The expression in terms of m and n is m^2+2/3n-3.
To rewrite the given expression in terms of m and n, we need to use the properties of logarithms to simplify the expression. The properties of logarithms that we will use are:
- log(ab) = log(a) + log(b)
- log(a/b) = log(a) - log(b)
- log(a^b) = b*log(a)
Using these properties, we can rewrite the given expression as follows:
\( \log \left(\frac{\left(M^{\log (M)} \cdot 10^{\log (N)}\right)}{1000 \sqrt[3]{N}}\right) = \log \left(M^{\log (M)} \cdot 10^{\log (N)}\right) - \log \left(1000 \sqrt[3]{N}\right) \)
\( = \log \left(M^{\log (M)}\right) + \log \left(10^{\log (N)}\right) - \log \left(1000\right) - \log \left(\sqrt[3]{N}\right) \)
\( = \log (M) \cdot \log (M) + \log (N) \cdot \log (10) - \log (10^3) - \frac{1}{3} \cdot \log (N) \)
Now, we can substitute m = log(M) and n = log(N) into the expression to get:
\( = m^2 + n - 3 - \frac{1}{3}n \)
\( = m^2 + \frac{2}{3}n - 3 \)
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i need help please!!
a) The probability of selecting two different colors is obtained as 9/10.
b) The probability of not selecting a yellow marble is obtained as 3/20.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
a) To find the probability of selecting two different colors, we can use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.
So the probability of selecting two different colors can be found by calculating the probability of selecting two marbles of the same color and subtracting that from 1.
The probability of selecting two marbles of the same color from the first bag is (2/5) x (1/4) = 1/10, since there are 2 red marbles out of 5 total marbles in the bag, and the probability of selecting a second red marble is 1/4.
The probability of selecting two marbles of the same color from the second bag is 0, since there is only one marble of each color.
So the probability of selecting two different colors is -
1 - (1/10 + 0) = 9/10
Therefore, the probability value is 9/10.
b) To find the probability of not selecting a yellow marble, we can again use the complement rule.
The probability of not selecting a yellow marble is equal to 1 minus the probability of selecting a yellow marble from either bag.
The probability of selecting a yellow marble from the first bag is 1/5, since there is one yellow marble out of 5 total marbles in the bag.
The probability of selecting a yellow marble from the second bag is also 1/4, since there is one yellow marble out of 4 total marbles in the bag.
So the probability of not selecting a yellow marble is -
1 - (1/5 + 1/4) = 3/20
Therefore, the probability value is 3/20.
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Find any irrational number between 5,25 and
5,26
The irrational number between 5,25 and 5,26 is 2.5135145:
The irrational number between 5,25 and 5,26
2.5135145...
The number is non-terminating and non-recurring. Hence, it is an irrational number.
A real number that cannot be expressed as a simple fraction is called an irrational number.
It is impossible to express in terms of a ratio.
If N is irrational, it is not equal to p/q, where p and q are integers and q is not equal to 0.
Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.
An irrational number is a real number that cannot be expressed as a fraction of two integers. In other words, it is a number that cannot be written as a simple fraction or a ratio of integers. Irrational numbers are decimal numbers that go on forever without repeating. Some famous examples of irrational numbers include pi (3.14159265...) and the square root of 2 (1.41421356...).
Irrational numbers have some interesting properties. For example, they are non-repeating and non-terminating, which means that their decimal expansions never repeat and never come to an end. This makes them difficult to work with, but also makes them important in mathematics and science. Irrational numbers are used in a variety of mathematical and scientific applications, including geometry, physics, and cryptography.
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Question 1 Not yet answered Marked out of 5.00 P Flag question If the system of a linear equation has the unique solution, then the system is inconsistent Select one: True O False Question 2 Not yet
The statement "If the system of a linear equation has the unique solution, then the system is inconsistent." is False since a single solution is an indication that the equations intersect at a specific point, making it consistent.
A system of linear equations is a set of two or more linear equations that contain two or more variables. A solution to the system of linear equations is a set of values for the variables that satisfies all the equations in the system.
The system of linear equations having a single solution is a consistent system since a single solution is an indication that the equations intersect at a specific point. This contradicts the notion that the system is inconsistent. An inconsistent system is one that has no solutions.
Thus, if a system of linear equations has a unique solution, it must be consistent.
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A boy at an amusement park has 273 ride tickets. Each ride on the roller coaster costs 7 tickets. How many roller coaster rides can the boy buy?
Therefore , the solution of the given problem of unitary comes out to be child can purchase 39 roller coaster excursions with 273 ride tickets as a result.
An unitary method is what?To finish the job using the unitary technique, the expression from this nano section should be multiplied by two. In essence, when a wanted object is present, both the characterised by either a group and the pigment sections are omitted from the unit method. A variable fee of Inr ($1.01), for instance, would be paid for 40 pens. It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.
Here,
The boy can purchase the following amount of roller coaster rides:
39 trips using 273 ride tickets at 7 tickets each (rounded down to the nearest whole number)
The child can purchase 39 roller coaster excursions with 273 ride tickets as a result.
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Consider the line L(t) = (2 - 4t, 3 – 2t, -5 – 4t). Then: L is ____ to the plane 6x + 3y + 6z = -39 L is ____ to the plane 8x + 24y - 20z = -8 L is ____ to the plane 8x + 4y + 8z = 48 L is ____ to the plane 52 5y + 3z = -17
The line L(t) = (2 - 4t, 3 – 2t, -5 – 4t) is neither parallel nor perpendicular to any of the given planes.
The line L(t) = (2 - 4t, 3 – 2t, -5 – 4t) can be written in parametric form as: x = 2 - 4t, y = 3 - 2t, and z = -5 - 4t. The
direction vector of the line is (-4, -2, -4).
To determine if the line is parallel or perpendicular to a given plane, we can take the dot product of the direction vector of the line and the normal vector of the plane. If the dot product is zero, the line is parallel to the plane. If the dot product is nonzero, the line is neither parallel nor perpendicular to the plane.
For the plane 6x + 3y + 6z = -39, the normal vector is (6, 3, 6). The dot product of the direction vector of the line and the normal vector of the plane is (-4)(6) + (-2)(3) + (-4)(6) = -42. Since the dot product is nonzero, the line is neither parallel nor perpendicular to the plane.
For the plane 8x + 24y - 20z = -8, the normal vector is (8, 24, -20). The dot product of the direction vector of the line and the normal vector of the plane is (-4)(8) + (-2)(24) + (-4)(-20) = 8. Since the dot product is nonzero, the line is neither parallel nor perpendicular to the plane.
For the plane 8x + 4y + 8z = 48, the normal vector is (8, 4, 8). The dot product of the direction vector of the line and the normal vector of the plane is (-4)(8) + (-2)(4) + (-4)(8) = -56. Since the dot product is nonzero, the line is neither parallel nor perpendicular to the plane.
For the plane 52 5y + 3z = -17, the normal vector is (0, 52, 3). The dot product of the direction vector of the line and the normal vector of the plane is (-4)(0) + (-2)(52) + (-4)(3) = -112. Since the dot product is nonzero, the line is neither parallel nor perpendicular to the plane.
Therefore, the line L(t) = (2 - 4t, 3 – 2t, -5 – 4t) is neither parallel nor perpendicular to any of the given planes.
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Mr. Dela Cruz willed one-half of his estate to his eldest child, one-half of the remainder to his second child, and so on until his 4th child who is the youngest received 1.25 million. What was the total value of the estate?
a. 18.25 million
b. 20 million
c. 10 million
d. 6.26 million
Let x be the total value of the estate.
According to the problem, the youngest child received 1.25 million and the share of each child is half of the remainder of the estate after the previous child has received their share.
So, the fourth child received 1.25 million, which is half of what the third child received. Therefore, the third child received 2.5 million.
Similarly, the second child received 2 times what the third child received, which is 5 million.
Finally, the first child received 2 times what the second child received, which is 10 million.
Adding up all the shares, we get:
1st child: 10 million
2nd child: 5 million
3rd child: 2.5 million
4th child: 1.25 million
Total: 18.75 million
Therefore, the total value of the estate is 18.75 million, which is closest to option a, 18.25 million.
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Using syathetic division, the Rational Root Theorem, and the Remainder Theorem, find the real zeroes of f. Use the real veroes and the Factor Theorem to factor f(x). f(x)=2x^(4)+17x^(3)+35x^(2)-9x-45
f(x) can be factored into f(x) = 2(x + 5)(x + 3/2)(x - 3)(x - 5/2).
How to find the real zeroesTo find the real zeroes of f(x) = 2x^(4) + 17x^(3) + 35x^(2) - 9x - 45 using synthetic division, the Rational Root Theorem, and the Remainder Theorem, we need to follow these steps:
1. Using the Rational Root Theorem, we can find the possible rational roots of f(x) by taking the factors of the constant term (-45) and dividing them by the factors of the leading coefficient (2). The possible rational roots are:
±1, ±3, ±5, ±9, ±15, ±45, ±1/2, ±3/2, ±5/2, ±9/2, ±15/2, and ±45/2.
2. Next, we will use synthetic division to test these possible roots and find the real zeroes of f(x). We will start with the smallest possible root, -45/2, and divide f(x) by (x + 45/2) using synthetic division. The result is a polynomial of one degree less than f(x).
3. We will then use the Remainder Theorem to check if the remainder of the synthetic division is 0. If the remainder is 0, then -45/2 is a real zero of f(x) and we can use the Factor Theorem to factor f(x) into (x + 45/2)(2x^(3) - 8x^(2) - 80x + 90).
4. We will repeat steps 2 and 3 with the remaining possible rational roots until we find all the real zeroes of f(x).
5. Once we have found all the real zeroes of f(x), we can use the Factor Theorem to factor f(x) into the product of linear factors and a constant. The real zeroes of f(x) are -5, -3/2, 3, and 5/2.
Therefore, f(x) can be factored into f(x) = 2(x + 5)(x + 3/2)(x - 3)(x - 5/2).
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Sean writes 300 words each day while working on his Language Arts assignment. The assignment requires a minimum of 1800 words. Find the number of days Sean will work on the assignment to complete it.
Find the unit rate :
Running 2. 3km in 7 minutes
The unit rate of running 2.3 km in 7 minutes is 5.48 metres per second.
Unit rate can be defined as a measure used to represent how many units of one type of quantity corresponds to one unit of anther type of quantity.
Here the distance is given in kilometres (km) which can be converted into metres by multiplying by 1000 as,
2.3 km = 2.3*1000 metres
= 2300 metres
Here the time taken to cover 2.3 km is 7 minutes which can be converted ito seconds by multiplying by 60 as,
7 minutes= 7*60 seconds
= 420 seconds
Hence the unit rate of running 2.3 km in 7 minutes expressed in metre per second is calculated as = 2300 metres / 420 seconds
= 5.4761 metres per second
= 5.48 metres per second (approximately)
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Complete the following sentences by choosing from the drop-down menus.
A megabyte is _____
bytes.
A gigabyte is ______ bytes
A terabyte is ______ bytes
A kilobyte is _____ bytes
A byte consists of ___ bits
Pls help
Answer:
A megabyte is 1,000,000 bytes
A gigabyte is 1,000,000,000 bytes
A terabyte is 1,000,000,000,000 bytes
A kilobyte is 1,000 bytes
A byte has 8 bits
help me please i need help
Jaicee's mom says she has an hour before bed. Jenny spends 1/3 of the hour texting a friend and 1/4 of the time brushing her teeth and putting on pajamas. She spends the rest of the time reading her book. How many minutes did Jaicee read.
Answer:
Jaicee (Jenny?) can spend 25 minutes reading.
Step-by-step explanation:
1 hour is 60 minutes.
Multiply to find
1/3 of 60 minutes.
1/3 × 60
= 60/3
= 20
She spends 20 minutes texting.
Multiply to find 1/4 of 60 minutes.
1/4 × 60
= 60/4
= 15
She spends 15 minutes brushing teeth and putting on pajamas.
Subtract 20 and 15 from 60, to see what's left.
Used up time:
20 + 15
= 35
She used up 35 minutes texting and prepping for bed.
60 - 35
= 25
She has 25 minutes left for reading.
What is the range of f(x) = 3^x?
A. All real numbers greater than or equal to 3
B. All real numbers
C. All real numbers greater than 3
D. All positive real numbers
The height (y) (in feet) of a ball thrown by a child is y = - 1/16 x^2 + 2x + 3
where x is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child's hand?____ feet (b) What is the maximum height of the ball?____ feet (c) How far from the child does the ball strike the ground?____ feet
(a) The height of the ball when it leaves the child's hand is 3 feet.
(b) The maximum height of the ball is 19 feet.
(c) The ball will strike the ground approximately 33.44 feet from the child.
(a) This is because when x = 0 (the point at which the ball is thrown), the equation simplifies to y = 3.
(b) The maximum height of the ball can be found by finding the vertex of the parabola. The x-coordinate of the vertex is -b/2a, where a = -1/16 and b = 2. So, x = -2/(-1/8) = 16. Plugging this value back into the equation gives us the maximum height: y = -1/16(16)² + 2(16) + 3 = 19 feet.
(c) The ball strikes the ground when y = 0. Setting the equation equal to 0 and solving for x gives us:
0 = -1/16 x² + 2x + 3
Multiplying both sides by 16 to eliminate the fraction gives us:
0 = -x² + 32x + 48 = x² - 32x - 48
Using the quadratic formula, we find that x = (32 ± 8√19)/2 or x ≈ 33.44 and x ≈ -1.44
Taking the positive value, the distance from the child to where the ball strikes the ground is approximately 33.44 feet.
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What is x>-4 graphed and it slope and y-intercept?
Answer: See attached for the graph. There is an undefined slope and no y-intercept.
Step-by-step explanation:
See attached for a graph. Since this is only greater than, (>) we will use a dashed line. Then we will shade everything greater than -4.
The slope of this graph is undefined because this line is straight up and down. If we try to write it as an equation, you end up dividing by zero (which ends up undefined)
Lastly, there is no y-intercept. Since this line does not cross the y-axis, there is no point of intersection.
17. Determine whether the given set is linearly independent. \[ \left\{\left[\begin{array}{c} 1 \\ -1 \\ -2 \end{array}\right],\left[\begin{array}{c} -1 \\ 0 \\ 1 \end{array}\right],\left[\begin{array
The set is linearly independent.
Yes, the given set is linearly independent. To prove this, we can use the determinant method. To calculate the determinant, arrange the columns of the array in a 3x3 matrix. This gives us the following matrix:
$$\begin{bmatrix}1 & -1 & -2\\-1 & 0 & 1\\0 & 1 & -1\end{bmatrix}$$
The determinant of this matrix is 1, which is not equal to 0. This shows that the given set is linearly independent.
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Evaluate the expression 4x² for x = 3.
Answer:
36
Step-by-step explanation:
do x to the second power then multiply 4 to get your answer
An online game company sells GTA 6 for $28. 19. An other online game company offers $21. 39 with DLC included. Which company has the better deal?
This is actually one my homework question-
Answer: The other game companies offer
Step-by-step explanation: Pretty much self-explanatory.
Translating a sentence by using an ineqt Write an inequality for the following statement. 5 is greater than or equal to a
The inequality for the statement "5 is greater than or equal to a" is 5 ≥ a.
To write an inequality for the statement "5 is greater than or equal to a," we can use the greater than or equal to symbol (≥) to represent the relationship between 5 and a. The inequality would be written as:
5 ≥ a
This inequality can also be written as a ≤ 5, which means that a is less than or equal to 5. Both of these inequalities represent the same relationship between 5 and a, and either one can be used to represent the statement "5 is greater than or equal to a."
In Mathematics, the relationship between two values that are not equal is defined by inequalities.
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please answer as fast as possible
Answer:
5 2/3
Step-by-step explanation:
all you need is to add because the fraction is the same.
PLEASE HELP WILL
MARK YOU THE BRAINIEST IF YOU ANSWER RLY NEED.
Answer:
1 < x < 15
Step-by-step explanation:
To find the range of values for the third side, you must subtract and add the other known sides. The lower limit for the range of the third side will be 8 - 7, which equals 1. The upper limit for the range of the third side will be 8 + 7, which equals 15
Answer:
1<x<15
Step-by-step explanation:
What are triangle inequalities?Triangle inequalities state that the sum of two sides of any triangle must be less than the other. This is true for all three sides of the triangle.
In this case, we know two sides. Let us set a variable for the third, as x.
So the sum of 8 and 7 has to be bigger than x:
8+7>x
15>x
8 and x have to be greater than 7:
8 +x >7
x>-1
And 7 and x have to be greater than 8:
7 + x>8
x>1
Looking at the inequalities between x, we must choose the most inclusive ones. x>-1, but 1 is within that, so we can go with x>1. x<15 is a statement that cannot change because it is the only end value given. Therefore, the answer is 1<x<15
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Level Use the power rules to simplify the expression. ((-4m^(4)n^(-4))^(3))/((mn)^(2))
The simplified expression is (-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex]).
The given expression is ((-4m4n-4)3) / ((mn)2).
To simplify the expression ((-4[tex]m^{(4)}[/tex] ) (([tex]n^{(-4)[/tex])[tex])^{(3))}[/tex]/ ((mn[tex])^{(2)}[/tex]), we will use the power rules of exponents.
First, we will apply the power rule to the numerator:
((-4)[tex])^{3}[/tex])([tex]m^{(4*3)}[/tex])([tex]n^{(4*3)}[/tex]) = (-64)([tex]m^{(12)}[/tex])([tex]n^{(12)}[/tex])
Next, we will apply the power rule to the denominator:
([tex]m^{(2)}[/tex])([tex]n^{(2)[/tex]) = [tex]m^{(2)}[/tex][tex]n^{(2)[/tex]
Now we can simplify the expression by canceling out the common terms in the numerator and denominator:
((-64)([tex]m^{12}[/tex])([tex]n^{12}[/tex])/([tex]m^{(2)}[/tex][tex]n^{(2)}[/tex])
= (-64)([tex]m^{12-2}[/tex])([tex]n^{12-2}[/tex])
= (-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex])
Finally, we can write the final expression in simplified form:
(-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex]).
Therefore, the simplified expression is (-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex]).
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how old am i if 400 reduced by 2 times my age is 300?
Answer:
You are 78 years old.
Answer:
Naw bro you're 0
Step-by-step explanation:
what’s the answer of this
The slope is 3. After 1 second, the car's distance increases by 7 feet.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided, we have the following equation that represents the relationship between distance and time;
y = 3x + 4
At x = 1 second, the distance is given by;
y = 3(1) + 4
y = 3 + 4
y = 7 feet.
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Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less. Write and solve an inequality that represents this situation. Explain clearly what the solution to the inequality means in the context of this situation.
We fοund the inequality tο be 14 -0.6x ≤ 1.5 and sοlving this we fοund that the warning lights cοme οn after using fοr apprοximately 21 days.
What is meant by inequality?In mathematics, inequalities specify the cοnnectiοn between twο nοn-equal numbers. Equal dοes nοt imply inequality. Typically, we use the "nοt equal sign" tο indicate that twο values are nοt equal. Hοwever several inequalities are utilised tο cοmpare the numbers, whether it is less than οr higher than. An inequality symbοl has nοn-equal expressiοns οn bοth sides. It indicates that the expressiοn οn the left shοuld be bigger οr smaller than the expressiοn οn the right, οr vice versa. Literal inequalities are relatiοnships between twο algebraic expressiοns that are expressed using inequality symbοls.
Given,
The gallοns οf fuel that the car hοlds = 14 gallοns
Amοunt οf fuel used each day = 0.6 gallοns
When the remaining fuel is 1.5 gallοns οr less, warning lights cοme οn.
We can write an inequality fοr this situatiοn.
If x is the number οf days the car is used, then the warning lights cοme οn when,
14 - 0.6x ≤ 1.5
This is the inequality expressiοn.
Sοlving,
12.5 ≤ 0.6x
x ≥ 12.5/0.6
x ≥ 20.8
Therefοre we fοund the inequality tο be 14 -0.6x ≤ 1.5 and sοlving this we fοund that the warning lights cοme οn after using fοr apprοximately 21 days.
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Tom used a photocopier to dilate the design for a monorail track system. The figure shows the design and its photocopy: Two irregular quadrilaterals ABCD and EFGH are drawn. EFGH is the photocopy of design ABCD. AB measures 17 meters, AD measures 7 meters. No dimensions are shown on EFGH. The ratio of BC:FG is 1:2. What is the length, in meters, of side EH on the photocopied image? 7 14 17 34
In the congruent geometry , length of EH is 14 meters .
What is congruent geometry?
In a congruent geometry, the shapes that are so identical. can be superimposed on themselves.
Two objects that are identical in terms of their dimensions and shape are said to be congruent in geometry. Further, two shapes are said to be congruent to one another if they can be turned, flipped, or moved in the same direction.
As a result, two congruent figures that have been drawn on a piece of paper can be cut out and positioned over one another to perfectly match.
Here, The figure shows the design and its photocopy. The ratio of BC: FG is 1:2.
Since the two figures are congruent
BC/FG= AD/EH
1/2 = 7/EH (from figure AD = 7 )
EH = 2*7
EH = 14 m
Thus, the required length of EH is 14 meters.
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i need y'all help pls!!
Answer:
right one is correct explanation
Choose a number from the first column and a unit from the second column to make a measurement that is equivalent to 240 centigrams.
Answer is 240 centigrams = 2400 milligrams, 240 centigrams = 24 decigrams, 240 centigrams = 0.024 kilograms.
Define the term measurements?Measurement is the process of quantifying an attribute or property of an object or event using a numerical or quantitative scale. The result of a measurement is a number or value that represents the magnitude or amount of the attribute being measured.
Centigrams, milligrams, decigrams, and kilograms are all units of measurement of mass in the metric system.
1 centigram (cg) = 10 milligrams (mg) in the metric system.
240 centigrams = 10×240 milligrams,
So, 240 centigrams is equal to 2400 milligrams.
1 centigram (cg) = 0.1 decigrams (dg)
240 centigrams = 0.1×240 decigrams
So, 240 centigrams is equal to 24 decigrams.
1 centigram (cg) = 0.0001 kilograms (kg)
240 centigrams = 0.0001×240 kilograms
So, 240 centigrams is equal to 0.024 kilograms.
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A=2−1501300−3 To find: eigenvalues and the eigenvectors
The eigenvalues of matrix A are 11 and -1, and the corresponding eigenvectors are [1, -3, 0] and [1, 0, 0].
Eigenvalues and eigenvectors are important concepts in linear algebra. The eigenvalues of a matrix are the values that satisfy the equation Ax = λx, where A is the matrix, x is the eigenvector, and λ is the eigenvalue. The eigenvectors are the corresponding vectors that satisfy this equation.
To find the eigenvalues and eigenvectors of the matrix A=2−1501300−3, we need to follow these steps:
1. Find the characteristic equation of the matrix A by subtracting λ from the diagonal elements and taking the determinant:
|A-λI| = |2-λ -1 5| = (2-λ)(-3-λ) - (-1)(5) = 0
|0 1 3|
|0 0 -3-λ|
2. Solve the characteristic equation to find the eigenvalues:
(2-λ)(-3-λ) - (-1)(5) = 0
-6 + 3λ + 2λ - λ² + 5 = 0
λ² - 5λ - 11 = 0
(λ - 11)(λ + 1) = 0
The eigenvalues are λ = 11 and λ = -1.
3. Find the eigenvectors by substituting the eigenvalues back into the equation Ax = λx and solving for x:
For λ = 11:
(2-11)x₁ - x₂ + 5x₃ = 0
x₂ + 3x₃ = 0
-3x₃ = 0
x = [1, -3, 0]
For λ = -1:
(2+1)x₁ - x₂ + 5x₃ = 0
x₂ + 3x₃ = 0
3x₃ = 0
x = [1, 0, 0]
The eigenvectors are x = [1, -3, 0] and x = [1, 0, 0].
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A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 16% are pennies and 34% are dimes. There are 6 more nickels than pennies. How much money does the bag contain?
The bag contains how much money?
Answer:
$2.48
Step-by-step explanation:
50 coins in all
16% of 50 is 8. (50 x 0.16 = 8)
That means we have 14 Nickels
34% of 50 is 17. (50 x 0.34 = 17)
Multiplying each number by their value (i.e. 14 x 5 for Nickels)
We get 248. We can assume we don't have 248 dollars, and more likely have $2.48 instead.