Answer:
[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]
Step-by-step explanation:
(3a³-6b³) (4a² + 5b²) -> Simplify not Multiply
Expand (3a³-6b³) (4a² + 5b²) using the FOIL Method.
Apply the distributive property.
[tex]3a^3(4a^2+5b^2)-6b^3(4a^2+5b^2)[/tex]
[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2+5b^2)[/tex]
[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]
Simplify each term.
Rewrite using the commutative property of multiplication.
[tex]3*4a^3a^2+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]
↓
[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]
Equation Simplified.
---------------------------------------------------------------------------------------
Hope this helped!
HELP ME PLEASE !!!!!!!
Suppose g(x) = f(x-3) -4. Which statement best compares the graph of
g(x) with the graph of f(x)?
A. The graph of g(x) is shifted 3 units right and 4 units up.
B. The graph of g(x) is shifted 3 units left and 4 units down.
C. The graph of g(x) is shifted 3 units left and 4 units up.
D. The graph of g(x) is shifted 3 units right and 4 units down.
Answer:
D. The graph of g(x) is shifted 3 units right and 4 units down.
Step-by-step explanation:
The graph of g(x) is shifted 3 units right and 4 units down
The Rainbow Motor Motel is a 50-room facility with a restaurant to accommodate its guests. The motel is open 365 days a year, even on leap years; as Lurena Boucha, the proprietor, closes down the facility every February 29, her birthday, for an all day celebration of four years of successful operations. On the average, 98% of the rooms are available for sale. For the year just ended, the actual number of rooms sold totaled 15,000 and the number of guests for the year totaled 20,000. The projected occupancy rate for the next year is 82% of the available rooms based on past experience. The food information is as follows:
Sales $150,000, Beg Inventory 8,000, Purchases $70,000, Ending Inventory, $ 13,000 Consumption by employees (free of charge) $3,000, Number of checks 64,139. Cost of sales ?
From the information given, the cost of sales is $65,000. See the explanation below.
What is the definition of cost of sales?Add your initial inventory to the purchases made over the time period, remove that amount from your ending inventory, and that is your cost of sales.
Cost of Sales = (Bi + P) - Ei
Where Bi is Beginning Inventory
P is Purchases; and
Ei is Ending Inventory.
So the derivation of the solution above is?Beginning Inventory = 8,000
(add) Purchase = 70,000
Bi + P = 78,000
Ending Inventory = 13,000
Cost of sales = 78,000 - 13,000
= $65,000
Learn more about cost of sales at;
https://brainly.com/question/24561653
#SPJ1
Using the Empirical Rule, it is found that:
Scores between 80% and 96% are within 2 standard deviations of the mean.
68 scores are within one standard deviation of the mean.
It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Considering the mean of 88% and the standard deviation of 4%, the scores that are within 2 standard deviations of the mean are:
88 - 2 x 4 = 80%.
88 + 2 x 4 = 96%.
68% are within 1 standard deviation of the mean, hence, out of 100:
0.68 x 100% = 68 scores.
What is the median of the above answer? Pls help fast.
Considering that the mean of the normal distribution is the same as the median, the median is of 88%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For the normal distribution, the median is the same of the mean, that is, the median is of 88%.
More can be learned about the Empirical Rule and the normal distribution at https://brainly.com/question/24537145
#SPJ1
Angle RSU is complementary to angle UST. Angle QSR is congruent to angle RSU.
Lines Q, R, U, and T extend from point S from left to right. Angle R S T is a right angle.
Which statement is true about angles UST and QSR?
They are complementary.
They are supplementary.
They are congruent.
They are obtuse.
Answer:
Statement 1 is correct
Angles UST and QSR are complementary.
Step-by-step explanation:
Complementary angles are those angles whose addition gives result of 90°
Congruent angles are those angles which are equal to each other.we can say that there values are same.
Here angle RSU is complementary to angle UST.
Therefore there addition is equal to 90°
∠RSU + ∠UST = 90° - (i)
Here angle QSR is congruent to angle RSU.
It means ∠QSR =∠RSU -(ii)
From equation (i) and (ii)
∠QSR + ∠UST = 90°
So angles UST and QSR are complimentary angles.
Learn more about complimentary angles here -https://brainly.in/question/35749822
#SPJ10
Answer: A. They are complementary.
Step-by-step explanation: RIGHT ON EDGE 2023
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 60% pure fruit juice. The company is attempting to produce a fruit drink that contains 45% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice?
32 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the pints of 60% pure fruit juice
0.60x + 0.35(40 - x) = 0.40(40)
x = 8
= 40 - 8 (pints of 35% juice)
= 32
Thus, 32 pints and 8 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ1
The average THC content of marijuana sold on the street is 10.9%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street
(a) X ≈ N (0.10 , 0.02²)
(b) The probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11% is 31%.
(c) The 60th percentile is 11%.
The complete question is:The average THC content of marijuana sold on the street is 10%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to two decimal places and give THC content in units of percent. For example, for a THC content of 11%, write "11" not 0.11.A. X ~ N( , )
B. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11%.
C. Find the 60th percentile for this distribution.
According to the question,
The random variable X is defined as the THC content for a bag of marijuana that is sold on the street.
(a)The random variable X is Normally distributed with mean, μ = 0.10 and standard deviation, σ = 0.02.
Therefore, X ≈ N (0.10 , 0.02²)
(b) The value of P (X > 0.11) as follows:
P (X > o.11_ = P(X -μ/a > [tex]\frac{0.11-0.10}{0.02} \\[/tex])
= P(Z > 0.50)
= 1 -P (Z <0.50)
= 1- 0.69146
= 0.30854 ≈ 0.31
Hence,
the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11% is 31%.
(c)Let x represent the 60th percentile value.
Then, P (X < x) = 0.60.
⇒ P (Z < z) = 0.60
The value of z is,
z = 0.26.
Now put the value of x as follows:
z = x - μσ
0.26 = x - 0.100.02
x = 0.10+ ( 0.26 x 0.02)
x = 0.1052
x ≈ 0.11
Therefore,
The 60th percentile is 11%
Learn more about Probability here:
https://brainly.com/question/23345093
#SPJ1
cho hàm số f(x) liên tục trên đoạn [a;b] và có nguyên hàm F(x) thỏa F(a)=10;F(b)=2022 Khi đó \int _a^b\: f(x) dx bằng
The result follows from the fundamental theorem of calculus.
[tex]\displaystyle \int_a^b f(x) \, dx = F(b) - F(a) = 2022 - 10 = \boxed{2012}[/tex]
Evaluating a piece-wise function. 10 pts
Consider the function f(x)=3^x and the translation if f(x) named g(x). Janeen created a table for select values of x. What can be concluded about the relationship between two functions?
The conclusion about the relationship is
The functions have the same base.The functions have the same range.The functions have the same domain.g(x) is a translation left 1 unit.What is function?The complete question is:
Consider the function f(x) = 3x and a translation of f(x) named g(x). Janeen created a table for select values of x. Her table is shown below. What can be concluded about the relationship between the two functions? Check all that apply.
The functions have the same base.
The functions have the same range.
The functions have the same exponent.
The functions have the same domain.
g(x) is a translation left 1 unit.
g(x) is a translation right 2 units.
g(x) is a translation up 2 units.
Given function is:
f(x) = [tex]3^{x}[/tex]
g(x) = [tex]3^{x+1}[/tex]
Firstly, the functions have the same base i.e., base 3.
second, the functions have the same range.
As the range of f are all the values that f can assume. i.e., positive numbers and the range of g are all the values that g can assume. i.e., positive numbers.
third, both functions have the same domain as x = {0,1,2,3}.
Fourth, g(x) = f(x+1). So, g(x) is a translation left 1 unit.
Learn more about this concept here:
https://brainly.com/question/12612621
#SPJ1
Assume that 900 births are randomly selected and 4 at the births are girls. Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither
The number of girls are significantly low.
What is Probability ?Probability is the study of likeliness of an event to happen.
It is given that
900 births are randomly selected
The probability of birth of a boy or a girl is 1/2 = 0.5
Total chances of a girl is 900 * 0.5 = 450
The birth of girl observed is 4
Therefore the number of girls are significantly low.
To know more about Probability
https://brainly.com/question/11234923
#SPJ1
What is the result of M x H?????
I have asked 4 tutors and none of them know how to answer this.
Answer: m x H = [ -9 36 - 9/2 ]
Step-by-step explanation:
what is the median \
66, 51, 77, 68, 60, 75, 54, 80
cos^2 x = (1 - cos 2x)/2 A. True B. False
We know that cos2x=cos²x-sin²x
=cos²x-(1-cos²x) [since, cos²x+sin²x=1]
=cos²x-1+cos²x
=2cos²x-1
So, cos2x=2cos²x-1
Hence, cos²x= (1+cos2x)/2
Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables occurring on both sides of an equation. Geometrically, these identities involve certain trigonometric functions (such as sine, cosine, tangent) of one or more angles.
Most common trigonometric identities are:
- cos²x + sin²x = 1
- sec²x - tan²x = 1
- cosec²x - cot²x = 1
- cos2x = cos²x - sin²x
Therefore we get that the statement cos² x = (1 - cos 2x)/2 is false.
Learn more about trigonometric identities here-
brainly.com/question/12537661
#SPJ10
can you help me to solve this
Answer:
Is the question even complete ?
Step-by-step explanation:
How many units were started into production in a period if there were zero units of beginning work in process inventory, 4,714 units in ending work in process inventory, and 20,661 completed and transferred out units?
The number of the units were started into production in a period will be 25,375.
What is inventory?A industry's fully prepared kinds of goods, as well as the primary materials needed to make them, are considered to as inventory.
If there were zero units of beginning work in process inventory, 4,714 units of ending work in process inventory, and 20,661 completed and transferred out units.
Completed and transferred out = 20,661
Ending Inventory = 4,714
Units accounted for = 25,375
Beginning Inventory = 0
Units started into production = [Units accounted for – Beginning work in progress Inventory] = 25,375
Units accounted for = 25,375
More about the inventory link is given below.
https://brainly.com/question/14184995
#SPJ1
write the following situation as a proportion, 10 sandwiches feed 8 kids, how many sandwices will feed 30 kids
Help please I will give you a lot of points
Answer:
2 5/7 5/7 -1/7, -5/7, 1 2/7, -2 2/7, -1 5/7
Mrs. Martin brought 100 cookies to her class. She gave each student the same number of cookies, and had 5 cookies left over. there are more than 10 students and less than 50 students in Mrs. Martin's class. How many students are in her class?
Answer:
Mrs. Martin has 19 Students
Step-by-step explanation:
first step: 100-5=95
second step: 95/19=5
So, 95 divided by the possible number of students which is 19 it yields the answer of 5 which is the number of cookies each of her student recieved.
If f(x) = x², and
g(x) = x1, then
f(g(x)) = ?
will give brainliest answer !!
Answer: 1, -2, 1
Step-by-step explanation:
[tex]f(g(x))=f(x-1)=(x-1)^{2}=x^{2}-2x+1[/tex]
Choose True or False, (T or F). Grouped data is a data that has not been organized into intervals.
The statement "Grouped data is a data that has not been organized into intervals" is false.
Data presented in class intervals, such as 0-20, 20-40, and so on, is referred to as "grouped data."
Ungrouped data is information presented as individual values or integers, such as 15, 63, 34, 20, 25, and so on.
Assume we have a set of data with values between 0 and 50, such as 2, 17, 0, 1, 8, 19, 43, 2, 1, 32, and so on. In this situation, we may divide the data into categories like 0-10, 10-20,...,40-50. The data in this case are simply grouped.
Hence, the statement "Grouped data is a data that has not been organized into intervals" is false.
Learn more about grouped data here-
brainly.com/question/6759188
#SPJ10
Help !! I’ll mark brainliest !!
Answer:
9
Step-by-step explanation:
The opposite sides of a parallelogram are congruent.
Answer:
9
Step-by-step explanation:
Parallel sides are always equal. :)
What is the solution of the following system?
Use the substitution method.
{3x+2y=11x−2=−4y
A.) The only solution is (12, - 5/2)
B.) The only solution is (4, - 1/2)
C.) There is no solution
D.) There are an infinite number of solutions
Answer:
B.) The only solution is (4, - 1/2)
Step-by-step explanation:
To solve this system of equations using the substitution method, we need to use one equation to find an expression for one of the terms or variables that can be substituted for that term or variable in the other equation.
__
expression for xHere, it is convenient to use the second equation to write an expression for x:
x -2 = -4y
x = 2 -4y . . . . add 2 to both sides
substituteUsing this expression for x, we can write the second equation as ...
3x +2y = 11
3(2 -4y) +2y = 11 . . . . . substitute for x
6 -10y = 11 . . . . . . . . eliminate parenthses
solveThis 2-step equation can be solved in the usual way:
-10y = 5 . . . . . . . subtract the constant to isolate the variable term
y = -5/10 = -1/2 . . . . . divide by the coefficient of the variable
x = 2 -4(-1/2) = 2 +2 = 4 . . . . . find the corresponding x-value
The only solution is (x, y) = (4, -1/2).
The only solution is (x, y) = (4, -1/2). so, the correct option is B.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
we have the system of equations;
3x+2y=11
x−2=−4y
By the substitution method;
use the second equation to write an expression for x:
x -2 = -4y
x = 2 -4y
substitute
3x +2y = 11
3(2 -4y) +2y = 11
6 -10y = 11
solve
-10y = 5
y = -5/10 = -1/2
x = 2 -4(-1/2)
x = 2 +2 = 4
Thus, The only solution is (x, y) = (4, -1/2). so, the correct option is B.
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ1
Terry brings home $14 per hour he works. When he started this job, he had
$40 in the bank. Write and graph the equation that would represent how
much money Terry has in the bank (y) after x hours of work. Identify the x-
and the y-intercepts. Do they make sense in this context. If so, what do they
tell us about Terry's situation? Find the point (3, 82) on the graph. What does
that point represent in the context of Terry's situation?
The point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.
Given that, Terry brings home $14 per hour he works. When he started this job, he had $40 in the bank.
We need to write and graph the equation that would represent how much money Terry has in the bank (y) after x hours of work.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, y=40+14x
Graph the line using the slope and y-intercept, or two points.
Slope: 14
y-intercept: (0, 40)
The coordinates to plot the graph are (0, 40), (1, 54), (2, 68) and (3, 82).
The graph for the given equation is given below.
Therefore, the point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
g(x) f(x) = −6x − 3 cosine function with y intercept at 0, negative 3 h(x) = 2 cos(x + π) − 1 Using complete sentences, explain which function has the greatest y-intercept. (10 points)
full step by step process please.
A function assigns the values. The function that has the greatest y-intercept is h(x).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
There are three function, g(x){given in the graph below}, f(x)= -6x-3, and -3h(x) = 2 cos(x + π) − 1, the y-intercept of the function is the point at which the graph intersects the y-axis. Therefore, the y-intercept are,
g(x) = -3
f(x) = -3
h(x) = 1
Hence, the function that has the greatest y-intercept is h(x).
Learn more about Function:
https://brainly.com/question/5245372
#SPJ1
Drag each tile to the correct box.
Using the order of operations, what are the steps for solving this expression?
Step-by-step explanation/Answer:
PE(MD)(AS) (a good way to remember how to solve order of operations)
Start:
P: Parenthesis
E: Exponent
M: Multiplication & D: Division
A: Addition & S: Subtraction
:End
*Multiplication and Division are grouped together because they are on the same level, you decide which to do first depending on which comes first in the equation. The same applies for addition and subtraction.
So:
first thing we can look is the parenthesis, but before we can solve the whole thing we must notice the exponent only on the four. Since it is inside the parenthesis we must solve it first.
1. 4^2 = 16
now we will solve the addition inside the parenthesis
2. 16-13 = 3
now lets continue with pemdas, no more parenthesis so we tackle exponents
3. 5^2 = 25
Lets rewrite our equation with the changes we have made
8 × 3 ÷ 3 + 25 + 4 × 3
Now we solve multiplication and division
Equations is worked left to right, like english is read, so we will start on the left side and continue to the right, only solving multiplication and division.
4. 8 x 3 = 24
5. 24 ÷ 3 = 8
6. 4 x 3 = 12
new equation: 8 + 25 + 12
now we can use addition and subtraction (no subtraction luckily!)
7. 8 + 25 = 33
8. 33 + 12 = 45
Given a_4=135\;and\;a_6=1215a
4
=135anda
6
=1215, find the explicit rule for the geometric sequence, given that the common ratio is positive.
Answer:
Step-by-step explanation:
let a be first term and r be c.r.
a_{n}=ar^{n-1}
a_{4}=ar^{4-1}=ar^3=135
a_{6}=ar^{6-1}=ar^5=1215a_{4}=1215 \times 135
divide
r^2=1215
r=√1215=35
a_{n}=35 a_{n-1}
Given log base 2 =1/6, what is log base 4
Answer:
log x to the base 2 +log x to the base 4 =2
or log x/ log 2+ log x /lig 4 =2
or log x /log2 + log x /2.log 2 = 2
or log x/log 2(1+1/2)= 2
or log x/log 2 = 4/3
or 3.log x =4.log2
or logx^3=log 2^4
or x^3= 2^4
or x =(2)^4/3 or 2.(2)^1/3 ,Answer.
hope this helps
Step-by-step explanation:
A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which there
were 2039 class attendees. The data is summarized in the table below.
Class Type and Member Status of Class
Attendees
Class Type
Barre
Boot Camp
Boxing
Spinning
Yoga
Member
.240
204
288
191
177
Non-Member
185
155
234
271
94
What is the probability that a class attendee is a non-member of the gym and is attending a barre class or is a member of the gym and is attending a boot camp class?
Enter a fraction or round your answer to 4 decimal places, if necessary.
The probability that a class attendee is a non-member of the gym and is attending a barre class or is a member of the gym and is attending a boot camp class is 0.009.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The marketing team has gathered data from a random month, in which there were 2039 class attendees.
The probability that a class attendee is a non-member of the gym and is attending a barre class
= 185/2039
= 0.09
The probability that a class attendee is a member of the gym and is attending a boot camp class
= 204/2039
= 0.10004
The probability for both the event would be
= 0.09 x 0.10004
= 0.009
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ1
Which ordered pair is a solution of the equation?
y=4x−7
Answer:
Unknown
Step-by-step explanation:
Hi! so you didn't add the ordered pair options but I will do my best :) so if you see the ordered pair (0.7) that could definitely be a solution because using the slope intercept form equation you gave I know that's our y Intercept. the slope is 4/1 so moving up 4 and to the right 1 or down 4 and to the left 1 on a graph could show you more points! If you don't want to draw it you could use Desmos and just put this equation in or give me the ordered pairs and I will give you your answer!
hope this helps :)
15 points help! Select the correct answer from the drop-down menu.
Consider the equation (x^m)³ = (113)5 x(x−8)—5
The value of mis
Reset
Next
Answer:The value of m for the given equation is, 35
Step-by-step explanation:
Given an equation: https://tex.z-dn.net/?f=x%5E%7B3m%7D%3D(x%5E%7B65%7D)*(x%5E%7B40%7D)
Use the above property on RHS in equation [1];
Since the base are same i.e, x ; we can add the exponents.
or
Using: , then a=b.
Therefore, 3m=105.
Divide 3 on both sides of an equation:
Simplify:
m=35
Therefore, the valur of m is, 35.
