Answer:
b. Conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.
Step-by-step explanation:
Before testing, we need to understand the central limit theorem and subtraction of normal variables.
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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Samples of 31 weeks. The mean attendance on Tuesday evening is calculated as 5,060, with a population standard deviation of 540.
This means that:
[tex]\mu_{T} = 5060, s_T = \frac{540}{\sqrt{31}} = 97[/tex]
The mean attendance on Wednesday evening is calculated as 5,390, with standard deviation of 480.
This means that:
[tex]\mu_{W} = 5390, s_W = \frac{480}{\sqrt{31}} = 86.21[/tex]
A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening.
At the null hypothesis we test if there is no difference, that is:
[tex]H_0: \mu_T - \mu_W = 0[/tex]
At the alternate hypothesis, we test if there is difference, that is:
[tex]H_a: \mu_T - \mu_W \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples collected:
[tex]X = \mu_T - \mu_W = 5060 - 5390 = -330[/tex]
[tex]s = \sqrt{s_T^2+s_W^2} = \sqrt{97^2+86.21^2} = 129.77[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-330 - 0}{129.77}[/tex]
[tex]z = -2.54[/tex]
Pvalue of test and decision:
The pvalue of the test is finding the probability of the sample mean difference differing by 0 by at least 330, that is, P(|z| > 2.54), which is 2 multiplied by the pvalue of z = -2.54.
Looking at the z-table, z = -2.54 has a pvalue of 0.0067.
2*0.0067 = 0.0134
The pvalue of the test is 0.0134 < 0.05, which means that there is evidence that the mean attendance differs. The correct answer is given by option b.
Rose decided to buy a photocopy machine that is projected to yield cash savings of RM2,000 per year over a 20 years period. Using a 15% discount rate, calculate the present value of the savings.
(Assume that the cash savings occur at the end of the year)
Answer:
RM832.29
Step-by-step explanation:
Calculate PV Savings
To calculate the present value of the savings, we can use the formula:
PV = cash savings / (1 + r)^t
Where PV is the present value, r is the discount rate, and t is the number of years.
Plugging in the values given in the problem, we get:
PV = RM2,000 / (1 + 0.15)^20
= RM2,000 / 1.15^20
= RM832.29
So the present value of the savings is RM832.29.
Answer: RM25,919.89.
Step-by-step explanation:
The present value of the cash savings is the sum of the present value of each year's cash savings.
To calculate this, the formula for the present value of a single cash flow is used:
Present Value = Future Value / (1 + r)^n
Where r is the discount rate, and n is the number of years.
So, for the first year's cash savings, the present value would be:
PV = 2000 / (1 + 0.15)^1 = 1739.13
For the second year's cash savings, the present value would be:
PV = 2000 / (1 + 0.15)^2 = 1510.71
This can be repeated for the remaining 18 years, and the sum of all the present values is the total present value of the cash savings over 20 years:
Total PV = 1739.13 + 1510.71 + .... + 437.66 = RM25,919.89
Therefore, the present value of the cash savings over 20 years with a 15% discount rate is RM25,919.89.
The amount of time in seconds, t, it takes for a bungee jumper to free fall is given by the function t equals the square root of the quantity d over 16 end quantity comma where d represents the distance that the object falls, in feet. If a bungee jumper free falls for 5 seconds, how far does the jumper fall? (5 points)
400 feet
160 feet
6,400 feet
80 feet
If the amount of time in seconds, t, it takes for a bungee jumper to free fall is given by the function t equals the square root of the quantity d over 16. The distance the jumper fall is: A 400 feet.
How to find the distance?Using this formula to find the distance by solving for d
t=√d/q
Where:
t = Time = 5 seconds
d = Distance = ?
q = Quantity = 16
So,
5 seconds=√d/16
d=16x5²
d=16 × 25
d= 400 feet
Therefore we can conclude that the correct option is A.
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A town has a population of 18000 and grows at 2% every year. What will be the population after 11 years, to the nearest whole number?
Answer:
~22381
Step-by-step explanation:
a=starting value = 18000
r=rate = 2%=0.02
Exponential Growth:
b=1+r=1+0.02=1.02
b=1+r=1+0.02=1.02
Write Exponential Function:
y=18000(1.02)^x
y=18000(1.02)
x
Put it all together
\text{Plug in time for x:}
Plug in time for x:
y=18000(1.02)^{11}
y=18000(1.02)
11
Evauate:
y= 22380.73755
y=22380.73755
Round:
y\approx 22381
y≈22381
Could someone use my Gauthmath code 8APGFB to help me gain more tickets? My math review sheet is crazzzzzzy.
Answer:
Okay
Step-by-step explanation:
I will try to help you
Answer:
Ok I also have a code: F5LS4F
Step-by-step explanation:
I heard you can get tickets in their discord community or something like that.
3) Mr. Johnson uses 2.34 yards of yarn to knit a scarf. If Mr. Johnson has a total of 30.42 yards of yarn, how many scarfs will he be able to knit?
she will be able to knit 13 scarfs
Given ,
Mr. Johnson uses 2.34 yards of yarn to knit a scarfMr. Johnson has a total of 30.42 yards of yarnTo Find : Scarfs Mr John will be able to make if he has 30.42 yards of yarn
2.34 yards of yarn = 1 scarf
30.42 yards of yarn = [tex]\frac{30.42}{2.34}[/tex]
= 13 scarfs
Hence , the number of scarfs Mr John will make with 30.42 yards of yarn is 13
please help it’s due in half an hour
Answer:
(a) They asked for one value of x
but I'll give you both
They're 2 and -2
(b)g(-1) = 4
Step-by-step explanation:
For (a) they're are looking for the value of x that is corresponding to 1 on the y axis
If you observe from your graph only -2 and 2 will have a corresponding value of 1 therefore they're the answers
for (b) Just look for the corresponding value of -1(x -axis) on the y axis which is 4
For a given arithmetic sequence, the first term, 47, is equal to 26, and the 37 th term, a37, is equal to 278. th Find the value of the 4th term, a4.
9514 1404 393
Answer:
47
Step-by-step explanation:
Given:
a1 = 26, a37 = 278
Find:
a4
Solution:
Filling in the given values in the formula for the general term of an arithmetic sequence, we have ...
an = a1 +d(n -1)
a37 = 26 +d(37 -1) = 278
d = (278 -26)/36 = 7 . . . . . . solve for d
Then the 4th term is ...
a4 = 26 +7(4 -1)
a4 = 47
I need help because I don't understand and I need an explanation of how to do it, please.
Answer:
Step-by-step explanation:
a.we konw DC=2b and DO=OC, so the coordinate of D(-b, 0), C(b, 0)
b.we konw the height of rectangle is h, so the coordinate of A(-b, h), B(b, h).
Anna has 60 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exactly four times as many pennies as dimes, how many pennies are in her piggy bank?
A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours.
(a) Identify the parameters in this situation.
(b) Identify the statistics in this situation.
(c) Suppose we were to make a histogram of the finishing times of all participants in the duathlon. Which of the following would the histogram be a display of?
i. Population distribution
iii. Distribution of a sample
ii. Sampling distribution of means
(d) Suppose the process of taking random samples of size 30 is repeated 200 times and a histogram of 200 sample means is created. Which of the following would the histogram be a display of?
i. Population distribution
ii. Distribution of a sample
iii. Sampling distribution of means
(e) What is the standard error for the mean finish time of 30 randomly selected participants?
(f) If one participant is selected at random, what is the probability that his/her time will be less than 1.59 hours.
(g) What is the probability that another sample of 30 randomly selected participants will have a mean finishing time of 1.59 hours or less?
Answer:
A.) Parameter = 1.67 ; 0.25
B.) Statistic = 1.59, 0.30
C.) Population distribution
D.) Sampling distribution of means
E.) 0.058
F.) 0.395
G.) 0.072
Step-by-step explanation:
A.) The parameters are measured quantities or characteristics derived from the population. The parameter here describes the mean and standard deviation of all participants ;
Population mean = 1.67
Population standard deviation = 0.25
B.) Statistic are measured quantities which are characteristics of the sample. Here, we have the sample mean and standard deviation
Sample mean = 1.59
Sample standard deviation = 0.30
C.) The population distribution is the plot of the histogram prepared using data from the population (all participants)
D.) The plot of the mean value obtained from the repeated measurement or simulation of the sample data is called sampling distribution of the means.
E.) Mean finish time of 30 randomly participants :
Sample size, n = 30
Standard Error = s/√n
Standard Error = 0.30 /√30 = 0.0548
F.) If one participant is selected at random, what is the probability that his/her time will be less than 1.59 hours
P(x < 1.59)
Z = (xbar - μ) / σ ; (1.59 - 1.67) / 0.30 = - 0.267
P(Z < - 0.267) = 0.395 (Z probability calculator)
G.) P(x < 1.59)
Z = (xbar - μ) / s ; (1.59 - 1.67) / (0.30/√30) = - 1.46
P(Z < -1.46) = 0.072 (Z probability calculator)
Lee’s fish is 4 centimeters long.
Tia’s fish is 11 centimeters long.
What is the geometric mean of 12 and 15?
Answer:
The geometric mean is 9.798
Step-by-step explanation:
Answer:
13.416407864998738
A student made two patterns to show multiplication of a decimal by powers of ten. the equations shown for both patterns are incorrect. pattern A
3.675. 10 =3.7650
3.675. 100= 3.67500
3.675.1,000= 3.675000
pattern B
3.675. 10=3.0675
3.675.0.01= 3.00675
3.675. 0.001= 3.000675
explain why the equations in each of the patterns are false. Include in your explanation the values that should appear on the right side of each equation in both patterns to make the equations true.
If a student made two patterns to show multiplication of a decimal by powers of ten. All the value are incorrect. The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.
How to find the correct value?Pattern A
3.675×10 =3.7650 Incorrect
3.675×10 = 36.75 Correct
3.675× 100= 3.67500 Incorrect
3.675×100= 367.5 Correct
3.675×1,000= 3.675000 Incorrect
3.675×1,000 = 3,675 Correct
Pattern B
3.675×10=3.0675 Incorrect
3.675× 10= 36.75 Correct
3.675×0.01= 3.00675 Incorrect
3.675×0.01= 0.03675 Correct
3.675×0.001= 3.000675 Incorrect
3.675×0.001= 0.003675 Correct
The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.
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5. Mariel volunteers at the
animal shelter 3 times a month.
After 6 months, how many
times has she volunteered at
the animal shelter?
If the radius is 10 ft, what will be the area of the circle!
Answer:
314
Step-by-step explanation:
Formula for area -> A= PI times radius squared
10x10=100x3.14+314
Answer:
314.16ft
Step-by-step explanation:
Diameter = 2
×
Radius
Diameter = 2
×
10
Diameter = 20 feet
Can you please help me faster please help me if you know???!!!
Answer:
29%
Step-by-step explanation:
5+48+22=75
22/75=0.2933
nearest % is 29%
evaluate (4√81)³.............
Please help, thank you
Answer:
9.42
Step-by-step explanation:
Using the law of Sines we get
[tex]a = 14 \times \frac{ \sin(41) }{ \sin(77) } = 9.426[/tex]
The angle (77) was found by subtracting 41 and 62 from 180.
180 - 41 - 62 = 77
Answer:
Chapppppppp kid l Hfhssh
Can someone tell me the answer?
Answer:
I believe the train arrived at 5:30 am.
Answer:
5:30 AM
Step-by-step explanation:
Add the two times it took to travel together, and add it to 8:55 PM, you'll end up with 5:30 AM
you can use a calculator if you want. No links please help this is very important i will give you brain thing if its correct
Answer:
A, D
Step-by-step explanation:
1.67+1.4>3, 4.6-1.47>3.
Answer:
A and D
Step-by-step explanation:
How many -pound bags of soap flakes can Mr. Newman fill?
Answer:
where is the other part of the question
A chef makes small and large snacks to sell at a local art show. He cannot make more than 30
snacks before the show, with no more than 6 large snacks. The chef must make at least 10 small snacks to
earn a profit.
Part A
Let x represent the number of small snacks and y represent the number of large snacks. Given x ≥ 0 and
y 20, select all the inequalities that represent the situation.
0 x≤6
O y ≥ 10
Ox+y≤ 30
O 10x+6y≤ 30
0y≤6
0 x ≥ 10
-01:25
the inequalities that represent the situation are,
Ox+y≤ 30
0y≤6
0 x ≥ 10
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
Here, given that,
A chef makes small and large snacks to sell at a local art show.
He cannot make more than 30
snacks before the show, with no more than 6 large snacks.
The chef must make at least 10 small snacks to earn a profit.
Let,
x represent the number of small snacks
and y represent the number of large snacks.
Given x ≥ 0 and y 20
So, we get,
the inequalities that represent the situation are,
Ox+y≤ 30
0y≤6
0 x ≥ 10
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Find the slope of the line through each pair of points.
(4, 18), (4, -11)
Answer:
undefined
Step-by-step explanation:
slope formula:
m =y2-y1 / x2-x1
m= -11-18 / 4-4= -29/0
you cannot divide by zero so the slope is undefined
8. If 5/12.5 is equivalent to -4/2x, what is the value of x?
Answer:
-5
Step-by-step explanation:
[tex]\frac{5}{12.5} = \frac{-4}{2x}[/tex]
[tex]5 \cdot 2x = 12.5 \cdot -4[/tex]
[tex]10x = -50[/tex]
[tex]x=-5[/tex]
Question 6 of 40
Multiply (x2 + 2x + 3)(4x2 – 2x + 1).
O A. 5x2 + 4
O B. 4x + 10x + 17x2 + 8x + 3
O C. 44 + 6x3 + 9x2 - 4x + 3
O D. 44 - 4x2 + 3
Jdjdjdjd
Help jajasjjaj
Answer:
x=57
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
(x-5) + (2x-7) + 21 = 180
Combine like terms
3x +9 = 180
Subtract 9 from each side
3x+9-9= 180-9
3x = 171
Divide by 3
3x/3 =171/3
x =57
maybe explain what a dependent is in math pls
4. Choose the expression that matches the following statement: three times the difference of
two times a number and 7 taken from 8 of a number.
a) 2x+21
b) 2x - 21
c) -2x - 21
d) -2x - 7
Toby buys packs of 12 racing cars for R49,99 and sells each racing car for R10 at school
1.1 Determine the cost price per racing car
1.2 calculate the profit toby makes per racing car
1.3 Determine toby's profit margin on one pack 12 racing car
Answer:
1.1 R5.83
1.2 R70.01
1.3 58.34%
Step-by-step explanation:
Given that he buys a pack of 12 racing cars for R49,99 then the unit cost for a car which is the total cost divided by the number of cars in a pack
= R49,99/12
= R4.17
If each car is sold for R10 then the profit made on each car which is the difference between the cost and the selling price
= R10 - R4.17
= R5.83
The profit margin on one pack of 12 racing cars
Profit margin is the ratio of the profit to the total selling price
The total profit (profit on one pack of 12 racing cars)
= R5.83 * 12
=R70.01
Total selling price = R10 * 12
=R120
Margin = R70.01 / R120
= 58.34%
1. The sum of two angles is 85°, one angle is five more than the measure of the other angle. Write the equation that represents this scenario and find the measure of each angle. Be sure to show your
work.
On solving the provided question, we can say that - by equation angles will be, x + 5x = 85 => 6x = 85 => x = 14.1666666667
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
let one angle be = x
other angle be 5x
then, x + 5x = 85
6x = 85
x = 14.1666666667
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