the prime factorization of 455.

(a) The population of ants doubled in one week, so it took 1 week.

(b) The population of ants tripled in two weeks.

(c) The population of ants reached 10,000 in 13.29 weeks.

(d) There were 200 ants per anteater after 7.64 weeks.

Here is the explanation for each answer:

(a) The population of ants doubled in one week, so it took 1 week.

The population of ants is an exponential function of time, which means that it grows at a rate that is proportional to its current size. In other words, the more ants there are, the faster the population grows.

The population of ants doubled in one week, which means that it grew by a factor of 2. This means that the growth rate of the population is 2 per week.

The time it takes for the population to double is inversely proportional to the growth rate. In other words, the faster the population grows, the less time it takes to double.

Since the growth rate of the population is 2 per week, it took 1 week for the population to double.

(b) The population of ants tripled in two weeks.

The population of ants is an exponential function of time, which means that it grows at a rate that is proportional to its current size. In other words, the more ants there are, the faster the population grows.

The population of ants tripled in two weeks, which means that it grew by a factor of 3. This means that the growth rate of the population is 3 per week.

The time it takes for the population to triple is inversely proportional to the growth rate. In other words, the faster the population grows, the less time it takes to triple.

Since the growth rate of the population is 3 per week, it took 2 weeks for the population to triple.

(c) The population of ants reached 10,000 in 13.29 weeks.

The population of ants is an exponential function of time, which means that it grows at a rate that is proportional to its current size. In other words, the more ants there are, the faster the population grows.

The population of ants reached 10,000 in 13.29 weeks, which means that it grew by a factor of 10,000. This means that the growth rate of the population is 10,000 per 13.29 weeks.

The time it takes for the population to reach a certain size is inversely proportional to the growth rate. In other words, the faster the population grows, the less time it takes to reach a certain size.

Since the growth rate of the population is 10,000 per 13.29 weeks, it took 13.29 weeks for the population to reach 10,000.

(d) There were 200 ants per anteater after 7.64 weeks.

The population of anteaters is also an exponential function of time, but it doubles every 2.8 weeks. This means that the growth rate of the population of anteaters is 1/2.8 = 0.357 per week.

The population of ants is growing at a much faster rate than the population of anteaters. This means that the number of ants per anteater will continue to increase over time.

After 7.64 weeks, the population of ants will be 200 times the population of anteaters. This means that there will be 200 ants per anteater.

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Answer:

Step-by-step explanation:

\(y=-2x+8\\\\x=20\)

Substitute ; x =20 in given equation

\(y =-2(20 )+8\\\\y = -40+8\\\\y = -32\)

The angle bisector from a vertex to the opposite side of a triangle is unique. We get AD = BE by subtracting BD from both sides of AB + BD = BE.

Proposition 4.4 states that in every triangle, there exists an angle bisector from a vertex to the opposite side and the angle bisector is unique.

Proof:

Let ΔABC be the given triangle and suppose AD is the angle bisector from A to BC. To prove that AD is unique, suppose BE is another angle bisector from B to AC.

We need to show that AD = BE.

Construct the incenter I of ΔABC. Draw lines AI and BI. AI bisects ∠A and BI bisects ∠B.

So, ∠AIB = 90° + ½ ∠C (proved in proposition 4.3).

Again, ∠AIB = ∠AID + ∠BIE [angle addition property of equality]

Therefore, ∠AID + ∠BIE = 90° + ½ ∠C...(1)

Since AD is the angle bisector from A to BC, we have

∠BAD = ∠CAD

Also, BE is the angle bisector from B to AC, so

∠EB = ∠EC

Adding these two equations, we get

∠BAD + ∠EB = ∠CAD + ∠EC...(2)

Since ∠A + ∠B + ∠C = 180° (angle sum property of a triangle),

∠C/2 + ∠B/2 + ∠A/2 = 180° (angle bisector property)

Therefore, ∠A/2 + ∠B/2 = 90° - ∠C/2

So, 2∠A/2 + 2∠B/2 = 180° - ∠C...(3)

Adding equations (1), (2), and (3), we get

∠AID + ∠BIE + ∠BAD + ∠EB + 2∠A/2 + 2∠B/2 = 360° - ∠C/2 + 180° + ∠C/2 + 180° - ∠C

∠AID + ∠BIE + ∠BAD + ∠EB + ∠A + ∠B = 360°(simplifying)

Therefore,

∠AID + ∠BIE + ∠BAD + ∠EB = 180°...(4)

Now, consider ΔABD and ΔEBD.

∠ABD = ∠EBD (∵ AD and BE are angle bisectors)

∠BAD = ∠BED [from equation (2)]

Therefore, ΔABD ≅ ΔEBD (∵ SAS congruence criterion)

So, BD = BD [by CPCTC]

Thus, we get AD = BE [by subtracting BD from both sides of AB + BD = BE]

Hence, the angle bisector from a vertex to the opposite side of a triangle is unique.

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Answer:

solutions are all values greater than 6

Step-by-step explanation:

add 15 to each side to get:

3x > 18

divide each side by 3 to get:

x > 6

solutions are all values greater than 6

Using the Poisson distribution, the probability of an earthquake in the 0.8-0.9 magnitude range sometime in the next 30 years is

1 - 1.9287 x 10⁻²².

It is given that mean recurrence of an earthquake is the 8.0-9.0 magnitude is approximately 1500 years.

We have to find the probability of an earthquake in this magnitude range sometime in the next 30 years.

Since, an occurrence of an earthquake is a rare event, we can use Poisson distribution here.

Poisson distribution gives the probability of occurrence of any event in a given time interval.

Let the average number of event per year in 30 years of period is λ.

\(\lambda = \frac{1500}{30}\)

λ = 50

Let, the occurrence of an earthquake is a random variable x.

Then the probability that at least an earthquake occur in next 30 years is calculated as:

P(x ≥ 1) = 1 - P(x<1)

P(x ≥ 1) = 1- P(x=0)   -----(1)

PDF of Poisson distribution with parameter λ is given as:

\(P(X = x) = \dfrac{e^{-\lambda}{\lambda}^x}{x!}\)

So, in this case

\(P(x=0)= \dfrac{e^{-50}{(50)}^0}{0!}\)

\(P(x=0)= \dfrac{1.9287 \times 10^{-22}}{1}\)

\(P(x=0)={1.9287 \times 10^{-22}\)

Substitute this value in equation (1)

P(x ≥ 1) = 1 - 1.9287 x 10⁻²²

Hence, the probability of an earthquake in next 30 years is

1 - 1.9287 x 10⁻²².

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Alleles in a population are represented as p and q, with p being the dominant allele and q being the recessive allele. In a population, the frequency of the alleles p and q must equal

1. If q equals 0.25, then p equals 0.75. This is because p + q = 1, so p = 1 - q. In this case, p = 1 - 0.25 = 0.75

.The frequency of p in this population is 0.75.

A resource population is any part of the environment that can be used to meet another organism's needs.

The first population acts as this because the second population is surviving by eating the first.

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The least number of computers that must be shipped is 10.

In order to determine the least number of computers that must be shipped, the equation that represents the cost of shipping should be equal to the selling price of the computers.

3000 + 100x = 400x

In order to determine the value of x, take the following steps:

3000 = 400x - 100x

3000 = 300x

x = 3000 / 300

x = 10

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Answer:

A

Step-by-step explanation:

Plug in the Input(x) for x in the equation.

y = 6(2) + 7

y in this case should equal 19 according to table A

19 = 6(2) + 7

19 = 12 + 7

19 = 19

Answer:

table A

Step-by-step explanation:

you can get this answer by putting an input number into the equation to get your output number. Make sure to subsitiute all Xs in the equation for said input number. And do this for each input number on your table.    

Answer:

5

25/5=5

Step-by-step explanation:

One of the variables that is categorical in the survey is the type of operating system used by the students.

This variable categorizes the students' responses into different categories based on the type of operating system they have on their personal computers.

Categorical variables are qualitative and represent characteristics or attributes that cannot be measured numerically.

In this case, the categories for the operating system variable might include options such as Windows, Mac, Linux, or Other.

Other variables in the survey may include numerical or quantitative data, such as the amount of RAM or the storage capacity of the students' computers.

These variables can be measured and expressed numerically.

However, since you asked for a variable that is categorical, the type of operating system is the relevant variable in this case.

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Answer:

-Scalene

- Isosceles

-Perpendicular lines

Answer: 96 miles cubed.

Step-by-step explanation: First, are you sure that the unit of measure is miles? But, anyway, you probably know how to calculate the area of a rectangle or square: length × width. With a 3D shape you do length × width × height. So we have 3 × 4 × 8 = 96.

a. The final result is obtained as (5 - 4z^(-3)) / (1 - z^(-1)).

b. The inverse Z-transform of -2jw * sin(7w) is -2j * δ(t - 1).

c. The final solution is 4w^2 + 12w + 37

The given question involves various operations and concepts related to the Z-transform. It includes finding the Z-transform of a given sequence, using operational theorems to determine the Z-transform and inverse Z-transform of different functions, and solving a second-order difference equation using the Z-transform technique.

(a) The Z-transform of the sequence {5-4Uk-3} is found using the definition of the Z-transform. By splitting the sequence into two terms and applying the shifting property, the final result is obtained as (5 - 4z^(-3)) / (1 - z^(-1)).

(b) (i) To find F(2e^(3jt)e^(-6t)), the operational theorem for the Z-transform is used. By applying the theorem and considering the Z-transform of 2, the expression becomes (2 * z^6) / (z - 1).

(ii) The inverse Z-transform of -2jw * sin(7w) is determined using the operational theorem. By considering the inverse Z-transform of -2j * δ(t - 1), where δ(t) is the Dirac delta function, the result is -2j * δ(t - 1).

(iii) The inverse Z-transform of 4w^2 + 12w + 37 is found using the operational theorem for derivatives. By taking the first derivative of the given expression and applying the inverse Z-transform, the final result can be obtained.

(c) The Z-transform technique is used to solve a second-order difference equation, Yk+2 - 3yk+1 + 2yk = 5, with initial conditions yo = -1 and y₁ = 2. By applying the Z-transform to the difference equation and solving for Y(z), the inverse Z-transform can be obtained to find the solution for the given difference equation.

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The height function for the baseball dropped from a stadium seat 77 feet above the ground is  s(t) = 77 - 16t^2.

To determine the height of the baseball after a given time, we need the specific function or equation that represents the relationship between the height and time. The problem statement mentions s(t) as the height function, but it does not provide the specific equation.

In general, when an object is dropped from a height and falls freely under the influence of gravity, the height function can be described by the equation:

s(t) = s0 - 16t^2

where s(t) represents the height of the object at time t, s0 is the initial height, and 16t^2 represents the distance traveled due to gravitational acceleration.

In this case, the initial height of the baseball is given as 77 feet above the ground, so we can substitute s0 = 77 into the equation:

s(t) = 77 - 16t^2

This equation represents the height of the baseball at any given time t in seconds.

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Vector equation of the line tangent to the graph of r(t) at the point p0 on the curve r(t) = (3t - 1) i + 13t j + 4 k.

To find a vector equation of the line tangent to the graph of r(t) at the point P0 on the curve r(t) = (3t - 1) i + 13t j + 16 k, where P0 is given as (-1,4), we can use the following steps:

Step 1: Find the derivative of r(t) with respect to t:

r'(t) = 3 i + 13 j

Step 2: Evaluate the derivative at the point P0:

r'(-1) = 3 i + 13 j

Step 3: Use the point P0 and the vector r'(-1) to form the vector equation of the tangent line:

r(t) = P0 + r'(-1) t

where t is a scalar parameter.

Plugging in the values, we get:

r(t) = (-1)i + 4j + (3i + 13j)t

Simplifying, we get:

r(t) = (3t - 1) i + 13t j + 4 k

Therefore, the vector equation of the line tangent to the graph of r(t) at the point P0 on the curve

r(t) = (3t - 1) i + 13t j + 16 k  is

r(t) = (3t - 1) i + 13t j + 4 k.

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Answer:

Step-by-step explanation:

-7y=42

we have to divide by 7

-y=6

multiply by -1

y=-6

Answer:

y=-6

Step-by-step explanation:

divide by -7 on both sides.

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

$22,880

Step-by-step explanation:

40 (hours a week) * 52 (weeks in a year) = 2,080

2080  * 11 (dollars an hour) = 22,880

So unless I a messing up somewhere I think it is $22,880  :)

Answer:

159

Step-by-step explanation:

The angle below is a co-interior angle

This means that both angle should add up to 180

Have a lovely day :)

Answer:

Step-by-step explanation:

Because we know that the two lines going diagonal are equivalent, we also know that they are parallel because equivalent lines have the same slope, meaning they are parallel. We also know that the two interior angles should add to 180. Follow the steps in the image for the rest.

-Hope this helped

The value of the t test is 13.36, we have to conclude that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

H0: u = 24000

H1: u > 24000

we have n = 84 homes

bar x = 27500

s = 2400

Next we have to find the test statistic

The formula for this is given as

\(t = \frac{x-u}{s/\sqrt{n} }\)

When we out in the values we would have

\(t = \frac{27500-24000}{2400/\sqrt{84} }\)

This would give us the answeer of the t test as

t test = 13. 3658

We have alpha = 0.02

the degree of freedom = 84 - 1 = 83

we have to find tα/2, df

=  ±2.0865

Given that the value of the test statistic is greater than critical value we would have to then reject the null hypothesis.

Hence the conclusion that we can make is that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

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Step-by-step explanation:

arithmetic sequence means every new term is the previous term plus a certain constant.

as we can see, this constant is +4 in our case.

15 + 4 = 19

19 + 4 = 23

23 + 4 = 27

...

so, we have

a1 = 15

a2 = a1 + 4 = 15 + 4 = 19

a3 = a2 + 4 = a1 + 4 + 4 = a1 + 2×4 = 15 + 8 = 23

...

an = an-1 + 4 = a1 + (n-1)×4 = 15 + (n-1)×4

The evaluation approach described in the given scenario is B.) forced distribution.

Forced distribution is an evaluation approach where performance ratings are distributed among employees according to predetermined percentages. In this case, the professor has predetermined that 10% of the class will receive an "A", 20% will receive a "B", 40% will receive a "C", 20% will receive a "D", and 10% will receive an "F".

This approach imposes a forced ranking system that restricts the distribution of grades based on predetermined proportions. Forced distribution can be useful in certain contexts as it helps differentiate performance levels and prevent grade inflation or deflation.

However, it also has limitations, as it may not accurately reflect individual performance and can create a competitive environment among students. It is important for educators to carefully consider the implications and potential drawbacks of using forced distribution in educational settings.

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Answer:

3:5

Before simplifying was 6:10

6:10 is the same as 3:5

Step-by-step explanation:

Answer:

the lengths of the sides of the yard.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

this reason is because the sides tell how big your backyard is

Answer:

90

Step-by-step explanation:

Positive 72 - (-18), is the same as 72 + 18, because two negatives cancel out and is the same as if you were adding. In other words, if you subtract a negative number, you are contradicting the negative, so you have one positive.

Hopefully that will help. :)

Answer: The required product of two given algebraic expressions =15abc +10b²c²

Step-by-step explanation:

Here we need to multiple two algebraic expressions: 3ab+2bc, 5bc

i.e. The required product = (3a+2bc)  x (5bc)

= 3a x 5bc + 2bc x 5bc    [Using right distributive property: (a+b)c= ac+bc]

= (3x 5)  abc + (2 x 5) (bc)²

= 15abc +10b²c²

Therefore, the required product of two given algebraic expressions = 15abc +10b²c²

Always choose the alpha level as 0.05.

The given statement;

When conducting a significance test in practice, how should you choose the alpha( α ) level,

→ When the repercussions of incorrectly rejecting the null hypothesis are more severe, use a greater alpha. Since it's the most appropriate in every case, choose alpha ( α ) = 0.05 always. When the repercussions of incorrectly rejecting the null hypothesis are more severe, use a smaller alpha.

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A statistic might read, "The mean weekly amount spent on groceries by fifty randomly selected households in one county." Hence option 1 is true.

Used the concept of statistics that states,

Statistics are truths discovered by the analysis of numerical data, such as information on how frequently something occurs

Now, in the example, "Fifty households randomly sampled in one county have a mean weekly amount spent on groceries."

Because it is a numerical summary or measurement obtained from a sample of data, the median weekly grocery expenditure qualifies as a statistic.

The statistic gives details on the typical spending patterns of the sampled homes, but it does not accurately reflect the county's complete household population.

Therefore, option 1 is true.

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Answer:

48π units³

OR

≈ 150.72 units³

Step-by-step explanation:

Volume formula for a cylinder is: πr²h

Using the measurements given, we get:

π×4²×3=

π×16×3=

π×48=

48π≈

150.72 units³

Answer:

Brainliest

Step-by-step explanation:

V= π r^2 h

see picture