PLEASE HELP THIS IS TIMED!!!

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]

Answer:

Step-by-step explanation:

a. annual premium: 79.35

b. monthly premium: 7.14

Marcie Ann Weber, age 32, takes out $15,000 of a term insurance for a ten-year term. Annual premium = $1,500 per year and monthly premium = $125 per month.

One type of operation is division in mathematics. In this procedure, the phrases or numbers are divided into the same number of components.

Given: Marcie Ann Weber,

insured amount of term insurance plan = $15,000.

Number of year = 10 year

To find the amount of annual premium:

Divide the total insured amount by number of years.

Annual premium = Insured amount of term insurance plan / Number of year

Annual premium = $15,000 / 10

Annual premium = $1,500 per year

To find the amount of monthly premium:

Monthly premium = Insured amount of term insurance plan / Number of month in 10 year

Monthly premium = 15,000 / (10 x 12)

Monthly premium = 15,000 / 120

Monthly premium = $125 per month.

Therefore, annual premium = $1,500 per year and monthly premium = $125 per month.

To learn more about the division;

https://brainly.com/question/13263114

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Answer:

8

x

3

+

2

x

2

−

3

x

+

18

Step-by-step explanation:

simply the answer thought bc i didn't simplify

Answer:

circle area = 50.24 units²

Step-by-step explanation:

circle area = πr² = 3.14(4²) = 3.14(16) = 50.24 units²

Answer:

It's 3[tex]x^{2}[/tex]/86

hope this helps:)

Answer:

Sum = 4 + 5 = 9

Step-by-step explanation:

Equation

2*(x - 2)(x-2) = (x - 3)(x + 4)

Solution

2*(x^2 - 4x + 4) = x^2 + 4x - 3x - 12

2x^2 - 8x + 8  = x^2 +x - 12                     Subtract the right side from the left

x^2 - 9x + 20 = 0

(x - 4)(x - 5) = 0

The possible values for x are

x - 4 = 0

x = 4

x - 5 = 0

x = 5

Check

(4 - 2)^2 = (4) = 4

(x - 3)(x + 4) = (4 - 3)(8) = 8

This checks

(5 - 2)^2 = 3^2 = 9

(5 - 3)(5 + 4) = 2 * 9 = 18

Answer:

-1.4  ; -0.7  ; 0.003   ; 3%    ;  0.3   ;  2/3  ;    7/8  ;   100/50

Step-by-step explanation:

0.003 ;  -1.4 ;  100/50 = 2 ;  0.85 ; 2/3 = 0.67  ; 3% = 3/100 = 0.03 ; 7/8 = 0.875 ;

0.3 , -0.7

0.003 ;  -1.4 ;   2 ;  0.85 ;  0.67  ;   0.03 ;   0.875 ; 0.3    ; -0.7

Least to greatest:

-1.4 ; - 0.7   ; 0.003  ;   0.03  ;   0.3   ;  0.67  ; 0.85    ;2

-1.4  ; -0.7  ; 0.003   ; 3%    ;  0.3   ;  2/3  ;    7/8  ;   100/50

Negative numbers have least value.Then  in decimal numbers, the number having the least value in tenth is the least

Answer:

−1+1.732051i

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The probability is 1/3

Answer:

i am unsure

Step-by-step explanation:

I HEART POINTS

Answer:I believe D

Step-by-step explanation: Hope you get it right

Answer:

Relative frequency

Step-by-step explanation:

8 x 7s = 56s

8 x (-2) = -16

so 8(7s - 2) = 56s - 16

50. 150 divided by 3

Answer:what’s classification

Step-by-step explanation:

Answer without Explanation:

B

Answer:

a) 1/2, 0.5, 50% b)3/4, 0.75, 75% c) 1/12, 0.08333, 8.333% d) 5/12, 41.6667%, 0.416

Step-by-step explanation:

Answer:

a] 1/2 b] 5/6 c] 1/6 d] 5/4

Step-by-step explanation:

no of even no present/total numbers and so on

try it later

Answer:

375

Step-by-step explanation:

500-125(25% of 500)=375

Answer:

20 people chosen to March

Step-by-step explanation:

The sample can be explained as a random subset of the population. It is a given number of draws or selection made usually at Random from the entire or larger population set. The sample is usually smaller Than the population and if done randomly will be representative of the population set. The entire spectator attending the baseball game is the population of interest while the 20 selected from the entire pool to March in the victory parade is the sample data obtained from the population set.

Answer:

x = 0

Step-by-step explanation:

hi there!

im not sure if the x between the 2's is a x as in a variable or if it is multiplication sign. im going to solve the problem as if it is a multiplication sign but if that is wrong then please let me know!

2 * 2 + x - 4 = 0

is our equation that we are working with ^

first step is, following the pemdas we multiply *2 with its self

( ^ parentheses, exponents, multiplication/ division making sure to solve it left to right, addition and subtraction still making sure to follow the left to right rule )

2 * 2 + x - 4 = 0

2 * 2

= 4 + x - 4 + 0

then we add positive 4 and negative 4 together, canceling eachother out the giving us the answer of  x = 0

4 + x - 4 + 0

4 + - 4 = 0

x = 0

i hope this helps you! have a good rest of your day :)

Answer:

A vertical line

Answer:

-12/35

Step-by-step explanation:

-3×4/5×7

-12/35

Answer:

m∠R = 123°

m∠S = 91°

Step-by-step explanation:

The measure of an inscribed angle is 1/2 the measure of the intercepted arc

m of arc QRS = 2 m∠P = 2(57) = 114

Now m of arc SPQ = 360 - 114 = 246

So, m∠R = 1/2(246) = 123

m of arc RSP = 2 m∠Q = 2(89) = 178

m of arc PQR = 360 - 178 = 182

m∠S = 1/2(182) = 91

Answer: (4+1)*5=25; (25+1)*5=130; (130+1)*5=655.

Step-by-step explanation:

Answer:

c = [tex]\sqrt{58}[/tex]

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

c² = 7² + 3² = 49 + 9 = 58 ( take the square root of both sides )

c = [tex]\sqrt{58}[/tex]

Answer:

Step-by-step explanation:

According to Pythagoras Theorem:

[tex] {7}^{2} + {3}^{2} = {c}^{2} [/tex]

Hence,

[tex] = > {c}^{2} = {7}^{2} + {3}^{2} [/tex]

[tex] = > {c}^{2} = 49 + 9[/tex]

[tex] = > {c}^{2} = 58[/tex]

[tex] = > c = \sqrt{58} [/tex]

So,

[tex]c = \sqrt{58} [/tex]

Is the answer.

Answer:

(a) His speed when he runs from C to A is [tex]4.\overline {285714}[/tex] m/s

(i) The bearing of B from A is approximately 127.18°

(ii) The bearing of A from B is approximately 307.18°

Step-by-step explanation:

(a) The given parameters are;

The distance from A to B = 120 m

The speed with which Olay runs from A to B, v₁ = 4 m/s

The distance from B to C = 180 m

The speed with which Olay runs from B to C, v₂ = 3 m/s

The distance from C to A = 150 m

His average speed for the whole journey = 3.6 m/s

We find

The total distance of running from A back to A, d = 120 m + 180 m + 150 m = 450 m

The time it takes to run from A to B, t₁ = 120 m/(4m/s) = 30 seconds

The time it takes to run from B to C, t₂ = 180 m/(3m/s) = 60 seconds

Let t₃ represent the time it takes Olay to run from C to A

We have;

The total time it takes to run from A back to A = t₁ + t₂ + t₃

Therefore;

[tex]Average \ velocity = \dfrac{Total \ distance }{Total \ time} = \dfrac{d}{t_1 + t_2 + t_3}[/tex]

Substituting the known values for the average velocity, 'd', 't₁' and 't₂'  gives;

[tex]Average \ velocity = 3.6 \, m/s = \dfrac{450 \, m}{30 \, s + 60 \, s + t_3}[/tex]

3.6 m/s × (30 s + 60 s + t₃) = 450 m

3.6 m/s × 30 s + 3.6 m/s × 60 s + 3.6 m/s × t₃ = 450 m

108 m + 216 m + 3.6 m/s × t₃ = 450 m

∴ 3.6 m/s × t₃ = 450 m - (108 m + 216 m) = 126 m

t₃ = 126 m/(3.6 m/s) = 35 s

The speed with which Olay runs from C to A, v₃ = Distance from C to A/t₃

The speed with which he runs from C to A = 150 m/(35 s) = 30/7 m/s =[tex]4.\overline {285714}[/tex] m/s

(i) The given bearing of C from A = 210°

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(A)

∴ cos(A) = (b² + c² - a²)/(2·b·c)

Where;

a = The distance from B to C = 180 m

b = The distance from C to A = 150 m

c = The distance from A to B = 120 m

We find;

cos(A) = (150² + 120² - 180²)/(2 × 150 × 120) = 0.125

A = arccos(0.125) ≈ 82.82°

The bearing of B from A ≈ 210° - 82.82° ≈ 127.18°

The bearing of B from A ≈ 127.18°

(ii) The angle, θ, formed by the path of the bearing of A from B is an alternate to the supplementary angle of the bearing of B from A

Therefore, we have;

θ ≈ 180°- 127.18° ≈ 52.82°

The bearing of A from B = The sum of angle at a point less θ

∴ The bearing of A from B = 360° - 52.82° ≈ 307.18°

The bearing of A from B ≈ 307.18°.

Answer:

:-):-)

Step-by-step explanation:

1) p<1000

2)p>500

3)By combining the above two, we get: 500<p<1000

Andre will agree as he thinks that the no. of paper clips in the box is less than 1000. But lin will not as she thinks that the no. of clips is more than 500.

4)This time, they both will agree as the no. of paper clips is more than 500 but less than 1000.