Normal time taken for operation = 7.7
Charlene's work performance is faster than normal time.
Need to define Charlene's average time:
8.4 + 8.6 + 8.3 + 8.5 + 8.7 + 8.5)/6
Avg time taken= 8.5.
Performance rating = 110/100 = 1.1
normal time taken: 8.5/1.1
normal time taken= 7.7
hence, 8.5 [tex]\geq[/tex] 7.7
Charlene is faster than normal time.
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the circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm. (a) use differentials to estimate the maximum error (in cm2) in the calculated surface area. (round your answer to the nearest integer.) cm2 what is the relative error? (round your answer to three decimal places.) (b) use differentials to estimate the maximum error (in cm3) in the calculated volume. (round your answer to the nearest integer.) cm3 what is the relative error? (round your answer to three decimal places.)
a) the maximum error in surface area and the relative error is 25.4 cm² and 1.25%
b) the maximum error in the volume and the the relative error is 162.1 cm³ and 1.875%
As we know the formula for surface area is
Surface Area , S= 4*π*r^2.
So differentiating both sides we get
dS/dr = 8*π*r .....1
and the formula for the circumference is :2*π*r
, so the error on the circumference will be respect to radius
=> Δc = 2*π*Δr
=> Δr = ΔC / (2*π)
substituing the value ofΔr in the equation 1, we get
The maximum error in surface area which is :
ΔS = 8*π*r*Δr = 4*r*Δc
= (2/π)*c*Δc.
= 25.4
where for the relative error
ΔS/S = 4*r*Δc/(4*π*r^2)
= Δc/(π*r)
= 2*Δc/c
= 1.25%
Now Since the formula for the volume of a sphere is :
V = 4/3*π*r^3
dofferentiating both sides we get ,
=> dV/dr = 4*π*r^2.
So, the the maximum error in the calculated volume will be :
ΔV = 4*π*r^2*Δr
= 2*r^2*Δc
= 1/(2*π^2)*c^2*Δc
=162.1
Where as the relative error for the volume will be
ΔV/V = 3*Δr / r = 3*ΔC/C = 1.875%
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PLS BE DONE RIGHT AWAY. NO NEED TO GRAPH JUST SOLVE
Answer:
x/1
Step-by-step explanation:
8=-4x-4
4=-4x
(divide by -4)
1=x
Answer:
[tex]-1\geq x[/tex]
Step-by-step explanation:
[tex]8\leq -4(x-1)[/tex]
[tex]8\leq -4x+4[/tex]
[tex]8-4=-4x+4-4[/tex]
[tex]4\leq -4x[/tex]
[tex]\frac{4}{-4} \leq \frac{-4x}{-4}[/tex]
Inequality is reversed:
[tex]-1\geq x[/tex]
Hope this helps
mnm corporation gives each of its employees an aptitude test. the scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. a simple random sample of 25 is taken from a very large population. what is the probability that the average aptitude test score in the sample will be less than 78
a) The expected value is 75, the standard deviation is 3 and the shape is approximately normal.
b) 0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.
c) 0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68.
d) 0.8907 = 89.07% probability that the average aptitude test in the sample will be less than 78.69.
e) The value of C = 81.51.
What is meant by Normal probability distribution?When the distribution is normal, we use the z-score formula.
In a set with mean [tex]$\mu$[/tex] and standard deviation [tex]$\sigma$[/tex], the z-score of a measure X is given by:
[tex]$Z=\frac{X-\mu}{\sigma}$[/tex]
The Z-score calculates the deviation of the measure from the mean in standard deviations. We glance at the z-score table after determining the Z-score to determine the p-value connected to it. The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the p-value.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]$\mu$[/tex] and standard deviation [tex]$\sigma$[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]$\mu$[/tex] and standard deviation [tex]$s=\frac{\sigma}{\sqrt{n}}$[/tex].
The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15.
This means that [tex]$\mu=75, \sigma=15$[/tex]
a. By the Central Limit Theorem, it will be approximately normal, with expected value [tex]$\mu=75$[/tex] and standard deviation [tex]$s=\frac{15}{\sqrt{25}}=3$[/tex]
b. The p-value of Z when X = 82.14 subtracted by the p-value of Z when X = 70.14.
X = 82.14
[tex]$Z=\frac{X-\mu}{\sigma}$[/tex]
By the Central Limit Theorem
[tex]$Z=\frac{X-\mu}{s}$[/tex]
[tex]$Z=\frac{82.14-75}{3}$[/tex]
Z = 2.38
Z = 2.38 has a p-value of 0.9913.
[tex]$Z=\frac{X-\mu}{s}$[/tex]
substitute the values in the above equation, we get
[tex]$Z=\frac{70.14-75}{3}$[/tex]
Z = -1.62 has a p-value of 0.0526
0.9913 - 0.0526 = 0.9387
0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.
c. This is 1 subtracted by the p-value of Z when X=82.68.
[tex]$Z=\frac{X-\mu}{s}[/tex]
substitute the values in the above equation, we get
[tex]$&Z=\frac{82.68-75}{3} \\[/tex]
Z = 2.56 has a p-value of 0.9948.
1 - 0.9948 = 0.0052
0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68
d. This is the p-value of Z when X=78.69. So
[tex]$&Z=\frac{X-\mu}{s} \\[/tex]
substitute the values in the above equation, we get
[tex]$&Z=\frac{78.69-75}{3} \\[/tex]
Z = 1.23 has a p-value of 0.8907
0.8907 = 89.07 % probability that the average aptitude test in the sample will be less than 78.69.
e. Find a value, C, such that P((x>C) = 0.015.
This is X when Z has a p-value of 1 - 0.015 = 0.985.
So X when Z = 2.17.
[tex]$Z=\frac{X-\mu}{s}$[/tex]
substitute the values in the above equation, we get
[tex]$2.17=\frac{X-75}{3}$[/tex]
X - 75 = 3 × 2.17
X = 81.51
Therefore, the value of C = 81.51
The complete question is:
MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 25 is taken from a population of 500.
a. What are the expected value, the standard deviation, and the shape of the sampling distribution of?
b. What is the probability that the average aptitude test in the sample will be between 70.14 and 82.14?
c. What is the probability that the average aptitude test in the sample will be greater than 82.68?
d. What is the probability that the average aptitude test in the sample will be less than 78.69?
e. Find a value, C, such that P(( x>C) = .015.
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find the 41st term 11, 16, 21…
Answer:
You can add up to 5 each time, so we just need to multiply 5 by 40 although we already have the first three terms.
A: 40*5 = 200
Step-by-step explanation:
21 + 200 = 221
draw and label tape diagram to model each number sentence
ANSWER:
We can see the answer in the drawing.
STEP-BY-STEP EXPLANATION:
In this case, we make the diagram as follows:
Which set of points would NOT define a function? A) {(-2,-2), (-1,-1), (0, 0), (1, 1), (2, 2)} B) {(-2,9), (0, 1), (1,0), (3, 4), (4,9)} C) {(-1,0), (0, 1), (0, -1), (3, 2), (3,-2)} D) {(-6, 2), (-5, 1), (-4,0), (-3, 1), (-2, 2)}
In order to a set o points define a function, a value of x can't have two different values of y.
Looking at every option, we have in the option C that the value of x = 0 has two different values of y (1 and -1), therefore this set of points do not define a function.
So the answer is C.
A 21-foot bean is to be cut into three pieces so that the second and third piece are each 3 times the length of the first piece. If x represents the length of the first piece, find the length of each piece
Answer: 3, 9, and 9
Step-by-step explanation:
X+3x+3x=217x=21x=33, 9, 9=21
solve and show working:- log(x^2 + 7) base 4 = 2
The value of x for the given logarithm equation log(x^2 + 7) base 4 = 2 is x = ± 3.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
It is known that [tex]log_{a}b[/tex] = c can be written as [tex]a^{c}[/tex] = b.
Given that, log(x^2 + 7) base 4 = 2
Therefore, x² + 7 = 4²
x² + 7 = 16
x² = 16 - 7 = 9
x² = 9
x = ±3
Hence "The value of x for the given logarithm equation log(x^2 + 7) base 4 = 2 is x = ± 3".
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ILL Give one hundred points and Branly only if you do it right though
Answer:
1) -2
2) -2
3) -2
4) -3
5) -4
6) -15
7) -13
8) 3
1b) -9
2b) -2
3b) 7
4b) 17
5b) -4
6b) -9
7b) -16
8b) 0
1c) -5
2c) -3
3c) 0
4c) -2
5c) -8
6c) -11
7c) -3
8c) 15
Jeez, I hope this helps xD
If m2 = 12x - 15 and m27 = 3x + 21, what is the measure of 21?
In the given figure, m∠2 and m∠7 are "Alternate Exterior Angles" and they are always congruent (equal).
So we can equate them and solve for x.
[tex]\begin{gathered} m\angle2=m\angle7 \\ 12x-15=3x+21 \\ 12x-3x=21+15_{} \\ 9x=36 \\ x=\frac{36}{9} \\ x=4 \end{gathered}[/tex]So, m∠2 is
[tex]\begin{gathered} m\angle2=12x-15 \\ m\angle2=12(4)-15 \\ m\angle2=48-15 \\ m\angle2=33\degree \end{gathered}[/tex]According to the straight-line angle property, the sum of m∠1 and m∠2 must be equal to 180°
[tex]\begin{gathered} m\angle1+m\angle2=180\degree \\ m\angle1+33\degree=180\degree \\ m\angle1=180\degree-33\degree \\ m\angle1=147\degree \end{gathered}[/tex]Therefore, the measure of m∠1 is 147°
Find the difference between the product of 2.5 and 7.5and the sum of 2.7 and 9.55
albert brought a blanket for 32.75, a pillow for 12.75,and a glove for 16.25. he paid 50 and the rest he borrowed from his friend. if albert for 5.25 in change from the cashier, how much did he borrow from his friend to pay for all of the items.
Albert borrowed $17 from his friend.
Given,
Albert brought some items:
Cost of blanket = $32.75
Cost of pillow = $12.75
Cost of glove = $16.25
Amount paid by Albert = 50
Amount borrowed by Albert from his friend = x
Cashier gave back the change = $5.25
We have to find the amount borrowed by Albert from his friend:
This is simply arithmetic operations:
Total cost in shop = 32.75 + 12.75 + 16.25 = $61.75
Total amount given to the cashier = 61.75 + 5.25 = 67
Amount borrowed by Albert from his friend = Total amount given to the cashier - Amount paid by Albert
x = 67 - 50
x = 17
That is,
Albert borrowed $17 from his friend.
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Which statement is true about the equations –3x + 4y = 12 and One-fourthx – One-thirdy = 1?
The system of the equations has exactly one solution at (–8, 3).
The system of the equations has exactly one solution at (–4, 3).
The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.
Answer: The answer is c) The system of the equations has no solution; the two lines are parallel.
Step-by-step explanation: edge 2022
Answer: C
Step-by-step explanation:
A cyclist leaves New York traveling at an average speed of 9 miles per hour. 4 hours later, a car leaves Bay Shore, on the same route, traveling at an average speed of 21 miles per hour. How many hours after the car leaves New York will the car catch up to the cyclist? *
The car will catch up with cyclist in 3 hours
What is time ?Time refers to the interval in seconds , minutes or hours it took for an event to take place
How to calculate How many hours it will take the car to catch up with cyclistInformation given for the question include
A cyclist has average speed of 9 miles per hour
A car leaves has average speed of 21 miles per hour
following same route when
The question is asking at what time will the distance be equal if the cyclists have advantage of 4 hours already
Calculation of distance covered by the cyclist
average speed = distance / time
distance = 9 mph * (x + 4)
Calculation of distance covered by the car
average speed = distance / time
distance = 21 mph * x
equating both gives
9 mph * (x + 4) = 21 mph * x
9x + 36 = 21x
36 = 21x - 9x
12x = 36
x = 3
hence the car will meet the cyclist in 3 hours
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Kirby is buying a new grill that has been reduced for an end of summer sale by 25% to $496. what was the original price of the grill?
Given:
percentage decerease = 25%
current price of the grill = $496
Let the original price of the grill be x
We can calculate percentage decrease using the formula:
[tex]\text{Percent decrease = }\frac{Orig\text{ inal value - new value}}{Orig\text{ inal value}}\text{ }\times\text{ 100}[/tex]Substituting the given values we have:
[tex]\begin{gathered} 25\text{ = }\frac{x-496}{x}\times\text{ 100} \\ 25\text{ = }\frac{(x-496)\times100}{x} \end{gathered}[/tex]Cross-Multiply:
[tex]\begin{gathered} 25x\text{ = 100x - 49600} \\ \text{Collect like terms:} \\ -75x\text{ = -49600} \\ \text{Divide both sides by -75} \\ \frac{-75x}{-75}\text{ = }\frac{-49600}{-75} \\ x\text{ }\approx\text{661.33} \end{gathered}[/tex]Hence, we can conclude that the original price of the grill is approximately $661.33
Answer:
$661.33
5 Let A(-2,5) and B(5,0) be the endpoints of AB. What is the length of the segment?
The equation for finding the length between two points is:
[tex]l\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]where point 1 has coordinates (x1, y1) and point 2 has coordinates (x2, y2).
We assign A to be point 1 and B be point 2
Therefore,
[tex]\begin{gathered} l\text{ = }\sqrt[]{(0_{}-5_{})^2+(5_{}-(-2)_{})^2} \\ l\text{ = }\sqrt[]{(-5)_{}^2+(7_{})^2} \\ l\text{ = }\sqrt[]{25+49^{}} \\ l\text{ =}\sqrt{\text{74}} \end{gathered}[/tex]I don’t understand can someone help me? Create a linear equation for the following data:
Given the data shown in the table, you can identify that these two points are on the line:
[tex](-1,7)(2,-2)[/tex]By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
You can find the slope of the line using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where these two points are on the line:
A plumber charges $25 for a service call plus $50 per hour of survice write an equation in slope-intercept form the cost for,C, after h hours of survice
The total cost for 8 hours of work is $425.
The total cost for 10 hours of work is $525.
The total amount the plumber earns is made up of a fixed charge and a variable charge. A fixed charge is a charge that remains constant regardless of the number of hours the plumber works. The fixed charge is $25. The variable charge is the charge that increases per hours worked. The variable charge is $50 per hour.
Cost = fixed charge + variable charge
C = $25 + $50h
The total cost for 8 hours
$25 + $50(8)
$25 + $400
= $425.
The total cost for 10 hours
$25 + $50(10)
$25 + $500
$525.
What is 420÷6 hellllll,lllllllllllllllpppppp I n ee d it now
Answer:
70
Step-by-step explanation:
A chemical company makes two brand of antifreeze. The first brand is 70 % pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 110 gallons of a mixture that contains 85% pure antifreeze, how many gallons of each brand of antifreeze must be used?first brand:_____gallonssecond brand:_____gallons
Since the 1st brand is 70% pure antifreeze
Since the 2nd brand is 95% pure antifreeze
Since we need to obtain 110 g of a mixture that contains 85% pure antifreeze
Let the quantity of the first is x and the second is y
Then
[tex]\frac{70}{100}x+\frac{95}{100}y=\frac{85}{100}(110)[/tex][tex]0.7x+0.95y=93.5\text{ (1)}[/tex][tex]x+y=110\text{ (2)}[/tex]Now let us solve the two equations to find x and y
Multiply equation (2) by -0.7
[tex]\begin{gathered} (-0.7)x+(-0.7)y=(-0.7)110 \\ -0.7x-0.7y=-77\text{ (3)} \end{gathered}[/tex]Add equations (1) and (3)
[tex]\begin{gathered} (0.7x-0.7x)+(0.95y-0.7y)=(93.5-77) \\ 0+0.25y=16.5 \\ 0.25y=16.5 \end{gathered}[/tex]Divide both sides by 0.25
[tex]\begin{gathered} \frac{0.25y}{0.25}=\frac{16.25}{0.25} \\ y=66 \end{gathered}[/tex]Substitute the value of y in equation (2) to find x
[tex]x+66=110[/tex]Subtract 66 from both sides
[tex]\begin{gathered} x+66-66=110-66 \\ x+0=44 \\ x=44 \end{gathered}[/tex]First brand: 44 gallons
Second brand: 66 gallons
75% of the marbles in a bag are orange and the rest are blue. What fraction of the orange marbles must be removed from the bag so that 50% of the remaining marbles are orange?
Answer:
1/2
Step-by-step explanation:
75% of the marbles in a bag are orange and the rest are blue. The percentage for blue will be:
= 100% - 75%
= 25%
The fraction of the orange marbles that must be removed from the bag so that 50% of the remaining marbles are orange will be:
= 75% - 25%
= 50%
= 1/2
Fill in the missing. How many solutions does the equation have? what does the simplified equation mean?
5.5x - 2.1 = 3 + 5.5x
5.5x - 2.1 - _____ x = 3 + 5.5x - _____ x
_____ = _____
The equation 5.5x - 2.1 = 3 + 5.5x has no solution. Then the number of the solution is zero.
What is the solution to the equation?The allocation of weights to the relevant variables that produce the calculation's equilibrium is referred to as a direct consequence.
Simplicity is the quality of making anything less complicated and more manageable in terms of both execution and comprehension.
The equation is given below.
5.5x - 2.1 = 3 + 5.5x
Subtract 5.5x on both sides, then simplify the equation.
5.5x - 5.5x - 2.1 = 3 + 5.5x - 5.5x
0x - 2.1 = 3
The equation 5.5x - 2.1 = 3 + 5.5x has no solution. Then the number of the solution is zero.
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1) the owner of a video store has determined that the cost c, in dollars, of operating the store is approximately given by where x is the number of videos rented daily. find the lowest cost to the nearest dollar. a) $400 b) $500 c) $650 d) $550
The lower cost will occur at the extreme point, that is if the number of videos rented daily is 8 pieces and the cost will be $550.
The cost function is given by:
C(x) = 2x² - 32x + 678
The lowest cost happens at the extreme point. In this point the derivative of C(x) is equal to zero.
Take the derivative:
C'(x) = 4x - 32 = 0
4x = 32
x = 32/4 = 8
Hence, the lowest cost will occur if the number of video rented daily is 8 pcs.
Substitute x = 8 into the cost function:
C(8) = 2(8)² - 32.(8) + 678 = 550
Complete question:
The owner of a video store has determined that the cost c, C(x) = 2x² - 32x + 678 in dollars, of operating the store is approximately given by where x is the number of videos rented daily. find the lowest cost to the nearest dollar
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Roger and Rita each drive at a constant speed between Phoenix and San Diego. Each driver’s distance (miles) is shown for the same elapsed time (hours) of the trip. Who had a head start, and how many miles was the head start?
If each driver’s distance (miles) is shown for the same elapsed time (hours) of the trip. The person that had a head start is: Rita had a 28-mile head start.
Determining the speedSlope for speed = (y² - y1) / (x² - x1)
Slope for speed = (130 - 65) / (2 - 1)
Slope for speed= 65 / 1
Slope for speed= 65 mph
Determining Roger's starting position if Roger distance is 65.
Hence,
Mile of head start = Slope of speed - Roger distance
Mile of head start = 65 mph - 65 miles
Mile of head start = 0 miles
Rita starting position if Rita distance is 93
Slope for speed = (y² - y1) / (x² - x1)
Slope for speed = (158 - 93) / (2 - 1)
Slope for speed = 65 / 1
Slope for speed = 65 mph
Mile of head start = Slope of speed - Rita distance
Mile of head start = 93 - 65
Mile of head start= 28 miles
Therefore we can conclude that Rita has a head start of 28 miles.
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Answer:
Rita had a 28-mile head start.
Step-by-step explanation:
EDGE
Help Me Please
A B, C, or D.
Answer correctly
Answer: D
Step-by-step explanation:
as when 3746 is rounded to the nearest hundred t is 4000
whereas when 3746 is rounded to the nearest ten it is 3800.
4000 is larger than 3800 so the answer is D.
A triangle has 2 angles measuring 40 degrees and 50 degrees. What is the measure of the 3rd angle and classify the triangle.
A triangle has all three angles summing up to 180. If two of the sides measure 40 degrees and 50 degrees, then the third side measures as follows;
[tex]\begin{gathered} 40+50+A=180 \\ A=180-40-50 \\ A=90 \end{gathered}[/tex]The third angle, which is labelled as angle A measures 90 degrees, and that means the triangle is a "right angled triangle."
Solve the following inequality.xe^x ≥7Choose one:1. x ≤ 1.522. no solution3. x ≤ 1.954. x ≥ 1.955. x ≥ 1.52
1) Considering e =2.72
Then let's plug it in the inequality, and calculate the natural logarithm.
[tex]\begin{gathered} xe^x\ge7 \\ x2.72^x\ge7 \\ 2.72^x\ge\frac{7}{x}^{} \\ \ln 2.72^x\ge\ln (\frac{7}{x}) \\ x\text{ }\ge1.52 \end{gathered}[/tex]2) Then option 5 is the answer
X≥ 1.52
I need help with #10 It says to also round to the nearest hundredth. Please help!
In general, one can obtain the volume of a sphere and a cube using the formulas below
[tex]\begin{gathered} V_{cube}=l^3 \\ l\rightarrow\text{ side of the cube} \\ V_{sphere}=\frac{4}{3}\pi r^3 \\ r\rightarrow\text{ radius} \end{gathered}[/tex]In our case, we need to subtract the volume of the hollow sphere from the volume of the cube, as shown below
[tex]\begin{gathered} V_{cube}=18^3 \\ and \\ V_{sphere}=\frac{4}{3}\pi(9)^3 \\ \Rightarrow V_{foam}=V_{cube}-V_{sphere} \\ \Rightarrow V_{foam}=2778.371... \end{gathered}[/tex]Rounding to the nearest hundredth,
[tex]\Rightarrow V_{foam}\approx2778.37[/tex]The answer is 2778.37in^3
What is the answer for the equation:
7x+31 = 8x -1/3(27x+3) ?
The answer for the equation:
7x+31 = 8x -1/3(27x+3) is x=-4
there will be 5 songs and 3 dances in a performance how many distinguished way to arrange the shows if all dances cannot be next to each other? and how many ways to arrange the shows if all dances must be next to each other?
In a performance there will be 5 songs and 3 dances
Total objects 5+3 = 8
Number of ways of arranging this objects is 8! = 40,320...........(1)
If all the dances must be next to each other than all dances should take as an object as 3!
Number of ways of arranging performing taking dance to each other
is = (5+1)! 3!
= 6! 3!
= 4320 ....................(2)
Number of ways to arrange the shows if all dances can not be next to each other = (1) - (2)
= 40320-4320
= 3600 ways
Number of ways to arrange the shows if all the dances must be next to each other is 4320 ways.
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