Answer:
yes
Step-by-step explanation:
no
maybe
perhaps
done
Where is the treasure?
A treasure is hidden under a number on the hundreds chart.
Use the clues to shade the other 99 numbers. The number
that is left unshaded holds the treasure.
• Shade the numbers in the patterns described below.
A. Start at 3. The rule is: Subtract 2, and then add 5.
B. Start at 2. The rule is: Add 6.
C. Start at 5. The rule is: Add 12.
D. Start at 83. The rule is: Subtract 12.
E. Start at 1. The rule is: Add 3.
Answer:
The treasure is hidden under 95.
Step-by-step explanation:
The numbers are:
[tex]1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\\21, 22, 23, 24, 25,26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40\\41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60\\61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80\\81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,100[/tex]
Clue A:Start at 3. The rule is: Subtract 2, and then add 5.
3-2+5=6
6-2+5=9
Therefore, this rule eliminates all multiples of 3.
[tex]1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20\\22, 23, 25,26, 28, 29, 31, 32, 34, 35, 37, 38, 40\\41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, \\61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80\\82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100[/tex]
Clue B:Start at 2. The rule is: Add 6.
The numbers are:2,8,14,...
We have left:
[tex]1, 4, 5, 7, 10, 11, 13, 16, 17, 19, \\22, 23, 25, 28, 29, 31, 34, 35, 37, 40\\41, 43, 46, 47, 49, 52, 53, 55, 58, 59, \\61, 64, 65, 67, 70, 71, 73, 76, 77, 79, \\82, 83, 85, 88, 89, 91, 94, 95, 97, 100[/tex]
Clue C: Start at 5. The rule is: Add 12.
The numbers are: 5,17,29,...
We have left:
[tex]1, 4, 7, 10, 11, 13, 16, 19, \\22, 23, 25, 28, 31, 34, 35, 37, 40\\ 43, 46, 47, 49, 52, 55, 58, 59, \\61, 64, 67, 70, 71, 73, 76, 79, \\82, 83, 85, 88, 91, 94, 95, 97, 100[/tex]
Clue D: Start at 83. The rule is: Subtract 12.
The numbers are 83,71,59,...
We have left:
[tex]1, 4, 7, 10, 13, 16, 19, \\22, 25, 28, 31, 34, 37, 40\\ 43, 46, 49, 52, 55, 58, \\61, 64, 67, 70, 73, 76, 79, \\82, 85, 88, 91, 94, 95, 97, 100[/tex]
Clue E: Start at 1. The rule is: Add 3.
The numbers are 1,4,7,...
We are left with:
[tex]95[/tex]
The treasure is hidden under 95.
The number of hours per week that high school seniors spend on computers is normally distributed, with a mean of 6 hours and a standard deviation of 2 hours. 80 students are chosen at random. Let y be the mean number of hours spent on the computer for this group.
Find the probability that y is between 6.2 and 6.9 hours.
To find the probability that y is between 6.2 and 6.9 hours, calculate the z-scores and use the standard normal distribution table.
Explanation:To find the probability that y is between 6.2 and 6.9 hours, we need to calculate the z-scores corresponding to these values and then use the standard normal distribution table. The formula to calculate the z-score is z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
For 6.2 hours: z = (6.2 - 6) / 2 = 0.1
For 6.9 hours: z = (6.9 - 6) / 2 = 0.45
Using the standard normal distribution table, the probability that y is between 6.2 and 6.9 hours is P(0.1 ≤ z ≤ 0.45). Thus, in the z table the P(Z x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 4.02 and x = 0.89 in the z table which has an area of 0.99997 and 0.81327 respectively.}
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Question:A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, of which 1062 support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, of which 900 support the candidate. A 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is:A. 0.050 to 0.112.B. 0.035 to 0.127.C. 0.040 to 0.122.D. 0.037 to 0.119.
Answer:
The correct option is (A).
Step-by-step explanation:
The (1 - α)% confidence interval for difference in proportion formula is,
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha /2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
The given information is:
n₁ = n₂ = 200,
X₁ = 1062,
X₂ = 900.
Compute the sample proportion as follows:
[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{1062}{2000}=0.531\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{900}{2000}=0.45[/tex]
For the 95% confidence level, the z-value is,
z₀.₀₂₅ = 1.96
*Use a z-table.
Compute the 95% confidence interval for the difference in proportion as follows:
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha /2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
[tex]=(0.531-0.45)\pm1.96\sqrt{\frac{0.531(1-0.531)}{2000}+\frac{0.45(1-0.45)}{2000}}[/tex]
[tex]=0.081\pm 0.031\\=(0.050, 0.112)[/tex]
Thus, the 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is (0.050, 0.112).
The correct option is (A).
plz ban mewerf32wfwef
Answer:
Why do they delete your question and answers too??
Step-by-step explanation:
A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (> r) from the center of the circle. Find the volume of the torus.
Consider a circle with radius [tex]r[/tex] centered at some point [tex](R+r,0)[/tex] on the [tex]x[/tex]-axis. This circle has equation
[tex](x-(R+r))^2+y^2=r^2[/tex]
Revolve the region bounded by this circle across the [tex]y[/tex]-axis to get a torus. Using the shell method, the volume of the resulting torus is
[tex]\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx[/tex]
where [tex]2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}[/tex].
So the volume is
[tex]\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx[/tex]
Substitute
[tex]x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt[/tex]
and the integral becomes
[tex]\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt[/tex]
Notice that [tex]\sin t\cos^2t[/tex] is an odd function, so the integral over [tex]\left[-\frac\pi2,\frac\pi2\right][/tex] is 0. This leaves us with
[tex]\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt[/tex]
Write
[tex]\cos^2t=\dfrac{1+\cos(2t)}2[/tex]
so the volume is
[tex]\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}[/tex]
Suppose he makes two stops of 10 minutes each during his journey. Will he be
able to reach the town in 4 hours if he keeps the speed the same?
Answer:
No, he would not be able to reach the town in 4 hours with two 10 minutes stops and same speed
Completed question;
Max travels to see his brother's family by car. He drives 216 miles in 4 hours. What is his rate in miles per hour? Suppose he makes two stops of 10 minutes each during his journey. Will he be able to reach the town in 4 hours if he keeps the speed the same?
Step-by-step explanation:
Average speed = total distance travelled/time taken
Given;
Total distance travelled= 216 miles
Total time taken = 4 hours
Average speed v = 216/4 = 54 miles per hour
v = 54 mph
Suppose he makes two stops of 10 minutes each during his journey.
Total time on stops = 2 × 10 = 20 minutes = 0.33 hours
Total time spent on motion = 4 - 0.33 hours = 3.67 hours
Total distance covered in 4 hours with two stops;
d = 3.67 × 54 mph = 198.18 miles
Since d < 216 miles
No, he would not be able to reach the town in 4 hours with two 10 minutes stops and same speed
3x^2-5=43 how do i solve this using the square root property
Answer:
x = 4
x = -4
Step-by-step explanation:
bro i dont know but i hope this help a little, sorry
Need Help What Is -10r+9r
Answer:
-1r
Step-by-step explanation:
The value for the expression -10r + 9r is -1r.
what is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
-10r+9r
Now, perform operations to solve
=-10 r + 9r
= r( -10 + 9)
Using properties of integers
(-) x (+ )= -
So,
= r( -1)
= -1r
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You earned $96,000 last year. Your effective tax rate went as follows; Federal: 16.3, FICA: 7.65, state: 4.5. If you added them all and subtracted them from your gross income what would remain of your income from last year?
Answer:68688
Step-by-step explanation:123 Thats EZ
The income remaining after taxes from last year is $68,688.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
To calculate the amount of income remaining after taxes, we need to subtract the total taxes paid from the gross income.
The total tax rate is the sum of the federal tax rate, FICA tax rate, and state tax rate.
Total tax rate = Federal tax rate + FICA tax rate + State tax rate
Total tax rate = 16.3% + 7.65% + 4.5%
Total tax rate = 28.45%
So the total amount of taxes paid is:
Total taxes = Gross income x Total tax rate
Total taxes = $96,000 x 28.45%
Total taxes = $27,312
To find the income remaining after taxes, we subtract the total taxes paid from the gross income:
Income after taxes = Gross income - Total taxes
Income after taxes = $96,000 - $27,312
Income after taxes = $68,688
Therefore, the income remaining after taxes from last year is $68,688.
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The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger? Round to four decimal places.
Answer:
[tex]P(X\geq 3.4)=0.0228[/tex]
Step-by-step explanation:
Given the mean is 3.2, standard deviation is 0.8 and the sample size is 64.
-We calculate the probability of a mean of 3.4 as follows:
#First determine the z-value:
[tex]z=\frac{\bar X -\mu}{\sigma/\sqrt{n}}\\\\=\frac{3.4-3.2}{0.8/\sqrt{64}}\\\\=2.000[/tex]
#We then determine the corresponding probability on the z tables:
[tex]Z(X\geq 3.4)=1-P(X<3.4)\\\\=1-0.97725\\\\=0.0228[/tex]
Hence, the probability of obtaining a sample mean this large or larger is 0.0228
To find the probability of obtaining a sample mean of 3.4 pounds or larger, calculate the z-score and find the corresponding probability using the standard normal distribution table.
Explanation:To find the probability of obtaining a sample mean of 3.4 pounds or larger, we need to calculate the z-score for the sample mean and then find the corresponding probability using the standard normal distribution table.
First, calculate the z-score using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we have: z = (3.4 - 3.2) / (0.8 / √64) = 0.2 / (0.8 / 8) = 0.2 / 0.1 = 2.
Next, we can find the probability by looking up the z-score of 2 in the standard normal distribution table. The probability of obtaining a sample mean of 3.4 pounds or larger is approximately 0.0228 or rounded to four decimal places.
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Kate’s math homework had a set of equations and one word problem. She took 3 minuets to solve each other equation, then 7 minuets to solve the word problem. If it took her 52 minuets in total, how many equations did she solve?
Answer:
the answer will be 15
Step-by-step explanation:
If it took her 52 minuets in total, then 7 questions she solved.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be number of equations.
From the given information, we know that Kate took 3 minutes to solve each equation, so the total time she spent on equations is 3x minutes.
We also know that it took her 7 minutes to solve the word problem.
So, the total time she spent on equations and the word problem is:
3x + 7
According to the problem, this total time is 52 minutes:
3x + 7 = 52
Subtracting 7 from both sides, we get:
3x = 45
Dividing both sides by 3, we get:
x = 15
Therefore, Kate solved 15 equations.
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In estimating the mean score on a fitness exam, we use an original sample of size n 3 and a bootstrap distribution containing 5000 bootstrap samples to obtain a 95% confidence interval of 67 to 73. A change in this process is described below. If all else stays the same, which of the following confidence intervals (A, B, or C) is the most likely result after the change: Using an original sample of size n 16
O A. 66 to 74
O B. 67 to 73
c. 67.5 to 72.5
Increasing the sample size in a statistical analysis, from n=3 to n=16, will likely lead to a decrease in the width of the confidence interval, making it more precise. Therefore, the most likely confidence interval after the change would be option C, 67.5 to 72.5.
Explanation:In statistics, increasing the sample size reduces the standard error of the mean. The standard error defines the width of the confidence interval for a given sample size. If we increase the sample size from n=3 to n=16, the standard error and thus the width of the confidence interval will likely decrease, assuming all else stays the same. Hence, the confidence interval will be more precise.
Considering the given options, option C, a confidence interval of 67.5 to 72.5, represents a narrower interval and is therefore the most likely result after increasing the sample size from n=3 to n=16.
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Members of an online gaming group have been increasing by 25% every year. The group started with 75 members. How many members will the group have after 4 years?
183 member will the group have after 4 years, if the members of an online gaming group have been increasing by 25% every year. The group started with 75 members.
Step-by-step explanation:
The given is,
Members of an online gaming group is 75
Increasing by 25% every year
Step:1
Formula to calculate the members in gaming group after few years with an rate of increase,
[tex]F = P(1+r)^{t}[/tex].......................(1)
Where, F - Members in gaming group after 4 years
P - Members in gaming group in initially
r - Rate of increase in year
t - No. of years
Step:2
From the given,
P = 75 members
r = 25 %
t = 4 years
Equation (1) becomes,
[tex]F = 75(1+0.25)^{4}[/tex]
[tex]= 75(1.25)^{4}[/tex]
= ( 75 ) ( 2.441406 )
= 183.105
F ≅ 183 members
Result:
183 member will the group have after 4 years, if the members of an online gaming group have been increasing by 25% every year. The group started with 75 members
If angle A and angle B are supplementary angles and angle A is eight times as large as angle B, find the measures of angle A and angle B.
Step-by-step explanation:
A=8B
A+B=180
8B+B=180°
9B=180°
B=20°
so
angle A =8×20=160°
angle B= 20°
The requried measures of angles A and B are 160° and 20° respectively.
What are the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
Angle A and angle B are supplementary angles and angle A is eight times as large as angle B,
The sum of the supplementary angle is 180°
A + B = 180
8B + B = 190
B = 20
Now,
A = 8B
A = 160°
Thus, the requried measure of angles A and B are 160° and 20° respectively.
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At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is 50° Celsius. This causes the cake to cool and the temperature difference loses (1/5) of it's value every minute.
Write a function that gives the temperature difference in degrees Celsius, D(t), t minutes after the cake was put in the cooler.
Answer:: D(t)= 50(4/5)^t
Step-by-step explanation: If 1/5 of the temperature difference is lost each minute, that means 4/5 of the difference remains each minute. So each minute, the temperature difference is multiplied by a factor of 4/5 (or 0.8).
If we start with the initial temperature difference, 50° Celsius, and keep multiplying by 4/5, this function gives us the temperature difference t minutes after the cake was put in the cooler.
Answer:
See answer below
Step-by-step explanation:
Hi there,
The prompt is trying to showcase exponential functions, and specifically exponential decay, where over the course of the independent variable (time in this example) the dependent variable (temp difference) exponentially drops.
To start, when a math prompt says something like "at the moment xyz begins" it usually means time zero. Thus, we have 1 point already, the y-intercept:
[tex]D(0)= 50 \ C[/tex]°
Now, we notice that it says it "loses 1/5 of its original value every minute" which is code for exp. decay. So, to account for this, the remaining value is just b = 1 - 0.2 = 0.8.
Exponential Decay formula:
[tex]f(x) = a (1-r)^x[/tex] where a is a constant, and constant r [tex]< 1[/tex]
[tex]D(t) = 50 * (0.8)^t \ C[/tex]° where t is in minutes
thanks,
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What is the area of the irregular figure below?
A figure can be broken into a parallelogram and triangle. The parallelogram has a baes of 4 inches and height of 6 inches. The triangle has a base of 4 inches and height of 6 inches.
36 Inches squared
48 Inches squared
144 Inches squared
288 Inches squared
We just need to find the area of the parallelogram and the triangle, and then add.
Parallelogram: The area is base times height. So, we can write 4 * 6 = 24 in^2.
Triangle: The area is base times height divided by two. So, it's 4 * 6 / 2 = 12 in^2.
24 + 12 gives us an answer of 36 inches squared.
Answer:
36 inches squared
Step-by-step explanation:
Which of the following data displays does not show individual data values, but rather shows the number of values that fall within a series of
specified ranges?
A.histogram
B. box plot
C. dot plot
D. scatter plot
Answer:
The answer is A.histogram
Step-by-step explanation:
Statistical data can be represented on charts such as histograms, box plots, etc.
The (a) histogram shows the number of values within series of a range
From the question, we understand that:
The required chart does not show individual data valuesThe required chart shows data in rangeThe chart that supports the above highlights is the histogram.
This is so because, it can be used to illustrate grouped data (i.e. data in series of a range), while others are not suitable for grouped data.
Hence, the chart is (a) histogram
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The triangles below are similar. Triangle G H F. Angle G is 65 degrees, H is 24 degrees, F is 91 degrees. Triangle J K L. Angle J is 24 degrees, K is 91 degrees, L is 65 degrees. Which similarity statement expresses the relationship between the two triangles? Triangle F G H is similar to Triangle K L J Triangle F G H is congruent to Triangle K L J Triangle F G H is similar to triangle J K L Triangle F G H is similar to triangle J K L
Answer:
Triangle F G H is similar to Triangle K L J
Step-by-step explanation:
Angle H = Angle J
Angle G = Angle L
Angle F = Angle K
KLJ is similar to FGH
If the lengths are also equal, then they're congruent
Triangle FGH is similar to triangle JKL.
To express the relationship between the two triangles using a similarity statement, we need to match corresponding angles.
Since the triangles are similar, corresponding angles are congruent.
In triangle FGH,
the angles are 65° , 24° , and 91 °
In triangle JKL,
the angles are 24° ,91° , and 65°
We see that the angles 24° , 91°, and 65° in triangle JKL match the angles in triangle FGH respectively.
So, the similarity statement expressing the relationship between the two triangles is:
Triangle FGH is similar to triangle JKL.
An open box is made from a 30-cm by 70-cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 1536 cm2. What is the length of the sides of the squares?
To find the length of the sides of squares cut from a piece of tin to create an open box, we use the dimensions of the tin and the area of the box's base to set up and solve a quadratic equation.
Explanation:The student is asking for the length of the sides of the squares that are cut out from a piece of tin to create an open box. Given that the tin measures 30 cm by 70 cm, and the area of the base of the resulting box is 1536 cm2, we can set up an equation to solve for the side length of the squares.
Let's denote the side length of the squares as x. After the squares are cut out, the length and width of the base of the box will be (70 - 2x) and (30 - 2x) respectively. The area of the base is given by:
Area = length × width
1536 cm2 = (70 - 2x)(30 - 2x)
By expanding this and solving the quadratic equation for x, we can find the length of the sides of the squares cut from each corner of the tin.
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A commuter must pass through five traffic lights on her way to work, and she will have to stop at each one that is red. After years of commuting she has developed the following probability distribution for the number of red lights she stops at each day on her way to work: No. of red lights x 0 1 2 3 4 5 Probability .05 .25 .30 .20 .15 .05 Note that the standard deviation of the above probability distribution is SD(X) = 1.27.
Answer:
Step-by-step explanation:
Hello!
You have the information about the number of red lights a commuter pass on her way to work and the probability of them stoping her:
Be x: number of red lights
X: 0, 1, 2, 3, 4, 5
hi: 0.05, 0.25, 0.30, 0.20, 0.15, 0.05
a. What is the expected number of red lights at which she will stop on her way to work?
The expected number of red lights is the sample mean, you can calculate it using the following formula:
[tex]X[bar]= sum Xi*hi= (0*0.05)+(1*0.25)+(2*0.30)+(3*0.20)+*(4*0.15)+(5*0.05)=2.3[/tex]
She's expected to be stopped by 2.3 red lights on the way to work.
b. Suppose each red light delays the commuter 1.8min. What is the standard deviation od the number of minutes that she is delayed by red lights?
If each light delays the commuter 1.8 min then you can determine a new variable of interest:
Be Y: the time a commuter is delayed by red lights on the way work, then Y= X*1.8min
Meaning if X= 0, then Y=0 (the commuter will be delayed 0 min), if X=1, then Y= 1.8min, if X=2, then Y= 3.6min and to on....
The properties of variance state that if
Y= X*k (Where K= constant)
Then the sample variance of Y will be
V(Y)= V(X*k)= k²*V(X)
Then the standard deviation of Y will be the constant k by the standard deviation of X:
Sy= k*Sx= 1.8 * 1.27= 2.286
I hope it helps!
5 260 people are randomly chosen at a shopping mall to taste-test a new brand of fruit drink. They are asked to rate the drink on a scale from 1 to 7, with 1 being very bad and 7 being very good. The results of the survey reveal that the average rating is 5.22 with a standard deviation of 2.31. The marketing division of the fruit drink distributor is only interested in selling this drink if the true mean rating is more than 4.75.
What is the alternative hypothesis for testing whether the fruit drink distributor should sell this drink?
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 4.75
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 4.75
Step-by-step explanation:
We are given that 260 people are randomly chosen at a shopping mall to taste-test a new brand of fruit drink. The results of the survey reveal that the average rating is 5.22 with a standard deviation of 2.31.
The marketing division of the fruit drink distributor is only interested in selling this drink if the true mean rating is more than 4.75.
Let [tex]\mu[/tex] = true mean rating.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 4.75
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 4.75
Here, null hypothesis states that the true mean rating is less than or equal to 4.75.
On the other hand, alternate hypothesis states that the true mean rating is more than 4.75.
Also, The test statistics that will be used here is One-sample t test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
Hence, the alternative hypothesis for testing whether the fruit drink distributor should sell this drink is [tex]\mu[/tex] > 4.75.
A botanist collected one leaf at random from each of 10 randomly selected mature maple trees of the same species. The mean and the standard deviation of the surface areas for the 10 leaves in the sample were computed.Assume the distribution of surface areas of maple leaves is normal. What is the appropriate method for constructing a one-sample confidence interval to estimate the population mean surface area of the species of maple leaves, and why is the method appropriate?
Answer:
One sample t-test for population mean would be the most appropriate method.
Step-by-step explanation:
Following is the data which botanist collected and can use:
Sample meanSample Standard DeviationSample size (Which is 10)Distribution is normalWe have to find the best approach to construct the confidence interval for one-sample population mean. Two tests are used for constructing the confidence interval for one-sample population mean. These are:
One-sample z test for population meanOne-sample t test for population meanOne sample z test is used when the distribution is normal and the population standard deviation is known to us. One sample t test is used when the distribution is normal, population standard deviation is unknown and sample standard deviation is known.
Considering the data botanist collected, One-sample t test would be the most appropriate method as we have all the required data for this test. Using any other test will result in flawed intervals and hence flawed conclusions.
Therefore, One-sample t-test for population mean would be the most appropriate method.
Ignoring those who said they weren't sure, there were 297 men asked, and 183 said yes, they had driven a car when they probably had too much alcohol. Does this provide statistically significant evidence that a majority of men in the population (that is, more than half) would say that they had driven a car when they probably had too much alcohol, if asked
Answer:
[tex]z=\frac{0.616-0.5}{\sqrt{\frac{0.5(1-0.5)}{297}}}=3.998[/tex]
[tex]p_v =2*P(z>3.998)=0.0000639[/tex]
With the most common significance levels used [tex]\alpha= 0.1, 0.05, 0.01[/tex] we see that the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can say that the true proportion is significantly higher than 0.5
Step-by-step explanation:
Information given
n=297 represent the random sample of male taken
X=183 represent the men who said yes, they had driven a car when they probably had too much alcohol
[tex]\hat p=\frac{183}{297}=0.616[/tex] estimated proportion of men who said yes, they had driven a car when they probably had too much alcohol
[tex]p_o=0.5[/tex] is the value that we want to test
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Hypothesis to test
We need to conduct a hypothesis in order to test the claim that the majority of men in the population (that is, more than half) would say that they had driven a car when they probably had too much alcohol, and the system of hypothesis are:
Null hypothesis:[tex]p\leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
After replace we got:
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.616-0.5}{\sqrt{\frac{0.5(1-0.5)}{297}}}=3.998[/tex]
Decision
We have a right tailed test so then the p value would be:
[tex]p_v =2*P(z>3.998)=0.0000639[/tex]
With the most common significance levels used [tex]\alpha= 0.1, 0.05, 0.01[/tex] we see that the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can say that the true proportion is significantly higher than 0.5
Find the perimeter 8ft 11ft
Answer:
38ft
Step-by-step explanation:
I'm assuming that you mean that the dimensions are 8ft by 11ft
If so, you need to add all the sides together, there should be two 8ft sides and two 11ft sides
8*2 = 16 (or 8+8
11*2= 22 (or 11+11
16+22 = 38
A new screening test for a disease is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Four hundred (400) people are screened at a clinic during the first year the new test is implemented. (Assume the true prevalence of the disease among clinic attendees is 10%.)Calculate the following values11) The number of false positives is:A. 108B. 132C. 24D. 252
Answer:
The number of false positives is 108. The right answer is A
Step-by-step explanation:
According to the given data we have the following:
probability of negative results which are correcly identified =0.7
probability of negative results which are wrongly identified =1-0.7 =0.3
hence, probability of negative result = 1-0.1 =0.9
Therefore, in order to calculate the number of false positives we would have to use the following formula:
false positives =total number * probability of negative results which are wrongly identified * probability of negative result=400 * 0.9*(1-0.7) = 108
false positives = 400 * 0.9*(1-0.7)
false positives = 108
The number of false positives is 108
14-8+5-2+6-11= a(4) b(8) c (20) d (26)
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 430 gram setting. It is believed that the machine is underfilling the bags. A 17 bag sample had a mean of 423 grams with a variance of 676. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses
Answer:
[tex]H_o:\mu\geq 430\\\\H_a:\mu<430[/tex]
Step-by-step explanation:
-let [tex]\mu[/tex] denote the population mean in grams.
-The claim under investigation is that the machine is underfilling the bags.
-The investigator intends to determine whether or not the population mean is less than 430 grams.
#The stated hypotheses are:
The null hypothesis(mean gram of the bags is greater or equal to 430g):
[tex]H_o:\mu\geq 430\\\\[/tex]
-Alternative hypothesis is the population mean is less than 430g:
[tex]H_a:\mu<430[/tex]
AllElectronics carries 1000 products, P1, . . . , P1000. Consider customers Ada, Bob, and Cathy such that Ada and Bob purchase three products in common, P1,P2, and P3. For the other 997 products, Ada and Bob independently purchase seven of them randomly. Cathy purchases 10 products, randomly selected from the 1000 products. In Euclidean distance, what is the probability that dist(Ada,Bob) > dist(Ada,Cathy)
Answer:
The probability that dist(Ada,Bob)>(Ada,Cathy) is very small as there is very large number of range to choose the product ==4.7*10^-9.
Step-by-step explanation:
Given:
Ada ,bob and cathy purchase electronics carries
Ada and bob commonly take 3 products and 7 independently.
And Cathy take 10 products on its own .
To Find:
probability that dist(Ada,bob)>dis(Ada,Cathy)?
Solution:
Using Euclidean distance is distance formula used in coordinate geometry simply known as Distance formula,
this problem is related to Euclidean Distance and Jaccard Similarity in Data mining.
1st calculate probability for x such that ,
[tex]3\leq x\leq 10[/tex] as there are 3 common products.
P([tex]3\leq x\leq 10[/tex])
=[tex]\frac{7C(x-3)*990C(10-x)}{997C7}[/tex].............. where x=3,4,5....10. ..........(equation 1).
Now calculate for each term,we get
When
x=3,P(x=3)=0.95
x=4,P(x=4)=[tex]6.8*10^{-3}[/tex]
x=5,P(x=5)=[tex]4.1*10^{-5}[/tex]
x=6,P(x=6)=2.1*10^-7
x=7,P(x=7)=8.5*10^-10
x=8,P(x=8)=2.6*10^-12
x=9,P(x=9)=5.2*10^-15
x=10,P(x=10)=5.3*10^-18.
Now calculating the Euclidean distance,
It is distance between two points ,
So there are total of 2 points as Ada and bob
they have 3 products in common
and 7 independent products ,7 Ada and 7 bob
Total of 17 products .
1,2,3,4,5,6..........,16,17.
Consider each product number as distance between them ,
(Suppose 5 product and 1 product distance will be 4)
Similarly,
Suppose Ada is at 3rd number at the 3 product (as they have 3 product same.)
and bob at product 17.
Hence when 3 products are similar distance between Ada and bob will be of 14.
Euclidean distance =[tex]\sqrt{14}[/tex].
Hence the Jaccard similarity =(Ada intersection Bob)/(Ada union bob)
=3/14
When 4 products are same means both will selected 6 and 6 independent product so that the each one will get 10 products i.e. starting condition should remain same .
Hence now bob will be at 16th term as it will take one more same product in between them
So no of same products will be 4,
Hence Ada will be at 4th term and bob will be at 16
So Euclidean distance =[tex]\sqrt{12}[/tex].
Similar For Next terms we can conclude as follows:
When
X=5 , dist(ada,bob)=[tex]\sqrt{10}[/tex],
X=6,dist(Ada,Bob)=[tex]\sqrt{8}[/tex]
X=7,dist(Ada,Bob)=[tex]\sqrt{6}[/tex]
X=8,dist(Ada,Bob)=[tex]\sqrt{4}[/tex]
X=9,dist(Ada,Bob)=[tex]\sqrt{2}[/tex]
X=10,dist(Ada,Bob)=[tex]\sqrt{0}[/tex].
Now for( Ada and cathy)
Here X ranges different but use same concept as above
Each term analog to the distance between them
Suppose 1st and 3rd term distance will be 2
First calculate
P([tex]1\leq x\leq 10[/tex]) as Cathy selects 10 products with no common between them.
P([tex]1\leq x\leq 10[/tex])
=[tex]\frac{10Cx*990C(10-x)}{1000C10}[/tex]..................equation (2)
Calculate for each term As x=1,2,3...8,9,10.
Hence
P(X=1)=9.23*10^-3 P(X=5)=3*10^-11 P(X=9)=3.8*10^-21
P(X=2)=8.4*10^-5 P(X=6)=1.5*10^-13 P(X=10)=3.8*10^-21
P(X=3)=6.9*10^-7 P(X=7)=6.1*10^-16
P(X=4)=4.9*10^-9 P(X=8)=1.9*10^-18
So Ada will have 10 products and Cathy will have 10 products
Namely,
1,2,3,4,5.......18,19,20.
So suppose 1 product is same between them will be ,
both will have 1 product so remaining will be 19 products.
Jaccard similarity =1/19
Distance to reach 1 to 19th product will be 18
So Euclidean distance =[tex]\sqrt{18}[/tex]
For next when they will 2 products in same remaining will be 18
Jaccard similarity =2/18
And Distance to reach 2 to 18 th product will be 16
Euclidean distance =[tex]\sqrt{16}[/tex]
Similar for other
When
x=3 dist(Ada, Cathy)=[tex]\sqrt{14}[/tex]
x=4 dist(Ada, Cathy)=[tex]\sqrt{12}[/tex]
x=5 dist(Ada, Cathy)=[tex]\sqrt{10}[/tex]
x=6 dist(Ada, Cathy)=[tex]\sqrt{8}[/tex]
x=7 dist(Ada, Cathy)=[tex]\sqrt{6}[/tex]
x=8 dist(Ada, Cathy)=[tex]\sqrt{4}[/tex]
x=9 dist(Ada, Cathy)=[tex]\sqrt{2}[/tex]
x=10 dist(Ada, Cathy)=[tex]\sqrt{0}[/tex]
This sqrt(0) means both are holding same products hence they are at same point on the graph so distance with itself will be zero.
Now the Probability of distance of dist(Ada,Bob)>dist(Ada,cathy) will be
=multiplying both the probabilities equations (Adding each term probabilities and multiplying )
=Equation(1) *Equation( 2).
=Summation Of P(3≤x≤10)*summation of P(1≤x≤10)
=4.7*10^-9.
In larger number of product event of in large space ,it is difficult( less likely) that they will chose same product .
This question involves complex probability in high dimensional spaces, making it difficult to provide an exact mathematical solution. Using a simulated method like Monte Carlo simulations could potentially provide an estimated answer, but it's key to remember that these are just approximations.
Explanation:This question involves a complex application of probability and distance in a high dimensional space (analogous to the recommendation system in e-commerce). The Euclidean distance between Ada and Bob would be zero for the first three products. For the other seven products that Ada and Bob independently purchase, the probability that they choose the same product would influence the Euclidean distance between them. However, getting an exact mathematical model for this is quite complex. The distance between Ada and Cathy is even more complicated because Cathy is selecting products randomly from all 1000 products.
Because of the randomness and high dimensionality involved, this question may not have an exact solution but could be estimated using simulations. In settings like these, Monte Carlo simulations, which involve running many trials with randomized inputs and calculating the averages, can be useful. However, it's important to remember these are only estimates and not exact mathematical solutions.
Learn more about Probability in high dimensional spaces here:https://brainly.com/question/16328656
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The prior probabilities for events A1 and A2 are P(A1) = 0.30 and P(A2) = 0.55. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits.a) Are A1 and A2 mutually exclusive? b) Compute P(A1 ∩ B) and P(A2 ∩ B). c) Compute P(B). d) Apply Bayes’ theorem to compute P(A1 | B) and P(A2 | B).
We're given the following probabilities:
[tex]P(A_1)=0.30[/tex]
[tex]P(A_2)=0.55[/tex]
[tex]P(A_1\cap A_2)=0[/tex]
[tex]P(B\mid A_1)=0.20[/tex]
[tex]P(B\mid A_2)=0.05[/tex]
(a) Yes, [tex]A_1[/tex] and [tex]A_2[/tex] are mutually exclusive. This is exactly what zero probability of their intersection means. The two events cannot occur simultaneously.
(b) Use the definition of conditional probability to expand:
[tex]P(A_1\cap B)=P(A_1)P(B\mid A_1)=0.30\cdot0.20=0.06[/tex]
[tex]P(A_2\cap B)=P(A_2)P(B\mid A_2)=0.55\cdot0.05=0.0275[/tex]
(c) By the law of total probability,
[tex]P(B)=P(A_1\cap B)+P(A_2\cap B)=0.06+0.0275=0.0875[/tex]
(d) Bayes' theorem says
[tex]P(A_1\mid B)=\dfrac{P(A_1)P(B\mid A_1)}{P(B)}=\dfrac{0.30\cdot0.20}{0.0875}\approx0.686[/tex]
[tex]P(A_2\mid B)=\dfrac{P(A_2)P(B\mid A_2)}{P(B)}=\dfrac{0.55\cdot0.05}{0.0875}\approx0.314[/tex]
Using probability concepts, it is found that:
a) Since [tex]P(A1 \cap A2) = 0[/tex], events A1 and A2 are mutually exclusive.
b) P(A1 ∩ B) = 0.06, P(A2 ∩ B) = 0.0275.
c) P(B) = 0.0875.
d) P(A1|B) = 0.6857 and P(A2|B) = 0.3143.
-----------
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.-----------
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which
P(B|A) is the probability of B happening when A has happened.P(A|B) is the probability of A happening when B has happened.-----------
Item a:
Two events A and B are mutually exclusive if they cannot happen together, that is, [tex]P(A \cap B) = 0[/tex].Since [tex]P(A1 \cap A2) = 0[/tex], events A1 and A2 are mutually exclusive.-----------
Item b:
To compute these probabilities, we use conditional probability.
A1 and B:
[tex]P(B|A1) = \frac{P(A1 \cap B)}{P(A1)}[/tex]
Since [tex]P(A1) = 0.3, P(B|A1) = 0.2[/tex]
[tex]0.2 = \frac{P(A1 \cap B)}{0.3}[/tex]
[tex]P(A1 \cap B) = 0.2(0.3) = 0.06[/tex]
Thus P(A1 ∩ B) = 0.06.
A2 and B:
[tex]P(B|A2) = \frac{P(A2 \cap B)}{P(A2)}[/tex]
Since [tex]P(A2) = 0.55, P(B|A1) = 0.05[/tex]
[tex]0.05 = \frac{P(A2 \cap B)}{0.55}[/tex]
[tex]P(A2 \cap B) = 0.05(0.55) = 0.0275[/tex]
Thus P(A2 ∩ B) = 0.0275.
-----------
Item c:
P(B) can be written as:
[tex]P(B) = P(A1)P(B|A1) + P(A2)P(B|A2) = 0.3(0.2) + 0.55(0.05) = 0.06 + 0.0275 = 0.0875[/tex]
Thus P(B) = 0.0875.
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Item d:
Applying Bayes Theorem, first for A1 given B.
[tex]P(A1|B) = \frac{P(A1)P(B|A1)}{P(B)} = \frac{0.3(0.2)}{0.0875} = 0.6857[/tex]
Then for A2 given B.
[tex]P(A2|B) = \frac{P(A2)P(B|A2)}{P(B)} = \frac{0.55(0.05)}{0.0875} = 0.3143[/tex]
Thus P(A1|B) = 0.6857 and P(A2|B) = 0.3143.
A similar problem is given at https://brainly.com/question/22428992
0.000000452 in scientific notation
0.000000452 in scientific notation would be 4.52 × [tex]10^{-7}[/tex]