Biologists stock a lake with 160
160
fish, and estimate the carrying capacity of the lake to be 9100
9100
fish. The number of fish tripled in the first year.
(a) Assuming that the fish population satisfies logistic growth, the fish population can be modeled by:()=/[1+55.875−1.13506]

From the given information about this population, determine the constant
that completes the model.

The area of a circle is pi x r^2

Area of full circle: 3.14 x 11^2

Area = 379.94 square miles.

To find the area of the bounded arc, multiply the full area by the fraction of a full circle the arc is:

379.94 x 300/360 = 316.62 square miles

Answer:

316.62 miles²

Step-by-step explanation:

Area of circle = 3.14 ×  r²

3.14 × 11²

= 379.94 (area of whole circle)

We need to find the area of the blue shaded sector.

300/360 × 379.94

= 316.62

Explanation:

Two points on this line are (0,1) and (2,0)

Use the slope formula

m = (y2-y1)/(x2-x1)

m = (0-1)/(2-0)

m = -1/2

The negative slope means the line goes downhill as you move from left to right.

Answer:

  (–8, –6)

Step-by-step explanation:

The given points represent the x- and y- intercepts of the line, so we can write the equation in intercept form as ...

  x/(x-intercept) +y/(y-intercept) = 1

  x/(-2) +y/2 = 1 . . . use the given intercepts

  x - y = -2 . . . . . multiply by -2

Then the system is ...

Using the first to substitute into the second, we get ...

  x - (2x +10) = -2

  -8 = x . . . . . . . . . . . add x+2, simplify

  y = 2(-8) +10 = -6

The solution is (x, y) = (-8, -6).

Answer:

(-8,-6)

Step-by-step explanation:

Got it right on edge soooo <3

Answer:

a) CI = ( 148,69 ; 243,31 )

b) n = 189

Step-by-step explanation:

a)  If the Confidence Interval is 95 %

α = 5 %     or   α = 0,05     and   α/2  = 0,025

citical value for α/2  =  0,025     is    z(c) = 1,96

the  MOE   ( margin of error is )  

1,96* s/√n

1,96* 163,7/ √46

MOE =  47,31

Then  CI  =  196 ± 47,31

CI = ( 148,69 ; 243,31 )

CI look very wide ( it sems that if sample size was too low )

b) Now if s (sample standard deviation) is 175, and we would like to have only 50 ppm width with Confidence  level 95 %, we need to make

MOE = 25 = z(c) *  s/√n

25*√n = z(c)* 175

√n   =  1,96*175/25

√n  = 13,72

n = 188,23

as n is an integer number we make n = 189

Answer:

c. -13/4.

d. -13/3.

Step-by-step explanation:

c. f(3/2) = (1/2)(3/2) - 4

= 3 / 4 - 4

= 0.75 - 4

= -3.25

= -3 and 1/4

= -13/4.

d. f(-2/3) = (1/2)(-2/3) - 4

= -2/6 - 4

= -1/3 - 4

= -1/3 - 12/3

= -13/3.

Hope this helps!

Answer:

  0.0228

Step-by-step explanation:

A suitable probability calculator (or spreadsheet) can tell you this.

It is about 0.0228.

Answer: 52%

Step-by-step explanation:

Let the original price be 100.

After 40% reduction, price will be 100 - 40% = 60

After further 20% reduction, price will be 60 - 20% = 48

%age = (cur val - orig. val ) / orig val x 100

= (48 - 100) / 100 x 100%

= -52

The actual percentage of reduction is 52%

The first reduction is given as:

[tex]r_1 = 40\%[/tex]

The second reduction is given as:

[tex]r_2 = 20\%[/tex]

Assume that the original price of the item is x.

After the first reduction of 40%, the new price would be:

[tex]New = x\times (1 -r_1)[/tex]

So, we have:

[tex]New = x\times (1 -40\%)[/tex]

[tex]New = x\times 0.6[/tex]

[tex]New = 0.6x[/tex]

After the second reduction of 20% on the reduced price, the new price would be:

[tex]New = 0.6x\times (1 -r_2)[/tex]

So, we have:

[tex]New = 0.6x\times (1 -20\%)[/tex]

[tex]New = 0.6x\times 0.8[/tex]

[tex]New = 0.48x[/tex]

Recall that the original price is x.

So, the actual reduction is:

[tex]Actual = \frac{x - 0.48x}{x}[/tex]

[tex]Actual = \frac{0.52x}{x}[/tex]

Divide

[tex]Actual = 0.52[/tex]

Express as percentage

[tex]Actual = 52\%[/tex]

Hence, the actual percentage of reduction is 52%

Read more about percentage change at:

https://brainly.com/question/809966

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

So, we are given:

[tex]\frac{3}{x}=\frac{4x+3}{x^2}[/tex]

First, we should immediately rule out 0 as an answer. This is because the if [tex]x=0[/tex], the equation would be undefined.

[tex]x\neq 0[/tex]

Now, cross multiply.

[tex]3(x^2)=x(4x+3)[/tex]

[tex]3x^2=4x^2+3x[/tex]

Divide everything by x (and we can do this safely because we already know x cannot be equal to zero).

[tex]3x=4x+3[/tex]

[tex]-x=3[/tex]

[tex]x=-3[/tex]

We didn't run into any possibilities for extraneous solutions.

Answer: The investment will be 6314 after 9 years.

Step-by-step explanation:

Formula to calculate the accumulated amount in t years:

[tex]A=P(1+r)^t[/tex], whereP= principal amount, r= rate of interest ( in decimal)

Given: P = $4,625

r= 3.52% = 0.0352

t= 9 years

Then, the accumulated amount after 9 years would be:

[tex]A=4625(1+0.0352)^9\\\\=4625(1.0352)^9\\\\=4625(1.36527)\approx6314[/tex]

Hence, the investment will be 6314 after 9 years.

Answer:

(0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.

First graph in top row is the answer.

Step-by-step explanation:

The given function is, f(x) = x⁴ - 4x³ + x² + 6x

For zeros of the given function, f(x) = 0

x⁴ - 4x³ + x² + 6x = 0

x(x³ - 4x² + x + 6) = 0

Therefore, x = 0 is the root.

Possible rational roots = [tex]\frac{\pm 1, \pm 2, \pm 3, \pm 6}{\pm1}[/tex]

                                      = {±1. ±2, ±3, ±6}

By substituting x = -1 in the polynomial,

x⁴ - 4x³ + x² + 6x = (-1)⁴ - 4(-1)³+ (-1)² + 6(-1)

                           = 1 + 4 + 1 - 6

                           = 0

Therefore, x = -1 is also a root of this function.

For x = 2,

x⁴ - 4x³ + x² + 6x = (2)⁴ - 4(2)³+ (2)² + 6(2)

                           = 16 - 32 + 4 + 12

                           = 0

Therefore, x = 2 is a root of the function.

For x = 3,

x⁴ - 4x³ + x² + 6x = (3)⁴ - 4(3)³+ (3)² + 6(3)

                           = 81 - 108 + 9 + 18

                           = 0

Therefore, x = 3 is a root of the function.

x = 0, -1, 2, 3 are the roots of the given function.

In other words, (0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.

From these points, first graph in top row is the answer.

Answer:

12%

Step-by-step explanation:

3/25 = .12

.12 x 100 = 12%

Answer:

12%

Step-by-step explanation:

All you have to do is divide this on a calculator and multiply it by 100. 3/25 = 0.12; 0.12 x 100 = 12%.

Answer:

B. The set is linearly independent because at least one of the vectors is a multiple of another vector.

Step-by-step explanation:

A set of n vector of length n is linearly independent if the matrix with these vectors as column has none of zero determinant. The set of vectors is dependent if the determinant is zero. In the given question the vectors have no zero determinants therefore it is linearly independent.

Answer:

C) $143.

Step-by-step explanation:

We are given an equation: y = 0.0714x + 44.8.

x is the number of miles, and y is the cost.

y = 0.0714 * 1,375 + 44.8

y = 98.175 + 44.8

y = 142.975

So, the cost is about C) $143.

Hope this helps!

Answer:

2 is the only even prime number

Answer:

2

Step-by-step explanation:

2 is the only even prime number. There is no even prime number other than 2. Prime numbers are the numbers which can only be divided by 1 and the number itself.

Answer:

The probability that the insurer pays at least 1.44 on a random loss is 0.18.

Step-by-step explanation:

Let the random variable X represent the losses covered by a flood insurance policy.

The random variable X follows a Uniform distribution with parameters a = 0 and b = 2.

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b\\\\\Rightarrow f_{X}(x)=\frac{1}{2}[/tex]

It is provided, the probability that the insurer pays at least 1.20 on a random loss is 0.30.

That is:

[tex]P(X\geq 1.2+d)=0.30\\[/tex]

⇒

[tex]P(X\geq 1.2+d)=\int\limits^{2}_{1.2+d}{\frac{1}{2}}\, dx[/tex]

                [tex]0.30=\frac{2-1.2-d}{2}\\\\0.60=0.80-d\\\\d=0.80-0.60\\\\d=0.20[/tex]

The deductible d is 0.20.

Compute the probability that the insurer pays at least 1.44 on a random loss as follows:

[tex]P(X\geq 1.44+d)=P(X\geq 1.64)[/tex]

                        [tex]=\int\limits^{2}_{1.64}{\frac{1}{2}}\, dx\\\\=|\frac{x}{2}|\limits^{2}_{1.64}\\\\=\frac{2-1.64}{2}\\\\=0.18[/tex]

Thus, the probability that the insurer pays at least 1.44 on a random loss is 0.18.

ANSWER

(a+b)(a^2+ab+b^2)=(3x+4y) 9x^2+12xy+16y^2)

Answer:

a. P(0 < z < 3.00) =  0.4987

b. P(0 < z < 1.00) =  0.3414

c. P(0 < z < 2.00) = 0.4773

d. P(0 < z < 0.79) = 0.2852

e. P(-3.00 < z < 0) = 0.4987

f. P(-1.00 < z < 0) = 0.3414

g. P(-1.58 < z < 0) = 0.4429

h. P(-0.79 < z < 0) = 0.2852

Step-by-step explanation:

Find the area under the standard normal probability distribution between the following pairs of​ z-scores.

a. z=0 and z=3.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 3.00) = 0.9987

Thus;

P(0 < z < 3.00) = 0.9987 - 0.5

P(0 < z < 3.00) =  0.4987

b. b. z=0 and z=1.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 1.00) = 0.8414

Thus;

P(0 < z < 1.00) = 0.8414 - 0.5

P(0 < z < 1.00) =  0.3414

c. z=0 and z=2.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 2.00) = 0.9773

Thus;

P(0 < z < 2.00) = 0.9773 - 0.5

P(0 < z < 2.00) = 0.4773

d.  z=0 and z=0.79

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 0.79) = 0.7852

Thus;

P(0 < z < 0.79) = 0.7852- 0.5

P(0 < z < 0.79) = 0.2852

e. z=−3.00 and z=0

From the standard normal distribution tables,

P(Z< -3.00) = 0.0014  and P(Z< 0) = 0.5

Thus;

P(-3.00 < z < 0 ) = 0.5 - 0.0013

P(-3.00 < z < 0) = 0.4987

f. z=−1.00 and z=0

From the standard normal distribution tables,

P(Z< -1.00) = 0.1587  and P(Z< 0) = 0.5

Thus;

P(-1.00 < z < 0 ) = 0.5 -  0.1586

P(-1.00 < z < 0) = 0.3414

g. z=−1.58 and z=0

From the standard normal distribution tables,

P(Z< -1.58) = 0.0571  and P(Z< 0) = 0.5

Thus;

P(-1.58 < z < 0 ) = 0.5 -  0.0571

P(-1.58 < z < 0) = 0.4429

h. z=−0.79 and z=0

From the standard normal distribution tables,

P(Z< -0.79) = 0.2148  and P(Z< 0) = 0.5

Thus;

P(-0.79 < z < 0 ) = 0.5 -  0.2148

P(-0.79 < z < 0) = 0.2852

Answer:

You can use your graphing calculator to find the answer.

Go to STAT, then TESTS, and hit "1: Z-Test..."

Make sure it is set to Stats, then for mu0, do 70; for standard deviation, do 9; for mean, you do 62; for sample size, you do 19. For mu, you do not equal to mu0. Then you hit "Calculate".

You then get a z-value (critical value) of -3.874576839, and a p-value of 0.00010685098.

This means that...

We reject the null hypothesis that the average height of lodgepole pines in Yellowstone is 70 feet because p = 0.0001 is less than the significance level of alpha = 0.01. There is sufficient evidence to suggest that the mean height of lodgepole pines in Yellowstone is NOT equal to 70 feet.

Hope this helps!

Answer:

(42, 0)

Step-by-step explanation:

Since we know the slope and y-intercept we can write the equation of the line in slope-intercept form which is y = mx + b; therefore, the equation is y = -3/7x + 18. To find the x-intercept, we just plug in y = 0 which becomes:

0 = -3/7x + 18

-18 = -3/7x

x = 42

[tex]\text{In order to find your x intercept, plug in 0 to y and solve:}\\\\0=-\frac{3}{7}x+18\\\\\text{Subtract 18 from both sides}\\\\-18=-\frac{3}{7}x\\\\\text{Multiply both sides by 7}\\\\-126=-3x\\\\\text{Divide both sides by 3}\\\\42 = x\\\\\text{This means that the x-intercept is (42,0)}\\\\\boxed{\text{x-intercept: (42,0)}}[/tex]

Answer:

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Step-by-step explanation:

To identify outliers the interquartile range of the dataset can be used

Outliers can be identified as data values that are

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Using the interquartile range concept, it is found that:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

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

[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]

Thus:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

A similar problem is given at https://brainly.com/question/14683936

Answer:

$1137

Step-by-step explanation:

Solution:-

We will define the random variable as follows:

                       X: Monthly social security (OASDI) payments

The random variable ( X ) is assumed to be normally distributed. This implies that most monthly payments are clustered around the mean value ( μ ) and the spread of payments value is defined by standard deviation ( σ ).

The normal distribution is defined by two parameters mean ( μ ) and standard deviation ( σ ) as follows:

                       X ~ Norm ( μ , σ^2 )

We will define the normal distribution for (OASDI) payments as follows:

                       X ~ Norm ( μ , 116^2 )

We are to determine the mean value of the distribution by considering the area under neat the normal distribution curve as the probability of occurrence. We are given that 1/4 th of payments lie above the value of $1214.87. We can express this as:

                      P ( X > 1214.87 ) = 0.25

We need to standardize the limiting value of x = $1214.87 by determining the Z-score corresponding to ( greater than ) probability of 0.25.

Using standard normal tables, determine the Z-score value corresponding to:

                     P ( Z > z-score ) = 0.25 OR P ( Z < z-score ) = 0.75

                     z-score = 0.675

- Now use the standardizing formula as follows:

                     [tex]z-score = \frac{x - u}{sigma} \\\\1214.87 - u = 0.675*116\\\\u = 1214.87 - 78.3\\\\u = 1136.57[/tex]

Answer: The mean value is $1137

Answer:

The missing side is [tex]B = 6.0\ cm[/tex]

The missing angles are [tex]\alpha = 56.2[/tex] and [tex]\theta = 93.8[/tex]

Step-by-step explanation:

Given

[tex]A = 10\ cm[/tex]

[tex]C = 12\ cm[/tex]

[tex]\beta = 30[/tex]

The implication of this question is to solve for the missing side and the two missing angles

Represent

Angle A with [tex]\alpha[/tex]

Angle B with [tex]\beta[/tex]

Angle C with [tex]\theta[/tex]

Calculating B

This will be calculated using cosine formula as thus;

[tex]B^2 = A^2 + C^2 - 2ACCos\beta[/tex]

Substitute values for A, C and [tex]\beta[/tex]

[tex]B^2 = 10^2 + 12^2 - 2 * 10 * 12 * Cos30[/tex]

[tex]B^2 = 100 + 144 - 240 * 0.8660[/tex]

[tex]B^2 = 100 + 144 - 207.8[/tex]

[tex]B^2 = 36.2[/tex]

Take Square root of both sides

[tex]B = \sqrt{36.2}[/tex]

[tex]B = 6.0[/tex] (Approximated)

Calculating [tex]\alpha[/tex]

This will be calculated using cosine formula as thus;

[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]

Substitute values for A, B and C

[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]

[tex]10^2 = 6^2 + 12^2 - 2 * 6 * 12 * Cos\alpha[/tex]

[tex]100 = 36 + 144 - 144Cos\alpha[/tex]

Collect Like Terms

[tex]100 - 36 - 144 = -144Cos\alpha[/tex]

[tex]-80 = -144Cos\alpha[/tex]

Divide both sides by -144

[tex]\frac{-80}{-144} = Cos\alpha[/tex]

[tex]0.5556 = Cos\alpha[/tex]

[tex]\alpha = cos^{-1}(0.5556)[/tex]

[tex]\alpha = 56.2[/tex] (Approximated)

Calculating [tex]\theta[/tex]

This will be calculated using cosine formula as thus;

[tex]C^2 = B^2 + A^2 - 2BACos\theta[/tex]

Substitute values for A, B and C

[tex]12^2 = 6^2 + 10^2 - 2 * 6 * 10Cos\theta[/tex]

[tex]144 = 36 + 100 - 120Cos\theta[/tex]

Collect Like Terms

[tex]144 - 36 - 100 = -120Cos\theta[/tex]

[tex]8 = -120Cos\theta[/tex]

Divide both sides by -120

[tex]\frac{8}{-120} = Cos\theta[/tex]

[tex]-0.0667= Cos\theta[/tex]

[tex]\theta = cos^{-1}(-0.0667)[/tex]

[tex]\theta = 93.8[/tex] (Approximated)

Answer:

The answer is option A.

Step-by-step explanation:

here, 5x^2-18x+9

=5x^2-(15+3)x+9

=5x^2-15x-3x+9

=5x(x-3)-3(x-3)

=(5x-3)(x-3)

so, the answer from the above options is (5x-3).

hope it helps..

Answer:

Length of the drain pipe is 72.15 feet.

Step-by-step explanation:

From the figure attached,

A drain pipe is to be laid between two pints P and Q.

Point P is 15 ft higher than the other point Q.

Angle of elevation of point P from point Q is 12°.

Let the length of pipe is l feet.

By applying Sine rule in the given right triangle PRQ,

Sin(∠Q) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

Sin(12) = [tex]\frac{\text{PR}}{\text{PQ}}[/tex]

0.20791 = [tex]\frac{15}{l}[/tex]

[tex]l=\frac{15}{0.20791}[/tex]

[tex]l=72.146[/tex]

l = 72.15 ft

Therefore, length of the drain pipe is 72.15 feet.

Answer:

-52, and the opposite of this is 52.

Step-by-step explanation:

If we are losing 52 pounds, then our number is -52 since we are losing 52 pounds (adding a negative number to a positive number is the same as subtracting that number).

The opposite of a number is when we negate the number, or multiply it by -1.

A negative number times a negative number is a positive number.

[tex]-52\cdot-1 = 52\cdot1 = 52[/tex]

Hope this helped!

Answer:

Hey there!

Loss of 52 pounds, -52

Opposite, 52

Hope this helps :)

Answer: y=3

Step-by-step explanation:

To solve the equation, we want to get the same terms onto the same side and solve.

y+3=-y+9                 [add y on both sides]

2y+3=9                    [subtract 3 on both sides]

2y=6                        [divide 2 on both sides]

y=3

Answer:

y=3

Step-by-step explanation:

Answer:

[tex]v=wr[/tex]

Step-by-step explanation:

The formula relating linear velocity v and angular velocity ω for a circle of radius r is

[tex]v=wr------1[/tex]

where v = linear velocity in m/s

           w= angular velocity in rad/s

            r= radius of curve

Both linear and angular velocity relates to speeds of objects, while linear velocity is to objects that moves, angular velocity is to objects that turns

Answer: 0.388 m

Step-by-step explanation:

Ok, if the ball is dropped from 1.8 meters, then the height after the first bounce will be 3/5 times 1.8 meters:

h1 = (3/5)*1.8m = 1.08m

now we can think that the ball is dropped from a height of 1.08 meters, then the height after the second rebound will be:

h2 = (3/5)*1.08m = 0.648m

Now, using the same method as before, the height after the third bounce will be:

h3 = (3/5)*0.648m = 0.388 m

Notice that we can write this relation as:

h(n) = 1.8m*(3/5)^n

where n is the number of bounces.

if n = 0 we have the initial height, and if n = 3 we are on the third bounce, then:

h(3) = 1.8m*(3/5)^3 = 0.388 m

Answer:

The proportion of these light bulbs that will last less than the advertised time is 18.94% or 0.1894

Step-by-step explanation:

The first thing to do here is to calculate the z-score

Mathematically;

z-score = (x - mean)/SD

= (1500-1550)/57 = -50/57 = -0.88

So the proportion we will need to find is;

P( z < -0.88)

We shall use the standard score table for this and our answer from the table is 0.1894 which is same as 18.94%

Answer:

[tex]B'(x,y) = (0,-2)[/tex]

Step-by-step explanation:

Given

The attached grid

Translation rule: [tex](x,y) = (x + 5, y - 2)[/tex]

Required

Determine the coordinates of B'

First, we have to write out the coordinates of B

[tex]B(x,y) = (-5,0)[/tex]

Next is to apply the translation rule [tex](x,y) = (x + 5, y - 2)[/tex]

[tex]B(x,y) = (-5,0)[/tex] becomes

[tex]B'(x,y) = B(x+5,y-2)[/tex]

Substitute -5 for x and 0 for y

[tex]B'(x,y) = (-5+5,0-2)[/tex]

[tex]B'(x,y) = (0,-2)[/tex]