Answers
Considering an arithmetic sequence, it is found that:
8. Two consecutive terms in the sequence of eruption times are: 94, 106.
9. The common difference of the sequence of eruption times is of 12.
10. The general rule of the sequence of eruption times is: [tex]a_n = 46 + 12(n - 1)[/tex]
What is an arithmetic sequence?An arithmetic sequence has the difference between consecutive terms assuming always the same value, being called common difference d.
The nth term of an arithmetic sequence is given by the following general rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
In the context of this problem, the sequence is given as follows:
46, 58, 70, 82, ...
Hence the common difference is given by:
d = 82 - 70 = 70 - 58 = 58 - 46 = 12.
The next two terms of the sequence are:
82 + 12 = 94.94 + 12 = 106.Considering that the first term is of 46, the general rule for the sequence is given by:
[tex]a_n = 46 + 12(n - 1)[/tex]
What is the missing information?The sequence of eruption times is given by:
46, 58, 70, 82, ...
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Related Questions
A cone and a cylinder both have a radius of 3 inches and a height of 7 inches. If you wanted to adjust the cone's radius so that both solids have the same volume, what should the cone's radius be?
Answers
Answer:
radius = 5.196 ins. to nearest thousandth.
Step-by-step explanation:
Volume of the cylinder = π (3)^2 7
= 63π in^3.
Volume of the cone = 1/3 π r^2 7 where r is the new radius of the cone
So, 63π = 7/3 π r^2
r^2 = 63 / 7/3
= (63*3)/7
= 27
r = 5.196 in.
put these numbers in order, smallest ton largest
3.7 3.77 7.3 3.07 7.33
Answers
Answer:
3.07 - 3.7 - 3.77 - 7.3 - 7.33
Step-by-step explanation:
The numbers from smallest to largest^
Solving Inequalities with One Variable
Show work
2(7 − 2) > 9 + 6
Answers
Answer: no solution
Step-by-step explanation:
2× (7-2)>9+6
Calculate the sum or difference
2×5>9+6
Calculate the sum or difference
2 × 5 > 15
2×5>15
Calculate the product or quotient
10 > 15
10 > 15
The solution of the inequality
no solution
What is the area of this trapezoid 13 cm 15cm 29cm
Answers
Answer:315
Step-by-step explanation:
if an angle and its half form a pair of supplementary angles , what are the measures of the angles
Answers
Answer:
100 degrees
Explanation:
2x + x + 30 = 180
3x + 30 = 180
3x = 180 - 30
3x = 150
x =
150
3
x = 50
both angles
2x = 2
×
50 = 100
x + 30 = 50 +30 = 80
larger angle is of 100 degrees
Answer the questions below to find the total surface area of the can.
Answers
The total surface area of the can is 61.23 square inches
The total surface area of can S = 2πr(r+h)
where:
h is the height
r is the radius
A cylinder's surface area is the area that its surface takes up in three dimensions. A three-dimensional structure known as a cylinder has circular bases that are parallel to one another. There are no vertices on it. Area of three-dimensional shapes often refers to surface area. Square units are used to denote the surface area. Examples include cm2, m2, and so forth.
Given
h = 5in
r = 1.5in
S = 2(3.14)(1.5)(1.5 + 5)
S = 6.28(1.5)(6.5)
S = 61.23 square inches
Hence the total surface area of the can is 61.23 square inches
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I need Algebra II help. Solve for x. 6x-10≤8 or 1/3x+6>12
If you can, please add an explanation. Thank you sm!
Answers
The solution of the inequality is x ≤ 3 or x > 18.
An inequality in mathematics is a relation that compares binary number or other mathematical in an unequal way.
The majority of the time, size comparisons between two figures on the number line are made. Different types of inequalities are represented by a variety of notations . The symbol for "larger than" that is divided in half by the word "not" can also be used to denote the relationship not greater than. For not fewer than and and a b, the same holds true.Now let us solve the inequality:
6x - 10 ≤ 8
adding 10 on both sides:
or, 6x -10+10 ≤ 8+10
or, 6x ≤ 18
dividing both sides by 6 we get :
or, 6x ÷ 6 ≤ 18 ÷ 6
or, x ≤ 3
For the second inequality:
1/3x+6>12
subtracting 6 from both sides :
or, 1/3x+6 - 6 > 12 - 6
or, 1/3 x > 6
Multiplying both sides by 3
or, x > 18
Therefore the complete solution is x ≤ 3 or x > 18 .
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Match each equation with the slope m and y-intercept of its graph.
A. m = -6, y-int = (0, 12)
1.5x-6y=30
B. m = -6, y-int = (0,5)
C. m = -, y-int = (0, 1)
D. m = 2, y-int = (0, 1)
E. m = 2, y-int = (0, -1)
F. m = , y-int = (0, -5)
2. y = 5-6x
3.y = x+1
4.5x-6y=6
5.5x+6y=6
6.6x + y = 12
Answers
For 5x-6y=30, slope = m = 5/6 and y-intercept = (0, -5)
For y = 5-6x, slope = m = -6 and y-intercept = (0, 5)
For y = x+1, slope = m = 1 and y-intercept = (0, 1)
For 5x-6y=6, slope = m = 5/6 and y-intercept = (0, -1)
For 5x+6y=6, slope = m = -5/6 and y-intercept = (0, 1)
For 6x + y = 12, slope = m = - and y-intercept = (0, 12)
What is the slope-intercept form of a line?
The line with m as the slope, 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. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
Given, the first equation is 5x - 6y = 30
Solving the equation for y, we get: y = (5/6)x + (-30/6) = (5/6)x + (-5)
Comparing this to the standard slope intercept form in literature, we have, slope = m = 5/6 and y-intercept = (0, -5)
The second equation is y = 5 - 6x
Solving the equation for y, we get: y = (-6)x + 5
Comparing this to the standard slope intercept form in literature, we have, slope = m = -6 and y-intercept = (0, 5)
The third equation is y = x + 1
Solving the equation for y, we get: y = x + 1
Comparing this to the standard slope intercept form in literature, we have, slope = m = 1 and y-intercept = (0, 1)
The fourth equation is 5x - 6y = 6
Solving the equation for y, we get: y = (5/6)x + (-6/6) = (5/6)x + (-1)
Comparing this to the standard slope intercept form in literature, we have, slope = m = 5/6 and y-intercept = (0, -1)
The fifth equation is 5x + 6y = 6
Solving the equation for y, we get: y = (-5/6) + (6/6) = (-5/6)x + (1)
Comparing this to the standard slope intercept form in literature, we have, slope = m = -5/6 and y-intercept = (0, 1)
The sixth equation is 6x + y = 12
Solving the equation for y, we get: y = (-6)x + 12 = (-6)x + 12
Comparing this to the standard slope intercept form in literature, we have, slope = m = - and y-intercept = (0, 12)
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How do you solve Mr.Fillbach drinks 1 cup of orange juice every morning He bought a 1 gallon jug of orange juice How many mornings will he be able to have orange juice before having to buy more juice
Answers
Mr. Fillbach will be able to have orange juice before having to buy more juice for 16 mornings.
The gallon is a unit of volume in imperial units and us a customary device. 3 one-of-a-kind variations are in modern use: the imperial gallon.
A clean manner to discern from liters to gallons, for an instance, is that a quart is a bit much less than a liter and 4 liters is a touch extra than 1 gallon. To be specific, 1 liter is 0.264 gallons (a bit greater than a quart), and four liters is 1.06 gallons. Q-I need to shop for a 35 mm. A gallon is equal to approximately 3.78541 liters. consequently, a gallon is larger than 3 liters.
Cups and liters each measure the extent of beverages, so whether or not you need to know how many cups are in a liter or water, oil or a bottle of soda, there will constantly be approximately four.3 cups in a liter! The liter is a metric measurement closest to the quart in imperial measurements.
Given,
Mr.Fillbach drinks 1 cup of orange juice every morning.
He bought a 1-gallon jug of orange juice.
Since there are 16 cups in 1 gallon.
Therefore, he is able to have orange juice before having to buy more juice = for 16 days
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pls help it’s a math question will mark brainliest
Answers
Answer: B the lines are neither parallel nor perpendicular.
Step-by-step explanation:
To make this easier we can make both equations into y-intercept statements.
y = 5x - 7
-8y = -x - 6
y = 1/8x + 6/8
By looking at the slopes of both equations (5 and 1/8) we can see that they are neither the same nor opposite reciprocals.
2. Kelley makes her own potting soil mix for planting flowers. She uses 2 scoops of compost with 9 scoops of top soil. If she uses 18 scoops of compost, how many scoops of top soil will she use?
Answers
Answer: 81
Step-by-step explanation: If we divide the numbers given to use, (2 factors of compost), you get 9, (do 18 divided by 2). 9 times 9 is 81.
Stefan sells jin a bicycle for $113 and a helmet for $19. The total cost for jin is 110% of what stefan spent originally to buy the bike and helmet. How much did stefan spend originally? How much money did he make by selling the bicycle and helmet to jin?
Answers
Stefan spent originally to buy a bike $95 and $15 to buy a helmet and he made $17.27 by selling the bicycle and $1.73 by selling the helmet to Jin.
The selling cost for Stefan bicycle = $113 and
the selling cost of a helmet = $19.
The total cost for Jin is 110% of the money spent by Stefan
Let us assume purchasing cost of a bicycle = $x.
Purchasing cost of a helmet = $y.
For bicycle
110% of x is $113
=> 1.10 × x = 113
Dividing both sides by 1.10, we get
x=$102.72.
Stefan spent for his bicycle = 102.72
For helmet.
110% of y is $19.
=> 1.10 × y = 19.
Dividing both sides by 1.10, we get
y = $17.27
Stefan spent for his helmet = 17.27
money made by selling the bicycle is $113 - 102.72 = $10.72
money made by selling the helmet is $19 - 17.27 = $1.73.
Therefore, Stefan spent originally to buy a bike $95 and $15 to buy a helmet and he made $17.27 by selling the bicycle and $1.73 by selling the helmet to Jin.
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What number is 150 decreased by 15%?
Answers
Step by step
150 decreased (subtract) by 15% (.15) = x
150 - ( .15 * 150) = x
150 - 22.5 = x
127.5 = your number x
Answer:127.5
Step-by-step explanation:
A parasail is $\frac{3}{100}$
mile above the water. After 5 minutes, the parasail is $\frac{1}{50}$
mile above the water. Find the change in height of the parasail.
The change is height is
mile.
Answers
The change in height of the parasail = 1/100
What is height?Height of defined as the measurement that is taken for an object which starts from its base to the topmost point. This is usually measured in meters.
From the question,
The height of the parasail above the water level= 3/100
The height of the parasail above the water level after 5 minutes= 1/50
The change in height of the parasail is determined by finding the difference between the two heights.
That is, = 3/100 - 1/50
= 0.03- 0.02 = 0.01
When changed to fraction is = 1/100
Therefore, the change in height after 5 minutes is = 1/100
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|z-18|-15=-5 , what's the absolute value for Z?
Answers
Answer:
8
Step-by-step explanation:
absolute value of z-18 = z + 18
z + 18
-15
______
z + 3
z + 3 - 3 = -5 - 3
z = -8
|z| = |-8|
z = 8
hope this helped ^^
PLEASE HELP QUICK !!
Answers
Answer:
The second option: f(x) = -(200/x)
Step-by-step explanation:
We can see that the input of the function is 20 and the output is -10. For the inverse, these values will swap: -10 will be the input and 20 will be the output.
Given that, we can substitute -10 into each equation and use trial and error to find out which one gives 20 as the output.
The first one, f(x) = -(0.5/x) will give an output of -(0.5/-10) = 1/20, which is incorrect.
The second one, f(x) = -(200/x) will give an output of -(200/-10) = 20, which is correct. Therefore, this must be the inverse. There will only be one inverse, so we don't need to try the rest.
Please awnser fast due tommorow worth 40 pts(I need all of the answered)1 Which of the following could be the graph of the equation y =-2x + 5? How do you know?
Answers
Answer: Your image is too blurry to read, but the third graph from the left is correct for y=-2x+5
Step-by-step explanation: This equation is already in the slope-intercept form: y=mx+b. In the slope-intercept form, m=slope of the line and b=intercept. For your equation, the slope is -2 and the y-intercept is where y=5. To graph the line, the -2 slope is down 2 on the y-axis for every +1 on the x-axis. Please see my attached image for the graph.
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean = 90 and standard deviation = 20. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
(a) x is more than 60
(b) x is less than 110
(c) x is between 60 and 110
(d) x is greater than 125 (borderline diabetes starts at 125)
Answers
The probability that x is between 60 and 110.
P(60 < x<110) = 0.6436
Step( i ) :-
Given data the random variable 'X' will have a distribution that is approximately normal with mean μ = 83 and standard deviation σ = 27.
Mean of the Population 'μ' = 83
Standard deviation of the Population 'σ' = 27.
Step(ii):-
Given X =60
Step(iii):-
Given X = 110
The Probability that between 60 and 110
P(60 < x<110) = P( -0.851 < z< 1)
= P( Z≤1) - P(Z≤ -0.851)
= (0.5 + A(1)) - (0.5- A(-0.851))
= (0.5 +0.3413)- (0.5 - 0.3023) ( check normal table yellow mark)
= 0.8413 - 0.1977
P(60 < x<110) = 0.6436
The probability that x is between 60 and 110.
P(60 < x<110) = 0.6436
What happen in uniform probability distributions?In case of uniform probability distributions, the likelihood of each possible outcome happening or not is the same. This property means that, for any given trial, the probability that an event will be successful does not change. Take the probability of rolling a 5 on a die for instance, no matter how many trials are performed, there is always a 1 in 6 probability for each trial.
Therefore, The probability that x is between 60 and 110.
P(60 < x<110) = 0.6436
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4. An object will most effectively absorb the
sun's rays if it is
(A) polished, and dark in color.
(B) polished, and light in color.
(C) rough, and light in color.
(D) rough, and dark in color.
Answers
instructions! answer the question, add me as a friend, put funny explanation, and tell name:)
666666 X 4443332221119111
i will make brainliest to best one!
Answers
The numbers are 666666 X 4443332221119111. The number solved multiplication is [tex]2.962218518 \times10^{21}[/tex].
Given that,
The numbers are 666666 X 4443332221119111
We have to solve the number multiplication.
Multiplication means the fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.
666666 X 4443332221119111
[tex]2.962218518 \times10^{21}[/tex]
Therefore, the number solved multiplication is [tex]2.962218518 \times10^{21}[/tex].
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find the area of this circle
Answers
Answer:
Formula given : Area = πr²
where r is the radius
the given radius is 5 inches
and pi is 3.14
so 3.14x 5²
3.14 x 25
the area is 78.5 in²
hope it helps, mark as brainliest :D
Answer:
A = 78.54 in²
Step-by-step explanation:
A = πr²
A = π(5²)
A = 25π
A = 78.54 in²
Find
(3.2x10¹0) (3.75x10⁰)
(4x10°) (6x105)
expressed in scientific notation.
PLEASE HELP!!! I WILL GIVE BRAINLIEST
Answers
The scientific notation of the given numbers is 12 x [tex]10^{10}[/tex] and 24 x [tex]10^{5}[/tex].
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, the scientific notation for 650,000,000 is 6.5 x [tex]10^{8}[/tex]
The given numbers are
(3.2 x [tex]10^{10}[/tex] ) (3.75 x [tex]10^{0}[/tex])
and (4 x [tex]10^{0}[/tex]) (6 x [tex]10^{5}[/tex])
So, Considering these numbers one by one,
(3.2 x [tex]10^{10}[/tex] ) (3.75 x [tex]10^{0}[/tex])
We multiply 3.2 and 3.75 and add the exponents of 10.
(3.2 x [tex]10^{10}[/tex] ) (3.75 x [tex]10^{0}[/tex]) = 12 x [tex]10^{10}[/tex]
Now the second number that we have is (4 x [tex]10^{0}[/tex]) (6 x [tex]10^{5}[/tex])
We multiply 4 and 6, and we add the exponents of 10.
(4 x [tex]10^{0}[/tex]) (6 x [tex]10^{5}[/tex]) = 24 x [tex]10^{5}[/tex]
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At the mall, Timmy bought a T-shirt and a book for a total of $23. The book cost $12. How much did the T-shirt cost? Let x represent the unknown information. Write an addition equation that models the problem
Answers
The equation can be modelled by 23 = 12 + x
How to determine the addition equation?The given parameters are
Cost of book = $12
Total purchase = $23
The total purchase can be calculated by adding the cost of the book and the cost of the T-shirt
This is represented as
Total purchase = Cost of book + Cost of T-Shirt
So, we have
23 = 12 + x
Where x represent the unknown information.
Hence, the addition equation is 23 = 12 + x
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this is difficult please help I need to know the answer I give more point pls help.
Answers
Answer:
decagon
Step-by-step explanation:
all angles measure 360, divide by 10 sides, answer is 36. lmk if you need a more in depth explanation
Solve the following system of linear equations by graphing:-X+ y = -74x + 4y = 20
Answers
1) Let's solve this Linear System, using the method of Elimination/Addition
-x+y=-7 Multi
4x+4y = 20
2. Three families bought food at a basketball game. The Davis family spend $16.50 on 3 hotdogs, 2
drinks, and 1 pretzel. The Ruiz family spend $26 on 4 hotdogs, 4 drinks, and 2 pretzels. The Cho family
spend $13.75 on 2 hotdogs, 1 drink, and 3 pretzels. Write a system of equations and solve for the price of each item
Answers
Answer:
x = $3.5
y = $2.25
z = $1.5
Step-by-step explanation:
let x = price of a hotdog
y = price of a drink
z = price of a pretzel
according to the question:
Davis family spends: 3x+2y+z = $16.50 (equation 1)
Ruiz family spends: 4x+4y+2z = $26 (equation 2)
Cho family spends: 2x+y+3z = $13.75 (equation 3)
from eq. 1
z = 16.50-3x-2y
substituting in eq.2
4x+4y+2(16.50-3x-2y) = 26
4x+4y+33-6x-4y=26
-2x=26-33
thus x = $3.5
from eq. 3
y = 13.75-2x-3z
y = 13.75-2(3.5)-3z
y = 13.75-7-3z
y=6.75-3z
thus,
z = 16.50-3(3.5)-2(6.75-3z)
z = 16.50-10.5-13.5+6z
z-6z = -7.5
-5z = -7.5
thus z = $1.5
thus
y = 6.75-3(1.5)
y = $2.25
Ben has a side job where he stuffs envelopes for a business. If he can fill 36 envelopes in
30 minutes, how long will it take him to fill 48 envelopes?
Answers
After solving basic arithmetic, we have come find that it will take 40 mins for Ben to fill 48 envelopes.
What is arithmetic?The word "arithmetic," which comes from the Greek word "arithmos," which means "number," is one of the oldest and most basic branches of mathematics. The study of numbers, particularly the characteristics of conventional operations, including:
Addition
Subtraction
Multiplication
Division
These operations are the basis for the arithmetic operators ‘+’, ‘-’, ‘×’ and ‘÷’.
The foundational subject in mathematics, arithmetic covers operations with numbers. These include addition, subtraction, multiplication, and division. One of the vital branches of mathematics, arithmetic serves as the cornerstone for students studying the subject of mathematics.
Given that he can fill 36 envelopes in 30 minutes
So time he would take to fill 1 envelope = 30/36
Therefore, time he would take to fill 48 envelopes = (30/36) × 48
= 40 mins.
Thus, It will take 40 mins for Ben to fill 48 envelopes.
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4. Cindy has $2.50 to spend on milk and
candy. The milk costs $0.70. Her favourite
candies cost $0.12 each.
a) Write an equation that models the
number of candies that Cindy can afford.
b) Solve the equation.
Answers
x = 15
Hafsa has planted a total of 40 plants in her new garden. 22 of these are flowering cacti. What percentage of the plants are flowering cacti?
Answers
Answer:
55%
Step-by-step explanation:
22 ÷ 40 × 100 = 55
Hope this could help you
Copy and complete the prime factor trees
for 21 and 33.
What is the highest common factor (HCF)
of 21 and 33?
21
33
Answers
Answer:
21 = 3 * 7
33 = 3 * 11
HCF 3
