41% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
Answers
Answer:
a) 0.2087 = 20.82% probability that the number of U.S. adults who have very little confidence in newspapers is exactly five.
b) 0.1834 = 18.34% probability that the number of U.S. adults who have very little confidence in newspapers is at least six.
c) 0.3575 = 35.75% probability that the number of U.S. adults who have very little confidence in newspapers is less than four.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they have very little confidence in newspapers, or they do not. The answers of each adult are independent, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
41% of U.S. adults have very little confidence in newspapers.
This means that \(p = 0.41\)
You randomly select 10 U.S. adults.
This means that \(n = 10\)
(a) exactly five
This is \(P(X = 5)\). So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 5) = C_{10,5}.(0.41)^{5}.(0.59)^{5} = 0.2087\)
0.2087 = 20.82% probability that the number of U.S. adults who have very little confidence in newspapers is exactly five.
(b) at least six
This is:
\(P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)\)
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 6) = C_{10,6}.(0.41)^{6}.(0.59)^{4} = 0.1209\)
\(P(X = 7) = C_{10,7}.(0.41)^{7}.(0.59)^{3} = 0.0480\)
\(P(X = 8) = C_{10,8}.(0.41)^{8}.(0.59)^{2} = 0.0125\)
\(P(X = 9) = C_{10,9}.(0.41)^{9}.(0.59)^{1} = 0.0019\)
\(P(X = 10) = C_{10,10}.(0.41)^{10}.(0.59)^{0} = 0.0001\)
Then
\(P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.1209 + 0.0480 + 0.0125 + 0.0019 + 0.0001 = 0.1834\)
0.1834 = 18.34% probability that the number of U.S. adults who have very little confidence in newspapers is at least six.
(c) less than four.
This is:
\(P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{10,0}.(0.41)^{0}.(0.59)^{10} = 0.0051\)
\(P(X = 1) = C_{10,1}.(0.41)^{1}.(0.59)^{9} = 0.0355\)
\(P(X = 2) = C_{10,2}.(0.41)^{2}.(0.59)^{8} = 0.1111\)
\(P(X = 3) = C_{10,3}.(0.41)^{3}.(0.59)^{7} = 0.2058\)
So
\(P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0051 + 0.0355 + 0.1111 + 0.2058 = 0.3575\)
0.3575 = 35.75% probability that the number of U.S. adults who have very little confidence in newspapers is less than four.
Related Questions
Wavelength and Frequency
Examine the following wavelength
What is the ratio of the wavelengths of these two notes?
a. 5 to 4
b. 3 to 2
c. 6 to 5
d. 2 to 1
Please select the best answer from the choices provided
Answers
Answer:
D. 2 to 1
Step-by-step explanation:
I calculated it logically
Answer:
D - 2 to 1
Step-by-step explanation:
I think the answer is 2 ratio 1 because of the wavelength of the blue note of 1/2 less than the wavelength of the red note.
Please see attached picture.
Need help answering.
Answers
In the given graph, the x-intercepts are (2,0) and (6,0).
The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.
The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).
The sign of the leading coefficient is positive, since it is 1/2.
To find the equation of the quadratic function, we start by using the vertex form:
\(y = a(x - h)^2 + k\)
where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:
\(y = a(x - 4)^2 - 2\)
Next, we use the other two points to find two additional equations:
\(6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))\)
Simplifying these equations, we get:
\(6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\\)
So the equation of the quadratic function is:
\(y = (1/2)(x - 4)^2 - 2\)
Now, we can answer the questions:
The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:
\(y = (1/2)(0 - 4)^2 - 2 = 6\)
So the y-intercept is (0,6).
To find the x-intercepts, we set y = 0 in the equation:
\(0 = (1/2)(x - 4)^2 - 2\)
Simplifying, we get:
\((x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6\)
So the x-intercepts are (2,0) and (6,0).
The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.
The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).
The sign of the leading coefficient is positive, since it is 1/2.
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What would be the BEST formula to model the volume of a tree trunk?
Answers
like a hand help model?
Answer:
Volume of a cylinder.
Step-by-step explanation:
a researcher wants to examine the effect of fertilizer and the effect of sunlight on the yield of tomatoes. she bought 60 tomato plants at a local garden store. she randomly assigned 30 tomato plants to be planted on the sunny side of the hill and 30 to be planted on the shady side. the 30 plants which are planted on the shady side are randomly assigned to one of three groups. the first group are grown with no fertilizer, the second group with a small amount of fertilizer, and the third group with a large amount of fertilizer. the 30 plants which are planted on the sunny side are likewise randomly assigned to one of three groups. the first group are grown with no fertilizer, the second group with a small amount of fertilizer, and the third group with a large amount of fertilizer. all tomato plants are planted at the same time and are all treated alike (in terms of how much they are watered, weeded, etc.), and the person who tends the plants does not know which group each is in. each plant is grown to maturity. the total weight of tomatoes obtained from each plant is recorded. Describe the design of the experiment (completely randomized or blocked).
Completely randomized over one factor (location), blocked by fertilizer
Blocked by fertilizer, blocked by location
Completely randomized over one factor (fertilizer)
Completely randomized over one factor (fertilizer), blocked by location
Completely randomized over two factors (fertilizer and location)
Answers
The design of the experiment is Completely randomized over two factors (fertilizer and location).
Randomization is a statistical technique used in experimental design to ensure that all possible combinations of the factors being studied are represented in the study groups. It is used to eliminate bias and control for confounding variables that may affect the outcome of an experiment.
The researcher randomly assigned the tomato plants to be planted on either the sunny or the shady side of the hill. This creates two groups or two levels of the factor "location". She also randomly assigned the tomato plants to one of three groups based on the amount of fertilizer given, creating three groups or three levels of the factor "fertilizer".
The random assignment of plants to the different groups for both factors helps to ensure that any differences in the yield of tomatoes is due to the independent variables (fertilizer and location) being tested, and not due to other extraneous factors.
Therefore, The design of the experiment is Completely randomized over two factors (fertilizer and location).
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I need help please I can only find 2 of these solutions
Answers
Step 1: Isolate the Sin Operator
\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)
Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable
Note that since trig functions have 2 general solutions, this will give us one of our general solutions.
\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)
x₁= 0.48
Solving for x₂
Use the period identity for Sin Functions
\(sin(x)=sin(\pi -x)\)
X in this case is arcsin(0.25)
\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)
So our two general solutions are 0.48 and 5.52
Step 3: Period
Trig Functions have periodic behavior and this function period is
\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)
So our general solutions are
0.48±12k, where k is an integer
5.52±12k, where k is an integer
Let k=1, and we get our next set of solutions:
12.48 and 17.52
So our answer is 0.48,5.52,12.48,17.52
When the sum of a number and 14 is
divided by 3, the result is 4.
Answers
Answer:
it is 4.6 sorry girl
Step-by-step explanation:
Answer:
Step-by-step explanation:
4.6=4 3/5=23/5
Contributions to the annual Grayson School fund raising campaign were 10% greater in 1984 than they were in 1983. In 1983, contributions were 15% greater than they were in 1982. If contributions for 1984 total $8855, what was the total in 1982?
Answers
Answer:
6774.075
Step-by-step explanation:
1984: 8855
1983: 8855*10/100=885.5
8855-885.5
7969.5
1982
7969.5*15/100=1195.425
7969.5-1195.425
6774.075
A
-pound bag of Kitty Kibbles is
. An
-pound bag of Feline Flavor is
. Which statement about the unit prices is true?
Feline Flavor has a higher unit price of
/pound.
Kitty Kibbles has a higher unit price of
/pound.
Kitty Kibbles has a higher unit price of
/pound.
Feline Flavor has a higher unit price of
/pound.
Answers
The statement about the unit prices which is true is Kitty Kibbles has a lower unit price of $1.30/pound.
The correct answer choice is option D.
How to solve unit prices?Cost of 16-pound bag of Kitty Kibbles = $20.80
Unit price of kitty kibbles = Price / number of pounds
= $20.80 / 16
= $1.30 per pound.
Cost of 8-pound bag of Feline flavor = $11.20
Unit price of feline flavor = Price / number of pounds
= $11.20 / 8
= $1.40 per pound
Ultimately, the unit price of kitty kibbles and feline flavor is $1.30 and $1.40 respectively.
Complete question:
A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true?
A. Feline Flavor has a lower unit price of $1.40/pound.
B. Feline Flavor has a lower unit price of $1.30/pound.
C. Kitty Kibbles has a lower unit price of $1.40/pound.
D. Kitty Kibbles has a lower unit price of $1.30/pound.
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-1/4 x [ x 12 -32 ] = [ 5 -3 y ]
![-1/4 x [ x 12 -32 ] = [ 5 -3 y ]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/MoWELz3Foh0WDK1NC6K1wfbtzYwwuPzh.png)
Answers
The x and y values for the given equation are x= -20 and y=8
What is meant by scalar multiplication?One of the fundamental operations defining a vector space in linear algebra in mathematics is scalar multiplication (or more generally, a module in abstract algebra). When a real Euclidean vector is multiplied scalarly by a positive real number, the direction of the vector remains unchanged, but the magnitude of the vector increases. A scalar is anything that scales vectors, which is how the word "scalar" itself came to be. It is important to distinguish between the inner product of two vectors and scalar multiplication, which is the multiplication of a vector by a scalar with a vector as the product.
Given,
-1/4[ x 12 -32 ] = [ 5 -3 y ]
[(-1/4)x (-12/4) (-32/-4)]=[5 -3 y]
-x/4=5
-x=20
x= -20
-32/-4=y
y=8
Therefore, the x and y values for the given equation are x= -20 and y=8
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Help me please, I’m very confused on what to do
Answers
Just add the powers while it is multiply
-1+(-3)
= -1 - 3
= -4
So it is \(2^{-4}\)
How many solutions does this system of equations have y = -1/3x + 7. y = -2x^3 + 5x^2 + x - 2
Answers
The system of equations has one solution.
How many solutions does this system has?To check this, we can graph the two equations of the system:
y = (-1/3)x + 7
y = -2x³ + 5x² + x - 2
On the same coordinate axis, and check how many times do the graphs intercept.
The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.
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The dot plot shows the lengths of the 12 trailers sold at a store last month.
Trailers Sold
6 7 8 9 10 11 12 13 14 15 16 17
Length (feet)
Which statement about the data is true?
Answers
Answer:
6
Step-by-step explanation:
.
how do i refund and stop my subscription for brainly
Answers
To refund and stop your subscription for Brainly.
Visit the Brainly website and log into your account using your credentials.Navigate to your account settings or profile page.Look for the "Subscription" or "Billing" section and click on it.In the subscription settings, locate the option to cancel or stop your subscription.Follow the provided instructions to cancel your subscription. This may involve confirming your cancellation or providing a reason.Once your subscription is canceled, check the terms and conditions for refund eligibility. If you are eligible for a refund, follow the refund process specified.If there is no refund available or if you encounter any issues, contact Brainly's customer support through their website or via email.Explain your situation and request assistance with the refund process.Be sure to monitor your bank or credit card statements to confirm that the subscription charges have been stopped.For such more questions on subscription
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i still need help 1 more after this
Answers
Answer:
4.2
Step-by-step explanation:
0.2^(3)-:0.4*60+3.6-:1.2 = 4.2
Answer:
4.2
Step-by-step explanation:
Find the linear function with the following properties.
f(0)=8
Slope of f=−6
Answer
Answers
Therefore , the solution of the given problem of function comes out to be f(x) = -6x + 8 .
Describe function.Numerous subjects, including numbers, numbers, as well as their subsets, as well as building, construction, and both real and fictitious geographic locations, are covered in the mathematics programme. The relationships between variable elements that all cooperate to create the same outcome are covered in a work. A utility is composed of several unique parts that, when combined, give particular outcomes for each input.
Here,
The linear function with a slope of -6 can be written in slope-intercept form as:
=> f(x) = -6x + b
where "b" is the y-intercept. We are also given that f(0) = 8, so we can substitute those values in to solve for "b":
=> f(0) = -6(0) + b = 8
=> b = 8
Therefore, the linear function we are looking for is:
=> f(x) = -6x + 8
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If Thomas travels 120 miles in 2 hours how many will it take him to travel 300 miles
Answers
Answer:
5hours
Step-by-step explanation:
120÷2=60
60=1 hour
300÷60=5
5hours
Roscoe is exchanging $ 121 for Euros for his upcoming trip to Germany. If $2 can be exchanged for 1.78 Euros,how many Euros will Roscoe have?
Answers
Answer:
€107.69
Step-by-step explanation:
If $2=€1.78 then $1= €0.89
0.89*121= €107.69
The 107.69 Euros will Roscoe have for trip to Germany.
It is required to find how many Euros will Roscoe have for trip to Germany.
What is arithmetic?The arithmetic refers to working with numbers by doing addition, subtraction, multiplication, and division. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.
Given:
Roscoe is exchanging $ 121 for Euros.
If $2 can be exchanged for 1.78 Euros.
$2=€1.78
then $1= €0.89
For $ 121=
=0.89*121
= €107.69
Therefore, the 107.69 Euros will Roscoe have for trip to Germany.
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A package of 25 fishing hooks costs $9.95 , while a package with 40 hooks costs $13.99 . Which is the better buy? Round your answer to the nearest cent if necessary.
Answers
Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.
To determine which package is the better buy, we need to compare the cost per hook for each package.
For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:
Cost per hook = $9.95 / 25 = $0.398
Rounding to the nearest cent, the cost per hook is $0.40.
For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:
Cost per hook = $13.99 / 40 = $0.3498
Rounding to the nearest cent, the cost per hook is $0.35.
Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.
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Please help me with this question I am trying to help my son but I have forgotten how to solve these problems. The formula for the lateral surface area of a cylinder is S=2πrh, where r is the radius of the bases and h is the height.Solve for r.r=2hπ/Sr=h/2πSr=2Sπhr=S/2πh
Answers
We have the following formula:
\(S=2\pi\text{ rh}\)and we need to isolate the radius r. Then, we can rewrite the formula as
\(S=(2\pi h)\cdot r\)then, by dividing both side by 2Pi h, we have
\(\frac{S}{2\pi h}=\frac{2\pi h}{2\pi h}\cdot r\)since
\(\frac{2\pi h}{2\pi h}=1\)we get
\(\begin{gathered} \frac{S}{2\pi h}=1\cdot r \\ or\text{ equivalently} \\ \frac{S}{2\pi h}=r \end{gathered}\)By comparing this result with the given options, the answer is the last option:
\(r=\frac{S}{2\pi h}\)Can someone help me with this question plz Show work.
Answers
Answer:
D. 32.3
Step-by-step explanation:
Length-a
Width-b
A=ab=6.8×4.75=32.3
Which expressions are equivalent to 4m + 12? Choose ALL that apply.
Answers
Answer:
Your answers are 6m-2m+12 and 4(m+3).
Step-by-step explanation:
This is because for 6m-2m+12, you are dealing with like terms. You are subtracting 6m-2m.
4(m+3) on the other hand, you are using the distributive property. You would carry the 4 to the m and to the 3.
Once you've done that with both of those expressions, they will both equal 4m+12.
Expression is a set of numbers, variables, and mathematical operations formed. The expression 4m+12 can be written as 4(m+3).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
In the given expression 4m + 12, there are 2 terms and both of these terms have 4 as the common factor, therefore, we can write the expression as,
\(4m +12\\\\= 4m+(4 \times 3)\\\\ = 4(m + 3)\)
Hence, the expression 4m+12 can be written as 4(m+3).
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Regina charges c dollars per hour to babysit. If she increases her rate by 15%, which expression represents her new rate, in dollars per hour?
PLZZ HELPPPPPPPPPPPPPPPPPP
A- c + 0.15
B- c + 15
C- c + 0.15c
D- c +15c
Answers
Answer: Correct answer is C
If x and y are consecutive positive integers and x2 – y2 = 11, what is the value of y?
E. 1
F. 3
G. 5
H. 6
please provide explanation
Answers
Answer:
y = 5
Step-by-step explanation:
We khow that x and y are consecutive integers and that x^2 is greater than y^2 since x^2-y^2=11
● so x is greater than y
● wich means that x = y+1
● x^2-y^2=11
● (y+1)^2-y^2 = 11
● y^2+2y+1-y^2=11
● 2y + 1 = 11
● 2y +1-1 = 11-1
● 2y = 10
●2y/2 = 10/2
● y = 5
The smallest plus three times the largest of three consecutive integers is three less than five times the middle integers. Find the smallest of the integers.
Answers
The smallest integer is 1 and middle integer is 2 and largest integer is 3
Solution:
Given that , three times the largest increased by two is equal to five times the smallest increased by three times the middle integer.
We have to find the three consecutive integers
So, let the smallest integer be n, then the next two consecutive middle and largest integers will be n + 1, n + 2 respectively
Then, by the given statement,
Three times the largest increased by two is equal to five times the smallest increased by three times the middle integer.
Thus the smallest integer = n = 1
Middle integer = n + 1 = 1 + 1 = 2
Largest integer = n + 2 = 1 + 2 = 3
Please helppp i will mark brainlist
Answers
Answer:
18.84
Step-by-step explanation:
6 times 3.14
= 18.84
Answer:
56.52
Step-by-step explanation:
1/2(π*radius^2)
Find the remainder when you divide 28282828282838·28282828282839 by 28.
Answers
Answer:
1.010101e+12
Step-by-step explanation:
28282828282838.28282828282839 / 28
Answer:
The answer to the question is 26.
293+290+287+284+...+2
Answers
Answer:
\(281\)
Explanation:
\(-3n+296\)
\(-3(5)+296\)
\(-15+296\)
Answer:
281
Step-by-step explanation:
Select the graph of y=cot x.
Answers
Answer:Suppose y= cot x is our parent function then remember general rules of transformation.1) y= -f(x), reflects the graph of f(x) across x-axis.2) y= cf(x), stretches the graph of f vertically by factor of c , for c >1.Now, apply these rules to y= -4 cot(x)the -ve sign reflects the graph of cot(x) across x-axis and the number 4 will stretch it vertically by 4 units.The graph of both parent function (y=cot x ) and transformed function (y= -4 cot(x)) are attached below.
Darren's birthday party will cost $40 if he invites 5 guests. If there are 6 guests, how muchwill Darren's birthday party cost? Assume the relationship is directly proportional.
Answers
Let y be the cost of the party and x the number of guests. Since we are told to assume that the relationship is directlly proportional, we have that
\(y=kx\)where k is a positive constant.
We are told that y is 40 whenever x is 5. So we have the equation
\(40=k\cdot5\)so, multiplying both sides by 5, we get
\(k=\frac{40}{5}=8\)So we have the equation
\(y=8x\)Now, we are interested in finding y when x=6. So we have that
\(y=8\cdot6=48\)So the cost for a party of 6 is 48.
Here are a few pairs of positive numbers whose sum is 34. (3 pts)
a. Find the product of each pair of numbers.
First
Number
1
4
8
14
Second
Number
33
30
26
20
b. Which pair of numbers that have a sum of 34 will produce the largest possible
product? What is that product?
Answers
Answer: 280
Step-by-step explanation:
The products of each pair of numbers are:
1 x 33 = 33
4 x 30 = 120
8 x 26 = 208
14 x 20 = 280
b. To find the pair of numbers that will produce the largest possible product, we need to look for the pair with the closest product to 340 (the square of 17, which is the average of the two numbers).
The pair of numbers with the closest product to 340 is 14 and 20, whose product is 280. Therefore, the pair of numbers that will produce the largest possible product is 14 and 20, and the product is 280.