Let x and y be the two numbers
x + y = 72 ------------------------------(1)
x - y = 4 ----------------------------------(2)
Add equation (1) and equation (2)
2x = 76
Divide both-side of the equation by 2
x = 38
substitute x = 38 into equation (1) and then solve for y
38 + y = 72
subtract 38 from both-side of the equation
y = 72 - 38
y = 34
The two numbers are 34 and 38
Yon buys tickets to a concert for himself and a friend. There is a tax of 6% on the price of the tickets andan additional booking fee of $20 for the transaction. Enter an algebraic expression to represent the priceper person. Simplify the expression if possible. Use variablet for the price of the 2 tickets in dollars.The algebraic expression is
Let the price of each ticket be represented by
[tex]=x[/tex]The price of two tickets will be
[tex]t=2x[/tex]The tax on the price of the tickets is 6% which be represented as
[tex]\begin{gathered} =\frac{6}{100}\times t \\ =\frac{6t}{100}=0.06t \end{gathered}[/tex]The price of the two tickets after tax will be
[tex]\begin{gathered} the\text{price of the two tickets+the tax on the two tickets} \\ =t+0.06t \\ =1.06t \end{gathered}[/tex]Therefore,
The price of the tickets after adding an additional booking fee of $20 will be given below as
[tex]=1.06t+20[/tex]Since,
We were asked to get the algebraic expression person, we would therefore divide the above expression by 2
[tex]\begin{gathered} =\frac{1.06t+20}{2}=\frac{1.06t}{2}+\frac{20}{2} \\ =0.53t+10 \end{gathered}[/tex]Hence,
The algebraic expression to represent the price per person using variable t is
=0.53t + 10
AnimalPossible Locations Relativeto Ocean's Surface25. Reasoning Suppose you plot the locations ofthe animals on a number line. Which animalwould be represented by the point farthest fromO on the number line? Explain. MP2Bloodbelly comb jellyDeep sea anglerfish-0.8 km- km- 2 kmFanfin anglerfishGulper eel-1.1 km26. Which animal is closest to a depth of -0.7 km?Pacific blackdragon- šo kmSlender snipe eel-0.6 km
Number line
[tex]\ldots-5<-4<-3<-2<\text{ -1< 0<1<2<3<4<5}\ldots[/tex]Let's
[tex]undefined[/tex]Angela bought a calculator on sale for 15% off. Sales tax is 7.5%. If the calculator cost x dollars, which expression represents the total cost of the calculator?A). (x-0.15) (0.075)B). (x-0.15) (1.075)C). (x-0.15x) (0.075)D). (x- .015x) (1.075)
Original price = x
Price with 15% off = x - 0.15x
Price with 15% off and 7.5% tax = (x - 0.15x)(1.075)
Answer:
Option B: (x - 0.15x)(1.075)
Can you help me answer part A and part B?
Part A.
Given:
P = (5, 4), Q = (7, 3), R = (8, 6), S = (4, 1)
Let's find the component of the vector PQ + 5RS.
To find the component of the vector, we have:
[tex]=\lparen Q_1-P_1,Q_2-P_2)=<7-5,3-4>[/tex]For vector RS, we have:
[tex]=\lparen S_1-R_1,S_2-R_2)=<4-8,1-6>[/tex]Hence, to find the vector PQ+5RS, we have:
[tex]\begin{gathered} =<7-5,3-4>+5<4-8,1-6> \\ \\ =\left(2,-1\right)+5\left(-4,-5\right) \\ \\ =\left(2,-1\right)+\left(5\ast-4,5\ast-5\right) \\ \\ =\left(2,-1\right)+\left(-20,-25\right) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} =<2-20,-1-25> \\ \\ =<-18,-26> \end{gathered}[/tex]Therefoee, the component of the vector PQ+5RS is:
<-18, -26>
• Part B.
Let's find the magnitude of the vector PQ+5RS.
To find the magnitude, apply the formula:
[tex]m=\sqrt{\left(x^2+y^2\right?}[/tex]Thus, we have:
[tex]\begin{gathered} m=\sqrt{\left(-18^2+-26^2\right?} \\ \\ m=\sqrt{324+676} \\ \\ m=\sqrt{1000} \\ \\ m=\sqrt{10\ast10^2} \\ \\ m=10\sqrt{10} \end{gathered}[/tex]Therefore, the magnitude of the vector is:
[tex]10\sqrt{10}[/tex]ANSWER:
Part A. <-18, -26>
Part B. 10√10
An electrician needs 6 rolls of electrical wire to wire each room in a house. How many rooms can he wire with 3/62 of a roll of wire?
Use a rule of three to find the amount of rooms wire with 3/62 rolls:
[tex]x=\frac{\frac{3}{62}rolls*1room}{6rolls}=\frac{\frac{3}{62}}{6}rooms=\frac{3}{6*62}rooms=\frac{3}{372}rooms=\frac{1}{124}rooms[/tex]Then, with 3/62 of a roll can be wire 1/124 parts of a room4 groups of a number
Answer:
[tex]4x[/tex]Step-by-step explanation:
In math, a group is a set equipped with an operation that combines any two elements of the set to produce a third element of the set.
Therefore, for 4 groups of a number.
Let x be the missing number
So, 4 multiply x:
[tex]4x[/tex]1 + c + 1.4 = c + 2.4I need help
1 + c + 1.4 = c + 2.4
c + 2.4 = c + 2.4
c = c + 2.4 - 24
c = c
Solve. 0.25(60) + 0.10x = 0.15(60+x)
[tex]15 + 0.10x = 0.15(60) + 0.15(x) \\ 15 + 0.10x = 9 + 0.15x \\ \\ 0.10x - 0.15x = 9 - 15 \\ - 0.05x = - 6 \\ \frac{ - 0.05x}{ - 0.05} = \frac{ - 6}{ - 0.05} \\ x = 120[/tex]
ATTACHED IS THE SOLUTION
452 pointsTo factor x2 + bx + c, the numbers you choose to fill in the empty spots of (x + )(x + ).1mustchoose your answer...to equal c.2Previous34Сл
The Quadratic format is
[tex]\begin{gathered} x^2\text{ + bx + c } \\ \text{The b is gotten by adding the factors } \\ \text{But the c is gotten by multiplying the factors } \end{gathered}[/tex]The answer to the question is that the factors must multiply to form c
Mrs. Laurence just bought a new car for 26,304. She plans to pay her car off in 24 months. Mr. Gannon just bought a new car for 20,480 and plans to pay his car off in 20 months. How much more money a month does Mrs. Laurence pay in her car payment?
The amount of extra money a month that Mrs. Laurence pays in her car payment is $72.
How much more money does Mrs. Laurence pay each month?We can get the amount of extra amount that Mrs. Laurence pays each month when compared to Mr. Gannon by dividing the amount that they pay by the number of months they need to make these payments.
This can be done as follows:
26304 ÷ 24 = 1096
20480 ÷ 20 = 1024
1096 - 1024 - 72
So, the amount of extra money that Mrs. Laurence has to pay each month when compared to that of Mr. Gannon is $72.
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Given f <-2, 3> and g <1, -5> find f + 2g
Here are the steps in adding vector f and vector 2g.
1. First, multiply vector G by 2. To do this, simply multiply each component of g by 2.
[tex]<2(1),2(-5)>\Rightarrow<2,-10>[/tex]2. Add the result in step 1 to vector f.
To add, simply add each component of vector f to its corresponding component of vector g.
[tex]\begin{gathered} <-2,3>+<2,-10> \\ <-2+2,3+(-10)> \\ <0,-7> \end{gathered}[/tex]The result is <0, -7>.
Hence, f + 2g = <0, -7>. (Option 3)
Hence, f + 2g = <0, -7>. (Option 3)
Math for Liberal Arts Lecture Class, Fall 2021 = Homework: Ch... Question 2, 1.1.3 Part 2 of 3 HW Score: Points: An election is held to choose the chair of a department at a university. The candidates are Professors Arg for short). The following table gives the preference schedule for the election. Use the table to complete pa Number of Voters 7 9 2 5 3 6 1st choice А A B D A 2nd choice B D D А E E 3rd choice D B E C B B 4th choice E C A B C D 5th choice C E C D A C (a) How many people voted in this election? ... 32 voters (Type a whole number.) (b) How many first-place votes are needed for a majority?
a) In this election voted: 7+9+2+5+3+6=32
b) For a majority you can follow the next rule:
The 50% of 32 is: 32*0.5=16, then, are needed at least 17 votes
c) Candidate A had 3 last-place votes, candidate B had 0 last-place votes, candidate C had 15 last-place votes, candidate D had 5 last-place votes and candidate E had 9 last-place votes.
Thus, the candidate with the fewest last-place votes is candidate B
The data below show the number of hits on a website per week over a random sample of five weeks. Compute the followingstatistics.
We have a sample that is:
[tex]115,39,160,240,176[/tex]a) We can find the median by first sorting the sample:
[tex]39,115,160,176,240[/tex]The median is the value that has 50% of the values below its values.
In this case, this value is in the third place of the sorted sample and has a value of 160.
b) We have to find the mean.
We can calculate it as:
[tex]\begin{gathered} \bar{x}=\frac{1}{n}\sum_{n\mathop{=}1}^5x_i \\ \\ \bar{x}=\frac{1}{5}(115+39+160+240+176) \\ \\ \bar{x}=\frac{1}{5}(730) \\ \\ \bar{x}=146 \end{gathered}[/tex]c) We have to calculate the variance. To find its value we will use the mean value we have just calculated:
[tex]\begin{gathered} s^2=\frac{1}{n}\sum_{n\mathop{=}1}^5(x_i-\bar{x})^2 \\ \\ s^2=\frac{1}{5}[(115-146)^2+(39-146)^2+(160-146)^2+(240-146)^2+(176-146)^2] \\ \\ s^2=\frac{1}{5}[(-31)^2+(-107)^2+(14)^2+(94)^2+(30)^2] \\ \\ s^2=\frac{1}{5}(961+11449+196+8836+900) \\ \\ s^2=\frac{1}{5}(22342) \\ \\ s^2=4468.4 \end{gathered}[/tex]d) We have to calculate the standard deviation. As we have already calculated the variance, we can calculate it as:
[tex]\begin{gathered} s=\sqrt{s^2} \\ s=\sqrt{4468.4} \\ s\approx66.85 \end{gathered}[/tex]e) We now have to find the coefficient of variation:
[tex]CV=\frac{s}{\bar{x}}=\frac{66.85}{146}\approx0.457876\cdot100\%\approx46\%[/tex]Answer:
a) 160
b) 146
c) 4468.4
d) 66.85
e) 46%
What does the point (2, 24 ) represent in the situation ?K =
Given point:
(2, 24)
To find the constant proportionality:
In general, the constant proportionality is
[tex]\begin{gathered} k=\frac{y}{x} \\ k=\frac{24}{2} \\ k=12 \end{gathered}[/tex]Hence, the constant proportionality is 12.
Using the Smith's BBQ Report, all of your hourly personnel are getting a promotion this week. As a result, your hourly wages for next week will be 8% more than the current week. What will be the approximate Total Payroll Variance from the current week to next week if all other factors remain the same?A 156B 9265C 842D 686
Given:
The current week hour wage is 8579
Total payroll =14081.
The hourly wage will be increased 8 %.
The 8% of 8579 is
[tex]=\frac{8}{100}\times8579=686.32[/tex]The hourly wage will be increased by 686 next week.
The total payroll also will be increased by 686.
So the total Payroll Variance from the current week to next week is 686.
Hence option D is correct.
Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you'll find out. Consider AABC, whose vertices are A (2,1), B (3, 3), and C (1,6) ; let AC represent the base of the triangle. Part A Find the equation of the line passing through B and perpendicular to AC.
Answer: y = x/5 + 12/5
Explanation:
The first step is to find the equation of line AC
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept.
The formula for calculating slope of a line is expressed as
m = (y2 - y1)/(x2 - x1)
Considering line AC with points, A(2, 1) and C(1, 6),
x1 = 2, y1 = 1
x2 = 1, y2 = 6
m = (6 - 1)/(1 - 2) = 5/- 1 = - 5
Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Negative reciprocal of - 5 is 1/5
Thus, slope of the perpendicular line passing through B(3, 3) is m = 1/5
We would find the y intercept, c of the line by substituting m = 1/5, x = 3 and y = 3 into the slope intercept equation. We have
3 = 1/5 * 3 + c
3 = 3/5 + c
c = 3 - 3/5
c = 12/5
By substituting m = 1/5 and c = 12/5 into the slope intercept equation, the equation of the line is
y = x/5 + 12/5
Given the matrices A and B shown below, find 4B – į A.3A=( 1215B5
Step 1 : To determine the matrices as shown below
Find the surface area of a right cone that has a radius of 9 inches and a height of 12 inches. Round your answer to the nearest hundredth. The surface area is about ⬜ square inches.
The surface area of the right cone is:
[tex]678.58in^2[/tex]Explanation:The surface area of a right cone is:
[tex]A=\pi r(r+\sqrt[]{r^2+h^2})[/tex]Here, r = 9 in, and h = 12 in
so
[tex]\begin{gathered} A=9\pi(9+\sqrt[]{9^2+12^2}) \\ \\ =9\pi(9+15) \\ =216\pi \\ =678.58in^2 \end{gathered}[/tex]determine values of the variables that will make the following equation true, if possible. if not, state “not possible”
Given:
[tex]4\begin{bmatrix}{-r} & & {} \\ {-s} & {} & {} \\ & {} & {}\end{bmatrix}-\begin{bmatrix}{-2r} & & \\ {-2s} & {} & \\ {-2t} & {} & {}\end{bmatrix}=\begin{bmatrix}{-3} & & \\ {-1} & {} & {} \\ {5} & & {}\end{bmatrix}[/tex]As the first matrix has 2 rows and 1 column. And the second matrix has 3 rows and 1 column.
The dimension of both the matrix is not the same.
For the subtraction of two matrices must have the same size.
So, we can not determine the values of variables.
Answer: not possible.
If 340 grams of a substance are present initially and 50 years later only 170 grams remain, how much of the substance will be present after 120 years?Round to the nearest tenth of a graim.grams
Given -
Substance present initially = 340 grams
Substance present 50 years later = 170 grams
To Find -
How much of the substance will be present after 120 years =?
Step-by-Step Explanation -
Since the substance was reduced to half of what it is initially in 50 years.
So,
The half-life time of the substance = 50 Years.
It means that every 50 years, the substance will reduce to half of its quantity.
And, we know the formula:
[tex]\text{ A = S\lparen}\frac{1}{2}\text{\rparen}^{\frac{t}{h}}[/tex]Where,
A = the remaining amount of Substance =?
S = the amount of Substance you start with = 340grams
t = the amount of time in years = 120 years
h = the half-life time = 50 years
Simply putting the values, we get:
[tex]\begin{gathered} A\text{ = 340}\times(\frac{1}{2})^{\frac{120}{50}} \\ \\ A\text{ = 17\lparen}\frac{1}{2}\text{\rparen}^{2.4} \\ \\ A\text{ = 17}\times(0.5)^{2.4} \\ \\ A\text{ = 17}\times0.1894 \\ \\ A\text{ = 3.22 gram} \end{gathered}[/tex]Final Answer -
The substance that will remain after 120 years = 3.22 gram
a scale drawing of a school bus is 1 inch to 5 feet. if the length of the school bus is 5 inches on the scale drawing. what is the actual length of the bus?
Answer:
25 feet
Step-by-step explanation:
we can set up the proportional relationship of the drawing vs the actual size
so 1 inch to 5 feet would be 1:5
so then if we scale up 1 inch to 5 inch
then we have 1:5=5:Actual length of the bus
so then we have 5*5=25 feet
In the figure below, m∠1 = 8x and m∠2 = (x-9). Find the angle measures.
Answer:
• m∠1 =168 degrees
,• m∠2 =12 degrees
Explanation:
From the diagram, Angles 1 and 2 are on a straight line.
We know that the sum of angles on a straight line is 180 degrees.
Therefore:
[tex]m\angle1+m\angle2=180^0[/tex]Substituting the given values, we have:
[tex]\begin{gathered} 8x+x-9=180^0 \\ 9x=180+9 \\ 9x=189 \\ x=\frac{189}{9} \\ x=21 \end{gathered}[/tex]The measures of angles 1 and 2 are:
[tex]\begin{gathered} m\angle1=8x=8\times21=168^0 \\ m\angle2=x-9=21-9=12^0 \end{gathered}[/tex]The measures of angles 1 and 2 are 168 degrees and 12 degrees respectively.
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 143 subjects with positive test results, there are 24
false positive results; among 150 negative results, there are 5 false negative results. If one of the test subjects is randomly selected, find the probability that the subject
tested negative or did not use marijuana. (Hint: Construct a table.)
The probability that a randomly selected subject tested negative or did not use marijuana is.
(Do not round until the final answer. Then round to three decimal places as needed.)
The probability that the subject tested negative or did not use marijuana is 145/293.
What is probability?
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.
As given in the question,
Total positive results are 143 out of which 24 are false, and
total negative results are 150 out of which 5 are false.
We know that,
probability = favorable outcome/ Total outcome
so,
Total outcome = total tests
total tests = 143 + 150
total outcome = 293
and favorable outcome = true negative outcome
true negative outcome = total negative outcome - false negative outcome
true negative outcome = 150 - 5
favorable outcome = 145
Therefore, the probability is equal to 143/293
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help meeeeeeeeee pleaseee !!!!!
The function 2x + 3x^2 represents the result of adding the two provided functions, f(x) and g(x).
Composite performance.An operation known as "function composition" takes two functions, f and g, and produces a new function, h, that is equal to both g and f and has the property that h(x) = g.
Given the f(x) = 2x and g(x) = 3x^2 functions
The sum of the two functions must be calculated as illustrated;
f(x) + g = (f+g)(x)
Put the provided functions in place of (f+g)(x) to have:
(f+g)(x) = 2x + 3x^2
Standard version of the expression is (f+g)(x) = 2x + 3x^2
Consequently, the sum of the functions f(x) and g(x) is2x + 3x^2
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If the calculator gives us the following values number 7
we know that
The equation is of the form
y=ax+b
The given values are
a=0.872
b=25.263
substitute
therefore
The equation is
y=0.872x+25.263Find the number that belongsin the green box.[?]109°13°6Round your answer to the nearest tenth.
step 1
Find the measure of the third interior angle of triangle
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
x+109+13=180
solve for x
x=180-122
x=58 degrees
step 2
Applying the law of sines
?/sin(13)=6/sin(58)
solve for ?
?=(6/sin(58))*sin(13)
?=1.6 unitsSuppose you are looking to purchase some cans to use for food storage. The can you are looking at has a diameter of 5in. and a height of 7in. What is the volume of the can? Round to the nearest hundredth
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
We are given the diameter is 5
r = d/2 = 5/2 = 2.5 in
V = pi ( 2.5)^2 (7)
V =pi ( 6.25)*7
V = 43.75 pi
Assuming a value for pi of 3.14
V =137.375 in ^3
Rounding to the nearest hundredth
V = 137.38 in ^3
Assuming a value for pi by using the pi button
V = 137.44468
Rounding to the nearest hundredth
V = 137.44 in ^3
What is 16m + 24n? (P.S, this is about factoring expressions.)
aWe can factorize by a common factor
[tex]16m+24n[/tex][tex](8\times2)m+(8\times3)n[/tex][tex]8(2m+3n)[/tex]ANSWER
8(2m+3n)
Which graph represents the solution set of the
inequality 4x>-8?
Answer:
The answer is C.
Step-by-step explanation:
In order to solve this, you must use an inequality from one side of the equation.
Inequality is the growing inequality between rich and poor.
4x>-8First thing you do is divide by 4 from both sides.
[tex]\sf{\dfrac{4x}{4} > \dfrac{-8}{4}}[/tex]
Solve.
Divide these numbers goes from left to right.
-8/4=-2
[tex]\boxed{\sf{x > -2}}[/tex]
Therefore, the graph represents the solution set of the inequality of 4x>-8 is C, which is our answer.
I hope this helps, let me know if you have any questions.
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the equation. (3, 7); y=3x+7
The linear equation parallel to y= 3x + 7 is:
y = 3x - 2
How to find the linear equation?A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Two lines are parallel only if the lines have the same slope and different y-intercepts.
So a line parallel to y = 3x + 7 will be of the form:
y = 3x + c
To find the value of c we use the point (3, 7) which must belong to the line, replacing the values in the linear equation:
7 = 3*3 + c
7 = 9 + c
7 - 9 = c
-2 = c
The linear equation is y = 3x - 2
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