Let A1,A2,A3,A4 be the 4 A.M.s between 4 and 19.
Then,
4,A1, A2,A3, A4,19 are in A.P. of 6 terms.
An=a+(n−1)d
a6=19=4+(6−1)d
Or d = 3 ...... (i)
Now,
A1=a+d=+3=7
A2=A1+d=7+3=10
A3=A2+d=10+3=13
A4=A3+d=13+3=16
The 4 A.M.s between 4 and 19 are 7, 10, 13, 16.
what is arithmetics?Arithmetic is a fundamental branch of mathematics that studies the characteristics of classical operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction. The term "arithmetic" derives from the Greek arithmtik (tekhn), which means "(art) of counting," and from the Greek arithmos, which means "number.".
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You roll a 6-sided die two times.
What is the probability of rolling a 3 and then rolling a 6?
Answer: 2/6 or 2/12 (Go with 2/6)
Step-by-step explanation:
1/6 probability of rolling any one number. Add the probabilities for rolling a 3 (1/6) and rolling a 6 (1/6) and there is a 2/6 chance of rolling those numbers. it can also be 2/12 if you are looking at both dice rolls like one function.
it it is 1/6 because it the probability of rolling a 3 and then rolling a 6
suppose 3% of cotton fabric rolls and 2% of nylon fabric rolls contain flaws. of the rolls used by a manufacturer, 70% are cotton and 30% are nylon. what is the probability that a randomly selected roll used by the manufacturer contains flaws? round your answer to three decimal places (e.g. 0.987).
The probability that a roll chosen at random and utilized by the manufacturer has problems is 0.032.
Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics. Probability is a mathematical representation of the likelihood or potential that an event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%. Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics.
So, the probability
[tex]=\frac{80}{100}*0.03+\frac{20}{100}*0.04\\=0.8*0.03+0.2*0.04\\=0.024+0.008\\=0.032[/tex]
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if the owner have a kiving room with lenght 12 meter and widht 5 meter, than decides to increase the living room dimensions by 20%, what is the new length and width of the living room floor?
The new length of the living room floor would be 14.4 meters and the new width would be 6 meters.
1. Original Length = 12 meters
2. Original Width = 5 meters
3. Increase by 20%
4. New Length = 12 + (20% of 12) = 12 + 2.4 = 14.4 meters
5. New Width = 5 + (20% of 5) = 5 + 1 = 6 meters
The original length of the living room floor was 12 meters and the original width was 5 meters. The owner decided to increase the living room dimensions by 20%, so the new length of the living room floor is 14.4 meters and the new width is 6 meters. This is calculated by adding 20% of the original length and width to the original values. For the length, this is 12 + (20% of 12) which is 12 + 2.4 = 14.4 meters. For the width, this is 5 + (20% of 5) which is 5 + 1 = 6 meters. The increase of 20% in the dimensions of the living room floor makes it look more spacious and inviting.
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Read the problem and answer the question below:
Jason and his 3 brothers want to buy a gift for their mother. They have $314 saved. Each of them will save $17 a week until they have at least $515 for her gift. How much money will they save after 3 weeks? Will they have enough money to buy the gift?
1. What are the hidden questions?
2. Write an equation that can be used to answer each hidden question.
3. Write and solve an equation to find how much money they will save after the 3 weeks. Will they have enough money to buy the gift?
Answer:
see below
Step-by-step explanation:
4 brothers in total, each saves 17 per week, in 3 weeks
314+(17*4)*3 =518
yes they do have enough
How many weeks will it take for them to save enough $ to buy the gift
515 = x *(17*4) + 314
How much each of them must save per week to have enough?
515= 3(x*4) +314
38. data was collected on hand grip strength of adults. the histogram below summarizes the data. which statement is true about the distribution of the data shown in the graph?
As a general rule of data ; a class is represented by Lower Limit to Upper Limit. So, by comparison. Lower Limit = 40 and Upper Limit - 60
The lower limit of the first class
The attached histogram has overlapping interval, and the intervals are:
40 to 60, 60 to 80, 80 to 100, and so on....
The first class data here is:
40 to 60
As a general rule; a class is represented by Lower Limit to Upper Limit.
So, by comparison.
Lower Limit = 40
Upper Limit - 60
and hence limit can also be calculated by checking the continuity of a function
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The distribution appears to be approximately bell-shaped and symmetric. The majority of the data falls between 40 and 80 units of hand grip strength, with the highest frequency occurring around 60 units.
The data appears to be unimodal, with a single clear peak in the middle. The distribution does not appear to be skewed to the left or right.
Overall, the distribution appears to be relatively normal, with the majority of the data falling within one or two standard deviations of the mean. This suggests that the data is relatively normally distributed and that the mean and standard deviation would be appropriate measures of central tendency and variability, respectively.
Overall, the histogram suggests that the data is relatively normally distributed. This means that the mean and standard deviation would be appropriate measures of central tendency and variability, respectively. Additionally, because the distribution appears to be relatively symmetrical, the median would also be a reasonable measure of central tendency.
It is worth noting that the histogram provides a visual representation of the data, but it does not provide exact measures of central tendency or variability. Therefore, to make any quantitative inferences about the data, it would be necessary to calculate these statistics based on the raw data.
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Data was collected on hand grip strength of adults. the histogram below summarizes the data. which statement is true about the distribution of the data shown in the graph?
A. There m have been a mistake made n data collection because the distribution should be bell shaped.
B. The graph is useless because it is bimodal
C. The graph shows that two different groups may have been combined into one collection
D. The best estimate of typical grip strength is 90 pounds because it is in the center of the distribution
7/9 divided 578 +2/9+578
The simplified value of the expression 7/9 divided 578 + 2/9 + 578 is,
(27071271/46818).
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
The expression 7/9 divided 578 + 2/9 + 578 is,
= 7/9 ÷ 578 + 2/9 + 578
= (7/9) × (1/578) + 2/9 + 578.
= (7/5202) + (2 + 9×578)/9.
= (7/5202) + (5204/9).
= (7×9 + 5202×5204)/(5202×9).
= (63 + 27071208)/(46818).
= (27071271/46818)
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Question 6 mathematics
The quadratic regression equation is given as follows:
y = -0.02x² + 0.14x + 19.6.
How to obtain the regression equation?Regression equations are obtained inserting the points of a data-set into a calculator.
In this problem, we want to find the quadratic regression equation, hence a quadratic regression calculator is used.
The points for this problem are given as follows:
y = -0.02x² + 0.14x + 19.6.
Meaning that the fourth option is the correct option.
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Half the fish in a tank are rainbow fish. 20% are Gouramis and the rest are Corydoras. Write the ratio of rainbow fish to gouramis to corydoras in the simplest form.
Originally, there were 20fish. 3 more rainbow fish are added. What fraction of the fish in the tank are now rainbow fish?
all possible samples of size n are selected from a population, and the mean of each sample is determined. what is the mean of the sample means? it is larger than the population mean. it cannot be estimated in advance. it is the population mean. it is smaller than the population mean.
The a) mean of the sample means is equal to the population mean.
This is because the mean of all of the sample means is a measure of the center of all of the samples, which is the same as the center of the population. This can be shown by calculating the arithmetic mean of the sample means.
The arithmetic mean of the sample means is calculated by summing the means and dividing by the number of samples. Since the sum of all the sample means is the same as the sum of the population, the mean of the sample means must also be equal to the population mean.
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20. The sample mean is an unbiased estimator for the population mean. This means: (a) The sample mean always equals the population mean. (b) The average sample mean, over all possible samples, equals the population mean. (c) The sample mean is always very close to the population mean. (d) The sample mean will only vary a little from the population mean. (e) The sample mean has a normal distribution.
4 cm
4 cm
4 cm
9 cm
The area of one of the bases of the figure shown above is about 6.9 cm².
What is the surface area, in cm², of the figure? Round your answer to the
nearest tenth.
The surface area is of the triangular prism is 121.8 cm²
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
The surface area is gotten by adding each individual area of each surface of a three dimensional shape.
The area of the base is 6.9 cm². This is a triangular prism with height of 9 cm and each base side is 4 cm
The surface area = area of base + (9 cm * 4 cm) + (9 cm * 4 cm) + (9 cm * 4 cm) + area of base
Surface area = 6.9 + 6.9 + 36 + 36 + 36 = 121.8 cm²
The surface area is 121.8 cm²
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7 cups of blue paint and 1 cup of red paint percentage
Answer:
Blue paint = %90, Red Paint = 10%
Step-by-step explanation:
Out of 100, blue takes up more of the equation. It's 7/8's of the equation while there's only a quarter for red paint, making this equation, Blue > Red, aka, 90 > 10
90 > 10 = 90% of blue paint and 10% of red paint
based on the scatterplot and residual plot shown, is a linear model appropriate for summarizing the relationship? a linear model is appropriate because the residual plot shows no pattern. a linear model is appropriate because the mean of the residuals appears close to zero. a linear model is not appropriate because there are potential outliers in the residual plot. a linear model is not appropriate because of the random scatter of points in the residual plot.
Answer:A linear model is appropriate because the scatterplot shows a strong, positive linear relationship.
Step-by-step explanation:
Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.
sin(45°) = StartFraction B C Over 9 EndFraction
sin(45°) = StartFraction 9 Over B C EndFraction
9 tan(45°) = AC
(AC)sin(45°) = BC
cos(45°) = StartFraction B C Over 9 EndFraction
The equations that could be used to solve for the unknown lengths of △ABC are cos45° = AC/9 and sin45° = BC/9.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecent/hypotenuse and
tan = opposite/adjacent.
The opposite side to the reference angle is BC and the adjacent is the height.
We know, cos = adjacent/hypotenuse
Therefore, To determine AC we'll use cos45° = AC/9.
Also, To determine BC we'll use sin45° = BC/9.
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Triangle B'C'D' is the image of triangle BCD under a rotation 90° clockwise about the origin
followed by a reflection.
D
с
B
9
8
7
6
5
4
3
2
+
-10 9 8 7 6 5 4 3 2 1 1
-2
23
3
4
-5
6
-7
-8
9
10
Write the rules for the rotation and reflection.
Rotation: (x, y) →
Reflection: (x, y) + (
C'
D₁
8 9 10
B
the Image of Point C(-5, 3) under a rotation 90° clockwise about the origin followed by a reflection about the x-axis will be C'(3, -5).
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given A triangle BCD that has rotated clockwise 90° about the origin and then reflected about the x-axis.
Rule of reflection and rotation a point:
Rotation about 90° : (x, y) → For clockwise (y, -x) For counterclockwise (x, y)
Reflection about x-axis : (x, y) => (x, -y)
For point C (-5, 3):
After Rotation 90 about origin clockwise:
As per the rule mentioned above
C(-5, 3) => C" (3, 5)
After reflection about the x-axis:
As per the rule mentioned above
C" (3, 5) => C'(3, -5)
therefore, the Image of Point C under a rotation 90° clockwise about the origin followed by a reflection about the x-axis will be C'(3, -5).
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Please help me. I have been stuck on this for too long.
The required two column proof is explained below.
What betweenness of points?When a set of three points 1, 2 and 3 are arranged on a straight path, then a betweenness relationship holds that the addition of segments joining points 1 to 2, and 2 to 3 is the same as segment 1 to 3.
These points divide the line segment joining 1 to 3 into parts.
Considering the given guide, the two column proof required is explained thus:
STATEMENT REASON
1. BC = EF Given
2, AC = AB + BC Betweenness
3. AC > BC Part of a line segment
4. AC > EF Addition property of a segment
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1.81 find some values of z. find the value normal variable that satisfies each of the following conditions. (if you use table a, report the value of that comes closest to satisfying the condition.) in each case, sketch a standard normal curve with your value of marked on the axis. a. 68% of the observations fall below b. 75% of the observations fall above
The value of z that corresponds to 68% of the observations falling below is 0.84, and the value of z that corresponds to 75% of the observations falling above is 1.15.
A. To find the value of z that corresponds to 68% of the observations falling below, we can use the z-score formula. The z-score formula is z = (x-μ)/σ, where x is the value we are looking for, μ is the mean of the normal distribution, and σ is the standard deviation. Using this formula and a standard normal table, we can find that the value of z is 0.84. This means that 68% of the observations fall below z = 0.84. We can sketch a standard normal curve with this value of z marked on the axis by drawing a bell-shaped curve with the value of 0.84 marked on the x-axis.
B. To find the value of z that corresponds to 75% of the observations falling above, we can use the same formula and a standard normal table. We can find that the value of z is 1.15. This means that 75% of the observations fall above z = 1.15. We can sketch a standard normal curve with this value of z marked on the axis by drawing a bell-shaped curve with the value of 1.15 marked on the x-axis.
The value of z that corresponds to 68% of the observations falling below is 0.84, and the value of z that corresponds to 75% of the observations falling above is 1.15.
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Machine Trades How long will it take to machine 45 pins if each pin
requires 6 minutes? Allow 1 minute per pin for placing stock in the lathe.
Answer: 315
Step-by-step explanation:
(45 * 6) + 45
Since there are 45 pins and each takes 6 minutes, then you multiply those 2 first, and then each pin takes 1 minute each, so add 45 to your last answer, which will be your final answer of 315. :)
Answer:
315 minutes
Step-by-step explanation:
We know
One pin requires 6 minutes, with 1 minute per pin for placing stock in the lathe, which means 7 minutes to machine 1 pin.
7 times 45 = 315 minutes
So, it will take 315 minutes to machine 45 pins
the photo shows a woman watching a row of machines in a factory. a photo of a woman standing between two long rows of sewing machines in a factory. what advantages did machinery provide for factory owners?
A photo of a woman standing between two long rows of sewing machines in a factory. The factory owners relied on skilled workers to run the machines. Thus, option b is correct.
The manufacturing system's key advantages were lower costs for the business and increased worker productivity. The factory administration had direct control over the workers, allowing for regular monitoring of their output. Resources may be used more efficiently if they are shared across several employees.
First, equipment hastened the production of goods. This is because a machine might perform routine tasks skillfully and dependably. The ability of equipment to decrease the number of people required to complete a task is its second advantage. They were able to avoid paying employees by doing this, which allowed them to save money.
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The complete question is-
The photo shows a woman watching a row of machines in a factory. A photo of a woman standing between two long rows of sewing machines in a factory. what advantages did machinery provide for factory owners?
a. machines could do the work faster than skilled workers by hand.
b. factory owners relied on skilled workers to run the machines.
c. the machines produced a better product than skilled workers by hand.
d. factory owners needed more unskilled workers to run the machines.
Help please :(. Grade 8
Answer:
A
Step-by-step explanation:
The easiest way to see whether a table is a function is to check the Input and Output. If one Input has two outputs, then that table is not a function. So, the answer is A
A linear function goes through the points (-3,1) and (1,-3). What are the coordinates for the y-intercept of this function?
Answer:
y = (0,-2)
Step-by-step explanation:
change in y/ change in x.
-4/4 ---> slope is -1
plug x and y coordinates AND SLOPE into y=mx+b
-3= -4/4(1)+b
-3= -1 +b
-2=b
compare the two rates. has faulting taken place at a constant rate, or has the rate increased or decreased over time? explain in as much detail as possible.
The solution is, a. Climate change takes place at a constant rate over time.
What is climate?Climate is the long-term weather pattern in a region, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years.
here, we have,
A climate can be define as the average state of the everyday weather condition which remain probably stable for a period of 30 years. It is measured by various parameters like atmospheric pressure, temperature and humidity.
so,
On the basis of the above description, a.Climate change takes place at a constant rate over time. is the correct option.
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1)
(-7, 5) and (-2, 7)
find the slope given two points
The slope of the given points is [tex]\frac{2}{5}[/tex] or 0.4.
Step-by-step explanation:1. Name the ordered pairs.Let (-7, 5) be ordered pair 1.
Let (-2, 7) be tordered pair 2.
2. Identify the coordinates.Since point (-7, 5) is ordered pair 1: [tex]x_{1} =-7[/tex] and [tex]y_{1} =5[/tex].
Since point (-2, 7) is ordered pair 2: [tex]x_{2} =-2[/tex] and [tex]y_{2} =7[/tex]
3. Apply the slope formula.Formula: [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Substitute the variables in the formula by the identified coordinates in step 2 and calculate.
[tex]m=\frac{(7)-(5) }{(-2) -(-7) }=\frac{7-5}{-2+7}=\frac{2}{5}[/tex]
4. Conclude.The slope of the given points is [tex]\frac{2}{5}[/tex].
-------------------------------------------------------------------------------------------------------
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Answer: 2/5
Step-by-step explanation:
(-7,5) (-2,7)
change in y 2
------------------ = -----
change in x 5
sin(180+0) =
a. sin 0
b. -sin 0
c. cos 0
please explain thoroughly and in basic concepts I’m really bad at math thank you!
b.
because if you use math it tells you b
a30 arithmetic sequence of 1,-4,-9,-14
The 30th term a30 of the sequence is -1445
How to determine the value of a30?The definition of the function is given as
arithmetic sequence of 1,-4,-9,-14
The above definitions imply that we simply subtract 5 from the previous term to get the current term
Using the above as a guide,
so, we have the following representation
First term, a = 1
Common difference, d = 5
An arithmetic sequence is represented as
a(n) = a + (n - 1)d
For the 30th term, we have
a(30) = a + 29d
So, we have
a(30) = 1 + 29 * -5
Evaluate
a(30) = -144
Hence, the value of a30 is -144
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a woman who has five children (all boys) is planning to have another child. what is the probability that this child will be a boy?
The probability of the sixth child being born as a boy is 0.5 or 50%. It is irrespective to the five boys born previously.
Since probability of a girl or boy being born is 50%,
Probability of Girl being born, P(G) = ½
Probability of boy being born, P(B) = ½
When one is calculating the probability of any one of the two events occurring or both evens have a chance of occurring, considering the events are non-mutually exclusive, the rule of addition is used.
Rule of addition: P(A or B)= P(A) + P(B) –P(A+B)
Where P(A)- probability that event A takes place
P(B)- Probability that event B takes place
P(A+B)- probability of both events taking place.
In this case, both events cannot take place simultaneously, i.e., they are mutually exclusive, hence,
P(G or B)= ½ + ½ = 2/4 = ½ = 0.5.
Therefore, Probability of boy being born is 0.5
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an experimenter surveyed two acres of a desert preserve and found six cactus wren nests. assuming that the habitat is fairly uniform, how many nests would he expect to be in the entire 200-acre preserve?
600 cactus wren nests the experimenter would expect to be in the entire 200-acre preserve.
To estimate the number of cactus wren nests in the entire 200-acre preserve, we can use the ratio of the area surveyed to the number of nests found.
Let's call the number of nests in the entire 200-acre preserve "N".
The ratio of the area surveyed to the number of nests found is:
2 acres / 6 nests = 200 acres / N nests
We can use this ratio to find the number of nests in the entire 200-acre preserve:
N nests = 200 acres * (6 nests / 2 acres)
N nests = 200 * 3
N nests = 600
So the experimenter would expect to find approximately 600 cactus wren nests in the entire 200-acre preserve, assuming that the habitat is fairly uniform.
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A company makes two kinds of trading cards.
Regular cards are $0.40 each and premium
cards that cost $0.65 each. A box of 25 assorted
cards sells for $14. How many of each card type
are included? pls show work to help
The system of equations are solved and the number of regular and premium cards are 9 and 16 respectively
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , let the regular cards be x
And , the premium cards be y
The cost of one regular card x = $ 0.40
The cost of one premium card y = $ 0.65
The total cost = $ 14
The total number of cards = 25
Substituting the values in the equation , we get
x + y = 25 be equation (1)
0.40x + 0.65y = 14 be equation (2)
Multiply by 100 on both sides of equation (2) , we get
40x + 65y = 1400
Divide by 5 on both sides of the equation , we get
8x + 13y = 280 be equation (3)
Multiply equation (1) by 8 , we get
8x + 8y = 200 be equation (4)
Subtracting equation (4) from equation (3) , we get
13y - 8y = 280 - 200
5y = 80
Divide by 5 on both sides of the equation , we get
y = 16
So , the number of premium cards is 18
Substitute the value of y in equation (1) , we get
x + 16 = 25
Subtracting 16 on both sides of the equation , we get
x = 9
So , the number of regular cards is 9
Hence , the equations are solved
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How do I scale a graph with the ordered pairs (6,37) (1,14.50) (0,10)
The equation of line is y = 4.5x + 10 and the slope is m = 4.5
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the first point be P ( 6 , 37 )
Let the second point be Q ( 1 , 14.50 )
Let the third point be R ( 0 , 10 )
Now , the slope of the line be represented as m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 37 - 14.50 ) / ( 6 - 1 )
Slope m = ( 22.50 ) / 5
Slope m = 4.5
And , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying the equation , we get
y - 10 = 4.5 ( x - 0 )
y - 10 = 4.5x
Adding 10 on both sides of the equation , we get
y = 4.5x + 10
Hence , the equation of line is y = 4.5x + 10 and the graph is plotted
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Duretta is collecting coins and has 5/6 as many quarters as dimes. If Duretta has collected
$7.40 in all, how many of each coin does she have?
The number of dimes is 24.
The number of quarters is 20.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
10 dimes = $1
1 dime = $0.1
4 quarters = $1
1 quarter = $0.25
Now,
Number of dimes = x
Number of quarters = (5/6)x
Now,
Duretta has collected $7.40 in all.
This means,
0.1x + 0.25(5/6)x = 7.40
0.1x + 0.21x = 7.40
0.31x = 7.40
x = 7.40/0.31
x = 23.87
x = 24
And,
(5/6)x
= 5/6 x 24
= 20
We can cross-check.
24 x 0.1 + 20 x 0.25 = 7.40
2.4 + 5 = 7.40
7.40 = 7.40
Thus,
Number of dimes = 24
Number of quarters = 5/6 x 24 = 20
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consider three different processors p1, p2, and p3 executing the same instruction set. p1 has a 3 ghz clock rate and a cpi of 1.5. p2 has a 2.5 ghz clock rate and a cpi of 1.0. p3 has a 4.0 ghz clock rate and has a cpi of 2.2. true or false
Part a: P2 processors therefore performs the best out of the three.
Part b: Number of Cycles are found.
Part c: New Clock rate for each processors is found.
Explain about the highest performance of processors processors?High-speed data processing and intricate calculations are capabilities of high-performance computing (HPC).
1.
P1: 3GHz / 1.5 = 2 × 10^9 instructions / second
P2: 2.5GHz / 1.0 = 2.5 × 10^9 instructions / second
P3: 4GHz / 2.2 = 1.82 × 10^9 instructions / second
2. Number of Cycles:
P1: 3GHz × 10 = 3 * 10^10 cycles
P2: 2.5GHz × 10 = 2.5 × 10^10 cycles
P3: 4GHz ×10 = 4 × 10^10 cycles
Number of instructions:
P1: 3GHz × 10 / 1.5 = 2 × 10^10 instructions
P2: 2.5GHz × 10 / 1.0 = 2.5 × 10^10 instructions
P3: 4GHz × 10 / 2.2 = 1.82 × 10^10 instructions
3. Execution time = (Number of instructions * CPI) / (Clock rate)
Therefore, if CPI rises by 20% but we aim to cut the execution time to 30%, we have:
Execution time × 0.7 = (Number of instructions × CPI × 1.2) / (New Clock rate)
New Clock rate = Clock rate × 1.2 / 0.7 = 1.71 * Clock rate
New Clock rate for every processor:
P1: 3GHz × 1.71 = 5.13 GHz
P2: 2.5GHz × 1.71 = 4.27 GHz
P3: 4GHz × 1.71 = 6.84 GHz
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The correct question is-
Performance:
Consider three different processors, P1 P2 and P3, executing the same instruction set.
P1 has a 3 GHz clock rate and a CPI of 1.5. P2 has a 2.5 GHz clock rate and a CPI of 1.0.
P3 has a 4.0 GHz clock rate and a CPI of 2.2.
1. Which processor has the highest performance expressed in instructions per second?
2. If the processors each execute a program in 10 seconds, find the number of cycles and the number of instructions.
3. We are trying to reduce the execution time by 30% but this leads to an
increase of 20% in the CPI. What clock rate should we have to get this time reduction?