Answer:
$4,562.5
Step-by-step explanation:
The amount Arvin has to invest, P = $10,000
The interest paid on the investment in the term deposit = 5%/year
The interest paid om the investment in Canada savings bonds = 3.4%/year
The amount Arvin earned at the of the year as simple interest, A = $413
Let, x, represent the amount Arvin invested in the term deposit and let, y, represent the amount he invested in Canada savings bonds, we can get the following system of equations
x + y = 10,000...(1)
0.05·x + 0.034·y = 413...(2)
Making y the subject of equation (1) and substituting the value in equation (2), we get;
From equation (1), we get, y = 10,000 - x
Plugging the above value of y in equation (2) gives;
0.05·x + 0.034 × (10,000 - x) = 413
∴ 0.05·x - 0.034·x + 340 = 413
x = (413 - 340)/(0.05 - 0.034) = 4,562.5
Therefore, the amount Arvin invested in the term deposit at 5%, x = $4,562.5
(y = 10,000 - x
∴ y = 10,000 - 4,562.5 = 5,437.5
The amount Arvin invested in Canada savings bonds, y = $5,437.5.)
whats the lowest common multiple of 120 and 19600
Answer:
Multiples of 120 are 120, 240, 360, 480, 600, 720, 840 etc; Multiples of 150 are 150, 300, 450, 600, 750, 900 etc; Therefore, the least common multiple of 120 and 150 is 600.
Least common multiple (LCM) of 19600 and 19619 is 384532400.
Answer: 19600
Step-by-step explanation:
19600/120 = 160
Please help me with this problem
Answer:
6a = 6 * a
2a * b = 2ab
Step-by-step explanation:
2a * 2b = 4ab not 2ab
6 * a is the same as 6a
5a = 5 * a not 5 + a
3ab has different variables then 3c therefore the expression cannot be true
2ab is the same as 2a * b
-6x=48-6y
-4x=50-6y
HELP PLZZZ
Answer:
[tex]x=1,\\y=9[/tex]
Step-by-step explanation:
When solving a system of equations, one of the faster methods to solve this system is the process of elimination. This process involves manipulating one of the equations (by multiplying it by a certain value), such that when one adds the two equations in the system, one of the variables cancels. One can then solve for the other variable in the system. Then backsolve for the other variable; by substituting the value of the found variable into the system, simplifying and using inverse operations to solve for the other variable.
[tex]-6x=48-6y\\\\-4x=50-6y[/tex]
Manipulate, multiply one of the equations by a certain value such that the coefficient of the like term in the other equation is the additive inverse of it.
[tex](-6x=48-6y)*(-1)\\\\-4x=50-6y[/tex]
Simplify,
[tex]6x=-48+6y\\\\-4x=50-6y[/tex]
Add the equations in the system,
[tex]6x=-48+6y\\\\-4x=50-6y[/tex]
[tex](6x)+(-4x)=(-48)+(50)+(6y)+(-6y)[/tex]
Simplify,
[tex](6x)+(-4x)=(-48)+(50)+(6y)+(-6y)[/tex]
[tex]2x=2[/tex]
Inverse operations,
[tex]2x=2[/tex]
[tex]x=1[/tex]
Backsolve to find the value of (y).
[tex]-4x=50-6y[/tex]
[tex]x=1[/tex]
Substitute,
[tex]-4(1)=50-6y[/tex]
Simplify,
[tex]-4=50-6y[/tex]
Inverse operations,
[tex]-4=50-6y[/tex]
[tex]-54=-6y[/tex]
[tex]9=y[/tex]
A line passes through the points (-1, -1)
and (5,8). Which points lie on the same
line? Select all that apply.
(-3, -4)
(9, 14)
(1, 2)
(4, 7)
(3,5)
(-2,-2)
Given:
A line passes through the points (-1, -1) and (5,8).
To find:
Which points lie on the same line?
Solution:
If a line passes through two points, then the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:
[tex]y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))[/tex]
[tex]y+1=\dfrac{8+1}{5+1}(x+1)[/tex]
[tex]y+1=\dfrac{9}{6}(x+1)[/tex]
[tex]y+1=\dfrac{3}{2}(x+1)[/tex]
Multiply both sides by 2.
[tex]2(y+1)=3(x+1)[/tex]
[tex]2y+2=3x+3[/tex]
[tex]2y=3x+3-2[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex]
So, the equation of the line is [tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex].
Now, check each point for this equation.
Putting [tex]x=-3[/tex], we get
[tex]y=\dfrac{3}{2}(-3)+\dfrac{1}{2}[/tex]
[tex]y=\dfrac{-9+1}{2}[/tex]
[tex]y=\dfrac{-8}{2}[/tex]
[tex]y=-4[/tex]
Similarly,
For [tex]x=9,y=15[/tex].
For [tex]x=1,y=2[/tex].
For [tex]x=4,y=6.5[/tex].
For [tex]x=3,y=5[/tex].
For [tex]x=-2,y=-2.5[/tex].
Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.
PLEASE HELP !!!
Annabelle went to the store to buy some apples. The price per pound of the apples is $3.75 per pound and she has a coupon for $3.25 off the final amount. With the coupon, how much would Annabelle have to pay to buy 3 pounds of apples? Also, write an expression for the cost to buy pp pounds of apples, assuming at least one pound is purchased.
final cost of 3 pounds: ______
final cost of p pounds: ______
Answer:
final cost of 3 pounds: 8 dollars
final cost of p pounds: 3.75p - 3.25 dollars
Step-by-step explanation:
Each pound costs $3.75, so 3 pounds cost 3*3.75 = 11.25 dollars. Subtract off the $3.25 to get the final cost to be 11.25-3.25 = 8 dollars. This takes care of the first part.
For the second part, the expression for the final cost is 3.75p - 3.25; where the 3.75p is the cost before the coupon is applied. If you plugged p = 3 into that expression, you should get 8 as a result. The variable p is some positive whole number. It's a place holder for the number of pounds of apples.
At Billy's school, 80 students come to school by bicycle or by car. Together, the vehicles they arrive to school in have 270 wheels. How many of each are used
Answer:
x = number of bicycles = 35
y = number of cars = 55
Step-by-step explanation:
Let
x = number of bicycles
y = number of cars
x + y = 80 (1)
2x + 4y = 270 (2)
From (1)
x = 80 - y
Substitute x = 80 - y into (2)
2x + 4y = 270 (2)
2(80 - y) + 4y = 270
160 - 2y + 4y = 270
- 2y + 4y = 270 - 160
2y = 110
y = 110/2
y = 55
Substitute y = 55 into (1)
x + y = 80 (1)
x + 55 = 80
x = 80 - 55
x = 35
x = number of bicycles = 35
y = number of cars = 55
What's a boxplot? Also provide an example...
Answer:
BOXPLOT is a simple way of representing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, usually with a vertical line inside to indicate the median value. The lower and upper quartiles are shown as horizontal lines either side of the rectangle.
Step-by-step explanation:
Example 1: Draw a box-and-whisker plot for the data set {3, 7, 8, 5, 12, 14, 21, 13, 18}.
From our Example 1 on the previous page, we had the five-number summary:
Minimum: 3, Q1 : 6, Median: 12, Q3 : 16, and Maximum: 21.
CHECK THE ABOVE PICNotice that in any box-and-whisker plot, the left-side whisker represents where we find approximately the lowest 25% of the data and the right-side whisker represents where we find approximately the highest 25% of the data. The box part represents the interquartile range and represents approximately the middle 50% of all the data. The data is divided into four regions, which each represent approximately 25% of the data. This gives us a nice visual representation of how the data is spread out across the range.
Step-by-step explanation:
In descriptive statistics, a box plot or boxplot (also known as box and whisker plot) is a type of chart often used in explanatory data analysis. Box plots visually show the distribution of numerical data and skewness through displaying the data quartiles (or percentiles) and averages.
What is the volume of the prism?
A rectangular prism with cubic units arranged in two rows of two with six total layers. Each cubic unit is one cubic meter.
14 m3
24 m3
30 m3
44 m3
Answer:
24 m³
Step-by-step explanation:
We need to find the volume of the prism. Given that , rectangular prism with cubic units arranged in two rows of two with six total layers . And the volume of each unit is 1 m³ .
Volume of one unit :-
[tex]\rm\implies Volume_{one\ unit } = 1m^3 [/tex]
By Unitary Method :-
Volume of two cubes , will be :-
[tex]\rm\implies Volume_{two\ unit } = 2m^3 [/tex]
Volume of one layer :-
[tex]\rm\implies Volume_{one\ layer } = 4m^3 [/tex]
Volume of six layers :-
[tex]\rm\implies Volume_{6\ layers } = 4m^3\times 6 \\\\\rm\implies \boxed{\rm Volume_{6\ layers } = 24 \ m^3} [/tex]
what is the solution to -6 - -25=
Answer:
19
Step-by-step explanation:
(-6)-(-25)=(-6) +25 = 19
Find the scale factor of the dilation. Then tell whether the
dilation is a reduction or an enlargement
Answer:
Enlargement
k =[tex]\frac{18}{4}[/tex] = [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
k = [tex]\frac{new}{old}[/tex]
If k > 1 then its an enlargement.
If k < 1 then its a reduction
Lola needs to sign 96 invitations. Using a stopwatch that measures time to tenths of a second, it takes Lola 5.3 seconds to sign her full name. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of seconds Lola needs to sign all 96 invitations?
508 seconds
510 seconds
509 seconds
508.8 seconds
Answer:
508.8 seconds
Step-by-step explanation:
The most accurate determination mathematically is to assume that Lola will maintain an average of 5.3 seconds per signature as she signs all 96 invitations.
Therefore, multiply the time it takes her to sign each invitation (5.3 seconds) by the total number of invitations there are (96 invitations) to get the projected total amount of time that it will take Lola to sign all 96 invitations:[tex]96\cdot 5.3=\boxed{508.8\text{ seconds}}[/tex]
Answer:
508.8 seconds (8.48 minutes)
Step-by-step explanation:
96 × 5.3 = 508.8
PLZ ANSWER ILL GIVE BRAINLIEST
Answer:
B. neither perpendicular nor parallel
Step-by-step explanation:
to be perpendicular, the slopes have to be complete opposites. in this case, the second term would have to be y=-0.5x to be perpendicular. to be parallel, the two would have to have the same slopes; so y=2x and y=2x
Which of the following graphs represents the equation y-2 = 3(x - 1)?
Answer:
Graph B
Step-by-step explanation:
The vertical intercept I am getting is (0,-1) and B is the only one with that point. Therefore, it should be B.
factorise the following. x²-4
(x-2)(x+2) is factorize is given eq
an object falls from a height, h m, varies directly as the square of its time, t s on planet Q. given that the object falls from the height of 5 m in 2 s, calculate the time taken in seconds, for the object to fall from a height of 45 m on the planet.
Answer:
18 seconds
Step-by-step explanation:
5x9=45 so 2x9=18
David is paid a salary of $1850 per month. He is also paid time and a half for work in excess of 40 hours a week. He worked 62 hours last week. What is his gross pay?
Answer:
$1,471.5625
Step-by-step explanation:
Monthly salary = $1850
Weekly salary = $1850/4 weeks
= $462.5
Hourly rate = $462.5/40 hours
= $11.5625
Overwork time = 62 hours - 40 hours
= 22 hours
Time and a half = 1.5 times the normal salary
Overwork time payment per hour = 1.5 × $11.5625
= $17.34375
Overwork time payment for 22 hours = 22 × $17.34375
= $381.5625
Last week salary = weekly salary + overtime payment
= $462.5 + $381.5625
= $84.0625
Gross salary for the month = 3 weeks regular salary + last week salary
= (3 × $462.5) + $84.0625
= $1387.5 + $84.0625
= $1,471.5625
Help, please answer this for me
Answer:
For this problem, we need to add to the price of the phone (50 $) the cost of the data usage (which is 0.20 $ per minute).
If he spends on average 200 minutes, we can calculate what that costs by multiplying the number of minutes by the cost of each one: 200 * 0.2 = $40
And we can now add to the $50 the $40: 50 + 40 = $90
Answer:
$40
Step-by-step explanation:
$.20×200=$40
it's pretty simple
It would be great if someone could help me with this problem
Express sin O as a fraction in simplest form
Answer:
sin o = opposite/hypotenuse
sin o= 7/12
What is the correct expansion of (2x+3) (2x^2-5)
Answer:
4x^3 + 6x^2 -10x - 15
Step-by-step explanation:
* means multiply
4x^3 + 6x^2 -10x - 15
2x * 2x^2 = 4x^3
2x * -5 = 10x
3 * 2x^2 = 6x^2
3 * -5 = -15
Answer:
4x³ + 6x² - 10x - 15
Step-by-step explanation:
(2x+3) (2x²-5)
4x³ - 10x + 6x² - 15
4x³ + 6x² - 10x - 15
PLEASE HELP ASAP !!!
compare and contrast how to graph x=2 and y=-4
Answer:
I attached pictures of the two graphs, I hope they help!
Step-by-step explanation:
Answer:
x = 2 is a vertical line going through 2 on the x-axis. It has an undefined slope.
y = 4 is a horizontal line going through 4 on the y-axis. It has a slope of zero
They are perpendicular.
Step-by-step explanation:
For the function f(x) =x 1/5 /8, find f-1(x)
Second option is correct
What is the distance between (-1,2) and (-5, 2)
Answer:
4
Step-by-step explanation:
The distance between the points (-1,2) and (-5,2)
[tex] \sqrt{( - 5 - ( - 1)) ^{2} + (2 - 2) ^{2} } \\ = \: \sqrt{( - 4)^{2} + (0) ^{2} } \\ = \sqrt{16 + 0} \\ = \sqrt{16} \\ = 4[/tex]
Answered by GAUTHMATH
p(x)=x2-1;x=-2 find wheter the following zeroes of the pollynomials are indicated towsrds them
Given:
The polynomial is:
[tex]p(x)=x^2-1[/tex]
To find:
Whether [tex]x=-2[/tex] is a zero of the given polynomial or not.
Solution:
If [tex]x=c[/tex] is a zero of a polynomial, then [tex]f(c)=0[/tex].
We have,
[tex]p(x)=x^2-1[/tex]
Putting [tex]x=-2[/tex] in the given polynomial.
[tex]p(-2)=(-2)^2-1[/tex]
[tex]p(-2)=4-1[/tex]
[tex]p(-2)=3[/tex]
Since [tex]p(-2)\neq 0[/tex], therefore [tex]x=-2[/tex] is not a zero of the given polynomial.
A single equation representing both lines x+y=0 and x+2y = 0 is ?
Answer:
The single equation is [tex]y = 0[/tex]
Step-by-step explanation:
We are given the following system of equations:
[tex]x + y = 0[/tex]
[tex]x + 2y = 0[/tex]
From the first equation:
[tex]x = -y[/tex]
Replacing in the second equation:
[tex]-y + 2y = 0[/tex]
[tex]y = 0[/tex]
The single equation is [tex]y = 0[/tex]
Select the expression that represents the following statement: add 24 to the quotient of 16 and 8.
Answer:
16/8 + 24
Step-by-step explanation:
what is the answer for 9x² + 3xy - 12x - 4y
Answer:
(3x + y)(3x - 4)
Step-by-step explanation:
9x² + 3xy - 12x - 4y =
There is no common factor in the 4 terms.
Since there are 4 terms, we try factoring by grouping.
Find a common factor in the first two terms, and find a common factor in the last two terms.
= 3x(3x + y) - 4(3x + y)
Now factor out the common factor 3x + y.
= (3x + y)(3x - 4)
On evaluating the expression 10(x - 20y) + 100x, the answer will be
Answer:
110x -200y
Step-by-step explanation:
10(x - 20y) + 100x
Distribute
10x-200y +100x
Combine like terms
110x -200y
Answer:
110x−200y
Step-by-Step Explanation:
Given:
10(x−20y)+100x
First Step: Distribute
(10)(x)+(10)(−20y)+100x
10x+−200y+100x
Second Step: Combine Like Terms:
10x+−200y+100x
(10x+100x)+(−200y)
110x+−200y
Answer:
=110x−200y
I have no idea how to do this, it is due in two days. Hopefully someone sees this before then.
Hello,
[tex]m\ \widehat{ABC}=x\\m\ \widehat{BAC}=2*x\\\\So:\\ x+2x=90^o\\x=30^o\\[/tex]
[tex]cos(30^o)=\dfrac{\sqrt{3} }{2} \\[/tex]
In the triangle ABC,
[tex]cos(30^o)=\frac{BC}{BA} \\\\BA=\dfrac{cos(30^o)}{BC} \\\\BA=\frac{\dfrac{\sqrt{3} }{2} }{24} =16*\sqrt{3} \\\\[/tex]
[tex]sin(30^o)=\dfrac{1 }{2} =\dfrac{AC}{AB} \\\\AC=\dfrac{1}{2} *16\sqrt{3} =8\sqrt{3}[/tex]
In the triangle ACB,
[tex]cos(30^o)=\dfrac{AC}{AL} \\\\AL=\dfrac{8\sqrt{3} *2}{\sqrt{3} } =16\\[/tex]
Please help me finish these for summer school :)