To find the first quartile (Q1) of the given data set, we first need to sort the data in ascending order: 198, 199, 199, 200, 202, 215, 223, 223, 223, 301. The data set contains 10 values.
Q1 represents the value at the 25th percentile, which means it divides the data into the lower 25% of the distribution. To calculate the position of Q1, we use the formula (25/100) * (n + 1), where n is the number of values in the data set. In this case, (25/100) * (10 + 1) = 2.75.
Since the position is not an integer, we take the average of the values at the positions 2 and 3. These values are 199 and 199. Therefore, the Q1 of the data set is (199 + 199) / 2 = 199. Based on the given options, the correct answer is d. 199.
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teri ran 4 kilometers . one mile is approximately equal to 1.6 kilometers. how many miles did teri run
Answer:
2.5 Miles
Step-by-step explanation:
4 k = ? Mile
1.6 k = 1 mi
4/1.6 is 2.5
1x2.5 equals 2.5
so 4 km should be 2.5 mi
4 k = 2.5 Mile
(x2.5)1.6 k = (x2.5)1 mi
The miller’s are comparing babysitting services for their two children. the babysitters block charges a rate of $15 an hour per child plus an initial fee of $25 per household. super sitters charges a flat rate of $20 an hour per child. for …. hours of service both babysitting services would cost the same
Answer:
2.5 hours
Step-by-step explanation:
BB = 25 + (15x)2
SS = (20x)2
25 + 30x = 40x
10x = 25
x = 2.5
Answer:
5 hours
Step-by-step explanation:
15 times 5 is 75 plus 25 is 100
20 times 5 is also 100
A cello string is 0.695 m long, and transmits waves at 204 m/s. What frequency does it produce? (Unit = Hz)
Answer:
The frequency produced is: F = 146.76 Hz
Step-by-step explanation:
We are given:
Length of string = 0.695 m
Waves speed = 204 m/s
We need to find Frequency
The formula used is: \(F=\frac{v}{2L}\)
where F is frequency, L is length of string and v is wave speed
We have :
L = length of string = 0.695
v= Wave speed = 204 m\s
Finding frequency by putting values in formula:
\(F=\frac{v}{2L}\\F=\frac{204}{2(0.695)}\\F=\frac{204}{1.39}\\F=146.76\:Hz\)
So, The frequency produced is: F = 146.76 Hz
Answer:
146.76 Hz
hope it helps you
make y the subject of the formula
X= 4-3y/y-5
Step-by-step explanation:
X= 4-3y/y-5
x(y-5) = 4-3y
xy -5x = 4 -3y
xy+3y = 4+5x
y(x+3)= 4+5x
y = (4+5x)/(x+3)
help me with this question please
Answer:
N+1
Step-by-step explanation:
It begins with = 2
then n+1=3
then n+2=4 and so on it is n+1
Angle of Triangle ( x )
Answer:
117°
Step-by-step explanation:
The angle in the bottom left is 180 - 101 = 79°; straight angle is supplementary
79° + 38° = 117°; 2 angles combined opposite from exterior angle is equal to the ext angle
Answer:
117º
Step-by-step explanation:
The angle measure of a line is 180º, so the measure of the angle next to the one with measure 101º is 180-101=79º.
The Exterior Angle Theorem says that an exterior angle (like x) is equal to the sum of the opposite interior angles. So, x=38+79=117º.
Humberto evaluates the expression 4t 2 for t = 3. He correctly substitutes 3 for t in the expression, but then says that the value is 144. Fill in the blanks to explain Humberto’s error
The correct value of the expression is 36.
What is Expression?An expression is combination of variables, numbers and operators.
Given that Humberto evaluates the expression 4t² for t = 3.
He correctly substitutes 3 for t in the expression, but then says that the value is 144.
Humberto solution has an error the correct answer should be 36.
Humberto first multiplied 4 by 3 to get 12, then he multiplied 12 by itself to get 144.He should have first multiplied 12 by itself then he should multiplied the result 9 by 4.
The correct value of the expression is 36.
Hence, the correct value of the expression is 36.
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verify that the mean value theorem can be applied to the function f(x)=x3/4 on the interval [0,16]. then find the value of c in the interval that satisfies the conclusion of the mean value theorem.
The value of c that satisfies the conclusion of the mean value theorem is c≈7.69.
The mean value theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists at least one point c in (a,b) where the value of the derivative of f(x) is equal to the slope of the line connecting the endpoints of the interval, i.e., \(f'(c)=(f(b)-f(a))/(b-a).\)
Here, the function \(f(x)=x^(3/4)\) is continuous on the closed interval [0,16] and differentiable on the open interval (0,16), as the derivative of f(x) is \(f'(x)=(3/4)x^(-1/4)\), which is defined for all x in (0,16).
Therefore, we can apply the mean value theorem to this function on the interval [0,16].
To find the value of c that satisfies the conclusion of the mean value theorem, we first calculate the slope of the line connecting the endpoints of the interval: \((f(b)-f(a))/(b-a)=[(16)^(3/4)-(0)^(3/4)]/(16-0)\)=\(2sqrt(2).\) Then, we set f'(c)=2sqrt(2) and solve for c:
\(f'(c)=(3/4)c^(-1/4)=2sqrt(2)c^(-1/4)=(8/3)sqrt(2)c=(3/2)^(4/3)≈7.69\)
Therefore, the value of c that satisfies the conclusion of the mean value theorem is c≈7.69.
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Probability of a pair of dice landing on a 4 and on a 6
Answer:
1/3
Step-by-step explanation:
It would be 2 options out of 6 total which means 2/6. 2/6 reduces down to 1/3
Which value of x makes the equation
-4x + 8 = -12 true?
Answer:
x=5
Step-by-step explanation:
-4x + 8 = -12
-4x = -12-8
-4x = -20
x = -20÷-4
x = 5
What current is drawn by a 90 W light bulb on a 110 V household circuit?
plzzz answer and fast
Answer:
10 and 1 i belive
Step-by-step explanation:
Write the equation of the line (in slope-intercept form) that has an x-intercept at -6 and a y-intercept at 2. Provide a rough sketch of the line indicating the given points. [1 mark]. Exercise 2. For the polynomial f(x) = −3x² + 6x, determine the following: (A) State the degree and leading coefficient and use it to determine the graph's end behavior. [2 marks]. (B) State the zeros. [2 marks]. (C) State the x- and y-intercepts as points [3 marks]. (C) Determine algebraically whether the polynomial is even, odd, or neither.
To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.
To write the equation of the line with an x-intercept at -6 and a y-intercept at 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
In this case, the y-intercept is given as 2, so the equation becomes y = mx + 2. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (-6, 0) and (0, 2). We find that the slope is 1/3. Thus, the equation of the line is y = (1/3)x + 2.
For the polynomial f(x) = -3x² + 6x, the degree is 2 and the leading coefficient is -3. The end behavior of the graph is determined by the degree and leading coefficient. Since the leading coefficient is negative, the graph will be "downward" or "concave down" as x approaches positive or negative infinity.
To find the zeros, we set the polynomial equal to zero and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two solutions: x = 0 and x = 2.
The x-intercept is the point where the graph intersects the x-axis, and since it occurs when y = 0, we substitute y = 0 into the polynomial and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two x-intercepts: (0, 0) and (2, 0).
To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.
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15 yd
19 yd
Area =
Parallelogram
15*19=285
base times height is the formula
Nadia’s bookshelf contains 10 fiction books, two reference books, and five nonfiction books. What is the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book? StartFraction 1 Over 289 EndFraction StartFraction 10 Over 289 EndFraction StartFraction 5 Over 136 EndFraction One-tenth.
The probability that Nadia randomly picks up a reference book and then, without replacing it, picks up a nonfiction book is 5/136.
We have,17 total number books out of which,10 are fiction books, 2 are reference books, 5 are non-fiction books.
What are combination and probability?The combination is the number of ways of selecting things.
Probability is to quantify the possibilities.
Number of ways in which a reference book can be picked = ²C₁
Probability of picking a reference book = ²C₁ / ¹⁷C₁ = 2/17
Now, the total number of books left on the bookshelf is 16
The number of ways in which a non-fiction book can be picked after a reference book is already picked up( no replacement) = ⁵C₁ / ¹⁶C₁ = 5/16
Total probability =multiplication of both the possibilities
Total probability =(2/17)×(5/16) = 5/136
Therefore, the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book is 5/136
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Answer:
C. 5/156
Step-by-step explanation:
Edge 2023
5. Tony wants to buy a ticket for $15.75. He
has $9.25. How much must he earn to
buy the ticket?
Answer:
$6.50
Step-by-step explanation:
You just have to subtract the 2 so you get $6.50 which is how much he needs to earn
Answer:
$6.5
Step-by-step explanation:
all you have to do is find the difference between the two values
15.75-9.25=6.5
John's son will start college in 10 years. John estimated a today's value of funds to finance college education of his son as $196,000. Assume that after-tax rate of return that John is able to earn from his investment is 8.65 percent compounded annually. He does not have this required amount now. Instead, he is going to invest equal amounts each year at the beginning of the year until his son starts college. Compute the annual beginning of-the-year payment that is necessary to fund the estimation of college costs. (Please use annual compounding, not simplifying average calculations).
John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.
To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.
The present value of an annuity formula is given by:
P = A * [(1 - (1 + r)^(-n)) / r],
where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.
In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:
196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].
Simplifying the expression inside the brackets:
196,000 = A * (1 - 0.469091).
196,000 = A * 0.530909.
Dividing both sides by 0.530909:
A = 196,000 / 0.530909.
A ≈ 369,238.68.
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Determined three ways have a total cost of six dollars each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.
The cost of the apples is 2.9 dollars.
The cost of the bananas is 5.7 dollars.
How to find the number of fruits bought?The total cost is 6 dollars, each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.
Therefore,
let
x = number of apples
y = 2x
where
y = number of bananasTherefore, using equations,
1.5(x) + y(0.30) = 6
Hence,
where
y = 2x
1.5(x) + 2x(0.30) = 6
1.5x + 0.6x = 6
2.1x = 6
divide both sides by 2.1
x = 6 / 2.1
x = 2.9 dollars
y = 2(2.9) = 5.7 dollars
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Are these repeating or terminal?
Answer:-5 1/3 is repeating and 1 1/4 is terminal
Step-by-step explanation:
Answer: Terminal
Step-by-step explanation: yw :)
Which of the following is the graph of the equation below? y=3x+4
Answer:
(0,4) , (1,7) , (2,10) and (-1,1)
Step-by-step explanation:
Since you did not supply a graph, maybe I could give you some points that you should find the line on the correct graph goes through.
y = 3(0) + 4
y = 4
y = 3(1) + 4
y = 7
y = 3(2) + 4
y = 10
y = 3(-1) + 4
y = 1
The points (0,4) , (1,7) , (2,10) and (-1,1) should be on the line of the correct graph. In general, your graph should be of a straight line that crosses the y-axis at 4.
Four friends take turns driving on a road trip. Kelly drives 28 miles in the first half hour. John drives 82 miles in the following hour. Ebise then drives 58 miles in the next 45 minutes. Write an inequality to determine how many miles Eric can drive in the final 45 minutes of the trip so that the average speed over their whole trip does not exceed 70 miles per hour. Then explain how you can solve the inequality.
2.5 hours the Kelly spent driving.51 minutes John spent for driving.1.20 hours Ebise spent driving.Since average speed = distance/time +> distance = speed*time,
What is the inequalityx =the number of hours the Kelly spent driving.
y = the number of hours John spent driving.
Z= the number of hours Ebise spent driving.
Since average speed = distance/time +> distance = speed*time,
y = x + 1.
By resolving the system of equations
y = x + 1
x*28 + y*82 + Z* 58,
average speed = 70
we discover that
x = 2.5 hours
y = 51 minutes, respectively.
Z = 1. hr 20 minutes
2.5 hours the Kelly spent driving.
51 minutes John spent for driving.
1.20 hours Ebise spent driving.
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A) Which of the following statement is not true about the Poisson distribution:
(1) In Poisson distribution, the experiment consists of counting the number of times certain in a given unit of time
(2) The number of events in a Poisson distribution can also be over a given area, volume, or any other unit of measurement
(3) The probability of occurrence in a given unit of time has fixed number of trial
(4) The mean number of events or occurrence in a Poisson distribution is denoted by u
(5) The Poisson distribution is described by only one parameter which is u
The statement (3) The probability of occurrence in a given unit of time has a fixed number of trials is not true about the Poisson distribution.
In the Poisson distribution, the number of trials is not fixed, and each event in the Poisson distribution is considered a trial. The Poisson distribution is a type of discrete probability distribution that is used to calculate the probability of a certain number of events occurring in a specified interval of time or space. It is often used to model situations where the number of occurrences is rare but the average occurrence rate is known. The Poisson distribution is described by a single parameter, λ (lambda), which is equal to the expected number of occurrences in the specified interval. The Poisson distribution can also be used to calculate the probability of a certain number of events occurring over a given area, volume, or any other unit of measurement. This makes it a versatile tool in many different fields, including physics, biology, and finance. It is worth noting that the Poisson distribution assumes that the events are independent of each other, meaning that the occurrence of one event does not affect the probability of the occurrence of another event.
In conclusion, the statement (3) The probability of occurrence in a given unit of time has a fixed number of trials is not true about the Poisson distribution. The number of trials is not fixed, and each event in the Poisson distribution is considered a trial.
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a culture of bacteria has an initial population of 8600 bacteria and doubles every 5 hours. using the formula p t
The exponential growth formula for bacteria growth is P(t) = 8600 \((2)^(t/5)\).
What is exponential growth?
Exponential growth is a pattern of data that exhibits a greater increase over time, resulting in an exponential curve. Exponential is also a mathematical term meaning "with exponents". For example, if you raise a number to the 10th power, the number increases exponentially. Exponential growth is growth that increases at a constant rate.
Here given take Initial number of bacteria = 8600. rate of growth = 2.
It doubles every year. Then doubling time = 5 hours.
Now population growth after t years,
P(t) = Po \((2)^(t/5)\)
=> P(t) = 8600 \((2)^(t/5)\)
Therefore exponential growth formula is P(t) = 8600 \((2)^(t/5)\).
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Leslie planted a tree that grows at an average rate of 6 inches each year. What is the
slope of the line?
Answer:
you stated the question wrong, a tree grows upwards. state the question again
Answer:
slope = 6
Step-by-step explanation:
since the rate is 6 in/yr, the slope is 6.
-7,5 + 4,2 =?
-0,9 * 2,7 =?
\(-7,5 + 4,2 = -3.3\)
\(-0,9 \cdot 2,7 = -2.43\)
or write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. at a community barbecue, mrs. dotson and mr. kent are buying dinner for their families. mrs. dotson purchases 2 hot dog meals and 3 hamburger meals, paying a total of $33. mr. kent buys 1 hot dog meal and 3 hamburger meals, spending $27 in all. how much do the meals cost? hot dog meals cost $ each, and hamburger meals cost $ each.
Let's use the variables x and y to represent the cost of a hot dog meal and a hamburger meal, respectively.
Then, we can write the following system of equations to describe the situation:
2x + 3y = 33 (Mrs. Dotson's purchases)
1x + 3y = 27 (Mr. Kent's purchases)
To solve this system of equations using elimination, we can multiply the second equation by 2 and subtract it from the first equation:
2x + 3y = 33
-2x - 6y = -54
0x - 3y = -21
Simplifying the equation, we get:
y = 7
Substituting this value of y into either equation, we can solve for x:
2x + 3(7) = 33
2x + 21 = 33
2x = 12
x = 6
Therefore, hot dog meals cost $6 each, and hamburger meals cost $7 each.
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If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, which tool should you use?
A. X-bar and R chart
B. p-chart
C. Pareto chart
D. Scatter plot diagram
E. Affinity diagram
If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the
correlation between variables, you should use the tool: D. Scatter plot diagram. therefore, option D.Scatter plot
diagram is correct.
A scatter plot diagram is a graphical representation of the relationship between two variables. It can help you visualize
the correlation between the input and output variables, making it easier to determine if there is a potential cause-and-
effect relationship.
The tool that you should use to examine the correlation between variables is D. Scatter plot diagram.
A scatter plot diagram is a graphical representation that displays the relationship between two variables.
The x-axis represents the input variable, while the y-axis represents the output variable.
By plotting the data points on the scatter plot diagram, you can visually analyze the correlation between the variables.
If there is a strong positive or negative correlation between the variables, it suggests that the input variable may affect
the key characteristic (output variable).
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D. Scatter plot diagram is the tool that should be used to examine the correlation between variables to determine if an input variable may affect your key characteristic (output variable).
The scatter plot diagram is a graphical representation that displays the relationship between two variables, and it is commonly used to identify patterns, trends, and correlations between variables. By examining the scatter plot diagram, you can determine whether there is a positive, negative, or no correlation between the variables, which can help you to identify potential cause-and-effect relationships.
To determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, you should use:
A scatter plot diagram is a graphical tool that helps visualize the relationship between two variables, allowing you to identify any correlation between the input and output variables.
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Identify the x-intercepts, vertex, and axis of symmetry of the graph of f(x)=-0.25(x+2)(x+8)
The characteristics of the quadratic function f(x) = -0.25(x + 2)(x + 8) are given as follows:
x-intercepts: x = -8 and x = -2.Vertex: (-2.5, -2.25).Axis of symmetry: x = -2.5.x-interceptsThe x-intercepts of a function are the values of x for which the function is zero, that is:
f(x) = 0.
Hence:
-0.25(x + 2)(x + 8) = 0.
The roots are already factored, as follows:
x + 2 = 0 -> x = -2.x + 8 = 0 -> x = -8.VertexIn expanded form, the function is:
f(x) = -0.25(x + 2)(x + 8)
f(x) = -0.25(x² + 10x + 16)
f(x) = -0.25x² -2.5x - 4
The coefficients are:
a = -0.25, b = -2.5, c = -4.
The x-coordinate of the vertex is given as follows:
\(x_v = -\frac{b}{2a} = -\frac{-2.5}{4(-0.25)} = -2.5\)
Which is also the axis of symmetry of the quadratic equation.
The y-coordinate of the vertex is:
\(y_v = -\frac{b^2 - 4ac}{4a} = -\frac{(-2.5)^2 - 4(-0.25)(-4)}{4(-0.25)} = -2.25\)
Hence the vertex is:
(-2.5, -2.25).
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find the p-value (to two significant digits) for the following test. h0: μ ≤ 0, h1: μ > 0, σ = 1, z = 1.5 hint: the population follows the standard normal distribution.
The p-value for the given test is approximately 0.067, rounded to two significant digits. This was calculated by finding the area to the right of z=1.5 under the standard normal distribution.
It is given that Null hypothesis: H0: μ ≤ 0, Alternative hypothesis: H1: μ > 0, Population standard deviation: σ = 1, Test statistic: z = 1.5
To find the p-value, we need to calculate the probability of observing a z-value of 1.5 or greater under the null hypothesis. Since the population follows the standard normal distribution, we can use a standard normal table or a calculator to find this probability.
Using calculator, we can find that the area to the right of z = 1.5 is approximately 0.0668 (rounded to four decimal places).
Since this is a one-tailed test with the alternative hypothesis in the right tail, the p-value is equal to the area in the right tail beyond the observed z-value. Therefore, the p-value for the test is approximately 0.067 (rounded to two significant digits).
So, the p-value for the given test is 0.067 (rounded to two significant digits).
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I NEED HELP THIS WORKSHEET IS DUE IN AN HOUR!!!!!!!!
14/15 + x = 4/9
Answer:
So let's rearrangeWe get x= -22/45