Examine the two normal probability curves and complete the statements.
The mean of the shorter normal curve is ["equal to", "greater than", "less than"] the mean of the taller normal curve.
The standard deviation of the shorter normal curve is ["less than", "greater than", "equal to"] the standard deviation of the taller normal curve.
The area under the shorter normal curve is ["equal to", "greater than", "less than"] the area under the taller normal curve.

Answer:

Y = 2/3X + 4/3

Step-by-step explanation:

(1,2) (4,4)

M = 2/3

Y = 2/3X + b

4 = 8/3 + b

12 = 8 + 3b

4 = 3b

B = 4/3

Y = 2/3X + 4/3

Answer:

Step-by-step explanation:

Answer:

Area of  square = 100 square cm

Step-by-step explanation:

Let the sides of a square be = a

Perimeter of a square = 4a

Let area of square = [tex]a^2[/tex]

Let the Length of rectangle be = [tex]l[/tex]

Given: width of the rectangle = 6 cm

Area of rectangle = length x breadth

          Perimeter of rectangle and square is equal.

          That is,

                     [tex]2(length + width) = 4a\\\\2(l + 6) = 4a\\\\l + 6 = 2a\\\\l = 2a - 6[/tex]

Therefore ,

    Area of rectangle

                              [tex]= Length \times width \\\\= (2a - 6) \times 6\\\\=6(2a - 6)[/tex]

Given area of rectangle is 16 less than area of square.

That is ,

         [tex]( 6(2a- 6) ) = a^2 - 16\\\\12a - 36 = a^2 - 16\\\\a^2 - 12a +20= 0\\\\a^2 - 2a -10a + 20 = 0\\\\a(a - 2) - 10(a - 2) = 0\\\\(a -10) ( a-2) = 0\\\\a = 10 , \ a = 2[/tex]

Check which value of 'a ' satisfies the equation:

[tex]\underline {when \ a = 2 }\\\\Length\ of \ rectangle \ l = 2a - 6 = 2 ( 2 ) - 6 = 4 - 6 = - 2. \\\\Length \ cannot \ be \ negative \ number. \\\\ \underline{ when \ a = 10 }\\\\Length \ of \ rectangle \ , l = 2a - 6 = 2 (10) - 6 = 20 - 6 = 14\\\\satisfies \ the \ conditions. \\\\Therefore , a = 10[/tex]

That is , side of the sqaure = 10

Therefore , area  of the square = 10 x 10 = 100 square cm.

[tex]V = 864\pi[/tex]

Step-by-step explanation:

Since one of the boundaries is y = 0, we need to find the roots of the function [tex]f(x)=-2x^2+6x+36[/tex]. Using the quadratic equation, we get

[tex]x = \dfrac{-6 \pm \sqrt{36 - (4)(-2)(36)}}{-4}= -3,\:6[/tex]

But since the region is also bounded by [tex]x = 0[/tex], that means that our limits of integration are from [tex]x=0[/tex] (instead of -3) to [tex]x=6[/tex].

Now let's find the volume using the cylindrical shells method. The volume of rotation of the region is given by

[tex]\displaystyle V = \int f(x)2\pi xdx[/tex]

[tex]\:\:\:\:\:\:\:= \displaystyle \int_0^6 (-2x^2+6x+36)(2 \pi x)dx[/tex]

[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \int_0^6 (-2x^3+6x^2+36x)dx[/tex]

[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \left(-\frac{1}{2}x^4+2x^3+18x^2 \right)_0^6[/tex]

[tex]\:\:\:\:\:\:\:= 864\pi [/tex]

Answer:

19.3 miles per gallon

Step-by-step explanation:

First, subtract 54,042.8-53,737.7. The answer is 305.1

Then, find the unit rate. 305.1/15.8

You get 19.31012658. The prompt says to round to the nearest tenth, so round, and you get 19.3.

That's your answer!

Answer:

D. No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.

Answer:

80 telephones should be sampled

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

89% confidence level

So [tex]\alpha = 0.11[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.11}{2} = 0.945[/tex], so [tex]Z = 1.6[/tex].

How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence?

n telephones should be sampled, an n is found when M = 0.09. We have no estimate for the proportion, thus we use [tex]\pi = 0.5[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.09 = 1.6\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.09\sqrt{n} = 1.6*0.5[/tex]

[tex]\sqrt{n} = \frac{1.6*0.5}{0.09}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.6*0.5}{0.09})^2[/tex]

[tex]n = 79.01[/tex]

Rounding up(as 79 gives a margin of error slightly above the desired value).

80 telephones should be sampled

Answer:

[tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative Property [Addition/Subtraction]:                                                            [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                               [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \frac{3x + 5}{\sqrt{x}}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

​Robbin's grade point average must be at least 2.75 in order to be unconditionally accepted into the program. ​

Step-by-step explanation:

An unconditional acceptance into a graduate program at a university will be given to students whose GMAT score plus 100 times the undergraduate grade point average is at least 1075

Considering the GMAT score x, and the GPA y, this situation is modeled by the following inequality:

[tex]x + 100y \geq 1075[/tex]

Robbin's GMAT score was 800.

This means that [tex]x = 800[/tex], and thus:

[tex]x + 100y \geq 1075[/tex]

[tex]800 + 100y \geq 1075[/tex]

[tex]100y \geq 275[/tex]

What must her grade point average be in order to be unconditionally accepted into the​ program?

Solving the above inequality for y:

[tex]100y \geq 275[/tex]

[tex]y \geq \frac{275}{100}[/tex]

[tex]y \geq 2.75[/tex]

Thus:

​Robbin's grade point average must be at least 2.75 in order to be unconditionally accepted into the program. ​

Answer:

The number of ways = 151200

Step-by-step explanation:

Below is the calculation of the number of ways:

Total number of people = 10

Total number of posts = 6

The number of ways = 10P6

The number of ways = [tex]\frac{10!}{10! - 6!}[/tex]

The number of ways = 10 x 9 x 8 x 7 x 6 x 5

The number of ways = 151200

Answer:

-10

Step-by-step explanation:

Step-by-step explanation:

hope it helps

Answer:

[tex]\bar x = 13.739[/tex]

[tex]\sigma^2 = 4.923[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{cc}{Class} & {Frequency} & 10.01 - 11.50 & 44 & 11.51 - 13.00 & 27 & 13.01 - 14.50 & 38 & 14.51 - 16.00 & 33 & 16.01 - 17.50 & 40 \ \end{array}[/tex]

Required

The sample mean and the sample variance

First, calculate the midpoints

[tex]x_1 = \frac{10.01 + 11.50}{2} = 10.755[/tex]

[tex]x_2 = \frac{11.51 + 13.00}{2} = 12.255[/tex]

And so on...

So, the table becomes:

[tex]\begin{array}{ccc}{Class} & {Frequency} & {x} & 10.01 - 11.50 & 44 & 10.755 & 11.51 - 13.00 & 27 & 12.255 & 13.01 - 14.50 & 38 & 13.755 & 14.51 - 16.00 & 33 & 15.255 & 16.01 - 17.50 & 40 & 16.755 \ \end{array}[/tex]

So, the sample mean is:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

[tex]\bar x = \frac{44 * 10.755 + 27 * 12.255 + 38 * 13.755 + 33 * 15.255 + 40 * 16.755}{44 + 27 + 38 + 33 + 40}[/tex]

[tex]\bar x = \frac{2500.41}{182}[/tex]

[tex]\bar x = 13.739[/tex]

The sample variance is:

[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]

[tex]\sigma^2 = \frac{44 * (10.755 - 13.739)^2 + 27 * (12.255 - 13.739)^2+ 38 * (13.755 - 13.739)^2 + 33 * (15.255 - 13.739)^2+ 40 * (16.755- 13.739)^2}{44 + 27 + 38 + 33 + 40-1}[/tex]

[tex]\sigma^2 = \frac{890.950592}{181}[/tex]

[tex]\sigma^2 = 4.923[/tex]

Answer:

The problem is incomplete, but it is solved using a binomial distribution with [tex]n = 8[/tex] and [tex]p = 0.16[/tex]

Step-by-step explanation:

For each adult who regret getting tattoos, there are only two possible outcomes. Either they say that they were too young, or they do not say this. The answer of an adult is independent of other adults, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

​16% say that they were too young when they got their tattoos.

This means that [tex]p = 0.16[/tex]

Eight adults who regret getting tattoos are randomly​ selected

This means that [tex]n = 8[/tex]

Find the indicated probability.

The binomial distribution is used, with [tex]p = 0.16, n = 8[/tex], that is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = x) = C_{8,x}.(0.16)^{x}.(0.84)^{8-x}[/tex]

Answer:

C.No, the two triangles can only be proven congruent through SSS.

Answer:

Step-by-step explanation:

It is a  28×12 rectangle, minus a 5×6 cutout.

area of 28×12 rectangle = 336 ft²

area of 5×6 cutout = 30 ft²

area of carpet = 336-30 = 330 ft²

Answer:

the larger number is 69

the smaller number is 16

Step-by-step explanation:

x is the smaller number

y is the larger number

x + y = 85

y - 4x = 5

y = 5 + 4x

x + 5 + 4x = 85

5x = 80

x = 16

y = 69

Answer:

In general gf(x) is not equal to fg(x)

Some pairs of functions cannot be composed. Some pairs of functions can be composed only  for certain values of x.

Only with they can be composed some values of x are the ranges of g(x) and f(x) are the same, and their domains are also the same. Or else lies inside it.

Step-by-step explanation:

g(x) = 3x + 6 - 8, f(x) = √x.

The domain of a composed function is either the same as the domain of the first function, or  else lies inside it

The range of a composed function is either the same as the range of the second function, or else lies inside it.

Or vice versa

Now only positive numbers, or zero, have real square roots. So g is defined only for numbers

greater than or equal to zero. Therefore g(f(x)) can have a value only if f(x) is greater than or

equal to zero. You can work out that

f(x) ≥ 0 only when x ≥3/2

.

Answer:

300%

Step-by-step explanation:

because 9/3×100=900/3=300 so it is 300%

Answer:

300%

Step-by-step explanation:

9/3 * 100%

900%/3 = 300%

Answer:

m(x) is a dilation of scale factor K = 1/5 of f(x).

Step-by-step explanation:

The transformation is a horizontal dilation

The general transformation is defined as:

For a given function f(x), a dilation of scale factor K is written as:

g(x) = f(x/K)

If K > 1, then we have a dilation (the graph contracts)

if 0 < K < 1, then we have a contraction (the graph stretches)

Here we have m(x) = f(5*x)

Then we have a scale factor:

K = 1/5

So this is a contraction.

Then the transformation is:

m(x) is a dilation of scale factor K = 1/5 of f(x).

Answer:

0.7671 = 76.71% probability that he was taught by method A

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Person learned Spanish successfully.

Event B: Method A was used.

Probability of a person learning Spanish successfully:

70% of 80%(using method A)

85% of 20%(using method B)

So

[tex]P(A) = 0.7*0.8 + 0.85*0.2 = 0.73[/tex]

Probability of a person learning Spanish successfully and using method A:

70% of 80%, so:

[tex]P(A \cap B) = 0.7*0.8 = 0.56[/tex]

What is the probability that he was taught by method A?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.56}{0.73} = 0.7671[/tex]

0.7671 = 76.71% probability that he was taught by method A

Solution :

a). [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y)$[/tex]

  Now, if X = Y, then :

  [tex]P(X|Y)=\left\{\begin{matrix} 1,& \text{if } x=y \\ 0, & \text{otherwise }\end{matrix}\right.[/tex]

Then, E[X|Y] = x = y

So, [tex]$\text{Var} (X|Y) =E((X-X)^2 |Y)$[/tex]

                      [tex]$=E(0|Y)$[/tex]

                      = 0

Therefore, this statement is TRUE.

b). If X = Y , then Var (X) = Var (Y)

And as Var (X|Y) = 0, so Var (X|Y) ≠ Var (X), except when all the elements of Y are same.

So this statement is FALSE.

c). As defined earlier,

  [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y=y)$[/tex]

  So, this statement is also TRUE.

d). The statement is TRUE because [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y=y)$[/tex].

e). FALSE

   Because, [tex]$\text{Var} (X|Y) =E ((X-E(X|Y=y))^2 |Y=y)$[/tex]

Answer:

0.3573 = 35.7%

Step-by-step explanation:

We roll a pair of dice 10,000 times so the mean and standard deviation is,

μ  = 10000/36  =277.7          σ = [tex]\sqrt{10000*\frac{35}{36^{2} } } =16.4[/tex]

[tex]z_{1}[/tex] = (280 - 277.7)/16.4 = .14

[tex]z_{2}[/tex] = (300 - 277.7)/16.4 = 1.35

Probablity (range)  

0.3573  

Z(low)=0.14        0.555766357

Z(upper)=1.36        0.91304644

Answer:

4g+2x=r

Step-by-step explanation:

4g+r=2r-2x

collecting like terms

4g+2x=2r-r

4g+2x=r

Answer:

please provide an image.

Answer:

By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.

Step-by-step explanation:

For examples,

Let's consider squares of 3, 11, 25, 37 and 131.

[tex] {3}^{2} = 9[/tex]

8 is a multiple of 4, and 9 is more than 8.

[tex] {11}^{2} = 121[/tex]

120 is a multiple of 4 and 121 is one more than it.

[tex] {25}^{2} = 625[/tex]

624 is a multiple of 4 and 625 is one more than it.

[tex] {37}^{2} = 1369[/tex]

1368 is a multiple of 4 and 1369 is one more than 1368.

[tex] {131}^{2} = 17161[/tex]

17160 is a multiple of 4.

Answer:

The probability of getting two good coils is 77.33%.

Step-by-step explanation:

Since a batch consists of 12 defective coils and 88 good ones, to determine the probability of getting two good coils when two coils are randomly selected (without replacement), the following calculation must be performed:

88/100 x 87/99 = X

0.88 x 0.878787 = X

0.77333 = X

Therefore, the probability of getting two good coils is 77.33%.

Answer:

5 1/4

Step-by-step explanation:

* is multiplication

1 3/4 is 1.75

so

24/1.75 = 72/×

1.75 * 72 = 24 * x

126 = 24x

24x = 126

x = 5.25 or 5 1/4

Total [tex]5\frac{1}{4}[/tex] cups of butter required to make 72 cookies.

The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of .

According to the given question.

Number of cups or butter required for making 24 cookies = [tex]1\frac{3}{4} =\frac{7}{4}[/tex]

⇒ Number of cups of butter required to make 1 cookie = [tex]\frac{\frac{7}{4} }{24} =\frac{7}{(24)(4)}[/tex]

Therefore,

The number of cups of butter required to make 72 cookies

= [tex]72[/tex] × [tex]\frac{7}{(24)(4)}[/tex]

= [tex]\frac{21}{4}[/tex]

= [tex]5\frac{1}{4}[/tex]

Hence, total [tex]5\frac{1}{4}[/tex] cups of butter required to make 72 cookies.

Find out more information about unitary method here:

https://brainly.com/question/22056199

#SPJ3

Answer:

"D" is the correct answer

Step-by-step explanation:

Answer: A.

Step-by-step explanation:

Hope this helps!