If A is any set then n(A)=4 then n[P(A)]=____________ * 1)16 2)4 3)8 4)6

Hey there! :)

Answer:

y = 8x + 6

Step-by-step explanation:

Slope-intercept form of an equation is:

y = mx + b

Rearrange the given equation to be in this format by isolating the 'y' variable:

8x - y = -6

Subtract -8x from both sides:

-y = -8x - 6

Divide both sides by -1:

y = 8x + 6

This is the slope-intercept form!

Answer:

Step-by-step explanation:

write down the expression:

x*z-y

lets plug in the variables to evaluate the expression:

8*4.6-(-0.1)

36.8+0.1

36.9

Answer:

Given,

X=8

y=-0.1

z=4.6

Now,

[tex]xz - y \\ = 8 \times 4.6 - ( - 0.1) \\ = 36.8 - ( - 0.1) \\ = 36.8 + 0.1 \\ = 36.9[/tex]

hope this helps..

Good luck on your assignment..

Answer:

The degree of the polynomial is 3.

By the fundamental theorem of algebra, the function has three roots.

Two roots are given, so there must be one root remaining.

By the complex conjugate theorem, imaginary roots come in pairs.

The final root must be real.

Step-by-step explanation:

The number of roots remaining of the polynomial function f(x) = x³ − 7x − 6, with two roots -2, and 3 already given is 1. The nature of the root will be real.

A polynomial function is a function (say f(x)), which is defined over a polynomial expression in x. It is of the form,

f(x) = a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ, where a₀, a₁, a₂, ..., aₙ are constants, x is a variable, and n ≥ 0.

Degree of the polynomial function = n, the highest power of x.

The fundamental theorem of algebra is that the number of roots or solutions of a polynomial function = The degree of the polynomial function.

According to the complex conjugate theorem, if a polynomial function has complex roots, they will always exist in conjugate pairs, that is, if one root is of the form a + bi, the other root will be a - bi.

We are given a polynomial function f(x) = x³ - 7x - 6. Two roots of the equation are given as -2, and 3.

The degree of the equation = 3, so by the fundamental theorem of algebra number of roots = 3.

2 roots are given, so the number of roots remaining = 1.

Since none of the given roots are complex, the third root can not be complex, as complex roots always exist in conjugate pairs, coming from the complex conjugate theorem. So, the remaining root will be real in nature.

Learn more about the fundamental theorem of algebra and the complex conjugate theorem at

https://brainly.com/question/11855858

https://brainly.com/question/13792775

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Answer:

60°

Step-by-step explanation:

Two angles are complementary if one of the angles is double the other angle find the two angles

Complementary angles mean that the two angles, when added together, equal 90°. Let's call the first angle x, and its second, complementary angle 2x. So, we have x + 2x = 90. ... The second angle, 2x, is just twice the first angle, so its measurement is 60°.

Answer:

4(x+8) + 5(x-3)

= 4x + 32 + 5x - 15

= 9x + 17

Answer:

9x+17

Step-by-step explanation:

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Answer:

C.

Step-by-step explanation:

[tex]1.5^2\pi =2.25\pi[/tex]

Answer:

sin x = 0.998

cosx = 0.046

Step-by-step explanation:

Given that:

tan x = 21

where interval of x is [tex][0,\dfrac{\pi}{2}][/tex].

We know that the trigonometric identity for tan x is:

[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]

Comparing with:

[tex]tan x = \dfrac{21}{1}[/tex]

Perpendicular = 21 units

Base = 1 unit

As per pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\[/tex]

[tex]\Rightarrow \text{Hypotenuse}^2 = 21^2 +1^2\\\Rightarrow \text{Hypotenuse} = \sqrt{442} = 21.023\ units[/tex]

interval of x is [tex][0,\dfrac{\pi}{2}][/tex] so values of sinx and cosx will be positive because it is first quadrant where values of sine and cosine are positive.

We know that

[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}\\cos\theta = \dfrac{Base}{Hypotenuse}[/tex]

So, sine x :

[tex]\Rightarrow sinx =\dfrac{21}{21.023}\\\Rightarrow sinx = 0.998[/tex]

Similarly, value of cos x :

[tex]\Rightarrow cosx =\dfrac{1}{21.023}\\\Rightarrow cosx = 0.046[/tex]

Answer:  b) reflexive property

Step-by-step explanation:

When you are stating that a line is congruent to itself, you are using the Reflexive Property.

a) Associative Property: a + (b + c) = (a + b) + c

b) Reflexive Property: AB = AB

c) Substation Property: not a real property - does not exist

d) Transitive Property: If a = b and b = c, then a = c

Answer:

c. One response and one or more explanatory variables are related.

Step-by-step explanation:

Regression shows the relationship between a given variable and its covariates, which can be one or more. The initial variable is the dependent or response variable selected to show its level of variation with respect to one or more independent or explanatory variables.

Therefore, regression modeling describes how one response is related to one or more explanatory variables.

Answer:

0.253 m/s

Step-by-step explanation:

radius r of the circular rise = 13 mm = 0.013 m

apparent weight loss = 50%

acceleration of the new weight = 0.5 x 9.81 = 4.905 m/s^2

centripetal acceleration = 9.81 -  4.905 =  4.905 m/s^2

centripetal acceleration = [tex]\frac{v^{2} }{r}[/tex]

where v is the acceleration at the rise and r is the radius of the rise

centripetal force = [tex]\frac{v^{2} }{r}[/tex]  = [tex]\frac{v^{2} }{0.013}[/tex]

4.905 = [tex]\frac{v^{2} }{0.013}[/tex]

[tex]v^{2}[/tex] = 0.063765

v = [tex]\sqrt{0.063765}[/tex] = 0.253 m/s

Answer:

$65,351+/-$3,661.73

= ( $61,689.27, $69,012.73)

Therefore, the 90% confidence interval (a,b) = ( $61,689.27, $69,012.73)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $65,351

Standard deviation r = $7,711

Number of samples n = 12

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

$65,351+/-1.645($7,711/√12)

$65,351+/-1.645($2,225.973962860)

$65,351+/-$3661.727168905

$65,351+/-$3,661.73

= ( $61,689.27, $69,012.73)

Therefore, the 90% confidence interval (a,b) = ( $61,689.27, $69,012.73)

Answer:

"The probability that the egg will be with cholesterol content greater than 220 milligrams" is 0.37070 (37.070% or simply 37%)

Step-by-step explanation:

We have here a normally distributed random variable. The parameters that characterize this distribution is the mean, [tex] \\ \mu[/tex], and the standard deviation, [tex] \\ \sigma[/tex].

In this question, we have that:

And we want to know the probability that a randomly selected single egg "will be with cholesterol content greater than 220 milligrams."

To answer the latter, we need to use the following key concepts:

The z-scores are standardized values and represent the distance (for the raw score) from the mean in standard deviations units. A positive z-score indicates that it is above [tex] \\ \mu[/tex] and, conversely, a negative result that the value is below it.

The cumulative distribution function generates the values for the cumulative standard normal distribution displayed in the standard normal table.

The standard normal distribution is employed to find probabilities for any normally distributed data and we only need to calculate the corresponding z-score (or standardized value). This distribution has a [tex] \\ \mu = 0[/tex] and [tex] \\ \sigma = 1[/tex].

As we can see, all of these concepts are intertwined, and each of them is important because:

Finding the probability

We can get the z-score using the formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where x is the raw value we want to standardize using the previous formula, and, in this case is 220 milligrams, [tex] \\ x = 220[/tex] milligrams.

Thus (without using units):

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ z = \frac{220 - 215}{15}[/tex]

[tex] \\ z = \frac{5}{15}[/tex]

[tex] \\ z = \frac{5}{5} * \frac{1}{3}[/tex]

[tex] \\ z = 1 * \frac{1}{3}[/tex]

[tex] \\ z = 0.3333333...[/tex]

To consult the standard normal table, we only need [tex] \\ z = 0.33[/tex], because it only has values for two decimal digits. As a result, the value will be a little inexact (but near to the true value) compared to that obtained using statistical software (or maybe a more precise table).

With this value (which is positive and, therefore, above the mean), we need to carefully see the first column of the mentioned table to find z = 0.3. Then, in the first row, we only need to select that column for which we can add the next digit, in this case, 3 (it appears as +0.03). That is, we are finding the probability for [tex] \\ z = 0.33[/tex].

Then, the cumulative probability for [tex] \\ z = 0.33[/tex] is:

[tex] \\ P(x<220) = P(z<0.33) = 0.62930[/tex]

However, the question is asking for "cholesterol content greater than 220 milligrams" or

[tex] \\ P(x>220) = P(z>0.33)[/tex]

Since

[tex] \\ P(x<220) + P(x>220) = 1[/tex]

Which is the same for a standardized value:

[tex] \\ P(z<0.33) + P(z>0.33) = 1[/tex]

Then

[tex] \\ P(z>0.33) = 1 - P(z<0.33)[/tex]

Therefore

[tex] \\ P(x>220) = P(z>0.33) = 1 - P(z<0.33)[/tex]

[tex] \\ P(x>220) = 1 - P(z<0.33)[/tex]

[tex] \\ P(x>220) = 1 - 0.62930[/tex]

[tex] \\ P(x>220) = 0.37070[/tex]

Thus, "the probability that the egg will be with cholesterol content greater than 220 milligrams" is 0.37070 (37.070% or simply 37%).

The graph below shows a shaded area that corresponds to the found probability.  

Answer:

9/3

Step-by-step explanation:

could also be simplified to 3, but just the reciprocal is 9/3

Answer:  9/3

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

= 5(2) + 3(4)

= 10 + 12

= 22

Answer:

D) 22

Step-by-step explanation:

y-1= -7(x-3)

y= -7x+21+1

x=0 ⇒ y-intercept is equal to:

So y -intercept is 22, option D

Answer:

22

Step-by-step explanation:

y-1 = -7(x-3)

This is point slope form

Distribute

y-1 = -7x +21

Add 1 to each side

y-1+1 = -7x+21+1

y = -7x+22

This is slope intercept form where y = mx+b and b is the y intercept

22 is the y intercept

Answer:

2731

Step-by-step explanation:

3 - 1 = 2 = 2^1

11 - 3 = 8 = 2^3

43 - 11 = 32 = 2^5

171 - 43 = 128 = 2^7

683 - 171 = 512 = 2^9

Following the pattern, add 2^11 to 683.

683 + 2^11 = 683 + 2048 = 2731

Hi,

We have the sequence 1 , 3 , 11 , 43 , __.

Let us say  [tex]a_{1}=1 , a_{2}=3 , a_{3}=11 , a_{4}=43[/tex]  and it is required to find out [tex]a_{5}[/tex] .

As, we can see the pattern from the given four terms that,

[tex]a_{2}=a_{1}+2[/tex] i.e. [tex]a_{2}=a_{1}+2^{1}[/tex]

[tex]a_{3}=a_{2}+8[/tex] i.e. [tex]a_{3}=a_{1}+2^{3}[/tex]

[tex]a_{4}=a_{3}+32[/tex] i.e. [tex]a_{4}=a_{1}+2^{5}[/tex]

Since, the next term is obtained by adding the previous terms by odd powers of two.

Therefore, [tex]a_{5}=a_{4}+2^{7}[/tex] i.e. [tex]a_{5}=a_{4}+128[/tex] i.e [tex]a_{5}=43+128[/tex] i.e. [tex]a_{5}=171[/tex]

So, [tex]a_{5}=171.[/tex]

Hence, the next term of the sequence is 171.

Let us say  [tex]a_{1}=1 , a_{2}=3 , a_{3}=11 , a_{4}=43[/tex], [tex]a_{5}[/tex] [tex]= 683[/tex] and it is required to find out [tex]a_{6}[/tex].

Therefore, [tex]a_{6}=a_{5}+2^{9}[/tex] i.e. [tex]a_{6}=a_{5}+512[/tex] i.e [tex]a_{6}=683+512[/tex] i.e. [tex]a_{6}=1195[/tex]

So, [tex]a_{6}=1195.[/tex]

Hence, the next term of the sequence is 1195.

Answer:

V = 137.2

Step-by-step explanation:

We are given the volume equation. Simply plug in your r into the equation and calculate and you should get 137.189 as your answer.

Answer:

x = pi/2 + 2 pi n                            x = pi + 2 pi n   where n is an integer

x = 5pi /3 + 2 pi n                      

Step-by-step explanation:

8 cos^2 x + 4 cos x-4 = 0

Divide by 4

2 cos^2 x +  cos x-1 = 0

Let u = cos x

2 u^2 +u -1 =0

Factor

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

Using the zero product property

2u-1 =0    u+1 =0

u = 1/2      u = -1

Substitute cosx for u

cos x = 1/2    cos x = -1

Take the inverse cos on each side

cos ^-1(cos x) = cos ^-1(1/2)   cos ^-1( cos x) =cos ^-1( -1)

x = pi/2 + 2 pi n                            x = pi + 2 pi n   where n is an integer

x = 5pi /3 + 2 pi n                      

Answer:

[tex] P(0.55 <X<1.1)= F(1.1) -F(0.55) [/tex]

And replacing we got:

[tex] P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})[/tex]

[tex] P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457[/tex]

And rounded the answer would be 0.246

Step-by-step explanation:

For this case we can define the random variable X as "The commute time for people in a city" and for this case the distribution of X is given by:

[tex] X \sim exp (\lambda = \frac{1}{0.66}= 1.515)[/tex]

And for this case we want to find the following probability:

[tex] P(0.55 <X<1.1)[/tex]

And we can use the cumulative distribution function given by:

[tex] F(x) =1- e^{-\lambda x}[/tex]

And using this formula we got:

[tex] P(0.55 <X<1.1)= F(1.1) -F(0.55) [/tex]

And replacing we got:

[tex] P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})[/tex]

[tex] P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457[/tex]

And rounded the answer would be 0.246

Answer:

q1: 80

q2:85

q3:91.5

Work:

- rearrange the numbers from least to greatest

68,78,82,84,86,89,94,100

q1- add 78 and 82, divide by 2

q2: add 84 and 86, divide by 2

q3- add 89 and 94, divide by 2

Answer:

Option D

Step-by-step explanation:

Cost for the materials to resurface 1 meter of the road is $750.

∵ 1 kilometer = 1000 meter

∴ 0.25 kilometer = 0.25 × 1000

                            = 250 meters

∵ Cost to resurface 1 meter of road = $750

∴ Cost to resurface 250 meter of road = 750 × 250

                                                                = 187,500

The cost of materials to resurface 0.25 kilometer of a road is $187,500.

Option D is the answer.

Answer:

b. At least 2 abandoned cars in the next week.

Answer:

5

Step-by-step explanation:

y=5x-2

y=23

23=5x-2

25=5x

x=5

Hope this helps!

Answer:

x=5

Step-by-step explanation:

y=5x-2

23=5x-2

25=5x

x=5

[tex]32500[/tex]

[tex]0.00604[/tex]

[tex]2.4 \times 10^6[/tex]

[tex]1.47 \times 10^{-3}[/tex]

Answer:

A) 32500

B) 0.00604

C) [tex]2.4 * 10^6[/tex]

D) [tex]1.47 * 10^{-3}[/tex]

Answer:

The sequence converges to 5/9.

Step-by-step explanation:

Suppose we have a sequence [tex]a_{n}[/tex]

Limit test:

[tex]L = \lim_{n \to \infty} a_{n}[/tex]

If L is a constant number, the sequence converges to L.

If L = 0, the test is inconclusive.

Otherwise, the sequence diverges.

In this question:

[tex]a_{n} = \frac{5n}{1 + 9n}[/tex]

Test:

[tex]L = \lim_{n \to \infty} (\frac{5n}{1 + 9n})[/tex]

Infinity limit, we consider the term with the highest degree in the numerator and in the denominator.

[tex]L = \lim_{n \to \infty} (\frac{5n}{1 + 9n}) = \lim_{n \to \infty} \frac{5n}{9n} = \lim_{n \to \infty} \frac{5}{9} = \frac{5}{9}[/tex]

The sequence converges to 5/9.

You can check whether the sequence is decreasing or not in this case and use them with the limit.

The answers are:

a) The sequence converges. The limit is 5/9

b) The sequence converges. The limit is 0

There are many methods to find that. But one reverse test to be sure that the given sequence is not converging is that the limit when n tends to infinity, won't come as a finite point.

[tex]a_n = \dfrac{5n}{1+9n}[/tex]

We have this sequence upper bounded by: [tex]\dfrac{5n}{9n} = \dfrac{5}{9}[/tex]  (assuming n starts from 1) since the less the denominator, the bigger the term is (since 9n is positive and 1 is positive so 1 + 9n > 9n )

The sequence is lower bounded by  [tex]\dfrac{5n}{n + 9n} = \dfrac{5n}{10n} = \dfrac{5}{10} = \dfrac{1}{2}[/tex]

Checking if the sequence is monotonic:

[tex]a_{n+1} - a_n = \dfrac{5(n+1)}{1+9(n+1)} - \dfrac{5n}{1+9n} = \dfrac{(5n + 5)(1+9n) - (5n)(10 + 9n)}{(10 + 9n)(1+ 9n)} \\\\=a_{n+1} - a_n = \dfrac{5}{(10+9n)(1+9n)} > 0[/tex]

Thus the sequence is monotonically increasing sequence.

Thus, since the sequence is bounded and monotonic, thus it is converging.

The limit of this sequence is found by:

[tex]lim_{n \rightarrow \infty}\dfrac{5n}{1+9n} = lim_{n \rightarrow \infty}\dfrac{5}{1/n+9} = \dfrac{5}{9}[/tex]

Thus, the limit of this sequence is 5/9

Checking the convergence of second given sequence:

Since the given sequence is always bigger than 0, thus it is lower bounded by 0.

Now the given sequence is monotonic decreasing since each term is less than or equal to previous term. Thus, due to it being monotonic decreasing and being bounded (and all terms are smaller or equal to 1, thus upper bounded too), we have this sequence as converging.

The limit of this sequence is taken by:

[tex]a_n = \dfrac{1}{mod(n, 2)}\\\\\rm As \: n \rightarrow \infty, \text{ we have mod(n,2)} \rightarrow \infty\\Thus, a_{\infty}= 0[/tex]

Thus, the given sequence converges to 0.

Learn more about convergence of sequence here:

https://brainly.com/question/20945705

Answer:

23.6

Step-by-step explanation:

Finding AC:

Cos 61 = [tex]\frac{adjacent}{hypotenuse}[/tex]

0.48 × 10 = Adjacent

AC = 4.8

Now, CB:

Cos 29 = [tex]\frac{adjacent}{hypotenuse}[/tex]

0.87 × 10 = CB

CB = 8.8

The perimeter:

=> 10+4.8+8.8

=> 23.6

Answer:

23.6

Step-by-step explanation:

The correct answer is A

Explanation:

An orthographic drawing shows a three-dimensional figure from different perspectives or sides. Indeed, the orthographic drawing in the question shows how the object looks if you see this the front, side, and top of this. This implies the foundation drawing needs to match the figures of the orthographic drawing.

According to this, the correct figure is A because this is the only one that has a rectangle shape, and due to this, if you look at this from any different sides you will always see a rectangle. For example, the top view shows a rectangle of approximately 2x3 squares, and this view only fits with option A because B and C are not complete rectangles and therefore their top view is not a rectangle.

Answer:

The correct answer would be option 4

12x+20

 5y3

Hope that helps.Thank you!!!

Step-by-step explanation:

1,2,3,4,5,6 is a set of 6 elements; therefore it has 2⁶=64 subsets

Answer:

3/4 or 0.75

Step-by-step explanation:

You have four options available

Lets say P(A) is pick a rocket

P(A) = 2/4 because there are two rockets in the four choices

simplify it to 1/2

P(B) pick a big = 2/4 because there are two bigs and two smalls.

simplify it to 1/2

P(A ∩ B) = Pick a big rocket = 1/4

P(AUB) = P(A)+P(B)- P(A ∩ B)

P(AUB) = 1/2+1/2- 1/4 = 3/4 or 0.75