A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 6.5% and the tax in the second city was 4.5% The total hotel tax paid for the two cities was $582.50
. How much was the hotel charge in each city before tax?

Step-by-step explanation:

[tex]6.\\\\\dfrac{\tan x}{\cot x}\qquad\text{use}\ \cot x=\dfrac{1}{\tan x}\\\\=\dfrac{\tan x}{\frac{1}{\tan x}}=\tan x\cdot\dfrac{\tan x}{1}=\tan x\cdot\tan x=\left(\tan x\right)^2\qquad\text{use}\ \tan x=\dfrac{\sin x}{\cos x}\\\\=\left(\dfrac{\sin x}{\cos x}\right)^2\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\dfrac{\sin^2x}{\cos^2x}\qquad\text{use}\ \sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\=\dfrac{\sin^2x}{1-\sin^2x}[/tex]

[tex]7.\\\\\cos x\cdot\cot x+\sin x\qquad\text{use}\ \cot x=\dfrac{\cos x}{\sin x}\\\\=\cos x\cdot\dfrac{\cos x}{\sin x}+\sin x=\dfrac{\cos^2x}{\sin x}+\dfrac{\sin^2x}{\sin x}=\dfrac{\cos^2x+\sin^2x}{\sin x}=\dfrac{1}{\sin x}[/tex]

Suppose [tex]y_2(x)=y_1(x)v(x)[/tex] is another solution. Then

[tex]\begin{cases}y_2=vx^3\\{y_2}'=v'x^3+3vx^2//{y_2}''=v''x^3+6v'x^2+6vx\end{cases}[/tex]

Substituting these derivatives into the ODE gives

[tex]x^2(v''x^3+6v'x^2+6vx)-x(v'x^3+3vx^2)-3vx^3=0[/tex]

[tex]x^5v''+5x^4v'=0[/tex]

Let [tex]u(x)=v'(x)[/tex], so that

[tex]\begin{cases}u=v'\\u'=v''\end{cases}[/tex]

Then the ODE becomes

[tex]x^5u'+5x^4u=0[/tex]

and we can condense the left hand side as a derivative of a product,

[tex]\dfrac{\mathrm d}{\mathrm dx}[x^5u]=0[/tex]

Integrate both sides with respect to [tex]x[/tex]:

[tex]\displaystyle\int\frac{\mathrm d}{\mathrm dx}[x^5u]\,\mathrm dx=C[/tex]

[tex]x^5u=C\implies u=Cx^{-5}[/tex]

Solve for [tex]v[/tex]:

[tex]v'=Cx^{-5}\implies v=-\dfrac{C_1}4x^{-4}+C_2[/tex]

Solve for [tex]y_2[/tex]:

[tex]\dfrac{y_2}{x^3}=-\dfrac{C_1}4x^{-4}+C_2\implies y_2=C_2x^3-\dfrac{C_1}{4x}[/tex]

So another linearly independent solution is [tex]y_2=\dfrac1x[/tex].

Answer:

(x+2) (x-1)

Step-by-step explanation:

x^2+x-2

What 2 numbers multiply together to give -2 and add together to give 1

2 * -1 = -2

2 + -1 = 1

(x+2) (x-1)

Answer:

(x+2) (x-1)

Step-by-step explanation:

Answer: 0.9887

Step-by-step explanation:

Given : The true probability of a baby being a boy : [tex]0.527[/tex]

The number of selected births : [tex]7[/tex]

Now, the when next seven randomly selected births in the​ country, then the probability that at least one of them is a girl​ is given by :_

[tex]\text{P(at least one girl)=1-P(none of them girl)}\\\\=1-(0.527)^7=0.988710510435\approx0.9887[/tex]

Hence, the probability that at least one of them is a girl​ =0.9887

Final answer:

The probability of at least one girl being born among seven births in a country where a boy has a 0.527 chance of being born is calculated by subtracting the probability of all seven being boys from 1.

Explanation:

The question asks about the probability of at least one girl being born among the next seven randomly selected births in a country where the true probability of a baby being a boy is 0.527. To find this, we can use the complement rule, which focuses on the probability that all seven births will be boys, the opposite of what we want to find.

First, we find the probability of all seven being boys:

P(all boys) = (0.527)⁷

Next, we subtract this from 1 to get the probability of at least one girl:

P(at least one girl) = 1 - P(all boys)

This gives us the probability that at least one of the next seven births will be a girl.

Answer:

22 yd

Step-by-step explanation:

Length is four times its width   ----->    L=4W

area of rectangle is 196           ----->   196=LW

Plug L=4W into 196=LW giving you 196=(4W)W

Simplify a bit 196=4W^2

Divide both sides by 4:   196/4=W^2

Simplify a bit:   49=W^2

Square root both sides:  7 or -7=W

The width is 7 yd

The length is 4(7)=28 yd

Now its final part is for you to find the perimeter of this rectangle.  The rectangle is a 7 yd by 4 yd rectangle.

Double both then add.. 14+8=22 yd

Answer:

21 yd

Step-by-step explanation:

Length of a rectangle is four times its width =

L = 4 × w

The area of the rectangle is 196

L = 4W

A = L*W = 196

---

4W*W = 196

W*W = 196/4

W*W = 49

W = 7

L = 28

---

Answer:

P = 2(L + W)

P = 2(28 + 7)

P = 14 + 7

P = 21 yd

The probability that a randomly selected dropout aged 16 to 17 is white, given the provided statistics, is 67.39%.

The student is asking a question related to conditional probability in the field of Mathematics. The question prompts us to find out the probability that a randomly selected high school dropout in the age range of 16 to 17 is white. To find the answer, we use the following formula:

P(A|B) = P(A ∩ B) / P(B)

Where:
P(A|B) is the probability of event A happening given that event B has occurred.
P(A ∩ B) is the probability of both event A and event B happening together.
P(B) is the probability of event B happening.

From the problem statement, we know that P(B), the percentage of dropouts who are 16-17 years old, is 9.2%. Also, P(A ∩ B), the percent of dropouts who are both white and 16-17 years old, is given as 6.2%. We are supposed to find P(A|B), the probability that a dropout is white given that they are 16-17 years old.

Therefore, by substituting these values into the formula, we get:

P(A|B) = 6.2% / 9.2% = 67.39%

Rounded to two decimal places, the answer is 67.39%. So, there is approximately a 67.39% chance that a random high school dropout aged 16-17 is white.

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Answer: There are 26000 miles that will both be due at the same time.

Step-by-step explanation:

Since we have given that

Number of miles required by new vintage = 400

Number of miles if these services have must been performed by the dealer = 13000

We need to find the number of miles from now that will both be due at the same time.

We would use "LCM of 400 and 13000":

As we know that LCM of 400 and 13000 is 26000.

So, there are 26000 miles that will both be due at the same time.

Answer: 0.9713

Step-by-step explanation:

Given : Mean : [tex]\mu = 5.2\text{ day}[/tex]

Standard deviation : [tex]\sigma = 1.7\text{ days}[/tex]

The formula of z -score :-

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

At X = 2 days

[tex]z=\dfrac{2-5.2}{1.7}=-1.88235294118\approx-1.9[/tex]

Now, [tex]P(X>2)=1-P(X\leq2)[/tex]

[tex]=1-P(z<-1.9)=1- 0.0287166=0.9712834\approx0.9713[/tex]

Hence, the probability of spending more than 2 days in recovery = 0.9713

Answer:

There is a 98.54% probability of spending more than 2 days in recovery.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 5.7, \sigma = 1.7[/tex]

What is the probability of spending more than 2 days in recovery?

This probability is 1 subtracted by the pvalue of Z when X = 2. So:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2 - 5.7}{1.7}[/tex]

[tex]Z = -2.18[/tex]

[tex]Z = -2.18[/tex] has a pvalue of 0.0146.

This means that there is a 1-0.0146 = 0.9854 = 98.54% probability of spending more than 2 days in recovery.

Answer:

  (1/3(5-√34), 1/27(-205+32√34)) and (1/3(5+√34), 1/27(-205-32√34))

Step-by-step explanation:

The slope of the given line is the x-coefficient, 4. Then you're looking for points on the f(x) curve where f'(x) = 4.

  f'(x) = 3x^2 -10x +1 = 4

  3x^2 -10x -3 = 0

  x = (5 ±√34)/3 . . . . . x-coordinates of tangent points

Substituting these values into f(x), we can find the y-coordinates of the tangent points. The desired tangent points are ...

  (1/3(5-√34), 1/27(-205+32√34)) and (1/3(5+√34), 1/27(-205-32√34))

_____

The graph shows the tangent points and approximate tangent lines.

To find where the tangent line to the function f(x)=[tex]x^3-5x^2+x[/tex] is parallel to the line y=4x+23, we need to find where the derivative of the function is equal to the slope of the given line.

In the field of mathematics, the problem asks us to find at which points the tangent line to function f(x)=[tex]x^3-5x^2+x[/tex] is parallel to the line y=4x+23. A line is tangent to a function at a point where the derivative of that function equals the slope of the line. The first step in solving this problem is to calculate the derivative of function f(x).

The derivative of the function f(x) is f'(x) =[tex]3x^2 - 10x +1[/tex]. Next, we set this equal to the slope of the given line, which is 4. Solving this quadratic equation will give us the x-values where the tangent line is parallel to y=4x+23.

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f(x) = 3x^2 - 5x +2

Let me show you the picture below and the answer is (0 , 2)

Answer:

(0,2)

Step-by-step explanation:

the y-intercept of the function, f(x) = 3x² -5x + 2 when : x = 0

f(0) = 3(0)² - 5(0)+2 = 2

For this case we have the following expression:

[tex](\frac {-27x ^ 0 * y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

By definition we have to:

[tex]a^0 = 1[/tex]

So:

[tex](\frac {-27y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

Simplifying:

[tex](\frac {-y ^ {- 2}} {2x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So, rewriting the expression we have:

[tex](-1)^{-2}\frac{-y^{-2*-2}}{2^{-2}*x^{-5*-2}*y^{-4*-2}}=\\\frac{1}{(-1)^2}*\frac{-y^{4}}{2^{-2}x^{10}*y^{8}}=[/tex]

SImplifying:

[tex]+1*\frac{y^{4-8}}{2^{-2}x^{10}}=\\\frac{y^{-4}}{2^{-2}x^{10}}=\\\frac{2^2}{x^{10}y^{4}}[/tex]

Answer:

[tex]\frac{4}{x^{10}y^{4}}[/tex]

Answer:

[tex]\sqrt[3]{17}= 2.57128=257128[/tex]×[tex]10^{-5}[/tex]

Step-by-step explanation:

We need to find: [tex]\sqrt[3]{17}[/tex] in decimals. To do this, we are going to need the help of a calculator. After plugging the values, we get that:

[tex]\sqrt[3]{17}= 2.57128 = 257128[/tex]×[tex]10^{-5}[/tex]

In this case, I just considered 5 significant figures!

Answer: Third Option

[tex]f(t)=21,386[/tex]

Step-by-step explanation:

We know that the equation that models the number of trees in the forest is:

[tex]f(t)=\frac{32,000}{1+12.8e^{-0.065t}}[/tex]

Where t represents the time elapsed in years

To calculate the number of trees after 50 years substitute [tex]t = 50[/tex] in the equation

[tex]f(t)=\frac{32,000}{1+12.8e^{-0.065(50)}}[/tex]

[tex]f(t)=21,386[/tex]

Answer:

II. Angle C cannot be a right angle.

III. Angle C could be less than 45 degrees.

The given altitude of triangle ABC is h, is located inside the triangle and

extends from side AB to the vertex C.

The true statements are;

I. Triangle ABC could be a right triangle

II. Angle C cannot be a right angle

Reasons:

I. Triangle ABC could be a right triangle

The altitude drawn from the vertex C to the line AB = h

The length of h = AB

Where, triangle ABC is a right triangle, we have;

The legs of the right triangle are; h and AB

The triangle ABC formed is an isosceles right triangle

Therefore, triangle ABC could be an isosceles right triangle; True

II. Angle C cannot be a right angle: True

If angle ∠C is a right angle, we have;

AB = The hypotenuse (longest side) of ΔABC

Line h = AB is an altitude, therefore, one of the sides of ΔABC is hypotenuse to h, and therefore, longer than h and AB, which is false

Therefore, ∠C cannot be a right angle

III. Angle C could be less than 45 degrees; False

The minimum value of angle C is given by when triangle ABC is an isosceles right triangle. As the position of h shifts between AB, the lengths of one of the sides of ΔABC increases, and therefore, ∠C, increases

Therefore, ∠C cannot be less than 45°

The true statements are I and II

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Answer:

  (x, y, z) = (0, 0, 0) +t(1, 5, 4)

Step-by-step explanation:

Such a parametric equation can be written in the form ...

  (first point) + t×(change in point values)

where the change in point values is the difference between the point coordinates.

Since the first point is (0, 0, 0), the change is easy to find. It is exactly equal to the second point's coordinates. Hence our equation is ...

  (x, y, z) = (0, 0, 0) +t(1, 5, 4)

The sum can be "simplified" to ...

  (x, y, z) = (t, 5t, 4t)

_____

Comment on answer forms

I like the first form for many uses, but the second form can preferred in some circumstances. Use the one consistent with your reference material (textbook or teacher preference).

Answer:

[tex]5x+2 , 2x^2+5x-2,\frac{x^2+5x}{2-x^2}[/tex]

Step-by-step explanation:

We are given f(x) and g(x)

1. (f+g)(x)

(f+g)(x) = f(x) + g(x)

           = [tex]x^2+5x+2-x^2[/tex]

           = [tex]5x+2[/tex]

Domain : All real numbers as it there exists a value of (f+g)(x) f every x .

2. (f-g)(x)

(f-g)(x) = f(x)-g(x)

          = [tex]x^2+5x-2+x^2[/tex]

          =[tex]2x^2+5x-2[/tex]

Domain : All real numbers as it there exists a value of (f-g)(x) f every x .

Part 3 .

[tex](\frac{f}{g})(x)\\(\frac{f}{g})(x) = \frac{f(x)}{g(x)}\\=\frac{x^2+5x}{2-x^2}[/tex]

Domain : In this case we see that the function is not defined for values of x for which the denominator becomes 0 or less than zero . Hence only those values of x are defined for which

[tex]2-x^2>0[/tex]

or [tex]2>x^2[/tex]

   Hence taking square roots on both sides and solving inequality we get.

[tex]-\sqrt{2} <x<\sqrt{2}[/tex]

Answer:

  x = 4

Step-by-step explanation:

Add 8 to both sides of the equation:

  6x -8 +8 = 16 +8

  6x = 24

Divide both sides of the equation by 6:

  6x/6 = 24/6

  x = 4

For this case we have the following equation:

[tex]6x-8 = 16[/tex]

We must find the value of the variable "x":

Adding 8 to both sides of the equation we have:

[tex]6x = 16 + 8\\6x = 24[/tex]

Dividing between 6 on both sides of the equation we have:

[tex]x = \frac {24} {6}\\x = 4[/tex]

Thus, the solution of the equation is[tex]x = 4[/tex]

Answer:

[tex]x = 4[/tex]

Answer:

  a) growth will reach a peak and begin declining after about 42.6 days. 5000 people will be infected at that point

  b) the infected an uninfected populations will be the same after about 42.6 days

Step-by-step explanation:

We have assumed you intend the function to match the form of a logistic function:

[tex]P(t)=\dfrac{Kpe^{rt}}{K+p(e^{rt}-1}[/tex]

This function is symmetrical about its point of inflection, when half the population is infected. That is, up to that point, it is concave upward, increasing at an increasing rate. After that point, it is concave downward, decreasing at a decreasing rate.

a) The growth rate starts to decline at the point of inflection, when half the population is infected. That time is about 42.6 days after the start of the infection. 5000 people will be infected at that point

b) The infected and uninfected populations will be equal about 42.6 days after the start of the infection.

Answer:

The 1st & 2nd option

Step-by-step explanation:

Ans1: 16/3

Ans2: 30

Ans3: 11/7×surd6

Ans4: 2/3×surd11

Rational number is a number that can be expressed in ratio (quotient)

It can be expressed in the form of repeating or terminating decimal

Example:

16/3 is equal to

5.3333333333....(repeating decimal)

thus it is a rational number

1/4 is equal to

0.25 (terminating decimal)

thus it is a rational number

Answer:

It diverges to positive infinity  

Step-by-step explanation:

I see it was 4/(x-6)^3 not 4(x-6)^3... but still can't make out everything else.

[tex] \int_6^8 \frac{4}{(x-6)^3} dx [/tex]

The integrand does not exist at x=6.

[tex] \int_6^8 \frac{4}{(x-6)^3} dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} } \int_z^8 4(x-6)^{-3} dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} }\frac{4(x-6)^{-2}}{-2} |_z^8dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} }[\frac{4(8-6)^{-2}}{-2} -\frac{4(z-6)^{-2}}{-2} ] [/tex]

[tex] \frac{1}{-2} - -\infty [/tex]

[tex] \infty [/tex]

So it diverges

Answer:

I could not properly read this but here was what I could make out

Step-by-step explanation:

Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)

home this helped ;)

Answer:

  Pablo and Elena will be 38 miles apart in 19/2 hrs.

Step-by-step explanation:

Their separation speed is 13 mph - 9 mph = 4 mph. Using the relation ...

  time = distance/speed

we can find the time from ...

  time = (38 mi)/(4 mi/h) = 38/4 h = 19/2 h

Answer: 0.8186

Step-by-step explanation:

Given: Mean : [tex]\mu=1.01\text{ inch}[/tex]

Standard deviation :  [tex]\sigma=0.003\text{ inch}[/tex]

Sample size :  [tex]n=9[/tex]

The formula to calculate z-score :-

[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x=1.009 inch

[tex]z=\dfrac{1.009-1.01}{\dfrac{0.003}{\sqrt{9}}}=-1[/tex]

For x=1.012 inch

[tex]z=\dfrac{1.012-1.01}{\dfrac{0.003}{\sqrt{9}}}=2[/tex]

Now, The p-value =[tex]P(-1<z<2)=P(2)-P(-1)=0.9772498-0.1586553=0.8185945\approx0.8186[/tex]

Hence, the required probability = 0.8186

Answer:

792

Step-by-step explanation:

₁₂C₅ = (12!) / (5! (12-5)!)

₁₂C₅ = (12!) / (5! 7!)

₁₂C₅ = 792

There are 792 different selections are​ possible.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

We are given that in a Power Ball​ lottery, 5 numbers between 1 and 12 inclusive are drawn. These are the winning numbers.

Therefore, the selections are​ possible as;

₁₂C₅ = (12!) / (5! (12-5)!)

₁₂C₅ = (12!) / (5! 7!)

₁₂C₅ = 792

Hence, there are 792 different selections are​ possible.

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Answer: Hello your in college please help me with my latest problem please :(

Step-by-step explanation:

Answer:

[tex]\large\boxed{x=\sqrt6-3}[/tex]

Step-by-step explanation:

[tex]Domain:\\2x+3\geq0\to x\geq-1.5[/tex]

[tex]f(x)=\sqrt{2x+3},\ g(x)=x^2\\\\f(g(x))-\text{substitute x = g(x) in}\ f(x):\\\\f(g(x))=f(x^2)=\sqrt{2x^2+3}\\\\g(f(x))-\text{substitute x = f(x) in}\ g(x):\\\\g(f(x))=g(\sqrt{2x+3})=(\sqrt{2x+3})^2=2x+3\\\\f(g(x))=g(f(x))\iff\sqrt{2x^2+3}=2x+3\qquad\text{square of both sides}\\\\(\sqrt{2x^2+3})^2=(2x+3)^2}\qquad\text{use}\ (\sqrt{a})^2=a\ \text{and}\ (a+b)^2=a^2+2ab+b^2\\\\2x^2+3=(2x)^2+2(2x)(3)+3^2\\\\2x^2+3=4x^2+12x+9\qquad\text{subtract}\ 2x^2\ \text{and 3 from both sides}[/tex]

[tex]0=2x^2+12x+6\qquad\text{divide both sides by 2}\\\\x^2+6x+3=0\qquad\text{add 6 to both sides}\\\\x^2+6x+9=6\\\\x^2+2(x)(3)+3^2=6\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+3)^2=6\iff x+3=\pm\sqrt6\qquad\text{subtract 3 from both sides}\\\\x=-3-\sqrt6\notin D\ \vee\ x=-3+\sqrt6\in D[/tex]

Answer:

D. {(7, 11), (0,5), (11, 7), (7,13)}

Step-by-step explanation:

Because the relations (7, 11), (7,13) are false.

f(7) = 11

f(7) = 13

=> 11 = 13 (F)

Answer:

The correct answer option is: D. {(7, 11), (0,5), (11, 7), (7,13)}.

Step-by-step explanation:

We are given some paired values of inputs and outputs (x and y) for a function and we are to determine whether which of them is not a function.

For a relation to be function, no value of x should be repeated. It means that for each value of y, there should be a unique value of x (input).

In option D, two of the pairs have same value of x. Therefore, it is not a function.

{(7, 11), (0,5), (11, 7), (7,13)}

Answer:

P (Math or English) = 0.90

Step-by-step explanation:

* Lets study the meaning of or , and on probability

- The use of the word or means that you are calculating the probability

  that either event A or event B happened

- Both events do not have to happen

- The use of the word and, means that both event A and B have to

  happened

* The addition rules are:

# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen

  at the same time)

# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they  

   have at least one outcome in common)

- The union is written as A ∪ B or “A or B”.  

- The Both is written as A ∩ B or “A and B”

* Lets solve the question

- The probability of taking Math class 71%

- The probability of taking English class 77%

- The probability of taking both classes is 58%

∵ P(Math) = 71% = 0.71

∵ P(English) = 77% = 0.77

∵ P(Math and English) = 58% = 0.58

- To find P(Math or English) use the rule of non-mutually exclusive

∵ P(A or B) = P(A) + P(B) - P(A and B)

∴ P(Math or English) = P(Math) + P(English) - P(Math and English)

- Lets substitute the values of P(Math) , P(English) , P(Math and English)

 in the rule

∵ P(Math or English) = 0.71 + 0.77 - 0.58 ⇒ simplify

∴ P(Math or English) =  0.90

* P(Math or English) = 0.90

To find the probability that a randomly selected student is taking a math class or an English class, use the principle of inclusion-exclusion. The probability is 90%.

To find the probability that a randomly selected student is taking a math class or an English class, we can use the principle of inclusion-exclusion. We know that 71% of students are taking a math class, 77% are taking an English class, and 58% are taking both.

To find the probability of taking either math or English, we add the probabilities of taking math and English, and then subtract the probability of taking both:

P(Math or English) = P(Math) + P(English) - P(Math and English)

= 71% + 77% - 58%

= 90%

Therefore, the probability that a randomly selected student is taking a math class or an English class is 90%.

Answer:

  use a suitable calculator

Step-by-step explanation:

For finding values related to a normal probability distribution function, it is convenient to use a suitable calculator or spreadsheet. (See below)

___

If all you have is a z-table, you must calculate the corresponding z-value and look it up in the table.

  z = (X -µ)/σ = (56 -54)/8 = 1/4

You are interested in the area above z=1/4. The table in the second attachment gives the area between z=0 and z=1/4. So, the area of interest is the table value subtracted from 0.5 (the total area above z=0.):

  0.5000 -0.0987 = 0.4013

Answer:

n = 1067

Step-by-step explanation:

Since nothing is known, we would assume that 50% of the computers use the new operating system.

So, standard error = 0.5/SQRT(n)

Z-value for a 95% CI = 1.9596

So, margin of error = 1.9596 x 0.5 / SQRT(n) = 0.03

So, n = 1067 (approx.)

This will be your approximate answer : n = 1067

Answer: 2401

Step-by-step explanation:

Formula to find the sample size is given by :-

[tex]n= p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex]

, where p = prior population proportion.

[tex]z_{\alpha/2}[/tex] = Two -tailed z-value for [tex]{\alpha[/tex]

E= Margin of error.

As per given , we have

Confidence level : [tex]1-\alpha=0.95[/tex]

⇒[tex]\alpha=1-0.95=0.05[/tex]

Two -tailed z-value for [tex]\alpha=0.05 : z_{\alpha/2}=1.96[/tex]

E= 2%=0.02

We assume that nothing is known about the percentage of computers with new operating systems.

Let us take p=0.5  [we take p= 0.5 if prior estimate of proportion is unknown.]

Required sample size will be :-

[tex]n= 0.5(1-0.5)(\dfrac{1.96}{0.02})^2\\\\ 0.25(98)^2=2401[/tex]

Hence, the number of computer must be surveyed = 2401

Answer:

Step-by-step explanation:

Anwer -1

Answer:

-1

Step-by-step explanation:

You could solve for x... or just plug those values in to see which would make the inequality true

Let's check x=3

-3(3-4)>6(3-1)

-3(-1)>6(2)

3>12  this is false  so not x cannot be 3

Let's check x=-1

-3(-1-4)>6(-1-1)

-3(-5)>6(-2)

15>-12 this is true so x can take on the value -1

Let's check x=7

-3(7-4)>6(7-1)

-3(3)>6(6)

-9>36 is false so x cannot be 7

Let's check x=2

-3(2-4)>6(2-1)

-3(-2)>6(1)

6>6 is false so x cannot be 2