Answer:
6115
Explanation:
[tex]70000(1-0.15)^{15} \approx 6115[/tex]
The volume of the cube is claimed to be 27 inches, correct to within 0.027 in3. Use differentials to estimate the propagated error in the measurement of the side of the cube.
The propagated error in the measurement of the side of the cube is 0.001.
We know that,
the volume of a cube is dependent on the length of the edge, s, which is given by the equation,
V = [tex]s^{3}[/tex].
With this we determine that the given cube has an edge of 27 = [tex]s^{3}[/tex]
⇒ s = 3 inches.
Now we can acquire the differential of the equation for the volume of the cube with the following equations.
V = [tex]s^{3}[/tex]
dV = d([tex]s^{3}[/tex])
dV = 3[tex]s^{2}[/tex] ds
We have given that volume of the cube is 0.027.
That is dV = 0.027 and s = 3
we simply plug in the given and then solve for ds to determine the error in the measurement of the edge of the cube.
dV = 3[tex]s^{2}[/tex] ds
0.027 = 3(3)²ds
0.027 = 27ds
0.001 = ds
Therefore, there is an error in measurement of the edge of the cube up to 0.001 inches.
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Line l Intersects line m. Find the value of a,b, x. Give reasons
The angles in the intersected lines are as follows:
a = 80 degreesb = 80 degreesx = 92 degreesHow to find angles when lines intersect?When lines intersect angle relationships are formed such as vertically opposite angles, linear angles etc.
Angle a is vertically opposite to angle b.
Vertically opposite angles are congruent.
Therefore,
∠a ≅ ∠b
Hence,
x + 8 = 100(vertically opposite angles)
x = 100 - 8
x = 92
b + x + 8 = 180(sum of angles on a straight line)
b + 92 + 8 = 180
b = 180 - 100
b = 80 degrees.
Hence,
a = 80 degrees
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Show me how to write a phrase as an expression then solve when x equals 5 and Y equals 26 more than the product of 8 and a number is X
The expression used to represent the given phrase is given by x =5 and
y = 26 + 8x and value of the given expression when x =5 is equal to
y = 66.
As given in the question,
Given phrase is:
x equal 5
y equals 26 more than the product of 8 and a number x
Required expression to represent the given phrase is:
x = 5
y = 26 + 8x
Value of the expression y = 26 + 8x when x = 5 is given by :
y = 26 + 8( 5 )
⇒ y = 26 + 40
⇒ y = 66
Therefore, the required expression for the given phrase is x =5 and
y=26 +8x , the value of the expression y = 66 when x = 5.
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find the area of the shaded figure
ASAPPPPPP
Answer:
[tex]A=20 units^2[/tex]
Step-by-step explanation:
I would separate out the shape into two equal right triangles over a square. The total area can then be found by adding these areas together:
[tex]A_t=2A_\Delta +A_s\\A_t=2(\frac{1}{2}bh)+(s)^2\\b=2 units\\h=2units\\s=4units\\A_t=2[\frac{1}{2}(2units)(2units)]+(4units)^2\\A_t=4units^2+16units^2\\A_t=20units^2[/tex]
I need help with 9 10 and 11
Suppose that X and Y have a discrete joint distribution for whichthe joint p.f. is defined as follows:f(x,y) = (1/30)(x+y) for x = 0,1,2 and y = 0,1,2,3.and 0 otherwise.a) Determine the marginal p.f.'s of X and Y.b) Are X and Y independent?
The probability mass function (pmf) of X formally displays the likelihood of events where X=xk.
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.
The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.
The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .
According to our question-
We can list the components of RX if X is a discrete random variable since RX is a countable set. In other words, RX=x1,x2,x3,... can be written.
Note that the random variable X here has the potential values x1, x2, x3
While we typically use capital letters to designate random variables, we typically use lowercase letters like x, x1, y, and z to denote the integers in the range.
We are interested in learning the probability that a discrete random variable, X, equals a certain value, xk.
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If you vertically stretch the exponential function f(x) = 2x by a factor of 4, what is the equation of the new function?
The equation of the new function is g(x) = 4(2ˣ)
How to determine the equation of the new function?The exponential equation is given as
f(x) = 2ˣ
Then, we have the transformation to be:
Vertically stretch by a scale factor of 4
The scale factor can be represented as k
So, we have
k = 4
The rule of vertical stretch by a scale factor of k is represented a
g(x) = kf(x)
So, we have
g(x) = 4 * 2ˣ
This gives
g(x) = 4(2ˣ)
Hence, the equation is g(x) = 4(2ˣ)
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Rick rents a car from a company that charges him $25 per day plus 10 cents per mile driven. Which expression can represent the amount he owned on resent retal.
The expression that can be use to represent the amount owned on rental is 0.1x + 25y
How to find the expression that represent the amount?Rick rents a car from a company that charges him $25 per day plus 10 cents per mile driven.
The expression that can be use to represent the amount owned on rental can be represented as follows:
let
x = number of miles driven
y = number of days
Let's convert cent to dollars
100 cents = 1 dollars
10 cents = ?
cross multiply
amount in dollars = 10 / 100 = 0.1 dollars
Therefore,
the expression = 0.1x + 25y
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a military unit wants to pass through a forested arwa, but wants to check the area for possible enemy troops first. a team of speciaists will place 15 motion sensors throughout the area. each sensor has a probability of 0.95 of operating for a 24-hour period
By using Binomial distribution, it can be calculated that
a) Probability that the operation is successful = 0.8290
b) Number of sensors expected to operate during the 24 hour period = 14.25
What is Binomial Distribution?
Binomial Distribution is a discrete type probability distribution whose probability mass function is given by
P(X = x) = [tex]{n \choose x}p^xq^{n-x}[/tex]
p is the probability of success and q is the probability of failure.
a) This is a problem on Binomial Distribution
Probability that the operation is successful = P(X [tex]\geq[/tex] 14)
= P(X = 14) + P(X = 15)
P(X = 14) =
[tex]{15 \choose 14}(0.95)^{14}(1- 0.95)^{15 - 14}\\15 \times 0.95^{14}\times 0.05\\0.3657\\[/tex]
P(X = 15) =
[tex]{15 \choose 15} 0.95^{15}(1-0.95)^{15 - 15} = 0.4633[/tex]
Probability that the operation is successful = 0.3657+0.4633 = 0.8290
b) Number of sensors expected to operate during the 24 hour period = [tex]15 \times 0.95[/tex] = 14.25
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Roger Marl wung a bat which had a ma of 2kg at a velocity of 45m/. How many joule of kinetic energy could he give to the ball
Total kinetic energy that is generated will be 2025 joules
What is kinetic energy?
The K.E. of an object is that the energy that it possesses because of its motion. it's outlined because the work required to accelerate a body of a given mass from rest to its expressed velocity.
Main body:
According to question :
mass = 2 kg
velocity = 45 m/s
formula for kinetic energy = (1/2) mv²
substituting these values in formula,
K.E. = (1/2) 2* 45²
K.E. = 45²
K.E. = 2025 joules.
Hence kinetic energy generated is 2025 joules.
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27. P is (-1, 3) and Q is (5, -1).
(a) Find the coordinates of the midpoint of PQ.
(b) Find the gradient of the line PQ
36 +16
(c) Given that the length of PQ-2√n units, where n is an integer, find the value of n
=
(N2013/1/19)
a) Coordinates of the midpoint: (2,1)
b) Gradient of the line PQ = -2/3
c) n = 13
What is the midpoint of a line segment?
The midpoint is defined as the point which divides the line segment into two equal halves.
Given P = (-1,3) , Q = (5,-1)
Coordinates of the midpoint are given by
X' = (X1+ X2)/2
Y' = (Y1+ Y2)/2
(X1,Y1 ) and (X2,Y2) are the endpoints of the line segment.
Putting the values in the above formula X' = (-1+5)/2 = 2
Y' = (3-1)/2 = 1
hence midpoint = (2,1)
The Slope or Gradient of the line is given by = (Y2-Y1)/X2-X1)
= (-1-3)/(5-(-1))
= -4/6 = -2/3
Gradient = -2/3
Distance between 2 points is given by the formula
[tex]\sqrt{(x_{1}-x_{2}) ^{2}+(y_{1}-y_{2}) ^{2} }[/tex]
[tex]\sqrt{(-1-5)^{2}+(3-(-1))^{2} }[/tex]
[tex]\sqrt{6^{2}+4^{2} }[/tex]
= [tex]2\sqrt{13}[/tex]
hence n = 13
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Given f(x)=3x+4f(x)=3x+4, find f(4)f(4).
Answer:
f(x) = 3x + 4
f(4) = 3(4) + 4 = 12 + 4 = 16
Write an equation of the line that passes through (−5, −2) and is parallel to y=2/3x+1.
Answer:
[tex]y=\frac{2}{3}x+1\frac{1}{3}[/tex]
Step-by-step explanation:
when a line is parallel the slope is the same for both
y=mx+b is slope intercept form where m is slope and b is intercept
we know the slope is 2/3 so to find b we just fill it in with coordinates
-2=2/3(-5)+b
-2=-10/3+b
+10/3 +10/3
4/3=b
y=2/3x+4/3
hopes this helps please mark brainliest
A group of friends wants to go to the amusement park. They have no more than $170 to spend on parking and admission. Parking is $7. 25, and tickets cost $23. 25 per person, including tax. Write and solve an inequality which can be used to determine xx, the number of people who can go to the amusement park.
If the inequality which can be used to determine x is 7.25 + 23.25x ≤ 170 and the number of people who can go the amusement park is 7
The maximum amount that he can spend = $170
The cost of the parking ticket = $7.25
The cost of the ticket including tax = $23.25 per person
Then the inequality will be
7.25 + 23.25x ≤ 170
Subtract both side of the inequality by 7.25
23.25x ≤ 162.75
Divide both side of the inequality by 23.25
23.25x / 23.25 ≤ 162.75/23.25
x ≤ 7.006
Hence, the inequality is 7.25 + 23.25x ≤ 170 and 7 people can go to the amusement park
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Leslie spent $43. 50 to purchase a combination of drinks, sandwiches, and chips for herself and her friends. A drink costs $1. 75, a sandwich costs $6. 25, and chips cost $1. 50. Identify the linear equation that represents this situation.
The linear equation that represents the given situation is 1.75x + 6.25y + 1.50z = 43.50
Total amount that she spent = $43.50
The cost of drinks = $1.75
The cost of sandwich = $6.25
The cost of chips = $1.50
The linear equation is defined as the equation in which the highest power of the variable is 1
The linear equation the represents this situation is
1.75x + 6.25y + 1.50z = 43.50
Where the number of drinks is x, number of sandwiches is y and the number of chips is z
Hence, the linear equation is 1.75x + 6.25y + 1.50z = 43.50
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in your own words, explain why the speedup of a parallel algorithm will eventually reach some limit.
The speedup of a parallel algorithm will eventually reach some limit.
What is parallel algorithm?
An algorithm is a set of instructions that takes input from the user and, after doing some calculations, generates an output. A parallel algorithm is one that can carry out multiple operations simultaneously on various processing units and then combines all of the separate outputs to get the desired outcome.
An algorithm that can execute several instructions concurrently on various processing devices and then aggregate all of the individual outputs to produce the final result is known as a parallel algorithm.
Because a parallel algorithm's speedup is never equal to the number of processors, it ultimately reaches a limit beyond which it can no longer be accelerated. At that point, the algorithm will no longer be accelerated and the speedup will stop.
Hence, the speedup of a parallel algorithm will eventually reach some limit.
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solve the system of equations using any method
3x-3= y
6x-5y=12
(please i need help im begging you)
Answer:
(1/3, - 2)-------------------------------
Given system3x - 3 = y6x - 5y = 12Solve by substitution6x - 5(3x - 3) = 126x - 15x + 15 = 12- 9x = 12 - 15- 9x = - 3x = - 3 / - 9x = 1/3Find y:
y = 3 * 1/3 - 3y = 1 - 3y = - 2a marketing class polled 270 people at a shopping center to determine how many read the daily news and how many read the weekly gazette. they found the following: 124 read the daily news. 33 read both. 19 read neither. How many read the Weekly Gazette?
128 were Daily News readers. 19 read neither while 35 read both. Weekly Gazette A marketing class conducted a survey of 270 shoppers at a mall to find out how many of them read the Weekly Gazette and how many the Daily News.
What is News readers?
150 attendees were surveyed by a marketing class to find out how many read the Weekly Journal and how many the National News. In this section, word problems will be solved using Venn diagrams. The areas of a Venn diagram that indicate quantities as opposed to will have numbers in them. Confidence interval for difference of two formula You may have read statements like the ones below in newspapers, for instance. law in numerous nations.
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Homework Progress
37/ 105 Marks
Gigi is going to buy 100 stickers.
Here is some information about the cost of stickers in two shops.
Stickers4u
Pack of 25 stickers for £2.25
World Stationery
Pack of 10 stickers for £1.75
Buy 1 pack get 1 pack free
Gigi wants to buy the stickers for the best possible price.
Which shop should Gigi buy the 100 stickers from?
You must show how you get your answer.
Show your workin
Gigi should buy stickers from World Stationery.
Define Expressions.
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Let's see the information about Stickers4u
Here, pack of 25 stickers is = £2.25
1 sticker cost = 2.25 / 25
= £0.09 per sticker
Now, information about World Stationery
Here, pack of 10 stickers is = £1.75
1 sticker cost = 1.75/10
= £0.175 per sticker
In this shop, the offer is also there i.e, Buy 1 pack get 1 pack free.
Therefore, Gigi should go with this shop for best possible price.
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The graph represents the money collected at the movie theater on Saturday. Find the domain when the maximum number of people allowed in the movie theater is 60 people.
graph of y equals 2 times x plus 40 with x axis labeled Number of People and y axis labeled Amount of Money
The domain when the maximum number of people allowed in the movie theater is 60 people would be: B. 0 ≤ x ≤ 60.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) for a function while a range is the set of all possible output values (y-values) of a function.
Since the maximum number of people that are allowed in the movie theater is 60 people, we can logically deduce that the input values (x-values) for its function is less than or equal to 60. Therefore, the domain of the function on this graph is given by:
Domain = [0, 60]
Domain = 0 ≤ x ≤ 60.
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Complete Question:
The graph represents the money collected at the movie theater on Saturday. Find the domain when the maximum number of people allowed in the movie theater is 60 people.
40 ≤ y ≤ 160
0 ≤ x ≤ 60
40 ≤ x ≤ 160
0 ≤ y ≤ 60
Answer:
the answer is 0 is less than or equal to x which is less than or equal to 60
Step-by-step explanation:
Domain is the x value
Since the max amount of people is 60, and people is x value the answer i put above is a reasonable domain.
Hope this helps!
In the context of hypothesis testing, what is a test statistic?
a. The confidence level that is to be used to except or reject the null hypothesis.
b. A parameter determine from a sample, such as mean or standard deviation, used to test a hypothesis.
c. A value, determined from sample information, used to test the null hypothesis.
In the context of hypothesis testing, a test statistic is; c. A value, determined from sample information, used to test the null hypothesis.
How to Interpret Hypothesis Testing?Hypothesis testing is defined as the method that is used to find the probability of the hypothesis to be proved in the future on the basis of the small population sample. The null hypothesis is said to be a hypothesis where no important difference between the random variables
The test statistic is defined as a value that is computed from the sample data that is used when making a decision about whether or not to reject the null hypothesis.
Looking at the options and based on the definitions above, option C adequately describes the test statistic.
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7(x-1)=3x+2 in a improper fraction
Answer:x=9/4 nine over 4 for improper fraction I hope this is helpful mark me brainlist if this sounds good
Step-by-step explanation:
7(x-1)=3x+2
Distribute through the parentheses
7x-7=3x+2
Move the variable to the left-hand side and change its sign
7x-7-3x=2
or Move the constant to the right-hand side and change its sign
7x-7-3x=2
Collect like terms
4x=2+7
And then Add the numbers
4x=9
Divide both sides of the equation by 4
x=9/4
Mixed number is 2 1/4
help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
Write the equation of the line that passes through (4,2) and is parallel to y =3x + 1 in point-slope form
Answer:
y=3x-10
Step-by-step explanation:
y=mx+b
2=3(4)+b
2=12+b
b=-10
y=3x-10
Please answer asap! find the magnitude and direction angle of m=(-15,16) and n=(2,-6)
The magnitude and the direction angle of the vector are given as follows:
Magnitude: 27.80.Direction angle: θ = -52.3.What are the magnitude and the direction of the vector?The points that define the vector are given as follows:
m(-15, 16) and n(2,-6).
Considering m as the starting point and n as the endpoint, the vector is defined by the subtraction of the coordinates of n by the coordinates of m, hence:
v = (2 - (-15), -6 - 16) = (17, -22).
The magnitude of the vector is given by square root of the sum of the squares of the components, hence:
|v| = sqrt(17² + (-22)²) = 27.80.
The direction angle is the arc tangent of the division of the vertical component of the vector by the horizontal component of the vector, hence:
θ = arctan(-22/17)
θ = -52.3.
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Three consecutive integers have a sum of â€""21. which equation can be used to find the value of the three numbers? x x x = negative 21 x 2 x 3 x = negative 21 x (x 1) (x 2) = negative 21
This equation x + (x + 1) + (x + 2) = negative 21 will be used.
Let the first Number is x.
We have to take 3 consecutive integers.
second Number is x+1
third Number is x+2.
Sum of these 3 consecutive integers is x+(x+1)+(x+2).
Sum of these 3 consecutive integers is given as negative21.
so we can write x+(x+1)+(x+2)=negative 21.
by using above equation we can find the value of 3 numbers.
So the final equation will be x + (x + 1) + (x + 2) = negative 21.
Given Question is incomplete, Complete Question here:
Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers? x + x + x = negative 21 x + 2 x + 3 x = negative 21 x + (x + 1) + (x + 2) = negative 21 x + (x + 2) + (x + 4) = negative 21
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Ana conducts a study using a /-test to see if there is a difference in the mean number of cups of coffee consumed between men and women. The null hypothesis would state that the population mean number of cups of coffee that women drink would _______ the population mean number cups of coffee that men drink.
The null hypothesis would state that the population mean number of cups of coffee that women would drink 32% the population mean number cups of coffee than men drink.
What is meant by percentage?The term "percentage" comes from the Latin phrase "per centum," which means "by the hundred." With 100 as the denominator, percentages are fractions. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam received 30% on his math test, he received 30 points out of 100. It is expressed as 30/100 in fractional form and 30:100 in ratio form.
A certain number or quantity in every hundred is referred to as a percentage. It is a fraction, and the denominator is 100.
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The table below shows that the number of miles driven by Abigail is directly
proportional to the number of gallons she used.
Gallons Used Miles Driven
15
517.5
33
1138.5
36
1242
What is the constant of proportionality between the
number of miles driven and the number of gallons
used?
Answer: 34.5
Step-by-step explanation:
To find the constant of proportionality between miles driven and number of gallons used, we will divide the miles driven by the gallons used.
517.5 / 15 = 34.5
1138.5 / 33 = 34.5
1242 / 36 = 34.5
due now pls help mee!!!!!!
Answer:
(-2,-4)
Step-by-step explanation:
3x+2=-2x-8
+2x. +2x
5x+2=-8
-2. -2
5x=-10
/5. /5
x= -2
y=3(-2)+2
y=-6+2
y= -4
(-2,-4)
Hopes this helps please mark brainliest
Which relation is a function?
Select all that apply.
Responses
{(2, 1), (2,3), (3, 4), (4,5)} {(2, 1), (2,3), (3, 4), (4,5)}
{(2, 1), (−2,1), (3, 2), (4,2)} {(2, 1), (−2,1), (3, 2), (4,2)}
{(−1, 2), (−2,2), (−3, 2), (−4,2)} {(−1, 2), (−2,2), (−3, 2), (−4,2)}
{(2, 1), (2,3), (−2, 5), (−2,7)} {(2, 1), (2,3), (−2, 5), (−2,7)}
{(2, 2), (3,3), (4, 4), (5,5)}
The relations which are functions as required to be identified in the task content are;
{(2, 1), (−2,1), (3, 2), (4,2)} {(−1, 2), (−2,2), (−3, 2), (−4,2)}{(2, 2), (3,3), (4, 4), (5,5)}Which relations are functions among the given answer choices?It follows from the task content that the relations which are functions among the given answer choices are to be identified.
Since the definition of a function is such that; a function is a special kind of relation in which case only one output value is assigned to each input values.
Put simply, a function has only one output value for each input value.
Therefore, it follows from the definition above that the relations which are functions among the given answer choices are as listed above.
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