Answer:
1/16 pound
Step-by-step explanation:
1/4 ÷ 4 = 1/4 x 1/4 = 1/16
According to 2013 report from Population Reference Bureau, the mean travel time to work of workers ages 16 and older who did not work at home was 30.7 minutes for NJ State with a standard deviation of 23 minutes. Assume the population is normally distributed.
Required:
a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?
b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.
c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?
Answer:
a) 48.80% probability that his travel time to work is less than 30 minutes
b) The mean is 30.7 minutes and the standard deviation is of 3.83 minutes.
c) 13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes
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 normally distributed samples are solved using 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.
In this question, we have that:
[tex]\mu = 30.7, \sigma = 23[/tex]
a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?
This is the pvlaue of Z when X = 30. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 30.7}{23}[/tex]
[tex]Z = -0.03[/tex]
[tex]Z = -0.03[/tex] has a pvalue of 0.4880.
48.80% probability that his travel time to work is less than 30 minutes
b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.
[tex]n = 36[/tex]
Applying the Central Limit Theorem, the mean is 30.7 minutes and the standard deviation is [tex]s = \frac{23}{\sqrt{36}} = 3.83[/tex]
c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?
This is 1 subtracted by the pvalue of Z when X = 35. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35 - 30.7}{3.83}[/tex]
[tex]Z = 1.12[/tex]
[tex]Z = 1.12[/tex] has a pvalue of 0.8687
1 - 0.8687 = 0.1313
13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes
Which expression is equivalent to 36 a minus 27?
9 (4 a minus 3)
3 (18 a minus 9)
9 (4 a minus 27)
3 (12 a minus 6)
Answer:
[tex]9(4a)-9(3)[/tex]
Step-by-step explanation:
[tex]36a-27[/tex]
[tex]9(4a)-9(3)[/tex]
[tex]9(4a-3)[/tex]
Answer:
it is 9(4a-3)
Step-by-step explanation:
Solve for B. R = x(A + B)
Answer:
B = R/x -A
Step-by-step explanation:
[tex]\text{Divide the equation by x:}\\\\\dfrac{R}{x}=A+B\\\\\text{Subtract A:}\\\\\dfrac{R}{x}-A = B\\\\\text{The solution is ...}\\\\\boxed{B=\dfrac{R}{x}-A}[/tex]
Answer:
[tex] b = \frac{r - ax}{x} \\ [/tex]
Step-by-step explanation:
[tex]r = x(a + b) \\ r = ax + bx \\ r - ax = bx \\ \frac{r - ax}{x} = b[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What is the equation of the line perpendicular to y = 2/3 x +1 that passes through the point (12, – 6)?
Answer:
y= -3/2x+12
Step-by-step explanation:
the slope of perpendicular lines multiplied together would be -1, so the slope of the perpendicular line is -3/2. y=-3/2x+b, so -6=-18+b, so b= 12. the equation of the line is y=-3/2x+12.
2x+3=-7 twenty Chanda long-standing look
Answer:
x =-5
Step-by-step explanation:
Answer:
x=-5
Step-by-step explanation:
Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.
60
25
Answer:
65
Step-by-step explanation:
C^2= A^2 + B^2
C^2 = (60)^2 + (25)^2
C^2 = 4225
Take the square root of C
C = 65
Answer:
65
Step-by-step explanation:
Use the Pythagorean Theorem to find the length of the hypotenuse.
[tex]a^2+b^2=c^2[/tex]
I'm assuming that '60' and '25' are measures of the legs, since the question asks to find the hypotenuse.
[tex]60^2+25^2=c^2\\\rightarrow 60^2=3600\\\rightarrow 25^2 = 625\\3600+625=c^2\\4225=c^2\\\sqrt{4225}=\sqrt{c^2}\\\boxed{65=c}[/tex]
The hypotenuse should measure 65 units.
Please help this is urgent!
Answer:
Isosceles
Obtuse
Step-by-step explanation:
1) When two sides of a triangle are the same length, the triangle is an isosceles triangle.
2) When one angle of the triangle is greater than 90 degrees, the triangle is an obtuse triangle.
I hope this helps! Have a great day!
Answer:
Isosceles, obtuse
Step-by-step explanation:
There are three types of triangles based on their sides:
Equilateral: a triangle with 3 equal sidesIsosceles: a triangle with 2 equal sidesScalene: a triangle with no equal sidesThis triangle here as sides of 28 cm, 16 cm, and 16 cm
This triangle has two equal sides of 16 cm, indicating it is an isosceles triangleThere are three types of triangles based on their angles:
Acute: when all angles are less than 90° Right: when the triangle has one angle that is 90° Obtuse: when one of the angles is greater than 90°This triangle has angles of 26°, 26°, and 128°
This triangle has one angle that is greater than 90° → 128°, indicating that this is an obtuse triangleA state end-of-grade exam in American History is a multiple-choice test that has 50 questions with 4 answer choices for each question. A student must get at least 25 correct to pass the test, and the questions are very difficult. Question 1. If a student guesses on every question, what is the probability the student will pass
Answer:
0.004% probability the student will pass
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 50, p = \frac{1}{4} = 0.25[/tex]
So
[tex]\mu = E(X) = np = 50*0.25 = 12.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.25*0.75} = 3.06[/tex]
If a student guesses on every question, what is the probability the student will pass
Using continuity correction, this is [tex]P(X \geq 25 - 0.5) = P(X \geq 24.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 24.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24.5 - 12.5}{3.06}[/tex]
[tex]Z = 3.92[/tex]
[tex]Z = 3.92[/tex] has a pvalue of 0.99996
1 - 0.99996 = 0.00004
0.004% probability the student will pass
The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width. What is the length and width in yards?
Answer:
160 yards
Step-by-step explanation:
P=2l+2w
P=2(3w-8)+2(w)
432=2(3w-8)+2(w)
432=6w-16+2w
432=8w-16
432+16=8w
448=8w
w=448/8
w=56yards
l=3(56)-8
l=168-8=160yards
Which of the following linear equations has the steepest slope?
A. Y = -2x +11
B. y=+x+4
C. y - x +7
D. y - 7+2
Answer:
A --- unless d is supposed to be "y= -7x + 2"
Step-by-step explanation:
The slope is m in y=mx + b
So:
a. y= -2x + 11 slope= -2
b. y= x + 4 slope= 1
c. y= -x + 7 slope= -1
d. y= -7 + 2 (I don's see an x but if there were an x I assume that the slope would equal -7)
The higher the m value, the steeper the slope because it is m/1
So, -2/1 is steeper than 1/1 or -1/1
what is the positive solution for the equation
Answer:
x=3
Step-by-step explanation:
4x^2 - 36 = 0
Add 36 to each side
4x^2 -36 +36 = 0+36
4x^2 = 36
Divide each side by 4
4x^2/4 =36/4
x^2 = 9
Take the square root of each sdie
sqrt(x^2) = ±sqrt(3)
x = -3,+3
We want the positive square root
x=3
choose the most convenient method to graph the line y=−3
Answer:
the line just goes straight up the y-axis. so, place your dot at -3 and draw the line straight up
Step-by-step explanation:
The line is shifted downward by 3 units from the x-axis, and the slope of the line is zero. The intercept of the line is at (0, -3).
What is the graph of the function?The collection of all coordinates in the planar of the format [x, f(x)] that make up a variable function's graph.
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation of the line is given below.
y = –3
The line y = –3 is parallel to the x-axis.
The slope of the line is zero.
The line is shifted downward by 3 units from the x-axis.
The intercept of the line is at (0, -3).
The graph of the line y = –3 is given below.
More about the graph of the function link is given below.
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Maria has $39.00 that she can spend on school supplies. If she spends $18.00 on pens and pencils, how many packs of notebook paper can she buy if the notebook paper costs $3.00 a pack, including tax? Choose the graph that shows your answer.
Answer:
Please show the graph choice it sounds linear xy (positive)
or parallel depending on how much pens and pencils were.
We know $18 purchased more than 1 pack so this divided by notebook shws us at least 6 per notepack paper or so many packs of pen that cost $18 ffor pens were ratio to 1 pack of paper. ie) if pens were £2 pack then while we understand it could have been as many as 9 we divide by how many we find or bought by the amount of notepaper books to determine the rate and distribution of the money.
Step-by-step explanation:
$39 - $18 = $21 left over
21/3 = 7 packs of note paper can be purchased..
Please answer this correctly
Mark all of the values that are between 61 and 80. See the diagram below. You should mark exactly 6 values.
Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many real number
solutions does the equation have?
Discriminant = b2-4ac
0
1
2
o 12
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Submit
Mark this and return
le
Step-by-step explanation:
work is shown and pictured
The discriminant of quadratic equation is,
⇒ D = 0
What is Quadratic equation?
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form: ax² + bx + c = 0
We have to given that;
Quadratic equation is,
⇒ - 3 = x² + 4x + 1
Now, We can write as;
⇒ x² + 4x + 1 + 3 = 0
⇒ x² + 4x + 4 = 0
Hence, Discriminant of quadratic equation is,
⇒ D = b² - 4ac
⇒ D = (4)² - 4×1×4
⇒ D = 16 - 16
⇒ D = 0
Thus, The discriminant of quadratic equation is,
⇒ D = 0
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Express 1.8meter in seconds given answer in scientific notation
Answer:
Dear user,
Answer to your query is provided below
Scientific notation = 1.8x10^0
Step-by-step explanation:
This is usually expressed simply as 1.8 (Recall that 10^0 = 1.)
1.8×10^0
find the equation ( in form of y = mx+c) of line which has a gradient of -3 and a y intercept of -2
Answer:
The answer is y = -3x - 2.
Step-by-step explanation:
Given that in slope-form equation, m represents gradient and c is y-intercept. So you have to sbustitute the values into the equation :
[tex]y = mx + c[/tex]
[tex]let \: m = - 3 \\ let \: c = - 2[/tex]
[tex]y = - 3x - 2[/tex]
Find the nth term and the 150th term of the following sequence 7,11,15,19,23,...
Answer:
for the 9th it is 39 for the 150th it is 607
what is 0.035 as a simplified reduced fraction
Answer:
7/200
Step-by-step explanation:
0.035= 35/1000= 7*5/200*5=7/200
A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes. How long to finish filling the remaining jugs
Answer:
Step-by-step explanation:
=20
This take 30 minutes to finish filling the remaining jugs.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes.
Now,
Let the time to finish filling the remaining jugs = x
Since, A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes.
Hence, By definition of proportion we get;
⇒ 20 / x = 2 / 3
⇒ 20 × 3 / 2 = x
⇒ x = 30
Thus, The time to finish filling the remaining jugs = 30 minutes
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Sample Space: Tutorial
Activity
In this exercise, you'll use the formula for the probability of the complement of an event.
Another game you've set up at casino night involves rolling a fair six-sided die followed by tossing a fair coin. In this game, players earn points
depending on the number they get on the die and which side of the coin turns up. For example, the player earns 5 points for getting (2, tails).
Question 1
Find the total number of possible outcomes in each trial of this game.
Answer:
The number of possible outcomes in each trial of this game is 12
Step-by-step explanation:
Given
Rolling of a 6 sided die followed by tossing of a fair coin
Required
Number of possible outcomes
The first step is to list out the possible outcomes of rolling a die and tossing a coin
Rolling a fair die = {1,2,3,4,5,6}
Tossing a coin = {Head, Tail}
Let Head be represented by H and Tail be represented by T;
So,
Rolling a fair die = {1,2,3,4,5,6}
Tossing a coin = {H, T}
The question states that a roll of a 6 sided die is followed by a toss of a fair coin
This means that each trial is {A roll of die and A toss of coin}
So, the sample space is as follows
Sample Space = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}
Number of outcomes in the sample space is 12.
Hence, the number of possible outcomes in each trial of this game is 12
Answer:
the total number of possible outcomes in each trial of this game is 12
Step-by-step explanation:
uhhhhhh none :) kk bye <3
find the area of this figure to the nearest hundredth use 3.14 to approximate pi A=? ft squared
Answer:
[tex]105.13ft^2[/tex]
Step-by-step explanation:
Rectangle
[tex]A=lw\\=10*8\\=80ft^2\\[/tex]
Semicircle
[tex]A=\frac{1}{2} \pi r^2\\=\frac{1}{2}* \pi *4^2\\=25.13ft^2[/tex]
Add both values together
[tex]80+25.13\\=105.13ft^2[/tex]
Answer: 105.13
Step-by-step explanation:
You are at a playground with a see-saw and a large merry-go-round. You put your phone on the see-saw and find it slides when it is tilted at an angle of 38 degrees. How far can you put your phone from the center of the merry-go-round (in m) when it makes one rotation every 3 s
Answer: r_max = 1.75m
Step-by-step explanation:
Below is a rather brief analysis to solving this problem.
The phone starts sliding when along incline,
when F_net = m g sin(theta) - fs_max = 0
and fs_max = us N = us m g cos(theta)
m g sin(theta) - us m g cos(theta) =
us = tan(theta) = tan38 = 0.781
On merry - go - round,
fs_max = us N = us m g
Using F = m a
fs_max = m w^2 r_max and w = 2pi / T
us m g = m (2 pi / T)^2 (r_max)
0.781 x 9.81 = (2 pi / 3)^2 (r_max)
r_max = 1.75 m
cheers i hope this helped !!
Suppose that a large mixing tank initially holds 100 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 4 lb/gal, determine a differential equation (in lb/min) for the amount of salt A(t) (in lb) in the tank at time t > 0. (Use A for A(t).)
Answer:
dA/dt = 12 - 2A/(100 + t)
Step-by-step explanation:
The differential equation of this problem is;
dA/dt = R_in - R_out
Where;
R_in is the rate at which salt enters
R_out is the rate at which salt exits
R_in = (concentration of salt in inflow) × (input rate of brine)
We are given;
Concentration of salt in inflow = 4 lb/gal
Input rate of brine = 3 gal/min
Thus;
R_in = 4 × 3 = 12 lb/min
Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min
So, after t minutes, there will be (100 + t) gallons in the tank
Therefore;
R_out = (concentration of salt in outflow) × (output rate of brine)
R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min
R_out = 2A(t)/(100 + t) lb/min
So, we substitute the values of R_in and R_out into the Differential equation to get;
dA/dt = 12 - 2A(t)/(100 + t)
Since we are to use A foe A(t), thus the Differential equation is now;
dA/dt = 12 - 2A/(100 + t)
help solve the above equation
Answer:
[tex]\dfrac{1}{27}[/tex]
Step-by-step explanation:
[tex]n^{-\frac{2}{3}}=9[/tex]
Rewrite:
[tex]\dfrac{1}{\sqrt[3]{n^2}}=9\\\\9\sqrt[3]{n^2}=1[/tex]
Cube both sides:
[tex]729n^2=1[/tex]
Divide both sides by 729:
[tex]n^2=\dfrac{1}{729}[/tex]
Take the square root of both sides:
[tex]n=\sqrt{\dfrac{1}{729}}=\dfrac{1}{27}[/tex]
Hope this helps!
One number is 4 plus one half of another number. Their sum is 31. Find the numbers.
Answer:
18, 13
Step-by-step explanation:
x=4+1/2y
x+y=31
4+1/y+y=31
3/2y=27
y=18
x=31-18=13
Answer:
13 & 18
Step-by-step explanation:
Create the formulas:
0.5x+4=y
x+y=31
0.5x+4=y
Multiply both sides by 2
x+8=2y
x+y=31
Subtract 31 from both sides
x+y-31=0
Subtract y from both sides
x-31= -y
Multiply both sides by -1
-x+31=y
Multiply both sides by 2
-2x+62=2y
Combine equations:
-2x+62=x+8
Add 2x to both sides
62=3x+8
Subtract 8 from both sides
3x=54
Divide both sides by 3
x=18
0.5x+4=y
Subtract y from both sides
0.5x-y+4=0
Subtract 0.5x from both sides
-y+4= -0.5x
Multiply both sides by -1
y-4=0.5x
Multiply both sides by 2
2y-8=x
x+y=31
Subtract y from both sides
x= -y+31
Combine equations:
2y-8= -y+31
Add y to both sides
3y-8=31
Add 8 to both sides
3y=39
Divide both sides by 3
y=13
Nathan spins 2 different spinners at the same time.There are a total of 10 possible outcomes.which pair of spinners did Nathan spin?
Answer:
The one divided into five part and the one divided into two parts
Step-by-step explanation:
find the option with one that has five parts and one with two parts :3
hope this helps!!
It is the graph with 5 numbers and 5 letters
I ready diagnostic
the sum of the three numbers in 2003,two of the numbers are 814 and 519 what is the third number
Answer:
idk dont ask me
Step-byi-step explanation:
Answer:
a+b+c=2003
a+b=814
2003-819=189
Step-by-step explanation:
Bonita said that the product of 5/6 x 1 2/3 is 7/3. How can you tell that her answer is wrong.
Answer:=
1 7/18
Step-by-step explanation:
Turn the improper fraction into a mixed fraction.
Please help me with this problem I am lost
Answer:
[tex]\frac{49}{15}[/tex]
Step-by-step explanation:
[tex]\frac{2}{5} \times \frac{7}{-6} \times -7[/tex]
[tex]\frac{2}{5} \times \frac{7}{-6} \times \frac{-7}{1}[/tex]
[tex]\frac{2 \times 7 \times -7}{5 \times -6 \times 1}[/tex]
[tex]\frac{-98}{-30}=\frac{98}{30}=\frac{49}{15}[/tex]
Answer:
-3.26 repeating
Step-by-step explanation:
2×7=14
5×(-6) = -30
14/30×(-7)= -3.26 repeating
