which is more effective for reducing
stress. They randomly selected 100 people who suffer from high stress to participate in the study. The
subjects will either be given a 10-week course in a meditation program or they will participate in a 10-
week exercise program. The researchers must decide how to assign the subjects to these programs.
One option would be random assignment of the subjects into the programs. Another option is to allow
each subject to choose a program.
Which of the following is the main advantage of randomly assigning subjects to one of the two
programs rather than allowing them to choose?
Answer:
This is not math...
Step-by-step explanation:
In ΔEFG, e = 310 inches, m m∠G=89° and m m∠E=27°. Find the length of f, to the nearest 10th of an inch.
The length of f to the nearest 10th of an inch is 308.8 inches.
What is law of sines?A trigonometric rule known as the Law of Sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. To put it another way, we may write: If we have a triangle with sides a, b, and c, and opposing angles A, B, and C:
Sin(A) / a = b / a sin(B) / c / sin (C)
Using the Law of Sines we have:
f / sin(89°) = e / sin(27°)
f = sin(89°) * 310 / sin(27°)
f ≈ 308.8 inches
Hence, the length of f to the nearest 10th of an inch is 308.8 inches.
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Answer:
613.7 in
Step-by-step explanation:
You want the length of side f in ∆EFG with e = 310 in, E = 27°, G = 89°.
Law of sinesThe law of sines tells you ...
f/sin(F) = e/sin(E)
Angle F is the third angle in the triangle, so its measure is ...
F = 180° - 89° -27° = 64°
Then the length of f is ...
f = e·sin(F)/sin(E) = (310 in)·sin(64°)/sin(27°) ≈ 613.7 in
The length of f is about 613.7 inches.
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Use the following function to complete this question:
f(x)=(x-1)^3+5
Graph the function and fill in the blanks.
If the transformation listed is not applicable write none.
Fill in the blanks in the form:
4 left
5 up
Write infinity in the form: inf
Horizontal shift:
Vertical shift:
Vertical stretch factor:
Vertical compression factor:
Axis of reflection:
Domain:
Range:
Inflection Point:
Pic is attached below
The following is deduced from the equation f(x)=(x - 1)^3 + 5
Horizontal shift: 1 left
Vertical shift: 5 down
Vertical stretch factor: 1
Vertical compression factor: 1
Axis of reflection: -x + 6
Domain: all real numbers
Range: all real numbers
Inflection Point: (1, 5)
What is vertical stretch factor?The vertical stretch factor is a term used in mathematics to describe the transformation that changes the height of a graph while leaving the horizontal axis unchanged. In other words, it's a factor by which the y-values of a function are multiplied to produce a new, stretched or compressed version of the original graph.
The stretch factor is usually represented by the symbol "k". For example, if the equation of a function is y = f(x), then the equation of its vertically stretched image would be y = k * f(x). A positive value of k stretches the graph upward, while a negative value of k compresses the graph downward. If k > 1, the graph is stretched vertically; if 0 < k < 1, the graph is compressed vertically; if k = 1, the graph remains unchanged.
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If sec 0 = √2, find 0 and identify all angles 0° < 0 < 360° that are co-terminal with the
given angle.
In the trigonometry relation the value of θ is 45 degrees and the coterminal angle between 0° < θ < 360° is 315 degrees
How to find conterminal of the angleCoterminal angles are angles that have the same terminal side in a given circle. They are angles that differ by a multiple of 360 degrees.
In other words, if two angles are coterminal, they have the same trigonometric functions, despite having different degrees.
If sec θ = √2
θ = arc sec (√2)
θ = arc cos (1/√2))
θ = 45 degrees
coterminal of angle 45 degrees between 0° < θ < 360°
360 - 45 = 315.
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Please help I dont understand how to get the length of segment DF
the measure of the angle will be 70°.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception.
The sum of all angle of triangle = 180
The given triangle two angles are given 44° and 68°
The other angle is 180° - (44+68) = 180 - 110 = 70°
Hence the measure of the angle will be 70°.
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What are the quotient and remainder of (3x^4+ 2x² - 6x + 1) + (x + 1)?
Answer:
The quotient is 3x^3 + 2x and the remainder is 0.
Step-by-step explanation:
Quotient: 3x³ + 2x
Remainder: -5
Answer:
3x^3 - 3x^2 + x - 1
x + 1 | 3x^4 + 2x^2 - 6x + 1
- (3x^4 + 3x^3)
---------------
-x^3 - 6x + 1
- (-x^3 - x^2)
-------------
-5x^2 - 6x + 1
-(-5x^2 - 5x)
------------
-x + 1
Therefore, the quotient is 3x^3 - 3x^2 + x - 1, and the remainder is -x + 1.
i cant figure out the second number
PLEASE HURRY I REALLY NEED HELP WITH THIS PROBLEM
5. Suppose a poll is to be conducted in an elementary school by interviewing 50 students. Explain whether or not the following samples are representative of the students at the school. a. The first 50 students leaving the cafeteria. b. Fifty randomly chosen names from a computer-generated list of names of all students at the school. c. Ten students randomly chosen from each of the 5 areas of campus. d. Five students from 10 teachers' classes.
If a poll is to be conducted in an elementary school by interviewing 50 students, the following samples have been described as either representative or not representative as follows:
a. The first 50 students leaving the cafeteria. Not representative
b. Fifty randomly chosen names from a computer-generated list of names of all students at the school. Representative
c. Ten students randomly chosen from each of the 5 areas of campus. Representative
d. Five students from 10 teachers' classes. Representative
What is a representative sample?A representative sample is a small collection from a larger group from which any information obtained will be as good as the larger group. While choosing a representative sample, the researcher should take care not to zone the participants from a given section of the population. This will cause the information to be skewed and not objective.
Selecting 50 students leaving a cafeteria will not be representative because this might only represent a section of the school that will be giving their response based on a certain mood.
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What is [ 8- (2/3) ^2] / ( 5 1/3 - 4 2/3 + 1 1/6 x 2)
Please Help!
Answer: To solve this expression, we first need to simplify the terms in the denominator:
5 1/3 - 4 2/3 + 1 1/6 x 2
We can convert each fraction to a mixed number:
5 1/3 = 5 + 1/3
4 2/3 = 4 + 2/3
1 1/6 x 2 = 2 x 1/6 + 2 = 2 + 1/3
Now we can perform the subtraction:
(5 + 1/3) - (4 + 2/3) + (2 + 1/3)
= 5 + 1/3 - 4 - 2/3 + 2 + 1/3
= 5 + 1/3 - 4 + 2 + 1/3 + 1/3
= 7
So the denominator simplifies to 7.
Next, we simplify the numerator:
8 - (2/3)^2
We can first square the fraction:
(2/3)^2 = 4/9
Now we can perform the subtraction:
8 - 4/9
= 8 - 4/9
= 8 x 9/9 - 4/9
= 72/9 - 4/9
= 68/9
So the numerator simplifies to 68/9.
Finally, we divide the numerator by the denominator:
68/9 ÷ 7 = 9.71
So, the expression simplifies to 9.71.
Step-by-step explanation:
Laurence earned scores of 87, 80, 75, and 85 on four biology tests. What score must he earn on his next test to have an 85 average?.
To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.
We can use the formula for the average (or mean) of a series of variables to determine Laurence's next biology test score in order to achieve an average of 85:
Average = (sum of values) / (number of values)
The total of Laurence's marks on the first four biology exams can be calculated using the following formula:
Sum of scores = 87 + 80 + 75 + 85
= 327
We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.
Therefore, We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.
By deducting Laurence's first four scores from the desired total of all five scores, and dividing the result by one (the number of scores left), we can get the score that Laurence has to achieve in his next biology exam:
Next score = (sum of all five scores) - (sum of first four scores)
= (85 x 5) - 327
= 25
Therefore, To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.
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Find angles m<1 and m<2
Answer:
Step-by-step explanation:Angles 1 and 2 form a linear pair and are supplementary. So to find m∠2, subtract m∠1 from 180o. m∠2 = 180o - 135o = 45o.
...
Solution
m∠1 + 32 = 90 Substitute 32 for m∠2.
m∠1 = 58 Subtract 32 from each side.
m∠1 + m∠ 2 = 90 Definition of complementary angles.
The population, P, in millions, of Ethiopia was 72.5 million in 2004
2.5%. Let t be time in years since
and growing at an annual rate of
2004.
an amal rate of 2,8%. Let (B) Express P as an exponential function using base e
Answer:
P = 72.5 * e^(0.025t)
Step-by-step explanation:
Here's a step by step solution with all the details and calculus involved.
(a) Express P as a function in the form P = Poat.
Since the population is growing continuously at a rate of 2.5% per year, we can use the formula for continuous growth:
P = Po * e^(rt)
where Po is the initial population (72.5 million), r is the continuous growth rate (0.025), and t is the time elapsed in years since 2004.
The continuous growth rate, r, is related to the annual growth rate, g, by:
r = g / 100
So, the continuous growth rate is 0.025.
Substituting the values into the formula for continuous growth, we get:
P = 72.5 * e^(0.025t)
This is the expression for the population as a function of time in the form P = Poat.
(b) Express P as an exponential function using base e.
The exponential function using base e is already in the desired form. So, we can simply write:
P = 72.5 * e^(0.025t)
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Consider the expansion of (3x² - k/x)^9, where k > 0.
The coefficient of the term in x^6 is 6048. Find the value of k.
(Show your work)
Answer:
The expansion of (3x² - k/x)^9 can be found using the binomial theorem. The binomial theorem states that for any real numbers a and b and any positive integer n, the expansion of (a + b)^n is given by:
(a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1)b^1 + C(n, 2)a^(n-2)b^2 + ... + C(n, n-1)a^1b^(n-1) + C(n, n)a^0b^n
where C(n, k) = n! / (k! (n-k)!).
Using this formula, we can find the coefficient of the term in x^6 in the expansion of (3x² - k/x)^9. The term in x^6 will be of the form C(9, 3) (3x²)^3 (-k/x)^6. We can find the value of C(9, 3) as follows:
C(9, 3) = 9! / (3! (9 - 3)!) = 84.
So, the coefficient of the term in x^6 is 84 * (3^3) * (-k/x)^6 = 84 * 27 * (-k)^6.
Since we are told that this coefficient is 6048, we can set these two expressions equal to each other:
6048 = 84 * 27 * (-k)^6
Dividing both sides by 84 * 27, we get:
k^6 = -6048 / (84 * 27) = -1.
Taking the sixth root of both sides, we find:
k = -1^(1/6).
So the value of k is approximately -1.122462048309372981433.
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 71° is changed to 93°, which of the following measures changes the most and what is the new value?
Mean 82.3°
Median 86.5°
Range 48°
IQR 34°
The measure that changes the most is the mean and the new value is 74.33°
How to find the measure that changes the most?If a value of 71° is changed to 93°, we have:
58, 61, 93, 77, 91, 100, 105, 102, 95, 82, 66, 57
Mean = (58+ 61+ 93+77+ 91+ 100+ 105+ 102 + 95 + 82+ 66+ 57)/12 = 74.33°
To find the median, arrange the data in order of size and pick the middle number. That is:
57, 58, 61, 66, 77, 82, 91, 93, 95, 100, 102, 105
Median = (82+91)/2 = 86.5°
Range = 105 - 57 = 48°
IQR = 97.5 - 63.5 = 34°
Therefore, the measure that changes the most is the mean and the new value is 74.33°
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Answer: it is 86.5 i got the answer correct on test trust me i want to help you guys out.
Step-by-step explanation:
Find the total number of lattice points on the
graph of
x² + y² + 11x - 13y + 73 = 0.
The total number of lattice points on the graph of x²+y²+11x-13y+73=0 is 0.
What is a lattice point?A point in a regularly spaced array of points, known as a point lattice, that is at the intersection of two or more grid lines is referred to as a lattice point.
Since in a Cartesian coordinate system, a lattice point is a point whose x-coordinate and y-coordinates are both integers. Therefore, it a defined point on the plane with both the coordinates known.
Further, if the given set of equation or function is plotted on the graph, then the graph of the function does not exist in the xy-plane.
Hence, there will be no lattice points on the given graph.
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If the x-values are equal for two points, then the two points are on a ____ line
If the x-values are equal for two points, then the two points are on a vertical line.
When will x - values for two points be equal ?When there is a vertical line, then it will cross the x - axis at only a single point. This point will be such that all the x - values on the line would be - values because the line stands on only one point on the x - axis.
The same applies to the y - axis for horizontal lines. This is because the horizontal line would cross the y - axis at a single point. For instance, all the points on y = 2, would have a y - value of 2.
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what is the least common denominator for 5/18, 11/12, and 6/13
Answer:
LCD → 468
Step-by-step explanation:
[tex]\frac{5}{18} = \frac{5}{18} * \frac{26}{26} = \frac{130}{468}[/tex]
[tex]\frac{11}{12} = \frac{11}{12} * \frac{39}{39} = \frac{429}{468}[/tex]
[tex]\frac{6}{13} = \frac{6}{13} * \frac{36}{36} = \frac{219}{468}[/tex]
Hence, the least common denominator for these three fractions would be 468.
