A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately five per square metre. If a forester randomly locates ten 1-square-metre sampling regions in the area, find the probability that none of the regions will contain seedlings.

Answer:

5.5

Step-by-step explanation:

From the table; one cup of oat contains 103.4 carbohydrates.

568.7/103.4 = 5.5 cups

Step-by-step explanation:

5x - 2y

5(-2) - 2(-2)

-10 + 4

= - 6

Answer:

f[g(x)]= 7x + 27

Step-by-step explanation:

g(x) = x + 2,

f(x) = 7x + 13,

f[g(x)] means you substitute the value of g(x) into the variable of f(x);

Which is 7( x+2) + 13 = 7x +14 +13

= 7x + 27

Answer: X = -5

Step-by-step explanation:

1) Multiply both sides by 6, which is 4x - 3 = 2 + 5x

2) Move the terms, 4x - 5x = 2 + 3

3) Combine like terms, -x = 5

4) Multiply both sides by -1, x = -5

Answer:

a. 15

b. based on the result of part a, 15 standard deviation above the mean.

c. 2.5

d.  Earl's height is unusual

Step-by-step explanation:

We have that "x" would be the height of Earl = 196, the mean m = equals 181 and the standard deviation (sd) = 6, now:

a. the positive difference between the mean and Earl's height:

D = x - m

D = 196 - 181 = 15

b. based on the result of part a, 15 standard deviation above the mean.

c. The z value is given by:

z = x - m / sd

replacing:

z = (196 - 181) / 6

z = 2.5

d. the z-score is unusual since the value of z is 2.5 which is a value greater than than 2 standard deviations above the mean, which means that Earl's height is unusual

Answer:

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

On this case n =6 and x =6 we got:

[tex] 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1[/tex]

Step-by-step explanation:

The utility for the combination formula is in order to find the number of ways to order a set of elements

For this case we want to find the following expression:

[tex] 6C6[/tex]

And the general formula for combination is given by:

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

On this case n =6 and x =6 we got:

[tex] 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1[/tex]

Answer:

llolololol

Step-by-step explanation:

Answer:80 grams

Step-by-step explanation:

Answer:

B then C

Step-by-step explanation:

First screenshot:

Shape B because the net has a square base.

Second screenshot:

It is C

C does not make a cube

Answer:

3769.57

Step-by-step explanation:

the perimeter of semicircle is

P = d + πd/2

251.86 = d + (3.14d/2)

multiply both side with 2

503.72 = 2d + 3.14d

503.72 = 5.14 d

d = 98 miles

d is diameter, then the radius is 98 : 2 = 49

Area of semicircle

A = ½ π r²

A = 0.5 x 3.14 x 49²

A = 3769.57 miles²

Answer: 3769.57 miles²

Step-by-step explanation:

The perimeter of the semi circle is the sum of the curve and the diameter.

Perimeter of curve

[tex]\dfrac{1}{2}C=\dfrac{1}{2}2\pi r\\\\\\.\quad =\pi r\\[/tex]

Diameter of the semi circle = 2r

[tex]P = \pi r+2r\\\\\\251.86=r(\pi +2)\\\\\\\dfrac{251.86}{\pi +2}=r\\\\\\\dfrac{251.86}{5.14}=r\\\\\\49=r[/tex]

Area of the curve

[tex]\dfrac{1}{2}A=\dfrac{1}{2}\pi r^2\\\\\\.\quad =\dfrac{1}{2}(3.14)(49)^2\\\\\\.\quad =\large\boxed{3769.57}[/tex]

Answer:

Hello There Again. The Correct answer is C.

Explanation: Because it shows that the numbers need to be least median then greater of the breakfast lunch.

Hope It Helps! :)

Answer: 290 degrees

Step-by-step explanation:

subtract the minor arc's measure from 360 to get the major arc's measure

Answer:

a) 19,600 fishes were originally put in the pond.

b) Population of fishes after 10 years = 3,863

Population of fishes after 20 years = 1,733

Population of fishes after 30 years = 1,403

Step-by-step explanation:

The population follows a logistic model

P(t) = d (1 + ke⁻ᶜᵗ)

For a fish pond,

d = 1400, k = 13, c = 0.2

Inserting the values of these constants

P(t) = 1400 (1 + 13 e⁻⁰•²ᵗ)

a) How many fish were originally put in the pond?

At the start of the whole thing, t = 0

P(t=0) = 1400 (1 + 13 e⁰) = 1400 × 14 = 19,600

Hence, 19,600 fishes were originally put in the pond.

b) Find the population after 10, 20, and 30 years.

P(t) = 1400 (1 + 13 e⁻⁰•²ᵗ)

At t = 10, 0.2t = 0.2 × 10 = 2

P(t=10) = 1400 (1 + 13e⁻²) = 1400 (1 + 1.759) = 3,863.1 = 3,863

At t = 20, 0.2t = 0.2 × 20 = 4

P(t=20) = 1400 (1 + 13e⁻⁴) = 1400 (1 + 0.238) = 1,733.3 = 1,733

At t = 30, 0.2t = 0.2 × 30 = 6

P(t = 30) = 1400 (1 + 13e⁻⁶) = 1400 (1 + 0.00248) = 1,403.47 = 1,403

Hope this Helps!!

Answer:

0.3891 = 38.91% probability that only one is a second

Step-by-step explanation:

For each globet, there are only two possible outcoes. Either they have cosmetic flaws, or they do not. The probability of a goblet having a cosmetic flaw is independent of other globets. So we use the binomial probability distribution 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.

17% of its goblets have cosmetic flaws and must be classified as "seconds."

This means that [tex]p = 0.17[/tex]

Among seven randomly selected goblets, how likely is it that only one is a second

This is P(X = 1) when n = 7. So

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

[tex]P(X = 1) = C_{7,1}.(0.17)^{1}.(0.83)^{6} = 0.3891[/tex]

0.3891 = 38.91% probability that only one is a second

Answer:

The mean and standard deviation of the combined distribution is 16 and 7.192 respectively.

Step-by-step explanation:

We have given that a distribution consists of three components with frequencies 200, 250, and 300 having means 25, 10, and 15 and standard deviations 3, 4, and 5 respectively.

And we have to find the mean and standard deviation of the combined distribution.

Firstly let us represent some symbols;

[tex]n_1[/tex] = 200           [tex]\bar X_1[/tex] = 25                 [tex]\sigma_1[/tex] = 3

[tex]n_2[/tex] = 250            [tex]\bar X_2[/tex] = 10                  [tex]\sigma_2[/tex] = 4

[tex]n_3[/tex] = 300            [tex]\bar X_3[/tex] = 15                  [tex]\sigma_3[/tex] = 5  

Here, [tex]\bar X_1, \bar X_2 , \bar X_3[/tex] represent the means and [tex]\sigma_1,\sigma_2,\sigma_3[/tex] represent the standard deviations.

Now, as we know that Mean of the combined distribution is given by;

                         [tex]\bar X = \frac{n_1 \times \bar X_1+n_2 \times \bar X_2+n_3 \times \bar X_3}{n_1+n_2+n_3}[/tex]

Putting the above values in the formula we get;

                         [tex]\bar X = \frac{200 \times 25+250 \times 10+300 \times 15}{200+250+300}[/tex]

                         [tex]\bar X = \frac{5000+2500 +4500}{750}[/tex]

                         [tex]\bar X = \frac{12000}{750}[/tex]  =  16

Similarly, the formula for combined standard deviation is given by;

       [tex]\sigma = \sqrt{\frac{n_1\sigma_1^{2} + n_1(\bar X_1-\bar X)^{2}+n_2\sigma_2^{2} + n_2(\bar X_2-\bar X)^{2}+n_3\sigma_3^{2} + n_3(\bar X_3-\bar X)^{2} }{n_1+n_2+n_3} }[/tex]

       [tex]\sigma = \sqrt{\frac{(200 \times 3^{2}) + 200 \times (25-16)^{2}+(250 \times 4^{2}) + 250 \times (10-16)^{2}+(300 \times 5^{2}) + 300 \times (15-16)^{2} }{200+250+300} }[/tex]

       [tex]\sigma = \sqrt{\frac{1800 + (200 \times 81)+4000 + (250 \times 36)+7500 +( 300 \times 1) }{750} }[/tex]        

       [tex]\sigma = \sqrt{\frac{1800 + 16200+4000 + 9000+7500 +300 }{750} }[/tex]  

       [tex]\sigma = \sqrt{\frac{38800 }{750} }[/tex]  =  7.192

Hence, the mean and standard deviation of the combined distribution is 16 and 7.192 respectively.

Answer:

[tex]\frac{-1}{(\sqrt{8}+\sqrt{9} )}[/tex]

Answer:

the water here is wet.

Step-by-step explanation:

Answer:

A = 55.15

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adjacent/ hypotenuse

cos A = 4/7

Take the inverse cos of each side

cos^-1 cos A = cos^-1 (4/7)

A = 55.15009542

To the nearest hundredth

A = 55.15

Answer:

Step-by-step explanation:

Work done is given as the product of force and distance.

The liquid in the cylindrical tank weighs 62.4 lb/ft^3.

This means that each ft^3 of the tank has 62.4 lb of the liquid.

To find the wight of the liquid in the entire tank, we multiply 62.4 by the volume of the cylindrical tank.

The volume of a cylinder is given as:

[tex]V = \pi r^2h[/tex]

where r is its radius and h is its height

The radius of the tank is 6 ft (since its diameter is 12 ft) and its height is 20 ft.

Therefore, the weight of the liquid in the tank is given as:

[tex]V = \pi * 6^2 * 20 = 2261.95 lb[/tex]

This weight is a force.

The height of the tank is 20 ft.

Therefore, the work done in pumping the liquid to the top of the tank is:

W = 2261.95 * 20 = 45239 ft.lb

Answer:

r = 3cm

Step-by-step explanation:

Use the formula for the surface area of a cylinder and solve to obtain r=3cm

Hence radius of base is 3 cm of right circular cylinder.

The cylinder is known as a right circular cylinder when the axis (one of the rectangle's sides) is perpendicular to the radius ((r)). The base and top of the right circular cylinder are both round and parallel to one another. The general formula for the total surface area of a cylinder is T. S. A. =[tex]2\pi rh+2\pi r^{2} .[/tex]

Given total surface area of right circular cylinder =84[tex]\pi cm^{2}[/tex]

Using formula for right circular cyinder =.[tex]2\pi rh+2\pi r^{2} .[/tex]=84

and height=11 cm

[tex]2\pi r11+2\pi r^{2} =84.\pi[/tex]

⇒[tex]11r+ r^{2} =84/2[/tex]

⇒[tex]11r+ r^{2} =42[/tex]

⇒[tex]r^{2} +11r-42=0[/tex]

⇒r = [tex]\frac{-11+-\sqrt{11^{2}-4(1)42 } }{2}[/tex]

⇒r=[tex]\frac{-11+-17}{2}[/tex]

⇒r=3,-1

Hence radius of base is 3 cm as value can't be negative .

Learn more about surface area of cylinder https://brainly.com/question/12763699

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Answer:

Step-by-step explanation:

To factor the expression we need to look for a value that is unique to both terms in the expression.

Given the expression

[tex]24g - 36h[/tex]

The available factors common to both terms are 2,3,4,6,8,12. but since we are expected to factor the expression completely we will use the greatest common factor (gcf) to find the solution

The greatest but common factor is 12, hence we have

[tex]=12(2g- 3h)[/tex]

Answer:

257 people are satisfied

Step-by-step explanation:

11/15 is the fraction that are satisfied

11/15 * 350 =256.6(repeating)

Rounding to the nearest whole person

257 people are satisfied

Answer:

In first quadrant, [tex]\tan B=\frac{8}{15}[/tex]

In second quadrant, [tex]\tan B=\frac{-8}{15}[/tex]

Step-by-step explanation:

Given: [tex]\sin B=\frac{8}{17}[/tex]

To find: [tex]\tan B[/tex]

Solution:

Trigonometry explains the relationship between the sides and the angles of the triangle.

Here,

[tex]\sin B=\frac{8}{17}[/tex]

So, B can be in first or second quadrant as sine is positive both first and second quadrants.

Cosine and tangent are positive in first quadrant but negative in second quadrant.

In first quadrant:

[tex]\cos B=\sqrt{1-\sin ^2B}=\sqrt{1-\left ( \frac{8}{17} \right )^2}=\sqrt{1-\frac{64}{289}}=\sqrt{\frac{225}{289}}=\frac{15}{17}[/tex]

So, [tex]\tan B=\frac{\sin B}{\cos B}=\frac{\frac{8}{17}}{\frac{15}{17}}=\frac{8}{15}[/tex]

In second quadrant:

[tex]\cos B=-\sqrt{1-\sin ^2B}=-\sqrt{1-\left ( \frac{8}{17} \right )^2}=-\sqrt{1-\frac{64}{289}}=-\sqrt{\frac{225}{289}}=\frac{-15}{17}[/tex]

[tex]\tan B=\frac{\sin B}{\cos B}=\frac{\frac{8}{17}}{\frac{-15}{17}}=\frac{-8}{15}[/tex]

Answer:

A.2 x minus y = negative 6 and 3 x minus y = negative 5

Step-by-step explanation:

A ) 2x-y=-6, and 3x-y=-5

Consider the provided information.

First convert the statement into mathematical representation.Consider the smaller number is x and the larger number is y.

y, is equal to twice the sum of a smaller number and 3.    

This information can be written as: y=2(x+3)

The larger number is also equal to 5 more than 3 times the smaller number.

This information can be written as: y=5+3x

Answer:

A ) 2x-y=-6, and 3x-y=-5

Step-by-step explanation:

Answer:

The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

Step-by-step explanation:

I hope this helped ;)

Answer:

The team ordered 7 black T-shirts.

The team ordered 14 red T-shirts.

Step-by-step explanation:

The team ordered 140 T-shirts.

How many black T-shirts did the baseball team order?

Of those, 5% are black.

0.05*140 = 7

The team ordered 7 black T-shirts.

How many red T-shirts?

Of those, 10% are red.

0.1*140 = 14

The team ordered 14 red T-shirts.

Step-by-step explanation:

The distance traveled varies directly with the time spent in motion. If d is distance and t is time taken. Then,

[tex]d\propto t[/tex]

or

[tex]d=kt[/tex]

k is the constant of variation

If d = 150 miles and t = 4 hours

[tex]k=\dfrac{d}{t}\\\\k=\dfrac{150}{4}\\\\k=37.5\ mph[/tex]

Answer:

A) A is an invertible matrix ( TRUE )

B) A is a row equivalent to the n x n identity matrix ( n = 3 ) ( TRUE )

C ) The equation Ax = 0 has only the trivial solution ( TRUE )

D ) The columns of A form a linearly independent set ( TRUE )

Step-by-step explanation:

Assuming a matrix A

[tex]\left[\begin{array}{ccc}1&2&1\\-1&0&3\\4&1&5\end{array}\right][/tex]

det A = 1 [ 0 -3 ] +  2 [12 + 5 ]  + 1[-1]

        = -3 + 34 -1 = 30 ≠ 0

THEREFORE  det A = 30 ≠ 0

Attached is the detailed solution of the given statements above

Answer:

24.15° = 24° to the nearest degree

Step-by-step explanation:

If we draw the triangle we would see that the KL is the longest side and the hypothenus;

Also MK would-be the height and ML is the base of the triangle.

Since L and M are the angles at the base;

From Trigonometry Sin L = MK/ KL

= 2.7/6.6

L = Sin^{-1} (2.7/6.6)

L = Sin^{-1} (0.4091)

=24.15°

Note : sin a = height/ longest side

= Opposite/hypothenus

Answer:

see below

Step-by-step explanation:

cube has 6 square faces so 6*s*s

s =3 in =3*2.54 cm = 7.62 cm

1 in = 2.54 cm

1 cube needs 6*7.62² = 348.3864 cm²

10 cubes = 10*348.3864 =3483.864 cm²