The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.
The area of a square with sides of one inch is equal to one square inch (plural: square inches).
We have that:
Let the dimension of the paper be x and y.
Such that:
Length = [tex]x[/tex]
Width = [tex]y[/tex]
So:
Area = [tex]x*y[/tex]
Substitute 128 for Area
[tex]128=x*y[/tex]
Make x the subject.
[tex]x=\frac{128}{y}[/tex]
When 1 inch margin is at top and bottom
The Length becomes:
[tex]Length =x+1+1[/tex]
[tex]Length = x+2[/tex]
When 2-inch margin is at both sides
The width becomes:
[tex]Width = y+2+2[/tex]
[tex]Width = y+4[/tex]
The New Area (A) is then calculated as:
[tex]A = (x+2)*(y+4)[/tex]
Substitute [tex]\frac{128}{y}[/tex] for x
[tex]A = (\frac{128}{y}+2 )*(y+4)[/tex]
Open Brackets
[tex]A = 128 + \frac{512}{y} + 2y + 8[/tex]
Collect Like Terms
[tex]A = \frac{512}{y} + 2y + 8+128[/tex]
[tex]A = \frac{512}{y} +2y+136[/tex]
[tex]A = 512y^{-1} +2y + 136[/tex]
To calculate the smallest possible value of y, we have to apply calculus.
Differentiate A with respect to y
[tex]A' = -512y^{-2}+2[/tex]
Set
[tex]A' = 0[/tex]
This gives:
[tex]0=-512y^{-2}+2[/tex]
Collect Like Terms
[tex]512y^{-2} = 2[/tex]
Multiply through by [tex]y^{2}[/tex]
[tex]y^{2} *512y^{-2} = 2*y^{2}[/tex]
[tex]512 = 2y^{2}[/tex]
Divide through by 2.
[tex]256 = y^{2}[/tex]
Take square roots of both sides.
[tex]\sqrt{256= y^{2} }[/tex]
[tex]16 =y\\\\y=16[/tex]
Recall that:
[tex]x = \frac{128}{y}[/tex]
[tex]x = \frac{128}{16}[/tex]
[tex]x=8[/tex]
Recall that the new dimensions are:
[tex]Length = x+2[/tex]
[tex]Width = y+4[/tex]
So:
[tex]Length = 8+2[/tex]
[tex]Length = 10[/tex]
To double-check.
Differentiate A'
[tex]A' = -512y^{-2}+2[/tex]
[tex]A'' = -2 * -512y^{-3}[/tex]
[tex]A'' = 1024y^{-3}[/tex]
[tex]A'' = \frac{1024}{y^{3} }[/tex]
The above value is:
[tex]A'' = \frac{1024}{y^{3} } > 0[/tex]
In other words, the estimated numbers are at their lowest.
Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.
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The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.
The area of a square with sides of one inch is equal to one square inch (plural: square inches).
We have that:
Let the dimension of the paper be x and y.
Such that:
Length = x
Width = y
So:
Area = xy
Substitute 128 for Area
128 = xy
Make x the subject.
x=128/y
When 1 inch margin is at top and bottom
The Length becomes:
length = x+2
When 2-inch margin is at both sides
The width becomes:
width = y+4
The New Area (A) is then calculated as:
A = (x+2)(y+4)
Substitute for x
A = (128/y +2)(y+4)
Open Brackets
A = 128 +512/y + 2y +8
Collect Like Terms
A = 512/y + 2y +136
To calculate the smallest possible value of y, we have to apply calculus.
Differentiate A with respect to y
A' = -512/y*y +2
Set
A' = 0
This gives:
y = 16
Recall that:
x = 128/y
x = 8
Recall that the new dimensions are:
Length = x +2
Width = y+4
So:
Length = 10
To double-check.
Differentiate A'
A'' = 1024/y*y*y
The above value is greater than 0
In other words, the estimated numbers are at their lowest.
Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.
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Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.
10%
30%
50%
90%
Answer: 90%
Step-by-step explanation: To find the probability of not choosing a red marble, we need to calculate the total number of marbles in the bag and subtract the number of red marbles. The total number of marbles is 3 red + 3 green + 15 yellow + 9 purple = 30. So, the probability of not choosing a red marble is P(not red) = (30 - 3) / 30 = 27 / 30 = 9 / 10=90/100=90%
When X has the pdf: f(x) = λe^{-λx}λe^(-λx)λe^-λx for x>0
P(X>x) =
A. 1-λe^{-λx}λe^(-λx)λe^-λx
B. 1-λe^{-λx}λe^(-λx)e^-λx
C. λe^{-λx}λe^(-λx)λe^-λx
D. λe^{-λx}λe^(-λx)e^-λx
The probability that X is greater than x is P(X>x) = 1-λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{-\lambda x}[/tex]. Thus, option (A) is correct.
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain.
P(X>x) is the probability that X takes on a value greater than x, which means that X is in the tail of the distribution. The cumulative distribution function (CDF) of X, denoted F(x), is defined as F(x) = P(X ≤ x). Since the CDF is a cumulative probability, we can find P(X>x) by subtracting the cumulative probability of X being less than or equal to x from 1:
P(X > x) = 1 - P(X ≤ x) = 1 - F(x)
Now, to find F(x), we can use the cumulative density function (pdf) of X. The pdf of X is given by f(x) = λ [tex]e^{- \lambda x}[/tex] for x > 0. To find the cumulative probability, we need to find the definite integral of the pdf from 0 to x:
F(x) = [tex]\int_0^x \lambda e^{- \lambda x}dx[/tex]
= [tex]-e^{-\lambda x} \int_0^x \lambda de^{\lambda x}[/tex]
= [tex]-e^{-\lambda x}[e^{\lambda x}]_0^x[/tex]
= [tex]-e^{-\lambda x}(e^{\lambda x} - 1)[/tex]
= [tex]1 - e^{-\lambda x}[/tex]
Therefore, the probability that X is greater than x is:
P(X>x) = 1 - F(x) = 1 - (1 - [tex]e^{- \lambda x}[/tex] = [tex]e^{- \lambda x}[/tex]
Hence, the probability that X is greater than x is P(X>x) = 1-λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{-\lambda x}[/tex].
Option (A) is correct.
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Let F(t) be the outside temperature (*F)t hours after 3 A.M. Explain the meaning of F(4) < F(5)
F(4) < F(5) means that the temperature at 7 A.M. is less than the temperature at 8 A.M.
What is an inequality?An inequality is used to compare two or more expressions.
For example -
ax + b > c
ax + b < c
Given is that F(t) is the outside temperature (*F)t hours after 3 A.M.
It is given that -
F(4) < F(5)
This means that the temperature at 7 A.M. is less than the temperature at 8 A.M.
Therefore, F(4) < F(5) means that the temperature at 7 A.M. is less than the temperature at 8 A.M.
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Need help please on this
The line has an equation y = 0.03x + 20, with a slope of $0.03 per GB and the y intercept of $20.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on
The slope intercept form of a linear equation is:
y = mx + b
where m is the rate of change and b is the y intercept
Let y represent the total cost of buying x gigabyte of data
The line passes through the point (0, 20) and (2000, 80). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-20=\frac{80-20}{2000-0} (x-0)\\\\y = 0.03x + 20[/tex]
The slope is 0.03 and the y intercept of the line is 20.
The second line passes through the point (0, -2) and (-2, -5). Hence:
[tex]y-y_1=\frac{y_1-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-2)=\frac{-5-(-2)}{-2-0} (x - 0)\\\\y=1.5x-2[/tex]
The equation of the line is y = 1.5x + 1 and y = 1.5x - 2
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A bicycle store costs $4000 per month to operate. The store pays an average of $50 per bike. The average selling price of each bicycle is $150. How many bicycles must the store sell each month to break even
Answer:27
Step-by-step explanation:
Answer:
The store would need to sell 40 bikes to break even.
Step-by-step explanation:
In order to break even the store needs to make $4000 a month. They spend $50 per bike and sell them for $150, an easy equation to get their profit per bike is to subtract how .uch they pay for a bike from how much they make per bike which is $150-50=$100. So now we just need to divide $4000 by $100 to find out how many bikes they need to sell. $4000÷$100=40.
Work out the area of a rectangle with base,
b
= 14mm and height,
h
= 10mm.
Answer:
70mm
Step-by-step explanation:
(14*10)/2=70
Height and Width multiplied against each other divided by two is the area of a triangle
Why do fractions need to have a common denominator before you add or subtract them? Tell me in the comments below
Explanation: Fractions must have a common denominator to add or subtract because if you think of pieces of a pizza, if you split one pizza into quarters and one into fifths, then each piece won't be the same size, so 1/5 isn't equivalent to 1/4. Therefore, if you subtract or add fractions you need to find a common denominator. One easy way to find a common denominator is list out the multiples of the two (or more) denominators and find the LCM (Least common multiple). Then find the quotient of the LCM divided by the denominator, and multiply that number by the numerator, and you have successfully changed your fraction to an equivalent fraction with a different denominator. Hope this helped. Please vote me brainliest.
Claudia is walking at a constant speed in front of a motion sensor. After 1 s she is 2. 5 m from the sensor. 2s later and she is 4. 0 m from the sensor. Find the equation in the form d=mt+b that describes her motion
The distance is 5.5 meters from the sensor.
Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.
Let us assume that d means distance and t means time.
When t = 1, d = 2.5
When t = 3, d = 4
d = mt + b
2.5 = m + b [t = 1]
4.0 = 3m + b [t = 2]
1.5 = 2m [subtract]
m = .75 = slope
b = 1.75 = d-intercept
d = .75t + 1.75
d = 15/4 + 7/4 [t = 5]
d = 22/4 = 5.5 m from sensor
Thus, the distance is 5.5 meters from the sensor.
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Exponential Functions
In the exponential function y = 3 × q⁵ the starting value is 3.
What is an exponential function?
The formula for an exponential function is f(x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The given exponential function is -
y = 3 × q⁵
The exponential function is written in the form abˣ.
Here, a is considered to be the initial value, b is considered to be the base and x represents the growth factor.
So, the initial or starting value in function y = 3 × q⁵ is -
a = 3
Therefore, the starting value is 3.
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for the same frame, complete the free-body diagram of the system abc by adding the forces that act on it.
The total force acting on the system ABC. The total force is equal to the sum of the force of gravity, normal force, friction force, tension force and applied force (Ftotal = Fg + FN + Ff + T + Fapp).
The force of gravity (Fg) acts on the system in the downward direction. This force is equal to the mass of the body multiplied by the acceleration due to gravity (Fg = mg).
The normal force (FN) is the force that acts perpendicular to the surface on which the body is resting. This force is equal to the weight of the body multiplied by the coefficient of friction between the body and the surface (FN = m * g * μ).
The force of friction (Ff) is the force that acts in the opposite direction of the motion of the body. This force is equal to the coefficient of friction multiplied by the normal force (Ff = μ * FN).
The tension force (T) is the force exerted by a string or a cable on the body. This force is equal to the mass of the body multiplied by the acceleration due to the applied force (T = m * a).
The applied force (Fapp) is the force that is applied to the body by an external force. This force is equal to the mass of the body multiplied by the acceleration due to the applied force (Fapp = m * a).
By combining all of these forces, we can determine the total force acting on the system ABC. The total force is equal to the sum of the force of gravity, normal force, friction force, tension force and applied force (Ftotal = Fg + FN + Ff + T + Fapp).
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Complete question:
What is the free-body diagram of the system ABC?
adding and subtracting mixed numbers with unlike denominators worksheets
Adding and subtracting mixed numbers with unlike denominators requires converting them into equivalent fractions with a common denominator. for example 3 3/5 + 2 1/7 = 5 8/35.
3 3/5 + 2 1/7 = 5 8/35, 5 1/5 - 3 2/3 = 1 7/15, 4 1/4 + 2 2/7 = 6 11/28, 6 3/4 - 3 5/6 = 2 13/24, 1 1/2 + 3 4/7 = 4 11/14, 2 5/6 - 1 1/4 = 1 7/12, 5 1/2 + 3 3/4 = 9 1/4, 3 1/5 - 2 3/7 = 0 16/35, 4 2/3 + 2 4/5 = 6 17/15 , 2 3/4 - 1 5/6 = 1 1/12
To add or subtract mixed numbers with different denominators, you must convert them into identical parts with common factors. Similarities can be found by looking at the most unusual differences between the two denominators. Mixed numbers are converted to bad parts, added or subtracted, and returned to perfect mixed numbers. How to find the common factor, that is,
Switch completely to unwise parts, extend or subtract, then switch completely to mixed numbers. Consider exact calculations of mixed numbers with different denominators.
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sum of independent negative binomial random variable and geometric random variable
The sum of independent negative binomial and geometric random variables does not have a closed-form distribution and must be computed numerically.
What is binomial random variable ?
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success or failure.
Let X be a negative binomial random variable with parameters r and p, and let Y be a geometric random variable with parameter q. The sum Z = X + Y is also a random variable.
The cumulative distribution function (CDF) of Z is given by:
F_Z(z) = P(Z <= z) = P(X + Y <= z) = ∑_{x=0}^{z} P(X = x) * P(Y = z - x)
This expression is a double sum and does not have a closed-form solution, but it can be computed numerically.
Alternatively, the probability mass function (PMF) of Z can be found by counting the number of ways that X and Y can take on their respective values, and summing up their joint probabilities:
f_Z(z) = P(Z = z) = ∑_{x=0}^{z} P(X = x) * P(Y = z - x)
The sum of independent negative binomial and geometric random variables does not have a closed-form distribution and must be computed numerically.
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i need help with thus..
Answer: -35/18
Step-by-step explanation: Hello!
The main thing that you need to know when dividing fractions is what the reciprocal is. Here is an example of finding the reciprocal:
1/2 divided by 2/3 = 1/2 x 3/2.
Basically, you flip the second fraction upside down (Put the number under the fraction line over the fraction line and put the number above the fraction line under the fraction line). Then, you multiply the two fractions. Then, you will find the answer. Here is how to do that with the problem you have:
5/3 divided by (-6/7) = ?
After finding the reciprocal, you would get:
5/3 x (-7/6)
To find the answer, multiply the numerators together (5 and -7) and the denominators (3 and 6) together.
For the new numerator, you get -35. For the new denominator, you get 18. Put the new numerator above the fraction line and the new denominator below the fraction line.
The answer is:
-35/18
An archer is able to hit the bull's-eye 49% of the time. If she shoots 10 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.
a. 0.1267
b. 0.2130
c. 0.7870
d. 0.0010
e. 0.0576
Probability of hitting bull's eye exactly 4 time sin 10 arrows is 0.213
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, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Properties of Probability:
Phi or a null set is the probability of an impossibly unlikely event.Its sample space represents an event's highest probable probability.Any occurrence has a probability between 0 and 1. A probability can also be zero (0).An event's probability cannot be negative.The chance of A or B happening is equal to the probability of A plus the probability of B if A and B are two outcomes that cannot both occur simultaneously.The probability of hitting a bull's Eye is 49% = 49/100 = 0.49
The probability of not hitting a bull's Eye is = 1- 0.49 = 0.51
Probability of hitting bull's Eye 4 times = (0.49)⁴
Probability of not hitting Bull's eye 6 times = (0.51)⁶
The total number of combinations possible with 10 sets are ¹⁰C₄.
Probability of hitting bull's eye 4 time sin 10 arrows is
¹⁰C₄*(0.49)⁴*(0.51)⁶ = 0.213
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the picture. please answer it
Answer:5 pounds, and x+y pounds.
Step-by-step explanation:
3 pounds + 2 pounds would equal 5 pounds ,and x pounds plus y pounds are veriables, and we do not have information on how to solve for them, so the answer would just be x pounds plus y pounds.
Step-by-step explanation:
1. If Jaxson buys 2 pounds of kiwi and 3 pounds of raspberries, he buys a total of 2 + 3 = 5 pounds of fruit.
2.If he buys a pounds of kiwi and 7 pounds of raspberries, he buys a total of a + 7 = a + 7 pounds of fruit.
let f(x) be a function with domain double-struck r. (a) show that e(x) = f(x) f(−x) is an even function. (simplify your answers completely.) e(x) = f(x) f(−x)
The given equation e(x)=f(x)f(-x) is an even function since e(x)=e(-x) and f(x)^2=f(-x)^2.
let f(x) be a function with domain double-struck r. (a) show that e(x) = f(x) f(−x) is an even function. (simplify your answers completely.) e(x) = f(x) f(−x) = f(x) f(x) = f(x)^2 e(x) = f(x)^2
e(x) = e(-x) Therefore, e(x) is an even function.
(-x) is an even function, we need to show that e(x)=e(-x).
We start by replacing -x with x in the equation:
e(x)=f(x)f(-x)
e(x)=f(x)f(x)
e(x)=f(x)^2
Now, we replace x with -x in the equation:
e(-x)=f(-x)f(-x)
e(-x)=f(-x)^2
Since the left-hand side of both equations are the same (e(x)=e(-x)), and the right-hand sides of both equations are the same (f(x)^2=f(-x)^2), we can conclude that e(x) is an even function.
The given equation e(x)=f(x)f(-x) is an even function since e(x)=e(-x) and f(x)^2=f(-x)^2.
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How do we solve this’!???
Answer:
n=32 That's all and the stepss
What is x + y + z if [tex]\frac{x}{4-x} = \frac{y}{5-y} = \frac{z}{6-z} = 2[/tex]
A. 8
B. 10
C. 16
D. 6
Step-by-step explanation:
DISCUSSION QUESTIONS (DQ's).
1. Is division always a negative in a religious faith? Why or why not?
clay made 4/5 of a pound of a trait mix if he puts 2/5 of a pound into each bag how many bags can clay fill
Answer: 2 bags
Step-by-step explanation:
To determine the number of bags Clay can fill, we need to divide the total amount of the trail mix by the amount of trail mix in each bag.
First, we'll convert the amounts to a common denominator of fifths:
4/5 of a pound of trail mix is 4/5 * 5/5 = 4 fifths
2/5 of a pound is 2/5 * 5/5 = 2 fifths
Now, we can divide the total amount of trail mix by the amount in each bag:
4 fifths ÷ 2 fifths/bag = 2 bags
So, Clay can fill 2 bags with 2/5 of a pound of trail mix each.
Consider the vector A == Axi + Ayj + Azk. Find the components AhA2' A3 of the vector A in a skewed coordinate system whose axes have directions specified by the following unit vector triad:
the components of A in this system will be: Ah = Axi1 + Ayj1 + Azk1, A2 = Axi2 + Ayj2 + Azk2, and A3 = Axi3 + Ayj3 + Azk3. To find the components of A in a skewed coordinate system, we first need to express the vector A in terms of the unit vectors of the system.
i = i1i2i3
j = j1j2j3
k = k1k2k3
Ah = Axi1 + Ayj1 + Azk1
A2 = Axi2 + Ayj2 + Azk2
A3 = Axi3 + Ayj3 + Azk3
To find the components of A in a skewed coordinate system, we first need to express the vector A in terms of the unit vectors of the system. The unit vectors of the skewed coordinate system are given by i = i1i2i3, j = j1j2j3, and k = k1k2k3.
Therefore, the components of A in this system will be: Ah = Axi1 + Ayj1 + Azk1, A2 = Axi2 + Ayj2 + Azk2, and A3 = Axi3 + Ayj3 + Azk3.
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please convert the following decimal numbers to binary numbers: (to receive full credit, you must show how you reach your answers. 1 point each, total 5 points): 1) 13 2) 121 3) 252 4) 1023 5) 2049
Answer:
1101 1111001111111001111111111100000000001Step-by-step explanation:
2/13=6 reminder 1
2/6= 3 reminder 0
2/3= 1 reminder 1
2/1= 0 reminder 1
13 becomes 1101 base two/ binary form
The conversion of number from decimal to binary:
[tex](13)_{10}=(1101)_{2}[/tex]
[tex](121)_{10}=(1111001)_{2}[/tex]
[tex](252)_{10}=(11111100)_{2}[/tex]
[tex](1023)_{10}=(1111111111)_{2}[/tex]
[tex](2049)_{10}=(100000000001)_{2}[/tex]
Recursively multiplying the given decimal number by two is one way to convert a decimal number to a binary number. The remainders are then recorded until we arrive at 0 as the final quotient. The remainders are then entered in reverse order to obtain the binary equivalent of the provided decimal number.
The number is 13.
13 ÷ 2 = 6, Remainder = 1
6 ÷ 2 = 3, Remainder = 0
3 ÷ 2 = 1, Remainder = 1
1 ÷ 2 = 0, Remainder = 1
So, [tex](13)_{10}=(1101)_{2}[/tex]
The number is 121.
121 ÷ 2 = 60, Remainder = 1
60 ÷ 2 = 30, Remainder = 0
30 ÷ 2 = 15, Remainder = 0
15 ÷ 2 = 7, Remainder = 1
7 ÷ 2 = 3, Remainder = 1
3 ÷ 2 = 1, Remainder = 1
1 ÷ 2 = 0, Remainder = 1
So, [tex](121)_{10}=(1111001)_{2}[/tex]
The number is 252.
252 ÷ 2 = 126, Remainder = 0
126 ÷ 2 = 63, Remainder = 0
63 ÷ 2 = 31, Remainder = 1
31 ÷ 2 = 15, Remainder = 1
15 ÷ 2 = 7, Remainder = 1
7 ÷ 2 = 3, Remainder = 1
3 ÷ 2 = 1, Remainder = 1
1 ÷ 2 = 0, Remainder = 1
So, [tex](252)_{10}=(11111100)_{2}[/tex]
The number is 1023.
1023 ÷ 2 = 511, Remainder = 1
511 ÷ 2 = 255, Remainder = 1
255 ÷ 2 = 127, Remainder = 1
127 ÷ 2 = 63, Remainder = 1
63 ÷ 2 = 31, Remainder = 1
31 ÷ 2 = 15, Remainder = 1
15 ÷ 2 = 7, Remainder = 1
7 ÷ 2 = 3, Remainder = 1
3 ÷ 2 = 1, Remainder = 1
1 ÷ 2 = 0, Remainder = 1
So, [tex](1023)_{10}=(1111111111)_{2}[/tex]
The number is 2049.
2049 ÷ 2 = 1024, Remainder = 1
1024 ÷ 2 = 512, Remainder = 0
512 ÷ 2 = 256, Remainder = 0
256 ÷ 2 = 128, Remainder = 0
128 ÷ 2 = 64, Remainder = 0
64 ÷ 2 = 32, Remainder = 0
32 ÷ 2 = 16, Remainder = 0
16 ÷ 2 = 8, Remainder = 0
8 ÷ 2 = 4, Remainder = 0
4 ÷ 2 = 2, Remainder = 0
2 ÷ 2 = 1, Remainder = 0
1 ÷ 2 = 0, Remainder = 1
So, [tex](2049)_{10}=(100000000001)_{2}[/tex]
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Find the equation of the line passing through (-8,3) and (-6, 7). Write your equation in point-slope AND slope-intercept forms. Use the first point in your point-slope form!
point-slope form:
slope-intercept form:
Answer:
point-slope form: y - 3 = 2(x+8)
slope-int form: y = 2x + 19
Step-by-step explanation:
For slope-int form, find the slope of the line.
7-3 / -6-(-8) = 4/2 = 2
This becomes y = 2x + b
To find b: plug in a y-coordinate for the y in the equation and plug in an x-coordinate for the x
7 = 2(-6) + b
7 = -24/2 + b
7 = -12 + b
7 + 12 = -12 + 12 +b
19 = b
The final equation is: y = 2x + 19
What quantity of 62% acetic acid solution must be mixed with a 19% acetic acid solution to produce 334. 78 mL of 47% solution?
x = 217.9927 = amount of mL of the 62% acid solution
y = 116.7873 = amount in mL of the 19% acid solution
This can be solved using a system of two equations and two variables.
Let x = amount of mL of the 62% acid solution
Let y = amount in mL of the 19% acid solution
We know the total mL of the mixture of the two solutions is 600 mL,
so x + y = 334.78 ..... eq(1)
62% of solution x is acid which can be written as 0.62x and similarly acid from the second solution can be written as 0.19y. We know that 47% of the 334.78 mL solution will be acid or 0.47(334.78).
The acid in the mixture solution comes from the acid in solution x and solution y. So 0.62 x + 0.19 y = 0.47 (334.78) ... eq(2)
from equation (1)
x = 334.78-y
So, x = 217.9927
y = 116.7873.
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what is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=44−x2−−−−−√ and the x- and y-axes is revolved about the y-axis?
The volume of the solid generated is [tex]\pi (2/3) (44)^{3/2}.[/tex]
We have,
To find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of y = √(44 - x²) and the x- and y-axes about the y-axis, we can use the method of cylindrical shells.
The volume can be calculated using the following integral:
V = ∫[a,b] 2πx f(x) dx
where [a, b] is the interval of x-values that defines the region in the first quadrant.
In this case, the curve y = √(44 - x²) intersects the x-axis when y = 0, which gives us:
0 = √(44 - x²)
Squaring both sides and solving for x, we get:
x² = 44
x = ±√44
Since we're considering the region in the first quadrant, we take the positive square root:
x = √44 = 2√11
Now we can set up the integral:
V = ∫[0, 2√11] 2πx (√(44 - x²)) dx
Simplifying the integrand:
V = 2π ∫[0, 2√11] x (√(44 - x²)) dx
To evaluate this integral, we can make the substitution u = 44 - x²,
du = -2x dx:
V = 2π ∫[0, 44] (√u) (-du/2)
V = -π ∫[0, 44] (√u) du
Integrating:
V = -π [2/3 u^(3/2)] [0, 44]
V = -π [2/3 (44)^(3/2) - 0^(3/2)]
V = -π (2/3) (44)^(3/2)
Finally, taking the absolute value and simplifying:
V = π (2/3) (44)^(3/2)
So, the volume of the solid generated is π (2/3) (44)^(3/2).
Thus,
The volume of the solid generated is [tex]\pi (2/3) (44)^{3/2}.[/tex]
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For each of the examples below, identify the bearing of D from C.
a)
250°
N
110°
D
b)
145°
D
N
C
215°
Not drawn accurately
a) The bearing of D from C is 250.
b) The bearing of D from C is 145.
What is Bearing in Angle?Angles are measured in bearings clockwise from north. The direction of north must be identified before taking a bearing measurement. The math exam question will typically include this north direction. The required angle is then measured in a clockwise fashion.
Given:
a) 250°N, 110°D
As, we know that Bearings are angles, measured clockwise from north. To measure a bearing, we must first know which direction is north.
So, the bearing of D from C is 250.
b) The bearing of D from C in second case is 145.
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a data analyst creates a scatterplot with a lot of data points. it is difficult for the analyst to distinguish the individual points on the plot because they overlap. what function could the analyst use to make the points easier to find? 1 point geom line() geom jitter() geom point() geom bar()
The analyst could use the geom_jitter() function to make the points easier to find.
What is data analyst ?
Analytics is the systematic computational analysis of data or statistics. It is used for the discovery, interpretation, and communication of meaningful patterns in data.
The function geom_jitter() can help to resolve this issue by randomly offsetting the x and y position of each point. By adding a small amount of "jitter" to each point, the overlap is reduced and the individual data points become more visible. In ggplot2 library, which is a popular plotting library in R, geom_jitter() is used as a layer in a plotting pipeline to add jitter to a scatterplot.
To use geom_jitter(), you will first create a scatterplot using the geom_point() function, then add a geom_jitter() layer to it. This will apply the jitter to the points and improve their visibility. For example, in ggplot2 the following code would create a scatterplot with jittered points:
ggplot(data, aes(x=x, y=y)) +
geom_jitter() +
geom_point()
The analyst could use the geom_jitter() function to make the points easier to find.
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The analyst could use the geom_jitter() function to make the points easier to find.
Analytics is the systematic computational analysis of data or statistics. It is used for the discovery, interpretation, and communication of meaningful patterns in data.
The function geom_jitter() can help to resolve this issue by randomly offsetting the x and y position of each point. By adding a small amount of "jitter" to each point, the overlap is reduced and the individual data points become more visible. In ggplot2 library, which is a popular plotting library in R, geom_jitter() is used as a layer in a plotting pipeline to add jitter to a scatterplot.
To use geom_jitter(), you will first create a scatterplot using the geom_point() function, then add a geom_jitter() layer to it. This will apply the jitter to the points and improve their visibility. For example, in ggplot2 the following code would create a scatterplot with jittered points:
ggplot(data, aes(x=x, y=y)) +
geom_jitter() +
geom_point()
The analyst could use the geom_jitter() function to make the points easier to find.
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also this one would help me out alot
The line that connects the coordinates (7,5) and (9,5) has the equation y = 5.
What is coordinates?A point or shape's location in a two-dimensional plane can be found using coordinates, which are a pair of numbers. The terms "x-coordinate" and "y-coordinate" are used to define a point's location on a 2D plane. A group of values that exhibit precise positioning On graphs, it is typically represented by a pair of numbers: the first number indicates the length along, while the second number indicates the length up or down. The point (12,5), for instance, is 12 units down and 5 units up. In order to determine a point's coordinates in a coordinate system, you must do the opposite.Due to the fact that the slope of the line across the two points (x1, y1) and (x2, y2) [tex]$\mathrm{m}=\frac{\mathrm{y}_2-\mathrm{y}_1}{\mathrm{x}_2-\mathrm{x}_1}$[/tex] Now, as shown below, we can determine the slope of the line through points (7,5) and (-9,5):
[tex]$\mathrm{m}=\frac{5-5}{-9-7}=\frac{0}{-16}=0[/tex]
As a result, the line's slope is o.
Find the y-intercept now by using the slope and one of the two points.
y = mx + b
5 = (0)(7) + b
b = 5
Equation in slope intercept form is written as follows:
y = mx + b
y = (0)x + 5
y = 5
Consequently, y = 5 is the line's equation.
The complete question is:
Find the equation of the line that passes through the points (7,5) and (−9,5)
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The slope of the line given by the coordinates of two points (x1, y1) = (-7, 5) and (x2, y2) = (-7, 9) is undefined. The slope of the line for coordinates (2, 3) and (2, -3) is undefined.
What is slope of the line?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Given that,
The coordinates of two points are:
(x1, y1) = (-7, 5) and
(x2, y2) = (-7, 9).
The slope of the line is given by the following equation:
m = (y2 - y1) / (x2 - x1)
Substituting the value of the given coordinates we have:
m = (9 - 5) / (-7 - (-7))
m = (4)/ -7 + 7 = undefined
The slope of the line given by the coordinates of two points (x1, y1) = (-7, 5) and (x2, y2) = (-7, 9) is undefined.
Similarly, for the coordinates (2, 3) and (2, -3):
m = (y2 - y1) / (x2 - x1)
m = (-3 -3) / (2 - 2)
m = undefined.
Hence, the slope of the line for coordinates (2, 3) and (2, -3) is undefined.
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One year old baby often weighs 250% of its birth weight. What should a one year old baby weigh if it was 8 pounds at birth?
Answer:
20 pounds
Step-by-step explanation:
250% = 2.5
8 times 2.5 = 20 pounds
So, a one-year-old baby weighs 20 pounds.
A population has u = 80 and a standard deviation of o = 5. 2. What are the mean and standard deviation of the sampling distribution
& if a sample of 100 were taken? (2 points)
CH-80,02 -0. 52
CH-80,0 -0. 052
H-80,0 - 5. 2
H-80,0 - 52
H-80. 0 - 520
The mean of the sampling distribution is 80 and the standard deviation is 0.52.
What is Normal Distribution?A normal distribution in statistics is defined as the type of continuous probability distribution where the data are arranged in a symmetrical bell shaped graph.
Given that,
Population mean, μ = 80
Population standard deviation, σ = 5.2
Mean of a sampling distribution in a normally distributed sample is same as the population mean and the standard deviation of the sampling distribution = σ / √n, where n is the sample size.
Sample size, n = 100
Mean of the sampling distribution = 80
Standard deviation of the sampling distribution = 5.2 / √100 = 5.2/10 = 0.52.
Hence mean and the standard deviation of the sampling distribution is 80 and 0.52 respectively.
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what will always be a solution to a homogenous set of equations
Homogeneous systems of linear equations can have either a unique solution or infinitely many solutions, depending on the rank of the matrix representing the system.
A homogeneous set of equations is a set of linear equations that has a trivial solution (that is, a solution consisting of only the zero vector). In other words, if the coefficients of the variables in a set of linear equations are all equal to zero, the set of equations is considered homogeneous.
The trivial solution, that is, the solution in which all variables are equal to zero, will always be a solution to a homogeneous set of equations. This is because, if all coefficients are equal to zero, then each equation in the set will reduce to 0 = 0, which is always true. Thus, the trivial solution is always a solution to a homogeneous set of equations.
In addition to the trivial solution, a homogeneous set of equations may also have non-trivial solutions, which are solutions that are not equal to only the zero vector. To find these non-trivial solutions, we typically use techniques such as Gaussian elimination, row reduction, or the use of matrices and determinants.
It is important to note that homogeneous systems of linear equations can have either a unique solution or infinitely many solutions, depending on the rank of the matrix representing the system.
Therefore, homogeneous systems of linear equations can have either a unique solution or infinitely many solutions, depending on the rank of the matrix representing the system.
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