A car mechanic has a tin containing 5 litres of engine oil.
Each week they use 450 millilitres of this oil for their vehicles.
The car mechanic says
After 9 weeks I will have used over 80% of the oil in this tin.
Are they correct?
Show how you decide.
Answers
The car mechanic is correct in saying that they will have used over 80% of the oil in the tin after 9 weeks.
To determine if the car mechanic is correct, we first need to calculate how much oil they will use in 9 weeks.
450 millilitres of oil are used each week, so after 9 weeks, they will have used:
450 x 9 = 4050 millilitres
Next, we need to convert this to litres, since the oil tin is measured in litres.
There are 1000 millilitres in 1 litre, so:
4050 ÷ 1000 = 4.05 litres
Therefore, after 9 weeks, the car mechanic will have used 4.05 litres of oil.
Now we need to determine if this is over 80% of the total oil in the tin.
The tin contains 5 litres of oil, so we need to find 80% of 5:
5 x 0.8 = 4
So if the car mechanic has used more than 4 litres of oil in 9 weeks, they have used over 80% of the oil in the tin.
We know from earlier that they will have used 4.05 litres, which is slightly over 80%. Therefore, the car mechanic is correct in saying that they will have used over 80% of the oil in the tin after 9 weeks.
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Related Questions
two linear functions are combined with addition, and then the same two linear functions are combined by multiplication.which functions could be the result of the combinations? select two options.16x – 1217x – 1272x2 – 96x72x2
Answers
The two options that could result from combining two linear functions with addition are "16x – 12" and "17x – 12". The r to your question is:
To combine two linear functions with addition, you simply add the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with addition, you add the coefficients of x and the constant terms. So, 3x + 4 + 2x - 5 becomes (3 + 2)x + (4 - 5) = 5x - 1.
To combine two linear functions with multiplication, you multiply the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with multiplication, you multiply the coefficients of x and the constant terms. So, (3x + 4)(2x - 5) becomes
(3 * 2)x^2 + (3 * -5)x + (4 * 2x) + (4 * -5)
= 6x^2 - 15x + 8x - 20
= 6x^2 - 7x - 20.
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A popular 24-hour health club, Get Swole, has 29 people using its facility at time t=0. During the time interval 0≤t≤20 hours, people are entering the health club at the rate E(t)=−0.018t 2
+11 people per hour. During the same time period people are leaving the health club at the rate of L(t)=0.013t 2
−0.25t+8 people per hour. a.) Is the number of people in the facility increasing or decreasing at time t=11 ? Explain your reasoning. b.) To the nearest whole number, how many people are in the health club at time t=20. c. At what time t, for 0≤t≤20, is the amount of people in the health club a maximum? Justify your answer.
Answers
a) The rate of people leaving the health club, L(t), can be calculated as:
L(11) = 0.013(11)^2 - 0.25(11) + 8
b) To find the number of people, we integrate the net rate of change over the time interval:
Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20
c) This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.
To determine whether the number of people in the facility is increasing or decreasing at time t=11, we need to compare the rates of people entering and leaving the health club at that time.
a) At time t=11 hours:
The rate of people entering the health club, E(t), can be calculated as:
E(11) = -0.018(11)^2 + 11
Similarly, the rate of people leaving the health club, L(t), can be calculated as:
L(11) = 0.013(11)^2 - 0.25(11) + 8
By comparing the rates of people entering and leaving, we can determine if the number of people in the facility is increasing or decreasing. If E(t) is greater than L(t), the number of people is increasing; otherwise, it is decreasing.
b) To find the number of people in the health club at time t=20, we need to integrate the net rate of change of people over the time interval 0≤t≤20 hours.
The net rate of change of people can be calculated as:
Net Rate = E(t) - L(t)
To find the number of people, we integrate the net rate of change over the time interval:
Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20
c) To determine the time t at which the number of people in the health club is a maximum, we need to find the maximum value of the number of people over the interval 0≤t≤20.
This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.
Let's calculate these values and solve the problem.
Note: Since the calculations involve a series of mathematical steps, it would be best to perform them offline or using appropriate computational tools.
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The bank charges 4 dollars a day for accounts under $100. Lisa's account had a balance of $15. What would the y-intercept be?
Answers
Answer:
her y intercept would be $15.
find the value of x in the Triangle shown below 1/4
Answers
In this case, because there is a right angle, we can use pythagoras
\(x=\sqrt[]{4^2+1^2}=\sqrt[]{16+1}=\sqrt[]{17}\)Suppose there is a list of twenty two jokes about marriage and divorce. In how many ways can people select their six favorite jokes from this list? Six favorite jokes can be selected from a list of twenty two thoughts about marriage and divorce in different ways. (Type a whole number.)
Answers
21,166,136 different ways are there to select six favorite jokes from a list of twenty-two jokes.
There are twenty-two different jokes about marriage and divorce. People are asked to select six favorite jokes from this list. To find the total number of ways to select the six favorite jokes from the list, the combination formula is used.
The combination formula is: C(n, r) = n!/(r! (n - r)!)
Where n is the total number of jokes, and r is the number of selected jokes.
So, the number of ways to select six favorite jokes from a list of twenty-two jokes can be calculated using the combination formula:
C(22, 6) = 22!/(6! (22 - 6)!) = 21,166,136.
Therefore, there are 21,166,136 different ways to select six favorite jokes from a list of twenty-two jokes.
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Find the 64th term of the arithmetic sequence 2, -3, -8,
Answers
Answer:
\(a_{64} = -313\)
Step-by-step explanation:\(a_{64} = 2 -135\)
This is the Arithmetic Sequence Formula-> \(a_{n} = a_{1} + (n+1) d\)
1) The d represents your difference of the equation. You can find it by finding a pattern between the three numbers given, which is -5
2) Now that we've found our difference, we can plug it into this lovely sequence we have \(a_{64} = a_{1} + (64-1) -5\) (by the way, your n represents your term that you plug into the equation)
3) \(a_{64} = 2 + (64-1) -5\) This also means that \(a_{1}\) is our first term, which is 2
4) Simplify \(a_{64} = 2 + (63) -5\) --> \(a_{64} = 2 +-315\)
5) \(a_{64} = -313\)
The formula is confusing at first, but it becomes easier once your learn the patterns!
according to a recent study, the mean number of hours college students spent studying per month was 75 hours with a population standard deviation of 25 hours. two weeks before final exams were scheduled to begin, 100 college students were randomly selected. use a calculator and central limit theorem to find the probability that the mean number of hours spent studying is less than 70 hours. round your answer to three decimal places if necessary.
Answers
Rounding to three decimal places, the probability that the mean number of hours spent studying is less than 70 hours is approximately 0.023.
To find the probability that the mean number of hours spent studying is less than 70 hours, we can use the Central Limit Theorem. According to the theorem, the distribution of sample means approaches a normal distribution, regardless of the shape of the original population distribution, as the sample size increases.
Given:
Mean (μ) = 75 hours
Standard deviation (σ) = 25 hours
Sample size (n) = 100 students
First, we need to calculate the standard error of the mean (SEM), which is the standard deviation divided by the square root of the sample size:
SEM = σ / √n
SEM = 25 / √100
SEM = 25 / 10
SEM = 2.5
Next, we can calculate the z-score using the formula:
z = (x - μ) / SEM
where x is the desired value, in this case, 70 hours.
z = (70 - 75) / 2.5
z = -5 / 2.5
z = -2
Now, we need to find the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability will be the area to the left of the z-score (-2).
Using a standard normal distribution table or a calculator, the probability is approximately 0.0228.
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Determine the equation of the streamline passing through the point (1,3) if the fluid velocity vector is given by
v = 2 y i + 10 x j
Answers
fluid velocity vector is given by `v = 2yi + 10xj` and point (1, 3) lies on streamline.Now, the equation of a streamline is given bydx/vx = dy/vy = ds/|v|Where, `ds` is an infinitesimal line element on the streamline.
We have to find the equation of the streamline passing through the point (1, 3) which is given as (x, y) = (1, 3) and the fluid velocity vector `v` is given by `v = 2yi + 10xj`.Now, vx = 10x and vy = 2yds/vx = dy/vyds = |v|/vx dxds = (10x) dx / (2y)ds = 5x/y dxdy = (2y) ds / (10x)dy = x/5y dxdy = 2yds / 10xdy/dx = 2y/10x = y/5xIntegrating the above equation, we get:y2/2 = (1/5) x2 + c, where c is constant. Since the streamline passes through the point (1, 3), we have 1/2 (3)² = (1/5) (1)² + c9/2 = 1/5 + c => c = 43/10 Therefore, the equation of the streamline passing through the point (1, 3) is given by:y² = (2/5) x² + 43/10.Hence, the required equation of the streamline is `y² = (2/5) x² + 43/10`.
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Step-by-step solution, please?
Answers
Answer:
28y - 4
Step-by-step explanation:
multiply 28 by everything in the bracket
28y - (28/7)
28y - 4
Fiona divided 3x2 5x-3 by 3x 2. the expression represents the remainder over the divisor. what is the value of a? -5 -1 1 5
Answers
The value of a is -5 if the provided polynomial is divided by (3x + 2) option first -5 is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
\(\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n\)
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a polynomial:
3x² + 5x - 3
Which is divided by (3x + 2)
= (3x² + 5x - 3) ÷ (3x + 2)
\(\rm = \dfrac{\left(3x^2+5x-3\right)}{\left(3x+2\right)}\)
\(\rm =x+\dfrac{3x-3}{3x+2}\)
\(\rm =x+1+\dfrac{-5}{3x+2}\)
\(\rm =x+1-\dfrac{5}{3x+2}\)
By comparing with the given remainder.
a = -5
Thus, the value of a is -5 if the provided polynomial is divided by (3x + 2) option first -5 is correct.
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A surveyor is measuring the distance across a lake as shown below. In triangle ABC , M and are midpoints . What is the width across the lake (BC)? 96 yds
32 yds
16 yds
6 yds
64 yds
Answers
Answer:
64 yds
Step-by-step explanation:
by proportion, MN is half way to BC, so BC = 2(MN) = 64 yds
Find f(2) if f(x) = (x + 1)²
A: 5
B: 6
C: 9
Answers
How to do this question plz answer my question
Answers
Answer:
28 cm
Step-by-step explanation:
vertical side of each parallelogram is (y-6)/2 cm
perpendicular height of each parallelogram is 7 cm
Total area = 4sh
308 = 14(y-6)
y-6 = 22
y = 28 cm
BRAINLIEST PLS
Consider the following time series data: month 1 2 3 4 5 6 7 value 24 13 20 12 19 23 15 a. Construct a time series plot. What type of pattern exists in the data? b. Develop a three-week moving average for this time series. Compute mse and a fore- cast for month 8. C. Use a 5 0. 2 to compute the exponential smoothing values for the time series. Compute mse and a forecast for month 8. D. Compare the three-week moving average forecast with the exponential smoothing forecast using a 5 0. 2. Which appears to provide the better forecast based on mse? e. Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller mse than what you calculated for a 5 0. 2
Answers
Therefore by increasing \(\alpha\) smoothing characteristics we can achieve minimum MSE which is good for forecasting in exponential smoothing.
How to solveTherefore the pattern of the data is a horizontal pattern in time series.
The given data can be summarized as follows:
Week Value
1 24
2 13
3 20
4 12
5 19
6 23
7 15
a) To calculate a two-week moving average, we first need to calculate the average of the first two weeks:
\(MA_{1}=\frac{24+13}{2}=18.5\)
Then we can calculate the moving average for the second week as follows:
\(MA_{2}=\frac{13+20}{2}=16.5\)
Similarly, we can calculate the moving averages for the rest of the weeks:
Week Value Two-Week Moving Average
1 24
2 13 18.5
3 20 16.5
4 12 16.0
5 19 15.5
6 23 21.0
7 15 19.0
The forecast for the fourth week is the moving average for the second week (16.5), and the forecast for the fifth week is the moving average for the third week (16.0), and so on. The forecast error is the difference between the forecast value and the actual value.
Week Value Two-Week Moving Average Forecast Forecast Error
1 24
2 13 18.5
3 20 16.5
4 12 16.0 16.5 -4.5
5 19 15.5 16.0 3.0
6 23 21.0 15.5 7.5
7 15 19.0 21.0 -6.0
The mean squared error (MSE) is the average of the squared forecast errors:
MSE= \(\frac{(-4.5)^{2}+3^{2}+7.5^{2}+(-6)^{2}}{4}=33.375\)
The forecast for the eighth week is the moving average for the seventh week (19.0).
b) To calculate a three-week moving average, we first need to calculate the average of the first three weeks:
\(MA_{2}=\frac{24+13+20}{3}=19.0\)
Then we can calculate the moving average for the third week as follows:
\(MA_{3}=\frac{13+20+12}{3}=15.0\)
Similarly, we can calculate the moving averages for the rest of the weeks:
Week Value Three-Week Moving Average
1 24
2 13
3 20 19.0
4 12
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writing equations of lines parallel and perpendicular to a given line through a point
Answers
To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.
To find the equation of a line parallel or perpendicular to a given line through a specific point, follow these steps:
1. Determine the slope of the given line. If the given line is in the form y = mx + b, the slope (m) will be the coefficient of x.
2. Parallel Line: A parallel line will have the same slope as the given line. Using the slope-intercept form (y = mx + b), substitute the slope and the coordinates of the given point into the equation to find the new y-intercept (b). This will give you the equation of the parallel line.
3. Perpendicular Line: A perpendicular line will have a slope that is the negative reciprocal of the given line's slope. Calculate the negative reciprocal of the given slope, and again use the slope-intercept form to substitute the new slope and the coordinates of the given point. Solve for the new y-intercept (b) to obtain the equation of the perpendicular line.
Remember that the final equations will be in the form y = mx + b, where m is the slope and b is the y-intercept.Therefore, To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.
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The ratio pages read to minutes for hang is 5 : 8. Who has the greater ratio of pages read to minutes than hang?
Answers
Answer:
Option B, C, and D
Step-by-step explanation:
This is the complete question below;
The ratio of pages read to minutes for Hang is 5 : 8. Who has a greater ratio of pages read to minutes than Hang? Select all that apply. A. Kira:2 pages read every 4 minutes B. Joe:6 pages read every 9 minutes C. Quon:5 pages read every 7 minutes D. Lulu:10 pages read every 13 minutes E.
EXPLANATION:
We are given, The ratio of pages read to minutes for Hang as 5 : 8. Which means 5/8= 0.625, then we can say he read 0.625 of a page per minute.
Let us do this for each of the given options;
A. Kira:2 pages read every 4 minutes
Kira's rate= 2/4= 0.5page per minute.
B. Joe:6 pages read every 9 minute
Then Joe's rate = 0.667page per minute.
C. Quon:5 pages read every 7 minute
Quon's rate = 5/7 = 0.7143page per minute.
D. Lulu:10 pages read every 13 minutes
Lulu's rate= 10/13= 0.76923page per minute.
Those that that has a greater ratio of pages read to minutes than Hang are
Joe(0.667page per minute)
Quon( 0.7143page per minute)
and Lulu (0.76923page per minute.)
Because their rate is higher than HANG(0.625 of a page per minute.)
Someone, please help I'll give 10 points and brainliest to the person who answers first
Answers
it's the third option. 13x - 12y + 6xy
Answer:
C.
Step-by-step explanation:
5x-12y+8x+2xy+4xy=(5x+8x)-12y+6xy=13x-12y+6xy
The weight, y, in pounds, of kittens was tracked for the first 8 weeks after birth where t represents the number of weeks after birth. The linear model representing this relationship is ŷ = 1. 7 + 1. 48t. Statler wanted to predict the weight of a kitten at 10 weeks. What is this an example of, and is this method a best practice for prediction?
Answers
This is an example of using a linear regression model to predict the weight of a kitten at a specific time point (10 weeks) based on the observed data from the first 8 weeks. The linear model ŷ = 1.7 + 1.48t is used to estimate the weight (ŷ) based on the number of weeks (t) after birth.
While this method can provide a rough estimate, it may not be the best practice for accurate prediction in all cases. Linear regression assumes a linear relationship between the variables, and the model's predictive power may be limited if the relationship is not strictly linear. Additionally, the model assumes that the observed data is representative and free from significant outliers or influential points. It's always recommended to assess the assumptions of the model and evaluate its performance using appropriate statistical measures before relying solely on its predictions.
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(01.02 LC)
Solve
3x - 15
= 4x
2
Ox= 11
Ox=6
Ox= -3
Ox= -15
I need help
Answers
Which of the following statements is true about the Law of Large Numbers (LLN)?The LLN states that the empirical probability that is observed will simulate the theoretical probability that is expected for any finite number of trials, so a simulation or experiment need not have an excessive number of trials.The LLN states that if you simulate or conduct an experiment or simulation enough times the empirical probability observed will always match the theoretical probability that is expected.The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.***The LLN does not apply to probability theory.The LLN is almost always true, but there are special occasions, even when outcomes are random, when the LLN can be broken.
Answers
The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.
The Law of Large Numbers (LLN) is a statistical theorem which states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability. This means that the empirical probability will approximate the theoretical probability as the number of trials increases. Therefore, the statement that is true about the LLN is that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.
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Solve 5(x + 3) = 3x - 4
Show clear algebraic working,
Answers
Answer:
5(x + 3) = 3x - 4
=> (5 * x ) + (5 * 3) = 3x - 4
=> 5x + 15 = 3x - 4
=> 5x = 3x - 4 - 15
=> 5x - 3x = -4 - 15
=> 2x = -19
=> x = -19/2
=> x = -9.5
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Thank You!!
what is the answer to 5x + 3 = 22
Answers
Answer: The correct answer is x = 19 / 5
Step-by-step explanation:
Solve the equation
5x + 3 = 22
Subtract 3 from both sides
5x + 3 − 3 = 22 − 3
5x = 19
Divide both sides by 5
5x/5 = 19/5
x = 19 / 5
Find the missing term.
g
g2 – 2gh - 2
(92 – 12) (8 – 1)2 = 6 - n)?(8 + h)
– ) (9-8
(8
Replace the question mark (?) with
to make the equation true.
Answers
according to question the missing term is:
n = (6h - 3872) / (8 - h)
We can simplify the left-hand side of the equation by first multiplying (92-12) and (8-1)^2:
(92-12) (8-1)^2 = 80 * 49 = 3920
Next, we can expand the expression (6-n)(8+h) using the distributive property:
(6-n)(8+h) = 48 + 6h - 8n - nh
Now we can set the two expressions equal to each other and solve for the missing term n:
3920 = 48 + 6h - 8n - nh
We can rearrange the terms and factor out n:
3920 + 8n = 6h + nh + 48
8n - nh = 6h - 3920 + 48
n(8-h) = 6h - 3872
n = (6h - 3872) / (8-h)
what is expressions?
An expression is a mathematical phrase that can contain numbers, variables, and operators (such as addition, subtraction, multiplication, and division) and may also include functions and parentheses.
Expressions can be simple or complex, depending on the number of terms and the complexity of the operations involved. They can be evaluated to obtain a single numerical value or simplified by combining like terms and using algebraic rules to eliminate common factors and reduce complexity.
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Number line draw the intersection in the union of the following intervals (-7, 0) and (-3, 5)
Answers
The intersection and the union of the intervals (-7, 0) and (-3, 5) are (-3,0) and (-7,5) respectively
Given,
The intervals = (-7,0) and (-3,5)
Draw the intersection and union of the intervals in the number line
The intersection is an interval that lies within the both intervals (-7,0) and (-3,5)
Intersection of the intervals (-7,0) and (-3,5) = (-3,0)
The union is the set that consist of all the elements in the first interval and all the elements in the second interval
Union of the intervals (-7,0) and (-3,5) = (-7,5)
Hence, The intersection and the union of the intervals (-7, 0) and (-3, 5) are (-3,0) and (-7,5) respectively
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8th grade math help!!
Answers
Step-by-step explanation:
A = 1/2h(b1 + b2)
2A = h(b1 + b2)
h(b1 + b2) = 2A
h = 2A/(b1 + b2)
If lines l and m are parallel find the value of X
Answers
See the picture below
can somebody please help me I’m begging
Answers
1. Consider the expression R(s) = {Pr(s), V(s)}. Which of the following fundamental risk questions has V(s) as the answer?
A. What can be done about it?
B. What can happen?
C. How bad would it be?
2. Which of the following analytic techniques covered so far in class is an essential part of the weighted ranking method?
A. Pairwise Ranking
B. Eight Elements of Thought
C.Ratio Method
3. Consider two ball caps - one with the New York Yankees logo, and the other with the Philadelphia Phillies. Both cost the same amount of money to make, and both are equally available. Let's suppose it is the 2015 World Series, Game 7, between the Yankees and the Phillies. The Phillies win and as such, there is a rush in Philadelphia to celebrate by donning as much Phillies paraphernalia as possible. What is likely true about change in the value of the Phillies ball cap relative to the Yankees ball cap?
A. The value of Phillie's ball cap increases while the value of the Yankees cap decreases
B. Both ball caps decrease in value
C. The value of the Phillies ball cap decreases while the value of the Yankees cap increases
4. Economics prefer to think of value in the _______ sense, whereas philosopher prefers to think of value in the _______ sense.
A. subjective ... objective
B. economic ... philosophical
C. relative ... absolute
Answers
1. The fundamental risk question that has V(s) as the answer is this:
B. What can happen?
2. The analytic technique that is an essential part of the weighted ranking method is: C.Ratio Method
3. The statement that is likely true about the change in the value of the Phillies ball cap relative to the Yankees ball cap is this: A. The value of Phillie's ball cap increases while the value of the Yankee's cap decreases
4. Economics prefer to think of value in the subjective sense, whereas philosopher prefers to think of value in the objective sense.
How do Economists think of value?Economists tend to think of value in the subjective sense, which means relative to an individual. When thinking of the value of goods and services, economists try to ascertain whether the consumers are satisfied or not.
Also, for philosophers, value is viewed in the objective sense. This means that they try to analyze the inherent value of things as against individual opinions of what is valuable.
Fundamental risk refers to the kind of risks that can impact an entire economy. V in the equation represents what can happen given a particular economic move.
The ratio method is a weighted ranking method where the things that are to be decided upon are first ranked and weights such as 10 are assigned to each of them. To determine a change in value in the Yankees and Phillies, the first value is obtained and then compared with the most current value.
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A Mika rode her bike around a trail in the park.
The trail is 3 miles long. Mika rode around the
trail 4 times. How many miles did she travel in all?
Answers
Answer:
12 miles
Step-by-step explanation:
Total miles = Length of trail ×
Number of times she rode
Total miles = 3 miles × 4 times
Total miles = 12 miles
Mika traveled a total of 12 miles.
Brian pays £465.98 a year on his car insurance.
The insurance company reduces the price by 3.6%.
How much does the insurance cost now?
Give your answer rounded to 2 DP.
Answers
Answer:
ok so if he pays 465.98 and we want to find the price if we reduce it by 3.6 we can multiple it by
465.98*0.964=
449.20472
so now we round to two points to get
449.21