The question can be addressed using the principles of Normal Distribution. Given the z-chart, 8 ounces is the observed value for the 99.5th percentile, which equates to approximately 2.58 standard deviations. Therefore, the mean setting of the coffee machine should be set around 8 ounces for the cup to overflow only 0.5% of the time.
Explanation:The situation described in the question is a typical case of application of Normal Distribution. As a reminder, in a Normal Distribution, 99.7% of the values lie within 3 standard deviations of the mean. The question states that the cup should overflow only 0.5% of the time. Therefore, we need to consider the 99.5% of the left side under the normal curve (as we're considering the upper limit), which corresponds to around 2.58 standard deviations under the normal curve.
Given that the standard deviation (σ) is 0.4 ounces, using the formula X = μ + Zσ (where Z is the Z-score corresponding to the desired percentile, μ is the mean we want to find, and X is the threshold value where the cup overflows at 8 ounces), we can substitute the known values and solve for μ.
Therefore, 8 = μ + 2.58 * 0.4 Solving for μ gives us around μ = 7.966, or about 8 ounces. Hence, the mean setting of the coffee machine should be set around 8 ounces to ensure that the cup will overflow only 0.5% of the time.
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Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura. How long would Tammy take to do the job alone?
3 hrs.
4 hrs.
6 hrs.
The number of hours that Tammy takes to do the job alone will be 4 hours. Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura.
The equations are given as,
T + J + L = 1 + 20/60
T + J + L = 1.333 ....1
J = 2T ....2
J = 2 + L ....3
The rate for Laura, Tammy, and Jeri will be given as,
Laura DATA:
Time = x hr/job ; Rate = 1/x job/hr
Jeri DATA:
Time = x+2 hr/job ; Rate = 1/(x+2) job/hr
Tammy DATA:
Time = (x+2)/2 hr/job ; Rate = 2/(x+2) job/hr.
Together DATA:
Time = 4/3 hr/job ; Rate = 3/4 job/hr
The equation is given as,
Rate + Rate + Rate = Together rate
1/x + 1/(x+2) + 2/(x+2) = 3/4
Multiply the equation by 4x(x+2) to get:
4(x+2) + 4x + 8x = 3x(x+2)
16x + 8 = 3x^2+6x
3x^2-10x-8 = 0
3x^2-12x+2x-8 = 0
3x(x-4)+2(x-4) = 0
(x-4)(3x+2) = 0
x = 4, - 2/3
The number of hours that Tammy takes to do the job alone will be 4 hours. Then the correct option is B.
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Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 3 + x - 3x2 = 9 A) (x - 1 6 )2 = 71 36 B) (x - 1 3 )2 = 71 36 C) (x - 1 6 )2 = - 71 36 Eliminate D) (x - 1 3 )2 = - 71 36
what is the volume of the cylinder?
radius=7 height=18
A.126
B.252
C.2268
D.882
Answer:
Option D. [tex]882\pi\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
In this problem we have
[tex]r=7\ units[/tex]
[tex]h=18\ units[/tex]
substitute
[tex]V=\pi (7^{2})(18)=882\pi\ units^{3}[/tex] -----> exact value of the volume
A spherical ball of wax with a radius of 4 inches is melted and poured into a container shaped like a rectangular prism with a 6 inch x 6 inch base. What is the height of the melted wax in the new shape?
Phil is offered a 3-year contract with a law firm. His first year earnings would be $81,000 with an annual raise of 15%.
What would Phil's total earnings be over the term of the contract?
Enter your answer, rounded to two decimal places, in the box.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%. Phil's total earnings would be over the term of the contract is $281272.5.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%.
First year
= $81000
Second year
1.15 x ($81000)
= $93150
Third year
1.15 x ($93150)
= $107122.50
Phil's total earnings would be over the term of the contract
= $81000 + $93150 + $107122.50
= 281272.5
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Anyone know?
A. 99
B. 100
C. 121
D. Cannot be determined
Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.
By being congruent, the corresponding angles and sides are equal.
Therefore, [tex]\angle A = \angle F[/tex], [tex]\angle B = \angle G[/tex], [tex]\angle C = \angle H[/tex], [tex]\angle D= \angle I[/tex], [tex]\angle E = \angle J[/tex].
By using [tex]\angle A = \angle F[/tex]
So, [tex]100^\circ = \angle 1[/tex]
Therefore, the measure of angle 1 is 100 degrees.
So, Option B is the correct answer.
The antarctic peninsula is less than 700 miles from what continent
PLEASE HELP: Question above ☝☝☝
I'm actually pretty sure it's B
A 3-lb force acting in the direction of the vector (3,-1) moves an object just over 9 ft from point (0,5) to (6,-2). Find the work done to move the object to the nearest foot-pound
Answer: The Work done to move the object is [tex]=23.15 \text { foot pounds }[/tex]
Step-by-step explanation:
Given;
Force F=3 [tex]l b s[/tex]
Vectors of F= (3,-1)
Moves object to a distance=9 [tex]f t s[/tex]
Let A and B be the displacements Vectors
A= (0,-5)
B= (6,-2)
To Find:
Work done in foot-pounds
Solution:
Work done [tex]W=F \times D[/tex]
Direction of force vector= (3,-1) (i, j)
=3i-j
Unit of force vector [tex]=\sqrt{3^{2}+\left(-1^{2}\right)}[/tex]
[tex]=\sqrt{9+1}[/tex]
Force vector=(Force/Unit Vector)Direction of force vectors
F=[tex]3 / \sqrt{10} \times(3 i-j)[/tex]
Direction of motion vector= (B-A)
= (6,-2)-(0,-5) x i,j)
=(6-0),(-2-5) x (i, j)
=(6,-7) x (i, j)
=6i-7j
Unit of motion vector [tex]=\sqrt{6^{2}+\left(-7^{2}\right)}[/tex]
[tex]=\sqrt{36+49}[/tex]
[tex]=\sqrt{85}[/tex]
Motion Vector= (Distance moved by the object/Unit motion vector) × (Direction of motion vectors)
[tex]D=9 / \sqrt{85} \times(6 i-7 j)[/tex]
Workdone [tex]W=F \times D[/tex]
[tex]= [3/ \sqrt{10} \times (3i-j)] \times [9/ \sqrt{85} \times (6i-7j)][/tex]
[tex]= [3/ \sqrt{10} \times 9/ \sqrt{85}] \times [(3i-j) \times(6i-7j)][/tex]
[tex]= [3/3.1623 \times 9/9.2195] \times [(3\times6) + ((-1) \times (-7))][/tex]
[tex]= [0.94867 \times 0.97619] \times [18+7][/tex]
[tex]=23.15 \text { foot pounds }[/tex]
Result:
Work done to move an object [tex]=23.15 \text { foot pounds }[/tex]
Answer:
[tex]W = 25.617\,lbf\cdot ft[/tex]
Step-by-step explanation:
The work done to move the object is:
[tex]W = F \cdot s \cdot \cos \alpha[/tex]
The angle of the force with respect to change in the position vector is:
[tex]\alpha = \tan^{-1}\left(-\frac{7}{6} \right) - \tan^{-1}\left(-\frac{1}{3} \right)[/tex]
[tex]\alpha \approx 18.415^{\textdegree}[/tex]
The magnitude of the work done is:
[tex]W = (3\,lbf)\cdot (9\,ft)\cdot \cos 18.415^{\textdegree}[/tex]
[tex]W = 25.617\,lbf\cdot ft[/tex]
The recursive rule for a sequence is shown. an=an−1+7 a1=17 what is the explicit rule for this sequence?
The explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
The recursive rule is given as:
[tex]a_n=a_{n-1}+7[/tex]
[tex]a_1 = 17[/tex]
The above shows that the sequence is an arithmetic sequence.
Start by calculating a2
We have:
[tex]a_n=a_{n-1}+7[/tex]
Substitute 2 for n
[tex]a_2=a_1+7[/tex]
This gives
[tex]a_2 = 17 + 7[/tex]
[tex]a_2 = 24[/tex]
So, we have:
a1=17
a2 = 24
The common difference (d) is:
d =a2 - a1
d = 24 - 17
d = 7
The explicit rule is then calculated as:
[tex]a_n = a_1 + (n - 1)d[/tex]
This gives
[tex]a_n = 17 + (n - 1) * 7[/tex]
Expand
[tex]a_n = 17 - 7 + 7n[/tex]
[tex]a_n = 10 + 7n[/tex]
Hence, the explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
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The range of y=1x−2+3 is y=0.
true
false
On a highway, Nick's car uses 12.5 gallons of gas to travel 240 miles. The gas tank in Nick's car holds 20 gallons of gas. How far can Nick's car travel on a highway using a full tank of gas?
Answer:
Nick's car can travel 384 miles using a full tank of gas.
Step-by-step explanation:
How would I write #3
He altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 89000 square centimeters?
Which path is a Hamiltonian circuit?
A circle has a radius of 7.2 feet and a central angle aob that measures 112°. what is the area of sector aob? use 3.14 for pi and round your answer to the nearest tenth.
Solve for x in the image below
The value of x in the equation given is 8
Using the equations given for our Calculation;
7/8 - 1/x = 3/4Take the L.C.M of 8 and x ; which is 8x
(7x - 8) / 8x = 3/4
Now we cross multiply;
4(7x - 8) = 3 * 8x
open the bracket
28x - 32 = 24x
28x - 24x = 32
4x = 32
x = 8
Hence, the value of x = 8
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Evaluate the expression
A. arctan ( - \sqrt{3} )
B. Arctan ( - \sqrt{3} )
Pls help i need this asap!
The requried both A and B refer to the same calculation, which is finding the inverse tangent of -√3. The result is -60 degrees or -π/3 radians.
A. The expression "arctan(-√3)" represents the inverse tangent function of the value -√3. The inverse tangent function returns an angle whose tangent is equal to the given value.
To evaluate arctan(-√3), we can use a calculator or reference table that provides trigonometric function values. In this case, the value is approximately -60 degrees or -π/3 radians.
B. The expression "Arctan(-√3)" is the same as "arctan(-√3)" and represents the inverse tangent function of -√3. The uppercase "Arctan" notation is commonly used in mathematical literature and calculators to represent the inverse tangent function.
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Select the equations that are equivalent to the equation y – 2 = 3(x + 6). Select all that apply.
y = 3x + 20
y = 3x + 6
2x - y = -3
3x - y = -20
Jesse earns $420 a week, and he works 5 days a week. What is his daily wage?
A. $84
B. $415
C. $60
D. $425
Morgan uses 1/4 of her supply of raisins to make a trail mix and 3/8 of her supply of raisins to make cookies.If Morgan uses 5 pounds of raisins, how many pounds of raisins are in her supply.
You are looking at two different houses. house #1 would have a daily 5-mile commute to work, while house #2 would have a daily 20-mile commute. how much more co2 would you produce annually if you buy house #2? (hint: driving 1 mile produces 1.1 lb of co2 and you work 240 days/year.)
Answer:
B: 3960 lb
Step-by-step explanation:
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The length of a rectangle is 5 yd less than three times the width, and the area of the rectangle is 28 yd2 . find the dimensions of the rectangle.
The dimensions of the rectangle are width = 4 yds and length = 7 yds.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that the length of a rectangle is 5 yds less than three times the width,
The area of the rectangle is 28 yds square.
Let the width of the rectangle is x
So the length of the rectangle = 3x - 5
The area of a rectangle = x × (3x - 5)
28 = 3x² - 5x
3x² - 5x - 28 = 0
(3x + 7)(x - 4) = 0
3x + 7 = 0 and and x - 4 = 0
x = -7/3 and x = 4
Take x = 4 as the width
So the length of the rectangle = 3(4) - 5 = 12 - 5 = 7
Therefore, the dimensions of the rectangle are width = 4 yds and length = 7 yds.
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In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. to avoid confusion between "o" and zero and between "i" and one, the letters "o" and "i" are not used. how many distinct license plates can be formed in this state?
Find the equation of the line that passes through (-2,5) and is parallel toy= -1/3x+2
Tracy can wallpaper 7 rooms in a new house in 21 hours. together with her trainee they can wallpaper the 7 rooms in 12 hours. how long would it take the trainee working by herself to do the job? round to the nearest tenth.
Lines that are not in the same plane are called _____ lines. A.perpendicular B.transversal C.skew D.parallel
Lines that are not in the same plane are called skew lines.
What is a line?"A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely."
Given, two lines are not in the same plane.
Here, perpendicular lines, transversal lines, and parallel lines should be in the same plane.
Two lines are called skew lines are two lines if they do not intersect and are not parallel.
Therefore, skew lines are not in the same plane.
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ind the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)
Which of the following is not an example of like terms? A. 2 and –6 B. 2b and –6b C. 2b and 2 D. 2b^2 and 6b^2
PLEASE HELP!!! ASAP!!!!!!!!!!!!!!! 10 POINTS
Expand the number 1800 into its corresponding exponential form.
2^3 · 3^2 · 5^2
9^2 · 100
8 · 9 · 25
2^2 · 3^3 · 5^2
Select expression equal to ^3√320
4
4^3√5
5^3√4
5^3√5