Answer:
it would be A 1251
Step-by-step explanation:
The question involves hypothesis testing of proportions. Based on a sample where 80% favour Candidate A, we may infer the true population proportion is significantly greater than 75%, however, actual mathematical calculations are needed for confirmation.
Explanation:The question examines whether the proportion of the population favouring Candidate A is significantly more than 75% based on a sample of 100 people where 80 favoured Candidate A. This is a problem of hypothesis testing for proportions. The null hypothesis (H₀) is that the true population proportion is 75% (p = 0.75), versus the alternative hypothesis (H₁) stating the true population proportion is more than 75%. Using a significance level of 0.05, we examine the data.
With a sample proportion of 80 out of 100 (p' = 0.80) and given the large sample size, we apply the Normal approximation to the Binomial distribution, followed by a one-sample z-test. If the resulting p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the true population proportion of individuals favouring Candidate A is significantly greater than 75%.
However, without performing the actual calculations, we cannot definitively determine the conclusion. From a practical perspective, an 80% sample proportion showing favour in a sample as large as 100 might indicate a significantly higher proportion than 75%, but an exact mathematical test should be done to confirm this.
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Your jewelry business orders $1320 in supplies each month. In each month, you can usually sell an earring/ring set for about $55 each. How many sets do you need to sell each month to break even?
If you found that your total profit for a month was $715, how many sets did you sell?
If you had a month where 7 sets were sold, how much profit did you make?
Answer:
Given,
The jewelry business orders $ 1320 in supplies each month.
That is, the invested amount = $ 1320,
Also, the selling price of each earring/ring set = $ 55,
Part 1 : Let x be the number of set that have been sold each month to break even ( in which revenue and invested amount are equal )
So, Total revenue ( the cost of x sets) = 55x,
⇒ 55x = 1320
Divide both sides by 55,
We get,
x = 24
Hence, 24 sets are needed to sell each month to break even.
Part 2 : Let y be the number of sets in which the profit is $ 715,
Total revenue = 55x
Profit = Total revenue - invested amount
⇒ 55x - 1320 = 715,
⇒ 55x = 715 + 1320
⇒ 55x = 2035
⇒ x = 37
Hence, 37 sets are sold for the total profit of $715.
Part 3 :
Revenue in selling 7 sets = 55 × 7 = $ 385
Profit = $ 385 - $ 1320 = - $ 935
Hence, the profit is - $ 935 after selling 7 sets.
A company is considering a new manufacturing process. It knows that the rate of savings (in dollars per year) from the process will be about S(t) = 3000(t+2), where t is the number of years the process has been in use. Find the total savings during the first year. Find the total savings during the first 5 years. . The total savings during the first year is S (Simplify your answer.)
Answer:
i). [tex]\$ 7500[/tex]
ii).[tex]\$ 67500[/tex]
Step-by-step explanation:
Given in the question-
Saving rate is s(t)= 3000(t+2)
We know that savings in the 1st year can be calculated as
[tex]\int_{0}^{1}3000(t+2).dt[/tex]
[tex]3000\left [ \frac{t^{2}}{2}+2t \right ]_0^1[/tex]
[tex]3000\left [ \frac{1}{2}+2 \right ][/tex]
= [tex]\$ 7500[/tex]
So savings in the first 5 years can be calculated as
[tex]\int_{0}^{5}3000(t+2).dt[/tex]
[tex]3000\left [ \frac{t^{2}}{2}+2t \right ]_0^5[/tex]
[tex]3000\left [ \frac{25}{2}+5 \right ][/tex]
= [tex]\$ 67500[/tex]
Basing your answer on the appearance of the figures below, identify whether the mathematical expression is true or false.
ΔROB ≅ ΔDFE
True or False
Answer:
The mathematical expression is false
Step-by-step explanation:
* Lets use the figure to answer the question
- There are four triangles in the figure
- Δ ROB and Δ PTA appear congruent because:
# The side RO appears equal the side PT
∴ RO ≅ PT
# The side OB appears equal the side TA
∴ OB ≅ TA
# The side RB appears equal the side PA
∴ RB ≅ PA ⇒ SSS
∴ Δ ROB ≅ Δ PTA
- Δ DEF and Δ YXW appear congruent because:
# The side DE appears equal the side YX
∴ DE ≅ YX
# The side EF appears equal the side XW
∴ EF ≅ XW
# The side DF appears equal the side YW
∴ DF ≅ YW
∴ Δ DEF ≅ Δ YXW ⇒ SSS
- Δ ROB and Δ DEF have different shapes and sizes
∵ Δ ROB not appear congruent to Δ DEF
∴ Δ ROB ≠ Δ DEF
∴ The mathematical expression is false
Answer : The mathematical expression is false.
Step-by-step explanation :
As we are given 4 triangles in which ΔROB & ΔPTA and ΔDEF & ΔYXW are appears congruent.
First we have to show that ΔROB and ΔPTA appear congruent.
Side RO appears equal to Side PT
Side OB appears equal to Side TA
Side RB appears equal to Side PA
∴ ΔROB ≅ ΔPTA (by SSS)
Now we have to show that ΔDEF and ΔYXW appear congruent.
Side DE appears equal to Side YX
Side EF appears equal to Side XW
Side DF appears equal to Side YW
∴ ΔDEF ≅ ΔYXW (by SSS)
According to given expression, ΔROB and ΔDEF have different shapes and sizes.
So, ΔROB not appear congruent to ΔDEF
Therefore, the mathematical expression is false.
A participant in a cognitive psychology study is given 50 words to remember and later asked to recall as many of the words as she can. She recalls 17 words. What is the (a) variable, (b) possible values, and (c) score?
Answer:
A participant in a cognitive psychology study is given 50 words to remember and she recalls 17 words.
So, here variable will be the number of words the participant can remember, out of 50.
The possible values can be the whole numbers 0, 1, 2, 3, 4, upto... 50.
And the score is 17. That is the score she remembers out of 50.
The people at a party tried to form teams with the same number of people on each team, but when they tried to split up into teams of 2, 3, 5, or 7, exactly one person was left without a team. What is the smallest amoutn of people who could have been at the party?
Answer:
211 people
Step-by-step explanation:
1. This is a least common multiple question, otherwise known as an LCM question. We know this because if the one extra person had not shown up to the party, all groups would have been formed evenly. This means the amount of people at the party is 1 more than a number 2, 3, 5, and 7 can go into.
2. We also know this is an LCM question because we are being asked for the smallest amount of people who could have possibly attended the party.
3. From this we know the amount of people at the party must be an odd number. If the number were even, there would have been no left over when groups of 2 were formed.
4. The amount of people at the party must end in a 1. This is because all multiples of 5 always end in a 0 or 5. Because there is on extra person, we must add 1 to all multiples of 5 we check. However, 5 + 1 is 6. This is a problem because 6 is an even number, and as we already established, the amount of people at the party must end in an odd number. So, we now know the smallest amount of people at the party will end in a 1.
5. Because we know the largest teams attempted to be formed with 1 left over is teams of 7 people, we only need to check multiples of 7. It is the largest number, so doing this will save us time.
6. Since we know the amount of people at the party must end in a 1, and we are only checking multiples of 7, we only need to check multiples of 7 that end in a 0. This is because any multiple of 7, 7 will go into evenly without a remainder. So we must add 1 to every multiple we check in order to make a remainder of 1. The only number we can add 1 to in order to get 1 is 0, so we only need to check multiples of 7 that end in 0. The only multiples of 7 that end in a 0 are when 7 is multiplied by a ten, ex: 10, 20, 30, 40, 50, ect.
7. Only searching for odd numbers, numbers that end in 1, and multiples of 7 means we only have to check if any possible answer when divided by 3 has a remainder of 1. We only have to check by the number 3 because any number ending in 1 will automatically have a remainder of one for 2 and 5, and because we are using multiple of 7 we don't need to check through 7.
8. Now that we know all our rules, all we need to do is list multiples of 7 that end in 0. Then we will add 1 to them and check to see if they have a remainder of 1 when divided by 3.
Using these rules will narrow our search drastically.
Applicable multiples of 7
(7 × 10) = 70 → 70 + 1 = 71 → 71/3 = 23 R2 → not possible
(7 × 20) = 140 → 140 + 1 = 141 → 141/3 = 47 → not possible
(7 × 30) = 210 → 210 +1 = 211 → 211/3 = 70 R1 → possible
The smallest possible amount of people at the party is 211.
Final answer:
The smallest amount of people who could have been at the party is 210.
Explanation:
To find the smallest amount of people who could have been at the party, we need to find the least common multiple (LCM) of the numbers 2, 3, 5, and 7. The LCM is the smallest number that is divisible by all of the given numbers without leaving a remainder.
Prime factorize each of the given numbers:Therefore, the smallest amount of people who could have been at the party is 210.
Solve y''+2y' - 3y = 0, y(0) = 3, y'(0) = 11 Preview y(t) = |2e^(-3t)+5e^t Points possible: 1 This is attempt 3 of 3 Score on last attempt: 0. Score in gradebook: 0 License Submit
[tex]y''+2y'-3y=0 [/tex]
Second order linear homogeneous differential equation with constant coefficients, ODE has a form of,
[tex]ay''+by'+cy=0[/tex]
From here we assume that for any equation of that form has a solution of the form, [tex]e^{yt}[/tex]
Now the equation looks like this,
[tex]((e^{yt}))''+2((e^{yt}))'-3e^{yt}=0[/tex]
Now simplify to,
[tex]e^{yt}(y^2+2y-3)=0[/tex]
You can solve the simplified equation using quadratic equation since,
[tex]e^{yt}(y^2+2y-3)=0\Longleftrightarrow y^2+2y-3=0[/tex]
Using the QE we result with,
[tex]\underline{y_1=1}, \underline{y_2=-3}[/tex]
So,
For two real roots [tex]y_1\neq y_2[/tex] the general solution takes the form of,
[tex]y=c_1e^{y_1t}+c_2e^{y_2t}[/tex]
Or simply,
[tex]\boxed{y=c_1e^t+c_2e^{-3t}}[/tex]
Hope this helps.
r3t40
ASAP PLEASE RESPOND
To win the game, Eitan has to roll a sum of 11 or more using two six-sided number cubes.
Asher has a better probability of winning than Eitan has. Which could be the outcome that Asher needs to win the game? Check all that apply.
rolling a sum of 4
rolling a sum of 9
rolling a sum that is less than 5
rolling a sum that is greater than 5 but less than 7
rolling a sum that is greater than 9 but less than 11
rolling a sum that is greater than 2 but less than 4
There are 36 total possible outcomes.
Rolling a sum of 11 or higher, there are 3 possible rolls, to make a 3/36 = 1/12 probability.
Rolling a sum of 4 there are also 3 possibilities, so the chance would be the same.
Rolling a sum of 9, there are 4 possibilities, which is a better chance.
Rolling a sum less than 5, there is 6 possibilities, which is a better chance.
Rolling greater than 5 but less than 7 means rolling a sum of 6, there are 5 chances, which is a better chance.
Rolling greater than 9 but less than 11, means rolling a 10, there are 3 possibilities, which is the same.
Rolling greater than 2 and less than 4 means rolling a 3, there are 2 possibilities, which is less.
The answers would be:
Rolling a sum of 9,
Rolling a sum less than 5
Rolling greater than 5 but less than 7
Answer:
B, C, D
Step-by-step explanation:
I got it right on Edg
On a single roll of a pair of dice, what are the odds against rolling a sum of 3? The odds against rolling a sum of 3 are nothing to nothing.
Answer: Odds against rolling a sum of 3 = 17:1
Step-by-step explanation:
On rolling a pair of dice,
Total number of outcomes = 6 × 6 = 36
Outcomes with a sum of 3:
there is only 2 outcomes whose sum is 3, that is, (1,2) and (2,1)
∴ Favorable outcome = 2
Unfavorable outcome = 34
Odds against refers to the ratio of unfavorable outcomes to the favorable outcomes
so,
odds against rolling a sum of 3 = [tex]\frac{unfavorable\ outcomes}{favorable\ outcomes}[/tex]
= [tex]\frac{34}{2}[/tex]
= 17:1
An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11.What is the μM ?• A. 8• B. 11• C. 25• D. 64
Answer: C. 25
Step-by-step explanation:
Given : The average rat (of this strain) can learn to run this type of maze in a box without any special coloring : [tex]\mu=25[/tex]
The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper= [tex]M= 11[/tex]
We know that the sampling distribution D is given by :-
[tex]\mu_D=\mu[/tex]
Similarly the mean of the distribution M in the given situation is given by :_
[tex]\mu_M=\mu=25[/tex]
The mean of the distribution M in the given situation is 25. Then the correct option is C.
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
An experimental psychologist is interested in whether the color of an animal's surroundings affects the learning rate.
He tests 16 rats in a box with colorful wallpaper.
The average rate (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution.
The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11.
We know that the sampling distribution D is given by
μD = μ
Similarly, the mean of the distribution M in the given situation is given by
μD = μ = 25
More about the normal distribution link is given below.
https://brainly.com/question/12421652
At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 20 knots and ship B is sailing north at 21 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
Step-by-step explanation:
I just found the answer and I hope that this helps :)!!
The rate at which the distance between the ships is changing at 4 PM depends on their velocities.
Explanation:To find the rate at which the distance between the ships is changing, we can use the concept of relative velocity. Let's consider ship B as the reference point. Ship A is moving west at 20 knots (which is equivalent to 20 nautical miles per hour), and ship B is moving north at 21 knots. The distance between the ships can be considered as the hypotenuse of a right triangle, with the velocities of the ships representing the triangle's sides.
Using the Pythagorean theorem, we can write the equation: d^2 = x^2 + y^2, where d is the distance between the ships, x is the velocity of ship A, and y is the velocity of ship B. We need to find the rate of change of d with respect to time (dt).
Taking the derivative on both sides of the equation with respect to time, we get: 2d * (dd/dt) = 2x * (dx/dt) + 2y * (dy/dt).
Substituting the given values, x = -20 knots (negative because ship A is moving west), y = 21 knots, and dx/dt = dy/dt = 0 (since ship B is not changing its velocity), we can solve for dd/dt, which represents the rate at which the distance between the ships is changing.
Therefore, dd/dt = 2x * (dx/dt) + 2y * (dy/dt) = 2 * -20 knots * 0 + 2 * 21 knots * 0 = 0.
Thus, the distance between the ships is not changing at 4 PM.
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Problem Page
Find the slope and the y -intercept of the line.
Write your answers in simplest form.
2x + 5y = -3
Answer:
slope -2/5
y-intercept -3/5
Step-by-step explanation:
Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.
Our goal is to write 2x+5y=-3 into y=mx+b to determine the slope and y-intercept.
So we need to isolate y.
2x+5y=-3
Subtract 2x on both sides:
5y=-2x-3
Divide both side by 5:
[tex]y=\frac{-2}{5}x-\frac{3}{5}[/tex]
Compare this to y=mx+b.
You should see m is -2/5 and b is -3/5
so the slope is -2/5 and the y-intercept is -3/5
Answer:
The slope is: [tex]-\frac{2}{5}[/tex] or [tex]-0.4[/tex]
The y-intercept is: [tex]-\frac{3}{5}[/tex] or [tex]-0.6[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
To write the given equation in this form, we need to solve for "y":
[tex]2x + 5y = -3\\\\5y=-2x-3\\\\y=-\frac{2}{5}x-\frac{3}{5}[/tex]
Therefore, you can identify that the slope of this line is:
[tex]m=-\frac{2}{5}=0.4[/tex]
And the y-intercept is:
[tex]b=-\frac{3}{5}=-0.6[/tex]
Solve the given linear Diophantine equation. Show all necessary work. A) 4x + 5y=17 B)6x+9y=12 C) 4x+10y=9
Answer:
A) (-17+5k,17-4k)
B) (-4+3k,4-2k)
C) No integer pairs.
Step-by-step explanation:
To do this, I'm going to use Euclidean's Algorithm.
4x+5y=17
5=4(1)+1
4=1(4)
So going backwards through those equations:
5-4(1)=1
-4(1)+5(1)=1
Multiply both sides by 17:
4(-17)+5(17)=17
So one integer pair satisfying 4x+5y=17 is (-17,17).
What is the slope for this equation?
Let's put it in slope-intercept form:
4x+5y=17
Subtract 4x on both sides:
5y=-4x+17
Divide both sides by 5:
y=(-4/5)x+(17/5)
The slope is down 4 and right 5.
So let's show more solutions other than (-17,17) by using the slope.
All integer pairs satisfying this equation is (-17+5k,17-4k).
Let's check:
4(-17+5k)+5(17-4k)
-68+20k+85-20k
-68+85
17
That was exactly what we wanted since we were looking for integer pairs that satisfy 4x+5y=17.
Onward to the next problem.
6x+9y=12
9=6(1)+3
6=3(2)
Now backwards through the equations:
9-6(1)=3
9(1)-6(1)=3
Multiply both sides by 4:
9(4)-6(4)=12
-6(4)+9(4)=12
6(-4)+9(4)=12
So one integer pair satisfying 6x+9y=12 is (-4,4).
Let's find the slope of 6x+9y=12.
6x+9y=12
Subtract 6x on both sides:
9y=-6x+12
Divide both sides by 9:
y=(-6/9)x+(12/9)
Reduce:
y=(-2/3)x+(4/3)
The slope is down 2 right 3.
So all the integer pairs are (-4+3k,4-2k).
Let's check:
6(-4+3k)+9(4-2k)
-24+18k+36-18k
-24+36
12
That checks out since we wanted integer pairs that made 6x+9y=12.
Onward to the last problem.
4x+10y=9
10=4(2)+2
4=2(2)
So the gcd(4,10)=2 which means this one doesn't have any solutions because there is no integer k such that 2k=9.
Q8. the average Ferris wheel rotates at 6.9 miles per hour. What circular distance, in feet dose the average Ferris wheel cover in a 5 minutes ride?
Answer:
303.6 feet
Step-by-step explanation:
Given,
The average Ferris wheel rotates at 6.9 miles per hour.
So, the speed of the wheel = 6.9 miles per hour,
We know that,
Distance = Speed × Time
So, the distance covered by the wheel in 5 minutes ( or 1/12 hours because 1 hour = 60 minutes ) ride = [tex]6.9\times \frac{1}{12}[/tex]
[tex]=\frac{6.9}{12}[/tex]
[tex]=0.575\text{ miles}[/tex]
Since, 1 mile = 5280 feet,
Hence, the distance covered by the wheel in 5 minutes = 0.575 × 528 = 303.6 feet.
The average Ferris wheel covers a circular distance of 3024 feet in a 5-minute ride.
Explanation:To calculate the circular distance covered by the average Ferris wheel in a 5-minute ride, we need to convert the speed from miles per hour to feet per minute. There are 5,280 feet in a mile and 60 minutes in an hour, so we can convert 6.9 miles per hour to feet per minute using the formula:
6.9 miles/hour x 5,280 feet/mile x 1 hour/60 minutes = 604.8 feet/minute
Now that we know the Ferris wheel covers 604.8 feet in 1 minute, we can calculate the circular distance covered in 5 minutes by multiplying the feet per minute by the number of minutes:
604.8 feet/minute x 5 minutes = 3024 feet
Therefore, the average Ferris wheel covers a circular distance of 3024 feet in a 5-minute ride.
Industry standards suggest that 13 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday. (Round your mean answer to 2 decimal places and the other answers to 4 decimal places.) What is the probability that none of these vehicles requires warranty service
Answer: 0.1880
Step-by-step explanation:
The binomial distribution formula is given by :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
where P(x) is the probability of x successes out of n trials, p is the probability of success on a particular trial.
Given : The probability of new vehicles require warranty service within the first year : p =0.13.
Number of trials : n= 12
Now, the required probability will be :
[tex]P(x=0)=^{12}C_0(0.13)^{0}(1-0.13)^{12-0}\\\\=(1)(0.13)^{0}(0.87)^{12}=0.188031682201\approx0.1880[/tex]
Thus, the probability that none of these vehicles requires warranty service = 0.1880
A particular fruit's weights are normally distributed, with a mean of 353 grams and a standard deviation of 6 grams. If you pick one fruit at random, what is the probability that it will weigh between 334 grams and 344 grams?
Answer: 0.0660
Step-by-step explanation:
Given : A particular fruit's weights are normally distributed with
Mean : [tex]\mu=353\text{ grams}[/tex]
Standard deviation : [tex]\sigma=6\text{ grams}[/tex]
The formula to calculate the z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Let x be the weight of randomly selected fruit.
Then for x = 334 , we have
[tex]z=\dfrac{334-353}{6}=-3.17[/tex]
for x = 344 , we have
[tex]z=\dfrac{344-353}{6}=-1.5[/tex]
The p-value : [tex]P(334<x<353)=P(-3.17<z<-1.5)[/tex]
[tex]P(-1.5)-P(-3.17)=0.0668072-0.000771=0.0660362\approx0.0660[/tex]
Thus, the probability that it will weigh between 334 grams and 344 grams = 0.0660.
1.) Given P(E or F) = 0.82, P(E) = 0.18, and P(E and F) = 0.09, what is P(F)?
Answer:
p(F)=0.73
Step-by-step explanation:
we have by identity
[tex]p(A\cup B)=p(A)+p(B)-p(A\cap B)[/tex]
Thus for given events E and F
we have[tex]p(E\cup F)=p(E)+p(F)-p(E\cap F)[/tex]
Applying values we get
[tex]p(F)=p(E\cup F)+p(E\cap F)-p(E)[/tex]
Thus
p(F) = 0.82+0.09-0.18
p(F) = 0.73
The foreman of a bottling plant has observed that the amount of soda in each \16-ounce" bottle is actually a normally distributed random variable, with a mean of 15.9 ounces and a standard deviation of 0.1 ounce. If a customer buys one bottle, what is the probability that the bottle will contain more than 16 ounces
Answer: 0.1587
Step-by-step explanation:
Given : The foreman of a bottling plant has observed that the amount of soda in each 16-ounce bottle is actually a normally distributed random variable, with
[tex]\mu=15.9\text{ ounces}[/tex]
Standard deviation : [tex]\sigma=0.1\text{ ounce}[/tex]
Let x be the amount of soda in a randomly selected bottle.
Z-score : [tex]\dfrac{x-\mu}{\sigma}[/tex]
[tex]z=\dfrac{16-15.9}{0.1}=1[/tex]
The probability that the bottle will contain more than 16 ounces using standardized normal distribution table :
[tex]P(x>16)=P(z>1)=1-P(z<1)\\\\=1-0.8413447=0.1586553\approx0.1587[/tex]
Hence, the probability that the bottle will contain more than 16 = 0.1587
An auto license plate consists of 6 digits; the first three are any letter (from the 26 alphabets), and the last three are any number from 0 to 9. For example, AAA 000, ABC 123, and ZZZ 999 are three possible license plate numbers. How many different license plate numbers may be created?
Answer: There are 17576000 ways to generate different license plates.
Step-by-step explanation:
Since we have given that
Numbers are given = 0 to 9 = 10 numbers
Number of letters = 26
We need to generate the license plate numbers.
Since there are repetition allowed.
We would use "Fundamental theorem of counting".
So, the number of different license numbers may be created as given as
[tex]26\times 26\times 26\times 10\times 10\times 10\\\\=26^3\times 10^3\\\\=17576\times 1000\\\\=17576000[/tex]
Hence, there are 17576000 ways to generate different license plates.
Graph the function y = √ x + 4 – 2. Then state the domain and range of the function.
Answer:
Domain : [-4, ∞)
Range : [ -2, ∞)
Step-by-step explanation:
The given function is y = [tex]\sqrt{(x+4)}-2[/tex]
Domain of the given function will be
(x + 4) ≥ 0
[ Since square root of numbers less than 0 is not possible ]
Domain : x ≥ (-4)
Or [-4, ∞) will be the domain
Now range of the function will be x ≥ -2
[ -2, ∞) will be the range of the given function.
let A={2, 4, 6, 8} and B={2, 3, 5, 7, 9} compute n(A)
Answer with explanation:
Given two sets
A={2, 4, 6, 8} and B={2, 3, 5, 7, 9}
⇒n(S)=Cardinality of a set
Means the number of distinct elements in a Set is called it's cardinal number.
→In Set A,total number of distinct elements is 4.
n(A)=4
It is 76 miles from Waterton to Middleton. It is 87 miles from Middleton to Oak Hill. Driving directly, it is 134 miles from Waterton to Oak Hill. It is 39 miles from Oak Hill to Jackson. If Juan drives from Waterton to Middleton, then from Middleton to Oak Hill, and finally home to Waterton, how many miles does he drive?
Answer: 297 miles
Step-by-step explanation:
The drive from Waterton to Middleton is 76 miles, from Middleton to Oak Hill is 87 miles, and from Oak Hill directly to Waterton it is 134 miles.
Then: [tex]76+87+134=297[/tex]
So Juan drives 297 miles.
Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for x from the first equation. Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0)=4 and y(0)=5, what are x and y?
The general solution of this differential equation is y(t) = c1 cos(5t) + c2 sin(5t), where c1 and c2 are constants determined by the initial conditions.
Differentiating the second equation with respect to t, we get: d^2y/dt^2 = -5 dx/dt, Substituting dx/dt from the first equation, we get: d^2y/dt^2 = -5(-5y) = 25y.
This is a second order differential equation in y. The general solution of this differential equation is y(t) = c1 cos(5t) + c2 sin(5t), where c1 and c2 are constants determined by the initial conditions.
To find x as a function of t, we can substitute y(t) into the first equation and solve for x: dx/dt = -5y = -5(c1 cos(5t) + c2 sin(5t)) , Integrating both sides with respect to t, we get: x(t) = -c1 sin(5t) + c2 cos(5t) + k
where k is a constant of integration. Using the initial conditions x(0) = 4 and y(0) = 1, we can solve for the constants c1, c2, and k: x(0) = -c1 sin(0) + c2 cos(0) + k = c2 + k = 4, y(0) = c1 cos(0) + c2 sin(0) = c1 = 1
Substituting c1 = 1 and c2 + k = 4 into the equation for x, we get:
x(t) = -sin(5t) + 4
So the solution to the system of differential equations with initial conditions x(0) = 4 and y(0) = 1 is x(t) = -sin(5t) + 4 and y(t) = cos(5t).
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1. A researcher is interested in studying whether or not listening to music while jogging makes people run faster. He thinks that listening to music will make people run faster. Luckily, he knows that, for the population he interested in (runners in Washington, DC), the mean running speed (μ) is 6mph, and the standard error is 2mph. He collects data from a sample of runners that only listen to music, and finds they have a mean running speed (M) of 9mph. No Sample Size givenA. State the hypothesisH0:H1:B. The researcher would like to conduct a One-Sample Z-test. Please calculate the Z-statistic (Z-obtained):
Step-by-step explanation:
1.Assuming the same sample size and considering the same value for the errors ( not taking into consideration the type of music, the volume of the sound and cow familiar the runner is with that type of stimuli, age group, time of the day/ number of days, running conditions like wether and equipment, distance) one can state:
A. Music has no influence over the running speed ( when jogging) in Washington DC
B.When listening to music, people ( in Washington DC) run faster while jogging
The mean running speed is a simple, ponderate or other type of mean ( that takes into consideration the variations of speed at the beginning and by the end of the race?
A tenth of a number in algebraic expression
Answer:
Step-by-step explanation: manej
Final answer:
In algebra, a tenth of a number is algebraically represented by multiplying the number by [tex]10^{-1}[/tex], which is equivalent to dividing the number by 10. This application of negative exponents simplifies expressions, especially in scientific notation, making it easier to work with large and small quantities.
Explanation:
In algebra, when we refer to a tenth of a number, we are usually dealing with fractions or exponential notation. A tenth of a number can be represented algebraically as the number divided by 10, which is the same as multiplying the number by [tex]10^{-1}[/tex]. This is because negative exponents indicate the reciprocal of a number; in other words, 10-1 equals 1/10 or 0.1.
This concept relates to the powers of ten and how each power of 10 affects the size of a number. For instance, 102 is 100, and 101 is 10, which is ten times smaller than 100. Conversely, 100 is 1, which is ten times smaller than 10, and thus, logically, [tex]10^{-1}[/tex] is 0.1, which is ten times smaller still. In expressing measurements in scientific work, especially for very small numbers, we frequently use this exponential form.
Thus, a tenth of an algebraic expression would mean multiplying the expression by [tex]10^{-1}[/tex] or dividing the expression by 10. This process is a form of simplification and re-scaling of numbers that are commonly used in scientific notation, which includes both positive and negative exponents. By understanding these principles, one can efficiently work with both large and small quantities in scientific and mathematical contexts.
If a 2-kg block compresses a spring 800mm from its relaxed state, how much potential energy does the block have due to the spring? Assume the spring constant, k = 25 N/m.
Answer:
8 Joule
Step-by-step explanation:
Mass of block = 2 kg
Displacement = x = 800 mm = 0.8 m
Spring constant = k = 25 N/m
Potential Energy of a spring
Work done = Difference in Potential Energy
Work Done = Δ P.E.
[tex]\Rightarrow \Delta\ P.E.=\frac{1}{2}kx^2[/tex]
⇒P.E. = 0.5×25×0.8²
⇒P.E. = 8 Nm = 8 Joule
Here already the spring constant and displacement is given so the mass will not be used while calculating the potential energy.
10. (Section 4.7) John filled his gas tank and noted that the odometer read 38,320.8 miles. After the next filling, the odometer read 38,735.5 miles. It took 14.5 gal to fill the tank. How many miles per gallon did John get?
Find the number of miles he drove by subtracting the odometer readings:
38735.5 - 38320.8 = 414.7 miles.
Now divide the number of miles driven by the number of gallons:
414.7 / 14.5 = 28.6 miles per gallon.
also find the measure of BEF as well
Answer:
∠ABC = 84°
∠BEF = 64°
Step-by-step explanation:
∠ABC is supplementary to the 96° angle shown, so is 180° -96° = 84°.
__
∠ABD, marked as (x+y)°, is a vertical angle with ∠EBC, so has the same measure, 96°. ∠BEF, marked as y°, is a vertical angle with the one marked 2x°.
These relationships can be expressed as two equations:
x + y = 962x = yUsing the second of these equations to substitute for y in the first equation, we have ...
x + 2x = 96
x = 96/3 = 32
y = 2x = 2·32 = 64 . . . . . . substitute the value of x into the second equation
Then ∠BEF = 64°.
Assume that women's heights are normally distributed with a mean given by mu equals 62.3 in, and a standard deviation given by sigma equals 2.4 in.(a) If 1 woman is randomly selected, find the probability that her height is less than 63 in.(b) If 47 women are randomly selected, find the probability that they have a mean height less than 63 in.
Answer: a) 0.6141
b) 0.9772
Step-by-step explanation:
Given : Mean : [tex]\mu= 62.3\text{ in}[/tex]
Standard deviation : [tex]\sigma = \text{2.4 in}[/tex]
The formula for z -score :
[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
a) Sample size = 1
For x= 63 in. ,
[tex]z=\dfrac{63-62.3}{\dfrac{2.4}{\sqrt{1}}}=0.29[/tex]
The p-value = [tex]P(z<0.29)=[/tex]
[tex]0.6140918\approx0.6141[/tex]
Thus, the probability is approximately = 0.6141
b) Sample size = 47
For x= 63 ,
[tex]z=\dfrac{63-62.3}{\dfrac{2.4}{\sqrt{47}}}\approx2.0[/tex]
The p-value = [tex]P(z<2.0)[/tex]
[tex]=0.9772498\approx0.9772[/tex]
Thus , the probability that they have a mean height less than 63 in =0.9772.
Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Compute the point estimate for the proportion of citizens who are in favor of gun control legislation. Round to four decimal places.
Answer: [tex]\hat{p}=0.5625[/tex]
Step-by-step explanation:
Given : Sample size : [tex]n=4000[/tex]
The number of people who are in favor of gun control legislation =2250
The proportion of people who are in favor of gun control legislation will be :-
[tex]p_0=\dfrac{2250}{4000}=0.5625[/tex]
We assume that the the given situation is normally distributed.
Then , the point estimate for the proportion [tex]\hat{p}[/tex] of citizens who are in favor of gun control legislation is equals to the sample proportion.
i.e. [tex]\hat{p}=0.5625[/tex]
Find a compact form for generating function of the sequence 1, 8, 27,.........., k^3,.........
The generating function is [tex]f(x)[/tex] where
[tex]f(x)=\displaystyle\sum_{k=0}^\infty a_kx^k[/tex]
with [tex]a_k=k^3[/tex] for [tex]k\ge0[/tex].
Recall that for [tex]|x|<1[/tex], we have
[tex]g(x)=\dfrac1{1-x}=\displaystyle\sum_{k=0}^\infty x^k[/tex]
Taking the derivative gives
[tex]g'(x)=\dfrac1{(1-x)^2}=\displaystyle\sum_{k=1}^\infty kx^{k-1}=\sum_{k=0}^\infty(k+1)x^k[/tex]
[tex]\implies g'(x)-g(x)=\dfrac x{(1-x)^2}=\displaystyle\sum_{k=0}^\infty kx^k[/tex]
Taking the derivative again, we get
[tex]g''(x)=\dfrac2{(1-x)^3}=\displaystyle\sum_{k=2}^\infty k(k-1)x^{k-2}=\sum_{k=0}^\infty(k^2+3k+2)x^k[/tex]
[tex]\implies g''(x)-3g'(x)+g(x)=\dfrac{x^2+x}{(1-x)^3}=\displaystyle\sum_{k=0}^\infty k^2x^k[/tex]
Take the derivative one last time to get
[tex]g'''(x)=\dfrac6{(1-x)^4}=\displaystyle\sum_{k=3}^\infty k(k-1)(k-2)x^{k-3}=\sum_{k=0}^\infty(k^3+6k^2+11k+6)x^k[/tex]
[tex]\implies g'''(x)-6g''(x)+7g'(x)-g(x)=\dfrac{x^3+4x^2+x}{(1-x)^4}=\displaystyle\sum_{k=0}^\infty k^3x^k[/tex]
So the generating function is
[tex]\boxed{f(x)=\dfrac{x^3+4x^2+x}{(1-x)^4}}[/tex]