The definition of the f, h, and g functions, indicates the possible damains, range and composite functions are as follows;
(a) The domain of f is the set of real numbers except x = 5
The range is the set of all real numbers except f(x) = 0
(b) (f○g)(x) = 1/(3·x + 1)
(f○h)(x) = 1/(cos(x + 1) - 5)
(g○f)(x) = (6·x - 27)/(x - 5)
(c) g⁻¹(x) = (x - 6)/3
(d) The domain is; x ∈ R, and x ≠ 5
What is the domain of a function?The domain of a function is the set of the possible input values of the function.
The specified functions are;
f(x) = 1/(x - 5), g(x) = 3·x + 6, h(x) = cos(x + 1)
(a) The domain of f is the set of numbers such that the rational polynomial, 1/(x - 5) is defined
The polynomial, f(x) = 1/(x - 5) is defined when x - 5 ≠ 0, therefore;
x - 5 + 5 ≠ 0 + 5 = 5
x - 0 ≠ 5
x ≠ 5
The polynomial, f(x) = 1/(x - 5) is difined where x ≠ 5
The domain is the set of all real numbers, such that x ≠ 5
The range of the function, is the set of the possible output values, such that as (x - 5) ≠ 0, f(x) ≠ 0
The range is therefore; -∞ < f(x) < ∞, f(x) ≠ 0
(b) The composite functions (f○g)(x) = f(g(x))
Therefore; (f○g)(x) = f(g(x)) = f(3·x + 6)
Plugging in x = (3·x + 6) in the function, f(x) = 1/(x - 5), we get;
f(g(x) = 1/((3·x + 6) - 5) = 1/(3·x + 1)
f(g(x) = 1/(3·x + 1)
(f○g)(x) = 1/(3·x + 1)(f○h)(x) = f(h(x))
h(x) = cos(x + 1), therefore; (f○h)(x) = f(cos(x + 1))
Plugging in x = cos(x + 1) in f(x) = 1/(x - 5), we get;
(f○h)(x) = f(cos(x + 1)) = 1/((cos(x + 1)) - 5)
(f○h)(x) = 1/((cos(x + 1)) - 5)(g○f)(x) = g(f(x))
g(f(x)) = g(1/(x - 5)) = 3/(x - 5) + 6 = (6·x - 27)/(x - 5)
(g○f)(x) = (6·x - 27)/(x - 5)(c) g⁻¹(x)
g⁻¹(x) is the inverse of the function, g(x), which can be foiund as follows;
Plugging in; y = g(x) = 3·x + 6
y = 3·x + 6
y - 6 = 3·x
x = (y - 6)/3
Therefore;
g⁻¹(x) = (x - 6)/3(d) (f + g)(x) = f(x) + g(x)
f(x) + g(x) = 1/(x - 5) + 3·x + 6
The use of a graphing calculator indicates that we get;
1/(x - 5) + 3·x + 6 = (3·x² - 9·x - 29)/(x - 5)
Therefore; (f + g)(x) = (3·x² - 9·x - 29)/(x - 5)
The domain is therefore, the possible values of x at which the denominator is not zero, that is x ≠ 5
The domain is the set real numbers except x = 5, which is; x ∈ R, x ≠ 5
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A student received a coupon for 14% off the total purchase price at a clothing store. let b be the original price of the purchase. use the expression c - 0.14c for the new price of the purchase. write an equivalent expression to show another way to represent the new price.
Answer:
The equivalent expression to show another way to represent the new price is b - 0.86b = c .
Step-by-step explanation:
Given that the original price of the purchase is b and the coupon gives a 14% discount, the new price of the purchase is given by:
c = b - 0.14b
To write an equivalent expression, we can multiply both sides of the equation by 100% - 14% to simplify:
c * 100% = b * 100% - 0.14b * 100%
c * 100% = b * (100% - 14%)
c * 100% = b * 86%
c = b * 86%
So, another way to represent the new price of the purchase is c = b * 86%.
What number compared to 10 is the same as 28 compared to 5 A. 46 B. 36 C. 56 D. 66
HELP ME PLEASE
The number 56 when compared to 10 is the same as 28 compared to 5.
Option- C(56)
Let x be the number when compared to 10 is same as 28 compared to 5.
So, finding the value of x by comparing the ratios of the above stated values.
Therefore,
[tex]\frac{x}{10} = \frac{28}{5}[/tex]
So, Cross multiplying the above equation,
x × 5 = 28 × 10
5x = 280
x = [tex]\frac{280}{5}[/tex]
x = 56
So, 56 when compared to 10 bears the same ratio as 28 compared to 5.
Option number - C
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Write an exponential function that has a y-intercept of -4 and passes through the points (1, -1.6) and (2, -0.64) .
The exponential function is y = 4(0.4)^x
How to determine the exponential functionFrom the question, we have the following parameters that can be used in our computation:
y-intercept of -4 passes through the points (1, -1.6) and (2, -0.64) .An exponential function s represented as
y = ab^x
Where
a = the y-intercept
a = -4
Also, we have
b = -0.64/-1.6
b = 0.4
So, we have
y = -4(0.4)^x
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a non-square rectangle has integer dimensions. the number of square units in its area is triple the number of units in its perimeter. what is the smallest possible perimeter of the rectangle?
The perimeter of this rectangle is 94, which is the smallest possible perimeter for a non-square rectangle with integer dimensions that has an area that is triple its perimeter.
Let's call the length of the rectangle "L" and the width of the rectangle "W". The area of the rectangle is then L * W, and the perimeter is 2 * (L + W).
According to the problem, the number of square units in the rectangle's area is triple the number of units in its perimeter:
L * W = 3 * (2 * (L + W))
Expanding the right side and solving for L:
L * W = 6L + 6W
L * W - 6L = 6W
L * (W - 6) = 6W
L = 6W / (W - 6)
Since L and W are both positive integers and L can't be equal to W (because the rectangle can't be a square), we know that W must be greater than 6. Let's try W = 7:
L = 6 * 7 / (7 - 6) = 6 * 7 = 42
This gives us a rectangle with dimensions 42 x 7, which satisfies the conditions of the problem.
The perimeter of this rectangle is 2 * (42 + 7) = 94, which is the smallest possible perimeter for a non-square rectangle with integer dimensions that has an area that is triple its perimeter.
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31) Find the sum in scientific notation, and then write the answer in standard form.
(3.49x10^-2)+(4.39×10^-2)
32) Find the difference in scientific notation, and then write the answer in standard form
(8.75×10^-8)-(3.75×10^-8)
Answer:
Sum: (3.49x10^-2) + (4.39x10^-2) = 7.88x10^-2
In standard form, this can be written as 0.0788.
Difference: (8.75x10^-8) - (3.75x10^-8) = 5x10^-8
In standard form, this can be written as 0.00000005.
Step-by-step explanation:
A jet ski costs $3,204. If you want to make 36 equal payments, how much is each payment?
Answer:
$89 for each payment
Step-by-step explanation:
3,204 / 36 = 89
Answer: Each payment is 89 dollars
Step-by-step explanation:
Divide 3,204 by 36 to get how much each payment will be.
Solve the System of Equations Using Elimination.
3m-4n=-14
3m+2n=-2
The solution of this system of equations is ( , ).
Answer:
(m,n) is (-2,2)
Step-by-step explanation:
Elimination means that we should rewrite one of the two equations as an expression of one of the variables isolated, and then use that definition isn the other equation. It is also called "substitution."
Lets use the first equation and rewrite it so that the variable m is isolated:
3m-4n=-14
-4n = -3m-14
n = (3/4)m +(7/2)
Now use this definition of n in the second equation:
3m+2n=-2
3m+2((3/4)m +(7/2)) = -2
3m + (3/2)m + 7 = -2
4.5m = -9
m = -2
Now use m= -2 in either equation to find n.
3m-4n=-14
3(-2)-4n=-14
-6 -4n = -14
-4n = -8
n = 2
The solution of this system of equations is (-2,2).
See the attached graph, with x and y used in place of m and n.
The angle of a sector of a circle of perimeter is 24 degree Celsius. Find the radius of the sector
In light of the query we've got The circle's radius is equivalent to 3.832 units.
Describe perimeter :In geometry, the perimeter is the overall area of a shape's boundary. A shape's perimeter is computed by adding the lengths of all of its sides and edges. Linear measurements like cm, metres, inch, and feet are used to express its dimensions.
The answers to our problem is that area
A = (θ/360) * π * r^2
π = 3.14
Perimeter is 24 degree, The formula for circumference is:
C = 2 x πr
Now, we can calculate the radius using the circumference:
r = C / (2 x π)
Substituting the value of C from the equation above, we get:
r = (24 / (2 x π))
Therefore, the radius of the circle is approximately equal to 3.832 units.
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there are 5 students in my class. i want to pick 2 to treat them to a lunch. the 1st picked gets 100% lunch cost covered and the 2nd picked gets 50% of the lunch cost covered. in how many ways can i do this?
So there are ten different combinations of two pupils out of five when there are five kids in my class and I want to choose two to treat to lunch.
What is combination?A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.
Here,
To determine the number of ways to pick 2 students out of 5 to treat them to lunch, you can use the combination formula, which is given by nCr, where n is the number of items to choose from, r is the number of items to choose, and nCr is the number of combinations of n items taken r at a time. In this case, n = 5 and r = 2, so the number of ways to pick 2 students out of 5 is:
5C2 = 5! / (2! * (5 - 2)!) = 10
So, there are 10 possible combinations of 2 students out of 5 when there are 5 students in my class and I want to pick 2 to treat them to a lunch.
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two fair, $6$-sided dice are thrown. what is the probability that the product of the two numbers is a multiple of $5$? express your answer as a common fraction.
The probability of the product of the two numbers being a multiple of 5 are 9/36.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
We can approach this problem by listing out all the combinations of two numbers from 1 to 6 and counting the number of combinations for which the product is a multiple of 5.
There are 6 x 6 = 36 possible combinations of two numbers from 1 to 6.
The combinations for which the product is a multiple of 5 are: (1, 5), (5, 1), (2, 5), (5, 2), (3, 5), (5, 3), (4, 5), (5, 4), and (5, 5).
So, there are 9 possible combinations for which the product is a multiple of 5.
The probability that the product of the two numbers is a multiple of 5 is 9/36. Expressing this as a common fraction, we have:
P(product is a multiple of 5) = 9/36 = 1/4
The probability that the product of the two numbers is a multiple of 5 is 9/36.
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What is the y-intercept of the line shown? (4 points)
A coordinate plane is shown. A line passes through the point -4 comma 1 and through the y-axis at 4.
The y-intercept of the line shown is (0,4).
What is y-intercept of a function?The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.
Assume that we've got: y = f(x)
At y-axis, we've got x = 0, so putting it will give us the y-intercept.
Thus, y-intercept of y = f(x) is y = f(0)
Given;
A line passes through the point -4 comma 1 and through the y-axis at 4.
Now,
y=mx+c
1=m*-4+c
Line passes through 4 at y-axis
(0,4)
Therefore, the y intercept will be (0,4).
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Please help ASAP
Frequency Distribution table
The answer is:
A frequency distribution for a collection of data is shown in the accompanying table.
The intervals or ranges of the data are displayed in the left column of the table, and the frequency or number of observations within each interval is displayed in the right column.
For instance, the first row demonstrates that 3 observations fall within the range of 10 to 19, the second demonstrates that 5 observations fall within the range of 20 to 29, and so on.
We only combine the frequencies to determine the total number of observations:
Total observations are equal to 3 + 5 + 7 + 4 + 1 = 20.
By averaging the bottom and upper interval bounds, we can also determine each interval's midpoint. As an illustration, the first interval's midway (10-19) is as follows:
Midpoint: (14.5) (10 + 19) / 2
This may be done for each interval, and to display the midpoints, we can add a third column to the table.
The cumulative frequency, which is the overall frequency as we progress from the shortest interval to the longest interval, can then be calculated. The cumulative frequency can be displayed in the table by using a fourth column.
The finished table is shown here:
Interval Frequency Midpoint Cumulative Frequency
Oct-19 3 14.5 3
20-29 5 24.5 8
30-39 7 34.5 15
40-49 4 44.5 19
50-59 1 54.5 20
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Valeria practices the piano 910 minutes in 5 weeks. Assuming she practices the same amount every week, how many minutes would she practice in 4 weeks?
Answer:
728
Step-by-step explanation:
910/5 = 182 per week
4 weeks = 4*182 =728
Which expression is equivalent to ∣∣b∣∣>6
?
Responses
b > –6 and b < 6
b > –6 and b < 6
b < –6 and b > 6
b < –6 and b > 6
Answer:
b > –6 and b < 6
Step-by-step explanation:
The expression "|b| > 6" means that the absolute value of b is greater than 6. Therefore, b can either be greater than 6 or less than -6. So, the equivalent expression is b > –6 and b < 6.
Bonnie and Kelly are part of a group going to a basketball game. The group has two court-side seats, five upper-level seats, and four seats in general admission. If the group randomly chooses seats, what is the probability that both Bonnie and Kelly will sit court side at the basketball game if they are the first two to choose seats? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
1. 8%
98. 2%
3. 3%
18. 2%
The probability that both Bonnie and Kelly will sit courtside at the basketball game if they are the first two to choose seats is 2%.(option 2)
When the group selects their seats at random, we must take into account all possible outcomes in order to calculate this. There are a total of 11 seats, two of which face the court. 11 are there! possible methods by which the group can select their seats. There is only one option for Bonnie and Kelly to sit courtside out of these, and that is for them to select a seat courtside first. As a result, there is a one in eleven chance that Bonnie and Kelly will sit side by side in court., or 2%.
We can divide the probability by 100 to put this into percentage form. The question has been answered by this, which gives us 2%.
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Complete Question:
Bonnie and Kelly are part of a group going to a basketball game. The group has two court-side seats, five upper-level seats, and four seats in general admission. If the group randomly chooses seats, what is the probability that both Bonnie and Kelly will sit court side at the basketball game if they are the first two to choose seats? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
1. 8%
2. 2%
3. 3%
4. 12%
What are possible coordinates of point D if ΔDEF is congruent to ΔABC? (–6,1) (–6,2) (–5,1) (–5,2)
(–6,2) is the possible coordinates of point D if ΔDEF is congruent to ΔABC.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Shapes are congruent if you can turn one into the other by moving, rotating or flipping.
We can use this symbol to show that two things are congruent.
Two triangles are congruent if and only if all the corresponding legs are congruent.
The only point that makes the corresponding legs to be congruent is
(–6,2)
because we can match these two triangles by flipping the red one two times and moving it into the blue one.
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Sally sold a table for $180.00, her commission is 21.5%. What is the amount of Sally's Commission?
Answer:
$38.70
Step-by-step explanation:
21.5% = 0.215
$180.00 times 0.215 = $38.70
So, Sally's Commission is $38.70
in 2017, 77 out of 100 americans claimed to have read at least one book during the year. write this ratio as a percent.
Step 1: Calculate the ratio.
The ratio is 77 out of 100.
Step 2: Convert the ratio to a percent.
To convert the ratio to a percent, divide the numerator by the denominator and multiply the result by 100.
Therefore, 77 out of 100 can be written as 77/100 x 100 = 77%.
The conversion process known as "ratio to percentage" aids in turning a ratio into a percentage. As is common knowledge, two quantities of the same unit are compared using the ratio. A percentage, on the other hand, is a particular kind of ratio where the value of the sum is always equal to 100. Let's go over the formula, the value of the ratio to percentage for some of the most commonly used numbers, and several solved examples in depth in this article.
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can someone please help me asap?
The amount that Reuben owe after 9 years, rounded to the nearest cent is $19,252.95..
What is the accrued amount after 9 years?The formula compound interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $8,000Interest rate r = 10% = 10/100 = 0.1Compounded semi annually n = 2 Time t = 9 years Accrued amount A = ?Plug the given values into the above formula and solve for A.
A = P( 1 + r/n )^( n × t )
A = $8,000( 1 + 0.1/2 )^( 2 × 9 )
A = $8,000( 1 + 0.05 )¹⁸
A = $8,000( 1.05 )¹⁸
A = $19,252.95
Therefore, the accrued amount is $19,252.95.
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Is Ariel correct? Complete the statements.
Ariel is ?
For any value of y,
the statement -12 = 3 is always ?
The equation has ?
For the given equation, we can complete the statements below:
Ariel is correct. For any value of y, the statement -12 = 3 is always true.
The equation has no solutions.
What is an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The first part of the question is as given below.
Ariel simplifies the equation 3y - 12 = 3(y+1) and says it has no solution.
We are asked to complete the statements based on the above information.
Simplifying the equation,
3y - 12 = 3(y+1)
3y - 12 = 3y + 3
-12 = 3
Since the y term in the above equation is not present, the given equation has indeed no solution.
Also if we take any value of y, the final answer will always be -12 = 3.
Therefore we can complete the statements as below:
Ariel is correct. For any value of y, the statement -12 = 3 is always true.
The equation has no solutions.
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Answer: Ariel is correct. For any value of y the statement -12=3 is always false and it’s no solution
Step-by-step explanation:
Grace has 1. 35 pounds of strawberries, 1. 4 pounds of bananas, and some apples. She has more pounds of apples than pounds of strawberries, but fewer pounds of apples than pounds of bananas. How many pounds of apples could Grace have? Explain the strategy you used
Grace could have weighed 1.36 pounds, 1.37 pounds, 1.38 pounds, or 1.39 pounds of apples.
Let a be the number of pounds of apples.
We are told that Grace has 1.35 pounds of strawberries. It has more kilograms of apples than kilograms of strawberries.
This means that a is greater than 1.35. We can represent this information as an inequality as follows:
We were also told that Grace had 1.4 pounds of bananas. It has fewer kilograms of apples than kilograms of bananas. This means that a is less than 1.4. We can represent this information as an inequality:
Combining the two inequalities we get:
Therefore, Grace can be 1.36 lbs., 1.37 lbs., 1.38 lbs., or 1.39 kilos of apples.
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Which number set correctly represents the range of the given data? {(0, 0), (2.0), (3, 0), (5,0)}
The set of range of given data is {0,0,0,0}
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The y coordinates are the range values
range = {0,0,0,0}
The set of range of given data is {0,0,0,0}
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Please Help ASAP. No links or files. I will report!
Answer: 18
Step-by-step explanation: Solve using algebra and angles given.
A person decides to take a walk. They walk ten miles north (up), tw east (right), and ten miles south (down). How far was the person disclaced?
We can quickly determine that the person has been moved by 10 miles by logical reasoning.
What is logical reasoning?A mental process called logical reasoning seeks to reach a conclusion in a precise way.
By beginning with a set of premises and reasoning to a conclusion supported by these premises, it takes the shape of inferences or arguments.
Propositions, or true or false statements about the reality of a situation, are what the premises and the conclusion are.
They have a disagreement as a group.
In the sense that it seeks to develop correct arguments that any sane person would find persuasive, logical reasoning is norm-governed.
Logic is the primary academic field that studies logical reasoning.
So, using logical thinking, we can easily tell that the person is displaced by 10 miles.
(refer to the image attached below)
Therefore, we can quickly determine that the person has been moved by 10 miles by logical reasoning.
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Find the number that makes the ratio equivalent to 8:1. :11
Answer:
88
Step-by-step explanation:
We can set up the proportion 8/1 = x/11. By cross-multiplying, we get that x = 88.
Employee Performance
Adequate
Good
Outstanding
5%
8%
10%
The employee wage is 22 per hour.
What is the new wage if the performance is Adequate?
Round annual wages to the nearest dollar.
Note: do not enter commas or dollar signs, numbers only
The new wage if the performance is Adequate is $23.1 per hour.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
If an employee's performance is adequate, then he will get a raise of 5%.
The employee wage is 22 per hour.
The performance is Adequate.
That means,
the wage is,
= 22 + 22x 0.05
= 23.1
Hence, $23.1 is the wage per hour.
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Mr. Adams divides 730 cookies onto plates with of 35 cookies on each plate. How many plates will he fill? How many extra cookies will he have?
Answer:
Step-by-step explanation:
Mr. Adams will fill 21 plates, and he will have 5 extra cookies.
To find the number of plates filled by Mr. Adams, we need to divide 730 cookies by 35 cookies per plate:
730 ÷ 35 = 21
So, Mr. Adams will fill 21 plates.
To find the number of extra cookies, we use the modulo operator to find the remainder after dividing 730 by 35:
730 % 35 = 5
So, Mr. Adams will have 5 extra cookies.
g what is the probability that the hand contains 4 cards of the same suit, and 1 of another suit?
We got that the probability that the hand contains 4 cards of the same suit and 1 of another suit = 0.042917
In the given question the hand contains 4 cards of the same suit, and 1 of another suit and we have to find the probability of this.
As we know that in standard card deck have 4 suits and 13 ranks in each suit and each deck have total 52 cards. If 13 ranks separated then 39 cards are left.
So the probability that the hand contains 4 cards of the same suit and 1 of another suit is
Probability = [tex]\frac{|^{13}C_{4}\times^{39}C_{1}|+|^{13}C_{4}\times^{39}C_{1}|+|^{13}C_{4}\times^{39}C_{1}|+|^{13}C_{4}\times^{39}C_{1}|}{^{52C_{5}}}[/tex]
Probability = [tex]\frac{|715 \times 39| + |715 \times 39|+|715 \times 39|+|715 \times 39|}{2,598,960}[/tex]
Probability = (27,885 + 27,885 + 27,885 + 27,885)/2,598,960
Probability = 111,540/2,598,960
Probability = 0.042917
we got that the probability that the hand contains 4 cards of the same suit and 1 of another suit = 0.042917
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The complete question is:
A 5-card hand is (randomly) drawn from a standard 52 card deck. What is the probability that the hand contains 4 cards of the same suit, and 1 of another suit?
Steve bought 1 burger and 3 fries. The burger cost $5 and the total cost was $14.75. How much is each order of fries?
Consider the equation a^3 - b^3 / (a-b)^3 = 91 where a and b are real numbers a>b>0. Find b/a.
The value of b/a is b/a = 91/3 {(1-b/a)²}.
What is the Cubic equation?Cubic equations are polynomials of degree 3. That means the maximum degree of the polynomial is three.
And the standard form of a cubic equation is;
f(x) = ax³ + bx² +cx +d, where a, b, c, and d are constant coefficients a ≠ 0.
Given:
A cubic equation,
a³ - b³ / (a-b)³ = 91 where a and b are real numbers a>b>0.
Simplifying,
(a-b)(a²+b²+ab)/(a-b)³ = 91
(a²+b²+ab)/(a-b)² = 91
(a²+b²+ab-3ab+3ab)/(a-b)³ = 91
3ab/(a-b)² = 91
b/a = 91/3 {(a - b)²/a²}
b/a = 91/3 {(a - b/a)²}
b/a = 91/3 {(1-b/a)²}
Hence, b/a = 91/3 {(1-b/a)²}.
To learn more about the cubic equation;
brainly.com/question/13730904
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