Andreas wants to estimate how many fish there are in a lake. One day he catches 20 fish,marks them,and returns them to the lake. The next day he catches 10 fish of which four are marked. Estimate the number of fish in the lake.

Step-by-step explanation:

. 345,000 cm³.

b. 124,300 hl.

c. 9,000 cm³.

d. 32.5 dm³.

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

a. 3,450 deciliters to cubic decimeters:

1 deciliter=100 cubic decimeters

(3,450dl)(\frac{100cm^{3}}{1dl})=345,000cm^{3}(3,450dl)(

1dl

100cm

3

)=345,000cm

3

b. 124.3 hectoliters to deciliters:

1 hectoliter=1,000 deciliters

(124,3hl)(\frac{1,000dl}{1hl})=124,300hl(124,3hl)(

1hl

1,000dl

)=124,300hl

c. 9 liters to cubic centimeters:

1 liter=1,000 cubic centimeters

(9L)(\frac{1,000cm^{3}}{1L})=9,000cm^{3}(9L)(

1L

1,000cm

3

)=9,000cm

3

d. 32.5 liters to cubic decimeters:

1 liter=1 cubic decimeter

32.5L=32.5dm^{3}32.5L=32.5dm

3

your answer follow me plzzz

Answer:

The first one is 345,000 cm³.

The second is 124,300 hl.

the Third is 9,000 cm³.

Anddd the fourth one is 32.5 dm³

:)

Answer:

speed=3.33m/s

Step-by-step explanation:

speed= distance÷time

3.33 m/s

length = ?

Answer:

Length  : 50m

Speed   : 5 m  /  s

im sorry if im too late :'(

Answer:

a

   $10,151   [tex]< \mu <[/tex]  $11448.12

b

  [tex]n = 158[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample size is  n  =  19

    The  sample mean is  [tex]\= x =[/tex]$10,800

     The  standard deviation is  [tex]\sigma =[/tex]$1095  

    The  population mean is  [tex]\mu =[/tex]$225

Given that the confidence level is 99%  the level of significance is mathematically represented as

       [tex]\alpha = 100 -99[/tex]

      [tex]\alpha = 1[/tex]%

=>    [tex]\alpha = 0.01[/tex]

Now the critical values of [tex]\alpha = Z_{\frac{\alpha }{2} }[/tex] is obtained from the normal distribution table as

        [tex]Z_{\frac{0.01}{2} } = 2.58[/tex]

The reason we are obtaining values for [tex]\frac{\alpha }{2}[/tex] is because [tex]\alpha[/tex] is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while [tex]\frac{\alpha }{2}[/tex]  is the area under the normal distribution curve for just one tail and we need the  value for one tail in order to calculate the confidence interval

Now the margin of error is obtained as

     [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

    [tex]MOE = 2.58* \frac{1095 }{\sqrt{19} }[/tex]

     [tex]MOE = 648.12[/tex]

The  99% confidence interval for the population mean yearly premium is mathematically represented as

    [tex]\= x -MOE < \mu < \= x +MOE[/tex]

substituting values

   [tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]

    [tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]

   $10,151   [tex]< \mu <[/tex]  $11448.12

The  largest sample needed is mathematically evaluated as

      [tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{\mu} ][/tex]

substituting values

       [tex]n = [ \frac{ 2.58 * 1095}{225} ]^2[/tex]

      [tex]n = 158[/tex]

Answer:

2π/7

Step-by-step explanation:

A cosine wave is:

y = A cos(2π/T x + B) + C

where A is the amplitude,

T is the period,

B is the horizontal shift,

and C is the vertical shift.

In this case:

7 = 2π/T

T = 2π/7

Answer:

The period the la function  is with the formula that will be explained below

Step-by-step explanation:

The period is calculated with this formula:

                   2 π

                     b

The absolute value is the distance between a number and zero, therefore the distance between zero and 7 is therefore 7; therefore we finally have:

Periodo:  

2 π

  7  

Answer:

The answer is option C

Step-by-step explanation:

Total surface area of a cylinder is

2πr( r + h)

The curved surface area of a cylinder is

2πrh

where r and h are the radius and height respectively

h = 10cm

r = 7cm

Total surface area is

2π×7( 7 + 10)

14π ( 7 + 10)

98π + 140π

238π

Which is

748 cm²

The curved surface area is

2π (7)(10)

140π

Which is

440cm²

The difference between the total surface area and the curved surface area of the cylinder is

748 cm² - 440cm²

Hope this helps you

Answer: The average rate of change for this function for the interval from x=3 to x=5 is 12.

Step-by-step explanation:

Complete question is provided in the attachment below.

Formula: The average rate of change for this function y=f(x) for the interval from  x= a to x= b :

[tex]Rate =\dfrac{f(b)-f(a)}{b-a}[/tex]

Let y= f(x) for the given table:

At x= 3 , f(3)=8 and f(5)=32

Then, the average rate of change for this function for the interval from x=3 to x=5:

[tex]Rate=\dfrac{f(5)-f(3)}{5-3}\\\\=\dfrac{32-8}{2}\\\\=\dfrac{24}{2}=12[/tex]

Hence, the average rate of change for this function for the interval from x=3 to x=5  is 12.  (Option A is correct.)

Answer:

51.339

Step-by-step explanation:

Hello,

At the beginning Holly has $500

After one year

   he will get 500*(1+6.75%)=500*1.0675

After n year (n being real)

   he will get

   [tex]500\cdot1.0675^n[/tex]

and we are looking for n so that

   [tex]500\cdot1.0675^n=14,300\\<=> ln (500\cdot1.0675^n)=ln(14,300)\\<=>ln(500)+n\cdot ln(1.0675)=ln(14,300)\\<=> n= \dfrac{ln(14,300)-ln(500)}{ln(1.0675)}=51.338550...\\[/tex]

so we need 51.339 years

Hope this helps

Answer:

x = 22

<a = 88°

<b = 92°

Step-by-step explanation:

To solve for x, <a, and <b, we'd need to recall some of the properties of parallel lines, then apply them in solving this problem.

To find the value of x, recall that consecutive interior angles are supplementary. (5x - 18), and (3x + 22) are consecutive interior angles. Therefore:

[tex] (5x - 18) + (3x + 22) = 180 [/tex]

Solve for x

[tex] 5x - 18 + 3x + 22 = 180 [/tex]

[tex] 5x + 3x - 18 + 22 = 180 [/tex]

[tex] 8x + 4 = 180 [/tex]

Subtract 4 from both sides:

[tex] 8x + 4 - 4 = 180 - 4 [/tex]

[tex] 8x = 176 [/tex]

Divide both sides by 8

[tex] \frac{8x}{8} = \frac{176}{8} [/tex]

[tex] x = 22 [/tex]

=>Find <a:

According to the properties of parallel lines, alternate interior angles are equal. Therefore:

<a = 3x + 22

Plug in the value of x

<a = 3(22) + 22 = 66 + 22

<a = 88°

=>Find <b:

According to the properties of parallel lines, corresponding angles are said to be equal. Therefore,

<b = 5x - 18

Plug in the value of x to find <b

<b = 5(22) - 18

<b = 110 - 18 = 92°

*check attachment for the correct figure given in this question with the right labelled angles

Answer:

[tex] x = 86, y = 67, z = 94 [/tex]

Step-by-step explanation:

From the given figure attached below, values of x, y, and z can be found as follow:

Value of x:

[tex] x = 180 - (38 + 56) [/tex] => sum of angles in a triangle

[tex] x = 180 - 94 [/tex]

[tex]x = 86[/tex]

Value of z:

[tex] z = 180 - 86 [/tex] => angles on a straight line

[tex]z = 94[/tex]

Value of y:

[tex] y = 180 - (19 + 94) [/tex] => sum of angles in a triangle.

[tex] y = 180 - 113 [/tex]

[tex]y = 67[/tex]

[tex] x = 86, y = 67, z = 94 [/tex]

Answer:

"If an angle has measure 90°, then it is a right angle" , True

Step-by-step explanation:

We have the following:

"If an angle is a right angle, then it’s measure is 90"

The idea is to write the opposite of the previous conditional statement.

We know that if the statement is "If p, then q", then its inverse will be "If q, then p".

So the opposite of our given statement will be :

"If an angle has measure 90°, then it is a right angle"

And this statement is true since every angle that measures 90 ° is considered a right angle.

Answer:

101.98 yards.

Step-by-step explanation:

Please refer to the diagram that I drew (sorry for the messiness; I do not own a stylus and so I was using my mouse to try to draw it).

Since the triangle is a right triangle, you can use SOH CAH TOA. In this case, you are trying to figure out the opposite length, but you are given the adjacent. So, we will use tangent to solve this (TOA = Tangent, Opposite over Adjacent).

The angle is 22.6 degrees, and the tangent of the angle is equivalent to the opposite length, x, divided by the adjacent length, 245 yards.

tan(22.6) = x / 245

x / 245 = tan(22.6)

x = tan(22.6) * 245

x = 0.4162598242 * 245

x = 101.9836569

So, you are about 101.98 yards from the cabin.

Hope this helps!

Answer:

3.924×10∧-9

Step-by-step explanation:

Royal flush contains five cards and it's probability is 0.3924%≈0.003924

Straight contain five cards and it's probability is 0.0001%≈0.000001

The probability including straight and royal flushes will be 0.003924×0.000001≈3.924×10∧-9

Answer:

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Step-by-step explanation:

Coordinates of points A and C are (-8, 6) and (2, 5).

If a point B intersects the segment AB in the ratio of 2 : 5

Then coordinates of the point B will be,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.

For the coordinates of point B,

x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]

  = [tex]-\frac{36}{7}[/tex]

y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]

  = [tex]\frac{40}{7}[/tex]

Therefore, coordinates of pint B will be,

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Answer:

17.5 days

Step-by-step explanation:

The half life of this element is five days.

For the first five days it will decrease to 100*0.5=50%.

For the second five days it will decrease to 50*0.5= 25%

For the third five days it will decrease to 25*0.5 = 12.25%

It means in each day in the five days it reduce 0.1 of the it's remaining amount.

12.5 - 9 = 3.5 %

0.5 of 12.5 = 6.25%

It's going to be 15 days + 2.5 days= 17.5 days

Answer:

h = -9

Step-by-step explanation:

5h+2(11-h)= -5

Distribute

5h +22 -2h = -5

Combine like terms

3h +22 = -5

Subtract 22 from each side

3h +22-22 = -5-22

3h = -27

Divide by 3

3h/3 = -27/3

h = -9

Answer:

The probability that Pat will pass the exam is 0.02775.

Step-by-step explanation:

We are given that exam consists of 100 true-false questions. Pat plans to guess the answer to each question without reading it.

If a grade on the exam is 60% or more, Pat will pass the exam.

Let X = grade on the exam by Pat

The above situation can be represented through binomial distribution such that X ~ Binom(n = 100, p = 0.50).

Here the probability of success is 50% because there is a true-false question and there is a 50-50 chance of both being the correct answer.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]100 \times 0.50[/tex] = 50

and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]

                                                                  = [tex]\sqrt{100 \times 0.50 \times (1-0.50)}[/tex]

                                                                  = 5

So, X ~ Normal([tex]\mu=50, \sigma^{2} = 5^{2}[/tex])

Now, the probability that Pat will pass the exam is given by = P(X [tex]\geq[/tex] 60)

         P(X [tex]\geq[/tex] 60) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{60-50}{5}[/tex] ) = P(Z [tex]\geq[/tex] 2) = 1 - P(Z < 2)

                                                       = 1 - 0.97725 = 0.02275

Hence, the probability that Pat will pass the exam is 0.02775.

Answer:

58 hours

Step-by-step explanation:

First week: 25 5/8 hours = 25 hrs 37 mins and 30 sec

Second weeK: 32 5/6 hrs = 32 hrs and 50 mins

To find the toal time in minutes

(37 + 50) mins = 1 hr 27 mins

Threfore, total number of hours he worked in two weeks:

(25 + 32 + 1) hrs = 58 hours

Answer:

A). 55

Step-by-step explanation:

Number of Variegated Fritillaries for each year is

2009 = 7

2010= 95

2011= 63

The sum total of the samples= 7+95+63

The sum total of the samples= 165

Number of years= 3

The average= total/number of years

The average= 165/3

The average= 55

Answer: A

Step-by-step explanation: I have a massive brain (•-*•)

Answer:

x = ±sqrt(7)

Step-by-step explanation:

x^2 - 8 = -1

Add 8 to each side

x^2 - 8+8 = -1+8

x^2 = 7

Take the square root of each side

sqrt(x^2) = ±sqrt(7)

x = ±sqrt(7)

Answer:

(C) The area of the cylinder's base is [tex]\dfrac{1}{4} \pi x^2[/tex] square units.

(E)The height of the cylinder is 4x units.

Step-by-step explanation:

If the Base Diameter = x

Therefore: Base radius = x/2

Area of the Base

[tex]=\pi (x/2)^2\\=\dfrac{ \pi x^2}{4} $ square units[/tex]

Next, we know that:

The volume of a cylinder = Base Area X Height

[tex]\pi x^3=\dfrac{ \pi x^2}{4} \times Height\\Height =\pi x^3 \div \dfrac{ \pi x^2}{4}\\=\pi x^3 \times \dfrac{ 4}{\pi x^2}\\\\Height=4x$ units[/tex]

Therefore, the correct options are: C and E.

Learn more:  https://brainly.com/question/16856757

Answer:

You didn't put an attachment to show what solid you wanted rounded

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

A proportion is setting two ratios equal to each other.

Look at the info you are given for price in $ and area in sq ft:

$385 for 70 sq ft

That allows you to write a ratio. The ratio of dollars to square feet is

385/70    (notice it's dollars divided by sq ft)

Now you look at the part of the problem that has an unknown, and you set up the same type of ratio (dollars to sq ft) using x for the unknown.

x dollars to 200 sq ft

The ratio is

x/200     (notice that, again, it's dollars divided by sq ft)

In both cases the ratios are dollars to sq ft.

To set up a proportion, you just set the ratios equal to each other.

385/70 = x/200

Now we solve the proportion. We can cross multiply.

385/70 = x/200

70x = 385 * 200

70x = 77,000

x = 1100

They would charge $1100 to install 200 sq ft of tile.

The unit price is obtained by dividing a cost by the corresponding area in sq ft. you can use either ratio.

unit price = ($385)/(70 sq ft) = $5.5/sq ft

($1100/200 sq ft also works since it is also equal to $5.5/sq ft)

Answer:

The answer is option B

Step-by-step explanation:

To find cos 45° we must first find the adjacent and the hypotenuse

Let the adjacent be x

Let the hypotenuse be h

To find the adjacent we use tan

tan ∅ = opposite / adjacent

From the question

the opposite is 9

So we have

tan 45 = 9 / x

x tan 45 = 9

but tan 45 = 1

x = 9

Since we have the adjacent we use Pythagoras theorem to find the hypotenuse

That's

h² = 9² + 9²

h² = 81 + 81

h² = 162

h = √162

h = 9√2

Now use the formula for cosine

cos∅ = adjacent / hypotenuse

The adjacent is 9

The hypotenuse is 9√2

So we have

cos 45 = 9/9√2

We have the final answer as

Hope this helps you

Answer:

f(0) = 0

Step-by-step explanation:

f(x) = -sqrt(x)

Let x= 0

f(0) = -sqrt(0)

f(0) = 0

Value of the given function [tex]f(x) = -\sqrt{x}[/tex] for [tex]f(0) = 0.[/tex]

" A function is defined as the relation between the given variable represents set of all input value should have one output each."

According to the question,

Given function,

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

Substitute the different values for 'x' for the given function we get,

[tex]x=1 , f(1) = -\sqrt{1}[/tex]

                 [tex]=-1[/tex]

[tex]x=4 , f(4) = -\sqrt{4}[/tex]

                 [tex]=-2[/tex]

[tex]x=0, f(0) = -\sqrt{0}[/tex]

                 [tex]=0[/tex]

Therefore, given relation is a function.

Hence, value of the given function [tex]f(x) = -\sqrt{x}[/tex] for [tex]f(0) = 0.[/tex]

Learn more about function here

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Answer:

3/8

Step-by-step explanation:

The bag contains 4 green marbles, 8 yellow marbles and 20 red marbles.

The total number of marbles is 32.

She chooses one from the bag.

The probability of the marble not being red is:

P(not red) = 1 - P(red)

P(not red) = 1 - (20 / 32) = 1 - 5/8

P(not red) = 3/8

The probability of it not being red is 3/8.

Answer:

A. -9

Step-by-step explanation:

If one of the variables were negative than, it would not be able to equal 2/7.

Answer:

The correct answer is the first one.

Step-by-step explanation:

Let's analyse the effect of each modification in the function.

The value 6 multiplying the cot function means a vertical stretch.

The value of 3 multiplying the x inside the function is a horizontal compression, which causes the period to be 3 times lower the original period.

The original period of the cotangent function is pi, so the horizontal compression will make the period be pi/3.

The value of -pi/2 inside the cotangent function normally causes a horizontal shift of pi/2 to the right, but the x-values were compressed by a factor of 3 (horizontal stretch), so the horizontal shift will be 3 times lower: (pi/2) /3 = pi/6

And the value of 4 summing the whole equation is a vertical shift of 4 units up.

So the correct answer is the first one.

Answer:

option 1

Step-by-step explanation:

Answer:

Option E

Step-by-step explanation:

y = x /3

let x = 1, 2, 3

y = 0.333, 0.667, 1

y = x/2 + 40

let x = 1, 2, 3

y = 40.5, 41, 41.5

y = x

let x = 1, 2, 3

y = 1, 2, 3

y = 2x + 50

let x = 1, 2, 3

y = 52, 54, 56

y = 3x - 20

let x = 1, 2, 3

y = -17, -14, -11

The standard deviation is the spread of data, the data that is most spread is option E.

Answer:

3 and 8

Step-by-step explanation:

Given the proportion:

[tex] \frac{3}{4} = \frac{6}{8}[/tex]

Required:

Find the extreme values.

When given an equation like the one we have here, there is always a very easy way to find the extreme value.

First make rewrite to a ratio form:

Example:

a:b = c:d

Just know that extreme values are the values on the outside of the ratio(a & d)

Therefore,

3:4 = 6:8

When it is written this way extreme values are 3 & 8

Extreme values = 3 and 8