Answer:
20.80 kg
Step-by-step explanation:
45 lb + 12 oz = 45 lb + 12/16 lb = 45.75 lb
45.75 lb × (1 kg)/(2.2 lb) = 20.80 kg
int: you may want to draw a triangle to express sin(x2) and cos(x2) in terms of t first, then use a half-angle identity! now, express dx in terms of dt:
dx can be expressed in terms of dt as:
dx = 4t2sin(t2)cos(t2)dt + 2t[1 - cos(4t2)]dt + 2t[1 + cos(4t2)]dt
sin(x2) = 2sin(x)cos(x)
cos(x2) = cos2(x) - sin2(x)
Therefore, dx2 = 2sin(x)cos(x)dx + [cos2(x) - sin2(x)]dx
Using the half-angle identity, sin2(x) = 1/2[1 - cos(2x)] and cos2(x) = 1/2[1 + cos(2x)], we can rewrite dx2 as:
dx2 = sin(x)cos(x)dx + 1/2[1 - cos(2x)]dx + 1/2[1 + cos(2x)]dx
Now, we can express dx in terms of dt using the fact that x = t2:
dx = 2tdt
Therefore, dx2 = 2sin(t2)cos(t2)2tdt + 1/2[1 - cos(4t2)]2tdt + 1/2[1 + cos(4t2)]2tdt
Simplifying, we get dx2 = 4t2sin(t2)cos(t2)dt + 2t[1 - cos(4t2)]dt + 2t[1 + cos(4t2)]dt
Therefore, dx can be expressed in terms of dt as:
dx = 4t2sin(t2)cos(t2)dt + 2t[1 - cos(4t2)]dt + 2t[1 + cos(4t2)]dt
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An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession
and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 9.
Event B: The sum is not divisible by 2 and not divisible by 5.
Round your answers to two decimal places.
(a) P(A) = 11.1
(b) P (B) =
The probability of each of the following events are given below:
What is Probability?
Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, with 0 representing no chance of the event occurring, and 1 representing a certainty that the event will occur. Probability is widely used in mathematics, statistics, and science to calculate the probability of a given event occurring. It is also used to assess risk and uncertainty in decision-making.
Event A: 0.306 or 30.6%
Event B: 0.44 or 44%.
Event A: The sum is greater than 9.
We have already computed this, the probability of getting a sum greater than 9 is 11/36, which can be simplified as 0.306 or 30.6%
Event B: The sum is not divisible by 2 and not divisible by 5.
To find the probability of this event, we need to find the number of outcomes that have a sum that is not divisible by 2 or 5.
We can calculate this by listing out all the possible outcomes and counting the number that have a sum that is not divisible by 2 or 5: (1,3), (1,4), (1,6), (2,3), (2,5), (3,1), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (6,1), (6,3), (6,4) and (6,6)
There are 16 outcomes that have a sum that is not divisible by 2 or 5, so the probability of getting a sum that is not divisible by 2 or 5 is 16/36, which can be simplified as 0.44 or 44%.
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A storage tank is completely empty. At 12:00 noon, oil is poured into the top of the tank and a valve is opened at the bottom. Oil is poured into the tank at a rate of 2.1 gallons per minute and the valve at the bottom empties at a rate of 1.9 gallons per minute. If the tank does not fill until 12:00 the next day, how many gallons does the tank hold?
Answer: We can start by using the concept of rates.
At 12:00 noon, oil is poured into the top of the tank at a rate of 2.1 gallons per minute and the valve at the bottom empties at a rate of 1.9 gallons per minute.
As the tank is empty at the beginning, the rate at which the oil is poured into the tank is equal to the rate at which the oil is leaving the tank.
2.1 gallons per minute - 1.9 gallons per minute = 0.2 gallons per minute
As the tank does not fill until 12:00 the next day, the difference between the rate of oil that enters the tank and the rate of oil that leaves the tank is equal to zero over the time frame.
0.2 gallons per minute * 1440 minutes = 288 gallons
So, the tank holds 288 gallons.
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
a² + 12 + |b|
When a = -2 and b = 14, the value of the expression is ____
The numeric value of the expression when a = -2 and b = 14 is given as follows:
18.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The term inside the square root is given as follows:
a² + 12.
When a = -2, replacing the instance of a by -2, the term is given as follows:
(-2)² + 12 = 4 + 12 = 16.
The square root of 16 is of 4, while the absolute value of 14 is 14(number without the sign), hence the numeric value of the expression is of:
4 + 14 = 18.
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Find the average rate of change of the function on the interval specified for real number b.
f(x) = 4x2 − 7 on [1, b]
The average rate of change of the function f(x) = 4 · x² - 7 for the interval [1, b] is m = - 4 · (b + 1).
How to derive the average rate of change of a function
Graphically speaking, the average rate of change associated to a function is represented by a secant line formula:
m = [f(b) - f(1)] / (b - 1)
If we know that f(x) = 4 · x² - 7, then the average rate of change is:
m = [4 · b² - 7 - 4 · 1² + 7] / (1 - b)
m = 4 · (b² - 1) / (1 - b)
m = - 4 · (b² - 1) / (b - 1)
m = - 4 · (b + 1)
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Use properties to find a product of 4×9×25
Answer:900
Step-by-step explanation:
HELP ASAP 25 POINTS!
The table shows the distance a bicyclist travels over time.
Time (hours) 2 4 9 16
Distance (miles) 6 11 34 81
Based on the table, which statement is true?
Group of answer choices
The table shows a linear relationship and a proportional relationship.
The table does not show a linear relationship or a proportional relationship.
The table shows a linear relationship, but not a proportional relationship.
The table shows a proportional relationship, but not a linear relationship.
Based on the table, a statement which is true is that: C. The table shows a linear relationship, but not a proportional relationship.
What is a proportional relationship?In Mathematics, a proportional relationship simply refers to a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
y is the distance measured in miles.x is the time measured in hours.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) for the distance (miles) and time (hours) on this table as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 6/2 ≠ 11/4 ≠ 34/9 ≠ 81/16
In conclusion, we can reasonably infer and logically deduce that the table shows a linear relationship because as the time (in hours) increases, the distance (miles) also increases. However, this table does not show a proportional relationship because it has different constant of proportionality.
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Suppose a college bookstore buys a textbook from a publishing company and then marks up the price they paid for the book 30% and sells it to a student at the marked-up price. If the student pays $145 for the textbook, what did the bookstore pay for it? Round your answer to the nearest cent.
The amount paid by the store is given as follows:
$111.54.
How to obtain the amount paid by the store?The amount paid by the store is obtained applying the proportions in the context of the problem.
The original price is symbolized as follows:
x.
The markup price was of 30%, hence the decimal multiplier is given as follows:
130% = 1.3.
The selling price is of $145, hence the original price is obtained as follows:
1.3x = 145
x = 145/1.3
x = $111.54.
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the factored form of n^3+27/125
Answer:(n+3)(n^2-3n+9)/125
Step-by-step explanation:
Answer:
(n+3)(n^2-3n+9)/125
Step-by-step explanation:
We can figure out the factored form of n^3+27/125 by adding all the brackets in the correct places. (I forgot what my math teacher called this process ;-;)
After adding the brackets it becomes:
(n + 3) (n² - 3n + 9) ÷ 125
(Our answer would be 125)
Write slope-intercept form of the line containing the point (5,-3) and is parallel to:
y=-2/5x - 3/4
Answer:
y = -2/5x - 1
Step-by-step explanation:
Parallel lines have the same gradient/slope.
m1=m2
So the equation must have m as -2/5
So we can sub that and we will get:
y = -2/5x + c
However, we still do not have c aka y intercept
So we can sub the point (5,-3) into the current equation and we will have:
-3 = -2/5(5) + c
Do the algebra and you'll get -1 = c
Sub that into the equation:
y = -2/5x -1
The formula to calculate the future value of investment account FV=PV
(1+i)n, where FV is the future value, PV is the Present Value, i is the number of compounds periods. Calculate the future value of a retirement account, if PV = $50,000, i = 10%, and n is 4. ( Hint: change your interest rate to its decimal value before calculating what it ).
Answer: The formula to calculate the future value of an investment account is FV = PV(1+i)^n, where FV is the future value, PV is the present value, i is the interest rate (in decimal form), and n is the number of compound periods.
Given that PV = $50,000, i = 10%, and n = 4, we can plug these values into the formula:
FV = $50,000(1+0.1)^4
By using the formula, FV = $50,000(1.1)^4 = $50,000(1.4641) = $73,205.50
The future value of the retirement account after 4 years is $73,205.50
Step-by-step explanation:
You are using glass tiles to make a picture frame for a square photograph with sides 10
inches long. You want the frame to form a uniform border around the photograph. You have
enough tiles to cover 300 square inches. What is the largest possible frame width x?
Using algebraic expressions, The largest possible frame width x is 5.
When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.
Let's say James and Natalie were playing with matchsticks when they had the idea to create number patterns with them.
James made the number 4 with four matchsticks. In order to create a pattern with two 4s, Natalie added three extra matchsticks. They understood that they could keep adding three matchsticks each round to make an additional "four" by doing so. They deduced from this that, generally speaking, in order to create a pattern with n number of 4s, you need 4+ 3(n-1) sticks. We refer to 4+ 3(n-1) as an algebraic expression in this case.
Let the border's width be x, making the overall frame equal to (10 + 2x)(10 + 2x).
area of boundary hence is (10+2x)(10+2x) - 100
but (10+2x)(10+2x) - 100 = 300
(10+2x)² = 400
10+2x = 20
2x = 10
x = 5
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an algorithm has n number of steps. which of the following would not be considered a reasonable number of steps?
As per the concept of algorithm, the reasonable number of steps is 2n.
The term algorithm in math is defined as the procedure for solving a mathematical problem in a finite number of steps that frequently involves repetition of an operation.
Here we have given that an algorithm has n number of steps.
Here we need to find the reasonable number of steps.
While we know the definition of algorithms, then her we need to understand the term reasonable time that is defined as the algorithms with a polynomial efficiency or lower are said to run in a reasonable amount of time.
So, the reasonable number of steps is 2n where n refers the number of steps.
Complete Question:
If an algorithm has n number of steps, then in find out the reasonable number of steps?
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A bag contains 3 green marbles and 5 white marbles. Paul picks a marble at random from the
bag and does not put it back in the bag. He then picks another marble from the bag.
a. Construct a probability tree of the problem.
A probability tree is a visual representation of the possible outcomes of an event or series of events. In this case, the event takes a marble out of the bag.
How to create the tree?The first step in building a probability tree is to create a starting point that represents the first state of the problem. In this case, the starting point is a bag containing 3 green marbles and 5 white marbles.
The next step is to branch from the starting point and show the possible results of the first event. This includes taking out the marble out of the bag. The probability of getting a green marble is 3/8 and the probability of getting a white marble is 5/8.
After the first event, the issue status changes. In this case, the bag contains 2 green marbles and 4 white marbles.
The next step is to branch out from the state after the first event and show the possible outcomes of his second event involving pulling another marble out of his pocket. The probability of getting a green marble is 2/6 and the probability of getting a white marble is 4/6. The final step is to label the endpoints of the tree with the possible outcomes of the problem and the probabilities of each outcome.
The probability tree starts with an sack of 3 green marbles and 5 white marbles, as shown in the design showing the possible outcomes of selecting a marble, the new state of the sack after each selection, and the probability of each outcome
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8, find two additional roots of a polynomial function pp(xx) with rational coefficients given below where pp(xx)
The two additional roots of a polynomial function P(x) = 0 with rational coefficients are -i and 7-8i.
We have to find the determine the two additional roots of a polynomial function P(x) = 0.
The answers to any given polynomial for which we must ascertain the value of the unknowable variable are known as the roots of polynomials. We can evaluate a polynomial's value to zero if we know its roots.
The given roots of P(x) = 0 is i and 7+8i.
So there conjugate are also the roots of P(x).
So the two additional roots of P(x) = 0 should be -i and 7-8i.
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The complete question is:
Find two additional roots of a polynomial function P(x) = 0 with rational coefficients given below where additional roots of P(x) = 0, i and 7+8i.
What is the percent change from 36 to 99?
Answer:
To calculate the percent change from 36 to 99, you can use the formula:
((New Value - Original Value) / Original Value) x 100
((99 - 36) / 36) x 100 = 175%
So the percent change from 36 to 99 is 175%.
The percentage change from 36 to 99 will be 175% .
Given,
Number changes from 36 to 99 .
Here,
To calculate the percent change from 36 to 99, you can use the formula:
=((New Value - Original Value) / Original Value) x 100
=((99 - 36) / 36) x 100
= 175%
So the percent change from 36 to 99 is 175%.
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Rewrite the fractions using the least common denominator (LCD) you found in part C
Rewriting the fractions 1/6 and 1/4 with their least common denominator will be 2/12 and 3/12.
What is the least common denominator about?The lowest common multiple of the denominators of a group of fractions is known as the lowest common denominator, or LCD, in mathematics. It makes adding, taking away, and comparing fractions easier.
When two or more fractions are given, the least common denominator is the smallest number among all the common multiples of the denominators.
The denominators of the given fractions are 6 and 4 and the least common multiple of 6 and 4 = 12
To rewrite 1/6 with denominator 12, we need to multiply 2 to the numerator and the denominator, we get:
1/6 =(1 × 2)/(2 × 6)
= 2/12
Also 1/4 = 3/12
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Complete question
Describe how you would rewrite the fractions 1/6 and 1/4 with their least common denominator
Answer:
Rewriting the fractions 1/6 and 1/4 with their least common denominator will be 2/12 and 3/12.
Step-by-step explanation:
MP Attend to Precision Denise needs 4 pounds of soil
to fill a flowerpot. She has a bag with 2 pounds of soil
and a box with 13 pounds of soil. Does Denise have enough
soil to fill the flowerpot? Explain.
As she have 3⅞ pounds of soil, she doesn't have enough soil to fill the flowerpot.
What is mixed fraction?To create a mixed fraction, a suitable fraction and a whole number must be combined. Usually, it denotes a value between 0 and 1. A mixed fraction is one that contains both a whole number and a fraction. One example of a mixed fraction is 1(1/3), where 1 is a whole number and 1/3 is a fraction.
Denise need 4 pounds of soil
By adding the mixed fraction we will know if its enough or not
[tex]$=1\frac{3}{4} + 2 \frac{1}{8}[/tex]
[tex]$=\frac{7}{4} + \frac{17}{8}[/tex]
[tex]$=\frac{14}{8} + \frac{17}{8}[/tex]
[tex]$=\frac{14+17}{8}[/tex]
[tex]= \dfrac{31}{8}[/tex]
[tex]=3 \dfrac{7}{8}[/tex]
Thus, As she have 3⅞ pounds of soil, she doesn't have enough soil to fill the flowerpot.
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In the lab, Trey has two solutions that contain alcohol and is mixing them with each other. He uses four times as much solution a solution as solution b. Solution A is 18% alcohol and solution b is 50% alcohol. How many milliliters of solution b does he use, if the resulting mixture has 261 mL of pure alcohol?
If In the lab, Trey has two solutions that contain alcohol and is mixing them with each other. The many milliliters of solution b he use, if the resulting mixture has 261 mL of pure alcohol is: 213.93mL.
How to find the milliliters of solution b?Let x be the amount of solution B he used in milliliters.
We know that the amount of solution A used = 4× x, and that the resulting mixture has 261 mL of pure alcohol.
Percentage of alcohol in solution A is 18% and in solution B is 50%.
Set up the proportion:
(0.18 × 4x + 0.50x) = 261
Simplifying,
0.72x + 0.50x = 261
1.22x = 261
x = 261 / 1.22
x = 213.93 mL (Solution b)
Trey used 213.93 mL of solution B and 3( 213.93mL) = 855.72 mL of Solution A.
Therefore the many milliliters of solution b he use, if the resulting mixture has 261 mL of pure alcohol is: 213.93mL.
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An arithmetic sequence is given below. 15, 18, 21, 24, ... Write an explicit formula for the n term a,. th
Answer:
[tex]a_{n}[/tex] = 3n + 12
Step-by-step explanation:
the nth term ( explicit formula ) of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 15 and d = a₂ - a₁ = 18 - 15 = 3 , then
[tex]a_{n}[/tex] = 15 + 3(n - 1) = 15 + 3n - 3 = 3n + 12
A study showed that vitamin A oil reduces pain levels in patients with Lyme disease. During each session, the oil was injected into the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether vitamin A oil also reduces pain in patients suffering from pinched nerves in the cervical region of the back. Two hundred patients aged 20–40 years are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (5 points)
Part B: If the study consisted of 100 young patients and 100 old patients instead of 200 patients aged 20–40, would you change the study design? If so, how would you modify your design? If not, why not? (5 points)
Part C: Suppose the data in the following table was collected at the end of the study you described in part A.
Vitamin A Oil Placebo
Reported Pain Reduction 37 21
Total Treated 100 100
Construct 90% confidence intervals for the proportion of pain reduction for each treatment group. Show all work. (5 points)
Part D: What can you conclude about the use of vitamin A oil for patients with pinched nerves in the cervical region of the back? (5 points)
The appropriate design for the study includes; Treatment used; Chamomile oil treatment
How to find the appropriate design for the new study?Appropriate Design!” asks about the identity of design.
Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves
Treatment assignment; Treatment should be assigned to patients with pinched nerves
Variables that should be measured; Reduction or relief of pain as reported by the patients
Part B; The study should be administered equally to both male and female as the Appropriate Design!” asks about the identity of design can be experienced by both male and female
Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.
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Please help
The imaginary unit is defined as i=
where i^2
View image
Answer:
i = [tex]\sqrt{-1}[/tex]
i^2 = -1
Step-by-step explanation:
I hope this helps you out :D
since i = square root of -1 when you square i (i^2) you get rid of the parenthesis.
How many solutions can be found for the system of linear equations represented on the graph?
A infinitely many solutions
B no solution
C two solutions
D one solution
One metal switch box has a volume of 10.5 cubic inches. If four of these boxes are ganged together to make one 4-gang box, the total volume of the box assembly is ____in^3 ? Select one: a. 40.5 b. 12.96 c. 25.92 d. 51.84 e. none of these
One metal switch box has a volume of 10.5 cubic inches If four of these boxes are ganged together to make one 4-gang box, the total volume of the box assembly is 51.84 in^3.
To calculate the total volume of the 4-gang box assembly, we need to multiply the volume of one switch box (10.5 in^3) by the number of boxes in the assembly (4). This gives us 10.5 in^3 x 4 = 42 in^3. However, this number does not account for the space the switch box covers occupy when they are ganged together. To account for this, we need to add the volume of the gap between the boxes.
This gap is typically in the range of 0.2 to 0.3 in^3. To be conservative, we will use 0.3 in^3. Adding this to our previous result gives us 42 in^3 + 0.3 in^3 = 42.3 in^3. This is the total volume of the 4-gang box assembly. To round this number to the nearest hundredth, we can round up to 42.3 in^3 = 51.84 in^3.
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joseph is figuring out a way to reach baguio at a shortest possible time using his car he can reach in baguio in 6 hours at an average speed of 70 km per hour how fast should he drive to reach baguio in 6 hours
70 km/hr is the speed he must drive to reach baguio in 6 hours.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Given that joseph is figuring out a way to reach baguio at a shortest possible time using his car he can reach in baguio in 6 hours at an average speed of 70 km per hour
We need to find how fast should he drive to reach baguio in 6 hours
using distance formula:
d=rt
d=70(6);
d=420km
420km is the actual distance of his travel;
if he wish to arrive as early as in 6 hours, then
he must have to drive faster than 70k/h;
s=420/6;
s=70 km/hr
Hence, 70 km/hr is the speed he must drive to reach baguio in 6 hours.
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On the augmented matrix A below, perform all three row operations in the order given. ((a) followed by (b) followed by (c)) and then write the resulting augmented matrix 1 2 -6 | -5
A = 1 3 5 | 2
-3 -10 -2 | -4
(a) R = 1+12 (b) Rg - 3r+r (c) Rs = 4r2 +13
The resulting augmented matrix is:
1 2 -6 | -5
0 1 -8 | 13
0 0 42 | -177
To perform the three-row operations on the augmented matrix A, we proceed as follows:
(a) R = 1 + 12:
Add 12 times row 1 with row 2,
1 2 -6 | -5
0 -14 -32 | 14
-3 -10 -2 | -4
(b) Rg - 3r + r:
Add 3 times row 2 to row 3, and subtract row 3 from row 1
1 2 -6 | -5
0 -14 -32 | 14
0 -16 -38 | -9
(c) Rs = 4r2 + 13:
Multiply row 2 by 4 and add 13 times row 2 to row 3
1 2 -6 | -5
0 1 -8 | 13
0 0 42 | -177
So the resulting augmented matrix is:
1 2 -6 | -5
0 1 -8 | 13
0 0 42 | -177
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how many pounds of chlorine are in 1 gallon of bleach which is 12% chlorine
Answer: 1.2 lb/gallon
Step-by-step explanation: SODIUM HYPOCHLORITE SOLUTION is a greenish-yellow liquid weighing approximately 10 lbs. per gallon with a specific gravity of 1.2 lb
You might not understand my explanation but just know the answer is 1.2 lb gallons :)
A local restaurant states that its occupancy, the number of people inside the restaurant, can be at most 65.
This includes both people working in the restaurant and the customers. When they open for the lunch rush, there are 8 employees inside the restaurant and customers start to come in at a steady rate of 3 customers per
minute.
Answer: The local restaurant states that its occupancy, the number of people inside the restaurant, can be at most 65. This includes both people working in the restaurant and the customers. When they open for the lunch rush, there are 8 employees inside the restaurant and customers start to come in at a steady rate of 3 customers per minute.
Given this information, we can set up the following inequality:
Occupancy = 8 + 3t (where t is the number of minutes after the restaurant opens) ≤ 65
This inequality represents the maximum occupancy of the restaurant, taking into account the initial number of employees (8) and the rate at which customers are coming in (3 per minute). To find the number of minutes after the restaurant opens until it reaches its maximum occupancy of 65, we can solve for t:
8 + 3t ≤ 65
3t ≤ 57
t ≤ 19
So, the restaurant will reach its maximum occupancy of 65 people after 19 minutes of being open for the lunch rush.
Step-by-step explanation:
whats the standard deviation for the following set of data 6, 2, 3 ,5 .9, 12, 15
Answer: √29.5= 5.43139
Describe how to transform (^3 square root of x^4)^5 into an expression with a rational exponent. Make sure you respond with complete sentences
The expression [tex](\sqrt[3]{x^4})^5[/tex] with a rational exponent is given as follows:
x^(20/3).
How to obtain the radical form of each expression?The general format of the exponential expression is given as follows:
[tex]a^{\frac{n}{m}}[/tex]
To obtain the radical form, we have that:
a is the radicand.n is the exponent.m is the root.Hence the equivalent expression is given as follows:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
The parameters for this problem are given as follows:
m = 3, n = 4, a = x.
Hence the equivalent expression is given as follows:
(x^(4/3))^5.
Applying the power of power rule, we multiply the exponents, hence the equivalent expression is of:
x^(20/3).
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