Choose the symbol that goes in the blank to make the statement true.
163_136

Answer:

I answered your last question also

2 log3x – 2 logx3 -3 <0

\(\mathrm{Subtract\:}2\log ^3\left(x\right)\mathrm{\:from\:both\:sides}\)

\(2\log ^3\left(x\right)-2logx^3-3-2\log ^3\left(x\right)<0-2\log ^3\left(x\right)\)

\(\mathrm{Simplify}\)

\(-2logx^3-3<-2\log ^3\left(x\right)\)

\(\mathrm{Add\:}3\mathrm{\:to\:both\:sides}\)

\(-2logx^3-3+3<-2\log ^3\left(x\right)+3\)

\(\mathrm{Simplify}\)

\(-2logx^3<-2\log ^3\left(x\right)+3\)

\(Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)\)

\(\left(-2logx^3\right)\left(-1\right)>-2\log ^3\left(x\right)\left(-1\right)+3\left(-1\right)\)

\(\mathrm{Simplify}\)

\(2lx^3og>2\log ^3\left(x\right)-3\)

\(\mathrm{Divide\:both\:sides\:by\:}2lx^3o;\quad \:l>0\)

\(\frac{2lx^3og}{2lx^3o}>\frac{2\log ^3\left(x\right)}{2lx^3o}-\frac{3}{2lx^3o};\quad \:l>0\\\)

\(\mathrm{Simplify}\)

\(g>\frac{2\log ^3\left(x\right)-3}{2lx^3o};\quad \:l>0\)

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

This is pretty easy all you have to do is rise/run to find your answer

Answer:

1. Yes it does. It's a function because it pass in the vertical line test, which tell us that if you can draw an vertical line through the graph and this line touches the graph in only one point, it is a function.

2. B. I and II only

3. A. y = 8/7 x +5

The largest possible volume of the box, given the constraint of 1700 square centimeters of material, is approximately 18709.5437 cubic centimeters. This volume is achieved by making the base of the box with a side length of approximately 23.2379 centimeters.

To determine the largest possible volume of the box with a square base and an open top, we need to maximize the volume.

Let's assume that the length of each side of the square base is 's' centimeters, and the height of the box is 'h' centimeters.

The volume of a box with a square base is given by V = s² * h.

We have that the total surface area of the material available is 1700 square centimeters. The surface area of the box consists of the base and four sides, so we have:

Surface area = s²+ 4sh

Since the top is open, we don't need any material for it.

Now, we can rewrite the surface area equation as:

s² + 4sh = 1700

To maximize the volume, we can solve this equation for 'h' in terms of 's' and substitute it into the volume equation:

h = (1700 - s²) / (4s)

V = s² * [(1700 - s²) / (4s)

Simplifying further:

V = (1/4)(1700s - s³)

To determine the largest possible volume, we need to maximize this function. We can take the derivative of V with respect to s, set it to zero, and solve for 's'.

dV/ds = 1700/4 - (3/4)s²

Setting dV/ds = 0, we have:

1700/4 - (3/4)s² = 0

Simplifying further:

1700 = 3s²

s² = 1700/3

s ≈ 23.2379 cm

Substituting this value of 's' into the volume equation, we get:

V ≈ (1/4)(1700 * 23.2379 - (23.2379)^3)

V ≈ 18709.5437 cubic centimeters

Therefore, the largest possible volume of the box is approximately 18709.5437 cubic centimeters.

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Answer:

3x√5 + 6√10x + 5√3x + 10√6

Step-by-step explanation:

(√3x + √5)(√15x + 2√30)

The above expression can be evaluated as follow:

(√3x + √5)(√15x + 2√30)

Expand

√3x (√15x + 2√30) + √5(√15x + 2√30)

x√45 + 2√90x + √75x + 2√150

Express in the best possible surd form.

x•3√5 + 2•3√10x + 5√3x + 2•5√6

3x√5 + 6√10x + 5√3x + 10√6

We can not simplify further.

Therefore,

(√3x + √5)(√15x + 2√30) =

3x√5 + 6√10x + 5√3x + 10√6

Note that the Perimeter of the red polygon is 338 in.

The perimeter of a polygon is the total of its sides' measurements. In this question, the polygon is built by taking the tangents from a specified circle.

The idea here is that if we draw two tangents from the same point outside on a given circle, the length of both tangents will always be equal.

There are 8 sides of this polygon , That means there are four pairs because length of them are equal .

So perimeter is equal to two times the sum of four sides given to us .

Perimeter = 2( 22+27+22+98)

Perimeter = 2(169)

Perimeter = 338 in

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Full Question:

Although part of your question is missing, you might be referring to this full question:

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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The Maclaurin series for \(\(f(x) = \sin\left(\frac{\pi x}{2}\right)\)\) is given by:

\(\[\sin\left(\frac{\pi x}{2}\right) = \frac{\pi}{2} \left(x - \frac{\left(\pi^2 x^3\right)}{2^3 \cdot 3!} + \frac{\left(\pi^4 x^5\right)}{2^5 \cdot 5!} - \frac{\left(\pi^6 x^7\right)}{2^7 \cdot 7!} + \ldots\right).\]\)

The radius of convergence, \(\(R\)\) , for this series is infinite since the series converges for all real values of \(\(x\).\)

Therefore, the Maclaurin series for \(\(f(x) = \sin\left(\frac{\pi x}{2}\right)\)\) is:

\(\[\sin\left(\frac{\pi x}{2}\right) = \frac{\pi}{2} \left(x - \frac{\left(\pi^2 x^3\right)}{2^3 \cdot 3!} + \frac{\left(\pi^4 x^5\right)}{2^5 \cdot 5!} - \frac{\left(\pi^6 x^7\right)}{2^7 \cdot 7!} + \ldots\right)\]\)

with an associated radius of convergence \(\(R = \infty\).\)

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a. Expected Time and Variance Calculation: Calculate the expected time and variance for each task using the provided formulas.

b. Critical Path and Time: Draw the network diagram to find the critical path, which is A -> C -> E -> G.

c. Probability of Completing Critical Path in 23 Weeks: The probability of completing the critical path in 23 weeks is approximately 99.94%.

d. Deadline with 87% Certainty: The deadline for completing the critical path with 87% certainty is estimated to be around 20.66 weeks.

a. Expected Time and Variance Calculation:

To calculate the expected time and variance for each task, we will use the formula:

Expected Time (TE) = (Optimistic Time + 4 x Normal Time + Pessimistic Time) / 6

Variance (V) = ((Pessimistic Time - Optimistic Time) / 6)²

Task A:

TE(A) = (2 + 4 x 4 + 6) / 6

         = 4

V(A) = ((6 - 2) / 6)²

       = 0.44

Task B:

TE(B) = (3 + 4 x 5 + 9) / 6

         = 5

V(B) = ((9 - 3) / 6)²

         = 1.33

Task C:

TE(C) = (4 + 4 x 5 + 7) / 6

         = 5

V(C) = ((7 - 4) / 6)²

       = 0.11

Task D:

TE(D) = (4 + 4 x 6 + 10) / 6

         = 6

V(D) = ((10 - 4) / 6)²

       = 0.89

Task E:

TE(E) = (4 + 4 x 5 + 7) / 6

         = 5

V(E) = ((7 - 4) / 6)²

       = 0.11

Task F:

TE(F) = (3 + 4 x 4 + 8) / 6

         = 4

V(F) = ((8 - 3) / 6)²

       = 0.56

Task G:

TE(G) = (3 + 4 x 5 + 8) / 6

         = 5

V(G) = ((8 - 3) / 6)²

       = 0.56

b. Critical Path and Time:

To find the critical path and time, we draw the network diagram and identify the longest path.

The critical path consists of tasks with zero slack, meaning any delay in these tasks will directly impact the project's duration.

The critical path is A -> C -> E -> G.

c. Probability of Completing Critical Path in 23 Weeks:

To find the probability that the critical path will be completed in 23 weeks, we need to calculate the z-score using the formula:

Z = (Target Time - Expected Time) / √Variance

For the critical path:

TE(critical path) = TE(A) + TE(C) + TE(E) + TE(G)

                          = 4 + 5 + 5 + 5

                          = 19

V(critical path) = V(A) + V(C) + V(E) + V(G)

                        = 0.44 + 0.11 + 0.11 + 0.56

                        = 1.22

Z = (23 - 19) / √1.22

   ≈ 3.27

Using a standard normal distribution table or calculator, we find that the probability of completing the critical path in 23 weeks is approximately 0.9994 or 99.94%.

d. Deadline with 87% Certainty:

To determine the deadline with 87% certainty, we need to find the z-score corresponding to the desired probability. In this case, the desired probability is 0.87.

Z = InvNorm(0.87) ≈ 1.15

Using the z-score formula, we can calculate the deadline:

Deadline = Expected Time + (Z x √Variance)

Deadline = 19 + (1.15 x √1.22)

               ≈ 20.66 weeks

Therefore, with 87% certainty, the deadline for completing the critical path is approximately 20.66 weeks.

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In the following table task durations are given in weeks.

Activity     Predecessor    Optimistic    Normal  Pessimistic

A                  None                  2                  4                  6

B                  None                  3                  5                  9

C                  A                        4                  5                  7

D                  A                        4                  6                  10

E                  B,C                     4                  5                  7

F                  D                        3                  4                  8

G                  E                        3                  5                  8

Use the information to answer the questions:

a. Calculate the expected time and variance for each task

c. Find the probability that the critical path will be completed in 23 weeks?

b. Draw the network and find the critical path and time

d. Suppose you want to give your client a deadline you are 87% certain you can meet. What is that deadline?

Answer:

\(\huge \boxed{{10x^2 + 12x \mathrm{\ units^2 }} }\)

Step-by-step explanation:

area of shaded region = area of whole rectangle - area of unshaded region

Area of a rectangle is length × width.

A = 5x(3x+2) - (x(5x-2))

Expand brackets.

A = 15x² + 10x -(5x² - 2x)

Distribute negative sign.

A = 15x² + 10x - 5x² + 2x

Combine like terms.

A = 10x² + 12x

Answer:

90-27= 63°

the sum of the angles are 180°

Step-by-step explanation:

Answer is 63°

Since the sample space contains  \(36\) equally likely outcomes, each outcome has a probability of \(1/36\)

The sample space consists of all possible outcomes when rolling two number cubes. Each cube has six equally likely outcomes, so the total number of outcomes is\(6\times6=36.\)

P(1 and 2) refers to the probability of rolling a 1 on the first cube and a 2 on the second cube. There is only one outcome that satisfies this condition, which is \((1, 2)\) .

Therefore, the probability of rolling a 1 and 2 is:

P(1 and 2) = (number of outcomes that satisfy the condition)/(total number of possible outcomes)

P(1 and 2) \(= 1/36\)

Therefore, the probability of rolling a \(1\) and  \(2\) is  \(1/36\) .

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Answer:

Since the sample space contains 36 equally likely outcomes, each outcome has a probability of 1 / 36.

We know that probability is defined as number of favourable outcomes divided by total number of outcomes.

Step-by-step explanation:

An experiment occurs of rolling two fair number cubes.

We have given number of favourable outcomes = 2 {(2,1), (1,2)}

Number of Total Outcomes = 36

So ,

Probability = Number of favourable outcomes / Total Outcomes

P(1 and 2) refers to the probability of rolling a 1 on the first cube and a 2 on the second cube. There is only one outcome that satisfies this condition, which is (1, 2).

P(1 and 2) = 2 / 36

P(1 and 2) = 1 / 18

Hence , 1 / 18 is the answer as a fraction in simplest form.

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Answer:

\( \sf \large \: x=6\)

Step-by-step explanation:

Let's solve your equation step-by-step.

6x−11=180−155

Step 1: Simplify both sides of the equation.

6x−11=180−155

6x+−11=180+−155

6x−11=(180+−155)(Combine Like Terms)

6x−11=25

6x−11=25

Step 2: Add 11 to both sides.

6x−11+11=25+11

6x=36

Step 3: Divide both sides by 6.

6x/6 = 36/6

x=6

A node or event with a duration of 0 days is a b. milestone

A milestone refers to an important event in a project that has a duration of zero days. It signifies the completion of a significant phase or task within the project. Milestones are numbers placed on roads, such as roads, railroads, canals, or borders. They can show distances to cities, towns, and other places or regions; or they can set their work on track with respect to a reference point.

They are found on the road, often by the roadside or in a warehouse area. They are also called mile markers (sometimes abbreviated MM), milestones, or mileposts (sometimes abbreviated MP). "mile point" is the term used for the medical field where distance is usually measured in kilometers rather than miles. "Distance marking" is a general term that has nothing to do with units.

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Answer:

I believe it is C but it's good to double check

Step-by-step explanation:

Answer:

Step-by-step explanation:

b

Answer:

2(-x+4)+5x-3 = 11

-2x+8+5x-3=11

-2x+5x+8-3=11

-3x+5=11

-3x=11-5

-3x=6

x=6/-3

x=-3/1

or x=-3. answer

Step-by-step explanation:

please mark me brainliest please

Answer:

x = 3

Step-by-step explanation:

2(-x + 4) + 5x - 3 = 11​

~Simplify

-2x + 8 + 5x - 3 = 11

~Combine like terms

3x + 5 = 11

~Subtract 5 to both sides

3x = 6

~Divide 3 to both sides

x = 3

Best of Luck!

Answer:

x=-1

Step-by-step explanation:

5x-2x-7=-10

3x-7=-10

3x-7+7=-10+7

3x=-3

x=-1

\(\text{Hey \: there!}\)

\(\text{5x - 7 - 2x = 10}\)

\(\bf{(5x - 2x) \: which \: gives \: us \: 3x}\)

\(\text{3x - 7 + 7 = 10 + 7}\)

\(\bf{ - 7 + 7 \: because \: it \: gives \: you \: 0}\)

\(\bf{10 + 7 = 17}\)

\( \frac{3x}{3} = \frac{17}{3} \)

\(\text{we \: cant \: divide \: 17 \: from \: 3 \: because \: itll \: give \: us \: a \: decimal}\)

\(\boxed{\bf{thus \: your \: answer \: is \: \bf{ \frac{17}{3} }}}\)

~

\(\frak{loveyourselffirst:)}\)

The  line at the coffee shop during rush hour is 15 people long.

Given:

- 5 people arrive at the coffee shop each minute.

- Each person has to wait for 3 minutes to be served.

Since 5 people arrive each minute,  the rate of people entering the line is 5 people/minute.

Now, Each person has to wait for 3 minutes to be served.

So, Average length of line = Rate of people entering * Time for a person to be served

Average length of line = 5 people/minute * 3 minutes

Average length of line = 15 people

Therefore, on average, the line at the coffee shop during rush hour is 15 people long.

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Answer:

option B. It's graph must-have a constant slope ; is not true about a direct proportion

1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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Given: point (-2, 7)

The given line is perpendicular to the line we are to find.

For a line to be perpendicular to another, the slope of one will be the negative reciprocal of the other slope.

slope of the line perpendicular to the given line = negative reciprocal of the slope

slope = 1/2

reciprocal of the slope = 2/1 = 2

negative reciprocal = -2

2nd slope = -2

To get the equation of line with slope -2, we will use the point given:

Th equation of line Perpendicular to the line -4y + 2x = -3 that passed through the point (-2, 7):

Answer:

0 < x < 1/3

Step-by-step explanation:

Hello! The answer I provided is correct, you know this because any value you can use for X that is in between 0 and 1/3 would make the inequality true.

Answer:

36 violin player is my final answer

The standard deviation is relatively small when the data are all concentrated close to the mean, exhibiting little variation or spread.

The standard deviation could be a degree of the changeability or spread of a set of information. It is calculated by finding the square root of the normal of the squared contrasts between each information point and the cruel(mean).

In other words, it tells us how much the information values are scattered around the mean.

When the information is all concentrated near the cruel(mean), it implies that the contrasts between each information point and the cruel are moderately little.

This comes about in a little while of squared contrasts, which in turn leads to a little standard deviation. On the other hand, when the information is more spread out, it implies that the contrasts between each information point and the cruel are bigger.

This comes about in a bigger entirety of squared contrasts, which in turn leads to a bigger standard deviation.

For case, let's consider two sets of information:

Set A and Set B.

Set A:

2, 3, 4, 5, 6

Set B:

1, 3, 5, 7, 9

Both sets have the same cruel(mean) (4.0), but Set A encompasses a littler standard deviation (1.4) than Set B (2.8).

This is because the information values in Set A are all moderately near to the cruel(mean), while the information values in Set B are more spread out.

Subsequently, we will say that the standard deviation is generally small when the information is all concentrated near the mean, showing a small variety or spread.

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The values of x and y as a result of the code are 8 and 8

The code is given as:

int x = 25, y = 8;

x = y;

At the first line, we have

x= 25 and y = 8

On the second line, where we have

x = y

This means that

x = 8 and y = 8

Hence, the values of x and y as a result of the code are 8 and 8

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Answer:

Step-by-step explanation:

1-2sin²∝=cos 2∝

1-2sin²(105)=cos(2×105)

=cos 210

=cos (180+30)

=-cos 30

\(=-\frac{\sqrt{3}}{2} \\\)

The correct answer is option A which is the value of the expression is -√3/2.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

The expression will be solved as:-

1-2sin²∝=cos 2∝

1-2sin²(105)=cos(2×105)

1-2sin²(105=cos 210

1-2sin²(105=cos (180+30)

1-2sin²(105=-cos 30

1-2sin²(105 = -√3/2.

Therefore the correct answer is option A which is the value of the expression is -√3/2.

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We must determine the value of y at x = 0.2 in order to numerically solve the equation y = (x + 1) with the initial condition y(0) = 1 and a step size of h = 0.1. The right response is 1.2.

We can utilise the Euler's method or any other numerical integration method to solve the issue numerically. By making small steps of size h and updating the value of y in accordance with the derivative of the function, Euler's approach approximates the value of y at a given x.

We can iteratively proceed as follows, starting with y(0) = 1, as follows:

At x = 0, y = 1.

Y = y(0) + h * f(x(0), y(0)) = 1 + 0.1 * (0 + 1) = 1.1 when x = 0.1.

Y = y(0.1) + h * f(x(0.1), y(0.1)) = 1.1 + 0.1 * (0.1 + 1) = 1.2 for x = 0.2.

So, 1.2 is the right response. This is the approximate value of y at x = 0.2 that was determined by applying a step size of h = 0.1 when solving the given problem numerically.

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