Monthly salary = $1120
Comission percentage = 14%
Janet's sales = $94,100
1. Amount of commission
Multiply the sales amount (94,100) by the Commission percentage in decimal form (divided by 100).
94,100 x (14/100) =
94,100 x 0.14 = $13,174
2. Gross pay
Add the amount of commission and the monthly salary:
13,174+1120 = $14,294
What are the solutions to the equation ? e^1/4x = (4x) [tex]e^1/4x =abs( 4x)[/tex](Round to the nearest hundredth). The solutions are about x = and
The solution of the equation e^(x/4) = |4x| for the x by graphical approach is 0.27 and -0.24.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
A formula known as an equation uses the same sign to denote the equality of two expressions.
As per the given expression,
e^(x/4) = |4x|
The function e^(x/4) is an exponential function and the plot of this function has been plotted below.
The mode function |4x| has also been plotted below.
The point of intersection is the point where both will be the same or the solution meets.
The first point of intersection is (0.267,1.0691) so x = 0.267 ≈ 0.27
The second point of intersection (-0.2357,0.9428) so x = -0.2357 ≈ -0.24
Hence " The solution of the equation e^(x/4) = |4x| for the x by graphical approach is 0.27 and -0.24.".
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[tex]((1.25 \times {10}^{ - 15} ) \times (4.15 \times {10}^{25} )) \div ((2.75 \times {10}^{ - 9}) \times (3.4299 \times {10}^{8} ))[/tex]solve. final answer in scientific notation
done
[tex]\text{result = 5.4999 x 10}^{10}[/tex][tex]Inscientificnotation=5.4999x10^0[/tex]Finding a specify term of a geometric sequence given the common ratio and first term
A geometric sequence is defined as:
[tex]\begin{gathered} a_1=a*r^0=a*r^{1-1}, \\ a_2=a*r^1=a*r^{2-1}, \\ a_3=a*r^2=a*r^{3-1}, \\ ... \\ a_7=a*r^6=a*r^{7-1}, \\ ... \end{gathered}[/tex]Where r ≠ 0 is the common ratio and a ≠ 0 is the first term of the sequence.
From the statement, we know that r = 2/3 and the first term is a = 5.
Replacing these numbers in the expression of the 7th term, we get:
[tex]a_7=5*(\frac{2}{3})^6=5*\frac{64}{729}=\frac{320}{729}.[/tex]Answer320/729
Hello! Need some help on part c. The rubric, question, and formulas are linked. Thanks!
Explanation:
The rate of increase yearly is
[tex]\begin{gathered} r=69\% \\ r=\frac{69}{100}=0.69 \end{gathered}[/tex]The number of lionfish in the first year is given beow as
[tex]N_0=9000[/tex]Part A:
To figure out the explicit formula of the number of fish after n years will be represented using the formula below
[tex]P(n)=N_0(1+r)^n[/tex]By substituting the formula, we will have
[tex]\begin{gathered} P(n)=N_{0}(1+r)^{n} \\ P(n)=9000(1+0.69)^n \\ P(n)=9000(1.69)^n \end{gathered}[/tex]Hence,
The final answer is
[tex]f(n)=9,000(1.69)^n[/tex]Part B:
to figure out the amoutn of lionfish after 6 years, we wwill substitute the value of n=6
[tex]\begin{gathered} P(n)=9,000(1.69)^{n} \\ f(6)=9000(1.69)^6 \\ f(6)=209,683 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow209,683[/tex]Part C:
To figure out the recursive equation of f(n), we will use the formula below
From the question the common difference is
[tex]d=-1400[/tex]Hence,
The recursive formula will be
[tex]f(n)=f_{n-1}-1400,f_0=9000[/tex]WhichIs 9.56556555... a rational or irrationalnumber? Highlight the correct answer below.181a)Whicha) Rational numberb) Irrational numberthat ap
Answer
Option B is correct.
9.56556555... is an irrational number.
Step-by-step Explanation
Rational numbers are numbers that can be expressed as a clear fraction consisting of the numerator and the denominator both being integers.
The decimal form or decimal expansion of a rational number terminates after a particular/finite number of digits (e.g., 0.25, 0.762 etc.) or begins to repeat/recur the same sequence over and over again (e.g., 0.333..., 0.267267... etc)
Anything other than these two rules, the number is regarded as an irrational number.
The number given is 9.56556555...
The dots indicate thst the numbers after the decimal point conbtinue till eternity.
Observing the numbers after the decimal point for the given number, one can see that 565 repeats once and then the number after the second 565 is 55, indicating that the 565 doesn't recur till infinity.
Since the numbers after the decimal point doesnt contain a finite number of digits and the numbers don't recur till infinity, we can conclude that 9.56556555... isn't a rational number.
Hope this Helps!!!
Find the common difference and the recursive formula. 22,19,16,13
The common difference between each term is -3.
19 - 22 = -3
16 - 19 = -3
13 - 16 = -3
The recursive formula of an arithmetic sequence follows the pattern below:
[tex]a_n=a_{n-1}+d,n\ge2[/tex]where d = common difference and number of terms "n" must be more than or equal to two.
To be able to get the recursive formula, we will plug in the common difference assuming that first term a₁ = 22. Therefore, the recursive formula is:
[tex]a_n=a_{n-1}-3,for\text{ n}\ge2[/tex]Find the length of line segment MN. Round to the nearest hundredths place.
First, look th the graph and set the coordinate of the points:
M = (mx,my)= (-1,2)
N = (nx,ny)= (4,0)
Now, apply the distance formula:
[tex]\text{Distance =}\sqrt[]{(mx-nx)^2+(my-ny)^2}[/tex]Replace with the coordinates:
[tex]D\text{ =}\sqrt[]{(-1-4)^2+(2-0)^2}[/tex][tex]D=\sqrt[]{(-5)^2+2^2}=\sqrt[]{25+4}=\sqrt[]{29}\text{ =5.3}9[/tex]Distance: 5.39
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
perimeter: add p + m + n
area: use (p × m)/2
find missing side: use p^2 + m^2 = n^2
What is the constant of proportionality of x 0 4 8 12 y 0 3 6 9
Answer:
3/4
Step-by-step explanation:
As y is changing by 3, x is changing by 4
hi can you see if I did this estimate right?
Mr Manet need 5 guitars for his 4 grandsons and 1 granddaughter.
Each guitar costs $88,
So the total cost of guitars is $88 x 5 = $440
The best estimate among the choices is Choice B. $450
The estimate should always be higher than the actual cost.
could you help me no other tutor will help and its heartbreaking so please try your hardest
The triangle has sides
a=8
b=14
c=19
You need to determine the measure of x
To determine the value of x you have to use the Law of Cosines that states that:
[tex]a^2+b^2-ab\cos \theta=c^2[/tex]Where a, b, and c are the sides of the triangle, and theta represents the angle we are looking for.
So first step is to replace the formula with the given data and solve the exponents
[tex]\begin{gathered} 8^2+14^2-8\cdot14\cos thetha=19^2 \\ 64+196-112\cos \theta=361 \\ 260-112\cos \theta=361 \end{gathered}[/tex]Next solve for the cosine of theta:
[tex]\begin{gathered} -112\cos \theta=361-260 \\ -112\cos \theta=101 \\ \cos \theta=\frac{101}{-112} \\ \cos \theta=-\frac{101}{112} \end{gathered}[/tex]And calculate the inverse cosine to determine the measure of the angle
[tex]\begin{gathered} \theta=\cos ^{-1}(-\frac{101}{112}) \\ \theta=154.39 \end{gathered}[/tex]Given the figure below, determine the angle that is a same side interior angle with respect to
We remember that two interior angles are those inside the are of the lines, Thus, the angles in the area:
Are interior. Now, we identify two sides, the right side, and the left side, which have been separated by the transversal line.
Thus, the angle that is is the same side as ∡3, and also that is interior is ∡5.
Help please!!!!!!!!!!!!!!!!!!!!!!!!!Which is the best buy?a. $18.09 for 9 bottles of juiceb. $22.33 for 11 bottles of juice
Answer:
The correct option is option a.
$18.08 for 9 bottles is the better buy.
Explanation:
The best buy is the item with the lesser price tag.
Let us chech which of the given items has the lesser price tag.
a. $18.08 for 9 bottles of juice
Let us find how much one bottle costs.
1 bottle = 18.08/9
= 2.01
1 bottle of juice costs $2.01 approximately
b. $22.23 for 11 bottles of juice
1 bottle = 22.23/11
= 2.03
1 bottle of juice costs $2.03 approximately.
Comparing these prices per bottle of juice, we realise that the one with $18.08 for 9 bottles is the better buy.
How many different arrangements of letters can be formed if the letter must be repeats of letters are allowed?
Solution:
There is 2 possibility for the first letter from the left.
Then there are 2 possibilities for the second letter. Then and so on till the 5-th letter.
In this way, you will get
[tex]2^{5\text{ }}=32[/tex]Each is unique, and each is achievable in this way.
There are no other arrangements. So that, we can conclude that the correct answer is:
[tex]32[/tex]
The pie chart below shows the percentage of total revenue that a publisher receives from publications.A) which category accounts for approximately 1/5 of publishers total revenue type in which one (textbooks, cookbooks, magazines, paperbacks,poetry, nonfiction B)Approximately percentage total revenue from paperbacks poetry combined C) if revenue from nonfiction 10% total revenue approximately percentage total comes from poetry
a) To determine which category represents approximately one-fifth of the publisher's revenue, you can compare the given pie chart with a pie chart divided into 5 parts.
The category that is approximately one-fifth of the revenue, that is, 20% of the total revenue, is textbooks.
To solve parts b and c you can use the following pie chart to compare with the given chart for the publisher's revenue:
b) Looking at the pie charts, the categories "paperback" and "poetry" are approximately 20% of the total revenue.
c) The category "Nonfiction" is 10% of the total revenue, the category "poetry" is approximately half of the size of the category "nonfiction" so you can say that it corresponds to 5% of the total revenue.
Eliminate the y in the following system of equations. What is the result when you add the two equations? [tex]x + y = 8 \\ 5x - 3y = 24[/tex]A: 6x = 32B: 8x = 32 C: x = 0D: 8x = 48
EXPLANATION
x + y = 8 ----------------------------------------(1)
5x - 3y = 24 ------------------------------------------(2)
If we are to eliminate y in the equations, we first need to multiply through equation (1) by 3.
3x + 3y = 24 ----------------------------------------(3)
Add equation (2) and equation (3).
If we add equation(1) and equation(3) together, -3y will cancel-out 3y.
(5x + 3x) = (24 + 24)
8x = 48
Therefore, the correct option is D. 8x = 48
I need help with a 8th-grade math assignment:China has a population of approximately 1,382,323,332 people. The United States has a population of about 324,118,787 people.Part AUsing scientific notation, give the approximation for each population. Round the first factor to the nearest tenth.China: United States: Part BAbout how many more people live in China than in the United States? Express your answer using scientific notation. Round the first factor to the nearest hundredth.
We have the next given information:
China has a population of approximately 1,382,323,332 people.
The United States has a population of about 324,118,787 people.
a) We need to use scientific notation which is given by the next form:
[tex]ax10^n[/tex]Where a is the coefficient rounded to the nearest tenth.
and a is the terms moved to the decimal point.
For China:
1382323332.0, we moved the decimal point nine spaces to the right.
then
1.382323332
Expressed in scientific notation and rounded to the nearest tenth:
[tex]1.4x10^9[/tex]For the United States:
324,118,787 with the decimal point 324,118,787.0
then
324118787.0
Move the decimal point 8 spaces to the right, then:
3.24118787
Expressed in scientific notation and rounded to the nearest tenth:
[tex]3.2x10^8[/tex]
Part b:
To find how many more people live in China than in the United States, we need to subtract between China and the United States:
Then:
1,382,323,332 - 324,118,787 = 1,058,204,545
Now
1,058,204,545 equal to 1058204545.0
We need to move the decimal point 9 spaces:
1.058204545
Expressed as scientific notation and rounded to the nearest hundredth:
[tex]1.06x10^9[/tex]solve p(x+q)^4=r for x
Given the following equation:
[tex]p\mleft(x+q\mright)^4=r[/tex]You can solve for the variable "x" as following:
1. You need to apply the Division property of equality by dividing both sides of the equation by "p":
[tex]\begin{gathered} \frac{p\mleft(x+q\mright)^4}{p}=\frac{r}{p} \\ \\ \mleft(x+q\mright)^4=\frac{r}{p} \end{gathered}[/tex]2. Remember that:
[tex]\sqrt[n]{a^n}=a[/tex]Then:
[tex]\begin{gathered} \sqrt[4]{(x+q)^4}=\sqrt[4]{\frac{r}{p}} \\ \\ x+q=\sqrt[4]{\frac{r}{p}} \end{gathered}[/tex]3. Now you have to apply the Subtraction property of equality by subtracting "q" from both sides of the equation:
[tex]\begin{gathered} x+q-(q)=\sqrt[4]{\frac{r}{p}}-(q) \\ \\ x=\sqrt[4]{\frac{r}{p}}-q \end{gathered}[/tex]The answer is:
[tex]x=\sqrt[4]{\frac{r}{p}}-q[/tex]relation and functionFunction OperationComposition of functionsymmetryfunction Inversesrate of change scartterplotsMINIMUM STEPS PLEASE!
In order to find f(2) we just have to replace x by 2 in its equation:
f(x) = 3x - 1
↓
f(2) = 3 · 2 - 1
f(2) = 6 - 1
f(2) = 5
Finding g(x) = f(2)Since g(x) = f(2) is
g(x) = 5
using the equation of g, we have that
2x - 3 = 5
In order to find x we just solve the previous equation
2x - 3 = 5
↓ adding 3 both sides of the equation
2x - 3 + 3 = 5 + 3
2x = 8
↓ dividing by 2 both sides of the equation
2x/2 = 8/2
x = 4
Answer- D: x = 4
nction.
f(x) = -x² + 3x + 11
Find f(-1)
Answer:
f(-1) = 7
Step-by-step explanation:
Hello!
You can evaluate for f(-1) by substituting -1 for x in the equation.
Evaluate f(-1)f(x) = -x² + 3x + 11f(-1) = -(-1)² + 3(-1) + 11f(-1) = -1 -3 + 11f(-1) = -4 + 11f(-1) = 7f(-1) is 7.
Answer:
f(-1) = 7
Step-by-step explanation:
Hello!
You can evaluate for f(-1) by substituting -1 for x in the equation.
Evaluate f(-1)f(x) = -x² + 3x + 11f(-1) = -(-1)² + 3(-1) + 11f(-1) = -1 -3 + 11f(-1) = -4 + 11f(-1) = 7f(-1) is 7.
A bag contains 5 red and 3 blue marbles. Two marbles are drawn simultaneously from the bag. DETERMIN the probability that at least one is red.
total number of balls = 5 + 3 = 8
The possibilities are:
RR (two red) and RB (one red and one blue)
RR and RB are mutually exclusive
P(RR) =
Which of the following tables represents a function?
Answer:
Table A represents a function
Step-by-step explanation:
Table A represents function because it is the only table that doesn't repeat an output or input number.
Use the sequence below to complete each task. 34, 25, 16, 7, ... a. Identify the common difference (a). b. Write an equation to represent the sequence. c. Find the 20th term (azo)
Problem
Solution
We have the following sequence of terms 34,25,16,7,....
Part a
The common difference for this case would be:
25-34= -9
16-25=-9
7-16= -9
Then the answer for part a would be -9
Part b
We want to write the following form:
an = a1 + (n-1) d
For this case d=-9, a1= 34
And then we can write the genral expression like this:
an = 34 + (n-1 ) (-9)
With n = 1,2,3,4....
Part c
In order to find the 20 th term we can replace n =20 and we got:
a20= 34 + (20-1) (-9) = 34-171= -137
Please help! I have 3 questions that I'm not sure what to do about :( if you could answer them that would be great
The resultant matrix for the given expressions are as follows -
[A] → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]
[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]
[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]
What is a Matrix?Matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. A matrix has [n] rows and [m] columns. The order of a matrix is given by - [m] x [n].
Given are the three different matrices as -
A = [tex]\left[\begin{array}{ccc}9&-6\\7&5\\\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}4&3\\-7&-6\\\end{array}\right][/tex]
C = [tex]\left[\begin{array}{ccc}0.5&3.6\\2.4&-3.2\\\end{array}\right][/tex]
We can solve the given expressions as follows.
[A] → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]
[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]
[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]
Therefore, the resultant matrix for the given expressions are as follows -
[A] → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]
[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]
[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]
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A straight line is 180 degrees. Find the value of X.
Given a straight line angle = 180
So, the angles (9x-100) and (40-x) are supplementary angles
So,
[tex](9x-100)+(40-x)=180[/tex]Solve for x:
[tex]\begin{gathered} (9x-x)+(40-100)=180 \\ 8x-60=180 \\ 8x=180+60 \\ 8x=240 \\ x=\frac{240}{8}=30 \end{gathered}[/tex]So, the answer will be x = 30
How many different 3 digit combinations can there be for a combination lock that has a six digit wheel?
The number of 3 digit combinations possible for the six digit wheel combination lock is; 216 combinations.
Combinations and selections.It follows from the task content that the number of possible 3 digit combinations for the six digit wheel as required is to be determined.
The number of possible selections in a given sample space is defined by the combination which defines the situation.
On this note, each digit from the 3 digit combinations could be any of the six digits on the wheel.
Therefore, the number of possible combinations is; 6 × 6 × 6 = 216 combinations.
Ultimately, the number of possible combinations is; 216 combinations.
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I need help pls 1. Is this graph sine or cosine 2. What’s the amplitude of graph 3. What’s the equation of the midline 4. Whats the period of the function Whats the equation of the function Whats the domain and range?
As per given by the question,
There are given that a graph.
Now,
1. The given graph is cosine graph.
2. The aplitute of the given graph is,
From the graph, it is lie between -2 to 2.
So,
The amplitude of the given graph is 2.
Now,
3. The equation of the midline is,
[tex]y=-2[/tex]Now,
4.The period of the fumction is,
[tex]P=\frac{2\pi}{3}[/tex]Now,
The equation of the function.
First the general form of cosine graph function is,
[tex]y=A\cos (bx+c)+d[/tex]Then,
[tex]y=2\cos (3x+c)+d[/tex]Now,
[tex]y=2\cos (3x-1)+3[/tex]Where, D is vertical shift.
Hence, the equation of the function is,
[tex]y=2\cos (3x-1)+3[/tex]Given that A = {1, 2,2 3} and B = {4, 6}, then find B×A
The solution for set B × A is {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
Given,
The sets,
A = {1, 2, 3}
B = {4, 6}
We have to find B × A.
Here,
Consider the Cartesian product:
The set of all ordered pairs (x, y) such that x belongs to A and y belongs to B is referred to as the Cartesian Product of sets A and B in mathematics. For instance, the Cartesian Product of A and B is (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), and (2, 5) if A = [1, 2] and B = [3, 4, 5].
The Cartesian product of B × A = {(b, a) | b € B, a € A}
So,
B × A = {4, 6} × {1, 2, 3}
B × A = {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
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Given a and b are the first-quadrant angles, sin a=5/13, and cos b=3/5, evaluate sin(a+b)1) -33/652) 33/653) 63/65
We know that angles a and b are in the first quadrant. We also know this values:
[tex]\begin{gathered} \sin a=\frac{5}{13} \\ \cos b=\frac{3}{5} \end{gathered}[/tex]We have to find sin(a+b).
We can use the following identity:
[tex]\sin (a+b)=\sin a\cdot\cos b+\cos a\cdot\sin b[/tex]For the second term, we can replace the factors with another identity:
[tex]\sin (a+b)=\sin a\cdot\cos b+\sqrt[]{1-\sin^2a}\cdot\sqrt[]{1-\cos^2b}[/tex]Now we know all the terms from the right side of the equation and we can calculate:
[tex]\begin{gathered} \sin (a+b)=\sin a\cdot\cos b+\sqrt[]{1-\sin^2a}\cdot\sqrt[]{1-\cos^2b} \\ \sin (a+b)=\frac{5}{13}\cdot\frac{3}{5}+\sqrt[]{1-(\frac{5}{13})^2}\cdot\sqrt[]{1-(\frac{3}{5})^2} \\ \sin (a+b)=\frac{15}{65}+\sqrt[]{1-\frac{25}{169}}\cdot\sqrt[]{1-\frac{9}{25}} \\ \sin (a+b)=\frac{15}{65}+\sqrt[]{\frac{169-25}{169}}\cdot\sqrt[]{\frac{25-9}{25}} \\ \sin (a+b)=\frac{15}{65}+\sqrt[]{\frac{144}{169}}\cdot\sqrt[]{\frac{16}{25}} \\ \sin (a+b)=\frac{15}{65}+\frac{12}{13}\cdot\frac{4}{5} \\ \sin (a+b)=\frac{15}{65}+\frac{48}{65} \\ \sin (a+b)=\frac{63}{65} \end{gathered}[/tex]Answer: sin(a+b) = 63/65
Leo is constructing a tangent line from point Q to circle P. What is his next step? Mark the point of intersection of circle P and segment PQ. Construct arcs from point P that are greater than half the length of segment PQ. Construct a circle from point Q with the radius PQ. Plot a new point R and create and line perpendicular to segment PQ from point R
The next step to constructing a tangent line from Q to circle P is to construct the perpendicular bisector of the segment PQ.
For this, Leo can construct arcs from point P and from point Q that are greater than half the length of segment PQ.
AnswerThe next step is to construct arcs from point P that are greater than half the length of segment PQ.
