Determine the common ratio for each of the following geometric series and determine which ones have an infinite sum

Complete question :

The manager of Pia’s Taco Casa makes a deposit into the restaurant’s checking account at the end of the day. She has 2 fifty-dollar bills, 16 twenty-dollar bills, 4 ten-dollar bills, 1 five-dollar bill, 24 quarters, 12 dimes, and 3 nickels. She wants to receive 20 one-dollar bills to use as change the next day. How much is the total deposit

Answer:

$452.35

Step-by-step explanation:

1 Nickel = 25 cents = $0.25

1 dime = 10 cent = $0.10

1 quarter = 5 cent = $0.05

Notes deposited :

2 fifty-dollar bills = $50 * 2 = $100

16 twenty-dollar bills = $20 * 16 = $320

4 ten-dollar bills = $10 * 4 = $40

1 five-dollar bill = $5 * 1 = $5

24 quarters = 24 * $0.25 = $6

12 dimes = 12 * $0.1 = $1.2

3 nickels = 3 * $0.05 = $0.15

Total deposit :

$(100+320+40+5+6+1.2+0.15) =$472.35

Amount to withdraw:

20 $1 bill = $1 * 20 = $20

Net deposit :

Deposit - withdraw

$472.35 - $20

= $452.35

1. Cosine is a function that represents the ratio of adjacent over hypotenuse. The range of values for cosine varies from -1 to 1. Therefore, a cosine value of 2 is impossible. Hence, there is no angle in the 3rd quadrant that has a cosine value of 2.

.2. A tangent function has an undefined value whenever it results in a denominator that equals zero. Thus, any angles with tangent functions having a denominator of zero will have an undefined value. Tangent is undefined at angles 90 degrees and 270 degrees. These angles lie on the positive and negative y-axes, respectively.3. -360° < 0 < 360° is a possible range for an angle. Any angle that is an integer multiple of 360 degrees (n*360) is a coterminal angle.

This means that all coterminal angles have the same reference angle, or the smallest angle between the terminal side of an angle and the x-axis, which can be found by calculating the remainder when the angle is divided by 360. Thus, all coterminal angles can be expressed as α + n(360), where α is the reference angle and n is an integer.

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Answer:

The Correct answer is

57°

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D has the answer of 69/64 which is bigger then the others :)

The equation of the tangent line with derivatives is y - y₁ = m(x - x₁)

The derivative of a function tells us the slope of the tangent line at any given point on the curve. Thus, we can find the slope of the tangent line to the curve at a specific point by taking the derivative of the function at that point.

Once we have the slope of the tangent line, we need to find its y-intercept. We can do this by using the point-slope form of a line. The point-slope form of a line is

=> y - y₁ = m(x - x₁),

where m is the slope of the line, and (x₁, y₁) is any point on the line. Since we already have the slope of the tangent line and the point at which it touches the curve, we can plug these values into the equation and solve for y-intercept.

Therefore, to find the equation of the tangent line with derivatives, we need to follow these steps:

Find the derivative of the function at the given point.

Plug in the x-coordinate of the given point into the derivative to find the slope of the tangent line.

Use the point-slope form of a line with the slope and the given point to find the y-intercept of the tangent line.

Write the equation of the tangent line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the tangent line at a different point on the curve, we would need to repeat these steps for that point.

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Answer:

b. F' (3, 0), G' (-6, -1), H' (-5, -3)

It indicates that the test is highly accurate in correctly identifying individuals with hepatitis C (high sensitivity) and accurately ruling out individuals without the disease (high specificity).

Sensitivity and specificity are two important measures of a diagnostic test's performance. Sensitivity refers to the test's ability to correctly identify individuals who have the condition, while specificity refers to its ability to correctly identify individuals who do not have the condition.

In the case of the ELISA test for hepatitis C, a sensitivity of 95% means that the test will correctly identify 95% of individuals who actually have hepatitis C as positive. This indicates a high probability of detecting the disease when it is present.

On the other hand, a specificity of 90% means that the test will correctly identify 90% of individuals who do not have hepatitis C as negative. This suggests that there is a 10% chance of a false positive result, where individuals without the disease are mistakenly identified as positive.

Overall, the high sensitivity and specificity of the ELISA test for hepatitis C make it a valuable tool in the diagnosis and screening of individuals for this infectious disease. However, it is important to consider that no test is 100% accurate, and false results can still occur. Therefore, additional confirmatory tests may be required in certain cases to ensure accurate diagnosis and appropriate medical intervention.

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Ruth can contribute $2400 as the maximum amount as an additional contribution for the tax year.

People enrolling in high-deductible health plan (HDHP) receive Healthy Savings Account (HSA) with tax advantages. It offers no income tax on the money saved, which can also be carried forward in case of job switch, retirement and varied health plans.

It allows total contribution of $3400 for medical expenses from employers and employees.

Based on this data, the maximum contributional amount can be = 3400 - 1000

Maximum contributional amount = $2400

Hence, the maximum contributional amount is $2400.

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Answer:

2824 pigs

Step-by-step explanation:

You divide 101667 by 36. The resulting number, 2824 , rounded to the nearest whole number, 2824, is your answer.

Answer: 2a+5

5a-2-3a+7

First gather together the like terms

5a-3a  and  -2+7

then solve

5-3=2   and -2+7=5

answer = 2a+5

Answer:

the answer should be b. it just makes sense

The time that it take to knit the scarf from start to finish is 10 hours.

From the information, the volunteer knits a 5-foot long scarf at a constant rate and after 4 hours, the volunteer still has to knit 3 feet of the scarf.

Therefore, the volunteer used 4 hours to knit 2 scarf. The time used per scarf is 4/2 = 2 hours.

In this case, the time taken to finish the scarf will be:

= Time per feet × Total feet

= 2 × 5

= 10 hours.

It'll take 10 hours.

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Answer:  D) 2.95 units

Step-by-step explanation:
I just took this

The probability of waiting longer than one hour for a taxi is approximately 0.5488

Let X be the time between arrivals of taxis at the intersection. Then, X follows an exponential distribution with a mean of 10 minutes, i.e., E(X) = 10.

We want to find the probability of waiting longer than one hour (i.e., 60 minutes) for a taxi. Let Y be the waiting time for a taxi. Then, Y = kX, where k is a constant.

We can find k as follows

E(Y) = E(kX) = kE(X) = 10k

Since the mean waiting time is one hour (i.e., 60 minutes), we have

E(Y) = 60 minutes = 1 hour

Therefore, we get

10k = 1

k = 1/10

Now we can find the probability of waiting longer than one hour for a taxi as follows

P(Y > 60) = P(kX > 60) = P(X > 6) [since k = 1/10]

where the last step follows from the fact that X follows an exponential distribution with mean 10, so P(X > x) = e^(-x/10) for any x > 0.

Therefore, we get

P(Y > 60) = P(X > 6) = e^(-6/10) = e^(-0.6) ≈ 0.5488

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The given question is incomplete, the complete question is:

The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. (a) What is the probability that you wait longer than one hour for a taxi?

Answer:

Hope this is right.

1. 7(4x-5)

2. 28x-35

Step-by-step explanation:

Answer:

the area would be 15 if you use are equals 1/2 base times height

The plan that is most useful for demonstrating a new technology or service or to reach a market that is widely spread out is a proof-of-concept website

The statement about the market section of the classic business plan that is not true is that some people prefer to relocate the competition and competitive advantage section from the market section to the industry section.

A critical risk to the success of your business plan is Overlooked competition.

The pitch deck categories that is sometimes given in the form of a user's experience is Problem slide.

There are two goals you can seek in the "ask" of your elevator pitch. One is to build your network and the other is to get the listener to Make a micro-commitment

A good marketing strategy is most likely to focus on the longer-term competitive plan.

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Answer:

the first is 26 and the second is 84.5 or 84 or 85 depending or if you need to round it and whether you round up or down

Answer:

26 cups of flour for the first pizza, 2 pizza's made with 13 cups of flour

Step-by-step explanation:

One Pizza uses 6.5 cups of flour (divide 39/6)

For the second fill in the blank, multiply 6.5*4 to get 26

For the last one, divide 13 by 6.5 to get 2

Hope this helps!

Answer:

35/8; 5 2/8

Step-by-step explanation:

7/8 × 5 = 35/8

35/8 should be simplified down to 5 and 2/8th tanks

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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The exact probability that the absolute value of the difference between the sample sum of the labels and -581.4 exceeds 31.54 is approximately 0.1128 or 11.28%.

To find the exact probability, we will use the properties of the normal distribution.

Let X be the random variable representing the sum of the labels on the tickets. We know that the mean of X (μ) is -581.4 and the standard deviation of X (σ) is √(17) × 4.5.

We want to find the probability that the absolute value of the difference between X and -581.4 exceeds 31.54. In other words, we want to find P(|X - (-581.4)| > 31.54).

Convert the inequality into a standard normal distribution form.

The standard normal distribution has a mean of 0 and a standard deviation of 1. To convert X to a standard normal random variable Z, we use the formula:

Z = (X - μ) / σ

In our case:

Z = (X - (-581.4)) / (√(17) * 4.5)

Calculate the Z-score.

Z = (31.54) / (√(17) * 4.5) ≈ 1.591

Find the probability using a standard normal distribution table or a calculator.

P(Z > 1.591) ≈ 0.0564 (rounded to four decimal places)

Account for both tails of the distribution.

Since we are interested in the absolute difference, we need to consider both tails of the normal distribution. Therefore, the total probability of the absolute difference exceeding 31.54 is:

P(|X - (-581.4)| > 31.54) = 2 P(Z > 1.591) ≈ 2 × 0.0564 ≈ 0.1128

So, the exact probability that the absolute value of the difference between the sample sum of the labels and -581.4 exceeds 31.54 is approximately 0.1128 or 11.28%.

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Answer:

Step-by-step explanation:

\(a^{m} * b^{m}\) = \((ab)^{m}\)

Yes, he can!!

\(5^{c} * 2^{c} = (2 * 5 )^{c}\) = \(10^{c}\)

For example,

2³ × 3³ = 8 × 27 = 216

6³ = 216

The expression can not be simplified as it do not have same base, and can be written as \(10^c\)

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, Phillips says he cannot simplify the expression \(5^c.2^c\)

She can not simplify the expression because the bases of the expression are not same, and this expression is same as

\(5^c.2^c\\\\= (5.2)^2\\\\=10^c\)

Hence, the expression can not be simplified as it do not have same base, and can be written as \(10^c\)

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Answer:

x=5

Step-by-step explanation:

4x-9=29

4x=29-9

4x=20

x=20/4

x=5

Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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Main Answer:The approximate probability is 0.033

Supporting Question and Answer:

How do we calculate the expected average and standard deviation for a sample?

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

Body of the Solution:

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Final Answer:Therefore, the approximate probability is 0.033, accurate to three decimal places.

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The approximate probability is 0.033

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Therefore, the approximate probability is 0.033, accurate to three decimal places.

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To find the minimum score of the top 2.5% of students, we need to calculate the z-score corresponding to the 97.5th percentile and then convert it back to the original SAT score scale.

First, let's calculate the z-score using the formula:

z = (x - μ) / σ

where x is the SAT score, μ is the mean (1175), and σ is the standard deviation (120).

To find the z-score corresponding to the 97.5th percentile, we need to find the z-score value that leaves 2.5% in the tail of the distribution (to the right).

Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the 97.5th percentile is approximately 1.96.

Now we can solve for x (the SAT score) in the z-score formula:

1.96 = (x - 1175) / 120

Multiply both sides by 120:

1.96 * 120 = x - 1175

235.2 = x - 1175

Add 1175 to both sides:

235.2 + 1175 = x

1410.2 = x

Therefore, the minimum score of the top 2.5% of students is approximately 1410.

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Answer:

f(x) is going to be on the y axis or intercept and what number it is on the line is in quotes f(x)="6"+2(1.05)^x it would be at 6 on the y axis.

Answer:

3x

Step-by-step explanation:

because if f is -5, -5=-3x-4, -5+4, -1=-3 divide and get 3=x