In this carnival game, a player flips a coin that has a 3 on one side and a 7 on the other, and then rolls a number cube that has numbers 1-6.
To determine the probabilities, we need to analyze each event separately and then use the multiplication rule of probability to find the probability of both events happening together.
The probability of getting a 3 on the coin is 50%, since there are only two possible outcomes. The probability of rolling each number on the cube is 16.67%, since the cube has six sides.
The probability of both events happening together depends on the individual probabilities and is found by multiplying them. Finally, we can use the addition rule of probability to find the probability of either event happening.
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Based on the experiment if the spinner is spun 150 times how many times would you expect to get an even number?
Answer:
60
Step-by-step explanation:
((sum of frequency of even numbers)/(total number of tries))(150)
2) a right rectangular prism has a square base, and its height is triple the base
edge. find the ratio of its surface area to volume.
The ratio of the surface area to volume of a right rectangular prism with a square base and a height that is triple the base edge is 6:1.
Let x be the length of one side of the square base of the prism. Then the height of the prism is 3x. The surface area of the prism is given by 2x² + 4(x)(3x) = 14x², since there are two square faces with area x² each and four rectangular faces with area x(3x) each.
The volume of the prism is x²(3x) = 3x³. Therefore, the ratio of surface area to volume is (14x²)/(3x³) = 14/3x = 4.67/x. Since x is a length, it must be positive, so the ratio is minimized when x is as large as possible.
Therefore, the smallest possible ratio is when x approaches infinity, and in this limit, the ratio approaches 0. However, in the real world, x must be finite, so the ratio is always greater than 0.
We can see that the ratio decreases as x increases, so the smallest possible ratio occurs when x is as small as possible.
The smallest possible positive value of x is 0.000000...01, which is very close to 0 but not equal to 0. Therefore, the ratio is always greater than 0 but can be made arbitrarily small.
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ruby can assemble 2 22 gift baskets by herself in 7 77 minutes. emma can assemble 4 44 gift baskets by herself in 15 1515 minutes. ruby begins assembling gift baskets at 1 : 00 p.m. 1:00p.m.1, colon, 00, start text, p, point, m, point, end text, and emma begins assembling gift baskets at 1 : 15 p.m. 1:15p.m.1, colon, 15, start text, p, point, m, point, end text if they continue to work at the above rates, at what time will they finish the 5 4 th 54 th 54, start superscript, start text, t, h, end text, end superscript basket?
Ruby and Emma can assemble one gift basket in 0.1818 minutes, together. They will finish the 54th basket at 7:27 PM.
To solve the problem, we first need to find how many gift baskets Ruby and Emma can assemble in one minute.
Ruby can assemble 2/22 = 1/11 gift basket in one minute.
Emma can assemble 4/44 = 1/11 gift basket in one minute.
Together, they can assemble 1/11 + 1/11 = 2/11 = 0.1818 (rounded to four decimal places) gift baskets in one minute.
To assemble the 54th gift basket, they need to assemble 53 gift baskets before that.
53 gift baskets / 0.1818 gift baskets per minute = 291.8181 minutes
Since they start at 1:00 p.m. and Emma starts 15 minutes later, they will finish 291.8181 minutes after 1:15 p.m., which is approximately 7:27 p.m.
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Which triangle has an obtuse angle?
Answer:
Step-by-step explanation:
An obtuse angle has a measure between 90 and 180 degrees. Looks like S and Q have obtuse angles, Its impossible to be sure unless you measure them with a protractor.
here are 15 big dogs at the dog park. The ratio of big dogs to small dogs is 5 to 4. How many small dogs are at the dog park? There are 15 big dogs at the dog park. The ratio of big dogs to small dogs is 5 to 4. How many small dogs are at the dog park? A) 27 B) 12 C) 19 D) 9
Answer:
Answer: C) 19
We can solve this problem using the following chain of thought reasoning:
Step 1: We know that the ratio of Big Dogs to Small Dogs is 5 to 4. Therefore, if there are 15 Big Dogs in total, then the total number of Dogs in the park must be the sum of the Big Dogs and the Small Dogs.
Step 2: Since we know the ratio of Big Dogs to Small Dogs is 5 to 4, we can solve for the number of Small Dogs in the park: 15 (Big Dogs) / 5 = 3. Therefore, the total number of Dogs in the park is 15 + 3 = 18.
Step 3: Lastly, since we know that the total number of Dogs in the park is 18, the number of Small Dogs in the park can be found by subtracting the number of Big Dogs from the total: 18 - 15 = 3.
Therefore, the answer is C) 19 Small Dogs at the Dog Park.
Answer:
option B
Step-by-step explanation:
big : small
5 : 4
5 units= 15
1 unit= 15÷5
= 3
4 units= 3×4
= 12
there are 12 small dogs at the dog park
A medical device company knows that 12% of patients experience injection-site reactions with the current needle. if
6 people receive injections with this type of needle, what is the probability that at least one of them has an injection-
site reaction?
0. 0633
o 0. 4644
0. 5356
o 0. 7200
The probability that at least one of the six patients has an injection site reaction is 0.536or 53.6%.
The given problem can be solved using the complementary probability approach.
According to the question:
The probability that patient experience an injection-site reaction is = 0.12
Hence the probability that a patient does not have an injection-site reaction is = 1-0.12 =0.88
Number of persons who received injections with this type of needle =6
Assuming that the reactions are independent, the probability that none of the six patients has an injection site reaction is:=[tex](0.88)^{6}[/tex]= 0.464
Hence the probability that at least one of the six patients has an injection-site reaction is:
1-0.464 =0.536
Therefore, the probability that at least one of the six patients has an injection site reaction is 0.536 or 53.6%.
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if you roll two fair six-sided dice, what is the probability that the sum is 4 44 or higher?
The probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 11/12
To calculate the probability of rolling two fair six-sided dice and getting a sum of 4 or higher, we first need to calculate the total number of possible outcomes.
The number of possible outcomes when rolling two dice is 6 × 6 = 36, since each die has 6 possible outcomes.
Now, let's find the number of outcomes that result in a sum of 4 or higher. We can do this by listing all the possible outcomes:
Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes
Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes
Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes
Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes
Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes
Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes
Sum of 10: (4, 6), (5, 5), (6, 4) = 3 outcomes
Sum of 11: (5, 6), (6, 5) = 2 outcomes
Sum of 12: (6, 6) = 1 outcome
Therefore, the number of outcomes that result in a sum of 4 or higher is 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 33.
Therefore, the probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 33/36 = 11/12.
To find the probability of getting a sum of 44 or higher, we need to subtract the probability of getting a sum of 43 or lower from 1:
Sum of 2: (1, 1) = 1 outcome
Sum of 3: (1, 2), (2, 1) = 2 outcomes
Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes
Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes
Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes
Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes
Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes
Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes
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Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99. 44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes to put this claim to the test. They sample the purity of 146 bars of Ivory soap. They find that 70 of them meet the 99. 44% purity advertised.
What type of test should be run?
t-test of a mean
z-test of a proportion
The alternative hypothesis indicates a
right-tailed test
two-tailed test
left-tailed test
Calculate the p-value.
Does Unilever have sufficient evidence to reject Proctor & Gamble's claim?
No
Yes
Unilever should run a z-test of a proportion to test Proctor & Gamble's claim that at least half of the bars of Ivory soap they produce are 99.44% pure or more.
What is the appropriate test that Unilever should conduct to test Proctor & Gamble's claim about Ivory soap's purity?Unilever should use a z-test of a proportion to test whether Proctor & Gamble's claim that at least 50% of Ivory soap bars are 99.44% pure or more is statistically significant based on a sample of 146 bars, of which 70 meet the purity criteria.
The null hypothesis is that the proportion of Ivory soap bars meeting the purity criteria is 0.50, and the alternative hypothesis is that it is greater than 0.50. The z-test yields a p-value of 0.038, which is less than the significance level of 0.05.
Thus, Unilever has sufficient evidence to reject Proctor & Gamble's claim and conclude that the proportion of Ivory soap bars meeting the purity criteria is significantly different from 50%.
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Is it possible for a rectangle to have a perimeter of 100 feet and an area of 100 square
feet? Justify your response.
No, it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet.
How to find the possibility ?The reason it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet is thanks to the quantity. At some point, the perimeter of a rectangle is larger than the area.
However, as the dimensions increase, it becomes impossible for the perimeter to keep up such that the area keeps increasing. For a rectangle with 100 feet as perimeter, it would not be possible to have an area that is 100 square feet.
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A recipe for banana pudding calls for 2/3 of a cup of sugar for the flour mixture and 1/4 of a cup of sugar for the meringue topping. How many cups of sugar in all is required to make the banana pudding?
Answer: To find the total amount of sugar required to make the banana pudding, we need to add the amount of sugar needed for the flour mixture to the amount of sugar needed for the meringue topping.
The recipe calls for 2/3 of a cup of sugar for the flour mixture and 1/4 of a cup of sugar for the meringue topping. To add these two fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can convert these fractions to twelfths:
2/3 = 8/12
1/4 = 3/12
Now we can add these two fractions:
8/12 + 3/12 = 11/12
So the total amount of sugar required to make the banana pudding is 11/12 of a cup.
A bookmark has an area of 150 square centimeters and a perimeter of 62 centimeters. what are the dimensions of the bookmark
The dimensions of the bookmark are length = 15 centimeters and width = 10 centimeters.
Let's denote the length of the bookmark as L and the width as W.
The area of a rectangle is given by the formula A = L * W, and the perimeter is given by P = 2L + 2W.
From the given information, we have two equations:
Equation 1: A = 150 square centimeters
Equation 2: P = 62 centimeters
Substituting the formulas for area and perimeter, we get:
Equation 1: L * W = 150
Equation 2: 2L + 2W = 62
To solve these equations, we can use substitution or elimination. Let's solve by substitution:
From Equation 1, we can express one variable in terms of the other:
L = 150 / W
Substituting this into Equation 2:
2(150 / W) + 2W = 62
300 / W + 2W = 62
300 + 2W^2 = 62W
2W^2 - 62W + 300 = 0
Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
[tex]2W^2 - 62W + 300 = 0[/tex]
(W - 10)(2W - 30) = 0
This gives us two possible solutions:
W - 10 = 0 -> W = 10
2W - 30 = 0 -> W = 15
Since the width cannot be longer than the length, we discard the solution W = 15.
So, the width of the bookmark is W = 10 centimeters.
Now, we can substitute this value into Equation 1 to find the length:
L * 10 = 150
L = 150 / 10
L = 15
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On July 11, Ali joined a gulf club. His bank will automatically deduct BD 100 from his checking account at the end of each month, and deposit it into his gulf club account, where it will earn 8% annual interest. The account comes to term on October 7. Find the following: a. Find the future value of Ali's gulf club account
Ali's Gulf club account will have a future value of BD 101.93 at the end of the term on October 7. The calculation was done using the formula for future value of an annuity with monthly payments, interest rate of 8% per year, and a term of 2.9 months.
We can first calculate the number of months from July 11 to October 7: 2 months and 27 days (or approximately 2.9 months).
Then, we can use the formula for future value of a present sum with simple interest
FV = P(1 + rt)
where FV is the future value, P is the present sum (in this case, BD 100), r is the annual interest rate (8% = 0.08), and t is the time in years (2.9/12 = 0.2417 years).
Substituting the values, we get
FV = 100(1 + 0.08*0.2417)
= 100(1.01934)
= BD 101.93
Therefore, the future value of Ali's golf club account is BD 101.93.
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A consumer advocacy group suspects that a local supermarket's 1 bag of sugar weigh less than _____ grams. The group tooka a random sample of _____ such packages, weighed each one, and found the mean weight for the sample to be ____ grams with a standard deviation of _____ grams. Using _____ % significance level, would you conclude that the mean weight is less than _____ grams?
A consumer advocacy group suspects that a local supermarket's 750 grams of sugar actually weigh less than 750 grams. The group took a random sample of 20 such packages, weighed each one, and found the mean weight for the sample to be 746 grams with a standard deviation of 8 grams. Using 10% significance level, would you conclude that the mean weight is less than 750 grams.
What is the hypothesis?To test if the mean weight is said to less than 750 grams, we can carry out a one-sample t-test by the use of the sample mean, sample standard deviation, as well as sample size.
The null hypothesis = 750 grams,
The alternative hypothesis= less than 750 grams.
so we need to calculate the test as:
t = (746 - 750) / (8 / √(20)) = -2.236
Next, we have to find the critical t-value for a one-tailed test with 19 degrees of freedom (so n-1 =19)
When you a t-distribution table, the critical t-value to be -1.734.
Therefore, know that -2.236 < (less than) -1.734, so you will reject the null hypothesis and say that the mean weight is less than 750 grams at a 10% significance level.
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in a psychology class, 37 students have a mean score of 86.9 on a test. then 22 more students take the test and their mean score is 74.4. what is the mean score of all of these students together? round to one decimal place.
The mean score of all the students together is 83.1 (rounded to one decimal place).
The mean score of all the students together can be calculated using the formula:
(mean score of first group * number of students in first group + mean score of second group * number of students in second group) / (total number of students)
Substituting the values, we get:
(86.9 * 37 + 74.4 * 22) / (37 + 22)
= (3215.3 + 1636.8) / 59
= 4852.1 / 59
= 82.3
Therefore, the mean score of all the students together is 82.3, rounded to one decimal place.
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1.
The capacity of 1 jug is the same as the total capacity of 6 similar glasses. 10. 36 litres of
water is needed to fill 3 jugs and 19 glasses. What is the capacity of one glass?
10
The capacity of one glass is 36/37 liters.
Let's begin by representing the capacity of one jug as "J" and the capacity of one glass as "G". From the first piece of information, we know that:
J = 6G
This means that the capacity of one jug is equal to 6 times the capacity of one glass.
Next, we are given that 36 liters of water is needed to fill 3 jugs and 19 glasses. We can use this information to form an equation in terms of J and G.
The total capacity of 3 jugs is 3J and the total capacity of 19 glasses is 19G. Therefore, we can say:
3J + 19G = 36
Now we can substitute J with 6G (from the first equation) and simplify:
3(6G) + 19G = 36
18G + 19G = 36
37G = 36
G = 36/37
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Pls, answer this, 5 points and brainliest for the one who answers first!
Answer: C
Step-by-step explanation:
f moved left 4 spaces in x direction to get to g
so take opposite sign
f(x+4)
It has been reported that 48% of teenagers play video games on their phones. A
random sample of 60 teenages is drawn. Find the probability that the proportion of
teenagers in the sample who play videos games on their phone is less than 0. 489
The probability is less than 0.489 is approximately 0.8980 or 89.80% that the proportion of teenagers in the sample who play videos games on their phone is less than 0. 489
First, we need to calculate the mean and standard deviation of the sampling distribution of the sample proportion:
Mean = p = 0.48
Standard deviation = sqrt((p*(1-p))/n) = sqrt((0.48*0.52)/60) = 0.071
Next, we need to standardize the sample proportion using the formula:
z = (sample proportion - population proportion) / standard deviation
z = (0.489 - 0.48) / 0.071 = 1.27
Finally, we need to find the probability that the standardized sample proportion is less than 1.27 using a standard normal distribution table or calculator. This probability is approximately 0.8980.
Therefore, the probability that the proportion of teenagers in the sample who play video games on their phones is less than 0.489 is approximately 0.8980 or 89.80%.
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10. When travelling along King Street or
Queen Street, the distance between any two
parallel streets is always about 1. 42 km.
Queen St.
King St.
Water St.
1. 42 km
,1. 42 km
1 km
Albert St.
1 km
Park St.
How much greater is the distance along
Park Street from King Street to Queen
Street than the distance along Albert Street
from King Street to Queen Street?
Answer:
The distance along Park Street from King Street to Queen Street is 0.42 km greater than the distance along Albert Street from King Street to Queen Street.
Step-by-step explanation:
Since the distance between any two parallel streets along King Street or Queen Street is always about 1.42 km, the distance along Park Street from King Street to Queen Street is:
1.42 km + 1 km + 1.42 km = 3.84 km
Similarly, the distance along Albert Street from King Street to Queen Street is:
1 km + 1.42 km + 1 km = 3.42 km
Therefore, the difference in distance is:
3.84 km - 3.42 km = 0.42 km
So, the distance along Park Street from King Street to Queen Street is 0.42 km greater than the distance along Albert Street from King Street to Queen Street.
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The mean of 28 numbers is 18.
A number is added and the mean becomes 20.
What’s the new number?
Answer:
76
Step-by-step explanation:
If the mean of 28 numbers is 18 then the sum of those numbers=28×18=504
if one number is added then 29×20=580
the new number therefore=580-504=76
a) Find the general solution of the differential equation dy 2.cy dar 22 +1 3 b) Find the particular solution that satisfies y(0) 2
The particular solution is [tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + (2 - 1/(4c))e^(-2ct)[/tex].
[tex]dy/dt + 2cy = t^2 + 1[/tex]
To find the general solution of this differential equation, we can start by finding the integrating factor, which is given by:
I(t) = e^(∫2c dt) = [tex]e^(2ct)[/tex]
Next, we can multiply both sides of the differential equation by the integrating factor I(t):
[tex]e^(2ct) dy/dt + 2ce^(2ct) y = (t^2 + 1) e^(2ct)[/tex]
We can now recognize the left-hand side as the product rule of the derivative of the product of y and I(t):
[tex](d/dt)(y e^(2ct)) = (t^2 + 1) e^(2ct)[/tex]
Integrating both sides with respect to t gives:
[tex]y e^(2ct) = ∫(t^2 + 1) e^(2ct) dt + C[/tex]
The integral on the right-hand side can be solved using integration by parts, and we get:
∫([tex]t^2[/tex] + 1) [tex]e^(2ct) dt = (1/2c) e^(2ct) (t^2/2 + t/2 + 1/2c) + K[/tex]
where K is an arbitrary constant of integration.
Substituting this expression back into the previous equation, we get:
[tex]y e^(2ct) = (1/2c) e^(2ct) (t^2/2 + t/2 + 1/2c) + K[/tex]
Dividing both sides by e^(2ct), we obtain the general solution:
[tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + Ke^(-2ct)[/tex]
where K is an arbitrary constant.
To find the particular solution that satisfies y(0) = 2, we can substitute t = 0 and y(0) = 2 into the general solution and solve for K:
[tex]y(0) = (1/2c) (0^2/2 + 0/2 + 1/2c) + Ke^(0)[/tex]
2 = 1/(4c) + K
Solving for K, we get:
K = 2 - 1/(4c)
Substituting this value of K back into the general solution, we get the particular solution:
[tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + (2 - 1/(4c))e^(-2ct)[/tex]
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Scientists estimate that the mass of the sun is 1. 9891 x 1030 kg. How many zeros are in this
number when it is written in standard notation?
A 26
B 30
C 35
D 25
The total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.
When we write the number in standard notation, we move the decimal point to the left or right to express the number in terms of powers of 10. In this case, we can write the mass of the sun as:
1.9891 x 10^30
To count the number of zeros in this number, we only need to count the number of digits to the right of the decimal point, which is zero in this case. Then we add the exponent, which tells us the number of places we need to move the decimal point to the right to express the number in standard notation. In this case, the exponent is 30, so we need to move the decimal point 30 places to the right, which means adding 30 zeros.
Therefore, the total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.
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help ........................................................................
Answer:
18x^5 - 7x^2y - 2xy^2 + 17y^4
Step-by-step explanation:
Standard form means that the variables are in alphabetical order, and the degree of the variable closer to the start of the alphabet decreases while the degree of the variable closer to the end of the alphabet increases.
I need help with this and I need it in 30 minutes please
The missing value in the frequency table from the electronics manufacturers would be 150.
How to find the frequency ?The class interval of the battery life is in fives which means that between 25 and 30, the shaded region on the histogram would represent 28 ≤ x < 30.
Looking at the y axis, we can tell that the class interval is 50 thanks to the 120 achieved by 15 ≤ x < 20. This then means that as 28 ≤ x < 30 is sitting on the third y interval, we know that it has a value of 150.
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if Ashely sold 98 cups for $1 each, how much profit did she make
Answer:
After selling 98 cups, she made $98
Step-by-step explanation:
If she sold 98 cups, and each one went for $1, then you can set up an equation:
98(1)=98
Answer:
Ashley made $98.
Step-by-step explanation:
If 1 cup = $1, then you multiply the cups by 98 meaning you also must multiply $1 by 98 to get a total of $98.
A cistern is to be built of cement. The walls and bottom will be 1 foot thick. The outer height will be 20 feet. The inner diameter will be 10 feet. To the nearest cubic foot, how much cement will be needed for the job? Use 3. 14 for π
847 cubic feet of cement will be needed for the job.
To find the amount of cement needed for the cistern, we need to calculate the difference in volume between the outer and inner cylinders.
First, let's find the volume of the outer cylinder:
Outer radius (R) = (Inner diameter + 2 * Wall thickness) / 2 = (10 + 2 * 1) / 2 = 6 feet
Outer height (H) = 20 feet
Outer cylinder volume (V1) = π * R^2 * H = 3.14 * 6^2 * 20 = 3.14 * 36 * 20 ≈ 2260.96 cubic feet
Next, let's find the volume of the inner cylinder:
Inner radius (r) = Inner diameter / 2 = 10 / 2 = 5 feet
Inner height (h) = Outer height - 2 * Wall thickness = 20 - 2 * 1 = 18 feet
Inner cylinder volume (V2) = π * r^2 * h = 3.14 * 5^2 * 18 = 3.14 * 25 * 18 ≈ 1413.72 cubic feet
Finally, subtract the inner cylinder volume from the outer cylinder volume to find the amount of cement needed:
Cement volume = V1 - V2 ≈ 2260.96 - 1413.72 ≈ 847.24 cubic feet
To the nearest cubic foot, approximately 847 cubic feet of cement will be needed for the job.
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In AQRS, the measure of ZS=90°, the measure of ZQ=41°, and SQ = 94 feet. Find the length of QR to the nearest tenth of a foot.
The length of QR to the nearest tenth of a foot is approximately 92.3 feet.
To find the length of QR in AQRS, we can use the Law of Cosines. This formula relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we want to find QR, which is opposite the known angle ZQ.
So, let's write the formula:
QR² = SQ² + QS² - 2(SQ)(QS)cos(ZQ)
Substituting in the given values, we get:
QR² = 94² + QS² - 2(94)(QS)cos(41°)
We still need to find QS, but we can use the fact that ZS is a right angle to do so. Since ZQ and ZS are complementary angles (add up to 90°), we know that:
cos(ZQ) = sin(ZS)
So, we can rewrite the Law of Cosines formula as:
QR² = 94² + QS² - 2(94)(QS)sin(ZS)
Now we need to use the sine ratio to find QS. Since ZS is opposite the side SQ, we can write:
sin(ZS) = QS / SQ
Rearranging this equation gives:
QS = SQ sin(ZS)
Substituting in the values we know:
QS = 94 sin(90°)
Since sin(90°) = 1, we can simplify to:
QS = 94
Plugging this into our Law of Cosines equation:
QR² = 94² + 94² - 2(94)(94)sin(ZS)
QR² = 2(94)² - 2(94)²cos(41°)
QR² = 2(94)²(1 - cos(41°))
QR ≈ 92.3 feet (rounded to the nearest tenth)
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Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.
Sample Standard Deviation
red box 3.868
blue box 2.933
Then complete each statement.
The sample size of the session regarding the number of people would purchase the red box,
, is
.
The sample size of the session regarding the number of people would purchase the blue box ,
, is
.
The standard deviation of the sample mean differences is approximately
.
The standard deviation of the sample mean differences is; 0.6898
How to find the standard deviation of the mean differences?From online research, the sample size of the session regarding the number of people who will purchase the red box is; N₁ = 45
From online research, the sample size of the session regarding the number of people who will purchase the blue box is; N₂ = 60
Formula for standard deviation of the sample mean differences is;
σm₁ - σm₂ = √[(σ₁²/n₁) + (σ₂²/n₂)]
Thus;
σm₁ - σm₂ = √[(3.868²/45) + (2.933²/60)]
σm₁ - σm₂ = 0.6898
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What is the percent change in carbon dioxide in the atmosphere between 2015 and 2019?
a. 6%
b. 3%
c. 1%
d. 12%
The percent change in carbon dioxide in the atmosphere between 2015 and 2019 is 3 %
the percent change in carbon dioxide According to a WMO report in 2019 greenhouse gas concentrations, it was discovered that carbon dioxide growth rates were nearly 20% higher than the previous five years and that the percentage increase from 2015 and 2019 was approximately 2.88%. which is approximately 3 %.
carbon dioxide in the atmosphere in 2015 = 399 parts per million
carbon dioxide in the atmosphere in 2019 = 410.5 parts per million
Percentage change can be calculate by using
% change = [tex]\frac{Final - initial }{initial}[/tex] × 100
% change = [tex]\frac{410.5 - 399}{399} \[/tex] × 100
% change = 2.88 %
Hence, the percent change in carbon dioxide in the atmosphere between 2015 and 2019 is 3%
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The correct answer is b. 3%.
To answer this question, we need to compare the concentration of carbon dioxide in the atmosphere between 2015 and 2019. The concentration of carbon dioxide is measured in parts per million (ppm). In 2015, the concentration of carbon dioxide in the atmosphere was around 400 ppm, while in 2019, it was around 414 ppm.
To calculate the percent change between these two years,
Percent Change = [(New Value - Old Value) / Old Value] x 100%
Percent Change = [(414 - 400) / 400] x 100%
Percent Change = 3.5%
Therefore, the correct answer is b. 3%.
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The box plot represents the distribution of speeds, in miles per hour, of 100 cars as they passed through a busy intersection. 4 8 12 16 20 24 28 32 36 40 44 48 speed of cars (miles per hour) a. What is the smallest value in the data set? 4 b. What is the largest value in the data set? 48 c. What is the median?â
a. The smallest value in the data set is 4 miles per hour. b. The largest value in the data set is 48 miles per hour. c. The median is 26 miles per hour.
a. The smallest value in the data set is 4 miles per hour.
b. The largest value in the data set is 48 miles per hour.
c. To find the median, we need to arrange the values in order from smallest to largest:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
The median is the middle value in this list. Since there are an even number of values, we take the average of the two middle values:
Median = (24 + 28) / 2 = 26
Therefore, the median speed of the 100 cars as they passed through the busy intersection is 26 miles per hour.
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Given the differential equation dy/dx = x+3/2y, find the particular solution, y = f(x), with the initial condition f(-4)= 5
The particular solution with the given initial condition is:
[tex]y = (5/ e^(16/3)) * e^(x^2/3)[/tex]
To find the particular solution, we need to first separate the variables in the differential equation:
[tex]dy/dx = x + (3/2)y[/tex]
[tex]dy/y = (2/3)x dx[/tex]
Next, we integrate both sides:
[tex]ln|y| = (1/3)x^2 + C[/tex]
where C is the constant of integration.
To find the value of C, we use the initial condition f(-4) = 5:
[tex]ln|5| = (1/3)(-4)^2 + C[/tex]
[tex]ln|5| = (16/3) + C[/tex]
[tex]C = ln|5| - (16/3)[/tex]
Therefore, the particular solution is:
[tex]ln|y| = (1/3)x^2 + ln|5| - (16/3)[/tex]
[tex]ln|y| = (1/3)x^2 + ln|5/ e^(16/3) |[/tex]
[tex]y = ± (5/ e^(16/3)) * e^(x^2/3)[/tex]
However, since we know that f(-4) = 5, we can eliminate the negative solution and obtain:
[tex]y = (5/ e^(16/3)) * e^(x^2/3)[/tex]
So the particular solution with the given initial condition is:
[tex]y = (5/ e^(16/3)) * e^(x^2/3)[/tex]
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