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]
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. -6 ≤ y ≤ 9
Step-by-step explanation:
→Looking at the graphed function, you can see that the line starts at when y = -6. Then the function slowly increases, until it finally stops when y = 9.
→This means that the range (y-values) of the function can be from -6 through 9.
The correct answer should be "A. -6 ≤ y ≤ 9."
Which equation can be used to solve for b?
B
5 cm
С
10 cm
b
30
A
O tan(30)=5/b
O tan(30)=b/5
O tan(30)=10/b
O tan(30)=b/10
Answer:
The answer is option 1.
Step-by-step explanation:
You have to apply Tangent Rule, tanθ = opposite/adjacent:
[tex] \tan(θ) = \frac{oppo.}{adj.} [/tex]
[tex]let \: oppo. = 5 \\ let \: adj. = b \\ let \: θ = 30[/tex]
[tex] \tan(30) = \frac{5}{b} [/tex]
The correct answer is option (A) tan(30)=5/b
Tangent functionThe tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.How to solve this problem?The steps are as follow:
The right angle triangle is given whose sides are as follow:AB = 10 cm
BC = 5 cm
AC = b cm
To find the tan(30) we will use following formula:tan(x) = opposite side / adjacent side
tan(30) = BC / AC
tan(30) = 5 / b
So, the correct answer is option (A) tan(30)=5/b
Learn more about Tangent function here:
https://brainly.com/question/6904750
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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
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:
5. There are 400 students in the senior class at Oak Creek High School. All 2 points
of these students took the SAT. The distribution of their SAT scores is
approximately normal. The number of students who scored within 2
standard deviations of the mean is approximately *
-3
-2
0
1
2.
3
Answer:
The number of students who scored within 2 standard deviations of the mean is 380.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
The number of students who scored within 2 standard deviations of the mean is approximately
By the Empirical Rule, 95% of the students scored within 2 standard deviations of the mean
Out of 400
0.95*400 = 380
The number of students who scored within 2 standard deviations of the mean is 380.
Answer: 380
Step-by-step explanation: 95% of 400 is 380
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
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.
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.)
I Need help ASAP!!!
Answer:
x = 15, AOB = 15, BOC = 165
Step-by-step explanation:
Assume that this is a straight line
2x - 15 + 11x = 180
Combine like terms
13x - 15 = 180
Add 15 on both sides
13x = 195
Divide 13 on both sides
x = 15
Substitute x for 15 in both equations
2(15) - 15 = 15
11(15) = 165
(For checking purposes, 165 + 15 = 180)
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.
the sum of the measures of the angles of any triangle is 180 degrees. in triangle ABC, angles A and B have the same measure, of bile the measure of angle C is 72 degrees larger than each of A and B. what are the measures of the three angles?
Answer:
A=36
B=36
C=108
Step-by-step explanation:
A =B
2A+C=180
C is greater than A
2A+(A+72) =180
SIMPLIFY
3A +72=180
-72 ON BOTH SIDES
3A=108
DIVIDE BY 3
A=36
SO
B=36
36 TIMES 2 IS 72
180-72=108
SO
C=108
hope this helps
Answer:
Angle C= 108
Angles A and B=36
Step-by-step explanation:
180-72=108
108-72= 36
Check
36+36=72
72+108=180
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
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
When renting a car two options listed below are given. You need the car for 3 days. How many miles must you travel in order for option 2 to be the better option? Tell me your variable and what it represents. Then use that variable to set up an equation for each option. Graph each line and use the graph to answer the question. You will need to upload a picture or screenshot of your graphs.
Answer:
it´s b
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
A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 80 businesses at random. Of these, 46 return the questionnaire mailed by the committee.
a) What is the population for this sample survey?
The population in this situation is _______ (none, some, most, or all) of the __________(local business or college students) .
b) What is the sample?
The sample is the ______(enter exact number) of ___________ (local business or college students) selected.
c) What is the rate (percent) of nonresponse?
Answer:
a) The population population in this situation is all the local business
b) The sample is the 80 of local business selected.
c) The rate of nonresponse is 42.5%.
Step-by-step explanation:
Sampling
This is a common statistics practice, when we want to study something from a population, we find a sample of this population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
The population for this survey is all New York State residents, while the sample are the 1000 New York State residents.
From telephone book listings, the committee chooses 80 businesses at random.
Survey: 80 businesses.
Population: All businesses in the college town.
Then
a) What is the population for this sample survey?
The population population in this situation is all the local business
b) What is the sample?
The sample is the 80 of local business selected.
c) What is the rate (percent) of nonresponse?
80 - 46 = 34 non-responses, out of 80
34/80 = 0.425
0.425*100 = 42.5%
The rate of nonresponse is 42.5%.
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:
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
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]
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
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
Laura placed a bucket of water in her garden. Over the course of a week, she watched the water evaporate and recorded the volume of water left in the bucket each day.
Laura found the linear model that best fit the data was V=5.00−0.25n, where n is the number of days since she first placed the bucket and V is the volume of water, in liters, remaining in the bucket.
How many liters of water evaporated from the bucket every day?
How may liters where inside the bucket when Laura first placed it in the garden?
Answer:
1. 0.5 L; 2. 5.00 L
Step-by-step explanation:
V = 5.00 - 0.5n
If you include units, the equation becomes
V(in litres) = 5.00 L - (0.5 L/day) × (n days)
1. Rate of evaporation
When you include the units, it becomes easier to see that the water is evaporating at a rate of 0.5 L/day.
That is, 0.5 L of water evaporates each day.
The negative sign shows that the volume of water is decreasing.
2. Volume at the beginning
At the beginning of the experiment, n = 0. Then
V = 5.00 -0.5×0 = 5.00 - 0 = 5.00 L
The bucket originally contained 5.00 L of water.
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.
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
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]
2- = - 6 – 4.0
Solve for x:
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.
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.
