choose the correct statement of the rule; then complete the table for missing values. A merchant adds $3.00 to his cost to determine his selling price.
Answers
We have to find a relation between selling price in function of cost C.
If C is the cost, then the selling price is a function of C: f(
Related Questions
Perform the indicated operation -27÷-9
Answers
-27/9 = -3
answer is -3
Which Venn diagram correctly shows the relationships between the subsets of rational numbers?
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By definition, consider that natural numbers are all numbers from 1 to infinity. Whole numbers are the same natutal numbers plus zero. Integers are all numbers from minus infinity to infinity and rational are all number with finite decimals, and periodic infinite decimals.
Then, based on the previous description, the diagram which correctly shows the subsets of rational numbers is:
diagram F.
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 6z
Answers
Answer:
(-1, 7, - 4)(1, -1, 4)=====================
Given systemx² + z² = 174x + y = 3y + z = 3Rearrange the last two equation4x = 3 - yz = 3 - yThis gives us:
z = 4xSubstitute the value of z into fist equationx² + (4x)² = 17x² + 16x² = 1717x² = 17x² = 1x = 1 and x = - 1Find values of z and yx = 1 ⇒ z = 4*1 = 4 ⇒ y = 3 - 4 = - 1 x = - 1 ⇒ z = 4*(-1) = - 4 ⇒ y = 3 - (-4) = 7Answer:
[tex](x,y,z)=\left(\; \boxed{-1,7,-4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y,z)=\left(\; \boxed{1,-1,4} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x^2+z^2=17\\\;4x+y=3\\\;\;\;y+z=3\end{cases}[/tex]
To solve by the method of substitution, first rearrange the third equation to make y the subject:
[tex]\implies y=3-z[/tex]
Substitute this into the second equation and solve for z:
[tex]\begin{aligned}\implies 4x+(3-z)&=3\\3-z&=3-4x\\-z&=-4x\\z&=4x\end{aligned}[/tex]
Substitute the found expression for z into the first equation and solve for x:
[tex]\begin{aligned}\implies x^2+(4x)^2&=17\\x^2+16x^2&=17\\17x^2&=17\\x^2&=1\\x&=\pm1\end{aligned}[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}\implies x=-1 \implies 4(-1)+y&=3\\-4+y&=3\\y&=7\end{aligned}[/tex]
[tex]\begin{aligned}\implies x=1 \implies 4(1)+y&=3\\4+y&=3\\y&=-1\end{aligned}[/tex]
Substitute the found values of x into the derived expression for z and solve for z:
[tex]\begin{aligned}\implies x=-1 \implies z&=4(-1)\\z&=-4\end{aligned}[/tex]
[tex]\begin{aligned}\implies x=1 \implies z&=4(1)\\z&=4\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y,z)=\left(\; \boxed{-1,7,-4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y,z)=\left(\; \boxed{1,-1,4} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
What is the equation for the linear model in the scatterplot obtained by choosing the two points closest to the line
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consider two points closest to the line. say ,
[tex]\begin{gathered} (x_1,y_1)=(6,0) \\ (x_2_{}_{}_{},y_2)=(8,1) \end{gathered}[/tex]let us find the slope, m by the formula
[tex]m=\frac{y_2-y_1}{x_2_{}_{}-x_1}[/tex]subsitute the points in the formula,
[tex]\begin{gathered} m=\frac{1-0}{8-6} \\ m=\frac{1}{2} \end{gathered}[/tex]let us find the y - intercept.
[tex]y=mx+b\ldots(1)[/tex]subsitute the one of the point (6,0) in the above equation.
[tex]\begin{gathered} 0=\frac{1}{2}\times6+b \\ 0=3+b \\ b=-3 \end{gathered}[/tex]thus,
subsitute m= 1/2 and b = - 3 in the equation (1),
[tex]y=\frac{1}{2}x-3[/tex]1. P, Q and R are three buildings. A car began its journey at P, drove to Q, then to R and returned to P. The bearing of Q from P is 058º and R is due east of Q. PQ = 114 km and QR = 70 km. © Draw a clearly labelled diagram to represent the above informationen on the diagram TƏRund (a) the north/south direction (b) the bearing 058° (c) the distances 114 km and 70 km. (ii) Calculate (a) the measure of angle POR (b) the distance PR [3] (c) the bearing of P from R [3]
Answers
Step 1
Given;
[tex]\begin{gathered} The\text{ bearing of Q from P is 058}^o\text{ } \\ R\text{ is due east of Q} \\ PQ=114km \\ QR=70km \end{gathered}[/tex]Step 2
Draw the diagram
Step 2
Calculate the measure of angle PQR
[tex]\angle PQR=58+90=148^o[/tex]This is because using alternate exterior angles are equal theorem, the first part of angle Q 58 degrees. Since R is due east of Q, then the other part must be 90 degrees, when summed we get 148 degrees
Step 3
Calculate the distance PR. To do this we will use the cosine rule
[tex]\begin{gathered} PR^2=PQ^2+QR^2-2PQ\left(QR\right?cosQ \\ PR^2=114^2+70^2-2\left(114\right)\left(70\right)cos\left(148\right) \\ PR^2=17896+13534.84761 \\ PR=\sqrt{31430.84761} \\ PR=177.2874717 \\ PR\approx177.3km\text{ to the nearest tenth} \end{gathered}[/tex]Step 4
Calculate the bearing of P from R.
Use sine rule and find angle R
[tex]\frac{sin\text{ 148}}{177.2874717}=\frac{sinR}{114}[/tex][tex]\begin{gathered} 114sin148=177.2874717sinR \\ R=\sin^{-1}\frac{\mleft(114sin148\mright)}{177.2874717} \\ R=19.92260569 \end{gathered}[/tex]The bearing of P from R = (90-angle R)+90+90=250 degrees approximately to the nearest whole number
[tex]\begin{gathered} =\left(90-19.92260569\right)+90+90 \\ =250.07739 \\ \approx250^o \end{gathered}[/tex]The bearing of P from R =250 degrees approximately to the nearest whole number
what is the surface area, in square centimeters, of the pyramid ?
Answers
If you have a 77.2% and you got 34% on a test and it’s worth 60% of your grade, what would you grade be now?
Answers
Answer:
51.28%
Step-by-step explanation:
since the test is worth 60% of your grade, the rest is worth 40%
calculate your new grade by multiplying each grade percent (as written) by the percent of your grade (as a decimal):
77.2(0.4) = 30.88
34(0.6) = 20.4
then add them together: 30.88 + 20.4
I need help with triangles
Answers
Suppose a binomial trial has a probability of success of 0.3 and 450 trials are performed. What is the standard deviation of the possible outcomes?6.3614.8511.629.72
Answers
The standard deviation of a binomial distribution with n trials and a probability of success of p is given by the formula:
[tex]\sigma=\sqrt[]{n\cdot p\cdot(1-p)}[/tex]From the problem, we identify:
[tex]\begin{gathered} n=450 \\ p=0.3 \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sigma=\sqrt[]{450\cdot0.3\cdot(1-0.3)}=\sqrt[]{450\cdot0.3\cdot0.7} \\ \sigma\approx9.72 \end{gathered}[/tex]A carpenter cuts a 5-ft board in two pieces. One piece must be three times as longas the other. Find the length of each piece.
Answers
3.75 ft and 1.25 ft
Explanation
Step 1
Diagram
Step 2
set the equations
let x represents the longest piece
lety represents the smaller piece
so
a)A carpenter cuts a 5-ft board in two pieces, hence
[tex]x+y=5\Rightarrow equation(1)[/tex]b)One piece must be three times as long as the other,then
[tex]x=3y\Rightarrow equation(2)[/tex]Step 3
finally, solve the equations:
a) replace the x value from equation (2) into equation(1)
[tex]\begin{gathered} x+y=5\Rightarrow equation(1) \\ (3y)+y=5 \\ add\text{ like terms} \\ 4y=5 \\ divide\text{ both sides by 4} \\ \frac{4y}{4}=\frac{5}{4} \\ y=1.25 \end{gathered}[/tex]b) now, replace the y value into equation (2) to find x
[tex]\begin{gathered} x=3y\Rightarrow equation(2) \\ x=3(1.25) \\ x=3.75 \end{gathered}[/tex]therefore, the lengths of the pieces are
3.75 ft and 1.25 ft
I hope this helps you
Which graph represents the function f(x) = -x + 31?
Answers
Answer:
Step-by-step explanation:
I hope this helps! :) If it does could you please mark me brainliest?
Answer:
Slope : -1
y = intercept : (0,31)
Step-by-step explanation:
The graph of f(x) = x² is translated to formg(x) = (x-2)2-3.--5-4-3-2-1-2+Which graph represents g(x)?#
Answers
Step 1
Plot the graph of f(x)
[tex]f(x)=x^2[/tex]Step 2
The function of g(x) suggests that f(x);
[tex]\begin{gathered} 1)\text{ it was moved 2 units towards the right} \\ 2)\text{ It was then moved 3 units down} \end{gathered}[/tex]Thus, the graph of g(x) will look like this;
Answer;
Algebraically determine whether each of the following functions is even, odd or neither. then graph it B. y = x^3 – 3 C. y = 2x^3 - x
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According to the even and odd function rules, we found out that the function [tex]y=x^{3}-3[/tex] is neither even nor odd and the function [tex]y=2x^{3}-x[/tex] is an odd function.
It is given to us that the functions are -
B. [tex]y=x^{3}-3[/tex]
C. [tex]y=2x^{3}-x[/tex]
We want to determine each of the following functions is even, odd or neither.
To see if the function is even, we have to check if [tex]f(-x)=f(x)[/tex]
To see if the function is odd, we have to check if [tex]f(-x)=-f(x)[/tex]
B. Here, we have
[tex]y=x^{3}-3\\= > f(x)=x^{3}-3\\= > f(-x)=(-x)^{3}-3\\= > f(-x)=-x^{3}-3[/tex]
We see that [tex]f(-x)\neq f(x)[/tex]. This implies that the function is not even.
Also, [tex]f(-x)\neq -f(x)[/tex]. This implies that the function is not odd.
Therefore, this function is neither even nor odd.
C. Here, we have
[tex]y=2x^{3}-x\\= > f(x)=2x^{3}-x\\= > f(-x)=2(-x)^{3}-(-x)\\= > f(-x)=-2x^{3}+x[/tex]
We see that [tex]f(-x)\neq f(x)[/tex]. This implies that the function is not even.
However,
[tex]f(-x)=-2x^{3}+x\\= > f(-x)= -(2x^{3}-x)\\ = > f(-x)=-f(x)[/tex]
This implies that the function is odd.
Therefore, this function is odd.
Thus, the function [tex]y=x^{3}-3[/tex] is neither even nor odd and the function [tex]y=2x^{3}-x[/tex] is an odd function.
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An account earns an annual rate of 5.4% compounded monthly. If $3,000 is deposited into this account, then after 3 years there is $___. Round your answer to two decimals.
Answers
Given:
rate (r) = 5.4% or 0.054 in decimal form
Principal (P) = $3,000
time in years (t) = 3 years
number of conversions per year (m) = 12 (because it says monthly)
Find: future value or maturity value
Solution:
The formula for getting the future value of a compound interest is:
[tex]F=P(1+\frac{r}{m})^{mt}[/tex]Let's plug in the given data to the formula above.
[tex]F=3,000(1+\frac{0.054}{12})^{12\times3}[/tex]Then, solve for F or future value.
[tex]\begin{gathered} F=3,000(1.0045)^{36} \\ F=3,000(1.17532999) \\ F\approx3,526.30 \end{gathered}[/tex]Answer: After 3 years, the deposited money will become $3, 526.30.
Question content area topPart 1A medical researcher administers an experimental medical treatment to patients. The patients in the study are categorized by blood types A, B, AB, and O. The researcher observed that the treatment had a favorable outcome for of the patients with blood type A, of the patients with blood type B, of the patients with blood type AB, and none of the patients with blood type O. Use this information to complete parts (a) through (d).
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
total patients = 300
type A:
total patients = 90
favourable patients = 27
type B:
total patients = 124
favourable patients = 31
type AB:
total patients = 6
favourable patients = 6
type O:
total patients = 80
favourable patients = 0
Step 02:
empirical probability:
probability = favourable outcomes / total outcomes
probability (A) = 27/ 90 = 0.3
probability (B) = 31 / 124 = 0.25
probability (AB) = 6 / 6 = 1
probability (O) = 0 / 80 = 0
That is the full solution.
in DEF, K is the centroid. If KH=12 find DH
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the lines that cross the centroid are divided into 2 by this the short line corresponds to 1/3 of the complete line and the long line corresponds to 2/3 of the complete line
so KH is 1/3 of DH
if KH=12, then
[tex]\begin{gathered} DH=3KH \\ DH=3\times12 \\ DH=36 \end{gathered}[/tex]the value of DH is 36
what digit is in the
Answers
Rounding each number to the nearest ten:
• 96 = 100
,• 63 = 60
,• 27 = 30
,• 76 = 80
Sum with rounded numbers:
[tex]100\text{ + 60+30+80=270}[/tex]Answer = 270
you are selling snacks at the border trade fair. you are selling nachos and lemonade. each nachos costs $2.50 and each lemonade cost $2.25. at the end of the night you made a total of $112.50. you sold a total of 94 nachos and lemonade combined. how many nachos and lemonades were sold?
Answers
In order to determine the number of nachos and lemonade sold, you first write the given situation in an algebraic way.
If x is the number of nachos and y the number of lemonades, then, you have:
2.50x + 2.25y = 112.50 cost of the nachos and lemonade sold
x + y = 94 nachos and lemonade sold
Next, solve the previous system.
Multiply the second equation by 2.50. Next, subtract the equation to the first one:
(x + y = 94)(2.50)
2.50x + 2.50y = 235
2.50x + 2.25y = 112.50
-2.50x - 2.50y = -235
-0.25y = -122.5
solve the previous equation for y:
y = -122.5/(-0.25)
y = 490
Next, replace the previous value of y into the expression x + y = 94 and solve for x:
x + y = 94
x + 490 =
Simplify. Assume that all variables result in nonzero denominators.
2n^3 y−8n^2 y/3y^4 * 12/n-4
Answers
The simplified form of given expression 2n^3 y−8n^2 y/3y^4 * 12/n-4 is 8n^2/y^3
In this question, we have been given an expression.
2n^3 y−8n^2 y/3y^4 * 12/n-4
We need to simplify given expression.
2n^3 y − 8n^2 y/3y^4 * 12/n-4
= [2n^2y (n - 4)] / 3y^4 * 12/(n - 4)
= 4 * (2n^2y)/y^4
= 8n^2/y^3
Therefore, the simplified form of given expression 2n^3 y−8n^2 y/3y^4 * 12/n-4 is 8n^2/y^3
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Hi!A particle moves along a straight line, so its speed is () = ^2 − + 6, where t is the time measured in seconds and the speed is measured in meters timessecond.a) Calculate the distance traveled between the seconds t=1 and t=3
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In this problem
the distance traveled between the seconds t=1 and t=3 is given by
[tex]\int_1^3(t^2-t+6)dt=\frac{50}{3}\text{ m}[/tex]The answer is
50/3 metersor 16.67 metersExplanation of integrals
In this problem we have
[tex]\int_1^3(t^2-t+6)dt=\int_1^3t^2dt-\int_1^3tdt+\int_1^36dt[/tex][tex]\begin{gathered} \int_1^3t^2dt=\frac{t^3}{3} \\ Evaluate\text{ at 3 and 1} \\ \frac{(3)^3}{3}-\frac{1^3}{3}=\frac{27}{3}-\frac{1}{3}=\frac{26}{3} \end{gathered}[/tex][tex]\begin{gathered} -\int_1^3tdt=-\frac{t^2}{2} \\ evaluate\text{ at 3 and 1} \\ -\frac{3^2}{2}+\frac{1^2}{2}=-\frac{9}{2}+\frac{1}{2}=-4 \end{gathered}[/tex][tex]\begin{gathered} \int_1^36dt=6t \\ evaluate\text{ at 3 and 1} \\ 6(3)-6(1)=12 \end{gathered}[/tex]substitute
[tex]\int_1^3t^2dt-\int_1^3tdt+\int_1^36dt=\frac{26}{3}-4+12=\frac{50}{3}[/tex]17. In trapezoid FGJK, what is the value of x? N CO 18.6 L K 23.6 9.3 11.8 ET O 13.6
Answers
Given data:
The given figure is shown.
The expression for the trapezium is,
[tex]\begin{gathered} \frac{x}{18.6}=\frac{18.6}{23.6} \\ 23.6x=18.6^2 \\ x=14.6 \\ =15 \end{gathered}[/tex]Thus, thi
If 20 assemblers can complete a certain job in 6 hours, how long will the same job take if the number of assemblers is cut back to 8?
Answers
ANSWER
[tex]15[/tex]EXPLANATION
For 1 assembler, it will take;
[tex]\begin{gathered} 20\times R\times6=1 \\ R=\frac{1}{120} \end{gathered}[/tex]For 8 assemblers;
[tex]8\times R\times T=1[/tex]Substitute R
[tex]\begin{gathered} 8\times R\times T=1 \\ 8\times\frac{1}{120}\times T=1 \\ \frac{8T}{120}=1 \\ 8T=120 \\ T=\frac{120}{8} \\ =15 \end{gathered}[/tex]Hello I need help with this I’m in a rush thanks
Answers
Recall that:
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)},[/tex]and that the domain of a rational function consists of all real numbers such that the denominator is different from zero.
If f(x)=5x+3 and g(x)=4x-5 we get that:
[tex]\frac{f}{g}(x)=\frac{5x+3}{4x-5}\text{.}[/tex]The domain of the above rational function is:
[tex]\begin{gathered} \mleft\lbrace x|g(x)\ne0\mright\rbrace=\lbrace x|4x-5\ne0\rbrace \\ =\lbrace x|4x\ne5\rbrace=\lbrace x|x\ne\frac{5}{4}\rbrace\text{.} \end{gathered}[/tex]Answer: Last option.
A toy factory makes 5.7 x 10³ toys each day.At this rate, how many toys will be made in 9 days?Express the answer in scientific notation.
Answers
First We will put the number of toys per day in simple form:
[tex]5.7\times10^3=5.7\times1000=5700[/tex]Then, to know how many toys will be made in 9 days, let's multiply the number of toys per day by the given number of days:
[tex]5700\times9=51300[/tex]Now We will put the number in scientific notation:
[tex]5.13\times10^4[/tex]find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores. z= 1 and z= 1.9
Answers
The area, to the nearest thousandth, of the standard normal distribution between the z-scores z= 1 and z= 1.9 is 0.130
Write the expression in the standard form a + bi.
Answers
SOLUTION
Write out the expression
[tex]i^{22}[/tex][tex]\begin{gathered} i^{22} \\ \text{can be written as} \\ (i^2)^{11} \end{gathered}[/tex]Recall that
[tex]i^2=-1[/tex]Replace into the expression above
[tex](-1)^{11}=-1[/tex]Hence
[tex]i^{22}=-1[/tex]Therefore
The first option is Right
Determine the equation of the graphed circle below!Equation should look like the example below!
Answers
Step 1:
Write the formula for the equation of a circle.
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{Center = ( a , b )} \\ \text{Radius = r} \end{gathered}[/tex]Step 2:
Locate and write the center and radius of the circle.
Step 3:
Write the equation of the circle with center (-7, -2) and radius r = 2
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (x-(-7))^2+(y-(-2))^2=2^2 \\ (x+7)^2+(y+2)^2=\text{ 4} \end{gathered}[/tex]Final answer
[tex](x+7)^2+(y+2)^2=\text{ 4}[/tex]which measurement could create more than one triangle measuring 20 cm / 9 cm and 10cm be a triangle with sides measuring 10 cm and 20 cm and included angle measurement 65 C a right angle with acute angles measuring 45 and 45 d a triangle with sides measuring 15 in 20 in and 25 in
Answers
Input data
The triangles created by the measurements of options A, B and D have specific side lengths. Therefore, you cannot create more than one triangle.
However, for a triangle with acute angles measuring 45° and 45°, a countless number of similar triangles (triangles with the same shape but different sizes) can be created.
The correct choice is C.
Find the values of x and y in the equation below.a³b4a²b= a*b²X=
Answers
To divide, subtract exponents to same base variables.
[tex](ab^3)^6[/tex]Multiply exponents of exponents
[tex]a^6b^{18}[/tex]x= 6
y= 18
Josslyn has nickels and dimes in her pocket. The number of nickels is three more than seven times the number of dimes let d represent the number of dimes. Write the expression for the number of nickels
Answers
to solve this we need to translate into math terms, so
Step 1
a) let d represents the number of dimes
let n represents the number of nickles
so
re write the expressions
[tex]\begin{gathered} number\text{ of dimes=d} \\ seven\text{ times the number of dimes = 7d} \\ \end{gathered}[/tex]The number of nickels is three more than seven times the number of dimes in other words you have to add 7 to seven times the number of dimes to obtain the number of nickles
hence
[tex]n=7d+3[/tex]therefore , the expression for the number of nickles is
[tex]7d+3[/tex]I hope this helps you