Are the ratios 1:2 and 8:20 equivalent?

A recursive sequence is a sequence of numbers whose values are determined by the numbers that come before them in the sequence.

We’re given a sequence whose (n + 1)-th term f(n + 1) depends on the value of the n-th term f(n), specified by the recursive rule

f(n + 1) = -4 f(n) + 3

We’re also given the 1st term in the sequence, f(1) = 1. Using this value and the recursive rule, we can find the next term f(2). (Just replace n with 1.)

f(1 + 1) = -4 f(1) + 3

f(2) = -4 • 1 + 3

f(2) = -1

We do the same thing to find the next term f(3) :

f(2 + 1) = -4 f(2) + 3

f(3) = -4 • (-1) + 3

f(3) = 7

One more time to find the next term f(4) :

f(3 + 1) = -4 f(3) + 3

f(4) = -4 • 7 + 3

f(4) = -25

The probability that there are at least two people with the same birthday in a class of 95 students is about 0.9156 or 91.56%. This is a high probability due to the large number of students in the class.

To calculate the probability of at least two people having the same birthday in a class of 95 students, we can use the formula:
P(at least 2 people have the same birthday) = 1 - P(all 95 students have different birthdays)
The probability that the first student has a unique birthday is 1 (since there are no other students to share a birthday with yet). The probability that the second student has a unique birthday is 364/365 (since there is now one day taken up by the first student's birthday). The probability that the third student has a unique birthday is 363/365, and so on. We can multiply all of these probabilities together to get the probability that all 95 students have different birthdays:
P(all 95 students have different birthdays) = 1 x 364/365 x 363/365 x ... x 272/365
Using a calculator, we can find that this probability is approximately 0.0844.
Therefore, the probability that at least two people have the same birthday is:
P(at least 2 people have the same birthday) = 1 - 0.0844
P(at least 2 people have the same birthday) ≈ 0.9156
So the probability that there are at least two people with the same birthday in a class of 95 students is about 0.9156 or 91.56%. This is a high probability due to the large number of students in the class.

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The net pay amount for January would be $86,761.

Given the following information: Gross earnings in Vaughn Company were $114,000. All earnings are subject to 7.65% FICA taxes. Federal income tax withheld was $16,500, and state income tax withheld was $2,000.To calculate the net pay for January, first, we have to calculate the deductions:Gross earnings are:$114,000The FICA taxes for the earnings will be:7.65% of $114,000 = 0.0765 × $114,000 = $8,739State income tax withheld was $2,000Federal income tax withheld was $16,500Deductions are: 8,739 + 2,000 + 16,500 = $27,239The net pay amount for January would be:$114,000 - $27,239 = $86,761Answer: $86,761.

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The gender of the manatees could be an important variable when studying manatees. Gender is an a. categorical variable.

An example of a categorical variable is one that divides data into categories. Here, the categorical variable represents a particular gender while studying manatees. Rather than using numerical values, categorical variables are typically expressed by labels or terms like owns or rents. Researchers may more readily identify and analyse data by employing categorical variables. Thus, a categorical variable here is gender.

Variables that typically fall into separate categories or groups are known as categorical variables, and they cannot be quantified on a continuous scale. Gender is a categorical variable in study of manatees because it may be categorised into distinct groups, such as male or female, without the need of quantitative measures.

Complete Question:

Gender of the manatees could be an important variable when studying manatees. what type of variable is gender?

a. Categorical

B. Quantitative

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Let ABC be the given triangle. We can construct two triangles PAB and PBC such that they share the same height from P to AB and P to BC, respectively. We can label the side lengths of PAB and PBC as x and y, respectively. The total area of the triangle ABC is the sum of the areas of PAB and PBC:

Area_ABC = Area_PAB + Area_PBC We can write the area of each of the sub-triangles in terms of x and y by using the formula for the area of a triangle: Area_PAB = (1/2)(12)(x) = 6xArea_PBC = (1/2)(15)(y) = (15/2)y Setting the areas equal to each other and solving for y yields: y = (4/5)x Substituting this into the equation for the area of PBC yields:

Area_PBC = (1/2)(15/2)x = (15/4)x The area of ABC can also be written in terms of x by using the formula: Area_ABC = (1/2)(AB)(PQ) = (1/2)(12)(PQ) + (1/2)(15)(PQ) = (9/2)(PQ) Setting the areas equal to each other yields:(9/2)(PQ) = 6x + (15/4)x(9/2)(PQ) = (33/4)x(9/2)(PQ)/(33/4) = x(6/11)PQ = x(6/11)Thus, we can see that the longest possible integer length of the third altitude is $\boxed{66}$.

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Answer:

Yes, you are right. Great job!

Step-by-step explanation:

all even except 4th equation

Step-by-step explanation:

an even equation is the one who proves that f(-x) = f(x)

Answer:

A. 40.021

Step-by-step explanation:

Unlimited calls = $40

Text message = $0.021

NOTE:There is a difference between the value you gave for cost of text messages in the question and the values given in the group of answers. I will use $0.021 for cost of text messages since it is common to all answer choices.

Total cost = Cost of unlimited calls + cost of text messages

C = $40 + $0.021

= $40.021

Therefore, the equation which represent the total cost in dollars for a month is 40.021

A. 40.021

Answer:

he is right^ A.

Step-by-step explanation:

Answer:

it’s correct

Step-by-step explanation:

Answer:

\(\fbox {See below} \downarrow\)

Step-by-step explanation:

When taking the perpendicular of the line, it should be done at the midpoint of the line. Hence, by taking arcs from both endpoints, it should be done. This is why this is incorrect.

Answer:

42.25 feet ³

Step-by-step explanation:

Volume of the box = length × width × height

Length = 6 1/2 feet = 6.5 feet

Width = 3.25 feet

Height = 2 feet

Volume of the box = length × width × height

= 6.5 feet × 3.25 feet × 2 feet

= 42.25 feet ³

Volume of the box = 42.25 cubic foot

−196,16

.....................

Answer:

30

Step-by-step explanation:

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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Answer:

1) Isosceles

2) Scalene

3) Scalene

Step-by-step explanation:

The 1st choice is isosceles because 2 side lengths are equal.

The 2nd and 3rd choice are scalene because none of the sides equal the other sides.

Answer:

Part A

The rational equation that can be used to determine how long it would take Lara to clean the tank alone is; 6/9 + 6/x = 1

Part B

It would take Lara 18 hours to clean the tank if she works by herself

Step-by-step explanation:

Part A

The time it takes Kevin to clean an aquarium tank alone = 9 hours

The time it takes Kevin and Lara to clean the tank together = 6 hours

Let '1/x' represent Lara's cleaning rate, we have;

The time it would take Lara to clean 1 tank alone = 1/(1/x) = x

Kevin's cleaning rate, y = 1/9 tank per hour

The number of tanks, z =  tank

The total time it takes both of them to clean the tank, t = 6 hours

Therefore, we get;

t × y + t × 1/x = z

When t = 6, y = 1/9, and z = 1, we get;

6 × (1/9) + 6·(1/x) = 1

Therefore, the rational equation that can be used to determine how long it would take Lara to clean the tank if she work by herself, '1/x', is given as follows;

6/9 + 6·(1/x) = 1

6/9 + 6/x = 1

Part B

Solving the rational equation gives;

1/x = (1 - 6/9)/6 = 1/18

∴ 1/x = 1/18)

∴ x = 18

The time it would take Lara to clean the tank if she worked by herself, x = 18 hours

The process to find w involves using the fact that the angles around a point add up to 360°, and substituting expressions for the angles in terms of w to solve for it. , w = 102°

Let the angles formed by the three intersecting lines be A, B, and C as shown below:

A

/

B--C

We can see that A + B + C = 180° (since they form a straight line) and A + B = 76° (since that's the given angle).

Substituting A + B in terms of 76° in the first equation, we get:

A + B + C = 180°

76° + C = 180°

C = 104°

So, the equation that represents the relationship between the angles is: A + B + C = 180°.

To find w, we need to use the fact that the angles around a point add up to 360°.

Looking at the diagram below, we can see that the angles w, 76°, and x form a straight line, so we have:

w + 76° + x = 180°

We also know that the angles w, y, and 76° form a straight line, so we have:

w + y + 76° = 180°

Finally, we know that the angles x, y, and z form a straight line, so we have:

x + y + z = 180°

To solve for w, we can substitute x and y in terms of w using the first two equations:

x = 180° - 76° - w = 104° - w

y = 180° - 76° - w = 104° - w

Substituting these expressions in the third equation and solving for z, we get:

x + y + z = 180°

(104° - w) + (104° - w) + z = 180°

z = 2w - 128°

Now, we can substitute x, y, and z in terms of w in the first equation and solve for w:

w + (76°) + (104° - w) + (104° - w) + (2w - 128°) = 360°

4w - 48° = 360°

4w = 408°

w = 102°

Therefore, the process to find w involves using the fact that the angles around a point add up to 360°, and substituting expressions for the angles in terms of w to solve for it.

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Answer:

\(x = ( - 29)\)

Step-by-step explanation:

\( \frac{x + 1}{x + 5} = \frac{7}{6} \\ use \: \: \: cross \: \: multipication \\ 7(x + 5) = 6(x + 1) \\ 7x + 35 = 6x + 6 \\ 7x - 6x = - 35 + 6 \\ x = - 29\)

hope this helps you.

Answer:42.83 i think

Step-by-step explanation:

Answer:

42.83

Hope this helps and have a great day!!!

ENJOY!

The total number of ways to assign the pages to the printers is 6^5 = 7776.

(a)There are five printers. Each of the 125 pages can be assigned to one of these five printers. Thus, there are 5 choices of printers for the first page, followed by 5 choices for the second page, and so on, until there are 5 choices for the last page. By the multiplication principle, the total number of ways to assign the pages to the printers is 5 × 5 × ... × 5 = 5^125.

(b) The first and last pages must be printed in color, so two of the five printers must be chosen to do the color printing. There are 5 choices of printers for the first page and 5 choices for the last page, but once the two printers for the color pages are chosen, there are only 3 printers left to assign the remaining 123 black-and-white pages to.

Thus, by the multiplication principle, the total number of ways to assign the pages to the printers is 5 × 3^123.(c) Each printer can be assigned either 0, 25, 50, 75, 100, or 125 pages. Since there are five groups of 25 pages, the number of pages assigned to each printer must be a multiple of 25.

Thus, there are six choices for how many pages each printer will be assigned (0, 25, 50, 75, 100, or 125), and once those choices are made, there is only one way to assign each group of 25 pages to the corresponding printer. Thus, the total number of ways to assign the pages to the printers is the product of the number of ways to choose the number of pages assigned to each printer (6 choices for each of the 5 printers) and the number of ways to assign each group of 25 pages to the corresponding printer (1 way for each of the 5 groups).

Therefore, the total number of ways to assign the pages to the printers is 6^5 = 7776.

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Answer:1. 0.35. 0.35

Step-by-step explanation:

I did the question on edgenuity

The change for each consecutive time given is: 1

The change of each consecutive height given is: 0.35

The rate of change for the relationship between time and height is: 0.35

The table that displays the height of water when a pool is being filled against time is shown in the image attached. (See attachment).

Recall:

Rate of change can be calculated as: change in output / change in input

Change in output = difference between consecutive outputs

Change in input = difference between consecutive inputs

In the question given,

Time is input

Height is output

Thus:

Change for each consecutive input (time):

Therefore, the change of each consecutive input (time) is: 1

Change for each consecutive output (height):

Therefore, the change of each consecutive output(height) is: 0.35

Rate of change of the relationship between time and height:

Rate of change = change in height / change in time

Rate of change = 0.35/1 = 0.35

In summary:

The change for each consecutive time given is: 1

The change of each consecutive height given is: 0.35

The rate of change for the relationship between time and height is: 0.35

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Answer:

Step-by-step explanation:

Area of circle equation:

Circumference of circle equation:

Use circumference equation to find the radius:

Find the area:

The positive predictive value (PPV) and negative predictive value (NPV) of a test can be calculated using conditional probabilities and Bayes' formula. In this scenario, the sensitivity of the test is 99%, specificity is 98%, and the prevalence of the disease is 0.005. PPV represents the probability that a person with a positive test result actually has the disease, while NPV represents the probability that a person with a negative test result does not have the disease.

To calculate the positive predictive value (PPV), we need to find the probability that someone with a positive test actually has the disease. We can use Bayes' formula, which states that:

PPV = (Sensitivity * Prevalence) / [(Sensitivity * Prevalence) + [(1 - Specificity) * (1 - Prevalence)]]

Plugging in the given values, we have:

PPV = (0.99 * 0.005) / [(0.99 * 0.005) + [(1 - 0.98) * (1 - 0.005)]]

Simplifying the equation gives us:

PPV ≈ 0.3328 or 33.28%

Therefore, the positive predictive value of the test is approximately 33.28%.

Similarly, to calculate the negative predictive value (NPV), we need to find the probability that a person with a negative test result does not have the disease. The formula for NPV is:

NPV = (Specificity * (1 - Prevalence)) / [(Specificity * (1 - Prevalence)) + [(1 - Sensitivity) * Prevalence]]

Using the given values, we can calculate:

NPV = (0.98 * (1 - 0.005)) / [(0.98 * (1 - 0.005)) + [(1 - 0.99) * 0.005]]

Simplifying the equation gives us:

NPV ≈ 0.9999 or 99.99%

Therefore, the negative predictive value of the test is approximately 99.99%.

In summary, the positive predictive value (PPV) of the test is approximately 33.28%, indicating the probability that someone with a positive test actually has the disease. The negative predictive value (NPV) is approximately 99.99%, representing the probability that someone with a negative test result does not have the disease.

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Karen has made 76 calls today to secure donations at the call center.

Let's assume that Karen has made x calls so far today. According to the information given, she has convinced 18% of the people she has called to donate. This means that 18% of x calls have resulted in successful donations, which can be written as 0.18x.

Karen wants to be just over the 25% mark by convincing 12 out of the next 30 people she calls to donate. This means that the total number of successful donations should be slightly more than 25% of the total number of calls made. Representing this mathematically, we have (0.18x + 12)/(x + 30) > 0.25.

Simplifying the inequality, we have 0.18x + 12 > 0.25(x + 30). Solving for x, we find that x > 76.

Therefore, Karen has made 76 calls so far today to secure donations at the call center in order to be just over the 25% mark by convincing 12 out of the next 30 people she calls to donate.

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Answer:

187 games

Step-by-step explanation:

Calculation for how many games have the Hawks played this season

Numbers of games played=112 games/0.60

Numbers of games played=187 games

Therefore the numbers of games that Hawks

have played this season is 187 games

The number of individuals in the sample, n = 31

A one-sample (or one mean) t-test is applied to test whether the population-parameter is significantly different from some hypothetical value.

The degrees of freedom of the t-test, df = n – 1

Given,

The degrees of freedom of the t-test, df = 30

We have to find the sample size, n = df + 1

Therefore, the number of individuals in the sample:

n = df + 1

  = 30 + 1

  = 31

That is, the number of individuals in the sample, n = 31.

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\(\lim_{x\to1}{f(x)}\\\) does not exist.

Ally will be able to cover 285 miles for the trip

Ally wants to rent the car for one day

The rents costs $35 and $0.35 per mile

Ally has $134.75 to spend for the trip

The number of miles Ally can drive for the trip can be calculated as follows

134.75 - 35

= 99.75

99.75/0.35

= 285

Hence Ally will be able to drive 285 miles for the trip  

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