Answer:
13 km
Step-by-step explanation:
By Triangle Inequality Theorem: The sum of two smallest sides is greater than the third side.
Small Values of X:
X + 26 > 38
X > 38 - 26
X > 12
If we know that 38 km is the longest side, then the sum of other two sides must be greater than 38 km. Therefore the minimum value of X is 13 km.
Stonewall receives ¢250 per year in simple interest from an amount of money he invested in
ADB, Barclays and GCB. Suppose ADB pays an interest of 2%, Barclays pays an interest of
4% and GCB pays an interest of 5% per annum and an amount of ¢350 more was invested in
Barclays than the amount invested in ADB and GCB combined. Also, the amount invested in
Barclays is 2 times the amount invested in GCB.
a) Write down the three linear equations and represent them in the matrix form AX = B.
b) Find the amount of money Stonewall invested in ADB, Barclays and GCB using Matrix
Inversion
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]
The ratio of pears to green apples is 1:3 if there are 150 green apples how many pears are there
50. 150 divided by 3
The side of a square has the length (x-2), while a rectangle has a length of (x-3) and a width of (x+4). If the area of the rectangle is twice the area of the square, what is the sum of the possible values of x? I CAN'T ACCESS A FILE SO PLEASE JUST LOOK AT THE PICTURE YOURSELF, AND THEN TELL ME. THANKS!
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
During a professional baseball game, every
spectator placed his or her ticket stub into one of
several containers. After the game, the coach
chose twenty people to march in the victory
parade. What is the sample in this situation?
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.
Pleaseee answer these two questions helppppp ill give you brainliest answer if you knowwww help pleaseeee
Answer:
The theoretical probabilty of the coin landing on tails is 50/50 so their is a 50% chance of it landing on tails so theoretically it would land on tails 15 out of 30 times
Step-by-step explanation:
HELP!! :'(
An exponential function does not have a constant rate of change, but it has ____.
A. a slope
B. a parabolic shape
C. None of these
D. constant ratios
HELP PLEASEE
I’m stuck
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.
Plzzzzz I need help asap thank you
No links plzzzzz
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
HELP NQNSJNDNXJJXnwnfnf
Answer:
C. 14 is the answerStep-by-step explanation:
1. Write the question.
17 - 2x = -11
2. Subtract 17 from both sides
-17 -17
- 2x = -28
3. Negatives cancel
2x = 28
4. Divide both sides by 2
/2 /2
x = 14
5. Check the answer, write the equation.
17 - 2x = -11
6. Substitute x with the value
17 - 2(14) = -11
17 - 28 = -11
-11 = -11
The answer is correct!
So, 14 is the answerHope this helped,
Kavitha
What is the product of 2x + 3 and 4x^2 - 5x + 6
Answer:
8
x
3
+
2
x
2
−
3
x
+
18
Step-by-step explanation:
simply the answer thought bc i didn't simplify
3333 divided by 77. i really need help
Answer:
43.2857142857
plz mark me as brainliest
Answer:
476.142857143
Step-by-step explanation:
Antonio has six white socks, two black socks, and four gray socks in a drawer. If he randomly chooses a sock from the drawer, what is the probability he will choose a gray sock?
A.1/12
B.1/4
C.1/3
D.1/2
Answer:
C
Step-by-step explanation:
The probability is 1/3
I need help pls is due today
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
Convert:
35 pounds, 24 ounces=_ ounces
Answer:
Step-by-step explanation:
1 pound = 16 ounces
35 pounds = 560 ounces + 24 ounce = 584ounces
35 pounds,24ounces = 16 ounces
Help me please I have an f in this class I will give you 44 points
8 x 7s = 56s
8 x (-2) = -16
so 8(7s - 2) = 56s - 16
A smartphone regularly sells for $125. It is on sale this week for $85. The sale
price is what percent of the regular price?
Answer:
68%
Step-by-step explanation:
85 divided by 125 = .68 * 100 = 68
Answer: The sale price is 40 percent of the regular price
Step-by-step explanation:
Fill in the blank using a term found in the vocabulary list. The ratio of the value of a subtotal to the value of the total is called _________________.
Answer:
Relative frequency
Step-by-step explanation:
the bearing of c from a is 210°
(i) find the bearing of B from A
(ii) find the bearing of A from B
if you could also solve the question above I'd be very grateful
I need it in at least 10 minutes so please answer it!! ♡♡
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°.
need help with this one??
Answer:
the correct one would be quadrant 3
Step-by-step explanation:
Choose the correct classifacation of 4x^4-4x^3+10x^6
Answer:what’s classification
Step-by-step explanation:
could someone help me with this
What is -3/5 multiplied by 4/7?
Pls show answer with step by step answers explained pls
Answer:
-12/35
Step-by-step explanation:
-3×4/5×7
-12/35
Find the missing length PLEASE HELP NEED IT ASAP
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:
58Step-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.
A horse 64 feet from the center of a merry-go-round makes 27 revolutions. In order to travel the same distance, how many revolutions would a horse 16 feet from the center have to make?
-1.2k + 3.9 - g + .5g + 7 + .3k
Answer:
hi
Step-by-step explanation:
.2 How many millilitres of chutney are needed?
Answer:
Step-by-step explanation:
In this scenario, You've asked about the Chutney (Sauce/Raita).
Ok, So let's suppose you are making a "Chutney"
The first you need is the right amount of ingredients.Their quantity and they must be fresh "To make every effort of yours worth it!"Add it into a bowl or a dish that you have at the time (Or a big one to be on the safe side)At the end mix the ingredients well, So that they don't spoil taste of the one who is taking it.The amount of milliliters (Weight measurement) depends upon the amount of usage/intake that one is taking.
It could be a few hundred (gms. or some Kg's).
That totally depends up on your choice
PLEASE HELP ME OUT! QUICK POINTS FOR YOU!
All information needed can be found in the image below
Thank you in advance.
Answer:
circle area = 50.24 units²
Step-by-step explanation:
circle area = πr² = 3.14(4²) = 3.14(16) = 50.24 units²
Choose the best term from the box.
The ?
of an object is how heavy the object is.
?
weight
length
capacity
15
1/4 of my shirts are red, the rest are blue. Show the ratio of red to blue shirts
Answer:
1:3 red to blue
Step-by-step explanation:
you have x shirts. Let's call the number of red shirts r and the number of blue shirts b.
r = x * 1/4
b = x - r = x - (x * 1/4) = x * 3/4
r:b = (x * 1/4):(x * 3/4) = (1/4):(3/4) = 1:3
A gardener made a scale drawing of a lawn with a scale factor of 1:4 The dimensions of her drawing are 15 inches long by 10 inches wide. Her partner plans to make another scale drawing of the lawn, but with a scale factor of 1:20. What are the dimensions of her scale drawing? O A. The length is 50 inches and the width is 75 inches, OB. The length is 3 inches and the width is 2 inches. O Q. The length is 75 inches and the width is 50 inches. O D. The length is 2 inches and the width is 3 inches.
Answer:
B is the correct answer
Step-by-step explanation:
