The domain of \(f(x)=\sin^{-1}x\) is \([-1, 1]\) and the range is \([-π/2, π/2]\).
This is because the inverse sine function, \(sin^{-1}x\), is defined only for values of x between -1 and 1, resulting in a domain of \([-1, 1]\). The range of \(sin^{-1}x\) is the set of all possible output values, which are angles between \(-π/2\) and \(π/2\).
Therefore, the domain of \(f(x)=\sin^{-1}x\) is \(\boxed{[-1, 1]}\) and the range is \(\boxed{[-π/2, π/2]}\).
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Help me find the answer
The exponential function that represents a vertical compression by a factor of 2 of [tex]f(x) = 2^x[/tex] is given as follows:
[tex]g(x) = 0.5(2)^x[/tex]
How to define the exponential function?The standard definition of an exponential function is given as follows:
[tex]y = a(b)^x[/tex]
In which:
a is the value of y when x = 0.b is the rate of change.When a function is vertically compressed by a factor of a, we have that the output of the function is multiplied by 1/a = divided by a, hence, considering the factor of 2, the function g(x) is given as follows:
g(x) = 1/2 x f(x)
[tex]g(x) = 0.5(2)^x[/tex]
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Consider the sequence n an o[infinity] n=1 = n√ 2, q 2 + √ 2, r 2 + q 2 + √ 2, s 2 + r 2 + q 2 + √ 2, · · · o . Notice that this sequence can be recursively defined by a1 = √ 2, and an+1 = √ 2 + an for all n ≥ 1.
(a) Show that the above sequence is monotonically increasing. Hint: You can use induction.
(b) Show that the above sequence is bounded above by 3. Hint: You can use induction.
(c) Apply the Monotonic Sequence Theorem to show that limn→[infinity] an exists.
(d) Find limn→[infinity] an.
(e) Determine whether the series X[infinity] n=1 an is convergent
(a) By help of induction, it is proved the sequence is monotonically increasing for all n ≥ 1.
(b) The sequence is bounded above by 3 for all n ≥ 1.
(c) Applying the Monotonic Sequence Theorem, it is proved that the limit of the sequence exists.
(d) limn→[infinity] an is 2.
(e) The series X[infinity] n=1 an is convergent
(a) To show that the sequence is monotonically increasing, we can use induction. Let's first consider the base case, n = 1. We have a1 = √2 and a2 = √2 + a1 = √2 + √2 > a1, so the sequence is increasing for n = 1. Now, let's assume that the sequence is increasing for n = k, so ak+1 > ak. Then, for n = k+1, we have ak+2 = √2 + ak+1 > √2 + ak = ak+1, so the sequence is also increasing for n = k+1. Therefore, by induction, the sequence is monotonically increasing for all n ≥ 1.
(b) To show that the sequence is bounded above by 3, we can also use induction. Let's first consider the base case, n = 1. We have a1 = √2 < 3, so the sequence is bounded above by 3 for n = 1. Now, let's assume that the sequence is bounded above by 3 for n = k, so ak < 3. Then, for n = k+1, we have ak+1 = √2 + ak < √2 + 3 = 3.2 < 3, so the sequence is also bounded above by 3 for n = k+1. Therefore, by induction, the sequence is bounded above by 3 for all n ≥ 1.
(c) By the Monotonic Sequence Theorem, if a sequence is both monotonically increasing and bounded above, then the limit of the sequence exists. Since we have shown that the sequence is monotonically increasing in part (a) and bounded above by 3 in part (b), we can conclude that the limit of the sequence exists.
(d) To find the limit of the sequence, we can use the fact that an+1 = √2 + an for all n ≥ 1. Taking the limit of both sides as n approaches infinity, we get limn→∞ an+1 = limn→∞ √2 + an. Since the limit of the sequence exists, we can write this as L = √2 + L, where L is the limit of the sequence. Solving for L, we get L = 2, so the limit of the sequence is 2.
(e) To determine whether the series X∞ n=1 an is convergent, we can use the fact that the limit of the sequence is 2. Since the sequence converges to 2, the terms of the sequence are getting closer and closer to 2 as n approaches infinity. This means that the terms of the series are getting smaller and smaller, and the series is convergent.
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Determine if the relation defines y as a function of x. y 4+ 3+ 3 2 . 1 2 1+ 2+ -3+ 4+ Yes, this relation defines y as a function of x. Х 5 No, this relation does not define y as a function of x.
No, this relation does not define y as a function of x.
A function is a relation in which each input (x-value) is paired with exactly one output (y-value). In this relation, the x-value of 2 is paired with two different y-values (3 and -3), which violates the definition of a function.
Therefore, this relation does not define y as a function of x.
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Create utilities for location and price combinations considering restrictions listed on the case study (200-level seats cannot be less than $60, 300-midcourt seats cannot be less than $35).
Based on the results,
1.which location & price combination is the best alternative to raise prices? Which location & price combination is the best alternative to lower prices?
2. How much could administration raise 300 mid-level seat prices to give them the same level of attractiveness as the next best alternative? Should they raise the prices to the calculated level? Please explain.
1. To raise prices, the best alternative is to increase the price of 200-level seats to $60 or higher. To lower prices, the best alternative is to reduce the price of 300-midcourt seats to $35 or lower.
2. Administration could raise 300 mid-level seat prices to make them as attractive as the next best alternative. To calculate the optimal level, the cost of the next best alternative (200-level seats) needs to be compared with the cost of the 300-midcourt seats. If the cost of the 300-midcourt seats is lower than the cost of the 200-level seats, administration should raise the price of the 300-midcourt seats to match the cost of the 200-level seats. The attractiveness of the two options should be assessed to determine if the 300-midcourt seats should be priced at the calculated level.
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Select the correct answer from each drop-down menu.
Determine how the figure helps to verify the triangle inequality theorem.
*
The two sides with lengths of 7 and 5 will (meet at a third vertex, only meet when they lie on the third side, never meet) ,which shows that the (sum, difference) of the lengths of the two sides of a triangle must be (less than, greater than, equal to)
the length of the third side.
The two sides with lengths of 7 and 5 will never meet, which shows that the sum of the lengths of the two sides of a triangle must be equal to the length of the third side.
What is the triangle inequality theorem?In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < n < b + c
Where:
n, b, and c represent the side lengths of this triangle.
b - c < n < b + c
7 - 5 < n < 7 + 5
2 < n < 12
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Evaluate the integral by changing to cylindrical coordinates. 7 −7 49 − y2 − 49 − y2 11 xz dz dx dy x2 + y2
The value of the triple integral is 49π ln(49) - 24.5π.
To evaluate this triple integral using cylindrical coordinates, we need to express the limits of integration in terms of cylindrical coordinates. We can convert the Cartesian coordinates to cylindrical coordinates as follows:
x = r cos(θ)
y = r sin(θ)
z = z
The region of integration is a cylinder centered at the origin with radius 7 and height 14 (from -7 to 7 in the y-direction). Therefore, the limits of integration are:
0 ≤ r ≤ 7
0 ≤ θ ≤ 2π
-7 ≤ z ≤ 7
Substituting these limits of integration and the Cartesian-to-cylindrical conversion into the integral, we get:
∫∫∫ 7 −7 (49 - [tex]y^2 - r^2[/tex]) / ([tex]x^2 + y^2)[/tex] dz dx dy
= ∫[tex]0^7[/tex]∫[tex]0^2π[/tex] ∫-7^7 (49 - [tex]r^2[/tex]sin^2(θ) - r^2) / (r^2cos^2(θ) + r^2sin^2(θ)) dz r dθ dr
= ∫0^7 ∫0^2π ∫-7^7 (49 - r^2) / r^2 dz r dθ dr
= ∫0^7 ∫0^2π [ln|49-r^2|] from -7 to 7 dθ dr
= ∫0^7 2π ln|49-r^2| dr
This integral is now a single-variable integral that can be evaluated using integration by substitution or by parts. Let u = 49 - r^2 and du = -2r dr. Then:
∫0^7 2π[tex]ln|49-r^2|[/tex] dr = ∫49^0 -πln|u| du/-2
= π/2 [u ln|u| - u] from 49 to 0
= π/2 [49 ln(49) - 49] = 49π ln(49) - 24.5π
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Unit 2: Chapter 7b HW Score: 719 3/4 answered Save Question 3 Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample of 245 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.26 and 0.44? (Enter your answer as a number accurate to 4 decimal places.) Question Help: Message instructor
The probability that the sample proportion is between 0.26 and 0.44 is 0.9998, or 99.98%.
The probability that the sample proportion is between 0.26 and 0.44 can be found using the normal distribution formula.
First, we need to find the mean and standard deviation of the sample proportion. The mean of the sample proportion is equal to the population proportion, which is 0.37. The standard deviation of the sample proportion can be found using the formula:
σ = √(p(1-p)/n)
Where p is the population proportion, and n is the sample size. Plugging in the given values, we get:
σ = √(0.37(1-0.37)/245) = 0.0196
Next, we need to find the z-scores for the given sample proportions. The z-score can be found using the formula:
z = (x - μ)/σ
Where x is the sample proportion, μ is the mean of the sample proportion, and σ is the standard deviation of the sample proportion. Plugging in the values for the lower bound of the sample proportion (0.26), we get:
z = (0.26 - 0.37)/0.0196 = -5.61
Similarly, for the upper bound of the sample proportion (0.44), we get:
z = (0.44 - 0.37)/0.0196 = 3.57
Now, we can use the standard normal table to find the probabilities corresponding to these z-scores. The probability for z = -5.61 is 0, and the probability for z = 3.57 is 0.9998.
Finally, to find the probability that the sample proportion is between 0.26 and 0.44, we subtract the lower probability from the upper probability:
P(0.26 < p < 0.44) = 0.9998 - 0 = 0.9998
Therefore, the probability that the sample proportion is between 0.26 and 0.44 is 0.9998, or 99.98%.
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The price of nails, n, is $1.29/lb, the price of washers, w, is $0.79/b,
and the price of bolts, b, is $2.39/b.
PartA Write an expression to represent the
total price of the supplies.
PartB What is the total cost of buying 2 pounds of nails, 4 pounds of
washers, and 3 pounds of bolts
Th expression for total price of the supplies is $ 12.91 .
What is Expression ?Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
Anything that is variable, or without a fixed value, is a variable. Alphabetic characters like a, b, c, m, n, p, x, y, z, and so on are typically used to denote expression variables. By combining several variables and numbers, we can create a wide range of expressions.
Given : price of nails, n = $1.29/b
price of washers, w = $0.79/b
price of bolts, b = $2.39/b
He bought 2 pounds of nails, 4 pounds of washers, and 3 pounds of bolts.
So, The total supplies will be :
= $1.29/b × 2 + $0.79/b × 4 + $2.39/b × 3
= 2.58 + 3.16 + 7.17
= $ 12.91
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Consider this function in explicit form.
f(n)=5n−2 for n≥1
Select the equivalent recursive function.
A.
{f(1)=3f(n)=f(n−1)+5 for n≥2
B.
{f(1)=3f(n)=5f(n−1) for n≥2
C.
{f(1)=−2f(n)=f(n−1)+5 for n≥2
D.
{f(1)=−2f(n)=5f(n−1) for n≥2
For n≥2, the corresponding recursive function is f (1) =3f(n)=f(n1) +5.
Describe a function?In mathematics, a function is a rule that pairs each element from the domain with exactly one from the range or codomain of two sets.
In a recursive function, the output value at a certain input value is defined as a function of the output value at the previous input value. In this instance, we may use the definition to derive the recursive function from the explicit function:
f (n) = 5n - 2 f (n) = 5n - 3 f (n) = 5(2) - 8 f (n) = 5(3) - 13
The right response is: A. When n=2, f(1) = 2f(n)= f(n1) + 5.
As a result, the recursive function can be written as: f (1) =3f(n)=f(n1) +5 for n2.
Thus, for n≥2, the analogous recursive function is f (1) =3f(n)=f(n1) +5.
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PLEASE HELPPP!!
and thank you in advance!!!
The requried value of the expression [tex]\sum_{n=11}^{30}n-\sum_{n=1}^{10}n[/tex] is 355.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
To evaluate the expression:
[tex]\sum_{n=11}^{30}n-\sum_{n=1}^{10}n[/tex]
we can first simplify each summation separately and then subtract the second summation from the first.
[tex]\sum_{n=11}^{30}n[/tex]= 11 + 12 + 13 + ... + 29 + 30
We can use the formula for the sum of an arithmetic series to simplify this expression:
S = (n/2)(a + l)
In this case, a = 11, l = 30, and n = 20 (since we're summing 20 terms).
So, we have:
S = (20/2)(11 + 30)
S= 410
Similarly,
[tex]\sum_{n=1}^{10}n[/tex] = 1 + 2 + 3 + ... + 9 + 10
S = 55
Finally, we can subtract the second summation from the first:
= 410 - 55 = 355
Therefore, the value of the expression is 355.
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quired
1) Coordinate point B is at (4,3). What will the coordinates be for B' after a
translation of (x-2y+3)?
OB' (5,4)
OB' (2,6)
OB' (6,2)
OB' (-2,3)
The coordinates after the translation are (2, 6).
Which will be the coordinates after the translation?Here we start with the point (4, 3) and we want to apply the translation defined by (x - 2, y + 3)
This would be a translation of 2 units to the left and 3 units up, using a "coordinate-axis" notation.
So we just need to subtract 2 from the x-value and add 3 to the y-value, we will get the new coordinates:
(4 - 2, 3 + 3) = (2, 6)
These are the coordinates of point B after the translation, the correct option is the second one.
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Answer:
OB' (2,
Step-by-step explanation:
take your first point (B) (4,3) and plug it into the x and y in (x-2, y+3) so you get (4-2, 3+3) which will give you (2,
Please help me :(( I need the answer :(
Answer:
[tex]\theta = 60^\circ \;and\; \theta = 300^\circ[/tex]
Step-by-step explanation:
Given
[tex]\sin \left(2\theta\right)=\sin \left(\theta\right)[/tex]
Use the identity: [tex]\sin(2\theta) = 2 \sin(\theta)\cos(\theta)[/tex]
=> [tex]2 \sin(\theta)\cos(\theta) = \sin(\theta)[/tex]
Divide both sides by [tex]\sin(\theta)[/tex]
=> [tex]2 \cos(\theta) = 1[/tex]
[tex]= > \cos(\theta) = \dfrac{1}{2}[/tex]
[tex]= > \,\theta=\cos^{-1}\left(\dfrac{1}{2}\right)[/tex]
[tex]\cos^{-1}\left(\dfrac{1}{2}\right) \;is\: \dfrac{\pi}{3}} \text{ in the first quadrant and $\dfrac{5\pi}{3}$ in the fourth quadrant}}[/tex]
In degrees this corresponds to
[tex]\dfrac{\pi}{3} = \dfrac{\pi}{3} \times \dfrac{180^\circ}{\pi} = 60^\circ\\\\and\\\\\dfrac{5\pi}{3} = \dfrac{5\pi}{3} \times \dfrac{180^\circ}{\pi} = 300^\circ\\[/tex]
Answer
[tex]\theta = 60^\circ \;and\; \theta = 300^\circ[/tex]
The distance between two station is 300km two motorcyclist start simultaneously
The the distance between the two stations is 300km, then the speed of first motorcyclist is 63 km/h and speed of second-motorcyclist is 70 km/h.
The distance between the "two-stations" is given to be 300 km;
Let the speed of first-motorcyclists be x km/h
and let the speed of second-motorcyclists be (x + 7) km/h,
So, the Distance covered by first motorcyclist after 2 hours is = 2x km
and distance covered by second motorcyclist after 2 hours is = 2(x+7) km
⇒ 2x + 14 km,
So, the distance not covered by them after 2 hours is = 300 - (2x+2x+14) km.
The distance between the motorcyclist after 2 hours is 34 km,
Which means ,
⇒ 300-(4x+14) = 34
⇒ 300 - 4x - 14 = 34
⇒ 4x = 300 - 48
⇒ x = 63,
So, Speed of first-motorcyclists is 63 km/h, and
Speed of second-motorcyclist is = (63 + 7) = 70 km/h.
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The given question is incomplete, the complete question is
The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclist.
what's the answer to this question
The statements are
Slope = 3y-intercept = 0Equation of the line: y = 3xHow to complete the statementsFrom the question, we have the following parameters that can be used in our computation:
In 6 minutes, Jose can run 18 laps
Using the above as a guide, we have the following:
Rate or Slope = 18/6
Evaluate
Slope = 3
For the equation, we have
y = Slope * Number of minutes
So, we have
y = 3 * x
This gives
y = 3x
Hence, the equation is y = 3x
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The width of Aubrey's bed is 40 inches and the distance between opposite corners is 85 inches. What is the length of Aubrey's bed?
Answer: 75 inches
Step-by-step explanation:
Using Pythagorean's Theorem, a² + b² = c², let a represent the length of the bed.
a² + 40² = 85²
a² + 1600 = 7225
a² = 5625
a = 75
The length of the bed is 75 inches.
Hope this helps!
Answer: 75
Step-by-step explanation: We can think of Aubrey’s bed as a triangle, Since the area doesn't matter. The base would be width (40) and the hypotenuse (length from corners) would be 85. So, since A^2+B^2=C^2 and c is 85 and a is 40. The equation is 40^2+?^2=85^2 so if we solve the numbers whit exponents we would get this: 1600+?=7225. Then we would just subtract 1600 from 7225 which is: 5625. Now we are not done. 5625 is just the square version of 5625. So we would need to find the square root. Which is 75.
Assume 12% of a population of credit applications are fraudulent. (i.e each loan has a 12% probability of being fraudulent.)
Based on a random sample of 25 applications find the probability the number of fraudulent applications in the sample is
Equal to 0 [ Select ] Equal to 3 [ Select ] Equal to 3 or less [ Select ] Equal to 5 or more [ Select ] More than 3 [ Select ]
The probability of fraudulent applications are:
Equal to 0 [0.0410] Equal to 3 [0.2387] Equal to 3 or less [0.4088] Equal to 5 or more [0.1734] More than 3 [0.5912]How to determine the probability of fraudulent applicationsThe given parameters are
n = 25
p = 0.12
The individual probability can be calculated as
P(x) = C(n, x) * p^x * (1 - p)^(n - x)
So, we have
Probability the number of fraudulent applications in the sample is 0
P(0) = C(25, 0) * 0.12^0 * (1 - 0.12)^(25 - 0)
P(0) = 0.0410
Probability the number of fraudulent applications in the sample is 3
P(3) = C(25, 3) * 0.12^3 * (1 - 0.12)^(25 - 3)
P(3) = 0.2387
Probability the number of fraudulent applications in the sample is 3 or less
P(x ≤ 3) = P(0) + ... P(3)
Using the formula above, we have
P(x ≤ 3) = 0.4088
Probability the number of fraudulent applications in the sample is 5 or more
P(x ≥ 5) = P(5) + ... P(25)
Using the formula above, we have
P(x ≥ 5) = 0.1734
Probability the number of fraudulent applications in the sample is more than 3
P(x > 3) = 1 - P(x ≤ 3)
By substitution, we have
P(x > 3) = 1 - 0.4088
P(x > 3) = 0.5912
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Kell high school sells child and adult football tickets. last Friday they sold 412 tickets for 2,725,50 if a child ticket costs 3 and an adult ticket costs 7.50 how many of each type of ticket did they sell
Answer:
Step-by-step explanation:
Let's assume that the number of child tickets sold is x and the number of adult tickets sold is y.
From the problem statement, we know that:
The total number of tickets sold is 412, so x + y = 412.
The total amount of money collected from selling these tickets is 2,725.50, so 3x + 7.50y = 2,725.50.
We can use these two equations to solve for x and y. One way to do this is to use substitution:
Solve the first equation for x: x = 412 - y.
Substitute this expression for x into the second equation: 3(412 - y) + 7.50y = 2,725.50.
Simplify and solve for y: 1,236 - 3y + 7.50y = 2,725.50, so 4.50y = 1,489.50, and y = 330.
Use the first equation to find x: x = 412 - y, so x = 82.
Therefore, Kell High School sold 82 child tickets and 330 adult tickets.
Find the value of x to the nearest degree
The value of x to the nearest degree is 30°.
What is Triangle ?
A triangle is one that has three sides, three angles, and whose total angles is always 180 degrees.
Three line segments are linked end to end to make a triangle, a two-dimensional geometric structure with three angles. These line segments are known as sides, and their intersections are known as vertices.
The measurements of a triangle's sides and angles are used to categorize it.
We can use trigonometric ratios to get the value of x in the right triangle given:
sin(x) = opposite/hypotenuse
[tex]sin(x) = 8/17x = sin^{-1(8/17)}x = 29.74^{o} $ (approx.) $[/tex]
Therefore, the value of x to the nearest degree is 30°.
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Please do the foll calculation. When improper, rewrite number or integel 2.2+(3)/(5)
The final answer is 3
The calculation you are looking to solve is 2.2 + (3)/(5). To solve this, we first need to convert the improper number 2.2 to a fraction. We can do this by multiplying the whole number by the denominator of the fraction and then adding the numerator. In this case, we would multiply 2 by 5 and then add 2, giving us 12/5. Now, we can add this fraction to the other fraction:
12/5 + 3/5 = 15/5
Next, we can simplify the fraction by dividing both the numerator and denominator by the greatest common factor. In this case, the greatest common factor is 5, so we can divide both the numerator and denominator by 5:
15/5 = 3
Therefore, the final answer is 3.
In summary, 2.2 + (3)/(5) = 3.
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5. LetA=[142231]. Find a basis forRow(A)⊥using the dot product.
The vector x = [2, -3, 1] is a basis for Row(A)⊥. This means that any vector in Row(A)⊥ can be written as a multiple of x.
To find a basis for Row(A)⊥ using the dot product, we need to find a vector that is orthogonal to all the rows of A. This means that the dot product of the vector and each row of A should be equal to 0.
Let's say the vector we are looking for is x = [x1, x2, x3]. Then we need to solve the following system of equations:
x1 * 1 + x2 * 4 + x3 * 2 = 0
x1 * 2 + x2 * 2 + x3 * 1 = 0
x1 * 3 + x2 * 1 + x3 * 1 = 0
We can write this system of equations in matrix form as:
[1 4 2] [x1] = [0]
[2 2 1] [x2] = [0]
[3 1 1] [x3] = [0]
We can use Gaussian elimination to solve this system of equations. After performing the necessary row operations, we get:
[1 0 -2] [x1] = [0]
[0 1 3] [x2] = [0]
[0 0 0] [x3] = [0]
From the last equation, we can see that x3 can be any value. Let's choose x3 = 1. Then, from the second equation, we get x2 = -3, and from the first equation, we get x1 = 2.
So, the vector x = [2, -3, 1] is a basis for Row(A)⊥. This means that any vector in Row(A)⊥ can be written as a multiple of x.
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write an equation that represents that 35 pizzas can be sold in 7 hours.
50 pizzas can be sold in 10 hours, according to this equation p = 5h.
What is equation ?In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is usually called the "left-hand side" (LHS) of the equation, while the expression on the right side of the equal sign is called the "right-hand side" (RHS) of the equation.
Let's use the variable p to represent the number of pizzas sold, and the variable h to represent the number of hours it takes to sell those pizzas. We can use the formula for finding the rate of sales (also known as the unit rate) to write an equation that represents the situation:
rate = amount of sales ÷ time
In this case, we know that 35 pizzas are sold in 7 hours. So, the rate of sales is:
rate = 35 pizzas ÷ 7 hours
Simplifying this expression, we get:
rate = 5 pizzas per hour
Therefore, the equation that represents the situation is:
p = 5h
This equation tells us that the number of pizzas sold (p) is equal to 5 times the number of hours it takes to sell those pizzas (h). For example, if we want to know how many pizzas can be sold in 10 hours, we can plug in h = 10 and solve for p:
p = 5h
p = 5(10)
p = 50
Therefore, 50 pizzas can be sold in 10 hours, according to this equation p = 5h
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Linear Equations Digital Escape! Can you find the slope-intercept equation of each line and type the correct code? i need help on this.
Therefore , the solution of the given problem of slope comes out to be slope-intercept equation y = 2x + 1.
Slope intercept: What does that mean?The y-intersection axis's with the slope of the line marks the inflection point in arithmetic where the y-axis intersects a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is the equation for the long line. The y-intercept (b) and slope (m) of the line are emphasised in the equation intercept form. An solution with the intersecting form (y=mx+b) has m and b as the slope and y-intercept, respectively.
Here,
Y = mx + b, where m is the line's slope and b is the y-intercept, is the slope-intercept version of a linear equation. Given two points (x1, y1) and (x2, y2), we can use the following method to determine the slope of the line:
=> m = (y2 - y1) / (x2 - x1) (x2 - x1)
For instance, if the two locations (2, 5) and (4, 9) are provided, we can determine the slope as follows:
=> m = (9 - 5) / (4 - 2) = 2
The y-intercept can then be determined by using one of the locations and the slope. Let's use points 2 and 5:
=> y = mx + b
=> 5 = 2(2) + b
=> 5 = 4 + b
=> b = 1
As a result, the line going through the points (2, 5) and (4, 9) has the slope-intercept equation y = 2x + 1.
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Simplify ((4m^(2)n^(2)p^(2))/(3mp))^(4). Assume that the denominator does zero. A. (256mn^(2)p)/(81) B. (256m^(4)n^(6)p^(4))/(81) C. (256m^(4)n^(8)p^(4))/(81) D. (256m^(4)n^(8)p^(4))/(81mp)
The correct answer is C. (256m^(4)n^(8)p^(4))/(81).
To simplify ((4m^(2)n^(2)p^(2))/(3mp))^(4), we need to first apply the power of 4 to each term inside the parentheses. This gives us:
(4^(4)m^(8)n^(8)p^(8))/(3^(4)m^(4)p^(4))
Next, we can simplify the terms with the same base by subtracting the exponents. This gives us:
(256m^(4)n^(8)p^(4))/(81)
Therefore, the correct answer is C. (256m^(4)n^(8)p^(4))/(81).
It is important to note that we assumed that the denominator does not equal zero, as dividing by zero is undefined.
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does anyone know the answer?!?
Step-by-step explanation:
Lets find the slope of the line first so we can write the equation.
Counting the slope, we can see the slope of the line is [tex]\frac{3}{1}[/tex] or 3, so we have to write the equation of the line in slope intercept form [tex]y=mx+b[/tex] where m is the slope and b is the y intercept.
We know that the y intercept is -4 by looking at the graph, so we simply plug in our slope and y intercept.
[tex]y=3x-4[/tex]
To tell if equations are parallel or perpendicular:
Parallel: The slope is the same
Perpendicular: The slope is the opposite reciprocal
Lets look at the equations and see if there parallel:
1. [tex]y=-3x+10[/tex] is neither.
2. The equation of the line is in point slope form, however we are already given the slope in the equation. The slope is [tex]-\frac{1}{3}[/tex], which is the opposite reciprocal of 3, therefore it is perpendicular.
3. [tex]\frac{1}{3}[/tex] is not the opposite reciprocal of 3, it is neither.
4. The equation of the line is in standard form, which means we must solve for y to get it in slope intercept form
[tex]-3x+y=1[/tex]
Subtract -3x on both sides
[tex]y=1-(-3x)[/tex]
Simplify
[tex]y=3x+1[/tex]
The equation has the same slope, so it is parallel.
DBA QUESTION #3
How is the distributive property used when finding the product of two polynomials?
Give an example.
How are polynomials closed under multiplication?
Answer:
The distributive property is used when finding the product of two polynomials by distributing one polynomial to each term of the other polynomial. For example, if we wanted to multiply (3x - 4)(2x + 5), we would use the distributive property by first multiplying 3x(-4) and 2x(5) and then adding the results together.
Polynomials are closed under multiplication, meaning that when two polynomials are multiplied together, the result is always another polynomial. This is true because a polynomial is a combination of constants and variables raised to non-negative integer powers, and when two polynomials are multiplied, the result is a combination of constants and variables raised to non-negative integer powers, which is a polynomial.
After your collection, you obtain an average disc width of 18.76cm with a sample size of 56.
1) Enter in the appropriate null mean.
2)According to your null distribution, what is the probability of obtaining your sample estimate or more extreme? what is the p-value?
a)18
b)0.023
1) The null mean for the disc width is assumed to be 18.
2) According to your null distribution, the probability of obtaining a sample estimate of 18.76 cm or more extreme is 0.023, and the p-value is 0.023.
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Number of sodas sold:
Number of hot dogs sold:
35
Check
✓ 36
At a basketball game, a vender sold a combined total of 135 sodas and hot dogs. The number of hot dogs sold was 31 less than the number of sodas sold. Find
the number of sodas sold and the number of hot dogs sold.
0
✓ 37
✓38
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The number of sodas sold is 83 and the number of hot dogs sold is 52.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let's call the number of sodas sold "x".
According to the problem, the number of hot dogs sold is 31 less than the number of sodas sold, so we can write the number of hot dogs sold as "x - 31".
We also know that the combined total of sodas and hot dogs sold is 135, so we can write an equation:
x + (x - 31) = 135
Simplifying this equation:
2x - 31 = 135
Adding 31 to both sides:
2x = 166
Dividing both sides by 2:
x = 83
So the number of sodas sold is 83.
To find the number of hot dogs sold, we can use the equation we came up with earlier:
x - 31 = 83 - 31 = 52
So the number of hot dogs sold is 52.
Therefore, the number of sodas sold is 83 and the number of hot dogs sold is 52.
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Farmer TC is drinking 17 cups of tea by the sea. His cows are grazing behind him, and he notices that the square of the fifth root of the number of cows he has is 1 less than the number of cups of tea he is drinking. How many cows does TC have?
We can determine that TC owns one cow using exponential calculations.
Exponential equations: what are they?Exponent-based equations are those in which the exponent, or a portion of the exponent, is a variable.
For illustration, [tex]3^{x}[/tex] = 81.
In the question given,
TC is drinking no. of cups = 17
Let no. of cows TC has = x
Now according to the question, we can for the equation as:
[tex](\sqrt[5]{x} )^{2}[/tex] = 17 -1
⇒ x = [tex]\sqrt[5]{4}[/tex]
⇒ x = 1.319
⇒ x ≈ 1
Hence, TC owns 1 cow.
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Please help
A cereal box manufacturer changes the size of the box to increase the amount of cereal it contains. The expressions 15 + 7.6n and 11 + 8n, where n is the number of
smaller boxes, are both representative of the amount of cereal that the new larger box contains. How many smaller boxes equal the same amount of cereal in the large
box?
The larger box of cereal has as much cereal as
(Type a whole number.)
smaller boxes
Answer:
Step-by-step explanation:
A cereal box manufacturer changes the sizeof the box to increase the amount of cereal itcontains. The equations 12 + 7.6n and 6 + 8n,where n is the number of smaller boxes, areboth representative of the amount of cereal thatthe new larger box contains. How many smallerboxes equal the same amount of cereal in thelarger box?
Jonah has read 1/4 of his mystery book. He has 36 pages. How many pages are in the mystery book