absolute magnitude of a star that has a period of 50 days

Answer:

O Confirm, because the p-value is much smaller.

Step-by-step explanation:

The p-value is the probability used to determine whether to accept or reject an null hypothesis. Higher p-value means that there is evidence in favour of the null hypothesis while smaller p-value means that there is stronger evidence in favour of the alternative hypothesis. For the case above, the p-value is smaller which means that the new study confirms the results of the first study which also have a small p-value.

Final answer:

To find the population of a town after 12 years with an initial population of 17,000 and an annual growth rate of 4%, use the exponential growth formula. After the calculations, the town's estimated future population would be around 26,533 residents.

Explanation:

To calculate the future population of a town that currently has 17,000 residents and grows at a rate of 4% per year, we can use the formula for exponential growth: future population = current population ×  [tex](1 + growth \ rate)^n,[/tex] where n is the number of years the population is growing. In this case, the formula becomes  [tex]17000 \times (1 + 0.04)^n[/tex], because we're looking to find the population after 12 years.

Calculating this, we have: future population =  [tex]17,000 \times (1.04)^{12}[/tex]. Using a calculator, we get approximately 26,533, meaning after 12 years, the population of the town is expected to be around 26,533 residents.

Answer:

Q2

a) total sweets: 5 + 3 = 8

i) P(red) = 5/8

ii) P(yellow) = 3/8

b) for the second one:

4 red and 3 yellow left

i) P(red) = 4/7

ii) P(yellow) = 3/7

c) for the second one:

5 red and 2 yellow left

i) P(red) = 5/7

ii) P(yellow) = 2/7

Q3

a) total probability is 1

⅙ + ¼ + ⅓ + x = 1

x = 1 - (⅙ + ¼ + ⅓)

x = ¼

b) most likely is the color with highest probability, which is green

c) P(not red) = 1 - P(red)

= 1 - ⅙ = ⅚

Answer:

The percentage of ounces Leah has left of her coffee is 68.18%.

Step-by-step explanation:

The decrease percentage is computed using the formula:

[tex]\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100[/tex]

It is provided that Leah originally had 22 ounce coffee.

Then she drinks 7 ounces of coffee.

Decrease = 7 ounces

Original = 22 ounces

Compute the percentage of ounces Leah has left of her coffee as follows:

[tex]\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100[/tex]

                 [tex]=\frac{22-7}{22}\times 100\\\\=\frac{15}{22}\times 100\\\\=68.1818182\%\\\\\approx 68.18\%[/tex]

Thus, the percentage of ounces Leah has left of her coffee is 68.18%.

Given:

It is given that the function represents the data in the table.

We need to determine the function.

Slope:

The slope can be determined using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let us substitute the coordinates (1,6.5) and (4,8) in the above formula, we get;

[tex]m=\frac{8-6.5}{4-1}[/tex]

[tex]m=\frac{1.5}{3}[/tex]

[tex]m=0.5[/tex]

Thus, the slope is 0.5

y - intercept:

The y - intercept is the value of y when x = 0.

Thus, from the table, when x = 0 the corresponding y value is 6.

Therefore, the y - intercept is [tex]b=6[/tex]

Equation of the function:

The equation of the function can be determined using the formula,

[tex]y=mx+b[/tex]

Substituting the values [tex]m=0.5[/tex] and [tex]b=6[/tex], we get;

[tex]y=0.5x+6[/tex]

Thus, the equation of the function is [tex]y=0.5x+6[/tex]

Hence, Option C is the correct answer.

Answer:

5

Step-by-step explanation:

20+20=40

50-40=10

10/2=5

To check our work we find the perimeter with our new width. 20+20+5+5=50

So we are right!!!

You solve this question by finding the maximum possible number of different combinations, then adding one extra person.

3 possible shirts * 2 possible pants for each shirt = 6 combinations of pants and shirts.

6 + 1 = 7

Therefore, the minimum is:

7 People

Answer:

[tex]a.\ \mu_p=750\ \ , \sigma_p=0.005\\\\b.\ \mu_p=150\ \ , \sigma_p=0.0113\\\\c.\ \mu_p=75\ \ , \sigma_p=0.0160[/tex]

Step-by-step explanation:

a. Given p=0.15.

-The mean of a sampling proportion  of n=5000 is calculated as:

[tex]\mu_p=np\\\\=0.15\times 5000\\\\=750[/tex]

-The standard deviation is calculated using the formula:

[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\=\sqrt{\frac{0.15(1-0.15)}{5000}}\\\\=0.0050[/tex]

Hence, the sample mean is μ=750 and standard deviation is σ=0.0050

b. Given that p=0.15 and n=1000

#The mean of a sampling proportion  of n=1000 is calculated as:

[tex]\mu_p=np\\\\=1000\times 0.15\\\\\\=150[/tex]

#-The standard deviation is calculated as follows:

[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{1000}}\\\\\\=0.0113[/tex]

Hence, the sample mean is μ=150 and standard deviation is σ=0.0113

c. For p=0.15 and n=500

#The mean is calculated as follows:

[tex]\mu_p=np\\\\\\=0.15\times 500\\\\=75[/tex]

#The standard deviation of the sample proportion is calculated as:

[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{500}}\\\\\\=0.0160[/tex]

Hence, the sample mean is μ=75 and standard deviation is σ=0.0160

Answer:

y=10

Step-by-step explanation:

(y-10)^2=0

Take the square root of each side

sqrt((y-10)^2)=sqrt(0)

y-10 =0

Add 10 to each side

y-10+10=0+10

y = 10

Final answer:

The Central Limit Theorem explains the sampling distribution of the sample mean. We calculate probabilities using z-scores in the normal distribution for different scenarios. Understanding the concepts of sampling distributions and z-scores is essential for handling such questions in statistics.

Explanation:

The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the population distribution.

(a) The mean of the sampling distribution of x  equals the population mean, which is 74, and the standard deviation of the sampling distribution σ/√n equals 6/√36 = 1.

(b) To find Upper P(x > 75.9), we standardize the value: z = (75.9 - 74) / 1 = 1.9. Consulting a z-table, we find P(z > 1.9) ≈ 0.0287.

(c) For Upper P(x< 71.95), we standardize: z = (71.95 - 74) / 1 = -2.05. From the z-table, P(z < -2.05) ≈ 0.0202.

(d) To find Upper P(73 < x < 75.75), we standardize both values, giving z(73) = (73 - 74) / 1 = -1 and z(75.75) = (75.75 - 74) / 1 = 1.75. Then, P(-1 < z < 1.75) = P(z < 1.75) - P(z < -1) ≈ 0.9599 - 0.1587 = 0.8012.

Answer:

a) [tex]654.16-2.01\frac{164.55}{\sqrt{52}}=608.29[/tex]    

[tex]654.16+2.01\frac{164.55}{\sqrt{52}}=700.03[/tex]    

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

b) [tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]

Step-by-step explanation:

Part a

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=52-1=51[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,51)".And we see that [tex]t_{\alpha/2}=2.01[/tex]

Replacing we got:

[tex]654.16-2.01\frac{164.55}{\sqrt{52}}=608.29[/tex]    

[tex]654.16+2.01\frac{164.55}{\sqrt{52}}=700.03[/tex]    

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

Part b

The margin of error is given by :

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

The desired margin of error is ME =50/2=25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex]   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got [tex]z_{\alpha/2}=1.960[/tex], and we use an estimator of the population variance the value of 175 replacing into formula (b) we got:

[tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]

Answer:

95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].

Step-by-step explanation:

We are given that 15% of a random sample of 300 U.S. public high school students were obese.

Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;

                        P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample % of U.S. public high school students who were obese = 15%

           n = sample of U.S. public high school students = 300

           p = population percentage of all U.S. public high school students

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                             of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

95% confidence interval for p = [[tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]

  = [ [tex]0.15-1.96 \times {\sqrt{\frac{0.15(1-0.15)}{300} } }[/tex] , [tex]0.15+1.96 \times {\sqrt{\frac{0.15(1-0.15)}{300} } }[/tex] ]

  = [0.110 , 0.190]

Therefore, 95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].

The correct answer is option (c). The approximate 95% confidence interval is [tex]\[0.1108 \text{ to } 0.1892\][/tex]

To determine the approximate 95% confidence interval for the percentage of all U.S. public high school students who are obese, we'll use the standard error provided and the normal model.

The formula for the confidence interval is:

[tex]\[\hat{p} \pm Z \cdot \text{SE}\][/tex]

Now, we calculate the margin of error:

[tex]\[\text{Margin of Error} = Z \cdot \text{SE} = 1.96 \cdot 0.020 = 0.0392\][/tex]

Then, we determine the confidence interval by adding and subtracting the margin of error from the sample proportion:

[tex]\[\hat{p} - \text{Margin of Error} = 0.15 - 0.0392 = 0.1108\][/tex]

[tex]\[\hat{p} + \text{Margin of Error} = 0.15 + 0.0392 = 0.1892\][/tex]

Therefore, the approximate 95% confidence interval is:

[tex]\[0.1108 \text{ to } 0.1892\][/tex]

Answer:

76 inches

Step-by-step explanation:

It should be understood that 15.2cm is equal to 5 inches.

Since the height = 5 * size of the foot

= 5 * 15.2 = 76

Therefore, a person with 15.2cm as the size of the foot will have the height of 76 inches.

Using the regression model produced by the technology output. The best predicted value for the person's height would be 123.288 cm.

Using the Regression equation produced by the technology used :

For a foot length of 15.2 cm :

The predicted height value can be calculated by substituting the foot length value into the equation thus :

Height = 52.0 + 4.69(15.2)

Height = 52.0 + 71.288

Height = 123.288 cm

The best predicted value for the person's height would be 123.288 cm.

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Answer:

6.575 trillion BTUs

Step-by-step explanation:

Let represent the annual energy consumption of the town as E

The rate of annual energy consumption *  energy consumption at time past

dE/dt * E

dE/dt =K

k = the proportionality constant

c= the integration constant

(dE/dt=) kdt

lnE = kt + c

E(t) = e^kt+c ⇒ e^c e^kt  e^c is a constant, and e^c = E₀

E(t) = E₀ e^kt

The initial consumption of energy is E(0)=4.4TBTU

set t = 0 then

4.4 = E₀ e⇒ E₀ (1)

E₀ = 4.4

E (t) = 4.4e^kt

The consumption after 5 years is t = 5, e(5) = 5.5TBTU

so,

E(5) = 5.5 = 4.4e^k(5)

e^5k = 5/4

We now take the log 5kln = ln(5/4)

5k(1) = ln(5/4)

k = 1/5 ln(5/4) = 0.04463

We find  the town's annual energy consumption, after 9 years

we set t=9  

E(9) = 4.4e^0.04463(9)

= 4.4(1.494301) = 6.5749TBTUs

Therefore the annual energy consumption of the town after 9 years is

= 6.575 trillion BTUs

9514 1404 393

Answer:

  81m^4·n^4

Step-by-step explanation:

"Simplify" in this context means "remove parentheses." The applicable rule of exponents is ...

  (ab)^c = (a^c)(b^c)

__

  [tex](3mn)^4=3^4m^4n^4=\boxed{81m^4n^4}[/tex]

Find the attachment for complete solution

Answer:

A)sample proportion = 0.17,  the sampling distribution of p can be calculated/approximated with normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281

B) 0.869

C)0.9668

Step-by-step explanation:

A) p ( proportion of population that spends more than $100 per week) = 0.17

sample size (n)= 800

the sample proportion of p = 0.17

standard error of p = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex] = 0.013281

the sampling distribution of p can be calculated/approximated with

normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281

B) probability that the sample proportion will be +-0.02 of the population proportion

= p (0.17 - 0.02 ≤ P ≤ 0.17 + 0.02 ) = p( 0.15 ≤ P ≤ 0.19)

z value corresponding to P

Z = [tex]\frac{P - p}{standard deviation}[/tex]

at P = 0.15

Z =  (0.15 - 0.17) / 0.013281 = = -1.51

at P = 0.19

z = ( 0.19 - 0.17) / 0.013281 = 1.51

therefore the required probability will be

p( -1.5 ≤ z ≤ 1.5 ) = p(z ≤ 1.51 ) - p(z ≤ -1.51 )

                           = 0.9345 - 0.0655 = 0.869

C) for a sample (n ) = 1600

standard deviation/ error = 0.009391 (applying the equation for calculating standard error as seen in part A above)

therefore the required probability after applying

z = [tex]\frac{P-p}{standard deviation}[/tex] at p = 0.15 and p = 0.19

p ( -2.13 ≤ z ≤ 2.13 ) = p( z ≤ 2.13 ) - p( z ≤ -2.13 )

                               = 0.9834 - 0.0166 = 0.9668

The sampling distribution of the sample proportion can be approximated by a normal distribution. The probability of the sample proportion being within a certain range can be calculated using z-scores.

a. The sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries, can be approximated by a normal distribution with a mean of p and a standard deviation of √[(p(1-p))/n], where p is the population proportion and n is the sample size.

b. To find the probability that the sample proportion will be within ±0.02 of the population proportion, we calculate the z-scores for both values and find the area under the normal curve between those z-scores.

c. The probability of the sample proportion being within ±0.02 of the population proportion will remain the same for a sample of 1600 households, as long as the population proportion remains the same.

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Answer:

A C(x) =2x³+2x²-18x-11

Step-by-step explanation:

C(x) = W(x) - D(x)

plug W(x) and D(x) into equation

C(x) = 3x³+4x²-18x+4 - (x³+2x²+15)

add like terms now

C(x) =2x³+2x²-18x-11

Answer:

B

Step-by-step explanation:

choose brainliest

This is a composite function problem in high school mathematics. To solve the problem, first evaluate g(-4), then substitute that result into the function f(x). Using these steps, the composite function f(g(-4)) equals -114.

First, it is crucial to identify that this is a question involving composite functions, specifically applying the function f(g(x)). In this case, the function g(x) is not provided in the question, so I'll assume we have a typo. If g(x) has been given as 3x + 1, then g(-4) would equal -11. We substitute -11 into the function f(x)=10x-4, we get f(-11)=10*(-11)-4, which results in f(-11)=-114.

The composite function f(g(-4)) is thus -114.

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Answer:

There u go

Step-by-step explanation:

(-x+3x+3)×x=2x^2+3x

2x^2+3x=x(2x+3)

The sum of the functions f(x) = -x and g(x) = 3x + 3 is computed as (f+g)(x) = f(x) + g(x), which simplifies to 2x + 3. This denotes a polynomial in simplest form.

The question is asking to compute the sum of two functions, f(x) = -x and g(x) = 3x+3 and to express it as a polynomial or a rational function in simplest form.

The sum of the two functions can be computed by adding together the outputs of the individual functions. In mathematical bricolage, this is known as function addition. The function sum (f+g)(x) can be calculated as f(x) + g(x).

If f(x) = -x and g(x) = 3x + 3, then (f+g)(x) can be calculated as follows:

(-x) + (3x + 3) = (-1x + 3x) + 3 = 2x + 3

So, (f+g)(x), in this case, is 2x + 3 which is a polynomial function in simplest form.

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Answer:

w = 3(2a + b) - 4

w = 6a + 3b - 4

a = (w - 3b + 4) / 6

Answer:

[tex]a = \frac{w + 4 - 3b}{6} [/tex]

Step-by-step explanation:

[tex]w = 3(2a + b) - 4 \\ w + 4 = 6a + 3b \\ w + 4 - 3b = 6a \\ \frac{w + 4 - 3b }{6} = \frac{6a}{6} \\ \\ a = \frac{w + 4 - 3b}{6} [/tex]

Answer:

asdasd

Step-by-step explanation:

miles ÷ miles/hour = hours

Just divide the miles by the mph

4.5/12.5 = 0.36 hours

(0.36 hours)(60 min/hour) = 21.6 minutes

(0.6 minutes)(60 seconds/minute) = 36 seconds

Time:  21 minutes 36 seconds

Answer:

0.36 hours

Step-by-step explanation:

Miles ÷ Miles/hour = hours

4.5 miles ÷ 12.5 mph = 0.36 hours

Answer:

The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 500, \pi = \frac{421}{500} = 0.842[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 - 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.81[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 + 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.874[/tex]

The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).

The 95% confidence interval is (0.81,0.874) and this can be determined by using the confidence interval formula and using the given data.

Given :

The formula for the confidence interval is given by:

[tex]\rm CI = p\pm z\sqrt{\dfrac{p(1-p)}{n}}[/tex]  --- (1)

where the value of p is given by:

[tex]\rm p =\dfrac{421}{500}=0.842[/tex]

Now, the value of z for 95% confidence interval is given by:

[tex]\rm p-value = 1-\dfrac{0.05}{2}=0.975[/tex]

So, the z value regarding the p-value 0.975 is 1.96.

Now, substitute the value of z, p, and n in the expression (1).

[tex]\rm CI = 0.842\pm 1.96\sqrt{\dfrac{0.842(1-0.842)}{500}}[/tex]

The upper limit is 0.81 and the lower limit is 0.874 and this can be determined by simplifying the above expression.

So, the 95% confidence interval is (0.81,0.874).

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Complete Question

Suppose that the money demand function takes the form

(M/P)^d = L(i,Y) = Y/(5i)

a. If output grows at rate and the nominal interest rate is constant, at what rate will the demand for real balances grow

b. What is the velocity of money in this economy

Answer:

a. See explanation below

b. Velocity = 5i

Step-by-step explanation:

a. Suppose that the nominal interest rate remains constant, the demand for real balances will grow at the same rate at which the output grows.

b.

Given that (M/P)^d = L(i,Y) = Y/(5i)

Money equation is written as;

Total Spending = MV

Where M = Amount of Money..

V = Velocity of Circulation

Total Spending = PY;

So, PY = MV --- Make V the subject of formula

PY/M = V --- Rearrange

V = PY/M ---- (1)

Also,

M/P = Y/5i --- Cross Multiply

M * 5i = P * Y --- Make 5i the subject of formula

5i = PY/M ---- (2)

Compare 1 and 2

5i = V = PY/M

So, 5i = V

V = 5i

Hence, Velocity = 5i

Answer: 0.63333333333

Step-by-step explanation: Use a calculator.

Answer: 19/30

Step-by-step explanation:

You want to find a common denominator that works for all fractions and add a subtract them and the simplify

Answer:

in many random samples, 95% of the confidence intervals will contain a sample average between 24cm and 27cm.

Step-by-step explanation:

We then interpret this interval that  95% would contain a sample average forearm length between 24cm and 27cm.

The average is defined as the mean  equal to the ratio of the sum of the values ​​of a given number to the total number of values ​​in the set.

The formula for finding the average of given numbers or values ​​is very simple. We just need to add all the numbers and  divide the result by the given number of values. So the  formula for mean in mathematics is given as follows:

Mean = sum of values/ number of values ​​

Suppose we have given  n as number of values ​​like x1, x2, x3 ,..., xn. The average or  mean of the given data is equal to:

Mean = (x1 x2 x3 … xn)/n

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Answer:

The scroll is 1949 years old, thus the archeologists are right.

Step-by-step explanation:

The decay equation of ¹⁴C is:

[tex] A = A_{0}e^{-\lambda*t} [/tex]   (1)

Where:

A₀: is the initial activity

A: is the activity after a time t = 79%*A₀

λ: is the decay rate

The decay rate is:

[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]    (2)

Where [tex]t_{1/2}[/tex]: is the half-life of ¹⁴C = 5730 y

By entering equation (2) into equation (1) we can find the age of the scrolls.

[tex] A = A_{0}e^{-\lambda*t} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t} [/tex]

Since, A = 79%*A₀, we have:

[tex]\frac{79}{100}A_{0} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]

[tex]ln(\frac{79}{100}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]

Solving the above equation for t:

[tex]t = -\frac{ln(79/100)}{\frac{ln(2)}{t_{1/2}}}[/tex]

[tex]t = -\frac{ln(75/100)}{\frac{ln(2)}{5730 y}} = 1949 y[/tex]

Hence, the scroll is 1949 years old, thus the archeologists are right.

I hope it helps you!

Answer:

The hypothesis is correct.

Step-by-step explanation:

Using the half-life equation, the number of years (1,900) can be substituted for t and the half-life (5,730) can be substituted for h. Since the original amount is not known but the percent remaining is known, any value can be used for the original amount. Using 100 will be the easiest. Plugging these values into the equation gives 79.47 remaining. If 79.47 of the original 100 units are left, that is 79.47 percent. Since radiometric dating gives an estimate of age, the archeologists’ hypothesis is correct.