Answers
The composite functions (fg)(x) and (f/g)(x) when evaluated are (fg)(x) = (-5x) * (4^x) and (f/g)(x) = (-5x)/(4^x)
Evaluating the composite functionsGiven that
f(x) = -5x and g(x) = 4^x.
We have
(fg)(x) = f(x) * g(x)
So, we have
(fg)(x) = (-5x) * (4^x)
The domain of (fg)(x) is the set of all real numbers because both f(x) and g(x) are defined for all real numbers.
Next, we have
(f/g)(x) = f(x)/g(x)
So, we have
(f/g)(x) = (-5x)/(4^x)
The domain of (f/g)(x) consists of all real numbers except for and x = log(4)(5) i.e. {x ∈ ℝ | x ≠ log(4)(5)}
Next, we have
(fg)(1) = (-5) * (4) = -20
(f/g)(1) = (-5)/(4) = -5/4
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Related Questions
8. Which graph represents the equation y = 2x +3?* 1 point Option 1 Option 2math
Answers
ANSWER
Option 2
EXPLANATION
Graph of option 1 has a slope of 0, since it's an horizontal line.
Graph of option 2 has it's y-intercept at y = 3 and the slope is 2, so that's the graph of the equation.
Value 2000 is decresed to 100. What is the percent decreased
Answers
Answer:
PD = 95%
Step-by-step explanation:
(2,000 - 100) / 2,000 times 100
( (original - new) ) / original times 100
= 1,900 / 2,000 times 100
= 0.95 times 100
= 95% decrease
Step-by-step explanation:
John walks 3/5km per hour ,At this rate ,how far would he walk in 1/2 hour.provide answer in decimal notation
Answers
answer: 0.3km
explanation:
distance in 1 hour = 3/5km
distance in 1/2 hour = 3/5km ÷ 2
= 3/10km
= 0.3km
hence, john would have walked 0.3km in half an hour.
Meiling and Jackie are playing a game of chance with a six-sided number cube. The sides of the cube are numbered 1 to 6. Meiling scores a point each time she rolls a number greater than 4.
Answers
Answer:
D. Jackie rolls a number that is less than 3.
Step-by-step explanation:
Every time Meiling rolls a number greater than a four, she will get a point. This gives her two numbers that she can get a point off of, 5 and 6. So If Jackie were to roll a number less than a three, Jackie would also get two numbers that she can get a point off of, 1 and 2. So the answer "Jackie rolls a number that is less than 3" will give Jackie an equally likely chance for a point.
A common abuse of bar graphs is
Answers
Answer:
A common abuse of bar graphs is to. replace bars by pictures and increase both height and width as the variable plotted increases. If a bar graph is to be accurate, it is essential that. the bars all have the same width.
Write an equation for the function whose graph is shown to the right. The graph shows a transformation of a common function.An equation for the function of the given graph is___
Answers
The graph is square root function graph.
It has undergo a transformation and has been shifted to the left by 2 units
Hence, the equation for the function of the given graph is:
\(y=(x+2)^{\frac{1}{2}}\)the width of a rectangle is half as long as the length. the rectangle has an area of 72 square feet. what are the length and width of the rectangle
Answers
Answer:
w-6 l-12
Step-by-step explanation:
Let's put this into a system of equations.
w=0.5L
wL=72
Let's plug in the w value in the second equation.
0.5L(L)=72
L²=144
L=12
Now we plug our L value into the first equation.
w=1/2(12)
w=6
The width is 6 and the length is 12.
10 minutes! help!
suppose f(x) is given by following graph
Answers
Answer:
this is hard
Step-by-step explanation:
is it trigonometry?
What is the median of the following set of numbers? 35, 33, 36, 34, 33, 33, 32, 38, 35
A.35
B. 34
C.33
D.36
Answers
Median of the set is 34, as it is the middle value of the ordered set (32, 33, 33, 33, 34, 35, 35, 36, 38).
To find the middle of a bunch of numbers, the initial step is to organize the numbers all together from least to most prominent. For this situation, the arranged set is: 32, 33, 33, 33, 34, 35, 35, 36, 38.
The middle is the center number in the arranged set. On the off chance that there is an odd number of values, the middle is the center worth. On the off chance that there is a considerably number of values, the middle is the normal of the two center qualities.
For this situation, there are nine qualities in the set, which is an odd number. The center worth is the fifth worth, which is 34. Thusly, the middle of the set is B. 34.
To confirm, we can count four qualities before 34 and four qualities after 34 in the arranged set. Since there are an equivalent number of values when the middle, we can infer that 34 is for sure the middle.
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Let (1=1,2,3, 4, 5, 6, 7, 8, 9, 10
Answers
The list of elements in the sets are as follows:
A. A ∩ B = {2, 9}
B. B ∩ C = {2, 3}
C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D. B ∪ C = {2, 3, 5, 7, 9, 10}
How to find the elements in a set?Set are defined as the collection of objects whose elements are fixed and can not be changed.
Therefore,
universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 7, 8, 9}
B = {2, 3, 5, 9}
C = {2, 3, 7, 10}
Therefore,
A.
A ∩ B = {2, 9}
B.
B ∩ C = {2, 3}
C.
A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D.
B ∪ C = {2, 3, 5, 7, 9, 10}
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D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is mZDEF?
Answers
Answer: \(m\angle DE F=90^{\circ}\)
Step-by-step explanation:
The slope of \(DE\) is \(\frac{7-3}{5-4}=4\).
The slope of \(EF\) is \(\frac{3-2}{4-8}=-\frac{1}{4}\).
Thus, \(DE \perp EF\), meaning \(m\angle DE F=90^{\circ}\).
Bigco Corporation is one of the nation’s leading distributors of food and related products to restaurants, universities, hotels, and other customers. A simplified version of its recent income statement contained the following items (in millions).
Cost of sales $ 11,571
Income taxes 249
Interest expense 23
Net earnings 1,442
Sales 16,400
Earnings before income taxes 1,691
Selling, general, and administration expense 3,543
Other revenues 428
Total expenses (excluding income taxes) 15,137
Total revenues 16,828
Prepare an income statement for the year ended June 30, current year. (Hint: First order the items as they would appear on the income statement and then confirm the values of the subtotals and totals.)
Answers
Step-by-step explanation:
I hope this answer is helpful ):
on a separate sheet of paper, sketch the rectangle for each problem using any method round and estimate to check your answer problem 1 5 x 4,751
Answers
The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.
What is rounding of a number?Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.
The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.
1. 5 x 4751 ≈ 5 x 4800 = 24,000.
To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.
2. 7 x 6000 = 42,000.
To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.
3. 6 x 5214 ≈ 6 x 5200 = 31,200.
To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.
4. 8 x 3867 ≈ 8 x 3900 = 31,200.
To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.
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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.
What is rounding of a number?The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.
In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.
Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.
1. 5 x 4751 ≈ 5 x 4800 = 24,000.
To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.
2. 7 x 6000 = 42,000.
We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.
3. 6 x 5214 ≈ 6 x 5200 = 31,200.
By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.
4. 8 x 3867 ≈ 8 x 3900 = 31,200.
To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.
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encontrar el numero que cumple que la suma de su doble y de su triple es igual a 100
Answers
Answer:
33.33
Step-by-step explanation:
Answer: 20
Step-by-step explanation:
2x+3x=100x
Combine like terms:
2x+3x=5x
5x=100
Divide by 5 on both sides:
5x/5=100/5x
x=20
Solve x and y 3x-4y=18,9x-2y=12
Answers
Answer:
3x-4y=18
1xy=18
xy=18 ans
Answer:
X=2/5
Y=-21/5
Step-by-step explanation:
solve your system by substitution.
3x−4y=18;9x−2y=12
Step: Solve3x−4y=18for x:
3x−4y=18
3x−4y+4y=18+4y(Add 4y to both sides)
3x=4y+18
3x/3=4y+18/3
(Divide both sides by 3)
x=4/3y+6
Step: Substitute 4/3y+6 for x in 9x −2y=12:
9(4/3y+6)−2y=12
10y+54=12(Simplify both sides of the equation)
10y+54+−54=12+−54(Add -54 to both sides)
10y=−42
10y/10=-42/10 . (Divide both sides by 10)
y=-21/5
Step: Substitute
21/5 fory in x= 4/3y+6
x= 4/3y (-21/5) +6
X=2/5 (Simplify both sides of the equation)
Answer:
X=2/5
Y=-21/5
HAVE A NICE DAY!!!!!
Find the value of x.
Answers
Answer:
x = 124
Step-by-step explanation:
You want the value of the exterior angle x°, given that the remote interior angles are 83° and 41°.
Exterior angleThe exterior angle of a triangle is equal to the sum of the remote interior angles:
x° = 83° +41°
x° = 124°
x = 124
__
Check
The interior angle adjacent to x° is its supplement:
180° -124° = 56°
The sum of the interior angles of the triangle is 180°:
83° +41° +56° = 180° . . . . . true
The theorem we cite above is a consequence of the fact that the missing interior angle is supplementary to both x° and the sum of the other two interior angles. It saves having to find the measure of the missing interior angle.
PLEASE ANSWERING THIS QUESTION!
By completing the square, the expression \(\sf{x^2-12x+101}\) equals (x+A)^2+B
where A = (Blank)
and B = (Blank)
Show your work!
Do not spam answers!
Explain your answer!
Thanks!
Answers
The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65
A = -6 and B = 65
Completing the squareFrom the question, we are to express the given expression in the form (x + A)^2+B by completing the square
The given expression is
x² -12x + 101
Using the completing the square method
x² -12x + 101
Divide the coefficient of x by 2 and then square it
The coefficient of x is -12
Dividing by 2, we get
-12/2 = -6
Squaring
(-6)²
Now, add and subtract this value from the expression
x² -12x + (-6)² + 101 - (-6)²
Then, we can write that
(x - 6)² + 101 - (-6)²
(x - 6)² + 101 - 36
(x - 6)² + 65
Thus,
The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65
By comparison,
A = -6
and
B = 65
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what is 14: x :: 28:7
Answers
The value of x in 14 : x : : 28 : 7 is 3.5.
What is a ratio?The ratio is a comparison between two or more than two similar things in simplest form. There are two types of proportion in ratio one is direct proportion and another is inverse proportion. In direct proportion, all quantities increase or decrease simultaneously and in inverse proportion if one quantity increases another decrease.
We know we can write a : b as a/b and: : as an equal to sign.
The given statement says 14 : x is in proportion to 28 : 7.
∴ 14 : x : : 28 : 7.
14/x = 28/7.
28x = 98.
x = 98/28.
x = 3.5.
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please i need help!! Translate these words into symbols: The sum of fifteen and a number q equals the product of six and a number q
Answers
Answer:
15 + q = 6q
Step-by-step explanation:
The following are the ages (years) of 5 people in a room: 13 , 22 , 15 , 14 , 15 A person enters the room. The mean age of the 6 people is now 16. What is the age of the person who entered the room?
Answers
Answer:
17
Step-by-step explanation:
Add up the values (13, 22, 15, 15, 14) and subtract from the product of 16 and 6
Answer:
17
Step-by-step explanation:
the mean is calculated as
mean = \(\frac{sum}{count}\)
let x be the age of the person entering the room, then sum of 6 is
sum = 13 + 22 + 15 + 14 + 15 + x = 79 + x
\(\frac{79+x}{6}\) = 16 ( multiply both sides by 6 to clear the fraction )
79 + x = 96 ( subtract 79 from both sides )
x = 17
the age of the person who entered the room is 17
I need help solving/answering this, it’s from my ACT prep guide
Answers
Given the sum:
\(\sum ^{\infty}_{n\mathop=1}\frac{3n^5}{6n^6+1}\)Analyzing the argument:
\(\frac{3n^5}{6n^6+1}=\frac{3n^5}{n^6(6+\frac{1}{n^6})}=\frac{1}{n}\cdot(\frac{3}{6+\frac{1}{n^6}})\)Where:
\(\lim _{n\to\infty}(\frac{3}{6+\frac{1}{n^6}})=\frac{3}{6+0}=\frac{1}{2}\text{ (Bounded)}\)It is known that the harmonic sum diverges:
\(\sum ^{\infty}_{n\mathop=1}\frac{1}{n}=\infty\)And we have a multiplication between a term that diverges and a bounded term, so we can conclude that the product diverges. Then:
\(\begin{gathered} \sum ^{\infty}_{n\mathop=0}\frac{1}{n}\cdot(\frac{3}{6+\frac{1}{n^6}})=\infty \\ \\ \Rightarrow\sum ^{\infty}_{n\mathop{=}1}\frac{3n^5}{6n^6+1}=\infty \end{gathered}\)Solve for N. 5/3 = N/12
Answers
Answer:
N = 20
Step-by-step explanation:
5/3 = 1 2/3
20/12 = 1 8/20
They are equivalent
You get the answer by simplifying both sides of the equation, then isolating the variable.
Hope this helps! :))
1500 meters in 6 seconds as a fraction and in simplest form
Answers
Answer:
250 m/s
Step-by-step explanation:
1500/6=250
Because the units are meters per second (m/s), the final answer would be 250 m/s.
Answer:
Answer:
250 m/s
Step-by-step explanation:
1500/6=250
Because the units are meters per second (m/s), the final answer would be 250 m/s.
Which overlapping triangles are congruent by ASA?
Answers
The overlapping triangles which are congruent by ASA are ΔEBC and ΔADC which is therefore denoted as option C.
What is a Congruent triangle?This is a scenario in which all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Taking ΔEBC and ΔADC, we have the following below:
∠B=∠D (90°)
CB= CD (Given)
∠BCE=∠ACD( Common)
Therefore, by ASA we can deduce that,
Δ EBC ≅ΔADC.
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how do i solve this Please give me a advise
Answers
The probability of spinning an even number, flipping tails, then spinning an odd number is:
1/9 (as fraction) or 11.11% (as percent)
How to find the probability of spinning an even number, flipping tails, then spinning an odd number?
To find the probability of spinning an even number, flipping tails, then spinning an odd number. We need to consider the individual probabilities. That is:
We have only one even number in the spinner, and that is 2. Thus,
P(even number) = 1/3
For a coin, the probability of head or tail is 1/2. Thus,
P(tail) = 1/2
We have two odd number in the spinner, and that is 1 and 3. Thus,
P(odd number) = 2/3
Therefore, the probability of spinning an even number, flipping tails, then spinning an odd number will be:
P(even, tail, odd) = 1/3 * 1/2 * 2/3
= 2/18
= 1/9 (as fraction)
In percent:
P(even, tail, odd) = 1/9 * 100
= 11.11%
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i’ll mark brainlist !! pls help
Answers
Answer:
so hard oh my god
Step-by-step explanation:
I don't know sorry I'm not good in math I'm bobo in math
3.
The probability that a standardized normal random variable, Z, is less than 50 is
approximately 0.
A) True
B) False
Answers
Hope this helps you out!
Using the normal distribution, it is found that this statement is False, hence option B is correct.
Normal Probability DistributionIn a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem, we have a standard normal variable, which means that \(\mu = 0, \sigma = 1\).
The probability that it is less than 50 is the p-value of Z when X = 50, hence:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{50 - 0}{1}\)
\(Z = 50\)
\(Z = 50\) has a p-value of 1.
The probability is approximately 1, hence the statement is False and option B is correct.
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7. N.CN.7 Determine the zeroes for the equation below. Select all that apply.
x² - 6x +13=0
A. 1
B. 5
C. 13
D. -3 + 2i
E. 3+2i
F. 3+4i
G. 6 + 4i
H. 3-21
I .6-41
Answers
Answer:
D. -3 + 2i and E. 3+2i are the zeroes for the equation.
Step-by-step explanation:
Two system of equations 2y =14-2x and y=-x + 7 is graphed. What is the solution to the system of equations
Answers
To solve this system, we will use the graphing method.
Based on the graph shown below, we can conclude that this system has infinite solutions, because they are the same line.
Answer:
Infinitely many solutionsStep-by-step explanation:
Given equations
2y =14-2x and y= -x + 7Rewriting the first equation
2y = 14 - 2x2y = -2x + 14y = -x + 7As we see it is same as the second equation. So same two lines, overlapping when graphed and the system has infinitely many solutions
Suppose $14,000 is invested with 4% interest for 5 yr under the following
compounding options. Complete the table.
Compounding Option
n Value
Result
a. Daily
b. Continuously
Answers
To complete the table, we need to calculate the value resulting from the $14,000 investment with a 4% interest rate for 5 years under the given compounding options.
a. Daily compounding:
To calculate the value with daily compounding, we use the formula:
Value = Principal × (1 + (Rate / n))^(n × Time)
In this case, the principal (P) is $14,000, the rate (R) is 4% (or 0.04), the time (T) is 5 years, and the compounding period (n) is 365 (since it's daily compounding).
Value = 14000 × (1 + (0.04 / 365))^(365 × 5)
Calculating this value will give you the result for the daily compounding option.
b. Continuously compounding:
To calculate the value with continuous compounding, we use the formula:
Value = Principal × e^(Rate × Time)
In this case, the principal (P) is $14,000, the rate (R) is 4% (or 0.04), and the time (T) is 5 years.
Value = 14000 × e^(0.04 × 5)
Calculating this value will give you the result for the continuously compounding option.
Please note that e represents the mathematical constant approximately equal to 2.71828.