The 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center is (2.166, 2.634). So, the correct option is B).
To find the 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center, we can use the formula:
CI = X ± z*(σ/√n)
where X is the sample mean, σ is the sample standard deviation, n is the sample size, and z is the z-score associated with the desired confidence level (90% in this case).
The z-score for a 90% confidence level is 1.645.
Plugging in the values given in the problem, we get:
CI = 2.4 ± 1.645*(2.1/√220)
Solving this equation gives us a confidence interval of (2.166, 2.634) rounded to three decimal places.
Therefore, the correct answer is (2.166, 2.634) and option is B).
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a telephone survey of 1000 randomly selected us adults found that 31% of them say they believe in ghosts. does this provide evidence that more than 1 in 4 us adults believe in ghosts? clearly show all details of the test.
How can a telephone survey of 1000 randomly selected US adults provide evidence that more than 1 in 4 US adults believe in ghosts?The survey results provide evidence that more than one in four US adults believe in ghosts. The telephone survey was conducted on a random sample of 1000 US adults. The survey found that 31 percent of US adults believed in ghosts.
To determine whether more than one in four US adults believe in ghosts, the null and alternative hypotheses will be tested.The null hypothesis in this scenario is that less than or equal to 25% of US adults believe in ghosts. The alternative hypothesis is that more than 25% of US adults believe in ghosts.Therefore, the level of significance (α) will be determined.
The α level is typically set to 0.05. This means that the likelihood of making a type I error is 5%. Then, the z-score will be calculated as follows:z = (0.31 - 0.25) / sqrt[(0.25 x 0.75) / 1000]z = 2.83The obtained z-score will be compared to the critical z-value using a z-distribution table. The critical z-value is 1.96. Since the obtained z-score is greater than the critical z-value, the null hypothesis will be rejected. Therefore, there is evidence to suggest that more than one in four US adults believe in ghosts.
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alemu earn birrs 10000 per month,calculate
a, the income tax he has to pay
b.the net income after deducting income tax
Alemu's net income after deducting income tax is 9,470 birrs per month, assuming he lives in Ethiopia and the income tax rates for the current tax year apply.
We must take into account the income tax rates in Alemu's nation for the current tax year in order to determine how much income tax he must pay. We cannot provide an exact response since we are unsure about Alemu's country of residence. The income tax rates in Ethiopia, where the first 6,000 birr of income are tax-free and the remaining amount is subject to progressive taxes, range from 10% to 30%, can be used as an example, though.
Alemu's monthly taxable income, assuming he resides in Ethiopia, would be 4,000 birrs (between 10,000 and 6,000). He must pay the following amount of income tax:
180 birr (10% of the first 1,800 birr)
15% of the following 1,800 birrs is 270 birrs.
80 birrs are 20% of the remaining 400 birrs.
Alemu would therefore pay 530 birrs in total income tax each month.
Alemu's net income would be 9,470 birrs after income tax. This is the sum of cash he would have on hand to cover personal costs, savings, investments, and any other debts. It is crucial to remember that the net income amount may change depending on a number of variables, including deductions for social security, health insurance, or any other needed legal payments.
In conclusion, assuming Alemu lives in Ethiopia and the income tax rates for the current tax year are applicable, Alemu's net income after income tax is 9,470 birrs each month.
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Three people are sitting on a bus. Austin is seated 12 feet directly behind Bernard and 9 feet directly left of Keenan. How far is Bernard from Keenan?
Answer: I would say 21 feet.
Step-by-step explanation:
Bernard is 12 feet ahead of Austin
So add 12 feet to get to Austin first
Then add the 9 feet that is apart from Austin and Bernard
12+9 = 21
21 feet would be the answer
Hope this helps ! ^^
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an algebra class has 8 students and 8 desks. for the sake of variety, students change the seating arrangement each day. how many days must pass before the class must repeat a seating arrangement? days must pass before a seating arrangement is repeated. suppose the desks are arranged in rows of 4. how many seating arrangements are there that put larry, moe, curly, and shemp in the front seats? there are seating arrangements that put them in the front seats. what is the probability that larry, moe, curly and shemp are sitting in the front seats? the probability is .
Solving the probability and permutations, we get (a) 20,160. (b) Larry, Moe, Curly, and Shemp can be arranged in the four front seats in 24 ways, and the ILB block can be arranged with the remaining students in 720 ways, and (c) 1/280.
(a) The number of possible seating arrangements can be calculated using the formula for permutations of n objects taken r at a time: P(n,r) = n!/(n-r)!. In this case, there are 8 students and 8 desks, so there are 8! possible seating arrangements.
To find the number of days before a seating arrangement is repeated, we need to subtract 1 from this number (since the first day is a unique arrangement) and divide by 2 (since there are two possible ways to arrange the students in any given seating arrangement, by simply rotating the arrangement). So the number of days before a seating arrangement is repeated is (8! - 1)/2 = 20,160.
(b) Larry, Moe, Curly, and Shemp must occupy the four front seats, so we need to choose four of the remaining four desks for the other students to sit at. This can be done in 4!/(4-4)! = 4! = 24 ways.
(c) We can treat the block of three students (ILB) as a single object, and then arrange the five remaining objects (M, O, A, X, and the ILB block) in a row. The ILB block can be arranged in 3! = 6 ways, and the other five objects can be arranged in 5! = 120 ways.
So the total number of potential seating arrangements in which ILB remains together is 6 x 120 = 720.
(d) The probability that Larry, Moe, Curly, and Shemp are sitting in the front seats is the number of possible seating arrangements in which they occupy the four front seats (24, from part b) divided by the total number of possible seating arrangements ([tex]8![/tex], from part a). So the probability is 24/8! = 1/280.
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Find three different ways to write the number 534,000 using powers of 10.
Answer:
534×10³
5340×10²
53400×10
Write the series using sigma notation with lower limit n=4.
[tex]\begin{array}{cccccccccc} &\frac{-1}{4}\left( -\frac{1}{2} \right)&\frac{1}{8}\left( -\frac{1}{2} \right)&\frac{-1}{16}\left( -\frac{1}{2} \right)&\frac{1}{32}\left( -\frac{1}{2} \right)\\ -\cfrac{1}{4}&\cfrac{1}{8}&-\cfrac{1}{16}&\cfrac{1}{32}&-\cfrac{1}{64}... \end{array}\hspace{5em}\stackrel{\textit{common ratio}}{r=-\frac{1}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\qquad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ r=-\frac{1}{2}\\ a_1=-\frac{1}{4} \end{cases}\implies \sum_{n=1}^{n=4}~-\frac{1}{4}\left( -\frac{1}{2} \right)^{n-1}[/tex]
Equation for line of best fit
correlation positive/negative
r=
The equation for the line of best fit is a useful tool in data analysis to describe the relationship between two Variables and make predictions based on that relationship.
The equation for the line of best fit is a mathematical formula that describes the relationship between two variables in a data set. It is used in regression analysis to estimate and predict the value of one variable based on the value of another.
To find the equation for the line of best fit, we use the method of least squares, which minimizes the sum of the squares of the differences between the observed data points and the predicted values from the equation.
The equation takes the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept is the value of y when x = 0.
The coefficient of determination, denoted as r, is a measure of how well the line fits the data. It ranges from -1 to 1, where a value of 1 indicates a perfect fit, and a value of 0 indicates no correlation. A negative value indicates an inverse relationship.
In summary, the equation for the line of best fit is a useful tool in data analysis to describe the relationship between two variables and make predictions based on that relationship.
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6) In the diagram below, ABC → A'B'C'. List all the corresponding sides.
A
B
C
B'
A'
C'
Required corresponding sides are side AB corresponds to side A'B', side BC corresponds to side B'C', side AC corresponds to side A'C'
What is corresponding side?
In geometry, when two figures are similar, their corresponding sides are the sides that are in the same position and have the same relative orientation in each figure.
For example, consider two triangles ABC and DEF, where angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F. If the length of AB is proportional to the length of DE, BC is proportional to EF, and AC is proportional to DF, then side AB corresponds to side DE, side BC corresponds to side EF, and side AC corresponds to side DF.
To list all the corresponding sides of two triangles ABC and A'B'C', we need to identify which side of triangle ABC corresponds to which side of triangle A'B'C'. Corresponding sides are those that are in the same position relative to each triangle.
We can identify the corresponding sides by comparing the positions of the vertices. For example, the side opposite vertex A in triangle ABC corresponds to the side opposite vertex A' in triangle A'B'C'. Similarly, the side opposite vertex B in triangle ABC corresponds to the side opposite vertex B' in triangle A'B'C', and so on.
Therefore, the corresponding sides are side AB corresponds to side A'B', side BC corresponds to side B'C', side AC corresponds to side A'C'.
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a group of friends wants to know how many students bike to school. how can the median of the samples help you make an inference about the population?
The median of the samples can give an idea of the central tendency of the data and can help in making an inference about the population.
In this case, since the percent of students that bike to school varies from 20% to 50% in the samples, the median of the samples can provide an estimate of the median percent of students who bike to school in the population.
By analyzing the median of the samples, it may be possible to make an inference about the central tendency of the population, which could inform decisions about encouraging or improving biking to school.
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--The given question is incomplete, the complete question is given
" a group of friends wants to know how many students bike to school. Survey Results In the samples, the percent of students that bike to school varies from 20% to 50% 19 20 21 22 14 15 16 17 18 Number of Students that Bike to School How can the median of the samples help you make an inference about the population? "--
Find the surface area of the rectangular prism.
need help
The surface area of the rectangular prism with a length of 4 units, a width of 3 units, and a height of 5 units is 94 square units.
To find the surface area of a rectangular prism, you need to add up the area of all six faces. The formula for the surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism.
So, to find the surface area of a rectangular prism, you simply need to plug in the values for l, w, and h into this formula and solve.
For example, if the length of the rectangular prism is 4 units, the width is 3 units, and the height is 5 units, the surface area would be:
Surface Area = 2(4)(3) + 2(4)(5) + 2(3)(5)
Surface Area = 24 + 40 + 30
Surface Area = 94 square units
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A clothing truck has a base of 8 square meters. If it holds 12 cubic meters, what is the height of the truck?
Answer:
1.5 m
Step-by-step explanation:
Volume = base * height
12 = 8 * h
12/8 = h
1.5 = h
a principal wants to know if students want to change the start time of the school day. which strategy is most likely to produce a representative sample?
A. ask each teacher to select one student.
B. select a day at random. Ask the first students who arrive at school that day.
C. Select students from a list of all students at random. Ask those students
D. Select tables in the library at random. Ask the students sitting at those tables..
Answer:
Either A or c
Step-by-step explanation:
EXPIRED!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The option B is the correct answer for the above question. The line of symmetry should have been 4 instead -4 is correct.
How to find the symmetry?Line of symmetry - A line of symmetry is a line in mathematics that splits a form or object into two congruent halves, such that if one portion is reflected over the line of symmetry, it will coincide with the other component. A line of symmetry is also known as an axis of symmetry.
Now, we will see to find the line of symmetry for the quadratic equation [tex]f(x) = x^2 - 8x + 15[/tex],
Line of symmetry: [tex]x = \frac{-b}{2a}[/tex]
Vertex: [tex](x,y) = (\frac{-b}{2a}, f(\frac{-b}{2a}))[/tex]
where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c.[/tex]
In this case, [tex]a = 1, b = -8, and\ c = 15[/tex], so we can substitute these values into the formulas:
Line of symmetry: [tex]x = \frac{-(-8)}{21} = 4[/tex]
And, From this value of x, we will get the correct value of y.
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Solve this question for me?
The tree's height changes 2.5ft bases per time.
What's the rate of change?The rate of change function is defined as the rate at which one volume changes relative to another volume. In simple terms, the rate of change is the quantum of change in one item divided by the corresponding quantum of change in another.
Equation:We can find the rate of change in the tree's height by calculating the slope of the line that represents the direct function relating the tree's height to the number of times since it was planted.
To do this, we can use the slope formula
Slope = ( change in height)/( change in time)
Let's choose the points
( 1,4.5) and( 4, 12)
Change in height = 12-4.5 = 7.5
Change of time = 4- 1 = 3
Slope = (7.5/ 3) = 2.5
So, the tree's height changes 2.5 bases per time.
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Can someone please help me with this question. I know the answer is B, but I literally do not understand how to do it, because we are required to use the box method, and I don’t really get how to use it.
Thank you. Can someone please help me with this question. I know the answer is B, but I literally do not understand how to do it, because we are required to use the box method, and I don’t really get how to use it.
Thank you.
The child should be given 8.75 mL of the medicine. option B
How to solveTo determine the correct dosage, we first need to find out how much paracetamol the child needs based on their weight and then convert that amount to the appropriate volume of the medicine.
Calculate the required amount of paracetamol based on the child's weight:
Child's weight: 14 kg
Dosage: 15 mg per 2 kg of body weight
Required_paracetamol = (Child's weight / Dosage per kg) * Dosage
Required_paracetamol = (14 kg / 2 kg) * 15 mg
Required_paracetamol = 7 * 15 mg
Required_paracetamol = 105 mg
The child needs 105 mg of paracetamol.
Convert the required paracetamol amount to the appropriate volume of the medicine:
Medicine concentration: 120 mg of paracetamol per 10 mL
Required_volume = (Required_paracetamol / Medicine concentration) * 10 mL
Required_volume = (105 mg / 120 mg) * 10 mL
Required_volume = 0.875 * 10 mL
Required_volume = 8.75 mL
The child should be given 8.75 mL of the medicine.
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how to calculate a baseball player has a batting average of 0.365. what is the probability that he has exactly 1 hits in his next 7 at bats? Round your answer to four decimal places. The probability the baseball player has exactly 4 hits in his next 7 bats is
The probability that the baseball player has exactly 1 hit in his next 7 at-bats is 0.2908, rounded to 4 decimal places.
It is a statistic that measures the performance of baseball players. It is the ratio of the number of hits to the number of at-bats.
Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1.
Static means the precise value of something, without approximation or estimation.
It is a process of approximating a number to a specific number of decimal places.
A baseball player has a batting average of 0.365. The probability that he has exactly 1 hit in his next 7 at-bats is to be found.
Step 1: Calculate the probability of getting a hit in one at-bat. The probability of getting a hit in one at-bat is equal to the batting average of the player.
P(hit) = 0.365
Step 2: Calculate the probability of not getting a hit in one at-bat. The probability of not getting a hit in one at-bat is equal to the difference between 1 and the batting average.
P(not hit) = 1 - 0.365 = 0.635
Step 3: Calculate the probability of getting exactly 1 hit in 7 at-bats. The probability of getting exactly 1 hit in 7 at-bats can be calculated using the binomial probability formula:
P(1 hit in 7 at-bats) = 0.2908 (rounded to 4 decimal places)
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A company is marketing a new video game. Market research indicates that 24% of the the market has seen an advertisement for the new game.
Suppose 42% of those who see the ad have purchased the game and 93% of those who have not seen the advertisement have not purchased the game. If you choose a person who purchased the game, what is the probability he or she did not see the ad?
Express your answer as a decimal, rounded to the nearest thousandth (three decimal places).
Answer =
The probability that a person who purchased the game did not see the advertisement is:0.659.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probability is used in many areas, including statistics, mathematics, science, finance, and gambling.
In the given question,
To solve this problem, we will use Bayes' theorem, which allows us to update our beliefs about the probability of an event based on new information.
Let A be the event that a person has seen the advertisement, and B be the event that a person has purchased the game. We want to find the probability of A given B, i.e., the probability that a person who has purchased the game has also seen the advertisement.
We know that P(A) = 0.24 (24% of the market has seen the advertisement), P(B|A) = 0.42 (42% of those who see the ad have purchased the game), and P(~A|~B) = 0.93 (93% of those who have not seen the advertisement have not purchased the game).
We can use the complement rule to find P(B|~A), the probability of purchasing the game given that the person has not seen the advertisement:
P(B|~A) = 1 - P(~B|~A) = 1 - 0.93 = 0.07
Now we can use Bayes' theorem:
P(A|B) = P(B|A) * P(A) / P(B)
where P(B) = P(B|A) * P(A) + P(B|~A) * P(~A)
Plugging in the values, we get:
P(B) = 0.42 * 0.24 + 0.07 * (1 - 0.24) = 0.2956
P(A|B) = 0.42 * 0.24 / 0.2956 = 0.3408
Therefore, the probability that a person who purchased the game did not see the advertisement is:
1 - P(A|B) = 1 - 0.3408 = 0.659
Rounded to the nearest thousandth, the answer is 0.659.
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NEED HELP RIGHT NOW!!!
The number of users on a website is 2600 and is growing exponentially at a rate of 54% per year. Write a function to represent the number of users on the website after t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent.
Therefore , the solution of the given problem of function comes out to be the monthly percentage rate of change is roughly 4.56%, to the closest hundredth of a percent.
What is the function?There will be a range of questions in each subject on the midterm test, including inquiries about both imagined and real locations and also inquiries regarding the design of numerical variables. a schematic illustrating the connections between various components that work together to produce the same outcome.
Here,
The exponential development equation is:
=>[tex]N(t) = N_0 * e^{(rt)}[/tex]
We must first convert the annual growth rate from a percentage to a decimal, which we must then split by 12 to obtain the monthly rate:
Monthly rate at r = 54% is 0.54; r/12 is 0.045.
=>[tex]N(t) = 2600 * e^{(0.045)}[/tex]
=> [tex]N(t) = 2600 * 1.0469^t[/tex]
We can use the following method to determine the monthly percentage rate of change:
=> Monthly Rate of Change equals 100% * (e^(Monthly Rate) - 1)
By substituting the previously calculated monthly rate, we obtain:
=> [tex](e^{(0.045)} - 1)[/tex]* 100% = 4.56% for the monthly rate of change.
In light of this, the monthly percentage rate of change is roughly 4.56%, to the closest hundredth of a percent.
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Triangle ABC has coordinates A(4,-2), B(5,5), C(-1,3). Determine if triangle ABC is an equilateral triangle.
Triangle ABC is an ........ triangle because ..........
Triangle ABC's sides are not equal in length, hence it's not an equilateral triangle.
What does Class 7 equilateral triangle mean?It has three equal sides. The three angles are equal. Every edge of an equilateral is 60 degrees since the total of the inner angles equals 180 degrees. It has three regular sides and is a polygon. A vertex's height and median are represented by a single line.
What is equilateral, exactly?A triangular with equally length sides is known as an equilateral in geometry. The three angles opposing the three equal sides are equal in size because the three are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle.
Using the distance formula, we can find the lengths of the three sides:
[tex]AB = \sqrt{((5 - 4)^2 + (5 - (-2))^2)} = \sqrt{(2^2 + 7^2)} = \sqrt{(53)}[/tex]
[tex]BC = \sqrt{((-1 - 5)^2 + (3 - 5)^2) } = \sqrt{((-6)^2 + (-2)^2)} = \sqrt{(40)}[/tex]
[tex]CA = \sqrt{((4 - (-1))^2 + (-2 - 3)^2)} = \sqrt{(5^2 + 5^2)} = \sqrt{(50)}[/tex]
Since AB, BC, and CA have different lengths, the triangle is not equilateral.
Therefore, the answer is: Triangle [tex]ABC[/tex] is not an equilateral triangle because its sides have different lengths.
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Since AB and AC have the same length, but BC has a different length, Therefore, ΔABC is not an equilateral triangle.
What is an equilateral triangle?Equilateral triangles are those with three sides that are all the same length.
In other words, all three sides of an equilateral triangle are of the same length, and all three angles within the triangle are also equal to 60 degrees.
Equilateral triangles are a type of regular polygon, which means that they have congruent sides and congruent angles.
Triangle ABC is not an equilateral triangle because its side lengths are not all equal.The lengths of the sides can be determined using the distance formula:
AB = √((5-4)² + (5-(-2))²) = √(1 + 49) = √(50)
BC = √((5-(-1))² + (5-3)²) = √(36 + 4) = √(40)
AC = √((4-(-1))² + (-2-3)²) = √(25 + 25) = √(50)
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Find the shaded area. Round your answer to the nearest tenth, if necessary.
Use 3.14 for pi.
Area of the Rectangle =
Area of the Circle =
Total Shaded Area =
Answer:
Area of the rectangle - 144 in^2
Area of the circle - 28,26 in^2
Total shaded area - 115,74 in^2
Step-by-step explanation:
[tex]a(rectangle) = 18 \times 8 = 144 \: {in}^{2} [/tex]
[tex]a(circle) = \pi \times {r}^{2} = {3}^{2} \times \pi = 9\pi = 9 \times 3.14 = 28.26 \: {in}^{2} [/tex]
[tex]a(shaded) = a(rectangle) - a(circle)[/tex]
[tex]a(shaded) = 144 -28.26 = 115.74 \: {in}^{2} [/tex]
HELP PLEASE IT WAS DUE 10!!!
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
A- 14 and 1 over 7 in2
B -23 and 4 over 7 in2
C -47 and 1 over 7 in2
D - 84 and 6 over 7 in2
A,B,C,D which one
Answer:
Step-by-step explanation:
Surface area of a cylinder = 2πr(r + h)
radiius = 1/2 diameter so the radius is 1/2 of 2 = 1
Surface are = 2(22/7)(1 )[(1 + 1.25)]
44/7 (2.25) = 99/7
This is for ONE muffin - mulitply by 6 to find out how much paper for
6 muffins,
6 × 99/7 = 594/7 = 84 6/7 in²
a trapezoid in a coordinated plane has vertices (-2,5) (-3, -2) (2, -2) and (1,5) what is the height of the trapazoid
Answer: 7
Step-by-step explanation:
If you draw it out, you can visually tell it's 5 units, but you can also tell by looking at the two distinct y values, -2 and 5. The distance between them is 7 units, as you take the absolute value of both of them, then add to get 7.
Help please need this asap
The mean, median, and standard deviation of the given data set are approximately 114.4, 110, and 10.12, respectively.
What is mean?In statistics, the mean is a measure οf central tendency οf a data set, alsο referred tο as the average. It is calculated by summing up all the values in the data set and then dividing by the tοtal number οf values. The mean represents the typical οr cοmmοn value in the data set.
The mean of the given data set is:
(135 + 115 + 120 + 110 + 110 + 100 + 105 + 110 + 125) / 9 = 114.44 (rounded to the nearest tenth)
To find the median, we first need to arrange the data set in ascending order:
100, 105, 110, 110, 110, 115, 120, 125, 135
Since the data set has an odd number of values, the median is the middle value, which is 110.
To find the standard deviation, we first need to calculate the variance. The variance is the average of the squared differences between each value and the mean. We can use the following formula to calculate the variance:
variance = [(value1 - mean)² + (value2 - mean)² + ... + (value9 - mean)²] / 9
Plugging in the values from the data set and the mean we calculated earlier, we get:
variance = [(135 - 114.44)² + (115 - 114.44)² + ... + (125 - 114.44)²] / 9
Simplifying this expression, we get:
variance = 102.46
The standard deviation is the square root of the variance, which is:
[tex]\sqrt{(102.46)[/tex] = 10.12 (rounded to the nearest tenth)
Therefore, the mean, median, and standard deviation of the given data set are approximately 114.4, 110, and 10.12, respectively.
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Suppose you toss two number cubes. Find the probability that both cubes will show a 4.
Therefore, the probability of both cubes showing a 4 is 1/36 or approximately 0.028 or 2.8%.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. Probability can also be expressed as a percentage between 0% and 100%, with 0% indicating impossibility and 100% indicating certainty.
In probability theory, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you flip a fair coin, there are two possible outcomes: heads or tails. Since each outcome is equally likely, the probability of getting heads is 1/2 or 0.5 or 50%.
Assuming that the number cubes are fair and each face has an equal chance of landing face up, the probability of getting a 4 on any one of the cubes is 1/6, since there are six equally likely outcomes (numbers 1 to 6) and only one of them is a 4.
To find the probability of getting a 4 on both cubes, we need to multiply the probability of getting a 4 on the first cube by the probability of getting a 4 on the second cube, since the outcomes of the two cubes are independent of each other.
So, the probability of getting a 4 on both cubes is:
1/6 x 1/6 = 1/36
Therefore, the probability of both cubes showing a 4 is 1/36 or approximately 0.028 or 2.8%.
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The altitude of an airplane is decreasing at a rate of 44 feet per second. What is the change in altitude of the airplane over a period of 37 seconds?
the altitude of the airplane would decrease by 1628 feet over a period of 37 seconds.
What is Rate?
A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.
When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.
To find the change in altitude, we need to multiply the rate of decrease by the time period:
change in altitude = rate of decrease × time period
So, in this case:
change in altitude = 44 feet/second × 37 seconds
change in altitude = 1628 feet
Therefore, the altitude of the airplane would decrease by 1628 feet over a period of 37 seconds.
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Geometric probability
Find the probability that a randomly selected point within the square falls in the red shaded area
The probability that a randomly selected point within the square falls in the red shaded area is approximately 0.2146 or about 21.46%.
To find the probability that a randomly selected point within the square falls in the red shaded area, we need to compare the area of the red shaded region to the area of the entire square.
Let the side length of the square be 2 units, and let the center of the circle be at the center of the square. Then, the radius of the circle is also 1 unit.
The area of the square is [tex](side length)^2[/tex] = [tex]2^2[/tex] = 4 square units.
The area of the circle is π[tex](radius)^2[/tex] = π[tex](1)^2[/tex] = π square units.
The red shaded area is the difference between the area of the square and the area of the circle, which is 4 - π square units.
Therefore, the probability that a randomly selected point within the square falls in the red shaded area is:
(red shaded area) / (area of the square) = (4 - π) / 4 ≈ 0.2146
So the probability is approximately 0.2146 or about 21.46%.
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Help me with my homework please!
The values of the sides are;
11. SR = 25
12. RU = 25
13. SU = 35.4
14. Perimeter = 100 units
15. Area = 625 square units
How to determine the valueIt is important to note that a square have 4 equal sides and 4 equal angles.
From the information given, we have that;
Line SR = line RU
But we have that;
SR = 2k + 7
RU = 3k - 2
Equate the sides, we have;
2k + 7 = 3k - 2
collect the like terms
2k - 3k = - 2 - 7
subtract the terms
-k = - 9
k = 9
Then, SR =2(9) + 7 = 25
RU = 3(9) - 2 = 25
The line SU is the hypotenuse side
Using the Pythagorean theorem
SU² = 25² + 25²
SU² = 625 + 625
SU = √1250
SU = 35. 4
15. The perimeter of a square is expressed as;
Perimeter = 4a
Perimeter = 4(25)
Perimeter = 100 units
16. The area of a square is expressed as;
Area = a²
Area = 25²
Area = 625 square units
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Mary stocked books to sell at a street fair the ratio of comic books to mystery books is 2:5 Lina stocked no more than 100 of each type of book complete the table to determine how many comic books and mystery books Mary may have stocked
The question you posted is incomplete and does not have a table to complete. Can you please provide the table or the missing information so that I can answer your question properly?
Can someone pls help me with c!!
Answer:
Either plane XYS or plane Q
Step-by-step explanation:
They are the only points lying on the plane in general.
Can someone help me to figure out this problem
Answer:
Step-by-step explanation:
17f+1i
6f+5f+4f=15f
11i+4i+10i=25i ---------> 2f+1i
1feet=12inch