Answers
a) k = 1/2 then v = 1 cubic unit
b) k = 0.6 then v = 1.728 cubic units
c) k = 1 then v = 8 cubic units
d) k = 1.5 then v = 27 cubic units
The value of scale factor k, which is used to obtain a solid with volume v cubic units by 8 cubic unit is, ∛v / 2.
The volume of the solid is 8 cubic units.The scale factor of dilation is kThe volume of new solid obtained is v.Here the new volume of the solid is find out by the volume of 8 units and the scale factor k. Thus the scale factor k should be equal to the ratio of the volume of these two solid.
The volume of the solid is represents in cubic units. Thus, k = ∛(v/2)
k = (∛v) / 2
a) k = 1/2
(1/2)³ * 2³ = v
v = 1 cubic units
b) k = 0.6
(0.6)³ * 8 = v
0.216 * 8 = v
v = 1.728 cubic units
c) k = 1
1³ * 8 = v
v = 8 cubic units
d) k = 1.5
(1.5)³ * 8 = v
3.375 * 8 =v
v = 27 cubic units
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Related Questions
Multiple (3x+y) by (4x+2y)
Answers
Answer:
12x² + 10xy + 2y²
Step-by-step explanation:
(3x + y)(4x + 2y) =
= 12x² + 6xy + 4xy + 2y²
= 12x² + 10xy + 2y²
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
evaluate the line integral by the two following methods. line integral xy dx x2 dy c is counterclockwise around the rectangle with vertices (0, 0), (3, 0), (3, 4), (0, 4). (a) directly (b) using green's theorem
Answers
main answer: line integral by the two following methods [tex]xy dx x^{2} dy c[/tex]
supporting answer: A line integral in Calculus is an integral in which the function to be integrated is evaluated along a curve. A path integral, curve integral, or curvilinear integral are all names for a line integral. This article will go over the definition of the line integral, formulas, examples, and how to use line integrals in real life
body of the answer : given
line integral xy dx x^{2} dy c
c is counter clockwise
according to greens theorem
∫ₐpdx+qdy
∫∫ₓdq/dx-dp/dq
we evaluate the 1st line integral from (0,0) to (0,4)
an equation of straight line joining (0,0) and (0,4)in the xy plane is y=4
l₁=∫⁰₄ x(4)dx+ x²(4)=∫⁰₄ 4xdx+4x²
=[4.x²/2+4x³/3]₄⁰
=4(16)/2+4(64)/3
=32+256/3
=117
we evalute second integral from (0,4)to (3,0)
an equation of straight line joining (0,4)and(3,0)in xy plain is x=3 dx=0
the second line integral now becomes
l₂=∫³₀ (3)y(0)+3²dy
=∫³₀ 9dy
=27
we now evaluate the third line integral from (3,0) to (3,4)
an equation of straight line joining (3,0)and (3,4) in xy plain is y=4,dy=0
the third integral now becomes,
l₃=∫³₃ x(0)dx+ x²(4)
=∫³₃ 4x²
=4*9=36
36-36=0
now evalute the 4th line integral from (3,4) to(0,0)
an equation of straight line joining from (3,4) to (0,0) in xy plane is x=0
∫₄⁰(3)y(0)+ 9dy
∫⁰₄ 9dy
=9*4=36
sum of all line integral=36+27+0+117
=180
final answer:therefore ∫ₐ pdx +qdy
∫∫ₓdq/dx-dp/dq=180
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Line integral by the two following methods is 180
What is integral calculus?
A line integral in Calculus is an integral in which the function to be integrated is evaluated along a curve. A path integral, curve integral, or curvilinear integral are all names for a line integral. This article will go over the definition of the line integral, formulas, examples, and how to use line integrals in real life
Given
line integral xy dx x^{2} dy c
c is counter clockwise
According to greens theorem
∫ₐpdx+qdy
∫∫ₓdq/dx-dp/dq
We evaluate the 1st line integral from (0,0) to (0,4) an equation of straight line joining (0,0) and (0,4)in the xy plane is y=4
l₁=∫⁰₄ x(4)dx+ x²(4)=∫⁰₄ 4xdx+4x²
=[4.x²/2+4x³/3]₄⁰
=4(16)/2+4(64)/3
=32+256/3
=117
We evaluate second integral from (0,4) to (3,0)
an equation of straight line joining (0,4) and (3,0) in xy plain is x=3 dx=0
the second line integral now becomes
l₂=∫³₀ (3)y(0)+3²dy
=∫³₀ 9dy
=27
We now evaluate the third line integral from (3,0) to (3,4)
an equation of straight line joining (3,0)and (3,4) in xy plain is y=4,dy=0
the third integral now becomes,
l₃=∫³₃ x(0)dx+ x²(4)
=∫³₃ 4x²
=4*9=36
36-36=0
Now evaluate the 4th line integral from (3,4) to(0,0)
an equation of straight line joining from (3,4) to (0,0) in xy plane is x=0
∫₄⁰(3)y(0)+ 9dy
∫⁰₄ 9dy
=9*4=36
Sum of all line integral=36+27+0+117
=180
Therefore ∫ₐ pdx +qdy
∫∫ₓdq/dx-dp/dq=180
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The monthly rents (in dollars) paid by 9 people are given below. (Note that these are already ordered from least to greatest.)
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210
Suppose that one of the people moves. Her rent changes from $1210 to $1480.
Answer the following.
What happens to the mean=____ it decreases by __$
____ it increases by __$
____ it stays the same
What happens to the median=____ it decreases by __$
____ it increases by __$
____ it stays the same
Answers
The mean of a data-set is given by the sum of the values of all observations in the data-set divided by the number of elements in the data-set.
In this problem, the data-set is given as follows:
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210.
Hence the mean is of:
M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1210)/9 = 1035.
After the change, the data-set is of:
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1480.
Hence the mean will be of:
M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1480)/9 = 1065.
Then the increase will be of:
1065 - 1035 = 30.
What is the median of a data-set?The median of a data-set is the middle element of the data-set, the value which:
50% of the data-set is lesser than.50% of the data-set is greater than.The median is not affected by the values at the bounds of the distribution, such as 1210 and 1480 are in this distribution, hence it remains constant.
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Elephants sometimes damage trees in Africa. It turns out that elephants dislike bees. They recognize beehives and avoid them. Can this information be used to keep elephants away from trees? Will elephant damage be less in trees with hives? Will empty hives even keep elephants away? Researchers want to design an experiment to answer these questions using 72 acacia trees. Identify the experimental units, treatments, and the response variable.
Answers
a) The experimental units are the Acacia Trees.
b) The treatments carried used are; active beehives, empty beehives and no single beehive.
c) The response variable is the damage that the elephants caused to the trees.
How to interpret experimental research design?Experimental design is defined as the process of carrying out research in a manner that is objective and controlled such that precision is maximized and then specific conclusions can possibly be drawn regarding a hypothesis statement. Generally, the purpose of this is to establish the effect that a factor or independent variable has on a dependent variable.
From this question, it is very clear that the experimental units are the Acacia Trees. This is because they are the primary interest or objective of the research.
The treatments carried out here are the active beehives, empty beehives and no single beehive.
The response variable is defined as the result of the experiment where the explanatory variable is manipulated. In this case, the response variable is the damage that the elephants caused to the trees.
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a 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?
Answers
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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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.
Answers
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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If you vertically stretch the exponential function f(x) = 2x by a factor of 4, what is the equation of the new function?
Answers
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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Question 8(Multiple Choice Worth 5 points) (Two-Step Linear Inequalities MC) A Solve the inequality and graph the solution. -3p+ 6.7> -4.4 (HELP ASAP!)
Answers
Answer: p < [tex]-\frac{11.1}{3}[/tex]
Step-by-step explanation:
To solve, we will isolate the p variable.
Given:
-3p + 6.7 > -4.4
Subtract 6.7 from both sides of the equation:
-3p > -11.1
Divide both sides of the equation by 3:
Note, you must switch the sign since you're dividing by a negative.
p < [tex]-\frac{11.1}{3}[/tex]
Answer:
p < 3.7
Step-by-step explanation:
-3p + 6.7 > -4.4
1- subtract 6.7 to leave -3p alone
-3p + 6.7 -6.7 > -4.4 - 6.7
-3p > -11.1
2- Divide both sides by -3. NOTE; u must change the > sign to < because u r dividing by a negative
-3p/-3 = p
-11.1/-3= 3.7
p < 3.7
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
Answers
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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solve for x: x/7 < or equal to -6
Answers
Step-by-step explanation:
x
— - 6 = 0
7
Subtracting a whole from a fraction
Rewrite the whole as a fraction using 7 as the denominator :
6 6 • 7
6 = — = —————
1 7
x - (6 • 7) x - 42
——————————— = ——————
7 7
x - 42
—————— = 0
7
x-42
———— • 7 = 0 • 7
7
x-42 = 0
x = 42 Answer
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Determine if the table how a proportional relationhip. X 25. 6 72. 8 77. 2 y 6. 4 18. 2 19. 3 Ye, it i proportional becaue all y over x ratio are equivalent to one fourth. Ye, it i proportional becaue all y over x ratio are equivalent to one third. No, it i not proportional becaue 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8. No, it i not proportional becaue 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
Answers
Proportional relationship for the given table is true and is define as
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
As given in the question,
Value of x and y in the given table are :
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
To check the proportional relationship there should exist constant of proportionality that ratio of corresponding y/x should be constant.
y / x for all the values of x and y:
First values:
y /x = 6.4 / 25.6
= 0.25
Second values:
y/x = 18.2/ 72.8
= 0.25
Third values :
y /x = 19.3/ 77.2
= 0.25
0.25 is equivalent to One fourth ( 1/4).
Constant of proportionality exist = 0.25 or One fourth.
Therefore, in the table first option: yes, it is proportional because all y over x ratio are equivalent to one fourth is correct.
The complete question is:
Determine if the table how a proportional relationship.
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
Yes, it is proportional because all y over x ratio are equivalent to one third.
No, it is not proportional because 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8.
No, it is not proportional because 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
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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?
Answers
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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Find the olution to the following lhcc recurrence:
an=−6aₙ₋₁−5aₙ₋₂ for n≥3 with initial condition a0=28,a1=−76
Answers
aₙ = 6aₙ₋₁ - 5aₙ₋₂ then the values for n≤3, then a₀ = 28; a₁ = -76 ; a₂ = -596 ; a₃ = -3196. The Sequence is 28, -76, -596, -3196.
How can the sequence's solution be found?
a = 2 and d = 3 decide the order. Using the method for locating the nth term, we can locate a particular term in an arithmetic series. Step 1: An arithmetic sequence's nth term is determined by the formula an = a + (n - 1)d. Therefore, enter the values a = 2 and d = 3 into the formula to find the nth term.Given:
a₁ = -76 ; a₀ = 28
aₙ = 6aₙ₋₁ - 5aₙ₋₂
Then the arithmetic sequence is followed by:
a₂= 6a₂₋₁ - 5a₂₋₂
= 6a₁ - 5a₀
= 6(-76) - 5 (28)
= -456 - 140
a₂ = -596
a₃ = 6a₃₋₁ - 5a₃₋₂
= 6a₂ - 5a₁
= 6(-596) - 5(-76)
= - 3576 + 380
a₃ = -3196
The values for n≤3, then a₀ = 28; a₁ = -76 ; a₂ = -596 ; a₃ = -3196. The Sequence is 28, -76, -596, -3196.
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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.
Answers
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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less than (<), greater than (>), and not (not equal to) are examples of ____.
Answers
Answer: Less than (<), greater than (>), and not (not equal to) are examples of comparison operators.
Step-by-step explanation: They show a comparison between the two operands.
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
Answers
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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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?
Answers
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
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
Answers
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 diameter of a dime is 17.91 mm. The diameter of a strand of human hair is
6.0 x 10-2 mm. How many times greater is the diameter of a dime than the diameter of
the strand of human hair?
Answers
The diameter of a dime tells us the circumference of a dime is approximately 299 times larger than human hair.
What is DiameterThe diameter of an object is used to calculated the circumference or area of the object. This also helps us to know the width of a circular object.
In this problem, the diameter tells us about the length of the each quantity.
The diameter of a dime tells us how wide the coin is and the diameter if a hair tells us the width of the hair.
Comparing both values
Dime = 17.91mm
Hair = 6.0*10^-2
Divide both quantity together.
17.91 / 6.0*10^-2 = 298.5≅299
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What error did the student make? in line 2, the student forgot to multiply the right side of the equation by 2. in line 3, the student should have subtracted the equations instead of adding them. in line 3, the student added the two equations incorrectly. in line 5, the student used an incorrect equation when solving for x.
Answers
Answer: the student forgot to multiple by right side of equation 2 in line 2
Step-by-step explanation: your welcome :)
m angle KHG= (4x+6) and m angle HGW= (6x-16) and m angle NGX=(y+9)
5. Find the value of x
6. Find the value of y
7. m angle KHG=
8. m angle HGW=
9. m angle NGX=
Answers
Question 5
Using the alternate interior angles theorem,
[tex]4x+6=6x-16\\\\6=2x-16\\\\22=2x\\\\x=11[/tex]
Question 6
Using the corresponding angles theorem,
[tex]4x+6=y+9\\\\4(11)+6=y+9\\\\50=y+9\\\\y=41[/tex]
Question 7
[tex]m\angle KHG=4(11)+6=50^{\circ}[/tex]
Question 8
[tex]m\angle HGW=6(11)-16=50^{\circ}[/tex]
Question 9
[tex]m\angle NGX=41+9=50^{\circ}[/tex]
Solve for x:
2 + 4x = 30
Answers
-2 -2
4x = 28
Then you’ll divide 28/4 = 7
Which X would be 7
x = 7
If you need the point/x-intercept:
( 7, 0 )
Answer:2 + 4x = 30
-2 -2
4x = 28
= 28/4 = 7
X is 7
x = 7
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
Answers
Answer:
15095.39
Step-by-step explanation:
[tex]A=13000(1+(0.03)/4)^{(4)(5)} \approx 15095.39[/tex]
Why are factorial designs useful in testing theories?
a. They allow researchers to explore the construct validity of a theory.
b. Results from factorial designs are typically straightforward and easy to interpret.
c. They allow researchers to understand the nuances of how variables interact.
d. Results from factorial designs are always intuitive.
Answers
Factorial design are useful in testing theories because they enable researchers to investigate a theory's construct validity. so the correct answer is option (a).
What is factorial designs?A key technique for identifying the impact of numerous variables on a response is the factorial design. Traditionally, experiments are planned to ascertain how one variable affects just one response.
What is testing theories?The corpus of knowledge supporting the analysis and application of test results. The definition and measurement of reliability are of primary relevance. Classical test theory, generalizability theory, and item response theory are examples of theoretical frameworks.
a) They enable academics to investigate a theory's construct validity.
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prove: if the bisector of an exterior angle of a triangle is parallel to a side of the triangle, the triangle is isosceles
Answers
The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .
In the question ,
it is given that ,
the angle bisector of the exterior angle of a triangle is parallel to a side .
we have to prove that the triangle will be an isosceles triangle .
In the triangle ABC given below , AB is extended to AD ,
SO , the exterior angle will be angle DAC ,
let AE be the bisector of the the angle .
So , the equal angles are angle DAC and angle EAC .
it is given that AE is parallel to BC , where BC is base .
we know that ,
if any line intersects two parallel lines then every pairs of alternative Interior angles are same and also their corresponding angles are equal .
Here AE is parallel to BC and line BD intersects them ,
So , angle ABC = angle DAE ( corresponding angles )
angle ACB = angle EAC ( alternate angles )
Now , as AE is the bisector of angle DAC ,
we have , angle DAC = angle EAC
So , we get , angle ABC = angle ACB .
In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal
that means , AB=AC
Hence , the given Triangle is an isosceles triangle .
Therefore , it is proved that the triangle ABC is an isosceles triangle .
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Given f(x)=3x+4f(x)=3x+4, find f(4)f(4).
Answers
Because:
f(4)= 3(4) + 4
f(4) = 12 +4
f(4) = 16
Answer:
f(x) = 3x + 4
f(4) = 3(4) + 4 = 12 + 4 = 16
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
Answers
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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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.
Answers
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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Write the equation of the line that passes through (4,2) and is parallel to y =3x + 1 in point-slope form
Answers
Answer:
y=3x-10
Step-by-step explanation:
y=mx+b
2=3(4)+b
2=12+b
b=-10
y=3x-10
