The value of n in the sequence is ≅ 15
How to solve an Arithmetic Progression?We should know that Arithmetic progression is a type of sequence in which the consecutive terms are gotten by the addition or subtraction of a constant term known as the common difference.
The given parameters are>
a+6d--13 ........................................ (1)
a+8d=47............................................ (2)
Subtracting equation 1 from [a+8d=47]-[a+8d=-13
⇒ 2d=60
d=30
Put d=30 in equation 1
a+6(30)=-13
a+180=-13
Collecting like terms
a=-13-180
a=-193
The nth term of an AP is given by
nth term = a+(n-1)d
where nth = 217
⇒ 217=-193+(n-1)30
Simplifying the expressing
217+223=30n
440/3=30n/30
n=14.7
Therefore n≅15
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find the number of solutions to the equation 3x-1=1/3(9x-5)
Answer:
No Solution
Step-by-step explanation:
-1 is not equal to -5/3
prove: if the bisector of an exterior angle of a triangle is parallel to a side of the triangle, the triangle is isosceles
The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .
In the question ,
it is given that ,
the angle bisector of the exterior angle of a triangle is parallel to a side .
we have to prove that the triangle will be an isosceles triangle .
In the triangle ABC given below , AB is extended to AD ,
SO , the exterior angle will be angle DAC ,
let AE be the bisector of the the angle .
So , the equal angles are angle DAC and angle EAC .
it is given that AE is parallel to BC , where BC is base .
we know that ,
if any line intersects two parallel lines then every pairs of alternative Interior angles are same and also their corresponding angles are equal .
Here AE is parallel to BC and line BD intersects them ,
So , angle ABC = angle DAE ( corresponding angles )
angle ACB = angle EAC ( alternate angles )
Now , as AE is the bisector of angle DAC ,
we have , angle DAC = angle EAC
So , we get , angle ABC = angle ACB .
In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal
that means , AB=AC
Hence , the given Triangle is an isosceles triangle .
Therefore , it is proved that the triangle ABC is an isosceles triangle .
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f(x) =
2/9x2+18x-216
Answer:
Domain: all real numbers
Step-by-step explanation:
The function is:
[tex] f(x) = \dfrac{2}{9}x^2 + 18x - 216 [/tex]
The domain of a function is the set of values of the x-coordinates of the points of the function.
In this function, there is no restriction on x, so the domain is all real numbers.
solve for x: x/7 < or equal to -6
Step-by-step explanation:
x
— - 6 = 0
7
Subtracting a whole from a fraction
Rewrite the whole as a fraction using 7 as the denominator :
6 6 • 7
6 = — = —————
1 7
x - (6 • 7) x - 42
——————————— = ——————
7 7
x - 42
—————— = 0
7
x-42
———— • 7 = 0 • 7
7
x-42 = 0
x = 42 Answer
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help for 50 points!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The slope of the line given the information in the table is 1.
What is the slope?The slope is found in linear functions. The slope measures the rate of change of the dependent variable with respect to the independent variable. In this question, the independent variable is x and the dependent variable is y.
Slope = change in the value of y / change in the value of x
Slope = (0 - - 1) / (1 - 0) = 1
Slope = (1 - 0) / (2 - 1) = 1
Slope = (2 -1 ) / (3 - 2) = 1
Based on the value of the slope, it means that for every one percent change in the value of x, the value of y changes by 1%.
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Answer:
Step-by-step explanation:
look at the x and axis and the irrational fractions and you should find your slope
This graph shows the revenue, cost, and profit functions of a company. How can this company become profitable?
A graph shows the Price per Unit on the x-axis and dollars on the y-axis. A downward parabola revenue vertex at (25, 12,000) intercepts the origin and x-axis at (30, 0) linear function costs intercept the y axis at (0, 13,000).
A.
by increasing its production
B.
by increasing its prices
C.
by reducing its costs
D.
by reducing its prices
Based on this graph which shows the revenue, cost, and profit functions of a company, the way in which this company can become profitable is: C. by reducing its costs.
What is a profit?In Mathematics, a profit can be defined as a measure of the amount of money that is generated when the cost price is deducted from the selling price (revenue) of a good or service, which is usually provided by producers.
Mathematically, the profit made by an entrepreneur or business organization can be calculated by using this mathematical expression:
Profit = Revenue - Cost
In this scenario, the most effective and efficient way in which this company can become profitable is simply by reducing (lowering) its costs because it is incurring more cost than the amount of revenue it generates.
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the cargo plane delivering the relief supplies must be at another location after dropping off the supplies at your site. this requires the unloading tasks to be completed in 70 minutes. the current process is taking 2 people to complete all tasks in 86 minutes
Total number of people required is 3 to complete it in 57.33 days.
What is indirect proportion ?Basically in this proportion, two quantities generally follow the opposite trend of each other like if one is increasing other one is decreasing.
As an example, if the time takes to run 10 m is inversely proportional to the speed you can run at - if you double your given speed, it takes you half as much long.
Initially,
Total People = 2
Total time taken = 86 minutes
Total time we have= 70 minutes
As people and time are inversely proportional to each other.
[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{86}[/tex]
x = (86 × 2) / 3
x= 57.33
Hence, total number of people required is 3 to complete it in 57.33 days.
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if the points below represent a direct variatin find the missing value (2, -6) and (5, y)
The missing value if the point is a direct variation is -15
How to determine the missing value?From the question, we have the following ordered pairs
(2, -6) and (5, y)
These ordered pairs are direct variation
A direct variation is represented as
k = y/x
This means that
y/5 = -6/2
Evaluate the quotient
y/5 = -3
Multiply both sides by 5
y = -15
Hence, the value of y is -15
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Which polygon appears to be regular?
Answer:
Figure b
Step-by-step explanation:
the sides are equal
The monthly rents (in dollars) paid by 9 people are given below. (Note that these are already ordered from least to greatest.)
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210
Suppose that one of the people moves. Her rent changes from $1210 to $1480.
Answer the following.
What happens to the mean=____ it decreases by __$
____ it increases by __$
____ it stays the same
What happens to the median=____ it decreases by __$
____ it increases by __$
____ it stays the same
The mean of a data-set is given by the sum of the values of all observations in the data-set divided by the number of elements in the data-set.
In this problem, the data-set is given as follows:
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210.
Hence the mean is of:
M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1210)/9 = 1035.
After the change, the data-set is of:
910, 930, 965, 980, 1000, 1040, 1115, 1165, 1480.
Hence the mean will be of:
M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1480)/9 = 1065.
Then the increase will be of:
1065 - 1035 = 30.
What is the median of a data-set?The median of a data-set is the middle element of the data-set, the value which:
50% of the data-set is lesser than.50% of the data-set is greater than.The median is not affected by the values at the bounds of the distribution, such as 1210 and 1480 are in this distribution, hence it remains constant.
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Why are factorial designs useful in testing theories?
a. They allow researchers to explore the construct validity of a theory.
b. Results from factorial designs are typically straightforward and easy to interpret.
c. They allow researchers to understand the nuances of how variables interact.
d. Results from factorial designs are always intuitive.
Factorial design are useful in testing theories because they enable researchers to investigate a theory's construct validity. so the correct answer is option (a).
What is factorial designs?A key technique for identifying the impact of numerous variables on a response is the factorial design. Traditionally, experiments are planned to ascertain how one variable affects just one response.
What is testing theories?The corpus of knowledge supporting the analysis and application of test results. The definition and measurement of reliability are of primary relevance. Classical test theory, generalizability theory, and item response theory are examples of theoretical frameworks.
a) They enable academics to investigate a theory's construct validity.
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H(d) models the basketball's height (in meters) at a horizontal distance of dd meters from Kaori. What does the statement H(R)=4H(R)=4 mean
The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.
It is given that Kaori is taking a free-throw. H(d) models the basketball's height (in meters) at a horizontal distance of d meters from Kaori.
The given statement is H(R) = 4H.
Here we have H(R) instead of H(d) and it shows the height of basketball. So it clear that the height of basketball's is 4H because H(R)=4H at d = R
Since d represents the horizontal distance from Kaori, therefore the horizontal distance from Kaori is R.
Thus, Answer: The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.
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a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 402402 gram setting. is there sufficient evidence at the 0.020.02 level that the bags are overfilled? assume the population is normally distributed. state the null and alternative hypotheses for the above scenario.
Yes there is sufficient evidence that the alternative hypothesis is;
bag filling machine works incorrectly at the 402 gram setting which is;
H_o ; μ ≠ 402
Null hypothesis; H_o ; μ = 402
Alternative hypothesis; H_o ; μ ≠ 402
The null hypothesis states that there is no difference in the test which is denoted by H_o. However, the sign of null hypothesis is denoted by the signs of = or ≥ or ≤.
Meanwhile, the alternative hypothesis is one that defers from the null hypothesis. This therefore implies a significant difference in the test. Thus, the signs of alternative hypothesis is denoted by; < or > or ≠.
Now, the question we have is a two tailed test. Thus;
The null hypothesis is;
bag filling machine works correctly at the 402 gram setting which is;
H_o ; μ = 402
The alternative hypothesis is;
bag filling machine works incorrectly at the 402 gram setting which is;
H_o ; μ ≠ 402
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What error did the student make? in line 2, the student forgot to multiply the right side of the equation by 2. in line 3, the student should have subtracted the equations instead of adding them. in line 3, the student added the two equations incorrectly. in line 5, the student used an incorrect equation when solving for x.
Answer: the student forgot to multiple by right side of equation 2 in line 2
Step-by-step explanation: your welcome :)
Given n sets a₁, a₂. Aₙ. The inclusion-exclusion principle states that the cardinatlity of a₁∪ a₂∪. ∪aₙ is the sum of the individual cardinalities minus the sum of the cardinalities of intersections of any two sets plus the sum of the cardinalities of intersections of any three sets minus the sum of the cardinalities of intersections of any four sets and so on. This alternating sum ends with the cardinality of the intersection of all n sets. How many terms are there in this formula that are intersections of 3 sets?.
There are total of 7 terms in the formula of intersection of 3 sets.
What is intersection?In set theory, the intersection of two sets A and B, denoted {A,B}, is the set containing all the elements of A that also belong to B, or all the elements that also belong to B.A cut operation is represented by the symbol ∩.The set A ∩ B - pronounced "intersection B" or "intersection of A and B" - is defined as the set consisting of all elements that belong to both A and B.A controlled intersection has signs, signals, and lane markings that tell drivers and others what to do.The most common controlled intersections are stop sign controlled intersections.Stop signs and traffic lights are also used depending on the flow of traffic passing through that particular intersection.The formula of the given sets is,
n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C).
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Determine if the table how a proportional relationhip. X 25. 6 72. 8 77. 2 y 6. 4 18. 2 19. 3 Ye, it i proportional becaue all y over x ratio are equivalent to one fourth. Ye, it i proportional becaue all y over x ratio are equivalent to one third. No, it i not proportional becaue 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8. No, it i not proportional becaue 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
Proportional relationship for the given table is true and is define as
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
As given in the question,
Value of x and y in the given table are :
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
To check the proportional relationship there should exist constant of proportionality that ratio of corresponding y/x should be constant.
y / x for all the values of x and y:
First values:
y /x = 6.4 / 25.6
= 0.25
Second values:
y/x = 18.2/ 72.8
= 0.25
Third values :
y /x = 19.3/ 77.2
= 0.25
0.25 is equivalent to One fourth ( 1/4).
Constant of proportionality exist = 0.25 or One fourth.
Therefore, in the table first option: yes, it is proportional because all y over x ratio are equivalent to one fourth is correct.
The complete question is:
Determine if the table how a proportional relationship.
x : 25. 6, 72. 8, 77. 2
y : 6. 4, 18. 2, 19. 3
Yes, it is proportional because all y over x ratio are equivalent to one fourth.
Yes, it is proportional because all y over x ratio are equivalent to one third.
No, it is not proportional because 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8.
No, it is not proportional because 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3
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What is the solution to the system of equations?
1/3x-5=y
1/6x+y=4
Answers:
(18, 1)
(9/2, -7/2)
(-2, 17/3)
Answer:
A. (18, 1)
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
The King family went out to eat. They ordered three combo meals, two sodas, and one iced tea. Write an expression representing their bill. Then, determine the cost of the dinner for the entire family.
½ Pound Cheeseburger - $3.50
Grilled Chicken Sandwich - $4.00 Combo Meal (with fries) - $5.25
Soda - $2.00
Iced Tea - $2.25
Milkshake - $3.75
Brownie a La Mode $4.00
The expression for their bill will be;
B = 3c + 2s + i
While the cost for the entire family for dinner will be $22.
What is a mathematical expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
The structure of an expression is:
Expression is (Number/variable, Math Operator, Number/variable)
Types of Algebraic ExpressionsAlgebraic expressions are classified on the basis of the number of terms in the expression.
The various types of algebraic expressions are:
Monomial expressions contain only one term.Binomial expressions contain two unlike terms. Trinomial expressions contain only three unlike terms.Polynomial expressions have two or more terms. This includes binomials and trinomials too and all other expressions with four or more terms.Solution:
From the question;
Let c = Combo Meal (with fries) - $5.25
s = Soda - $2.00
i = Iced Tea - $2.25
The family ordered 3 combo meals, 2 sodas and 1 iced tea
So, expressing it;
Bill = 3c + 2s + i
Substituting the prices for the meals
Bill = 3(5.25) + 2(2) + 2.25
Bill = 15.75 + 4 + 2.25
Bill = $22
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alexis likes to go for boat rides along a river with her family. in still water, the boat travels about 7 kilometers per hour. in the river, it takes them the same amount of time t to go upstream 4 kilometers as it does to travel downstream 8 kilometers. if the speed of the river is r, which of the following expressions represents the time it takes to travel 4 kilometers upstream?
It takes 51.33 min or 6/7 hrs to travel upstream 4 km.
What is relative velocity?
it is the speed measured with respect to an observer whether he is moving or stationary and it might differ for different observers.
speed of boat = 7 km/hr
speed of river = r km/hr
speed upstream = 7-r km/hr
speed downstream = 7+r km/hr
time taken to go upstream 4 km = 4/(7-r)
time taken to go downstream 8 km = 8/(7+r)
as time taken is equal in both scenario:
4/(7-r) = 8/(7+r)
on solving we get:
r = 7/3 km/hr
put this value in time taken for upstream
4/(7-(7/3)) = 6/7 km/hr or 51.33 min
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Using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.
What is relative velocity?Think about two trains that are traveling in the same direction and at the same pace.
Even though the tracks, buildings, and trees on either side of the track indicate that both trains are moving, to the observer of one train, the other train appears to be stationary.
The other train seems to be moving at a constant speed.
So, we know that:
Speed of boat = 7 km/hr
Speed of river = r km/hr
Now,
Speed upstream = 7-r km/hr
Speed downstream = 7+r km/hr
Time taken to go upstream 4 km = 4/(7-r)
Time taken to go downstream 8 km = 8/(7+r)
As the time taken is equal in both scenarios:
4/(7-r) = 8/(7+r)
On solving we get:
r = 7/3 km/hr
Put this value in time taken for upstream as follows:
4/(7-(7/3)) = 6/7 km/hr or 51.33 min
Therefore, using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.
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The diameter of a dime is 17.91 mm. The diameter of a strand of human hair is
6.0 x 10-2 mm. How many times greater is the diameter of a dime than the diameter of
the strand of human hair?
The diameter of a dime tells us the circumference of a dime is approximately 299 times larger than human hair.
What is DiameterThe diameter of an object is used to calculated the circumference or area of the object. This also helps us to know the width of a circular object.
In this problem, the diameter tells us about the length of the each quantity.
The diameter of a dime tells us how wide the coin is and the diameter if a hair tells us the width of the hair.
Comparing both values
Dime = 17.91mm
Hair = 6.0*10^-2
Divide both quantity together.
17.91 / 6.0*10^-2 = 298.5≅299
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Elephants sometimes damage trees in Africa. It turns out that elephants dislike bees. They recognize beehives and avoid them. Can this information be used to keep elephants away from trees? Will elephant damage be less in trees with hives? Will empty hives even keep elephants away? Researchers want to design an experiment to answer these questions using 72 acacia trees. Identify the experimental units, treatments, and the response variable.
a) The experimental units are the Acacia Trees.
b) The treatments carried used are; active beehives, empty beehives and no single beehive.
c) The response variable is the damage that the elephants caused to the trees.
How to interpret experimental research design?Experimental design is defined as the process of carrying out research in a manner that is objective and controlled such that precision is maximized and then specific conclusions can possibly be drawn regarding a hypothesis statement. Generally, the purpose of this is to establish the effect that a factor or independent variable has on a dependent variable.
From this question, it is very clear that the experimental units are the Acacia Trees. This is because they are the primary interest or objective of the research.
The treatments carried out here are the active beehives, empty beehives and no single beehive.
The response variable is defined as the result of the experiment where the explanatory variable is manipulated. In this case, the response variable is the damage that the elephants caused to the trees.
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The length of a rectangle i 4 inche more than it width. The area of the rectangle i equal to 4 inche le than 2 time the perimeter. Find l and w
12 inches in length and 3 inches in width when a rectangle's length is 4 inches longer than its width.
Given that,
A rectangle's length is 4 inches longer than its width. The area of rectangle is equal to 4 inches less than 2 times the perimeter of rectangle.
We have to find what is the length and width of rectangle.
We know that,
Let take length as l and width as w.
l=4w
Area of rectangle is l×w
Perimeter of rectangle is 2(l+w)
So,
l×w=2(2(l+w))-4
l×w=4(l+w)-4
Take l as 4w
4w×w=4(4w+w)-4
4w²=4(5w)-4
4w²=20w-4
4w²-20w+4=0
w²-5w+1=0
w=3
So,
l=4w
l=12
Therefore, 12 inches in length and 3 inches in width when a rectangle's length is 4 inches longer than its width.
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Multiple (3x+y) by (4x+2y)
Answer:
12x² + 10xy + 2y²
Step-by-step explanation:
(3x + y)(4x + 2y) =
= 12x² + 6xy + 4xy + 2y²
= 12x² + 10xy + 2y²
Find the olution to the following lhcc recurrence:
an=−6aₙ₋₁−5aₙ₋₂ for n≥3 with initial condition a0=28,a1=−76
aₙ = 6aₙ₋₁ - 5aₙ₋₂ then the values for n≤3, then a₀ = 28; a₁ = -76 ; a₂ = -596 ; a₃ = -3196. The Sequence is 28, -76, -596, -3196.
How can the sequence's solution be found?
a = 2 and d = 3 decide the order. Using the method for locating the nth term, we can locate a particular term in an arithmetic series. Step 1: An arithmetic sequence's nth term is determined by the formula an = a + (n - 1)d. Therefore, enter the values a = 2 and d = 3 into the formula to find the nth term.Given:
a₁ = -76 ; a₀ = 28
aₙ = 6aₙ₋₁ - 5aₙ₋₂
Then the arithmetic sequence is followed by:
a₂= 6a₂₋₁ - 5a₂₋₂
= 6a₁ - 5a₀
= 6(-76) - 5 (28)
= -456 - 140
a₂ = -596
a₃ = 6a₃₋₁ - 5a₃₋₂
= 6a₂ - 5a₁
= 6(-596) - 5(-76)
= - 3576 + 380
a₃ = -3196
The values for n≤3, then a₀ = 28; a₁ = -76 ; a₂ = -596 ; a₃ = -3196. The Sequence is 28, -76, -596, -3196.
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Let the random variable b represent the number of books a student buys at the next book fair. What is the expected value of b ?.
The expected value of the random variable b is given as follows:
2.404 books.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.
From the histogram given by the image at the end of the answer, the distribution is given as follows:
P(X = 1) = 0.285.P(X = 2) = 0.333.P(X = 3) = 0.168.P(X = 4) = 0.136.P(X = 5) = 0.063.P(X = 6) = 0.015.Then the expected value of the random variable b is obtained as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.
Missing InformationThe histogram is given by the image at the end of the answer.
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In an AOL survey of Internet users, this question was posted online: "Have you ever been hit by a computer virus?" Among the 170,063 responses, 63% answered "yes."
The population will be _______.
Question 11 options:
170,063 responses.
all internet users.
63% answered "yes."
an AOL survey.
The population based on the information will be B. all internet users.
What is a population?In statistics, a population is a group of similar items or events that are relevant to a particular question or experiment. A statistical population can be a group of existing objects or a hypothetical and potentially infinite group of objects conceived as an experience-based generalization.
A population is any complete group that shares at least one characteristic. Populations are more than just individuals. People, animals, businesses, buildings, motor vehicles, farms, objects, or events are examples of populations.
In this case, In an AOL survey of Internet there wwe'r 170,063 responses, and 63% answered "yes. The population is the internet users.
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if i have a b and then i get a 72% on a test that is 30% of my grade, what will my grade be?
Answer:
if you have about an 85 now than you shouldn’t go below a b
Step-by-step explanation:
estimate using compatibl numbers.
241 divided by 34
If 50% of a number is 120 and 80% of the same number is 192, find 30% of that
number.
Answer: the answer is 72
Step-by-step explanation:
if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240
Now we need to determine 30% of 240 and the procedure explaining it as such
Step 1: In the given case Output Value is 240.
Step 2: Let us consider the unknown value as x.
Step 3: Consider the output value of 240 = 100%.
Step 4: In the Same way, x = 30%.
Step 5: On dividing the pair of simple equations we got the equation as under
240 = 100% (1).
x = 30% (2).
(240%)/(x%) = 100/30
Step 6: Reciprocal of both the sides results in the following equation
x%/240% = 30/100
Step 7: Simplifying the above obtained equation further will tell what is 30% of 240
x = 72%
Therefore, 30% of 240 is 72
I hope this helps
Answer:
72
Step-by-step explanation:
You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.
SolutionThe 30% you want will be the difference between 80% and 50%:
80% -50% = 30%
192 -120 = 72
30% of the same number is 72.
