The number of batches of muffins and bread to be made in order to maximize the profits is 16 and 2.
Considering the x to be the number of batches of bread and y be the number of batches of muffins.
In the problem, it is mentioned that the preparation of both the bread and muffin takes 4 hours and 0.5 hours since the maximum preparation time is 16 altogether
The inequality equation for it will be [tex]4x+0.5y\leq 16[/tex]
For baking the bread and muffin it takes 1 hour and 0.5 hours, the maximum baking time all together is 10
The inequality equation for it will be [tex]x+0.5y\leq 10[/tex]
The profit got from one batch of bread if 35 $ and from one batch of muffins is 10$
f(x,y)= 35x+ 10y
for f(0,0)= 0, f(0,20)= 200, f(2,16)= 230 , f(4,0) =140
So it requires 2 batches of bread and 16 batches of muffins.
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A bakery is making whole-wheat bread and apple bran muffins. For each batch of break they make $35 profit. For each batch of muffins, they make $10 profit. The break takes 4 hours to prepare and 1 hour to back. The muffins take 0.5 hours to prepare and 0.5 hours to bake. The maximum preparation time available is 16 hours. The maximum bake time available is 10 hours. Let x = # of the batches of bread and y = # of batches of muffins. What constraints can be used to find the number of batches of bread and muffins that should be made to maximize profits?
Write the equation of the line through each point. Use slope-intercept form.
(-3,1) ; perpendicular to y = -(2/5)x-4
The equation of the line in slope-intercept form passing through point (-3 , 1) and perpendicular to y = -(2/5)x - 4 is y = (5/2)x + 17/2
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula
y = mx + b
where m is the slope of the line
b is the y- intercept
If the line is perpendicular to y = -(2/5)x - 4, then their slopes are negative reciprocal of one another.
y = -(2/5)x - 4 : m = -2/5
m = 5/2
Substitute the values of the slope and the point to solve for the y-intercept, b.
y = mx + b
1 = 5/2(-3) + b
b = 17/2
Write the equation of the line by plugging in the value of the slope and y-intercept.
y = mx + b
y = (5/2)x + 17/2
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Find the missing term(s) of each arithmetic sequence. -4.6,□ ,-5.2, . . .
The missing term of the sequence is - 4.9.
Here the sequence is -4.6, __, -5.2....
An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Here the sequence is in an arithmetic sequence, as there is a common difference between them.
The nth term of the sequence has a formula
[tex]a_{n}[/tex] = a + (n - 1) d
Here we know the 3rd term of the sequence so that we can find the common difference between them
[tex]a_{3}[/tex] = -4.6 +(3-1)d
-5.2 = -4.6 + 2d
0.6 = 2d
d = 0.3
So here the common difference is 0.3.
Now we have to find the 2nd term of the sequence,
[tex]a_{2}[/tex] = -4.6 + ( 2-1) 0.3
= -4.6 + 0.3
= - 4.9
Therefore the second term of the sequence is -4.9.
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A 95onfidence interval for population mean will be wider than a corresponding 99onfidence interval.
true/false
The statement "A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval." is true.
What is a confidence interval for population standard deviation?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
The formula for finding the confidence interval for population standard deviation as follows:
[tex]\rm s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, \ n-1}}} < \sigma < s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, \ n-1}}}[/tex]
Where s is the standard deviation.
n is the sample size.
α is the significance level.
σ is the confidence interval for population standard deviation.
Calculating the confidence interval for population standard deviation:
We know significance level = 1 - confidence level
The statement is:
A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval.
As we know,
A 95% confidence interval is narrower than a 99% confidence interval.
Thus, the statement "A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval." is true.
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For each function, determine whether y varies directly with x . If so, what is the constant of variation?
a. 5 x+3 y=0
-5/3 is the constant of variation where y varies directly with x.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
A DIRECT VARIATION is a mathematical relationship between two variables that can be stated mathematically by an equation in which one variable equals a constant times the other. y = kx
⇒ 5 x+3 y=0
⇒ 3y= -5x
⇒ y = -5x/3
Thus, y = -5/3 × x, here k is constant = -5/3
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Position and label the following triangle on the coordinate plane.
right ΔJ K L with legs JK and KL so that JK is a units long and leg KL is 4 b units long
The right angle triangle ΔJ K L with legs JK and KL has been plotted below where the third side will be √(16b² + a²).
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
Given the triangle ΔJ K L
Base = a and Perpendicular = 4b
By Pythagoras theorem,
Hyp² = Base² + Perp²
Hyp² = a² + (4b)²
LJ = √(16b² + a²).
Hence "The right angle triangle ΔJ K L with legs JK and KL has been plotted below where the third side will be √(16b² + a²)".
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Write each equation in slope-intercept form. -4 x+3 y=1
The slope - intercept form of the equation -4 x+3 y=1 is y = 4/3x + 1/3.
How do we find slope - intercept form?Calculate the slope (m). Keep in mind that the slope is determined by dividing the change in y by the change in x. (rise over run).Find the y-value of the y-intercept by solving (b).In the formula y=mx+b, swap out m and b with their respective values.The equation given is -
-4 x+3 y=1
As we know the slope - intercept form is -
y = mx + c
-4 x+3 y=1
Dividing the equation with 3
⇒ -4/3x + y = 1/3
Now, rearranging the equation
y = 4/3x + 1/3
where slope = 4/3
y - intercept = 1/3
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1) -7+5= 2) 7+5 3) 7+ (-5) 4) 2+9 5) 2+(-9) adicion de numeros enteros 6) -2+9 7) 8+(-8) 8) -5+5 9) -3+(-3) 10) -5+(-5) sustraccion de numeros enteros 1) 7- (-5) 2) -7- (-5) 3) 7- (+5) 4) 2- (-9) 5) -5- (-10) 6) 5-5 7) -8- (+20) 8) -3- (-3) 9) -5- (+12) 10) 8- (+10) porfi
The results of the expressions given are:
Part 1:
1) -2
2) 12
3) 2
4) 11
5) -7
6) 7
7) 0
8) 0
9) - 6
10) - 10
Part 2:
1) 12
2) - 2
3) 2
4) 11
5) 5
6) 0
7) - 28
8) 0
9) - 17
10) -2
We solve the equations respecting the level of hierarchy:
First the operations in parentheses, then brackets and finally braces.Of the arithmetic operations, first the multiplication and divisions and then the additions and subtractions.Two like signs add the values and keep the common sign.Two unlike signs subtract the values and use the highest value sign.Part 1:
1) -7+5= -2
2) 7+5 = 12
3) 7+ (-5) = 7 - 5 = 2
4) 2+9 = 11
5) 2+(-9) = 2 - 9 = -7
6) -2+9 = 7
7) 8+(-8) = 8 - 8 = 0
8) -5+5 = 0
9) -3+(-3) = - 3 - 3 = - 6
10) -5+(-5) = - 5 - 5 = - 10
Part 2:
1) 7- (-5) = 7 + 5 = 12
2) -7- (-5) = - 7 + 5 = - 2
3) 7- (+5) = 7 - 5 = 2
4) 2- (-9) = 2 + 9 = 11
5) -5- (-10) = - 5 + 10 = 5
6) 5-5 = 0
7) -8- (+20) = - 8 - 20 = - 28
8) -3- (-3) = - 3 + 3 = 0
9) -5- (+12) = - 5 - 12 = - 17
10) 8- (+10) = 8 - 10 = -2
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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3 3/8 - 2 1/4 ÷ 1 1/2 - in the simplest form of a fraction
Answer:
1 7/8
Step-by-step explanation:
First convert mixed fraction to improper fraction. Then do division using KCF method. Then do subtraction.KCF method.
Keep the first fractionChange division to multiplicationFlip the second fraction[tex]\sf 3 \dfrac{3}{8}-2\dfrac{1}{4} \div 1\dfrac{1}{2}= \dfrac{27}{8}-\dfrac{9}{4}\div\dfrac{3}{2} \\\\[/tex]
[tex]\sf = \dfrac{27}{8}-\dfrac{9}{4}*\dfrac{2}{3}\\\\=\dfrac{27}{8}-\dfrac{3}{2}\\\\=\dfrac{27}{8}-\dfrac{3*4}{2*4} \ [\text{LCM of 2 and 8 is 8}]\\\\=\dfrac{27}{8}-\dfrac{12}{8}\\\\=\dfrac{27-12}{8}\\\\=\dfrac{15}{8}\\\\=1\dfrac{7}{8}[/tex]
Write an equivalent expression by distributing the "-−" sign outside the parentheses: -(-8.2w+10) −(−8.2w+10)
The equivalent expression by distributing the sign outside the parentheses: -(-8.2w+10) −(−8.2w+10) will be 16.4w - 20.
How to calculate the value?It should be noted that bwsed on the information given, the expression is illustrated as:
-(-8.2w+10) −(−8.2w+10)
The signs should be taken into consideration. This will be:
-(-8.2w+10) −(−8.2w+10)
= 8.2w - 10 + 8.2w - 10
= 16.4w - 20
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Write a definite integral that represents the area of the region. (do not evaluate the integral.) y1 = x2 2x 3 y2 = 2x 12
The definite integral that represents the area of the region under the given curves is: [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]
What is the area of the region under a curve?By performing a definite integral between the two locations, one can determine the area under a curve between two points. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a & x = b. With the specified limits, integration can be used to calculate this area.Given:
[tex]y_1=x^2+2x+3[/tex][tex]y_2=2x+12[/tex]The points where the two intersect will be given by:
y₁ = y₂
=> x² + 2x + 3 = 2x + 12
=> x² + 3 = 12
=> x² = 9
=> x = ± 3
For x₁ = 3, y₁ = 2(3) + 12 = 18 => (x₁, y₁) = (3, 18)
For x₂ = -3, y₂ = 2(-3) + 12 = 6 => (x₂, y₂) = (-3, 6)
Now, for the area of the region under first curve [tex]y_1=x^2+2x+3[/tex]:
A₁ = [tex]\int\limits^3_{-3} {x^2+2x+12} \, dx[/tex]
For the area of the region under the second curve [tex]y_2=2x+12[/tex]:
A₂ = [tex]\int\limits^3_{-3} {2x+12} \, dx[/tex]
For the required area of the region bounded by the two curves will be given by:
A = A₂ - A₁ = [tex]\int\limits^3_{-3} {x^2+2x+3 - (2x +12)} \, dx[/tex]
A = [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]
Refer to the image for the area so bounded by the curves.
Hence, The definite integral that represents the area of the region under the given curves is: [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex].
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Determine whether each sequence is geometric. If so, find the common ratio. 1,2,3,4, . . . . .
The given sequence is not geometric.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 1, 2, 3, 4, ....
Here, 2/1 ≠ 3/2 ≠ 4/3
Since, the none of the ratio of the consequent and the previous term is not equal, the sequence does not satisfy the required condition and hence, is not geometric.
Hence, The given sequence is not geometric.
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-9(-4)-6 find the value of expression
Answer:
30
Step-by-step explanation:
-9 × -4 = 36 (the two negatives cancel each other out)
36 - 6 = 30
List the domain and range of each relation. (0,4)_,(4,0),(-3,-4),(-4,-3)
Range - { 4 , 0 , -4 , -3 } is the domain and range of each relation.
What does the math term domain mean?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.What is domain and range mathematics?
A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
Domain - { 0, 4 , -3 , -4 }
Range - { 4 , 0 , -4 , -3 }
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17. The depth d of an aquarium tank for dolphins must be within a 5 feet margin of 50/feet deep. Write the absolute
value inequality to represent this situation.
The absolute value inequality to represent this situation is |d - 50| <= 5
How to write the absolute value inequality to represent this situation?The given parameters are
Margin = 5 feet
Depth = 50 feet
The absolute value inequality to represent this situation is
|d - Depth| <= Margin
So, we have:
|d - 50| <= 5
Hence, the absolute value inequality to represent this situation is |d - 50| <= 5
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Greg bought a blanket for $36.62, a flag for $11.25, and a glove for $17.75. He paid $60 and the rest he borrowed from his friend. If Greg got $4.38 in change from the cashier, how much did he borrow from his friend to pay for all the items?
Answer:
$10
Step-by-step explanation:
Let's begin with adding all of the items Greg bought.
36.62 + 11.25 + 17.75 = 65.62
Let the money paid to the cashier be x.
Now, it's stated he paid 60 dollars to the cashier and that he also got $4.38 back from the cashier.
Then, it must be that x=65.62+4.38
x=70
The money he borrowed from friend = 70-60=10
Therefore, the money Greg borrowed from his friend to pay for all the items is $10.
Greg borrowed $1.24 from his friend.
What is Unitary Method?A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilise this technique for math computations.
This approach allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.
Given:
Greg bought a blanket for $36.62,
a flag for $11.25,
and a glove for $17.75.
Total expense of the objects he brought
= 36.62+ 11.25 + 17.75
= $65.62
He paid $60 then
=65.62 - 60 = $5.62 remaining
Also, he got $4.38 in change from the cashier
= 5.62 - 4.38
= $1.24.
Hence, Greg borrowed $1.24 from his friend.
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Write each equation in slope-intercept form. Then find the slope and y -intercept of each line. 5 x+y=4
The slope for equation y = -5x + 4 in slope - intercept form is -5 and y - intercept is (x, 4 ).
What is slope - intercept form of equation?The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is.
The slope - intercept form is y = mx + c
5x + y = 4
Now, Rearrange the equation -
y = -5x + 4
m = -5 and y intercept = (x , 4)
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Read the problem. Identify what you need to know. Then organize the data to solve the problem.
There are 10 sophomore, 8 junior, and 9 senior members in student council. Each member is assigned to help plan one school activity during the year. There are 4 sophomores working on the field day and 6 working on the pep rally. Of the juniors, 2 are working on the field day and 5 are working on the school dance. There are 2 seniors working on the pep rally. If each activity has a total of 9 students helping to plan it, what is the probability that a randomly selected student council member is a junior or is working on the field day?
F. 1/5
G. 4/18
H. 5/9
J. 2/3
Using the combination formula, the committee can be selected in 1,211,760 ways.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Combination formula is the number of different combinations of x objects from a set of n elements.
In this problem:
There are 10 sophomore, 8 junior, and 9 senior members in student council.
They are independent, so we can just multiply them, thus;
T = 18!/ 2! 16! x 12!/ 2! 10! x 10!/ 3! 7!
T = 1,211,760
Hence, The committee can be selected in 1,211,760 ways.
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-4(m+3)=24
SHOW YOUR WORK
Answer:
Answer: M=-9
Step-by-step explanation:
[tex]\frac{-4(m+3)}{-4} =\frac{24}{-4} M + 3 = -6 (Subtract -3 from 3 and -6) M = -9[/tex]
x2+6x−16 vertex form
Answer:
Hello,
Step-by-step explanation:
[tex]x^2+6x-16\\\\=x^2+2*3x+3^2-9-16\\\\=(x+3)^2-25\\[/tex]
#1: Jane has 6 feet of ribbon. If one
meter is about 3 feet, how many
meters of ribbon does Jane have?
O 12
02
O
O 1
Answer: jane has 1.5 meters of ribbon
Step-by-step explanation:
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
If p || q , then ∠2 and ∠8 are supplementary .
The statement "If p || q , then ∠2 and ∠8 are supplementary" is false because " If p || q , then ∠2 and ∠8 are congruent"
Given,
The statement "If p || q , then ∠2 and ∠8 are supplementary"
In the figure
p is parallel to q.
∠2 and ∠8 are lie on the opposite sides of the transversal and both are nonadjacent exterior angle
So, ∠2 and ∠8 are alternate exterior angles
If p || q , then ∠2 and ∠8 are congruent.
Hence, The statement "If p || q , then ∠2 and ∠8 are supplementary" is false because " If p || q , then ∠2 and ∠8 are congruent"
The complete question is :
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
If p || q , then ∠2 and ∠8 are supplementary .
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what's the pattern? 7,11,19,35
The pattern of each number changes.. they are all factors of 4, the 4 turns into 8, than the 4 or 8 turns into 16.
7+4=11
11+8=19
19+16=35
[4×2=8, 8×2=16]
a. Use your calculator to generate an arithmetic sequence with a common difference of -7 . How could you use a calculator to find the 6th term? The 8th term? The 20th term?
The 20th term of the arithmetic sequence is 122.
What is arithmetic sequence?nth term = a1 + d(n - 1) so here:
20th term = -30 + 8(20 - 1)
- 30 + 152
[tex]a_{20}[/tex] = 122.
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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Which is the equation of a line perpendicular to line AB?
Answer:
Step-by-step explanation:
y = -3x + 7
since the slope of the line AB = (4 - 2) /( 3 - (-3)) = 1/3
slope of line perpendicular to AB will be -3
Need da answer pls and thank u point will be 100
The lessons from Clare B. Dunkie's The Hollow Kingdom, and the quote it matches are:
"If you love her enough to give up your world for her, don't you think she would want to do the same for you?" - People are willing to make sacrifices for the people they care about.She looked around at the stars, the moon, the trees. These were things she could count on. - Nature can be a source of courage and comfort.What are some lessons from Clare B. Dunkie's The Hollow Kingdom?One lesson that we see is that people who care about someone, are able to make sacrifices to ensure the wellbeing of that person. We see it with the narrator saying that the person loved another so much that they sacrificed their world for that person.
Another less is that nature can often help us gain the courage we need to do something. This is shown with the subject looking to the moon and stars to back her up.
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The box-and-whisker plot below represents some data set. What is the value of the second quartile?
The median is at 55. Therefore, the second quartile of the data set is: 55.
What is the Second Quartile of a Data?50% of any given data set lies below the second quartile. Thus, the second quartile can be described as the median of a data set.
In a box-and-whisker plot, the median is the mark at where the vertical line divides the box of the box-and-whisker plot.
In the box-and-whisker plot given, the median is at 55. Therefore, the second quartile of the data set is: 55.
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Bo the baker makes the best cookies! His recipe for triple-chip cookies uses 1/2 cups of chocolate chips, 3/4 cup of butterscotch chips, and 5/8 cup of peanut butter chips. Yum! How many cups of chips does Bo use to make one batch of triple-chip cookies?
Answer:
1/2 + 3/4 + 5/8
4/8 + 6/8 + 5/8 = 15/8 or 1 7/8 cups
Step-by-step explanation:
probably right dunno
This is one batch right? if so shud be right
12x + 8x + 3 + x
Is it
3x+12
-9x+6 2/3
21x+3
24x
-15x+8.3
Answer:
see explanation
Step-by-step explanation:
a bit more info is needed so this may be wrong.
so first you add up the x values which is 12x+8x+x=21x
then you can see we have a problem, we dont know the x value so the answer would be 21x +3
but we can go a bit further to get an answer as 3(7x+1)
this is also known as factorisation.
so ans: 3(7x+1)
List the outliers. if there is more than one outlier, separate them by a comma. use "none", if applicable. for the data set 3 6 4 13 3 7 5 13 3 7 5 15 3 8 5 27 4 8 6 6 4 11
For the data set 3, 6, 4, 13, 3, 7, 5, 13, 3, 7, 5, 15, 3, 8, 5, 27, 4, 8, 6, 6, 4, 11, the outliers are 3, 3, 3, 3, 15, and 27.
In statistics, outlier refers to the data point from a given data set that differs significantly from the other data points.
One way to determine the outlier in a given data set is to calculate the interquartile range.
1. Arrange the data set in ascending or descending order.
3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27
2. Divide the data set into two sets and find the median.
{3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6} , {6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27}
Q1 median = 4
Q3 median = 8
3. Solve for the IQR.
IQR = Q3 - Q1
IQR = 8 - 4
IQR = 4
4. Determine the outlier if
high outlier ≥ Q3 + (1.5 x IQR) = 8 + (1.5 x 4) = 14
high outlier ≥ 14
low outlier ≤ Q1 − (1.5 x IQR) = 4 - (1.5 x 4) = 3
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Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. -5,10,-20,40, . . . . . . .
It is a geometric sequence since it has a common ratio. The next two terms are -80, 160
Let a sequence be:
a(1), a(2), a(3), a(4), a(5), ...
To determine whether the sequence is an arithmetic sequence, or a geometric sequence, or neither, we need to check how its consecutive terms relate to each other.
They have a common difference.The given sequence is:
-5,10,-20,40, . . .
Let us check whether they have a common difference:a(2) - a(1) = 10 - (-5) = 15
a(4) - a(3) = 40 - (-20) = 60
So they don't have a common difference.
Let us check whether they have a common ratioa(4)/a(3) = 40/(-20) = -2
a(3)/a(2) = -20/(10) = -2
a(2)/a(1) = 10/(-5) = -2
So they have a common ratio, i.e. r = -2.
Therefore, we can conclude that -5,10,-20,40, . . is a geometric sequence.
In a geometric sequence, the next term is equal to the previous term times the ratio.
We already have: -5,10,-20,40, ...
Hence:
Next term after 40 = 40 . (-2) = -80
Next term after -80 = -80 . (-2) = 160
Thus, the next two terms are -80, 160
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