A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function P(t) = 7bt, where t is the time in weeks after the release and b is a positive unknown base. According to the model, how many fish of the new species were released initially?

Answer:

a) [tex]P(X \leq 3) = 0.99328[/tex]

b) 0.6957

Step-by-step explanation:

Let X represent the number of 4's when  n = 5 independent spins

each has a probability of 0.2 (i.e p = 0.2)

This notation is represented as:

X [tex]\approx[/tex] Binomial (n = 5, p = 0.2)

Probability of  [tex]x[/tex]  number of 4's is:

[tex]P(X=x)= (\left \ n \atop x \right) p^x (1-p)^{(n-x)}[/tex]

here; [tex](\left \ n \atop x \right)[/tex] is the combinatorial expression

[tex](\left \ n \atop x \right)[/tex] = [tex]\frac{n!}{x!(n-x)!}[/tex]

[tex]P(X \leq3), n =5 , p = 0.2[/tex]

[tex]P(X \leq3) = 1-P(X > 3)[/tex]

So; let's first find:

[tex]P(X > 3)[/tex]

[tex]= P(3 <X \leq 5) \\ \\ = P(4 <X \leq 5) \\ \\ = P (X = 4, 5) \\ \\ = P (X=4)+P(X = 5 ) \ \ \ (disjoint \ events)[/tex]

[tex]P(X = 4) =( \left \ {{5} \atop {4}} \right. ) (0.2)^4 (1-0.2)^1 \\ \\ P(X = 4) = 5(0.2)^4(0.8)^1 \\ \\ P(X = 4) = 0.0064[/tex]

[tex]P(X = 5) =( \left \ {{5} \atop {5}} \right. ) (0.2)^5 (1-0.2)^0 \\ \\ P(X = 5) = 5(0.2)^5(0.8)^0 \\ \\ P(X = 5) = 0.00032[/tex]

[tex]P (X=4)+P(X = 5 ) \\ \\ = 0.0064 + 0.00032 = 0.006720 \\ \\ \approx 0.007[/tex]

[tex]P(X > 3 ) = 0.00672 \\ \\ P(X \leq 3) = 1- P(X > = 3 ) \\ \\ =1 - 0.00672 \\ \\ = 0.99328[/tex]

[tex]P(X \leq 3) = 0.99328[/tex]

b)

Given that:

The ratio of boys to girls at birth in  Singapore is quite high at 1.09:1

What proportion of Singapore families with exactly 6 children will have at least 3 boys?

Probability of having a boy = [tex]\frac{1.09}{1+1.09}[/tex] = 0.5215

Binomial Problem with n = 6

P(3<= x <=6) = 1 - P(0<= x <=2)

= 1 - binomial (6,0.5215,2)

= 0.6957

This problem can be solved by Conducting a Chi-square test for independence to explore the relationship between helmet usage and head injuries. We state our null and alternative hypotheses, then we carry out our plan by calculating the observed and expected counts, the test statistic, and the p-value. The conclusion is drawn based on the computed p-value.

The purpose of this analysis is to see if there is a relationship between the use of helmets and head injuries in skiers and snowboarders. In this case, we are dealing with two categorical variables: injury status (injured or not injured) and helmet use (helmet used or not). This falls under the field of statistics in math, specifically, Chi-square test for independence is appropriate here.

Step 1 - STATE: We're comparing the proportion of helmet users among skiers and snowboarders who have head injuries (p1) with the proportion of helmet users among uninjured skiers and snowboarders (p2). The null hypothesis is that the two proportions are equal, i.e., p1 = p2, while the alternative is that they are not equal, i.e., p1 ≠ p2.

Step 2 - PLAN: We are to use a Chi-square test for independence to investigate if helmet use is independent of injury status.

Step 3 - SOLVE: Calculate the observed and expected counts, the test statistic, and the p-value. The observed counts are given in the problem: 96 out of 578 injured subjects used helmets and 656 out of 2992 uninjured subjects used helmets. Expected counts and the test statistic would require a detailed calculation that isn’t shown here.

The conclusion depends on the computed p-value. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that helmet use is less common among skiers and snowboarders who have head injuries. However, bear in mind that correlation does not imply causation, and this is an observational study, not an experiment.

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Answer:

Ella has the greatest return in the current year.

Step-by-step explanation:

Debby would receive $0.80 for each of her 2000 common stock in the oil company,hence Debby's return on investment in the current year is $1600($0.80*2000)

Besides,Ella's return on the stock investment in the current year is computed thus:

Ella's return= 5%*1000*$50=$2,500

In addition,Unique's dollar return on the investment is computed as follows:

Unique's return on  investment=4%*2000*$20=$1,600

From the above computations,Ella seems to have the highest return in the current year of $2,500 whereas the two others managed to have $1600 return each

Answer:

C 32

Step-by-step explanation:

[tex]f(x) = 8 \sqrt{143 - x} \\ f(127) = 8 \sqrt{143 - 127} \\ f(127) = 8 \sqrt{16} \\ f(127) = 8 \times 4 \\ \huge \red{ \boxed{ f(127) = 32}}[/tex]

Answer:

represents the combinations of K and L that cost the firm the same amount of money.

Step-by-step explanation:

Isocost is a graph representing factor inputs ( labour, capital ) ; which costs firm the same level of total production expenditure.

The curve is analogous to consumer's budget line - product combinations costing same to consumers. So, it is likely a straight line downward sloping curve also. Such because : factors are inversely related, given same total cost; and the slope is constant = price ratios of the two factor inputs.

An isocost line represents combinations of capital (K) and labor (L) that cost the same total amount for a firm. Option 2 correctly defines an isocost line. The line's slope is determined by the prices of labor and capital.

An Isocost Line in Economics

An isocost line is a graphical representation in economics that shows all the combinations of inputs that cost a firm the same total amount. When referring to factors of production such as capital (K) and labor (L), the isocost line equation could be expressed as rK + wL = constant, where 'r' represents the cost of capital and 'w' represents the wage or cost of labor. If we are looking at the firm's input choices to minimize cost for a given level of output, the isocost line will have a negative slope that represents the trade-off between the quantities of capital and labor the firm can use subject to its budget constraint.

The correct option to describe an isocost line from the given choices would be 2) represents the combinations of K and L that cost the firm the same amount of money. This means that all input combinations lying on the same isocost line have the same total cost (TC). Also, the slope of the isocost line is determined by the ratio of the prices of the factors, i.e., -w/r.

In economic analysis, firms are often visualized as combining inputs of labor and capital in the most cost-efficient manner to produce a certain level of output, as shown by the isoquant curves. By finding the point where an isocost line is just tangent to an isoquant, a firm achieves the least-cost combination of labor and capital for producing the given quantity of output.

Answer:

a=-2

Step-by-step explanation:

Let me know if you need the steps tho.

Answer:

The correct option is (d).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two means with same sample size is:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm CV\times SD\times \sqrt{\frac{2}{n}}[/tex]

The width of the interval is:

[tex]\text{Width}=2\times CV\times SD\times \sqrt{\frac{2}{n}}[/tex]

From the formula of the width of the confidence interval it can be seen that the sample size is inversely related to the width.

That is, if the sample size is increased the width of the interval will be decreased and if the sample size is decreased the width of the interval will be increased.

It is provided that two confidence intervals are constructed for the difference between the means of two populations R and J.

One One confidence interval, will be constructed using samples of size 400 from each of R and J.

And the other confidence interval, will be constructed using samples of size 100 from each of R and J.

Determine the formula of width for both sample sizes as follows:

[tex]\text{Width}_{1}=2\times CV\times SD\times \sqrt{\frac{2}{400}}\\[/tex]

           [tex]=2\times CV\times SD\times \frac{\sqrt{2}}{20}[/tex]

[tex]\text{Width}_{2}=2\times CV\times SD\times \sqrt{\frac{2}{100}}\\[/tex]

           [tex]=2\times CV\times SD\times \frac{\sqrt{2}}{10}[/tex]

So, the width of I₄₀₀ is half times the width of I₁₀₀.

The correct option is (d).

Answer:

D

Step-by-step explanation:

I got 18/18

Answer:

Would ypu plz show us the number line so at least i could answer the question

Answer:

  7/15

Step-by-step explanation:

We assume you want xy+x. Put the numbers where the variables are and do the arithmetic.

  (1/3)(2/5) +(1/3) = 2/15 + 5/15 = 7/15

Answer:

exactly I need help with this one to

The number of 2-point shots and the number of 3-point shots if, The basketball team scored a total of 79 points last game, They made 35 shots, including 2-point shots and 3-point shots, are 26 and 9 respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

The basketball team scored a total of 79 points last game,

They made 35 shots, including 2-point shots and 3-point shots,

Write the equation as shown below,

x + y = 35

2x + 3y = 79

Here, x  is the number of 2-point shots and y is the number of 3-point shots,

Solve the equation by elimination method,

y = 9, x = 35 - 9 = 26

Thus, the number of 2-point shots is 26  and the number of 3-point shots is 9.

To know more about equation:

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The number of permutations of 3 objects taken 2 at a time without repetition is 3. The permutations are ml, mn, lm, ln, nm, nl.

The number of permutations of three objects taken two at a time without repetition is given by the formula 3P2 = 3!/(3-2)! = 3!/1! = 3.

The permutations of three objects (m, l, and n) taken two at a time without repetition are:

Answer:

The mean number of points she scored per game was 8.

Step-by-step explanation:

The mean number of points scored per game is the sum of total points scored divided by the number of games played:

Her point total for each game were 8,14,4,7,6,14,4 and 7.

This means that there were 8 total games.

She scored 8+14+4+7+6+14+4+7 = 64 total points

64/8 = 8

The mean number of points she scored per game was 8.

Without additional information, it's not possible to calculate the exact probability that Artemisia's conclusion is correct using conditional probability and Bayes' theorem.

To calculate the probability that Artemisia's conclusion about her new phone number being correct, we need to use the concept of conditional probability. Since she is 50% sure that the number is correct, and given the probability of any seven-digit phone number being busy is 1%, we need to consider both pieces of information. We can use Bayes' theorem to update the probability of Artemisia's belief in light of the new evidence (getting a busy signal).

However, we need additional information to accurately calculate this. Specifically, we would need to know the probability that Artemisia would get a busy signal if the number was incorrect. Without this information, we cannot provide a definitive answer to the student's question.

Answer:

a) The mean number is 745 and the standard deviation is 25.18.

b) 896 deaths is a significantly high number, which means that there is cause for concern.

Step-by-step explanation:

For each death, there are only two possible outcomes. Either it is attributable to myocardial infarctions, or it is not. The probability of a death being attributable to myocardial infarctions is independent of other deaths. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

A value X is significantly high is:

[tex]X > E(X) + 2\sqrt{V(X)}[/tex]

In this problem:

[tex]p = 0.149, n = 5000[/tex]

a. Find the mean and standard deviation for the number of such deaths that will occur in typical region with 5000 deaths.

[tex]E(X) = np = 5000*0.149 = 745[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{5000*0.149*0.851} = 25.18[/tex]

The mean number is 745 and the standard deviation is 25.18.

b. In one region, 5000 death certificates are examined, and it is found that 896 deaths were attributable to myocardial infarction. Is there cause for concern? Why or why not?

Is 896 a significantly high number?

[tex]E(X) + 2\sqrt{V(X)} = 745 + 2*25.18 = 795.36[/tex]

895 > 795.36

896 deaths is a significantly high number, which means that there is cause for concern.

Answer:

For  values

Hence the Dr.Clifford Jones claim is wrong about the bats mean weight

Step-by-step explanation:

Given:

Mean=1.659 grams

Standard deviation: 0.264

No of samples=200

To find :

Confidence intervals at

1)99.9% 2)99%  3)95% 4)80% and

Whether the Dr. Clifford with 1.7 mean weight is less or not?

Solution:

We know  interval estimation is given by ,

E=mean±Z value*{standard deviation/Sqrt(N)}

Now For Z value 99.9% =3.291

E=1.659±3.291{0.264/Sqrt(200)}

=1.659±0.0614

i.e.C.I.[1.6 to 1.72]

Now for Z value 99 % =2.576

E=1.659±2.576{0.264/Sqrt(200)}

=1.659±0.0481

i.e. C.I[1.61,1.71]

Now for Z value at 95% =1.96

E=1.659±1.96*(0.264/sqrt(200))

=1.659±0.0366

i.e. C.I.[1.62,1.7]

Now ofr Z value at 80% =1.28

E=1.659±1.28*(0.264/sqrt(20))

=1.659±0.0239

i.e. C.I.[1.64,1.68]

Using t distribution as ,

value for mean =1.7

raw i.p=1.659

Degree of freedom =N-1=200-1=199

Hence

t-score is similar to zscore

T-score =(Raw input -mean)/(standard deviation/Sqrt(n))

=(-1.7+1.659)/(0.264/Sqrt(200))

=-2.19721

Consider 1 tailed ,

p value =P(Z≤-2.19721)

=0.0143

i.e  P value is 0.0143

Hence The result is not significant at p<0.01

To find the confidence interval for the mean weight of all bumblebee bats, use the formula: Confidence Interval = Xbar ± (Z-Value) * (Standard Deviation / sqrt(n)). To test whether bumblebee bats weigh less on average than Dr. Clifford Jones claims, use the t-distribution technique.

To find the confidence interval for the mean weight of all bumblebee bats, we will use the formula:

Confidence Interval = Xbar ± (Z-Value) * (Standard Deviation / sqrt(n))

where Xbar is the sample mean, Z-Value is the critical value from the standard normal distribution table, Standard Deviation is the population standard deviation, and n is the sample size.

(a) For a 99.9% confidence interval, the Z-value corresponding to a 99.9% confidence level is 3.291. Using the given values, the confidence interval can be calculated as follows:

Confidence Interval = 1.659 ± (3.291) * (0.264 / sqrt(200)) = 1.659 ± 0.1153

So the 99.9% confidence interval for the mean weight of all bumblebee bats is (1.543, 1.774).

(b) For a 99% confidence interval, the Z-value corresponding to a 99% confidence level is 2.576. Using the given values, the confidence interval can be calculated as follows:

Confidence Interval = 1.659 ± (2.576) * (0.264 / sqrt(200)) = 1.659 ± 0.0942

So the 99% confidence interval for the mean weight of all bumblebee bats is (1.565, 1.753).

(c) For a 95% confidence interval, the Z-value corresponding to a 95% confidence level is 1.96. Using the given values, the confidence interval can be calculated as follows:

Confidence Interval = 1.659 ± (1.96) * (0.264 / sqrt(200)) = 1.659 ± 0.0734

So the 95% confidence interval for the mean weight of all bumblebee bats is (1.586, 1.732).

(d) For an 80% confidence interval, the Z-value corresponding to an 80% confidence level is 1.282. Using the given values, the confidence interval can be calculated as follows:

Confidence Interval = 1.659 ± (1.282) * (0.264 / sqrt(200)) = 1.659 ± 0.0547

So the 80% confidence interval for the mean weight of all bumblebee bats is (1.604, 1.714).

2) To test whether bumblebee bats weigh less on average than Dr. Clifford Jones claims, we will use the t-distribution technique. We will set up the following hypotheses:

Null hypothesis (H0): The mean weight of bumblebee bats is equal to 1.7 grams.

Alternative hypothesis (Ha): The mean weight of bumblebee bats is less than 1.7 grams.

We will use a one-tailed test since we are only interested in whether the bats weigh less on average. Calculate the test statistic t using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(n))

where the sample mean is 1.659 grams, the hypothesized mean is 1.7 grams, the sample standard deviation is 0.264 grams, and the sample size is 200. Using these values, the test statistic can be calculated as follows:

t = (1.659 - 1.7) / (0.264 / sqrt(200)) = -2.524

Using a t-table or calculator, we can find the critical value for a one-tailed test with a significance level of 0.05 and 199 degrees of freedom to be approximately -1.652.

Since the test statistic t is less than the critical value, we reject the null hypothesis. Therefore, there is evidence to suggest that bumblebee bats weigh less on average than Dr. Clifford Jones claims at a significance level of 0.05.

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Answer: y=3x

Step-by-step explanation:

Answer:

–3x + y = 0

Step-by-step explanation:

line through (0,0) always has zero constant, divide by 8 for simplicity we get –3x + y = 0

Answer:

true

Step-by-step explanation:

An object can never act on itself. Forces related to Newton's third law apply to different bodies, therefore they cannot cancel each other out. For example, the reaction to Earth's gravitational pull on the Moon is the Moon's pull on Earth.

Answer:

The answer will be 1/12 of

Step-by-step explanation:

Answer:

The optimal capital structure of a firm is the best mix of debt and equity financing that maximizes a company’s market value while minimizing its cost of capital. In theory, debt financing offers the lowest cost of capital due to its tax deductibility. However, too much debt increases the financial risk to shareholders and the return on equity that they require. Thus, companies have to find the optimal point at which the marginal benefit of debt equals the marginal cost.

Step-by-step explanation:

Answer:

[tex](C)\dfrac{9+\sqrt{14} }{9+\sqrt{14} }[/tex]

Step-by-step explanation:

To rationalize the expression:

[tex]\dfrac{5-\sqrt{7} }{9-\sqrt{14} }[/tex]

In order to rationalize any Surdic expression, what is needed is to multiply both the numerator and the denominator of the rational function by the conjugate of the denominator.

In the example above:

The denominator is: [tex]9-\sqrt{14}[/tex]

Its conjugate therefore is: [tex]9+\sqrt{14}[/tex]

Therefore, we multiply the fraction by the expression:

[tex]\dfrac{9+\sqrt{14} }{9+\sqrt{14} }[/tex]

Answer:

c

Step-by-step explanation:

Answer:

  1/343

Step-by-step explanation:

  [tex]\dfrac{7^{-1}}{7^2}=7^{-1-2}=7^{-3}=\dfrac{1}{7^3}=\boxed{\dfrac{1}{343}}[/tex]

__

The applicable rules of exponents are ...

  (a^b)/(a^c) = a^(b-c)

  a^-b = 1/a^b

Answer:

a

Step-by-step explanation:

Answer:

V = 3 * (70 + 230) / 2

V = 450 m^3

Step-by-step explanation:

Based on the two measured rates, and assuming that the rate of increase was uniform, the volume would be the average, hourly volumetric flow rate, multiplied by number of hours, or

Answer:

6.5 bottles

Step-by-step explanation:

convert liters to ml 1 bottle= 1000ml

divide how much she drank by 1000ml

6500÷1000=6.5

The number of sides of a polygon can be determined from the total interior angle or each exterior angle. The interior angle measures of a regular polygon can be used to find unknown quantities. The sum of the interior angles in an 11-gon is 1620° regardless of whether it is regular or irregular.

a. The sum of the interior angles of a polygon is given by the formula (n-2) * 180°, where n is the number of sides. To find the number of sides, you rearrange the formula to n = (sum of angles/180) + 2. For 1980°, n = (1980/180) + 2 = 13. For 900°, n = (900/180) + 2 = 7.

b. The sum of the exterior angles of any polygon is always 360°. If each exterior angle is 90°, divide 360 by 90 to get 4. This polygon has 4 sides, so it's a square.

c. In a regular pentagon, each interior angle is 108°. So, if 2x + 4 = 108°, solve for x to find x = 52°.

d. The sum of the exterior angles of a polygon is also 360°. If four of them are 57, 74, 56, and 66, add these up and subtract from 360 to find the remaining angle. It's 107°.

e. The sum of the interior angles of an 11-gon (n = 11) is (11-2) * 180 = 1620°. This is the same whether the polygon is regular or not.

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Answer:

a. 113.72

b. 115

c. 107, 120

d. 100

Step-by-step explanation:

Hypothesis is seen as an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true. In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review.

Sampling distribition can be seen as the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.

Please go to attachment for the detailed analysis.

Answer:

20m squared

Step-by-step explanation:

The formula for working the area os a triangle is

base x height/2

5x8=40

40/2= 20

hope it helps

Answer:

The hawk drops the prey from a height of 4 meters.

The prey reaches the ground 4 seconds after.

Step-by-step explanation:

Notice that the equation gives you information about the height of the prey at any time counting from the moment the hawk drops it. Therefore, if we want to find the height at which the hawk drops the prey, we just need to evaluate the expression for time = zero (the starting time). SUch gives as the answer to the first question:

[tex]h=4+11t-3t^2\\h=4+11\,(0)-3\,(0)^2\\h=4\, \,meters[/tex]

Now, in order to find the time at which the prey reaches the ground, we want "h" to be zero (height zero), and solve for "t".

Notice that this gives a quadratic equation that can be solved using the quadratic formula:

[tex]h=4+11t-3t^2\\0=4+11t-3t^2\\-3t^2+11t+4=0\\t=\frac{-11+-\sqrt{11^2-4\,(-3)(4)} }{2\,(-3)} \\t=\frac{-11+-\sqrt{121+48} }{-6} \\t=\frac{-11+-13 }{-6} \\t= 4\,\,and \,\, t=-\frac{1}{3}[/tex]

Since negative times will not make sense, we select the positive 4 (4 seconds)