"Conservationists have despaired over destruction of tropical rain forest by logging, clearing, and burning." These words begin a report on a statistical study of the effects of logging in Borneo. Here are data on the number of tree species in 12 unlogged forest plots and 9 similar plots logged 8 years earlier:

Answer:

A.

Step-by-step explanation:

Multiply straight across:

[tex]\frac{2}{x+1}\cdot \frac{5}{3x}=\frac{10}{3x(x+1)}[/tex]

Simplify:

[tex]=\frac{10}{3x^2+3x}[/tex]

This cannot be simplified further.

Answer:

[tex] \boxed{\sf \frac{10}{3 {x}^{2} + 3x}} [/tex]

Step-by-step explanation:

[tex] \sf Expand \: the \: following: \\ \sf \implies \frac{2}{x + 1} \times \frac{5}{3x} \\ \\ \sf \implies \frac{2 \times 5}{3x(x + 1)} \\ \\ \sf 2 \times 5 = 10 : \\ \sf \implies \frac{ \boxed{ \sf 10}}{3x(x + 1)} \\ \\ \sf 3x(x + 1) = (3x)(x) + (3x)(1) : \\ \sf \implies \frac{10}{ \boxed{ \sf (3x)(x) + (3x)(1)}} \\ \\ \sf (3x)(x) = 3 {x}^{2} : \\ \sf \implies \frac{10}{ \boxed{ \sf 3 {x}^{2}} + (3x)(1) } \\ \\ \sf (3x)(1) = 3x : \\ \sf \implies \frac{10}{3 {x}^{2} + 3x} [/tex]

Answer:

c. 0.40

Step-by-step explanation:

The probability that a student has an A or B in the class can be found by simply adding up the probabilities of both. Since 0.30 + 0.30 =0.60, the probability a student has an A or B is 0.60. Now to find the probability that they don't have a A or B is represented by 1-0.60, which equals 0.40, which is our answer.

The probability of receiving grade other than A or B is 0.60.

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

The probability of receiving A grade in class = 0.30

And probability of receiving B grade in class = 0.30

Probability of receiving grade A or B = 0.30 + 0.30 = 0.60

Let total probability is equal to 1.

The probability of receiving grade other than A or B = 1 - 0.60 = 0.40

The required probability is 0.40.

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Answer:

  r(n) = 1000·(2/5)^n

Step-by-step explanation:

Since the tortoise travels 3/5 the remaining distance, the remaining distance at the end of the day is 2/5 of what it was at the beginning of the day. So, the function can be modeled by an exponential with a "growth" factor of 2/5:

  r(n) = 1000·(2/5)^n

where r(n) is the number of remaining feet after n days of travel.

[tex]\text{Find the distance from one corner to the other}\\\\\text{In this question, we would use the Pythagorean theorem to find the length}\\\text{between corners}\\\\\text{Pythagorean theorem:}\\\\a^2+b^2=c^2\\\\\text{We are trying to find c}\\\\\text{Plug in and solve:}\\\\7^2+6^2=c^2\\\\49+36=c^2\\\\85=c^2\\\\\text{Square root}\\\\\sqrt{85}=\sqrt{c^2}\\\\\sqrt{85}=c\\\\\text{In decimal form, it's: 9.219544}\\\\\text{Round to the nearest tenths place}\\\\\boxed{9.2\,\, feet}[/tex]

Answer:

The series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Step-by-step explanation:

We are given with the following series options below;

a. 3, 5, 7, 9

b. 2, 4, 5, 8

c. 4, 6, 8,10

d. 2, 3, 4, 5

And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].

For this, we will put the values of n in the above expression and then will see which series is obtained as a result.

So, the given expression is ; [tex]X_n=2n+1[/tex]

If we put n = 1, then;

[tex]X_1=(2\times 1)+1[/tex]

[tex]X_1 = 2+1 = 3[/tex]

If we put n = 2, then;

[tex]X_2=(2\times 2)+1[/tex]

[tex]X_2 = 4+1 = 5[/tex]

If we put n = 3, then;

[tex]X_3=(2\times 3)+1[/tex]

[tex]X_3 = 6+1 = 7[/tex]

If we put n = 4, then;

[tex]X_4=(2\times 4)+1[/tex]

[tex]X_4 = 8+1 = 9[/tex]

Hence, the series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Answer:

The answer is below

Step-by-step explanation:

We have the following information:

Number of songs you like = 2

Total number of songs = 12

a) P(you like both of them) = 2/12 x 1/11 = 0.015

This is unusual because the probability of the event is less than 0.05

b) P(you like neither of them) = 10/12 x 9/11  = 0.68

c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30

d) If  a song can be replayed before all 12,

P(you like both of them) = 2/12 x 2/12  =0.027

This is unusual because the probability of the event is less than 0.05

P(you like neither of them) = 9/12 x 9/12  = 0.5625

P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25

Answer:

[tex]\chi^2 =\frac{15-1}{25} 16 =8.96[/tex]

The degrees of freedom are given by:

[tex] df = n-1 = 15-1=14[/tex]

The p value for this case would be given by:

[tex]p_v =P(\chi^2 <8.96)=0.166[/tex]

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes

Step-by-step explanation:

Information given

[tex]n=15[/tex] represent the sample size

[tex]\alpha=0.05[/tex] represent the confidence level  

[tex]s^2 =16 [/tex] represent the sample variance

[tex]\sigma^2_0 =25[/tex] represent the value that we want to  verify

System of hypothesis

We want to test if the true deviation for this case is lesss than 5minutes, so the system of hypothesis would be:

Null Hypothesis: [tex]\sigma^2 \geq 25[/tex]

Alternative hypothesis: [tex]\sigma^2 <25[/tex]

The statistic is given by:

[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]

And replacing we got:

[tex]\chi^2 =\frac{15-1}{25} 16 =8.96[/tex]

The degrees of freedom are given by:

[tex] df = n-1 = 15-1=14[/tex]

The p value for this case would be given by:

[tex]p_v =P(\chi^2 <8.96)=0.166[/tex]

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes

Step-by-step explanation:

If all three sides have the same length then it's an equilateral triangle, if two sides are congruent then it's an isosceles triangle, and if there are no sides that have the same length then it's a scalene triangle.

Answer:

Sample Response: First, look at the side lengths a, b, and c, where c is the longest. Then take the sum of a squared and b squared and compare it to c squared. If they are equal, the triangle is a right triangle. If c squared is less than a squared plus b squared, the triangle is acute. If c squared is greater than a squared plus b squared, the triangle is obtuse.

Step-by-step explanation:

booyah

Answer:

270 centimeters

Step-by-step explanation:

A = wl

A = 15 cm x 18 cm

A = 270 centimeters

Step-by-step explanation:

the average change H = Δy/ Δx

so H = ( f(4) - f(2) )/ (4 -2) = ( 0 -1 ) / 2 = -1/2

Answer:

B, C, A

Step-by-step explanation:

If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.

Draw the triangle.

AC (7) is opposite from B

AB (8) is opposite from C

BC (10) is opposite from A

From smallest to largest: 7>8>10

7, 8, 10

or

B, C, A

Answer:

3/20

Step-by-step explanation:

15%

15/100

/5  /5

3/20

Answer:

3×^2+2

The product of three times a number is multiplied with the same product and added with 2.

Answer:

a) k=2.08 1/hour

b) The exponential growth model can be written as:

[tex]P(t)=Ce^{kt}[/tex]

c) 977,435,644 cells

d) 2.033 billions cells per hour.

e) 2.81 hours.

Step-by-step explanation:

We have a model of exponential growth.

We know that the population duplicates every 20 minutes (t=0.33).

The initial population is P(t=0)=58.

The exponential growth model can be written as:

[tex]P(t)=Ce^{kt}[/tex]

For t=0, we have:

[tex]P(0)=Ce^0=C=58[/tex]

If we use the duplication time, we have:

[tex]P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08[/tex]

Then, we have the model as:

[tex]P(t)=58e^{2.08t}[/tex]

The relative growth rate (RGR) is defined, if P is the population and t the time, as:

[tex]RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k[/tex]

In this case, the RGR is k=2.08 1/h.

After 8 hours, we will have:

[tex]P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644[/tex]

The rate of growth can be calculated as dP/dt and is:

[tex]dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)[/tex]

For t=8, the rate of growth is:

[tex]dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140[/tex]

(2.033 billions cells per hour).

We can calculate when the population will reach 20,000 cells as:

[tex]P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81[/tex]

Answer:

c) there is 95% confidence that the population mean number of books read is between 13.77 and 15.83.

Step-by-step explanation:

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=14.8.

The sample size is N=1003.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{16.6}{\sqrt{1003}}=\dfrac{16.6}{31.67}=0.524[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=1003-1=1002[/tex]

The t-value for a 95% confidence interval and 1002 degrees of freedom is t=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.96 \cdot 0.524=1.03[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 14.8-1.03=13.77\\\\UL=M+t \cdot s_M = 14.8+1.03=15.83[/tex]

The 95% confidence interval for the mean number of books read is (13.77, 15.83).

This indicates that there is 95% confidence that the true mean is within 13.77 and 15.83. Also, that if we take multiples samples, it is expected that 95% of the sample means will fall within this interval.

Answer:

Step-by-step explanation:

Since there are  2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.

Probability that at least 1 ball was​ red, given that the first ball was replaced before the second can be calculated as shown;

Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.

Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49

Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49

The probability that at least 1 ball was​ red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49

If the balls were not replaced before the second draw

Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21

Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21

The probability that at least 1 ball was​ red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

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The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.

Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.

That is to say, 3+5 = 8 is greater than the third side which is 7.

Therefore, the set of numbers the would represent a triangle are 3,5,7.

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Answer:

a

Step-by-step explanation:

that is the only thing there

Answer:

1024/59049

Step-by-step explanation:

P( clear hurdle) = 2/3

There are 10 hurdles

P ( clear all hurdles) = P( clear hurdle) * P( clear hurdle)...... 10 times

                                 = 2/3 * 2/3 *....... 10 times

                                  = (2/3) ^ 10

                                  =1024/59049

Answer:

1024/59049, 1.7%

Step-by-step explanation:

One way to do it would to be simply multiply 2/3 by itself 10 times

2/3 x 2/3 x 2/3 x 2/3 and so on

That would be a really long equation so instead we can use exponents to shorten it. We can simply just do 2^10/3^10

2^10=1024

3^10=59049

1024/59049, 1.7%

Answer:

14.  C   41

15. k = 72

Step-by-step explanation:

14.

For parallel lines, alternate exterior angles must be congruent.

3x - 43 = 80

3x = 123

x = 41

15.

The sum of the measures of the angles of a triangle is 180 deg.

k + 33 + 75 = 180

k + 108 = 180

k = 72

Answer:

1. 32

2. 41

3. 72

Step-by-step explanation:

Answer: 35.0 units long.

Step-by-step explanation:

You can treat a rhombus as four right triangles, where there is a short side, a long side, and a hypotenuse.

The hypotenuse of a right triangle inside a rhombus will always be on the exterior.

To find the hypotenuse of one of the right triangles, use the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

We are given that a = 9 and b = 15, but in order to get the values needed for the theorem, we must divide them by 2 in order to get the sides for the triangles.

9 / 2 = 4.5, 15 / 2 = 7.5

Then, you can substitute your values into the Pythagorean theorem:

[tex]4.5^2 + 7.5^2 = c^2\\\\20.25 + 56.25 = 76.5\\\\c^2 = 76.5\\c = 8.7464[/tex]

Knowing that one of the external sides is 8.7464 units long, you can then multiply that value by 4 to get your perimeter, as there are four identical sides forming the perimeter:

8.7464 * 4 = 34.9856. Rounded: 35.0

Answer:

99% confidence interval for the mean of college students

A) 112.48 < μ < 117.52

Step-by-step explanation:

step(i):-

Given sample size 'n' =150

mean of the sample = 115

Standard deviation of the sample = 10

99% confidence interval for the mean of college students are determined by

[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom

ν = n-1 = 150-1 =149

t₁₄₉,₀.₀₁ =  2.8494

99% confidence interval for the mean of college students are determined by

[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]

on calculation , we get

(115 - 2.326 , 115 +2.326 )

(112.67 , 117.326)  

16, think of 4 plus 4 plus 4 plus 4.

Answer:

Step-by-step explanation:

BC/220=sin 60

BC=220 sin 60=220×√3/2=110√3≈190.5 ft

Answer:

190.5 ft

Step-by-step explanation:

For the 60-deg angle, BC is the opposite leg. AB is the hypotenuse.

The trig ratio that relates the opposite leg to the hypotenuse is the sine ratio.

[tex] \sin A = \dfrac{opp}{hyp} [/tex]

[tex] \sin 60^\circ = \dfrac{BC}{220} [/tex]

[tex] BC = 220 \sin 60^\circ [/tex]

[tex] BC = 190.5 [/tex]

Answer:

The probability is 12.66%.

This is a low probability, so it is unlikely for such a combined sample to test positive.

Step-by-step explanation:

If the probability of being infected is 0.005, the probability of not being infected is 0.995.

Then, to find the probability of at least one of the 27 people being infected P(A), we can find the complementary case: all people are not infected: P(A').

[tex]P(A') = 0.995^{27}[/tex]

[tex]P(A') = 0.8734[/tex]

Then we can find P(A) using:

[tex]P(A) + P(A') = 1[/tex]

[tex]P(A) = 1 - 0.8734[/tex]

[tex]P(A) = 0.1266 = 12.66\%[/tex]

This is a low probability, so it is unlikely for such a combined sample to test positive.

Answer:

Option A

Step-by-step explanation:

Equation of the given quadratic function is,

y = 2x² + 8x + 3

y = 2(x² + 4x) + 3

  = 2(x² + 4x + 4 - 4) + 3

  = 2(x + 2)² - 8 + 3

  = 2(x + 2)² - 5

By comparing this equation with the equation of a quadratic function in vertex form,

y = a(x - h)² + k

Here (h, k) is the vertex of the parabola

Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)

Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.

Option (A). Graph A will be the answer.

Answer: The point (-10,-20) becomes (-8,-16) & point (15,25) becomes (12,20).

Step-by-step explanation:

When a point (x,y) is dilated by a scale factor k from the origin, then the new points become

[tex](kx,ky).[/tex]

The given rule of dilation : (x,y) →(0.8x, 0.8y)

The first point is (-10,-20), so its image will be

[tex](-10,-20)\to (0.8\times-10,0.8\times-20)=(-8,-16)[/tex]

So, the point (-10,-20)  becomes (-8,-16).

The second point is (15,25), so its image will be

[tex](15,25)\to (0.8\times15,0.8\times25)=(12,20)[/tex]

So, the point (15,25) becomes (12,20).

Hence, the point (-10,-20) becomes (-8,-16) & point (15,25) becomes (12,20).

Step-by-step explanation:

With the packaging of 8

48 cookies = 48 ÷ 8 = 6 boxes

With the packaging of 24

48 cookies = 48 ÷ 24 = 2 boxes

Answer:

C

Step-by-step explanation:

write an equation for the costs:

if x is the number of sodas

and y is the number of waters

2.75x + 2y <= 15

(<= is less than or equal to)

if we substitute 3 for y

we get 2.75x + 2(3) <= 15

2.75x + 6 <= 15

2.75x <= 9

9 / 2.75 = 3.2727

however, you cannot buy part of a soda

so, round to 3

you also cannot buy negative sodas

so, the answer is C