Answer:
Normality assumptions are met.
The 90% confidence interval for the proportion of adult drivers that run at least one red light in the last month is (0.4892, 0.5356).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
A poll is conducted on a simple random sample of adult drivers and it is found that out of 1251 adult drivers, 641 of them have run at least one red light in the last month.
This means that [tex]n = 1251, \pi = \frac{641}{1251} = 0.5124[/tex]
Normality assumptions:
We need that: [tex]n\pi \geq 10, n(1-\pi)\geq 10[/tex]
We have that:
[tex]n\pi = 1251*0.5124 = 641[/tex]
[tex]n(1-\pi) = 1261*0.4876 = 610[/tex]
So normality assumptions are met.
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5124 - 1.645\sqrt{\frac{0.5124*0.4876}{1251}} = 0.4892[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5124 + 1.645\sqrt{\frac{0.5124*0.4876}{1251}} = 0.5356[/tex]
The 90% confidence interval for the proportion of adult drivers that run at least one red light in the last month is (0.4892, 0.5356).
This box is being packed without gaps or overlaps with unit cubes. Enter the volume of this box in cubic units.
Answer: 56
Step-by-step explanation:
Volume = length x width x height
You can find the length width and height by counting the cubes.
7x4x2= 56 cubic units
Answer:
56
Step-by-step explanation:
Help pleaseeeeeeee thanks
Answer:
so the answer is 5
Step-by-step explanation:
the equation will be for this is
7x + 20 = 55
7x = 55-22
7x = 35
x = 35÷7
x=5
Combine as indicated by the signs.
2x/y^2-x^2-x/y-x=
Answer:
x(2-xy^2-y-y^2)/y^2
Step-by-step explanation:
It mabye the above answer so x
y ^2 - 4 x y ^3
The expression will be simplified as [tex]\dfrac{x^2+2x-xy}{y^2-x^2}[/tex].
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The expression will be simplified as follows:-
[tex]\dfrac{2x}{y^2-x^2}-\dfrac{x}{y-x} = \dfrac{2x-x(y-x)}{y^2-x^2}\\\\[/tex]
[tex]=\dfrac{2x-xy+x^2}{y^2-x^2}[/tex]
[tex]= \dfrac{x^2+2x-xy}{y^2-x^2}[/tex]
Therefore the expression will be simplified as [tex]\dfrac{x^2+2x-xy}{y^2-x^2}[/tex].
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Is it 2 or 3?
Thank you!
Answer:
3
Step-by-step explanation:
Each of 5 friends got a full box of snacks and an extra 6 snacks. Write an equation to show how many snacks are in all those boxes and all those extra snacks.
need help
give explanation and i’ll give brain list
Answer:
x = 14.5°
Step-by-step explanation:
A+D = 180°
(8x-11) + (5y+2) = 180°
simplify:
5y + 8x = 189°
5y = 189 - 8x
D = B
(5y+2) = (4x+17)
simplify
5y = 4x + 15
then:
189 - 8x = 4x + 15
12x = 174
x = 14.5°
5y = 4(14.5) + 15
5y = 73
y = 14.6
check:
5(14.6) + 8(14.5) = 189
73 + 116 = 189
189 = 189
-3x + 7 = -x - 1
What is the variable
Answer:
x = 4
Step-by-step explanation:
also nice pfp d====(￣▽￣*)b
how much is 1 hundred of R800
The number of vinyl album sales (in millions) in a country x years after 2010 can be modeled by y = 0.1242 + 0.32 +3.3
for 2010 through 2016. Use this model to predict the number of vinyl album sales in the country in the year 2020 where
(2 = 10) (1 point)
• The number of vinyl album sales in the country in the year 2020 will be 20.5 million
The number of vinyl album sales in the country in the year 2020 will be 18.3 million
The number of vinyl album sales in the country in the year 2020 will be 7.74 million
O The number of vinyl album sales in the country in the year 2020 will be 21.12 million
Answer:
b) The number of vinyl album sales in the country in the year 2020 will be 18.3 million.
Step-by-step explanation:
Given - The number of vinyl album sales (in millions) in a country x years after 2010 can be modeled by y = 0.12 x² + 0.3 x +3.3 for 2010 through 2016.
To find - Use this model to predict the number of vinyl album sales in the country in the year 2020 where x = 10
a) The number of vinyl album sales in the country in the year 2020 will be 20.5 million.
b) The number of vinyl album sales in the country in the year 2020 will be 18.3 million.
c) The number of vinyl album sales in the country in the year 2020 will be 7.74 million.
d) The number of vinyl album sales in the country in the year 2020 will be 21.12 million.
Proof -
Given that,
The equation be - y = 0.12 x² + 0.3 x +3.3
Now,
Put x = 10 in above equation we get
y = 0.12×10² + 0.3×10 +3.3
= 0.12×100 + 3 + 3.3
= 12 + 6.3 = 18.3
⇒y = 18.3
∴ we get
The number of vinyl album sales in the country in the year 2020 will be 18.3 million.
So,
The correct option be - b) The number of vinyl album sales in the country in the year 2020 will be 18.3 million.
Find the slope and the y-intercept of the line. 2 y=- x+2 5
help please I need it now
Answer: Y = -x/2 + 12.5
Step-by-step explanation:
You wrote the equation strange so i don't really know if the end of the equation is a 25 or not
Exit Ticket
A map of Froggy Mountain Park is mapped on a coordinate plane
using units of one mile. There are two camp ground at the park.
Camp 1 is located at (-41, 3)
Camp 2 is located at (75,3)
How far is Camp 1 from Camp 2?
Show your work
Answer:
116 miles
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-41,3)[/tex] --- Camp 1
[tex](x_2,y_2) = (75,3)[/tex] --- Camp 2
Required
The distance between both camps
This is calculated using:
[tex]d^2 = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}[/tex]
[tex]d^2 = \sqrt{(-41-75)^2 + (3-3)^2}[/tex]
[tex]d^2 = \sqrt{(-116)^2 + (0)^2}[/tex]
[tex]d^2 = \sqrt{116^2}[/tex]
[tex]d = 116[/tex]
The distance is 116 miles
You know that in a specific population of rainbow trout 15% of the individuals carry intestinal parasites. Assume you obtain a random sample of 9 individuals from this population:a. Calculate the probability that __ (last digit of your ID number) carry intestinal parasites.b. Calculate the probability that at least two individuals carry intestinal parasites.
Answer:
a) 0.2316 = 23.16% probability that 0 carry intestinal parasites.
b) 0.4005 = 40.05% probability that at least two individuals carry intestinal parasites.
Step-by-step explanation:
For each trout, there are only two possible outcomes. Either they carry intestinal parasites, or they do not. Trouts are independent. This means that we use the binomial probability distribution 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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
You know that in a specific population of rainbow trout 15% of the individuals carry intestinal parasites.
This means that [tex]p = 0.15[/tex]
Assume you obtain a random sample of 9 individuals from this population:
This means that [tex]n = 9[/tex]
a. Calculate the probability that __ (last digit of your ID number) carry intestinal parasites.
Last digit is 0, so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{9,0}.(0.15)^{0}.(0.85)^{9} = 0.2316[/tex]
0.2316 = 23.16% probability that 0 carry intestinal parasites.
b. Calculate the probability that at least two individuals carry intestinal parasites.
This is
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{9,0}.(0.15)^{0}.(0.85)^{9} = 0.2316[/tex]
[tex]P(X = 1) = C_{9,1}.(0.15)^{1}.(0.85)^{8} = 0.3679[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.2316 + 0.3679 = 0.5995[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.5995 = 0.4005[/tex]
0.4005 = 40.05% probability that at least two individuals carry intestinal parasites.
We will see that the probabilities are:
a) 3.8*10^-8b) 0.26How to find the probability.
We know that 15% of the population have the parasites, then if we take a trout at random we have:
a probability of 0.15 that it has parasites.a probability of 0.85 that it does not have parasites.a) The probability that 9 of them carry intestinal parasites (so all of them have).
This is just the product of the individual probabilities, so we have 9 times a probability of 0.15, this gives:
P(9) = (0.15)^9 = 3.8*10^-8
b) Probability that 2 out of 9 have parasites.
Then we have 0.15 two times, and 0.85 seven times.
But we also need to take in account the permutations, the different groups of 2 trouts that we can make out of 9 trouts is given by:
[tex]C(9, 2) = \frac{9!}{(9-2)!*2!} = \frac{9*8}{2} = 36[/tex]
This means that there are 36 different pairs of 2 trouts that can be the ones with parasites.
Then the probability that 2 trouts have parasites is:
P(2) = 36*(0.15)^2*(0.85)^7 = 0.26
And just to be complete, the probabilty that x trouts have parasites is:
P(x) = C(9, x)*(0.15)^x*(0.85)^(9 - x)
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HELPP!!!! YOU'LL GET 80 POINTS AND BE BRAINLIEST
The city of El Paso is three hundred and twenty miles from the city of Tucson, Arizona, and seven hundred and twenty miles from San Diego, California. Tomorrow I'm going to travel from Tucson to San Diego. I plan to leave Tucson at six in the morning. If I drive 75 miles per hour the first four hours and 50 miles per hour the rest of the way, what time (Tucson time) will I get to San Diego?
We have that El Paso is 320 miles from Tucson and 720 miles from San Diego.
You're travelling from Tucson to San Diego.
First we have to find the distance from Tucson to San Diego. We can do this by finding the difference between the distance of Tucson from San Diego and El Paso from San Diego.
That is:
720−320
400 miles
You leave by 6:00 am.
You drive for 75 miles per hour in 4 hours for the first part of the journey.
You then drive for 50 miles per hour for the rest of the journey.
The first step is to find the distance that the rest of the journey took. We can do that by first finding the distance covered in the first part of the journey and subtracting that from the total distance (400 miles).
To find the distance for the first part of the journey, we apply the formula for speed (rate of change of distance with time):
s = d/t
⇒d = s⋅t
where d= distance; t = time
Therefore:
d=75⋅4
d=300 miles
The first part of the journey covered 300 miles. This means that the rest of the journey covered:
400 - 300 = 100 miles
Now, to find the time the rest of the journey took, we have to apply the same formula for speed:
s=d/t
t=d/s
Therefore:
t=100/50
t=2 hrs
To find the total time it took to complete the journey, we have to add the times for the first part and the rest of the journey.
That is:
T=4+2
T=6 hours
Since you left home by 6:00 am, the time you will get to San Diego is 6 hours after that, i.e. 12 noon (Tucson time)
That is the answer.
Please...I really need help
Answer: it’s the first one
Step-by-step explanation:
9514 1404 393
Answer:
(d) g(x) = -f(x -3)
Step-by-step explanation:
Reflection over the x-axis multiplies function values by -1. Translation to the right 3 units replaces x with x-3. The transformed function is ...
g(x) = -f(x -3)
(b)
Part B
What is the exact amount of fruit salad in cups?
cups
Enter your answer as a fraction or a mixed number.
The sum of four numbers is 540. One of the
numbers, x, is 50% more than the sum of the other
three numbers. What is the value of x?
Answer:
chale. necesita. 20 caracteres
Plot the points where the x coordinate is twice the value of the y coordinate.
GIVING BRAINLIEST
Answer:
Heres brainliest for who answered first
Step-by-step explanation:
Can you help me on question six
Answer:
B
promise it's B trust me
Please help quick explain
Answer:
Step-by-step explanation:
3/5, 12/20
PLEASE HELP PLESD PLED
Answer:B
Step-by-step explanation: ok its B because i need some $$$
Answer:
D and E
Step-by-step explanation:
The question asks which one would always form an image that is congruent to the pre-image.
Note that Translation, Reflection, and Rotation do not change the size or shape of the pre-image while Dilation will change the size of your pre-image.
Therefore, the most likely answer would be options D and E that do not include dilation in their series of transformations so the image will not change its size making it congruent to the pre-image.
How are .4 and .04 different
Answer: .4 is in the tenths column and .04 is in the hundredths column and
.4 is 40% and .04 is 4% and .4 is 2/5 and .04 is 1/25 so .4 is larger then .04 and .4 is 2:5 and .04 is 1:25
Step-by-step explanation: plz mark me brainliest.
How to mark brainliest
___________________
Click on the crown on the bottom right of an answer if there is no crown reload the page
Answer:
Well .4 is bigger then .04. 0.4 is equal to 2/5 and 0.04 is equal to 1/25
Step-by-step explanation:
The population of a bacterium doubles every hour. At 9 am, the population is 12 bacteria. The function P (t) = 12.2 models the bacteria population t hours after 9 am What is the value of P (5) and what does it
represent in context?
A) The population is 120 bacteria at 2 pm
B)The population is 120 bacteria at 5 pm
C) The population is 384 bacteria at 2 pm
D) The population is 384 bacteria at 5p.m.
Answer: B
Step-by-step explanation:
The correct answer is B
The population of the bacteria at the value of P (5) is 384, and it represents that the time is 5 pm
What is an exponential function?Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=a^x[/tex]
Here, a is the variable in the power of a number.
The population of a bacterium doubles every hour. At 9 am, the population is 12 bacteria.
The function models the bacteria population t hours after 9 am is,
[tex]P (t) = 12\times2^t[/tex]
Put the value of t as 5 at P (5) in the above exponential function as,
[tex]P (5) = 12\times2^5\\P(5)=12\times32\\P(5)=384[/tex]
Hence, the population of the bacteria at the value of P (5) is 384, and it represents that the time is 5 pm.
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You and your friend each deposit $50 in separate savings accounts. Your account earns 4% simple annual interest. Your friend’s account earns 6% simple annual interest. How long does it take for you to earn $12 in interest? How long does it take for your friend to earn $12 in interest?
Marcy sees a game, Rolling-in-Gold, in which a contestant rolls a
cube with five red sides one gold side. A player wins the game
by rolling a gold. Is Rolling-in-Gold a fair game? If not, how
could the game be made fair? Explain.
Answer:
it's not fair, because it's only a 1 in 6 chance of rolling gold.
it would be fair if 3 of the 6 sides were gold
Answer:
it aint fair it only 1/6 listen to the other guy
Step-by-step explanation:
i needed points sorry
Why does the quotient of 8 ÷ 1 not change when we add a place value in the dividend and the divisor to make 80 ÷ 10?
Answer:
Basically this is because division can be thought of as how many times does the divisor have to be multiplied in order to produce the dividend.
So you would need to multiply 1 8 times in order to produce the dividend,
Similarly, 10 goes into 80 8 times. The zeros are simply cancelled out in the division.
Question Help Estimation Acar takes 70.3 seconds to travel 1 mile. How long does it take the car to travel 6.6 miles? First round to the nearest whole number to find the estimated answer. Then find the exact answer. Estimate the answer. It takes the car about seconds to travel 6.6 miles.
Answer:
Estimated time = 490 seconds
Exact time = 463.98 seconds
Step-by-step explanation:
The car traveled 1 mile in 70.3 seconds.
We want to find how long it took to travel 6.6 miles.
We are told to estimate the given values to the nearest whole numbers before solving.
Thus;
1 mile was travelled in 70 seconds
Then; 6.6 miles ≈ 7 miles
Thus, 7 miles is travelled in; 70 × 7/1 = 490 seconds
Estimated time = 490 seconds
Now, exact time will be;
Exact time = 70.3 × 6.6/1
Exact time = 463.98 seconds
The maximum weight M that can be supported by a beam is jointly proportional to its width w in inches and the square of its height h in inches and inversely proportional to its length L in feet. (a) Write an equation that expresses this proportionality. (Use k as the constant of proportionality.) (b) Determine the constant of proportionality if a beam 4 in. wide, 6 in. high, and 15 ft long can support a weight of 3840 lb. k
Answer:
M = kwh^2/L
k = 400
Step-by-step explanation:
Given that the maximum weight M that can be supported by a beam is jointly proportional to its width w in inches and the square of its height h in inches and inversely proportional to its length L in feet
Then
M ∝ wh^2/L
M = kwh^2/L
where k is the constant of proportionality
if a beam 4 in. wide, 6 in. high, and 15 ft long can support a weight of 3840 lb then
3840 = k * 4 * 6^2/15
k = 3840 * 15 / (4 * 36)
k = 400
Suppose that the mean of your 50 rolls is x = 3.25. Are you suspicious about the fairness of the die? Justify your answer.
Answer:
3.25x50=21
Step-by-step explanation:
Sample size falls within the range from the mean Standard deviation (3.5±1.75).
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Given, Suppose that the mean of your 50 rolls is x = 3.25.
Uniform distribution. linear Shape according to the Central lamed Theorem the distribution will be q Normal distribution of of xi; with Mean Rx = 3.5 if the sample Size is large enough and a variance of (1.71)²/N. Where N is the sample size 3.25 falls within the interval of the 95% confidence Sample means and it also falls within the range from the mean Standard deviation (3.5±1.75). This result is nothing suspicious of out of the ordinaryTherefore, Sample size falls within the range from the mean Standard deviation (3.5±1.75).
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Complete question:
review the graph. What is the component form and direction of the vector shown
a.) ⟨7,-3⟩ and 23 degrees
b.) ⟨-7,3⟩ and 23 degrees
c.) ⟨7,-3⟩ and 157 degrees
d.) ⟨-7,3⟩ and 157 degrees
Answer:
D
Step-by-step explanation:
Ed2021
Three vertices of parallelogram DEFG are D(-4,-2), E(-3,1) and F(3, 3). Find the coordinates of G.
The coordinates of G are
Answer:
Coordinates of G = [tex](2,0)[/tex]
Step-by-step explanation:
Given: Three vertices of parallelogram DEFG are D(-4,-2), E(-3,1) and F(3, 3).
To find: coordinates of G
Solution:
Midpoints of a side joining points [tex](a,b),\,(c,d)[/tex] are given by [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
Diagonals of a parallelogram bisect each other.
So,
Midpoint of DF = Midpoint of EG
Midpoint of DF = [tex](\frac{-4+3}{2},\frac{-2+3}{2})=(\frac{-1}{2},\frac{1}{2})[/tex]
Midpoint of EG = [tex](\frac{-3+x}{2},\frac{1+y}{2})[/tex]
Let coordinates of G be [tex](x,y)[/tex]
Therefore,
[tex](\frac{-1}{2},\frac{1}{2}) =(\frac{-3+x}{2},\frac{1+y}{2})\\\\\frac{-1}{2}=\frac{-3+x}{2},\,\frac{1}{2}=\frac{1+y}{2}\\\\-1=-3+x,\,1=1+y\\\\x=-1+3,\,y=1-1\\x=2,\,y=0[/tex]
So,
Coordinates of G = [tex](2,0)[/tex]