Answer:
Step-by-step explanation:
Linear Programming Problems (LPP): Linear programming or linear optimization is a process which takes into consideration certain linear relationships to obtain the best possible solution to a mathematical model. It is also denoted as LPP. It includes problems dealing with maximizing profits, minimizing costs, minimal usage of resources, etc. These problems can be solved through the simplex method or graphical method.
Linear Programming For Class 12
Linear Programming
Linear Programming Worksheet
The Linear programming applications are present in broad disciplines such as commerce, industry, etc. In this section, we will discuss, how to do the mathematical formulation of the LPP.
Mathematical Formulation of Problem
Let x and y be the number of cabinets of types 1 and 2 respectively that he must manufacture. They are non-negative and known as non-negative constraints.
The company can invest a total of 540 hours of the labour force and is required to create up to 50 cabinets. Hence,
15x + 9y <= 540
x + y <= 50
The above two equations are known as linear constraints.
Let Z be the profit he earns from manufacturing x and y pieces of the cabinets of types 1 and 2. Thus,
Z = 5000x + 3000y
Our objective here is to maximize Z. Hence Z is known as the objective function. To find the answer to this question, we use graphs, which is known as the graphical method of solving LPP. We will cover this in the subsequent sections.
Graphical Method
The solution for problems based on linear programming is determined with the help of the feasible region, in case of graphical method. The feasible region is basically the common region determined by all constraints including non-negative constraints, say, x,y≥0, of an LPP. Each point in this feasible region represents the feasible solution of the constraints and therefore, is called the solution/feasible region for the problem. The region apart from (outside) the feasible region is called as the infeasible region.
The optimal value (maximum and minimum) obtained of an objective function in the feasible region at any point is called an optimal solution. To learn the graphical method to solve linear programming completely reach us.
Linear Programming Applications
Let us take a real-life problem to understand linear programming. A home décor company received an order to manufacture cabinets. The first consignment requires up to 50 cabinets. There are two types of cabinets. The first type requires 15 hours of the labour force (per piece) to be constructed and gives a profit of Rs 5000 per piece to the company. Whereas, the second type requires 9 hours of the labour force and makes a profit of Rs 3000 per piece. However, the company has only 540 hours of workforce available for the manufacture of the cabinets. With this information given, you are required to find a deal which gives the maximum profit to the décor company.
Linear Programming problem LPP
Given the situation, let us take up different scenarios to analyse how the profit can be maximized.
He decides to construct all the cabinets of the first type. In this case, he can create 540/15 = 36 cabinets. This would give him a profit of Rs 5000 × 36 = Rs 180,000.
He decides to construct all the cabinets of the second type. In this case, he can create 540/9 = 60 cabinets. But the first consignment requires only up to 50 cabinets. Hence, he can make profit of Rs 3000 × 50 = Rs 150,000.
He decides to make 15 cabinets of type 1 and 35 of type 2. In this case, his profit is (5000 × 15 + 3000 × 35) Rs 180,000.
Similarly, there can be many strategies which he can devise to maximize his profit by allocating the different amount of labour force to the two types of cabinets. We do a mathematical formulation of the discussed LPP to find out the strategy which would lead to maximum profit.
HELP PLEASE WITH THIS ASAP ASAP
Answer:
52
Step-by-step explanation:
62 - 42 = 20
20 / 2 = 10
42 + 10 = 52
52... i think :\
Use the Divergence Theorem to evaluate the surface integral
Compute the divergence of [tex]\vec F[/tex].
[tex]\mathrm{div}(\vec F) = \dfrac{\partial(2x^3+y^3)}{\partial x} + \dfrac{\partial (y^3+z^3)}{\partial y} + \dfrac{\partial(3y^2z)}{\partial z} = 6x^2 + 3y^2 + 3y^2 = 6(x^2+y^2)[/tex]
By the divergence theorem, the integral of [tex]\vec F[/tex] across [tex]S[/tex] is equivalent to the integral of [tex]\mathrm{div}(\vec F)[/tex] over the interior of [tex]S[/tex], so that
[tex]\displaystyle \iint_S \vec F\cdot d\vec S = \iiint_{\mathrm{int}(S)} \mathrm{div}(\vec F)\,dV[/tex]
The paraboloid meets the [tex]x,y[/tex]-plane in a circle with radius 3, so we have
[tex]\mathrm{int}(S) = \left\{(x,y,z) \mid x^2+y^2\le3 \text{ and } 0 \le z \le 9-x^2-y^2\right\}[/tex]
and
[tex]\displaystyle \iiint_{\mathrm{int}(S)} \mathrm{div}(\vec F) \,dV = \int_{-3}^3 \int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}} \int_0^{9-x^2-y^2} 6(x^2+y^2)\,dz\,dy\,dx[/tex]
Convert to cylindrical coordinates, with
[tex]\begin{cases}x = r\cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = r\,dr\,d\theta\,d\zeta\end{cases}[/tex]
so that [tex]x^2+y^2=r^2[/tex], and the domain of integration is the set
[tex]\left\{(r,\theta,\zeta) \mid 0 \le r \le 3\text{ and } 0 \le \theta\le2\pi \text{ and } 0 \le \zeta \le 9-r^2\right\}[/tex]
Now compute the integral.
[tex]\displaystyle \int_0^3 \int_0^{2\pi} \int_0^{9-r^2} 6r^2\cdot r\,d\zeta\,d\theta\,dr = 12\pi \int_0^3 \int_0^{9-r^2} r^3\, d\zeta \, dr \\\\ ~~~~~~~~~~~~ = 12\pi \int_0^3 r^3 (9 - r^2) \, dr \\\\ ~~~~~~~~~~~~ = 12\pi \int_0^3 (9r^3 - r^5) \, dr \\\\ ~~~~~~~~~~~~ = 12\pi \left(\frac94 r^4 - \frac16 r^6\right)\bigg|_0^3 = 12\pi \left(\frac94\cdot3^4-\frac16\cdot3^6\right) = \boxed{729\pi}[/tex]
Solve the system of equations algebraically and create a graphical model.
[tex]3x + 2y = 8 \\ x + 2y = 4[/tex]
Answer: [tex]x=2, y=1[/tex]
Step-by-step explanation:
Subtracting the second equation from the first yields [tex]2x=4 \longrightarrow x=2[/tex].
This means that [tex]y=1[/tex].
So, the solution is [tex]x=2, y=1[/tex]
An administrator surveys a random sample of 48 out of 900 middle school
students. Using the survey results, the administrator estimates that 225 students
are in favor of the new dress code. How many of the 48 students surveyed were
in favor of the new dress code?
Considering the definition of probability, 12 of the 48 students surveyed were in favor of the new dress code.
Definition of probabilityProbability is the greater or lesser chance that a given event will occur.
In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.
Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.
P(A)=number of favorable events÷ number of total events
Probability that students are in favor of the new dress codeIn this case, you know:
Total number of middle school students = 900 (number of possible cases)The number of students are in favor of the new dress code = 225 (number of favorable cases)Replacing in the definition of probability:
P(A)=225 students÷ 900 students
Solving:
P(A)= 0.25
Expressed as a percentage:
P(A)= 25%
Number of the 48 students surveyed were that in favor of the new dress codeIn this case, you know:
Total number of middle school students = 48 (number of possible cases)25% students are in favor of the new dress code (P(A)= 25%= 0.25)Replacing in the definition of probability:
0.25=students in favor of the new dress code÷ 48 students
Solving:
students in favor of the new dress code= 0.25×48 students
students in favor of the new dress code= 12 students
Finally, 12 of the 48 students surveyed were in favor of the new dress code.
Learn more about probability:
brainly.com/question/3283947
#SPJ1
Calcular el valor del ángulo que falta de un triangulo rectangulo si uno de sus lados mide 25 grados.
Considerando la definición de triángulo rectángulo y sus propiedades, el valor del ángulo que falta de un triángulo rectángulo es 65°.
Definición de triánguloUn triángulo es un polígono conformado por tres lados, así como por tres vértices y tres ángulos interiores.
Una de las propiedades de cualquier triángulo indica que la suma de los ángulos interiores es igual a 180°.
Definición de triángulo rectánguloEl triángulo rectángulo es una figura geométrica que se considera como un polígono formado por tres lados que forman un ángulo interior recto (es decir, mide 90°) y dos ángulos interiores agudos.
Valor del ángulo faltante en este casoEn este caso, sabes que:
Al ser un triángulo rectángulo, un ángulo interior mide 90°.Otro ángulo interior mide 25°.La suma de los ángulos interiores es igual a 180°.Entonces, el valor del ángulo faltante se puede calcular mediante:
90° + 25° + ángulo faltante= 180°
Resolviendo:
115° + ángulo faltante= 180°
ángulo faltante= 180° - 115°
ángulo faltante= 65°
Finalmente, el valor del ángulo que falta de un triángulo rectángulo es 65°.
Aprende más sobre los ángulos de un triángulo:
brainly.com/question/21439270
brainly.com/question/21729438
brainly.com/question/27901271
#SPJ1
Land is decreasing at a rate o 17.3 annually. In 2016 there was 3,400 acres. If t represents the number of years since 2016.
The equation that can be used to determine after how many years the town will have of 900 acres of undeveloped land is 900 = 3400 * (0.827)^t
Estimate the equation that can be used to determine after how many years the town will have of 900 acres of undeveloped landFrom the question, the given parameters are:
Initial value = 3400 acres
Rate, r = 17.3%
Final value = 900
An exponential function is represented using the following equation
y = a(1 - r)^t
Substitute the known values in the above equation
y = 3400 * (1 -17.3%)^t
Express 17.3% as decimal
y = 3400 * (1 -0.173)^t
Evaluate the difference
y = 3400 * (0.827)^t
Recall that:
Final value = 900
So, we have
900 = 3400 * (0.827)^t
Hence, the equation that can be used to determine after how many years the town will have of 900 acres of undeveloped land is 900 = 3400 * (0.827)^t
Read more about exponential functions at:
https://brainly.com/question/11464095
#SPJ1
Sketch the region enclosed by the given curves and find its area.
The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.
How to determine the area of a region enclosed by four functions
In this question we must determine the area generated by four functions: three linear functions and a radical function. First, we plot the four functions to determine the required combinations of definite integrals need for calculation:
[tex]A = \int\limits^{0.382}_0 {[f(x) - g(x)]} \, dx + \int\limits^2_{0.382} {[h(x) - g(x)]} \, dx[/tex], where f(x) = √x, g(x) = x - 3 and h(x) = - x + 1.
[tex]A = \int\limits^{0.382}_{0} {[\sqrt{x} - x + 3]} \, dx + \int\limits^{2}_{0.382} {[- 2 \cdot x + 4]} \, dx[/tex]
[tex]A = \int\limits^{0.382}_{0} {\sqrt{x}} \, dx - \int\limits^{0.382}_{0} {x} \, dx + 3 \int\limits^{0.382}_{0}\, dx - 2 \int\limits^{2}_{0.382} {x} \, dx + 4 \int\limits^{2}_{0.382}\, dx[/tex]
[tex]A= 2 \cdot x^{\frac{3}{2} }|_{0}^{0.382} - \frac{x^{2}}{2}|_{0}^{0.382} + 3\cdot x |_{0.382}^{2} - x^{2} |_{0.382}^{2}+4\cdot x |_{0.382}^{2}[/tex]
[tex]A = 2 \cdot (0.382^{\frac{3}{2} }-0^{\frac{3}{2} })-\left(\frac{1}{2} \right)\cdot (0.382^{2}-0^{2}) + 3 \cdot (2 - 0.382) - (2^{2}-0.382^{2})+4\cdot (2^{2}-0.382^{2})[/tex]
A = 16.815
The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.
Remark
The statement reports an inconsistency with at least one function and needs to be modified in order to apply definite integrals in a consistent manner. New form is shown below:
Sketch the region enclosed by the given curves and find its area: (i) x + y = 1, (ii) x - 3 = y, (iii) y = √x, (iv) x = 0.
To learn more on definite integrals: https://brainly.com/question/14279102
#SPJ1
Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of fat?
Answer:
40 apples
Step-by-step explanation:
x = (4·2)/(1/5) = 8/(1/5) = (8/1):(1/5) = (8/1)·(5/1) = 40/1 = 40 apples
It takes 10 apples to make a gram of fat. Multiply the 10 apples by 4 grams of fat to find that it takes 40 apples to make 4 grams of fat.
Which graph has a domain of -∞ < x < ∞ and a range of -∞ < y
The graph of the option in the question has a domain of -∞ < x < 3.5.
Please find attached the drawing of a graph that has a domain of -∞ < x < ∞ Which method can be used to find the graph that has a domain of -∞ < x < ∞?The domain of a graph are the possible x-values that can be obtained from the graph.
A graph that has a domain given by the inequality, -∞ < x < ∞ does not have a vertical asymptote.
An asymptote is a straight line to which a graph approaches, as either the x or y-value approaches infinity.
The given graph has a vertical asymptote at y ≈ 3.5
The domain of the given graph is therefore, -∞ < x < 3.5
Similarly, the graph has a horizontal asymptote at x ≈ 3
The range of the given graph is therefore, -∞ < y < 3.
A graph that has a domain of -∞ < x < ∞, extends to infinity to the left and the right of the graph.
A function that has a graph with a domain of -∞ < x < ∞ is one of direct proportionality.
An example is, y = x
A graph that has a domain of -∞ < x < ∞ is attached.Learn more about the domain and range of a graph here:
https://brainly.com/question/2083771
#SPJ1
a rectangular floor of a room measures 5.4m long and 4.2m wide .the room is to be covered with square tiles . Calculate the minimum number of the floor
Answer: 22
Step-by-step explanation:
Number of floor tiles = (5.4m × 4.2m) ÷ 1m²
Number of floor tiles = 22.68
Minimum number of floor tiles = 22
Make a table for each function rule. Then graph each equation using the points you created.
F (x) = 2x - 5
F (x) =-3x +6
F (x) =2/3x +4
Answer:
1.f(x)=2x-5
i will take the set {-2,-1,0,1,2}
f(-2)=2(-2)-5
=-4-5
=-9
f(-1)=2(-1)-5
=-2-5
=-7
f(0)=2(0)-5
=-5
f(1)=2(1)-5
=-3
f(2)=2(2)-5
=-1
so the coordinates of the function is {-9,-7,-5,-3,-1}
2.f(x)=-3x+6
i will the take the set {-2,-1,0,1,2} too
f(-2)=-3(-2)+6=6+6=12
f(-1)=-3(-1)+6=3+6=9
f(0)=-3(0)+6=6
f(1)=-3(1)+6=-3+6=3
f(2)=-3(2)+6=-6+6=0
{12,9,6,3,0}
3.f(x)=2/3.x+4
{-2,-1,0,1,2}
f(-2)=2/3(-2)+4=-4/3+4=(-4+12)/3=8/3
f(-1)=2/3(-1)+4=-2/3+4=(-2+12)/3=10/3
f(0)=2/3(0)+4=4
f(1)=2/3(1)+4=2/3+4=(2+12)/3=14/3
f(2)=2/3(2)+4=4/3+4=(4+12)/3=16/3
{8/3,10/3,4,14/3,16/3}
you're can graph those coordinates
actually you can take other coordinates...
CMIIW
,
Jake invested his whole life savings today in an investment that pays 6% interest, compounded annually. In ten years, this investment will be worth $531,402. What is Jake's life savings today?
Answer:
$ 296 732 .10
Step-by-step explanation:
FV = PV ( 1 + i)^n FV = future value = 531402 PV = ?
i = decimal interest per period = .06
n = periods = 10
531 402 = PV ( 1.06)^10 Solve for PV = 296 732 .10
(x^2-y^2)dx+2xydy=0
so this is a problem of a differential equation I've been trying so hard to match with the given answer but failed every time I tried. So, is there anyone who can really can help me out to catch the mistakes that I'm making?
* The last line of my workout is just a dump guess.
The pictures are my workouts also the answer to this question is attached. Please read my solutions by this order : pic-1, pic-3 & pic-2, if necessary.
[tex](x^2 - y^2) \, dx + 2xy \, dy = 0[/tex]
Multiply both sides by [tex]\frac1{x^2}[/tex].
[tex]\left(1 - \dfrac{y^2}{x^2}\right) \, dx + \dfrac{2y}x \, dy = 0[/tex]
Substitute [tex]y=vx[/tex], so [tex]v=\frac yx[/tex] and [tex]dy=x\,dv+v\,dx[/tex].
[tex](1-v^2) \, dx + 2v (x\,dv + v\,dx) = 0[/tex]
[tex](1 + v^2) \, dx + 2xv \, dv = 0[/tex]
Separate the variables.
[tex]2xv\,dv = -(1 + v^2) \, dx[/tex]
[tex]\dfrac{v}{1+v^2}\,dv = -\dfrac{dx}{2x}[/tex]
Integrate both sides
[tex]\displaystyle \int \frac{v}{1+v^2}\,dv = -\frac12 \int \frac{dx}x[/tex]
On the left side, substitute [tex]w=1+v^2[/tex] and [tex]dw=2v\,dv[/tex].
[tex]\displaystyle \frac12 \int \frac{dw}w = -\frac12 \int\frac{dx}x[/tex]
[tex]\displaystyle \ln|w| = -\ln|x| + C[/tex]
Solve for [tex]w[/tex], then [tex]v[/tex], then [tex]y[/tex].
[tex]e^{\ln|w|} = e^{-\ln|x| + C}[/tex]
[tex]w = e^C e^{\ln|x^{-1}|}[/tex]
[tex]w = Cx^{-1}[/tex]
[tex]1 + v^2 = Cx^{-1}[/tex]
[tex]1 + \dfrac{y^2}{x^2} = Cx^{-1}[/tex]
[tex]\implies \boxed{x^2 + y^2 = Cx}[/tex]
Your mistake is in the first image, between third and second lines from the bottom. (It may not be the only one, it's the first one that matters.)
You incorrectly combine the fractions on the left side.
[tex]\dfrac1{-2v} -\dfrac v{-2} = \dfrac1{-2v} - \dfrac{v^2}{-2v} = \dfrac{1-v^2}{-2v} = \dfrac{v^2-1}{2v}[/tex]
The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and point A is reflected across the x-axis to obtain point C. What are the coordinates of points B and C?
B(2, 3) and, C(−2, −3)
B(−2, −3) and C(2, 3)
B(2, −3) and C(−2, 3)
B(−2, 3) and C(2, −3)
Answer: B(2, -3) and C(-2, 3) which is choice 3
Further Explanation:
The rule for a y-axis reflection is [tex](\text{x}, \text{y}) \to (-\text{x}, \text{y})[/tex] meaning the x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same.
Therefore, point A(-2,-3) moves to B(2, -3) when reflecting over the y-axis.
A similar rule is [tex](\text{x}, \text{y}) \to (\text{x}, -\text{y})[/tex] to describe an x-axis reflection. This time the y coordinate flips in sign, and the x coordinate stays the same.
In this case, we move from A(-2,-3) to C(-2, 3)
The graph of all three points is shown below. I used GeoGebra to make the graph, but Desmos is another option. I also recommend graphing by hand on graph paper to get practice that way if possible.
PLEASEEEEEEEEEE HELPPPP. which of the following system of inequalities would produce the region indicated on the graph below?
Answer: C
Step-by-step explanation:
The line [tex]y=x+2[/tex] is shaded below and is solid.
This eliminates all the options except for C.
what percent of 15.5 is 12.9? round to the nearest hundredth of 8%
Answer:
83.23%
Step-by-step explanation:
Proportioned Value = 12.9
Total Value = 15.5
Percentage = Proportioned Value / Total Value * 100%
= [tex]\frac{12.9}{15.5}*100[/tex]
= 83.23% (nearest hundredth)
The answer is 83.23%.
To find the percentage, take the ratio between 12.9 and 15.5, and multiply by 100%.
12.9/15.5 × 100%0.8323 × 100%83.23%find the positive square roots by division method of 151,321 please tell me fast
Answer:
389 is the answer
Hope you like it!
HELP PLEASE will give brainliest
Answer:
This is an example of correlation because there is an obvious relationship between the two scenarios
Step-by-step explanation:
This is not cause-and-effect therefore cannot be causation or "cause"
Julio wants to calculate 200,000 × 300,000. When he used his calculator to multiply, it showed the result below:
6E+10
Write the number shown on the calculator display in standard form.
The number shown on the calculator display can be written in standard form as 6 x 10¹⁰.
Product of 200,000 and 300,000The product of 200,000 and 300,000 is calculated as follows;
200,000 × 300,000 = 6E+10
What is standard form?Standard form is a mathematical way or a standard way of presenting numbers as a mathematical expression.
It presents numbers in the simplest form.
Product of 200,000 and 300,000 in standard form200,000 × 300,000 = 6 x 10¹⁰
Thus, the number shown on the calculator display can be written in standard form as 6 x 10¹⁰.
Learn more about standard form here: https://brainly.com/question/19169731
#SPJ1
-|8-15| what is the answer
Answer:
-7
Step-by-step explanation:
8-15 = -7 but since it's an absolute value, it is 7 and then you add the negative sign in front since it is not in the absolute value.
David signed up to provide snacks for his daughter and her school group's camping trip. He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days. He also wanted to buy some boxes of fruit snacks, which were $4 each. He just needed to decide how many to buy, and then figure the total cost.
Select the expression that will help him to determine the total cost.
The expression that will help him to determine the total cost is as follows:
y = 60 + 4x
How to construct an expression?He signed up to provide snacks for his daughter and her school group's camping trip.
He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days.
He also wanted to buy some boxes of fruit snacks, which were $4 each.
The number to buy and the total cost can be expressed as follows:
let
y = total cost
x = number of boxes of fruit juice.
Therefore, the expression that will help him to determine the total cost is as follows:
y = 60 + 4x
learn more on expression here: https://brainly.com/question/1655876
#SPJ1
For the function f(x)=3x²-7, find the value of f(x) when x=3.
Answer:
Step-by-step explanation:
Simply plug in a 3 where you see an x in the function:
[tex]f(3)=3(3)^2-7[/tex] so
f(3) = 3(9) - 7 and
f(3) = 27 - 7 so
f(3) = 20
The lateral edges of a prism are
Step-by-step explanation:
in a survey of 100 people ,65 read Kantipur ,45 read Gorkhapatra, 40 read himalayan times dream,25 read Kantipur as well as Gorkhapatra ,20 read kantipur as well as himalaya times,15 read gorkhapatra,as well as himalaya times and 5 read all three news papers.
1)draw a Venn diagram to illustrate the above information.
2find how many people do not read all three news paper ?
The lateral edges are congruent and parallel. The correct option is D.
A prism is a 3-dimensional object that has two bases that are similar and congruent to each other and are connected to each other with straight lines. A few examples of the prism are given in the image below.
Lateral edges are the edges that connect the two bases of the prism.
Since the lateral edges are straight lines and connect the similar vertices of the bases. Therefore, the lateral edges are always congruent and parallel.
Hence, the correct option is D.
Learn more about Prism here:
https://brainly.com/question/4113799
#SPJ3
The given question is incomplete. Probably the complete question is:
The lateral edges of a prism are
A. congruent, only
B. congruent and perpendicular
C. perpendicular, only
D. congruent and parallel
m..................................find the value of x ...y and z..
Step-by-step explanation:
x =130.......................
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
Learn more about binomial probability here
https://brainly.com/question/15246027
#SPJ1
Which of the following represents all solutions to the equation
1/3x^2 +10 = 7
Answer:
1 +-3i
Step-by-step explanation:
Answer:
answer is 1) x=±3i
Step-by-step explanation:
Question: 1 An analysis of an unknown compound found it contained 40 g potassium, 52 g chromium and 56 g of oxygen. a) What is the empirical formula for this compound? b) What type of compound is it, ionic, covalent or a combination of both? Explain your choice.
1) The empirical formula for this compound is; K₂Cr₂O₇
2) It is an Ionic compound because it has two potassium ions (K+) and a negatively charged dichromate ion (Cr2O7-).
How to find the Empirical Formula?
1) Elements of the unknown compound are;
Potassium = 40 g
Chromium = 52 g
Oxygen = 56 g
Let us find the number of moles of each element;
Number of moles of Potassium = 40/39 = 1.026 mol K
Number of moles of Chromium = 52/52 = 1 mol Cr
Number of moles of oxygen = 56/16 = 3.5 mol O
Multiply through the number of moles by 2 and round up to the nearest whole number to get the empirical formula at; K₂Cr₂O₇
2) The compound K₂Cr₂O₇ is called Potassium dichromate. It is classified as an ionic compound because it has two potassium ions (K+) and a negatively charged dichromate ion (Cr2O7-).
Read more about Empirical Formula at; https://brainly.com/question/1603500
#SPJ1
[tex]\lim_{x \to 0 (\frac{x(x-2)}{2-2e^2x} )[/tex]
Help evaluting this limit
Answer: 0
Step-by-step explanation:
Substituting in x=0, we get
[tex]\frac{0(0-2)}{2-2e^{2}(0)}=0[/tex]
Find the area of circle Y. The image is represented by circle Y with a sector XYZ that has an area of 85.5 square meters. That sector has an arc that measures 117 degrees. The radius of the circle is unknown.
Answer:
263.08 m²
Step-by-step explanation:
The fraction of circle area that a sector represents is proportional to the central angle.
Proportioncircle area/circle angle = sector area/sector angle
circle area / 360° = 85.5 m² / 117°
Multiplying by 360°, we have ...
circle area = (360/117)(85.5 m²) = 263.08 m²
The area of the circle is about 263.08 m².
A vector U has initial point (-3,-2) and terminal point (-6,1) .
Write U in component form.
Answer:
<-3,3>
Step-by-step explanation:
