||u|| = 16.492; θ = 165.964° are the vector magnitude and direction of u.
What is a straightforward definition of a vector?
A quantity or phenomena with both size and direction being independent of one another is called a vector. Also, the phrase specifies how such a quantity is represented mathematically or geometrically. Examples of vectors in nature include weight, force, electromagnetic fields, momentum, and velocity.
Let's find the magnitude of each component:
Let
(x₁,y₁ ) = (4,4)
(x₂ , y₂ ) = (-12 , 8 )
u = ax + by
ll u ll = √a² + b²
So, let's find a and b:
a = l x₂ - x₁ l =l -12 - 4 l = l -16 l = 16
b = l y₂ - y₁ l = l 8 - 4 l = l4l = 4
so,
ll u ll = √16² + 4²
= √272
≈ 16.492
And the direction is:
θ = 180 - tan⁻¹ (b/a )
= 180 - tan⁻¹(4/16)
θ ≈ 180 - tan⁻¹ (4/16)
≈ 165.953.
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The volume of a cylinder is 1540cm^3 and the difference of its height and radius is 3cm then, find the total surface area of the cylinder.
The formula for the volume of a cylinder is [tex]r^{2}[/tex]h, where r is the radius and h is the height. To solve for h, h = r + 3, and to find the total surface area, lateral surface area = 2rh, top and bottom areas = 2[tex]r^{2}[/tex], and total surface area = 826.59 [tex]cm^{2}[/tex].
What is the total surface area of the cylinder?Let's calculate for the radius and height using the cylinder's volume formula:
Volume = π[tex]r^2h[/tex], where r is the radius and h is the height.
We have Volume = 1540 [tex]cm^3[/tex], so we can write:
1540 = π[tex]r^2h[/tex]
Also, we know that the difference between the height and radius is 3 cm:
h - r = 3
We can solve for h in terms of r by rearranging the above equation:
h = r + 3
Now we can substitute this into the formula for volume:
1540 = π[tex]r^2(r + 3)[/tex]
Simplifying and solving for r:
1540 = π[tex]r^3[/tex] + 3π[tex]r^2[/tex]
π[tex]r^3[/tex] + 3π[tex]r^2[/tex] - 1540 = 0
r ≈ 7.38 cm
Using the equation h = r + 3, we can find the height:
h = 7.38 + 3 = 10.38 cm
Now we can use the formulas for the lateral surface area and the top and bottom areas to find the total surface area of the cylinder:
Lateral surface area = 2πrh
Top and bottom areas = 2π[tex]r^2[/tex]
Substituting in the values we found, we get:
Lateral surface area = 2π(7.38)(10.38) ≈ 483.87 [tex]cm^2[/tex]
Top and bottom areas = 2π[tex](7.38)^2[/tex] ≈ 342.72 [tex]cm^2[/tex]
Total surface area = Lateral surface area + Top and bottom areas
Total surface area ≈ 826.59 [tex]cm^2[/tex]
Therefore, the total surface area of the cylinder is approximately 826.59 [tex]cm^2[/tex].
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Marcus saw the factorization shown below in his textbook, but part of the factorization was covered by a drop of ink. What expression was covered by the drop of ink?
-24x^5-16x^3=-8x^3(?+2)
The missing expression that was covered by the drop of ink is simply 3[tex]x^{2}[/tex].
What is Algebraic expression ?
An algebraic expressiοn is a statement in mathematics that can cοntain variables, integers, οperatοrs (including additiοn, subtractiοn, multiplicatiοn, and divisiοn), as well as grοuping symbοls like brackets.
The given expression is:
-24[tex]x^{5}[/tex] - 16[tex]x^{3}[/tex] = -8[tex]x^{3}[/tex] (? + 2)
To find the missing expression, we need to isolate the unknown factor, denoted by the question mark (?). We can begin by factoring out the common term of -8x³ from the left side of the equation:
-8[tex]x^{3}[/tex](3[tex]x^{2}[/tex] + 2) = -8[tex]x^{3}[/tex](? + 2)
Now, we can divide both sides by -8[tex]x^{3}[/tex], which gives:
3[tex]x^{2}[/tex] + 2 = ? + 2
Subtracting 2 from both sides yields:
3[tex]x^{2}[/tex] = ?
Therefore, the missing expression that was covered by the drop of ink is simply 3[tex]x^{2}[/tex].
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can yall pls help me with this?
The value of the given linear equation to satisfied the given expression of the equation is = [tex]\frac{-9}{10}[/tex]
What about linear equation?
A linear equation is a mathematical equation that represents a straight line in a Cartesian coordinate system. It is an algebraic equation in which the highest power of the variable is 1.
The general form of a linear equation in one variable is:
ax + b = 0 where "a" and "b" are constants and "x" is the variable. The solution to this equation is: x = -b/a
The general form of a linear equation in two variables is:
ax + by + c = 0
Define equation:
An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to represent a wide range of relationships between variables.
According to the given information:
Here, the value of x and y are given
Put the value of x and y in the given expression we have that,
⇒ 4y - x
⇒ 4 x [tex]\frac{-3}{20}[/tex] - [tex](\frac{3}{10} )[/tex]
⇒ [tex]\frac{-12}{20}[/tex] - [tex](\frac{3}{10} )[/tex]
⇒ [tex]\frac{-18}{20}[/tex]
⇒ [tex]\frac{-9}{10}[/tex]
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you want to save $12,000 for a downpayment on a house. how much should be put into an account that pays 3.95% interest compounded continuously for 5 years
The formula for continuous compounding is given by:
A = Pe^(rt)
where:
A = final amount
P = principal amount (initial investment)
e = 2.71828 (constant)
r = annual interest rate (as a decimal)
t = time in years
We can solve for P as follows:
P = A/e^(rt)
We know that we want to save $12,000, the interest rate is 3.95%, and the time is 5 years. Substituting these values into the formula, we get:
P = 12000/e^(0.0395*5)
P = 12000/e^0.1975
P = 12000/1.2183
P = 9854.16
Therefore, Max should put $9,854.16 into the account that pays 3.95% interest compounded continuously for 5 years.
g lemon and pepper are in very posh luxury cars. pepper starts at a point 30 miles north of where lemon starts. pepper starts driving east at 25 miles per hour and lemon starts driving north at 40 miles per hour. how fast is the distance between them changing after 15 minutes? is the distance increasing or decreasing?
To solve this problem, you will need to use the Pythagorean theorem. According to this theorem, a^2 + b^2 = c^2, where a and b are the two sides of a right-angled triangle and c is the hypotenuse or the longest side. In this case, the two sides are the distance traveled by Pepper and Lemon respectively, and the hypotenuse is the distance between them.
Distance between Lemon and Pepper. Let's say that after 15 minutes, Lemon has traveled a distance of d1, and Pepper has traveled a distance of d2. Since they are moving in perpendicular directions, we can say that the distance between them is the hypotenuse of the right-angled triangle formed by their paths.
Using the Pythagorean theorem, we can write this as:d^2 = d1^2 + d2^2Distance traveled by LemonIn 15 minutes, Lemon travels a distance of 40 x 15/60 = 10 miles.Distance traveled by PepperIn 15 minutes, Pepper travels a distance of 25 x 15/60 = 6.25 miles.Distance between Lemon and Pepper. Using the Pythagorean theorem, we can find the distance between Lemon and Pepper:d^2 = 10^2 + 6.25^2d^2 = 100 + 39.0625d^2 = 139.0625d = sqrt(139.0625)d = 11.7858 miles.
Differentiating this expression with respect to time (t), we get:d/dt (d^2) = d/dt (d1^2 + d2^2)2d * (dd/dt) = 2d1 * (dd1/dt) + 2d2 * (dd2/dt)(dd/dt) = (d1 * dd1/dt + d2 * dd2/dt)/dd/dt = (10 * 40/60) + (6.25 * 25/60)dd/dt = 6.25 + 2.6042dd/dt = 8.8542 miles per hourThe distance between Lemon and Pepper is increasing at a rate of 8.8542 miles per hour. Therefore, the answer is that the distance between them is increasing.
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Three ballet dancers are positioned on stage. Max is 2 feet straight behind Kenji and 4 feet directly left of Lindsey. When the music begins, Max twirls to Lindsey's position, then leaps to Kenji's position, and finally walks back to his original position. How far did Max travel? If necessary, round to the nearest tenth.
Answer: 8.5 feet
Step-by-step explanation:
To determine how far Max traveled, we can use the Pythagorean theorem to find the distances between the points.
Max twirls to Lindsey's position:
Since Max is 2 feet behind Kenji and 4 feet left of Lindsey, Max and Lindsey form a right triangle with legs of 2 feet and 4 feet. Using the Pythagorean theorem:
a² + b² = c²
2² + 4² = c²
4 + 16 = c²
20 = c²
Taking the square root of both sides:
c = √20 ≈ 4.47 feet (rounded to the nearest tenth)
Max leaps to Kenji's position:
Since Max was initially 2 feet behind Kenji, the distance between Lindsey and Kenji is also 2 feet.
Max walks back to his original position:
The distance between Max's original position and Kenji's position is 2 feet.
Adding up the distances:
4.47 feet (Max to Lindsey) + 2 feet (Lindsey to Kenji) + 2 feet (Kenji to Max's original position) = 8.47 feet
So, Max traveled approximately 8.5 feet (rounded to the nearest tenth) during his movements.
The distance Max traveled can be found by calculating the distance of each movement he makes and adding them up. First, we need to use the Pythagorean theorem to calculate the distance between Lindsey and Max:
sqrt(4^2 + 2^2) = sqrt(16 + 4) = sqrt(20) = 2*sqrt(5)
So, Max travels 2*sqrt(5) feet to get to Lindsey's position. Next, he travels the distance between Kenji and Lindsey, which is 4 feet:
distance = 4
Finally, he travels in a straight line back to his original position, which is 2 feet straight behind Kenji:
distance = 2
Adding these distances together, we get:
2*sqrt(5) + 4 + 2 = 2*sqrt(5) + 6
Rounding to the nearest tenth gives us a final answer of approximately 8.5 feet.
What is the end behavior of the function f of x equals 3 times the cube root of x? as x → â€"∞, f(x) → â€"∞, and as x → ∞, f(x) → ∞. as x → â€"∞, f(x) → ∞, and as x → ∞, f(x) → â€"∞. as x → â€"∞, f(x) → 0, and as x → ∞, f(x) → 0. as x → 0, f(x) → â€"∞, and as x → ∞, f(x) → 0.
The end behavior of the function is: as x → -∞, f(x) → -∞, and as x → ∞, f(x) → ∞.
The end behavior of the function f(x) = 3 * cube root of x can be determined by examining the function as x approaches negative and positive infinity.
1. As x → -∞, the cube root of a large negative number will also be negative, and 3 times a negative number is still negative.
Therefore, as x → -∞, f(x) → -∞.
2. As x → ∞, the cube root of a large positive number will be positive, and 3 times a positive number is still positive. Therefore, as x → ∞, f(x) → ∞.
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3) Texas enforces a 6% sales tax on items $75 and over. What would be a) the total tax and b)) the total cost on a purchase of items that cost $64, $78, $102 and $28 helppp pls
Caden’s school is due west of his house and due south of his friends Eva’s house. The distance between the school and Eva’s house is 5 kilometers and the straight-line distance between Caden’s house and Eva’s house is 13 kilometers. How far is Caden’s house from school?
Thus, the distance between Caden’s house and school is found as: 12 km.
Define about the Pythagorean theorem:Pythagoras theorem triangles are right triangles that adhere to the Pythagoras theorem. Pythagorean triples are the name given to the three sides that make up this triangle.
The axiom that the hypotenuse's square in a right triangle equals the sum of its squares on the other sides (c² = a² + b²)
Given data:
From the attached diagram for question:
Distance between Caden’s house and Eva’s house CA = 13 kilometers.
Distance between school and Eva’s house CB = 5 kilometers.
using Pythagorean theorem:
CA² = CB² + BA²
BA² = CA² - CB²
BA² = 13² - 5²
BA² = 169 - 25
BA = 12
Thus, the distance between Caden’s house and school is found as: 12 km.
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which recursive definition could be used to generate the sequence (3,6,3,6,3)
Answer: a1 = 3 and an = an-1 + 3(-1)n
Step-by-step explanation:
* start off with the first term being a1 = 3
* add on 3 to get to 6 as the second term
* add on -3, to get back to 3 once more
* add on the general term 3*(-1)^n (bc the pattern continues like, forever)
* term is found by a(n) = a(n-1) + 3*(-1)^n
I think This is correct as I found a similar brainly post
The coordinates of point A are (-6,4). The coordinates of point B are (3, 4). Which expression represents the distance, in units, between points A and B?
A. |-6| + |3|
C. |-6| + |-4|
B. |3| - |-6|
D. |4| - |-6|
Answer:
a
Step-by-step explanation:
6 - 6=0 the 0-3 -3 total of 9 and 6 + 3 is equal to 9
Help on this question
The average daily balance is $1,372.57 and the finance charge is $23.69.
What is the formula for the average daily balance?
The formula for the average daily balance is (1/number of days in billing period) x (sum of daily balances)
To calculate the finance charge, we need to first calculate the average daily balance for the billing period.
So, in this case, the billing period is 31 days (8 days for the previous unpaid balance plus 23 days for the current charges).
The sum of the daily balances is (8 x 1,876.00 + 10 x 778.12 + 3 x 2,112.50 + 10 x 1,544.31) = $42,559.42
Therefore, the average daily balance is (1/31) x 42,559.42 = $1,372.57
Next, we need to calculate the monthly periodic rate, which is the APR divided by 12 ,
19.2% / 12 = 1.6%
Then, we can calculate the finance charge using the following formula,
average daily balance x monthly periodic rate x number of days in billing cycle
$1,372.57 x 0.016 x 31 = $676.10
Rounding this amount to the nearest cent gives us a finance charge of $676.09, which is closest to option B: $23.69.
Therefore, the answer is B) $23.69.
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what is 1 and 2/3 simplified
Answer:
The improper/exact form=5/3 and the decimal form is 1.(6) (which is the 6 repeated)
Step-by-step explanation:
Technically, you can't simplify 1 2/3, but these are just two ways you could change it into.
here's another one we're doing
When we simplify an equatiοn and end up with a cοntradictiοn like this, it means that the equatiοn has nο sοlutiοn.
What is system οf linear equatiοns?The intersectiοns οr meetings οf the lines οr planes that represent the linear equatiοns are knοwn as the sοlutiοns οf linear equatiοns. The set οf values fοr the variables in every feasible sοlutiοn is knοwn as a sοlutiοn set fοr a system οf linear equatiοns.
Nοt a Sοlutiοn
If there is nο intersectiοn οf any lines, οr if the graphs οf the linear equatiοns are parallel, then the system οf linear equatiοns cannοt be sοlved.
The equatiοn 5 + 9z = 9z can be simplified as fοllοws:
5 + 9z = 9z
5 = 0
This is a cοntradictiοn since 5 cannοt be equal tο 0. Therefοre, there is nο sοlutiοn fοr this equatiοn.
In general, when we simplify an equatiοn and end up with a cοntradictiοn like this, it means that the equatiοn has nο sοlutiοn.
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Sam can paint a house in 3 days. With Clark's help, Sam can paint
the same house in 1.2 days. How long would it take Clark to paint
the house on his own?
(A) 2 days
(B) 0.86 days
(C)1.8 days
(D) 4 days
Answer:
C
Step-by-step explanation:
Because 1.2+1.8 equal to 3.
Select all the expressions that are equivalent to the number in the picture
Answer:
The expressions 10³÷10⁷, 10¹²/10¹⁶, and 10⁻²/10² are all equivalent to 10⁻⁴.
Step-by-step explanation:
When dividing exponents with the same base you subtract the exponents.
For visuals, in the equation 10³÷10⁷ it would be 10³⁻⁷ which would be 10⁻⁴ since 3 minus 7 is negative 4.
It is the same thing for 10¹²/10¹⁶, it would be 10¹²⁻¹⁶ which is equal to 10⁻⁴.
The same method can be used for 10⁻²/10² (10⁻²⁻²).
suppose 42% of the population has myopia. if a random sample of size 442 is selected, what is the probability that the proportion of persons with myopia will differ from the population proportion by less than 3% ? round your answer to four decimal places.
0.7994 portion of persons with myopia will differ from the population portion by less than 3%.
Here we have to implement the central limit theorem,
therefore,
the formula is Z = x- a /s where, a = mean , d= standard deviation
let us consider that 42% has myopia
then p = 0.42
size of random sample given is 442
therefore, n = 442
then, a = p = 0.42
standard deviation is
s = [tex]\sqrt{p(1-p)/n}[/tex]
=[tex]\sqrt{0.42* 0.58/442}[/tex]
=0.0235
portion between 0.42 +0.03 = 0.45 and 0.42 - 0.03 = 0.39
there for there are two values of X = 0.45 , X = 0.39
when X = 0.45Z = X - a/s
Z = 0.45 - 0.42 / 0.0235
Z = 1.28 have a p-value of 0.8997
when X = 0.39Z = X - a /s
Z = 0.39 - 0.42 / 0.0235
Z = -1.28 have a p-value of 0.1003
0.8997 - 0.1003 = 0.7994
0.7994 portion of persons with myopia will differ from the population portion by less than 3%.
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A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is yellow or green.
The probability to pick one candy at random that is yellow or green through which relation satisfied is [tex]\frac{65}{139}[/tex]
What about probability ?
Probability is a branch of mathematics that deals with the study of random events or experiments. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you roll a fair six-sided die, the probability of rolling a 3 is 1/6, since there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling any number from 1 to 6).
Probability theory is used in a wide range of fields, including statistics, economics, physics, engineering, and computer science, to model and analyze phenomena that involve uncertainty or randomness. It is also used in many practical applications, such as risk assessment, decision making, and game theory.
According to the given information:
The probability it is yellow:
[tex]\frac{20}{20+42+45+32} = \frac{20}{139}[/tex]
The probability it is green:
[tex]\frac{45}{45+20+42+32} = \frac{45}{139}[/tex]
P(green, yellow):
⇒ [tex]\frac{20}{139} + \frac{45}{139}\\\\\frac{65}{139}[/tex]
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Answer:
65/139
Step-by-step explanation:
Acellus
find the distance between 0,7 and 9,-6
Given:-
[tex] \textsf{(0 , 7) }[/tex][tex] \: [/tex]
[tex] \textsf{(9 , -6)}[/tex][tex] \: [/tex]
To find:-
[tex] \textsf{Distance between two points = ?}[/tex][tex] \: [/tex]
By using formula:-
[tex] \pink\bigstar \underline{{ \boxed{ \sf{ \color{lightgreen}Distance = \sqrt{( x_2 - x_1 )² + ( y_2 - y_1 )²}}}}}[/tex]
[tex] \: [/tex]
Solution:-
[tex] \sf{D = \sqrt{( x_2 - x_1 )² + ( y_2 - y_1 )²} }[/tex]
[tex] \: [/tex]
where ,
[tex] \sf \bold{0 = x_1 }[/tex][tex] \: [/tex]
[tex] \sf \bold{ 7 = y_1}[/tex][tex] \: [/tex]
[tex] \sf \bold{ 9 = x_2 }[/tex][tex] \: [/tex]
[tex] \sf \bold{ -6 = y_2}[/tex][tex] \: [/tex]
[tex] \sf \: D = \sqrt{( 9 - 0 )² + ( -6 - 7)²} [/tex]
[tex] \: [/tex]
[tex] \sf \: D = \sqrt{ ( 9 )² + ( - 13 )²}[/tex]
[tex] \: [/tex]
[tex] \sf \:D = \sqrt{ 81 + 169} [/tex]
[tex] \: [/tex]
[tex] \underline{ \underline{ \sf{ \color{hotpink} \: D = \sqrt{{250}\: }}}}[/tex]
[tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps:)
Complete the steps to solve the equation 2x2 + 12x-42=0 by completing the square.
2x² + 12x-42 = 0
Answer:
2(-3±√120)
Step-by-step explanation:
quadratic formula
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There are 13 possible toppings at the local ice cream shop. You can have 3 toppings on a large sundae. How many combinations of ice cream toppings are possible?
plsss i need this done yall! help a girl out!
Answer: 286 toppings
Step-by-step explanation:
Two cylinders are shown below. Find the volume of each cylinder. Use 3.14 for π
π
. Round your answers to the nearest hundredth.
Answer: cylinder a is 12.45cm^3
cylinder b is 49cm^3
Step-by-step explanation: been through this my guy it was a struggle frl but bro igy frls
your house is located at (0,0) to get from your house to school, you walk 2 blocks east and 1 block south. what ordered pair corresponds to the location of your school? b.
The ordered pair of the location of the school from the house is found to be (2,1).
It is said that the house is located at (0,0).
We can assume this point to be the origin so we can see that the house is located at the origin and the school is located 2 blocks east and one block south.
Now in the ordered pair the first term represents the X co-ordinate and the second term represents the Y co-ordinate.
As we are moving to the right we can say that we are moving towards the positive x axis and we are moving 1 block south, we can say that we are moving towards the positive y axis.
Han the corresponding ordered pair to the location of the school will be (2,1).
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sam buys a laptop for R6 840 (including VAT). Determine the price of the laptop
without VAT (excluding VAT). VAT = 15%
the price of the laptop without VAT (excluding VAT) is R5 814.
Value Added Tax (VAT) is a consumption tax added to the value of goods and services. In many countries, VAT is included in the selling price of goods and services. However, it is also important to know how much of the selling price is VAT and how much is the actual cost of the goods or services.
In this problem, Sam bought a laptop for R6 840, which includes VAT of 15%. To determine the price of the laptop without VAT, we need to subtract the VAT from the total cost.
The VAT amount can be found by multiplying the total cost by the VAT rate. In this case, the VAT rate is 15%, so the VAT amount is:
VAT = 15/100 * R6 840
VAT = R1 026
To find the price of the laptop without VAT, we need to subtract the VAT amount from the total cost:
Price without VAT = Total cost - VAT
Price without VAT = R6 840 - R1 026
Price without VAT = R5 814
Therefore, the price of the laptop without VAT (excluding VAT) is R5 814.
In summary, to determine the price of a product without VAT, we need to subtract the VAT amount from the total cost. The VAT amount can be found by multiplying the total cost by the VAT rate. Knowing the price without VAT can be helpful in making cost comparisons between different products or when calculating profit margins.
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three-guys vending inc. supplies vended food to a large university. because students often kick the machines out of anger and frustration, management has a constant repair problem. the machines break down on an average of three per hour, and the breakdowns are distributed in a poisson manner. downtime costs the company $230/hour per machine, and each maintenance worker gets $28 per hour. one worker can service machines at an average rate of five per hour, distributed exponentially; two workers working together can service seven per hour, distributed exponentially; and a team of three workers can repair eight per hour, distributed exponentially. what is the optimal maintenance crew size for servicing the machines? and why?
This is because, in this scenario, the total cost per hour (-$432/hour) is the lowest compared to the costs of having two or three workers (-$864/hour and -$1,066/hour, respectively).
To determine the optimal maintenance crew size for servicing the machines at Three-Guys Vending Inc., we need to consider the average rate of breakdowns, downtime costs, and worker costs for each crew size.
The breakdowns are distributed in a Poisson manner, and the service rates are distributed exponentially.
1. Average breakdown rate: 3 machines/hour
2. Downtime cost: $230/hour per machine
3. Worker cost: $28/hour per worker.
Crew Size Scenarios:
A. One worker: services 5 machines/hour
B. Two workers: service 7 machines/hour together
C. Three workers: service 8 machines/hour together
First, we'll calculate the downtime and worker costs for each scenario:
A. One worker:
Downtime cost = (3 breakdowns/hour - 5 services/hour) x $230 = -$460/hour
Worker cost = 1 x $28 = $28/hour
Total cost = -$460 + $28 = -$432/hour
B. Two workers:
Downtime cost = (3 breakdowns/hour - 7 services/hour) x $230 = -$920/hour
Worker cost = 2 x $28 = $56/hour
Total cost = -$920 + $56 = -$864/hour.
C. Three workers:
Downtime cost = (3 breakdowns/hour - 8 services/hour) x $230 = -$1,150/hour
Worker cost = 3 x $28 = $84/hour
Total cost = -$1,150 + $84 = -$1,066/hour
From the calculations above, the optimal maintenance crew size for servicing the machines is one worker.
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Jenna is responsible for the invetory at the boutique where she works the bar graph shows how many diffrent items she keeps in the three areas of the stores if jenna increases the number of aldults to 24 how many teens items should she pan to have in order to kee the ratio of adult to teens items the same?
Jenna should plan to have 8 teen items in the store to maintain the same ratio of adult to teen items.
What is ratio and proportion?When comparing quantities and figuring out how they relate to one another, ratio and proportion are two related mathematical ideas.
A ratio is a comparison between two values that is typically stated as a fraction. The ratio of red to blue marbles, for instance, would be 3/5 if there were 3 red and 5 blue marbles in a bag.
Contrarily, the proportion equation declares that two ratios are equivalent. For instance, if there are 3/5 red to 5/5 blue marbles in one bag and 6/10 red to blue marbles in the other, we have two bags of marbles.
From the given bar graph the ratio of adult to teen items is 18 : 6 or 3:1.
Thus for 24 items,
24:x = 3:1
Cross-multiplying, we get:
24 * 1 = 3 * x
x = 24/3
x = 8
Therefore, Jenna should plan to have 8 teen items in the store to maintain the same ratio of adult to teen items.
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The complete question is:
Multiply the polynomials simplify the answer and show your work please
Answer:
48a^3 + 14a^2 - 52a + 15.
Step-by-step explanation:
To multiply these two polynomials, we need to use the distributive property and multiply each term of the first polynomial by each term of the second polynomial, like this:
(6a^2 + 4a - 5) x (8a - 3)
= 6a^2 x 8a + 6a^2 x (-3) + 4a x 8a + 4a x (-3) - 5 x 8a - 5 x (-3)
= 48a^3 - 18a^2 + 32a^2 - 12a - 40a + 15
= 48a^3 + 14a^2 - 52a + 15
So the simplified answer is 48a^3 + 14a^2 - 52a + 15.
There are 46,000 adults living in Grand City. In examining attitudes toward the news, a research group asked a random sample of Grand City adults "What Is your main source of news?" The results are shown below.
We predict that approximately 17,204 adults in Grand City have television as their main source of news.
How to predict the number of adults in Grand City whose main source of news is television?To predict the number of adults in Grand City whose main source of news is television, we need to use the proportion of adults in the sample who selected television as their main source of news and apply it to the entire population of 46,000 adults.
The proportion of adults in the sample who selected television as their main source of news is:
135/361 = 0.374
To get the predicted number of adults in Grand City whose main source of news is television, we multiply this proportion by the total population:
0.374 x 46,000 = 17,204
Rounding this to the nearest whole number, we get:
17,204 adults
Therefore, we predict that approximately 17,204 adults in Grand City have television as their main source of news.
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The vector u has magnitude 3 and direction 160°. If vector v = 2u, then what is
the magnitude and direction of vector v?
In response to the stated question, we may state that As a result, vector v has a magnitude of 6 and a direction of 160°.
What is Vector?A vector in mathematics is a mathematical object with both magnitude (or length) and direction. Vectors are frequently depicted as arrows, with the length of the arrow representing the magnitude and the direction of the arrow representing the vector's direction. A vector, for example, might represent an object's velocity, where the magnitude of the vector indicates the object's speed and the direction of the vector represents the direction of motion.
Assuming that u has a magnitude of 3 and a direction of 160°.
Vector u can be represented by its components as follows:
3 cos(160°)i + 3 sin(160°)j = u
where I and j are unit vectors pointing in the x and y directions.
We now know that vector v = 2u, implying that the magnitude of vector v is:
|v| = |2u| = 2|u| = 2(3) = 6
As a result, the magnitude of vector v is 6.
We can use the fact that vector v is in the same direction as vector u but scaled by a factor of two to determine its direction. As a result, the vector v's direction is also 160°.
As a result, vector v has a magnitude of 6 and a direction of 160°.
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what is the length of the line
Step-by-step explanation:
rise = height = 5 units run = base = 2
Use Pythagorean theorem
L^2 = 5^2 + 2^2
L^2 = 29
L = sqrt (29)