49% 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.
Answer:
a) P(x=5) = 0.2456
b) P(x≥6) = 0.3526
c) P(x<4) = 0.1887
Step-by-step explanation:
We can model this as a binomial experiment, with sample size n=10 and p=0.49.
To calculate the probability of having k subjects with very little confidence in the sample of 10, we solve:
[tex]P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}[/tex]
a) We have to calculate P(x=5).
For a binomial variable with n=10 and p=0.49, this can be calculated as:
[tex]P(x=5) = \dbinom{10}{5} p^{5}q^{5}=252*0.0282*0.0345=0.2456\\\\[/tex]
b) We have to calculate P(x≥6). This can be calculated as:
[tex]P(x\geq6)=P(x=6)+P(x=7)+P(x=8)+P(x=9)+P(x=10)\\\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0138*0.0677=0.1966\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.0068*0.1327=0.1080\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0033*0.2601=0.0389\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0016*0.51=0.0083\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.0008*1=0.0008\\\\\\P(x\geq6)=0.1966+0.1080+0.0389+0.0083+0.0008\\\\P(x\geq6)=0.3526[/tex]
c) We have to calculate P(x<4). That is:
[tex]P(x<4)=P(x=0)+P(x=1)+P(x=2)+P(x=3)\\\\\\P(x=0) = \binom{10}{0} p^{0}q^{10}=1*1*0.0012=0.0012\\\\P(x=1) = \binom{10}{1} p^{1}q^{9}=10*0.49*0.0023=0.0114\\\\P(x=2) = \binom{10}{2} p^{2}q^{8}=45*0.2401*0.0046=0.0494\\\\P(x=3) = \binom{10}{3} p^{3}q^{7}=120*0.1176*0.009=0.1267\\\\\\P(x<4)=0.0012+0.0114+0.0494+0.1267\\\\P(x<4)=0.1887[/tex]
8. Peter and his partner are conducting a physics experiment on pendulum motion. Their 30-cm
pendulur traverses an arc of 15 cm. To the nearest degree, how many degrees of rotation did
the pendulum swing?
Answer: 90/pi degrees
Step-by-step explanation:
It forms a 15cm arc from a circle of radius 30 cm.
The diameter is 30*2*pi = 60pi cm. So the arc is 15/60pi = 1/4pi of the way around a 360 degree circle. This is 1/4pi * 360 = 90/pi degrees.
Hope that helped,
-sirswagger21
The pendulum will swing 28.68° if the 30-cm pendulum traverses an arc of 15 cm.
What is a circle?It is defined as the combination of points that, and every point has an equal distance from a fixed point (called the center of a circle).
We know that relationship between arc length s and central angle θ:
s = rθ
Where r is the radius of the circle
We have s = 15 cm
r = 30 cm
15 = (30)(θ)
θ = 0.5 radians
To convert it to a degree, multiply it by 180/π
θ = 0.5(180/π)
θ = 28.647 ≈ 28.68°
Thus, the pendulum will swing 28.68° if the 30-cm pendulum traverses an arc of 15 cm.
Learn more about circle here:
brainly.com/question/11833983
#SPJ2
Given the two parallel lines determine the value of x
Answer:
D. 150°
Step-by-step explanation:
x= 150°
Choice D
Round 8326 to the nearest hundred
Answer:
The answer is 8300.
Step-by-step explanation:
1) We round the number up to the nearest hundred, if the last two digits in the number are 50 or above.
2) We round the number down to the nearest 100 if the last two digits in the number are 49 or below.
3) If the last two digits are 00, then we do not have to do any rounding because it is already to the hundred.
Among fatal plane crashes that occurred during the past 55 years, 415 were due to pilot error, 96 were due to other human error, 169 were due to weather, 622 were due to mechanical problems, and 68 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it?
Answer:
Relative frequency:
[tex]\text{Pilot error}=415/1370=0.30\\\\\text{Other human error}=96/1370=0.07\\\\\text{Weather}=169/1370=0.12\\\\\text{Mechanical problems}=622/1370=0.45\\\\\text{Sabotage}=68/1370=0.05\\\\[/tex]
The most serious threat to aviation safety is, according to this data, "mechanical failures". It can be improved by more rigorous inspection and better maintenance policies and execution.
Step-by-step explanation:
We have the data for fatal plane crashes. The sum of plane crashes is
We can calculate the relative frequency as:
[tex]\text{Pilot error}=415/1370=0.30\\\\\text{Other human error}=96/1370=0.07\\\\\text{Weather}=169/1370=0.12\\\\\text{Mechanical problems}=622/1370=0.45\\\\\text{Sabotage}=68/1370=0.05\\\\[/tex]
We can see that the most frequent cause is "mechanical problems", with a relative frequency of 0.45.
Moise Moliere
Mrs. Johnson has 159 chickens that she puts in shelters at night to keep safe. She places 12 chickens in a shelter
and continues putting this number of chickens in each shelter until she comes to the last one. How many chickens
will Mrs. Johnson put in the last shelter?
3
4
13
11
6
7
8 9 10
14
Back
2 3 4 5
9:3
INTL
Answer: she putz 9 in the last shelter
Step-by-step explanation:
If f(3x − 1) = 6x − 1, find f(x) and f(0)
f(3x - 1) = 6x - 1
Rewrite 6x - 1 as a function of 3x - 1:
6x - 1 = 6x - 2 + 1 = 2(3x - 1) + 1
That is,
f(3x - 1) = 2(3x - 1) + 1
which means
f(x) = 2x + 1
and so
f(0) = 2*0 + 1 = 1
Given that it was less then 80degrees on a given day, what is the probability that it also rained that day?
The probability that it also rained that day would be 0.30
Which is the value of this expression when a = negative 2 and b = negative 3? (StartFraction 3 a Superscript negative 3 Baseline b squared Over 2 a Superscript negative 1 Baseline b Superscript 0 Baseline EndFraction) squared
Answer:
27/8
Step-by-step explanation:
You seem to want to evaluate ...
[tex]\dfrac{3a^{-3}b^2}{2a^{-1}b^0}[/tex]
I like to simplify the expression first, even though the order of operations would have you evaluate it as is.
[tex]=\dfrac{3}{2}a^{-3-(-1)}b^{2-0}=\dfrac{3b^2}{2a^2}[/tex]
Substitute the given values for "a" and "b" and do the arithmetic.
[tex]=\dfrac{3(-3)^2}{2(-2)^2}=\dfrac{3\cdot 9}{2\cdot 4}=\boxed{\dfrac{27}{8}}[/tex]
Please help! Been stuck on this for hours Solve the inequality. Express your answer in interval form. (If there is no solution, enter NO SOLUTION.) 2 ≤ |x^2 − 4| < 4
Answer:
(-√8, -√6] ∪ [-√2, 0) ∪ (0, √2] ∪ [√6, √8)
Step-by-step explanation:
The inequality resolves into 4 inequalities. There are 4 intervals in the solution.
Starting at the left, for the absolute value argument less than 0:
2 ≤ -(x^2 -4) . . . . . . . for x^2 -4 ≤ 0
2 ≤ -x^2 +4
-2 ≤ -x^2
2 ≥ x^2 . . . . . . . . . . consistent with the above 4 ≥ x^2
-√2 ≤ x ≤ √2 . . . . . square root; may be limited by other constraints
For the absolute value argument greater than 0:
2 ≤ x^2 -4 . . . . . . . for x^2 -4 ≥ 0
6 ≤ x^2 . . . . . . . . . .consistent with x^2 ≥ 4
-√6 ≥ x ∪ x ≤ √6 . . . . take the square root
__
The inequality on the right can be written as the compound inequality ...
-4 < x^2 -4 < 4
0 < x^2 < 8 . . . . . add 4
0 < |x| < √8 . . . . take the square root
This resolves to ...
-√8 < x < 0 ∪ 0 < x < √8
__
So, the solution set is the set of values of x that satisfy these restrictions on x:
-√2 ≤ x ≤ √2
x ≤ -√6 ∪ x ≤ √6
-√8 < x < 0 ∪ 0 < x < √8
That is a collection of 4 intervals:
(-√8, -√6] ∪ [-√2, 0) ∪ (0, √2] ∪ [√6, √8)
_____
You may be expected to write √8 as 2√2.
__
These intervals are the portions of the red curve that lie between the two horizontal lines. The points on the upper (dashed) line are not part of the solution set. The points on the lower (solid) line are part of the solution set.
divide 41000 into two parts such that their amounts at 50% compound interest compounded annually in 2 and 3 years are equal
Answer:24600 , 16400
Step-by-step explanation:
Let the first part be x
So, second part will be 41000 - x
For amount x
SI = prt / 100
SI = x * 0.50 * 2
SI = 1x
For amount 41000 - x
SI = (41000-x) * 0.50 * 3
SI = 61500 - 1.5x
1x = 61500 - 1.5x
1.5x + x = 61500
2.5x = 61500
x = 61500 / 2.50 = 24600 for 2 years
2nd part = 41000 - 24600 = 16400 for three years
Identify a reason why we should be skeptical of any claim or statistical evidence involving the following: A study shows that during the early 20th century, a strong correlation existed between the number of people who owned radios and the number of people put into insane asylums. Therefore, people who owned a radio were more likely to be declared insane and put into an insane asylum.a. correlation does not imply causality b. misleading graph c. self-interest survey d. voluntary response survey
Answer:
Option A
Step-by-step explanation:
Correlation does not imply causality. Correlation shows whether and how strongly pairs of variables are related.
Causality shows a situation between two events where one event is affected by the other
We would be skeptical of this survey because it is very difficult to assume that people who owned a radio were more likely to be declared insane and put into an insane asylum as listening to the radio cannot cause insanity unless proven.
the revenue function for a school group selling n bookmarks is given by R(n) =2n and the total cost function is given by C(n)=144+0.08n. determine the number of books
Correction
The revenue function for a school group selling n bookmarks is given by R(n) =2n and the total cost function is given by C(n)=144+0.08n. Determine the number of bookmarks sold at which they break-even.
Answer:
75 bookmarks
Step-by-step explanation:
The break-even point is the point at which revenue earned is equal to the cost of production.
Given the cost and revenue functions respectively:
R(n) =2nC(n)=144+0.08nCost=Revenue
C(n)=R(n)
144+0.08n=2n
144=2n-0.08n
144=1.92n
Divide both sides by 1.92
n=75
When 75 bookmarks are sold, the school group will break even.
Austin is 103 years old Raquel is 35 years old how many years ago was Austin age 5 times Raquel age
Answer:
18
Step-by-step explanation:
Let x represent the years ago
103-x = 5(35-x)
103-x = 175 +5x
4x = 72
x = 18
Mr. Dylan asks his students throughout the year to record the number of hours per week they spend practicing math at
home. At the end of the year, he creates a scatter plot that models the relationship between exam score and time spent
practicing. Which line of best fit will give Mr. Dylan the most accurate linear equation in order to make predictions about
this relationship?
Answer:
see the attachment
Step-by-step explanation:
A "line of best fit" generally has about as much data above the line as below it. If the data has any trend, it generally follows the trend.
The best choice here is B.
Answer:Answer:
see the attachment
Step-by-step explanation:
A "line of best fit" generally has about as much data above the line as below it. If the data has any trend, it generally follows the trend.
The best choice here is B.
Step-by-step explanation:
The average number of children a Japanese woman has in her lifetime is 1.37. Suppose that one Japanese woman is randomly chosen. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X.X~ _____(_____,_____) d. Find the probability that she has no children. e. Find the probability that she has fewer children than the Japanese average.
Answer:
a. X: amount of children that a Japanese woman has in her lifetime.
b. X can take natural numbers (all positive integers) as values.
c. X~Poi(1.37).
d. P(X=0)=0.2541
e. P(X<1.37)=0.6022
Step-by-step explanation:
a) This can be modeled with a Poisson distribution.
We let the variable X be the amount of children that a Japanese woman has in her lifetime.
The parameter of the Poisson distribution is λ=1.37.
This is also the value of the mean and the standard deviation.
b) X can take all positive integer values.
c) X is modeled as a Poisson variable with λ=1.37.
d) This can be calculated as:
[tex]P(0)=\lambda^ke^{-\lambda}/k!=1.37^{0} \cdot e^{-1.37}/0!=1*0.2541/1=0.2541\\\\[/tex]
e) Having fewer children than the average means that she has one or none children.
This can be calculated as:
[tex]P(X<1.37)=P(0)+P(1)\\\\\\P(0)=1.37^{0} \cdot e^{-1.37}/0!=1*0.2541/1=0.2541\\\\P(1)=1.37^{1} \cdot e^{-1.37}/1!=1.37*0.2541/1=0.3481\\\\\\P(X<1.37)=0.2541+0.3481=0.6022[/tex]
2- = - 6 – 4.0
Solve for x:
Please help :( : Solve the equation 3x + 5y = 15 for y
Answer:
y = -3/5 x +3
Step-by-step explanation:
3x + 5y = 15
Subtract 3x from each side
-3x+3x + 5y = -3x+15
5y = -3x+15
Divide each side by 5
5y/5 = -3x/5 +15/5
y = -3/5 x +3
please help !!!
Find the probability that x = -10
Answer:
20%
Step-by-step explanation:
Use the table provided... it says -10 is .2 which is the same as 20%
Answer:
0.20
Step-by-step explanation:
requires decimal not percentage
If we divide the numerator and denominator of (6/8) by 2, will its value be changed?
(50 points)
1.No
2.Yes
3.sometimes
4.Maybe
Answer:
Step-by-step explanation:
6/8 in simplest form is 3/4 but value is still the same so
1. no
What’s the correct answer for this question?
Answer:
B:
Step-by-step explanation:
If we rotate the 3-D figure around y-axis we'll obtain a cone with a radius of 3 units
I was confused on how to go about this.
Find the area of the triangle.
A = 14 m^2
Step-by-step explanation:
The equation for the area of a triangle is...
[tex]A=\frac{1}{2}bh[/tex]
For this we need the base and the height. Looking at the picture, we can see that the height is 4. The base is split into 2 parts, so we just need to add the 3 and the 4 together, that will make our base 7. Now we can plug these into the equation, but I'm also just going to make the 1/2 a 0.5.
[tex]A=0.5*4*7[/tex]
[tex]A=[/tex]
14 m^2
The ability of ecologists to identify regions of greatest species richness could have an impact on the preservation of genetic diversity, a major objective of the World Conservation Strategy. A study used a sample of n = 33 lakes to obtain the estimated regression equation
y = 3.89 + 0.033x1 + 0.024x2 + 0.023x3 − 0.0080x4 − 0.13x5 − 0.72x6
where y = species richness, x1 = watershed area, x2 = shore width, x3 = poor drainage (%), x4 = water color (total color units), x5 = sand (%), and x6 = alkalinity.
The SSR and SSE have been calculated to be:_________.
SSR = 752.25 and SSE = 300.9.
ANSWER:
I believe you wish to calculate the sum of squares total (SST) for this regression analysis. The sum of squares total is 1053.15
Step-by-step explanation:
The sum of squares total is numerically derived by adding the sum of squares regression (regression sum of squares) to the sum of squares error (error sum of squares). The regression sum of squares here is 752.25 and the error sum of squares is 300.9
This gives us a total sum of squares of 1053.15
Sums of squares tell if a linear regression of one variable (or variables) on another is good or not.
The squared differences between the observed dependent variable and its mean is a measure of the total variability of the data set.
So the SST is equal to 752.25 + 300.9 = 1053.15
Display the values of the function in two ways: (a) by sketching the surface zequals=f (x comma y )f(x,y) and (b) by drawing an assortment of level curves in the function's domain. Label each level curve with its function value.
Answer:
(1) f(x,y) = 1-|x|-|y|
(a) 3d figure attached
(b) 2d figure attached
(2) f(x,y) = 6-2x-3y
(a) 3d figure attached
(b) 2d figure attached
Step-by-step explanation:
The Function is not given in the question. Lets solve this for 2 common function for the internet. Hopefully it can solves the given problem
(1) f(x,y) = 1-|x|-|y|
(2) f(x,y) = 6-2x-3y
All the figures are labelled to avoid confusion. (a) part of both functions have 3D sketches. (b) part of both functions have 2d sketches
Which rule describes the translation?
5
B
С
(x, y) - (x - 8, y-3)
O (x, y) — (x - 3, y + 8)
O (x, y) = (x + 8, Y-3)
O(x, y) = (x + 3, y + 8)
B'
A
5
D
A
D
5
Answer:
look to rule number five
Step-by-step explanation:
Rule Number 5 best explains the answer
What is true about the number 3.872? Check all that apply.
The 8 is in the tens place.
The 7 is in the hundredths place.
The 3 is in the ones place.
This number is read as "three and eight seventy-two hundredths."
3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).
Answer:
The 7 is in the hundredths place.
The 3 is in the ones place.
3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).
Step-by-step explanation:
Given the number 3.872, to check all the given options that are true apply to the number, let's take a look at each position occupied by each digit. In order words, let's consider their place value.
Thus,
The 3 is in the ones place and as such has a value of 3.
8 is in the tenths place having a place value of 0.8 (⁸/10)
7 is in the hundredths place having a place value of 0.07 (⁷/100)
2 is in the thousandths place having a place value of 0.002 (²/1000)
Going by these, the following statements are true :
"The 7 is in the hundredths place."
"The 3 is in the ones place."
"3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001)."
The number is pronounced as three and eight hundred seventy-two thousandths rather than the option given.
Therefore, only 3 if the options are correct
Answer: The 7 is in the hundredths place.
The 3 is in the ones place.
3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).
Step-by-step explanation:
In the question, 3 is in the ones place. The first number after the decimal point is the tenths. In the question, the place value of 8 is 8 tenths; 7 is in the hundredths place.
3.872 = (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001)
= 3 + 0.8 + 0.07 + 0.002
= 3.872
The number is pronounced as three and eight hundred seventy-two thousandths
Assume that random guesses are made for nine multiple choice questions on an SAT test, so that there are nequals9 trials, each with probability of success (correct) given by pequals0.55. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4.
Answer:
[tex]P(X=0)=(9C0)(0.55)^9 (1-0.55)^{9-0}=0.000757[/tex]
[tex]P(X=1)=(9C1)(0.55)^9 (1-0.55)^{9-1}=0.0083[/tex]
[tex]P(X=2)=(9C2)(0.55)^9 (1-0.55)^{9-2}=0.0407[/tex]
[tex]P(X=3)=(9C3)(0.55)^9 (1-0.55)^{9-3}=0.1160[/tex]
And adding we got:
[tex] P(X < 4) = 0.000757 +0.0083+0.0407 +0.1160= 0.2626[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of correct answers", on this case we now that:
[tex]X \sim Binom(n=9, p=0.55)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X < 4) =P(X=0) +P(X=1) +P(X=2) +P(X=3) [/tex]
And we can find the individual probabilities:
[tex]P(X=0)=(9C0)(0.55)^9 (1-0.55)^{9-0}=0.000757[/tex]
[tex]P(X=1)=(9C1)(0.55)^9 (1-0.55)^{9-1}=0.0083[/tex]
[tex]P(X=2)=(9C2)(0.55)^9 (1-0.55)^{9-2}=0.0407[/tex]
[tex]P(X=3)=(9C3)(0.55)^9 (1-0.55)^{9-3}=0.1160[/tex]
And adding we got:
[tex] P(X < 4) = 0.000757 +0.0083+0.0407 +0.1160= 0.2626[/tex]
Please help! Correct answer only, please! Consider the following table. A movie theatre is planning to increase each of their various ticket prices by $2. Which informational matrix operation below would correctly increase of their prices ticket prices by $2? A. B. C. D.
Answer: D
Step-by-step explanation:
In order to increase each ticket by $2, you are ADDING 2 to each value.
So you create a matrix of all 2's and add that to the given matrix.
[tex]\left[\begin{array}{cc}2&2\\2&2\\2&2\end{array}\right] +\left[\begin{array}{cc}8&10\\12&16\\6&8\end{array}\right]\quad =\quad \large \left[\begin{array}{cc}10&12\\14&18\\8&10\end{array}\right][/tex]
Answer:
Unit 8 test answers
Step-by-step explanation:
1: a.)3x4
2:b.)
3:a.)
4:b.)
5:c.) matrix CD would have the dimensions 7x7
6: a.)
7:67
8:c.)
9:b.) Scott sold 1 van
10:d.)
Which is the correct classification of StartFraction 3 Over 8 EndFraction?
Answer:
Classifications would include
Rational; Fraction; Can be turned into Decimal; Positive
Those would be classifications
Answer: rational number, 0.375
Step-by-step explanation:
Identify which type of sampling is used random, systematic, convenience, stratified, or cluster To determine customer opinion of their inflight service, Continental Airlines randomly selects 30 flights during a certain week and surveys all passengers on the flights. Which type of sampling is used?
A. Stratified
B. Cluster
C. Systematic
D. Random
E. Convenience
Answer:
B. Cluster
Step-by-step explanation:
Samples may be classified as:
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
Each Continental Airlines flight is a group.
30 of them are chosen, and in each group chosen, every passenger is surveyed.
So cluster sampling was used.
