A number cube is rolled. Event A is rolling an odd number, and event B is rolling a factor of 12. What is P(AU B)?
Explanation:
A = set of odd numbers = {1,3,5}
B = set of factors of 12 = {1,2,3,4,6}
A U B = union of set A and set B
A U B = {1,3,5} union {1,2,3,4,6}
A U B = {1,3,5, 1,2,3,4,6}
A U B = {1,2,3,4,5,6}
The set union operation combines two sets into one bigger set. Duplicates are tossed out.
There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.
Therefore, the probability event A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.
Side notes:
A U B can be read out as "event A or event B"; so P(A U B) is "the probability event A happens or B happens or both".A intersect B = {1,3} = values that are in both set A and set B at the same time. These are both odd and a factor of 12.How many significant figures are in the number
43.6? 43.6 has [?] significant figures.
Answer:
43.6 has 3 significant figures.
A wage earner receives a gross pay of $983.15 for 52.5 hours of work. What is his hourly rate of pay if a regular workweek is 44 hours and overtime is paid at time-and-a-half the regular rate of pay?
Is 6 inches in 10 seconds proportional to 12 inches in 60 seconds?
Answer: No
Step-by-step explanation:
to be proportional, both numbers have to increase by the same number
because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in
HELP!! WILL GIVE BRAINLIEST!!!
The direct proportion y=kx is given in the following table. Find the coefficient k, and fill in the table:
Answer:
Look at image
Step-by-step explanation:
image shown below, copy the answer from there.
The value of coefficient k is 5. The required values are y = 15.5 when x = 3.1, y = 12.5 when x = 2.5, y = 6 when x = 1.2, y = 4.5 when x = 0.9, x = 0.06 when y = 0.3, and x = 0.02 when y = 0.1.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
The direct proportion y = kx is given in the shown table.
Find the coefficient k, and fill in the table:
As per the question, we have
y = kx .....(i)
To determine the value of k, we substitute the value of x = 0.14 and y = 0.7 in equation (i),
⇒ 0.7 = k (0.14)
⇒ k = 0.7/0.14
⇒ k = 5
Substitute the value of k = 5 in equation (i), and we get
y = 5x .....(ii)
Now, we are finding the values of the table,
Substitute the value of x = 3.1 in equation (ii), and we get
y = 5(3.1)
y = 15.5
Similarly, the other required values are
y = 12.5 when x = 2.5, y = 6 when x = 1.2, y = 4.5 when x = 0.9, x = 0.06 when y = 0.3, and x = 0.02 when y = 0.1.
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1- An office supply company is shipping a case of wooden pencils to a store. There are 64 boxes of pencils in the case. If each box of pencils weighs 2.5 ounces (oz), what is the weight in pounds, in the case of wooden pencils?
Answer:
Total weight in lb = 10 lb
The weight of wooden pencils is 10 pounds.
Step-by-step explanation:
We are given that an office supply company is shipping a case of wooden pencils to a store.
There are 64 boxes of pencils in the case.
The weight each box of pencils is 2.5 ounces (oz)
We are asked to find the weight of wooden pencils in pounds.
Step 1: Find the total weight of pencils in ounces
Since there are 64 pencils and each pencil weighs 2.5 ounces,
Total weight in oz = 64×2.5
Total weight in oz = 160 oz
Step 2: Convert the total weight of pencils into pounds
We know that 1 pound has 16 ounces so we have to divide the total weight of the pencils by 16 to get the weight in pounds
Total weight in lb = 160/16
Total weight in lb = 10 lb
Therefore, the weight of wooden pencils is 10 pounds.
17/6749 find the remainder
Answer:
17Step-by-step explanation:
17 = 6749 × 0 + 17
Then
The remainder is 17
How many
1/5s are in 9?
A.5/9
B.9/5
C.45
D.4 1/2
Answer:
C 45
Step-by-step explanation:
Answer:
Answer and explanation
9 ÷ 1/59 × 5/1= 45For two n by n square matricies A and B,
suppose rankA = rankB = n-1.
Can rank(AB) become less than n-1 ?
(e.g. rank (AB) = n-2)
If so, I humbly ask you for an example.
Thank you very much.
No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.
According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.
If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.
Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.
However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.
Therefore, if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.
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you love to play pool at the local hall if it costs $10 just to play plus $2.30 per game played what is the most number of games that you can play in one night on $50
Answer:
4
Step-by-step explanation:
or 17
10 to enter i assume and then 2.30 per game
12.3 everytime u play
50/12=4
If l=5,b=3cm,c=2cm, find its volume
Answer:
30 cm³
Step-by-step explanation:
Volume = lbc
V = l x b x cV = 5 cm x 3 cm x 2 cmV = 30 cm³Answer:
The volume is 30 cm³
Step-by-step explanation:
Volume = l×b×c
=> 5×3×2
=> 30 cm³
The radius of a circle is 19 cm. Find the area
Answer: 1134.11
A=3.14*r^2
Step-by-step explanation:
Answer:
a ≈ 1134.11 cm2
Step-by-step explanation:
The formula:
\(a=\pi r^{2}\)
\(a=\pi (19)^{2} =361\pi\)
\(a=1134.11cm^{2}\)
Hope this helps
Suppose that ƒ is a function given as f(x) = 4x² + 5x + 3.
Simplify the expression f(x + h).
f(x + h)
Simplify the difference quotient,
ƒ(x + h) − ƒ(x)
h
=
Submit Question
The derivative of the function at x is the limit of the difference quotient as h approaches zero.
f(x+h)-f(x)
f'(x) =lim
h→0
h
ƒ(x + h) − f(x)
h
=
Answer:
f(x +h) = 4x² +4h² +8xh +5x +5h +3
(f(x+h) -f(x))/h = 4h +8x +5
f'(x) = 8x +5
Step-by-step explanation:
For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.
F(x+h)Put (x+h) where h is in the function, and simplify:
f(x+h) = 4(x+h)² +5(x+h) +3
= 4(x² +2xh +h²) +5x +5h +3
f(x +h) = 4x² +4h² +8xh +5x +5h +3
Difference quotientThe difference quotient is ...
(f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h
= (4h² +8xh +5h)/h
(f(x+h) -f(x))/h = 4h +8x +5
LimitWhen h=0, the value of this is ...
f'(x) = 4·0 +8x +5
f'(x) = 8x +5
__
Additional comment
Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.
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Arrange in order from smallest to largest.
6.187, 27.132, 3.55, 9.312
Answer: 3.55, 6.187, 9.312, 27.132
Step-by-step explanation:
The easiest way I do this is by rounding all the numbers to the nearest hundredths, tenths, or whole numbers.
3.55 = 4
6.187 = 6
9.312 = 9
27.132 = 27
A tank in the shape of a hemisphere has a diameter of 24 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid in the tank is approximately 12,628 pounds.
To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.
In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.
Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.
In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.
By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.
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use theorem 2.1.13 to prove that if $f$ and $g$ are continuous functions with open domains $u f$ and $u g$, and if $g(u g)\subseteq u f$, then $f \circ g$ is continuous on $u g$
Since function f andg are continuous and u g subseteq u f, Theorem 2.1.13 states that f circ g is continuous on u g.
In accordance with Theorem 2.1.13, if two functions,f andg, are continuous on open domains \($u f$\)and \($u g$\) respectively, and $g(u g)subseteq u f, then $ circ g is continuous on u g. This is the case since the domain of f, which is u g is a subset of the domain of f, which is u g, and the composition of continuous functions is continuous. The composition of these two functions will be continuous onu g because both of these functions are continuous and u g subseteq u f.
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I don’t know how to do this problem help me!!
\(x-9z^5+4z+11+2z^5+14=-5z^5-3z+25\\x=2z^5-7z\)
Therefore, it's \(2z^5-7z\).
10-10=69.420!!!!!!!!!!
Let y = 5x^2
Find change in y, deltay when x =2 and delta x = .1
Find the differential dy when x = 2 and dx = .1
Change in y when x =2 and Δx= 0.1 is 2.05 and the differential dy when x= 2 and dx = 0.1 is 2
Δy and dy can be calculates as follows
We already knew that Δy = f( x + Δx ) - f(x) and y = f(x)
so we just need to subtitute the values
Δy = f( x + Δx ) - f(x)
Δy = f( 2 + 0.1 ) - f(2) and back to y = f(x) we can subtitute the f(x) by \(5x^{2}\) so,
Δy = \(5(2.1)^{2} -5(2)^{2}\)
Δy = 2.05
and for the differential,
dy = f'(x) dx and we need to know diferential from y=\(5x^{2}\) is 10x
so we just subtitutes the values
dy = f'(x) dx
dy = f'(2) (0.1) and back to diferential from y=\(5x^{2}\) is 10x so subtitute the f'(x)
dy = 10(2) (0.1)
dy = 2
hence, change in y, Δy is 2.05 an the diferenyial dy is 2
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In a survey, 125 people were asked to choose one card out of five cards labeled 1 to 5. The results are shown in the table. Compare the theoretical probability and experimental probability of choosing a card with the number 1.
Answer: probably 4 cards each person
Step-by-step explanation:
An airplane flies 105 miles in ½ hour. How far can it fly in 1 ¼ hours at the same rate of speed?
Answer:
262.5 miles
Step-by-step explanation:
Correct me if I am wrong
y = |x - 5| + |x + 5| if x >5
Answer:
y = 2x
Step-by-step explanation:
You want the simplified form of y = |x -5| +|x +5| if x > 5.
Turning pointsThe graph of the whole function will have turning points where the absolute value expressions are 0:
x -5 = 0 ⇒ x = 5
x +5 = 0 ⇒ x = -5
For values of x > 5, we are concerned with that portion of the graph that is to the right of both of these turning points. Hence, both absolute value expressions are positive and unchanged by the absolute value bars.
y = (x -5) +(x +5) . . . . . . if x > 5
y = 2x . . . . . . . . . . . . . . collect terms
The simplified function is y = 2x.
__
Additional comment
The attached graph shows y=2x and the given function for x > 5. They are identical. (The y=2x graph is shown dotted, so you can see the red graph of the given function.)
Need help. This please
The domain of the quadratic function in this problem is given as follows:
All real values.
How to obtain the domain of the function?The domain of a function is the set of all the possible input values that can be assumed by the function.
On the graph, the domain of the function is given by the values of x of the function.
A quadratic function has no restrictions on the domain, hence it is defined by all the real values.
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In the following diagram, ABCDABCD is a square. The coordinates of the vertices A,B,CA,B,C and DD are (3,3),(8,3),(8,8)(3,3),(8,3),(8,8) and (3,8)(3,8) respectively.
The square is dilated from the origin by a factor of 1111 to give A′B′C′D′A′B′C′D′.
What are the coordinates of point C′C′? (NEED THIS ASAP)
Answer:
Step-by-step explanation:
To dilate the square by a factor of 1111 from the origin, we need to multiply each coordinate by 1111.
The coordinates of point C are (8,8). So, to find the coordinates of point C' after dilation, we can simply multiply each coordinate by 1111:
x-coordinate of C' = 1111 * 8 = 8888
y-coordinate of C' = 1111 * 8 = 8888
Therefore, the coordinates of point C' are (8888, 8888).
2.2.18Find the vertex of the graph of the quadratic function. Determine whether thegraph opens upward or downward, find the y-intercept, and sketch the graph.f(x) = - x2 - 2x+3The vertex is(Simplify your answer. Type an ordered pair.)
The quadratic function is given by the following expression:
\(f(x)=-x^2-2x+3\)The direction at which the graph opens is determined by the signal of the number multiplying x². If the number is positive then the graph opens upwards, if it is negative it opens downward. In this case it is negative so it opens donward.
The vertex of a quadratic expression can be found by the following expression:
\(x=\frac{-b}{2a}\)Where a is the number multiplying "x²", while b is the number multiplying "x". Applying the data from the problem we have:
\(x=\frac{-(-2)}{2\cdot(-1)}=\frac{2}{-2}=-1\)To find the value of "y" for the vertex we need to apply the coordinate for x on the expression. We have:
\(\begin{gathered} f(-1)=-(-1)^2-2\cdot(-1)+3 \\ f(-1)=-1+2+3=4 \end{gathered}\)The coordinates of the vertex are (-1,4).
To sketch a graph we need to find the x-intercept and y-intercept of the function. These are given when f(x) = 0 and x=0 respectively. Let's find these points.
\(\begin{gathered} 0=-x^2-2x+3 \\ -x^2-2x+3=0 \\ x_{1,2}=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(-1)(3)}}{2\cdot1} \\ x_1=-3 \\ x_2=1 \end{gathered}\)\(f(x)=-0^2-2\cdot0+3=3\)The x intercept happens in two points -3 and 1, while the y intercept happens in the point 3. With this and the vertex we can sketch the function.
If Coach Smith has 12 players and each player needs three uniforms, three shin guards, two balls, and three pairs of cleats. How much will he end up spending on his equipment for the entire soccer team?
you can't do that. there isn't enough detail. we don't know how much each item costs
The following formula gives the temperature's measure in degrees Fahrenheit F, where C is the measure in degrees Celsius:
F=9/5C+32
C+32F, equals, start fraction, 9, divided by, 5, end fraction, C, plus, 32
Rearrange the formula to highlight the measure in degrees Celsius. C=
Answer:
.............................
After rearrange the formula to highlight the measure in degrees Celsius is;
C = 5/9 ( F - 32 )
Given that;
Formula to measure temperature's in degrees Fahrenheit F is;
F = 9/5C + 32
We have to find the formula to highlight the measure in degrees Celsius
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Formula to measure temperature's in degrees Fahrenheit F is;
F = 9/5C + 32
The formula to highlight the measure in degrees Celsius is find as;
F = 9/5C + 32
Subtract 32 both sides;
F - 32 = 9/5 C + 32 - 32
F - 32 = 9/5 C
Multiply by 5 both sides;
5 ( F - 32 ) = 5*9/5 C
5 ( F - 32 ) = 9C
Divide by 9 both sides;
5/9 ( F - 32 ) = C
C = 5/9 ( F - 32 )
Hence, After rearrange the formula to highlight the measure in degrees Celsius is;
C = 5/9 ( F - 32 )
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helpppppp meeeeeeeee
Answer:
probably H but im not sure
Step-by-step explanation:
Answer:
H
Step-by-step explanation:
the equation is 5x=0.1y
Find the percent of decrease from 136 days to 85 days. Round the percent to the nearest tenth if necessary
The percent of decrease from 136 days to 85 days is, 37.5%.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
The days decrease from 136 days to 85 days.
Hence, The percent of decrease from 136 days to 85 days is,
Decrease percent = (136 - 85) / 136 × 100
= 37.5%
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Question 7(Multiple Choice Worth 5 points)
(04.02 MC)
The two-way frequency table contains data about students' preferred exercise.
Likes running 28
Does not like running 46
Column totals 74
What is the joint relative frequency of students who do not like to run and enjoy swimming?
O23%
37%
Enjoys swimming Enjoys cycling Row totals
62
90
64
110
126
200
46%
072%
The joint relative Frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.
The joint relative frequency of students who do not like to run and enjoy swimming, we need to find the intersection of the row and column corresponding to those categories in the two-way frequency table.
Given the following information from the table:
Likes running: 28
Does not like running: 46
Column totals: 74
Enjoys swimming: 62
Enjoys cycling: 90
Row totals: 110
The joint relative frequency, we divide the number of students who do not like running and enjoy swimming by the total number of students:
Joint relative frequency = (Number of students who do not like running and enjoy swimming) / (Total number of students)
From the table, the number of students who do not like running and enjoy swimming is given as 46.
Total number of students is given as 74.
Joint relative frequency = 46 / 74
Calculating this value, we find that the joint relative frequency is approximately 0.6216, which is equivalent to 62.16%.
Therefore, the joint relative frequency of students who do not like to run and enjoy swimming is approximately 62.16%.
In conclusion, the joint relative frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.
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Find the area of theparallelogram.9.9 in5.5 in[?] in2Enter the exact answer. Do not round
The area of a parallelogram is given by:
\(A=B\cdot H\)Where:
B = Base = 9.9 in
H = Height = 5.5 in
Therefore:
\(\begin{gathered} A=9.9\cdot5.5 \\ A=54.45in^2 \end{gathered}\)Answer:
54.45 in²