The weights of a certain type of captured fish can be described by a bell-shaped distribution (symmetric and unimodal) with a mean of 1050 grams and a standard deviation of 375 grams. What is the probability of fish that have weights above 675g

Answer:

x+3

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

(x-3)(x-2)(x-4)

Step-by-step explanation:

x+4             x^2 -16

---------------÷ -------------

x^2 - 5x+6     x+3

Copy dot flip

x+4                x+3

--------------- * -------------

x^2 - 5x+6     x^2 -16

Factor

x+4                x+3

--------------- * -------------

(x-3)(x-2)     (x-4)(x+4)

Cancel like terms

1                   x+3

--------------- * -------------

(x-3)(x-2)     (x-4)1

x+3

---------------   x cannot equal 3,2,4 -4

(x-3)(x-2)(x-4)

Answer:

2.56

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(3.5 - 1.5)² + (4.3 - 2.7)²

√(2)² + (1.6)²

√(4) + (2.56)

√6.56

= 2.56

Answer:

False

Step-by-step explanation:

Work Shown:

1 pack of white = 2 shirts = A

1 pack of blue = 6 shirts

5 packs of blue = 5*6 = 30 shirts = B

A+B = 2 white shirts + 30 blue shirts = 32 shirts total

Answer:

32 T-shirts in total

Step-by-step explanation:

1 white has 2

1 blue has 6

1*2=2 white T

5*6=30  blue T

30+2=32

Answer:

Sum is 20,935.

Step-by-step explanation:

This is an arithmetic progression.

Sum:

[tex]S = \frac{n}{2} (2a + (n - 1)d) [/tex]

n is the number of terms, n = 79

S is the sum

a is the first term, a = -8

d is common difference, d = -1-(-8) = 7

substitute:

[tex]S = \frac{79}{2} (2 \times - 8 + (79 - 1) \times 7)) \\ \\ S = \frac{79}{2} ( - 16 + 546) \\ \\ S = \frac{79}{2} (530) \\ S = 20935[/tex]

Answer:

is y=x^2 a proportional relationship?

[tex]{ \sf{yes. \: constant \: of \: proportionality = 1}}[/tex]

is y=2+x a proportional relationship?

[tex]{ \sf{no. \: unless \: y \: is \: proportinal \: to \: (2 + x)}}[/tex]

is y=2/x a proportional relationship?

[tex]{ \sf{yes. \: where \: proportianality \: constant \: is \: 2}}[/tex]

is y=2x a proportional relationship?

[tex]{ \sf{yeah. \: constant \: is \: 2}}[/tex]

Answer:

A. 4000 meters because

1 km = 1000 meters

and 4 km = 1000 × 4 = 4000

............

Answer:

167.64 cm

Step-by-step explanation:

I dont kno how to work it out

Answer: A & C

Step-by-step explanation:

[tex]i=\sqrt{-1}[/tex]

[tex]\sqrt{-1} *\sqrt{4} =\sqrt{-4}[/tex]

You can also simplify the above by taking the -4 out of the radical

It becomes 2 x [tex]\sqrt{-1}[/tex], which can be simplifed to C

Answer:

27

Step-by-step explanation:

x-y

We are subtracting and we want the smallest number

We want the smallest number for x and the largest number for y

The smallest number for x is 71

The largest number for y is 44

71-44

27

Answer:

i dont no the ans

Step-by-step explanation:

Answer:- 10[tex]m^{2}[/tex] + 3m -9

Step-by-step explanation: Given ;  

  A= -3 -m

  B= 3m -5[tex]m^{2}[/tex]

 2B + 3A

        solution

     2B + 3A

substitute A and B in the formula

    2(3m - 5[tex]m^{2}[/tex]) + 3(-3 -m)

    6m - 10[tex]m^{2}[/tex] - 9 - 3m   group like terms

    - 10[tex]m^{2}[/tex] + (6m -3m) -9

     - 10[tex]m^{2}[/tex] + 3m -9

Answer:

x = π/4.

Step-by-step explanation:

3sin(2x) = 2sin(2x) + 1

3sin(2x) - 2sin(2x) = 1

1sin(2x) = 1

sin(2x) = 1

When a variable n = π/2, sin(π/2) = 1 [refer to the unit circle].

2x = π/2

x = π/4.

Hope this helps!

9514 1404 393

Answer:

  (5, -6)

Step-by-step explanation:

x-coordinates measure the distance to the right of the y-axis. Moving a point 4 units to the right adds 4 to its x-coordinate.

y-coordinates measure distance up from the x-axis. Moving a point 4 units down subtracts 4 from its y-coordinate.

  (1, -2) +(4, -4) = (1 +4, -2 -4) = (5, -6) . . . . image of translated point

Answer:

The number of hits would follow a binomial distribution with [tex]n =10,\!000[/tex] and [tex]p \approx 4.59 \times 10^{-6}[/tex].

The probability of finding [tex]0[/tex] hits is approximately [tex]0.955[/tex] (or equivalently, approximately [tex]95.5\%[/tex].)

The mean of the number of hits is approximately [tex]0.0459[/tex]. The variance of the number of hits is approximately [tex]0.0459\![/tex] (not the same number as the mean.)

Step-by-step explanation:

There are [tex](26 + 10)^{6} \approx 2.18 \times 10^{9}[/tex] possible passwords in this set. (Approximately two billion possible passwords.)

Each one of the [tex]10^{9}[/tex] randomly-selected passwords would have an approximately [tex]\displaystyle \frac{10,\!000}{2.18 \times 10^{9}}[/tex] chance of matching one of the users' password.

Denote that probability as [tex]p[/tex]:

[tex]p := \displaystyle \frac{10,\!000}{2.18 \times 10^{9}} \approx 4.59 \times 10^{-6}[/tex].

For any one of the [tex]10^{9}[/tex] randomly-selected passwords, let [tex]1[/tex] denote a hit and [tex]0[/tex] denote no hits. Using that notation, whether a selected password hits would follow a bernoulli distribution with [tex]p \approx 4.59 \times 10^{-6}[/tex] as the likelihood of success.

Sum these [tex]0[/tex]'s and [tex]1[/tex]'s over the set of the [tex]10^{9}[/tex] randomly-selected passwords, and the result would represent the total number of hits.

Assume that these [tex]10^{9}[/tex] randomly-selected passwords are sampled independently with repetition. Whether each selected password hits would be independent from one another.

Hence, the total number of hits would follow a binomial distribution with [tex]n = 10^{9}[/tex] trials (a billion trials) and [tex]p \approx 4.59 \times 10^{-6}[/tex] as the chance of success on any given trial.

The probability of getting no hit would be:

[tex](1 - p)^{n} \approx 7 \times 10^{-1996} \approx 0[/tex].

(Since [tex](1 - p)[/tex] is between [tex]0[/tex] and [tex]1[/tex], the value of [tex](1 - p)^{n}[/tex] would approach [tex]0\![/tex] as the value of [tex]n[/tex] approaches infinity.)

The mean of this binomial distribution would be:[tex]n\cdot p \approx (10^{9}) \times (4.59 \times 10^{-6}) \approx 0.0459[/tex].

The variance of this binomial distribution would be:

[tex]\begin{aligned}& n \cdot p \cdot (1 - p)\\ & \approx(10^{9}) \times (4.59 \times 10^{-6}) \times (1- 4.59 \times 10^{-6})\\ &\approx 4.59 \times 10^{-6}\end{aligned}[/tex].

Answer:

N = 1000

Step-by-step explanation:

The population growth of species per capita of any geographical can be computed by using the formula:

[tex]\dfrac{dN}{dT}=rN (1 - \dfrac{N}{K})[/tex]

here;

N = population chance

T = time taken

K = carrying capacity

r = the constant exponential growth rate

From the given equation, we can posit that the value of r will be the greatest at the time the value of dN is highest:

As such, when the population chance = 1000

[tex]\dfrac{dN}{dT}=0.17 * 1000 (1 - \dfrac{1000}{10000})[/tex]

[tex]\dfrac{dN}{dT}=0.17 * 1000 (0.9)[/tex]

[tex]\dfrac{dN}{dT}= 153[/tex]

At N = 5000;

[tex]\dfrac{dN}{dT}= 85[/tex]

At N= 8000;

[tex]\dfrac{dN}{dT}= 34[/tex]

At N = 10000

[tex]\dfrac{dN}{dT}= 0[/tex]

Answer:

The first three terms in the geometric sequence are 18, 24, 32.

Step-by-step explanation:

A number when added to [tex]x,y,z[/tex] that yields consecutive terms of a geometric sequence is an unknown number [tex]t\in \mathbb{Z}[/tex]

Given

[tex]x = 1, y = 7, z = 15[/tex]

We know

[tex]\alpha _1 = 1+t[/tex]

[tex]\alpha _2 = 7+t[/tex]

[tex]\alpha _3 = 15+t[/tex]

Recall that a geometric sequence is in the form

[tex]\boxed{a_n = a_1 \cdot r^{n-1}}[/tex]

Therefore, once  [tex]\alpha_1, \alpha_2, \alpha_1[/tex] are consecutive terms,

[tex]15+t = (1+t) r^{3-1} \implies 15+t = (1+t) r^2[/tex]

To find the ratio, for

[tex]\dots a_{k-1}, a_k, a_{k+1} \dots[/tex]

we know

[tex]\dfrac{a_k}{a_{k-1}} =\dfrac{a_k}{a_{k-1}} =r[/tex]

Therefore,

[tex]\dfrac{(7+t)}{(1+t)} =\dfrac{(15+t)}{(7+t)} \implies (7+t)^2 = (15+t)(1+t)[/tex]

[tex]\implies 49+14t+t^2=15+16t+t^2 \implies -2t=-34 \implies t=17[/tex]

The ratio is therefore

[tex]r=\dfrac{4}{3}[/tex]

Therefore, the first three terms in the geometric sequence are 18, 24, 32.

Answer:

a

Step-by-step explanation:

g(1)=5

f(g(1))=f(5)

f(5)=2

Answer:

fyi b's answer has imaginary numbers in it...

Imaginary: 1 +[tex]\frac{\sqrt{2i} }{2 }[/tex]    

Imaginary: 1 -  [tex]\frac{\sqrt{2i} }{2 }[/tex]  

Step-by-step explanation:

[tex]2x^{2} - 4x -3 = 0[/tex]

[tex]\sqrt{-4^{2} -4(2)(3)}[/tex] = [tex]\sqrt{-8}[/tex] ... the negative root will produce imaginary solutions

9514 1404 393

Answer:

  1a. -4, 3/4

  1b. 1-0.71i, 1+0.71i

Step-by-step explanation:

The directions tell you to use the quadratic formula. Factoring may get you the solution somewhat more easily, but does not comply with the directions.

The quadratic formula tells you ...

  [tex]\text{The solution to }ax^2+bx+c=0\text{ is given by }\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

__

1a. a=4, b=13, c=-12

  [tex]x=\dfrac{-13\pm\sqrt{13^2-4(4)(-12)}}{2(4)}=\dfrac{-13\pm\sqrt{361}}{8}=\dfrac{-13\pm19}{8}\\\\x=\left\{-4,\dfrac{3}{4}\right\}[/tex]

__

1b. After adding 3 to both sides, a=2, b=-4, c=3

  [tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(2)(3)}}{2(2)}=\dfrac{4\pm\sqrt{-8}}{4}=1\pm\dfrac{\sqrt{2}}{2}i\\\\x=\left\{1-\dfrac{\sqrt{2}}{2}i,1+\dfrac{\sqrt{2}}{2}i\right\}\approx\{1-0.71i,1+0.71i\}[/tex]

Answer:

Yes, the graph is a function.

Vertical line test proves so.

Answer:

a first degree equation

Answer:

0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.

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: Positive test

Event B: Person has diabetes.

Probability of a positive test:

0.95 out of 0.1(person has diabetes).

0.007 out of 1 - 0.1 = 0.9(person does not has diabetes). So

[tex]P(A) = 0.95*0.1 + 0.007*0.9 = 0.1013[/tex]

Probability of a positive test and having diabetes:

0.95 out of 0.1. So

[tex]P(A \cap B) = 0.95*0.1 = 0.095[/tex]

What is the probability that a randomly selected person has diabetes, given that his test is positive?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.095}{0.1013} = 0.9378[/tex]

0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.

Answer:

Step-by-step explanation:

y = ½(x-4)² + 13

y = ½(x² - 8x + 16) + 13

y = ½x² - 4x + 21

Answer:

totally 16 numbers can be formed

It is hard and the condition of repeat of number should be clear if you have formula ( it is obvious to have) you can use that.

Step-by-step explanation:

X +1 + X + 2

X + X + 1 + 2

2x + 3

Therefore it's 2x + 3

Answer:

x=30.5

Step-by-step explanation:

Using midsegment 's theorea:

[tex]2=\dfrac{RG}{RS} =\dfrac{RH}{RQ} =\dfrac{GH}{SQ} \\\\4x-65=2x-4\\\\2x=61\\\\x=\dfrac{61}{2} \\\\x=30.5\\[/tex]

= 2025

When you are told to find the smallest length possible, you perform L.C.M(Least common multiples)

For this, you divide the given lengths using the numbers that divides all through.

I have added an image to this answer. Go through it for more explanation

Answer:

Point has co-ordinates, (0, 5)

Step-by-step explanation:

If they cut y-axis, then x = 0

[tex]2y - x = 10 \\ 2y - 0 = 10 \\ 2y = 10 \\ y = 5[/tex]