The function defined by M(t) = 2t + 1 has no maximum value on the interval [0,4) as the derivative of m(t) is not equal to zero.
The maxima of the function can be calculated by the derivative of the function. The derivative is equated to 0 to calculate the critical points. If the second derivative is negative at this critical point then a maximum exists at this point.
The function is M(t) = 2t + 1 . Differentiate the function with respect to t. Now equate the derivative to 0. This will give the critical point. Since 2 is not equal to 0, the critical point does not exist on the curve of the function. Therefore, the function M(t) = 2t + 1does not have a maxima. M(t) = 2t + 1
d/dt M(t) = d/dt 2t + 1
= 2
d/dt m'(t) = 0
2 not equal to 0
The function does not have a critical point. Therefore, the maxima do not exist for the function.
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Can anyone factor out the GCF of the 3 questions?
The GCFs of the given polynomials are 4, 7x² and 1
What are the greatest common factors?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Given are some polynomial, we need to find GCF,
a) 12x²-8x+4
12x² = 2×2×3×x×x
8x = 2×2×2×x
4 = 2×2
GCF = 2×2 = 4
b) 7x⁸-14x⁴+21x²
7x⁸ = 7×x×x×x×x×x×x×x×x
14x⁴ = 7×2×x×x×x×x
21x² = 7×3×x×x
GCF = 7×x×x
GCF = 7x²
c) 17x³+15x²-21x+3
17x³ = 17×x×x×x
15x² = 3×5×x×x
21x = 7×3×x
3 = 3×1
GCF = 1
Hence, the GCFs of the given polynomials are 4, 7x² and 1
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1
Select the correct answer.
What is the solution for x in the equation?
-2x + 14+ 10x = 34
O A.
OB.
O C.
O D.
2 =
= 6
2/5
2=
= 1/
2 =
1/0 10/2
Reset
Ne
Answer: Option D
Step-by-step explanation: Given: -2x + 14 + 10x = 34
-2x + 10x + 14 = 34
8x + 14 = 34
8x = 34 - 14
8x = 20
divide both sides by 8
8x/8 = 20/8
x = 5/2
Which example is a compound experiment?
finding the probability of heads on a coin and 4 on a number cube
finding the probability of 3 on a six spaced spinner
finding the probability of rolling a 6 on a number cube
finding the probability of drawing a King from a regular deck of cards
The compound experiment is the probability of heads on a coin and 4 on a number cube which is P = ( 1/12 )
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability be represented as P
Now , the equation will be
a)
The probability of heads on a coin and 4 on a number cube
Now , the probability of tossing a heads on a coin = 1/2
The probability of rolling a 4 on number cube = 1/6
So , the compound probability P = ( 1/2 ) ( 1/6 )
On simplifying the equation , we get
P = 1/12
b)
The probability of 3 on a six spaced spinner
The value of P = 1/6
c)
The probability of rolling a 6 on a number cube
The value of P = 1/6
d)
The probability of drawing a King from a regular deck of cards
The value of P = 4/52
On simplifying the equation , we get
The value of P = 1/13
Hence , the compound probability is P = 1/12
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showing your work solve the polynomial f(x) x^3-7x^2+2x+40
pleaseeee helpppppp
Answer:
(x+2)(x−5)(x−4)
Step-by-step explanation: These are the possible roots of the polynomial function. ± 1 , ± 40 , ± 2 , ± 20 , ± 4 , ± 10 , ± 5 , ± 8 Substitute − 2 and simplify the expression. In this case, the expression is equal to 0 so − 2 is a root of the polynomial. Tap for more steps... 0 Since − 2 is a known root, divide the polynomial by x + 2 to find the quotient polynomial. This polynomial can then be used to find the remaining roots. x 3 − 7 x 2 + 2 x + 40 x + 2 Divide x 3 − 7 x 2 + 2 x + 40 by x + 2 . Tap for more steps... x 2 − 9 x + 20 Write x 3 − 7 x 2 + 2 x + 40 as a set of factors. ( x + 2 ) ( x 2 − 9 x + 20 )
What is the area of triangle ABC?
two angles in the triangle are 60°, so the last one must be 60°, since all must add up to 180°, that means the triangle is equilateral
[tex]\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3}~ ~~ units^2[/tex]
Answer:
C.
Step-by-step explanation:
It is an equilateral triangle.
DB = 6, AB = 12, DC = height
[tex]DC=\sqrt{(CB)^{2}- (DB)^{2} } =\sqrt{144-36} =\sqrt{108}=\sqrt{(36)(3)} =6\sqrt{3}[/tex]
[tex]A=\frac{(DC)(AC)}{2} =\frac{(6\sqrt{3})(12) }{2} =\frac{72\sqrt{3} }{2} =36\sqrt{3}[/tex]
Hope this helps
Write the degree of each of the following polynomials:
(1) 5x³+4x²+7x
(ii) 4-y²
(iii) 5t-√√7
(iv) 3
Answer:
Step-by-step explanation:
evaluate the probability that the fuel tank (f) is empty, given also the observation that the battery is flat. which probability is lower? comment on the results.
Introduction:
Probability is a measure of the likelihood that a given event will occur. In this scenario, the event of interest is the fuel tank being empty, given the observation that the battery is flat. Evaluating the probability of this event involves finding the relationship between the fuel tank and the battery, and using this information to calculate the probability that the fuel tank is empty.
Detailed explanation:
To evaluate the probability of the fuel tank being empty given the observation that the battery is flat, we need to use Bayes' theorem. Bayes' theorem states that the probability of event A given event B can be calculated as follows:
P(A|B) = P(B|A) * P(A) / P(B)
Where P(A|B) is the probability of event A given event B, P(B|A) is the probability of event B given event A, P(A) is the probability of event A, and P(B) is the probability of event B.
In this scenario, event A is the fuel tank being empty, and event B is the battery being flat. To calculate the probability of the fuel tank being empty given the battery is flat, we need to find the values of P(B|A), P(A), and P(B).
Suppose we have the following information:
P(A) = 0.1 (the probability that the fuel tank is empty)
P(B|A) = 0.8 (the probability that the battery is flat given that the fuel tank is empty)
P(B) = 0.05 (the probability that the battery is flat)
Using these values, we can calculate P(A|B) as follows:
P(A|B) = P(B|A) * P(A) / P(B) = 0.8 * 0.1 / 0.05 = 0.16
This means that the probability that the fuel tank is empty given the battery is flat is 0.16.
In conclusion, the probability that the fuel tank is empty given that the battery is flat is lower than the probability that the fuel tank is empty, which was 0.1. This suggests that having a flat battery decreases the likelihood that the fuel tank is empty.
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72. Shoe Sales On Saturday night, the manager of a shoe store evaluates the receipts of the previous week's sales. Two hundred and forty pairs of two different styles of tennis shoes were sold. One style sold for $66.95 and the other sold for $84.95. The total receipts were $17,652. The cash register that was supposed to record the number of each type of shoe
sold malfunctioned. Can you recover the information? If so, how many shoes of each type were sold?
Answer:
To solve this problem, we can use a system of equations. Let x be the number of shoes sold at $66.95 and y be the number of shoes sold at $84.95. We know that:
x + y = 240 (because 240 pairs of shoes were sold in total)
66.95x + 84.95y = 17,652 (because this is the total amount of money earned from shoe sales)
To find the number of each type of shoe sold, we can use substitution method, by solving one equation for one variable and substituting that expression into the other equation.
We can solve the first equation for y:
y = 240 - x
Then we can substitute this expression into the second equation and solve for x:
66.95x + 84.95(240 - x) = 17,652
66.95x + 21,068 - 84.95x = 17,652
-18x = -3,416
x = 176
So, 176 pairs of shoes were sold at $66.95. To find the number of shoes sold at $84.95, we can substitute this value of x into the first equation:
y = 240 - 176 = 64
So, 64 pairs of shoes were sold at $84.95.
In conclusion, we can recover the information and the manager can know that 176 pairs of shoes were sold at $66.95 and 64 pairs of shoes were sold at $84.95.
how many monic polynomials of degree are there in Fp[x] that do not take on the value 0 for x ∈ Fp?
The number of monic polynomials of degree n in Fp[x] that do not take on the value 0 for x ∈ Fp is pⁿ - 1.
The number of monic polynomials of degree n in Fp[x] is pⁿ. In this case, "monic" means that the coefficient of xⁿ is 1.
In Fp[x], there are p possible values for the coefficient of each power of x, from x⁰ to xⁿ. Hence, there are pⁿ possible polynomials of degree n.
The number of polynomials that do not take on the value 0 for x ∈ Fp is pⁿ - 1 because if a polynomial is zero for all values of x in Fp, then it must be the zero polynomial. The zero polynomial is not counted because it is not monic, as it has a coefficient of 0 for the xⁿ term.
So, the number of monic polynomials of degree n in Fp[x] that do not take on the value 0 for x ∈ Fp is pⁿ - 1.
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2. The value of a stock increases gradually at a constant rate at the beginning
of the day. The value quickly decreases at a constant rate to below the original
value during the middle of the day. It then stays the same for the rest of the day.
A. Sketch a graph that represents the situation.
B. How would the graph change if the stock gradually decreased during the
middle of the day?
Answer:
A. The graph of the stock value would start at a low point on the left side of the graph and gradually increase in value as it moves to the right. The line representing the stock value would start to level off and then suddenly drop, representing the quick decrease in value. The line would then level off again and stay the same for the rest of the day.
B. If the stock gradually decreased during the middle of the day, the line on the graph would start at a high point, gradually decrease in value, and then level off.
1. Circle the correct word/symbol to create true statements about polynomials.
A polynomial is even if each term is an even function. f ( x ) = 2 x 4 − 3 x 2 − 5 f(x)=2x^4-3x^2-5 f(x)=2x4−3x2−5. Odd
What is odd and even polynomial?
The polynomial function f(x)=x2+x4+x6 is even. The polynomial function f(x)=x+x3+x5 is odd. The polynomial function f(x)=1+x+x2 is neither odd nor even.Here, the function f(x) is called an even function when we substitute -x in the place of x and get the expression the same as the original function. That means, the function f(x) is called an even function if f(-x) = x for all real values of x. Even function: f(-x) = f(x) Odd function: f(-x) = -f(x)A function is called an even function if for every input x.f(x)=f(−x)The graph of an even function is symmetric about the y- axis.A function is called an odd function if for every input x.f(x)=−f(−x)To learn more about polynomial refers to:
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true or false? [1,5] = { 1, 2, 3, 4, 5 }.
The statement [1,5] = { 1, 2, 3, 4, 5 is False.
In mathematics, there are two ways of representing a set of elements: by using curly braces {} or square brackets []. The curly braces {} are commonly used to represent sets, while square brackets [] are used to represent lists or arrays.
[1,5] is a list, which means it is ordered and has duplicates allowed. On the other hand, {1,5} is a set, which means it is unordered and has no duplicates allowed.
Therefore, [1,5] is not equal to {1, 2, 3, 4, 5} because the former is a list of two elements, while the latter is a set of five distinct elements.
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the branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population. the branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population. true false
The given statement "the branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population." is FALSE
In inferential statistics, sample data is analysed as opposed to the entire population since, in some cases, it is impossible to analyse the population of an entire country. As a result, inferential statistics uses analysis of sample data to make conclusions about the entire population. The population's sample data are chosen, and after analysis, the results can be utilised to draw conclusions about the entire population.
Hence, the given statement "the branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population." is false
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how many free variables does each augmented matrix have?
The number of free variables in an augmented matrix depends on the size of the matrix. An augmented matrix with an [tex]$m \times n$[/tex] matrix on the left side has n free variables.
An augmented matrix is composed of two parts, the left side and the right side. The left side is an [tex]$m \times n$[/tex] matrix, where m is the number of rows and n is the number of columns. The right side is a column of constants. The number of free variables in an augmented matrix is equal to the number of columns in the left side matrix, which is n.
The number of free variables in an augmented matrix depends on the size of the matrix. An augmented matrix with an[tex]$m \times n$[/tex] matrix on the left side has n free variables.
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band members are selling magazines to raise $150 for a shcool dance. The bar graph shows the amount of the sales so far. How much more money do the band members need to raise?
magazine sales
50
.j
40
30
.p .d
20
.m
10 .ji .b
0
student
p j ji d m b
$20 more money the band members need to raise.
What is the total amount?
Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A car that has been totaled in an accident is irreparably damaged.
Here, we have
Given: Band members are selling magazines to raise $150 for a school dance.
= 150 - (25 + 45 + 10 +25 + 15 + 10)
= 150 - 130
= 20
Hence, $20 more money the band members need to raise.
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Why will this declaration not work? animation: linear 5s 3 alternate-reverse; There needs to be an 's' after the number '3' There is no setting called 'alternate-reverse The animation-timing-function property has to follow 5s The animation name property is missing
The declaration won't work because the animation name property is missing.
Declaration : linear 5s 3 alternate-reverse
The absence of the animation name attribute prevents the declaration from functioning.
The name of the animation A CSS attribute specifies the names of one or more keyframes at-rules that describe the animation to be applied to an element.
Several keyframe at-rules are supplied as a list of names separated by commas. No properties are animated if the provided name does not match any keyframe at-rule. When setting all animation properties at once, it is frequently convenient to use the shortcut property animation.
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Ms. Langlois has 26 pencils and Mr. Cox has a certain number of pencils. Write an expression that represents the combined number of pencils Ms. Langlois and Mr. Cox have.
We know Ms. Langlois has 26 pencils.
We DO NOT know the amount of pencils that Mr.Cox has, we can use the variable "x" to represent Mr.Cox's number of pencils.
An expression is just an expression, not an equation, so it DOES NOT require a "="
The expression could be represented as 26+x
. imagine a hallway with 1000 doors numbered consecutively 1 through 1000. suppose all of the doors are closed to start with. then some dude with nothing better to do walks down the hallway and opens all of the doors. because the dude is still bored, he decides to close every other door starting with door number 2. then he walks down the hall and changes (i.e., if open, he closes it; if closed, he opens it) every third door starting with door 3. then he walks down the hall and changes every fourth door starting with door 4. he continues this way, making a total of 1000 passes down the hallway, so that on the 1000th pass, he changes door 1000. at the end of this process, which doors are open and which doors are closed?
A hallway having 1000 doors at the end of the process the doors which are open are all the factors of 24 i.e, 24,48,72,96,120,144...
A hallway has 1000 doors named 1 from 1000
So he opens all the doors of the hallway so all the doors are opened.
He decides to close every other door starting with door number 2 so 1st door is open and from 2nd door every alternate door is opened so factor of 2 is all close,
2, 4, 6, 8, 10, 12, 14, 16, 18, 20..................1000.
Then he decides to close very open door and open every close door from door three so,
3 is open it will be closed
6 was close so open
9 was open so it will be close
12 was close the it is open
so on 15,21, 27,33......999 will all be closed,
and all 18, 24, 30.....will be all open
then he walks down the hall and changes every fourth door starting with door 4
so 4 will be open so on
4, 8, 16,20, 28,32, 36,40........so on 1000 will all be open
and 12,24,48,60.............will be closed.
So all the door with factor of 12 i.e.12,24,36,48,60,72...will closed.
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The diagram shows a floor in the shape of a trapezium. 5 litres= 16.99 Has John got enough money to buy all the paint he needs? You must show how you get your answer.
To purchase all the paint, it will cost £ 186.89.
What is trapezoid?An open, flat shape with 4 straight sides and 1 set of parallel sides is a trapezoid, also known as a trapezium. The parallel sides of a trapezium are its bases, and the non-parallel sides are its legs.Parallel legs are another option for a trapezium. Having at least one pair of parallel sides, a quadrilateral form is known as a trapezoid in the US and Canada. Outside of those countries, this is what is referred to as a trapezium. Some claim that a trapezoid in the US and Canada has one pair of parallel sides, but a trapezium has none.-Following are the formulas for calculating the trapezium's area:
[tex]& A=\frac{1}{2}(a+b) h \\[/tex]
[tex]& a \| b \text { dimensions } \\[/tex]
[tex]& \therefore A=\frac{1}{2}(16+10) \times 7.6 \\[/tex]
[tex]& =98.8 \mathrm{~m}^2[/tex]
-Since 1 litre of paint covers an area of 1.9 sq m, we divide the area of the trapezium by this and multiply by the cost per litre to get the overall cost:
[tex]$& \text { Paint Used }=\frac{\text { Area }}{\text { Paint } / m^2} \\[/tex]
[tex]$& =\frac{98.8}{1.9} \\[/tex]
[tex]$& =52 \text { litres }[/tex]
-We are given that each 5 I tin of paint costs $£ 16.99$. We therefore divide the paint used by 5 and multiply by $£ 16.99$ :
[tex]$& =\frac{52}{5} \\[/tex]
[tex]$& =10.4-. > 11 \text { tins } \\[/tex]
[tex]$& \text { Cost }=11 \times 16.99 \\[/tex]
= £ 186.89
Hence, it will cost £ 186.89 to buy all the paint
Paint is only bought in 5 I tins. Hence, any fractional bit will necessitate the purchase of the whole 5 I tin
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i just want to know the Answer for fun lol I will give brain list what is one third divided by seven with an explanation
Answer:
1/21
Step-by-step explanation:
1/3 divided by 7
= 1/3 x 1/7
= 1/21
Helppp please!!! I don’t really understand
how to write cube root on mobius
The radius sign () with a little three (3) above it, followed by the number, can be used to represent a number's cube root. For instance, 8's cube root is represented by the symbol 8.
The number that remains the same after being multiplied twice by itself is known as a number's cube root. It can be written as the radical sign () followed by the number and a little three (3) above it. For instance, 8's cube root is represented by the symbol 8. When 8 is multiplied by itself twice (8 x 8 x 8), the result is 8; this is known as "the cube root of 8." In a similar way, 27's cube root can be expressed as 27, which, when multiplied by itself twice, also equals 27. Exponential expressions can also be used to represent cube roots. Because 8's cube root is expressed as 23, the result of multiplying 8 by itself three times (2 x 2 x 2) is also 8. Similarly, 33 can be used to represent the cube root of 27.
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Suppose that the number P(t) of bacteria in a culture after t days is given by the formula
P(t) = 95 (1.53)^t
How long does it take for the population to triple in size?
The answer indicates that it will take 2.38 yrs to for population to treble in size.
Which demographic do you refer to?A population is any large group that has at least one resource is common. People do not make up all populations. Population numbers can include, but aren't limited to, people, animals, groups, organizations, buildings, houses, trucks, farms, and things.
Let's call the population after it has tripled "P_triple". Then:
P(t) = 3P(0) = 3 * 95
P_triple = 285
We want to find the time t such that P(t) = 285, so we'll set the two expressions equal to each other:
95 (1.53)^t = 285
Dividing both sides by 95:
(1.53)^t = 3
Taking the natural logarithm of both sides:
t = log(3) / log(1.53)
Approximating using a calculator:
t = approximately 2.38 years
So it will take approximately 2.38 years for the population to triple in size.
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evaluate the definite integral. e81 dx x ln x e16
The definite integral of x * ln(x) from [tex]x = e^{1/8} \ to \ x = \frac{e^{-1/6}}{2}[/tex]
To find the definite integral of x * ln(x) from x = [tex]e^{(1/8)}[/tex] to x = [tex]e^{(1/6)[/tex] it can be evaluated using integration by substitution.
Let u = ln(x), then du/dx = 1/x and dx = [tex]e^u du[/tex]. The integral becomes:
[tex]\int e^{(1/8)} e^{(1/6) }x \ ln(x) dx = \int e^{(1/8)} e^{(1/6)} e^u u du[/tex]
= [[tex]e^{(2u)[/tex]/2] evaluated at u = ln([tex]e^{(1/6)[/tex]) and u = ln([tex]e^{(1/8)}[/tex]), which gives the final result:
[e[tex]^{(2u)[/tex]/2] evaluated at u = 1/6 - 1/8 = -1/12
[tex]= e^{(-2/12)}/2 = e^{(-1/6)}/2[/tex]
The integral is a mathematical concept that refers to the sum of the values of a function over a specific interval or region. It is a tool used to calculate the area under a curve or the total change in a quantity over a given interval.
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Mercedes is running a special in which all SUVs are marked down 15%. Mr. Estes purchased a G wagon for $160,000. What did he pay for the SUV after the discount was applied?
136,000
125,000
105,000
110,000
Mr. Estes paid $136,000 for the SUV after the discount was applied.
What is Markdown Percentage?Markdown percentage is defined as the decrease in the price which is calculated as a percent of the selling price.
We have the formula,
Selling price = (1 - markdown rate) Original price
Here,
Markdown percentage = 15%
Markdown rate = 15/100 = 0.15
Original price of the car = $160,000
Selling price = (1 - 0.15) × 160,000
= 0.85 × 160,000
= 136,000
Hence the selling price of the car is $136,000.
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similar to the hospital schedule in example 2.9, suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries. a. how many different sequences are possible? b. how many different sequences have all hip, knee, and shoulder surgeries scheduled consecutively? c. how many different schedules begin and end with a knee surgery?
a. The different sequences possible are 1200.
b. The different sequences have all hip, knee, and shoulder surgeries scheduled consecutively are 720.
c. The different schedules begin and end with knee surgery is 6.
(a) To find the number of different sequences, we can use the permutation formula n!/(n-r)!
where n is the total number of surgeries and r is the number of surgeries of each type that we need to schedule.
For knee surgeries, n = 5 (total surgeries) and r = 3 (number of knee surgeries), so the number of different sequences for knee surgeries is 5!/(5-3)! = 5!/(2!) = 54 = 20.
Similarly, the number of different sequences for hip surgeries is 5!/(5-2)! = 5!/(3!) = 54*3 = 60.
Hence, the total number of different sequences is 20 * 60 = 1200.
(b) To find the number of different sequences with all hip, knee, and shoulder surgeries scheduled consecutively, we first need to find the number of sequences for each type of surgery.
For knee surgeries, n = 3 (number of knee surgeries) and r = 3 (number of knee surgeries), so the number of different sequences for knee surgeries is 3!/(3-3)! = 3!/(0!) = 3! = 6.
Similarly, the number of different sequences for hip surgeries is 2!/(2-2)! = 2!/(0!) = 2! = 2.
For shoulder surgeries, the number of different sequences is 5!
Hence, the total number of different sequences with all hip, knee, and shoulder surgeries scheduled consecutively is 6 * 2 * 5! = 720.
(c) In order to find the number of different schedules that begin and end with knee surgery, we first need to find the number of sequences for the middle surgeries.
There are 2 hip surgeries and 2 knee surgeries left to schedule, so the number of different sequences for these surgeries is (2+2-1)!/(2!2!) = 3!/(2!1!) = 3.
Hence, the total number of different schedules that begin and end with a knee surgery is 3 * 2 * 1 = 6.
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The complete question is -
A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries.
(a) How many different sequences are possible?
(b) How many different sequences have all hip, knee, and shoulder surgeries scheduled consecutively?
(c) How many different schedules begin and end with knee surgery?
6] A ship sails 70 km on a bearing of 38° and then changes course and sails 40 km on
a bearing of 150° By making a scale diagram find: -
a) The final distance of the port from the ship.
b) The final bearing of the port from the ship.
The final distance of the port from the ship is 75.63 km and the final bearing of the port from the ship is 263.57° using cosine and sine rules.
How to evaluate for the final distance and bearingConsidering the triangle formed by the ship ∆ABC where A, B and C are the points for; the port, where the ship changes its course, and its final bearing. The final distance "a" of the port from the ship is calculated with cosine rule as follows;
a² = b² + c² - 2(b)(c)cosA
a² = 40² + 70² - 2(40)(70)cos82°
a² = 1600 + 4900 - 5600cos82°
a² = 5720.63 {take square root of both sides}
a = 75.63
For the triangle ABC, by sine rule;
a/sinA = b/sinB = c/sinC
75.63/sin82° = 70/sinC
C = sin⁻¹(70 × sin82°/75.63) {by cross multiplication}
C = 66.43
angle C = 60 + 6.43 {60° is an alternate angle with angle 30° at the point B where the ship chenged course and 6.43° is a complementary angle at the 3rd quadrant of point C}
The final bearing of the port from the ship is calculated as;
180° + (90 - 6.43)° = 263.57°
Therefore, the final distance of the port from the ship is 75.63 km and the final bearing of the port from the ship is 263.57° using cosine and sine rules.
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Solve for the given variable. 2(3c + 5) = 82
find the area of the shaded region. r2 = sin(2)
The area of the shaded region is equal to sin(2).
The shaded region is a sector of a circle with radius r and central angle 2. To find the area of the shaded region, we first need to find the radius of the circle, which is given by r2 = sin(2). Taking the square root of both sides, we get r = sqrt(sin(2)).
Next, we need to find the area of the sector, which is given by:
A = (r^2 * 2) / 2 = r^2
Substituting r = sqrt(sin(2)), we get:
A = (sqrt(sin(2)))^2 = sin(2)
Therefore, the area of the shaded region is equal to sin(2).
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QUESTION CORRECTION: Find The Area Of The Shaded Region. R² = Sin (2Ф).
Which expression has a term with a coefficient greater than 1?
The expression that has a term with a coefficient greater than 1 is
3) 5 + 3m.
What are coefficients and like terms?A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.
Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.
We know a coefficient is a constant term that is with a variable.
By observing the given options we conclude that the expression
5 + 3m has a coefficient which is 3 and it is greater than 1.
Q. Which expression has a term with a coefficient greater than 1?
1) m -5×3.
2) 5 + m.
3) 5 + 3m.
4) 5/6m + 3.
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