The volume, L liters, of paint in a plastic tub may be assumed to be normally distributed with mean 10.25 and variance σ^2.
(a) assuming that variance = 0.04, determine P(L<10).
(b) Find the value of standard deviation so that 98% of tubs contain more than 10 liters of paint.
Answers
Assuming a variance of 0.04, determine the probability P(L < 10) and find the standard deviation that ensures 98% of tubs contain more than 10 liters of paint, we need to calculate the appropriate value.
(a) To determine the probability P(L < 10), we need to calculate the cumulative distribution function (CDF) of the normal distribution with a mean of 10.25 and a variance of 0.04. By standardizing the variable using the z-score formula and looking up the corresponding value in the standard normal distribution table, we can find the probability.
The z-score is given by (10 - 10.25) / sqrt(0.04) = -1.25. Looking up -1.25 in the standard normal distribution table, we find that the probability is approximately 0.1056. Therefore, P(L < 10) is approximately 0.1056.
(b) To find the standard deviation that ensures 98% of tubs contain more than 10 liters of paint, we need to calculate the corresponding z-score. We want to find the z-score such that the area to the right of it in the standard normal distribution is 0.98. Looking up the value 0.98 in the standard normal distribution table, we find that the z-score is approximately 2.05.
Now we can set up an equation using the z-score formula: (10 - 10.25) / σ = 2.05. Solving for σ, we have σ ≈ (10.25 - 10) / 2.05 ≈ 0.121. Therefore, a standard deviation of approximately 0.121 would ensure that 98% of tubs contain more than 10 liters of paint.
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Related Questions
True or False: A discrete probability distribution can be expressed in a graph, table, or formula, as long as it gives the probability associated with each value of the discrete random variable.
Answers
The given statement is True. A discrete probability distribution can be expressed in a graph, table, or formula, as long as it gives the probability associated with each value of the discrete random variable.
A Discrete probability distribution is a statistical term used to describe the probability distribution of a random variable that can take on a finite or countably infinite number of distinct outcomes. In other words, a discrete random variable is one that can only take on a specific set of values, while a continuous random variable can take on any value within a specified range.Examples of discrete random variables include the number of children in a family, the number of accidents that occur in a given day, and the number of red cars that pass through an intersection in an hour. A discrete probability distribution is a way of describing the probabilities associated with each of these possible outcomes.In summary, a discrete probability distribution can be expressed in a graph, table, or formula, as long as it gives the probability associated with each value of the discrete random variable. This is because a discrete random variable can only take on a specific set of values, making it easy to calculate the probabilities associated with each outcome.
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3m+2n=7 solve for M
It’s late night my brain is stemming. Help
Answers
Answer:
M= 7/3 hope that helps ya out
Plz help me and send a picture of what u wrote❤️
Answers
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PLEASE ANSWER TODAY ASAP WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER.
Kelli and Karl each have a job. Kelli earns $20 an hour. She also receives a $100 weekly bonus.
Kelli made a table to show how much she earns in a given week.
Hours 0 5 10 15 20 25 30 35 40
Weekly Earnings 100 200 300 400 500 600 700 800 900
Karl earns $25 an hour and receives a $50 weekly bonus.
Karl made a graph to show how much he earns per hour in a given week.
How many hours will it take Kelli and Karl to earn the same amount of money?
Enter your answer in the box.
____hours
Answers
Answer:
I'm think it is 40hours (or 1 1/2 days)
Does (5, 6) satisfy the inequality 2x - 3y> 6?
Answers
Answer:
yes
Step-by-step explanation:
Answer:
Nope, it does not satisfy the equation.
Step-by-step explanation:
2x - 3y > 6
2(5) - 3(6) > 6
10 - 18 > 6
-8 > 6
Hope this helps and I hope u have an Amazing day!
a bus drives for 3 and a half hours at an average speed of 56mph how far does the bus drive?
Answers
Answer:
196 miles
Step-by-step explanation:
distance (D) is calculated as
D = S × T ( S is average speed and T is time in hours )
here T = 3 and a half hours = 3.5 hours and S = 56 , then
D = 56 × 3.5 = 196 miles
a persons salary is $2,500 per month. she received a 10% raise. What is her new salary in dollars per month?
Answers
Answer:
2750
Step-by-step explanation:
10% of 2500 is 250
250 + 2500 = 2750
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Use the constraints of the real-world situation to predict the height of the water balloon at 15 seconds. Use complete sentences to support your answer.
Answers
The linear model is represented as
A. An increasing lines goes up from left to right. This is shown from 0 to 2
B. A horizontal line would show the height remaining the same. This is shown from 2 to 3
C. The steeper the line the faster the decrease. This is shown from 3 to 4
D. The height of the balloon at 10 seconds would be O as it hits the zero mark at 6 seconds and the arrow continues along the O line.
What is Linear Model ?
A linear model is an equation that describes a relationship between two quantities that show a constant rate of change.
Part A the balloons height is increasing when the line is going up
It is increasing between 0 and 2
0 ≤ t ≤ 2
Part B the balloons height remains the same when the line is flat
It is constant between 2 and 3
2 ≤ t ≤ 3
Part C the balloons height is decreasing when the line is going down
It is decreasing the fastest when the line is going down the quickly and that is between 3 and 4. The slope is (80-20)/(4-3)= 60/160. The larger the slope, the faster the height decreases.
3 ≤ t ≤ 4
Part D At 10 second the balloon will be on the ground. At 6 second the height is zero and remains at 0.
The linear model is represented as
A. An increasing lines goes up from left to right. This is shown from 0 to 2
B. A horizontal line would show the height remaining the same. This is shown from 2 to 3
C. The steeper the line the faster the decrease. This is shown from 3 to 4
D. The height of the balloon at 10 seconds would be O as it hits the zero mark at 6 seconds and the arrow continues along the O line.
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One pack of sliced cheese weighs 350 grams. How many packages would you need tobuy to have at least 1 kilogram of cheese?
Answers
Answer:
3
Step-by-step explanation:
Divide 1kg or 1000g by 350 and round up to the next integer. That's it.
Answer:
3 packages
Step-by-step explanation:
350+350=700
700+350=1100
1000 grams=1 kilograms
A line contains the points (-3,-9) and (4,5). What is the point-slope form of the line? A. y + 9 = -2 (x + 3)
B. y - 5 = 3 (x - 2)
C. y - 9 = 2 (x + 3)
D. y + 9 = 2 (x + 3)
Answers
Answer:
D
Step-by-step explanation:
First find the slope.
\(Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{5-[-9]}{4-[-3]}=\dfrac{5+9}{4+3}\\\\\\=\dfrac{14}{7}=2\)
Point slope form:
y - y1 = m(x -x1)
y -[-9] = 2 (x - [-3])
y +9 = 2 (x + 3)
Question 11(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of carbohydrates from 10 different tortilla sandwich wraps sold in a grocery store was collected.
Which graphical representation would be most appropriate for the data, and why?
Circle chart, because the data is categorical
Line plot, because there is a large set of data
Histogram, because you can see each individual data point
Stem-and-leaf plot, because you can see each individual data point
Question 12(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10, 16, 20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 14, with a median of 14
Bus 18, with a mean of 12
Bus 14, with a mean of 14
Bus 18, with a median of 12
Answers
The correct answer is: option D. Bus 18, with a median of 12.
How did we get our assertion?To determine which bus typically has the faster travel time, we need to compare the measures of center of the two sets of data. The measure of center that we use depends on the shape of the data. In this case, since the data is not symmetric, we should use the median as the measure of center.
Looking at the line plots, we can see that the median travel time for Bus 14 is approximately 14 minutes (the value with four dots above it), while the median travel time for Bus 18 is approximately 12 minutes (the value with two dots above it).
Since the median is less affected by extreme values than the mean, it is a more appropriate measure of center for this data. Therefore, we can conclude that Bus 18 typically has the faster travel time, with a median of 12 minutes, compared to Bus 14's median of 14 minutes.
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Which of the following is true about k-means clustering Group of answer choices A tree diagram is used to illustrate the steps in the clustering analysis We choose the value for k before doing the clustering analysis It is a type of hierarchical clustering The cluster analysis will give us an optimum value for k In a cluster analysis, the distance between the clusters should be: Group of answer choices Maximized Minimized Even Zero THANK YOU :)
Answers
Prior to performing the clustering analysis, we choose the value for k. In a cluster analysis, the distance between the clusters should be minimized.
K-means clustering is an unsupervised machine learning technique used to identify clusters of data points. Before performing the clustering analysis, we must first choose the value of k (the number of clusters we wish to identify). The cluster analysis will then attempt to find the k clusters by minimizing the distances between the data points in each cluster. Once the clusters have been identified, the distance between them should be minimized to ensure that the clusters are as distinct as possible.
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I really need help with this
Answers
Answer:
I don't have a grid with me but look at it this way. if you look at the first set of points look at where they are starting. and. then look at the second set of points. see if the points plotted bend over the x axis or the y axis:)
the terms of this sequence increase by the same amount each time _,_,17_,_,29
Answers
Answer:
9, 13, 17, 21, 25, 29
Step-by-step explanation:
Since there is an equal increase of the same amount, the sequence is arithmetic with n th term
Substituting a = 9 and d = 4 into the n th term expression
\(a_{n}\) = 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5
\(a_{n}\) = a + (n - 1)d
where a is the first term and d the common difference
The third term and sixth term are therefore
a + 2d = 17 → (1)
a + 5d = 29 → (2)
Subtract (1) from (2) term by term, eliminating a, that is
3d = 12 ( divide both sides by 3 )
d = 4
Substitute d = 4 into either of the 2 equations and solve for a
Substituting into (1)
a + 2(4) = 17
a + 8 = 17 ( subtract 8 from both sides )
a = 9
Thus the first term is 9 and the common difference d = 4
The sequence of terms is therefore
9, 13, 17, 21, 25, 29
Substituting a = 9 and d = 4 into the n th term expression
\(a_{n}\) = 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5
a quantity with an initial value of 800 grows exponentially at a rate of 5.5% every 10 minutes. what is the value of the quantity after 30 minutes, to the nearest hundredth?
Answers
940 is the initial value, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.
Given that,
An amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.
We have to find what is the quantity's value, to the closest hundredth, after 30 minutes.
We know that,
Formula is
S=a(r+1)ⁿ
Here,
S is initial value
a is 800
r is 5.5%
n is time 30/10
800×(5.5%+1\()^{30\div10}\)
=939.3931
Therefore, 940 is the quantity's value, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.
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Answer:
939.39
Step-by-step explanation:
marvin was completing the square, and his work is shown below. identify the line where he made his mistake. (2 points) f(x)
Answers
He made the mistake on line 1.
2x^2 - 8x + 5....move the 5 to the other side
2x^2 - 8x = -5....now divide by 2
x^2 - 4x = -5/2
x^2 - 4x + 4 = -5/2 + 4
(x - 2)^2 = -5/2 + 8/2
(x - 2)^2 = 3/2
x - 2 = (+-)sqrt 3/2
x = 2 + sqrt 3/2 or x = 2 - sqrt 3/2
He made mistake on line 1.
Complete question -Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake. f(x) = 2x2 − 8x + 5. Line 1: f(x) = 2(x^2 − 8x) + 5 Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32 Line 3: f(x) = 2(x − 4)^2 − 27
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kevin buys a lether jacket listed for $190 he receives a 15% discount at the register what is the new price of the lether jacket.
Answers
Answer:
161.50
Step-by-step explanation:
Answer:
take $190 and multiply it by 0.15 (28.5) and subtract that from $190= $161.50
Step-by-step explanation:
PLZ MAKE ME BRAINLIEST TRYNG TO REACH TOP RANK ON LEADER BOARD
The owner of a pizza restaurant needs to buy a new pizza oven for the restaurant. The oven costs $600, is expected to last 10 years, and will be depreciated using the straight line method. If the total cash inflows from the new oven are constant at $880 for the next 5 years, and the total cash outflows are constant at $240 for the next 5 years,
determine the cash flow for the pizza restaurant in the second year assuming the tax rate is 34%.
Answers
The cash flow for the pizza restaurant in the second year, considering a tax rate of 34%, is $442.80.
To determine the cash flow for the pizza restaurant in the second year, considering a tax rate of 34%, we need to calculate the net cash flow.
Given information:
Cost of the pizza oven: $600
Expected lifespan: 10 years
Cash inflows: $880 per year for the next 5 years
Cash outflows: $240 per year for the next 5 years
Tax rate: 34%
Calculate the annual depreciation expense:
Depreciation Expense = Cost of the pizza oven / Expected lifespan
Depreciation Expense = $600 / 10 = $60 per year
Calculate the taxable income:
Taxable Income = Cash Inflows - Depreciation Expense - Cash Outflows
Taxable Income = $880 - $60 - $240 = $580
Calculate the tax amount:
Tax Amount = Taxable Income * Tax Rate
Tax Amount = $580 * 34% = $197.20
Calculate the net cash flow:
Net Cash Flow = Cash Inflows - Cash Outflows - Tax Amount
Net Cash Flow = $880 - $240 - $197.20 = $442.80
Therefore, the cash flow for the pizza restaurant in the second year, considering a tax rate of 34%, is $442.80.
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The cash flow for the pizza restaurant in the second year, assuming a tax rate of \(34\%\), is \(\$442.80\).
To determine the cash flow for the pizza restaurant in the second year, we need to calculate the net cash flow by subtracting the total cash outflows from the total cash inflows, taking into account the tax rate.
Given:
Cost of the oven: $600
Expected life of the oven: 10 years
Cash inflows per year: $880
Cash outflows per year: $240
Tax rate: 34%
First, we calculate the annual depreciation expense using the straight-line method:
Depreciation expense per year = Cost of the oven / Expected life of the oven
Depreciation expense per year =\(\$600 / 10 = \$60\)
Next, we calculate the taxable income for each year:
Taxable income per year = Cash inflows per year - Depreciation expense per year - Cash outflows per year
Taxable income per year = \(\$880 - \$60 - \$240 = \$580\)
Then, we calculate the tax payable for each year:
Tax payable per year = Taxable income per year * Tax rate
Tax payable per year =\(\$580 * 0.34 =\$197.20\)
Finally, we calculate the net cash flow for the second year:
Net cash flow = Cash inflows per year - Cash outflows per year - Tax payable per year
Net cash flow =\(\$880 - \$240 -\$197.20 = \$442.80\)
Therefore, the cash flow for the pizza restaurant in the second year, assuming a tax rate of \(34\%\), is \(\$442.80\).
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Diego is trying to find the value of X in 5 • x = 35. He draws his diagram but it’s not certain how to proceed. 1. Complete the tape diagram so represents the equation 5•x = 352. Find the value of x.Type the answer in the box belowX=__(Please use pictures or screenshots.
Answers
The tape diagram is:
Then we have that x times x equals to 35
What number multiplied 5 times is 35? The answer is 7
The answer to two is 7
We have the equation:
\(x\cdot5=35\)this means, that x is a number that multiplied by 5 is equal to 35. We can then divide both sides by 5:
\(x\cdot\frac{5}{5}=\frac{35}{5}\)By the multiplication table, we know that 5 *7 = 35. Thus:
\(x=7\)The answer is x = 7
What is the Value of this expression??
Q => (2/3 - 5/6)
--------------
3/4
A =>
1) - 2/9
2) - 1/8
3) 1/8
4) 2/9
Answers
Answer:
1) -2/9
Step-by-step explanation:
(2/3 - 5/6) / (3/4) =
(2*2/(3*2) - 5/6) / (3/4) = ==> the LCM of 3 and 6 is 6. 3*2=6. 6*1=6.
(4/6 - 5/6) / (3/4) = ==> simplify
((4-5)/6) / (3/4) =
(-1/6) / (3/4) =
-1/6 * 4/3 = ==> dividing by a number is equivalent to multiplying by its
reciprocal. Here, the reciprocal of 3/4 is 4/3 since the
numerator and denominator are swapped.
(-1*4)/(6*3)=
-4/18=
-2/9 ==> simplified form of -4/18
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Use the coordinate system selected in part b and find the x and y components of the acceleration of the box, ax and ay, respectively
Answers
By substituting the values of the total acceleration and the angle θ, we can calculate the x and y components of the acceleration.
Remember to consider the coordinate system selected in part b and any given information to determine if there are forces acting in the x and y directions. If there are, you can use the equations above to calculate the x and y components of the acceleration.
To find the x and y components of the acceleration of the box, we need to consider the coordinate system that was selected in part b.
In a Cartesian coordinate system, the x-axis represents horizontal motion and the y-axis represents vertical motion. The acceleration of an object can be broken down into its x and y components.
To find the x-component of the acceleration (ax), we look at the acceleration in the horizontal direction. This could be due to forces like friction or an applied force. If there are no horizontal forces acting on the box, the x-component of the acceleration would be zero.
To find the y-component of the acceleration (ay), we look at the acceleration in the vertical direction. This could be due to forces like gravity or a normal force. If there are no vertical forces acting on the box, the y-component of the acceleration would also be zero.
However, if there are forces acting on the box in both the x and y directions, we can calculate the x and y components of the acceleration using trigonometry. Let's say the total acceleration of the box is represented by a, and the angle it makes with the x-axis is represented by θ.
The x-component of the acceleration (ax) can be calculated using the equation:
ax = a * cos(θ)
The y-component of the acceleration (ay) can be calculated using the equation:
ay = a * sin(θ)
By substituting the values of the total acceleration and the angle θ, we can calculate the x and y components of the acceleration.
Remember to consider the coordinate system selected in part b and any given information to determine if there are forces acting in the x and y directions. If there are, you can use the equations above to calculate the x and y components of the acceleration.
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3,7,2,4,7,5,7,1,8,8
What is the mean
Answers
a) The mode of the list is 7
b) The median of the list is 7.
c) The mean is 5.4
d) The range is 7
What is the Mean, Mode and Median?
Mean: The mean is the average of a set of numbers, calculated by adding up all the numbers and dividing by the total number of numbers in the set.
Mode: The mode is the most frequently occurring number in a set of numbers.
Median: The median is the middle value in a set of numbers when the set is sorted in ascending or descending order.
a) Mode: The mode of the list is 7, as it is the number that occurs most frequently (3 times).
b) Median: To find the median, the list must first be sorted in ascending order:
1, 2, 3, 4, 5, 7, 7, 7, 8, 8
The median of the list is 7.
c) Mean: The mean is found by adding up all the numbers in the list and dividing by the total number of items:
(3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8)/10 = 54/10 = 5.4
d) Range: The range is the difference between the largest and smallest numbers in the list:
8 - 1 = 7
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PLZ IM ON A TEST AND HAVE 2 MIN LEFT
Which equation does NOT represent a direct variation?
1.-3x+2y=0
2.-2y=x
3.y=50x
4. 5x+2y=10
Answers
Answer:
2.-2y=x
Step-by-step explanation:-2y=x
y=kx for constant k
Deandra spent $14.00 of the $20.00 in her wallet. What decimal is equivalent to the fraction of the $20.00
Deandra spent?
Answers
Answer:
0.7
Step-by-step explanation:
i converted the fraction 14/20 to decimal form lol
determine the probability that the first child of clara and charles will be a boy with both albinism and hemophilia.
Answers
The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.
The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%. Albinism and hemophilia are both recessive genetic conditions, meaning that both parents must have the recessive gene in order for a child to be born with either condition. Since neither Clara nor Charles have either condition, the probability that their first child will be a boy with both albinism and hemophilia is 0%.
The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.
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Hugo is serving fruit sorbet at his party. he has 1 gallon of fruit sorbet to serve to 32 friends. if each person receives the same amount, how many cups of fruit sorbet will each person get? 14 cup 12 cup 34 cup 1 cup
Answers
If each person receives the same amount, each person at Hugo's party will get 0.5 cups, or 1/2 cup, of fruit sorbet.
To determine how many cups of fruit sorbet each person will get, we need to convert the volume of the sorbet from gallons to cups, and then divide by the number of people who will be served.
Since 1 gallon is equal to 16 cups, we can multiply the number of gallons by 16 to get the total number of cups of sorbet. In this case, 1 gallon x 16 cups/gallon = 16 cups of fruit sorbet.
To find out how many cups of sorbet each person will get, we simply divide the total number of cups by the number of people. In this case, 16 cups ÷ 32 people = 0.5 cups/person.
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Is √8 a rational or irrational number
Answers
Answer:
irrational
Step-by-step explanation:
irrational because there will still be a 2 under the root when you simplify to 2√2
The price of flour increased from $10 to $12.50 per five pound bag. What is the percentage of increase?
Answers
Answer:
25% increase
Step-by-step explanation:
10*.25=2.5
Answer:
The iteam increased by $2.50
Step-by-step explanation: 12.50 - 10 = 2.50
Simplify using synthetic division (show all work)
(6x^4 - 24 x^3-33x^2+20x+3) divided(x-5)
Answers
Answer:
Here is the answer:
x4−5x3+7x2−34x−1x−5=x3+7x+1+4x−5 = x^3+7x+1+4/x-5
-----------------------------------------------------------
x-5
Write down the first coefficient without changes:
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
We have completed the table and have obtained the following resulting coefficients: 1,0,7,1,4.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus, the quotient is x^3+0x^2+7x+1 and the remainder is 4.
What is the gradient of the graph shown?
Give your answer in its simplest form.
Answers
Answer:
1/3
Step-by-step explanation:
Gradient or slope can be found using the point-slope formula:
\(y-y_{1} =m(x-x_{1} )\)
We can rearrange the equation to find slope (m) like so:
\(m=\frac{y-y_{1} }{x-x_{1} }\)
To use this formula we need to find two well-defined points and use their coordinates.
Let's use (0,2) and (3,3) because they are clear points on the graph.
(0,2) will represent \(x\) and \(y\) in the equation respectively, and (3,3) our other point will represent \(x_{1}\) and \(y_{1}\).
Now we just need to plug the numbers into the equation:
\(m=\frac{2-3}{0-3} \\\\m=\frac{-1}{-3} \\m=\frac{1}{3}\)
The gradient of the graph is 1/3.
Hope this helped!