The shortest distance between planet Q and planet R is 1.64 × 10⁷ .
What is planet distance?RP = 1.6 * 10⁷
most compact distance
The Pythagoras theorem x₂ = R * P² + Q * P² is then used to determine the shortest distance (x).
This results in x = (3.6 * 10⁶) + (1.6 * 10⁷) = 2.
x² = 12.96 * 10¹² + 2.56 * 10¹⁴ should be evaluated.
Write the equation as: x²= 12.96 * 10¹² + 256 * 10¹²
Sums x² = 268.96*10¹² should be evaluated.
multiply both sides' square roots.
x = 16.4 * 10⁶
Replace with: x = 1.64 * 10⁷
In light of this, the distance between planet Q and planet R is 1.64 * 10⁷ km.
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The complete question is
The distances between some planets are given below.
Planet Q is 3.6 x 10⁷ to the power of 6 km from planet P.
Planet R is 1.6 x 10⁷ to the power of 7 km from planet P.
Work out the shortest distance between planet Q and planet R. Give your answer in standard form.
A construction project calls for attaching plywood to floor joists using either nails or screws . When screws are used, there must be at least 2 screws for every square foot of flooring . When nails are used, there must be at least 4 nails per square foot. A floor that was 144 square feet was constructed using a mixture of screws and nails. The worker has planned to use no more than 500 screws and nails combined . Can he complete 90 square feet of flooring with nails?
Yes, we may install 90 square feet of flooring with 360 nails, as the total number of nails and screws used shouldn't exceed 500.
what is unitary method ?The facility is a method to problem-solving and involves essentially figuring out the price of a single unit, following multiplication that value to figure out the desired value. Clearly explained, the unit method is employed to derive a single property value out of a specified multiple. For contrast, 40 pens should cost (400 rupees, which is equal to the cost among one pen. This procedure might be standardized. undivided nation. anything does indeed have a distinctive element. Its adjoint and reciprocal are equal in terms of mathematics (algebra), abstract algebra, mathematical analysis, or mathematics of matrices or operators.
given
Let x be the number of screws and y be the number of nails,
then the answer to the question is 500.
For 90 square feet, it takes
144 = (2x + 4y) nails, or
4 nails per square foot, for a total of 360 nails.
Yes, we may install 90 square feet of flooring with 360 nails, as the total number of nails and screws used shouldn't exceed 500.
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Solve using elimination.
–3x + 10y = –7
–3x + 4y = –19
Answer:
Approximately 6.78
Step-by-step explanation:
–3x + 10y = –7 - - - - - - > (1)
–3x + 4y = –19 - - - - - - > (2)
(1) - (2) Because if same sign then you have subtract to cancel out the equal numbers therefore - 3x and - 3x is cancelled out
6y = +2
y = 2 ÷ 6
y = 1/3
Then to find the value of x substitute value of y
-3x + (4 × 1/3) = - 19
-3x + 4/3 = - 19
- 3x = - 19 - 4/3
- 3x = - 61/3
x = ( - 61/3 ÷ -3)
x = 6.78
right ascension 15 06 53.62 declination 62 20 10.0 1
The celestial coordinates of the given point are (0.92868, 0.36983, 0.04921).
The right ascension and declination of a particular point in the sky can be used to calculate its corresponding celestial coordinates. Right ascension (RA) is measured in hours, minutes and seconds, while declination (Dec) is measured in degrees, minutes and seconds.
The RA of the given point is 15 h 06 m 53.62 s. This can be converted to degrees by multiplying by 15. The result is 225.1045 degrees. The Dec of the given point is 62° 20' 10.0" which can be converted to radians by multiplying by pi/180. The result is 1.08269 radians.
The celestial coordinates can then be calculated using the formula:
sin(RA)cos(Dec) = sin(225.1045)*cos(1.08269) = 0.92868
cos(RA)cos(Dec) = cos(225.1045)*cos(1.08269) = 0.36983
sin(Dec) = sin(1.08269) = 0.04921
Therefore the celestial coordinates of the given point are (0.92868, 0.36983, 0.04921).
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a continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n) probability distribution. a. normal b. uniform c. exponential d. poisson
A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event, is an exponential probability distribution.
The probability density function or pdf of the exponential distribution is given by the formula
[tex]$$f(x) = \begin{cases} \lambda e^{-\lambda x} & \text{for } x \ge 0 \ 0 & \text{otherwise} \end{cases}$$[/tex]
where λ is the rate parameter and e is the natural logarithm base.
The pdf gives the probability distribution of a random variable x, which represents an exponential distribution.
The exponential distribution is a continuous probability distribution that simulates the interval between events with an average occurrence rate that is constant.
In this distribution, the likelihood that an event will occur in the future is independent of when that event occurred in the past
The time interval between customers joining a line, the interval between device failures, or the separation between two places in space are all frequently modeled using the exponential distribution.
The rate parameter, which denotes the average number of events per unit of time or space, is what defines the exponential distribution.
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write an equivalent expression to the following: 5y + 35 HINT: think distributive property.
Answer:
5(y+7)
Step-by-step explanation:
Answer:
5(y + 7)
Step-by-step explanation:
we plan to turn over the first 3 cards in a well-shuffled deck of 52 cards. compute the probability that both the second and third cards are the same suit.
Answer is 1/104. Probability is a branch of mathematics that deals with numerical descriptions of the probability of an event occurring or the probability that a statement is true.
What is the probability that both the second and third cards are the same suit?
Probability that the first card is a club = 1/4. (There are 13 club cards in the deck, and 13/52 = 1/4). Probability that the second card is a 3 = 1/13. (There are four 3 cards in the deck, and 4/52 = 1/13). Probability that the third card is red = 1/2. (There are 26 red cards in the deck, and 26/52 = 1/2). The probability of an event is a number between 0 and 1, where 0 represents approximately an impossibility and 1 represents a certainty. The higher the probability of an event, the more likely the event will occur. A simple example is mining a fair (impartial) coin. Since the coin is fair, both outcomes ("heads" and "tails") are equally likely; the probability of heads is equal to the probability of heads; and since no other outcome is possible, the probability of "heads" or "heads" is 1/2 (which can also be written as 0.5 or 50%).
Probability that the first card is a club, the second card is a 3, and the third card is red = 1/4 * 1/13 * 1/2
= 1/104
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Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine and it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag. The additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.50 each. Team B will sell the cotton candy for $0.75 per stick.
What is the least number of items Team B will need to sell to avoid losing money?
Team B will need to sell at least 192 candies to avoid losing money.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given total amount to be raised by each team is $100,
Team B wants to sell cotton candy,
rent of candy machine = $25
total cost to be earned for team B = $100 + $25 = $125
let the number of candies sold be x
cost used in candy sticks = $0.10 per stick
cost used in x candy sticks = $0.10x
the selling price of each candy = $0.75
the selling price of x each candy = $0.75x
total gain = $0.75x - $0.10x
total gain = $0.65x
minimum candies to be sold for no loss
$0.65x = $125
x = 125/0.65
x = 192.30
x = 192
Hence for no loss, at least 192 candies are to be sold.
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Trapezoid HRNB is shown with midsegment MS.
HM = (5x-3),
MB = (x + 5)
HR=(2y+3).
MS (4y - 3). and
BN= (10x+1)
What is the value of a?
What is the value of y?
the value of x=2 and y =5, for the given trapezoid.
What is trapezoid?
A trapezoid, commonly referred to as a trapezium, is a quadrilateral or polygon with four sides. It has a set of parallel opposite sides as well as a set of non-parallel sides. The bases and legs of the trapezoid are referred to as parallel and non-parallel sides, respectively. A trapezoid is a four-sided closed 2D figure with a perimeter and an area. The bases of the trapezoid are two of the shape's sides that are parallel to one another. The legs or lateral sides of a trapezoid are its non-parallel sides. The altitude is the shortest distance between any two parallel sides.
Given, HM =5x-3
BM = x+5
So 5x-3 = x+5
4x = 8
x = 2.
and (4y - 3) =(2y+3)+(10x+1) /2
8y-6 = 2y+3 + 10x+1
6y = 10+20
y =5
Hence the value of x=2 and y =5, for the given trapezoid.
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Find the area of △ABC. Where: A=(2,−1,−1), B=(1,−3,2), C=(2,−3,0)
The area of △ABC is equal to 6√6 / 2.
What is the area of triangle 3-dimensional space?
The area of a triangle in 3-dimensional space can be found using the cross product of two vectors formed by the three vertices of the triangle.
The formula for the area of a triangle with sides u and v is given by:
Area = |u × v| / 2
Where × represents the cross product of the two vectors u and v, and |•| represents the magnitude of the resulting vector.
To find the area of △ABC, we can form the vectors AB and AC and find their cross-product:
AB = B - A = (1 - 2, -3 - (-1), 2 - (-1)) = (-1, -2, 3)
AC = C - A = (2 - 2, -3 - (-1), 0 - (-1)) = (0, -2, 1)
Cross product of AB and AC: AB × AC =
| i j k |
|-1 -2 3 |
| 0 -2 1 |
= (6, 6, -6)
Area of △ABC = |AB × AC| / 2 = |(6, 6, -6)| / 2 = √(6^2 + 6^2 + (-6)^2) / 2 = 6√6 / 2
Hence, the area of △ABC is equal to 6√6 / 2.
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Whats the slope and y-intercept
2x-6y=24
I think I know the intercept I just don't know the slope.
Answer:
x-6y=-24
Step-by-step explanation:
do it
Answer:
Step-by-step explanation:
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the slope and y-intercept of the equation 2x - 6y = 24, you can first isolate y by adding 6y to both sides and then dividing both sides by -6. This gives you: y = (-1/3)x + 4
So, the slope is -1/3 and the y-intercept is 4.
which of the following is the midpoint riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width?
The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is 9980
The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is calculated by summing the area of each subinterval under the midpoint of the interval.
The formula for the midpoint Riemann sum is given by:
Sum = (width of interval) * (height of midpoint)
For this problem, since the width of each interval is 16/4 = 4, the midpoint Riemann sum is calculated by:
Sum = 4 * (1 + (16/4)^3 + (32/4)^3 + (48/4)^3)
Substituting the values for each midpoint, we get the following equation:
Sum = 4 * (1 + 4^3 + 8^3 + 12^3)
This simplifies to:
Sum = 4 * (1 + 64 + 512 + 1728)
Therefore, the midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is:
Sum = 4 * (2495)
Sum = 9980
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Determine the value of the variable that makes the equation true.
1=-10c
The value of the variable that makes the equation true -1/10
What is an equation?An equation is a mathematical statement that shows the equality of two or more things. that is An equation is a mathematical statement that shows that two mathematical expressions are equal
The given equation is 1=-10c
To make the statement true, we have to determine the value of the variable c
this is done by making the variable c the subject of the relation
Now, 1/-10 = -10c/-10
Therefore c = -1/10 makes the equation true
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If AE=6x-55 and EC=3x-16, find DB quetion 8 6. 3 polygon and quadrilateral geometry
The length of side DB can be expressed as [tex]\sqrt{ (15x - 55)(3x - 28).}[/tex]
To solve this, we can use the Pythagorean theorem:
[tex]DB^2 = AE^2 + EC^2[/tex]
Substituting the values of AE and EC:
[tex]DB^2 = (6x - 55)^2 + (3x - 16)^2[/tex]
[tex]DB^2 = 36x^2 - 720x + 3025 + 9x^2 - 96x + 256[/tex]
[tex]DB^2 = 45x^2 - 816x + 3281[/tex]
[tex]DB =[/tex] [tex]\sqrt{ (15x - 55)(3x - 28).}[/tex]
Key points:
The Pythagorean theorem states:
In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.Symbolically, this can be expressed as [tex]a^2 + b^2 = c^2[/tex], where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.The theorem can be used to find the length of one side of a right triangle if the lengths of the other two sides are known.It is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery and proof.The theorem has many applications in mathematics, physics, engineering, and construction, among others.Learn more about the Pythagorean theorem here:
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The complete question is:
In a quadrilateral ABCD, the length of sides AB and CD are equal and measure x units. If AE = 6x - 55 and EC = 3x - 16, find the length of side DB.
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the marginal benefit is the ___________________benefit associated with an increase in the activity.
The marginal benefit is the additional number of benefit associated with an increase in the activity.
The marginal benefit is the amount of benefit that is gained from a one-unit increase in the activity, and is measured by the additional satisfaction or utility that the individual or organization receives from the increase in the activity.
The marginal benefit is the additional number of benefit associated with an increase in the activity.
The marginal benefit is the additional benefit or satisfaction that is derived from an increase in the activity or product. It is the amount of pleasure or utility that a person or organization receives from the marginal increase in the activity or product. This is measured by the additional revenue, utility, or satisfaction that is experienced from the increase in activity. Marginal benefit can also refer to the additional money, time, or other resources that are invested in an activity or product, as well as the amount of value that is gained from the increase in the activity or product.
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There are 50 cds if 30% of them are country music and 40% are pop music how many cds are other types of music
Answer:
15 CDs
Step-by-step explanation:
The total percentage of the CDs is 100% because it basically means all the CDs. Therefore, the percentages of types need to add up to 100%. If 30% are country and 40% are pop, 100 - 30 - 40 = 30% are other.
30% is equivalent to 30/100 or 0.3 when written as a decimal. You would then multiply this by the number of CDs to get the number of other CDs:
[tex]50 * 0.3 = 15[/tex]
Therefore, 15 CDs are other types of music
Write an equation for this line.
Answer:
y = -2
Step-by-step explanation:
The equation is y = mx + b
But this line has no slope, but it has a y-intercept at (0,-2), so the equation is
y = -2
use the definition of a limit to fill in the blanks and prove the statement below. lim x → 2 1 2 x + 2 = 3
The limit of 1/2x + 2 as x approaches 2 is equal to 3.
The definition of a limit states that as the x-value approaches a specific number, in this case 2, the y-value of the expression 1/2x + 2 approaches 3. The definition states that for any ε > 0, there exists a δ > 0, such that for all 0 < |x - 2| < δ, we have |1/2x + 2 - 3| < ε. We can rearrange this to find that for all 0 < |x - a| < δ, we have |f(x) - L| < ε. This means that when x is close to 2, the difference between 1/2x + 2 and 3 is less than ε. Therefore, if we take ε to be very small, we see that 1/2x + 2 gets very close to 3, so the limit is 3. To prove this statement, we can calculate the y-value of the expression when x is equal to 1.5, 1.99, and 1.999. As we can see, the y-values get closer and closer to 3 as the x-values get closer and closer to 2. As x gets closer and closer to 2, the y-values of 1/2x + 2 get closer and closer to 3, so the limit of 1/2x + 2 as x approaches 2 is equal to 3.
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When the p-value is used for hypothesis testing, the null hypothesis is rejected ifa)p-value ≤ αb)α < p-valuec)p-value ≥ αd)p-value = 1 - α
If he p-value is used for hypothesis testing , then the Null Hypothesis is rejected if (a) p-value ≤ α .
In a hypothesis testing, the p-value represents the probability of observing a test statistic as extreme or more extreme than the one observed, provided that the null hypothesis is True.
The significance level, represented by "α" , is a pre-determined threshold which determines the level of evidence required to reject the null hypothesis.
If the p-value is less than or equal to α, this indicates that the observed test statistic is sufficiently unlikely to occur under the null hypothesis, and therefore the null hypothesis is rejected.
Therefore , the Null hypothesis is rejected if (a) p-value ≤ α .
The given question is incomplete , the complete question is
When the p-value is used for hypothesis testing, the null hypothesis is rejected if
(a) p-value ≤ α
(b) α < p-value
(c) p-value ≥ α
(d) p-value = 1 - α
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The correct answer is a) p-value ≤ α. In hypothesis testing, the null hypothesis is typically assumed to be true initially. The p-value is used to determine the probability of observing a test statistic as extreme or more extreme than the one obtained from the data, assuming that the null hypothesis is true.
The significance level (α) is chosen beforehand and represents the maximum acceptable probability of rejecting the null hypothesis when it is actually true.
If the p-value is less than or equal to the significance level (p-value ≤ α), then the result is considered statistically significant and the null hypothesis is rejected. This implies that the observed effect is unlikely to have occurred by chance alone and that the alternative hypothesis is more likely to be true.
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ZA and ZB are vertical angles. If mA = (8x 23)° and m/B = (6x - 5)°, then find the measure of ZA.
The numerical measure of angle A is 49 degrees.
What is the measure of angle A?Vertical angles are simply angles that are opposite one another when two starlight lines cross. They are congruent.
Given the data in the question;
∠A and ∠B are vertical angles
mA = ( 8x - 23)° mB = ( 6x - 5)°Numerical value of angle A = ?Since ∠A and ∠B are vertical angles and vertical angles are congruent,
∠A = ∠B
(8x - 23)° = (6x - 5)°
Solve for x
8x - 23 = 6x - 5
8x - 6x = -5 + 23
2x = 18
x = 18/2
x = 9
Now, the numerical value of angle A will be;
mA = ( 8x - 23)°
Plug in x = 9
mA = ( 8(9) - 23)°
mA = ( 72 - 23)°
mA = 49°
Therefore, the measure of mA is 49°.
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solve for x: x 2a-b=3(x a)-2(2a-b)
The expression x 2a-b=3(x a)-2(2a-b) has the result x = 2a / (2a + 3).
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The sum of 8 and 3 equals 11. 8 + 3 is an expression.
Here,
To solve for x, we can simplify the equation first:
x * 2a - b = 3(x + a) - 2(2a - b)
Expanding the right side:
x * 2a - b = 3x + 3a - 2 * 2a + 2b
Combining like terms:
x * 2a - b = 3x + 3a - 4a + 2b
x * 2a - b = 3x - a + 2b
Now, we can isolate x on one side of the equation:
x * 2a - 3x = a - b + 2b
x * 2a - 3x = a + b
Multiplying both sides by -1:
-x * 2a + 3x = -a - b
Adding 2a to both sides:
x * 2a + 3x + 2a = -a - b + 2a
Combining like terms:
x * 2a + 3x + 2a = -a + 2a
x * 2a + 3x + 2a = 2a
Finally, collecting all x terms on one side:
x * (2a + 3) = 2a
Dividing both sides by (2a + 3):
x = 2a / (2a + 3)
The value of x for the expression x 2a-b=3(x a)-2(2a-b) is x = 2a / (2a + 3).
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Please help need this done asap
A. KP = ST is given
B. Given as PR = TV is known
C. KP + PR = ST + TV using the addition property.
D. Segment addition in KP + PR = KR
E. ST + TV = SV
F. Segment addition has obtained this answer
G. KR = SV by substitution property
The solution has been obtained by using the concept of mathematical reasoning.
What is mathematical reasoning?
In mathematics, reasoning entails making logical deductions from data or presumptions.
A. For this, we are stated a reason that it is given.
So, the statement is KP = ST.
B. We are given the statement as PR = TV
The reason is that it is given.
C. For this, we are stated a reason that it is obtained by addition property.
So, the statement is KP + PR = ST + TV.
D. We are given the statement as KP + PR = KR
The reason is that it is obtained by segment addition.
E. ST + TV = SV is the statement
F. The reason for the statement is that it is obtained by segment addition.
G. For this, we are stated a reason that it is obtained by substitution property.
So, the statement is KR = SV.
Hence, the statements and their respective reasons have been arranged.
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find the inverse of the matrix, if it exists. use the algorithm for finding by row reducing i]
The matrix is now in row echelon form. The inverse is the right side of the augmented matrix: [tex]$$\begin{bmatrix}1 & 1 & 0 \\2 & 1 & 3 \\0 & 1 & 2\end{bmatrix}$$[/tex]
We will use the algorithm for finding the inverse of a matrix by row reducing.
Step 1: Augment the matrix with the identity matrix.
[tex]$$\begin{bmatrix}1 & 1 & 0 & | & 1 & 0 & 0\\2 & 1 & 3 & | & 0 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]
Step 2: Use row operations to transform the matrix into the identity matrix.
1. Multiply the first row by [tex]$\frac{1}{2}$[/tex] to get:
[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\2 & 1 & 3 & | & 0 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]
2. Subtract two times the first row from the second row to get:
[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]
3. Subtract the first row from the third row to get:
[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 2 & | & -\frac{1}{2} & 0 & 1\end{bmatrix}$$[/tex]
4. Multiply the third row by [tex]$\frac{1}{2}$[/tex] to get:
[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 1 & | & -\frac{1}{4} & 0 & \frac{1}{2}\end{bmatrix}$$[/tex]
5. Subtract [tex]$\frac{3}{2}$[/tex]times the second row from the third row to get:
[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 0 & | & \frac{7}{4} & -1 & \frac{1}{2}\end{bmatrix}$$[/tex]
Step 3: The matrix is now in row echelon form. The inverse is the right side of the augmented matrix:
[tex]$$\begin{bmatrix}1 & 0 & 0\\-1 & 1 & 0\\\frac{7}{4} & -1 & \frac{1}{2}\end{bmatrix}$$[/tex]
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What is the value of x in this triangle?
Enter your answer in the box.
Answer:102+31-180 = 47
so x = 47
Step-by-step explanation:
this is very simple
(exercise 2: find the critical points of the gompertz equation (1). (is y = 0 a critical point? does it solve the algebraic equation you get?).dy = ry In(K/y
y = k asymptotically stable critical point because f'(k) < 0 and f'(0) > 0. So y = 0 is an an asymptotically unstable critical point.
The Gompetz equation is dy/dt = ry In(K/y).
In order to find critical points equate dy/dt equal to zero
dy/dt = 0
ry In(k/y) = 0
Here, k and r are constants
y In(k/y) = 0
y = 0
In (k/y) = 0
Eliminating In
k/y = e^0
k/y = 1
Multiply by y on both side, we get
k = y
y = 0 and y = k
The critical points are 0 and k
Since zero is a critical point
dy/dt = f(y)
dy/dt = ry In(k/y)
Differentiation on both side
f'(y) = ry In(k/y) - ry × y/k × k/[tex]y^2[/tex]
f'(y) = r In(k/y) - r
f'(k) = r In(k/k) - r
f'(x) = -r < 0
So that, y = k asymptotically stable critical point because f'(k) < 0
f'(0) > 0
That means y=0 is asymptotically unstable critical point.
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the vector a2 is in w if and only if a2 can be written in the form c1a1 c2a2 c3a3 with
Vector a2 is in the subspace spanned by vectors a1, a2, and a3 if it can be written as a linear combination of these vectors.
What is vector ?
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields and weight.
Let W be a subspace of a vector space V and let a1, a2, and a3 be vectors in V. The vector a2 is in the subspace W if and only if it can be written as a linear combination of the vectors a1, a2, and a3. That is, there exist scalars c1, c2, and c3 such that:
a2 = c1 * a1 + c2 * a2 + c3 * a3
This equation can be written in matrix form as:
[a2] = [a1 a2 a3] * [c1; c2; c3]
where [a2] is the column vector representation of a2, [a1 a2 a3] is the matrix with a1, a2, and a3 as columns, and [c1; c2; c3] is the column vector of scalars c1, c2, and c3.
Vector a2 is in the subspace spanned by vectors a1, a2, and a3 if it can be written as a linear combination of these vectors.
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Need some help ASAP!
Given: AD, BE and FC intersect at point P. AD⊥FC.
Write at least 6 algebra equations to relate different pairs of angles. Justify your statements with the correct definition or theorem.
The required six algebraic equations to relate the given different pairs of angles are in the solution part.
What are supplementary angles?The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.
Given: AD, BE and FC intersect at point P.
AD⊥FC.
According to the given figure, the required equations would be as:
m∠APB = m∠EPD (vertical angles)
m∠FPD = m∠APC (right angles are congruent)
m∠EPC + m∠EPF = 180 degrees (linear pair)
m∠BPC = m∠EPD (vertical angles)
m∠APB + m∠BPC = 90 degrees (complementary angles)
m∠FPB + m∠BPC = 180 degrees (linear pair)
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sandeep, hee, sara, and mohammad play euchre with a standard deck consisting of 24 cards (a, k, q, j, 10 , and 9 from each of the four suits of a regular deck of playing cards). in how many ways can the deck be dealt so that each player receives 5 cards, with 4 cards left in the middle, one of which is turned face-up? the order of the 3 cards that are left face-down in the middle does not matter, but who receives a particular set of 5 cards (for example, sara or sandeep) does matter.
There are 23,311,945,600 possible ways to deal the cards to the four players and choose one card to be turned face-up in the middle.
We can calculate the number of ways to deal the cards to the four players and then multiply by the number of ways to choose which card is turned face-up in the middle.
First, there are 24 choose 5 ways to deal the first hand, since each player receives 5 cards. Then, there are 19 choose 5 ways to deal the second hand, since there are now 19 cards left. Similarly, there are 14 choose 5 ways to deal the third hand and 9 choose 5 ways to deal the fourth hand.
So, the number of ways to deal the cards to the four players is:
24 choose 5 * 19 choose 5 * 14 choose 5 * 9 choose 5 = (24! / (5! * 19!)) * (19! / (5! * 14!)) * (14! / (5! * 9!)) * (9! / (5! * 4!))
Now, we need to multiply this result by 4, since there are 4 possible cards to turn face-up in the middle. So, the final answer is:
4 * 24 choose 5 * 19 choose 5 * 14 choose 5 * 9 choose 5 = 4 * (24! / (5! * 19!)) * (19! / (5! * 14!)) * (14! / (5! * 9!)) * (9! / (5! * 4!)) = 4 * 5,827,986,400 = 23,311,945,600.
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in the standard normal curve, what percent of data lies between 0 and 1 standard deviation?
About 68% of the data in a typical normal curve is within one of the mean's standard deviation. Accordingly, 68% of the data should fall between -1 and 1 if the data's mean was 0 and its standard deviation was 1.
A theoretical continous probability distribution known as the "standard normal curve" depicts a bell-shaped, symmetrical curve. The normal distribution or the Gaussian distribution are other names for it. The standard normal curve, which serves as a benchmark for other normal distributions, has a means of 0 and a variance of 1. For simpler analysis and comparison, data sets can frequently be translated into the normal form standards. The distributions of many real-world events, including IQ scores, length, weight, and heart rate, to mention a few, is described by the curve, which is significant in statistics. Among other uses, the normalised curve is employed in statistical inference, quality control, and hypothesis testing.
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as an architect, you are designing a new house. a window has a height between 140 cm and 150 cm and a width between 74 cm and 70 cm. what are the smallest and largest areas that the window could be?
The smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
This problem is based on the area of rectangle .
Here, since the height and the width of the window are distinct, so the window can be assumed to be of rectangular shape.
Now, the area of a rectangle is given by = l x b where l and b are respectively the height and the width of the window respectively.
The area would be smallest when both the height and width are least i.e. 140 cm and 70 cm .
So, smallest area = lxb = 140 x 70 = 9800 sq. cm = 9.8 sq. m.
Similarly the largest area would be when both the height and the width are maximum i.e. largest area = lxb = 150x 74 = 11,100 sq cm. =11.1 sq metres.
Therefore, the smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
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The smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
This problem is based on the area of a rectangle.
Here, since the height and the width of the window are distinct, so the window can be assumed to be of rectangular shape.
Now, the area of a rectangle is given by = l x b where l and b are respectively the height and the width of the window respectively.
The area would be smallest when both the height and width are least i.e. 140 cm and 70 cm .
So, smallest area = lxb = 140 x 70 = 9800 sq. cm = 9.8 sq. m.
Similarly, the largest area would be when both the height and the width are maximum i.e. largest area = lxb = 150x 74 = 11,100 sq cm. =11.1 sq metres.
Therefore, the smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
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You'll earn 95 points! ASAP please
Suppose you bought 8 mangoes and four apples for $20 and 3 mangoes and 6 apples for $16.50. What is a system of equations that represents the situation? how much does each mango and each apple cost?
Answer: Apples: $2 Mangos: $1.50
Step-by-step explanation:
8m+3a = 183m+5a=14.5
Multiply the first equation by 5 and multiply the second equation by 340m+15a=909m+15a=43.5
Subtract the equations
31m=46.5m=46.5/31m=1.5
Substitute to find the price of apples
8(1.5)+3a=1812+3a=183a=18-123a=6a=2
Apples cost $2.00 each mangoes cost $1.50 each