the PERT weighted average is 9 days
What is PERT weighted average?
PERT can be defined as an estimating technique that uses a weighted average of three numbers to get a final estimate.
The formula for finding the PERT weighted average is given as;
PERT weighted average = (Optimistic + (4 X Most Likely) + Pessimistic)/6
We have;
Optimistic = 6 daysMost likely = 8 daysPessimistic = 16 daysSubstitute the values into the formula
PERT weighted average = [tex]\frac{6 + 4(8) + 16 }{6}[/tex]
PERT weighted average = [tex]\frac{54}{6}[/tex]
PERT weighted average = 9 days
Thus, the PERT weighted average is 9 days
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A random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important. The interval that is 95% certain to contain the proportion of all 18-24 year olds who believe that their health is extremely important is
Between 48% and 54% believe that their health is extremely important.
According to the statement
Given that a random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important.
Here
Sample size n =1001
sample proportion p = 0.51
By these values we calculate the Standard error of proportion.
So, Standard error of proportion = 0.0158.
Since sample size is sufficiently large we can take Z critical value for confidence interval
Z critical value for 95% = 1.96
Margin of error = ±1.96*std error
= ±0.0310
confidence interval = 0.51 ±0.0310
= (0.48, 0.54)
So, Between 48% and 54% believe that their health is extremely important.
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Instructions: Find the measure of the indicated angle to the nearest degree.
Answer:
15.78°
Step-by-step explanation:
Let the angle be x.
From the x, the known sides are the opposite side, O(13) and the adjacent side, A(46)
Therefore, The trigonometric ratio is the tangent ratio.
tan x = O/A
tan x =13/46
x = 15.78°
A student is overheard saying: "I don't need to learn the Primary Trig Ratios. I am just going to use the Sine
and Cosine Laws to solve problems." Show by example that the student is right. Explain the advantages and
disadvantages to this approach. Step by step. Thank you!
The sine and cosine rule is typically used to find the measure of angles in trigonometry.
How to illustrate the trigonometry?It should be noted that the sine rule is used when we are given:
two angles and one side.two sides and a non included angle.The cosine rule is used when we are given:
there sides two sides and the included angle.The advantage is that it can help us understand the connections between the sides and their angles.
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What is the GCF of:
9a^4b^4 - 27a^3b^3
Answer:
9a^3b^3
Step-by-step explanation:
The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number
Find the prime factors of each term in order to find the greatest common factor (GCF).
The gas co2 is diffusin at steady state through a tube 20 cm long having a diameter of 1 cm and containing n2 at 350 k . the total pressur is constant at 101.3kpa . the partial pressure of co2 at one end is 456 mmhg and 76 mmhg at the end . the diffusivity is 0.167 cm2 /s at 298 k . calculate the mass rate of co2 if the partial pressure remains constant.
The value is J = 1.71*10^-6 kmol/m^2.s
According to the given conditions we get,
The length the tube l= 0.20m
The diameter of the tube d= 0.01m
The total pressure inside the tube P= 101.32kPa
The partial pressure of CO2 at the first end is
P1= 456mm Hg = 60794.832 Pa
The partial pressure of CO2 at the other end is
P2= 76mm Hg = 10132.472 Pa
The temperature is T = 298 K
The diffusion coefficient D= 1.67* 10^-5 m^2/s
Generally the molar flux of CO2 is mathematically represented as
J= D{p1-p2} / R.T
Here R is the gas constant with value R= 8.314 j/kmol
So we get J= 1.71 * 10^-3 mol/m^2.sec
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Find Q2 of the following data set 3, 9, 12, 4, 6, 40, 25, 14, 10
Answer:
Q₂ = 10
Step-by-step explanation:
Given data set: 3, 9, 12, 4, 6, 40, 25, 14, 10
Q₂ is the median (the middle value) of the given data set when the data set is ordered from smallest to largest.
Order the values in the data set:
3, 4, 6, 9, 10, 12, 14, 25, 40
As the number of values is odd, the middle value is the 5th value.
Therefore, the median (Q₂) of the given data set is 10.
If the number of data values is even, and therefore there are two middle values, the median is halfway between them.
(HELP!) now consider 0=-120. Draw the angle 0=-120 on the circle below. Make sure you rotate clockwise for the negative angle. It needs to be approximate, but not precise.
The reference angle after rotating the unit circle anti-clockwise is; π/3 Radians
How to draw a Unit Circle?To draw the angle θ = -120° in the unit circle, we will move clockwise 90°, and thereafter another angle of 30°.
This tells us that we pass the fourth quadrant and stop in the third quadrant.
The reference angle of an angle theta in the third quadrant, is; θ + 180°.
Thus, the reference angle of -120° is; -120° + 180° = 60°.
Converting 60° to radians gives; (60/360) * 2π Radians = π/3 Radians
Thus, the Reference angle is π/3 Radians
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A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. during week 10 of the recall, the manufacturer fixed 200 cars. in week 15, the manufacturer fixed 175 cars. assume that the reduction in the number of cars each week is linear. write an equation in function form to show the number of cars seen each week by the mechanic. f(x) = 5x 250 f(x) = −5x 250 f(x) = 10x 200 f(x) = −10x 200
The linear function that shows that the number of cars seen each week by the mechanic is:
f(x) = -5x + 200.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.During the first week analyzed, the amount of cars was of 200, hence the y-intercept is of 200. In 5 weeks, the amount decayed by 25, hence the slope is given by:
m = -25/5 = -5.
Thus the linear function that shows that the number of cars seen each week by the mechanic is:
f(x) = -5x + 200.
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Answer:
f(x) = −5x + 250
Step-by-step explanation:
First, we must find the slope. We can take 2 points. (10, 100) and (15,175)
Using y2-y1/x2-x1=m, we find that the slope =-5. to find the y-intercept, we have to find that y= when x=0. Since 10 weeks passed since the begining, we can inverse the slope to find 5(cars)x10(weeks)=50.
so, 200(week10)+50(week 1)=250
f(x)=-5x+250.
WILL GIVE BRAINLIEST! I’m desperate for help! This assignment is due today I’m stuck! Pls help!
Which expression represents the following statement? Multiply 6 by 3, and then subtract the quotient of 18 and 9.
6 x (3 ÷ 18) + 9
6 + 3 + (18 ÷ 9)
(6 x 3) − 18 ÷ 9
6 x (3 + 18) + 9
Answer:
Step-by-step explanation:
the third one is correct
[tex]6 \times 3 - \frac{18}{9} \\ (6 \times 3) - (18 \div 9)[/tex]
what is 7+6-8x5=????
Answer:
Step-by-step explanation:
7+6-8x5=
7+6-40=
13-40=
-37
if the x is multiplying
If the function 5x+y=1 has the domain (-2,1,6) then what is the corresponding range?
The corresponding range of the domain is (11, -4, -29)
How to determine the range?The function is given as:
5x + y = 1
Make y the subject
y = 1 - 5x
The domain is given as:
(-2,1,6)
Substitute these values in y = 1 - 5x
y = 1 - 5(-2) = 11
y = 1 - 5(1) = -4
y = 1 - 5(6) = -29
Hence, the corresponding range of the domain is (11, -4, -29)
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Consider this expression.
x
2
+
x
−
72
Replace the values of a and b to rewrite the given expression.
Answer:
(x+9) (x-8)
Step-by-step explanation:
Edmentum/Plato
A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue
(C) [tex]\frac{1}{3}[/tex] fraction of the marbles now in the bag is blue.
What is a fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction that consists of a numerator above a line and a non-zero denominator below that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.To find what fraction of the marbles now in the bag is blue:
Important information is that immediately before the last step blue marbles formed [tex]\frac{1}{5}[/tex] from the marble in the bag. That means that there were [tex]x[/tex] blue and [tex]4x[/tex] other marbles, for some [tex]x[/tex]. When we double the number of blue marbles, there will be [tex]2x[/tex] blue and [tex]4x[/tex] other marbles. Hence, blue marbles now form [tex]\frac{1}{3}[/tex] all marbles in the bag.Therefore, (C) [tex]\frac{1}{3}[/tex] fraction of the marbles now in the bag is blue.
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Complete question:
A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?
(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/5
(E) 1/2
What is another name for XW?
Name a ray with an endpoint X.
Give another name for WX.
What’s another name for AXW?
Double points
Another name for AXW is <X
What is another name for XW?The arrow on XW implies that the segment XW is a ray, such that any of the points X or W can be the starting point
Hence, another name for XW is WX
Name a ray with an endpoint X.A ray with an endpoint X is a ray that ends at point X
An example of such ray is XY
Give another name for WX.The arrow on WX implies that the segment WX is a ray, such that any of the points X or W can be the starting point
Hence, another name for WX is XW
What’s another name for AXW?The name AXW represents an angle
An angle can be named after its middle point
Hence, another name for AXW is <X
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Miguel is making pudding. The recipe yields
6 servings and calls for 2
cups of milk. How
many cups of milk will Miguel need for 18
servings of pudding?
Using the given recipe, he will need 6 cups of milk to make 18 servings.
How many cups of milk will Miguel need for 18 servings of pudding?We know that the recipe for 6 servings, calls for 2 cups of milk.
Miguel wants to do 18 servings, Then he needs to use the recipe:
18 = x*6
Solving the linear equation for x:
x = 18/6 = 3
So he needs to use his recipe 3 times.
And we know that for 6 servings he needs 2 cups of milk, then for 18 he needs:
3*(2 cups) = 6 cups of milk.
Using the given recipe, he will need 6 cups of milk to make 18 servings.
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Drag the tiles to the correct boxes to complete the pairs.
Given: u = <-2, -7>, v = <3, -4>, and w = <5, 1>.
Based on the components of the given vectors, match each vector subtraction with the graph of the resulting vector.
Please help me figure out the correct pairs, godbless the one who answers! (See images attached)
Performing subtraction operations on the given vectors gives;
Graph 1 → u - vGraph 2 → u - wGraph 3 → w - vGraph 4 → v - u Which method can be used to complete the pairs correctly?
u - v = <-2 - 3, -7 - (-4) > = <-5, -3>
Therefore;
Graph 1 → u - vu - w = <-2 - 5, -7 - 1> = <-7, -8>
u - w = <-7, -8> which corresponds with graph 2
Therefore;
Graph 2 → u - ww - v = <5 - 3, 1 - (-4)> = <2, 5>
w - v = <2, 5> which corresponds with graph 3
Therefore;
Graph 3 → w - vv - u = <3 - (-2), -4 - (-7)> = <5, 3>
v - u = <5, 3> which corresponds with graph 4
Therefore;
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PLEASE HELP Which answer provides a counterexample to the following statement: "If a figure has an endpoint,
then it is a line segment"?
Answer:
ray
Step-by-step explanation:
Rays only have one endpoint, so it continues infinitely in one direction. Segments have TWO endpoints.
Which equation is equivalent to: 3r = 78 + 14 ?
A. −3r =−78+14
B. 3r =78−14
C. 3r−14 =78
D. −3r =78−14
Answer:
Step-by-step explanation:
B is the answer
A popular roller coaster ride lasts 10 minutes. There are 20 people on average on the roller coaster during peak time. How many people are stepping onto the roller coaster per minute at peak time
There are 2 people are stepping onto the roller coaster per minute at peak time
According to statement
Given Flow time = 10 minutes.
Given Inventory = 20.
We use the formula then
I = R × T,
Therefore R = I / T.
Substitute the values in formula then
Flow rate = 20 / 10 = 2 people per minute.
So, There are 2 people are stepping onto the roller coaster per minute at peak time
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The theater club of a local high school is planning a production. The amount of time t needed to assemble the set is inversely proportional to the number of people n working. Twelve people can assemble the set in 5 hours.
Write an equation to represent the situation.
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if a=7 feet and b=7 feet, what is c? if necessary, round to the nearest tenth.
The length of hypotenuse when the value of legs of a right angled triangle are 7 and 7 feet is 9.9 feet.
Given that a and b are legs and c is the hypotenuse. length of legs of a right angled triangle are 7 feet and 7 feet.
We have to find the value of c in the right angled triangle.
In this we have to apply pythagoras theorem because it says tat the square of hypotenuse is equal to the sum of squares of base and perpendicular of that right angled triangle.
[tex]H^{2} =P^{2} +B^{2}[/tex]
H=c
P=7 feet
B=7 feet.
Put the values in the above rule:
[tex]c^{2} =7^{2} +7^{2}[/tex]
[tex]c^{2}[/tex]=49+49
[tex]c^{2}[/tex]=98
c=9.899
After rounding off to nearest tenth we will get c=9.9.
Hence the value of c is 9.9 which is the length of hypotenuse.
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More than 93 percent of all blank______ are distributed as freestanding inserts in newspapers
More than 93 percent of all blank coupons are distributed as freestanding inserts in newspapers.
What is percent?
A percentage solution is a chemical or compound amount or volume per 100 mL of solution. It is a proportion of solute to solvent: X amount/100 ml = X% Percentage solutions are a simple and convenient way to record solution concentrations.A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. It is denoted by the symbol "%."To learn more about percentage visit:
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A sales tax of P9,000 is added to a purchase of P120,000 worth of
jewelry. What is the rate of sales tax?
Answer:
Find the rate of sales tax
R= 9000/120000
=0.075
=7.5%
So, the rate is 7.5%
what are the solutions to 5x^2 - x - 1 < 0
If the average (arithmetic
mean) of 2, 7, and x is 12,
what is the value of x?
Answer: 27
Step-by-step explanation:
Mean = Sum of data/Number of data = (2 + 7 + x)/3 = 12
(x+9)/3 = 12
x+9 = 36
x = 27
Which expression is equivalent to (r^5/4
Answer:
2
Step-by-step explanation:
• Multiplying two numbers with same bases is the same as adding their powers:
∴ [tex](\frac{4^{\frac{5}{4} } \cdot 4^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](\frac{4^{\frac{5}{4} } ^ + ^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
• Dividing two numbers with same bases is the same as subtracting their powers:
∴ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](4^{{\frac{6}{4} - \frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](4^{1})^{\frac{1}{2} }[/tex]
⇒ [tex]4^{\frac{1}{2}[/tex]
• Raising anything to the power of [tex]\frac{1}{2}[/tex] is the same as square-rooting it:
∴ [tex]4^{\frac{1}{2}[/tex]
⇒ [tex]\sqrt{4}[/tex]
⇒ 2
Some bacteria double in every hour. if there were 2 bacteria in the beginning, how many bacteria will be there after 6 hours? how many bacteria will be there after 24 hours?
Using an exponential function, it is found that:
After 6 hours, there will be 256 bacteria.After 24 hours, there will be 33,554,432 bacteria.What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the growth rate.The parameters for this problem are given as follows:
a = 2, b = 2.
Hence the number of bacteria after x hours is given by:
[tex]y = 2(2)^x[/tex]
After 6 hours, the amount is:
[tex]y = 2(2)^6 = 2^7 = 128[/tex]
After 24 hours, the amount is:
[tex]y = 2(2)^{24} = 2^{25} = 33554432[/tex]
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If the variance of a security is 0.01545, what is the standard deviation?
A. 0.1545
B. 0.1243
C. 0.0155
D. 0.1121
The standard deviation is 0.1243, given the variance to be 0.01545, making option B the right choice.
Dispersion is measured by variance. A metric called a "measure of dispersion" is used to assess how variable data are concerning an average value. There are two sorts of data: grouped and ungrouped. Data is referred to as grouped data when it is presented as class intervals. On the other hand, it is referred to as ungrouped data if it comprises just individual data points. For both types of data, the sample and population variances may be calculated.
The variance of the provided data is obtained by taking the square of the standard deviation. The standard deviation is used to determine how widely distributed the data points are about the mean. In other words, the standard deviation is used to determine how observations in a data collection deviate from the mean. While the standard deviation has the same unit as the population or the sample, variance is represented in square units.
In the question, we are asked to find the standard deviation, if the variance is 0.01545.
We know that Variance = (Standard Deviation)².
This gives us:
Standard Deviation = √Variance,
or, Standard Deviation = √0.01545,
or, Standard Deviation = 0.12429802894 ≈ 0.1243.
Thus, the standard deviation is 0.1243, given the variance to be 0.01545, making option B the right choice.
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One of the legs of a right triangle measures 10 cm and the other leg measures 7 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
12.2 cm
Step-by-step explanation:
we are going to use the formula (below).
Our a and b are going to be our two legs: 10cm and 7cm
[tex]C^{2} =10^{2} +7^{2} \\C^{2}=100+49\\C^{2}=149\\C=\sqrt{149} \\C=12.2cm[/tex]
make x the subject! w/ show work