Please help 20 POINTS. Problem below
An even function is when f(x) = f(-x) ... or ... g(x) = g(-x).
f(x) = - (x + 1)(x - 4)
= -(x² - 3x - 4)
= -x² + 3x + 4 f(x) = -x² + 3x + 4
f(-x) = -(-x)² + 3(-x) + 4
= -x² - 3x + 4 f(-x) = -x² - 3x + 4
f(x) ≠ f(-x) so it is NOT even.
********************************************************
g(x) = [tex]\frac{3}{2}|x|[/tex]
g(-x) = [tex]\frac{3}{2}|-x|[/tex]
= [tex]\frac{3}{2}|x|[/tex] since absolute value becomes positive
g(x) = g(-x) so it IS even
Answer: C
The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 20% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of nine adult friends, what is the probability of the following?
Given that about 20% of adults do one time fling.
That is probability of a person doing fling is [tex]\frac{20}{100}=0.2[/tex] . Let it be p.
Then we have to use binomial distribution formula for the given problems.
b(x;n,p)=[tex]n_{C_{x}}p^{x}(1-p)^{n-x}[/tex]
A)Probability of no one has done one time fling means x is 0 here.
Hence [tex]b(0;9,0.2)=9_{C_{0} }(0.2)^{0}(1-0.2)^{9}[/tex]
[tex]=1X1X0.8^{9}=0.1342[/tex]
b) Probability of at least one person has done fling=1-(probability of no one has done)
=1-0.1342=0.8658
c)Probability of no more than two people have done one time fling means we need to add the probabilities for x=1,x=2 along with x=0.
[tex]b(1;9,0.2)=9_{C_{1}}(0.2)^{1}(1-0.2)^{8}[/tex]
[tex]=9X0.2X0.8^{8}=0.302[/tex]
[tex]b(2;9,0.2)=9_{C_{2}}0.2^{2}(1-0.2)^{7}[/tex]
[tex]=36X0.04X0.8^{7}=0.302[/tex]
Hence probability = 0.1342+0.302+0.302 = 0.7382
Translate this sentence into an equation. 32 is the product of Mabel's age and 2 . Use the variable m to represent Mabel's age. URGENT
To translate the given sentence into an equation, use the equation 2m = 32 and then divide both sides by 2 to solve for Mabel's age, which is 16 years old.
The sentence '32 is the product of Mabel's age and 2' can be translated into an equation using the variable m to represent Mabel's age. The product of two numbers means you multiply them together. We are given that when you multiply Mabel's age by 2, you get 32. The equation that represents this relationship is:
2m = 32
To find Mabel's age, we simply divide both sides of the equation by 2 to isolate m, which gives us:
m = 32 / 2
m = 16
Mabel's age is 16 years old.
2x-5=x+25 what is the answer for x because am stuck
2x - 5 = x + 25
-x -x
x - 5 = 25
+5 +5
x = 30
Answer: x = 30
Three roads lead into a stadium's parking areas. Each road has four lanes (two in each direction) with a capacity oftwo parking attendants are required to park cars for each type a lot, while just one can handle each type b lot. Of the ten lots that will be used tonight, six are type a and four are type b. How many parking attendants are required for tonight's event?1,00vehicles/lane/hour. If 10,000 vehicles are expected for a game, how long will it take for all of them to enter the parking areas?
In this scenario, the combined capacity of the three roads leading to the stadium is 12,000 vehicles per hour. Therefore, to park 10,000 vehicles, it would take approximately 50 minutes.
Explanation:The question involves an understanding of traffic flow and rates. To find the total capacity of these roads leading to the stadium, we multiply the number of roads by the number of lanes on each road and the capacity of each lane, resulting in 4 lanes per road x 3 roads x 1,000 vehicles per lane per hour, equal to 12,000 vehicles per hour.
With 10,000 vehicles expected for the game, we can then divide the total number of vehicles by the total capacity of the roads per hour to find out how many hours it will take for all vehicles to enter the parking lots. Therefore, it will take approximately 10,000 vehicles / 12,000 vehicles per hour = 0.83 hours, or about 50 minutes.
The increased traffic due to a new manufacturing plant, increased businesses, and route changes in the nearby streets can also affect the traffic flow, however these factors are not quantified in the question. In the real world, proper planning and infrastructure can solve campus parking issues, as the example mentioned about Twelfth and Locust Streets.
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Add using a number line 5/6 plus - 1 1/6
Start at 5/6 on the number line. Move 11/6 spaces to the left (11/6 is negative; if you are adding a negative number, move to the left). You should land on -1.
Richard can read 1/4 of a book in 4/5 of an hour.At this rate ,how much can richard read in one hour
Assuming that Richard always reads with the same rate, there is a direct proportion between the time spent reading and the portion of book read:
[tex] \text{portion}_1 : \text{time}_1 = \text{portion}_2 : \text{time}_2 [/tex]
So, we can set up and solve the following proportion:
[tex] \dfrac{1}{4} : \dfrac{4}{5} = x : 1 \iff x = \dfrac{\frac{1}{4}}{\frac{4}{5}} = \dfrac{1}{4}\cdot \dfrac{5}{4} = \dfrac{5}{16} [/tex]
HELP WILL GIVE BRAINLIEST! 45 POINTS IF YOU GIVE CORRECT ANSWER!!!!
Among the following arithmetic operations, which could the symbol □ represent given that the equation is (2□1)4+(6□3)2=10
1. Addition
2. Subtraction
3. Division
It would be subtraction because 2-1 would result into 1 multiplied by 4 would make 4 your answer. And then 6-3 would equal to 3, multiply 3 by 2, you would get 6. Then finally when you add both 4 and 6, you would get the final answer of 10.
item 6 for what value of a is 8x−8+3ax=5ax−2a an identity?
Let's rewrite the expression as
[tex] 8x+3ax-5ax = 8-2a \iff 8x - 2ax = 8-2a \iff 2x(4-a) = 2(4-a) [/tex]
So, if [tex] a \neq 4 [/tex], you may divide both sides by [tex] 4-a [/tex], the equation becomes [tex] 2x=2 [/tex], and the only solution is [tex] x=1 [/tex], which means that this is not an identity (an indentity is tautologically true, no matter the value of x).
If instead [tex] a = 4 [/tex], you are multiplying both sides by zero, so the equation becomes
[tex] 2x \cdot 0 = 2 \cdot 0 \iff 0=0 [/tex]
So, it doesn't matter which value for x you choose, because you will always end up with [tex] 0=0 [/tex], which is obviously always true.
Paula is training take part in a fun run fir charity. Paula weighed 65.5 kilogram before she started her training. She has list 3500grams, how much does she weigh now in kilogram
is the relation a function?
(3,6)
(10,13)
(11,1)
(13,6)
A.Yes
B.No
Answer:
A
Step-by-step explanation:
yes
On Monday, Torrance practiced the violin for 4/10 of an hour. On Tuesday, he practiced for 1 6/8 of an hour. How much time did he practice in all?
Answer: [tex]2\frac{3}{20}[/tex]
Step-by-step explanation:
First, convert mixed numbers into improper fractions and simplify all fractions
[tex]\frac{4}{10}[/tex] ÷ [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{5}[/tex]
[tex]1\frac{6}{8}[/tex] = [tex]\frac{8(1) + 6}{8}[/tex] = [tex]\frac{14}{8}[/tex] ÷ [tex]\frac{2}{2}[/tex] = [tex]\frac{7}{4}[/tex]
Next, find their sum. Remember to find the LCD and convert the fractions so they have like denominators.
Monday + Tuesday = Total
[tex]\frac{2}{5}[/tex] + [tex]\frac{7}{4}[/tex] = Total the LCD of 5 and 4 is 20
[tex](\frac{4}{4})\frac{2}{5}[/tex] + [tex](\frac{5}{5})\frac{7}{4}[/tex] = Total
[tex]\frac{8}{20}[/tex] + [tex]\frac{35}{20}[/tex] = Total
[tex]\frac{43}{20}[/tex] = Total
Then, convert the improper fraction into a mixed number
[tex]\frac{43}{20}[/tex] = [tex]2\frac{3}{20}[/tex]
Charlie receives an email from his brother every 4th day and from his sister every 7th day. When will he receive an email from both on the same day?
I'm pretty sure its the 28th day?? If not let me know.
60 POINTS FOR THE THISS!!!
Does the following table show a proportional relationship between the variables x and y?
There is a certain pattern:
As x is increased by 1/4 every time, y is increased by 3 every time. You can make a proper ratio and set up proportions with these numbers.
Please Help It Is Past Due!
Prove the Pythagorean Theorem using similar triangles. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse. Be sure to create and name the appropriate geometric figures.
Explanation:
First we consider ΔABC and ΔBCD,
∠C=∠C (common)
∠B=∠D=[tex]90\textdegree[/tex]
So, ΔABC ≈ ΔBCD (By AA similarity rule )
So by taking corresponding sides in ratios we get
[tex]\frac{AB}{BD}=\frac{AC}{BC}=\frac{BC}{CD}[/tex]
Now
[tex]AC.CD=BC.BC\\BC^{2} =AC.CD[/tex] -------- Eqn (1)
Similarly,
We consider ΔABD and ΔABC
∠A=∠A (Commom)
∠B=∠D=[tex]90\textdegree[/tex]
So,
ΔABD ≈ ΔABC (By AA similarity rule )
So by taking corresponding sides in ratios we get
[tex]\frac{BC}{BD}=\frac{AC}{AB}=\frac{AB}{AD}[/tex]
Now,
[tex]AB.AB=AC.AD\\AB^{2} =AC.AD[/tex] --------Eqn (2)
By Adding both the equation we get
[tex]AB^2+BC^2=AC.CD+AC.AD\\AB^2+BC^2=AC(CD+AD)\\AB^2+BC^2=AC.AC\\AB^2+BC^2=AC^2[/tex]
Hence, we proved the pythagorean theorem by using similarity of triangle.
Select the postulate of equality or inequality that is illustrated.
Answer: Comparison Postulate
This is the idea that exactly one statement shown below is true
a > b
a = b
a < b
So if you compare two numbers, then either the left value is larger, the left is smaller, or the the left is the same as the value on the right.
what is the domain and range?
{(4,2), (-9,2), (5,4), (4,17)}
Answer:
Domain = {4,-9,5}
Range = {2,4,17}
Step-by-step explanation:
We are given ordered pairs as
{(4,2), (-9,2), (5,4), (4,17)}
This is a subset of cartesian product AXB where
A = {4,-9,5} and B = {2,4,17}
Note: Repeated values are written only once in the set.
Hence we find that 4 is mapped on to 2 and 17,
-9 to 2 and 5 to 4
Domain = I item in the ordered pair of mapping = {4,-9,5}
Range = II item in the ordered pair of mapping = {2,4,17}
Hey there!!
What is a coordinate form?
... Coordinate form is written as ( x , y )
What is domain?
... Domain are also called as the 'x' values.
What is the range?
... Range is the other word for the 'y' values.
Given ordered pairs :-
( 4 , 2 ) ; ( -9 , 2 ) ; ( 5 , 4 ) ; ( 4 , 17 )
Hence, the domain is :-
... { 4 , -9 , 5 )
Hence, the range is :-
... { 2 , 4 , 17 )
Remember :- The values "can not" be repeated!
Hope my answer helps!!
Use the graph for Parts A and B....
It is a function. It passes the vertical line test, meaning for each x there's at most one y.
When x=2 we see y=-3 as (2,-3) is a point on the graph
The question's subject is about interpreting and representing data using different types of graphs. Each type of graph is chosen based on what we want to show with our data. For instance, line graphs are useful for displaying change over time.
Explanation:The question refers to the use of graphs to illustrate data. These graphs represent the position of a moving object plotted against time. In the presented case, Part A of the graph begins with a nonzero y-intercept with a downward slope that levels off at zero, while Part B begins at zero with an upward slope that decreases in magnitude until the curve levels off.
When creating graphs, it's important to label the axes correctly and, if multiple datasets are shown on one graph, various symbols should be used to differentiate between them. In the example given, three types of graphs can be used: a line graph to show change over time, a bar graph to compare different categories, and a pie chart to represent proportions. The choice of graph depends on the type of data and what you want to show.
As mentioned, a graphing utility allows us to compare trajectories, highlighting the differences and similarities. It is crucial to use that visualization and analysis tool to make effective interpretations.
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What is greater one inch or one centimeter
One inch is greater than centimeter
Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.
Answer: k = -1 +/- √769
Step-by-step explanation:
48x - ky = 11
-48x -48x
-ky = -48x + 11
[tex]\frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}[/tex]
[tex]y =\frac{48x}{k} - \frac{11}{k}[/tex]
Slope: [tex]\frac{48}{k}[/tex]
*************************************************************************
(k + 2)x + 16y = -19
- (k + 2)x -(k + 2)x
16y = -(k + 2)x - 19
[tex]\frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}[/tex]
[tex]y = -\frac{(k + 2)x}{16} - \frac{19}{16}[/tex]
Slope: [tex]-\frac{(k + 2)}{16}[/tex]
**********************************************************************************
[tex]\frac{48}{k}[/tex] and [tex]-\frac{(k + 2)}{16}[/tex] are perpendicular so they have opposite signs and are reciprocals of each other. When multiplied by its reciprocal, their product equals -1.
[tex]-\frac{(k + 2)}{16}[/tex] * [tex]\frac{k}{48}[/tex] = -1
[tex]\frac{(k + 2)k}{16(48)}[/tex] = 1
Cross multiply, then solve for the variable.
(k + 2)(k) = 16(48)
k² + 2k - 768 = 0
Use quadratic formula to solve:
k = -1 +/- √769
Solve for x. y=bx+a Enter your answer in the box.
Answer:
The value of the equation is [tex]x=\frac{y-a}{b}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]y=bx+a[/tex]
We need to solve the provided equation for x.
Subtract a from both side.
[tex]y-a=bx+a-a[/tex]
[tex]y-a=bx[/tex]
Divide both sides by b.
[tex]\frac{y-a}{b}=\frac{bx}{b}[/tex]
[tex]x=\frac{y-a}{b}[/tex]
Hence, the value of the equation is [tex]x=\frac{y-a}{b}[/tex].
The variable 'x' as the subject of the formula of the equation y = bx + a is x = ( y - a )/b.
How to make 'x' the subject of the formula of the equation?Given the equation in the question:
y = bx + a
To make the variable 'x' the subject of the formula of the equationy = bx + a, first isolate term with the variable 'x'.
y = bx + a
To isolate the term containing variable 'x', first subtract 'a' from both sides of the equation:
y - a = bx + a - a
y - a = bx
Reaorder:
bx = y - a
Now, divide both sides by 'b':
bx/b = ( y - a )/b
x = ( y - a )/b
Therefore, the variable 'x' equals ( y - a )/b.
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I'd really appreciate it if anyone helped! :)
What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=−3+|x|?
Horizontal translation of 3 units left
Vertical translation of 3 units up
Vertical translation of 3 units down
Horizontal translation of 3 units right
Vertical translation of 3 units down
the graph of g(x) = - 3 + | x| is the graph of f(x) = | x| moved 3 units down ( - 3 ) vertically
Ube had made a banana cream pie. His brother he 1/3 of a pie and his sister had 2/5 of the pie how much less did his brother eat than his sister
Least common multiple of 26,39 using prime factorization
26 is a multiple of 2 but 39 isn't
39 is a multiple of 3 but 26 isn't
Dividng by the next three prime numbers, neither 26 nor 39 is a multiple of 5, 7, or 11
Moving up to the sixth prime number (13), we see that BOTH 26 and 39 are divisible by 13. 26 = 2 * 13 and 39 = 3 * 13 and 13 is the lowest common multiple of 26 and 39.
Candle food is on sale for 20% of the original price what is the discount of the key if the original price is $1.35
Hi there!
To calculate a discount or a mark-up in the price of a retail item, you need to multiply the given price of the item by the percentage, like so:
1.35 × 0.2 = 0.27
Then you add or subtract as necessary. In your case you would subtract since you are trying to find a discount price.
1.35 - 0.27 = 1.08
So the final price of the product after the discount is $1.08
Your friend, ASIAX
Carrie spent
1
4
of her allowance on a shirt,
1
3
of her allowance on a skirt, and $8 on a belt. If she spent $22 in all, how much was Carrie’s allowance?
Equation:
1
4
a +
1
3
a + 8 = 22
Carrie’s allowance was $
.
24 dollars.
1/4 + 1/3 = 3/12 + 4/12 = 7/12
7/12 a + 8 = 22
7/12 a = 14
a = 14 x 12/7
a = 24 dollars
HELP HELP HELP DUE TODAY PLEASEEE WILL GIVE ANYTHING
What is the recursive rule for the sequence?
4.4, 5.8, 7.2, 8.6, 10, …
an=an−1−1.4 , where a1=4.4
an=an+1+1.4 , where a1=4.4
an=an+1−1.4 , where a1=4.4
an=an−1+1.4 , where a1=4.4
Answer:
a_n=a_(n−1)+1.4 , where a_1=4.4
Step-by-step explanation:
Given a sequence as
4.4, 5.8, 7.2, 8.6, 10, …
We find that first term is 4.4
II term = 5.8 = 4.4+1.4
III term = 7.2 = 5.8+1.4
Iv term = 8.6 = 7.2+1.4
V term = 10.0 = 8.6+1.4
i.e. each term is got by adding 1.4 to the previous term.
In other words, this is an arithmetic sequence with I term =4.4 and d = common difference =1.4
I term = a_1 = 4.4
and a_2 = a_1+1.4 and so on.
Hence correct answer is
a_n=a_(n−1)+1.4 , where a_1=4.4
At a pet store ,davina counted 12parrots out of 20 birds ,which is an equivalent ratio of parrots to birds at the pet store
Every 3 Parrots there will be 5 Birds
3/5
Answer:
Every 3 Parrots there will be 5 Birds
3/5
Step-by-step explanation:
The distance between the baseball stadium and the airport is 1.6×10^6 centimeters.Which unit of measurement is most appropriate to measure this distance?
Answer:
'Kilometers' is the most appropriate unit to measure this distance.
Step-by-step explanation:
The distance between the baseball stadium and the airport is [tex]1.6\times 10^6[/tex] centimeters.
[tex](1.6\times 10^6)cm = (16\times 10^5)cm[/tex]
Now, 10⁵ centimeters is equal to 1 kilometer.
That means, [tex](16\times 10^5)cm = (16\times 1)km= 16 km[/tex]
So, 'Kilometers' is the most appropriate unit to measure this distance.
. Anna gets paid $8.75/hour working as a barista at Coffee Break. Her boss pays her
$9.00/hour for creating the weekly advertisement signs. She works a total of 25
hours each week.
a. Let x represent the hours that Anna works each week as a barista.
Write a function ℎ(x) to represent the amount of money that Anna earns working as
a barista.
b. Write a function, f(x) to represent the hours Anna works creating the signs.
c. Let s represent the number of hours that Anna works creating the signs.
Create a function g(s) to represent the money Anna earns creating the signs.
d. Find g( f(x) ). What does this composite function represent?
e. What functions could be combined to represent Anna’s total earnings?
Combine the functions to write an expression that can be used to represent
Anna’s total earnings, where x represents the number of hours she works as a
barista
Explanation:
Anna gets paid $8.75/hour working as a barista.
She gets paid $9.00/hour for creating weekly advertisement signs.
In total she works 25 hours a week.
Let 'x' represent the number of hours that she works as a barista, then [tex]25-x[/tex] would represent the number of hours she works to create signs.
A. We need to write a function h(x) that represents the amount of money that Anna earns working as a barista.
Since she is earning $8.75 per hour and she works as a barista for 'x' hours a week so the function is:
[tex]h(x)=8.75\times x=8.75x[/tex]
[tex]h(x)=8.75x[/tex]
B. We need to write a function f(x) to represent the hours Anna works creating the signs.
Since, in total she works for 25 hours a week so the function to represent the number of hours she work to create signs can be given by:
[tex]f(x)=(25-x)[/tex]
C. If 's' represents the number of hours that Anna works creating signs, we need to create a function g(s) that represents her earning creating signs.
So the number of hours Anna works creating signs for the coffee break is [tex]s[/tex], she gets paid $9.00 an hour for creating signs, so:
[tex]g(s)=9\times s=9s[/tex]
[tex]g(s)=9s[/tex]
D. We need to finf a composite function [tex]g(f(x))[/tex], to find the desired function we need to plug value of f(x) in the function g(s):
[tex]g(f(x))=9s=9(f(x))=9(25-x)=225-9x[/tex]
[tex]g(f(x))=225-9x[/tex]
The composite function g(f(x)) represents Anna's earnings while working just to create signs for the Coffee break.
E. To represent Anna's total earnings the functions that can be combined are h(x) and g(f(x)) because h(x) represents Anna's earnings while working as a barista and g(f(x)) represents Anna's earnings while she creates signs for the coffee break.
The function to represent Anna's total earnings can be given as:
[tex]T(x)=h(x)+g(f(x))=8.50x+225-9x[/tex]
where we must keep in mind that 'x' represents the number of hours she spent working as a barista in a 'week'.