Answer:
The trip will take 36 minutes.
Step-by-step explanation:
This question can be solved using a rule of three.
The boat maintains a constant speed of 15 knots (nautical miles per hour). How many minutes it will take to return to its home port 9 nautical miles away?
So in 60 minutes, 15 nautical miles. How many minutes for 9 nautical miles?
60 minutes - 15 nautical miles
x minutes - 9 nautical miles
[tex]15x = 60*9[/tex]
[tex]x = \frac{60*9}{15}[/tex]
[tex]x = 36[/tex]
The trip will take 36 minutes.
Business Week conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000 and for the female graduates it is $25,000. 1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why? 2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?
Answer:
1. Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean
2. 15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, 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.
1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why?
The lower the standard deviation, the less dispersed the values are, meaning it is more likely to find values within a certain threshold of the mean.
So
Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean.
2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?
We have that:
[tex]\mu = 168000, \sigma = 40000, n = 100, s = \frac{40000}{\sqrt{100}} = 4000[/tex]
This probability is the pvalue of Z when X = 168000 - 4000 = 164000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{164000 - 168000}{4000}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean
Which rule represents the translation from he pre-image, ABCD, to the image, A’B’C’D’?
Answer:
Option (4)
Step-by-step explanation:
From the figure attached,
Quadrilateral ABCD has been translated to form an image A'B'C'D' by shifting 'a' units right and 'b' units up.
Let the rule for translation is,
(x, y) → (x + a, y + b)
Coordinates of point A is (-4, 4) and the coordinates of the image A' are (-2, 5).
So, (-4, 4) → [(-4 + 2), (4 + 1)]
Therefore, the translation can be represented by [tex]T_{2, 1}(x, y)[/tex] (shifted 2 units right and 1 unit up).
Option (4) will be the answer.
Answer:
T2,1(x,y)
Step-by-step explanation:
is the inverse of the function shown below also a function?
Answer:
Yes
Step-by-step explanation:
Yes. Here's why: We can obtain the graph of the inverse of the function shown by reflecting the red graph about the line y = x. The resulting graph is true for all x values and for all y values; it passes the vertical line test.
Answer:
yes. ^^^^^^^^
Step-by-step explanation:
We can obtain the graph of the inverse of the function shown by reflecting the red graph about the line y = x. The resulting graph is true for all x values and for all y values; it passes the vertical line test.
Find the area of a rectangle with base 4ft and height 4 in.
Hey there!
Answer:
A = 192 in²
Step-by-step explanation:
Base = 4 ft
Height = 4 in
Convert the length of the base to inches:
4 ft = 4 ×12 = 48 in
Formula for the area of a rectangle: A = l × w (in this instance, 'l' is the height)
4 × 48 = 192 in²
Answer:
A =192 in^2
Step-by-step explanation:
Change the 4 ft to inches
4 * 12 = 48 inches
A = l*w
A = 48*4
A =192 in^2
Solve for x
There’s no options sorry ya’ll please answer I’m desperate
Answer & Step-by-step explanation:
The triangle shown is an isosceles triangles. Isosceles triangles have a pair of congruent angles which are found at the bottom. These angles are called the base angles. So, when you find the measurement of one of the base angles, then the other base angle will have the same measurement.
We can find the measurement of x by subtracting 130 from 180. We are doing this because all triangles have a sum measurement of 180°. After we do this, then we will divide that number by 2 to find the measurement of x.
180 - 130 = 50
Now, we divide 50 by 2.
50 ÷ 2 = 25
So, the measurement of x is 25°.
The following simple linear regression analyzes the relationship between the number of classes students are taking (the independent variable, labeled in the following output as X[,2]) and the number of books they have in their backpack (the response) at randomly chosen times. Assume all relevant assumptions are met. Which of the following are correct interpretations of the slope?
a. Each additional class a student takes is associated with about a 58.7% increase in the number of books in their backpack on average.
b. Each additional class a student takes is associated with about an additional 0.587 books in their backpack on average.
c. Taking an additional class causes students to carry 0.587 extra books with them on average.
d. The population average number of books in a studentâs backpack is 0.587.
Answer:
The answer is B.
Step-by-step explanation:
Why do we say that the answer is B?
For each additional class there is a significant increase that represents a minimum value over a total of books, that is, 100% that will always remain, therefore the increase will be an additional average over the other "books" that are already in backpack.
URGENT!! EASY IM DUMB MY LAST 2 QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
16. Which sentence would be a good counterexample to this statement?
A line can exist in only one plane.
A) A line intersects one plane and then another.
B) A line that is coplanar exists in more than one plane.
C) A line is the intersection of two planes.
D) A line is parallel to one plane at a time.
17. Which statement is needed to complete this syllogism?
If the angles of a triangle are all equal, then the sides of a triangle are all equal.
If the sides of a triangle are all equal, then the triangle is equilateral.
Therefore, if the angles of a triangle are all equal,then________________________.
A) the sides of a triangle are all equal
B) the angles of a triangle are all equal
C) the triangle is equiangular
D) the triangle is equilateral
Answer:
16. A
17. D
Step-by-step explanation:
16. By saying that a line intersects one plane and then another, you are saying that a line is existing on two planes. This is a direct contradiction to the statement.
17. The triangle is equilateral because syllogism is basically connecting the dots. If the angles in the triangle are all equal, it has all equal sides, and if it has all equal sides, then it is equilateral, therefore, it is D, not C.
Suppose that weekly income of migrant workers doing agricultural labor in Florida has a distribution with a mean of $520 and a standard deviation of $90. A researcher randomly selected a sample of 100 migrant workers. What is the probability that sample mean is less than $510
Answer:
[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]
And we can find the probability using the normal standard distribution table and with the complement rule we got:
[tex]P(z<-1.11)= 0.1335[/tex]
Step-by-step explanation:
For this problem we have the following parameters:
[tex] \mu = 520, \sigma = 90[/tex]
We select a sample size of n =100 and we want to find this probability:
[tex] P(\bar X <510) [/tex]
The distribution for the sample mean using the central limit theorem would be given by:
[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]
And we can solve this problem with the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score formula we got:
[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]
And we can find the probability using the normal standard distribution table and with the complement rule we got:
[tex]P(z<-1.11)= 0.1335[/tex]
A random two digit number (10-99) is drawn. Find P(odd number)
Answer:
P(odd number) = 0.5
Step-by-step explanation:
There are 90 members in the set (10, 11, 12, .. , 97, 98, 99)
When we have an even number of consecutive numbers, the number of even numbers equals the number of odd numbers. This means that half of the numbers in this set are even and half of them are odd.
So the probability of P(odd number) = 0.5
The sales price of a single family house in Charlotte is normally distributed with mean $210,000 and standard deviation $35,000. 1. A random sample of 49 single-family houses in Charlotte is selected. Let X ¯ be the mean sales price of the sample. What is the mean of X ¯?
Answer:
E(X ¯)=210,000.
Step-by-step explanation:
A sampling distribution for samples of size n=49 from a population with means μ=210,000 and standard deviation σ=35,000, has the following means anda standard deviation:
[tex]\mu_s=\mu=210,000\\\\\sigma_s=\sigma/\sqrt{n}=35,000/\sqrt{49}=35,000/7=5,000[/tex]
If X ¯ is the mean sales price of the sample, it will have a mean value of E(X ¯)=210,000.
Can someone help me?
Answer:
Step-by-step explanation:
a)4a-6a d)2x+4y-10x
=-2a. =-8-+4y
b)14-1-10
=3
c)2+8
=10
e)answer is 6 x raised to the power 3
f)7x raised to the power 2-5x-y
What is the square root of -1?
Answer:
i
Step-by-step explanation:
Why is i the square root of negative one?
The term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root.
5. The value of 25sqare -24sqare
Answer:
49
Step-by-step explanation:
25²-24²
625-576
=49
use calculator lah dehh
g Suppose you have $100 of endowment, and you are offered a chance to buy a lottery which costs $36. The lottery has 18% of chance to win a prize of $G, or you just lose and get nothing. Suppose your utility function on wealth is U(w)=\sqrt{w}. What is the least prize size G that you will be willing to buy the lottery?
Answer:
$301.23
Step-by-step explanation:
We have that the function of wealth is U (w) = w ^ (1/2)
So, since what you have at the start is 100, we replace:
U (w) = 100 ^ (1/2)
U = 10
Now we have two cases:
the first one we win, then the winnings would be 100 minus the cost of the lottery, that is 36 and to that add G of the prize:
100 - 36 + G = 64 + G
In the second case, where we lose, the subtraction of 100 that we have minus the cost of the lottery would be equal 36
100 - 36 = 64
Therefore, we have to win with an 18% probability, therefore losing would be 82% (100% - 18%)
0.18 * (64 + G) ^ (1/2) + 0.82 * 64 ^ (1/2)
solving:
0.18 * (64 + G) ^ (1/2) + 6.56
Now this is equal to U which is equal to 10:
10 = 0.18 * (64 + G) ^ (1/2) + 6.56
(10 - 6.56) /0.18 = (64 + G) ^ (1/2)
(64 + G) ^ (1/2) = 19.11
(64 + G) = 365.23
G = 365.23 - 64
G = 301.23
Therefore, the smallest G prize size that the lottery will be willing to buy is $ 301.23
a 680g patient comes in with diarrhea. the doctor orders anti-diarrhea medication at a dosage of 15 mcg/kg TID x 3 days. rhye medication concentration 50mcg/ml. What is the patients dose in MCG? What is the total volume of medication you will send home?
Answer:
dose in MCG = 10.2 mcg
Total volume to be sent home = 1.836 ml (1836μl)
Step-by-step explanation:
weight of patient = 680g
dosage in mcg of medication = 15mcg/kg
This means that
for every 1kg weight, 15mcg is given,
since 1kg = 1000g, we can also say that for every 1000g weigh, 15mcg is given.
1000g = 15mcg
1g = 15/1000 mcg = 0.015 mcg
∴ 680g = 0.015 × 680 = 10.2 mcg
Dosage in MCG = 10.2 mcg
Next, we are also told ever ml volume of the drug contains 50 mcg weight of the drug (50mcg/ml). This can also be written as:
50mcg = 1 ml
1 mcg = 1/50 ml = 0.02 ml
∴ 10.2 mcg = 10.2 × 0.02 = 0.204 ml
since the medication is to be taken TID (three times daily) for 3 days, the total number of times the drug is to be taken = 9 times.
therefore, the total volume required = 0.204 × 9 = 1.836 ml (1836 μl)
I’ll give the bralyist to the first correct answer
Let f be defined as shown.
What is f1 (-7)?
Answer:
The answer is 2
From the function when the input is 2 the output is -7. The inverse reverses the order so the input will be -7 and the output will be 2.
A rectangular box is 4 cm wide, 4 cm tall, and 10 cm long. What is the diameter of the smallest circular opening through which the box will fit? Round to the nearest tenth of a centimeter.
Answer:
The diameter of the smallest circular opening through which the box will fit is 5.7 cm to the nearest tenth
Step-by-step explanation:
The dimensions of the rectangle are :
height: 4 cm
length: 10 cm
breadth: 4 cm
The diameter of the smallest circular opening through which the box will fit will be equals to the diagonal of a face of the rectangular box.
The face we will try to fit in first will determine the diagonal that we will calculate.
Let us try to fit in the right side of the rectangular box. The face we will have at that side is a square of 4 cm by 4 cm which is formed by the height and the width of the box.
We can calculate the diagonal using Pythagoras Theorem:
diagonal = [tex]\sqrt{height^{2}+ breadth^{2}}= \sqrt{4^{2}+4^{2}}=5.657 \approx 5.7cm[/tex] to the nearest tenth
Consider the function y=f(x)=3x. The values of f(1/2) and f(1/4), rounded to the nearest hundredth, are_______ and__________ , respectively.
Answer:
f(1/2)=1.5
f(1/4)=0.75
The function f(x)=2x2−x+4; f ( x ) = 2 x 2 − x + 4 is defined over the domain 0 ≤ x ≤ 3 Find the range of this function. A. 4 < f(x) < 7 B. 4 < f(x )< 19 C. 4 ≤ f(x) ≤ 19 D. 4 ≤ f(x) ≤ 25
Answer:
C. 4 ≤ f(x) ≤ 19 . . . . . . best of bad answer choices
Step-by-step explanation:
When looking for the range of a function on an interval, one must check the function values at the ends of the interval, along with any local maxima or minima.
Here, the function values at the interval ends are ...
f(0) = 4
f(3) = 2·3² -3 +4 = 19
The axis of symmetry is located at ...
x = -b/(2a) = -(-1)/(2(2)) = 1/4
This is a value in the interval, so will be the location of the minimum value of the function.
f(1/4) = 2(1/4)² -1/4 +4 = 3.875
The range of f(x) on the interval [0, 3] is [3.875, 19]:
3.875 ≤ f(x) ≤ 19
__
All of the answer choices are incorrect. Please discuss question this with your teacher.
What’s 148+383-163=?
Answer:
368
Step-by-step explanation:
Anyone know how to solve this
Answer:
Y=1800+150x
Step-by-step explanation:
Answer:
4. Y = 150x + 1800
A magazine asks its readers to complete a survey on their favorite music and tv celebrities. Classify this sample
Answer:
All the elements in the sample share a common characteristic. All of them read the magazine, so we may have a biased sample. And we also have the bias of the fact that only the volunteers will respond to this survey, so this is a biased sample.
This type of sample is usually called convenience sampling, where the elements in the sample are the most readily available (and what is most readily available for a magazine than its own readers?)
Then the type of sample is a convenience sample and a biased sample.
Find the percent of area under a normal curve between the mean and the given number of standard deviations from the mean. (Note that positive indicates above the mean, while negative indicates below the mean.)0.20
Answer:
15.86%
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Percent of area between the mean and 0.20 standard deviations from the mean:
pvalue of Z = 0.2 subtracted by the pvalue of Z = -0.2
Z = 0.2 has a pvalue of 0.5793
Z = -0.2 has a pvalue of 0.4207
0.5793 - 0.4207 = 0.1586
So this percentage is 15.86%
luvenia can row 4mph in still water. She takes as long to row 7 mi upstream as 21 mi downstream. how
Answer:
The speed of the river is 2mph.
Step-by-step explanation:
I guess that we want to find the speed of the river.
First, remember the relation: speed*time = distance
If the speed of the river is Sr, when Luvenia moves downstream (in the same direction that the flow of the water) the total speed will be equal to the speed of Luvenia in still water plus the speed of the water:
Sd = 4mph + Sr
and at this speed, in a time T, she can move 21 miles, so we have:
Sd*T = (4mph + Sr)*T = 21 mi
When moving upstream, the speed will be:
Su = (4mph - Sr)
and in the same time T as before, she moves 7 miles, so we have the equation:
Su*T = (4mph - Sr)*T = 7 mi
Then we have two equations:
(4mph + Sr)*T = 21 mi
(4mph - Sr)*T = 7 mi
Now we can take the quotient of those two equations and get:
((4mph + Sr)*T)/((4mph - Sr)*T) = 21/7
The time T vanishes, and we can solve it for Sr.
(4mph + Sr)/(4mph - Sr) = 3
4mph + Sr = 3*(4mph - Sr) = 12mph - 3*Sr
4*Sr = 12mph - 4mph = 8mph
Sr = 8mph/4 = 2mph.
Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 the job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this.
30 + 15 x greater-than-or-equal-to 90
Which best describes the restrictions on the jobs Deepak will accept?
He only accepts jobs that last 4 or more hours.
He only accepts jobs that last 5 or more hours.
He only accepts jobs that last 8 or more hours.
He only accepts jobs that last 9 or more hours.
Hey there! I'm happy to help!
The only thing we have to do is solve our inequality to find the answer!
30+15x ≥ 90
We subtract 30 from both sides.
15x ≥ 60
Finally, we divide both sides by four.
x ≥ 4
Therefore, Deepak can only accept jobs that last 4 or more hours.
I hope that this helps! Have a wonderful day!
The solution for the inequality is x≥4. Therefore, option A is the correct answer.
Given that, Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The inequality for the given situation is 30+15x≥90
Subtract 30 on the both the sides of an inequality, which is
30+15x-30≥90-30
⇒ 15x≥60
Divide 15 on the both the sides of an inequality, that is
15x/15≥60/15
⇒ x≥4
The solution for the inequality is x≥4. Therefore, option A is the correct answer.
To learn more about the inequalities visit:
https://brainly.com/question/20383699.
#SPJ5
What’s the correct answer for this question?
Answer:
C:
Step-by-step explanation:
Both angles add up to 180°
<BCG + <BFG = 180°
2x+146+4x+238=180
6x+384 = 180°
6x = 180-384
6x = -204
Dividing both sides by 6
x = -34
If a line crosses the y-axis at (0,1) and has a slope of 4/5 what is the equation of the line
Answer:
y = 4/5x + 1
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
y = 4/5x + 1
Answer:4y-5x=5
Step-by-step explanation:
A company makes candles in the shape of a right cone. The lateral surface of each candle is covered with paper for shipping and each candle also has a plastic circular base. Find the amount of paper needed to cover the lateral surface of each candle. Then find the total amount of paper and plastic needed for the candle. Round to the nearest tenth. Use 3.14 for π.
Answer:
If we have a cone-shape candle with r=2 cm and h=3 cm, then the amount of paper needed is 18.84 cm^2 and the amount of plastic needed is 12.56 cm^2.
Step-by-step explanation:
The question is incomplete: no numerical values for the dimensions of the cone are given.
A right cone is defined by the radius r of the base and the height h.
The base area is the area of a circle with radius r:
[tex]A_b=\pi r^2[/tex]
The lateral area is calculated as:
[tex]A_l=\pi \cdot r\cdot l[/tex]
As the values for r and h are not given, we will use an example with r=2 and h=3.
Then, the amount of paper needed is:
[tex]A_l=\pi \cdot r\cdot l=3.14\cdot (2\,cm)\cdot (3\, cm)=18.84\,cm^2[/tex]
The amount of plastic needed is:
[tex]A_b=\pi r^2=3.14\cdot (2\,cm)^2=3.14\cdot 4\,cm^2=12.56\,cm^2[/tex]
In the diagram below, measure of arcABC = 230º.
What is the measure of
Answer:
65°
Step-by-step explanation:
Short arc AC is the difference between 360° and long arc ABC:
arc AC = 360° -230° = 130°
The inscribed angle ABC that intercepts this short arc will have half the measure of the arc:
∠ABC = 130°/2 = 65°
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 7 20 14 41
Female 3 4 19 26
Total 10 24 33 67
If one student is chosen at random,
Find the probability that the student was male OR got an "A".
Answer:
46/ 67
Step-by-step explanation:
The numbers of students irrespective of grades is;
The sum of the last roll of numbers:
10+24+ 33+ 67 = 134
The number of males irrespective of grades is the sum of the numbers in the male row ;
7 +20+ 14 +41= 82
The numbers of students with grade A is the first column at the last row and is 10;
Hence;
the probability that the student was male OR got an 'A' is
the probability that the student was male plus the probability that he/she got an 'A'.
The probability that it's a male is ;
Number of males/ total number of students
=82/134
The probability that he got an A is;
The number of students that got A/ the total number of students;
10/134
Hence
the probability that the student was male OR got an 'A' is;
82/ 134 + 10/134 = 92/134 = 46/ 67
