By solving a system of equations we will see that the cost a slice of pizza is $9.80
How to find the cost of a slice of pizza?Let's define the variables:
p = cost of a slice of pizza.
n = cost of the nachos.
We know that "Jeffery ordered 3 pieces of pizza an 2 nachos for total of 16.50"
So we can write:
3p + 2n = 16.50
"Hanah ordered a piece of pizza an 4 nachos for total of 16 "
p + 4n = 16
Then we can write the system of equations:
3p + 2n = 16.50
p + 4n = 16
We can isolate n on the second equation to get:
4n = 16 - p
n = (16 - p)/4
n = 4 - (1/4)p
Replacing that on the other equation we get:
3p + 2*(4 - (1/4)p) = 16.50
Now we can solve this for p.
3p - 8 - 1/2p = 16.50
(5/2)p - 8 = 16.50
(5/2)p = 16.50 + 8
p = (2/5)*(16.50 + 8) = 9.8
So the cost of a slice of pizza is $9.80
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One canned juice drink is 30% is orange juice, another is 5% orange juice. How many liters of each should be mixed together in order to get 25 Liters that is 27% orange juice?
The amount of juice for 30% orange juice is 22 liters,
and the amount of juice for 5% orange juice is 3 liters mixed together in order to get 25 Liters.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given One canned juice drink is 30% orange juice, another is 5% orange juice,
Let x and y be the amount of 30% and 5% orange juice respectively,
according to condition
0.30x + 0.05y = 0.27(25) .........(1)
x + y = 25.........(2)
Multiply the second equation by -0.05,
0.30x + 0.05y = 0.27(25)
-0.05x - 0.05y = -0.05(25)
Add equation to eliminate y,
0.30x - 0.05x + 0.05y - 0.05y = 0.27(25) - 0.05(25)
Solve for y,
0.25x = 5.5
x = 5.5/.25
x = 22
substitute value of x in equation,
x + y = 25
(22) + y = 25
y = 25 - 22
y = 3
Hence the amount of 30% orange juice is 22 liters and the amount of 5% orange juice is 3 liters.
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Factor the following examples of difference perfect squares for X to power of 2-9
Answer: X^2 - 9 can be factored into (X - 3)(X + 3) which is the difference of squares.
The difference of squares factorization of X^2 - 9 is (X - 3)(X + 3)
Step-by-step explanation:
determine its average speed when it goes around the closed path. express your answer to three significant figures and include the appropriate units.
The average speed is 0 m/s since the object does not move.
Since the object does not change its position, it does not move. Therefore, its average speed is 0 m/s.
The object in question does not move in a closed path, meaning that its position remains the same throughout the entire path. As a result, its average speed is 0 m/s. This is because average speed is the total distance traveled divided by the total time taken, and since the object does not move its distance traveled is 0 and its time taken is also 0. Therefore, when the object goes around the closed path, its average speed is 0 m/s.
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Given right triangle ABC, where side "c" is the hypotenuse, angle B measures 42 degrees, and side c measures 18 m, find the length of side b.
The length of side b of the given right angle triangle using law of sines is; b = 12.044 m
How to use the law of sines?The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C
Thus;
a/sin A = b/sin B = c/sinC
The parameters are;
B = 42°
c = 18m
Since c is the hypotenuse, it is the side that will be opposite the right angle and so;
C = 90°
Thus, using sine rule;
c/sinC = b/sin B
18/sin 90 = b/sin 42
b = (18 * sin 42)/1
b = 12.044 m
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Find the value for the following determinant
Answer:
42
Step-by-step explanation:
determinant of matrix
= 5(2) - 8(-4)
= 10 - (-32)
= 10 + 32
= 42
Answer:
32
Step-by-step explanation:
the determinant of matrix
[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex] = ad - bc
then
[tex]\left[\begin{array}{ccc}5&-4\\8&2\\\end{array}\right][/tex]
= (5 × 2) - (- 4 × 8) = 10 - (- 32) = 10 + 32 = 42
What is the chance of exactly 1 of population members A , B, and C being in a sample of 100 , drawn randomly from a population of 100,000?
The chance of exactly one of population members A, B, and C being in a sample of 100, drawn randomly from a population of 100,000 is 0.0003%.
What is the chance of exactly 1 of population members A , B, and C being in a sample of 100 , drawn randomly from a population of 100,000?The probability of exactly one of population members A, B, and C being in a sample of 100, drawn randomly from a population of 100,000, is equal to the product of the probability of selecting each of the members and the probability of not selecting the other two members. Mathematically, this is expressed as: P(A, not B, not C) = (1/100,000) x (99,999/100,000) x (99,998/100,000) The probability of exactly one of population members A, B, and C being in a sample of 100, drawn randomly from a population of 100,000, is equal to 0.00299970 or approximately 0.003.This is an example of the binomial probability formula which is used to calculate the chance of a certain number of successes in a given number of trials. In this example, the population members A, B, and C represent the successes and the 100 randomly selected sample of 100,000 is the number of trials.To learn more about the binomial probability formula refer to:
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The number N of locations of a popular coffeehouse chain is given in the table. (The numbers of locations as of October 1 are given.)Year 2004 2005 2006 2007 2008N 8,574 10,238 12,440 15,006 16,676a. Find the average rate of growth between each pair of years.2004 to 2006 _____ locations/ year2006 to 2007 _____ locations/ year2005 to 2006 _____ locations/ yearb. Estimate the instantaneous rate of growth in 2006 by taking the average of the last two rates of change in part (a).c. Estimate the instantaneous rate of growth in 2006 by measuring the slope of the tangent line through (2005, 10,238) and (2007, 15,006).d. Estimate the instantaneous rate of growth in 2007 by measuring the slope of the tangent line through (2006, 12,440) and (2008, 16,676).e. Compare the growth rates you obtained in part (c) and (d). What can you conclude?1. The rate of growth is increasing.2. The rate of growth is decreasing.3. The rate of growth is constant.4. There is not enough information.
a. To find the average rate of growth between each pair of years, we can use the formula: (end value - start value) / (end year - start year).
2004 to 2006: (12,440 - 8,574) / (2006 - 2004) = 3,866 / 2 = 1,933 locations/year
2006 to 2007: (15,006 - 12,440) / (2007 - 2006) = 2,566 / 1 = 2,566 locations/year
2005 to 2006: (12,440 - 10,238) / (2006 - 2005) = 2,202 / 1 = 2,202 locations/year
b. To estimate the instantaneous rate of growth in 2006, we can take the average of the last two rates of change from part (a).
(2,566 + 2,202) / 2 = 2,384 locations/year
c. To estimate the instantaneous rate of growth in 2006 by measuring the slope of the tangent line through (2005, 10,238) and (2007, 15,006), we can use the formula:
(15,006 - 10,238) / (2007 - 2005) = 4,768 / 2 = 2,384 locations/year
d. To estimate the instantaneous rate of growth in 2007 by measuring the slope of the tangent line through (2006, 12,440) and (2008, 16,676), we can use the formula:
(16,676 - 12,440) / (2008 - 2006) = 4,236 / 2 = 2,118 locations/year
e. Comparing the growth rates from part (c) and (d), we can see that the growth rate in 2007 is less than the growth rate in 2006. So we can conclude that 2. The rate of growth is decreasing.
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Can someone help is for geometry
A truth table deconstructs a logic function by outlining all possible outcomes the function might achieve.
Explain about the truth table?A truth table offers a way to map out the potential truth values in an expression and predict their results. The table has a row for each conceivable combination of truth values and a column for each variable in the expression. There is also a column that displays the results of each set of values.
For propositional logic formulations, this tool builds truth tables. There are numerous formats available for entering logical operators. As an illustration, the propositional formula p q r could be represented as p / q -> r, p and q => not r, or p && q ->!r. You can enter the connectives and as T and F.
P Q (Q ∧ P)
F F F
F T F
T F F
T T T
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Answer and Explain Please
a) The final coordinates are given as follows:
X(-5,-4) -> X'(-4,5).Y(2,-2) -> Y'(-2,-2).Z(-3,-6) -> Z'(-6,3).b) The rotation rule is given as follows: (x,y) -> (y,-x).
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x)The rotation in this problem is the last rotation, 270º counterclockwise about the origin, hence the rule is given as follows:
(x,y) -> (y,-x).
The rule is applied to each of the vertices X, Y and Z to obtain the vertices of the reflected triangle X', Y' and Z'.
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Sales of portable MP3 players grew approximately exponentially from $0.08 billion in 1999 to $0.88 billion in 2004. Predict the sales of MP3 players in 2008.
The sales of MP3 players in 2008 is $ billion.
(Type an integer or a decimal. Round the final answer to one decimal place as needed. Round all intermediate values to three decimal places as needed.)
Based on the exponential function, the sales of MP3 players in 2008 is $1.82 billion.
What is an exponential function?An exponential function is a function that has the general form y = abˣ
where
a ≠ 0,
b is the base b is a constant (b is a positive real number and b ≠ 1)
x is the independent variable whose domain is the set of real numbers.
Using the equation for exponential growth
y = ab^x
y = 0.88
a = 0.08
0.88 = 0.08bˣ
bˣ = 0.88/0.08
bˣ = 11
x = 4
Hence;
b⁴ = 11
b = 1.82
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Our school purchased 100 new computers. Of those are 1/5 broken. How many computers are broken?
Answer:
20
Step-by-step explanation:
1/5 = 20/100
please try on this and please give explanation
Answer: In the figure above, clearly the line L is perpendicular to x-axis and passing through the value 'c' on x- axis. So, the equation of a line perpendicular to x axis is x = c
please help me with this math problem i’ll give you brainlist
Answer:
42=3.5x+2y
Step-by-step explanation:
3.5 is the cost of the cakes and 2 is the cost of the oreos. 42 is how much Francis can spend
Santiago has planned a basketball game for the weekend.
The chance of snow on Saturday is 35%, with a 70% chance on
Sunday. If these probabilities are independent, what is the
chance that it will snow on both days?
The probability that it will snow on both days, given the chances of snow on Saturday and Sunday, is 24.5%.
How to find the probability ?The chance of it snowing on both days is calculated by multiplying the probability of it snowing on Saturday by the probability of it snowing on Sunday. If the probabilities are independent, we can assume that one event occurring doesn't affect the other event, therefore the probability of both events happening is just the product of the individual event probabilities.
So, the chance of it snowing on both days is:
P(Saturday and Sunday) = P(Saturday) x P(Sunday)
P(Saturday and Sunday) = 0.35 x 0.70
P(Saturday and Sunday) = 24.5 %
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5. a random sample of 500 subjects measured their systolic blood pressure, and if they were a smoker or not. the goal is to evaluate if average systolic blood pressure differs by smoking status. summary sample statistics on the dataset follow:
There is a difference in average systolic blood pressure between smokers and non-smokers.
To evaluate if average systolic blood pressure differs by smoking status, we need to calculate the mean systolic blood pressure for both smokers and non-smokers. We can calculate the mean systolic blood pressure for smokers by taking the sum of systolic blood pressure values for all smokers in the sample, divided by the number of smokers in the sample. This formula can be written as:
Mean Systolic Blood Pressure for Smokers = (Sum of Systolic Blood Pressure Values for all Smokers) / (Number of Smokers)
Similarly, we can calculate the mean systolic blood pressure for non-smokers by taking the sum of systolic blood pressure values for all non-smokers in the sample, divided by the number of non-smokers in the sample. This formula can be written as:
Mean Systolic Blood Pressure for Non-Smokers = (Sum of Systolic Blood Pressure Values for all Non-Smokers) / (Number of Non-Smokers)
Once we have calculated the mean systolic blood pressure for both smokers and non-smokers, we can compare the two means to evaluate if there is a difference in average systolic blood pressure between smokers and non-smokers.
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Which object is about 15 centimeters long? Responses pencil, desk, paper, clip or television
The object that is about 15 cm is pencil.
What is Measurement?The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.
Given:
Measurement = 15 cm
As, the average length for the pencil varies from 7 cm - 17 cm.
and, average length for the desk is 120 cm.
and, the average length for the paper is 30.3 x 40.6cm.
and, the average length for the clip is 4 cm.
and, the average length for the television is 40 cm.
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Write two different expressions you could use to represent the
combined area of the Activities and Quotations sections. What
information about the sections does each expression show?
The area expressions are (2x + 1) * (x^2 + 4x - 5) and 2x^3 + 9x^2 - 6x - 5
How to determine the area expressionsThe missing figure is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Length = 2x + 1
Width = x^2 + 4x - 5
The area is calculated as
Area = (2x + 1) * (x^2 + 4x - 5)
When expanded, we have
Area = 2x^3 + 8x^2 -10x + x^2 + 4x - 5
Evaluate the like terms
Area = 2x^3 + 9x^2 - 6x - 5
Hence, the area expression is 2x^3 + 9x^2 - 6x - 5
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A caterer for a wedding reception wants to use a recipe for eggplant salad that recommends using 0.7 kg of eggplant for guests. However, in her area, eggplant is only sold by the pound. If 70 guests are expected, how many pounds of eggplant should the caterer purchase?
By performing a change of units, we will see that the caterer should purchase 107.8 lb
How many pounds of eggplant should the caterer purchase?First, let's find how many kilograms are needed. We know that the recipe recomends using 0.7kg per person, and there are 70 guests, so an estimate of the mass needed is:
M = 70*0.7kg = 49 kg
Now weneedto do a change of units, we know that:
1 kg = 2.2 lb
Then we can rewrite:
49 kg = 49*(2.2 lb) = 107.8 lb
The caterer should purchase 107.8 pounds
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List the elements of each of the following sample spaces: (a) the set of integers between 1 and 50 divisible by 8. (b) the set S = (x1x2 + 4x - 5 -0. (c) the set of outcomes when a coin is tossed until a tail or three heads appear. (d) the set S = {x|2x - 4 20 and x < 1)
a)The set of integers between 1 and 50, divisible by 8 are given as.
S={ 8,16,24,32,40,48}
b ) Hence, the set {-5,1}
c) The list of set of outcomes when a coin is tossed until a tail or three heads appear will be.
S={T,HT,HHT,HHH}
d) S={Europe, Asia, Australia, North America, South America, Africa, Antarctica.}
a) We have to find a list of integers between 1 and 50, divisible by 8.
Keep in mind that the S is the event that represents the sample space. The set of integers between 1 and 50, divisible by 8 are given as.
S={ 8,16,24,32,40,48}
b) We need to list the set S= {[tex]x| x^2+4x-5=0}[/tex]}
[tex]x^2+4x-5=0\\\\x^2+5x-x-5=0\\x(x+5)-(x+5)==\\(x+5)(x-1)=0\\\\x=-5 , x=1[/tex]
Hence, the set {-5,1}
c) c) We have to find a list of the set of outcomes when a coin is tossed until a tail or three heads appear.
Let T denote the event that tail appeared.
Let H denote the event that head appeared.
The list of set of outcomes when a coin is tossed until a tail or three heads appear will be.
S={T,HT,HHT,HHH}
d) We need to list the set
S={x ∣ x is a continent}.
There are 7 continents:
S={Europe, Asia, Australia, North America, South America, Africa, Antarctica.}
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Part A Create the smallest cylinder possible with the tool, and record the values o cylinder by the given scale factors, and then record the resulting volumes ( cylinder. BI UX² X₂ 12pt Original Cylinder Radius (units) 2 Scale Factor (k) AV Radius Height (units) funite Height (units) A 6 Volume (V) 13 13 E Volume (cu. unit: 8 Vxk³. scaled cylinders are 2, 3, and 4
The original cylinder has a radius of 2 units and a height of 13 units, and its volume is given by the formula: V = πr²h = π * 2² * 13 = 104π cubic units.
How you can create the smallest cylinder?Original cylinder: The original cylinder has a radius of 2 units and a height of 13 units, and its volume is given by the formula: V = πr²h = π * 2² * 13 = 104π cubic units.
Scaled cylinder 1: The first scaled cylinder has a scale factor of 2, so its radius is 2 * 2 = 4 units and its height is 13 * 2 = 26 units. Its volume is given by: V = πr²h = π * 4² * 26 = 672π cubic units.
Scaled cylinder 2: The second scaled cylinder has a scale factor of 3, so its radius is 2 * 3 = 6 units and its height is 13 * 3 = 39 units. Its volume is given by: V = πr²h = π * 6² * 39 = 1764π cubic units.
Scaled cylinder 3: The third scaled cylinder has a scale factor of 4, so its radius is 2 * 4 = 8 units and its height is 13 * 4 = 52 units. Its volume is given by: V = πr²h = π * 8² * 52 = 3072π cubic units.
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Please answer this question for me
Using properties of triangles, Correct options are A,B and D. AE = EB, EG || AC and AC = 2 EG.
A triangle has three sides, three angles, and three vertices, which are its characteristics.
A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.
Any two triangle sides can add up to a length that is longer than the third side.
A triangle's total angles are always 180 degrees.
A triangle's outside angles are always a sum of 360 degrees.
The total of the parallel interior and exterior angles is additional.
From the given figure,
As E is the mid point of BA,
So, BE = EA
As it is clearly seen that EG is parallel to AC = EG||AC
Further,
As, EG is intersecting AB and BC at mid points,
⇒ AC = 2EG
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Write this in exponential form
5^2 x 5^6
How do I do this problem I do not get it do I add when I found the volume of both
Answer:
206
Step-by-step explanation:
cube volume = 5*5*5 +3*3*3 = 125+81 = 206
need the answer please
The number of feet that canyon wall away from the person will be 3,300 feet.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo.
Convert the speed in feet per second. Then we have
Speed = 750 x 5280 / 3600
Speed = 1,100 feet per second
Let 'n' be the number of seconds. Then the distance is given as,
1,100 = (d / 2) / n
d = 2,200 n
If n = 1.5, then we have
d = 2,200 x 1.5
d = 3,300 feet
The number of feet that canyon wall away from the person will be 3,300 feet.
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There are three quarters, five dimes, and twelve pennies in a bag.
Once a coin is drawn from the bag, it is not replaced. If two coins
are drawn at random, determine each probability.
1. P(a quarter and then a penny)
2. P(a nickel and then a dime)
3. P(two pennies)
4. P(a dime and then a quarter)
The probability for these are
Probability(a dime and then a quarter)=3/76
Probability(two pennies)=33/95
Probability(a quarter and then a penny)=9/95
What is probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.
Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes
Now,
Quarters=3, Dimes=5 and Pennies=12
Total=20
Probability(a dime and then a quarter)=5/20*3/19=15/380=3/76
Probability(two pennies)=12/20*11/19=132/380=33/95
Probability(a quarter and then a penny)=3/20*12/19=36/380=9/95
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1. You are trying to decide where the best place to get a pizza delivered from as quickly as possible. Here are the several delivery times of some local pizza places (in minutes).
Ronny’s: 24, 38, 31, 27, 40, 21, 34, 19
John and Mary’s: 18, 69, 22, 27, 32, 25, 16, 25
Penora’s: 19, 42, 23, 42, 24, 39, 20, 25
Use the information above to answer all five questions below. Be detailed in your answer and provide work for all but the five number summary.
A. Find the five number summary, mean, standard deviation, range and interquartile range for all three local pizza places.
B. Determine if there are any outliers for the three pizza places. List the outliers if any for each pizza place.
C. What place do you think Allison and Emily should order from? How did you determine this?
D. For each pizza place, which measure of central tendency (mean or the median) represents the data the best and why?
E. If you were to plot the data for each pizza company, how would the data be described? (Symmetric, Skewed left or Skewed right)
2. Ms. McGregor is a teacher at Wendover High. She surveyed her students to find out how far from school her students lived. The following data is the distance between the school and her students' homes, in miles:
9
10
7
7
8
10
11
10
5
9
8
7
5
2
10
10
14
8
7
4
Use the data provided above to answer the questions below:
Create a boxplot for Ms. McGregor’s class and display it on a number line. Make sure to label your number line clearly so it easy to determine the accuracy of your calculations.
Create a frequency table and histogram of the number of miles students are from the school in the space provided below for Mrs. McGregor’s class
Intervals
Frequency
0 - 3
3 - 6
6 - 9
9 - 12
12 - 15
3. Jonathan compared the ounces in and prices of several different cereals at the grocery store. Here are his results:
ounces
Price (in dollars)
32
$3.89
28
$2.79
42
$4.19
8
$1.00
27
$3.15
12
$2.25
Use the information listed above to answer all questions:
A. Find the line of best fit. Round any decimals to the hundredths place:
y = _____________________
Find the correlation coefficient and explain what it means in the context of the problem:
Correlation coefficient: _____ Explanation:
C. Estimate the price when you have a weight of 48 ounces. Show all work for credit.
D. Estimate the ounces when you have a price of $3.50. Show all work for credit.
E. Find the residuals for your data. You can provide a screenshot from your calculator or
show all work to identify your residuals.
F. Provide a screenshot of your residual plot from your calculator below.
G. Explain if your equation is a good fit for your data based on your screenshot from your
residual plot
Answer:
Step-by-step explanation:
In a right-skewed distribution, which of the following is true? The mean tends to be greater than the median.
h(n)=2/n -2 solve inverse function
Answer:
2/n+2
Step-by-step explanation:
a project consists of 150 jobs. the expected completion time for each job is given in days. the project has three critical paths with two jobs in common, j and k. in order to finish the project one day early, the completion time should be reduced one day for
Reducing the completion average time for Jobs J and K by one day will shorten the overall project completion time by one day, allowing the project to finish one day early.
In order to finish the project one day early, the completion time for Jobs J and K should be reduced by one day. This is because these two jobs are part of the three critical paths of the project. By reducing the completion time for these two jobs by one day, the entire project will be completed one day early. This is because the critical paths are the paths that will determine the overall project completion time. By reducing the completion time for these two jobs, the overall project completion time will be shortened. This will allow the project to be finished one day earlier than expected.
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Si el costo de 1 Kg de azucar es $8?cual es el precio de 3 3/4 kg?
On evaluating the fraction 3 3/4 the cost of 3 3/4 kg of sugar is $30.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
The cost of 1 kg of sugar is = $ 80
The amount of sugar is given in fractional form - 3 3/4 kg
The equation for cost of 3 3/4 kg sugar is -
Cost = 3 3/4 × 8
Solve the fractional part first -
Cost = 15/4 × 8
Simplify the equation -
Cost = 15/4 × 8
Cost = 120/4
Cost = 30
Therefore, the cost value is obtained as $ 30.
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If the cost of 1 kg of sugar is $8, what is the price of 3 3/4 kg?
What is the solution to the system of equations?
6x-2y=-14
4x-3y=-31
A:(2,1)
B:(-6,11)
C:(2,13)
D:(-2,1)
The solution to the system of equations is 6x – 2y = -14 with x = -4 and y = -5
How to get perfect solution?4x – 3y = -31
To find x or method, you must first make one of the words the same so that they may cancel out.
To determine the x terms, we will make the y terms the same in this example.
To do so, multiply the first equation by three, yielding:
18x – 6y = - 42
And multiply the second equation by two to get:
8x – 6y = - 62
Now that we have the y terms, you may cancel them out.
You now have the following two equations:
18x = -42
8x = -62
The next step is to combine them, since the preceding – and – form a +.
This implies that you are left with one equation
26x = -104
Now divide by 26 on each side to get:
x = -4
As you have x, you substitute it into one of the ORIGINAL equations.
6x – 2y = -14
Substitute x in:
6(-4) – 2y = -14
-24 – 2y = -14
Add 24 on each side to get:
-2y = 10
y = -5
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