What is the rate of change for the function in the table?

Answer:

ight so combine the 14x and the 4x thats 18x then divide by 18 90 divided by 18 is 5 so x is 5

Step-by-step explanation:

The probability that four of the first five patients will be helped by the medicine is 0.39. The probability that a particular medicine will help a person is an important aspect of medicine.

The probability that a certain medicine will help a person is 0.75. A doctor will be seeing 15 patients today.

To find out the probability of the following:

a) P(The medicine will help all 15 patients)When each patient is independent of the other, then the probability of the medicine helping all 15 patients can be calculated by multiplying 0.75 by itself 15 times.

Therefore:

= P(The medicine will help all 15 patients)

= 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75

= 0.0047.

Therefore, the probability that the medicine will help all 15 patients is 0.0047.

b) P(The medicine helps 9 or more patients)

To determine this, we have to calculate the probability of the medicine helping 9 patients, 10 patients, 11 patients, 12 patients, 13 patients, 14 patients and 15 patients.

We can calculate these probabilities using the binomial probability formula. The probability of the medicine helping at least 9 patients is the sum of the probabilities of the medicine helping 9 patients, 10 patients, 11 patients, 12 patients, 13 patients, 14 patients and 15 patients.

Therefore:

P(The medicine helps 9 or more patients) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

= 0.196 + 0.326 + 0.305 + 0.176 + 0.066 + 0.018 + 0.003

= 0.99

Therefore, the probability that the medicine helps 9 or more patients is 0.99.

c) P(The medicine helps exactly 10 patients)Using the binomial probability formula, we can find that the probability that the medicine will help exactly 10 patients is:

P(X = 10) = nCx * p^x * q^(n - x), where n = 15, x = 10, p = 0.75 and q = 0.25

Therefore:

P(X = 10) = 15C10 * (0.75)^10 * (0.25)^5

= 0.20

Therefore, the probability that the medicine helps exactly 10 patients is 0.20.

d) P(Four of the first five patients will be helped by the medicine)

Using the binomial probability formula, we can find that the probability that 4 of the first 5 patients will be helped by the medicine is:

P(X = 4) = nCx * p^x * q^(n - x)y, where n = 5, x = 4, p = 0.75 and q = 0.25

Therefore:

P(X = 4) = 5C4 * (0.75)^4 * (0.25)^1

= 0.39

Therefore, the probability that four of the first five patients will be helped by the medicine is 0.39.

The probability that a particular medicine will help a person is an important aspect of medicine. The likelihood of the medicine helping all 15 patients is very low, and the likelihood of the medicine helping 9 or more patients is very high. The likelihood of the medicine helping exactly 10 patients is relatively low, and the likelihood of four of the first five patients being helped by the medicine is relatively high.

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Paris earned a real interest rate of approximately 7.98% in 2021, calculated by subtracting the inflation rate of 10% from the nominal interest rate of 11%.

To calculate the real interest rate, we need to adjust the nominal interest rate using the Consumer Price Index (CPI) inflation rate. The CPI increased from 120 to 132, indicating an inflation rate of (132 - 120) / 120 = 0.1, or 10%.

The real interest rate can be calculated using the formula: Real Interest Rate = Nominal Interest Rate - Inflation Rate.

In this case, the nominal interest rate is 11%, and the inflation rate is 10%. Substituting the values into the formula:

Real Interest Rate = 11% - 10% = 1%.

However, it is important to note that this calculation provides the approximate real interest rate. Other factors such as compounding frequency and the specific calculation method used by the mutual fund may affect the actual real interest rate earned by Paris.

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The ability of typhoid to spread can be best attributed to bacteria in unclean water. Unclean water contaminated with the bacterium Salmonella typhi is a primary source of transmission for typhoid fever.

Typhoid fever is caused by the bacterium Salmonella typhi, which primarily spreads through the consumption of contaminated food and water. Unclean water sources, such as those contaminated with fecal matter containing the bacteria, can serve as a breeding ground for the transmission of typhoid.

When individuals consume or come into contact with water contaminated by the bacteria, they become susceptible to the infection. Other modes of transmission, such as contaminated food, can also contribute to the spread of the disease. However, the main factor behind the ability of typhoid to spread is the presence of the bacteria in unclean water, highlighting the importance of clean water sources and proper sanitation practices in preventing the transmission of typhoid.

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Answer:

you have it correct sir

Step-by-step explanation:

Answer:

Step-by-step explanation:

B. Because your domain is the number of songs someone will purchase

Answer: c = b/a

Step-by-step explanation:

ax+ b= a(x+ c)

ax+ b= ax+ ac

b= ac

c = b/a

Answer:

B

Step-by-step explanation:

Answer:

B) There were N people on the beach at 10:00a.m.

Step-by-step explanation:

As stated, "t" represents the hours past midnight. So the first part states that it is 10 hours after midnight. Since we know its ten hours after midnight, aka 10am, what we don't know is how many people are on the beach. therefore we know the answer is B.

Fron the given question, we can say that systematic sample because not all sample are possible.

Using the probabilistic sampling technique known as systematic sampling, researchers periodically choose individuals from a community. Choose each 15th of her, for instance, from the population list. You can simulate the advantages of straightforward random sampling by randomly sorting the population.

\(Since every 100th horse is selected in the sample. Thus, Systematic Sampling is used.\)

Further,

Sampling method is said to be Simple Random Sampling if unit from the population are picked randomly without any criteria, so that each unit as similar chance of selection.

If any criteria are used to select every sample, such as selecting every fourth unit, the sampling technique is said to be systematic sampling.

If the population is divided into various groups that share the same characteristic, the sampling method is said to be stratified sampling. Additionally, units are chosen at random from these groups.

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Answer:

D

Step-by-step explanation:

The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

y - 1 = (-1/8)(x - 2)

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

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The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

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9.53 fertilizer bags are required to cover a lawn that is rectangular and is 260 feet by 120 feet.

The nitrogen fertilizer type known as urea is inexpensive. This is as a result of its high nitrogen content and the ensuing low costs of storage and transportation.

When all that is required for a soil fertility program is nitrogen, urea can be the best fertilizer to use.

Finding the location of the lawn is the first stage.

Area: 110 feet by 260 feet.

28600 square feet.

Calculating how many bags of fertilizer to purchase is the next step.

Bags = Area x 3,000 feet

Bags: 28600 feet / 3000 feet

9.53 bags total are in the bag.

Inconclusion 9.53 sacks of fertilizer should be bought to cover a lawn that is rectangular and measures 260 feet by 120 feet.

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Answer:

Step-by-step explanation:

are the what???

The solution to the given quadratic expression using the completing the square is x = ±√-2 -5

This is a method of factoring quadratic expression. Given the quadratic function.

x^2 + 10x + 27 = 0

Subtract 27 from both sides

x^2 + 10x = -27

Complete the square

x^2 +10x +5^2 = -27 + 25

(x+5)² = -2
x +5 = ±√-2
x = ±√-2 -5

Hence the solution to the given quadratic expression using the completing the square is  x = ±√-2 -5

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A linear function with a slope of -0.5 is parallel to the line 2x + 4y =16.

A linear function is modeled by:

y = mx + b

In which:

In slope-intercept format, the linear equation given is:

4y = 16 - 2x

y = -0.5x + 4.

When two lines are parallel, they have the same slope, hence a linear function with a slope of -0.5 is parallel to the line 2x + 4y =16.

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Hey there!

3/4 • 5/7

= 3(5)/4(7)

3(5) = 15⮐ Solving for your NUMERATOR (TOP number)

4(7) = 28⮐ Solving for your DENOMINATOR (BOTTOM number)

= 15/28

Answer: 15/28

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The three conditions for a function to be continuous at a point x=a are:

a) The function is defined at x=a.

b) The limit of the function as x approaches a exists.

c) The limit of the function as x approaches a is equal to the value of the function at x=a.

The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.

The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.

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Answer:

5

Step-by-step explanation:

24- 4= 20/ 4 = 5

Answer:

5

Step-by-step explanation:

24 - 4 = 20

20 divided by 4 = 5

Hope this helps☺️

The radius of convergence, R, of the series. Σn=1[infinity] to \(n/3^n x^n\). R =3. the interval, I, of convergence of the series I=[-3, 3].

To find the radius of convergence, we can use the ratio test, which states that if

\(lim |(a_{n+1}/a_n)| = L\)

exists, then the series converges if L < 1 and diverges if L > 1. If L = 1, the test is inconclusive and we need to use another test.

Applying the ratio test to our series, we get:

\(lim |(a_{n+1}/a_n)| = lim |((n+1)/3)(x/(n+1))| = |x/3|\)

Since this limit exists for all x, the series converges for all x where |x/3| < 1, and diverges for |x/3| > 1. Thus, the radius of convergence is R = 3.

To find the interval of convergence, we need to check the endpoints x = -3 and x = 3 separately.

When x = -3, the series becomes:

Σn=1[infinity] to \(n/(-1)^n 3^n/3^n\)

which is a geometric series with ratio -1/3. By the formula for the sum of a geometric series, this series converges to:

S = 3/4

When x = 3, the series becomes:

Σn=1[infinity] to \(n3^n/3^n\)

which is also a geometric series, this time with ratio 1. Thus, this series diverges.

Therefore, the interval of convergence is (-3,3], which means the series converges for all x in the open interval (-3,3) and converges at x = -3, but diverges at x = 3.

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The vertices of the dilated image are P' (2, 2), R' (-2, -2), and S' (-2, 3).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/3 centered at the origin as follows:

Ordered pair P (6, 6) → Ordered pair P' (6 × 1/3, 6 × 1/3) = Ordered pair P' (2, 2).

Ordered pair R (-6, -6) → Ordered pair R' (-6 × 1/3, -6 × 1/3) = Ordered pair R' (-2, -2).

Ordered pair S (-6, 6) → Ordered pair R' (-6 × 1/3, 6 × 1/3) = Ordered pair S' (-2, 3).

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Answer:

1. slope is 2

2. a is 5

3. b is 6

4. 0

Step-by-step explanation:

Answer:

The answer is

24,3210

Answer:

the inverse is f^-1(x)=3x+6

Step-by-step explanation:

The probability of the golden marble is \(\frac{3}{38}\) .

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. The likelihood that an event will occur increases with its probability.

possible outcome =3

favorable outcomes = 38

Probability = \(\frac{favorable outcomes}{possible outcome}\)

Probability  \(=\frac{3}{38}\)

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The best lower bound for the volume is 24 cm³, and the best upper bound is 120 cm³ and the best lower bound for the surface area is 52 cm², and the best upper bound is 148 cm².

a. To determine the best upper and lower bounds for the volume of the rectangular parallelepiped, we can consider the extreme cases by rounding each side to the nearest centimeter.

Lower bound: If we round each side down to the nearest centimeter, we get a rectangular parallelepiped with sides 2 cm, 3 cm, and 4 cm. The volume of this parallelepiped is 2 cm * 3 cm * 4 cm = 24 cm³.

Upper bound: If we round each side up to the nearest centimeter, we get a rectangular parallelepiped with sides 4 cm, 5 cm, and 6 cm. The volume of this parallelepiped is 4 cm * 5 cm * 6 cm = 120 cm³.

Therefore, the best lower bound for the volume is 24 cm³, and the best upper bound is 120 cm³.

b. Similar to the volume, we can determine the best upper and lower bounds for the surface area of the parallelepiped by considering the extreme cases.

Lower bound: If we round each side down to the nearest centimeter, the dimensions of the parallelepiped become 2 cm, 3 cm, and 4 cm. The surface area is calculated as follows:

2 * (2 cm * 3 cm + 3 cm * 4 cm + 4 cm * 2 cm) = 2 * (6 cm² + 12 cm² + 8 cm²) = 2 * 26 cm² = 52 cm².

Upper bound: If we round each side up to the nearest centimeter, the dimensions become 4 cm, 5 cm, and 6 cm. The surface area is calculated as follows:

2 * (4 cm * 5 cm + 5 cm * 6 cm + 6 cm * 4 cm) = 2 * (20 cm² + 30 cm² + 24 cm²) = 2 * 74 cm² = 148 cm².

Therefore, the best lower bound for the surface area is 52 cm², and the best upper bound is 148 cm².

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Answer:

6.4 x10^ -4

Step-by-step explanation:

the number has to berween 1 and 9 ao multiply by 10000 and because you went from a small number to a bigger number ,it is a negative power

when sample size increases, everything else remaining the same, the width of a confidence interval decreases.

The sample size is defined as the the number of observations or participants included in a study.

The confidence interval is defined as the mean of the estimate plus and minus the variation in that estimate. That means when you do the test multiple times, then the value may be vary from the estimated value. The confidence interval is the range of those values.

So when the sample size increases the width of the confidence interval decreases

Hence, when sample size increases, everything else remaining the same, the width of a confidence interval decreases.

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Answer:

8.5%

Step-by-step explanation: