Answer:
the mistake was in subtracting 21.6 from 13.8
Step-by-step explanation:
the answer was suppose to be -7.8 and not 35.4
Answer:
the mistake was in subtracting 21.6 from 13.8
Step-by-step explanation
the answer was suppose to be -7.8 and not 35.4
a/4 - 5/6 = -1/2
URGENT!
ACTUALLY DO THE MATH
Get it right and ill make the first person the brainiest!
Answer:
a = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
[tex]\frac{a}{4}[/tex] - [tex]\frac{5}{6}[/tex] = - [tex]\frac{1}{2}[/tex]
multiply through by 12 ( the LCM of 4, 6 and 2 ) to clear the fractions
3a - 10 = - 6 ( add 10 to both sides )
3a = 4 ( divide both sides by 3 )
a = [tex]\frac{4}{3}[/tex]
Answer:
[tex]a=\frac{4}{3}[/tex]
Step-by-step explanation:
Move all terms not containing [tex]a[/tex] to the right side of the equation.
Add [tex]\frac{5}{6}[/tex] to both sides of the equation.
[tex]\frac{a}{4}=-\frac{1}{2} +\frac{5}{6}[/tex]
To write [tex]-\frac{1}{2}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{3}{3}[/tex].
[tex]\frac{a}{4}=-\frac{1}{2}*\frac{3}{3} +\frac{5}{6}[/tex]
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
[tex]\frac{a}{4}=-\frac{3}{2*3} +\frac{5}{6}[/tex]
[tex]\frac{a}{4}=-\frac{3}{6} +\frac{5}{6}[/tex]
Combine the numerators over the common denominator.
[tex]\frac{a}{4}=\frac{-3+5}{6}[/tex]
Add [tex]-3[/tex] and [tex]5[/tex] .
[tex]\frac{a}{4}=\frac{2}{6}[/tex]
Cancel the common factor of [tex]2[/tex] and [tex]6[/tex].
Factor [tex]2[/tex] out of [tex]2[/tex].
[tex]\frac{a}{4}=\frac{2(1)}{6}[/tex]
[tex]\frac{a}{4}=\frac{2*1}{2*3}[/tex]
Cancel the common factor.
[tex]\frac{a}{4}=\frac{1}{3}[/tex]
Multiply both sides of the equation by [tex]4[/tex].
[tex]4\frac{a}{4} =4(\frac{1}{3})[/tex]
Simplify both sides of the equation.
Simplify the left side.
Cancel the common factor of [tex]4[/tex].
[tex]a=4(\frac{1}{3})[/tex]
Simplify the right side.
Combine [tex]4[/tex] and [tex]\frac{1}{3}[/tex]
[tex]a=\frac{4}{3}[/tex]
how many ways are there to select 5 scoops of ice cream to put into a bowl, chosen from baskin robbins 31 flavors? a flavor may be selected multiple times.
In permutation, ³¹C₅ are there to select 5 scoops of ice cream to put into a bowl .
What are some examples of permutation?
A permutation is a set up of things in a specific order. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. The components of set A cannot be arranged in any other way, as you can see.Total ice cream flavor n = 31 flavor
selection of (r) = 5 scoop
total number of ways to select 5 scoops of ice cream from 31 flovers
= ³¹C₅
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Solve using proportions: If a 4-pound roast takes 140 minutes to cook, how long should a 5-pound roast take to cook?
Step-by-step explanation:
[tex]4pound \: roast \: = 140 \: minutes \\ 5 \: pounds \: roast \: = {?} \\ then cross multiplication \\ 140 \times 5 \: divide \: by \: 4 \\ 700 \div 4 = 175 \\ 5 \: pound \: roast \: take \: 175 \: minutes[/tex]
a popular resort hotel has 300 rooms and is usually fully booked. about 6% of the time a reservation is cancelled before the 6:00 p.m. deadline with no penalty. what is the probability that at least 275 rooms will be occupied? use the binomial distribution to find the exact value. a. 0.01 b. 0.96 c. 0.93 d. 0.85
When binomial distribution is used, the probability that at least 275 rooms are occupied is 0.96
Option b. is correct
We have the following parameters:
sample, n=300
proportions of rooms reserved, p=6%
We first get the sample mean,
Sample mean=n*p
=300*6%
=18
Now, we get population mean according to binomial distribution, μ'
μ=n-sample mean
=300-18
=282
We get the standard deviation, σ
σ=(sample mean*(1-p))^1/2
=(18*(1-6%))^1/2
=4.11
We now, calculate z-score:
z=(x-μ)/σ, given x should be at least 275
z=(275-282)/4.11
=-1.703
Now, we have p(x>275)=p(z>-1.703)
From z-score of probabilities, we have p(z>-1.703) as 0.95572
So, p(x>275)=0.95572
=0.96
Hence, the probability that at least 275 rooms are occupied is 0.96
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you want to obtain a sample to estimate a population proportion. based on previous evidence, you believe the population proportion is approximately 40%. you would like to be 90% confident that your estimate is within 1.5% of the true population proportion. how large of a sample size is required?
The largest sample size required is 2886.4.
Here we have to calculate how large of a sample size is required.
The formula:
(Z ∝I2/ E)² × P( 1- P)
The given data:
Margin error (E) = 1.5%
=0.015
As it is given that 90% confident that your estimate is within 1.5% of the true population proportion, therefore we have:
The level of significance(∝) = 1 - 0.90
= 0.10
The z value for the 90% confidence is 1.645
Therefore the largest of a sample size is required = ( 1.645/ 0.015)²× ( 0.4)(1- 0.4)
= 2886.4
The largest a sample size required is 2886.4
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pls help! Last year, 180 new houses were built in a neighborhood. So far this year, 5/6 of them have been sold. How many new houses have been sold this year? Write your answer in simplest form.
Answer:
150 Houses
Step-by-step explanation:
180/6=30. Every 1/6 is 30 houses. Therefore you multiply 30x5 to get 150. 150 is 5/6 of the houses sold.
a restaurant has special menu that features three choices of salad, six choices of entree, and eight choices of dessert. how many different three course meals could you order
72 three course meals we can order.
Question states that;
A restaurant offers a special menu with three salad options, six meal options, and eight dessert options.
Counting Principle:
The counting rule is another name for the Fundamental Counting Principle. It's a way to figure out how many possible outcomes there are in a probability word problem. Probability is the likelihood that an event will occur. An event's probability is always a number between 0 and 1. The probability of all events added together equals one.
We need to find how many three course meals we can order;
Total number of ways,
P(A) = 3 * 6 * 8
P(A) = 72
72 three course meals we can order.
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Ms. Grace bought 3 bags of dog treats for $7.38. What is the cost per bag of dog treats?
Answer:
$2.46
Step-by-step explanation:
7.38/3 = 2.46
2.46 x 3 = 7.38
a sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. determine the decision rule for rejecting the null hypothesis, h0, at the 0.10 level.
The alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
Given that;
A sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage.
To get decision rule for rejecting the null hypothesis, h0, at the 0.10 level;
n = 900
P = 0.34
p = 0.31
α = 0.10
Claim: More than 31% do not malfunction within the first 1000 hours of operation.
The null and alternative hypothesis must be stated.
This is a right-tailed test because the claim is directional to the right side (> type).
Therefore, the alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
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14. the mean price of a pound of ground beef in 75 cities in the midwest is $2.11 and the standard deviation is $0.56. suppose the histogram of the data shows that the distribution is unimodal and symmetrical. a local grocer is selling a pound of ground beef for $3.50. what is this price in standard units? assuming the empirical rule applies, would this price be unusual or not? round to the nearest hundredth.
For a unimodal distribution which is symmetrical with a mean price of $2.11 and standard deviation of $0.56, a local grocer’s price of $3.50 in standard units would be 2.282 and it is unusually expensive.
A unimodal distribution refers to a distribution with one clear peak as the values increase to a single highest point after which they. It can be symmetrical or non-symmetrical. A symmetrical distribution refers to a distribution whose mean, mode, and median are all equal.
The standard score (z) is given by:
z = (x - µ)/σ where µ is the mean and σ is the standard deviation.
To determine the value of z for $3.50 price:
z = (3.5 – 2.11)/0.56 = 2.482
From the z-table, the probability of z ≥ 2.282
P (z ≥ 2.282) = 1 – P (z < 2.282) = 1 – 0.98876 = 0.0112 or 1.12%
Hence, the price of $ 3.50 is unusually high.
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Sam catches a sale on airline tickets that are being discounted 15%. He purchases a flight that normally costs $235. What is the new price of the flight?
The new price of the flight is $208.25
How to determine the new price of the flight?In this question, we have the following parameters
Discount proportion = 15%
Cost of flight = $245
This means that
New price = Cost of flight x (1 - Discount proportion)
Substitute the known values in the above equation, so, we have the following representation
New price = $245 x (1 - 15%)
Evaluate the product
New price = $208.25
Hence, th new price is $208.25
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Sabrina needs more than 42 ft.³ of soil to top up her raised garden bed. each bag of soil contains 1.75 ft.³. Write and solve any inequality to find how many bags of soil Sabrina needs
The inequality that represents the quantity of bags of soil Sabrina needs is 1.75x > 42
The bags of soil needed is 24 bags
What is inequality?Inequality as used in math refers to relations that are not precisely equal
How to determine the bags of soil Sabrina needsSabrina needs more than 42 ft.³ of soil to top up her raised garden bed
> 42 ft³
each bag of soil contains 1.75 ft.³
let the number of bags of soil be x, such that
1.75x > 42
x > 42 / 1.75
x > 24
Sabrina needs at least 24 bags of soil
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PLEASE HELP MEEE!!!!!!!!!
Each function operation should be matched with what it is equivalent to as follows:
f(x) + g(x) = -2x² + x + 6.
g(x) - f(x) = -2x² - 5x + 2.
f(x) · g(x) = -6x³ - 10x² + 8x + 8.
h(x) - f(x) = 3x² - 7x - 2
f(x) · h(x) = 9x³ - 6x² - 8x.
f(x) + g(x) + h(x) = x² - 3x + 6.
How to determine the solutions of the given function?In order to determine the solutions of the given function, we would have to evaluate each of the function based on the required mathematical operations as follows.
From the information provided, we have the following functions:
f(x) = 3x + 2
g(x) = -2x² - 2x + 4
h(x) = 3x² - 4x
f(x) + g(x) = 3x + 2 + (-2x² - 2x + 4)
f(x) + g(x) = 3x + 2 - 2x² - 2x + 4
Next, we would rearrange the function by collecting like terms as follows:
f(x) + g(x) = -2x² + (3x - 2x) + (2 + 4)
f(x) + g(x) = -2x² + x + 6 (solution).
g(x) - f(x) = -2x² - 2x + 4 - (3x + 2)
Opening the bracket, we have:
g(x) - f(x) = -2x² - 2x + 4 - 3x - 2
Next, we would rearrange the function by collecting like terms as follows:
g(x) - f(x) = -2x² + (-2x - 3x) + (4 - 2)
g(x) - f(x) = -2x² - 5x + 2 (solution).
f(x) · g(x) = (3x + 2) × (-2x² - 2x + 4)
Opening the bracket, we have:
f(x) · g(x) = -6x³ - 6x² + 12x - 4x² - 4x + 8
Next, we would rearrange the function by collecting like terms as follows:
f(x) · g(x) = -6x³ + (-6x² - 4x²) + (12x - 4x) + 8
f(x) · g(x) = -6x³ - 10x² + 8x + 8 (solution).
h(x) - f(x) = 3x² - 4x - (3x + 2)
h(x) - f(x) = 3x² - 4x - 3x - 2
h(x) - f(x) = 3x² - 7x - 2 (solution).
f(x) · h(x) = (3x + 2) × (3x² - 4x)
f(x) · h(x) = 9x³ - 12x² + 6x² - 8x
f(x) · h(x) = 9x³ - 6x² - 8x (solution).
f(x) + g(x) + h(x) = 3x + 2 + (-2x² - 2x + 4) + (3x² - 4x)
f(x) + g(x) + h(x) = -2x² + x + 6 + 3x² - 4x
f(x) + g(x) + h(x) = x² - 3x + 6 (solution).
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4. A park charges $8 for adults and $4 for kids. How many of each type of ticket was sold if a total of 325 tickets were sold for a total of $1812?
Answer:
1300 and 750
Step-by-step explanation:
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the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that thesum of the four numbers on each face is the same. what is this common sum?
The common sum is 18 as "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same".
What is sum?A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. The outcome or conclusion we arrive at when we add two or more numbers is known as the SUM. Addends are the numbers that are added.
Here,
The sum of the numbers on one face of the cube is equal to the sum of the numbers on the opposite face of the cube; these 8 numbers represent all of the vertices of the cube.
=(1+2+3+4+5+6+7+8)/2
=18
Since "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same," the common sum is 18.
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Need help asap
Solve by using elimination. Express your answer as an ordered pair.
3x−2y=11
3x−y=7
The solution to the given set of systems of equations is (x, y) = (1, -4).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let's determine the solution using the elimination Method
3x−2y=11 (Equation 1)
3x−y=7(Equation 2)
Multiply the second equation by 2.
6x - 2y = 14 (Equation 3)
Now subtract the first equation from third to eliminate the y.
6x - 2y - (3x - 2y) = 14 - 11
3x = 3
x = 1
Now to find the value of y,
3x−y=7
3(1) − y = 7
y = 7 - 3
y = -4
Therefore, the solution to the given set of systems of equations is (x, y) = (1, -4).
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Find X in all three problems below
The lengths for the missing side of each case, determined by the use of trigonometric functions, are listed below:
Case D: 50.513
Case E: 46.165
Case F: 2.052
How to determine missing lengths of right triangles by trigonometric functions
In this problem we have three cases of right triangles, each of which has an unknown side length. Each length can be found by using trigonometric functions. Now we proceed to determine it for each case:
Case D
tan 29° = 28 / x
x = 28 / tan 29°
x ≈ 50.513
The missing side length is approximately 50.513 units.
Case E
tan 18° = 15 / x
x = 15 / tan 18°
x ≈ 46.165
The missing side length is approximately 46.165 units.
Case F
cos 70° = x / 46
x = 46 · cos 70°
x ≈ 2.052
The missing side length is approximately 2.052 units.
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Given f(x) = 19 - 4x|, find f (7)
The value of f(7) is 9 given that f(x) = |19 - 4x|
How to determine the value of f(7)?A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
Given: f(x) = |19 - 4x|
To find f(7), substitute x = 7 into f(x) = |19 - 4x|:
f(7) = |19 - 4(7)| = |19-28| = |-9| = 9
Note: The sign | | means absolute, the sign of any value inside it will be discarded and only the number is written
Therefore, f(7) is 9
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A construction company is planning the foundation for a house. Stakes have been placed in the ground to mark the corners of the foundation. The four sides formed are measured as 20 feet, 20 feet, 48 feet, and 48 feet. The diagonal of the quadrilateral formed is measured to be 54 feet.
What type of triangle is formed by the diagonal and two sides of the current foundation plan?
Answer:
See below
Step-by-step explanation:
It is NOT a right triangle or the diagonal would measure 52 feet (instead of 54 feet) ....it is an OBTUSE triangle
a small airline runs commuter flights with a plane that holds 10 people. each ticket-holder has a 10% chance of not showing up, so the airline sells 12 tickets for each flight. which is an appropriate plan for a simulation that uses a table of random digits to estimate the probability that exactly ten people show up for the flight?
The probability that exactly 10 people will show up is 0.230
Let X measure the number of people (out of 12) who show up for a flight. For each passenger
we have a 90% chance of showing up, so X is a binomial random variable with n = 12 and p = 0.90.
(b) Everyone gets a seat when X ≤ 10. We have to find the probability when exactly 10 people show up for the flight , so we use the binomial probability for P(10)
∴ P(10) = [tex]C^{n} _{x} p^{x}(1-p)^{n-x}[/tex]
P(10) = 0.230
So , the probability that exactly 10 people show up for the flight is 0.230 .
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Here you go LOL didn't get all the files. I need help TWT
Answer:
First option
Step-by-step explanation:
→ Define domain
The set of x values a function can take
→ Identify
2 to negative infinity
if a password is to have 4 digits, each from 0 to 9, what is the probability that there will be no repeats on the digits?
The probability that there will be no repeats on the digits is 0.504.
What is meaning of probability?
The ratio of favorable outcomes with the total number of outcomes is known as probability of that event.
The number of digits of the password is 4.
The numbers from 0 to 9 is 10.
If the digit can repeat, then we can chose first digit in 10 ways, the second digit in 10, third digit in 10 ways and fourth digit in 10 ways.
The total number of ways is 10 × 10 × 10 × 10 =10000.
If the digit can't repeat, then we can chose first digit in 10 ways, the second digit in 9 (because we can't use first digit) , third digit in 8 ways (because we can't use first digit and second digit) and fourth digit in 7 ways(because we can't use first digit, second digit, and third digit).
The total number of ways is 10 × 9 × 8 × 7 =5040.
The favorable outcomes for this event is 5040.
The total number of outcomes is 10000.
The required probability is 5040/10000 = 0.504.
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plsssssssshelpppppppppp
a) The correct equation to represent the given condition is;
⇒ 4 (x + $3) = $36
Where, x represents the amount Pablo parents added in each day.
b) The amount to added by his parents in his account = $6
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
For 4 days, Pablo put $3 into his account.
And, His parent also add the some money to his saving account.
In the end, there was a total $36 in his account.
Now,
Let the amount Pablo parents added in each day = x
So, We can formulate;
⇒ 4 (x + $3) = $36
Solve for x as;
⇒ 4x + $12 = $36
⇒ 4 x = $36 - $12
⇒ 4x = $24
Divide by 4 both side, we get;
⇒ x = $6
Thus,
a) The correct equation to represent the given condition is;
⇒ 4 (x + $3) = $36
Where, x represents the amount Pablo parents added in each day.
b) The amount to added by his parents in his account = $6
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What does negative 3 over 5 > −2 indicate about the positions of negative 3 over 5 and −2 on the number line? (1 point) a negative 3 over 5 is located on the right of −2 b negative 3 over 5 is located on the left of −2 c negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 d negative 3 over 5 is located on the left of 0 and −2 is located on the right of 0
This is worth 40 points pls help
Answer:
−2 c negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 d negative 3 over 5
Step-by-step explanation:
imma lose all my points but someone PLS HELP ME OUT WITH THIS I really need it done ASAP PLS
increase the amount of the ingredients by 5 and by 20
If increase the amount of the ingredients by 5 and by 20 is 51.75 grams and 207 grams respectively.
Given that, Ingredients: 2 teaspoons Worcestershire sauce
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
Converted to Metric measurements : 10.35 g
Increased by 5 = 10.35 × 5
= 51.75 grams
Increased by 20 = 10.35 × 20
= 207 grams
Therefore, if increase the amount of the ingredients by 5 and by 20 is 51.75 grams and 207 grams respectively.
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Which of the following equations have exactly one solution?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
6
x
−
6
=
15
x
+
15
6x−6=15x+156, x, minus, 6, equals, 15, x, plus, 15
(Choice B)
B
6
x
+
15
=
6
x
+
15
6x+15=6x+156, x, plus, 15, equals, 6, x, plus, 15
(Choice C)
C
6
x
−
15
=
6
x
+
15
6x−15=6x+156, x, minus, 15, equals, 6, x, plus, 15
(Choice D)
D
6
x
−
6
=
6
x
+
15
6x−6=6x+156
The equation which has exactly one solution is 6x - 6 = 15x + 15.
The correct answer option is option A
Solving equations with one solutionCheck all that applies:
6x - 6 = 15x + 15
6x - 15x = 15 + 6
- 9x = 21
divide both sides by -9
x = 21/-9
x = -2.33
6x + 15 = 6x + 15
6x - 6x = 15 - 15
0 = 0
False
6x - 15 = 6x + 15
6x - 6x = 15 + 15
0 = 30
False
6x - 6 = 6x + 15
6x - 6x = 15 + 6
0 = 21
False
In conclusion, the 6x - 6 = 15x + 15 has only one solution.
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Help find the Perimeter of 4,5,6 please
The perimeters of the given figures 4, 5, 6 are 27 m, 140.76 cm and 28 inches respectively.
We need to find the perimeter of given figures.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
4) Now, sum of all the sides
= 5+3.5+1.5+3.5+5+3.5+1.5+3.5 m
= 27 m
5) Here, radius = Diameter/2 = 17 cm
Perimeter = 2 semicircles+2(17) cm
= 2 × 1/2 πr + 2×17
= 2 × 3.14 × 17 + 34
= 140.76 cm
6) In the given figure here, there are 4 similar triangles
= 4(4+3) inches
= 4 × 7
= 28 inches
Therefore, the perimeters of the given figures 4, 5, 6 are 27 m, 140.76 cm and 28 inches respectively.
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A family of four goes to a movie theater and spends $26.50. They buy 2 children's tickets at
$3.50 per ticket, 2 adult tickets, and 3 boxes of popcorn at $2.50 per box. What is the cost of
an adult ticket?
(Algebra)
Answer:
$6.50
Step-by-step explanation:
3.50(2)+2x+2.50(3)=26.50
6.00+2x+7.50=26.50
13.50+2x=26.50
2x=13.00
x=6.50
Find the slope of the line that passes through the pair of points (8, −2), (1, 1)
The slope of the line that passes through the given pair of points is, -3/7.
What is slope of the line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.
Given: (8, -2), (1, 1)
Since, if two points [tex](x_1, y_1), (x_2, y_2)[/tex] are given then slope (m) is defined as,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex].
Here,
[tex](x_1, y_1) = (8, -2)\\(x_2, y_2)=(1, 1)[/tex]
So, the slope can be defined as,
[tex]m = \frac{1-(-2)}{1-8} \\m=\frac{3}{-7} \\m=-\frac{3}{7}[/tex]
Hence, the slope of the line that passes through the given pair of points is, -3/7.
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angelina drove at an average rate of 80 kmh and then stopped 20 minutes for gas. after the stop, she drove at an average rate of 100 kmh. altogether she drove 250 km in a total trip time of 3 hours including the stop. which equation could be used to solve for the time t in hours that she drove before her stop?
The equation that could be used to solve for the time t in hours that she drove before her stop is 80t + 100(8/3 - t) = 250.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let t = time she drove before her stop
If the total trip time is 3 hours including the stop, which took 20 minutes, then the time she drove after the stop is 3 - t - 1/3 or 8/3 - t.
If altogether she drove a distance of 250 km, then the sum of the products of the rate of speed and time each drive is equal to 250.
(80 km/h)(t) + (100 km/h)(8/3 - t) = 250
Simplify the equation.
80t + 100(8/3 - t) = 250
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