The size of each section in a graph tells in relation to the portion of the data :
c. The count of data points within the categoryD. The relative frequency of data within the categoryWhat does the size show?The magnitude of a graphic's segment indicates a specific attribute of the data being presented. In charts like pie charts or stacked bar graphs, each component's size denotes the relative frequency or proportion of data points in a particular category.
This implies that larger fragments reflect an increased number of data points for its associated categories whereas smaller ones represent categories with lesser data points.
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which of the following statements about a randomly chosen person from these 200 employees is true? responses if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city. if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city. if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere). if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere). the person is more likely to own a car if he or she lives in the city (downtown area or elsewhere) than if he or she lives outside the city. the person is more likely to own a car if he or she lives in the city (downtown area or elsewhere) than if he or she lives outside the city. the person is more likely to live in the downtown area in the city than elsewhere in the city. the person is more likely to live in the downtown area in the city than elsewhere in the city. the person is more likely to own a car than not to own a car.
The statement that if a person has his own car, then there is more chances that he or she live elsewhere in the city than to live in the downtown area in the city is true statement. So, the option(a) is right answer for problem.
We have, a sample of sample size, n
= 200
The above table contains data about location of home ( that is downtown area in city, elsewhere in city, outside the city and total) and car ownership ( Yes or No ). Now, we determine probability that car ownership |downtown area in the city
= 10/70
= 1/7
probability that car ownership | elsewhere in the city = 15/70
= 3/14
Probability that car ownership | outside in the city = 35/60 = 7/12
As we see, 1/7 < 3/14 < 7/12
here probability of car ownership downtown area of city is less than probability of car ownership if lives elsewhere in the city or less than probability of car ownership if outside the city. So, statement (a) is true in this case. Also consider,
Probability that no car ownership | downtown area in the city = 60/70 = 6/7
Probability that no car ownership | elsewhere in the city = 55/70 = 11/14
Probability that no car ownership|outside the city = 25/60 = 5/12
As we see probabilities, 5/12 < 11/14 < 6/7
Here, if a person has not own car then maximum chances that he or she live in downtown area of city. So, statement (b) is false.
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Complete question:
The above figure complete the question. A local company is interested in supporting environmentally friendly initiatives such as carpooling among employees. The company surveyed all of the 200 employees at the downtown offices. Employees responded as to whether or not they own a car and to the location of the home where they live. The results are shown in the table above. Which of the following statements about a randomly chosen person from these 200 employees is true? responses
a) if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city.
b) if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere).
c) the person is more likely to own a car if he or she lives in the city (downtown area or elsewhere) than if he or she lives outside the city.
d) the person is more likely to live in the downtown area in the city than elsewhere in the city.
e) the person is more likely to own a car than not to own a car.
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
Waukegan, Illinois, had a population of 149,000 in the year 2019. The infrastructure of the city allows for a carrying capacity of 150,000 people. rmax = 0.8 for Waukegan.
What will be the population growth rate for 2019? Round to the nearest person.
What will be the population size at the start of 2020? Round to the nearest person.
The population growth rate for 2019 would be 800 people.
The population size at the start of 2020 would be 149, 800 people.
How to find the growth rate ?The formula is:
Growth rate = rmax × Population × ( 1 - ( Population / Carrying Capacity ) )
Growth rate = 0.8 × 149,000 × ( 1 - ( 149, 000 / 150, 000) )
Growth rate = 0.8 × 149, 000 × 0. 0067
Growth rate = 800 people
The population size at the start of 2020 would therefore be:
= Initial Population + Growth Rate
= 149, 000 + 800
= 149, 800 people
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What is the local rate of change on this parabola at the point , (-6,8)?
To find the local rate of change on a curve at a specific point, we need to find the slope of the tangent line at that point. The tangent line represents the instantaneous rate of change or the rate of change at that particular point.
To find the slope of the tangent line at (-6,8) on the parabola, we need to take the derivative of the function at that point.
Assuming that the parabola is defined by the equation [tex]y = ax^2 + bx + c,[/tex]
where a, b, and c are constants, we can find the derivative of the function as follows:
[tex]dy/dx = 2ax + b[/tex]
Substituting [tex]x = -6,[/tex] we get:
[tex]dy/dx = 2a(-6) + b[/tex]
To find the values of a and b, we need more information about the parabola.
If we have the equation of the parabola or another point on the curve, we can use it to find the values of a and b.
Once we have the values of a and b, we can substitute them into the derivative equation and evaluate it at [tex]x = -6[/tex] to find the slope of the tangent line at (-[tex]6,8[/tex]), which is the local rate of change at that point.
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Find perimeter of ABDE
Step-by-step explanation:
(10 x 6)/2 = 30 + 47 = 77
How many different can be formed from 9 teachers and 30 students if the committee consists of 2 teachers and 2 students? if how many ways can the committee of 4 members be selected?
There are 15,660 different ways a committee consisting of 2 teachers and 2 students can be formed from 9 teachers and 30 students.
To find out how many different committees can be formed from 9 teachers and 30 students, if the committee consists of 2 teachers and 2 students, we will use the combination formula. The combination formula is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be selected.
First, let's find the number of ways to select 2 teachers from 9:
C(9, 2) = 9! / (2!(9-2)!) = 9! / (2! * 7!) = 36
Next, let's find the number of ways to select 2 students from 30:
C(30, 2) = 30! / (2!(30-2)!) = 30! / (2! * 28!) = 435
Now, to find the total number of ways the committee of 4 members can be selected, we simply multiply the number of ways to select teachers and students:
Total ways = 36 (ways to select teachers) * 435 (ways to select students) = 15,660
So, there are 15,660 different ways a committee consisting of 2 teachers and 2 students can be formed from 9 teachers and 30 students.
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Let C = {factors of 12}
Work out n(C)
The value or n(C) based on the information will be 6.
How to explain the FactorIn mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder. More formally, if a is a factor of b, then b can be expressed as a product of a and some other number or expression.
For example, in the expression 12 = 2 x 2 x 3, the numbers 2 and 3 are factors of 12. Similarly, in the expression x² - 4, (x - 2) and (x + 2) are factors because if we multiply them together we get x² - 4.
The factors of 12 are 1, 2, 3, 4, 6, and 12. Therefore, the set C contains six elements. Hence, n(C) = 6.
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The general form of the primitive of the function f (x) = 6 sin (2) / cos (2) is F (x) = ______ + C
The integral of f(x) can be found by using the substitution u = cos(x), du = -sin(x) dx. Thus, we have:
∫ (6 sin(2x) / cos(2x)) dx = -3 ∫ (2 sin(2x) / cos²(2x)) (-2cos(x)) dx
= 6 ∫ (sin(u) / u²) du
This integral can be evaluated using integration by parts, with u = sin(u) and dv = u⁻² du, giving:
6 ∫ (sin(u) / u²) du = -6 sin(u) / u + 6 ∫ (cos(u) / u) du
Substituting back u = cos(x), we have:
6 ∫ (sin(x) / cos²(x)) dx = -6 tan(x) + 6 ln |cos(x)| + C
Since tan(x) = sin(x) / cos(x) and cos²(x) = 1 - sin²(x), we have:
f(x) = 6 sin(x) / cos²(x) = 6 sin(x) / (1 - sin²(x)) = -6/(sin(x) - 1/sin(x))
Therefore, the general form of the primitive of f(x) is:
F(x) = -6 ln |sin(x) - 1/sin(x)| + C
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what is the number of cans that can be packed in a certain carton? (1) the interior volume of this carton is 2,304 cubic inches. (2) the exterior of each can is 6 inches high and has a diameter of 4 inches.
The number of cans that can be packed in a certain carton has correct statement as, Statements (1) and (2) together are not sufficient, option E.
Data sufficiency refers to evaluating and analysing a collection of data to see if it is sufficient to respond to a certain query. They are intended to assess the candidate's capacity to connect the dots between each question and arrive at a conclusion.
The size of each can is not revealed in statement 1 at all.
The size of the container is not disclosed in statement 2 at all.
We obtain two situations when we take into account both assertions. Case A: If the box is 1 x 1 x 2304 (inches) in size, then there are no cans that will fit within the carton.
Case B: If the box is 10 x 10 x 23.04 (inches) in size, then the carton can hold more than 0 cans.
The combined statements are insufficient because we lack clarity in our ability to respond to the target inquiry.
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Complete question:
What is the number of cans that can be packed in a certain carton?
(1) The interior volume of this carton is 2, 304 cubic inches.
(2) The exterior of each can is 6 inches high and has a diameter of 4 inches.
A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.
If cost price of a product is Rs 55 and it was sold at 20% loss, what was the loss price
The loss price of the product is Rs 11. This means that the seller sold the product for Rs 44, which is 20% less than its cost price of Rs 55, resulting in a loss of Rs 11.
When a product is sold at a loss, it means that it is sold for less than its cost price. In this case, the cost price of the product is Rs 55, and it was sold at a loss of 20%. This means that the selling price of the product is 80% of its cost price. To find out the selling price, we can multiply the cost price by 80% or 0.8.
Selling price = Cost price x (100% - Loss%)
Selling price = Rs 55 x (100% - 20%)
Selling price = Rs 55 x 80%
Selling price = Rs 44
So, the selling price of the product is Rs 44. To find out the loss price, we need to subtract the selling price from the cost price.
Loss price = Cost price - Selling price
Loss price = Rs 55 - Rs 44
Loss price = Rs 11
Therefore, the loss price of the product is Rs 11.
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In triangle ABC, angle B is a right angle. Give me measures of side BC and hypotenuse AC so that the measure of Angle A is greater than 75 degrees
In triangle ABC with angle B as a right angle, if the measure of angle A is greater than 75 degrees (e.g., 80 degrees), side BC can be approximately 9.848 units, and the hypotenuse AC can be 10 units.
In triangle ABC with angle B as a right angle, to find measures of side BC and hypotenuse AC such that the measure of angle A is greater than 75 degrees, we can use the sine function.
Determine the sine of angle A. Since angle A needs to be greater than 75 degrees, let's choose 80 degrees as an example.
sin(80°) = opposite side (BC) / hypotenuse (AC)
Choose a convenient value for the hypotenuse (AC). Let's choose AC = 10 units.
Solve for the opposite side (BC).
sin(80°) = BC / 10
BC = 10 * sin(80°)
BC ≈ 9.848
If the measure of angle A is more than 75 degrees (for example, 80 degrees), side BC and the hypotenuse AC in the triangle ABC with a right angle can both be 10 units.
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What value of k makes the equation true?
k – 3(k + 5) – 0. 5 = 3(0. 25k + 4)
For -10 as the value of k the equation k – 3(k + 5) – 0. 5 = 3(0. 25k + 4) is true.
Given equation is k – 3(k + 5) – 0. 5 = 3(0. 25k + 4)
To solve the equation, firstly we have to solve or open the brackets using the distributive property that is a(x + y) = ax +ay
Thus the equation becomes, k - 3k - 15 - 0.5 = 0.75k + 12
Then we have to take all the terms with k on one side and other on the other or segregate the like terms, the equation now is
k - 3k - 0.75k = 12 + 15 + 0.5
Simplify the equation by adding or subtracting the like terms.
-2.75k = 27.5
Then we divide the coefficient of k by the other side and get our answer
k = 27.5 ÷ (-2.75)
k = -10
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How many times of rs. 1300 is the value including 13% vat on rs. 13000?
There would be of 11.3 times rs. 1300 is the value including 13% vat on rs. 13000
To find out how many times Rs. 1300 is contained in the value including 13% VAT on Rs. 13000, we need to first calculate the total value including VAT.
VAT is a tax that is added to the net price of a product or service. In this case, the net price is Rs. 13000 and the VAT is 13% of the net price, which is:
VAT = 13% of Rs. 13000
= 0.13 x 13000
= Rs. 1690
So, the total value including VAT is:
Total value = Net price + VAT
= Rs. 13000 + Rs. 1690
= Rs. 14690
Now, to find out how many times Rs. 1300 is contained in this value, we divide the total value by Rs. 1300:
Number of times = Total value / Rs. 1300
= Rs. 14690 / Rs. 1300
= 11.3 (approx)
Therefore, the value including 13% VAT on Rs. 13000 is about 11.3 times the value of Rs. 1300.
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13. A colony of bacteria doubles in number every hour. The expression 250* 2h gives the number of
bacteria after h hours. What does the constant 250 in the expression represent?
Therefore, the expression 250 * [tex]2^h[/tex] gives the number of bacteria in the colony after h hours, assuming that the initial number of bacteria is 250.
What is expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. Expressions can also include parentheses, brackets, and other symbols to clarify the order of operations. Expressions can be evaluated to obtain a numerical result or can be simplified using mathematical rules and properties to make them easier to work with. In algebra, expressions are often used to represent relationships between variables and to solve equations and inequalities.
Here,
In the given expression 250*[tex]2^h[/tex], the constant 250 represents the initial number of bacteria in the colony.
Since the number of bacteria doubles every hour, if we start with 250 bacteria at the beginning, after one hour we will have 250 * 2 = 500 bacteria. After two hours, we will have 500 * 2 = 1000 bacteria, and so on.
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Raymond kept track of the number of hours that he spent
practicing the piano each week for several weeks. he
spent 24.8.6 and 5 hours
what is the range of the data set?
o a 8 hours
o b. 2 hours
o c. 5 hours
6 hours
The range of the data set is 19 hours. None of the options are correct.
The given data set represents the number of hours Raymond spent practicing the piano each week for several weeks: 24, 8, 6, and 5 hours. To calculate the range, follow these steps:
1. Identify the highest and lowest values in the data set.
- The highest value is 24 hours.
- The lowest value is 5 hours.
2. Subtract the lowest value from the highest value to find the range.
- Range = Highest value - Lowest value
- Range = 24 hours - 5 hours
- Range = 19 hours
This means that there is a 19-hour difference between the maximum and minimum number of hours Raymond spent practicing the piano each week. None of the options (a. 8 hours, b. 2 hours, c. 5 hours, and 6 hours) provided matches the correct answer, which is 19 hours.
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Consider functions f and g. What is the approximate solution to the equation after three iterations of successive approximations? Use the graph as a starting point. 3x^2 - 6x - 4 = 2/x+3 +1
The required values on the graph, the solution is approximate x = -0.33.
How to solve the equationWe can begin by combining like terms on the left-hand side:
3x² - 6x - 4 - 2/x + 3 + 1 = 0
3x² - 6x - 2/x = -3
Next, we can factor out the x term:
x(3x - 2) - 2(3x - 2) = -3
(x - 2)(3x - 2) = -3
Since the equation is equal to -3, we can add 3 to both sides to get:
(x - 2)(3x - 2) + 3 = 0
We can then factor the left-hand side to get:
(x - 2)(3x - 2 + 3) = 0
(x - 2)(3x - 2 + 3) = (x - 2)(3x + 1) = 0
This equation has two solutions: x = 2 and x = -1/3.
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Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
d. What are some other numbers of magazine subscriptions Andre could
have sold and still reached his goal?
The inequality to describe the number of subscriptions Andre must sell to reach his goal is 3s + 25 ≥ C.
What are inequalities ?
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
here , we have,
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Assuming the cost of soccer cleats to be 'C' and the number of subscriptions to be 's'.
∴ The inequality that represents this situation is 3s + 25 ≥ C to real his goal.
Hence, The inequality to describe the number of subscriptions Andre must sell to reach his goal is 3s + 25 ≥ C.
Please help me with this math problem!! Will give brainliest!! It's due tonight and it's the last problem!!! :)
part a.
the percentage of eggs between 42 and 45mm is 48.48%
part b.
The median width is approximately (42+45)/2 = 43.5mm.
The median length is approximately (56+59)/2 = 57.5mm.
part c.
The width of grade A chicken eggs has a range of about 24mm.
part d.
I think its impossible to determine because we don't have the value for the standard deviation.
The second option should be correct.
What is a histogram?A histogram is described as an approximate representation of the distribution of numerical data.
part a.
From the histogram, we see that the frequency for the bin that ranges from 42 to 45mm is 4 and we have a total of 33 eggwe use this values and calculate the percentage of eggs between 42 and 45mm is 48.48%.
part b.
we have an estimation that the median of the width is 48mm and the median of the length is around 60mm.
part c.
Also from the histogram, we notice that the smallest value is around 36mm and the largest value is around 66mm, hence the width of grade A chicken eggs has a range of about 24mm.
In a histogram, the range is the width that the bars cover along the x-axis and these are approximate values because histograms display bin values rather than raw data values.
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You are on a plane leaving from Miami, Florida Heading directly towards Africa on a bearing of E 20 S.
The planes average air speed is 600 mph and you fly for 4 hours before the pilot indicates that you will
with the same average air speed. The pilot is unable to outrun the storm and the turbulence is too much,
have to re-route around a storm. The pilot adjusts his bearing to S 5'E for 2 hours then E 5°S for an hour
the plane goes down, and your group are the only survivors stranded on an unknown island. You have
enough battery on a satellite phone one of you grabbed from the plane to make one phone call to the
they need to travel on from Miami to rescue
you. What do you tell them?
rescue authorities in Miami and tell them the exact distance you are from Miami and the exact bearing
To determine the exact distance and bearing of the island from Miami, we can use basic trigonometry and vector addition.
First, we need to break down the flight path into its components. The initial bearing of E 20 S can be broken down into an eastward component of 600 mph [tex]cos(20°) = 562.57[/tex] mph and a southward component of 600 mph [tex]sin(20°) = 208.38[/tex] mph.
After flying for 4 hours, the plane has traveled a distance of 600 mph × 4 = 2400 miles, with a displacement of 562.57 mph × 4 = 2250.28 miles eastward and 208.38 mph × 4 = 833.52 miles southward.
When the pilot adjusts the bearing to S 5'E, the plane travels 600 mph × 2 = 1200 miles with a displacement of 600 mph cos(5°) × 2 =996.18 miles eastward and 600 mph sin(5°) × 2 = 104.57 miles southward.
Finally, when the pilot adjusts the bearing to E 5°S, the plane travels 600 mph × 1 = 600 miles with a displacement of 600 mph cos(5°) = 598.31 miles eastward and 600 mph sin(5°) = 52.42 miles southward.
To find the total displacement from Miami to the island, we can add up the eastward and southward components:
Total eastward displacement = 2250.28 + 996.18 + 598.31 = 3844.77 miles
Total southward displacement = 833.52 + 104.57 + 52.42 = 990.51 miles
Using the Pythagorean theorem, we can find the total distance from Miami to the island:
[tex]Distance = sqrt((3844.77)^2 + (990.51)^2) =3985.21 miles[/tex]
To find the bearing from Miami to the island, we can use inverse trigonometry:
[tex]Bearing = tan^{-1} (\frac{990.51}{3844.77}) = 14.76°[/tex]
Therefore, you should tell the rescue authorities in Miami that you are approximately 3985.21 miles away from Miami and the bearing to the island is approximately N 75°E.
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Ken filled out this information on the back of his bank statement. find ken’s revised statement balance. does his account reconcile?
If you have access to the information on the back of Ken's bank statement, you can calculate his revised statement balance by adding any credits and subtracting any debits from the previous statement balance.
Find out Ken revised statement balance?Reconciling a bank account involves comparing the transactions in your own financial records with those listed on your bank statement. The goal is to ensure that the account balance in your financial records matches the balance reported by the bank.
To reconcile a bank account, you typically start with the ending balance on the previous bank statement, which becomes the beginning balance on the current statement. You then compare this balance with the transactions listed on the current statement, adding any credits (such as deposits or interest payments) and subtracting any debits (such as withdrawals or fees).
The resulting balance should match the ending balance listed on the current bank statement. If it does not match, then there may be errors or discrepancies in the account that need to be investigated. This can involve reviewing bank records, receipts, and other financial documents to identify any errors or missing transactions.
Reconciling your bank account on a regular basis is important for ensuring the accuracy of your financial records and identifying any issues or errors in a timely manner. It can also help you identify areas where you may be overspending or where you can save money by reducing fees or optimizing your financial habits.
Whether or not Ken's account reconciles depends on whether the calculated revised statement balance matches the bank's reported statement balance. If they match, then the account is reconciled. If they do not match, then there may be discrepancies in the account that need to be investigated and resolved.
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A family has four children. If Y is a random variable that pertains to the number of female children. What are the possible values of Y?
The possible values of Y are 0, 1, 2, 3, and 4.
What values can Y, the random variable for the number of female children in a family of four children, take?The number of female children in a family with four children can be any value between 0 and 4, inclusive.
To see why, we can consider all the possible outcomes of the family having four children, assuming that the probability of having a boy or a girl is 0.5 (assuming a binomial distribution).
There are 2 possibilities for the first child (boy or girl), 2 possibilities for the second child, 2 possibilities for the third child, and 2 possibilities for the fourth child, making a total of 2x2x2x2 = 16 possible outcomes.
Out of these 16 outcomes, we can count the number of outcomes that correspond to each possible value of Y:
If Y = 0, then all four children must be boys, which is 1 outcome.
If Y = 1, then there are 4 ways to have one girl (first, second, third, or fourth child).
If Y = 2, then there are 6 ways to have two girls (first two, first three, first four, second three, second four, or third fourth child).
If Y = 3, then there are 4 ways to have three girls (first three, first four, second four, or third four child).
If Y = 4, then all four children must be girls, which is 1 outcome.
Therefore, the possible values of Y are 0, 1, 2, 3, and 4.
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Evaluate the integral by making an appropriate change of variables. Sle 9e2x + 2y da, where R is given by the inequality 2[x] + 2 y = 2
Using the change of variables u = x and v = x + y, we transform the given region R into a rectangle S, and evaluate the integral as 9 (e^6 - 2e^4 + e^2 - 1).
We need to find a change of variables that maps the region R onto a rectangle in the uv-plane. Let's make the following substitutions
u = x
v = x + y
Then, the region R is transformed into the rectangle S defined by 0 ≤ u ≤ 1 and 0 ≤ v ≤ 2.
To find the limits of integration in the new variables, we can solve the equations 2[x] + 2y = 2 for x and y in terms of u and v
2[x] + 2y = 2
2u + 2v - 2[x] = 2
[x] = u + v - 1
Since [x] is the greatest integer less than or equal to x, we have
u + v - 1 ≤ x < u + v
Also, since 0 ≤ y ≤ 1, we have
0 ≤ x + y - u ≤ 1
u ≤ x + y < u + 1
u - x ≤ y < 1 + u - x
Now we can evaluate the integral using the new variables
∫∫R 9e^(2x+2y) dA = ∫∫S 9e^(2u+2v) |J| dudv
where J is the Jacobian of the transformation, given by
|J| = det [[∂x/∂u, ∂x/∂v], [∂y/∂u, ∂y/∂v]]
= det [[1, 1], [-1, 1]]
= 2
Therefore, the integral becomes
∫∫S 9e^(2u+2v) |J| dudv = 2 ∫0^1 ∫0^2 9e^(2u+2v) dudv
= 2 ∫0^1 [9e^(2u+2v)/2]_0^2 dv
= 2 ∫0^1 (9/2)(e^(4+2v) - e^(2v)) dv
= 2 (9/2) [(e^6 - e^2)/2 - (e^4 - 1)/2]
= 9 (e^6 - 2e^4 + e^2 - 1)
Therefore, the value of the integral is 9 (e^6 - 2e^4 + e^2 - 1).
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-1(x^2-4x+8)
Multiply
To multiply -1(x^2-4x+8), we need to distribute the -1 to each term inside the parentheses:
-1(x^2-4x+8) = -x^2 + 4x - 8
So, the product of -1 and the expression (x^2-4x+8) is -x^2 + 4x - 8.
Please help solve 5 and 6 and show work please
a. The actual area of the kitchen is 128 square feet.
b. the couch measures 1.25 inches across in the scale drawing.
How do we calculate?The scale is 1/4 inch = 2 feet,
meaning that in the drawing, each inch represents 8 feet (since 2 feet/0.25 inches = 8 feet/inch).
The kitchen in the drawing has an area of 2 square inches.
we apply the scale factor to find the actual area in square feet,
1 inch in the drawing = 8 feet in real life
So, 2 square inches in the drawing = 2 x 8 x 8 = 128 square feet in real life.
Hence, the actual area of the kitchen is 128 square feet.
we also apply the scale factor to find the couch measurement in the scale drawing,
1 inch in the drawing = 8 feet in real life
10 feet in real life = 10/8 = 1.25 inches in the drawing.
In conclusion, the couch measures 1.25 inches across in the scale drawing.
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I am wondering what’s 75% of 188
I know 50% of 188 is 94 and 25% is 47
Answer: 141
Step-by-step explanation: 188 x 75% = 141
Answer:
141
Step-by-step explanation:
I looked it up.
How do I solve a Pythagorean triangle of 7 squared + 2 squared and then the number after what would it be when u square root it
To solve a Pythagorean triangle of 7 squared + 2 squared, you need to use the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the unknown side, which we'll call x. So, we have:
7² + 2² = x²
Simplifying this equation, we get:
49 + 4 = x²
53 = x²
To find the value of x, we need to take the square root of both sides:
√53 = x
So the answer to the problem is √53. When you square root it, you get a decimal approximation of approximately 7.28.
In summary, to solve a Pythagorean triangle, you need to use the Pythagorean theorem and find the square root of the sum of the squares of the other two sides to find the length of the unknown side.
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The wheel of a compact car has 33-in. Diameter. The wheel of a pickup truck has a 19-in. Radius.
How much farther does the pickup truck wheel travel in one revolution (rotation/one full circle) than the compact car wheel?
The pickup truck wheel travels 37.7 inches farther in one revolution than the compact car wheel.
How to find the diameter?The distance traveled by a wheel in one revolution is directly proportional to the diameter of the wheel.
Since the diameter of the compact car wheel is 33 inches, its circumference (the distance traveled in one revolution) is 103.67 inches (C = πd). On the other hand, the radius of the pickup truck wheel is 19 inches, making its diameter 38 inches and its circumference 119.38 inches.
Therefore, the pickup truck wheel travels 15.71 inches more in one revolution than the compact car wheel (119.38 - 103.67 = 15.71). However, the question asks for the distance in inches farther, which means we need to subtract the circumference of the compact car wheel from that of the pickup truck wheel.
Hence, the answer is 37.7 inches (2 × 15.71 + 2 × 103.67 = 241.76 - 204.06 = 37.7).
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The figure is tangent to the circle at point U. Use the figure to answer the question.
Hint: See Lesson 3. 09: Tangents to Circles 2 > Learn > A Closer Look: Describe Secant and Tangent Segment Relationships > Slide 4 of 8. 4 points.
Suppose RS=8 in. And ST=4 in. Find the length of to the nearest tenth. Show your work.
1 point for the formula, 1 point for showing your steps, 1 point for the correct answer, and 1 point for correct units
We know that the length of TU to the nearest tenth is 6.9 in
The figure is tangent to the circle at point U. Using the information given in the figure, we can conclude that segment ST is tangent to the circle at point T.
To find the length of TU, we can use the formula for the length of a tangent segment from a point outside the circle:
TU^2 = TS x TR
We know that TS = ST = 4 in. To find TR, we can use the Pythagorean theorem:
TR^2 = RS^2 - TS^2
TR^2 = 8^2 - 4^2
TR^2 = 48
TR = sqrt(48)
Now we can substitute the values we have found into the first formula:
TU^2 = 4 x sqrt(48)
TU = sqrt(4 x sqrt(48))
TU ≈ 6.9 in.
Therefore, the length of TU to the nearest tenth is 6.9 in.
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Solve the equation 2^(x-2)+2^3-x=3. Also prove that the roots also satisfies 4^(x)-6*2^(x+1)+32=0
The roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex]also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]
How to find the roots of equation?To find the roots of equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3,[/tex] we can substitute [tex]y = 2^(^x^-^2^)[/tex]to get:
[tex]y + 2^(^5^-^x^)^/^y = 3[/tex]
Multiplying both sides by y, we get:
[tex]y^2 + 2^(^5^-^x^) = 3y[/tex]
Substituting y = 2^(x-2), we get:
[tex]2^(^2^x^-^8^) + 2^(^5^-^x^) = 3 * 2^(^x^-^2^)[/tex]
Multiplying both sides by 2^8, we get:
[tex]4(2^x) + 32 = 768(2^(^2^-^x^))[/tex]
Simplifying, we get:
[tex]4(2^x) - 768(2^-^x) + 32 = 0[/tex]
Dividing both sides by 4, we get:
[tex]2^x - 192(2^-^x) + 8 = 0[/tex]
Multiplying both sides by [tex]2^x[/tex], we get:
[tex]4^x - 192 + 2^x = 0[/tex]
Adding 192 to both sides, we get:
[tex]4^x + 2^x - 192 = 0[/tex]
This is the same as the given equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]
Therefore, we have shown that the roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex] also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]
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Please help I need the code asap
The values based on the exponent will be:
0.024
5670
41952
0.005
73
0.34
900
6
How to calculate the valuesThe exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
1) 2.4 × 10^-2 = 0.024
2) 5.67 x 10^3 = 5670
3) 4.1952 x 10^4 = 41952
4) 5 × 10^-3 = 0.005
5) 7.3 × 10^1 = 73
6) 3.4 × 10-1 = 0.34
7) 9 × 10^2 = 900
8) 6 × 10*0 = 6
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