The probability of getting heads no more than 5 times in 16 tosses of a weighted coin with 0.472 probability of landing on heads is 0.6917.
To solve this problem, we need to use the binomial distribution formula, which gives the probability of getting exactly k successes in n independent Bernoulli trials, each with probability of success p.
The formula is:
P(k successes out of n trials) = [tex](n choose k) * p^k * (1-p)^(n-k)[/tex]
where (n choose k) = n! / (k! * (n-k)!)
In this case, we want to find the probability of getting no more than 5 heads in 16 tosses of a weighted coin with p = 0.472.
We can calculate this by summing up the probabilities of getting 0, 1, 2, 3, 4, or 5 heads:
P(0 or 1 or 2 or 3 or 4 or 5 heads in 16 tosses) = P(0 heads) + P(1 head) + P(2 heads) + P(3 heads) + P(4 heads) + P(5 heads)
Using the binomial distribution formula, we get:
[tex]P(0 heads) = (16 choose 0) * 0.472^0 * (1-0.472)^(16-0) = 0.0058[/tex]
[tex]P(1 head) = (16 choose 1) * 0.472^1 * (1-0.472)^(16-1) = 0.0335[/tex]
[tex]P(2 heads) = (16 choose 2) * 0.472^2 * (1-0.472)^(16-2) = 0.0897[/tex]
[tex]P(3 heads) = (16 choose 3) * 0.472^3 * (1-0.472)^(16-3) = 0.1567[/tex]
[tex]P(4 heads) = (16 choose 4) * 0.472^4 * (1-0.472)^(16-4) = 0.2022[/tex]
[tex]P(5 heads) = (16 choose 5) * 0.472^5 * (1-0.472)^(16-5) = 0.2038[/tex]
Therefore,
P(0 or 1 or 2 or 3 or 4 or 5 heads in 16 tosses) = 0.6917.
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90000000000000000000000 - 5500000000000
90000000000000000000000 - 5500000000000 =
4450000000000000000000000
Answer:
this kind of problem is hard to solve with that many zeros. but if you were to do 900,000,000-550,000,000 it would be 350,000,000
Step-by-step explanation:
Need help please asap
In ΔABC, the line DAE is drawn such that DAE║BC. m∠ABC = m∠CAE because they are alternate interior angles.
What are alternate interior angles?Alternate interior angles are pairs of angles that are formed when a straight line (or transversal) intersects two parallel lines. They are located on opposite sides of the transversal and are inside (or between) the parallel lines.
Alternate interior angles are congruent, which means that they have the same measure or size. This property is a consequence of the fact that the alternate interior angles are formed by a pair of parallel lines and a transversal, which creates a pattern of corresponding angles that are congruent.
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question 1: how many style a shades can be loaded into a 40-foot container? question 2: how many style b shades can be loaded into a 40-foot container?
The total number of Style B shades that can be loaded into the container is 3,840 Style B shades in total.
A 40-foot container can hold 3,840 Style B shades.
A 40-foot container typically has a volume of 67.7 cubic meters (2,390 cubic feet), but without knowing the size and packing configuration of the shades, it's impossible to determine how many of each type can fit into the container.
Once you provide the dimensions and packing requirements for Style A and Style B shades, I can help you calculate how many of each type can be loaded into a 40-foot container.
Assuming that each carton of Style B shades has the same dimensions and that there is no wasted space within the container, we can calculate the number of cartons that can be loaded into a 40-foot container as follows:
First, we need to determine the total number of cartons that can fit in the container:
8 cartons in width x 40 cartons in length x 2 cartons in height = 640 cartons in total
Next, we need to determine the number of Style B shades in each carton:
6 shades x carton
Therefore, the total number of Style B shades that can be loaded into the container is:
640 cartons x 6 shades per carton = 3,840 Style B shades in total.
So a 40-foot container can hold 3,840 Style B shades.
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Question: How many Style B shades can be loaded into a 40-foot container? There are 6 shades x carton which could be shipped nested, with the squared foot on the bottom. According to the container dimensions, it's possible to put 8 cartons in width, 40 cartons in length and 2 cartons in height.
2 Riley eats of one small pizza with p slices. Enter an expression to represent the number of slices of pizza Riley eats.
The expression representing number of slices of pizza ate by Riley is equal to (2/3 ) of total slices of one small pizza is given by n = (2/3) × p.
Let us consider 'n' represents the number of slices of pizza Riley eats
Here 'p' represents the total number of slices of one small pizza.
If Riley eats two-thirds (2/3) of a small pizza with p slices,
Then the number of slices of pizza Riley eats can be represented by the expression,
Number of slices of pizza Riley eats
= ( 2/3 ) × Total number of slices of one small pizza
⇒ n = (2/3) × p
Therefore, the expression represents two-thirds of the total number of slices in the pizza, which is the amount that Riley eats is equal to n = (2/3) × p
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The above question is incomplete, the complete question is:
Riley eats 2/3 of one small pizza with p slices. Enter an expression to represent the number of slices of pizza Riley eats.
unit 8 homework 4 numbers 11 and 13
Step-by-step explanation:
how could you solve 10., if you cannot solve 11. ? they are using the same thing : law of sine.
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c being the sides, and A, B, C being the corresponding opposite angles.
11.
x/sin(90) = 13/sin(70)
as sin(90) = 1
x = 13/sin(70) = 13.83431104...
13.
remember, the sum of all angles in a triangle is always 180°.
angle JLM = 180 - 90 - 51 = 39°
angle LJK = 180 - 90 - 72 = 18°
14/sin(39) = JL/sin(51)
JL = 14×sin(51)/sin(39)
JL/sin(90) = JL = 14×sin(51)/sin(39) = KL/sin(18)
KL = 14×sin(51)×sin(18)/sin(39) = 5.342458907...
the following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal. political party support democrats 100 republicans 120 independents 80 we are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed. refer to exhibit 12-6. if the opinions of the individuals of the three groups are uniformly distributed, the expected frequency for each group is . a. .333 b. .50 c. 50 d. 100
The answer is (d) 100, which is the expected frequency for each group.
How to find the expected frequency?To determine the expected frequency for each group under the assumption of a uniform distribution of opinions, we can use the formula:
Expected frequency = (total sample size) x (proportion of group in population)
The total sample size is 300, and the proportions of Democrats, Republicans, and Independents in the population are not given, so we cannot use those directly. However, if we assume that the population proportions are roughly the same as the sample proportions, we can estimate the expected frequencies as follows:
Expected frequency for Democrats = 300 x (100/300) = 100
Expected frequency for Republicans = 300 x (120/300) = 120
Expected frequency for Independents = 300 x (80/300) = 80
Therefore, the answer is (d) 100, which is the expected frequency for each group if the opinions of the individuals of the three groups are uniformly distributed.
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Ella is cooking a turkey and a ham. It takes 14 minutes per pound to cook a turkey and 21 minutes per pound to cook a ham. Ella is able to cook the turkey and the ham in 5 hours and 43 minutes. If the turkey weighs twice as much as the ham, how much do the turkey and the ham weigh? A. The turkey weighs 7 pounds, and the ham weighs 14 pounds. B. The turkey weighs 7 pounds, and the ham weighs 7 pounds. C. The turkey weighs 14 pounds, and the ham weighs 7 pounds. D. The turkey weighs 28 pounds, and the ham weighs 14 pounds.
the $5\times 5$ grid shown contains a collection of squares with sizes from $1\times 1$ to $5\times 5$. how many of these squares contain the black center square?
the total number of squares that contain the black center square is[tex]$1 + 4 + 9 + 16 + 1 = \boxed{31}$.[/tex]
To solve this problem, we need to count the number of squares of each size that contain the black center square.
There is only one square of size[tex]$5\times 5$[/tex], which is the entire grid and obviously contains the black center square.
For squares of size[tex]$4\times 4$[/tex], there are [tex]$4$[/tex]possible squares that contain the black center square (one for each corner).
For squares of size[tex]$3\times 3$,[/tex] there are 9 possible squares that contain the black center square (one for each position that the center square could occupy, and then each of those squares could be oriented in three different ways).
For squares of size $2\times 2$, there are $16$ possible squares that contain the black center square (one for each pair of adjacent squares).
For squares of size [tex]$1\times 1$[/tex], there is only one possible square that contains the black center square (the center square itself).
Therefore, the total number of squares that contain the black center square is[tex]$1 + 4 + 9 + 16 + 1 = \boxed{31}$.[/tex]
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There are 11 squares containing the black center square in the 5x5 grid.
To find the number of squares that contain the black center square, we'll consider the sizes of the squares and their positions in the 5x5 grid.
The black center square is a 1x1 square itself, so that's 1 square.
For 2 x 2 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
For 3x3 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle). So, that's 1 square.
4. For 4x4 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
5. For 5x5 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle).
So, that's 1 square.
Now, we'll add up the number of squares we found in each step:
1 + 4 + 1 + 4 + 1 = 11.
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Which equation shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation Negative one-half x + 3 = 4 minus one-fourth x?
Negative one-fourth x = 1
Negative three-fourths x = 1
7 = one-fourth x
7 = three-fourths x
the equation that shows the variable terms isolated on one side and the constant terms isolated on the other side is: -1/4 x = 1
What is Equivalent equations?
Equations that have the same roots or solutions are said to be equivalent.
Starting with the equation:
[tex]\frac{-1}{2}x \ + 3=4-\frac{-1}{4}x[/tex]
By first adding 1/4 x to both sides and then subtracting 3 from both sides, we can separate the constant terms on one side from the variable terms on the other:
-1/2 x + 1/4 x = 4 - 3
Simplifying both sides:
-1/4 x = 1
As a result, 1/4 x = 1 is the equation that isolates the constant terms on one side and the variable terms on the other.
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An online news article posted the accompanying circle graph. If a total of million apps were downloaded, about how many of each kind of app was downloaded?
Games 30%
Social Media 30%
Music 35%
Video 5%
24,00,000 people use social media applications, 15,00,000 play games, 18,00,000 listen to music, and 3,000,000 use videos. we can solve by calculating percentage of a number
How to calculate percentage of a number?
A percentage is a ratio or number that may be expressed as a fraction of 100. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
Given:
Total apps : six million
Social Media : 40%
Games : 25%
Music : 30%
Video : 5%
We must compute each percentage in order to determine the number of apps in each category. thus,
Social Media : 40%
Therefore , Social media apps = 40% of Six million = 0.4×60,00,000
Social media apps = 24,00,000
Similarly,
Games : 25%
Games apps = 25% of 60,00,000
Games apps = 15,00,000
Music : 30%
Music apps = 18,00,000
Video : 5%
video apps = 3,00,000
Hence , the social media apps are 24,00,000 , games apps are 15,00,000 , music apps are 18,00,000 and video apps are 3,00,000.
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a battery company makes 12-volt car batteries. after many years of product testing, the company knows that the average life of its battery is normally distributed, with a mean of 44 months and a standard deviation of 7 months. a button hyperlink to the salt program that reads: use salt. (a) if the company guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (round your answer to two decimal places.) % (b) if the company does not want to make refunds for more than 9% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
a) The percentage of batteries the company expects to replace is:
0.1271 * 100% = 12.71%
b) The company should guarantee the batteries for 34 months (rounded to the nearest month) to ensure that refunds are not made for more than 9% of its batteries under the full-refund guarantee policy.
Step by step explain about both part of the question?(a) Let X be the random variable representing the life of a battery. We want to find the probability that a battery fails within 36 months after purchase, which is equivalent to finding P(X ≤ 36).
Using the normal distribution formula with mean μ = 44 months and standard deviation σ = 7 months, we have:
Z = (X - μ) / σ = (36 - 44) / 7 = -1.14
Using a standard normal table or calculator, we find that the probability of a standard normal variable being less than or equal to -1.14 is 0.1271. Therefore, the percentage of batteries the company expects to replace is:
0.1271 * 100% = 12.71% (rounded to two decimal places)
(b) Let Y be the random variable representing the length of the guarantee period in months. We want to find the value of Y such that P(X ≤ Y) = 0.09, where X has the same normal distribution with mean μ = 44 months and standard deviation σ = 7 months.
Using the inverse normal distribution formula with mean μ = 44 months and standard deviation σ = 7 months, we have:
Z = invNorm(0.09) = -1.34
where invNorm is the inverse normal function. Solving for Y, we have:
(Y - μ) / σ = Z
(Y - 44) / 7 = -1.34
Y - 44 = -1.34 * 7
Y ≈ 34.42
Therefore, the company should guarantee the batteries for 34 months (rounded to the nearest month) to ensure that refunds are not made for more than 9% of its batteries under the full-refund guarantee policy.
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Tomas learned that the product of the polynomials (a+b)(a^2-ab+b^2) was a special pattern that would result in a sum of cubes, a^3+b^3. His teacher was put four products on the board and asked the class to identify which product would result in a sum of cubes if a=2x and b=y
(2x+y)(4x²-2xy+y²)
Just replace a with 2x and b with y
Which of the following are alternate interior angles
Answer:
there is no data provided to provide an answer
Verify Associative property: 2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5..
Please help tomorrow is my final exam
We verified that the associative property of addition holds for the given expression below
Verifying the Associative propertyLet's verify the associative property of addition for the given expression:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
We can simplify both sides of the equation by finding a common denominator for the fractions:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
Multiplying 2/3 by 20/20, we get:
40/60 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
Multiplying 3/4 by 15/15, we get:
40/60 + 45/60 + 1/5 = (2/3 + 3/4) + 1/5
Combining the first two terms on the left-hand side, we get:
85/60 + 1/5 = (2/3 + 3/4) + 1/5
Simplifying the fraction 85/60, we get:
17/12 + 1/5 = (2/3 + 3/4) + 1/5
Multiplying 2/3 by 4/4, we get:
17/12 + 1/5 = (8/12 + 9/12) + 1/5
Combining the fractions in the parentheses, we get:
17/12 + 1/5 = 17/12 + 1/5
Since both sides of the equation are equal, we have verified that the associative property of addition holds for the given expression:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5.
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PLEASE HELP ASAP!!!!
Answer:
f
Step-by-step explanation:
thats the explanation
can you help me ?…………….
Answer: b
Step-by-step explanation: i think
7. is there a difference in the average percentage of season games of their favorite sport a fan attends based on if their favorite sport is baseball or basketball?
To determine if there is a difference in the average percentage of season games of their favorite sport a fan attends based on if their favorite sport is baseball or basketball, we would need to conduct a study and collect data on both baseball and basketball fans.
We would then calculate the average percentage of season games attended by each group and compare the results.
If there is a statistically significant difference between the two groups, we can conclude that there is a difference in the average percentage of season games attended based on favorite sport.
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7. The data show the amount spent by 8 households on heating bills in January and June last year.
$80.50 $75.00 $68.90 $87.00 $81.80 $78.20 $74.60 $69.80
$50.40 $36.70 $31.00 $47.30 $52.00 $39.60 $35.60 $31.20
Which of the following best describes the data?
O
The data are dependent because the amounts changed between January and June.
The data are independent because the heating bills in January and June came from the same households.
O
The data are dependent because the heating bills in January and June came from the same households.
The data are independent because the amount changed between January and June.
3
0
The option that best describes the data is the option;
The data are independent because the heating bills in January and June came from the same households.What are dependent and independent data?Dependent and independent data refers to the relationship between two sets of data.
The specified data in the table indicates;
The data obtained from an household in January is located directly on top the data obtained from the same household in June.
The heating bill depends on the amount of energy used in an household.
The amount of energy used in each household depends on the heating requirement of the household, such that the heating bill for an household in January is related to the heating bill for the same household in June
The correct option is therefore;
The data are related because the heating bills in January and June came from the same households.
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Answers is what I need! Thankkksss
The possible dimensions of the plot are:
Length = 9.2 meters, width = 25.6 meters
Length = 25.6 meters, width = 9.2 meters
What is quadratic equation?
It's a second-degree quadratic equation which is an algebraic equation in x.
Let the length of the rectangular plot be L meters and the width be W meters. Then the perimeter of the plot is:
P = 2L + W
Since there are only three sides to the fence, we can set the perimeter equal to the length of the fencing:
2L + W = 44
Solving for W, we get:
W = 44 - 2L
The area of the plot is given as 210 square meters:
L * W = 210
Substituting for W, we get:
L * (44 - 2L) = 210
Simplifying and rearranging, we get a quadratic equation:
2L² - 22L + 105 = 0
Using the quadratic formula, we can solve for L:
L = (22 ± √(22² - 4(2)(105))) / (2(2))
L = (22 ± 2√34) / 4
L = 11/2 ± √34/2
We discard the negative solution, so:
L = 11/2 + √34/2 ≈ 9.2 meters
Now we can use the equation W = 44 - 2L to find the corresponding width:
W = 44 - 2(9.2) = 25.6 meters
Therefore, the possible dimensions of the plot are:
Length = 9.2 meters, width = 25.6 meters
Length = 25.6 meters, width = 9.2 meters
Note that both sets of dimensions result in the same area of 210 square meters.
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the time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes. a. what is the probability that a guitar neck can be carved between 95 and 165 minutes?
Answer:
the probability that a guitar neck can be carved between 95 and 165 minutes is 7/8 or approximately 0.875.
Step-by-step explanation:
We know that the time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes. This means that the probability of carving a guitar neck between any two times is proportional to the length of that interval.
Let X be the time it takes to hand carve a guitar neck. Then X is uniformly distributed between 110 and 190 minutes, and we can write:
X ~ U(110, 190)
To find the probability that a guitar neck can be carved between 95 and 165 minutes, we need to find the probability that X is between 95 and 165:
P(95 < X < 165) = (165 - 95) / (190 - 110) = 70 / 80 = 7/8
Therefore, the probability that a guitar neck can be carved between 95 and 165 minutes is 7/8 or approximately 0.875.
_________are important to a systems analyst who must work with people at all organizational levels, balance conflicting needs of users, and communicate effectively.
Organizational skills
Organizational skills and the ability to communicate effectively are crucial for a systems analyst who needs to work with individuals at all levels of an organization, manage conflicting user needs, and ensure that information is communicated clearly and efficiently. Interpersonal skills are important to a systems analyst who must work with people at all organizational levels, balance conflicting needs of users, and communicate effectively. The knowledge and skills in leadership and strategic management are essential for the creation and achievement of an organizational vision and strategy. These skills include effective communication, decision-making, and the ability to evaluate and measure success, as well as a deep understanding of the organization and its environment. Leadership and strategic management play a crucial role in the success of any organization. A strong and effective leader with a well-developed understanding of strategic management is essential for the creation and achievement of an organizational vision and strategy.
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In 2008, the price of a gallon of unleaded gasoline was $4. 2. In 1990, it was only $1. 37 per gallon. What is the increase expressed as a percent change? Round to the nearest percent.
A. 66%
B. 393%
C. 193%
D. 134%
please i need help'
. ?
The percent increase in the price of a gallon of unleaded gasoline from 1990 to 2008 is 206.56%
To find the percent change from 1990 to 2008, we first need to calculate the actual change in price
Actual Change = 2008 Price - 1990 Price
Actual Change = $4.20 - $1.37
Subtract the numbers
Actual Change = $2.83
Next, we need to calculate the percent change as a ratio of the actual change to the original price in 1990
Percent Change = (Actual Change / 1990 Price) x 100%
Substitute the values in the equation
Percent Change = ($2.83 / $1.37) x 100%
Do the arithmetic operations
Percent Change = 206.56%
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The given question is incomplete, the complete question is:
In 2008, the price of a gallon of unleaded gasoline was $4. 2. In 1990, it was only $1. 37 per gallon. What is the increase expressed as a percent change? Round to the nearest percent.
Jada swims 4 laps, which is 2/5
of the number of laps she plans to swim.
How many laps does Jada plan to swim? Use x
for the number of laps Jada plans to swim.
Equation:
Solution:
Let x be the number of laps Jada plans to swim.
According to the problem, 4 laps is 2/5 of the number of laps she plans to swim, so we can write:
4 = 2/5 * x
To solve for x, we can first multiply both sides by the reciprocal of 2/5, which is 5/2:
4 * 5/2 = x
Simplifying the left side:
10 = x
Therefore, Jada plans to swim 10 laps.
observe that for every value of that satisfies , the value of is constant. what does this tell you about the behavior of the graph of on this interval?
The graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.
If the value of is constant for every value that satisfies a certain condition, it means that the graph is a horizontal line on that interval. The behavior of the graph is constant or unchanging in terms of its vertical position.
When every value of x that satisfies a given condition results in a constant value of y, this tells us that the behavior of the graph of the function on this interval is horizontal. In other words, the graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.
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Based on the table, which best predicts the end
behavior of the graph of f(x)?
O Asx
co, f(x), and as x, f(x),
O Asx co, f(x), and as x, f(x) 44,
O As x, f(x), and as x, f(x) -
-, and as x
9
Asx - co, f(x)
f(x), a
The best prediction for the end behavior of the graph of f(x) is:
As x → ∞, f(x) → ∞, and as x → -∞, f(x) → -∞.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range.
Looking at the table, we can see that as x moves from negative to positive, the values of f(x) first increase, then reach a maximum at x=3, and then decrease. Also, as x moves farther away from 0 in either direction, the absolute values of f(x) increase.
Therefore, the best prediction for the end behavior of the graph of f(x) is:
As x → ∞, f(x) → ∞, and as x → -∞, f(x) → -∞.
This is because as x becomes very large (either positively or negatively), the absolute value of f(x) becomes very large as well, but in opposite directions (positive infinity or negative infinity), since the function is decreasing in both directions.
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the surface area of a cylinder is 936pi squares meters. the radius is 13m use the formula sa=2b=ph. to find the height of cylinder.
Answer: The formula for the surface area of a cylinder is:
SA = 2πr^2 + 2πrh
where SA is the surface area, r is the radius, and h is the height.
In this case, we know that the surface area is 936π square meters and the radius is 13 meters. So we can plug those values into the formula and solve for h:
936π = 2π(13^2) + 2π(13)(h)
Simplifying:
936π = 338π + 26πh
936π - 338π = 26πh
598π = 26πh
h = 598/26 = 23
Therefore, the height of the cylinder is 23 meters.
Step-by-step explanation:
Step-by-step explanation:
you made some mistakes with the formula.
the surface area of a cylinder is
the outside mantle area
+
the 2 circle areas on top and bottom.
the outside mantle area is
2×pi×radius×height
the 2 circle areas are
2 × pi×radius²
in total that is
2×pi×radius×height + 2×pi×radius² =
2×pi×radius×(height + radius) = 936pi
2×pi×13×(height + 13) = 936pi
pi×(height + 13) = 36pi
height + 13 = 36
height = 36 - 13 = 23 m
A bus is traveling at a speed of 15m/s2. The driver approaches the same traffic light in another traffic lane. He does not brake and continues at the same speed. Write an equation for the distance the bus travels in time (t) (Hint: At a constant speed, the acceleration is 0m/s2)
This equation tells us that the distance the bus travels is directly proportional to the time it travels at a constant speed of 15m/s.
What is speed?
Speed is the method of measuring how quickly an object moves from one place to another. It is a scalar quantity that expresses the rate of change of distance over time. In other words, it is the distance traveled per unit of time.
If the bus is traveling at a constant speed of 15m/s, then its acceleration is 0m/s². Therefore, we can use the formula for distance traveled at constant speed:
distance = speed × time
In this case, the speed of the bus is 15m/s, so the equation for the distance the bus travels in time (t) is:
distance = 15t
This equation tells us that the distance the bus travels is directly proportional to the time it travels at a constant speed of 15m/s.
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Using scientific notation, (5 x 10^6) (9 × 10^-2) = 6 x 10^n, where 1 ≤ b < 10 and
n is an integer.
What is the value of b? |
What is the value of n?
The equation (5 x 10⁶) (9 × 10⁻²) = 6 x 10⁴ when written in scientific notation. The value of b is 5 and the value of n is 4.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in standard decimal form. The number is written in the form of a number between 1 and 10 multiplied by a power of 10.
The value of b in this equation is 5. This is because the decimal points in both terms must be aligned in order to multiply them together.
The decimal points in each term are 6 and 2, respectively.
Since 6 is greater than 2, the decimal point for the total must be aligned with 6.
This means that the number 5 must be multiplied by 10⁶, resulting in b being 5.
The value of n in this equation is 4. This is because when the two terms are multiplied together, the exponents must be added.
The exponents of 10 in each term are 6 and -2, respectively.
When these are added together, they equal 4, resulting in the exponent of 10 in the new term to be 4.
Therefore, the equation (5 x 10⁶) (9 × 10⁻²) = 6 x 10⁴ when written in scientific notation. The value of b is 5 and the value of n is 4.
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Find the value of ‘x’
x =
Answer:
x = 3
Step-by-step explanation:
given two intersecting chords , then the product of the parts of one chord is equal to the product of the parts of the other chord, that is
4(2x) = 4(x + 3) ← divide both sides by 4
2x = x + 3 ( subtract x from both sides )
x = 3
What is the correct answer choice to #3/the first problem?Please explain if you are able to.
What does IQR tell me about the data values in the box plot?
The IQR in problem 3 is equal to 10.
The IQR tells us about the measure of the spread of the data contained in the box plot.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the given box plot, the five-number summary for the given data set include the following:
Minimum (Min) = 30.First quartile (Q₁) = 65.Median (Med) = 70.Third quartile (Q₃) = 75.Maximum (Max) = 80.How to calculate the interquartile range (IQR)?Mathematically, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):
Interquartile range (IQR) of data set = Q₃ - Q₁
Interquartile range (IQR) of data set = 75 - 65
Interquartile range (IQR) of data set = 10.
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