Thomas has constant speeds for both running and walking. When a down-escalator is moving, Thomas can run down it in
15
seconds or walk down it in
30
seconds. One day, when the escalator was broken (and stationary), it took Thomas
20
seconds to run down it.
How long, in seconds, would it take Thomas to walk down the broken escalator?
Answers
Answer:
40 seconds
Step-by-step explanation:
Ratio of 15:30 = 1:2
20:x
x = 20 x 2 using ratio, also stop putting these Maths challenge qs on website.
x = 40 :)
Related Questions
help, please
Given the triangle shown on the grid below, which graph shows the triangle reflected over the x-axis?
Answers
Step-by-step explanation:
Answer attached.
Hope it helps :)
Two parallel lines are crossed by a transversal. Horizontal and parallel lines y and z are cut by transversal x. At the intersection of lines y and x, the top right angle is (2 k + 11) degrees. At the intersection of lines z and x, the bottom left angle is 131 degrees. What is the value of k?.
Answers
The number k is equal to 60 when the top right angle at the intersection of the lines y and x is (2 k + 11) degrees and the bottom left angle is 131 degrees.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A mathematical expression is a sentence that includes numbers, variables, or both. The equal sign is never used in expressions. A mathematical statement stating the equality of two expressions is known as an equation.
Here,
Those two angles have the same measure. so you have,
2k+11=131
22k=120
k=60
The value of k where at the intersection of lines y and x, the top right angle is (2 k + 11) degrees and at the intersection of lines z and x, the bottom left angle is 131 degrees is 60.
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From a table of integrals, we know that for ,≠0a,b≠0,
∫cos()=⋅cos()+sin()2+2+.∫eatcos(bt)dt=eat⋅acos(bt)+bsin(bt)a2+b2+C.
Use this antiderivative to compute the following improper integral:
∫[infinity]01cos(3)− = limT→[infinity]∫0[infinity]e1tcos(3t)e−stdt = limT→[infinity] if ≠1s≠1
or
∫[infinity]01cos(3)− = limT→[infinity]∫0[infinity]e1tcos(3t)e−stdt = limT→[infinity] if =1.s=1. help (formulas)
For which values of s do the limits above exist? In other words, what is the domain of the Laplace transform of 1cos(3)e1tcos(3t)?
help (inequalities)
Evaluate the existing limit to compute the Laplace transform of 1cos(3)e1tcos(3t) on the domain you determined in the previous part:
()=L{e^1t cos(3)}=
Answers
"From a table of integrals, we know that for \(\(a \neq 0\)\) and \(\(b \neq 0\):\)
\(\[\int \cos(at) \, dt = \frac{1}{a} \cdot \cos(at) + \frac{1}{b} \cdot \sin(bt) + C\]\)
and
\(\[\int e^a t \cos(bt) \, dt = \frac{e^{at}}{a} \cdot \cos(bt) + \frac{b}{a^2 + b^2} \cdot \sin(bt) + C\]\)
Use this antiderivative to compute the following improper integral:
\(\[\int_{-\infty}^{0} \cos(3t) \, dt = \lim_{{T \to \infty}} \int_{0}^{T} e^t \cos(3t) \, e^{-st} \, dt = \lim_{{T \to \infty}} \text{ if } s \neq 1, \, \text{ or } \lim_{{T \to \infty}} \text{ if } s = 1.\]\)
For which values of \(\(s\)\) do the limits above exist? In other words, what is the domain of the Laplace transform of \(\(\frac{1}{\cos(3)} \cdot e^t \cos(3t)\)\)?
Evaluate the existing limit to compute the Laplace transform of on the domain you determined in the previous part:
\(\[L\{e^t \cos(3t)\\).
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some data mining algorithms require that variables are standardized (sometimes called normalized) to zero mean and standard deviation of 1.0. what is the reason for this?
Answers
The reason why some data mining algorithms require that variables are standardized to zero mean and standard deviation of 1.0 is because it helps to normalize the data and make it more comparable across different variables.
Standardizing the data helps to remove the impact of the scale of the variables on the analysis, allowing for more accurate comparisons and correlations between variables. By doing this, it ensures that no one variable has an undue influence on the results of the analysis. Standard deviation is a statistical measure that is used to measure the amount of variability or dispersion in a dataset. When data is standardized, it allows for a more accurate assessment of the relationship between variables and can improve the accuracy of the analysis. Overall, standardizing variables is a crucial step in the data mining process, as it helps to ensure that the results of the analysis are reliable and accurate.
The reason some data mining algorithms require variables to be standardized (or normalized) to a zero mean and a standard deviation of 1.0 is to ensure consistent and comparable scales for all variables involved. Standardizing variables helps in improving the performance and accuracy of the algorithms.
When variables have different scales or units, it can be challenging for algorithms to interpret their relative importance accurately. By transforming variables to have a zero mean and a standard deviation of 1.0, the algorithms can more effectively process and analyze the data. This standardization process is particularly important for distance-based and gradient-based algorithms, where scale differences can significantly impact the results.
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Felipe calculated that he uses about 545 gallons of fuel each year. His car's owner's manual says that it is approved to use regular fuel. How much money can he save each year by switching from premium fuel, at $4.59 per gallon, to regular fuel at $4.18 per gallon?
$0.41
$2,501.55
$223.45
$2,278.10
$4,779.65
Answers
Answer:
$223.45
Step-by-step explanation:
premium fuel: 4.59 x 545
= 2501.55
regular fuel: 4.18 x 545
=2278.1
2501.55-2278.1 = 223.45
PLS HELP solve the equation.
sqrt (x-1)^2=1-x
Answers
Answer:
The value of x is 1
Step-by-step explanation:
√(x – 1)² = 1 – x
x – 1 = 1 – x
x – 1 + 1 + x = 1 + 1 – x + x
2x = 2
2x/2 = 2/2
x = 1
Thus, The value of x is 1
-TheUnknownScientist 72
A business has a beginning capital of $3000.the owner makes a contribution of $1000. the net income of $2500 the end capital is $4500. how much was the owner withdraw?A$6500B$2000C$3000D$11000
Answers
Let be x the amount the owner withdrew. Then, we can write and solve the following equation:
\(\begin{gathered} \text{ Beginning capital }+\text{ Contribution }+\text{ Net income }-\text{ Owner withdraws }=\text{ End Capital} \\ \text{\$}3,000+\text{\$}1,000+\text{\$}2,500-x=\text{\$}4,500 \\ \text{\$}6,500-x=\text{\$}4,500 \\ \text{ Subtract 6500 from both sides} \\ \text{\$}6,500-x-\text{\$}6,500=\text{\$}4,500-\text{\$}6,500 \\ -x=-\text{\$}2,000 \\ \text{ Multiply by -1 from both sids} \\ -x\cdot-1=-\text{\$}2,000\cdot-1 \\ x=\text{\$}2,000 \end{gathered}\)Answer
The owner withdraws $2,000.
Hello friends, I'm from brainly Indonesia. Here I just want to walk :v
I will make a Quiz
7⁴ =
Easy..
Good luck
Answers
Answer:
7⁴ IS 28
I HOPE IT IS HELPFUL
Answer:
2401
Step-by-step explanation:
7×7×7×7
2401
hope it helps
halp :<<<<<<<<<<<<<<<
Answers
Answer:
122 so its 70%
Step-by-step explanation:
The scatter plot shows the length of a spring, in inches, when a stretch force, in pounds, is applied. The equation represents the linear model for this data. y = 0.73x + 1 What does the number 0.73 in the equation mean in this context? The spring has a length of 0.73 inch when no force is applied. The spring will stretch 0.73 inch for every pound of force applied. The spring has no stretch when a force of 0.73 pound is applied. The spring stretches at a rate of 0.73 pound per inch. The spring stretches a distance of 1 inch when a force of 0.73 pound is applied.
Answers
the correct answer is: The spring has a length of 1 inch when no force is applied.
The scatter plot shows the length of a spring when a stretch force is applied. The equation represents the linear model for this data.
y = 0.73x + 1
pretty simple
Using linear function concepts, it is found that the meaning of the slope of 0.73 in this context is that:
The spring will stretch 0.73 inch for every pound of force applied.What is a linear function?A linear function is modeled by:
\(y = mx + b\)
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, y is the length of the spring, considering a stretch force of x pounds, and the equation is:
\(y = 0.73x + 1\)
The slope is of 0.73, which means that, considering what x and y are:
The spring will stretch 0.73 inch for every pound of force applied.You can learn more about linear functions at https://brainly.com/question/24808124
Find the value of x
please help :>
Answers
Answer:
x=7
Step-by-step explanation:
5x+55=90
5x+55−55=90−55
5x=35
x=7
how much volume in one grain of rice
Answers
A grain of rice contains about 0.029 milliliters of volume.
A grain of rice is a tiny, ingestible seed that comes from either Oryza sativa (Asian rice) or Oryza glaberrima, two types of grass (African rice). A single grain of rice is round or oval in shape and measures about 3–4 millimeters in length. A grain of rice has a volume of 0.029 milliliters and a mass of approximately 0.05 grams. The type of rice and the method of processing affect the size and form of a single grain of rice. Over half of the world's population relies heavily on rice as a source of nutrition and as a staple food in many different cultures. Sushi, risotto, rice pudding, and many more recipes all use rice as an ingredient.
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PLEASE HELP TY
show all work
Answers
Answer:
36 cm
Step-by-step explanation:
\(V= \frac{4}{3} \pi r^{3}\)
\(3V= 4\pi r^{3}\)
\(r^{3}=\frac{3V}{4\pi }\)
\(r= 3\sqrt{\frac{3V}{4\pi } }\)
\(r=3\sqrt{\frac{3* 24429 cm^{3} }{4\pi } }\)
r=18 cm
diameter= d= 2r
d= 2(18cm)= 36 cm
explain how the following problem could be solved. then, solve the problem. a full-grown dog is about one-eighth as heavy as a cow. together, they weigh 360 kg.
Answers
The problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.
The weight of the cow, on solving the equation, is found to be 320 kg.
The weight of the full-grown dog = (1/8)*320 kg = 40 kg.
We assume the weight of the cow to be x kg.
The weight of a full-grown dog is given to be one-eight of a cow, that is, the weight of a full-grown dog = (1/8)*x = x/8 kg.
Thus, the sum of the weights of the full-grown dog and the cow = x/8 + x kg.
But, we are given that together, they weigh 360 kg.
This can be shown as the linear equation in the one variable:
x/8 + x = 360.
Thus, the problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.
To solve the problem, we solve the equation as follows:
x/8 + x = 360,
or, (9/8)x = 360 {Simplifying},
or, x = 360*8/9 {Cross-Multiplying},
or, = 320.
Thus, the weight of the cow, on solving the equation, is found to be 320 kg.
The weight of the full-grown dog = (1/8)*320 kg = 40 kg.
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Pleeeeaseeeee help algebra 1 plzzz I’m frrr
Answers
Answer:
d
Step-by-step explanation:
Set up, but do not evaluate, an integral for the area of the surface
obtained by rotating
y = ln x, 1 ≤ x ≤ 3
about the x-axis
Answers
Therefore, the set up integral for the surface area is given as ∫[1, 3]2πln(x)√[1+(1/x)²]dx.
To obtain the area of the surface, obtained by rotatingy = ln x, 1 ≤ x ≤ 3about the x-axis, the integral must be set up as follows:
We have the curve given as y = ln x, with the limits of integration being 1 ≤ x ≤ 3.
To obtain the surface area obtained by rotating the curve around the x-axis, we need to apply the formula for surface area, which is given as:
S = ∫[a, b]2πy(x)√[1+(dy/dx)²]dxwhere y = ln x, a = 1, and b = 3
Substituting the given values, we get:S = ∫[1, 3]2πln(x)√[1+(dy/dx)²]dxFor √[1+(dy/dx)²], we need to take the derivative of y = ln x and square it as follows:dy/dx = 1/x (differentiating ln x)
Squaring this, we get:1+(dy/dx)² = 1 + (1/x)²
Substituting back into the integral, we get:S = ∫[1, 3]2πln(x)√[1+(dy/dx)²]dx= ∫[1, 3]2πln(x)√[1+(1/x)²]dx.
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hey can someone help me
Answers
Answer:
need more info on question
Step-by-step explanation:
only b can be found b=40
I WILL BRAINIEST!!!
The two-way frequency table contains data about how students access courses.
Traditional Online Row totals
Computer: |28| |62| |90|
Mobile device: |46| |64| |110|
Column totals: |74| |126| |200|
What is the joint relative frequency of students who use a mobile device in an online class?
Answers
Answer: 32%
Step-by-step explanation:
The reason on why this answer is 32% is because in order to calculate joint relative frequency, you must have two values.
The first value is the one the question is asking you about. For this, it's mobile device in online classes, which is 64 on the table. Simply divide this number by the total of the table, which is normally on the bottom right. In this case, it's 200.
Now all that needs to be done is this:
\(\frac{64}{200}\) = 0.32, which is 32%.
The answer is 32%, C.
The joint relative frequency of students who use a mobile device in an online class will be 32% as the "Student who use a mobile device in online class=64 and total students=200".
What is joint relative frequency?The ratio of a frequency that is not in the total row or column to the total number of values or observations is known as joint relative frequency. In a two-way frequency table, the marginal frequency is the entry in the "total" for the column and the "total" for the row. These are the frequencies in a given category divided by the total number of data values. The term "joint frequency" refers to the joining of one variable from the row and one variable from the column. The ratio of the frequency in a specific category to the total number of data values is known as joint relative frequency.
Here,
Title Traditional Online Row totals
Computer: |28| |62| |90|
Mobile device: |46| |64| |110|
Column totals: |74| |126| |200|
The joint relative frequency of students who use a mobile device in an online class,
Student who use a mobile device in online class=64
Total students=200
64/200=0.32
0.32*100=32%
As "Students who use a mobile device in an online class=64 and total students=200," the joint relative frequency of students who use a mobile device in an online class will be 32%.
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Drag steps of the solution into order to solve for x in the equation 6(x-5) = 54
A. 6x – 30 = 54
B. 6x = 84
C. 6x = 24
D. x = 14
I need to figure out what order to put these in to get the answer I can only use three!
Answers
The steps of the solution into order to solve for x in the equation 6(x-5) = 54 are:
A. 6x – 30 = 54 B. 6x = 84 D. x = 14Given the expression 6(x-5) = 54
Expand the expression in parenthesis using the distributive law;
6x - 6(5) = 54
6x - 30 = 54
Add 30 to both sides
6x - 30 + 30 = 54 + 30
6x = 84
Divide both sides by 6
6x/6 = 84/6
x = 14
Therefore the steps of the solution into order to solve for x in the equation 6(x-5) = 54 are:
A. 6x – 30 = 54 B. 6x = 84 D. x = 14Learn more on equations here; https://brainly.com/question/2972832
-5 = -y - 3x
Write the equation in slope-intercept form. Please help me. :)
Answers
Answer:
y = -3x + 5
Step-by-step explanation:
You want it in y = mx + b form
-5 = -y - 3x
Add y to both sides
-5 + y = -y + y - 3x
-5 + y = -3x
Add 5 to both sides
- 5 + 5 + y = -3x + 5
y = -3x + 5
independent variables are those which are beyond the experimenter's control. true false question. true false
Answers
The statement is true - Independent variables are beyond the experimenter's control.
The statement is true. Independent variables are those factors that cannot be manipulated by the experimenter. They are the variables that are naturally occurring and cannot be changed. For example, age, gender, or genetics are independent variables that are beyond the experimenter's control. In contrast, dependent variables are those variables that can be manipulated by the experimenter, such as the amount of light, the temperature, or the dosage of a drug. Understanding the difference between independent and dependent variables is crucial in designing and conducting experiments.
Independent variables are those variables that are beyond the control of the experimenter. They are naturally occurring factors that cannot be manipulated, whereas dependent variables are those that can be manipulated.
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Solve for x (please help I’m failing the class also can you show your work thanks)
Answers
Answer:
x = 11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsGeometry
Vertical Angles TheoremStep-by-step explanation:
Step 1: Define
Identify and set up
[Vertical Angles] 10x - 2 = 108
Step 2: Solve for x
[Addition Property of Equality] Add 2 on both sides: 10x = 110[Division Property of Equality] Divide 10 on both sides: x = 11Forrest Lumber purchased a table saw for $810. After 4 years the saw had a depreciated value of $450. What is the amount of yearly depreciation?
Answers
The amount of the annual depreciation has been $90.
The statement provides us with the following data:
The yearly depreciation of the table saw can be calculated by subtracting the depreciated value from the original cost and dividing by the number of years.
Yearly depreciation = (Original cost - Depreciated value) / Number of years
Yearly depreciation = ($810 - $450) / 4
Yearly depreciation = $360 / 4
Yearly depreciation = $90
Therefore, the amount of yearly depreciation for the table saw is $90.
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find the finance charge for a $25,000, three year loan with a 9.25% apr. How much interest is paid
Answers
Answer:
$6,937.50
Step-by-step explanation:
Interest = Principal x Rate x Time
I = 25000(.0925)(3)
what percentage of persons who lose weight are able to maintain it for more than a year?
Answers
Answer: 20%
Step-by-step explanation:
Solve the recurrence relation: T (n) = 2n. T(n-1) + 12 2
Answers
The Recurrence Relation T(n) for T(n) = 2n.T(n-1) + 12 2 is:
T(n) = 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0) = 2^n * n! * T(0).
To solve the given recurrence relation T(n) = 2n * T(n-1) + 12, we can use iteration or expansion methods. Let's use the expansion method to find an explicit formula for T(n).
Expanding the recurrence relation, we have:
T(n) = 2n * (2(n-1) * T(n-2) + 12) + 12
= 2n * 2(n-1) * T(n-2) + 2n * 12 + 12
= 2n * 2(n-1) * (2(n-2) * T(n-3) + 12) + 2n * 12 + 12
By continuing this process, we can observe a pattern. Each term in the expansion will be of the form 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0), where T(0) is the initial term.
The number of factors of 2 will depend on the value of n. We can see that for each term, the number of factors of 2 is n! (n factorial). Therefore, the explicit formula for T(n) is:
T(n) = 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0) = 2^n * n! * T(0).
In this case, T(0) represents the initial term of the sequence. Without knowing its value, we cannot provide a specific numerical solution. However, the above formula provides a general expression for T(n) in terms of n and T(0), satisfying the given recurrence relation.
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Just a little help please ☺️
Simplify
(3^8/3^5)3
3^9
3^39
3^10
3^6
Answers
\(\left(\dfrac{3^8}{3^5} \right)^3\\\\\\=\left(3^{8-5}\right)^3\\\\=(3^3)^3\\\\=(3)^{3\cdot 3}\\\\=3^9\)
As part of the Pew Internet and American Life Project, researchers surveyed a random sample of 800 teens and a separate random sample of 400 young adults. For the teens, 79% said that they own an iPod or MP3 player. For the young adults, this figure was 67%. Do the data give convincing evidence of a difference in the proportions of all teens and young adults who would say that they own an iPod or MP3 player? State appropriate hypotheses for a test to answer this question. Define any parameters you use.
Answers
the data provide convincing evidence of a difference in the proportions of teens and young adults who own an iPod or MP3
To determine if there is convincing evidence of a difference in the proportions of all teens and young adults who own an iPod or MP3 player, we can perform a hypothesis test.
Let's define the following parameters:
- p₁: Proportion of all teens who own an iPod or MP3 player.
- p₂: Proportion of all young adults who own an iPod or MP3 player.
The null hypothesis (H₀) assumes that there is no difference between the proportions:
H₀: p₁ = p₂
The alternative hypothesis (H₁) assumes that there is a difference between the proportions:
H₁: p₁ ≠ p₂
To test this hypothesis, we can use a two-proportion z-test. We calculate the test statistic using the formula:
z = ((p₁ - p₂) - 0) / √((\(\hat{p}_1\) * (1 - \(\hat{p}_1\)) / n₁) + (\(\hat{p}_2\) * (1 - \(\hat{p}_2\)) / n₂))
Where:
- \(\hat{p}_1\): Sample proportion of teens who own an iPod or MP3 player (79% or 0.79)
- \(\hat{p}_2\): Sample proportion of young adults who own an iPod or MP3 player (67% or 0.67)
- n₁: Sample size of teens (800)
- n₂: Sample size of young adults (400)
Using the given values, we can calculate the test statistic:
z = ((0.79 - 0.67) - 0) / √((0.79 * (1 - 0.79) / 800) + (0.67 * (1 - 0.67) / 400))
Calculating this yields the test statistic z = 5.525.
Next, we can determine the critical value or p-value associated with this test statistic using a significance level (α). Assuming a significance level of 0.05, for a two-tailed test, the critical values are approximately -1.96 and 1.96.
Since the calculated test statistic (5.525) is beyond the critical values of -1.96 and 1.96, we can reject the null hypothesis. There is convincing evidence to suggest that there is a difference in the proportions of all teens and young adults who own an iPod or MP3 player.
In conclusion, the data provide convincing evidence of a difference in the proportions of teens and young adults who own an iPod or MP3 player.
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The appropriate hypotheses for testing the difference in proportions of all teens and young adults who own an iPod or MP3 player are:
Null Hypothesis (H0): The proportion of teens who own an iPod or MP3 player is equal to the proportion of young adults who own an iPod or MP3 player.
Alternative Hypothesis (Ha): The proportion of teens who own an iPod or MP3 player is not equal to the proportion of young adults who own an iPod or MP3 player.
To test if there is a significant difference in the proportions of all teens and young adults who own an iPod or MP3 player, we need to set up appropriate hypotheses. Let's denote the proportion of teens who own an iPod or MP3 player as p1 and the proportion of young adults who own an iPod or MP3 player as p2.
The null hypothesis (H0) assumes that there is no difference between the proportions, so we can state it as:
H0: p1 = p2
The alternative hypothesis (Ha) assumes that there is a difference between the proportions, so we can state it as:
Ha: p1 ≠ p2
Here, p1 represents the true proportion of teens who own an iPod or MP3 player, and p2 represents the true proportion of young adults who own an iPod or MP3 player.
To test these hypotheses, we can use a significance level (α) of 0.05, which is a common choice in hypothesis testing. If the p-value (the probability of observing a test statistic as extreme as the one calculated) is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the proportions.
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PLEASE HELP ME (BRAINIEST) Please Show me how to do this.
Answers
M+L=10
= M = 10 - L
1.80M + 2.40 (10-M) = 21.60
3M + 4 (10 - m) = 36
M = 4
L = 6
Step-by-step explanation:
most of the solution is already written there.
in words :
you define 2 variables for the 2 unknown quantities.
per definition we pick
M = number of medium packs
L = number of large packs
in order to solve a system of 2 variables we need 2 different equations about these 2 variables (for 3 variables we need 3 equations and so forth).
she bought 10 packs.
that much we know. and we know how much she paid for these 10 packs in total.
and we know the individual prices for a single pack of medium and of large size.
so,
M + L = 10
we don't know how many of each, but the total number of packs is 10. so, that's what we are writing down, and it becomes our first equation to solve the 2 variables.
and combining our knowledge about individual prices and the total cost we say
1.80M + 2.40L = 21.60
in other words, we still don't know how many of each size she bought, but the sum of the unknowns "weighted" by their individual prices is known in the form of total cost.
and this is then our second equation.
to summarize these equations again :
M + L = 10
1.80M + 2.40L = 21.60
the first equation is the easiest to transform, and we use it to express one variable by the other (apply the same change to both sides, like here subtracting L from both sides) :
M = 10 - L
this identity we can now use in the second equation :
1.80×(10-L) + 2.40L = 21.60
you know, when you multiply 2 expressions, you need to multiply every term of one expression with every term of the other expression. so, we get
1.80×10 - 1.80L + 2.40L = 21.60
18 - 1.80L + 2.40L = 21.60
when you add 2 terms of the same variable, you can simply add the factors of the variable. so, we get
18 + 0.60L = 21.60
when transforming an equation, it is important to always apply the same changes on both sides. so, here, we subtract 18 from both sides :
0.60L = 3.60
now dividing both sides by 0.60 :
L = 6
and from
M = 10 - L
we get
M = 10 - 6 = 4
so, she bought 4 medium packs and 6 large packs.
In Mrs. Little’s first period classroom, there are 15 boys
and 8 girls on the roster. However, she would like the ratio
of girls to boys to be higher. If Mrs. Schwartz plans to set
Mrs. Little’s classroom such that 2/5
of the total students are
girls, how many more girls must she add to the classroom
roster?
Answers
Step-by-step explanation:
2/5 = x/15+x
= 10
she must add 2 girls to have above 40% girls in the class
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