Jennifer starts with a population of 100 amoebas that doubles in size every minute for a number of minutes, m. She writes the expression 100(2m) to find the number of amoeba after m minutes. Nathan starts with a population of 10 amoebas that increases 40% in size every minute for a number of minutes, m. He writes the expression (1+0.4)m to find the number of amoeba after m minutes. Use the drop-down menus to explain what each part of Jennifer's and Nathan's expressions mean.

Answer:

There is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same​ frequency.

Step-by-step explanation:

In this case we need to test whether there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same​ frequency.

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: The observed frequencies are same as the expected frequencies.

Hₐ: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

 [tex]\chi^{2}=\sum{\frac{(O-E)^{2}}{E}}[/tex]

The values are computed in the table.

The test statistic value is [tex]\chi^{2}=128.12[/tex].

The degrees of freedom of the test is:

n - 1 = 12 - 1 = 11

Compute the p-value of the test as follows:

p-value < 0.00001

*Use a Chi-square table.

p-value < 0.00001 < α = 0.05.

So, the null hypothesis will be rejected at any significance level.

Thus, there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same​ frequency.

Final answer:

To test the claim that professional basketball players are born in different months with the same frequency, a chi-square test for goodness of fit can be used. Calculations involve comparing the actual birthdate frequencies of the players against the expected frequencies if the distribution were uniform. A statistically significant result would support the author's claim, while a non-significant result would not.

Explanation:

Chi-Square Test for Uniform Distribution

To determine if there is sufficient evidence to support the author's claim that professional basketball players are born in different months with the same frequency, we can perform a chi-square test for goodness of fit. Given the frequency counts of the birthdates of professional basketball players for each month, we will compare them to the expected frequencies if births were uniformly distributed throughout the year.

Steps to Perform the Test

Firstly, calculate the total number of players in the sample by summing up the frequency counts for each month.

Determine the expected frequency for each month, which would be the total number of players divided by 12, assuming a uniform distribution.

Calculate the chi-square statistic using the formula: χ² = ∑((observed - expected)² / expected), where 'observed' is the frequency count for each month, and 'expected' is the expected frequency.

Compare the calculated chi-square value with the critical value from the chi-square distribution table with 11 degrees of freedom (since there are 12 months - 1) and a significance level of 0.05.

If the chi-square value is greater than the critical value, reject the null hypothesis (that the birth months are uniformly distributed), which supports the author's claim. Otherwise, do not reject the null hypothesis.

Interpretation

By performing the calculations, if the chi-square test statistic is greater than the critical value, it suggests that there is a statistically significant difference in the distribution of birth months among professional basketball players. This would support the author's claim that there may be more players born in the months immediately following July 31, which is the age cutoff date for nonschool basketball leagues. If the test statistic is not greater than the critical value, there is not enough evidence to support the claim.

Answer:

The volume of the cone is  63.3m³

Step-by-step explanation:

First of all to solve this problem we need to know the formula to calculate the volume of a cone

v = volume

r = radius  = 2.2m

h = height  = 12.5m

π = 3.14

v = 1/3 * π * r² * h

we replace with the known values

v = 1/3 * 3.14 * (2.2m)² * 12.5m

v = 1/3 * 3.14 * 4.84m² * 12.5m

v = 63.32m³

rount to the neares tenth

v = 63.32m³ = 63.3m³

The volume of the cone is  63.3m³

Answer: 63.4

Step-by-step explanation:

You round to the tenths giving you 63.4

Answer:

Laurens dog: 8 feet

Cheyenne's dog: 2 feet

Step-by-step explanation:

The first step is to evaluate the question, we know that you need to find the height each dog jumped, given the sum of both combined

next, you do simple math:

4x2= 8

10-8= 2

hope this helps

stay safe :))))

brainliest is apprceiated:))))

Answer:

The answer would be 2924. 82

Step-by-step explanation:

8x² − 8x + 2

2 (4x² − 4x + 1)

2 (2x − 1)²

Answer:

Angle A equals Angle B so 6x-2=4x+48 ---> 2x=50 ---> x=25. From this we find that both Angles A and B are equal to 148 degrees. :)

Answer: √3/2

Step-by-step explanation: Ok...so it would look like this:

(3√8)/(4√6)

I hope this helps!

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images for the step by step explanation to the question

Answer:

easy peasy lemon squeezy

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

First you use the equation [tex]2(\pi r^{2})[/tex] to find the area of the circles combined and you find the radius by diving the height by 2(getting 5)

Then you find the area of the squares with the circles(10 x 20= 200)

Finally you subtract the area of both circles and the total area. (200-157=43)

The equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Here, general equation of parabola in downward direction is

(y-y₁) = -4a(x-x₁)²

vertex of parabola (-1, 2)

(y-2) = -4a(x-(-1))²

(y - 2) = -4a(x + 1)²

put the value of x = 0 and y = -1

so we get, a = 3/4

put in equation of parabola

( y - 2 ) = -3 ( x + 1 ) ²

y = -3 (x + 1)² + 2

f(x) = -3 (x + 1)² + 2

Thus, the equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.

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Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The independent variable which will on on the x-axis is the price of a t-shirt.

The dependent variable which will on on the x-axis is the number of t-shirts sold.

The independent variable can be described as the variable that is used to determine the dependent variable. It is the variable that the researcher manipulates in the experiment.  

The dependent variable is the variable whose value is determined in the experiment. The value of the dependent variable depends on the independent variable.  

For example, assume that if the price of a shirt is $1. A person purchases 10 t shirts. If the price increases to $10, only one shirt would be sold. This means that the amount of shirts bought is dependent on the price of the t-shirt. The price of the shirt is the independent variable while the amount of shirts bought is the dependent variable.

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Answer:

The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).

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 = 55, \pi = \frac{24}{55} = 0.4364[/tex]

93% confidence level

So [tex]\alpha = 0.07[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.07}{2} = 0.965[/tex], so [tex]Z = 1.81[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4364 - 1.81\sqrt{\frac{0.4364*0.5636}{55}} = 0.3154[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4364 + 1.81\sqrt{\frac{0.4364*0.5636}{55}} = 0.5574[/tex]

The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).

Answer:

2 and 4

Step-by-step explanation:

A function assigns the values. The statements that are true about the given function are B and D.

A function assigns the value of each element of one set to the other specific element of another set.

To know the correct statements about the graph of the function f(x)=6x-4+x², we need to plot the graph, as shown below.

A.) The vertex form of the function is f(x)=(x-2)²+2.

To know if the vertex form of the function is f(x)=(x-2)²+2, solve the equation and check if it is of the form f(x)=6x-4+x².

[tex]f(x)=(x-2)^2+2\\\\ f(x)=x^2+4-4x+2\\\\f(x) = x^2-4x+6[/tex]

Since the two functions are not equal this is not the vertex form of the function is f(x)=6x-4+x².

B.) The vertex of the function is (-3, -13).

As can be seen in the image below, the vertex of the function lies at (-3,-13.) Therefore, the statement is true.

C.) The axis of symmetry for the function is x = 3.

As the vertex is at -3, therefore, the function symmetry will be about x=-3.

Hence, the given statement is false.

D.) The graph increases over the interval (-3).

The given statement is true since the graph will be showing a positive slope in the interval (-3, +∞).

E.) The function does not cross the x-axis.

It can be observed that the function intersects the x-axis exactly at two points, therefore, the given statement is false.

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3Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D has the most similarities than others

The option B is correct.

The option B quadrilateral is similar to the given quadrilateral.

Because the three corresponding angles are the same.

Therefore, option B is correct.

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Answer:

yes

Step-by-step explanation:

By definition, all sides are the same length, so the perimeter is simply the length of a side times the number of sides.

Since it is true that the distance between sides of a polygon are always the same.

A polygon is defined as a closed figure made up of three or more line segments connected end to end

For a regular polygon of any number of sides, then the sum of its exterior angle is 360° .

Exterior angle is an measure of rotation between one extended side of the polygon with its adjacent side which is not extended. Also, regular having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.

When a polygon is four sided (a quadrilateral), the sum of its angles is 360°

Based on the definition, all sides are the same length, thus the perimeter is simply the length of a side times the number of sides.

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Answer:

We conclude that the commuting times are same in the winter.

Step-by-step explanation:

We are given that the Census Bureau reports the average commute time for citizens of Cleveland, Ohio is 33 minutes. To see if the commute time is different in the winter, a random sample of 40 drivers were surveyed.

The average commute time for the month of January was calculated to be 34.2 minutes and the population standard deviation is assumed to be 7.5 minutes.

Let [tex]\mu[/tex] = average commute time in winter.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 33 minutes      {means that the commuting times are same in the winter}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 33 minutes      {means that the commuting times are different in the winter}

The test statistics that would be used here One-sample z test statistics as we know about population standard deviation;

                    T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean commute time for the month of January = 34.2

            [tex]\sigma[/tex] = population standard deviation = 7.5 minutes

            n = sample of drivers = 40

So, test statistics  =  [tex]\frac{34.2-33}{\frac{7.5}{\sqrt{40}}}[/tex]  

                              =  1.012

The value of z test statistics is 1.012.

Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the commuting times are same in the winter.

Also, P-value of the test statistics is given by;

         P-value = P(Z > 1.012) = 1 - P(Z [tex]\leq[/tex] 1.012)

                       = 1 - 0.84423 = 0.1558

Answer:    

She switched her say

Step-by-step explanation:

Answer:

Annie made the mistake of either swapping the numbers or the items in her comparison.

Step-by-step explanation:

The ratio of lollipops to cookies is:

6/9

This can be simplified to:

2/3

That means that for every two lollipops, there are three cookies. Therefore Annie made the mistake of either swapping the numbers or the items in her comparison.

Answer:

The model for the pollutant levels in the soil t years from the first measurement is:

[tex]Y(t)=65e^{0.044}[/tex]

Step-by-step explanation:

We have a first measurement of 65 parts per million (ppm) of pollutant.

We also know that the pollutant levels were growing exponentially at a rate of 4.5% a year.

We can model this as:

[tex]Y(t)=Y_0e^{kt}[/tex]

The value of Y0 is the first measurement, that correspond to t=0.

[tex]Y_0=65[/tex]

The ratio for the pollutant levels for two consecutive years is 1+0.045=1.045. This can be expressed as the division between Y(t+1) and Y(t), and gives us this equation:

[tex]\dfrac{Y(t+1)}{Y(t)}=\dfrac{Y_0e^{k(t+1)}}{Y_0e^{kt}} =\dfrac{e^{k(t+1)}}{e^{kt}}=e^{k(t+1-t)}=e^k=1.045\\\\\\k=ln(1.045)\approx 0.044[/tex]

Then, we have the model for the pollutant levels in the soil t years from the first measurement:

[tex]Y(t)=65e^{0.044}[/tex]

Answer:

  f(u +6) = u

Step-by-step explanation:

Put (u+6) in place of t and simplify:

  f(u+6) = (u+6) -6

  f(u+6) = u

Answer:

The volume of the sphere is 678.24 u³  

V = ⁴⁄₃ * π * (6u)³

Step-by-step explanation:

To calculate the volume of a sphere we have to use the following formula:

V = volume

r = radius  = 6 units

π = 3.14

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * 3.14 * (6u)³

V = 4.187 * 216 u³

V = 678.24 u³

The volume of the sphere is 678.24 u³

Answer:

9

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

cuzz im right

Answer:

A = $100(1.12)^2

Step-by-step explanation:

The standard formula for compound interest is given as;

A = P(1+r/n)^(nt) .....1

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case;

P = $100

t = 2years

n = 1

r = 12% = 0.12

Substituting the values, we have;

A = $100(1+0.12)^(2)

A = $100(1.12)^2

Answer:

[tex]z=\frac{0.47-0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=-1.897[/tex]  

We have aleft tailed test the p value would be:  

[tex]p_v =P(z<-1.897)=0.0289[/tex]  

The p value obtained is less compared to the significance level so then we have enough evidence to conclude that the true proportion is significantly lower than 0.5.

Step-by-step explanation:

Information given

n=1000 represent the random sample selected

X=470 represent the number of people who felt political news was reported fairly

[tex]\hat p=\frac{470}{1000}=0.470[/tex] estimated proportion of people who felt political news was reported fairly

[tex]p_o=0.5[/tex] is the value that we want to test

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

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

For this case we want to test if proportion for the U.S. is below .50 so then the system of hypothesis for this case are:

Null hypothesis:[tex]p \geq 0.5[/tex]  

Alternative hypothesis:[tex]p < 0.5[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info provided we got:

[tex]z=\frac{0.47-0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=-1.897[/tex]  

We have aleft tailed test the p value would be:  

[tex]p_v =P(z<-1.897)=0.0289[/tex]  

The p value obtained is less compared to the significance level so then we have enough evidence to conclude that the true proportion is significantly lower than 0.5.

Answer:

  299

Step-by-step explanation:

On average, it travels 52 miles in each hour. In 5 3/4 hours, it travels 5 3/4 times 52 miles.

  (5 3/4)(52 miles) = 299 miles

It travels 299 miles in the given time.

Answer:

The car will travel 195 miles.

Step-by-step explanation:

(3.75 hrs)(52 mph)=195 miles

Answer:

0.9552

Step-by-step explanation:

Probability of making home can be made by either of the options :-

So, probability of making out at home : Reach through flight or car =  0.72 + 0.2352 = 9.9552

Final answer:

The probability of making it home for the holidays can be calculated using conditional probability. The probability of the flight being canceled is 28 percent, and the probability of Walter having a seat in his car is 84 percent. The probability of making it home is approximately 60.48 percent.

Explanation:

The probability of making it home for the holidays can be calculated using the concept of conditional probability. The probability of the flight being canceled is given as 28 percent, which means there is a 72 percent chance that the flight is not canceled. The probability of Walter having a seat in his car is given as 84 percent. To calculate the probability of making it home, we need to calculate the probability of both events happening.

The probability of the flight not being canceled is 72 percent (0.72) and the probability of Walter having a seat is 84 percent (0.84). To find the probability of both events happening, we multiply the probabilities: 0.72 * 0.84 = 0.6048 or approximately 60.48 percent. So, there is a 60.48 percent probability of making it home for the holidays.

Answer:

54% probability that a person likes Italian food, but not Chinese food.

82% probaility that a person likes at least one of these foods

79% proability that a person likes at most one of these foods

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a person likes Italian food.

B is the probability that a person likes Chinese food.

We have that:

[tex]A = a + (A \cap B)[/tex]

In which a is the probability that a person likes Italian food but not Chinese and [tex]A \cap B[/tex] is the probability that a person likes both Italian and Chinese food.

By the same logic, we have that:

[tex]B = b + (A \cap B)[/tex]

The probability that a person likes both foods is 0.21.

This means that [tex]A \cap B = 0.21[/tex]

The probability that a person likes Chinese food is 0.28

This means that [tex]B = 0.28[/tex]

So

[tex]B = b + (A \cap B)[/tex]

[tex]0.28 = b + 0.21[/tex]

[tex]b = 0.07[/tex]

The probability that a person likes Italian food is 0.75

This means that [tex]A = 0.75[/tex]

So

[tex]A = a + (A \cap B)[/tex]

[tex]0.75 = a + 0.21[/tex]

[tex]a = 0.54[/tex]

Determine the probability that a person likes Italian, but not Chinese

This is a.

54% probability that a person likes Italian food, but not Chinese food.

Determine the probaility that a person likes at least one of these foods

[tex]P = a + b + (A \cap B) = 0.54 + 0.07 + 0.21 = 0.82[/tex]

82% probaility that a person likes at least one of these foods

Determine the proability that a person likes at most one of these foods

Either a person likes at most one of these foods, or it likes both. The sum of the probabilities of these events is decimal 1.

0.21 probability it likes both.

Then

0.21 + p = 1

p = 0.79

79% proability that a person likes at most one of these foods