Answer:
1/12
Step-by-step explanation:
Given
5/14 x 7/30Solving
This can easily be solved by using cross-multiplicationIf we are given a fraction a/b, it can be rewritten as a x 1/b⇒ 5 x 1/14 x 7 x 1/30Now combine (7 and 1/14) and (5 and 1/30)⇒ 7 x 1/14 x 5 x 1/30⇒ 7/14 x 5/30⇒ 1/2 x 1/6⇒ 1/12Answer:
\(\dfrac{1}{12}\)
Step-by-step explanation:
Rewrite the denominators as products of factors, then cancel the common factors.
\(\begin{aligned}\dfrac{5}{14} \times \dfrac{7}{30} & =\dfrac{5}{2 \cdot 7} \times \dfrac{7}{6 \cdot5}\\\\ & = \dfrac{5 \cdot 7}{2 \cdot 7 \cdot 6 \cdot 5}\\\\ & = \dfrac{1}{2 \cdot 6}\\\\ & = \dfrac{1}{12}{\end{aligned}\)
A person is skateboarding to their local skate shop to pick up some sick rims. They skate at 8 miles per hour. The store is 2.5 miles away. How long will it take them to get to the store in hours?
Answer: 0.3125 hours
Step-by-step explanation:
The formula for time taken to cover a distance is:
= Distance / Speed
Distance = 2.5 miles
Speed = 8 miles per hour
Time taken = 2.5 / 8
= 0.3125 hours
In minutes this is:
= 0.3125 * 60 mins
= 19 mins approx
Re-write the following system of equations in matrix format and solve them by using Cramer's rule. z+5x= 24 3x+2z+3y=7 -x+2y=-9
The solution of the given system of equations is (-3, 5/3, -4) by using Cramer's rule.
The given system of equations is given as,z + 5x = 243x + 2z + 3y = 7-x + 2y = -9
To solve the given system of equations by using the Cramer's rule, we have to first represent the given system in matrix format.
Matrix format: ⎡1 0 5⎤ ⎡x⎤ ⎡24⎤ ⎢0 3 2⎥ ⎢y⎥=⎢7⎥ ⎣-1 2 0⎦ ⎣z⎦ ⎣-9⎦
Using the formula for Cramer's rule, we know that,
x = Dx / D, y = Dy / D, z = Dz / D, whereD is the determinant of the coefficient matrix, Dx is the determinant of the matrix obtained by replacing the x column with the constant matrix, Dy is the determinant of the matrix obtained by replacing the y column with the constant matrix, and Dz is the determinant of the matrix obtained by replacing the z column with the constant matrix.
Calculation of D: D = | A | = ⎡1 0 5⎤ ⎡0 3 2⎥ ⎣-1 2 0⎦
Applying the Laplace expansion along the first column, D = 1 |⎡3 2⎤| - 0 |⎡-1 2⎤| + 5 |⎡-1 3⎤| |⎣2 0⎦| |⎣2 0⎦| |⎣2 0⎦| D = 6 Calculation of Dx: Dx = ⎡24 0 5⎤ ⎡3 2⎤ ⎢7 3 2⎥ ⎢-1 2⎥ ⎣-9 2 0⎦ ⎣2 0⎦
Applying the Laplace expansion along the first column, Dx = 24 |⎡3 2⎤| - 0 |⎡-1 2⎤| + 5 |⎡-9 2⎤| |⎣3 2⎦| |⎣3 2⎦| |⎣3 2⎦|
Dx = -18
Calculation of Dy: Dy = ⎡1 24 5⎤ ⎡0 2 2⎤ ⎢0 7 2⎥ ⎢-1 -1 0⎥ ⎣-1 -9 0⎦ ⎣2 0 0⎦
Applying the Laplace expansion along the second column, Dy = 0 |⎡1 5⎤| - 24 |⎡0 2⎤| + 5 |⎡0 2⎤| |⎣-1 0⎦| |⎣-1 0⎦| |⎣-1 0⎦|
Dy = 10
Calculation of Dz: Dz = ⎡1 0 24⎤ ⎡0 3 2⎥ ⎢0 3 7⎥ ⎢-1 2 -1⎥ ⎣-1 2 -9⎦ ⎣3 2 0⎦
Applying the Laplace expansion along the third column,
Dz = 24 |⎡3 2⎤| - 10 |⎡-1 2⎤| + 0 |⎡-1 3⎤| |⎣2 0⎦| |⎣2 0⎦| |⎣2 0⎦|
Dz = -24
Now we have the values of D, Dx, Dy and Dz.
Therefore, x = Dx / D, y = Dy / D, z = Dz / D,x = -18/6 = -3 y = 10/6 = 5/3 z = -24/6 = -4
Hence, the value of x, y, and z is (-3, 5/3, -4) respectively.
Therefore, the solution of the given system of equations is (-3, 5/3, -4) by using Cramer's rule.
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Evaluate f(x) = 5x – 8 when 8 when I = -3.0, and 4.
Answer:
f(3)=3
Step-by-step explanation:
Plugin 3 for x, and simplify
f(x) =5(x)−12
f(3) =5(3)−12
=15−12
f(3)=3
if the f is differentiable, then its derivative is the maximizing argument in the computation of the convex conjugate:
while the derivative of a differentiable function is important in the computation of the convex conjugate, it is not accurate to say that the derivative is the maximizing argument.
The statement you provided is not entirely accurate. While it is true that the derivative of a differentiable function can play a role in computing the convex conjugate, it is not accurate to say that the derivative is the maximizing argument in the computation of the convex conjugate.
Let's clarify the concepts involved:
Convex conjugate: Given a function f, its convex conjugate (also known as the Legendre-Fenchel transform) is denoted as f∗ and is defined as:
f∗(y) = sup(x)(⟨x, y⟩ - f(x))
Here, sup denotes the supremum (least upper bound), ⟨x, y⟩ represents the inner product of x and y, and f(x) is the original function.
Derivative: The derivative of a function f(x) with respect to x, denoted as f'(x) or df/dx, gives you the rate of change of the function at a particular point.
The relationship between the derivative and the convex conjugate can be seen through the Moreau-Rockafellar duality theorem, which states that if f is a proper, convex, and lower-semicontinuous function, then its convex conjugate f∗ is also proper, convex, and lower-semicontinuous.
In this duality relationship, the gradient (or derivative) of f plays a crucial role, but it is not the maximizing argument itself.
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Which are steps in the process of completing the square used to solve the equation? 1 = 2(x2 + 2x) 1 = 2x2 + 4x 2 = 2(x2 + 2x + 1) 3 = 2(x + 1)2 2 = 2(x + 1)2
Answer: 1 2 and 4 hope this helps
Step-by-step explanation:
Answer:
yes, the correct answers are:
A) 1 = 2(x2 + 2x)
B) 1 = 2x2 + 4x
D) 3 = 2(x + 1)2
Step-by-step explanation:
got it correct in edg 2020 hope this is of help :)
(a) what is the probability that the first sample following the mean shift produces a statistics that plots inside the control limits?
The probability that the first sample following the mean shift produces a statistics that plots inside the control limits: β ^{m-1}( 1-β )
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Pr(shift found on mth sample) = Pr (not detected for (m-1) samples) x Pr (detected on mth)
= [ 1-(1-β) ]^{m-1} ( 1-β )
=β ^{m-1}( 1-β )
the anticipated number of subgroups to be examined before the shift is seen
ARL=1/{1-β}
Shift not detected on the first sample following the shift:
Pr = 1-(1-β) = β
Pr n successive samples that are outside of the control limits
= ( 1- β )^{n}
f) the likelihood that at least one out of n consecutive statistical plots will fall outside the control limit.
=[1- ( 1- β )]^{n}
=β^{n}
Hence, The probability that the first sample following the mean shift produces a statistics that plots inside the control limits is β ^{m-1}( 1-β )
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If a spinner will land on red 45% of the time, yellow 15% of the time, and blue 40% of the time, what are the chances it wont land on red
Answer:
55%
Step-by-step explanation:
Chances it wont land on red = chances of blue + chances of yellow
= 55%
For every 3 minutes that Ryan runs on the treadmill, he burns 28
calories. How many calories can he expect to burn if he runs for 24
minutes?
Answer:
He will burn 224 calories.
Step-by-step explanation:
Multiply 8 by 28 to get your answers because he runs 8 times more in 24 minutes.
:))
4x + 33 = 10x + 3
show your work
Answer:
on 4x + 33 = 10x + 3, we could use inverse operation and move 10x to left side, which will create -6x+33=3. we could also use the same thing to 33 and get -6x=-30. if we divide -30 by -6, we would get 5
Step-by-step explanation:
4+33=10+3
4+33−33=10+3−33
4=10−3
=5
What is chi-square for association?
The Chi-Square Test for Association is used to determine if there is any association between two variables
The chi-square test of association is used to determine whether there is an association between two variables. It's really a hypothesis test of independence. The null hypothesis states that the two variables are unrelated, or independent. The alternative hypothesis is that the two variables are related. The following example shows how to perform this test using the SPC for Excel software (by Ajit Tamhane and Dorothy Dunlop, Prentice-Hall, from his Statistics and Data Analysis, 2000). A study was conducted to determine whether job satisfaction was related to income. A total of 901 people participated in the survey. The data are shown below. Use the chi-square test of association to determine whether two variables are associated.
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Which of these equations has infinitely many solutions?
A
W+ 12 = 6 + W + 6
B.
W-4 = W+4.
C
W+6 = 3(w+2)
D
W-1 = 4W-8
Answer:
A. W+ 12 = 6 + W + 6
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Meyer used 8 loads of gravel to cover 2/5 of his driveway. How many loads of gravel will he need to cover his entire driveway?
Answer:Meyer uses 2.5 loads
Step-by-step explanation:Why does he use 2.5? Because, he has 8 loads and with 1 load he covers 2/5 of his driveway so 2 loads covers 4/5 and 2.5 loads cover 5/5 of his driveway
HELP ASAP!! What is the average rate of change between x = -3 and x = 4 for the equation y = 8x2?
Answer:
\(x=-3\\y=8(-3)^2\\y=8(9)\\y=72\)
\(x=4\\y=8(4)^2\\y=8(16)\\y=128\)
128-72=56
average rate of change is 56
Step-by-step explanation:
Plz let me know if im right
Answer:
8 is the average rate of change
Step-by-step explanation:
Plugin -3 and 4 in for x.
y = 8(-3)^2
y = 72
y = 8(4)^2
y = 128
128-72/4-(-3) = the average rate of change
56/7=8
What is the solution to the system of equations y =- 3x 2 5x 2y 15?
The solution for system of equation provided as per the given question will be x = -19 and y = 55 or (-19,55).
It is given that the equations are:
y = –3x – 2
Simplifying it further, we get:
y + 3x = -2 (equation 1)
5x + 2y = 15 (equation 2)
Multiplying y + 3x = -2 by 2 and subtracting from 5x + 2y = 15, we get:
2y - 2y + 5x -6x = 15 + 4
-x = 19
x = -19
Plugging the value of x in the equation y + 3x = -2, we get:
y + 3 × - 19 = -2
y - 57 = -2
y = -2 + 57
y = 55
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use scenario 6-16. on average, how many people will the reporter have to stop before he finds his first democrat?
On an average, 1.67 people will have to be stopped by the reporter before he finds his first democrat.
What is democrat?A supporter of democracy, Democratic Party subscriber, a democratic government, or a system of government where the people rule, may be referred to as a Democrat, Democrat, or Democratic.
The central value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a given set of numerical data.
For instance, (2+3+4)/3 = 9/3 = 3 is the average of 2, 3, and 4. As a result, in this instance, 3, which also includes 2, 3, and 4, serves as the central value. Finding the average value of a group of numbers is what average means, then.
Average is calculated by dividing the total number of values by the sum of the individual values.
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Can someone help me please
Answer:
x= 70°
Step-by-step explanation:
the lines overlapping the two sides on the triangle mean that those two sides are congruent, meaning that both of those angles would be equal to 70°
witch expression is equivalent to |-5| + |3|
A -8
B -2
C 2
D 8
Answer:
D
Step-by-step explanation:
WHEN APPLY MOD | | , we consider making every values in it positive.
so, equation becomes:
+5 + (+3)
= +8
therefore, D 8
Answer:
D
Step-by-step explanation:
The absolute value function always gives a positive result, that is
| - a | = | a | = a
Given
| - 5 | + | 3 |
= 5 + 3
= 8 → D
2(8x +9) -8(7-5x)
Please can someone help
Answer:
56x-38
Step-by-step explanation:
2(8x+9)-8(7-5x)
16x+18
-8(7-5x)
-56+40x
16x+18-56+40x
Add all like terms
56x-38
Answer:16x + 18 -56+40x=0
16x+40x +18-56=0
56x-38=0
56x=38
X=19/28
Step-by-step explanation:
Newton's law of gravitation state that the force F of attraction between two bodies varies jointly as their masses M1 and M2 and inversely as the square of the distance between them. Two bodies whose centers are 500mi apart attract each other with a force of 15lb.What will be the force of attraction if their masses were tripled and the distance between their centers doubled?
how do i solve −3 1/3 ÷ 9
-3 1/3=-10/3
-10/3 / 9 = -10/3 * 1/9 = -10/27
Hope this helps! Good luck! Bye.
Answer:
0.1
Step-by-step explanation:
-10/3 / 9 = -10/3 * 1/9
aimee has 20 apples and wants to have the same amount of apples in each bag but ends up with more than one bag of apples and each bag to contain more than one apple
work out all the possibilities for all of the number of apples that she could use for each bag
Answer:
There are 4 possibilities: 2, 4, 5 or 10 apples in each bag.===========
Let the number of apples in each bag is x, then the number of bags is 20/x.
Since the number of apples in each bag is greater than one and number of bags is greater than one, we have the following conditions:
x > 1 , 20/x > 1 ⇒ x < 20,x is factor of 20.The factors of 20 between 1 and 20 are:
2, 4, 5, 10The possibilities are:
If x = 2, then the number of bags is 20/2 = 10;If x = 4, then the number of bags is 20/4 = 5;If x = 5, then the number of bags is 20/5 = 4;If x = 10, then the number of bags is 20/10 = 2.Find the equation of the line parallel to -2x +y = 3, that passes through the point
(-3,-1). Write your answer in slope-intercept form. Do not use spaces in your
answer. Enter any fractions like a/b or -a/b.
Answer:
y=-2x-9
Step-by-step explanation:
First, convert -2x+y=3 to an expression in slope-intercept form. This will be written as y=-2x+3.
Parallel lines have the same slope.
So, the slope of the new line will also be -2x.
Now, use the given coordinates and put them and the slope into point-slope form.
Point slope: y-y1=m(x-x1)
y+3=-2(x+3)
Finally, distribute -2 to (x+3) and simplify the equation.
y+3=-2x-6
y=-2x-9
Find an expression which represents the sum of (3x+9y)(3x+9y) and (5x+7y)(5x+7y) in simplest terms.
The expressions (7x - 6y) and (3x - 5y) added together result in 10x - 11y.
What is unitary method?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Consider your square as being composed of smaller unit squares.
The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.
Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.
According to our question-
(7x – 6y) and (3x – 5y
Then the sum of the expressions will be
(7x – 6y) + (3x – 5y)
7x – 6y + 3x – 5y
10x – 11y
Hence, The expressions (7x - 6y) and (3x - 5y) added together result in 10x - 11y.
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Find the perimeter
x + 7y
8x-x+y units
units
The perimeter is units.
(Simplify your answer. Do not factor)
Thus, the linear equation for the perimeter if the rectangle is found as:
P = 2(8x + 8y) units.
Explain about the perimeter of rectangle?P = (L + W) 2 is the perimeter rule for a rectangle, where P stands for perimeter, L for length, and W for width.
To find the perimeter of a rectangle with specified dimensions, all you need to do is enter the values of L and W into the formula.
The perimeter calculation can be used, for instance, to calculate how many feet with brick border are required overall if the rectangle depicts a garden that requires a brick border.
Given data:
Length = x + 7y units
Width = 8x-x+y units
perimeter P = 2(L + W)
P = 2(x + 7y + 8x - x + y)
adding the same variables.
P = 2(8x + 8y)
Thus, the linear equation for the perimeter if the rectangle is found as:
P = 2(8x + 8y) units.
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Complete question:
Find the perimeter
Length = x + 7y units
Width = 8x-x+y units
A craftsman wants to build this fiddle. He needs to know the area of the face of the fiddle. How could he use the measurements shown to find the area?
The Area of Trapezium is 50, 267 mm².
We have,
base 1 = 224 mm
base 2 = 77 mm
Height = 334 mm
Now, Area of Trapezium
= 1/2 (Sum of parallel side) x height
= 1/2 (224 + 77) x 334
= 1/2 x 301 x 334
= 50, 267 mm²
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Two containers P and Q are filled with different amounts of water. Each container has a small hole. The graph shows the amount of water, V milliliters, left in each container after x minutes.
Explain what the y-intercept means in this scenario.
Answer:
Step-by-step explanation:
Equation of the line for container O and container P will be in the form of,
y = mx + b
Here m = slope of the line = Change in amount of water per minute
b = y-intercept
From the graph attached,
y-intercept 'b' represents the initial amount of water in the container.
For container O, initial amount of water in the container is 1000 mL.
Similarly, initial amount in the container is 900 mL.
type the correct answer in the box. simplify the following expression into the form a bi, where a and b are rational numbers. ( 4 − i ) ( − 3 7 i ) − 7 i ( 8 2 i )
The final simplified expression is: -211/7i - 3/7
To simplify the given expression, let's work step by step:
(4 - i)(-3/7i) - 7i(8/2i)
First, let's simplify each multiplication:
(4 * -3/7i - i * -3/7i) - (7i * 8/2i)
Now, simplify further:
(-12/7i + 3/7i^2) - (56/2)
Remember that i^2 is equal to -1:
(-12/7i + 3/7(-1)) - (28)
Simplify the expression:
(-12/7i - 3/7) - 28
Combining like terms:
-12/7i - 3/7 - 28
Now, let's express the terms as a single fraction:
-12/7i - 3/7 - 196/7
Combine the numerators:
(-12 - 3 - 196)/7i - 3/7
Simplify further:
(-211)/7i - 3/7
The final simplified expression is:
-211/7i - 3/7
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Solve for the?
Pls actually help
problem: report error anabel's horse runs $24$ miles per hour. jackie's horse runs $28$ miles per hour. both horses stand at the starting line of a straight $2$-mile track, and jackie's horse starts running $30$ seconds after anabel's. how many miles from the starting line does jackie's horse catch up to anabel's?
The miles from the starting line does which jackie's horse catch up to Anabel's is 1.4 miles.
What is defined as the rate?The unit rate is distinct from the rate, which compares a certain number of units of first quantity to one unit of a second quantity. To put it another way, the second quantity with in comparison has always been 1. One minute, for example, has 60 seconds. As a result, we can convey that as 60 seconds per minute as a unit rate.Let the distance covered by Jackie's horse be 'd'.
Let the time taken be 't'.
Distance = time * rate
Jackie's horse travelled distance; d = 28t .....eq1
Anabel's horse travelled the distance d = 24t + 1/5. .....eq2
Equating equation 1 and 2.
28t = 24t + 1/5
Simplifying.
4t = 1/5
t = 1/20 hour.
The same distance can be covered in 1/20 hour ;
Put the value of t in eq 1.
d = 28t
d = 28(1/20)
d = 12/5 miles
d = 1.4 miles
Thus, the miles from the starting line does which jackie's horse catch up to Anabel's is 1.4 miles.
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A sphere has a radius of 6.2 centimeters. what is the approximate lateral surface area?
Answer:
483.05
Step-by-step explanation:
the surface area of sphere =
4×pi ×r^2=
4×pi×6.2