[tex]number \: of \: performances = 9 \\ note = \\ one \: insists \: on \: being \: last \\ number \: of \: flexible \: performances = 9 - 1 = 8 \\ \\ c( \gamma ) = 8P8 \times 1 \\ c( \gamma ) = 8! \\ c( \gamma ) = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \\ c( \gamma ) = 40320 \: ways[/tex]
Attached as a photo.
Applying the initial conditions, the specific solution is:
[tex]y = e^{-2x}(-3\sin{3x} + 4\cos{3x})[/tex]
What is the general solution?The general solution is given by:
[tex]y = e^{-2x}(C_1\sin{3x} + C_2\cos{3x})[/tex]
How to find the specific solution?We apply the initial conditions to find the specific solution.
First, we have that y(0) = 4, then:
[tex]4 = e^{-2(0)}(C_1\sin{3(0)} + C_2\cos{3(0)})[/tex]
Since cos(0) = 1, we have that:
[tex]C_2 = 4[/tex]
Then:
[tex]y = e^{-2x}(C_1\sin{3x} + 4\cos{3x})[/tex]
The derivative is:
[tex]y^\prime(x) = -2e^{-2x}(C_1\sin{3x} + 4\cos{3x}) + e^{-2x}(3C_1\cos{3x} - 4\sin{3x})[/tex]
Since y'(0) = -17, then:
[tex]-17 = -8 + 3C_1[/tex]
[tex]3C_1 = -9[/tex]
[tex]C_1 = -3[/tex]
Then the specific solution is:
[tex]y = e^{-2x}(-3\sin{3x} + 4\cos{3x})[/tex]
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m..................................find the value of x ...y and z..
Step-by-step explanation:
x =130.......................
) The following scatterplot shows the percentage of the vote a candidate received in the 2016 senatorial elections
according to the voter's income level based on an exit poll of voters conducted by a news agency. The income
levels 1-8 correspond to the following income classes:
1 = Under $15,000; 2 = $15-30,000; 3 = $30-50,000; 4 = $50-75,000; 5 = $75-100,000;
6 = $100-150,000; 7 = $150-200,000; 8 = $200,000 or more.
Use the election scatterplot to the find the critical values corresponding to a 0.01 significance level used to test
the null hypothesis of ρs = 0.
A) -0.881 and 0.881
B) -0.881
C) -0.738 and 0.738
D) 0.881
The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881
How to determine the critical values corresponding to a 0.01 significance level?The scatter plot of the election is added as an attachment
From the scatter plot, we have the following highlights
Number of paired observations, n = 8Significance level = 0.01Start by calculating the degrees of freedom (df) using
df =n - 2
Substitute the known values in the above equation
df = 8 - 2
Evaluate the difference
df = 6
Using the critical value table;
At a degree of freedom of 6 and significance level of 0.01, the critical value is
z = 0.834
From the list of given options, 0.834 is between -0.881 and 0.881
Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881
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Find the dy/dx using implicit differentiation
x³-3x²y+2xy² = 12
The dy/dx of equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].
Given an equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex].
We are required to find dy/dx of the equation.
Equation is like a relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.
Differentiation is basically finding the change in variables.
It may be linear equation, quadratic equation,cubic equation or many more depending on the power of the variable present in the equation.
Equation:[tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex]
Differentiating with respect to x.
3[tex]x^{2}[/tex]-3([tex]x^{2}[/tex]*dy/dx+y*2x)+2(x*2y*dy/dx+[tex]y^{2}[/tex])=0
3[tex]x^{2} -3x^{2} dy/dx-6xy+4xy dy/dx+2y^{2}[/tex]=0
Taking dy/dx at one side and take the other part to other end.
[tex]-3x^{2} dy/dx+4xy dy/dx[/tex]=[tex]6xy-3x^{2} -2y^{2}[/tex]
dy/dx=[tex](6xy-3x^{2} -2y^{2})/(4xy-3x^{2} )[/tex]
Hence the dy/dx of equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].
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Please help!
(02.01 HC)
Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x + 7, y − 1) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments. (10 points)
Using translation concepts, it is found that:
The new coordinates of A' are: (5,0).The new coordinates of B' are: (5,2).The new coordinates of C' are: (9,2).The new coordinates of D' are: (9,0).Since there are only two values for the x-coordinates and two values for the y-coordinates, if the corresponding vertices were connected with line segments, a rectangle would be formed.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule applied for each vertex of the rectangle is given as follows:
(x,y) -> (x + 7, y - 2).
The new coordinates of A' are given as follows:
(-2 + 7, 2 - 2) = (5,0).
The new coordinates of B' are given as follows:
(-2 + 7, 4 - 2) = (5,2).
The new coordinates of C' are given as follows:
(2 + 7, 4 - 2) = (9,2).
The new coordinates of D' are given as follows:
(2 + 7, 2 - 2) = (9,0).
Since there are only two values for the x-coordinates and two values for the y-coordinates, if the corresponding vertices were connected with line segments, a rectangle would be formed.
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Which sequence has a common difference of -8?
{63, 71, 79, 87, 95, …}
{800, 8, 12.5, 1.5625, …}
{536, 528, 520, 512, 504, …}
{1, -8, 64, -512, 4,096, …}
A 13km stretch of road needs repairs. Workers can repair 3 1/2 km of road per week.
How many weeks will it take to repair this stretch of road?
The computation shows that the number of weeks that it take to repair this stretch of road will be 4 weeks.
How to compute the number of weeks?From the information given, we are told that a thirteen kilometers stretch of road needs repairs and that the workers can repair three and half kilometers of road per week.
The question is simply for us to calculate the number or weeks that it will take to be able to repair the stretch of road.
Therefore, based on the information given, it should be noted that to get the number of weeks that will be used to repair the road, we simply have to divide the total distance or the road by the distance that is repaired every week.
Therefore, the number of weeks that it will take to be able to repair this stretch of road will be:
= 13/3.5
= 3.7
= 4 weeks approximately
Therefore, based on the information given, the number of weeks that's required is 4 weeks.
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As part of a summer internship, five people -- Cindy, Damaris, Eugenio, Fareed, and Guzal -- are to be assigned to floors 1-5 in a dormitory. Each person will occupy his or her own entire floor and no other people will be in the dormitory. The assignment of people to floors must follow the following rules: Eugenio lives immediately above Damaris. Cindy is not on the first floor. Fareed does not live immediately below Damaris. Guzal lives either on the first floor or the fifth floor. Which one of the five people could be assigned to live on any of the five floors in the dormitory?
Based on the information, it is expected Fareed can be assigned to live on any of the floors.
What condition limits Fareed's assignment?The only condition that limits the floor Fareed can be assigned to is that he cannot be immediately below Damaris. This means that as long as Damaris is not immediately above him, he can be assigned to all floors. Here are two possible arrangements:
Eugenio (5th floor)DamarisCindyFareedGuzal (1st floor)Guzal (5th floor)EugenioDamarisCindyFareed (1st floor)Learn more about arragements in: https://brainly.com/question/27909921
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I ordered a shoe a few days ago and the seller provided me with the tracking number for the hoodie but through Grailed but USPS has been stuck on "We are preparing your order for shipment" and "Delivery information will be available once the carrier has the updates." What does this mean? Also when I put my tracking number in USPS's Package Tracker, the number doesn't exist in its system. Does anyone know whats going on? Thanks!
find the fourth roots of i
Answer:
1∠22.5°, 1∠112.5°, 1∠202.5°, 1∠292.5°
Step-by-step explanation:
A root of a complex number can be found using Euler's identity.
ApplicationFor some z = a·e^(ix), the n-th root is ...
z = (a^(1/n))·e^(i(x/n))
Here, we have z = i, so a = 1 and z = π/2 +2kπ.
Using r∠θ notation, this is ...
i = 1∠(90° +k·360°)
and
i^(1/4) = (1^(1/4))∠((90° +k·360°)/4)
i^(1/4) = 1∠(22.5° +k·90°)
For k = 0 to 3, we have ...
for k = 0, first root = 1∠22.5°
for k = 1, second root = 1∠112.5°
for k = 2, third root = 1∠202.5°
for k = 3, fourth root = 1∠292.5°
Investments increase exponentially by
about 26% every 3 years. If you made a
$2,000 investment, how much money
would you have after 45 years?
Future Amount = $[?]
Hint: Future Amount = [(1 + r)t
-pt
↑
initial
amount
growth
rate
←time
periods
Round to the nearest dollar.
Answer:
9060$ is the final amount because 7060 is the interest
The amount of money after 45 years will be $64,060.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Investments increase exponentially by about 26% every 3 years.
If you made a $2,000 investment.
Then the equation will be
[tex]\rm A = 2000 \times \left (1.26 \right )^{\frac{t}{3}}[/tex]
Where t is the number of years.
Then the amount of money after 45 years will be
[tex]\rm A = 2000 \times \left (1.26 \right )^{\frac{45}{3}}[/tex]
Simplify the equation, then we have
A = 2000 × (1.26)¹⁵
A = 2000 × 32.03
A = $64,060
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Which of the following represents a quadratic function?
a. y = 3x - 2
b. y=6+5x + x²
c. x³10x = 21
d. y= 2² +4
Answer:
○ [tex]y = 6 + 5x + x^2[/tex]
Explanation:
What is a quadratic equation?A quadratic equation is an algebraic equation where the highest power of [tex]x[/tex] is 2. The general form of a quadratic equation is as follows:
[tex]\boxed{ax^2 + bx + c = 0}[/tex],
where a, b, and c represent known constants, and [tex]x[/tex] is the unknown.
In this question, if you take a look at the second option, you will see that it is possible to rearrange the equation to make it look the general form:
[tex]y = 6 + 5x + x^2[/tex]
⇒ [tex]y = x^2 + 5x + 6[/tex]
Therefore, this equation is quadratic.
The other three options are not quadratic equations because none of them have an [tex]x^2[/tex] term in them.
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
[tex]\leadsto[/tex] A quadratic equation is an algebraic equation of the second degree. The formula is:
▪ [tex]\longrightarrow \sf{y = ax^2 + bx + c}[/tex]
This can also be written as:
▪ [tex]\longrightarrow \sf{y = c + bx+ax^2}[/tex]
Comparing the equation above with each of the options, the equation that represents a quadratic function is:
[tex]\longrightarrow \sf{y=6+5 + x^2}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \large\bm{b. \: y=6+5x + x^2}[/tex]
Attached as photo. Please help
By Euler's method the numerical approximate solution of the definite integral is 4.189 648.
How to estimate a definite integral by numerical methodsIn this problem we must make use of Euler's method to estimate the upper bound of a definite integral. Euler's method is a multi-step method, related to Runge-Kutta methods, used to estimate integral values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:
∫ f(x) dx = F(b) - F(a) (1)
The steps of Euler's method are summarized below:
Define the function seen in the statement by the label f(x₀, y₀).Determine the different variables by the following formulas:The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the numerical approximation of the definite integral is:
y(4) ≈ 4.189 648 - 0
y(4) ≈ 4.189 648
By Euler's method the numerical approximate solution of the definite integral is 4.189 648.
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Name plane K using three noncollinear points.
Answer:
plane HNA, HMB, ANG ...
Step-by-step explanation:
Any combination of three points on plane K will work unless all three are on the same line.
sirs is making lemonade to sell at her lemonade stand. she made a batch of 8 pitchers of lemonade using 24 lemons, 12 cups of sugar, and 20 liters of water. she decides to make a second batch of 6 pitchers of lemonade. how many liters of water should she use to make the second batch of lemonade?
Answer:15
Step-by-step explanation: 20 divided by 8=2.5 x 6=15
4.) Determine the missing side of a rectangle with an area of 480 cm² and a length of 32 cm. Please show your work.
Answer:
w = 15 cm
Step-by-step explanation:
We want to find the width, as the area of a rectangle is length (l) * width (w).
Since we know the area and the length, we have 480 = 32w
Isolating w by dividing both sides by 32 gives us w = 15 cm
which theorem can be used to show that LABC is to LDEC
1/2-1/6
Jzjzhhzhzhzhhz
Answer:
ummm the answer is very simple
The answer is 0/6
Step-by-step explanation:
[tex] \frac{1}{2 \times 3} - \frac{1}{6} [/tex]
[tex] \frac{1}{6} - \frac{1}{6} [/tex]
[tex]1 - 1 = \frac{0}{6} [/tex]
Give the standard form for 7000+300+40+2
Answer:
7×10³+3×10²+4×10¹+2×10 or 7.342×10³
Find the slope of a line parallel to the line that crosses ( 3 , − 2 ) and the y -intercept is ( 0 , − 3 ) . I finally figured out how to write my equations in slope intercept form and NOW this pops up, can someone please explain it to me
Answer:
y = 1/3x - 3
Step-by-step explanation:
We can find the equation of the line, by finding the slope and combine with our y-intercept (-3).
We need to use the slope formula to find the slope.
Thus, we have (-3 - (-2)) / 0 - 3 = -1/-3 = 1/3
So our equation is y = -1/3x - 3
A string of 254cm from a ball of string measuring 4m.Calculate the string left on the ball
Answer:
1.46m or 14600cm are left over
Step-by-step explanation:
Assuming you mean that there were 4m of string and 254cm were used/removed.
A certain brand of coffee comes in two sizes. A 12.3-ounce package costs $2.99 . A 33.9-ounce package costs $8.74 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Answer:
[tex]12.3 - 33.9 = 21.6 \div 10 = 2.16[/tex]
Polygon WXYZ is dilated by a scale factor of 3 with vertex W as the center of dilation, resulting in polygon W'X'Y'Z'. The coordinates of point W are (3,2), and the coordinates of point X are (7,5). Select the correct statement. A. The slope of W'X' is , and the length of W'X' is 5. B. The slope of W'X' is , and the length of W'X' is 15. C. The slope of W'X' is , and the length of W'X' is 15. D. The slope of W'X' is , and the length of W'X' is 5.
Since the Dilating polygon WXYZ will alter the side lengths of the polygon. The correct option is option (b) the slope of WX is 3/4, and the length of W'X' is 15.
What is the vertex about?The coordinates in the question were:
(3,2), and (7,5).
Then the slope of WX is:
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
So m = [tex]\frac{{5} - 2 }{7-3} }[/tex]
=3/4
The length of WX is calculated by:
[tex]WX = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1}) ^ 2}[/tex]
[tex]\sqrt{(7-3)^2 + (5-2)^2} \\\\= \sqrt{25} \\\\= 5[/tex]
Since, The scale factor is = 3.
Hence, WX = 3 x 5 = 15
Therefore, Since the Dilating polygon WXYZ will alter the side lengths of the polygon. The correct option is option (b) the slope of WX is 3/4, and the length of W'X' is 15.
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Answer: slope 3/4 and length 15
Step-by-step explanation: plato
if X + Y = 212 and xy = 27 find the value of (x³+y³)
sin^4x rewrite the power as a product of two squared terms
sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)
How to rewrite the expression?The sine expression is given as
sin^4x
The above means
sin x raised to the power of 4
This in other words, the expression is represented as
(sin(x))^4
Express 4 as 2 + 2
(sin(x))^(2 + 2)
Apply the law of indices
(sin(x))^2 * (sin(x))^2
This gives
sin^2(x) * sin^2(x)
Hence, sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)
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Which of the following are true statements about a 30 69 90 triangle? Check all that apply
By the 30 - 60 - 90 theorem the right options of the multiple choice question is:
A. The hypotenuse is twice as long as the shorter leg.
D. The longer leg is √3 times as long as the shorter leg.
What are the properties of a 30 - 60 - 90 right triangles
In this problem we must look for the right choices in a multiple choice question. According to the Euclidean geometry, 30 - 60 - 90 have the following properties:
The length of the hypotenuse is √3 / 2 times as long as the longer leg.The length of the hypotenuse is twice as long as the shorter leg.The length of the longer leg is √3 times as long as the shorter leg.Thus, the right options of the multiple choice question is:
A. The hypotenuse is twice as long as the shorter leg.
D. The longer leg is √3 times as long as the shorter leg.
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In a population where 81 % of voters prefer Candidate A,
an organization conducts a poll of 15 voters. Find the
probability that 11 of the 15 voters will prefer Candidate
The probability of 11 voters out of 15 voting candidate A is 0.9770
According to the statement
we have given that the percentage of voters is 81% and poll conducts are 15 and we have to find the probability that 11 of the 15 voters will prefer Candidate
So, For this purpose,
the question in based on binomial probability which means the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes p and q and p+q=1
let probability of choosing candidate A be p
and probability of choosing candidate B be q
In question p=0.81 and q=0.16
n be total number of voters=15
x be number of successes
then P(x=x)= [tex]\frac{n}{x} p^{x} q^{n-x}[/tex]
P(x=11)= [tex]\frac{11}{15} 0.81^{11} 0.16^{4}[/tex]
= 0.9770
So, the probability of 11 voters out of 15 voting candidate A is 0.9770
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PLEASE HELP Find the value of x.
X
15
12
Answer: x = 9
Step-by-Step Solution:
Hypotenuse = 15 units
Base = 12 units
Altitude = x units
Using Pythagoras Theorem,
=> Hypotenuse^2 = Base^2 + Altitude^2
(15)^2 = (12)^2 + x^2
225 = 144 + x^2
225 - 144 = x^2
81 = x^2
x^2 = 81
x = √81
=> x = 9
Therefore, Altitude = 9 units
Solve the inequality for 3y+1 is less than -11 . Simplify your answer as much as possible.
MY LAST ONE PLEASE HELP
the inequality gives the 'y' value as -4
What is inequality?An inequality is a mathematical tool that compares two values, expressing when one is less than, greater than, or not equal to the other value.
For instance,
a ≠ b says that a is not equal to b
a < b says that a is less than b
a > b says that a is greater than b
From the information given, that 3y+1 is less than -11 . It can be expressed as;
3y + 1 ∠ -11
Let's collect like terms
3y ∠ -11 - 1
add like terms
3y ∠ -12
make 'y' the subject of formula
y ∠ -12/3
y ∠ -4
The inequality gives the 'y' value as -4
Thus, the inequality gives the 'y' value as -4
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Statistics students in Oxnard College sampled 9 textbooks in the Condor bookstore and recorded the number of pages in each textbook and its cost. The bivariate data are shown below:
Number of Pages (
x
) Cost(
y
)
322 41.2
895 103.5
232 22.2
618 74.8
394 51.4
814 89.4
884 97.4
919 89.9
929 109.9
A student calculates a linear model
y
=
x
+
. (Please show your answers to at least 4 decimal places)
Use the model to estimate the cost when number of pages is 407.
Cost = $
(Please show your answer to 2 decimal places.)
By using the linear function which models the data in the given table, the cost of a textbook with 402 pages is equal to $47.4478.
What is a scatter plot?A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:
y = 0.1057x + 4.9564
If x = 402, then y is given by:
y = 0.1057(402) + 4.9564
y = 42.4914 + 4.9564
y = $47.4478.
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