For a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.
L'Hospital's rule applies to limit expressions of the form 0/0 or infinity/infinity. Specifically, if we have a limit expression of form f(x)/g(x), where f(x) and g(x) both approach 0 or infinity as x approaches a certain value, then L'Hospital's rule may be applied to find the limit of the expression.
It is important to note that L'Hospital's rule can only be applied if the limit of the derivative of f(x) divided by the derivative of g(x) exists and is finite, or if the limit of the derivative of f(x) divided by the derivative of g(x) approaches infinity or negative infinity.
Therefore, for a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.
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Let S be the universal set, where:
S={1,2,3,...,23,24,25}
Let sets A and B be subsets of S, where:
The answer to this question according to given information is 10. The intersection of the sets A and C, denoted as (A∩C), is the set of all elements present in both A and C.
What is intersection?Intersection is a term used to describe the common elements between two or more sets. A set is called as a collection of distinct objects, usually represented by a list, table, or diagram. In other words, it is the overlap between the two sets. For example, the intersection of the set of even numbers and the set of prime numbers would be the set of all even prime numbers.
This is calculated by finding the common elements in the two sets. In this case, (A∩C) = {10, 13, 17, 23}.
Next, the intersection of (A∩C) and B, denoted as (A∩C)∩B, is the set of all elements which are common to all three sets. This is calculated by finding the common elements in (A∩C) and B. In this case, (A∩C)∩B = {10, 17}.
Finally, the number of elements in the set (A∩C)∩B is 10, since there are 10 elements in the set. To summarize, the number of elements in the set (A∩C)∩B is 10.
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The number of elements in the set (A∩C)∩B is 10. The intersection of the sets A and C, denoted as (A∩C), is the set of all elements present in both A and C.
What is intersection?Intersection is a term used to describe the common elements between two or more sets. A set is called as a collection of distinct objects, usually represented by a list, table, or diagram.
This is calculated by finding the common elements in the two sets.
In this case, (A∩C) = {10, 13, 17, 23}.
Next, the intersection of (A∩C) and B, denoted as (A∩C)∩B, is the set of all elements which are common to all three sets.
This can be calculated by finding the common elements in (A∩C) and B.
In this case, (A∩C)∩B = {10, 17}.
Finally, the number of elements in the set (A∩C)∩B is 10, since there are 10 elements in the set.
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A rectangle has an area of 24 square yards.the dimensions are whole numbers what are all the possible dimensions of the rectangle
Answer:
4 combination if order doesn't matter, 8 if order matter (for example is not the same 1x24 or 24x1)
Step-by-step explanation:
1x24
2x12
3x8
4x6
IF order matter also:
6x4
8x3
12x2
24x1
( [9(1) g(n) = g(n − 1) (-4) Find an explicit formula for g(n). g(n): g(1) = -29 1
Answer:
To find an explicit formula for g(n), we can start by using the recursive formula to generate some terms of the sequence:
g(1) = -29
g(2) = g(1) * (-4) = -29 * (-4) = 116
g(3) = g(2) * (-4) = 116 * (-4) = -464
g(4) = g(3) * (-4) = -464 * (-4) = 1856
We can see that each term in the sequence is obtained by multiplying the previous term by -4. More generally, we can write:
g(n) = (-4)^(n-1) * g(1)
Substituting g(1) = -29 and simplifying, we get:
g(n) = (-4)^(n-1) * (-29)
Thus, the explicit formula for g(n) is:
g(n) = -29 * (-4)^(n-1)
Note that this formula gives the same values as the recursive formula for all positive integers n.
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Each interior angle of a regular polygon is 140 Celcius.How many sides does the polygon have?
Answer:
9 sides
Step-by-step explanation:
180 - 140 = 40
360 ÷ 40 = 9
I NEED HELP ASAP PLS!!!! WILL GIVE BRAINLY IF THE EXPLANATION IS GOOD
Copiers A, B, and C are used to produce 3n copies, n on each copier. Copier A makes 18 copies per minute and copier B makes 9 copies per minute. If the average copy speed is 15 copies per minute, what is the rate in copies per minute at which copier C makes copies? The answer is 30, but I do not understand how.
all subnets exist in ospf area 0. which command, if issued on r3, would show all the lsas known by r3
The command that will allow you to set the interface link as preferred over another in OSPF is the "ip ospf cost 10" command. The correct answer is D).
The OSPF protocol uses the concept of cost to determine the best path for routing information to a remote network. The cost of a particular path is calculated based on the bandwidth of the interface and is inversely proportional to it. Therefore, the lower the cost, the more preferred the path is.
To set the preferred link, you can decrease the cost of the desired interface using the "ip ospf cost" command. For example, if you want to set the cost of interface GigabitEthernet0/0 to 10, you can use the following command:
ip ospf cost 10 interface GigabitEthernet0/0
This will make OSPF prefer the specified interface over other interfaces with a higher cost, ensuring that traffic is routed through the preferred link.
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____The given question is incomplete, the complete question is given below:
You need to setup a preferred link that OSPF will use to route information to a remote network. Which command will allow you to set the interface link as preferred over another?
A. ip ospf preferred 10
B. ip ospf priority 10
C. ospf bandwidth 10
D. ip ospf cost 10
Which of the following shows the correct evaluation for the exponential expression 1 over 5 to the power of 3 ? (2 points) a 1 over 5 times 3 equals 3 over 5 b 1 over 5 times 1 over 5 times 1 over 5 equals 1 over 125 c 1 over 5 plus 3 equals 3 and 1 over 5 d 1 over 5 divided by 3 equals 1 over 15
Answer:
b 1 over 5 times 1 over 5 times 1 over 5 equals 1 over 125
Help please! I have no idea!!!! PLEASEE
To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0.
What is graph?
In mathematics, a graph is a visual representation of a set of data, typically as a set of points or lines on a coordinate plane. Graphs are used to represent various types of data, such as numerical values, functions, relationships, and patterns.
Assuming that the graph is a coordinate plane with the x-axis and y-axis, do the following:
To highlight the point (9, 8) on the graph in red, locate the point (9, 8) on the coordinate plane and mark it with a red color.
To highlight the point (20, f(20)) on the graph in green, you need to know the value of f(20) first. Once you have that value, locate the point (20, f(20)) on the coordinate plane and mark it with a green color.
To highlight the line y = 5 on the graph in blue, draw a straight line passing through all points whose y-coordinate is 5. This line should be parallel to the x-axis and should be marked with a blue color.
Therefore To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0. This line should be parallel to the x-axis and should be marked with a black/grey color.
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Find the standard normal area for each of the following: round your answers to 4 decimal places
The answers to 4 decimal places are=
(a) 0.0884
(b) 0.0190
(c) 0.9596
(d) 0.2921
What is area?A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
According to our question-
a= 2.25-1.25
0.0884
b= 3.04-2.04
0.0190
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Let V,Wbe vector spaces and T:V→Wa linear transformation, then Tis injective iff Tpreserves linear independence".
The statement "T is injective iff T preserves linear independence" means that T maps distinct vectors in V to distinct vectors in W and that if a set of vectors in V is linearly independent, then their images under T are also linearly independent.
Now, let V and W be two vector spaces and let T: V→W be a linear transformation. We say that T is injective if and only if every distinct vector in V gets mapped to a distinct vector in W.
Now, the statement "T preserves linear independence" means that if a set of vectors in V is linearly independent, then their images under T (i.e., the vectors they get mapped to in W) are also linearly independent.
To see why this is true, suppose we have a linearly independent set of vectors v₁, v₂, ..., vₙ in V. If we assume that their images under T are linearly dependent, then there exist coefficients c₁, c₂, ..., cₙ such that
c₁Tv₁ + c₂Tv₂ + ... + cₙTvₙ = 0
But since T is linear, this is equivalent to
T(c₁v₁ + c₂v₂ + ... + cₙvₙ) = 0
which implies that c₁v₁ + c₂v₂ + ... + cₙvₙ = 0. But this contradicts the assumption that v₁, v₂, ..., vₙ are linearly independent. Therefore, their images under T must also be linearly independent.
Conversely, if T is injective, then it preserves linear independence because distinct vectors in V get mapped to distinct vectors in W. Therefore, if a set of vectors in V is linearly independent, then their images under T must also be linearly independent.
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x±Z./
x±t./
A highway safety researcher is studying the design of a freeway sign and is interested
in the mean maximum distance at which drivers are able to read the sign. The
maximum distances (in feet) at which a random sample of 9 drivers can read the sign are as follows:
400 600 600 600 650 500 345 500 440
The mean of the sample of 9 distances is 512 feet with a standard deviation of 105
feet.
(a) What assumption must you make before constructing a confidence interval?
•The population distribution is Uniform.
•The population distribution is Normal.
(b) At the 90% confidence level what is the margin of error on your estimate of the true mean maximum distance at which drivers can read the sign.
Answer= feet (round to the nearest whole number)
(c) Construct a 90% confidence interval estimate of the true mean maximum
distance at which drivers can read the sign.
Lower value= feet (round to the nearest whole number)
Upper value= feet (round to the nearest whole number)
(d) There is a 10% chance the error on the estimate is bigger than what value?
Answer= feet (round to the nearest whole number)
(e) The researcher wants to reduce the margin of error to only 15 feet at the 90% confidence level. How many additional drivers need to be sampled? Assume the sample standard deviation is a close estimate of the population standard deviation.
Answer=
In response to the stated question, we may state that The margin of error function is equal to the highest mistake on the estimate.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v
(a) The population distribution must be assumed to be normal before generating a confidence interval.
(b) The margin of error with 90% confidence is provided by:
Error Margin = Z (/2) * (/n)
Where Z (/2) is the confidence level/2 crucial value, is the population standard deviation (unknown), and n is the sample size.
Error Margin = t (/2, n-1) * (s/n)
Where t (/2, n-1) is the critical value for the degrees of freedom /2 and n-1, and s is the sample standard deviation.
(d) The margin of error is equal to the highest mistake on the estimate.
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A researcher tests whether cocaine use increases impulsive behavior in a sample of cocaine-dependent and cocaine-inexperienced mice.
Independent Variable: ________
Quasi-Independent Variable: ________
Dependent Variable: ________
Answer:
Independent variable: Cocaine Use
Quasi-Independent Variable: Cocaine-dependent and cocaine-inexperienced mice
Dependent variable: Increase in impulsive behavior
Pls help me! I only have 1 chances
Answer:
Neither parallel or perpendicular
Step-by-step explanation:
Parallel lines have the same slope. Perpendicular slopes are the negative reciprocals of each other.
30y +25x = -180 Subtract 25x from both sides
30y + 25x - 25x = -25x - 180
30y = -25x - 180 Divide all the way through by 30
[tex]\frac{30y}{30}[/tex] = [tex]\frac{-25}{30}[/tex] - [tex]\frac{180}{30}[/tex]
y = [tex]\frac{-5}{6}[/tex] - 6
y = [tex]\frac{-6}{5}[/tex] x + 6
Comparing the 2 equations, we have slope of
[tex]\frac{-5}{6}[/tex] and [tex]\frac{-6}{5}[/tex]
These slopes are not the same so they are not parallel.
These slopes are not negative reciprocals. so they are not perpendicular.
Perpendicular slopes would be [tex]\frac{-5}{6}[/tex] and [tex]\frac{6}{5}[/tex] or [tex]\frac{-6}{5}[/tex] and [tex]\frac{5}{6}[/tex]. One slope would have to be negative and the other slope would have to be positive which they are not.
Helping in the name of Jesus.
Mary is 21 years old. She buys 50/100/25 liability insurance, and collision and
comprehensive insurance, each with $500 deductibles. What is her total annual
premium? Round to the nearest dollar. Do not state the units. Be sure to show work.
Liability Insurance
Type Amount Premium
25/50 $240
50/100 $385
100/300 $450
Property damage 25 $210
50 $150
100 $140
Collision and comprehensive premiums
$250 $172 $112
$500 $102 $87
$750 $85 $52
Rating factor
Age
17-20 male Female
3.1 1.64
21-24. 2.53. 1.22
25-29 1.73 1.0
According to the given information, Mary's total annual premium is $574 (rounded to the nearest dollar).
What is multiplication ?In mathematics, multiplication is an arithmetic operation that combines two or more numbers to produce a product. It is represented by the symbol "×" or "*", or by placing the numbers next to each other with no symbol between them.
According to the given information:Mary is 21 years old, so according to the rating factor table, her rating factor is 1.22 for a female.
For liability insurance, Mary has chosen the 50/100/25 coverage, which means $50,000 for bodily injury per person, $100,000 for bodily injury per accident, and $25,000 for property damage per accident. The premium for this coverage is $385.
For collision and comprehensive insurance, Mary has chosen a $500 deductible, so her premiums are $102 for collision and $87 for comprehensive.
To find the total annual premium, we add up the premiums for liability insurance and collision/comprehensive insurance:
Total premium = Liability premium + Collision premium + Comprehensive premium
Total premium = $385 + $102 + $87
Total premium = $574
Therefore, according to the given information, Mary's total annual premium is $574 (rounded to the nearest dollar).
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Converting from decimal to non-decimal bases. info About A number N is given below in decimal format. Compute the representation of N in the indicated base. (a) N = 217, binary. (b) N = 99, hex. (c) N = 344, hex. (d) N =136, base 7. (e) N = 542, base 5. (f) N = 727, base 8. (g) N = 171, hex. (h) N = 91, base 3. (i) N = 840, base 9.
Hence the conversion of given numbers according to given demand is
a) N=217 in binary = 11011001
b) N=99 in hexadecimal = 63
c) N= 344 in hexadecimal = 158
d) N= 136 in base 7 = 253.
e) N= 542 in base 5 = 4132.
f) N= 727 in base 8= 1327
g) N= 171 in hexa =1011
h) N=91 in base 3=10101.
i) N= 840 in base 9 = 1133
a) A good method to convert a decimal number to binary is dividing it by 2 and using the remainder of the division as the converted number, starting by the most significant bit (the right one). We can't divide anymore. So we have:
217÷2 = 108 + 1
108÷2 = 54 + 0
54÷2 = 27 + 0
27÷2 = 13 + 1
13÷2 = 6 + 1
6÷2 = 3 + 0
3÷2 = 2 +1
2÷2 = 1
The binary equivalent to 217 is 11011001
b) To convert a number from decimal to hex we can divide the number by 16, taking out the decimal part and multiplying it by 16 using that as our most significant number while using the result of the original division to continue our conversion. So we have:
99÷16 = 6.1875
The decimal part is 0.1875, we multiply it by 16 and obtain 3 as our most significant number. Since we can't divide 6 by 16 we have that as our least significant number then the hexadecimal equivalent is 63.
c) We follow the same steps as in item b:
344÷16 = 21.5
The most significant number is 0.5*16 = 8
21÷16 = 1.3125
The next number is 0.3125*16 = 5
Since we can't divide it anymore we have our result which is 158 in hex.
d) To convert from decimal to base 7 we'll use the same method as to hex, but this time dividing and multiplying by 7.
136÷7 = 19.428571
The most significant number is 0.428571 * 7 = 3
19÷7 = 2.71428571
The next number is 0.71428571*7 = 5
Since we can't divide it anymore we have our result which is 253.
e) To convert from decimal to a base 5 we'll use the same method as before but dividing and multiplying by 5.
542÷5 = 108.4
The most significant number is 0.4*5 = 2
108÷5 = 21.6
The next number is 0.6*5 = 3
21÷5 = 4.2
The next number is 0.2*5 = 1
Since we can't divide it anymore we have our result which is 4132.
f) To convert from decimal to a base 8 we'll use the same method as before but dividing and multiplying by 8.
727÷8 = 90.875
The most significant number is 0.875*8 = 7
90÷8 = 11.25
The next number is 0.25*8 = 2
11÷8 = 1.375
The next number is 0.375*8 = 3
Since we can't divide anymore we have our result which is 1327
g) Following the same steps as before:
171÷16 = 10.6875
The most significant number is 0.6875*16 = 11
Since we can't divide anymore we have our result which is 1011
h) Following the same steps as before:
91÷3 = 30.333333333
The most significant number is 0.333333*3 = 1
30÷3 = 10
The next number is 0
10÷3 = 3.3333333333
The next number is 0.333333*3 = 1
3÷3 = 1
Since we have the final value remainder as 0 the least significant number is 1
Since we can't divide anymore we have our result which is 10101.
i) Following the same steps as before:
840÷9 = 93.333333
The most significant number is 0.33333*9 = 3
93÷9 = 10.3333333
The next number is 0.333333*9 = 3
10÷9 = 1.11111111
The next number is 0.11111111*9 = 1
Since we can't divide anymore we have our result which is 1133
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to enter their home the clayton family enters a 4 digit code how many codes are possible.
A Clayton family can therefore employ 10,000 different codes to access their house.
What makes fingers digits?In actuality, the habit of numbering to ten on the fingers is what gave rise to the custom of calling numbers by their digits. The English term "number" is derived from the Latin word digits, which originally meant "finger or toe." If the code is made up of four digits, and each digit can be any number from 0 to 9, then there are 10 possible choices for each of the four digits.
Hence, there are a total of the following codes:
10 x 10 x 10 x 10 = 10,000
Hence, the Clayton family has 10,000 different possible entry codes.
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-51+((-5+(-4)) all calculation
Answer:
the answer to that is -31
A test consists of 30 multiple choice questions, each with five possible answers, only one of which is correct. find the mean and the standard deviation of the number of correct answers. round the answers to the nearest hundredth.
The mean and standard deviation for 30 multiple-choice questions for the number of correct answers is Mean(μ) = 6 and Standard deviation(σ) = 2.19.
What is mean?
A collection of values are averaged to form the mean. The total points were divided by the total scores. When population samples are tiny, the mean is sensitive to extreme scores. For example, if two students in a class of 20 earned significantly higher than the rest, the mean will be skewed higher than the other students' scores might suggest. When using means, larger sample sizes are preferable.
Define standard deviation.
In statistics, a measure of variability known as the standard deviation ( standard deviation ) is frequently used. It demonstrates how different things are from the norm. (mean). When the SD is low, the data tend to be close to the mean, while when it is high, the data are dispersed over a wide variety of values.
Given: number of questions(n) = 30, p = [tex]\frac{1}{5}[/tex], q = [tex]\frac{4}{5}[/tex]
Mean μ = n*p
= 30 *[tex]\frac{1}{5}[/tex]
μ = 6
Standard deviation σ = [tex]\sqrt{n*p*q}[/tex]
= [tex]\sqrt{30*\frac{1}{5}*\frac{4}{5}}[/tex]
= [tex]\sqrt{4.8}[/tex]
σ = 2.19
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Raul's favorite gummy bear colors are yellow and red. He bought a package of gummy bears that only had his favorite colors. When he counted the gummy bears, he had 20 red and 23 yellow. What is the ratio of red gummy bears to yellow gummy bears?
Question 2 options:
23/20
23/43
20/23
20/43
The ratio between the number of red gummy bears to the number of yellow gummy bears is of:
20/23.
How to obtain the ratio?The ratio between the number of red gummy bears and the number of yellow gummy bears is obtained applying the proportions in the context of the problem.
To obtain the ratio between two amounts A and B, you need to divide the first amount by the second amount. The result of this division will give you the ratio of the two amounts.
The amounts for this problem are given as follows:
Amount A: 20 red gummy bears.Amount B: 23 yellow gummy bears.Hence the ratio between these two amounts is given as follows:
20/23.
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g suppose x and y are two random variables. you don't know their distribution, but someone tells you e[x]
When x and y are independent variables with x having uniform distribution (0,1) and y having exponential distribution respectively, then e (X+Y) is 3/2, E(XY) is 1/2, E (x-y)2 is 4/3, and e (x2 e24) is -1/3 22etyx u (0,1) > Independent y exp (1) > Independent
The exponential distribution is a continuous probability distribution used in probability theory and statistics that frequently addresses the amount of time until a given event occurs. Events occur continually, independently, and at a steady average pace during this process.
E (x) = 0+1/2 = 1/2
v (x) = [1 – 0]2 / 12 = 1/12
E x2 = v (x) + [Ex]2
= 1/12 + 1/4 = 1+3/12 = 4/12 = 1/3
E (y) = 1 v(y)=1
E y2= 1+1= 2
Eety = ∫0etye-ydy
Eety = ∫0e-y (1 – t)dy
a : E (x+y) = E (x) + E(y)
E (x+y) = 1/2+1 = 3/2
b: E (xy) = E (x) E(y) = 1/2 x 1 = 1/2
c: E (x+y)2 = E (x2 - 2xy+ y2)
= 1/3 - 2 x 1/2 + 2
= 1/3 + 1 = 4/3
d. E x2e24
= 1/3 x -1 = - 1/3
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Use the product of powers property to simplify the numeric expression. 2^2/5/2^1/10
Answer:
[tex] 2^\frac{3}{10} [/tex]
Step-by-step explanation:
[tex] \dfrac{2^\frac{2}{5}}{2^\frac{1}{10}} = [/tex]
[tex]= 2^{\frac{2}{5} - \frac{1}{10}}[/tex]
[tex]= 2^{\frac{4}{10} - \frac{1}{10}}[/tex]
[tex] = 2^\frac{3}{10} [/tex]
They did not explain why that was right. What kind of explanation is that?
An explanation without explaining why that was right is called
dogmatic explanation.
What is a dogmatic statement?An explanation without a reason why it is true is called a dogmatic statement.
We have,
Dogmatic statement:
This is a statement that is presented as true without providing any evidence or logical reasoning to support it.
It is often based on personal beliefs, opinions, or assumptions rather than objective facts or evidence.
Dogmatic statements can be problematic in academic or scientific contexts, where claims must be supported by evidence and logical reasoning.
It is important to be critical and skeptical of dogmatic statements and to seek out evidence and logical reasoning before accepting any claim as true.
Thus,
An explanation without explaining why that was right is called
dogmatic ex[planation.
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A shopkeeper sold 20 mobile sets of same brand for Rs 3,00,0000 at the same rate in a week. (a)What is the selling price of each mobile set? b, If he bought each mobile set for Rs 12,500, find his profit or loss percent. c, If each mobile set is 12 cm long, 6 cm broad and 1 cm thick, find the ratio of it length to the breadth.
Answer: 2:1
Step-by-step explanation:
a) The total selling price of 20 mobile sets is Rs. 3,00,000. Therefore, the selling price of each mobile set is:
Selling price of each mobile set = Total selling price ÷ Number of mobile sets sold
= 3,00,000 ÷ 20
= Rs. 15,000
Therefore, the selling price of each mobile set is Rs. 15,000.
b) The cost of each mobile set is given as Rs. 12,500. The total cost of 20 mobile sets is:
Total cost = Cost of each mobile set × Number of mobile sets sold
= 12,500 × 20
= Rs. 2,50,000
The profit made by the shopkeeper is the difference between the selling price and the cost price of the mobile sets:
Profit = Selling price - Cost price
= 3,00,000 - 2,50,000
= Rs. 50,000
Therefore, the profit made by the shopkeeper is Rs. 50,000.
The profit percent is given by:
Profit percent = (Profit ÷ Cost price) × 100
= (50,000 ÷ 2,50,000) × 100
= 20%
Therefore, the shopkeeper made a profit of 20%.
c) The ratio of the length to the breadth of each mobile set is:
Length:breadth = 12:6
= 2:1
Therefore, the ratio of the length to the breadth of each mobile set is 2:1.
Answer:
Step-by-step explanation:
a) To find the selling price of each mobile set, we need to divide the total amount sold by the number of mobile sets sold:
Selling price of each mobile set = Total amount sold / Number of mobile sets sold
Selling price of each mobile set = Rs 3,00,000 / 20
Selling price of each mobile set = Rs 15,000
Therefore, the selling price of each mobile set is Rs 15,000.
b) The cost price of each mobile set is Rs 12,500.
Profit or loss percent = [(Selling price - Cost price) / Cost price] x 100
Profit or loss percent = [(15,000 - 12,500) / 12,500] x 100
Profit or loss percent = 20%
Therefore, the shopkeeper has made a profit of 20%.
c) The ratio of the length to the breadth of the mobile set is:
Length : Breadth = 12 cm : 6 cm
Simplifying the ratio by dividing both sides by 6:
Length : Breadth = 2 : 1
Therefore, the ratio of the length to the breadth of the mobile set is 2 : 1.
As a sound wave travels, what happens to the particles in the medium it travels through i need help
As a sound wave travels, the particles in the medium it travels through vibrate back and forth in the same direction as the wave travels.
How to explain what happens to the mediumAs a sound wave travels through a medium, such as air or water, the particles in the medium vibrate back and forth in the same direction as the wave travels.
However, the particles themselves do not actually move along with the wave. Instead, the wave causes a disturbance in the particles, which then passes from one particle to the next, resulting in a wave-like pattern of motion that travels through the medium.
In other words, the sound wave is a disturbance that travels through the medium, causing the particles in the medium to oscillate back and forth around their equilibrium positions.
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g suppose that x and y are i.i.d. bernoulli(p) random variables (i.e., with the same value of p, 0
The product of expected value of xy is p^2.
If x and y are i.i.d. Bernoulli(p) random variables, then the probability mass function of each variable is:
P(x=1) = p
P(x=0) = 1-p
P(y=1) = p
P(y=0) = 1-p
To find the expected value of the product xy, we can use the definition of expected value:
E[xy] = Σ Σ xy P(x,y)
where the summation is over all possible values of x and y.
Since x and y can only take on the values of 0 or 1, there are only four possible outcomes:
x=0, y=0
x=0, y=1
x=1, y=0
x=1, y=1
We can calculate the probability of each outcome using the probability mass function:
P(x=0, y=0) = P(x=0)P(y=0) = (1-p)(1-p)
P(x=0, y=1) = P(x=0)P(y=1) = (1-p)p
P(x=1, y=0) = P(x=1)P(y=0) = p(1-p)
P(x=1, y=1) = P(x=1)P(y=1) = p^2
Therefore, we have:
E[xy] = (0)(0)(1-p)(1-p) + (0)(1)(1-p)p + (1)(0)p(1-p) + (1)(1)p^2
E[xy] = 0 + 0 + 0 + p^2
E[xy] = p^2
So the expected value of xy is p^2.
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____The given question is incomplete, the complete question is given below:
g suppose that x and y are i.i.d. bernoulli(p) random variables (i.e., with the same value of p, 0. find the product of expected value of xy.
For each of the following find:
I. lim f (x) as x approaches a from the negative
II. lim f (x) as x approaches a from the positive
III. lim f (x) as x approaches a
a. f(x)={ sin x/3, if x< or equal to pi a=pi
{ x(root3)/(2pi), if x>pi
b. f(x)= (x^2-36)/root(x^2-12x+36) a=6
Answer:
a. For the function:
f(x) = { sin x/3, if x ≤ π
{ x√3/2π, if x > π
I. To find lim f(x) as x approaches π from the negative side, we need to evaluate f(x) for values of x that are slightly less than π. In this case, since sin(x/3) is a continuous function, we can simply evaluate it at x = π:
lim f(x) as x approaches π- = f(π-) = sin(π/3) = √3/2
II. To find lim f(x) as x approaches π from the positive side, we need to evaluate f(x) for values of x that are slightly greater than π. In this case, we can simply evaluate the other part of the piecewise function at x = π:
lim f(x) as x approaches π+ = f(π+) = π√3/2π = √3/2
III. To find lim f(x) as x approaches π, we need to check whether the left-hand and right-hand limits are equal. In this case, since both the left- and right-hand limits exist and are equal, we have:
lim f(x) as x approaches π = √3/2
b. For the function:
f(x) = (x^2 - 36)/√(x^2 - 12x + 36)
I. To find lim f(x) as x approaches 6 from the negative side, we need to evaluate f(x) for values of x that are slightly less than 6. In this case, we can substitute x = 6 - h, where h is a positive number approaching zero, to get:
lim f(x) as x approaches 6- = lim f(6 - h) as h approaches 0
Substituting x = 6 - h into the function, we get:
f(6 - h) = [(6 - h)^2 - 36]/√[(6 - h)^2 - 12(6 - h) + 36]
= [h^2 - 12h]/√[h^2]
Simplifying the numerator and denominator separately, we get:
f(6 - h) = h(h - 12)/|h|
Since h approaches 0 from the positive side, we have:
lim f(6 - h) as h approaches 0+ = lim h(h - 12)/h as h approaches 0+ = lim (h - 12) as h approaches 0+ = -12
II. To find lim f(x) as x approaches 6 from the positive side, we need to evaluate f(x) for values of x that are slightly greater than 6. In this case, we can substitute x = 6 + h, where h is a positive number approaching zero, to get:
lim f(x) as x approaches 6+ = lim f(6 + h) as h approaches 0
Substituting x = 6 + h into the function, we get:
f(6 + h) = [(6 + h)^2 - 36]/√[(6 + h)^2 - 12(6 + h) + 36]
= [h^2 + 12h]/√[h^2]
Simplifying the numerator and denominator separately, we get:
f(6 + h) = h(h + 12)/|h|
Since h approaches 0 from the positive side, we have:
lim f(6 + h) as h approaches 0+ = lim h(h +
Step-by-step explanation:
PLEASE HELPPPP 30 POINTS!
Answer:
56
90
56
Step-by-step explanation:
easy easy lol.
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Which graph represents this equation?
= 3/2x^2 - 6x
The parabola is passing through (0, 0) and (9, 0).
What is the parabola?The locus of a moving point is the location that maintains a constant distance between a stationary point and a predetermined line.
The directrix is a non-moving line, while the focus is a non-moving point.
As you can see, the quadratic variable is not, which modifies the figure's orientation.
This parabola doesn't actually represent a function because it will open horizontally, specifically toward negative infinity, as the graphic linked illustrates.
The vertical line test will reveal that the vertical line in question intercepts the figure in two places, proving that it is not a function.
According to our question-
The equation of the parabola is given below.
y = (3/2)x² - 6x
Then the factor of the equation will be
y = 3x (x / 2 - 3)
Then the zeroes of the function will be
y = 0
x = 0, 9
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LOOK AT THE PHOTO PLS
Answer: 0.27272727 or 0.27 (with a dash on top of 27)
Step-by-step explanation:
mr.woodstock has a plot of land 36 meter long and 16 meters wide. he uses the land for mixed farming- rearing animals and growing crop? what length of wire does mr woodstock need to fence his land
To calculate the amount of wire needed to fence Mr. Woodstock's land, you will need to use the formula for the perimeter of a rectangular shape. The formula for perimeter is Length + Width x 2.
Plugging in the given dimensions for Length (36 meters) and Width (16 meters) will give us the following calculation:
36 + 16 x 2 = 88 meters
Therefore, Mr. Woodstock will need 88 meters of wire to fence his land.