The difference in ages of Marcelle and Megan is 95/12 as an improper fraction and as a mixed number is 7 whole number and the fraction 11/12.
How to evaluate the difference in the fraction of the agesWe shall convert the fractions to have similar denominators and simply apply subtraction for the numerators as follows:
Marcelle's age = 15 whole number, 1/2
Marcelle's age = 31/2
Megan's age = 7 whole number, 7/12
Megan's age = 91/12
LCM of 2 and 12 is 12 so;
Marcelle's age = 31/2 × 12/12
Marcelle's age = 186/12
difference in their age (186 - 91)/12
difference in their age = 95/12
Therefore, the difference in the ages of Marcelle and Megan is the fraction 95/12 or as a mixed number is 7 whole number and the fraction 11/12
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Consider a species that occupies a large, but fixed, number of islands. The distribution of the species across all islands is maintained by a balance between local extinctions and local colonization events. Devise a model for the relationship between the fraction of islands occupied by the species and time. Be clear to outline the assumptions you make and be sure to describe your key predictions
The most probable prediction( according to biogeography theory of islands) for this situation would be continued colonization of large species population( due to balance between immigration and extinction of species) through time on the island.
What is species?A species is a unit of biodiversity as well as the fundamental classification and taxonomic rank of an organism in biology.
Given:
Consider a species that occupies a large, but fixed, number of islands.
The distribution of the species across all islands is maintained by a balance between local extinctions and local colonization events.
According to island biogeography theory the population of an island is maintained constant through time when the immigration rate of new species to the island and extinction rate of species in the island is constant.
In a model for the relationship between the fraction of islands occupied by species and time, if the number of new species immigrating to the island will be equal to the number of species that become extinct in the island species population and will thrive continuously through time( will never become extinct) as the island species population will be maintained due to the existence of a dynamic equilibrium of species in the island.
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Can you please help with this question
Find the volume of the prism.
Answer:
1120
Step-by-step explanation:
A bag contains 2 snicker bars, 8 trix bars , and 5 crunch bars. A candy is chosen, replaced, then another is chosen, what is the probability of choosing a trix bar then a crunch bar?
The probability of choosing a trix bar then a crunch bar exists 8/45.
What is Probability?Mathematics' field of probability deals with numerical assessments of how likely an event is to occur.
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
Probability = Number of favorable outcome / Number of total outcome
Given,
Number of snicker bars = 2
Number of trix bars = 8
Number of crunch bars = 5
Total number of candy bars = 2 + 8 + 5 = 15
8 trix, so picking a trix would be 8/15
5 crunch bars, picking a crunch would be 5/15, which reduces to 1/3
Probability of both: 8/15 x 1/3 = 8/45
Therefore, the probability of choosing a trix bar then a crunch bar exists 8/45.
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The probability of choosing a trix bar then a crunch bar exists 8/45.
What is Probability?Probability theory deals with numerical evaluations of the likelihood that an event will occur.
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
A probability represents the likelihood or chance that a particular occurrence will take place. Probabilities can be expressed as ratios between 0 and 1, or as percentages between 0% and 100%.
Probability = Number of favorable outcome / Number of total outcome
Given,
Number of snicker bars = 2
Number of trix bars = 8
Number of crunch bars = 5
Total number of candy bars = 2 + 8 + 5 = 15
8 trix, so picking a trix would be 8/15
5 crunch bars, picking a crunch would be 5/15, which reduces to 1/3
Probability of both: 8/15 x 1/3 = 8/45
Therefore, the probability of choosing a trix bar then a crunch bar exists 8/45.
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in one year, the student enrollment increased from 560 to 588. This was an increase of what percent?
Answer:
5% Increase
Step-by-step explanation:
560 * 0.05 = 28
560 + 28 = 588
Answer: 5%
Step-by-step explanation:
Orig | 560 | 100
Change | 28 | x
new | 588 | n/a
560/28 = 100/x
1 x 5
5%
1) Alice decides to take a trip from the East Coast of the United States to the West Coast. While planning, she chooses to drive, fly, and ride a train. Her first leg of the trip is traveling by car, from Sacramento, California to Denver, Colorado. Along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. After driving for many hours, Alice finally makes it to Denver, Colorado spending $874.80 in gas.
a) Let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. Create an equation that models the situation.
b) If Alice purchases 87 gallons for regular unleaded gas, how many gallons of premium gas did she purchase? Show all work to receive full credit.
2) After spending a week in Denver, Alice decides to leave her car at a friend’s house in order fly from Denver, Colorado to Chicago, Illinois. Her plane ticket cost $475 and $35 per checked bag.
a) Write a function that models the number of checked bags, b, as it relates to the total cost, c(b).
b) Compete the table
Number of Bags (b) Total Cost c(b)
0
1
2
3
4
6
8
3) After spending time in Chicago, Alice decides to finish her trip by riding a train 700 miles to Washington D.C. The train travels at an average speed of 80mph. Answer the following questions using the graph.
a) Describe the y-intercept in this scenario.
b) Describe the x-intercept in this scenario
c) Finish the ordered pairs (2.5, ____ ) and (____,300).
d) What are the domain and range?
Domain: {h I ___ < h < ____}
Range: {f(h) I ___ < f(h) < ____}
We see Alice chose a journey to travel from the East coast United States to the West Coast. She had a starting place and ending place in mind and did not aimlessly find her way from Sacramento, California to Washington D.C. But rather, she made decisions along the way to accomplish her goal. One could also say your life is like a journey or race in which you are running. 1 Corinthians 9:24-25 (NIV version) says, “Do you not know that in a race all the runners run, but only one gets the prize? Run in such a way as to get the prize. Everyone who competes in the games goes into strict training. They do it to get a crown that will not last, but we do it to get a crown that will last forever.” How do you interpret this passage in the bible and what does it look like in your life?
All Answers:
1a) The equation that models the situation is: 4.65r + 4.95p = 874.80
1b) Using the equation from part 1a, we know that 4.65r + 4.95p = 874.80. If we know that Alice purchased 87 gallons of regular unleaded gas, we can substitute that value into the equation: 4.65(87) + 4.95p = 874.80. Solving for p, we get: 4.65(87) + 4.95p = 874.80
4.0995 + 4.95p = 874.80
4.95p = 869.805
p = 175.6 gallons
2a) The function that models the number of checked bags, b, as it relates to the total cost, c(b), is: c(b) = 35b + 475.
2b) Number of Bags (b) Total Cost c(b)
0 475
1 510
2 545
3 580
4 615
6 675
8 835
3a) The y-intercept in this scenario represents the total distance travelled when the time spent on the trip is zero. As the distance traveled is 700 miles when time is zero, the y-intercept is (0,700)
3b) The x-intercept in this scenario represents the total time spent on the trip when the distance travelled is zero. As time is zero when the distance traveled is zero, the x-intercept is (0,0)
3c) (2.5, 200) (10, 300)
3d) The domain and range are based on the permissible values of time and distance travelled. Based on the information provided, the domain would be {h | 0 < h < 10} and the range would be {f(h) | 0 < f(h) < 700}
About the last part of the question, it is referring to the fact that life is like a journey, and we should strive to be like runners who run to win the prize, not just to participate. This passage encourages us to put in the hard work and dedication necessary to achieve our goals in life, and to not be satisfied with simply going through the motions. It also reminds us that our ultimate goal should be eternal reward, not temporary ones. In your life, it might mean setting a goal, making a plan, and putting in the effort to achieve it, but also keeping a perspective of what is important in the long run, not just in the short run.
If Jamar can run 3/5 of a mile in 2 minutes 30 seconds, what is his rate in miles per minute? (Remember, distance = rate x time)
Answer:
6/25
Step-by-step explanation:
(3/5) / 2.5 = 6/25
The median is __________________ a value in a data set
A) never
B) always
C) sometimes
Please help, will give brainliest, 5 star, and thanks!
Answer:
[tex]y\geq -2[/tex]
Step-by-step explanation:
Credit: Desmos
What are personal assets?
Personal assets are the list of things which are owned by any person for the present or the future use such as house , saving accounts, Cash etc.
Personal assets the list of things all of which are owned by any personal or a family for the present or the future use.When an individual want to take loan of any purpose then bank give the loan by considering the present value of the personal assets.It represent the total property and cash owned by any individual for the present or the future use.Example of personal assets are : house, any other property , cash, certificate representing some value, jewelry, any vehicle etc.Therefore, the personal assets represent the valuable items owned by any individual for present or the future use.
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I need help I don’t get it
Answer:
its 2:3 if im not wrong
Step-by-step explanation:
Help me please I would really appreciate it
Step-by-step explanation:
The coordinates of the points are P1(2, 2) and P2(10, 2). The distance d between these two points are given by
[tex]d = \sqrt{ {(x\frac{}{2} - x\frac{}{1} ) }^{2} + ({y\frac{}{2} - y\frac{}{1}) }^{2} } \\ = \sqrt{ ({10 - 2})^{2} +( {2 - 2)}^{2}} \\ = 8[/tex]
choose the graph of the inequality X< 7
choose one:
3rd one. The circle is on 7 and is going to the left.
Is 2 by 7 recccuring decimal or terminating decimal
Given:
The number is 2 by 7.
To find:
Whether 2 by 7 recurring decimal or terminating decimal.
Solution:
If all the prime factors of denominator value of a fraction is either 2 or 5 or both, then the fraction is terminating decimal.
If the prime factors of denominator value of a fraction is other than 2 or 5 , then the fraction is recurring decimal.
The given number is:
[tex]\dfrac{2}{7}[/tex].
The denominator value is 7 and prime factor of 7 is 7, which is different from 2 and 5.
Therefore, the number 2 by 7 is recurring decimal.
How are the angles of the two figures related
Answer:
I believe its A
Step-by-step explanation:
Daija is creating a budget, and evaluating his purchases over the last month. Consider the following code segment which attempts to find the sum of all purchases made in the last month, stored in purchased List. N ← 1 sum ← 0 REPEAT UNTIL () { sum ← sum + purchase List[n] n ← n + 1 } What code can replace missing code to assign the total of all values in purchase List to sum
The missing code that can replace to assign the total of all values in purchase List to sum, is: REPEAT UNTIL (n > purchaseList.length)
What is syntax of REPEAT UNTIL?The syntax for a REPEAT UNTIL loop in most programming languages is as follows:
REPEAT {
// code to be executed
} UNTIL (condition)
or
DO {
// code to be executed
} UNTIL (condition)
What is looping?Looping is a programming construct that allows a certain block of code to be executed repeatedly. The two main types of loops are for loops and while loops.
A for loop is used to execute a block of code a specified number of times. It typically starts with a variable initialization, then a condition is checked, and if the condition is true, the code block inside the loop is executed, and then the variable is updated.
The missing code that can replace the empty parentheses in the REPEAT UNTIL statement to assign the total of all values in purchase List to sum, is:
REPEAT UNTIL (n > purchaseList.length)
This means that the loop will continue to execute until the value of n is greater than the length of the purchaseList. In each iteration, the value of purchaseList[n] is added to the sum, and then n is incremented by 1. So, this loop will iterate through all the elements in the purchaseList, adding each one to the sum, until it reaches the end of the list. This will give the total sum of all purchases made in the last month.
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........... I donr know what I'm doing-
Intercept = 1
Equation - y = -(2/5)x + 1
Write a rule to describe each reflection.
Rule:r() (x,y)=()
Who ever answers this question will get 25 points.
Answer: ok so if it is ok im sorry but like how is it like is there supposed to be a number? im sorryyy i thught i had it before i saw the picture
Step-by-step explanation:
How many one-cup servings of milk are in a two-liter bottle? Round your answer to the nearest tenth.
____________one-cup servings
The number of cups of serving that is possible in a two-liter bottle is 8.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know 1 liter is equal to 4 cups.
Therefore, The number of cups serves possible in a two-liter bottle is,
= (2×4) cups.
= 8 cups.
So, 8 cups of servings are possible from a two-liter bottle.
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John gains 5% by selling a book for 273. Find the cost price of the book
Answer:
$260
Step-by-step explanation:
$273 - 5% = $260
5% commission = $13
Answer:
260
Step-by-step explanation:
273-5%=260
How do you find the missing side of an obtuse triangle?
Answer:
Using the cosines law
Step-by-step explanation:
So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC
A truck uses 2.5 litres of fuel to travel 8 kilometres.
a How far will the truck travel on 1 litre of fuel?
b How far will the truck travel on 120 litres of fuel?
Answer:
a：20 km
b：384
Step-by-step explanation:
a：
[tex] \frac{2.5}{ 8} = \frac{1}{x} [/tex]
[tex]x = 20[/tex]
b：
[tex] \frac{2.5}{8} = \frac{120}{y} [/tex]
[tex]y = 384[/tex]
Solve the real-world situation by using the substitution method.
1. A standard rectangular highway billboard has a perimeter of 124 ft.
The length is 34 ft. more than the width. Let l represent the length
521 + 2w
124
and w represent the width. The system of equations
1 = 34 + w
Find the length and the width.
Answer:
521 plus 521 is equal to 10000
A store creates a mixture using only peanuts and almonds.
There are 20 pounds of the mixture.
Peanuts cost $2. 95 per pound.
Almonds cost $5. 95 per pound.
The mixture costs $4. 00 per pound.
How many pounds of peanuts are in the mixture?
There are 13 pounds of peanuts present in the mixture.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.
Let's consider Almonds be a and Peanuts be p.
from given conditions,
a + p = 20
and 5.95 a + 2.95 p = 4(20)
5.95 a + 2.95 p = 80
take, a = 20 - p
5.95 (20 - p) + 2.95 p = 80
119 - 5.95 p + 2.95 p =80
119 - 3 p = 80
3p = 39
p = 39/3
p = 13
Therefore, there are 13 pounds of peanuts present in the mixture.
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Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16
Vertices are at (-7, 5) and (-1, 5) and foci are at (-9, 5) and (1, 5) of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16.
As per the given data the given equation is:
[tex]\\$$\frac{ (x+4)^2}{9} - \frac{(y-5)^2 }{16}=1$$[/tex]
The standard form for the equation of a hyperbola with center (h, k) is [tex]\frac{(x-h)^{2} }{a^{2} } - \frac{(y-k)^2}{b^{2} } =1[/tex]
Your hyperbola opens left/right, because it is of form x - y.
Comparing terms, we find that
h = -4, k = 5, a = 3, y = 4
In the general equation, the coordinates of the vertices are at [tex]$(h \pm a, k)$[/tex].
Thus, the vertices of your hyperbola are at (-7,5) and (-1,5).
The foci are at a distance c from the center, with coordinates [tex]$(\mathrm{h} \pm \mathrm{c}, \mathrm{k})$[/tex], where [tex]$c^2=a^2+b^2$[/tex]
[tex]c^2=9+16=25$[/tex], so c = 5.
The coordinates of the foci are (-9, 5) and (-1, 5).
The Figure below shows the graph of the hyperbola with its vertices and foci.(attached at the end of solution)
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Help ill give u brainliest when I can
Answer:
A)82
b)16807
c)10
d)625
Step-by-step explanation:
a: 3^4 or 81
b 7^5. 16807
c 10^2 or 100
d 5^7 78125
Make a tree diagram to show sample space. Then select the total number of outcomes.
rolling a number cube, tossing a coin and choosing a card from cards marked A and B
a. 24
C.
18
b. 12
d. 6
HELP PLEASE
Answer:
a. 24
Step-by-step explanation:
Rolling a number cube: 6 outcomes
tossing a coin: 2 outcomes
At this point, we have 6 x 2 = 12 outcomes, because each of the 6 numbers on the cube can each have a heads or tails outcome
Choosing card A or card B gives us 2 more outcomes for each of the 12 outcomes we have so far.
12 x 2 = 24
y=-3x+15 create a word problem
Answer:
John starts with $12 dollars in his bank account, each day he spends $3.
Step-by-step explanation:
Andy is A years old. His brother Ron is R years old. Andy multiplies his own age by 3. He then subtracts twice Ron's age. The answer is 6. Ron subtracts his age from Andy's age. The answer is −2 aWrite a pair of simultanous equations that model Andy's and Ron's ages.
Answer:the pair of simultanous equations that model Andy's and Ron's ages are
3A-2R=6----Equation 1
R-A =2----Equation 2
Andy is 10 Years and Ron is 12 years
Step-by-step explanation:
Andy's age is represented as A
and Ron';s age is represented as R
Now if Andy multiplies his own age by 3. He then subtracts twice Ron's age. The answer is 6 can be expressed mathematically as
3A-2R=6
And if Ron subtracts his age from Andy's age. The answer is −2 can be expressed as
R-A =2
Therefore the pair of simultaneous equations that model Andy's and Ron's ages are
3A-2R=6----Equation 1
R-A =2----Equation 2
Solving becomes
3A-2R=6----Equation 1
R-A =2----Equation 2
Make R subject formulae in equation 2
R =2+A
Putting R =2+A in equation 1
3A-2(2+A)=6
3A -4-2A =6
A-4=6
A=6+4=10
From eqn 2,
R-A =2
R-10 =2
R=10+2=12
Andy is 10 Years and Ron is 12 years
Martina walked 34 of a mile in 35 of an hour. At this rate, how far can Martina walk in one hour?
Answer:
34 = 35
Step-by-step explanation:
34x35
Answer:
Martina can walk 1 1/4 miles in one hour.
Step-by-step explanation:
Find the reciprocal of 3/5 (by flipping the fraction)
5/3
Multiply 5/3 by 3/4
3/4(5/3)= 15/12= 1 1/4