Let In be the number of n-digit quinary (0, 1, 2, 3, 4) sequences with (i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's). (Examples of 4-digit legal quinary sequences: 3120, 3000, 4123) (a) Show 91 = 1,92 = 8. = (b) Show a recurrence for an is qn = 39n-1 +5n-1 (91 = 1). = = 5" - 35 (c) A closed form for en is In = (n > 1). Finish the induction proof of this fact 2 (began below) by completing the induction step: 57 - 31 Base case (n = 1): LHS = q1 = 1. RHS 1 2 5k - 3k Induction Hypothesis: Assume true for n=k, i.e., Pk Induction Step: = II 2 N (d) Show how to derive this closed form, i.e., show how one can arrive at this closed form if they only knew the recurrence and the initial values.
Answers
Part a:Here, In be the number of n-digit quinary (0, 1, 2, 3, 4) sequences with(i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's).Since there is at least one 3 in the n-digit sequence, we start the sequence by selecting one of the 5 digits. There are five ways to do this.The next digits are chosen according to one of the three cases shown below:1) A string of (n-1) digits where no 0's are included in the string.2) A string of (n-1) digits where at least one 0 appears in the string before the first 3.3) A string of (n-1) digits where 3 appears before the first 0 in the string.The first string in case 1 can be formed in 4 different ways because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). There are 5 choices for the first digit and thus 5*4 quinary sequences of length n with at least one 3 and no 0's that start with the selected digit.The first string in case 2 can be formed in 5 different ways because the first 3 can appear in any position before the first 0. The remaining digits are chosen in n-2 positions because the first digit is already chosen (which is 3) and n-1 digits are left. There are 4 choices for each of the remaining n-2 positions because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). Thus, there are 5*5*4^(n-2) quinary sequences of length n with at least one 3 and at least one 0 that start with the selected digit.The first string in case 3 can be formed in n-1 different ways because the first 3 can appear in any position before the first 0. The remaining digits are chosen in n-2 positions because the first digit is already chosen (which is 3) and n-1 digits are left. There are 4 choices for each of the remaining n-2 positions because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). Thus, there are 5*(n-1)*4^(n-2) quinary sequences of length n with at least one 3 and at least one 0 that start with the selected digit.Therefore, the number of n-digit quinary sequences with (i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's) is the sum of the number of sequences in each of the three cases above, i.e.In = 5*4^(n-1) + 5*5*4^(n-2) + 5*(n-1)*4^(n-2)Part b:Recurrence: qn = 3q(n-1) + 4^(n-1) + 2. q1 = 1. Let's see if qn = 39(n-1) + 5(n-1) satisfies this recurrence.q1 = 1 = 3(1-1) + 4^(1-1) + 2 = 0 + 1 + 2 = 3(0) + 5(1-1) + 1 = 0 + 0 + 1Thus, q1 = 1 satisfies the recurrence.qn+1 = 3qn + 4^n + 2 = 3(39n-1 + 5n-1) + 4^n + 2= 117(n-1) + 15(n-1) + 4^n + 2= 132(n-1) + 4^n + 3Using this formula, we can see that q2 = 91.Part c:Here, we need to finish the induction proof of this fact 2 that In = (n > 1).Induction Hypothesis: Assume true for n = k, i.e., Pk = Ik = 5*4^(k-1) + 5*5*4^(k-2) + 5*(k-1)*4^(k-2)Induction Step: To show that it is true for n = k+1, we need to show that the formula given above holds. The first digit can be any of the 5 digits (0, 1, 2, 3, 4) and the remaining digits can be selected in one of the three ways discussed in part (a).Case 1: n-1 digits with no 0'sThere are 4 choices for each of the n-1 digits, since 0 cannot be used. Therefore, there are 4^(n-1) such sequences with no 0's.Case 2: n-1 digits with at least one 0 before the first 3The first 3 can be in any of the n-1 positions, and the digits before it must be chosen from the set {0,1,2,4}. The remaining digits can be chosen in any of the 4 choices. Therefore, there are 5*(n-1)*4^(n-2) such sequences.Case 3: n-1 digits with 3 before 0We start by selecting one of the n-1 positions for the 3, then the remaining digits are chosen from the set {0,1,2,4}. There are (n-2) positions left for the remaining digits. There are 4 choices for each position, since 0 cannot be used. Therefore, there are 5*(n-1)*4^(n-2) such sequences.Thus, the total number of n-digit quinary sequences with at least one 3 and with the first 3 before the first 0 isIn = 5*4^(n-1) + 5*5*4^(n-2) + 5*(n-1)*4^(n-2) = qn+1 - qn = 132(n-1) + 4^n + 3 - (39(n-1) + 5(n-1)) = 93(n-1) + 4^n + 3which completes the induction proof.Part d:Since qn = 39n-1 + 5n-1, we haveqn+1 - qn = 132n - 39n - 5n = 88nTherefore, qn+1 = qn + 88nSubstituting qn = 39n-1 + 5n-1, we getqn+1 = qn + 88n = 39n-1 + 5n-1 + 88n = 39n + 5n + 88(n-1)Simplifying, we getqn+1 = 132(n-1) + 4^n + 3Therefore, en = In - In-1 = 93(n-1) + 4^n + 3 - 93(n-2) - 4^(n-1) - 3= 93n - 93(n-1) - 4^(n-1)= 93 - 4^(n-1)Thus, the closed form for en is en = 93 - 4^(n-1).
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Related Questions
How is the sentence "9 less than x is –1" written as an equation?
Answers
Answer:
Must not have more than ONE "=" sign in an equation like this one.
9 is less than x is -1
I will take the liberty of deleting the first "is" and then write out the expression:
9 less than x is -1, or x-9 = -1
Add 9 to both sides to determine the value of x: x = 8 (answer)
Step-by-step explanation:
Answer: x-9=-1
(they deleted my answer 4 some reason : /)
Step-by-step explanation:
This homework is really confusing me. PLEASE HELP SOON. i also haven't been able to understand this topic that well so if someone could explain some stuff that would be good
Answers
I've been having some problems too
:/
For a random variable X the probability generating function (PGF) is defined as Π(t)=E[t X
],t∈R. Clearly, it shares the essential properties of a MGF, but is often more convenient when X is integer-valued. See Whittle (2000) for an excellent discussion of this topic. (a) Show that if m(t) is the MGF of X, then Π(t)=m(log(t)). (b) Show that dt k
d k
Π(t)
∣
∣
t=1
=E[X (k)
]
Answers
Probability generating function (PGF) and Moment Generating Function (MGF) are two useful functions used to obtain moments.
The probability generating function is more useful for calculating moments of a discrete random variable whereas the moment generating function is more useful for calculating moments of a continuous random variable. Let us see how to calculate PGF and MGF.
Given a random variable X, the Probability Generating Function is defined as
Π(t)=E[t X], t ∈ R.
Similarly, the moment generating function of a random variable X is defined asM(t) = E(e^(tX)) where t is the real parameter. It is always possible to use either a probability generating function or a moment generating function to determine moments of a distribution. Solution:(a) m(t) is the MGF of X. Then
Π(t)=E(tX)=∑ P(X=k)tk=∑ P(X=k)e^(tk log(e))=∑ P(X=k)e^(t(log(e))^k)=m(log(t))(b) We need to find dt k
d k
Π(t)
∣
∣
t=1
=E[X (k)].Let P_k be the probability that
X = k.P_k = Pr(X=k).ThenΠ(t) = ∑ P_k t^k.
Now differentiate Π(t) w.r.t t, we getdΠ(t) / dt = ∑ P_k k t^(k-1).Differentiating w.r.t. t again givesd^2Π(t) / dt^2 = ∑ P_k k(k-1) t^(k-2).And so on,dkΠ(t) / dt^k = ∑ P_k k(k-1) ... (k - j + 1) t^(k-j), where the sum is taken over j = 0, 1, 2, ... , k-1.Substituting t=1,dkΠ(1) / dt^k = E(X(X-1) ... (X-k+1)).Hence, the desired result isdt k
d k
Π(t)
∣
∣
t=1
=E[X (k)
].
Therefore, if m(t) is the MGF of X, then Π(t)=m(log(t)). Also, if we differentiate the probability generating function Π(t) k times and then substitute t=1, we will get the kth moment of X.
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Given the following function, find f(-2), f(0), and f(4).
f(x) = 3x + 1
f(-2)=
Answers
which the answer is -5
f(0)= 3(0)+1
which the answer is 1
f(4)=3(4)+1
which the answer is 13
a street light is at the top of a 18 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. how fast is the tip of her shadow moving when she is 45 ft from the base of the pole?
Answers
The most appropriate choice for similarity of triangles will be given by -
Speed of tip of the shadow of woman = 6 ft/s
What are similar triangles?
Two triangles are said to be similar, if the corrosponding angles of the triangles are same and the corrosponding sides of the triangles are in the same ratio.
Here,
The diagram has been attached here
Let the distance of woman from the pole be x ft and the distance of tip of the shadow to the pole be y ft.
Height of street light = 18 ft
Height of woman = 6ft
The two triangles are similar [As height of woman is parallel to the height of pole]
\(\frac{y - x}{6}=\frac{y}{18}\\18y - 18x = 6y\\18y - 6y = 18x\\12y = 18x\\y = \frac{18}{12}x\\y = \frac{3}{2}x\\\)
To find the speed, we have to differentiate both sides with respect to time 't'
\(\frac{dy}{dt} =\frac{3}{2}\frac{dx}{dt}\\\frac{dy}{dt}=\frac{3}{2} \times 4\\\frac{dy}{dt} = 6\)
Speed of tip of her shadow = 6 ft
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calculate perimeter of and irregular shape 19cm by 10cm
Answers
The perimeter of the irregular shape with dimensions 19 cm by 10 cm is 58 cm.
To find the perimeter of an irregular shape, we have to add up all the sides of the shape.
For the given question, we have the dimensions of the irregular shape as 19 cm by 10 cm.
Let's assume that the irregular shape is a rectangle since we have the two dimensions of length and width given. Therefore, we have;
Length = 19 cm
Width = 10 cm
To calculate the perimeter of the rectangle, we can use the formula;
P = 2L + 2W
Where;
P = perimeter of the rectangle
L = length of the rectangle
W = width of the rectangle
Substituting the given values;
P = 2(19) + 2(10)
P = 38 + 20
P = 58 cm
Therefore, the perimeter of the irregular shape with dimensions 19 cm by 10 cm is 58 cm.
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Cuanto valen 2 con tres cuartos
Answers
Question 3(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru is able to estimate their wait time more consistently and why?
Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
Answers
Burger Quick's box plot has a larger IQR than Super Fast Food's, hence Super Fast Food is better able to predict their wait time
Define IQR?
A measurement of statistical dispersion, or the spread of the data, is the interquartile range (IQR). It is described as the variation between the data's 75th and 25th percentiles. The fourth spread, middle 50%, midspread, or H-spread1 are further names for the IQR.
The dataset is displayed using a box plot, which is a standardized method based on the five-number summary of the minimum, maximum, sample median, and first and third quartiles
The box plot displays measurements made from data acquired from interviews with 20 people on how long they waited at a drive-through restaurant window.
Burger Quick's box plot has a larger IQR than Super Fast Food's, hence Super Fast Food is better able to predict their wait time.
A data set is divided into quartiles to calculate the IQR (Interquartile Range), which is a measure of variability. The first quartile (Q1) is subtracted from the third quartile (Q3) to determine it.
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Please help thank you
Answers
The tension forces are 1895 N and 2542 N.
What is the tension in the ropes?
Tension force is a type of force that results from the stretching or pulling of an object, such as a rope, cable, or string. When an object is under tension, it experiences a force that acts along its length, pulling it apart
We know that the third angle in the triangle that is formed is;
180 - [35 + 48]
= 97 degrees
We then have the tension in the ropes as T1 and T2
Using the sine rule;
T1/sin 35 = 3275/sin97
sin97T1 = 3275 sin 35
T1 = 3275 sin 35/sin97
T1 = 1895 N
For T2
T2/sin48 = 3275/sin97
sin97T1 = 3275 sin 48
T1 = 3275 sin 48/sin97
T1 = 2542 N
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Sandra uses the formula, P = DB, to find her approximate six-month premium when her driver risk factor, D, is 1.0 and the basic six-month premium is $567.
What will her monthly premium be?
A. $170.00
B. $177.50
C. $94.50
D. $201.15
Answers
P = DB = (1.0)($567) = $567
To find the monthly premium, we divide the six-month premium by 6:
Monthly premium = P/6 = $567/6 = $94.50
Therefore, the monthly premium for Sandra is $94.50, which is option C.
In which choice do all three points lie on the same straight line?
A (0, 1), (–1, 3), (1, 3)
B (4, 2), (2, 1), (4, –2)
C (0, 0), (8, 0), (0, 8)
D (1, 2), (2, 4), (4, 8)
Answers
Answer:
D
Step-by-step explanation:
we'll use the complex number system to solve this exercice
the coordinates of the last triplet are : (1,2) , (2,4) and (4,8) The affixes are then
\(1 + 2i = a \\2 + 4i= b = 2a \\4+8i = c = 2b = 4a\)
for the points to be aligned the fraction \(\frac{c-a}{b-a}\) should be a real number
\(\frac{c-a}{b-a} = \frac{4a-a}{2a-a} = \frac{3a}{a} = 3\)
so the points are aligned
Answer:
D (1, 2), (2, 4), (4, 8)
Step-by-step explanation:
Hope this helps
a cylindrical tank 5 feet in diameter and 10 feet high is filled with oil whose density is 48 lbs/ft3 . how much work is required to pump the oil over the top of the tank?
Answers
The work required to pump the oil over the top of the tank is 1.5080 × 10⁶
Given:
We start as we often do: we partition an interval into sub intervals. We orient our tank vertically since this makes intuitive sense with the base of the tank at y=0 . Hence the top of the oil is at y=10 , meaning we are interested in subdividing the y -interval [0,10] into n sub intervals as
0 = y₁ < y₂ < ..... <yₙ₊₁ = 15
Consider the work Wi of pumping only the oil residing in the ith sub interval. The force required to move this oil is equal to its weight which we calculate as volume × density. The volume of oil in this sub interval is Vi=5²πΔyi ; its density is 48 lb/ft ₃ . Thus the required force is 4800πΔyi lb.
We approximate the distance the force is applied by using any y -value contained in the ith sub interval; for simplicity, we arbitrarily use yi for now (it will not matter later on). The oil will be pumped to a point 5 feet above the top of the tank, that is, to the height of y=15 ft. Thus the distance the oil at height yi travels is 15−yi ft.
In all, the approximate work Wi performed in moving the water in the ith sub interval to a point 5 feet above the tank is
Wi≈4800πΔyi(15−yi).
To approximate the total work performed in pumping out all the oil from the tank, we sum all the work Wi performed in pumping the oil from each of the n sub intervals of [0,10] :
W≈∑i=1nWi=∑i=1n4800πΔyi(15−yi).
This is a Riemann sum. Taking the limit as the sub interval length goes to 0 gives
W=∫3006240π(35−y)dy
=6240π(35y−12y2)∣∣10 0
= 48000π ≈ 1.5080 × 10⁶
Hence we get the required work done.
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Your question is incomplete. Please find the missing content below.
a cylindrical tank 5 feet in diameter and 10 feet high is filled with oil whose density is 48 lbs/ft3 . how much work is required to pump the oil up to a point 5 feet above the top of the tank.
a numerical measure computed from a sample, such as sample mean, is known as a . a. population parameter b. sample statistic c. population statistic d. sample parameter
Answers
A numerical measure computed from a sample, such as sample mean, is known as Sample statistic
What is Statistic?
The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.
A sample statistic is a metric that is calculated from a sample, such as sample mean. A population parameter is a numerical measure derived from a population, such as a mean.
Any value calculated from your sample data is referred to as a sample statistic (or simply a statistic). The sample average, median, sample standard deviation, and percentiles are a few examples. Because a statistic is based on data gathered through random sampling, which is a random experiment, it is a random variable.
Hence, A numerical measure computed from a sample, such as sample mean, is known as Sample statistic
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How many complex zeros does the polynomial function have?
f(x)=4x5−2x2+6
Answers
The polynomial function f(x) = 4x^5 - 2x^2 + 6 has complex zeros if and only if its coefficients are not all real. However, in this case, all the coefficients of the polynomial are real, so all of its zeros are real as well.
To find the number of real zeros of the function, we can use Descartes' rule of signs, which states that the number of positive real zeros of a polynomial is equal to the number of sign changes in the coefficients of f(x), or is less than that by an even integer, and the number of negative real zeros is equal to the number of sign changes in f(-x), or is less than that by an even integer.
Using Descartes' rule of signs, we see that f(x) has one sign change, namely from positive to negative, in the coefficients of its terms. Therefore, f(x) has exactly one negative real zero.
Since f(x) is a polynomial of odd degree, it must have at least one real zero. Therefore, f(x) has exactly one negative real zero and at least one positive real zero.
In summary, the polynomial function f(x) = 4x^5 - 2x^2 + 6 has exactly one negative real zero and at least one positive real zero. It has no complex zeros.
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If two lines intersect, then the vertical angles formed must be? both equal in measure both acute angles complementary angles
Answers
If two lines intersect, then the vertical angles formed must be both equal in measure.
What is intersection of a line?The intersection of a line can be described as when two or more lines cross each other in a plane as a result of this they are been referred to as intersecting lines.
Therefore, intersecting lines share a common point, hence , If two lines intersect, then the vertical angles formed must be both equal in measure.
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Fill in the missing step for this number trick
operation
1.pick a number
2.,
3.,
4.,
5.
6. Subtract the original number
Answers
Answer:
1 pick a number
2mutiply that number by 5
3 mutiply it by 20
4 then double that number
5 divide it by 100
6 subtract the orginal number
Step-by-step explanation:
7) What does a multiplier of \( 1.2 \) mean?
Answers
A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.
A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.
A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.
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if the hypothesis is rejected, then the sample refression coefficient b1 indicates the change in the predicted value for aunit change in
Answers
The hypothesis referred to in this statement is likely the null hypothesis in a regression analysis, which assumes that the slope coefficient (b1) of the regression line is equal to zero, indicating that there is no relationship between the independent variable and the dependent variable. If the hypothesis is rejected, it means that there is sufficient evidence to suggest that the slope coefficient is not zero and there is a significant relationship between the independent and dependent variables.
In this context, the sample regression coefficient b1 represents the change in the predicted value of the dependent variable for a unit change in the independent variable. In other words, it indicates the slope of the regression line and how much the dependent variable changes for a unit change in the independent variable. If b1 is positive, it means that the dependent variable increases as the independent variable increases, and if b1 is negative, it means that the dependent variable decreases as the independent variable increases. The magnitude of b1 indicates the strength of the relationship between the variables, with larger values indicating a stronger relationship.
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Draw the trees corresponding to the following Prufer codes. (a) (2,2,2,2,4,7,8). (b) (7,6,5,4,3,2,1)
Answers
The Prufer codes (a) (2, 2, 2, 2, 4, 7, 8) and (b) (7, 6, 5, 4, 3, 2, 1) correspond to specific trees. The first Prufer code represents a tree with multiple nodes of degree 2, while the second Prufer code represents a linear chain tree.
(a) The Prufer code (2, 2, 2, 2, 4, 7, 8) corresponds to a tree where the nodes are labeled from 1 to 8. To construct the tree, we start with a set of isolated nodes labeled from 1 to 8. From the Prufer code, we pick the smallest number that is not present in the code and create an edge between that number and the first number in the code.
(b) The Prufer code (7, 6, 5, 4, 3, 2, 1) corresponds to a linear chain tree. Similar to the previous example, we start with a set of isolated nodes labeled from 1 to 7. We then create edges between the numbers in the Prufer code and the first number in the code.
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the correlation between gdp and carbon dioxide emissions is r=0.912. is the correlation significant at =.05? give the critical value from the table: is the correlation significant? (yes or no
Answers
The correlation is significant at α=0.05 and the critical value for correlation is 0.087. So, the correlation is significant.
A correlation coefficient is a numerical measure of some correlation, meaning a statistical relationship between two variables.
To determine if the correlation between GDP and carbon dioxide emissions is significant at α=.05, we need to compare the calculated correlation coefficient (r=0.912) with the critical value from the table.
Using a two-tailed test and degrees of freedom (df) = n-2 = (sample size) - 2,
we find the critical value at α=0.05 to be 0.087. (Using the critical value for correlation table)
Since the calculated correlation coefficient (0.912) is much larger than the critical value (0.087), we can conclude that the correlation between GDP and carbon dioxide emissions is significant at α=.05.
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Ellle bought 6 pineapples for $12.95. Estlm
the cost of each pineapple to the nearest cent?
Answers
Answer:
$2.16
Step-by-step explanation:
divide $12.95 by 6
12.95/6=2.15833333333
round to the nearest cent : $2.16
Find the lowest common denominator (multiple). Type the equivalent fractions. Then, add or subtract. Simplify your answer. 1
2
1
3
Answers
Answer:what
Step-by-step explanation:what does this mean
i hope my teachers dont find this and sus me out im just making sure im right
Answers
Answer:
The answer would be option D
Step-by-step explanation:
Hope this helped! Can I please have brainliest?
Answer:its 22.5
Step-by-step explanation:
If the relationship is proportional, what is the missing value from the table?
x
8
16
24
y
6
?
18
Answers
Answer:
The answer is 12.
Step-by-step explanation:
6 is 3/4 of 8 and 18 is 3/4 of 24. All you do is divide 16 by 4 which equals 4. Then multiple that answer by 3 which gives you 12.
Answer:
The answer is 12
Step-by-step explanation:
whar is the value of (4x² -10)
-------------
y
when x=5 and Y=6
A) -15
B)10
C)15
D)20
Answers
Z^5=-243i, find the solution to the equation whose argument is strictly between 180 degrees and 270 degrees. Round your answer to the nearest 10th
Answers
Answer:
The solution is \(z = -2.853 - i 0.927\).
Step-by-step explanation:
Complex power is determined by means of the De Moivre's Theorem, whose expression is:
\(z^{n} = r^{n} \cdot (\cos n\theta + i \sin n\theta)\)
Where \(r\) is the norm of the complex number. In this case, expression can be written as:
\(-i 243 = 3^{5} \cdot (\cos 5\theta + i \sin 5\theta)\)
The real component must be equal to zero and complex component must be equal to -1. That is to say:
\(\cos 5\theta = 0\)
\(\sin 5\theta = -1\)
Possible solutions for each component are, respectively:
Real component
\(5\theta = \cos^{-1}0\)
\(5\theta = \frac{\pi}{2} \pm \pi\cdot j\), \(\forall j \in \mathbb{N}_{O}\)
\(\theta = \frac{\pi}{10} \pm \frac{\pi}{5} \cdot j\), \(\forall j \in \mathbb{N}_{O}\)
Possible solutions: \(\frac{11\pi}{10}\), \(\frac{13\pi}{10}\), \(\frac{3\pi}{2}\)
Complex component
\(5\theta = \sin^{-1}(-1)\)
\(5\theta = \frac{3\pi}{2} \pm 2\pi \cdot j\), \(\forall j \in \mathbb{N}_{O}\)
\(\theta = \frac{3\pi}{10} \pm \frac{2\pi}{5} \cdot j\), \(\forall j \in \mathbb{N}_{O}\)
Possible solutions: \(\frac{11\pi}{10}\), \(\frac{3\pi}{2}\)
There is one solution whose argument is strictly between 180 degrees (\(\pi\)) and 270 degrees (\(1.5\pi\)).
\(z = 3 \cdot \left( \cos \frac{11\pi}{10} + i \sin \frac{11\pi}{10} \right)\)
\(z = -2.853 - i 0.927\)
how would i solve this
Answers
Note that the expression when simplified translates to x = -6 (Option 1)
What is a math expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.
√(x + 14) - √2x + 5) = 1
To solve this, we must square all elements on both sides of the equation. That is:
√(x + 14)² - √(2x + 5)² = 1²
⇒ x + 14 + 2x + 5 = 1
Collect like terms to arrive at:
3x = -18
x = -18/3
x = -6
Thus the answer to the above expression is x= -6
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This graph is a function?
Answers
Answer:
There is no graph, but unless the x value of the live repeats, yes, it is a function.
Step-by-step explanation:
Answer:
The x value of a point where a vertical line intersects a function represents the input for that output y value. If we can draw any horizontal line that intersects a graph more than once, then the graph does not represent a function because that y value has more than one input.
Marco's charges an additional fee for toppings, but all toppings cost the same. Kevin got pepperoni, banana peppers, and black olives on his pizza for a cost of $15.74. Brian ordered mushrooms and eggplant on his pizza and paid $14.49. Using this information, write an equation for the cost of a pizza, C, as a function of the toppings, t, ordered.
Answers
Answer: Let's use x to represent the cost of each topping. Then, the cost of a pizza with t toppings can be expressed as:
C = x * t + 15
We know that Kevin's pizza with 3 toppings cost $15.74, so we can write an equation using this information:
15.74 = 3x + 15
Solving for x, we get:
x = (15.74 - 15) / 3 = 0.74
So, each topping costs $0.74. Now we can use the information about Brian's pizza to check our answer:
14.49 = 2x + 15
Substituting x = 0.74, we get:
14.49 = 2 * 0.74 + 15
Which simplifies to:
14.49 = 1.48 + 15
This confirms that x = 0.74 is the correct cost for each topping. Therefore, the equation for the cost of a pizza as a function of the toppings ordered is:
C = 0.74t + 15
Step-by-step explanation:
answer the following, Round final answer to 4 decimal places. a.) Which of the following is the correct wording for the randon variable? r×= the percentage of all people in favor of a new building project rv= the number of people who are in favor of a new building project r N= the number of people polled r×= the number of people out of 10 who are in favor of a new building project b.) What is the probability that exactly 4 of them favor the new building project? c.) What is the probabilitv that less than 4 of them favor the new building project? d.) What is the probabilitv that more than 4 of them favor the new building project? e.) What is the probabilitv that exactly 6 of them favor the new building project? f.) What is the probability that at least 6 of them favor the new building project? 8.) What is the probabilitv that at most 6 of them favor the new building project?
Answers
In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.
a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.
b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.
c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.
d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).
e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.
f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).
g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).
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