To ensure that the dimensions of the fish tank are adequate, we need to ensure that the volume of the fish tank is greater than or equal to 2625. Since we do not have any information about the dimensions of the fish tank,
What ensures dimensions of the fish tank are adequate?1. Let the dimensions of the fish tank be length, width, and height, represented by l, w, and h, respectively. V = l^1 × w^1 × h^1 = lwh. Therefore, the polynomial that represents the volume of the fish tank is V = lwh.
2. Then the volume of each hemisphere is (4/3)πr^3. Since there are two hemispheres, the total volume they take up is 2(4/3)πr^3 = (8/3)πr^3.
Therefore, the new volume of the fish tank after the hemispheres are installed is V - (8/3)πr^3, where V is the original volume of the fish tank. Substituting V = lwh, we get:
[tex]V_new = lwh - (8/3)πr^3[/tex]
3.The binomial that represents the length of the fish tank is l. To show that it is a factor of the polynomial V = lwh, we need to show that V is divisible by l, which means there exists a polynomial q such that V = lq. We can see that:
[tex]V = lwh = l(wh) = l(q)[/tex], where q = wh.
Therefore, l is a factor of V.
4. To determine if the binomial l is a factor of the polynomial V_new = lwh - (8/3)πr^3, we need to check if V_new is divisible by l. We can use polynomial long division to divide V_new by l:
Let the dimensions of the fish tank be length, width, and height, represented by l, w, and h, respectively.
Then the volume of the fish tank is V = lwh. We can use the properties of exponents to simplify this expression by multiplying the powers of the variables: [tex]V = l^1 × w^1 × h^1 = lwh[/tex] . Therefore, the polynomial that represents the volume of the fish tank is V = lwh.
The volume of each hemisphere is [tex](4/3)πr^3[/tex] . Since there are two hemispheres, the total volume they take up is [tex]2(4/3)πr^3 = (8/3)πr^3.[/tex]
Therefore, the new volume of the fish tank after the hemispheres are installed is V - (8/3)πr^3, where V is the original volume of the fish tank. Substituting V = lwh, we get:
V_new = l [tex]wh - (8/3)πr^3[/tex]
The binomial that represents the length of the fish tank is l. To show that it is a factor of the polynomial V = lwh, we need to show that V is divisible by l, which means there exists a polynomial q such that V = lq. We can see that:
V = lwh = l(wh) = l(q), where q = wh.
Therefore, l is a factor of V.
To determine if the binomial l is a factor of the polynomial V_new = lwh - (8/3)πr^3, we need to check if V_new is divisible by l. We can use polynomial long division to divide V_new by l:
Since there is a remainder of [tex]- (8/3)πr^3[/tex] , we can see that l is not a factor of V_new.
5. The average amount of tank allotted for each fish is represented by the binomial [tex](22 − 1)[/tex] . To determine if the dimensions of the new habitat are adequate for 125 fish, we need to check if the volume of the fish tank is greater than or equal to the space required for 125 fish.
Let the required space for each fish be v, then the total space required for [tex]125[/tex] fish is [tex]125v[/tex] . Substituting the given binomial, we have:
[tex]v = (22 - 1) = 21[/tex]
Therefore, the total space required for 125 fish is [tex]125v = 125(21) = 2625[/tex] . We cannot determine if it is adequate for the given number of fish.
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A boutique wants to determine how the amount of time a customer spends browsing in the store affects the amount the customer spends. 2 1 The equation of the regression line is Y - 2+0.98 40 30 . A browsing time of 17 minutes is found to result in an amount spent of 40.3 dollars. What is the predicted amount spent? Ex: 7.9 dollars 20 . 10 Where is the observed value in relation to the regression line? Pick 0 10 20 40 50 dollars Pick Browsing time in minutes) A browsing time of 14 minutes is found to result in a amount spent of 10.84 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? A browsing time of 28 minutes is found to result in a amount spent of 27.2 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? dollars ✓ Pick above below 2 on Check Next
EXPLANTION:
1. For a browsing time of 17 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X, where X is the browsing time in minutes.
Step-by-step:
Y = 2 + 0.98(17)
Y = 2 + 16.66
Y = 18.66 dollars
The observed value (40.3 dollars) is above the regression line, as it is higher than the predicted amount spent (18.66 dollars).
2. For a browsing time of 14 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X.
Step-by-step:
Y = 2 + 0.98(14)
Y = 2 + 13.72
Y = 15.72 dollars
The observed value (10.84 dollars) is below the regression line, as it is lower than the predicted amount spent (15.72 dollars).
3. For a browsing time of 28 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X.
Step-by-step:
Y = 2 + 0.98(28)
Y = 2 + 27.44
Y = 29.44 dollars
The observed value (27.2 dollars) is below the regression line, as it is lower than the predicted amount spent (29.44 dollars).
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Simplify. Remove all perfect squares from inside the square root. 18
A gas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. The total amount of gas pumped at the station in a month is a random variable Y (measured in 10,000 gallons) with a probability density function given by
y, 0< y < 1,
f(y) = 2 - y, 1<= y < 2,
0, elsewhere.
a Graph f(y)·
b Find F(y) and graph it.
c Find the probability that the station will pump between 8000 and 12,000 gallons in a
particular month.
d Given that the stati.on pumped more than 10,000 gallons in a particular month, find the probability that the station pumped more than 15,000 gallons during the month.
B. F(y) = 1, 2 ≤ y
C. P(8000 < Y < 12000) = 1 - 0.4 = 0.6
D. P(Y > 15000) = 1 - 1 = 0
A detailed explanation of the answer.
A. The graph of the probability density function, f(y), is shown below:
B. The cumulative probability distribution function, F(y), is given by:
F(y) = 0, 0 ≤ y < 1
F(y) = (y-1)/2, 1 ≤ y < 2
F(y) = 1, 2 ≤ y
The graph of F(y) is shown below:
C. The probability that the station will pump between 8000 and 12,000 gallons in a particular month is calculated by subtracting the cumulative probability at 8000 (0.4) from the cumulative probability at 12,000 (1):
P(8000 < Y < 12000) = 1 - 0.4 = 0.6
D. Given that the station pumped more than 10,000 gallons in a particular month, the probability that the station pumped more than 15,000 gallons during the month is calculated by subtracting the cumulative probability at 10,000 (1) from the cumulative probability at 15,000 (1):
P(Y > 15000) = 1 - 1 = 0
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what is the term for 2x + 4y - 2
Answer:
The term 2x+4y-2 is a binomial equation.
Step-by-step explanation:
Factoring said equation: 2(x+2y-1)
x intercepts: (1,0)
y intercepts: (0, 1/2)
what is the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud?
There is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.
To find the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud, we need to use the formula for the margin of error:
[tex]$$E = z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}$$[/tex]
where E is the margin of error, [tex]$z_{\alpha/2}$[/tex] is the critical value for the desired confidence level (let's assume 95%, so [tex]$z_{\alpha/2} = 1.96$[/tex]), p is the population proportion of websites experiencing click fraud, and n is the sample size.
We know that p=0.15, so we can plug in the values:
[tex]$$E = 1.96\sqrt{\frac{0.15(1-0.15)}{400}} = 0.05$$[/tex]
So the margin of error is 0.05. This means that there is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.
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Please help with 7! Thankyou :)
-12 will be the value of the variable x.
The given expression is:
-9 = (-6 +x)/2
Simplifying the expression,
-6+x = -18
x = -18 +6
x = -12
Therefore, the value of the variable x will be -12.
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Solve the equation by completing the square.
x^2−12x+35=0
After completing the square, the equation is _____, and the solution is x=5,x=7
Answer:
x:5,x:7
x^2-12x+35
x^2-12x=-35
x^2-12x+6^2=-35+36
(x+6)^2=1
insert a radical anywhere
x+6=1
x=1-6
x=-5. x=5
x=-1-6
x=-7. x=7
Which of the following is a cofactor for some enzymes and is a mineral whose primary route of excretion is through the feces and trace amounts in the urine?
A) chloride
B) copper
C) iron
D) manganese
E) calcium
Iron is required for the production of hemoglobin, which carries oxygen in red blood cells. It is also necessary for the functioning of many enzymes involved in energy metabolism.
The correct answer is (B) magnesium. Magnesium is a cofactor for some enzymes and is a mineral whose primary route of excretion is through the feces and trace amounts in the urine.
What is a cofactor?
A cofactor is a non-protein chemical that helps enzymes function correctly. It can be a metal ion or a small organic molecule. Cofactors work in tandem with the enzyme's active site to help catalyze reactions. Enzymes are protein molecules that assist in biochemical reactions, with each enzyme being specific to a certain reaction. Enzymes act as a catalyst by lowering the energy barrier required for a reaction to occur.
Magnesium is a cofactor for many enzymes that help to regulate nerve and muscle function, as well as glucose metabolism. It is needed for the production of proteins, DNA, and RNA, and it is a vital component of bone health. Magnesium is also necessary for the regulation of heart rhythm and blood pressure. Magnesium deficiencies can lead to muscle weakness, tremors, and seizures. The mineral magnesium's primary route of excretion is through the feces, with trace amounts being excreted in the urine.Calcium is an essential mineral that is involved in the formation and maintenance of bones and teeth, as well as blood clotting, nerve function, and muscle contraction.
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ʙʀᴀɴᴅᴏɴ ᴡᴀs ᴏɴ ᴠᴀᴄᴛɪᴏɴ ꜰᴏʀ 2 weeks ᴀɴᴅ 1ᴅᴀʏ ᴀɴᴅ ʜᴇ sᴘᴇɴᴅ ᴛʜᴇ sᴀɴᴇ ᴀᴍᴏᴜɴᴛ ᴏɢ ᴛɪᴍᴇs ᴡɪᴛʜ ᴇᴀᴄʜ 3 ʙʀᴏ ʜᴏᴡ ᴍᴀɴʏ sᴀʏs ᴅɪᴅ ʜᴇ sᴘᴇɴᴅ ᴡɪʀʜ ᴇᴀᴄʜ ʙʀᴏ ?
Answer:
5 days
Step-by-step explanation:
You want to know the amount of time that is 1/3 of 2 weeks and 1 day.
Total timeThere are 7 days in a week, so 2 weeks and 1 day will be a total of ...
2·7 +1 = 14 +1 = 15 . . . . days
Part timeIf this time is split into 3 equal parts, each part is 1/3 of the total.
1/3 · 15 days = 5 days
Brandon spent 5 days with each of his 3 bro.
A factory produces components of which 1% are defective. The components are
packed in boxes of 10. A box is selected at random
the probability that there are at most 2 defective components in the box is approximately 0.9044 and the probability of having at most 3 defective components out of 250 boxes is very close to zero.
a) Let X be the number of defective components in a box of 10 components. Then X follows a binomial distribution with n=10 and p=0.01, since the probability of a component being defective is 0.01. We want to find the probability that there are at most 2 defective components in the box, i.e., P(X ≤ 2).
Using the binomial probability formula, we get:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= (10 choose 0) × 0.01⁰ × 0.99¹⁰ + (10 choose 1) × 0.01¹ × 0.99⁹ + (10 choose 2) × 0.01² × 0.99⁸
= 0.90438222
Therefore, the probability that there are at most 2 defective components in the box is approximately 0.9044 (rounded to four decimal places).
b) We want to find the probability of having at most 3 defective components out of 250 boxes, each containing 10 components. Since np = 100.01 = 0.1 < 5 and n × (1-p)=10 × 0.99=9.9 > 5, we can use the normal approximation to the binomial distribution, with mean μ = np = 2.5 and standard deviation σ = √np(1-p) = 1.577.
Let X be the number of boxes with at most 3 defective components. Then X follows an approximate normal distribution with mean μ' = np=2.5250 = 625 and standard deviation σ' = √np(1-p)) = 12.5 × 1.577 = 19.712.
We want to find P(X ≤ 250), which can be written as P(X < 251) since X is a discrete variable. Using the continuity correction, we can approximate this probability as P(X < 251.5). Then we standardize the variable:
z = (251.5 - μ')/σ' = (251.5 - 625)/19.712 = -18.919
Using a standard normal table or calculator, we find that P(Z < -18.919) is a very small number, practically zero. Therefore, the probability of having at most 3 defective components out of 250 boxes is very close to zero.
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Complete Question
factory produces components of which 1% are defective. The components are packed in boxes of 10. A box is selected by random a) Find the probability that there are at most 2 defective components in the box b) Use a suitable approximation to find the probability of having at most 3 defective (inclusive 3 cases) components out of 250.
Hellppppppppppppppppp
Answer:
Step-by-step explanation:
asdfasdf
PLEASE HELP!
Jasmine invests $2658 in a retirement home account with a fixed annual interest rate of 9% compounded 4 times annually what will be the account balance after 5 years?
Work Shown:
A = P*(1+r/n)^(n*t)
A = 2658*(1+0.09/4)^(4*5)
A = 2658*(1+0.0225)^(20)
A = 2658*(1.0225)^(20)
A = 2658*1.56050920068472
A = 4147.83345541997
A = 4147.83
Find the measure of angle DBC.
The measure of angle DBC based on the information given will be 115°.
How to calculate the angleA circle is a geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius. A circle can also be defined as the set of all points that are a fixed distance away from the center point.
The total circle is 360 degrees. The sum of the arcs of the circle is 360
Arc DC = 360 - Arc CB - Arc BC
DC = 360 -30-100
DC =230
Inscribed Angle =1/2 Intercepted Arc
<DBC = 1/2 CD
<DBC = 1/2 (230)
= 115
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h(t) = -16t ² + 110t + 72
The function above models the height, h, in feet, of an object above the ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?
*
1 point
A The initial height, h, in feet, of the object.
B The maximum height, h, in feet, of the object.
C The initial speed, in ft per second, of the object.
D The maximum speed, feet per second, of the object.
Answer:
A. The initial height, h, in feet, of the object.
Answer:
A The initial height, h, in feet, of the object.
Step-by-step explanation:
Let t = 0
h(t) = -16t ² + 110t + 72
h(0) = -16(0)² + 110 × 0 + 72
h(0) = 72
The height at time zero is 72.
72 is the initial height.
Answer: A The initial height, h, in feet, of the object.
Solve the system of equations by elimination.
Answer:
(-1,1)
Step-by-step explanation:
A top tv costs r50 000. The dealer offers you two payments options
Option1:20% deposit and the balance paid back over 36 months (3 years) at 12% simple interest p. A
Option 2:no deposit ,but the product needs to be paid off in 42 months (3 1,2years )at 9% compound interest p. A
Calculate the deposit amount if option 1 is chosen
The deposit amount need to be paid in option 1 with 20% of the cost is equal to R10,000.
Cost of a tv = R50,000
Option 1.
Deposit amount = 20% of the cost.
Balance to be paid in 36 months
Simple interest = 12% p.a.
Deposit amount
= 20% of R50,000
= 0.2 x R50,000
= R10,000
Now,
Let x be the balance amount that needs to be paid.
x = R50,000 - R10,000
⇒ x = R40,000
Simple Interest = ( Principal × Rate of interest × time ) / 100
Total amount to be paid = Principal + Simple Interest
= R40,000 + (R40,000 x 0.12 x 3)
= R40,000 + R14,400
= R54,400
Therefore, the deposit amount for option 1 as per the given details is equal to R10,000.
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What is the weight of a 48 kg girl on Earth? Round the answer to the nearest whole number.
___N
Answer:
remember, in order to calculate the weight on earth, we need to multiply the mass of the object with the force of Gravity (9.8 m/s^2 on earth)
so, her weight would be:
48 x 9.8 = 470.4 >>>>>>> Will be 470 if we round it to the nearest whole number.
Step-by-step explanation: Hope this helps. Mark me brainliest!! :)))
Answer: 470
Step-by-step explanation:
A softball base is 15 inches long and 15 inches wide. How long is the diagonal? Leave your answer as a
simplified radical.
15 in
15 in
Length of diagonal =
explain how you know which type of feed the zookeeper will run out of first
Answer:
well since there is no math, the first feed that runs out, will be the animal that they have the most of, or the bigger animals. meaning lemurs for multiple or large meaning elephant, or your mother
Step-by-step explanation:
no offense, it's just faster to drive around the world than trying to print a picture of your mom
when the finite population correction factor is applied to the sample mean, the resulting standard error for the sample mean is equal to
The finite population correction factor (FPC) is a factor used when the sample size is more than 5% of the population size. It corrects for the bias that can occur when taking a sample from a finite population.
Applying the FPC to the sample mean results in the standard error for the sample mean being equal to the population standard deviation divided by the square root of the sample size times the FPC.
In other words, the standard error for the sample mean is equal to:
Standard Error = Population Standard Deviation/√(Sample Size*FPC)
The FPC is calculated by taking the reciprocal of the following formula:
FPC = (N-n)/(N-1), where N is the population size and n is the sample size.
In conclusion, applying the FPC to the sample mean reduces the bias that can occur when taking a sample from a finite population, and the resulting standard error for the sample mean is equal to the population standard deviation divided by the square root of the sample size times the FPC.
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if m<4 = 15, find the measure of <2
75°
Step-by-step explanation:Angle properties can help us find the measure of an unknown angle.
Vertical Angles
Before we find the measurement of angle 2, we need to find angle 1. Angle 1 and angle 4 are vertical angles.
Vertical angles are angles formed by 2 intersecting lines.We know that 1 and 4 are vertical angles because they are formed by the same lines. Vertical angles are always congruent. This means that if angle 4 is 15°, then angle 1 must equal 15°.
Complementary Angles
Now that we know angle 1, we can find angle 2. Angles 1 and 2 are complementary angles.
Complementary angles are angles that sum to 90°.We can tell that 1 and 2 are complementary angles because together they form a right angle. Using this information, we can set up an equation.
15 + x = 90x = 75This shows that angle 2 must equal 75°.
I need help ASAP please Just looking for an answer
Answer:
B
Step-by-step explanation:
In a lab experiment, 80 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 5 hours. How long would it be, to the nearest tenth of an hour, until there are 136 bacteria present?
Answer:
Step-by-step explanation:
We can use the formula for exponential growth to solve this problem:
N = N0 * 2^(t/T)
where N is the final number of bacteria, N0 is the initial number of bacteria, t is the time elapsed, and T is the doubling time.
We know that N0 = 80, and T = 5 hours. We want to find t when N = 136.
136 = 80 * 2^(t/5)
Dividing both sides by 80, we get:
1.7 = 2^(t/5)
Taking the logarithm of both sides (base 2), we get:
log2(1.7) = t/5
Solving for t, we get:
t = 5 * log2(1.7) ≈ 3.4 hours
Therefore, it would take approximately 3.4 hours, to the nearest tenth of an hour, until there are 136 bacteria present.
the first pentagon is dilated to form the second pentagon. drag and drop the answer to correctly complete the statement.
Hence, the correct answer to the question is: The second pentagon is either an enlargement or a reduction of the first pentagon, depending on the dilation factor.
The first pentagon is dilated to form the second pentagon. Drag and drop the answer to correctly complete the statement.The dilation is a transformation in which a figure is resized without changing its shape. It is an enlargement or a reduction of a geometric figure that maintains its similarity.
Therefore, if the first pentagon is dilated, the second pentagon will be an enlarged or a reduced form of the original pentagon.Since it is a dilation, the ratio of the corresponding sides of the pentagon will remain the same. Also, the angles of the pentagon will remain the same. Hence, both the pentagons will be similar to each other. The second pentagon will either be an enlargement or a reduction of the first pentagon. It will also have the same number of vertices and edges as the first pentagon.However, the size of the second pentagon will depend on the dilation factor. If the dilation factor is greater than 1, then the second pentagon will be an enlargement of the first pentagon. If the dilation factor is less than 1, then the second pentagon will be a reduction of the first pentagon.
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emma buys a gift basket online for 30% off the list price. she has to pay $5.50 for shipping. the total charge is $45.20. what is the list price of the gift basket?
The list price of the gift basket is $65.20. This can be determined by taking the total charge of the gift basket ($45.20) and subtracting the shipping charge of $5.50. The remaining $39.70 is the discounted amount of the gift basket.
Since the gift basket was discounted by 30%, the original list price can be determined by dividing the discounted amount by 70%, which is 0.7. Then, the list price can be calculated by multiplying the discounted amount by 1.43 (the reciprocal of 0.7). Therefore, the list price of the gift basket is $65.20.
This method of calculating the list price of the gift basket is called reverse-discounting. The process of reverse-discounting involves subtracting the discounted amount from the total charge to get the original list price. This method is useful when the discount rate is known and the total charge is given. It allows for the original list price of the item to be determined quickly and accurately.
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the medians of a triangle intersect at the ___
Answer:
orthocentre
Step-by-step explanation:
this is the answer to your question
During the first year she owned her car, Barbara spent $732 on repairs and maintenance. She spent $1,377 the second year she owned the car. What was the percentage
increase in maintenance and repair costs from the first year to the second year (to the nearest whole percent)?
79%
84%
88%
92%
None of these choices are correct.
There was 88% increase in maintenance and repair costs from the first year to the second year. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The four fundamental operations, often referred to as "arithmetic operations", are thought to be able to properly represent all real numbers. The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.
We are given that during the first year she owned her car, Barbara spent $732 on repairs and maintenance and she spent $1,377 the second year she owned the car.
So, the more amount she spent in the second year is obtained using subtraction operation which gives:
⇒ $1,377 - $732
⇒ $645
Now, the percentage increase is
⇒ $645 ÷ 7.32
⇒ 88.11%
Hence, there was 88% increase in maintenance and repair costs from the first year to the second year.
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20 points and brainly fast please!
Answer:
C
Step-by-step explanation:
the probability that a person in the united states has type b* blood is 12%. four unrelated people in the united states are selected at random. complete parts (a) through (d).
The probabilities of different events related to the type B' blood in four randomly selected people from the United States are 0.000207, 0.0600, 0.400. The events in parts (a) and (b) are considered unusual.
The probability that a person in the united states has type b* blood is 12%. four unrelated people in the united states are selected at random of different scenarios are calculated.
The probability that all four have type B' blood is 0.000207, The probability that none of the four have type B' blood is 0.0600, The probability that at least one of the four has type B' blood is 0.400, The events in parts (a) and (b) can be considered unusual because their probabilities are less than or equal to 0.05.
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_____The given question is incomplete, the complete question is given below:
The probability that a person in the United States has type B' blood is 12 % Four unrelated people in the United States are selected at random Complete parts (a) through (d) The probability that all four have type B' blood is 000207 (Round to six decimal places as needed) (b) Find the probability that none of the four have type B' blood The probability that none of the four have type B' blood is 0600 (Round to three decimal places as needed) (c) Find the probability that at least one of the four has type B' blood The probability that at least one of the four has type B' blood is 400 (Round to three decimal places as needed) (d) Which of the events can be considered unusual? Explain Select all that apply OA The event in part (a) is unusual because its probability is less than or equal to 0.05 OB. The event in part (c) is unusual because its probability is less than or equal to 0.05 O C. None of these events are r uual O D. The event in part (b) is unusual because its probability is less than or equal to 0.05 Click to select your answer and then click Check Answer
a new product is being tested by zed electronics to determine if it will continue to operate in a stable fashion under a variety of conditions. a sample of 400 items were tested, and 60 failed the test. determine a 90 percent confidence interval for the population proportion.
The 90% confidence interval for the population proportion is (0.1171, 0.1829).
To calculate the confidence interval, we first need to find the point estimate of the population proportion. The point estimate is the sample proportion which is given by:
p-bar = x/n = 60/400 = 0.15
where x is the number of items that failed the test and n is the sample size.
Next, we need to find the margin of error, which is given by:
ME = z*√(p_bar(1-p_bar)/n)
where z is the z-score corresponding to the confidence level, p_bar is the sample proportion, and n is the sample size.
For a 90% confidence level, the z-score is 1.645 (using a standard normal distribution table). Substituting the values, we get:
ME = 1.645*√(0.15(1-0.15)/400) = 0.0329
Finally, we can construct the confidence interval by adding and subtracting the margin of error from the point estimate:
CI = p_bar ± ME = 0.15 ± 0.0329 = (0.1171, 0.1829)
Therefore, we are 90% confident that the true population proportion of items that will fail the test is between 0.1171 and 0.1829.
Learn more about Confidence Interval:
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