An equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Given that, after 17 weeks, you have $570, and after 29 weeks, you have $822.
Here, (17, 570) and (29, 822)
Substitute (x₁, y₁)=(17, 570) and (x₂, y₂)=(29, 822) in m=(y₂-y₁)/(x₂-x₁)
= (822-570)/(29-17)
= 252/12
= 21
Substitute, m=21 and (x, y)=(17, 570) in y=mx+c, we get
570=21×17+c
570=357+c
c=213
Substitute, m=21 and c=213 in y=mx+c, we get
y=21x+213
Therefore, an equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.
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pleaseee help me!
.
Two numbers are consecutive positive multiples of 3. Three times the larger of the numbers is 7/10of 5 times the smaller. What are the numbers?
Answer:
18 and 21
Step-by-step explanation:
Let the smaller number = 3x
Let the larger number = 3x + 3
The three and the plus 3 insure that the numbers are multiples of 3 and are consecutive.
3* (3x + 3) = 7/10 * 5 (3x) Multiply both sides by 10
30*(3x + 3) = 7 * 5 * 3x Remove the brackets
90x + 90 = 7 * 5 * 3x Combine the right
90x + 90 = 105x Subtract 90x from both sides.
-90x -90x
90 = 15x Divide by 15
x = 90/15
x = 6
Let's see if it works.
3*(3x + 3) = 3*(18 + 3) = 3 * 21 = 63
7/10 * 5 *3x = 7/10 * 5 * 3*6 = 630 / 10 = 63
(PLS HELP QUICKLY!) (ONLY HAVE 10 MINUTES!!! PLS HELP)
A fundraiser is being held to raise money for a new school playground. Of every $20 raised, $16 will be spent on playground equipment. If the goal of the fundraiser is $320.00 for playground equipment, how much money will it need to raise?
Answer:
$400
Step-by-step explanation:
If $16 will be spent, then you should do 320/16=20 to find out how many times people are donating. Since that answer what 20, they need people to give 20*20=400 oo be able to raise enough money fOr playground equipment
Find the volume of the cylinder. Round your answer to the nearest tenth if necessary. Use 3. 14 for pi.
A can of juice has a radius of 5 inches and a height of 6 inches. What is the volume of the can?
The volume of the can based on mentioned radius and height of can is 471 inches³.
Volume of cylinder is defined the capacity or amount of fluid that can be held in the object. The mentioned object is can which is cylindrical in shape.
Use the below mentioned formula to calculate the volume -
V = πr²h, where V is volume, r is radius and h is height.
Keep the values in formula to find the value of volume of cylinder
V = 3.14×5²×6
Next step is to perform multiplication on Right Hand Side of the equation
V = 471 inches³
The obtained volume is already rounded off. Thus, the volume of the can is 471 inches³.
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Find x. Please help I’m stuck
Answer:
30 i think
Step-by-step explanation:
A spinner is divided into 7 equal regions, numbered 9 through 15. An arrow is spun and lands on one of the numbers. Which of the following best describes the probability of the arrow landing on a number that is greater than 13?
A.
0.143
B.
0.286
C.
0.429
D.
0.571
Therefore , the solution of the given problem of probability comes out to be P =0.286(approx).
Define probability.Probability is the likelihood or potential for something to event. For instance, there is only one way to get a head and a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) must equal 12. Classical: (equally likely results) (equally probable outcomes) S, the sample location (the collection of all distinct outcomes that could occur), Definition of Relative Frequency and Subjective Probability.
Here,
Given : S = {9,10,11,12,13,14,15}
If A is a subset of S, A could be {14,15}.
If a subset A represents the complement of spinning a number greater than 13, its sample space is A = {14,15}.
Thus,
To find the probability that it will land on number greater than 13
P = likelihood of event / total no of events
=> P = 2/7
=> P = 0.2857
=> P =0.286(approx)
Therefore , the solution of the given problem of probability comes out to be P =0.286(approx).
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using factorization middle school way ☹️
On solving the provided question, we can say that - by the prime factors we have x^2 + 1 +2x = X= -1, -1
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
here we have the equation,
[tex]x^2 + 1 + 2x\\[/tex]
(x+1)(x+1)
x = -1, -1
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Gregory(g) is 20 years older than his cousin Mark(m). Mark is 6 years younger than his
sister Louanne(L). Write an expression to represent the sum of their ages.
An expression to represent the sum of their ages is as follows.
g = 14 + L
How do you figure up the total age?If the ratio of the ages of X and Y is p:q and their sum is X, then the following formula can be used to calculate Y's age: Age of Y = Y/Total Ages x Total Ratios. Age of Y = (p+q) q x A.
According to the given information:Assume that L is Louannel's sister's age, m is Mark's age, and g is Gregory's age.
Gregory's age difference with his cousin Mark, who is 20 years older (m).
∴ g = 20 + m .............(1)
Also given that Mark is 6 years younger than his sister Louanne(L)
∴ m = L - 6 ............(2)
Now, substituting m = L - 6 from (2) in (1),
∴ g = 20 + L - 6
∴ g = 14 + L
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PLZ HELP! I WILL GIVE BRAINLIEST! Factor 400 completely. Write all prime factors in order and use the 'power' notation.
Answer:
400= 2 x 2 x 2 x 2 x 5 x 5 = 2/4 x 5/2
What is the least common denominator?
Answer:
LCD = 24xyz
Step-by-step explanation:
Answer:
24
hope this helps
have a good day :)
Step-by-step explanation:
(8.5 x 10^3) (2 x 10^5)
Answer:
Simplified = 1.7×109
1.7×109 = 185.3
The following magazines are in a rack at a doctor's office.
• 1 sports magazine
• 2 movie magazines
• 3 news magazines
• 3 science magazines
Gwen will choose a magazine at random, put it back, and choose another magazine. What is the probability that she will choose a science magazine and then a movie magazine?
A: 2/27
B: 1/12
C: 5/9
D: 7/12
help pls asap gotta ace this bc my grades bad
Answer:
This is super simple! No need to worry.
Step-by-step explanation:
Just add the two results from the aquarium and amusement park for both the teacher and the students!
Soooo it'd look something like this lol
8 + 32 = 40 students were polled
5 + 5 = 10 teachers were polled
Form the quadratic equation whose one root is 2 + 2^(1/2)
9514 1404 393
Answer:
x^2 -4x +2 = 0
Step-by-step explanation:
The other root is the conjugate of the given one, so is 2-√2. The quadratic equation in factored form is then ...
(x -2-√2)(x -2+√2) = 0
Expanding this, we get ...
(x -2)^2 -(√2)^2 = 0
x^2 -4x +4 -2 = 0
x^2 -4x +2 = 0 . . . . the equation you're looking for
Logan invested $180 in an account paying an interest rate of 2.6% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 12 years?
Answer:
250
Step-by-step explanation:
Compounded Continuously:
A=Pe^{rt}
A=Pe
rt
P=180 r=0.026 t=12
Given values
A=180e^{0.026(12)}
A=180e
0.026(12)
Plug in
A=180e^{0.312}
A=180e
0.312
Multiply
A=245.90784475
A=245.90784475
Use calculator (with e button)
A\approx 250
A≈250
What is the importance of constructing a probability distribution for a random variable in interpreting data?
A probability distribution model is a guide you use to fit a random variable in order to generalize its behavior.
A probability distribution is a list of all of the possible outcomes of a random variable, along with its corresponding probability values.
A probability distribution links each outcome of a random variable or process with its probability of occurrence.
A probability distribution model is a guide you use to fit a random variable in order to generalize its behavior.
These models have a mathematical background, and can be very picky. For them to work properly, the random variable you are trying to fit in must meet different assumptions so that the outcomes of the model have the correct probabilities, and also so that you can test and validate the model against real data from the random variable.
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How do you solve a math problem step by step?
Reading a math word problem through to the end will help you comprehend what you need to do in order to solve it. After reading it, you may determine which components of the issue that need to be resolved are the most important and which are not.
There are few basic steps to be followed while solving any mathematics problem:
1. Read and understand the problem.
2. Identify what is given and what is needed to solve the problem.
3. Choose an appropriate strategy to solve the problem.
4. Carry out the strategy.
5. Check your answer to make sure it is correct.
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3: 5 and 2:10 is are equivalent . explain
The ratios are not equivalent.
the piece wise defined function f(x) is graphed below. What is the value of f(2)? PLS HELP THIS IS TIMED
Answer:
B
Step-by-step explanation:
We have to look at the full dot
#1: The equation below describes the relationship between
the number of months (x) since a customer began renting a
storage unit and the total amount of money (y), in dollars, the
customer has paid to the storage facility.
`y=20x+35
Which statement describes a solution of the equation based
on the number of months the customer has rented the storage
unit?
A. After exactly 355 months, the customer has paid $16.
B. After exactly 16 months, the customer has paid $355.
C.After exactly 320 months, the customer has paid $16.
D.After exactly 16 months, the customer has paid $320.
The correct option for the given linear equation is option (B).
What is a linear equation?
An equation is said to be linear if the maximum power of the variable is always 1. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
The given equation is y =20x + 35
y = total amount of money
x = number of months the customer has been renting the storage unit
A) If x = 355
y = 20 * 355 + 35 = $7135
This is not the correct option.
B) If x = 16
y = 20*16 + 35 = $355
This is the correct option.
C) if x = 320
y = 20 * 320 + 35 = $6435
This is not the correct option.
D) If x = 16
y = 20*16 + 35 = $355
This is not the correct option.
Therefore the correct option for the given linear equation is option (B).
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Help please with this maths
The radius of the sphere is 9 centimeters.
What is the surface area of a sphere?The area of the outer surface of a sphere is the surface area of a sphere.
And its formula:
The surface area of the sphere is 4πr².
Where r is the radius of the sphere.
Given:
The surface area of the sphere is 4πr².
Where r is the radius of the sphere.
So,
surface area of the sphere = 4πr²
324π cm² = 4πr²
Simplifying,
r² = 324π/4π
r² = 324/4
r² = 81
r = 9
Therefore, the radius is 9 centimeters.
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During the summer holidays sarah earns pocket money by mowing lawn. She can mow 6 lawns in 1 1/2 and clean the pool in one-sixth of an hour
Answer:
It will take Sarah 2 1/2 hours to mow 10 lawns
It will take Sarah 1 2/3 hours to clean 10 pools
Step-by-step explanation:
During the summer holidays, Sarah earns pocket money by mowing the lawn. She can mow 6 lawns in 1 1/2 hour and clean a pool in one-sixth of an hour. How long does Sarah take to clean 10 pools and 10 lawns?
Number of lawns : Time to mow lawns = 6 : 1 1/2
= 6 : 3/2
Number of lawns : Time to mow lawns = 10 : x
6 : 3/2 = 10 : x
6 ÷ 3/2 = 10/x
6 * 2/3 = 10/x
12/3 = 10/x
Cross product
12 * x = 3 * 10
12x = 30
x = 30/12
x = 2 6/12
x = 2 1/2 hours
It will take Sarah 2 1/2 hours to mow 10 lawns
Number of pools cleaned : time taken = 1 : 1/6
Number of pools cleaned : time taken = 10 : x
1 : 1/6 = 10 : x
1 ÷ 1/6 = 10/x
1 * 6/1 = 10/x
6 = 10/x
Cross product
6 * x = 10
6x = 10
x = 10/6
x = 1 4/6
x = 1 2/3 hours
It will take Sarah 1 2/3 hours to clean 10 pools
Fill in the blank question.
Miss Wade's science class of 20 students is going on a field trip to the zoo. Each student will also take a train ride around the zoo. Mr. Sexton's class of 25 students is going on a field trip to the state park and will take a canoe trip. Admission to the zoo is twice that of the state park's entry fee as shown in the table. Each group will spend the same total amount of money.
The admission fee for the zoo and for the state park is given as follows:
Zoo: $13.State park: $6.5.How to model the situation?For the zoo, the costs are divided as follows:
Admission: 2x per student.Train ride: $3.25 per student.20 students are going to the zoo, hence the total cost spent at the zoo is given as follows:
20(2x + 3.25) = 40x + 65.
For the state park, the costs are divided as follows:
Admission: x per student.Train ride: $6.50 per student.25 students are going to the state park, hence the total cost spent at the state park is given as follows:
25(x + 6.50) = 25x + 162.50.
The costs spent at both parks are the same, hence the value of x can be obtained as follows:
40x + 65 = 25x + 162.5
15x = 97.5
x = 97.5/15
x = 6.5.
Hence the admission fees are given as follows:
Zoo: $13, as 2x = 13.State park: $6.5, as x = 6.5.Missing InformationThe table is given by the image presented at the end of the answer.
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(2x+6y) exponent 2 with solution po thanks
Answer: (2x+6y)^2 = (2x+6y)(2x+6y) = 4x^2 +12xy + 12yx + 36y^2 = 4x^2 + 24xy + 36y^2
So the result of (2x+6y)^2 is 4x^2 + 24xy + 36y^2
help pls, i'm stuck on this question
Answer:
∠x = 60°
Step-by-step explanation:
first:
∠a = 60° was given
the sides on each side of ∠a are equal so their opposite angles are equal also.
The sum of the interior angles of any triangle is 180°
The angles opposite ∠a are (180° - 60°)/2 = 60° each
Second:
∠b = 60° was given
so the angles opposite ∠b are also 60° each
Third:
the 2 angles opposite x are both 60° each because they are both vertical angles to 60°
That leaves ∠x to be 180° - 60° - 60° = 60°
I hate math. truly.
Question: Which is the solution to the inequality?
1/4 + x < 5/6
Answer Choices:
A: x < 7/12
B: x > 7/12
C: x < 1 1/12
D: x > 1 1/12
Answer:
A: x<7/12
Step-by-step explanation:
I hate math too :)
The sign wouldn't be flipped cause you don't have to divide, and 5/6 - 1/4 is 7/12. Hope this helps
The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys.
Company A: 1/5=5 25/5=5 50/10=5 75/15=5.
These ratios are all equivalent
This relationship is proportional.
company B: 5/1=5 20/5=4 40/10=4 69/15=4.
These ratios are not all equivalent.
This relationship is not proportional.
Is the ratio constant or varying for company B? Explain
When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.
Find the equivalent ratio by what method?Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you can determine the equivalent ratio. Finding equivalent fractions follows the same procedure.
A ratio formula is what?The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.
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Find the measure of the missing angles.
Answer:
c = 110-degrees
b = 70-degrees
Step-by-step explanation:
for c:
linear pair which means it equals 180-degrees
70 + c = 180 *subtract 70 from both sides*
c = 110
for b:
vertical angles are equal
b = 70-degrees
What is 0.632 as a fraction? Move numbers to the blanks to complete the fraction.
8
79
125
313
457
495
632
999
Answer:
Step-by-step explanation:
Converting 0.632 to a fraction, Step-by-Step
Step 1:
The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:
\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}
1×1000
0.632×1000
=
1000
632
Step 3:
Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:
\frac{632}{1000} = \frac{79}{125}
1000
632
=
125
79
Help no links
Mr. McGill is solving the following problem: 42x=163. Mr. McGill set 2x=3 and got x=32 as his answer. Tell the mistake Mr. McGill made and tell the correct answer.
Answer:
Hmmmm. Mr. McGill seems a little lost.
At first, I thought he might have divided both sides by 21 (to get 2x on the left), but look what happens on the right side of the equation!
[tex]42x=163\\\\2x=54\,\, 1/3[/tex] (not 3, for sure)
I think Mr. McGill needs to take the class you're in!