{4x+2y=10
y=2x-1

What is the value of x+y

A.3.125
B.2
C.4.5
D.3.5​

The following series is converges series.

The given series is,

\(\[\sum_{n=1}^\infty n^2e^{-n}\]\)

To determine whether the series converges or diverges, we use the ratio test. The ratio test states that if

\(\[\mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{a_{n + 1}}}}{{{a_n}}}} \right| = L < 1\]\)

then the series converges absolutely. If

\(\[\mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{a_{n + 1}}}}{{{a_n}}}} \right| = L > 1\]\)

then the series diverges. If

\(\[\mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{a_{n + 1}}}}{{{a_n}}}} \right| = L = 1\]\)

then the ratio test is inconclusive, and we need to use another method to determine convergence or divergence.

Let's apply the ratio test to the given series:

\(\[\mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{{(n + 1)}^2}{e^{ - (n + 1)}}}}{{{n^2}{e^{ - n}}}}} \right| = \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{{(n + 1)}^2}}}{{{n^2}}}{e^{ - 1}}} \right| = \mathop {\lim }\limits_{n \to \infty } {\left( {\frac{{n + 1}}{n}} \right)^2}e^{ - 1}\]\[ = \mathop {\lim }\limits_{n \to \infty } {\left( {1 + \frac{1}{n}} \right)^2}e^{ - 1} = e^{ - 1} < 1\]\)

Thus, by the ratio test, the given series converges.

Therefore, the series converges.

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Complete question is,

Determine whether the following series converges or diverges. Justify your answer. \(\[ \sum_{1}^{\infty} n^{2} e^{-n} \]\)

125 x (5^4)7 as a single power of 5 is 28*5^4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

125 x (5^4)7

Now, 125 x (5^4)7

=125x140

=17500

=28*5^4

Therefore, by algebra the answer will be 28*5^4.

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Answer:

17/2

Step-by-step explanation:

multiply 8x2 then add 1

Answer:

17/2

Step-by-step explanation:

The first step is to convert 8 into fractional form. 8=8/1, which is equal to 16/2. Adding this to the other 1/2, you get a total of 17/2. Hope this helps!

Answer:

4.) SAS

Step-by-step explanation:

to sides are congruent and both angles are 90 degrees

Answer:

4)It's RHS i.e. Right hand side

I don't know th full form of HL as there is difference in studies between countries. But right hand side applies when there is 90° angle , hypotenuse and a side equal in both the triangles. Would appreciate if you tell me what HL stands for.

5) ASA

6 SAS

Step-by-step explanation:

5) Angles are equal

the side is same for both the triangle.

6) Sides are given equal.

Angles are vertically opposite to each other.

Answer:

8

Step-by-step explanation:

The range is the difference between the smallest value and the largest value.  In order the numbers are:   37  41  42  42  43  44  45

The smallest number is 37, and the largest number is 45.

45 - 37 = 8

The range is 8.

Answer:

\(\frac{1}{24}\)

Step-by-step explanation:

24 is a common multiple so ill just use that as a denominator:

3/8 = 9/24

1/3 = 8/24

1/4 = 6/24

so then adding those up:

\(\frac{9}{24}\) + \(\frac{8}{24}\) + \(\frac{6}{24}\) = \(\frac{23}{24}\)

then whats left is 1/24 left to read, which cant be simplified so \(\frac{1}{24}\)

Answer:

   \(\frac{1}{24}\)

Step-by-step explanation:

Let x be the part of the book he read on fourth day.

\(\frac{3}{8} + \frac{1}{3} + \frac{1}{4} + x = 1\)

\(LCM \ of \ 8, 3 , 4 = 24.\ Therefore , \\\\\)

\(\frac{3}{8} + \frac{1}{3} + \frac{1}{4} + x = 1\\\\\frac{9 + 8 + 6 + 24x}{24} = 1\\\\23 + 24x = 24\\24x = 1\\x = \frac{1}{24}\)

\(On\ the\ fourth\ day\ he\ read\ \frac{1}{24} \ of\ the\ book\ to\ finish\ it.\)

Answer:

the answer is 11.

if 16 inches of wire cost 48 cents your goal i to figure out how many inches of wire cots 33 cents to do so you have to find out how many cents each inch is. to do that you have to divide 48 by 16 and you get 3 so that mean that 1 inch costs 3 cents. after you figure that out you do 33 divided by 3 and you get 11. the answer is 11 inches costs 33 cents.

Step-by-step explanation:

The items and the contained that best describes them between unit rate and rate include:

Rate:

Unit Rate:

A rate is a ratio that compares two different types of quantities, often with different units. A unit rate, on the other hand, is a specific type of rate that compares a quantity to one unit of another quantity.

1 page for every 4 students is a rate because it compares pages (one type of quantity) to students (a different type of quantity). 1 sheet per 4 paragraphs is also a rate because it compares sheets (one type of quantity) to paragraphs (a different type of quantity).

40 pages for each booklet is a unit rate because it compares pages (one type of quantity) to a single unit of another quantity, which in this case is 1 booklet.

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Answer:

Step-by-step explanation:

The diameter of a pearl is

The diameter of an atom is

How much larger than an atom is a pearl?

Correct option is D

The maximum probability that a photon with the polarization state will be transmitted through the A filter is 1/2

To solve this problem, we need to use Malus' law, which states that the intensity of light transmitted through a polarizer is proportional to the square of the cosine of the angle between the polarization direction of the incoming light and the axis of the polarizer.

To find the overall probability that a photon will be transmitted through all three filters, we need to multiply the probabilities of each filter

P = 1/2 × cos²(θ) × 1

We are not given the angle θ, so we cannot calculate the exact value of P. However, we can calculate the maximum value of P, which occurs when the rotated filter is aligned with the A filter (i.e., θ = 0). In this case, P = 1/2.

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The given question is incomplete, the complete question is:

H filter Rotated filter Rotated filter followed by A filter An unpolarized photon beam is incident on a linear polarizing filter. The incoming photon flux is is 2.34 x 101 photons/m' /sec.  What is the probability that a photo with the polarization state be transmitted through a subsequent filter, that is aligned with the direction?

Answer:

-3

Step-by-step explanation:

The equation is in slope-intercept form which is y=mx+b

m is the slope, or the rate of change defined by the change in y over the change in x

b is the y-intercept, which is where the graph of the equation will cross the y-axis or when x=0.

Since we are being asked to find the y-intercept and since the y-intercept is b, then b=-3, making the y-intercept -3

So -3 is the correct answer

Answer:

-3

Step-by-step explanation:

.

Answer:

145

Step-by-step explanation:

Cuánto es means what is the answer

35 - (-110)

Two negative signs equal a positive sign

35 + 110 = 145

The boat will coast approximately 16752.9 feet (or about 3.17 miles) in the first 2 minutes after its motor quits.

From the problem statement, we know that the velocity of the boat, v, changes from 83 ft/s to 23 ft/s over a period of 1 second. Therefore, we can write:

\(dv/dt = -k v^2\)

Separating variables and integrating from v = 83 at t = 0 to v = 23 at t = 1, we get:

\(∫83^23 dv / v^2 = ∫0^1 -k dt\)

=> [1/83 - 1/23] = k

So the equation for the velocity of the boat as it coasts is:

\(dv/dt = -[(1/83 - 1/23)] v^2\)

The differential equation is separable:

\(dv/v^2 = -[(1/83 - 1/23)] dt\)

Integrating both sides, we get:

-1/v = [(1/83 - 1/23)] t + C

where C is an integration constant. Using the initial condition v(0) = 83, we get:

C = -1/83

Substituting this back, we have:

-1/v = [(1/83 - 1/23)] t - 1/83

Solving for v, we have:

v(t) = 83 / [1 + (83/23 - 1) t]

To find the distance traveled, we integrate v(t) from t = 0 to t = 120:

s =\(∫0^120 v(t) dt\)

Substituting v(t) and simplifying, we have:

s = 23 ln(1 + 3.6087t) + 60.391t + C

where C is another integration constant. Using the initial condition s(0) = 0, we get:

C = 0

Therefore, the distance traveled by the boat in the first 2 minutes after its motor quits is:

s = 23 ln(1 + 3.6087t) + 60.391t

Evaluating this expression at t = 120 seconds, we get:

s = 23 ln(433.044) + 7246.92 ≈ 16752.9 ft

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The curve equation as F(x,y) = (x - 2)^2 + y^2 and the indicated point as P(a, b).

The distance between the curve and point P can be expressed as the square root of the square of the difference in x-coordinates plus the square of the difference in y-coordinates.

So, the distance function can be written as \(D(x,y) = \sqrt((x - a)^2 + (y - b)^2)\).

To find the minimum distance, we need to minimize the distance function subject to the constraint F(x,y) = 0. We can set up the Lagrange equation as follows:
L(x, y, λ) = D(x,y) + λF(x,y)
Taking the partial derivatives with respect to x, y, and λ, we have:

\(dL/dx = (x - a) / \sqrt((x - a)^2 + (y - b)^2) + 2\lambda(x - 2)\)
\(dL/dy = (y - b) / \sqrt((x - a)^2 + (y - b)^2) + 2 \lambda y\)
\(dL/dλ = F(x,y) = (x - 2)^2 + y^2\)

Setting each of these derivatives equal to zero, we can solve the resulting system of equations to find the critical points. Once we obtain the critical points, we can calculate the distance for each of them using the distance function D(x,y).

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When the two segments have the equal lengths then they are called congruent segments.

As given in the question,

Let us consider two different segments named AB and CD.

Length of the segment AB is equal to 5 cm __(1)

Length of the segment CD is equal to ( 6 - 1 ) cm.

⇒Length of CD = 5cm __ (2)

Length of segment AB is equal to the length of segment CD.

⇒ measure of (AB ) = measure of (CD)

This implies that the two segment with the same length are called congruent to each other.

Therefore, the segment having equal length are called congruent segments.

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Answer:

ucg

Step-by-step explanation:

Answer:

2x+1=86

Step-by-step explanation:

I think thats the answer, Im not sure though

The slope of the line forming the smallest right triangle, when a line is drawn through the point (1, 2), is 2.

The slope of the line forming the smallest right triangle with the positive x and y axes, when a line is drawn through the point (1, 2), can be determined as follows.

First, let's consider the two axes as the legs of the right triangle, and the line drawn through (1, 2) as the hypotenuse. The slope of the hypotenuse can be calculated by finding the difference in y-coordinates divided by the difference in x-coordinates between the two endpoints.

Since the x-coordinate of the point where the line intersects the x-axis is 0 (positive x-axis), and the y-coordinate of the point where the line intersects the y-axis is 0 (positive y-axis), the difference in y-coordinates is 0 - 2 = -2, and the difference in x-coordinates is 0 - 1 = -1.

Therefore, the slope of the line forming the smallest right triangle is -2/-1 = 2.

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Answer:

y=-1/6x-2

Step-by-step explanation:

Lets find the slope of the given line

6x-7=y,m=6

The slope of the perpendicular line would be=-1/6

Using the point-slope form y-y1=m(x-x1)

y--1=-1/6(x--6)

y+1=-1/6(x+6)

6y+6=-x-6

6y=-x-6-6

6y=-x-12

y=-1/6x-2

The volume of the tunnel is 225.476cm³

We should know that the volume of an object entails the quantity of things it can hold at a particular time.

The volume of the tunnel = Volume of semi circle + volume of the rectangle

This is given by

V=3/4\(\frac{4}{3} \pi r^{3}\) + lbh

volume of the tunnel = 4/3*3.142*(5/2)³ + 4*5*8

Simplifying the expression

(65.476 + 160)cm³

Volume = 225.476cm³

Given that the car exhaust  at 10m³

226cm = 2.26m

Note that 60 seconds = 1 Minute

Therefore 10*2.26=22.6m

=22.6/60 = 3 hours,  46 mins and 2 seconds.

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The probability that a randomly selected student in the course has received an A or B is 0.65 or 65%

To find the probability that a randomly selected student in the course has received an A or B, we can use conditional probability based on the given information.

Let's denote the event of doing homework regularly as A, and the event of getting a grade of A or B as B.

We know that P(A) = 0.8, which represents the probability of a student doing homework regularly.

We also know that P(B|A) = 0.75, which represents the probability of getting a grade of A or B given that the student does homework regularly.

Similarly, P(B|A') = 0.25, which represents the probability of getting a grade of A or B given that the student does not do homework regularly.

We can now calculate the probability of getting an A or B using the law of total probability:

P(B) = P(A) * P(B|A) + P(A') * P(B|A')

= 0.8 * 0.75 + 0.2 * 0.25

= 0.6 + 0.05

= 0.65

The probability that a randomly selected student in the course has received an A or B is 0.65 or 65%.

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The value of  zα for the following is :

(a)  α = 0.0089 is 2.37

(b) α = 0.09 is 1.34

(c)  α = 0.707 is -0.545

zα is the inverse function of the standard normal CDF.

(a) Central limit c= 1-α

for α = 0.0089 , c=1-0.0089

∴ c=0.9911

Hence confidence level in percentage= 99.5%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.9911)

zα =2.37

(b) Central limit c= 1-α

for α = 0.09 , c=1-0.09

∴ c=0.91

Hence confidence level in percentage= 91%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.91)

zα=1.34

(c) Central limit c= 1-α

for α = 0.707 , c=1-0.707

∴ c=0.293

Hence confidence level in percentage= 29.3%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.707)

zα= -0.545

Therefore zα value for 0.0089 is 2.37, for 0.09 is 1.34 and for 0.707 it is -0.545.

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True. System developers can initiate a formal project as early as the preliminary investigation stage, or later on, as analysis, design, and implementation activities occur.

When considering the initiation of a formal project, system developers need to assess the risks, costs, benefits, and constraints associated with the project. During the preliminary investigation stage, they conduct a feasibility study to determine whether the project is technically feasible, economically viable, and socially and legally acceptable. If the feasibility study shows that the project is feasible, the developers can initiate the project by defining its scope, objectives, deliverables, and requirements.

Once the project is initiated, the developers can proceed with the analysis, design, and implementation activities. The analysis phase involves gathering and documenting the requirements, analyzing the existing system, and identifying the functional and non-functional requirements of the new system.

True. System developers can initiate a formal project as early as the preliminary investigation stage, or later on, as analysis, design, and implementation activities occur. The decision on when to initiate a formal project depends on several factors, such as the complexity of the system, the available resources, and the level of certainty about the feasibility of the project.

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Answer: the scale factor is 5

Step-by-step explanation:

5 squares on the dilated shape and for the original shape it’s only 1 and the original shape is always going to be the denominator while the numerator is going to be the shape after it’s dilated so it’s 5/1 which equals 5

So THE ANSWER IS 5

The expression that will make the algebraic equation true for all values of x is: A. 3x - 3.

An algebraic equation is an equation where for a value of x, the right side and the left side of the equation must be balanced.

Given the algebraic equation, 15x - 15 = 5(?)

The missing expression, is 3x - 3, because:

15x - 15 = 5(3x - 3)

Open the bracket

15x - 15 = 15x - 15

Both sides are equal.

Therefore, the expression that will make the algebraic equation true for all values of x is: A. 3x - 3.

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Answer:

4,000

Step-by-step explanation: