A university considers giving only pass/fail grades to freshmen to reduce competition and stress. The student newspaper interviews faculty members and reports their opinions of the proposed policy. Suppose that 70% of the faculty favor the pass/fail proposal. Assuming 50 faculty members are interviewed. The goal is to find the probability that a majority (26 or more) will favor the proposal.

Answer:

the answer/expression you require is 40 - 1 = 1 day x - 1 = day 2 (repeat day 2 forever

Step-by-step explanation:

i say this because - 40 for the air conditioner and if it’s - 1 for electricity a day then unless your buying an air conditioner every day i don’t think you,l be repeating day 1 every day

:D

The solution of the given expression is 9*\(x^{4}\)/100.

GIven an expression equal to 27\(x^{12}\)/300\(x^{8}\).

We have to simplify the expression in which variable comes only once.

Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.

The given fraction is 27\(x^{12}\)/300\(x^{8}\).

When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.

=27\(x^{4}\)/300

Now divide numerator an denominator by 3.

=9\(x^{4}\)/300

Hence the expression 27\(x^{12} /300x^{8}\) will look like \(9x^{4} /100\) after simplifying.

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Answer:

\(Simplify:\sqrt\frac{27x^{12} }{300x^{8} }\)

\(O \frac{9}{100}x^{4}\)

✔ \(\frac{3}{10} x^{2}\)

\(O \frac{27}{300} x^{4}\)

\(O\frac{9}{10} x^{2}\)

Answer:

b

Step-by-step explanation:

The range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

Given that the function is f(x)=IxI+5.

We are required to find the range of the function.

Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have a corresponding value of y. The value of x is known as domain of the function and the value of y is known as codomain of the function. Range of a function is a limit of values in which the values of function lies.

Function is f(x)= IxI+5

We know that IxI=x for x>=0 and -x<0.

We have to just put the value of IxI in f(x) to get the range of function.

f(x)=x+5 for x>=0 and -x+5 for x<0.

Hence the range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

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Answer:

it needs 234 grass seeds for the acre

Step-by-step explanation:

2x + x + 57 = 90

3x = 33

x = 11

m1 = 2 × 11 = 22°

m2 = 11 + 57 = 68°

check: 22 + 68 = 90

Answer:

The answer is A

Step-by-step explanation:

Using z-scores and the normal distribution, it is found that the new value would be of 58.2.

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

We have to find the value of X, then:

\(Z = \frac{X - \mu}{\sigma}\)

\(1.645 = \frac{X - 50}{5}\)

\(X - 50 = 1.645(5)\)

\(X = 58.2\)

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The surface area of the cylinder with height 2 m and radius 2 m is: 50.265 m².

The surface area of a cylinder can be calculated by adding the area of the top and bottom circles (which have the same radius) to the area of the curved side (which is a rectangle that has a height equal to the height of the cylinder and a width equal to the circumference of the circle).

The formula for the surface area of a cylinder is:

Surface Area = 2πr² + 2πrh

Where:

π (pi) = 3.14

r is the radius of the circular base of the cylinder

h is the height of the cylinder

Given the following:

Height (h) = 2 m

Radius (r) = 2 m

Therefore, we have:

Surface area = 2πrh + 2πr² = 2·π·2·2 + 2·π·22 ≈ 50.265 m²

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Answer:

A = 59.63cm^2

Step-by-step explanation:

You have the following function for the surface area of the container:

\(A=\pi r^2+\frac{100}{r}\)                (1)

where r is the radius of the cross sectional area of the container.

In order to find the minimum surface are you first calculate the derivative of A respect to r, to find the value of r that makes the surface area a minimum.

\(\frac{dA}{dr}=\frac{d}{dr}[\pi r^2+\frac{100}{r}]\\\\\frac{dA}{dr}=2\pi r-\frac{100}{r^2}\)         (2)

Next, you equal the expression (2) to zero and solve for r:

\(2\pi r-\frac{100}{r^2}=0\\\\2\pi r=\frac{100}{r^2}\\\\r^3=\frac{50}{\pi}\\\\r=(\frac{50}{\pi})^{1/3}\)

Finally, you replace the previous result in the equation (1):

\(A=\pi (\frac{50}{\pi})^{2/3}+\frac{100}{(\frac{50}{\pi})^{1/3}}}\)

\(A=59.63\)

The minimum total surface area is 59.63cm^2

Answer:

12 sin 75°

Step-by-step explanation:

See the attached images!

Answer:

This is how you simplify it.

Answer:

Step-by-step explanation:

(3x⁵)^3
= {3x}^(15)     (According to rule)

Answer = (3x)^(15)  

Answer:

No, it isn't.

Step-by-step explanation:

The point on y = 5 should be on y = 7, and the point on x = 5 should be on x = 7. The attachment shown is what the graph should look like.

Answer:

D

Step-by-step explanation:

Answer:

csc 2 (csc \(\frac{5\pi}{6}\) = csc 150 = csc 30 = csc 2)

Step-by-step explanation:

csc \(\frac{5\pi}{6}\) is in the 2nd Quadrant where only sin, and csc are positive.

csc \((\frac{5\pi}{6})=csc (\pi -(\frac{5\pi}{6}))=csc(\frac{5\pi}{6})\)

but csc \(\frac{5\pi}{6}\) = \(\frac{1}{sin (\pi/6)} = \frac{1}{sin 30} = \frac{1}{1/2} =2\)

Answer: 8 is the anwser

Step-by-step explanation:

Answer:

Step-by-step explanation:

Dorința de a mă juca este mare.

de a (mă) juca - atribut verbal (care dorință?) exprimat prin verb la modul infinitiv;

Avea aerul a nu înțelege.

a nu înțelege - atribut verbal (ce fel de aer?) exprimat prin verb la modul infinitiv;

El dovedise un curaj de invidiat.

de invidiat - atribut verbal (ce fel de curaj?), exprimat prin verb la modul supin.

Casele aveau coșuri fumegânde.

fumegânde - atribut adjectival, exprimat prin verb la gerunziu acordat (cu valoare adjectivală)

Nevoia de a o lua din de a o lua dinloc din cauza frigului era mare.

de a o lua din loc - atribut verbal, exprimat prin locuțiune verbală la modul infinitiv;

A lipi bileţele pe un frigider este un mijloc de adus aminte.

de adus aminte - atribut verbal, exprimat prin locuțiune verbală la modul supin;

Fata ținând nasul pe sus a alunecat pe gheață.

ținând nasul pe sus - atribut verbal, exprimat prin locuțiune verbală la modul gerunziu (neacordat);

Blocul de acolo este înalt.

de acolo - atribut adverbial, exprimat prin adverb de loc;

Trezitul devreme nu-mi place.

devreme - atribut adverbial, exprimat prin adverb de timp;

Mersul de colo până colo l-a obosit.

de colo până colo - atribut adverbial exprimat prin locuțiune adverbială;

E o vreme brrr!

brrr - atribut interjecțional, exprimat prin interjecție.

The system of equations has an infinite number of solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

3x + 2y = 6 ____(1)

6x + 4y = 12 _____(2)

Applying the substitution method.

3x + 2y = 6

x = (6 - 2y)/3 in (2)

6 (6 - 2y)/3 + 4y = 12

2 (6 - 2y) + 4y = 12

12 - 4y + 4y = 12

12 = 12

This means,

It has an infinite number of solutions.

Thus,

An infinite number of solutions.

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The complete question is:

Graph the system of equations

3x + 2y = 6

6x + 4y = 12

and find the solution to the system.

Answer:

\(y = 2 + x\)

Step-by-step explanation:

x=0, y=2

x=1, y=3

x=2, y=4

x=3, y=5

Answer:

B

Step-by-step explanation:

3x - 2 + 2x + 1

5x - 1

Answer:

41

Step-by-step explanation:

So basically you need to use the pythagorean thrm. Essentially, the diagonal and the width and length create a triangle, the diagonal being the hypothenuse. So the formula goes as \(\sqrt[]{a^{2} +b^{2} }\). the variable "a" being the length and the variable "b" being the width.  So plug it in and there you have your answer!

Answer:

C. 41 units

Step-by-step explanation:

Edge 2021

a.) The area of the floor = 246.5ft²

b.) The amount that it will cost to put down the new floor would be = $2,711.5

C.) The new dimensions of the area rug would be= Length= 21ft, width = 18.5 ft.

d.) The area of the area rug would be = 388.5ft²

For question a.)

The floor has a rectangular shape. The area of a rectangle = length×width

area of the floor= 17×14.5

= 246.5ft²

For question b.)

For a square foot(1ft²) = $11

246.5ft² = 246.5×11 = $2,711.5

For question c.)

Since the rug will be extended by 2ft at each side, the new dimensions would be:

length = 2+2+17 = 21ft

width = 2+2+14.5 = 18.5ft

For question d.)

The area of the floor with the new dimensions = 21×18.5 = 388.5ft²

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Answer:

A) b>0 B) s<0 C) w≥-6

Step-by-step explanation:

A) greater than means >

B) less than means <

C) greater of equal means ≥

Answer:

(a)  b > 0

(b)  s ≤ 0

(c)  w ≥ -6

Step-by-step explanation:

Symbol notation

A negative real number is any real number that is less than zero.

A positive real number is any real number that is greater than zero.

Zero is neither positive nor negative.

If b is positive then it is greater than zero:

Nonpositive means not positive, so either negative or equal to zero.

If s is nonpositive then it is less than or equal to zero:

w is greater than or equal to -6:

Answer:

1/3

Step-by-step explanation:

a1=27

a2=9

common ratio=a2/a1=9/27=1/3

Answer:

3) Because the run go by 4 and the rise go up by 2

Step-by-step explanation:

Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

The y-intercept of the linear function means that her initial distance from the finish line is of 10 kilometers.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 10, hence the intercept b is given as follows:

b = 10.

The y-values represent the distance in the context of this problem, hence the initial distance is of 10 km.

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• Amount invested (,P,): $9500

• Annual interest rate (,r,): 10% = 0.1

• Accumulated amount (,A,): $19000 because it is double the amount invested.

• Time (,t,): ? years.

We replace the know values in the below formula, and we solve for t.

The time it takes to obtain the accumulated amount is approximately 6.9 years.

Lucio is 64 meters from the starting point.

The square has four sides of equal length, so Lucio has walked half the length of one side.

To return to the starting point, he needs to walk the other half of the side, which is 64 meters.

The angle Lucio turns is irrelevant, as long as he turns 180 degrees in total.

With this in mind, it can be seen that based on the parameters and the conditions, Lucio is 64 meters from the starting point because the angle to which he turns is irrelevant.

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The question in English:

In a square Lucio walks in straight sections, starting from the flagpole, at one point he changes direction turning 150º to his left, advances 64 meters and stops. To return to the pole you have to turn 75º to the left. How far are you from the starting point?