A statement 'He is not the winner, then, he is sick.' is a valid argument.
To test the validity of a given argument, we need to see if we can find a counter-example that makes one of the statements non-valid. If after analyzing the statements we can't find a counter-argument, then we can conclude that the argument is valid.
Here we will find that the argument is valid.
We can write given statement as:
1) If he participates in a race then he is the winner.
2) Either he participates in the race, or he is sick.
3) He is not the winner, then, he is sick.
Now, from the first statement, we know that this person participates in a race, he wins.
From the second statement we know that he only participates if he is not sick, we can rewrite that one as:
"If he is sick, then he does not participate in the race".
Finally, from the third one, if he does not win, then he is sick.
This makes sense, he only does not participate when he is sick, then the only races where he is not the winner, are these races where he does not participate, and he does not participate only if he is sick, then this is a valid argument.
Concluding, the 3 statements are valid, as we can't find any counter-argument to any of these 3.
Therefore, a statement 'He is not the winner, then, he is sick.' is a valid argument.
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Rebecca's boss pays her time and a half for overtime work at the comic book store. If her regular wage is $8.50, what is Rebecca paid for overtime work?
The amount that Rebecca will be paid for overtime work is $12.75.
How to calculate the value?From the information, Rebecca's boss pays her time and a half for overtime work at the comic book store. Her regular wage is $8.50.
The amount for overtime will be:
= (1.5 × $8.50)
= $12.75
Therefore, the amount that Rebecca will be paid for overtime work is $12.75.
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the time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list, along with the five-number summary. 9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58
Based on the 1.5 × IQR rule for outliers, there is no evidence to support the student's claim because there is only one outlier at 58 minutes.
What is an outlier?An outlier is also referred to as anomalous data and it can be defined as a numerical value that is either unusually too small or large (big) in comparison with the overall pattern of the numerical values contained in a data set.
What is an interquartile range?IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.
Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):
IQR = Q₃ - Q₁
Based on the given data set, the following interquartile ranges was calculated by using Excel:
Q₃ = 31.5
Q₁ = 20.5
Now, the interquartile range (IQR) is given by:
IQR = Q₃ - Q₁
IQR = 31.5 - 20.5
IQR = 11
Based on the 1.5 × IQR rule for outliers, we have:
1.5 × IQR = 1.5 × 11 = 16.5
Therefore, our fences will be 16.5 points below Q₁ and 16.5 points above Q₃:
Lower fence = 20.5 - 16.5 = 4.5
Upper fence = 4.5 + 31.5 = 36.
In conclusion, we can reasonably infer and logically deduce that there is no evidence to support the student's claim because there is only one outlier at 58 minutes.
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Complete Question:
The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list.
9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58
One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5 × IQR rule for outliers, is there evidence to support the student's claim?
can someone help me with this please and explain because i’m confused :)) thanks!
Answer: 0.2121...=7/33 ≈943 hits
Step-by-step explanation:
a.
[tex]99n=100n-n\\[/tex]
Divide both parts of the equation by 99:
[tex]\displaystyle\\n=\frac{100n-n}{99} \\\\n=\frac{100*0.2121...-0.2121...}{99} \\\\n=\frac{21.2121...-0.2121...}{99}\\\\n=\frac{21}{99} \\\\n=\frac{7*3}{33*3}\\\\n=\frac{7}{33}[/tex]
b.
[tex]\displaystyle\\200:\frac{7}{33}=\\\\200*\frac{33}{7} =\\\\\frac{200*33}{7}=\\\\\frac{6600}{7}=\\\\ \approx943[/tex]
There are 12 inches in 1 foot and 5,280 feet in 1 mile. Elena ran 212 miles how many feet is that
Based on the given parameters, there are 1119360 feet in 212 miles
How to determine the number of feet?The given parameters are
12 inches = 1 foot
5,280 feet = 1 mile.
Multiply both sides of 5,280 feet = 1 mile by 212
So, we have
212 * 5,280 feet = 1 mile * 212
Evaluate the product
1119360 feet = 212 miles
The above means that there are 1119360 feet is 212 miles
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Carlos jogged
5
3
4
laps around the school track in 8 minutes. What was his average speed in laps per minute?
Carlos took 8 minutes to complete 5 3/4 laps all around school track.
What would be Average speed?The total distance travelled divided by the time interval yields the average speed. For example, someone who drives 20 miles north and then 20 miles south in 40 minutes has an average speed of 40 miles divided by 40 minutes, and 1 mile per minute (60 mph)Now, to answer the question
5 3/4 laps = 23/4 laps
= (23/4)/8
Simplifying the equation;
=23/4 × 1/8
=23/32
Therefore, Carlos will take 23/32 laps per minute to running on school track.
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The correct question is-
carlos jogged 5 3/4 laps around the school track in 8 minutes. what was his average speed in laps per minute?
Simplify the following:
3(x + 1) - 4(2x - 5) + 10x
5x + 23
Step-by-step explanation:
[tex]{ \purple{ \tt{3(x + 1)}}} - { \purple{ \tt{4(2x - 5)}}} + { \purple{ \tt{10x}}}[/tex]
[tex] = { \purple{ \tt{3x + 3 - 8x + 20 + 10x}}}[/tex]
[tex] = { \purple{ \tt{3x + 2x + 23}}}[/tex]
[tex] = { \purple{ \tt{5x + 23}}}[/tex]
The grid above shows the graph of the parent function f(x)= land a translated functions graph.
Write the equation for the translated graph.
The blue graph is a translation of 2 units to the left and 1 unit up of the parent function, thus, the equation is:
g(x) = |x + 2| + 1
How to find the translated function?We know that the red graph is an absolute value function, so we have:
f(x) = |x|
And we want to find the equation of the blue absolute value function, which is a translation of the above one.
Notice that the vertex of the blue one is at (-2, 1), so we have a translation of 2 units to the left and one unit up, it is just written as:
y = |x + 2| + 1
We conclude that the translated function is:
g(x) = |x + 2| + 1
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the group given the treatment being studied during an experiment, such as a medication, fertilizer, or exposure to some other variable, is called the blank group. multiple choice question. test placebo control variable
The group given the treatment being studied during an experiment, such as medication, fertilizer, or exposure to some other variable, is called the (A) test group.
What is a test group?The term "test group" refers to the entire group of users who will be analyzed as part of a study. So, if you're running a mobile A/B test and the variables are sent to a predetermined proportion of users, your test group will be the total number of users who receive either variable. The test group is the group that receives the treatment being studied during an experiment, such as medication, fertilizer, or exposure to another variable. A common example of group testing is a string of light bulbs connected in series, one of which is known to be broken.Therefore, the group given the treatment being studied during an experiment, such as medication, fertilizer, or exposure to some other variable, is called the (A) test group.
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The correct question is given below:
The group given the treatment being studied during an experiment, such as medication, fertilizer, or exposure to some other variable, is called the _____?
(A) test group
(B) placebo group
(C) control group
(D) variable group
what is the area of triangle pqr on the grid? a triangle pqr is shown on a grid. the vertex p is on ordered pair 7 and 6, vertex q is on ordered pair 1 and 6, and the vertex r is on ordered pair 4 and 2.
The area of triangle par on the grid is the vertex p is on ordered pair 7 and 6.
What is vertex?Soccer on CBS Sports is various TV programs that have broadcasted soccer matches in the US on CBS, CBS Sports Organization, and Paramount+. These matches are from Global, European, and American contests. Affiliation football, all the more usually known as just football or soccer, is a group activity played between two groups of 11 players who essentially utilize their feet to impel the ball around a rectangular field called a pitch. Soccer, or football as it's known beyond North America, is the most famous game on the planet. Thus, how could it be played, who plays it, and a lot more inquiries are responded to here.
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tamika practiced oboe for 1/4 hour in the morning and 5/6 hour in the afternoon. how long did she practice in all? write your anwser as a mixed number.
Answer:
1/2
Step-by-step explanation:
- find the least common denominatir for the two. (12)
-multiply 4 and 3
-multiply 6 and 2
- Add 1 and 5
-Keep the denominator.
-simplify if needed
Answer:
Step-by-step explanation:
answer 1 1/12 hours
I need help pls Evaluate.
2^5/2^3
Answer:
I think it’s 4.
-2 2/3 x (-4 3/7)
Can someone help me?
Find the y-intercept of y=ax^2+bx+c
Answer:
c would be the y intercept,
Step-by-step explanation:
How many shrimps are in a colonie of fish
Answer:
The ideal starting count for your shrimp colony will be around 10 to 20 shrimp.
Step-by-step explanation:
Answer:
Step-by-step explanation:
20 to 10
which term best represents the intersection of two pages of an open book? line startfragment, line, angle startfragment, angle, point startfragment, point, plane
The term that best represents the intersection of two pages of an open book is point.
What is intersection?A third item made up of everything that is simultaneously contained in all of the other things is called an intersection of two or more objects in mathematics. In Euclidean geometry, for instance, the intersection of two lines in a plane that are not parallel is where they come together. More broadly, the set of elements that are a part of all of the sets is what is meant by the intersection of sets in set theory. The items being considered do not need to be in a shared space, unlike the Euclidean concept.
A point is the most frequent shape for an intersection in plane geometry, while there are other shapes that can be used as well. An intersection is an item of lesser dimension that is incident to each in incidence geometry, which is typically applied to flats.
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Find 5 numbers that have a mean of 40 and a median and deviationof 35 and a mode of 25.
The 5 number are 25, 25, 35, 45 and 70 that has the mean of 40 and a median and deviation of 35 and a mode of 25.
Mean:
Mean is the sum of all observations divided by the number of observations.
Median:
Median defines the value of the middlemost observation, obtained after arranging the data in ascending or descending order.
Mode:
The value which appears most often in the given data i.e. the observation with the highest frequency is called a mode of data.
Given,
Mean = 40
Median = 35
Mode = 25
We know that the mean value is is the sum of all observations divided by the number of observations.
So, Let us consider v,w,x,y,z are the five numbers.
So it can be written as,
[tex]Mean=\frac{v+w+x+y+z}{n}[/tex]
We know that,
Mean = 40 and n = 5.
Then,
[tex]40=\frac{v+w+x+y+z}{5}[/tex]
Therefore,
=> v + w + x + y + z = 40 x 5
=> v + w + x + y + z = 200 --------------------------(1)
Here we know that the Median is 35.
The median in equation (1) is x,
So x = 35
And the mode is 25, we know that definition of mode so let us consider it will occurs at least twice,
So, the values of v = 25 and u = 25
Now apply the values on the equation,
=> 25 + 25 + 35 + y + z = 200
=> 85 + y + z = 200
=> y + z = 200 - 85
=> y + z = 115
So, here we have to take the combinations that gives the value of 115 and the values must be greater than 35.
So, the values are 45 and 70.
Therefore, the five numbers are 25, 25, 35, 45 and 70.
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If Alice wants to have R12 000 saved in 4 years' time at 12% simple interest,
how much will she need to invest now?
Using simple interest, Alice need to invest 25000 now in order to get 12 000 saved in 4 years' time at 12% simple interest.
What is simple interest?The daily interest rate, the principle, and the number of days between payments are multiplied to determine simple interest. Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest. Simple interest loans are frequently used for auto loans and short-term personal loans.
Given,
simple interest = 12000
rate of interest = 12%
time = 4 years
Simple interest = P × R × T / 100
12000 = P × 12 × 4 / 100
P = 25000
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Find the slope and reduce.
P=(-2, 3) Q=(8, 3)
A
Slope = [ ?]
Hi!
Use the Slope Formula:
[tex]\begin{gathered}\\\bullet\implies\boldsymbol{\displaystyle\frac{y_2-y_1}{x_2-x_1}} \\\\\boldsymbol{Setting\:the\:Values}\\\bullet \boldsymbol{y_2=3}\\\bullet\boldsymbol{x_2=8}\\\bullet\boldsymbol{y_1=3}\\\bullet\boldsymbol{x_1=-2}\\\\\boldsymbol{Solving\:for\:the\:slope}\\\boldsymbol{\displaystyle\frac{3-3}{8-(-2)}}\\\boldsymbol{\dfrac{0}{8+2}}\\\boldsymbol{Slope\longrightarrow0}\end{gathered}[/tex]
I hope I helped! ^^
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The numbers given in scientific notation will be arranged from least to greatest as: 7.6×10⁻²⁰, 5.5×10⁻¹¹, 2.4×10², 8.9×10², 9.2×10⁴, 7.6×10²⁰.
Scientific notation of numbers may be defined as the way of representation of bigger numbers into powers of 10. This helps in reducing space as well as it helps in conveniently solving the problem. For example, scientific notation of 92000 may be written as 9.2×10⁴.
Here in the number 7.6×10⁻²⁰ the power of 10 is maximum but with a negative value so it is the least number. Then comes the number 5.5×10⁻¹¹ as its power are also negative but greater than the previous number. Similarly using the above logic, the other numbers will be placed, and the greatest number would be 7.6×10²⁰ as it has the maximum power of 10 that too with a positive sign.
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Solve by completing the square.
y² + 30y = -7
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
y =
Submit
or y =
Answer:
y = 0.24 or y = - 29.76==============================
Identity of the square of a sum of two numbers:
(a + b)² = a² + 2ab + b²Given equation:
y² + 30y = - 7We can see one of the numbers is y, and the second one is 15 as twice the product is 30y.
Add 15² = 225 to both sides to complete the square, then solve it:
y² + 2*15y + 15² = 225 - 7(y + 15)² = 218y + 15 = ± √218y = - 15 ± √218y = - 15 ± 14.76 (rounded to the nearest hundredths)y = 0.24 or y = - 29.76Answers:
y = ± 221.47, y = -0.24, y = -29.76
Step-by-step explanation:
y^2 + 30y = -7
Move -7 over to the other side
y^2 + 30y +7 = 0
This takes form of a quadratic equation of ax^2 + bx + c = 0, where y = x
Quadratic formula is x = (-b ± (sqrtb^2 - 4ac)/2a and replace everything so it's y = (-30 ± (sqrt30^2 - 4*1*7)/2*1. Once solved, the answer choices are y = ± 221.47, y = -0.24, or -29.76.
Could you help no time to wast
Answer:
Answers will be. ............ 36+38
Step-by-step explanation:
Try it on calculator
4⁄6 + 2⁄4 + 3⁄5 = answer
Answer: 53/30
Step-by-step explanation:
4/6 + 2/4 + 3/5 =
2/3 + 1/2 + 3/5 = ==> Simplify Denominators
30/30 * (2/3 + 1/2 + 3/5)= ==> Have matching denominators by multiplying by the LCM (Least common multiple) of the denominators
(2*30/3 + 1*30/2 + 3*30/5)/30=
(60/3 + 30/2 + 90/5)/30=
(20 + 15 + 18)/30=
(35 + 18)/30=53/30
One number is 6 less than five times another. Their difference is 22. Find the numbers.
The numbers in the equations are -4 and -26
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to find the numbers?Let the numbers be x and y
A system of linear equations is a collection of at least two linear equations. So, we have the following linear equations
y = 5x - 6
x - y = 22
Substitute y = 5x - 6 in x - y = 22
x -5x + 6 = 22
Evaluate the like terms
-4x = 16
Divide both sides by -4
x = -4
Substitute x = -4 in y = 5x - 6
y = 5 * -4 - 6
Evaluate
y = -26
Hence, the numbers are -4 and -26
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(-6) over 5 x (-6) over 8
Answer:
(-6 ÷ 5) × (-6 ÷ 8) = 9/10 or 0.9
Step-by-step explanation:
Which inequality is equivalent to -10 (x - 1) <13?
The inequality that is equivalent to the given inequality is -10x + 10 < 13
From the question, we are to determine the inequality that is equivalent to the given inequality
The given inequality is -10(x - 1) < 13
To determine the inequality that is equivalent to this inequality, we will solve the given inequality
Solving the inequality
-10(x - 1) < 13
Apply the distributive property
-10x + 10 < 13
Subtract 10 from both sides of the inequality
-10x + 10 - 10 < 13 - 10
-10x < 3
Divide both sides by -10 and reverse the sign
x > -3/10
From the steps of solving the inequality, the inequality that is equivalent to the given inequality is -10x + 10 < 13
Hence, the inequality that is equivalent to the given inequality is -10x + 10 < 13
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Answer:
C. -10x + 10 < 13
Draw a pair of intersecting lines that forms a pair of complementary angles. Explain your reasoning.
A pair of intersecting lines that forms a pair of complementary angles is as drawn below.
What are the pair of complementary angles?
Remember that complementary angles are defined as angles which sum is equal to 90°.
Besides, each of the pairs of opposite angles made by two intersecting lines are called vertical angles. Now, from congruent proofs, we know that that vertical angles are congruent. In another words, they have the same measure.
Thus, we have to draw two vertical angles that measure:
90° ÷2 = 45°
This image is as drawn below in the attached file.
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Convert 9 cubic centimeters to fluid ounces (to the nearest thousandth).
fl. oz.
Please help me with mathh
Answer:
16
Step-by-step explanation:
A____(6)_____B____(10)_____C
6+10=16
Hope this helps!
what is the final step to be performed in the mathematical expression, (σx)2? group of answer choices square the sum of the scores square each score add the squared scores add the scores
The final step to be performed in the mathematical expression, (Σx)2 is square the sum of the scores
What Is the Sum of Squares?Sum of squares is a statistical method for calculating the dispersion of data points in regression analysis. By deviating the least from the data, the sum of squares can be used to identify the function that fits the data the best. The purpose of a regression analysis is to assess how well a data series can be fitted to a function that could provide insight into the process by which the data series was created. In the world of finance, the sum of squares can be used to calculate the variation in asset values.
A statistical measure of departure from the mean is the sum of squares. Variation is another name for it. The squared differences of each data point are added together to calculate it. The sum of squares is calculated by squaring the separation between each data point and the line of best fit, then adding the results. The line of greatest fit will reduce this value to the minimum.
We first find the sum, and then square the sum.
ΣX = 1 + 0 + 2 + 4 = 7
So, ΣX + 1 = 8
Mean = ( 4+6+14 )/3 = 8
Mean = ΣX*f / Σf = (5*2 + 4*1 + 3*3 + 2*2 + 1*2) / (2+1+3+2+2) = 29/10
Subtract 3 points from the score X=3
Changing the lowest score to a lower one will increase the range.
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The final step to be performed in the mathematical expression, (Σx)2 is square the sum of the scores
What Is the Sum of Squares?Sum of squares is a statistical method for calculating the dispersion of data points in regression analysis. By deviating the least from the data, the sum of squares can be used to identify the function that fits the data the best. The purpose of a regression analysis is to assess how well a data series can be fitted to a function that could provide insight into the process by which the data series was created. In the world of finance, the sum of squares can be used to calculate the variation in asset values.
A statistical measure of departure from the mean is the sum of squares. Variation is another name for it. The squared differences of each data point are added together to calculate it. The sum of squares is calculated by squaring the separation between each data point and the line of best fit, then adding the results. The line of greatest fit will reduce this value to the minimum.
We first find the sum, and then square the sum.
ΣX = 1 + 0 + 2 + 4 = 7
So, ΣX + 1 = 8
Mean = ( 4+6+14 )/3 = 8
Mean = ΣX*f / Σf = (5*2 + 4*1 + 3*3 + 2*2 + 1*2) / (2+1+3+2+2) = 29/10
Subtract 3 points from the score X=3
Changing the lowest score to a lower one will increase the range.
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if a bacteria population starts with 100 bacteria and doubles every four hours, then the number of bacteria after t hours is n = f(t) = 100 · 2t⁄4. (a) find the inverse of this function.
The inverse of the given function,f(t) = 100 . 2^(t/4) is 4 * log2(x/100).
What is the inverse of a function?
An inverse of a function f(x), is defined as another function that undoes the operations performed on the function. It is denoted by f^(-1).
Calculation of the inverse of a function
We are given a function,
f(t) = 100 . 2^(t/4)
Let us assume that f^(-1) represents the inverse of a function
Replacing f(t) with y, we get,
y = 100 . 2^(t/4)
Now, replace further t with y and y with x
x = 100 . 2^(y/4)
Rearranging, we have,
2^(y/4) = x / 100
Taking log both sides, we get,
(y/4) log 2 = log (x/100)
y/4 = log2(x/100)
y = 4 * log2(x/100)
Further, replace x with t and y with f^(-1), i.e.
f^(-1) = 4 * log2(t/100)
Hence, the inverse of the given function, f(t) = 100 . 2^(t/4) is 4 * log2(x/100).
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