Answer:
The amount invested in ADB is ¢1363.[tex]\overline 3[/tex] =
The amount invested in Barclays is ¢3,427.[tex]\overline 3[/tex]
The amount invested in GCB is ¢1,713.[tex]\overline 3[/tex]
Step-by-step explanation:
The parameters of the investment Stonewall made are;
The amount in interest he receives from ADB, Barclays and GCB = ¢250
The amount of interest ADP pays = 2% per annum
The amount of interest Barclays pays = 4% per annum
The amount of interest GCB pays = 5% per annum
The amount invested in Barclays = The amount invested in ADB and GCB + ¢350
The amount invested in Barclays = 2 × The amount invested in GCB
a) Let 'x', represent the amount invested in ADB, 'y' represent the amount invested in Barclays, and 'z', represent the amount invested in GCB
We have;
y = x + z + 350
y = 2·z
0.02·x + 0.04·y + 0.05·z = 250
Therefore, we get the three linear equations as follows;
-x + y - z = 350...(1)
y - 2·z = 0...(2)
0.02·x + 0.04·y + 0.05·z = 250...(3)
Using Matrix inversion, we have;
[tex]\left[\begin{array}{ccc}-1&1&-1\\0&1&-2\\0.02&0.04&0.05\end{array}\right] \times \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}350&0&250\end{array}\right][/tex]
The transpose of the 3 by 3 matrix [tex]M^T[/tex] is given as follows;
[tex]M^T = \left[\begin{array}{ccc}-1&0&0.02\\1&1&0.04\\-1&-2&0.05\end{array}\right][/tex]
The Adjugate Matrix is given as follows;
[tex]Adj = \left[\begin{array}{ccc}0.13&-0.09&-1\\-0.04&-0.03&-2\\-0.02&0.06&-1\end{array}\right][/tex]
The inverse of the matrix = Adj/Det where, Det = -0.15, is therefore;
[tex]M^{-1} = \left[\begin{array}{ccc}\dfrac{-13}{15} &\dfrac{3}{5} &\dfrac{20}{3} \\\\\dfrac{4}{15} &\dfrac{1}{5} &\dfrac{40}{3} \\\\\dfrac{2}{15} &-\dfrac{2}{5} &\dfrac{20}{3} \end{array}\right][/tex]
We therefore, get the solution as follows;
[tex]\left[\begin{array}{ccc}\dfrac{-13}{15} &\dfrac{3}{5} &\dfrac{20}{3} \\\\\dfrac{4}{15} &\dfrac{1}{5} &\dfrac{40}{3} \\\\\dfrac{2}{15} &-\dfrac{2}{5} &\dfrac{20}{3} \end{array}\right]\times \left[\begin{array}{c}350&0&250\end{array}\right] = \left[\begin{array}{c}\dfrac{4,090}{3} \\&\dfrac{10,280}{3} \\ & \dfrac{5,140}{3} \end{array}\right][/tex]
[tex]\begin{array}{c}x = \dfrac{4,090}{3} \\&y = \dfrac{10,280}{3} \\ & z = \dfrac{5,140}{3} \end{array}[/tex]
The amount invested in ADB, x = ¢4,090/3 = ¢1363.[tex]\overline 3[/tex]
The amount invested in Barclays, y = ¢10,282/3 = ¢3,427.[tex]\overline 3[/tex]
The amount invested in GCB, z = ¢5,140/3 = ¢1,713.[tex]\overline 3[/tex]
if there are 24 boys and 6 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
Answer:
4:1, 6:2, 12:3, 24:6
Step-by-step explanation:
24 boy
6 girls
possible ratio
24 ÷ 6 = 4
6÷ 6 = 1
4 : 1
24 ÷ 3 = 6
6 ÷ 3 = 2
6 : 2
24 ÷ 2 = 12
6 ÷ 2 = 3
12 : 3
24 ÷ 1 = 24
6 ÷ 1 = 6
24 :6
HELP PLEASE Quadratic Equations Math Nation
Answer:
its 5/6
Step-by-step explanation:
we just group things around and we have this
36 m^2 - 60 m = -25
Alternate forms:
12 m (3 m - 5) = -25
36 m^2 - 60 m + 25 = 0
Solution:
m = 5/6
Which value of "X" is a solution to this equation?
4x2 +22x +10
Answer:
Two solutions: X = -5 and X = -0.5
Step-by-step explanation:
4x^2 + 22x + 10 = 0 // divide by 2
2x^2 + 11x + 5 = 0
delta = 11^2 - 4 * 2 * 5 = 121 - 40 = 81
sqrt(delta) = 9
x1 = (-11 - 9) / 4 = -5
x2 = (-11 + 9) / 4 = -0.5
please help me with the answer, ive been stuck on getting both answers for a while now ty
Answer:
[tex]3x + x - 17 + 13 = 116 \\ 4x = 120 \\ x = 30 \\ g = 73 \\ h = 43[/tex]
A roller coaster goes down 0 feet and then up 55 feet.
Answer:
was that the full question? i cant seem to understand what your asking
Step-by-step explanation:
Evaluate the expression below
(1/7)³
Answer:
1/49
Step-by-step explanation:
[tex] \purple{ \tt{ \huge{ \: ✨Answer ✨ \: }}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \red{ \boxed{ \boxed{ \tt{ \huge{{ \: {7}^{ - 3}}}}}}} [/tex]
Help please I’m being timed!!
Answer:d
Step-by-step explanation:
What is the surface area of the cone? (Use 3.14 for π.)
339.12 cm ^2
715.92 cm ^2
307.72 cm ^2
417.62 cm ^2
Answer:
tambil anseeciot
Step-by-step explanation:
three times than five times a number
Answer:
15
Step-by-step explanation:
Solve. Round to the nearest hundredth.
(Help! Will give brainliest)
What is the following product
Answer:
the answer is 7x^2-12x square root of 14 +72 (option 2)
Step-by-step explanation:
Position 3 Value of Term 8 20 Com
How could an Environmental Science and Protection Technician and an Environmental Engineering Technician be compared?
The careers are basically the same because both focus on protecting the environment.
Both focus on protecting the environment, but an Environmental Science and Protection Technician uses equipment to reduce the impact of issues while an Environmental Engineering Technician performs tests to identify issues.
Both focus on protecting the environment, but an Environmental Science and Protection Technician performs tests to identify issues while an Environmental Engineering Technician uses equipment to reduce the impact of issues.
The careers are different and belong to different career pathways within Manufacturing.
Answer:
the third one is correct. based on recent studies that i have read based on this topic. it should be right.
brainliest?
Step-by-step explanation:
3
Step-by-step explanation
edg
Please help!! Area!!
Answer:
5*8*4
Step-by-step explanation:
Multipy them together lol
Solve for the given variable in the equation: ½ n - 3 = 5
n = _______
Answer:
The correct solution is "n = 16".
Step-by-step explanation:
The given equation is:
⇒ [tex]\frac{1}{2} n-3=5[/tex]
On adding "3" both sides, we get
⇒ [tex]\frac{1}{2} n-3+3=5+3[/tex]
⇒ [tex]\frac{1}{2}n=8[/tex]
On applying cross multiplication, we get
⇒ [tex]n=8\times 2[/tex]
⇒ [tex]n=16[/tex]
MULTIPLE CHOICE !! HELP
Answer:
Its D
Step-by-step explanation:
What is the following product
Answer:
6 (square root )432 (option 3)
Step-by-step explanation:
Answer:
Step-by-step explanation:
⁶√(432)
Mike has a fish tank in the shape of a rectangular prism with dimesions of 6 feet by 5 feet by 3 feet. He has a canister that he uses to fill up the fish tank that is in the shape of a cylinder with a diameter of 2 feet and a height of 4 feet. How many tiems will he need to fil up the canister to fill up the tank?
Answer:
7 times
Step-by-step explanation:
To answer this question :
1. the volume of the rectangular prism has to b determined
2. the volume of the cannister has to be determined
3. divide the volume of the rectangular prism by the volume of the cannister
Volume of the rectangular prism = Width X Height X Length = 6 x 5 x 3 = 90ft³
Volume of a cylinder = πr²h
where
h = height
π = 3.14
Diameter = 2r
radius = 2/2 = 1 feet
3.14 x 1 x 4 = 12.56 feet
90 / 12.56 = 7.2 times
Approximating to the nearest whole number gives 7 times
Anyone know this cause my sister been lost for a day on this. I know it's nice t that hard to most of y'all but it's hard for her. ( will give big brain if I can)
Answer: The book tax is $1.10 and the video game is $3.40 so i'll let you figure this out
tell your sister that the nae nae frog has blessed her with the answer
The volume of the sphere is about (blank) ft.
Answer:
[tex]14.13[/tex]
Step-by-step explanation:
V=[tex]\frac{4}{3}[/tex][tex]\pi r^{3}[/tex]
Answer:
[tex] \displaystyle V_{ \text{sphere}} =14.13 \: \rm ft^{3} [/tex]
Step-by-step explanation:
we are given the redious of a sphere
we want to figure out the volume
remember that,
[tex] \displaystyle V_{ \text{sphere}} = \frac{4}{3} \pi {r}^{3} [/tex]
since we are given the redious we can substitute
[tex] \displaystyle V_{ \text{sphere}} = \frac{4}{3} \pi { \times 1.5}^{3} [/tex]
as the approximate value of π is given
substitute:
[tex] \displaystyle V_{ \text{sphere}} = \frac{4}{3} \times 3.14 { \times 1.5}^{3} [/tex]
we know the order of PEMDAS. Parentheses, Exponent, Multiplication or Division, Addition or substraction
so
simplify square:
[tex] \displaystyle V_{ \text{sphere}} = \frac{4}{3} \times 3.14 { \times 3.375}[/tex]
reduce fraction:
[tex] \rm\displaystyle V_{ \text{sphere}} = \frac{4}{ \cancel{ 3 \: }} \times 3.14 { \times \cancel{ 3.375}} \: ^{1.125} [/tex]
[tex] \displaystyle V_{ \text{sphere}} = 4\times 3.14 \times 1.125[/tex]
simplify multiplication:
[tex] \displaystyle V_{ \text{sphere}} =14.13[/tex]
since we cubed the redious and the redious is in feet, we of course use cubic feet
[tex] \displaystyle V_{ \text{sphere}} =14.13 \: \rm ft^{3} [/tex]
need help
problem/question in image below
Answer:
Option A would be the correct answer
I don't have an explanation to type but you can trust me :)
Please mark as brainliest for further answers :)Please help I can’t figure it out NO LINKS
LINKS= REPORT
Select the statement that describes this expression: 5 x (3 + 4) − 4. (2 points)
5 times the sum of 3 and 4, then subtract 4
5 times 3 plus 4 minus 4
5 more than the sum of 3 and 4, and then subtract 4
5 times 3 plus the difference of 3 and 4
Answer:
5 times the sum of 3 and 4, then subtract 4
Answer:
5 times the sum of 3 and 4, then subtract 4
Step-by-step explanation:
Hope this helps
******WORTH 85 POINTS******WILL MARK BRAINLIEST*****PLEASE ANSWER ALL QUESTIONS****
A catering company is setting up tables for a big event that will host 360 people. When they set up the tables they need 2 forks for each
child and 5 forks for each adult. The company ordered a total of 1470 forks. Set up a system of equations involving the number of adults,
a, and the number of children, c, and solve to find out how many of each attended the event.
A) Create an equation to represent the breakdown of people attending this event (children and adults).
B) Create an equation to model the number of forks used at this event.
C) Solve the system you created and write down the number of Children and Adults that attended.
180 c
70 a
360 divided by 2 = 180 c
360 divided by 5 = 70 a
63
Which expression is not equivalent to
66
A
62
B
1
216
1
D
Answer:1216
Step-by-step explanation:
It’s to big and if this helps plz but a brainly :)
what are systems of equations and inequalities definitions?
Answer:
A system of equations is a set of equations with the same variables. A system of inequalities is almost exactly the same, except you're working with inequalities instead of equations. To solve such a system, you need to find the variable values that will make each inequality true at the same time.
Step-by-step explanation:
Hope this helps. :D
What is the distance between the points (-5, 9) and (4, 9) on the coordinate plane? 9 9 1 1 10 10 90
Answer:
9 units
Step-by-step explanation:
Given: Two points on a coordinate plane are [tex](-5,9),\,(4,9)[/tex]
To find: distance between points [tex](-5,9),\,(4,9)[/tex]
Solution:
According to the distance formula,
Distance between points [tex](a,b)[/tex] and [tex](c,d)[/tex] is equal to [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]
Take [tex](a,b)=(-5,9),\,(c,d)=(4,9)[/tex]
Therefore,
Distance between points [tex](-5,9),\,(4,9)[/tex] [tex]=\sqrt{(4+5)^2+(9-9)^2}[/tex]
[tex]=\sqrt{(9)^2}[/tex]
[tex]=9[/tex] units
3)
The first number minus the second number
is always eight
Answer:
Well, I mean, that's a vague question. there are a ton of numbers where you can subtract a second number and have it equal eight. 15 - 7 = 8
Step-by-step explanation:
Hola me podría alguien ayudar con esto? Muchas gracias!
Answer:
Las respuestas estan a continuacion.
Step-by-step explanation:
Tres mas que un numero = a+3
La diferencia entr eun numero y 5 = a - 5
4 menos que n = 4 - n
Un numero aumenta en 1 = x + 1
Un numero disminuido en 10 = z - 10
El producto de dos numeros = x*y
Dos veces la suma de dos numeros = 2(a+b)
Doce veces un numero sumado a otro = 2a+b
El coceinte de dos numeros = a/b
Un numero aumentado en 3 = x+3
Un numero dismunuido en 2 = a - 2
El producto de m y n = m*n
El antecesor de un numero cualquiera = n - 1
El sucesor de un numero cualquiera = x+1
Espero te haya servido!
Hey I'm taking a math exam tomorrow please send words of encouragement please answer.
Answer:
did you study????? well if u did then why u scareddd shortteee.
