Answer:
The answer is option B. 240
28.
Car A and car B are 120 km apart. If they move towards each other, they will meet in 1 hour. If they
move in the same direction, car A will catch up with car B in 5 hours. Find the speed of car A and
the speed of car B. (Assume that the speeds of the cars are constant.)
Suppose that a committee is studying whether there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours. Construct a 95% confidence interval for the population mean time wasted. Which distribution should you use for this problem
Answer:
The t-distribution is used, as we have the standard deviation of the sample.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
Step-by-step explanation:
We have the standard deviation for the sample, which meas that the t-distribution should be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 81 - 1 = 80
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.99
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.99\frac{4}{\sqrt{81}} = 0.88[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 8 - 0.88 = 7.12 hours.
The upper end of the interval is the sample mean added to M. So it is 8 + 0.88 = 8.88 hours.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
Aubree is going to invest $27,000 and leave it in an account for 10 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Aubree to end up with $39,000?
Answer:
3.7%
Step-by-step explanation:
simple
The distance around the outside of an apartment is 0.3 mile. Keira ran 0.1 of the distance during her lunch. How far did she run?
Answer:
0.1
Step-by-step explanation:
What is x(3x+2)?Please give a reasonable explaination and answer.
Answer:
3x squared + 2x as you multiply everything in the bracket by what's on the outside of the bracket so it would be 3x multiply by x which equals 3x squared and 2 multiply x which equals 2x
Answer:
3x^2+2x
Step-by-step explanation:
multiply each of the two terms by x using the distributive property
Two trains on opposite tracks leave the same station at the same
time. One train travels at an average speed of 80 kilometers per
hour and the other travels at an average speed of 70 kilometers
per hour. How long after they leave the station will they be 50
km apart?
Answer:
20 minutes( 0.3333 hours) after they leave the station will they be 50 km apart, if the Two trains on opposite tracks leave the same station at the same time.
Step-by-step explanation:
One train travels at an average speed of 80 km/hr and the other travels at an average speed of 70 km/hr.
Simplify: 17b + 82c + 90 + e - 18 - 10c - b
Can y’all help me on question 27?!
Answer:
B and D
Step-by-step explanation:
A would be:
57 + 2j
C would be:
13-t
In ΔVWX, x = 9.1 inches, w = 5.4 inches and ∠W=161°. Find all possible values of ∠X, to the nearest 10th of a degree
Answer:
NO POSSIBLE TRIANGLES
Step-by-step explanation:
Answer:
no possible triangles
Step-by-step explanation:
Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 7.2 minutes and a standard deviation of 2.1 minutes. For a randomly received emergency call, find the probability that the response time is between 3 and 9 minutes. (Round your answer to four decimal places.)
Answer:
0.7823 = 78.23% probability that the response time is between 3 and 9 minutes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal distribution with a mean of 7.2 minutes and a standard deviation of 2.1 minutes.
This means that [tex]\mu = 7.2, \sigma = 2.1[/tex]
Probability that the response time is between 3 and 9 minutes.
This is the pvalue of Z when X = 9 subtracted by the pvalue of Z when X = 3. So
X = 9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9 - 7.2}{2.1}[/tex]
[tex]Z = 0.86[/tex]
[tex]Z = 0.86[/tex] has a pvalue of 0.8051
X = 3
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3 - 7.2}{2.1}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.8051 - 0.0228 = 0.7823
0.7823 = 78.23% probability that the response time is between 3 and 9 minutes.
Find the perimeter of the following shapes
3.6 cm
3 cm
7.2 cm
Step-by-step explanation:
Perimeter = 3.6 + 3 + 702
= 708.6 cm
A cone in the diagram below has a radius (r) of 10mm and its height (h) is 24mm calculate the length of the slant height
Answer:
26mm
Step-by-step explanation:
by the Pythagorean theorem,
[tex]x^2=10^2+24^2\\x^2=676\\x=26[/tex]
Amath class has a total of 45 students. The number of males is 13 more than the number of females. How many males and
how many females are in the class
Number of males:
Number of females
Answer:
Males: 29
Females: 16
Step-by-step explanation:
2x+ 13 = 45
2x = 45 - 13
2x = 32
x = 16
16 + 13 = 29
29 +16 = 45
Please answer this :/
Answer:
-60
Step-by-step explanation:
-45+s=-105
s=-105+45
s=-60
Which would be a good estimate for the tax on $97.95 if the tax is 9.5%?
$12
$10.50
$10
$8.50
Help please!!!!!! I don't have a lot of time
Answer:
Its 5,...................
Answer:
5
Step-by-step explanation:
simplify the exponent
35/8-1
simplify
35/7
simplify
5
g The average midterm score of students in a certain course is 70 points. From the past experience it is known that the midterm scores in this course are Normally distributed. If 29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points, find the probability that the average midterm score of these students is at most 75 points. (Round your final answer to 3 places after the decimal point).
Answer:
0.98 = 98% probability that the average midterm score of these students is at most 75 points.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average midterm score of students in a certain course is 70 points.
This means that [tex]\mu = 70[/tex]
29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points.
This means that [tex]\sigma = 13.15, n = 29, s = \frac{13.15}{\sqrt{29}} = 2.44[/tex]
Find the probability that the average midterm score of these students is at most 75 points.
This is the pvalue of Z when X = 75. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{75 - 70}{2.44}[/tex]
[tex]Z = 2.05[/tex]
[tex]Z = 2.05[/tex] has a pvalue of 0.98.
0.98 = 98% probability that the average midterm score of these students is at most 75 points.
Noah has $5.
1.
a.
Elena has 40% as much as Noah. How much does Elena have?
b.
Compare Elena's and Noah's money using fractions. Draw a diagram to
illustrate.
Answer:
a. $4
b. Noah has 5/5. Elena has 4/5.
Step-by-step explanation:
Noah has $5.
a.
Elena has 80% of Noah's money.
80% of $5 = 0.80 * $5 = $4
b.
Noah has $5. We can consider $5 to be the full amount.
A full amount is 100% or 1 or 5/5.
Elena has 80% of Noah's money, so she has 80/100 of Noah's money.
80/100 reduces to 4/5.
Noah has 5/5, and Elena has 4/5.
The money that Elena has is $2.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
The given problem can be solved as follows,
(a) The amount of money Elena has is 40% of that of Noah.
It can be written as follows,
40% × 5
= 40/100 × 5
= 2
(b) Since the Elena has 40% of the Noah's money,
In the form of fraction it can be written as follows,
40% = 40/100
= 2/5
This can be represented in a diagram as follows,
In the diagram shown the circle has in total 5 sectors of which 2 yellow sectors represent Elena's money.
Hence, the amount of money Elena has is $2 which is shown in the diagram.
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can somebody help me solve for x.
Answer:
8/3
Step-by-step explanation:
x : 4 = 4 : 6
x = 16/ 6
x = 8/3
The measure of an angle is 149.5°. What is the measure of its supplementary angle?
Answer:
30.5°
Step-by-step explanation:
Supplementary angles add up to 180°. You know one angle is 149.5°, so you can find the other angle.
Measure of its supplementary angle = 180° - 149.5°
= 30.5°
Q1. If sinθ = 3/5 and cosθ = 4/5, Find the value of tanθ (Use Pythagorean Identity)
Q2. If sinθ = 3/5 and cosθ = 4/5, Find the value of tanθ (Use Trignometric Identity)
Step-by-step explanation:
[tex]sinθ = \frac{3}{5} \: \: cosθ = \frac{4}{5} \\ now \\ tanθ = \frac{sinθ}{cos θ } \\ = \frac{3}{5 } \div \frac{4}{5} \\ = \frac{3}{5} \times \frac{5}{4} \\ = \frac{3}{4} [/tex]
Hope it will help :)❤
Find b and c so that y =
2x^2 + bx+c has vertex (0,-2)
b=
C=
Answer:
Step-by-step explanation:
the measures of the angles of a triangle are shown in the figure below. solve for x
Answer:
Brainliest????
Step-by-step explanation:
X=23°
i need help ////////
Answer:
[tex]1\frac{1}{2}[/tex] miles = 7920 feet
2[tex]\frac{1}{2}[/tex] miles = 13200 feet
3[tex]\frac{1}{2}[/tex] miles = 18480 feet
4[tex]\frac{1}{2}[/tex] miles = 23760 feet
5[tex]\frac{1}{2}[/tex] miles = 29040 feet
6[tex]\frac{1}{2}[/tex] miles = 34320 feet
Explanation:
1 mile = 5280 feet
[tex]\frac{1}{2}[/tex] miles = 2640 feet
to convert miles into feet, multiply the whole numbers by 5280 and add 2640 to find your overall feet
2[tex]\frac{1}{2}[/tex] : 2 x 5280 + 2640 = 13200 ft
3[tex]\frac{1}{2}[/tex] : 3 x 5280 + 2640 = 18480 ft
4[tex]\frac{1}{2}[/tex] : 4 x 5280 + 2640 = 23760 ft
5[tex]\frac{1}{2}[/tex] : 5 x 5280 + 2640 = 29040 ft
6[tex]\frac{1}{2}[/tex] : 6 x 5280 + 2640 = 34320 ft
Tom surveyed a random sample of the junior of his school to determine whether the Fall Festival should be held in October or November. Of the 80 students surveyed, 24.8% said they preferred November. Based on this information, about how many students in the entire 230-person class would be expected to prefer having the Fall Festival in November. SHOW YOUR WORK PLEASE!!!
a. 50
b. 60
c. 75
d. 80
9514 1404 393
Answer:
b. 60
Step-by-step explanation:
We assume the percentage for the sample holds for the whole class, so the estimated number preferring November is ...
0.248 × 230 = 57.04 ≈ 60
About 60 students prefer November.
WILL MARK!
For parallelogram ABCD, find x.
Answer:
x = 16
Step-by-step explanation:
If the figure is a parallelogram, the opposite sides are the same length
3x+20 = 5x-12
Subtract 3x from each side
3x+20 -3x = 5x-12-3x
20 = 2x-12
Add 12 to each side
20+12 = 2x-12+12
32 = 2x
Divide each side by 2
32/2 = 2x/2
16 =x
Which transformation should be applied to show similarity?
Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct, Since Richard has not attended a class recently, he doesn't know any of the answers, Assuming that Richard guesses on all 10 questions. Find the indicated probabilities.
A) What is the probability that he will answer all questions correctly?
B) What is the probability that he will answer all questions incorrectly?
C) What is the probability that he will answer at least one of the questions correctly?
Then use the fact that P(r1) = 1 P(r = 0).
D) What is the probability that Richard will answer at least half the questions correctly?
Answer:
a) 0.0000001024 probability that he will answer all questions correctly.
b) 0.1074 = 10.74% probability that he will answer all questions incorrectly
c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.
d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. 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.
Each question has five answers, of which only one is correct
This means that the probability of correctly answering a question guessing is [tex]p = \frac{1}{5} = 0.2[/tex]
10 questions.
This means that [tex]n = 10[/tex]
A) What is the probability that he will answer all questions correctly?
This is [tex]P(X = 10)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024[/tex]
0.0000001024 probability that he will answer all questions correctly.
B) What is the probability that he will answer all questions incorrectly?
None correctly, so [tex]P(X = 0)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]
0.1074 = 10.74% probability that he will answer all questions incorrectly
C) What is the probability that he will answer at least one of the questions correctly?
This is
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
Since [tex]P(X = 0) = 0.1074[/tex], from item b.
[tex]P(X \geq 1) = 1 - 0.1074 = 0.8926[/tex]
0.8926 = 89.26% probability that he will answer at least one of the questions correctly.
D) What is the probability that Richard will answer at least half the questions correctly?
This is
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264[/tex]
[tex]P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055[/tex]
[tex]P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008[/tex]
[tex]P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001[/tex]
[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0[/tex]
So
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328[/tex]
0.0328 = 3.28% probability that Richard will answer at least half the questions correctly
Branliest to correct answer explain how you solved it please
Answer:
0.03
Step-by-step explanation:
.25% for the tails times .5 for the odd number on the dice times 0.25 for the clubs because it is a 13/52 chance you will pull a clubs and put that all together and you get 0.03125 simplified and you get 0.03
Answer:
0.03
Step-by-step explanation:
The probability of landing on 1 tail is 1/2, since it is 1 out of 2 options, a tail or a head. If you want the probability of two tails, it would be 1/2 * 1/2 = 1/4.
Next we can take the probability of rolling an odd number on a fair die. A fair die has 3 even numbers: 2,4,6; and 3 odd numbers: 1,3,5. Since 3/6 or 1/2 of the numbers are odd, there is a 50% chance that it would roll an odd number.
Finally, drawing a club out of standard deck of cards is 1/4, since there are 4 choices: hearts, spades, clubs, or diamonds. You now get the idea, and you can figure out that the probability would be 1/4.
Our last step is to multiply all the answers we get, since to get all of them at once would lower your chances. 1/4 * 1/2 * 1/4 = 1/32 = 0.03125; rounded to 0.03.
The graphs below have the same shape. What is the equation of the graph of g(x)? A. g(x) = x^2 + 4
B. g(x) = x^2- 4
C. g(x) = (x - 4)^2
D. g(x) = (x + 4)^2
The given graph of g(x) is translated 4 units to left, so the function is g(x)=(x+4)². Therefore, option D is the correct answer.
What is the parabola?A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
From the graph, f(x)=x².
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (0,0)
Focus: (0,1/4)
Axis of Symmetry: x=0
Directrix: y= -1/4
In the graph we can graph of g(x) is translated 4 units to left, so the function is g(x)=(x+4)²
Therefore, option D is the correct answer.
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