The​ world's largest university​ (by enrollment) is University​ A, followed by University B. If the enrollment in University A is 3.5 million more students than University B and their combined enrollment is 9.5 million​ students, find the enrollment for each university?

Answer:

The aprox, numbers:

4.1633   and    8.3266

Step-by-step explanation:

a = 2b

a² - b² = 52

then:

(2b)² - b² = 52

4b² - b² = 52

3b² = 52

b² = 52/3

b² = 17.333

√b² = √17.333

b = 4.1633        aprox.

a = 2b

a = 2*4.1633

a = 8.3266

Check:

8.3266² - 4.1633² = 52

69.333 - 17.333 = 52

Answer:

Type I error is to Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.

Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.

Step-by-step explanation:

We are given the following hypothesis below;

Let p = proportion of people who write with their left hand

So, Null Hypothesis, [tex]H_0[/tex] : p = 0.22     {means that the proportion of people who write with their left hand is equal to 0.22}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.22      {means that the proportion of people who write with their left hand is different from 0.22}

Now, Type I error states that we conclude that the null hypothesis is rejected when in fact the null hypothesis was actually true. Or in other words, it is the probability of rejecting a true hypothesis.

So, in our question; Type I error is to Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.

Type II error states that we conclude that the null hypothesis is accepted when in fact the null hypothesis was actually false. Or in other words, it is the probability of accepting a false hypothesis.

So, in our question; Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.

Answer:

[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]

[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]

Step-by-step explanation:

Part a

We want to find:

[tex] P(X<6.4)[/tex]

And we just need to find the area below the curve until x=6.4, since we have a triangle we can do this:

[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]

Part b

For this case we want to find this probability:

[tex] P(X>4.8)[/tex]

And we can use the complement rule and we got:

[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]

Answer:

a = 10 1/4

Step-by-step explanation:

So with the following equation,

4/5a - 8 = 1/5,

we need to use the commutative property.

Which is the moving of whole numbers or variables.

So we add 8 to both sides.

4/5a = 41/5

Divide 4/5 by both sides

a = 10 1/4

So on of the equations could look like a = 10 1/4

Thus,

a = 10 1/4 could be one of the equations given which are equal to 4/5a - 8 = 1/5.

Hope this helps :)

Answer:

[tex]\huge\boxed{a=\dfrac{41}{4}=10\dfrac{1}{4}=10.25}[/tex]

Step-by-step explanation:

[tex]\dfrac{4}{5}a-8=\dfrac{1}{5}\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup\cdot\dfrac{4}{5\!\!\!\!\diagup}a-(5)(8)=5\!\!\!\!\diagup\cdot\dfrac{1}{5\!\!\!\!\diagup}\\\\4a-40=1\qquad\text{add 40 to both sides}\\\\4a-40+40=1+40\\\\4a=41\qquad\text{divide both sides by 4}\\\\\dfrac{4a}{4}=\dfrac{41}{4}\\\\a=10.25[/tex]

Answer:

Step-by-step explanation:

This problem is on the mensuration of solids, a box

we know that the volume of a box is give by the expression

[tex]Volume= L^3[/tex]

now to find the dimension of the box, we need to find L

Given data

volume = [tex]62,500 cm^3[/tex].

[tex]62,500 cm^3= L^3\\L=\sqrt[3]{62500} \\\L=39.69 cm[/tex]

Answer:

The dimensions of box that will minimize the amount of material used is [tex]39.69cm[/tex]

Step-by-step explanation:

Given information

Volume [tex]V=62500cm^3[/tex]

As given in question the box is of square shape:

So the volume will be

[tex]V=L^3[/tex]

where, L is the side of the square

[tex]V=L^3=62500\\L=\sqrt[3]{62500} \\L=39.69 cm\\[/tex]

Hence, The dimensions of box that will minimize the amount of material used is [tex]39.69cm[/tex].

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Answer:

180 goats

Step-by-step explanation:

3/3-1/3=2/3.

2/3=4/6 remaining.

4/6-1/6=3/6 which also equals 1/2.

If 90=1/2 then 90*2=180.

Hope this helps!! <3

Answer: Probability of visiting at most twice = 0.82

Step-by-step explanation: The probability distribution is of the form:

 X      0         1           2            3

P(X)  0.17   0.33      0.32       0.18

It wants the probability of visiting the gym at most twice in a month, which means the probability of never going to the gym, P(X=0), or going once, P(X=1), or going twice, P(X=2).

Using the "OR" probability:

P(visiting at most twice) = P(X=0) + P(X=1) + P(X=2)

P(visiting at most twice) = 0.17 + 0.33 + 0.32

P(visiting at most twice) = 0.82

Therefore, the probability of visiting the gym at most twice in a month is 0.82 or 82%

Step-by-step explanation:

Here,

the given polynomials are;

(x^2+5x+2)-(5x^2-x-2)

now, when we open bracket of second polynomial we get,

=x^2+5x+2-5x^2+x+2

combining like terms and simplifying them we get;

=x^2-5x^2+5x+x+2+2

=-3x^2+6x+4.

Therefore, the answer is-3x^2+6x+4 or, taking - (minus) commo it will be -(3x2-6x-4).

Hope it helps....

Answer:

  39.5 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between angles and sides of a right triangle.

  Tan = Opposite/Adjacent

This lets us write two equations in two unknowns:

  tan(67°) = AD/CD . . . . . . . . . . angle at guy point

  tan(39°) = AD/(CD+32) . . . . . .angle 32' farther

__

Solving the first equation for CD and using that in the second equation, we can get an equation for AD, the height of the tower.

  CD = AD/tan(67°)

  tan(39°)(CD +32) = AD . . . . eliminate fractions in the second equation

  tan(39°)(AD/tan(67°) +32) = AD

  32·tan(39°) = AD(1 -tan(39°)/tan(67°)) . . . simplify, subtract left-side AD term

  32·tan(39°)tan(67°)/(tan(67°) -tan(39°)) = AD . . . . divide by AD coefficient

  AD ≈ 39.486 . . . . feet

The tower is about 39.5 feet high.

[tex]\frac{257}{4}[/tex]

[tex]64\frac{1}{4}=\frac{64*4+1}{4}=\frac{256+1}{4}=\frac{257}{4}[/tex]

The conversion of this mixed number 64 1/4 into an improper fraction is 257/4.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In this exercise and scenario, we would convert the given mixed fraction into an improper fraction into a  by multiplying and adding as follows;

64 1/4 = ((4 × 64) + 1)/4

64 1/4 = 257/4

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Answer:

Step-by-step explanation:

6y = -5x + 18

y = -5/6x + 3

perp slope: 6/5

y - 7 = 6/5(x - 10)

y - 7 = 6/5x - 12

y = 6/5x - 5

Here, we are required to write an equation perpendicular to 5x + 6y = 18.

6x - 5y = 25.

Therefore, slope of equation 5x + 6y = 18 is -5/6.

Therefore, m1m2 = -1

Therefore, the slope of the required line, m2 is;

m2 = 6/5

Therefore, the equation of a line perpendicular to the equation 5x+6y=18 and passes through the point (10,7) is given as;

6/5 = (y - 7)/(x - 10).

By cross product; we have;

6x - 60 = 5y - 35

6x - 5y = 25.

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Answer:

(4, -8).

Step-by-step explanation:

If point W were to be rotated 90 degrees, it would rotate 90 degrees clockwise. The current point of W is (-2, 4). After a 90 degree rotation about the origin, the point will be (4, 2).

y = -3 is a horizontal line where y = -3. The y-value of the newly rotated point is 2. That is five units above the line where y = -3. So, a reflection would result in a y-value of y = -3 - 5 = -8. The x-value does not change.

So, the coordinate of W' is (4, -8).

Hope this helps!

Answer:

Hey there!

This can be modelled by an equation, y=2x+3.25

For one mile: y=2(1)+3.25, or y=5.25

For twenty miles: y=2(20)+3.25, or y=43.25

Hope this helps :)

Answer:  see below

Step-by-step explanation:

1) An inequality is an equation that uses >, ≥, <, or ≤ instead of an equal sign.

Example:  3x + 2 ≥ 10

2) A compound inequality is when 2 inequalities are combined using either "and" or "or".  

Example:     x > -2  and  x < 4       rewrite as: -2 < x < 4

Graph:        -2 o-----------------o 4        one line segment between the #'s

Example:          x < -2 or x > 4

Graph:        ←-----------o -2    4 o----------→      two lines in opposite directions

3) The GPA is dependent on the number of hours she studies.

Independent: hours Beth studies

Dependent: GPA

Answer: [tex]H_0:p=0.29[/tex]

[tex]H_a: p \neq0.29[/tex]

Step-by-step explanation:

A null hypothesis[tex](H_0)[/tex] is a type of statement used in statistics that proposes that there is no difference between particular characteristics of a population whereas the alternative hypothesis[tex](H_a)[/tex] proposes that there is a difference.

Let p be the population proportion of workers got their job through networking.

Given: 29% of workers got their job through networking.

i.e. [tex]H_0:p=0.29[/tex]

A researcher feels this percentage has changed.

i.e. [tex]H_a: p \neq0.29[/tex]

Hence, the required null and alternative hypotheses in symbolic form for this claim:

[tex]H_0:p=0.29[/tex]

[tex]H_a: p \neq0.29[/tex]

Answer:

3

Step-by-step explanation:

If the cube has 54 stickers across its six faces, and each face has the same number of stickers, first we can find the number of stickers in each face by dividing the number of stickers by the number of faces:

[tex]stickers\ per\ face = number\ of\ stickers / number\ of\ faces[/tex]

[tex]stickers\ per\ face = 54/6 = 9[/tex]

Each face has 9 stickers.

If each row and column has the same number of stickers, we can find the numbers of rows and columns by finding the square root of the number of stickers in the face:

[tex]\ number\ of\ rows = \sqrt{9} = 3[/tex]

If we have 3 rows, and each roll has the same number of stickers, the number of stickers per row or column is:

[tex]stickers\ per\ row = stickers\ per\ face / number\ of\ rows[/tex]

[tex]stickers\ per\ row = 9/3 = 3[/tex]

Answer:A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

Step-by-step explanation:

The cylinder is given by A = pi/4 the volume of the prism or π/4  x (4r²h) or π x r² x h

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Area circle is A = πr²

Area square with side s = s²

The side of the square is equal to the diameter of the circle

Area square = D²

A diameter of square is always twice the radius

Area square = (2r)² = 2²r² = 4r²

So , on simplifying , we get

Area circle/Area square = (πr²)/(4r²)

Area circle/Area square = π/4

Now , The volume Prism = Area Square x h

Volume Prism =  4r²h

Volume of Cylinder= Area Circle x h

Volume of Cylinder = π x r² x h

So , Volume Cylinder/Volume Prism = π x r² x h/4r² x h

Volume of Cylinder/Volume of Prism = π/4

Volume of Cylinder = π/4 x Volume Prism

And , The volume of Cylinder = π/4  x (4r²h)

Hence , the volume of cylinder is V = π/4  x (4r²h)

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Answer:

[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \sin \theta = \frac{12}{13}[/tex]

Where θ is an acute angle, and we want to find cot(θ).

Recall that sine is the ratio of the opposite side over the hypotenuse. In other words, our opposite side is measures 12 units and our hypotenuse measures 13 units.

Find the adjacent side:

[tex]\displaystyle \begin{aligned} a^2 + b^2 & = c^2 \\ \\ (12)^2 + b^2 & = (13)^2 \\ \\ b & = 5\end{aligned}[/tex]

Hence, our adjacent side is 5, our opposite side is 12, and our hypotenuse is 13.

Recall that cotangent is the ratio of the adjacent side to the opposite side. Therefore:

[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]

In conclusion:

[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]

Answer:

-5/12

Step-by-step explanation:

I just completed Quiz 2: Evaluation of Functions. Of which, this was one of the questions.

Answer: evaluate it is 52

Step-by-step explanation:

Answer:

33800

Step-by-step explanation:

100 x 338 = 33800

Answer:

33800

Step-by-step explanation:

338x10=3380 then 3380x10=33800

-------------------------------------------------------

Good luck with your assignment...

Answer:

[tex] f(x) =\sqrt{x} sin (x)[/tex]

And on this case we can use the product rule for a derivate given by:

[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]

Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]

And replacing we have this:

[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]

Step-by-step explanation:

We assume that the function of interest is:

[tex] f(x) =\sqrt{x} sin (x)[/tex]

And on this case we can use the product rule for a derivate given by:

[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]

Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]

And replacing we have this:

[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]

Answer:

A) cooling constant =  0.0101365

B) [tex]\frac{df}{dt} = k ( 60 - F )[/tex]

c)  F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]

D)137.46 ⁰

Step-by-step explanation:

water temperature = 60⁰F

temperature of Bar after 20 seconds = 120⁰F

temperature of Bar after 60 seconds = 100⁰F

A) Determine the cooling constant K

The newton's law of cooling is given as

= [tex]\frac{df}{dt} = k(60 - F)[/tex]

= ∫ [tex]\frac{df}{dt}[/tex] = ∫ k(60 - F)

= ∫ [tex]\frac{df}{60 - F}[/tex] = ∫ kdt

= In (60 -F) = -kt - c

       60 - F = [tex]e^{-kt-c}[/tex]

      60 - F = [tex]C_{1} e^{-kt}[/tex]       ( note : [tex]e^{-c}[/tex] is a constant )

after 20 seconds

[tex]C_{1}e^{-k(20)}[/tex] = 60 - 120 = -60  

therefore [tex]C_{1} = \frac{-60}{e^{-20k} }[/tex] ------- equation 1

after 60 seconds

[tex]C_{1} e^{-k(60)}[/tex] = 60 - 100 = - 40  

therefore [tex]C_{1} = \frac{-40}{e^{-60k} }[/tex] -------- equation 2

solve equation 1 and equation 2 simultaneously

= [tex]\frac{-60}{e^{-20k} }[/tex] = [tex]\frac{-40}{e^{-60k} }[/tex]

= 6[tex]e^{20k}[/tex] = 4[tex]e^{60k}[/tex]

= [tex]\frac{6}{4} e^{40k}[/tex] = In(6/4) = 40k

cooling constant (k) = In(6/4) / 40 = 0.40546 / 40 = 0.0101365

B) what is the differential equation  satisfied

substituting the value of k into the newtons law of cooling)

60 - F = [tex]C_{1} e^{0.0101365(t)}[/tex]  

F(t) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

The differential equation that the temperature F(t) of the bar

[tex]\frac{df}{dt} = k ( 60 - F )[/tex]

C) The formula for F(t)

t = 20 , F = 120

F(t ) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

120 = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

[tex]C_{1} e^{0.0101365(20)}[/tex] = 60

[tex]C_{1} = 60 * 1.291[/tex] = 77.46

C1 = - 77.46⁰ as the temperature is decreasing

The formula for f(t)

= F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]

D) Temperature of the bar at the moment it is submerged

F(0) = 60 + 77.46[tex]e^{0.01013659(0)}[/tex]

F(0) = 60 + 77.46(1)

     = 137.46⁰

Answer:

P (3 or fewer) =0.2650

Step-by-step explanation:

Mean = x` = 5

The Poisson distribution formula  is given by

P(X) = e-ˣ` x`ˣ/ x!

The mean is 5 and the X takes the values 0,1,2,and 3 which means 3 or fewer, so we add the probability of all the values of X to get the desired Value of X.

P(3 or fewer ) = e-⁵ (5)³/3!+  e-⁵ (5)²/2! +e-⁵ (5)/1!+e-⁵ (5)⁰/0!

Putting the Values

P (3 or fewer) = 0.006737 . 125 / 6 + 0.006737 . 25 / 2 +0.006737 . 5 / 1 + 0.006737 . 1 / 1

P (3 or fewer) = 0.140374 + 0.08422+ 0.03369 +0.006737

P (3 or fewer) =0.2650

Answer:

shape is how it looks like Square is a shape and size is how big something in like my size of my foot is 6 inches

Step-by-step explanation:

well idk your real question i think it is that your shape and size can change

Answer:

$26.

Step-by-step explanation:

Let's say that Matt started out with x dollars.

x - 6 - 7 - 10 = 3

x - 13 - 10 = 3

x -23 =  3

x = 26

He had $26 at the beginning of the day.

Hope this helps!

Answer:

97 m

Step-by-step explanation:

Perimeter = 2 * (length + width); perimeter = 344, width = 75 (solving for length)

344 = 2(length + 75)

172 = length + 75

length = 97

Answer:

C. 1/8

Step-by-step explanation:

Probability of shooting a goal on a throw is 2/4 = 1/2.

Probability of 3 in a row is (1/2)³ = 1/8.

Answer:

+40 to both sides of the = sign.

Step-by-step explanation:

x2-40=0

    +40=+40

x2=40

 /2=/2

x=20

Answer:

r = 2

h = 4

vol for r = 2  and h = 4 has the greater volume

Step-by-step explanation:

vol for r = 2, h = 4

= pi * r ² * h

= 50

vol for r = 1, h= 8

= pi * r ² * h

= 25

therefore : vol for r = 2  and h = 4 has the greater volume