Using the Central Limit Theorem, the sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.
The Central Limit Theorem establishes 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].
In this problem, the population has:
Mean of 11.4 minutes, thus [tex]\mu = 11.4[/tex].Standard deviation of 2.6 minutes, thus [tex]\sigma = 2.6[/tex]Samples of 84 are taken, thus, by the Central Limit Theorem:
[tex]n = 84, s = \frac{2.6}{\sqrt{84}} = 0.28[/tex]
The sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.
A similar problem is given at https://brainly.com/question/16364846
Graph: y - 3 = 1/2 (x + 2)
Answer:
Slope: [tex]\frac{1}{2}[/tex]
Y-intercept: (0,4)
Step-by-step explanation:
Put the equation into y = mx + b form, which is y = [tex]\frac{1}{2}[/tex] +4. Then create a table.
X: -2, -1, 0, 1, 2
Y: 3, [tex]\frac{7}{2}[/tex], 4, [tex]\frac{9}{2}[/tex], 5
Convert:
30 quarts
=
bushels
Round to the nearest hundredths.
Answer:
30 quarts= 0.8057 bushels
rounded to the nearest hundredths = 0.81
A bag contains only green balls and red balls. A bal is tim
of taking a green ball is 038. Write down the probability of
a red ball
Answer:
It would be 0.62.
Step-by-step explanation:
This is because the total probability is 1 and the chance of it being a green ball is 0.38, so:
1 - 0.38 = 0.62.
In a class of 23 students, 9 play an instrument and 7 play a sport. There are 3 students who play an instrument and also play a sport. What is the probability that a student does not play an instrument given that they play a sport?
Answer:
There are 23 students
-- 9 students play neither sport
-- therefore, 23 - 9 = 14 students play at least one of the two sports; some play both sports.
Inclusive or: the probability will be: 14 / 23 that a student chosen at random will play at least one of the two sports.
Exclusive or: we need to first find how many students play both sports.
Since 14 persons play sports and since 7 play basketball and 12 play baseball, this requires 7 + 12 = 19 students.
Subtracting 19 - 14 = 5 give the number of students who play both sports.
If we eliminate these 5 persons as well as the 9 who play neither sport, we have to eliminate 5 + 9 = 14 persons.
This gives 23 - 14 = 9 persons who play only one of the two sports.
The probability will be: 9/23 play a sport, but only one sport.
Step-by-step explanation:
The probability that a student does not play an instrument given that they play a sport is 6/7 or approximately 0.857.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
To find the probability that a student does not play an instrument given that they play a sport, we need to use conditional probability.
Let A be the event that a student plays a sport and B be the event that a student plays an instrument.
We want to find P(not B | A), which is the probability that a student does not play an instrument given that they play a sport.
We know that,
P(A) = 7/23, P(B) = 9/23, and P(A and B) = 3/23.
Using the formula for conditional probability, we have:
P(not B | A) = P(A and not B) / P(A)
We can find P(A and not B) by using the fact that,
P(A and B) = P(B) - P(A and not B).
P(A and not B)
= P(B) - P(A and B)
= 9/23 - 3/23
= 6/23
Substituting into the formula, we get:
P(not B | A) = (6/23) / (7/23) = 6/7
Therefore,
The probability that a student does not play an instrument given that they play a sport is 6/7 or approximately 0.857.
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Solve the inequality:
4-3x<16
Answer:
x > -4
Step-by-step explanation:
This is solved just like as if it was an equation. Its a two-step equation (inequality) The only thing that's different is with an inequality, it is imperative that you flip the inequality symbol if you multiply or divide by a negative number.
Here, we'll subtract 4 from both sides. Then divide by -3 on both sides. Flip! the < to a >.
see image.
x > -4.
Step-by-step explanation:1. Write the expression.[tex]4-3x < 16[/tex]
2. Subtract "4" from both sides of the equation.[tex]4-3x-4 < 16-4\\ \\-3x < 12[/tex]
3. Divide both sides by "-3" and switch the inequality symbol.[tex]\frac{-3x}{-3} < \frac{12}{-3} \\ \\x > -4[/tex]
Important. See that we switched the inequality symbol from "<" to ">", and this is because the symbol of the coefficient of variable "x" changed from negative to positive when it was divided by "-3". This rule will always be true, any time the symbol of the variable changed, the inequality symbol changes.
4. Verify.If x >-4 is the correct answer, then substituting x by "-4" in the inequation should make the inequation return the same value on both sides of the inequality symbol (>).
[tex]4-3(-4) > 16\\ \\4-(-12) > 16\\ \\4+12 > 16\\ \\16 > 16[/tex]
That's correct! x > -4 is the correct answer.
what is the sum of the IQR of the top data set and the IQR of the bottom data set
Answer:
IQR = 32 - 26 = 6
Step-by-step explanation:
Answer:
the answer is 11
Step-by-step explanation:
I took the algebra nation test
A pet shelter has 5 cats and 9 dogs.
Enter the ratios in the boxes.
ratio of cats to all animals:
ratio of dogs to cats:
The ratio of cats to all animals is 5:14
the ratio of dogs to cats is 9:5
Given-
Cats = 5
Dogs = 9
Total animals = cats+ Dogs
5+9=14
so the ratio of cats to all animals = 5: 14
and dogs to the cats= 9:5
Ratio give the relation between quantities of to identies.
Read more about the ratio: https://brainly.com/question/12024093
I’ll give brainliest to whoever answers this
Answer:
[tex] V_{prism} = 222\: cm^3 [/tex]
Step-by-step explanation:
For bottom portion:
l = 8 cm, w = 6 cm, h = 2 cm
[tex] V_1= lwh = 8*6*2= 96 \: cm^3 [/tex]
For top portion:
l = 6 cm, w = 3 cm, h = 9 - 2 = 7 cm
[tex] V_2= lwh = 6*3*7= 126 \: cm^3 [/tex]
[tex] V_{prism} = V_1 + V_2[/tex]
[tex] V_{prism} = 96 + 126[/tex]
[tex] V_{prism} = 222\: cm^3 [/tex]
Another way:
[tex] V_{prism} = 8*6*9-6*5*7[/tex]
[tex] V_{prism} = 432-210[/tex]
[tex] V_{prism} = 222\: cm^3 [/tex]
Carole worked her 40 regular hours plus 5 O.T. hours at time-in-a-half rate. Her gross pay was $1,163.75. What is her regular hourly rate?
Let her standard pay rate = x
She worked 40 hours for x per hour she also worked 5 hours at 1.5x ( time and a half)
Write an equation:
40x + 5(1.5x) = 1163.75
Simplify:
40x + 7.5x = 1163.75
Combine like terms:
47.5x = 1163.75
Divide both sides by 47.5
X = 24.50
Her regular hourly rate is $24.50
Answer:
let rate be x
by question
40x+7.5x=1163.75
x=1163.75/47.5=24.5
her regular income is $24.5 per hour.
Help me and I’ll give you brainliest
Answer: 45°
Step-by-step explanation:
The diagonals in squares are axes of symmetry.
This means the cut the corner angles in half.
90° ÷ 2 = 45°
Of 1936 people so came into a blood bank to give blood, 200 people had high blood pressure. Estimate the probability that the next person who comes in to give
blood will have high blood pressure’s
Answer:
person has a 10% chance of having high bp
Step-by-step explanation:
200 out of 1936 equals about 10%
Solve the triangle. Round to the nearest tenth.
39°
16
84°
B
Answer:
A. m<C = 57 degrees, a = 12, b = 19
Step-by-step explanation:
First we can start by calculating Angle C by using the rule that all interior angles of a triangle always add to 180 degrees:
180 - (39+84) = C
180 - 123 = C
C = 57
Now let's calculate side a. We can do this by using the sin rule: [tex]\frac{sin A}{a}=\frac{sin C}{c}[/tex]
According to the diagram we know that Angle A is 39 degrees, Angle C is 57 degrees, and side c is 16 so we can substitute these values into the formula and solve:
[tex]\frac{sin39}{a} =\frac{sin 57}{16} \\\\\frac{0.629320}{a} =\frac{0.838671}{16}\\\\0.629320=0.052417a\\0.629320/0.052417=a\\a= 12[/tex]
We can use the same method to solve for side b:
[tex]\frac{sin84}{b} =0.052417 \\0.994522=0.052417b\\0.994522/0.052417=b\\b= 19[/tex]
We now have the following values:
Angle C = 57 degrees, a = 12, b = 19
We can now see that A/Number 1 is the correct option.
Hope this helped!
7 movie tickets for $56 -help please lol-
Answer:
8
Step-by-step explanation:
If 7 tickets equals 56
56/7=8
Answer:
8 Dollars
Step-by-step explanation:
If the question you are asking is how much is a ticket, if 7 tickets cost a total of 56 dollars, then the answer is 8. This is because you would divide the total cost bu how many there are, which would look like 56 / 7 = 8.
Itzel purchased 18 pounds of oranges.
How many ounces of oranges did she
purchase?
Answer:
288
Step-by-step explanation:
1 pound is equal to 16 ounces
if Itzel purchases 18 pounds, to convert to ounces simply multiply 18 by 16.
Answer:
288
I wish you luck in your assignments.
(I just noticed someone got here in before me and answered WAY better. So I edited this to tell you to give them brainliest.)
Determine if the events are independent or dependent
Answer:
dependent
Step-by-step explanation:
there is no replacement
Answer:
Dependent
Step-by-step explanation:
The cards aren't replaced, so it depends on which ones are taken.
Find the missing side lengths. Leave your answers as radicals in simplest form.
Please help!!!! Due today
Answer:
B) x = 5sqrt2, y = 5
Step-by-step explanation:
(y) is equal to 5 because both angles are 45 degrees.
From here you can use the Pythagorean theorem to find (x):
a^2+b^2 = c^2
5^2+5^2 = c^2
25+25 = c^2
50 = c^2
sqrt50 = c
5sqrt2 = c (c is x in this case)
A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad.
The probability of drawing a bag with bad potatoes is less than 1.
True or False
The probability of drawing a bag with good potatoes is greater than 0.
True or False
What is the probability of drawing a bag with bad potatoes?
What is the expected probability of the complement of the event?
Answer:
The probability of drawing a bag with bad potatoes is less than 1. True
The probability of drawing a bag with good potatoes is greater than 0. True
What is the probability of drawing a bag with bad potatoes?
The probability of drawing a bag with bad potatoes is (2 bad bags) / (20 total bags) = 0.1 or 10%.
What is the expected probability of the complement of the event?
The complement of the event of drawing a bag with bad potatoes is drawing a bag with good potatoes. The probability of drawing a bag with good potatoes is (18 good bags) / (20 total bags) = 0.9 or 90%.
Uday Tahlan
Models come in different scales. A model of a G-scale railroad car has a scale ratio of 1:22.5, and the model is 3 in tall, how tall is the actual car?
Please help me answer this, this is due on Monday for me!!!
4 is the slope of a line y - 4x = 0 true or false
it is false but 4 is not y-4x=0
The quotient of s and 60
Answer:
60/s or s/60
Quotient means divide so you divide the following, s and 6 by each other.
Step-by-step explanation:
Hope it helps! =D
what is 900,000*9,000
Answer:
8,100,000,000
Step-by-step explanation:
I used a calculator lol
Refer to the figure in the picture to determine
the measure of each given angle.
Check the picture below.
The director of special events for Sun City believed that the amount of money spent on fireworks displays for the Fourth of July was predictive of attendance at the Fall Festival held in October. She gathered the following data to test her suspicion.
4th of July ($000) Fall Festival (000)
10.6 8.8
8.5 6.4
12.5 10.8
9.0 10.2
5.5 6.0
12.0 11.1
8.0 7.5
7.5 8.4
9.0 9.5
10.0 9.8
7.5 6.6
10.0 10.1
6.0 6.1
12.0 11.3
10.5 8.8
1. Determine the regression equation
2. Complete the ANOVA table.
Tgwre is no attached ANOVA chart.
Answer:
y = 0.762x + 1.72
Step-by-step explanation:
Given the data above , the regression model obtained using a Pearson linear regression calculator is :
y = 0.762x + 1.72
The regression equation cloud be interpreted as follows :
Slope, which is the increase in the value of y per unit increase in x = 0.762
The intercwpt, which is the value of x when y = 0 is 1.72
x = amount of money spent in fireworks for 4th July
y = Attendance at the October fall festival.
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(5x-17)®
(7x-3)
56°
The measurement of three angles in the triangle are 43°, 81°, 56°.
What are the angles of a triangle?A triangle's interior angles always add up to 180°, whereas its exterior angles are equal to the sum of the two interior angles that are not adjacent to it.
Given three angles,
∠A = (5x - 17)°
∠B = (7x - 3)°
∠C = 56°
We know that in a triangle ∠A + ∠B + ∠C = 180°
By substituting values,
(5x - 17) + (7x - 3) + 56 = 180
12x -20 + 56 = 180
12 x + 36 = 180
12x = 180 - 36
12x = 144
x = 144/12
x = 12
By substituting values of x we get,
∠A = (5x - 17)°
= 5 x 12 - 17
= 60 - 17
= 43
∠A = 43°
∠B = (7x - 3)°
= 7 x 12 - 3
= 84 - 3
= 81
∠B = 81°
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Help me with this !!!!!
Answer:
3. 30
4. 46
5. 55
Step-by-step explanation:
The average age of Elliot, Miya and Cara is 4 years more than the average
age of Elliot and Miya.
Cara is 9 years older than Elliot.
Four years ago, Elliot was double the age of Miya.
Work out the ages of Elliot, Miya and Cara.
Answer:
Elliot = 16 years old
Miya = 10 years old
Cara = 25 years old
Step-by-step explanation:
Define the variables:
x = Elliot's agey = Miya's agez = Cara's ageThe average age of Elliot, Miya and Cara is 4 years more than the average age of Elliot and Miya:
[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y}{2}+4[/tex]
[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y+8}{2}[/tex]
[tex]\implies 2(x+y+z)=3(x+y+8)[/tex]
[tex]\implies 2x+2y+2z=3x+3y+24[/tex]
[tex]\implies 2z=x+y+24[/tex]
[tex]\implies x=2z-y-24[/tex]
Cara is 9 years older than Elliot:
[tex]\implies z = x + 9[/tex]
Four years ago, Elliot was double the age of Miya:
[tex]\implies (x - 4) = 2(y - 4)[/tex]
[tex]\implies x - 4 = 2y-8[/tex]
[tex]\implies x +4 = 2y[/tex]
[tex]\implies y=\dfrac{1}{2}x +2[/tex]
Substitute the equations for z and y into the equation for x and solve for x:
[tex]\implies x=2z-y-24[/tex]
[tex]\implies x=2(x+9)-\left(\dfrac{1}{2}x +2\right)-24[/tex]
[tex]\implies x=\dfrac{3}{2}x-8[/tex]
[tex]\implies \dfrac{1}{2}x=8[/tex]
[tex]\implies x=16[/tex]
Substitute the found value of x into the equation for z and solve for z:
[tex]\implies z = 16 + 9[/tex]
[tex]\implies z = 25[/tex]
Substitute the found value of x into the equation for y and solve for y:
[tex]\implies y=\dfrac{1}{2}(16) +2[/tex]
[tex]\implies y=8+2[/tex]
[tex]\implies y=10[/tex]
Therefore, the ages of Elliot, Miya and Cara are:
Elliot = 16 years oldMiya = 10 years oldCara = 25 years oldits 9/16 close to 0, 1/2 or 1 explain
Answer: It's closer to 1/2
Step-by-step explanation: It's closer to 1/2 and here's why:
So, 1/2 (exact) is 8/16
0 = 0
1 = 16/16
Since 9/16 is the closest to 8/16 or around 1/2 in this case, it'd be about 1/2. I hope this helps!
DB =4.3cm BC=6.7cm
How do I find x° ?
Which statement is true for log3(x+1)=2?
Answer:
It is A: A: x+1=3^2 on EDG
Step-by-step explanation:
7. (a) A homeowner wishes to replace the three identical steps leading to her front door with a ramp. Each step is 10 cm high and 35 cm long. Find the length of the ramp. Give your answer correct to one decimal place.
Answer: To replace the three steps with a ramp, the height of the ramp must be equal to the total height of the steps. Since each step is 10 cm high, the total height of the three steps is 3 * 10 = 30 cm.
The length of the ramp must be equal to the length of the steps, since the ramp is replacing them. Since each step is 35 cm long, the total length of the three steps is 3 * 35 = 105 cm.
So the length of the ramp to replace the three steps leading to the front door is 105 cm, correct to one decimal place.
Step-by-step explanation: