MATHEMATICS COLLEGE

Before 1918, approximately 40% of the wolves in a region were male, and 60% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 60% of wolves in the region are male, and 40% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.) (a) Before 1918, in a random sample of 10 wolves spotted in the region, what is the probability that 7 or more were male

Answers

Answer 1

Answer:

P(≥ 7 males) = 0.0548

Step-by-step explanation:

This is a binomial probability distribution problem.

We are told that Before 1918;

P(male) = 40% = 0.4

P(female) = 60% = 0.6

n = 10

Thus;probability that 7 or more were male is;

P(≥ 7 males) = P(7) + P(8) + P(9) + P(10)

Now, binomial probability formula is;

P(x) = [n!/((n - x)! × x!)] × p^(x) × q^(n - x)

Now, p = 0.4 and q = 0.6.

Also, n = 10

Thus;

P(7) = [10!/((10 - 7)! × 7!)] × 0.4^(7) × 0.6^(10 - 7)

P(7) = 0.0425

P(8) = [10!/((10 - 8)! × 8!)] × 0.4^(8) × 0.6^(10 - 8)

P(8) = 0.0106

P(9) = [10!/((10 - 9)! × 9!)] × 0.4^(9) × 0.6^(10 - 9)

P(9) = 0.0016

P(10) = [10!/((10 - 10)! × 10!)] × 0.4^(10) × 0.6^(10 - 10)

P(10) = 0.0001

Thus;

P(≥ 7 males) = 0.0425 + 0.0106 + 0.0016 + 0.0001 = 0.0548

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The graph of the function f(x) = x^2 will be translated 3 units up and 1 unit left. What is the resulting function g(x)?

(12pts) Inequalities please help me !?

Answers

The correct answer would be C, or x > -2.

Because the line is going up from -2, we know that x is going to be greater than 2 for a fact.

We can tell that it wont be greater than or equal to because the circle is clear and not filled.

Thus, C is the correct answer.

A bacteria culture is initially 10 grams at t=0 hours and grows at a rate proportional to its size. After an hour the bacteria culture weighs 11 grams. At what time will the bacteria have tripled in size?

Answers

A bacteria culture is initially 10 grams at t=0 hours & grows at a rate proportional to its size , After an hour the bacteria culture weighs 11 grams , The bacteria takes 11.56 hours to have tripled in size.

To find the time of bacteria when increasing the growth to tripled.

Given : when time=0 hours , weight=10 grams.

when time=1 hours , weight=11 grams.

To find: when time= ? hours , weight=30grams.

Here according to question, initial size = 10 grams we have asked for tripled in size i.e. 30 grams.

Now we knows that,

The formula for exponential growth in population or size is

$\rm (P)=P_0e^(rt)$ where,

$\rm P_0=initial\;size\n\nr= rate\;of\;growth\n\nt= time \;period$

Now, we put the value in formula we get,

$\rm P_0=10\;grams \n\nwhen ,\n\;\;t=1\;hour P(t)=11 grams\nThen,\n11=10e^{r(1)\n1.1 =e^r\n\n\rm Taking \;log(natural)\;both\;the\; side \;on \;solving\;we\;get,\nln(1.1)=r\;ln(e)\nr=ln(1.1)\nr=0.953101798043\approx0.095$

Now when the bacteria increase its size to triple

$\rm P(t) = 3 * 10 = 30$

Then, according to the formula we substitute values in the formula,

$\rm 30=10e^(0.095t)\n\n3=e^(0.095t)\n\nAgain \;we \;take\;natural\;log\;on \;both\;the\;sides, we\;get\nln\;3=0.095t\n\nt=(\rm ln\;3)/(0.095)\n\n\n\n\rm t= (1.09861228867)/(0.095) \n\n\ t=approx \; 11.56$

Therefore, The bacteria takes 11.56 hours to have tripled in size.

Learn more about logical questions here : brainly.com/question/15046576

Answer: It will take 11.56 hours .

Step-by-step explanation:

Exponential growth in population or size formula :

$P(t)=P_0e^(rt)$

, where $P_0$ = initial size

r= rate of growth

t= time period

As per given , we have

$P_0=10$ grams

At t= 1 , P(t)= 11 grams

Then,

$11=10e^(r(1))\n\n 1.1= e^r\n\n\text{Taking natural log on both sides , we get} \n\n\ln (1.1)=r\ln (e)\n\n r=\ln (1.1)\n\n r=0.0953101798043\approx0.095$

When, the bacteria have tripled in size , P(t) = 3 x10 = 30

Then,

$30=10e^(0.095t)\n\n 3=e^(0.095t)$

$\text{Taking natural log on both sides , we get}\n\n \ln 3=0.095t\n\n t=(\ln3)/(0.095)\n\n t=(1.09861228867)/(0.095)\approx11.56$

Hence, it will take 11.56 hours .

Apply the Distributive Property 5(x + 3)

Answers

Answer: 5x + 15

Step-by-step explanation: The distributive property tells us that if we're given an expression such as 5(x + 3), we can multiply the 5 by both the x and the 3 to get 5x + 15.

Answer:

5x+15

Step-by-step explanation:

5*x+5*3

What is the sum of prime numbers between 40 and 56

Answers

Answer:

184

Step-by-step explanation:

The prime numbers between 40 and 56 are 41, 43, 47, and 53.

Add the prime numbers.

41 + 43 + 47 + 53

= 184

Answer:

184

Step-by-step explanation:

Prime numbers between 40 and 56: 41, 43, 47, 53.

41+43+47+53=

84+47+53=

131+53=

184

A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices - a, b, c, d, e- and only one correct answer. What is the probability that she answered neither of the problems correctly? Do not round your answer. (If necessary, consult a list of formulas.)

Answers

Answer:

there is a 64% chance that the student got both problems wrong

a 32% chance that they got only 1 correct

and a 4% chance that they got both correct

Step-by-step explanation:

There are 25 total possible combinations of answers, with 8 possible combinations where the student would get 1 answer right, and 1 combination where the student would get both answers correct.

$25-9=16$

$(16)/(25) =(x)/(100)$

$(64)/(100)$

$64$ %

$(8)/(25) =(y)/(100)$

$(32)/(100)$

$32$ %

$(1)/(25) =(z)/(100)$

$(4)/(100)$

$4$ %

If EN=16 and BN=20 what is the scale factor of the dilation?

Answers

The scale factor of the dilation is approximately 1.25.

To find the scale factor of the dilation, we need to compare the corresponding side lengths of the original figure and the dilated figure.

Let's consider the two corresponding side lengths:

Original side: EN = 16 units

Dilated side: BN = 20 units

The scale factor (k) of the dilation is the ratio of the corresponding side lengths in the dilated figure to the original figure. It can be calculated using the formula:

Scale factor (k) = Dilated side length / Original side length

Substituting the given values:

k = 20 / 16 ≈ 1.25

for such more question on scale factor

brainly.com/question/22973053

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