Answer: 240 miles in 2 hours
Step-by-step explanation:
we know the car is traveling 60 km per half hour (30 minutes)
so to find km per hour, multiply both by 2.
the rate of speed is 120 miles per 60 minutes (1 hour)
multiply 120 mph by the 2 hours given = 240 miles in 2 hours
Answer:
240 km in 2 hours
Step-by-step explanation:
If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:
Speed = distance ÷ time
Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour
Since the car is traveling at a constant speed, we can use the formula:
Distance = Speed × Time
To find how far the car will travel in 2 hours, we can substitute the values we have found:
Distance = Speed × Time
Distance = 120 km/hour × 2 hours
Distance = 240 km
Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.
Aaron sampled 101 students and calculated an average of 6.5 hours of sleep each night with a standard deviation of 2.14. Using a 96% confidence level, he also found that t* = 2.081.confidence intervat = x±s/√n A 96% confidence interval calculates that the average number of hours of sleep for working college students is between __________.
The average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night
According to the given data,
Sample size n = 101
Sample mean x = 6.5
Standard deviation s = 2.14
Level of confidence C = 96%
Using a 96% confidence level, the value of t* for 100 degrees of freedom is 2.081, as given in the question.
Now, the formula for the confidence interval is:x ± (t* × s/√n)Here, x = 6.5, s = 2.14, n = 101, and t* = 2.081
Substituting the values in the above formula, we get:
Lower limit = x - (t* × s/√n) = 6.5 - (2.081 × 2.14/√101) = 6.28
Upper limit = x + (t* × s/√n) = 6.5 + (2.081 × 2.14/√101) = 6.72
Therefore, the 96% confidence interval for the average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night.
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Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order.
y dA, D is bounded by y = x − 6; x = y2
D
The value of the double integral using the easier order, ydA bounded by y = x − 6; x = y² is 125/12.
The double integral, indicated by ', is mostly used to calculate the surface area of a two-dimensional figure. By using double integration, we may quickly determine the area of a rectangular region. If we understand simple integration, we can easily tackle double integration difficulties. Hence, first and foremost, we will go over some fundamental integration guidelines.
Given, the double integral ∫∫yA and the region y = x-6 and x = y²
y = x-6
x = y²
y² = y +6
y² - y - 6 = 0
y² - 3y +2y - 6 = 0
(y-3) (y+2) = 0
y = 3 and y = -2
[tex]\int\int\limits_\triangle {y} \, dA\\ \\[/tex]
= [tex]\int\limits^3_2 {y(y+6-y^2)} \, dx \\\\\int\limits^3_2 {(y^2+6y-y^3)} \, dx \\\\(\frac{y^3}{3} + 3y^2-\frac{y^4}{4} )_-_2^3\\\\\frac{63}{4} -\frac{16}{3} \\\\\frac{125}{12}[/tex]
The value for the double integral is 125/12.
Integration is an important aspect of calculus, and there are many different forms of integrations, such as basic integration, double integration, and triple integration. We often utilise integral calculus to determine the area and volume on a very big scale that simple formulae or calculations cannot.
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a bin can hold 28 pounds. each toy car weighs 7 ounces. how many toy cars can the bin hold? (2 points) 64 toy cars 72 toy cars 88 toy cars 92 toy cars
A bin can hold 28 pounds. each toy car weighs 7 ounces., so the bin can hold 64 toy cars.
How to determine the number of toy carsTo determine the number of toy cars the bin can hold, we must first convert the weight limit of the bin and the weight of the toy cars to a uniform unit of measure.
We'll then divide the weight limit of the bin by the weight of one toy car. After that, we'll multiply the resulting value by the number of ounces in one pound (16).
Here's how to solve the problem:
1 pound = 16 ounces
Therefore, a bin that can hold 28 pounds can hold:28 × 16 = 448 Ounces
The weight of one toy car is 7 ounces.
Divide the weight limit of the bin (448 ounces) by the weight of one toy car (7 ounces):
448 ÷ 7 = 64
Therefore, the bin can hold 64 toy cars.
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If P = 2y² + 4xy + 4
Q = − 3y² + 7 - 3xy
R=- 3xy + 8
Find P+Q=R.
Answer:
P = [tex]2y^{2}[/tex] + 4xy +4
Q = [tex]-3y^{2}[/tex] + 7 -3xy
R = -3xy +8
Step-by-step explanation:
Theorem: "If a and m are relatively prime integers and m > 1, then an inverse of a modulo m exists. Furthermore, this inverse is unique modulo m. (That is, there is a unique positive integer a less than m that is an inverse of a modulo m and every other inverse of a modulo m is congruent to a modulo m.)"Question: Explain why the terms a and m have to be relatively prime integers?
The reason why the terms a and m have to be relatively prime integers is that it is the only way to make sure that ax≡1 (mod m) is solvable for x within the integers modulo m.
Theorem:"If a and m are relatively prime integers and m > 1, then an inverse of a modulo m exists. Furthermore, this inverse is unique modulo m. (That is, there is a unique positive integer a less than m that is an inverse of a modulo m and every other inverse of a modulo m is congruent to a modulo m.)"If a and m are relatively prime integers and m > 1, then an inverse of a modulo m exists. Furthermore, this inverse is unique modulo m. (That is, there is a unique positive integer a less than m that is an inverse of a modulo m and every other inverse of a modulo m is congruent to a modulo m.)The inverse of a modulo m is another integer, x, such that ax≡1 (mod m).
This theorem has an interesting explanation: if a and m are not co-prime, then there is no guarantee that ax≡1 (mod m) has a solution in Zm. The reason for this is that if a and m have a common factor, then m “absorbs” some of the factors of a. When this happens, we lose information about the congruence class of a, and so it becomes harder (if not impossible) to undo the multiplication by .This is the reason why the terms a and m have to be relatively prime integers.
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Eddie est discutiendo con Tana sobre las probabilidades de los distintos resultados al lanzar tres monedas. Decide lanzar una moneda de un centavo, una de cinco centavos y una de die centavos. ¿ Cuál es la probabilidad de que las tres monedas salgan cruz?
The probability of getting tails in the three coins would be 0.125 or 12.5%.
How to calculate the probability?To calculate the probability of an event happening, first, we need to identify the rate of the desired outcome versus the total possible outcomes. Moreover, to determine the total probability of two or more events happening we need to calculate the probability of each event and then multiply the results.
Probability of getting tails in any of the three coins:
1 / 2 = 0.5
Total probabilityy:
0.5 x 0.5 x 0.5 = 0.125 or 12.5%
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determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span. a, S = {(1, −1), (2, 1)} b, S = {(1, 1)} c, S = {(0, 2), (1, 4)}
a. S = {(1, -1), (2, 1)}Let's begin by calculating the determinant of the matrix composed of the vectors of S, and checking if it is equal to 0. Because the two vectors are not colinear, they should span R2.|1 -1||2 1| determinant is not 0, therefore S spans R2. No geometric description is required for this example.
b. S = {(1, 1)} The set S contains one vector. A set containing only one vector cannot span a plane because it only spans a line. Therefore, S does not span R2. Geometric description: S spans a line that passes through the origin (0, 0) and the point (1, 1).c. S = {(0, 2), (1, 4)} Let's again begin by calculating the determinant of the matrix composed of the vectors of S, and checking if it is equal to 0.|0 2||1 4| determinant is 0, thus S does not span R2. In this scenario, S only spans the line that contains both vectors, which is the line with the equation y = 2x.
Geometric description: S spans a line that passes through the origin (0, 0) and the point (1, 2).
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I need help please show your work
Answer:
The 2nd equation is false.
Step-by-step explanation:
You don't even have to solve. DE is not 58, it's 40.
The 2nd equation is false.
The island of Martinique has received $32,000
for hurricane relief efforts. The island’s goal is to
fundraise at least y dollars for aid by the end of
the month. They receive donations of $4500
each day. Write an inequality that represents this
situation, where x is the number of days.
An inequality representing the amount that the island of Martinique can received for hurricane relief efforts, where x is the number of days is y ≤ 32,000 + 4,500x.
What is inequality?Inequality is an algebraic statement that two or more mathematical expressions are unequal.
Inequalities can be represented as:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The total amount received by the island = $32,000
The daily receipt of donations = $4,500
Let the number of days = x
Let the funds raised for aid = y
Inequality:y ≤ 32,000 + 4,500x
Thus, the inequality for the funds that the island can fundraise for hurricane relief aid by the end of the month is y ≤ 32,000 + 4,500x.
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A hawk flying at 19 m/s at an altitude of 228 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation y = 228 − x^2/57 until it hits the ground, where y is its height above the ground and x is its horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground. Express your answer correct to the nearest tenth of a meter.
The parabolic trajectory of the falling prey can be described by the equation y = 228 – x2/57, where y is the height above the ground and x is the horizontal distance traveled in meters. In this case, the prey was dropped at a height of 228 m and flying at 19 m/s. To calculate the total distance traveled by the prey, we can use the equation for the parabola to solve for x.
We can rearrange the equation y = 228 – x2/57 to solve for x, which gives us[tex]x = √(57*(228 – y))[/tex]. When the prey hits the ground, the height (y) is 0. Plugging this into the equation for x, we can calculate that the total distance traveled by the prey is[tex]x = √(57*(228 - 0)) = √(57*228) = 84.9 m.\\[/tex] Expressing this answer to the nearest tenth of a meter gives us the final answer of 84.9 m.
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Can anyone solve this ???
The result (recurrent value), A = sum j=1 to 89 ln(j), is true for every n. This is the desired result.
How do you depict a relationship of recurrence?As in T(n) = T(n/2) + n, T(0) = T(1) = 1, a recurrence or recurrence relation specifies an infinite sequence by explaining how to calculate the nth element of the sequence given the values of smaller members.
We can start by proving the base case in order to demonstrate the first portion through recurrence. Let n = 1. Next, we have:
Being true, ln(a1) = ln(a1). If n = k, let's suppose the formula is accurate:
Sum j=1 to k ln = ln(prod j=1 to k aj) (aj)
Prod j=1 to k aj * ak+1 = ln(prod j=1 to k+1 aj)
(Using the logarithmic scale) = ln(prod j=1 to k aj) + ln(ak+1)
Using the inductive hypothesis, the property ln(ab) = ln(a) + ln(b)) = sum j=1 to k ln(aj) + ln(ak+1) = sum j=1 to k+1 ln (aj)
(b), we can use the just-proven formula:
A = ln(1, 2,...) + ln + ln (89)
= ln(j=1 to 89) prod
sum j=1 to 89 ln = ln(prod j=1 to 89 j) (j).
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HELP PLS combine the like terms 3x+5-x+3+4x
Answer:
3x, 4x | 5, 3
Step-by-step explanation:
use the slicing method to find the volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles.
The volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles is 81/2*\sqrt3 by using the slicing method.
To find the volume of the solid whose base is the region inside the circle with radius 3, we need to integrate the area of the cross sections taken parallel to one of the diameters, which are equilateral triangles.
Let's consider a cross section of the solid taken at a distance x from the center of the circle.
Since the cross section is an equilateral triangle, all its sides have the same length.
Let this length be y. Since the triangle is equilateral, its height can be found using the Pythagorean theorem as follows:
[tex]height = \sqrt{(y^2 - (y/2)^2)} = \sqrt{(3/4y^2)}= \sqrt{3/2y}[/tex]
Therefore, the area of the cross section at a distance x from the center of the circle is:
[tex]A(x) = (1/2)y\sqrt{3/2y} = \sqrt{3/4y^2}[/tex]
Now, we need to integrate this area over the range of x from -3 to 3 (since the circle has radius 3):
[tex]V = \int\ [-3,3]\sqrt{3/4*y^2} dx[/tex]
To find the limits of integration for y, we need to consider the equation of the circle:
[tex]x^2 + y^2= 3^2[/tex]
Solving for y, we get:
[tex]y =\pm\sqrt{(3^2 - x^2)}=\pm\sqrt{(9^2 - x^2)}[/tex]
Since we want the cross sections to be equilateral triangles, we know that y is equal to the height of an equilateral triangle with side length equal to the diameter of the circle, which is 2*3 = 6. Therefore, we can write:
[tex]y = 3*\sqrt{3}[/tex]
Substituting this into the integral, we get:
[tex]V = \int\ [-3,3] \sqrt{3/4*(3\sqrt3)^2} dx[/tex]
[tex]= \int\ [-3,3] 27/4*\sqrt{3} dx[/tex]
Integrating, we get:
[tex]V = [27/4\sqrt{3x}]*[-3,3][/tex]
[tex]= 81/2*\sqrt{3}[/tex]
Therefore, the volume of the solid is [tex]81/2*\sqrt3[/tex]cubic units
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solve the proportion 7/11=18/x+1
Solve the equation [tex]7/11=18/x+1[/tex] we find the solution is [tex]x = 27.2857[/tex]
What is a formula or equation?Your example is an equation since an equation is any statement with an equals sign. Equations are frequently utilized for mathematical equations since mathematicians like equal signs. A set of instructions for achieving a certain result is called an equation.
A formula is it an expression?A number, a constant, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by such an assignment operator form an equation.
we can cross-multiply,
[tex]7(x+1) = 11(18)[/tex]
Expanding the left side,
[tex]7x + 7 = 198[/tex]
Subtracting [tex]7[/tex] from both sides,
[tex]7x = 191[/tex]
Dividing both sides by [tex]7[/tex],
[tex]x = 191/7[/tex]
Therefore, the solution to the proportion is
[tex]x = 27.2857[/tex]
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Solve equation for x
216=6^4x+5
Answer: x=211/1296
Step-by-step explanation:
in fig. 8-25, a block slides along a track that descends through distance h.the track is frictionless except for the lower section. there the block slides to a stop in a certain distance d because of friction. (a) if we decrease h,will the block now slide to a stop in a distance that is greater than, less than, or equal to d? (b) if, instead, we increase the mass of the block, will the stopping distance now be greater than, less than, or equal to d?
a block slides along a track that descends through distance h. The track is frictionless except for the lower section. There the block slides to a stop in a certain distance d because of friction. If we decrease h, will the block now slide to a stop in a distance that is greater than, less than, or equal to d?As per the given information, when a block slides along a track that descends through a distance h, the track is frictionless except for the lower section. There the block slides to a stop in a certain distance d because of friction. Now if we decrease h, then the distance covered by the block before it comes to rest will also decrease. So the block will slide to a stop in a distance that is less than d. Hence the answer is less than d.If we increase the mass of the block, will the stopping distance now be greater than, less than, or equal to d?
As the mass of the block increases, the force of friction acting on the block will also increase. Hence the stopping distance will also increase. So the stopping distance now will be greater than d. Hence the answer is greater than d.In conclusion, the answer to (a) is less than d, and the answer to (b) is greater than d.
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please help i have been trying to get an answer for 5+ hours
How is the quotient of 556 and 16 determined using an area model?
Enter your answers in the boxes to complete the equations. Your final answer should be a mixed number in simplest form.
Answer:
To use an area model to determine the quotient of 556 and 16, we can divide a rectangle of area 556 into 16 equal parts. Each part will have an area of 556/16.
We can start by dividing 556 into 16 groups of 10 (160), and then into 16 groups of 3 (48). That leaves us with a remainder of 4.
So we have:
556 = 16 x 34 + 48 + 4
This shows that 556 can be written as 16 times some whole number (34) plus a remainder of 48 + 4/16.
Simplifying the remainder, we have:
48 + 4/16 = 48 + 1/4 = 48.25
Therefore, the quotient of 556 and 16 is:
556/16 = 34 1/4
The quotient of 556 and 16 using an area model can be determined by producing a rectangle with the total area of 556 and one side of 16. The length of the other side will be the quotient. In this case, the quotient is 34 3/4.
Explanation:When asked to determine the quotient of 556 and 16 using the area model, one way to think of this is making a rectangle. The total area is 556 and one side is 16. The length of the other side will be the quotient.
Start by first estimating how many times 16 could fit into 556. Let's take 30 as an estimate, because 30*16 = 480, which is relatively close to 556. Draw a rectangle with the width of 16 and the length of 30.
Find the difference between the rectangle's area and 556. So, 556 - 480 = 76. Now, 76 is our remaining area to fill. 16 goes into 76 four more times, adding up to 64.
There is still a leftover area, which is 76-64 = 12. This is smaller than our width of 16. So, your final answer is 34 12/16 or 34 3/4 in simplest form.
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A sphere is to be designed with a radius of 72 in. Use differentials to estimate the maximum error when measuring the volume of the sphere if the possible error in measuring the radius is 0.5 in. 4 (Hint: The formula for the volume of a sphere is V(r) = ²³.) O 452.39 in ³ O 16,286.02 in ³ O 65,144.07 in ³ O 32,572.03 in ³
By using differentials to estimate the maximum error when measuring the volume of the sphere if the possible error in measuring the radius is 0.5. It will be 32,572.03 in³. Which is option (d).
How to measure the maximum error while measuring the volume of a sphere?The possible error in measuring the radius of the sphere is 0.5 in
The formula for the volume of a sphere is given by V(r) = 4/3πr³
The volume of the sphere when r=72 in is given by V(72) = 4/3π(72)³
When r= 72 + 0.5 in= 72.5 in, the volume of the sphere can be calculated using the formula:
V(72.5) = 4/3π(72.5)³
The difference between these two volumes, V(72) and V(72.5), gives us the maximum error while measuring the volume of a sphere. It can be calculated as follows:
V(72.5) - V(72) = 4/3π(72.5)³ - 4/3π(72)³= 4/3π [ (72.5)³ - (72)³ ]= 4/3π [ (72 + 0.5)³ - 72³ ]= (4/3)π [ 3(72²)(0.5) + 3(72)(0.5²) + 0.5³ ]≈ (4/3)π [ 777.5 ]= 3.28 × 10⁴ in³
Therefore, the maximum error while measuring the volume of a sphere with a radius of 72 in, where the possible error in measuring the radius is 0.5 in, is approximately 3.28 × 10⁴ in³ or 32,572.03 in³. Therefore coorect option is (D).
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Triangle ABC has coordinates A(4,1), B(5,9),and C (2,7). If the triangle is translated 7 units to left, what are the coordinates of B'?
Answer:
(-2,9)
Step-by-step explanation:
when moving it 5 units left on the x axis it would be 5-7
So in turn you would be given (-2,9)
Because the y stays the same you would still have (?,9)
An electric dipole with its center located at the origin of a Cartesian coordinate system oscillates along the z axis, creating an electromagnetic wave. At a position on the y axis far from the origin, what is the polarization of the wave and which axis are the magnetic (a) The wave is polarized parallel to the a axis and the magnetic field lines are parallel to b The wave is polarized parallel to the z axis and the magnetic field lines are parallel to (c) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (d) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (e) The wave is polarized parallel to the z axis and the magnetic field lines are parallel to field lines parallel to? the y axis the axis the r axis the z axis the z axis
The wave is polarized parallel to the y-axis, and the magnetic field lines are parallel to the x-axis. Here option D is the correct answer.
The oscillating electric dipole along the z-axis creates an electromagnetic wave with electric and magnetic fields perpendicular to each other and to the direction of wave propagation. At a position on the y-axis far from the origin, the electric field will be parallel to the y-axis.
The polarization of the wave refers to the orientation of the electric field vector. Since the electric field is parallel to the y-axis, the wave is polarized parallel to the y-axis.
According to the right-hand rule, the direction of the magnetic field lines will be perpendicular to both the electric field and the direction of wave propagation, which is along the z-axis. Therefore, the magnetic field lines will be parallel to the x-axis.
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for h(x) = 4x-1, find h(0) and h(2)
Answer:
- 1 and 7
Step-by-step explanation:
to find h(0) substitute x = 0 into h(x)
h(0) = 4(0) - 1 = 0 - 1 = - 1
to find h2) substitute x = 2 into h(x)
h(2) = 4(2) - 1 = 8 - 1 = 7
I need some help with this
Answer:
12
Step-by-step explanation:
i think its right
use the trapezoidal rule and simpson's rule to approximate the value of the definite integral for the given value of n. round your answer to four decimal places and compare the results with the exact value of the definite integral. 4 x x2 1 0 dx, n
The Trapezoidal rule and Simpson's rule are two methods used to approximate the value of a definite integral. The Trapezoidal rule approximates the integral by dividing the region between the lower and upper limits of the integral into n trapezoids, each with a width h. The approximate value of the integral is then calculated as the sum of the areas of the trapezoids. The Simpson's rule is similar, except the region is divided into n/2 trapezoids and then the integral is approximated using the weighted sum of the area of the trapezoids.
For the given integral 4 x x2 1 0 dx, with n = 200, the Trapezoidal rule and Simpson's rule approximate the integral to be 7.4528 and 7.4485 respectively, rounded to four decimal places. The exact value of the integral is 7.4527. The difference between the exact and approximate values is very small, thus indicating that both the Trapezoidal rule and Simpson's rule are accurate approximations.
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Anna wants to make 30 mL of a 60 percent salt solution by mixing togethera 72 percent salt solution and a 54 percent salt solution. How much of each solution should dhe use
Anna should use 10 mL of the 72% salt solution and 20 mL of the 54% salt solution to make 30 mL of a 60% salt solution
Let's assume that Anna will use x mL of the 72% salt solution, and therefore she will use (30 - x) mL of the 54% salt solution (since the total volume is 30 mL).
To find out how much of each solution Anna should use, we can set up an equation based on the amount of salt in each solution.
The amount of salt in x mL of 72% salt solution is
= 0.72x
The amount of salt in (30 - x) mL of 54% salt solution is
= 0.54(30 - x)
To make a 60% salt solution, the total amount of salt in the final solution should be
0.6(30) = 18
So we can set up an equation
0.72x + 0.54(30 - x) = 1
Simplifying the equation
0.72x + 16.2 - 0.54x = 18
0.18x = 1.8
x = 10 ml
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In a candy factory, each bag of candy contains 300 pieces. The bag can be off by 10 pieces.
Write an absolute value inequality that displays the possible number of candy pieces that a bag contains.
Answer:
[tex] |x - 300| \leqslant 10[/tex]
kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )
a. 1
b. x.x’
c. 1+ x.x’
d. (1+ x.x’)^2
e. exp (x+x’), for x.x’ ER
f. min (x.x’) for x.x’ E Z
Answer:
Step-by-step explanation:
kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )
A barista mixes 12lb of his secret-formula coffee beans with 15lb of another bean that sells for $18 per lb. The resulting mix costs $20 per lb. How much do the barista's secret-formula beans cost per pound?
Answer: $22.50
Step-by-step explanation:
Let x be the cost per pound of the secret-formula coffee beans.
The total cost of the secret-formula beans is 12x dollars.
The total cost of the other beans is 15 × 18 = 270 dollars.
The total cost of the mix is (12 + 15) × 20 = 540 dollars.
Since the barista mixed 12 pounds of the secret-formula beans with 15 pounds of the other beans, the total weight of the mix is 12 + 15 = 27 pounds.
We can set up an equation based on the total cost of the mix:
12x + 270 = 540
Subtracting 270 from both sides:
12x = 270
Dividing both sides by 12:
x = 22.5
Therefore, the barista's secret-formula coffee beans cost $22.50 per pound.
If the GM between √2 and 2√2 is a find the value of a.
Answer:
If the GM between √2 and 2√2 is a find the value of a.
Step-by-step explanation:
To find the geometric mean between two numbers, we simply take the square root of their product.
In this case, we want to find the geometric mean between √2 and 2√2.
Their product is:
√2 * 2√2 = 2√4 = 2*2 = 4
So, the geometric mean between √2 and 2√2 is the square root of 4, which is:
√4 = 2
Therefore, the value of a is 2.
The equation and graph show the distance traveled by a covertible and a limousine in miles, y, as a function of time in hours, x.
The rate of change of the distance for limousine is less than the rate of change of the convertible.
What is rate of change?How much a quantity changes over a specific time period or interval is the subject of the mathematical notion of rate of change. Several real-world occurrences are described using this basic calculus notion.
In mathematics, the ratio of a quantity change to a time change or other independent variable is used to indicate the rate of change. For instance, the rate at which a location changes in relation to time is called velocity, and the rate at which a velocity changes in relation to time is called acceleration.
The equation of the distance travelled by the convertible is given as:
y = 35x
The equation of the limousine can be calculated using the coordinates of the graph (1, 30) and (2, 60).
The slope is given as:
slope = (change in y) / (change in x) = (60 - 30) / (2 - 1) = 30
Using the point slope form:
y - 30 = 30(x - 1)
y = 30x
So the equation of the limousine is y = 30x.
Comparing the rates, that is the slope we observe that, the rate of change of the limousine is lower than the rate of change of the convertible.
Hence, the rate of change of the limousine is less than the rate of change of the convertible.
Learn more about rate of change here:
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Solve the following formula for t
S=12(V0+V1)t
Answer:
[tex]{ \rm{s = 12( v_{0} + v_{1} )t}} \\ \\{ \boxed { \rm{t = \frac{s}{12(v_{0} + v_{1})} \: \: }}}[/tex]
