Mimi and Rita both plan to run for a spot on the school
board in their city. They must each collect a certain
number of signatures to get their name on the ballot. So
far, Mimi has 30 signatures, but Rita just started and
doesn't have any yet. Mimi is collecting signatures at an
average rate of 8 per hour, while Rita can get 14
signatures every hour. Assuming that their rate of
collection stays the same, eventually the two will have
collected the same number of signatures. How many
signatures will they both have?
Create two tables showing hours and signatures. Write,
graph, and solve a system of equations for this situation.
Explain what your solution means for the situation.
Answers
Answer:
The equal number of signatures Mimi and Rita eventually collects are 70 signatures
Step-by-step explanation:
1) The initial number of signatures Mimi has = 30 Signatures
The average rate at which Mimi can collect signatures = 8 signatures per hour
The average rate at which Rita can collect signatures = 14 signatures per hour
The table of values showing the number of signatures Mimi and Rita can have at a given hour is presented as follows;
For Mimi, we have;
Hour [tex]{}[/tex] Number of Signatures
0 [tex]{}[/tex] 30
1 [tex]{}[/tex] 38
2 [tex]{}[/tex] 46
3 [tex]{}[/tex] 54
4 [tex]{}[/tex] 62
5 [tex]{}[/tex] 70
For Rita, we have;
Hour [tex]{}[/tex] Number of Signatures
0 [tex]{}[/tex] 0
1 [tex]{}[/tex] 14
2 [tex]{}[/tex] 28
3 [tex]{}[/tex] 42
4 [tex]{}[/tex] 56
5 [tex]{}[/tex] 70
2) The equation representing the number of signatures Mimi has at a given time, t, is given as follows;
The number of signatures Mimi has = 30 + 8 × t
The equation representing the number of signatures Rita has at a given time, t, is given as follows;
The number of signatures Rita has = 14 × t
3) Please find attached the required graph of the number of signatures Mimi and Rita has
4) The solution if the system of equations is given as follows;
30 + 8 × t = 14 × t
From which we have;
30 = 14 × t - 8 × t = 6 × t
t = 30/6 = 5 Hours
By substituting t = 5 hours in the above equations, the equal number of signature of signatures Mimi and Rita can have is therefore;
30 + 8 × 5 = 70 signatures = (14 × 5) signatures
The equal number of signatures Mimi and Rita eventually collects are 70 signatures
5) The meaning of the solution is that is Mimi and Rita continue collecting signatures at their respective constant rate of 8 and 14 signatures per hour, given that Mimi already has 30 signatures, they will have the same number of 70 signatures after 5 hours
Related Questions
What does an arrow as an endpoint
imply for a function? How does it
effect your domain and range?
I
Answers
Answer:
Step-by-step explanation:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis
Answer:
It menas that it keeps going.
Step-by-step explanation:
If you have a line with an arrow at the end it means that the numbers keep on going. So say that you had a number line that ended at ten but there is an arrow, this means that there is more or less.
<- ->
10 less than ten 10, more than ten.
8/9p=12/18 whats the p value?
Answers
Answer:
p = 12/18
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
8/9*p-(12/18)=0
Simplify.
Simplify more.
Find the Least Common Multiple
The left denominator is : 9
The right denominator is : 3
Jill made 20 muffins. She puts them into 3 boxes and has two muffins left. How many are in each box if they all contain the same amount of muffins?
Answers
Answer:
it would be 6 muffins each and muffins sounds so good right now TwT
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
20-2=18
18÷3=6
Therefore there are 6 muffins in each box
Simplify the expression. Write your answer as a complex number.
2 times the square root of 25 plus the square root of negative 16
Answers
Answer:
d
Step-by-step explanation:
In how many ways can 5 people sit around a circular table
Answers
Answer:
120 ways
Step-by-step explanation:
In the scenario described, there are 120 ways that 5 people can sit around a round table.
What is the coefficient in the expression 8x + 10
Answers
What is the slope of the equation: y = -3x +7
Answers
The slope of the equation is -3.
John's teacher bought three 64 ounce bottles of soda for a class party. At the end of the party, 1/6 of the soda remained. How many ounces of soda remained?
Answers
Answer: 10
Step-by-step explanation:
64/6=10 therefore it is 10
5 x (-1/3) do u know
Answers
Answer:
~-1.67
Step-by-step explanation:
Multiply. Note that when you multiply a negative and positive number, your answer will be negative:
5 x (-1/3) = (5 * -1)/3
Multiply, then divide:
5 * -1 = -5
-5/3 = ~-1.67 (rounded to the nearest hundredths).
~
Answer:
-5x/3
It just is, trust me.
-3x + 7= 28
what does x equal
Answers
1st step move the seven to the other side of the equal sign and change it from positive to negative like this
-3x=21
Step 2 divide 21 by -3 and the answer will be -7
Answer:
x = -7
Step-by-step explanation:
[tex]-3x+7=8[/tex] subtract 7 on both sides
[tex]-3x=21[/tex] divide -3 into both sides
[tex]x=-7[/tex]
To check
-3(-7) = 21 + 7=28
What's more selfish? Committing Death or forcing someone to stay in a world where they are so unhappy?
Answers
Answer:forcing someone to stay in the world they dont wanna be in
Step-by-step explanation:
At a carnival, Andrew went on rides and played games.
• Each ride cost $2.
• Each game cost $2.
• Andrew went on 3 rides and played g games.
Andrew wrote the expression below to represent the total
amount of money, in dollars, he spent at the carnival.
6 + 2g
Which of the following is another way Andrew could represent
the total amount of money, in dollars, that he spent at the
carnival?
a. 2 × 3g
b. 2(3 + g)
c. 4 × 3g
d. 4(3 + g)
Answers
Answer:
I thinks its b cause you have to multiply them both by 2 and add 3 and g together. hope it helps
The expression can also be 2(3 + g).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.
Variable: A symbol without a set value is referred to as a variable.
Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.
Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.
Given:
Each ride cost $2.
Each game cost $2.
Andrew went on 3 rides and played g games.
So, the ride costs = $6
and, games costs = $2g
Andrew pay in total = 6 + 2g
= 2 (3 + g)
Hence, the expression can also be 2(3 + g).
Learn more about Expression here:
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Latoya created a factor tree and wrote the prime factorization of 90 shown below. A factor tree of 90. 90 branches to 9 and 10. 9 branches to 3 and 3. 10 branches to 2 and 5. The equation is 90 = 2 times 3 times 5. What is Latoya's error? She should not have found the factors of 9. She should have included an exponent of 2 on the 3. She should have included 9 and 10 in the prime factorization. She should have started the tree with 2 times 45.
Answers
Answer:
B) She should have included an exponent of 2 on the 3.
Step-by-step explanation:
Just took the test. Good luck!
A spinner with 8 equally sized slices has 2 yellow slices, 3 blue slices, and 3 red slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellow or blue slice?
Answers
The probability that the dial stops on a yellow or blue slice will be 5/8.
What is mean by Probability?The term probability refers to the likelihood of an event occurring.
Given that;
A spinner with 8 equally sized slices.
It has 2 yellow slices, 3 blue slices, and 3 red slices.
Now,
Since, The dial is spun and stops on a slice at random.
Here, Number of yellow and blue slice = 2 + 3
= 5
And, Total number of slices = 8
So, The probability that the dial stops on a yellow or blue slice = 5 / 8
Learn more about the probability visit:
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____________________ A letter that represents one or more numbers. pick from these: Absolute Value Distributive Property Equation Evaluate Equivalent Simplify Expression Integers Like Terms Inequality Reciprocal Coefficient Variable Solution Ratio
Answers
Answer:
The answer is a Variable
Step-by-step explanation:
In algebra, symbols (usually letters) are used to represent numbers. To solve math problems, you should know what variables and constants are. Here is an introduction to the terms variables and constants. A variable is a letter or symbol used as a placeholder for an unknown value.
I hope this helps you :)
Please i need help thank you
Answers
In the neighborhood 72 families, 18 one or more cats as a fraction then express the fraction as a decimal
Answers
Answer:
poopie
Step-by-step explanation:
find three consecutive odd integers with a sum of 75
Answers
Answer:
23, 25, 27
Step-by-step explanation:
first integer will be X, second will be (X+2), and the third will be (X+4). They will all be summed up and set equal to 75.
[tex](x) + (x + 2) + (x + 4) = 75[/tex]
combine like terms:
[tex]3x + 6 = 75[/tex]
subtract 6:
[tex]3x = 69[/tex]
divide by 3 to find value of X:
[tex] \frac{3x}{3} = \frac{69}{3} [/tex]
[tex]x = 23[/tex]
plug in X in o red der to finger the rest of the integers.
(X+2)= (23+2)=25
(X+4)= (23+4)=27
The product of eight and a number x
Answers
Answer:
To write this down as an algebraic expression you would simply need to multiply the two terms together.
So in this case it would be 8 multiples by x which is 8x
Step-by-step explanation:
1) Find out the variables in the Expression
2) Find the operation that is done to the variables
3) Apply the operation to those variables.
The product of 8 and an unknown number x is 8x.
What is multiplication?Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.
Given the product of 8 and x
Product is also called multiplication.
Multiplication is an arithmetic operator which is applied in between two numbers or variables.
For example 2 × 4, 4 × 5.
So,
Product of 8 and x must be
8 × x = 8x
Hence "The product of 8 and an unknown number x is 8x".
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-28 + 2x = -18 what is x?
Answers
Answer: x=5
Step-by-step explanation:
To solve for x, we want to use algebraic properties to isolate x.
-28+2x=-18 [add both sides by 28]
2x=10 [divide both sides by 2]
x=5
Now, we know that x=5.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \text{x = 5}}}}}[/tex]
Step-by-step explanation:
[tex] \star{ \sf \: - 28 + 2x = - 18 }[/tex]
[tex] \tt{Step \: 1}[/tex] : Move 28 to right hand side and change it's sign
[tex] \hookrightarrow{ \sf{2x = - 18 + 28}}[/tex]
[tex] \tt{Step \:2}[/tex] : Subtract 18 from 28
The negative and positive integers are always subtracted but posses the sign of the bigger integer
[tex] \hookrightarrow{ \sf{2x = 10}}[/tex]
[tex] \tt{Step \: 3}[/tex] Divide both sides by 2
[tex] \hookrightarrow{ \sf{ \frac{2x}{2} = \frac{10}{2}}} [/tex]
[tex] \tt{Step \: 4}[/tex] Calculate
[tex] \hookrightarrow{ \sf{x = 5}}[/tex]
[tex] \tt{∴ \: The \: value \: of \: x \: is \: \bold{5}}[/tex]
[tex] \sf{Hope \: I \: helped !!}[/tex]
[tex] \sf{Best \: regards !!}[/tex]
~[tex] \text{TheAnimeGirl}[/tex]
Which Angel number supplementary to angel to AED
Answers
Answer:
Angle number 5
Step-by-step explanation:
The sum of supplementary angles equal 180°.
Angle AED, in the diagram given is labelled angle 4.
The angle labelled 4 forms a linear pair with the angle labelled 5.
Since a linear pair of angles = 180°, therefore:
m<AED + m<AEI = 180°.
That is:
m<4 + m<5 = 180°.
Both angles are supplementary.
Therefore, angle number 5 is supplementary to angle AED.
Choosing a car that coasts _____ instead of a car that costs _____ means that you’ll have more money available for other purchase. A. $12,000; $11,000 B. $9000; $7000 C. 10,000; $14,000 D. 18,000; $12,000
Answers
Answer:
C. : Choosing a car that costs 10,000 instead of a car that costs 14,000 means that you'll have more money available for other purchases
Step-by-step explanation:
or each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate. Anderson earns $6 per hour. Which equation can be used to solve for Carey’s hourly rate, c?
Answers
Answer:
6=[tex]\frac{c}{2}[/tex]+1
Step-by-step explanation:
anderson's $6 per hour is one half of carey's hourly rate, plus one.
Answer:
A)
6 = c/2 + 1
Step-by-step explanation:
edg2020
32. At 8 AM, the temperature was 3°F below zero. By 1pm, the temperature rose
14F and by 10 PM, dropped 12. Plot points and draw arrows on the number
line below to model this situation.
What was the temperature at 10 PM? Explain how the number line helped you
find your answer.
Answers
Answer: - 1°F
Step-by-step explanation:
Given that:
At 8a.m:
Temperature = 3°F below 0
By 1p.m ; Temperature rose by 14F ;
By 10pm ; temperature dropped by 12F
Temperature at 10 pm:
3°F below 0 = - 3°F
Temperature at 1pm: temperature increased by 14°F
-3°F + 14°F = 11°F
Temperature at 10pm: temperature dropped by 12°F
11°F - 12 = - 1°F
is the product of two rational numbers always a rational number?
Answers
Answer:
Yes, it's always rational.
Step-by-step explanation:
-7=y/-10
Help me, please
Answers
Answer:
70
Step-by-step explanation:
Solve any pre-algebraic equation with inverse operations:
-7 = y/-10
multiply both sides by -10
-7 * -10 = y
now simplify:
remember that multiplying two negatives with result in a positive
70 = y
2. |X-6|+ 1 =- 2x + 4
Answers
Answer:
i dont understand the question you are asking
Step-by-step explanation:
what is the slope intercept form of the equation 15x-4y=32
Answers
Answer: y = 15/4 x - 8
Step-by-step explanation:
A flower garden is 22.50m long. Sheila wants to make a border along one side using bricks that are 0.25m long. Find the number of bricks needed. a) 9 (b) 90 (c) 900 (d) none of these
Answers
Answer:
(b) 90
Step-by-step explanation:
Four bricks are needed for each meter of length:
4 × 22.5 = 90
90 bricks are needed.
what is the value of y?
Answers
Answer:
y +43⁰ +123⁰ =180⁰
=) y +160⁰ =180⁰
=) y = 20⁰
Answer:
Y = 34
Step-by-step explanation:
y + 43 + 123 = 180
y + 146 = 180
180 - 146. = y = 34
Y = 34