The best measure of variability for the data is standard deviation and player B is more consistent with IQR of 1.5
What is Standard Deviation?
The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Standard Deviation is calculated by
Each number's deviation from the mean must be determined, and then squared.
Next, add up all of these values.
Divide the result by the quantity of numbers.
Then calculate its square root.
σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²
Given data ,
Let the first table be represented as A
where A = { 2 , 1 , 3 , 8 , 2 , 1 , 4 , 3 , 1 }
Let the second table be represented as B
where B = { 2 , 3 , 1 , 3 , 2 , 2 , 1 , 3 , 6 }
And , mean of A = 25/9 = 2.778
And , mean of B = 23/9 = 2.5556
where the Standard Deviation of B = 1.5
Therefore , Player B is the most consistent, with an IQR of 1.5
Hence , player B is more consistent with IQR of 1.5
what is the value of b2-4ac for the following equation? 5x2+7x=6
Answer:
169
Step-by-step explanation:
Given data
The function is
5x^2+7x=6
rearrange
5x2+7x-6=0
From the above expression, we can see that
a=5
b=7
c=-6
Substitute into the expression b^2-4ac
=7^2-4*5*-6
= 49-(-120)
=49+120
=169
Hence the answer is 169
Liam reads 35 pages in 4 hours. How many pages can he read
in 6 hours?
Answer: 52.5
Step-by-step explanation:
Divide 35 by 4
Multiply the number you get by 6
Answer:
Liam reads 52.5 pages in 6 hours
Step-by-step explanation:
to solve this problem you need to start with finding how many pages he reads in 1 hour.
to do this, divide 35 by 4.
35/4 = 8.75
the unit rate is 8.75 pages per hour.
now just multiply the unit rate by the amount of hours.
8.75 * 6 = 52.5
The greatest rectangular area that the farmer can enclose with 100 m of fencing is
m2.
Considering the vertex of a quadratic equation, the greatest rectangular area that the farmer can enclose with 100 m is of 625 m².
What is the vertex of a quadratic equation?A quadratic equation is modeled by the rule presented as follows:
y = ax^2 + bx + c
The vertex has these following coordinates.
\((x_v, y_v)\)
In which:
\(x_v = -\frac{b}{2a}\)\(y_v = -\frac{b^2 - 4ac}{4a}\)Considering the coefficient a, we have that the vertex can represent either a maximum or a minimum point in the function, as follows::
If a < 0, the vertex is a maximum point of the function.If a > 0, the vertex is a minimum point of the function.In this problem, the coefficients of the quadratic equation representing the area are given as follows:
a = -1, b = 50.
The greatest rectangular area that the farmer can enclose with 100 m is the y-coordinate of the vertex of the quadratic equation, hence:
\(y_v = -\frac{50^2 - 4(-1)(0)}{4(-1)} = 625\)
The area is of 625 m².
Missing informationThe quadratic equation for the area is:
A(w) = -w² + 50w
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Answer:
625
explanation:
trust
Sum of roots of the equation
\(x_1+x_2=6x_1x_2\)
We're going to use Vieta's formula to solve the problem.
\(x_1+x_2=-\dfrac{b}{a}\\\\x_1x_2=\dfrac{c}{a}\)
Therefore
\(x_1+x_2=-\dfrac{-3}{2}=\dfrac{3}{2}\\\\x_1x_2=\dfrac{4m}{2}=2m\)
And so
\(\dfrac{3}{2}=6\cdot2m\\\\4m=\dfrac{1}{2}\\\\m=\dfrac{1}{8}\)
Solve. Round values to one decimal place, if necessary. Angle measure to be in degrees
An airplane climbs at an angle of 10• at an average speed of 400 mph. How long (in min.) will it take for the plane to reach an altitude of 5 miles:
It will take approximately 325.14 minutes (or 5 hours and 25 minutes) for the airplane to reach an altitude of 5 miles.
How long will it take for the plane to reach the altitude?
We can start by using trigonometry to determine the vertical component of the airplane's velocity, which will tell us how fast it is climbing. Since the angle of climb is 10 degrees, we can use the sine function:
sin(10) = opposite/hypotenuse
vertical velocity = hypotenuse * sin(10)
The hypotenuse is the airplane's speed of 400 mph, so we have:
vertical velocity = 400 * sin(10) ≈ 69.28 mph
To find how long it takes the airplane to reach an altitude of 5 miles, we need to convert 5 miles to feet (since velocity is given in miles per hour):
5 miles * 5280 feet/mile = 26,400 feet
Now we can use the formula:
time = distance/velocity
where distance is the altitude we want to reach (26,400 feet) and velocity is the vertical component of velocity (69.28 mph). However, we need to convert velocity to feet per minute to match the units of distance and get the time in minutes:
69.28 mph * 5280 feet/mile * 1/60 min/hour ≈ 81.22 feet/min
Now we can calculate the time:
time = 26,400 feet / 81.22 feet/min ≈ 325.14 min
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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 416 gram setting. It is believed that the machine is underfilling the bags. A 12 bag sample had a mean of 412 grams with a standard deviation of 11. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled
Based on the given information, we can perform a one-sample t-test to determine if there is sufficient evidence to support the claim that the chocolate chip bags are underfilled.
The null hypothesis (H0) states that the mean weight of the bags is equal to 416 grams, while the alternative hypothesis (H1) states that the mean weight is less than 416 grams.
Given the sample mean of 412 grams, standard deviation of 11 grams, and a sample size of 12 bags, we can calculate the t-statistic using the formula: t = (sample mean - population mean) / (standard deviation / √sample size).
The critical t-value for a one-tailed test at a 0.1 level of significance and 11 degrees of freedom (n-1) can be found in a t-distribution table. Comparing the calculated t-statistic to the critical t-value will help us determine whether to accept or reject the null hypothesis.
If the calculated t-statistic is less than the critical t-value, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the bags are underfilled at the 416-gram setting. If the t-statistic is greater than or equal to the critical t-value, we fail to reject the null hypothesis and cannot conclude that the bags are underfilled.
Remember to always consider the level of significance and the assumptions of the test (such as normality) when interpreting the results of a statistical hypothesis test.
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Plato classesWhich statement describes a key feature of function g
Solution:
Given:
\(\begin{gathered} f(x)=2^x \\ g(x)=f(x-4)=2^{x-4} \end{gathered}\)The graph of g(x) is shown;
From the graph of g(x), the horizontal asymptote is y = 0
Therefore, OPTION C is correct
The graph of y = 2x^2 - 8x + 7 is identical to the graph of y = a(x-h)^2 + k$ for some real numbers $a, h, k$.
What is the value of $k$?
The form:
y = a(x-h)^2 + k
Is the vertex form of the quadratic equation, by finding the vertex, we conclude that k = -1.
How to get the value of k?For any quadratic equation of the form:
y = a*x^2 + b*x + c
With a vertex (h, k), we can rewrite the equation as:
y = a*(x - h)^2 + k
And the value h of the vertex is given by:
h = -b/(2a)
In this case, the quadratic equation is:
y = 2x^2 - 8x + 7
Then the value h of the vertex is:
h = -(-8)/(2*2) = 2
Evaluating the quadratic equation in x = 2 we will get the value of k, so we have.
y = 2*(2)^2 - 8*2 + 7 = -1
Then the vertex is (2, -1), which means that the value of K is -1.
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The distribution of the wing lengths of house flies, in millimeters (mm), is approximately normal with mean wing length 4.55 mm and standard deviation 0.39 mm. A scientist is conducting an experiment to determine the effect of wing length on flight range. The first phase of the experiment will test houseflies with wing lengths that are between 3.77 mm and 4.16 mm. Based on the information, if a housefly is to be selected at random, what is the probability that the housefly's wing length will meet the requirements of the first phase of the experiment?
Answer:
Probability = 0.13591
Step-by-step explanation:
We are given;
Population mean; μ = 4.55
Population standard deviation: σ = 0.39
Now, we want to find the probability that the housefly's wing length will meet the requirements of the first phase of the experiment. This is;
P(3.77mm < X < 4.16mm)
Z-score formula is;
z = (x - μ)/σ
When x = 3.77mm
z = (3.77 - 4.55)/0.39
z = -2
When x = 4.16
z = (4.16 - 4.55)/0.39
z = -1
From online p-value calculator between 2 z-scores attached, we have;
P-value = 0.13591
Isabell will rent a car for a day. The rental company offers two pricing options: Option A and option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below. It’s Isabell drive the rental car 200 miles which option cost more?How much more does it cost than the other option?For what number of miles driven do the two options cost the same?If Isabell drives more than this amount, which option cost more?
From the graph of miles driven and pricing, it can be observed that for 200 miles option A price is $100 and option B price is $70.
So option A cost more than option B.
Determine the difference between $100 and $70 to obtain how much option A cost more than option B.
\(100-70=30\)So option A cost $30 more than option B.
From the graph, it can be observed that lines of option A and option B intersect each other at (50,40). So option A and option B cost same for 50 miles.
uppose the investigators had made a rough guess of 175 for the value of s before collecting data. what sample size would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%?
To determine the necessary sample size to obtain an interval width of 50 ppm for a confidence level of 95%, we need to use the formula for sample size calculation for estimating a population mean.
The formula for sample size calculation is:
n = (Z * σ / E)^2
n is the sample sizeZ is the Z-score corresponding to the desired confidence levelσ is the standard deviation of the populationE is the desired margin of error (half the interval width)In this case, the desired margin of error is 50 ppm, which means the interval width is 2 * E = 50 ppm. Therefore, E = 25 ppm.
The Z-score corresponding to a 95% confidence level is approximately 1.96.
Given that the investigators made a rough guess of 175 for the value of σ (standard deviation) before collecting data.
We can substitute these values into the sample size formula:
n = (1.96 * 175 / 25)^2
Simplifying the calculation:
n = (7 * 175)^2
n = 1225^2
n ≈ 1,500,625
Therefore, a sample size of approximately 1,500,625 would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%.
To obtain an interval width of 50 ppm with a confidence level of 95%, a sample size of approximately 1,500,625 is required. This is calculated using the formula for sample size estimation, considering a desired margin of error of 25 ppm and a standard deviation estimate of 175. The Z-score corresponding to a 95% confidence level is used to determine the sample size.
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7x+4y=24
4x-4y=0
Solve by using the elimination method. Show your work.
Answer:
as the last two months have a few minutes in a factory and we have a few minutes away and will also send the
n is an integer.
Write down the values of n such that -8 ≤ 4n < 12
Answer: -2; -1; 0; 1; 2
\(-8\leq 4n<12\\\\=> -2\leq n<3\)
because n is an integer => n ∈ {-2; -1; 0; 1; 2}
Step-by-step explanation:
Answer is : n ={-2; -1; 0; 1; 2}
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
given that,
-8 ≤ 4n < 12
=> -2≤ n <3
because, n is an integer => n ∈ {-2; -1; 0; 1; 2}
Hence, Answer is : n ={-2; -1; 0; 1; 2}.
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Hiiii Please help!!!
m/n(x), x≠
When we evaluate the quotient functions, (mn)(x) for x = -3
(mn)(-3) = 9 and (m/n) (x), x ≠ 0
How did we evaluate the quotient function?To evaluate the quotient function (mn)(x) for x = -3, we substituting x = -3 into the function mn(x).
This gives us (mn)(-3) = m(-3) × n(-3) = (-3)² × (-3) = 9.
We then need to evaluate (m/n)(x), x ≠ 0.
This is done by dividing the function m(x) by the function n(x). This gives us (m/n)(x) = m(x) / n(x) = x^2 / x = x. However, this expression is undefined when x = 0, because division by zero is undefine
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“The probability that you are given a car for your birthday.”
is that a conditional probability?
Answer:
No
Step-by-step explanation:
Conditional probability is an event repeating itself.
ex.) you have 3 red marbles and 4 blue ones in a hat, since you already drew a red one, there is conditional probability you will draw red again. So unless you have already gotten a car for your birthday previously, you cannot classify your question as conditional probability.
can we add 4x and 3y? why?
Answer:
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
no we cannot add them, though we can multiply or divide them. You cannot add them because they have different variables, we need the same variables to add or subtract those.
Step-by-step explanation:
Hope it helps
keep smiling :)
At a cherry farm, the cost per pound of cherries depends on the amount of cherries bought. For an amount up to 100 pounds, the cost is $1.75 per pound, and, for an amount over 100 pounds, the cost is $1.50 per pound. Ralph bought 60 pounds and Jeff bought 80 pounds separately. If they had bought the total amount jointly, how much would they have saved?
Answer:
they would have saved 35 dollars
Step-by-step explanation:
Ralph on his own would have paid 105 and jeff 140 but together with the discount they could save $35 by paying 210 in total with the discount.
two groups of rats were trained to navigate a runway for food. one group earned a single food pellet, the other received three pellets. what will happen when they are both shifted to a situation in which they earn the alternative reward
When both groups are shifted to a situation in which they earn an alternative reward after being trained to navigate a runway for food, the group that received three food pellets will continue to perform the task at a high level while the group that received one food pellet will experience difficulty.
It is known that rats have a natural preference for higher rewards. As a result, the group that received three pellets will be more motivated to complete the task since they have already tasted a higher reward. Therefore, they will continue to perform at a high level in the new environment.
On the other hand, the group that received only one pellet may find it challenging to adapt to the new situation since they are now receiving a lower reward. As a result, they may struggle to complete the task, and their performance may decrease.
In conclusion, the group that received three pellets will perform better than the group that received one pellet when both groups are shifted to a situation in which they earn an alternative reward. This is because the rats have a natural preference for higher rewards.
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Pls help! The sum of the digits of a certain two-digit number is 5. When you reverse its digits you
decrease the number by 9. What is the number?
answer: 32
Consider 2 digit numbers whose sum is 5
5
x
0
→
5
+
0
=
5
4
x
1
→
4
+
1
=
5
3
x
2
→
3
+
2
=
5
Now reverse the digits and compare with original 2 digit number. Starting with 4 1
4
x
1
→
1
x
4
and
41
−
14
=
27
≠
9
3
x
2
→
2
x
3
and
32
−
23
=
9
⇒
the number is
32
Complete the equation that involves multiplication contains the variable x, and has a solution of 7.
x = 56
Enter another equation that has the same solution and includes the same variable and numbers but uses division.
Answer:
56 divided by 8
Step-by-step explanation:
7 times 8 equals 56
therefore 56 divided by 8 equals 7 ANSWER
and 56 divided by 7 is 8
Fact families
Suppose a school has three periods (called 1, 2, and 3) during which a class can be scheduled. For each class, there are three variables. For example, for class A, there are variables XA1, XA2, and XA3. Setting XA2 = 1 represent scheduling class A during period 2. a. give a boolean expression that evaluates to 1 if and only if a is scheduled in at least one of the three periods.
The boolean expression that evaluates to 1 if and only if A is schedule in at least one of the three periods is \(x_{ A1}+x_{ A2} +x_{ A3}\).
A logical assertion that can only be TRUE or FALSE is called a Boolean expression. As long as both sides of the expression have the same fundamental data type, boolean expressions can compare data of any kind. Data can be tested to check if it is more than, less than, or equal to other data.
An expression that may only be evaluated as true or false is called a boolean expression (after mathematician George Boole). Let's examine some examples in everyday language: Pink is one of my favorite colors. I'm apprehensive about programming computers. • It's entertaining to read this book.
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How many thousands are in 9000
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
just breack it down
bus 1 leaves at 8 am at 80 mph from point b to point a, 550 miles away. bus 2 leaves point a at 8:30am to point b at 90 mph. what time will they pass each other?
The bus 2 will pass bus 1 at 12.30 pm, when both are at 360 miles.
The bus 1 starts half hour earlier than bus 2. But since bus 2 is faster, it will overtake at some point. At 8 am, bus 1 will start. By the time 8.30, it will cover a distance of 40 miles.
Bus 2 starts at 8.30, So it will be at 0 miles.
By 10, the bus 1 will be at 160 miles, bus 2 at 135 miles
By 10.30, the bus 1 will be at 200 miles, bus 2 at 180 miles.
By 11.30, bus 1 will be at 280 miles, bus 2 will be at 270 miles
By 12.30, bus 1 will be at 360 miles, bus 2 will be at 360 miles.
So at the 360 the, the both the buses passes each other.
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An officer printer prints 25 photos in 12.5 minutes. A home printer prints 15 photos in 6 minutes. Which printer is faster, How many more photos can you print in 12 minutes using the faster printer? You can print ____
more photos in 12 minutes using the faster printer.
Answer: The at home printer prints faster, and you can print 6 more photos with it than the office printer.
Step-by-step explanation:
25 ÷ 12.5 = 2
15 ÷ 6 = 2.5
2 x 12 = 24
2.5 x 12 = 30
Mr castle shares out 64 marbles between emily and asif in the ratio 7:1 how many marbles does each child get
Answer:
Emily: 72 marblesAsif: 8 marblesStep-by-step explanation:
first lets find in how many shares is the total amount of marbles divided into:
7+1=8
now, lets find how many marbles are in each share:
64/8=8
now that we know that each share of marbles contains 8 marbles, we can find how many each child got:
Emily got 7 shares: 8*7= 72 marbles
Asif got 1 share: 8*1= 8 marbles
Hence,
Emily got 72 marbles, while Asif got 8 marblesUse the distributive property to simplify
12 • 3 3/4
Answer:
We can first write 3 3/4 as an improper fraction:3 3/4 = 15/4Then, using the distributive property, we get:12 • 3 3/4 = 12 • (3 + 3/4) = 12 • 3 + 12 • 3/4 = 36 + 9 = 45Therefore, 12 • 3 3/4 simplifies to 45.
\(\huge\text{Hey there!}\)
\(\mathtt{12\times 3\dfrac{3}{4}}\)
\(\mathtt{= 12 \times \dfrac{3\times4+3}{4}}\)
\(\mathtt{= 12\times\dfrac{12 + 3}{4}}\)
\(\mathtt{= 12\times\dfrac{15}{4}}\)
\(\mathtt{= \dfrac{12}{1}\times\dfrac{15}{4}}\)
\(\mathtt{= \dfrac{12\times15}{4\times1}}\)
\(\mathtt{= \dfrac{180}{4}\rightarrow 180\div4 \rightarrow \bold{12(3 + \dfrac{3}{4}})\rightarrow 12(3) + 12(\dfrac{3}{4})\rightarrow 36 + 9}\)
\(\mathtt{= 45}\)
\(\huge\text{Therefore your answer should be:}\)
\(\huge\boxed{\mathtt{12(3 + \dfrac{3}{4})\ which\ gives\ you\ \bf 45}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
Please help me I need to pass this class
A line passes through the points (2, -1) and (9,3). What is the slope of the line?
Answer:
\( \huge{ \boxed{ \tt{ \frac{4}{7} }}}\)
Step-by-step explanation:
Let the points be A and B
\( \sf{A(2 \: , - 1) \longrightarrow \: (x1 \:, y1)}\)
\( \sf{B(9 \: ,3 \: ) \longrightarrow \: (x2 \:, y2)}\)
\( \underline{ \text{Finding \: the \: slope}}: \)
\( \boxed{ \rm{Slope \: ( \: m \: ) \: = \frac{y2 - y1}{x2 - x1} }}\)
\( \rm{Slope = \frac{3 - ( - 1)}{9 - 2} }\)
\( \rm{Slope = \frac{3 + 1}{9 - 2}} \)
\( \rm{Slope = \boxed{ \rm \frac{4}{7} }}\)
Hope I helped!
Best regards! :D
~TheAnimeGirl
Find the value of x (show your work)
simplify 3(6-3) -2x2 + 15 /5
Answer: \(\frac{3(6-3)-2x^{2}+15 }{5} : \frac{-2x^{2}+24 }{5}\)
You're welcome.