Final answer:
To find how much money Ethan gave to Dakota, we need to set up and solve an equation based on the given conditions, include the initial difference of $8, the 1/4 transfer of funds, and the resulting 5:2 ratio of their money.
Explanation:
Ethan had $8 more than Dakota. When he gave 1/4 of his money to Dakota, the ratio of Ethan's money to Dakota's became 5:2. To solve this, let's assume Dakota originally had D dollars and Ethan had D + 8 dollars. After giving away 1/4 of his money to Dakota, Ethan would have 3/4 of D + 8, and Dakota would have D plus 1/4 of D + 8.
The new ratio of Ethan's money to Dakota's money is 5/2, leading us to the equation 3/4(D + 8) / (D + 1/4(D + 8)) = 5/2. Solving this equation will not only give us the initial amounts of money each person had but also allow us to calculate the exact amount Ethan gave to Dakota, which is the 1/4 of Ethan's original money.
Linda's grandmother baked brownies on Saturday for her church's bake sale. She cut each batch of brownies into 9 large pieces. She made 81 brownies before lunch and by the end of the day, she had made 153 brownies altogether. How many batches of brownies did she make after lunch?
A)6
B)7
C)8
D)9
Answer:
C - 8
Step-by-step explanation:
153 - 81 = 72
72 ÷ 9 = 8
Answer:
C) 8
I looked at the other answer at the bottom.
What is the answer to 4 4/7
+ 3 6/7
Answer: 8 3/7
Step-by-step explanation:
32/7 + 3 6/7
= 32/7 + 27/7
= 59/7
= 8 3/7
Hope this helps!
Hello! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
So you are adding fractions, but not just any fractions, mixed numbers.
So, to start you are gonna wanna turn these mixed numbers into improper fractions.
Here are the steps!
1. Multiply the whole number by the denominator
2. Add that to the numerator
3. Write the number you now have over the original denominator
So 4 4/7 = 32/7
3 6/7 = 27/7
You can only add or subtract fractions with like denominators. This just means denominators with the same number. In our case, we already have like denominators. They are both seven! So the adding process easy. Simply add the numerators and keep the denominators the same!
32 + 27= 59/7
Bam! 59/7 is your answer! If you would like to turn this back into a mixed number, here are the steps:
1. Divide numerator by denominator
2. Put that number as the whole number
3. Use the remainder as the numerator
4. Keep the same denominator
So, 59/7 = 8 3/7
So your answer is 59/7, or, 8 3/7.
Have a great day! And feel free to reply with any questions! (〃^∇^)ﾉ
Simplify.
-4 (3-1) + 2
enter your answer below
Answer:
-6
Step-by-step explanation:
the first part is equal to -8 and then you add two which is -6
5. What is the solution to the system? *
Captionless Image
6. Explain what your solution means in terms of the scenario. *
trying to find the system to the solution you have to put in into slope intersecpt form so y=mx+b
so 4=m(3)+b
12=b
y=3x+12
HELP HELP HELP PLEASE
1. solve the eqation. First combine any like terms on each side of the equation
x-6 = -3+8 the solution is x =
2. Solve. First combine any like terms on each side of the equation.
3w - 8w = 35 w=
3. Solve the equation. First combine any like terms on each side of the equation.
- 4 x - 4 x = 44 - 4 the solution x =
4. Solve the equation. First combine any like terms on each side of the equation -5 -8 = 3x +2 - 2x the solution is x
5. Solve. First multiply to remove the parentheses.
3(3x - 3) = 10x x=
x - 6 = - 3 + 8
x = 5 + 6
x = 11
3w - 8w = 35
- 5w = 35
5w = - 35
w = - 35 : 5
w = - 7
3(3x - 3) = 10x
9x - 9 = 10x
- 9 = 10x - 9x
x = - 9
Answer:
1. x = 11,
2. w = -7,
3. x = -5
4. x = -5
5. x = -9
Step-by-step explanation:
1. x-6 = -3+8
x - 6 = 8 -3
x - 6 = 5
Adding 6 to both sides:
x - 6 + 6 = 5 + 6
x = 11
2. 3w - 8w = 35
3w - 8w = 35
-5w = 35
Divide both sides by -5
-5w/-5 = 35/-5
w = -7
3. - 4 x - 4 x = 44 - 4
- 4 x - 4 x = 44 - 4
-8x = 40
Divide both sides by -8
-8x/-8 = 40/-8
x = -5
4. 5 -8 = 3x +2 - 2x
Collecting like terms and rearranging equation
3x - 2x = 5 - 8 - 2
x = 5 - 10
x = -5
5. 3(3x - 3) = 10x
3(3x - 3) = 10x
Expanding and removing parenthesis
9x - 9 = 10x
Collecting like terms and rearranging equation
10x - 9x = -9
x = -9
2 Question
Type the correct answer in the box. Use numerals instead of words. If necessary, used for the fraction bar.
Geno is a running back for the Bayside Barn Owls. During the final drive of his last football game, he gained 4 yards three times, lose Iyard nice and
gained 6 yards twice.
The net change in Geno's field position is
yards!
Um
Submit
Answer:
Net Change in Geno's Field Position = 22 yards
Step-by-step explanation:
Assuming Geno initial position before change is 0
Geno Gained 4 yards three times = 4*3 = 12yards
Geno lose 1 yard twice = 1*(-2) = -2yards
Geno Gained 6 yards twice = 6*2 = 12yards
Net Change in Geno's Field Position = 12 + (-2) + 12 yards
= 22 yards
What expression represents x less than 5 times y
Answer:
5y-x
MathMathMathMath
Terri and Donna both sell crafts at two different craft shows each weekend. Terri is charged a 5% commission on the amount of money she earns and pays $35 for her booth. Donna is charged a 3% commission on the amount of money she earns and pays $55 for her booth.
On the last weekend in November, Terri and Donna both earned the same amount of money at their craft shows. They both paid their respective craft shows the same total amount of money for their booths and commission
Set up a system of equations to model the amount of money Terri and Donna pay each weekend at the craft shows. Let x represent the money earned from sales, let T represent the total amount Terri pays in one weekend, and let D represent the total amount Donna pays in one weekend.
Answer:
T = 0.05x + 35
D = 0.03x + 55
Step-by-step explanation:
i) On the last weekend in November both Terri and Donna earned from sales the amount of x.
ii) Terri pays the amount T = 0.05x + 35
iii) Donna pays the amount D = 0.03x + 55
the product of a linear monomial and a linear binomial is a
Answer:
Step-by-step explanation:
Example: (cx)×(ax + b) comes out to acx^2 + bcx, which is a linear quadratic (highest power of x is 2).
the product of a linear monomial and a linear binomial will be
[tex]\rm = (cx)\times(ax + b)[/tex] which will comes out to [tex]\rm acx^2 + bcx[/tex] that is a linear quadratic higgest power of x
Lets understand,
What is Linear monomial?A Linear monomial is an Expression that has only one given term & whose power or highest degree is one. It cannot take any addition or subtraction signs monomial is an linear expression that has only a single non-zero term. Monomials can be numbers, variables, or numbers multiplied with variables.
Examples of linear monomial:-
For example, [tex]\rm 2, ab, and\; 42\;xy[/tex] are examples of a monomial. A few other examples of monomials are [tex]\rm 5x, 5x^3 , 7xy,x^5 .[/tex]
Therefore, the product of a linear monomial and a linear binomial will be
[tex]\rm = (cx)\times(ax + b)[/tex] which will comes out to [tex]\rm acx^2 + bcx[/tex] that is a quadratic with higgest power of x.
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Nancy and Matilda are 60 miles apart, cycling towards each other on the same road. Matilda rides 12 miles per hour and Nancy rides 8 miles per hour. In how many hours will they meet?
Nancy and Matilda will meet in 3 hours.
Step-by-step explanation:
Given,
Distance to cover = 60 miles
Speed of Matilda = 12 miles per hour
Speed of Nancy = 8 miles per hour
Combined speed of Nancy and Matilda = 8+12 = 20 miles per hour
Let,
x be the time taken by them
Distance = Speed * Time
[tex]60=20*x\\60=20x\\20x=60[/tex]
Dividing both sides by 20
[tex]\frac{20x}{20}=\frac{60}{20}\\x=3[/tex]
Nancy and Matilda will meet in 3 hours.
Keywords: distance, speed
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In 3 hours Nancy and Matilda meet.
Given
Nancy and Matilda are 60 miles apart, cycling towards each other on the same road.
Matilda rides 12 miles per hour and Nancy rides 8 miles per hour.
What is speed?Speed is defined as the ratio of distance and time.
The time will take to meet Nancy and Matilda is given by;
[tex]\rm \dfrac{12}{8}=\dfrac{x}{60}\\\\8 \times x=60\times 12\\\\8x=720\\\\x = \dfrac{720}{8}\\\\x=90[/tex]
Therefore.
The time taken to meet them is;
[tex]\dfrac{12}{8}+\dfrac{90}{60}\\\\1.5+1.5= 3[/tex]
Hence, in 3 hours will they meet.
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Can someone please help me with this 7th grade math homework
Answer:
1) D
2) A, D, F
3) 3.5 mph
4) equation in explanation $15
Step-by-step explanation:
4) equation: 27.50-12.50
A concrete beam is used as a counterweight. The beam is 6 feet long with an 8-inch by 8-inch square base. If the beam has to be replaced by bags of sand, what is the volume (in ft^3) of the sand that will have the same weight as the beam?
Use the following densities for the materials involved (in pounds per cubic foot):
concrete 150
sand 100
4 cubic feet
Step-by-step explanation:
Step 1:
Length of the concrete beam = 6 feet
Side for the square base = 8 inch = 8/12 feet
So, volume of the concrete beam = 6*(8/12)*(8/12)= 2.67 cu ft
Hence mass of the beam = density of the beam * volume
= 150 * 2.67 = 400 kg
Step 2:
we need the the weight of sand equivalent to the concrete beam.
Mass of the sand bags = den of sand * vol
=> 100 * volume of sand = 400
=> Volume of sand = 400/100 = 4 cu feet.
(05.01 MC)
The graph of the following system of equations is
2x + y = 6
6x + 3y = 18
Your answer:
O
overlapping lines
O
parallel lines
O
intersecting lines
Answer:
overlapping lines
Step-by-step explanation:
look at shown picture
Annual student fees at the University of California rose from about $4,000 in the year 2000 to about $12,000 in 2010. Find the percent increase.
Answer: 200%
Step-by-step explanation:
We are asked to find the percent increase in student fees. The amount of increase in student fees is given by
final amount − initial amount = increase
12,000 − 4,000 = 8,000
We can now find the percent increase by finding what percent the amount of increase is of the initial amount. In other words, we want to find what percent 8,000 is ... of 4,000.
Let p be the percent. The question can be translated into an equation.
8,000 {is} {what percent} {of} 4,000
8,000 {=} { P } {x} 4,000
To solve for p, we can now divide each side by 4,000 and simplify.
8,000 = 4,000p
p=2
To convert p to a percent, multiply 2 by 100.
2 x 100
=200%
It follows that the percent increase in student fees was 200%.
Answer:
200%
Step-by-step explanation:
Find the amount of change.
12,000−4,000=8,000
Find the percent.
Change is what percent of the original amount?
Let p= the percent.
8,000 is what percent of 4,000?
Translate to an equation and simplify.
8,000 = p⋅ 4,000=
8,000 = 4,000p
Divide both sides by 4,000 and change to percent form.
2=p
200%=p
7(3+9) pls help me ASAP
Answer:
84
Step-by-step explanation:
Using PEMDAS: (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)
7*(3+9)
7*(12)
84
Answer:
83
Step-by-step explanation:
Edward is part of a bird watching club and keeps track of the robins in a local park. To do so, he puts tags on 20 robins and releases them. Later, he catches 120 robins; 12 robins were tagged.
What is the best estimate for the robin's population?
Answer:
Total population = 200
Step-by-step explanation:
recaptured tagged/recaptured total ≈ tagged/total population
The best estimate for the total population of Robin's is 200.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given that,
Number of robins which are tagged = 20
Let x be the total population of robins.
Her catches some other robins.
Number of robins that he catched = 120
Number of robins he catched also is tagged = 12
We can write the expression as,
20 / x = 12 / 120
Cross multiplying, we get,
12x = 120 × 20
12x = 2400
x = 2400 / 12
x = 200
Hence the number of robins is 200.
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12. Find 120% of 18. Show your work.
Answer:
21.6
Step-by-step explanation:
18 is the 100% of the given number, 120% is 18 + 20% of 18
to find 20% of 18 we multiply 18 by 20 and the divide it by 100
18 × 20 ÷ 100 = 3.6 now add this to 18 and the answer is 21.6
Answer:
21,6
Step-by-step explanation:
120% × 18 =
= 120×18/100
= 2160/100
= 21,6
Are priya’s and Hans expressions each equivalent to 8y - 24? explain your reasoning
Answer:
Step-by-step explanation:
8y-24=8(y-3)
Find a rule and write the missing number for each table
The question involves discovering rules for completing mathematical tables and requires skills in pattern recognition, multiplication, and data organization.
Explanation:The student's question requires finding a rule for each given table and writing the missing number. Utilizing mathematical skills to recognize patterns or apply known operations is the key to solving these problems. For example, when asked about the cube of a number such as (74)³, one would have to multiply 74 by itself three times to get the result. This translates to 74 * 74 * 74, which can also be expressed as 7.4 * 102 * 7.4 * 102 * 7.4 * 102. Furthermore, when working with tables of data, it's essential to organize the data accurately and calculate additional information such as relative frequency when required.
In another instance, if you're given a list of numbers corresponding to particular data points, like the roster of students or experimental results, the task could involve identifying patterns or utilizing statistical tools to complete the tables.
It's important to show work and approach each problem methodically, confirming the application of correct mathematical rules. By doing so, you gain deeper understanding and enhance your problem-solving skills.
The difference between four times a number and one
The difference between four times a number and one can be expressed as 4x - 1, where "x" represents the number. This expression involves multiplying the number by 4 and then subtracting 1.
The difference between four times a number and one can be succinctly expressed as the result of multiplying that number by four and then subtracting one from the product. In mathematical notation, this difference can be represented as:
4x - 1
Here, "x" represents the unknown number, and we are performing two operations: multiplying it by 4 and subtracting 1 from the result. Let's break this down further:
Four times a number: When you multiply a number by 4, you are essentially scaling it up by a factor of 4. For example, if the number is 5, then four times that number would be 4 * 5 = 20.
Subtracting one: After obtaining the result of four times the number, we subtract 1 from it. In our example, if the number is 5, then after four times the number (20), subtracting 1 results in 19.
So, the difference between four times a number and one is the value obtained after performing these two steps. It's a simple arithmetic expression that can be calculated for any given value of "x."
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Round tables seating 8 people and rectangular tables seating 12 people are being used at a banquet for 8th graders. The ratio of round tables to rectangular tables is 2 to 1. How many tables are used to seat 336 students at the banquet, if no table has an empty seat?
Answer:
36 tables are used to seat the students at the banquet: 12 rectangular and 24 round.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Round tables = 8 seats
Rectangular tables = 12 seats
Ratio of round tables to rectangular tables = 2:1
Number of students = 336
2. How many tables are used to seat 336 students at the banquet, if no table has an empty seat?
x = Number of rectangular tables
2x = Number of round tables
Let's solve for x, using this equation:
12x + 8 (2x) = 336
12x + 16x = 336
28x = 336
x = 336/28
x = 12 ⇒ 2x = 24
12 + 24 = 36
36 tables are used to seat the students at the banquet: 12 rectangular and 24 round.
Answer:
36
Step-by-step explanation:
Match the vocabulary word with the correct definition.
1. circle
a chord of a circle that contains the center of the circle
2. diameter
a segment joining the center of a circle to a point of the circle
3. congruent circles
the set of all points in a plane that are at a given distance from a given point in the plane
4. concentric circles
circles that have equal radii
5. radius
two or more circles that lie in the same plane an have the same center
Answer:
1) the set of all points in a plane that are at a given distance from a given point in the plane
2)a chord of a circle that contains the center of the circle
3)circles that have equal radii
4)two or more circles that lie in the same plane an have the same center
5)a segment joining the center of a circle to a point of the circle
A professor announced to her class that the average score for the 37 exams received was 86. She later discovered
three additional exams with scores of 76, 81 and 97. These exams were not included in the class average she
reported to the class. Is it possible to calculate the new class average? If so, what is it? If not, justify why.
Answer:
New average = 85.9.
Step-by-step explanation:
Yes, the new class average can be calculated.
The New total of the scores = 37*86 + 76 + 81 + 97
= 3436.
The new total of examinations sat = 37 + 3 = 40.
Therefore the new class average = 3436 / 40
= 85.9
The population of North Carolina in 2010 was 9,535,483 people. The population of South Carolina in 2010 was 4,625,364 people.
a) Approximately how much larger is the population of North Carolina than South Carolina? Show or explain your thinking.
b) Approximately how many times larger is North Carolina’s population than South Carolina’s population? Show or explain your thinking.
a) North Carolina has 4,910,119 more people than South Carolina
b) the population of North Carolina is 2.06 times larger than that of South Carolina
Step-by-step explanation:
a)
Here the question is asking "how much larger is the population of North Carolina than South Carolina". This means that we have to compare the absolute value of the population of North Carolina with the population of South Caroline.
We have:
NC = 9,535,483 is the population of North Carolina
SC = 4,625,364 is the population of South Carolina
In order two compare the two, we have to calculated the difference between NC and SC. Plugging into a calculator, we get:
[tex]NC-SC=9,535,483-4,625,34=4,910,119[/tex]
So, North Carolina has 4,910,119 more people than South Carolina.
b)
In this question, we are asked "how many times larger is North Carolina’s population than South Carolina’s population". This is equivalent to ask what is the ratio between the population of North Carolina to that of South Carolina.
As we said before, we have:
NC = 9,535,483 is the population of North Carolina
SC = 4,625,364 is the population of South Carolina
And by calculating the ratio, we find:
[tex]\frac{NC}{SC}=\frac{9,535,483}{4,625,364}=2.06[/tex]
So, the population of North Carolina is 2.06 times larger than that of South Carolina.
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Answer: the population of North Carolina is 2.06 times larger than that of South Carolina.
A cabin cruiser traveling with the current went 12 mi in 1 h. Traveling against the current, it took 2 h to go the same distance. Find the rate of the cabin cruiser in calm water and the rate of the current
The rate of the cabin cruiser in calm water is 9 mph and the rate of the current 3 mph
Step-by-step explanation:
Given:
Speed of cabin cruiser travelling with then current = 12 mi in 1 h.
Against the current, it took 2 h to travel the same distance.
To Find:
The rate of the boat in calm water and the rate of the current = ?
Solution:
Let boat speed in calm water be s
Let rate of the current be c
Then
(s-c) = effective speed upstream
and
(s+c) = effective speed downstream
Writing a distance equation for each trip:
distance = [tex]time \times \text{effective speed}[/tex]
1(s + c) = 12
2(s - c) = 12
On the first equation divide both sides by 1
On the second equation divide both sides by 2
s + c = 12
s - c = 6
Now addition of the above two equations gives
2s = 18
s = 9 mph, boat speed in calm water
Lets substitute s value to find c value
s + c = 12
9 + c = 12
c = 12 - 9
c = 3 mph is the current
Final answer:
The cabin cruiser's rate in calm water is 9 mph, and the rate of the current is 3 mph.
Explanation:
To solve this problem, we will let c represent the rate of the current and r represent the rate of the cabin cruiser in calm water. When traveling with the current, the effective speed of the cruiser is r + c, and against the current, it is r - c.
Using the given information:
With the current: 12 miles in 1 hour means the speed with the current is 12 mph. So, r + c = 12.Against the current: 12 miles in 2 hours means the speed against the current is 6 mph. So, r - c = 6.Now we can set up a system of equations:
r + c = 12r - c = 6Adding these two equations, we get:
2r = 18
Dividing both sides by 2, we find r = 9 mph. Thus, the rate of the cabin cruiser in calm water is 9 mph. To find the rate of the current, plug r = 9 into either of the original equations. Let's use equation (2):
9 - c = 6
Subtracting 9 from both sides, we find c = 3 mph. So the rate of the current is 3 mph.
Ajar contains 12 caramels, 7 mints and 16
dark chocolates. What is the probability of
selecting a mint expressed as a fraction?
Answer: 1/5
Step-by-step explanation: To find the probability of selecting a mint out of the jar, we use our ratio for the probability of an event which is shown below.
(P) event = number of favorable outcomes/total number of outcomes.
Since there are 7 mints in the jar, the number of favorable outcomes is 4 and since there are 35 candies in all,
the total number of outcomes is 35.
Therefore, the probability of selecting a mint is 7/35.
Notice however that 7/35 is not in lowest terms so we need to divide the numerator and denominator of 7/35 by their greatest common factor of 7 to get 1/5.
So our final answer for the probability of selecting a mint is 1/5.
What is the formula for the equation of a straigth line
Step-by-step explanation:
Formula of straight line is given as:
[tex]y= mx + c[/tex]
Where m = is the gradient or slope & c = y-intercept.
If Jesse bikes 3.2 kilometers in 2 hours. What is his rate
Answer:
He bikes 1.6 km per hour.
Step-by-step explanation:
If he bikes 3.2km un 2 hours, then:
3.2 km / 2 hours = 1.6 km / hour
a diesel train left berlin and traveled north at an average speed of 25 km/h. A cattle train left at the same time and traveled in the opposite direction with an average speed of 35 km/h. Find the number of hours the cattle train needs to travel before the trains are 600 km apart.
Answer:
10 hours
Step-by-step explanation:
Let [tex]N[/tex] represent the distance the train heading north has traveled
Let [tex]S\\[/tex] represent the distance the train heading south has traveled
Let [tex]t[/tex] represent the number of hours that has passed
[tex]N=25t\\S=35t[/tex]
[tex]600=N+S[/tex]
[tex]600=25t+35t\\600=60t\\t=10[/tex]
what’s the exact value of tan(6pi)
Answer:
0
Step-by-step explanation:
The period of the function [tex]y=\tan x[/tex] is equal to [tex]\pi.[/tex]
To find the exact value of [tex]\tan (6\pi)[/tex], first note that we can skip 6 periods of this function, so
[tex]\tan (6\pi)=\tan 0[/tex]
Use definition of [tex]\tan:[/tex]
[tex]\tan 0=\dfrac{\sin 0}{\cos 0}[/tex]
Since
[tex]\sin 0 = 0\\ \\\cos 0=1,[/tex]
we have that
[tex]\tan (6\pi)=\tan 0=\dfrac{\sin 0}{\cos 0}=\dfrac{0}{1}=0[/tex]