A bacteria doubles its original population in 16 hours (A=2A0). How big will its population be in 96 hours?

To find the perimeter of Amy's poster, convert all measurements to inches, resulting in a length of 12 inches and a width of 8 inches. Then use the formula for the perimeter of a rectangle, which is 40 inches in this case.

To calculate the perimeter of a poster, we must first have all dimensions in the same units. Amy's poster has a width of 8 inches and a length of 1 foot. Since there are 12 inches in a foot, the length is 12 inches. The perimeter of a rectangle is calculated by adding together the lengths of all the sides, or using the formula 2 * (length + width).

Using Amy's measurements, the perimeter of her poster would be:

2 * (12 inches + 8 inches) = 2 * 20 inches = 40 inches.

Therefore, the poster has a perimeter of 40 inches.

Answer:

The correct statement are (A) and (F).

Step-by-step explanation:

Events A and B are independent or mutually independent events if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.

That is,

[tex]P(A\cap B)=P(A)\times P(B)[/tex]

The conditional probability of event A given B is computed using the formula:

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

And the formula for the conditional probability of event B given A is:

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]

Consider that events A and B are independent.

Then the conditional probability of event A given B will be:

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

             [tex]=\frac{P(A)\times P(B)}{P(B)}\\\\=P(A)[/tex]

And the conditional probability of event B given A will be:

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]

             [tex]=\frac{P(A)\times P(B)}{P(A)}\\\\=P(B)[/tex]

Thus, the correct statement are (A) and (F).

In the context of independent events, the correct statements are that P(A | B) = P(A) and P(B | A) = P(B), indicating that the occurrence of one event does not affect the probability of the other event occurring. Other options presented do not accurately represent the properties of independent events in probability.

When assessing whether events A and B are independent, it is essential to understand the criteria for independence in probability theory. Specifically, two events are independent if the probability of one event occurring does not affect the probability of the other event occurring. This can be mathematically represented as follows: P(A AND B) = P(A)P(B), P(A|B) = P(A), and P(B|A) = P(B).

If events A and B are independent, the correct statements among the choices provided are:

Option A is true because if A and B are independent, the probability of A occurring given that B has occurred is the same as the probability of A occurring on its own.

Option F is also correct for the same reason applied to event B; the probability of B occurring given that A has occurred is the same as the probability of B occurring on its own.

The remaining options are incorrect because they do not align with the definition of independent events:

Answer:

4.635

Step-by-step explanation:

A confidence interval is:

CI = μ ± ME

where μ is the sample mean and ME is the margin of error.

In other words, the margin of error is half the width of the interval.

ME = (69.397 − 60.128) / 2

ME = 4.635

14

All you have to do is multiply the 1/2 by the 7.

Answer:

14

Step-by-step explanation:

there are 14  1/2 in 7

Answer:

The probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.

Step-by-step explanation:

We are given that the owner of the pizza chain wants to monitor the total weight of pepperoni. Suppose that for pizzas in this population, the weights have a mean of 250 g and a standard deviation of 4 g.

Management takes a random sample of 64 of these pizzas.

Let [tex]\bar X[/tex] = sample mean weight of the pepperoni.

The z score probability distribution for sample mean is given by;

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

where, [tex]\mu[/tex] = population mean weight = 250 g

            [tex]\sigma[/tex] = standard deviation = 4 g

            n = sample of pizzas = 64

Now, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is given by = P([tex]\bar X[/tex] > 251 g)

   P([tex]\bar X[/tex] > 251 g) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{251-250}{\frac{4}{\sqrt{64} } }[/tex] ) = P(Z > 2) = 1 - P(Z [tex]\leq[/tex] 2)

                                                     = 1 - 0.97725 = 0.02275

The above probabilities is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.

Hence, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.

Answer:

a) P ( X ≤ 26 ) = 0.0134

b) The significance of the cell phone causing brain cancer is 1.34 or 0.0134

Step-by-step explanation:

Solution:-

- From the entire population of cell phone users os size N = 346,145 media reported n = 26 people who developed cancer of brain or nervous system.

- The probability of a person developing cancer of the brain or nervous system, assuming that cell phones have no effect, is p = 0.000113.

- Denote a random variable X: The number people who developed cancer of brain or nervous system are normally distributed.

- The expected or mean number of people who developed cancer of brain or nervous system are u = 40.

- The standard deviation ( s ) for the distribution would be:

                          [tex]s = \sqrt{u*( 1 - p ) }\\\\s = \sqrt{40*( 1 - 0.000113 ) }\\\\s = 6.3242\\[/tex]

- The random variate X follows normal distribution with parameters:

                         X ~ Norm ( 40 , 6.3242^2 )

- The probability of X ≤ 26 cases from the total population of N = 346,145 can be determined by evaluating the Z-score standard value of the test statistics:

                        [tex]P ( X \leq 26 ) = P ( Z \leq [ \frac{X - u }{s} ) \\\\P ( Z \leq [ \frac{ 26 - 40 }{6.3242} ) = P ( Z \leq -2.21371 )[/tex]

- Using standard normal table compute the probability on the left side of Z-score value -2.21371. Hence,

                       P ( X ≤ 26 ) = 0.0134

- The probability of the less than 26 number of cases who developed cancer of the brain or nervous system is 0.0134 as per media reports.

- So 1.34% of population is a case brain cancer due to cell phones according to media reports.

Which is significant less than the expected number of cases ( 40 ) that occur regardless of cell phone effect.

Answer:  The significance of the cell phone causing brain cancer is 1.34 or 0.0134.

Answer:

   y = 6/19 = 0.316

Step-by-step explanation:

:)

Answer:

y=6/19

Step-by-step explanation:

15y − 1 = 11/2y + 2

15y-11/2y=3

30/2y-11/2y=3

19/2y=3

19y=6

y=6/19

Answer:

A. See diagram

B.y=80+4x

C.110000

Refer below.

Step-by-step explanation:

Refer to the pictures for complete illustration.

The alternative hypothesis suggests a significant relationship between years of experience and annual sales. The estimated regression equation, derived from the given data, can be used to predict the annual sales based on years of service. For instance, a salesperson with 9 years of experience is predicted to make annual sales of $120.5k.

To begin, let's identify the variables of interest. The years of experience is the independent variable (x) and the annual sales is the dependent variable (y).

(a) Alternative Hypothesis: There is a significant linear relationship between the years of experience and the annual sales. It suggests that as the years of experience increase, the annual sales also increase.

(b) Estimated Regression Equation: To create the estimated regression equation, we first need to calculate the slope and y-intercept of the line that best fits the data. For example, using statistical software or a calculator, you might find the slope (B1) and y-intercept (B0) to be around 4.5 and 79 respectively (these numbers are hypothetical and for illustration purposes), resulting in the equation: Annual Sales = 4.5*(Years of Experience) + 79.

(c) Predicting Annual Sales: With 9 years of experience, you would plug the value 9 into the sample regression equation to predict the annual sales: Annual Sales = 4.5*(9) + 79 = $120.5 (in $1000s).

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Answer:

The correct option is (D).

Step-by-step explanation:

To construct the (1 - α)% confidence interval for population proportion the distribution of proportions must be approximated by the normal distribution.

A Normal approximation to binomial can be applied to approximate the distribution of proportion p, if the following conditions are satisfied:

In this case p is defined as the proportions of students who ride a bike to campus.

A sample of n = 125 students are selected. Of these 125 students X = 6 ride a bike to campus.

Compute the sample proportion as follows:

[tex]\hat p=\frac{X}{n}=\frac{6}{125}=0.048[/tex]

Check whether the conditions of Normal approximation are satisfied:

[tex]n\hat p =125\times 0.048=6<10\\n(1-\hat p) =125\times (1-0.048)=119>10[/tex]

Since [tex]n\hat p <10[/tex], the Normal approximation to Binomial cannot be applied.

Thus, the confidence interval cannot be used to estimate the proportion of all students who ride a bike to campus.

Thus, the correct option is (D).

Answer:

The coefficient of variation for A is 24.6%.

The coefficient of variation for B is 33.7%.

Step-by-step explanation:

The coefficient of variation (CV) is well defined as the ratio of the standard deviation to the mean. It exhibits the degree of variation in association to the mean of the population.

The formula to compute the coefficient of variation is,

[tex]CV=\frac{SD}{Mean}\times 100\%[/tex]

Consider the data set A.

Compute the mean of the data set A as follows:

[tex]Mean_{A}=\frac{1}{n}\sum X[/tex]

            [tex]=\frac{1}{14}\times [36900+19400+...+26000+38400]\\=30064.2857[/tex]

Compute the standard deviation of the data set A as follows:

[tex]SD_{A}= \sqrt{ \frac{ \sum{\left(x_i - Mean_{A}\right)^2 }}{n-1} }[/tex]

        [tex]= \sqrt{ \frac{ 712852142.8571 }{ 14 - 1} } \\\approx 7405.051[/tex]

Compute the coefficient of variation for A as follows:

[tex]CV=\frac{SD_{A}}{Mean_{A}}\times 100\%[/tex]

      [tex]=\frac{7405.051}{30064.2857}\times 100\%\\=24.6\%[/tex]

The coefficient of variation for A is 24.6%.

Consider the data set B.

Compute the mean of the data set B as follows:

[tex]Mean_{B}=\frac{1}{n}\sum X[/tex]

            [tex]=\frac{1}{11}\times [2.1+5.0+...+4.1+1.7]\\=3.2455[/tex]

Compute the standard deviation of the data set B as follows:

[tex]SD_{B}= \sqrt{ \frac{ \sum{\left(x_i - Mean_{B}\right)^2 }}{n-1} }[/tex]

        [tex]= \sqrt{ \frac{ 11.9873 }{ 11 - 1} } \\\approx 1.0949[/tex]

Compute the coefficient of variation for B as follows:

[tex]CV=\frac{SD_{B}}{Mean_{B}}\times 100\%[/tex]

      [tex]=\frac{1.0949}{3.2455}\times 100\%\\=33.7\%[/tex]

The coefficient of variation for B is 33.7%.

Answer:

Hence A fish in an aquarium see the cat more than actual distance.

Step-by-step explanation:

Given:

A fish in aquarium with flat silde looks out to cat .

To find :

Appearance of fish to the cat.

Solution:

Now this problem is related to the refractive index of 2 mediums

So cat is  in air medium and a fish in water i.e. aquarium

R.I of water =1.33

R.I of air =1.00

We know the incident ray ,reflected ray,refracted ray and normal .

When a incident ray enter in denser medium it bends towards  normal.

But it diverges outward direction and goes beyond the actual object.

(Refer the Attachment).

Hence A fish in an aquarium see the cat more than actual distance.

Answer:

a) 0.691 = 69.1% probability that a battery lasts more than four hours

b) 25% value = 231

75% value = 299

c) 183 minutes

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 265, \sigma = 50[/tex]

a) What is the probability that a battery lasts more than four hours?

4 hours = 4*60 = 240 minutes

This is 1 subtracted by the pvalue of Z when X = 240. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{240 - 265}{50}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a pvalue of 0.309

1 - 0.309 = 0.691

0.691 = 69.1% probability that a battery lasts more than four hours

b) What are the quartiles (the 25% and 75% values) of battery life?

25th percentile:

X when Z has a pvalue of 0.25. So X when Z = -0.675

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.675 = \frac{X - 265}{50}[/tex]

[tex]X - 265 = -0.675*50[/tex]

[tex]X = 231[/tex]

75th percentile:

X when Z has a pvalue of 0.75. So X when Z = 0.675

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{X - 265}{50}[/tex]

[tex]X - 265 = 0.675*50[/tex]

[tex]X = 299[/tex]

25% value = 231

75% value = 299

c) What value of life in minutes is exceeded with 95% probability?

The 100-95 = 5th percentile, which is the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.645 = \frac{X - 265}{50}[/tex]

[tex]X - 265 = -1.645*50[/tex]

[tex]X = 183[/tex]

Answer:

200?

Step-by-step explanation:

its kinda simple but the 2 is in the hundreds place therefore it is 200.

hope it helped ;)

Answer:

use the distance formula,

by using it, prove the adjacent sides of the quadrilateral DEFG

hence, DEFG would be a rhombus

Answer:

6/5

Step-by-step explanation:

(4/7)  divided by (10/21) = (4/7) * (21/10) =  (3*4)/10= 6/5

Final answer:

The rate at which the water level is rising when the water level is 3 cm is approximately 2.92 cm/s.

Explanation:

To find the rate at which the water level is rising, we need to consider the volume of water being added per unit time and how that volume relates to the change in water level. The volume of a pyramid can be calculated using the formula V = (1/3)b*h, where b is the area of the base and h is the height. In this case, the base is a square with sides of length 6 cm, so the area is 6*6 = 36 cm^2. Substituting this into the formula, the volume of the pyramid is V = (1/3)*36*8 = 96 cm^3. Since the water is being filled at a rate of 35 cm^3/s, we can find the rate of the water level rising by taking the derivative of the volume equation with respect to time:

dV/dt = (1/3)*b*dh/dt

where dV/dt is the rate of change of volume, b is the area of the base, and dh/dt is the rate of change of the height (which is the same as the rate of change of the water level).

Substituting in the known values:

35 = (1/3)*36*(dh/dt)

dh/dt = (35*3)/(36) = 35/12 ≈ 2.92 cm/s

Answer: 25 in²

Step-by-step explanation: To find the area of a triangle, start with the formula for the area of a triangle which is shown below.

[tex]Area =[/tex] [tex]\frac{1}{2} bh[/tex]

In this problem, we're given that the base is 10 inches

and the height is 5 inches.

Now, plugging into the formula, we have [tex](\frac{1}{2})(10in.)(5 in.)[/tex].

Now, it doesn't matter which order we multiply.

So we can begin by multiplying (1/2) (10 in.) to get 5 inches.

Now, (5 in.) (5 in.) is 25 in².

So the area of the triangle is 25 in².

The coordinates of point Z(3, -3) after a 180° counterclockwise rotation around the origin are Z'(-3, 3).

The student has asked about the result of a 180° counterclockwise rotation around the origin for a point with given coordinates. When a point (x, y) is rotated 180° around the origin, both the x-coordinate and y-coordinate flip signs, which is a standard transformation in coordinate geometry.

For the point Z(3,−3), performing this rotation results in the point Z' having the coordinates (-3, 3).

This transformation follows the rule that (x, y) becomes (-x, -y) upon a 180° rotation about the origin.

Answer:

[tex](B)\sqrt[5]{16x^4}[/tex]

Step-by-step explanation:

We are required to evaluate:

[tex]\sqrt[5]{4x^2} X \sqrt[5]{4x^2}[/tex]

By laws of indices: [tex]\sqrt[n]{x}=x^{^\frac{1}{n} }[/tex]

Therefore: [tex]\sqrt[5]{4x^2} =(4x^2)^{^\frac{1}{5}[/tex]

Thus:

[tex]\sqrt[5]{4x^2} X \sqrt[5]{4x^2}=(4x^2)^{1/5}X(4x^2)^{1/5}\\$Applying same base law of indices:a^mXa^n=a^{m+n}\\(4x^2)^{1/5}X(4x^2)^{1/5}=(4x^2)^{1/5+1/5}=(4x^2)^{2/5}\\$Now, by index product law: a^{mn}=(a^m)^n\\(4x^2)^{2/5}=[(4x^2)^2]^{1/5}=[16x^4]^{1/5}\\[/tex]

[tex][16x^4]^{1/5}=\sqrt[5]{16x^4} \\$Therefore:\\\sqrt[5]{4x^2} X \sqrt[5]{4x^2}=\sqrt[5]{16x^4}[/tex]

Answer:

b in edge

Step-by-step explanation:

The question pertains to calculating the volume of a triangular prism using the given area of the base and height. The volume is found by multiplying the area of the base (75 square inches) by the height (15 inches) to yield an answer of 1125 cubic inches.

The question provided relates to the concept of finding the volume of a geometric shape, specifically a triangular prism, as it gives the area of the base and the height of the prism. In geometry, to find the volume of a triangular prism, we use the formula V = Area of base  imes Height. Given that the area of the base provided is 75 square inches and the height is 15 inches, we can calculate the volume of the triangular prism.

To calculate volume:

Thus, the volume of the triangular prism is 1125 cubic inches.

Answer:

$8.50C + $9.50 = ______

That's the expression.

Answer:

e= 0.8

Step-by-step explanation:

Get e by itself, so subtrct 1.2 from 2 to get 0.8

The solution to the equation [tex]\(e + 1.2 = 2\) is \(e = 0.8\).[/tex]

To solve the equation \(e + 1.2 = 2\), we need to isolate the variable \(e\) on one side of the equation. Here's how you can do it step by step:

1. **Subtract 1.2 from both sides:**

\[e + 1.2 - 1.2 = 2 - 1.2\]

\[e = 0.8\]

In the context of real numbers, this means that when you substitute \(e = 0.8\) back into the original equation, it holds true:

\[0.8 + 1.2 = 2\]

This equation verifies that \(e = 0.8\) is indeed the solution. In a broader sense, solving equations like this one is a fundamental concept in algebra and mathematics. It allows us to find unknown values in various real-life situations, making it a crucial skill in fields such as physics, engineering, economics, and many others.

Understanding how to manipulate equations helps us model and solve complex problems, making mathematics an essential tool in problem-solving and critical thinking.

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Answer:

When you multiply 8 by factors less than 1, your product is a number less than 8. An example of this would be when you multiply 8 by 1/2. Your product is 4. Another example is when you multiply 8 by 1/4. Your product is 2. When you multiply 8 by factors that are greater than 1, your product is a number greater than 8. One example of this is when you multiply 8 by 5. Your answer is 40. Another example is when you multiply the number 8 by 2. Your product is 16.

Step-by-step explanation:

Final answer:

When you multiply 8 by factors less than 1, the products will be smaller than 8. When you multiply 8 by factors greater than 1, the products will be larger than 8.

Explanation:

When you multiply 8 by factors less than 1, the products will be smaller than 8. For example, if you multiply 8 by 0.5, you get a product of 4. The further the factor is from 1, the smaller the product will be. Some other examples include multiplying 8 by 0.25 to get a product of 2, or multiplying 8 by 0.1 to get a product of 0.8.

On the other hand, when you multiply 8 by factors greater than 1, the products will be larger than 8. For example, if you multiply 8 by 2, you get a product of 16. The further the factor is from 1, the larger the product will be. Some other examples include multiplying 8 by 3 to get a product of 24, or multiplying 8 by 10 to get a product of 80.

Answer:

Give me more fees back on your equation

Step-by-step explanation:

Answer:

3/5, 0.6

Step-by-step explanation:

8/10 - 2/10 = 6/10

6/10/2= 3/5

PLEASE MARK AS BRAINLIEST

Step-by-step explanation:

8/10-2/10

it will be 6/10 both numbers arre divisible by 2 so 3/5

Final ANSWER

3/5

Answer:

3/6 = 1/2

Step-by-step explanation:

Important: 1/3 = 2/6

5/6-?=1/3

5/6-?=2/6

3/6=?

Answer:

the answer in scientific notation is 1.1235x10^10

Answer:

∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.

Step-by-step explanation:

tbh im not suuper sure but my educated guess is that by looking at it. Good Luck!

Two triangles are said to be similar by AA if two angles of both triangles are equal. The explanation that proves the similarity of [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] by AA is option (a)

Given that: [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex]

To prove that [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] are similar by AA, it means that two corresponding angles of both triangles must be congruent. So, the following must be true:

Hence, (a) is true

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