The 5-Number Summary for the heights (feet) of White Pine trees is as follows: Min: 50.5 Q1: 148.6 Med: 170.3 Q3: 196.4 Max: 290.9 Identify which of the following heights would be considered an outlier: 71.8 ft. 277.1 ft. 288.5 ft. 71.8 ft. 71.8 ft. & 288.5 Ft 71.8 ft. 277.1 ft. & 288.5 ft. O277 1 ft. & 288.5t
The height of 277.1 ft. would be considered an outlier based on the given 5-Number Summary for the heights of White Pine trees.
An outlier is a data point that is significantly different from other observations in a dataset. In order to identify outliers, we can use the 5-Number Summary, which includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value. Outliers can be identified as values that are more than 1.5 times the interquartile range (IQR) below Q1 or above Q3. The IQR is the distance between Q3 and Q1.
In this case, the IQR is 196.4 - 148.6 = 47.8 ft. The lower bound for identifying outliers is Q1 - 1.5IQR = 75.9 ft. and the upper bound is Q3 + 1.5IQR = 269.1 ft. Therefore, any value below 75.9 ft. or above 269.1 ft. would be considered an outlier.
Out of the given heights, only 277.1 ft. is greater than the upper bound of 269.1 ft., making it an outlier. The other values, including 71.8 ft. and 288.5 ft., are within the range defined by the 5-Number Summary and are not outliers.
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Question ) A company that builds burglar alarm systems designs a detection system that uses LDR sensors with a built-in electrical circuit; this circuit can contain lamps (resistors) in series or lamps (resistors) in parallel. When the sensors are activated, they turn on a siren that produces a loud sound in the house, these in turn turn on the circuit that accompanies it, causing the lighting of the lights in the environment. Spotlights are common, while the LDR sensor has the following characteristic graph (on a logarithmic-linear scale): a) How do you think the lights alarm is activated? explain
b) Estimate the value of the resistance of the sensor when it is activated. Justify.
c) Which of the circuits (series or parallel) will produce more light in the house? justify
d) Where in the house would you place each part of the detection system? explain
The lamps should be placed strategically around the house to provide adequate illumination in the event of an intrusion. It is important to ensure that the lamps are located in areas where they will not be easily disabled by an intruder. Additionally, the circuitry for the lamps should be placed in a secure location where it will not be easily tampered with by an intruder.
a) The lights alarm is activated when the LDR sensor detects a change in light intensity, which can occur when an intruder enters the premises or when there is a sudden change in ambient lighting conditions.
b) To estimate the value of the resistance of the sensor when it is activated, we need to refer to the characteristic graph of the LDR sensor. According to the graph, we can see that the resistance of the LDR sensor decreases as the light intensity increases. Therefore, when the sensor is activated (when there is a sudden increase in light intensity), we can expect the resistance of the LDR sensor to be at its lowest point on the graph. The exact value will depend on the specific characteristics of the LDR sensor being used and the intensity of the light triggering the activation.
c) The circuit with lamps in parallel will produce more light in the house compared to the circuit with lamps in series. This is because in a parallel circuit, each lamp receives the full voltage from the power source, whereas in a series circuit, the voltage is divided between the lamps. Therefore, the lamps in a parallel circuit will shine brighter than those in a series circuit, providing more illumination in the house.
d) The LDR sensors should be placed in strategic locations where they can detect any changes in light intensity caused by an intruder entering the premises. These may include entry points such as doors and windows or other areas where an intruder may try to gain access.
The siren should be placed in a central location in the house where it can be heard throughout the entire premises. This will help alert occupants to the presence of an intruder.
The lamps should be placed strategically around the house to provide adequate illumination in the event of an intrusion. It is important to ensure that the lamps are located in areas where they will not be easily disabled by an intruder. Additionally, the circuitry for the lamps should be placed in a secure location where it will not be easily tampered with by an intruder.
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Select all the correct answers.
63. 26
Which expressions are equal to
23 ?
Answer: The first option and the third option
Step-by-step explanation: You are not supposed to find something equivalent to the fraction, you have to divide the fraction.
13824 ÷ 8 = 1728
Then it is when you try to find a number equivalent to 1728. 12 to the power of 3 equals 1728
12×12=144
144×12=1728
12 to the power of 3 is equivalent to 1728
These are wrong: 2 to the power of three is unequivalent and so is 12 to the power of 6 and 6 to the power of 3
2 to the power of 6 is 64
2×2=4
4×2=8
8×2=16
16×2=32
32×2=64
3 to the power of 3 is 27
3×3=9
9×3=27
64 times 27 equals 1728 so it's equivalent and that means that our answers are A, the 1st option , and C, the 3rd option
The equivalent expression will be;
⇒ 12³
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 6³ × 2⁶ / 2³
Now,
Since, The expression is,
⇒ 6³ × 2⁶ / 2³
Solve as;
⇒ 6³ × 2⁶ × 2⁻³
⇒ 6³ × 2⁶⁻³
⇒ 6³ × 2³
⇒ (6 × 2)³
⇒ 12³
Thus, We get;
⇒ 6³ × 2⁶ / 2³ = 12³
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Solve for y in the two equations below using substitution.
3x - 9y = 9
-2x - 2y = 8
Answer:
C
Step-by-step explanation:
3x - 9y = 9 → (1)
- 2x +2y = 8 ( subtract 2y from both sides )
- 2x = - 2y + 8 ( divide through by - 2 )
x = y - 4
substitute x = y - 4 into (1)
3(y - 4) - 9y = 9
3y - 12 - 9y = 9
- 6y - 12 = 9 ( add 12 to both sides )
- 6y = 21 ( divide both sides by - 6 )
y = \(\frac{21}{-6}\) = - \(\frac{7}{2}\)
Would this be -4? Just wanna confirm!
Answer:
Yes
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The UAE Hope Probe is between 22,000 Km and 44,000 KM away from mars. This means its between _____________m and ______________m. PLease reply in 2 min and SHOW UR WORK :)
Answer:
This means it is between 22000000 m and 44000000 m.
Step-by-step explanation:
From the question, the UAE Hope Pobe is between 22 000 km and 44 000 km away from Mars.
Since,
1 000 m = 1 km
Then,
22 000 km = 22 000 x 1000 m
= 22000000 m
also,
44000 km = 44000 x 1000 m
= 44000000 m
Therefore, the Probe is between 22000000 m and 44000000 m.
2 How and why would lighting and ventilation needs
differ between the dining area and the kitchen used to prepare food
in a university dining center?
Divide into groups of two to three people. Visit t
Regular maintenance and inspections are essential to ensure the systems are functioning effectively and meeting the required standards.
The dining area and the kitchen used to prepare food in a university dining center have different lighting and ventilation needs due to their distinct purposes and requirements. Here's how and why their needs may differ:
1. Lighting:
- Dining Area: The dining area is primarily a space for eating and socializing. It requires comfortable and pleasant lighting to create a welcoming and inviting atmosphere.
The lighting should be evenly distributed to ensure visibility and allow people to see their food and interact with others. Warm and soft lighting can enhance the ambiance and promote a relaxed dining experience.
- Kitchen: The kitchen is a functional area where food is prepared, cooked, and plated. It requires bright and focused lighting to ensure proper visibility and facilitate safe and efficient food handling.
Bright task lighting is necessary for food preparation areas, cooking stations, and cutting surfaces to ensure accuracy, cleanliness, and food safety. Additionally, proper lighting helps staff identify food quality, monitor cooking processes, and prevent accidents.
2. Ventilation:
- Dining Area: The dining area typically requires adequate ventilation to maintain a comfortable and pleasant environment for diners. Ventilation systems in the dining area primarily focus on maintaining air circulation, controlling temperature, and removing odors.
- Kitchen: The kitchen, on the other hand, has more stringent ventilation requirements due to the nature of food preparation. A commercial kitchen generates heat, steam, smoke, and food odors, which can affect air quality and pose health risks if not properly managed.
The kitchen requires specialized ventilation systems, such as exhaust hoods, fans, and ductwork, to remove heat, steam, and grease-laden air. This helps maintain a clean and safe working environment, minimize odors, control humidity, and prevent the buildup of harmful contaminants.
It's important to note that specific regulations and guidelines may vary depending on local health and safety standards. Therefore, it's crucial for dining centers in universities to comply with applicable codes and regulations regarding lighting and ventilation in both the dining area and the kitchen.
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Use polar coordinates to find the volume of the given solid. Inside the sphere x^2 + y^2 + z^2 = 36 and outside the cylinder x^2 + y^2 = 1.
The required volume of the given solid is (√16 - r²) -(-√16 - r²).
What is volume?The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.
Volume and the notion of length are connected.
Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.
The cubic meter (m3), a derived unit, is the SI unit of volume.
So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.
We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.
The solid's volume is (√16 - r²) -(-√16 - r²).
Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).
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Correct question:
Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
A scale drawing of a rectangular park had a scale of 1 cm = 120 m.
What is the actual area of the park in meters squared?
Answer:
Solution
1 cm= 120 m
11.1 cm=120×11.1
=1332 m
5.4 cm=5.4×120
=648 m
area of rectangle=l×b
=1332×648
=863,136 m^2
hope it helps you
make me brainliest if u r satisfied
A Research company found that 11% of The people That they called agreed to Participate in a survey. If the company called 196 people, about how many would have be expected to participate in the survey?
Answer:
22
Step-by-step explanation:
11% of 196 = 21.56
Divide by 10 and divide by 100. Add them together
You must round this up because you cant really have .56 of a person.
Which is bigger 8 kg or 850 grams
Which is bigger 1 kg or 1000 grams
Which is bigger 3 liters or 3500 milliliters
Which is bigger 5 liters or 520 milliliters
PLZ ANSWER ALL 3 WILL GIVE 15 PIONTS
Which expression equals 9/10 ?
O 5√10+4√10
O5 10+4 10
O 5√10+43/10
O 5 10+4 10
Answer:
The second answer:
5cubrt10 + 4cubrt10
Step-by-step explanation:
In order to get a cubrt10 answer you have to add cubrt10's.
The first answer has squareroots, so that's a no.
The last two have cubrt + sqrt, which cannot be simplified.
5cubrt10 + 4cubrt10 = 9cubrt10
What is the equation of the linear function represented by the table?
O y=-X+9
O y=-x+ 13
O y=x+13
O Y = X+9
Answer:
y= -x+9
❤hope its helpful
THANK YOU.
Nancy, Jordan, and Krista all worked together to clean their neighbors house. They earned a total fo $30.75. If they split the money equally, how much will each person get?
Answer:
$10.25
Step-by-step explanation:
Nancy, Jordan and Krista all worked together to clean a neighbour house
They earned a total of $30.75
When the money is split among each person then the amount that each person will get can be calculated as follows
= 30.75/3
= 10.25
Hence each person will get $10.25
Choose the number in which the digit 2 is ten times greater than the digit 2 in 426.
Answer: 237
Step-by-step explanation:
Ok we can write 426 as:
400 + 20 + 6
Then the 2 in 426 is in the place of the tens and represents a 20.
If we want a number with a 2 that is 10 times greater than 20, we have that:
10*20 = 200.
Then we should find a number with a 2 in the hundreds place, an example can be:
237
where we can write this number as:
237 = 200 + 30 + 7
and the 2 is in the hundreds place.
Which relationships have a constant of proportionality equal to 25? Pick 2 answers
Answer:
B and C.
Step-by-step explanation:
If you divide the y value by the x value then it would be 25 for B and C. A and D do not work. A does not work because as you move along the graph 25 divided by 2 and anything higher is not 25. I hope this helps!!
Answer:
b and c
Step-by-step explanation:
because 75/3=25
125/5=25 and and you already have the graph!
PLEASE HELP WITH LOG MATH questions 9 and 10 attached below I WILL GIVE BRAINEST
If Paula divides her pencils among three friends and herself, everyone gets the same number of pencils. If Paula divides her pencils among
five friends and herself, everyone will get the same number of pencils.
How many pencils could Paula have?
A 28
B. 30
C. 42
D. 48
From a survey of coworkers you find that 42% of 150 have already received this year's flu vaccine. An approximate 95% confidence interval is (0.339.0.501). Which of the following are true? If not, explain briefly. ses a) 95% of the coworkers fall in the interval (0.339,0.501). b) We are 95% confident that the proportion of coworkers who have received this year's flu vaccine is between 33.9% and 50.1%. om c) There is a 95% chance that a randomly selected coworker has received the vaccine. d) There is a 42% chance that a randomly selected coworker has received the vaccine. e) We are 95% confident that between 33.9% and 50.1% of the samples will have a proportion near 42%.
The approximate 95% confidence interval for the proportion of coworkers who have received this year's flu vaccine is (0.339, 0.501). Based on this information, it is true that 95% of the coworkers fall within the interval (0.339, 0.501), and we can be 95% confident that the proportion of coworkers who have received the vaccine is between 33.9% and 50.1%. However, it is false to say that there is a 95% chance that a randomly selected coworker has received the vaccine or that there is a 42% chance for a randomly selected coworker to have received the vaccine.
The approximate 95% confidence interval for the proportion of coworkers who have received this year's flu vaccine is (0.339, 0.501). Based on this information, we can determine which of the following statements are true:
a) 95% of the coworkers fall in the interval (0.339, 0.501).
This statement is true. The 95% confidence interval represents the range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. Therefore, we can say that 95% of the coworkers fall within the interval (0.339, 0.501).
b) We are 95% confident that the proportion of coworkers who have received this year's flu vaccine is between 33.9% and 50.1%.
This statement is true. The 95% confidence interval (0.339, 0.501) provides us with a range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. Therefore, we can say that we are 95% confident that the proportion of coworkers who have received the vaccine is between 33.9% and 50.1%.
c) There is a 95% chance that a randomly selected coworker has received the vaccine.
This statement is false. The 95% confidence interval does not represent a probability or chance for an individual coworker. It provides a range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. It does not give information about the likelihood of an individual coworker receiving the vaccine.
d) There is a 42% chance that a randomly selected coworker has received the vaccine.
This statement is false. The 42% represents the proportion of coworkers in the survey who have received the flu vaccine, but it does not represent the chance or probability for a randomly selected coworker to have received the vaccine. The 42% is a point estimate, not a probability.
e) We are 95% confident that between 33.9% and 50.1% of the samples will have a proportion near 42%.
This statement is false. The confidence interval (0.339, 0.501) does not directly provide information about the proportion of samples that will have a proportion near 42%. The confidence interval represents the range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies, but it does not specifically address the proportion of samples near 42%.
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Procter and Gamble (PG) paid an annual dividend of $2.95 in 2018. You expect PG to increase its dividends by 7.4% per year for the next five years (through 2023), and thereafter by 2.6% per year. If the appropriate equity cost of capital for Procter and Gamble is 8.6% per year, use the dividend-discount model to estimate its value per share at the end of 2018.
The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.
To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.
First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:
Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22
After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)
where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.
In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:
PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.
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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.
To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:
Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22
After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.
In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.
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What is the value of k if one of the zeros of the quadratic polynomial K 2 x2 2x 5?
If one of the zeros in the quadratic polynomial is 4, then the value of k is 3.
What is polynomial?A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. A polynomial is a mathematical expression that only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in mathematics.
Here,
4 is a root/zero of polynomial
P(x) = (k-2) x² - 2 x - (k+5)
P(4) = 0
(k - 2) 4² - 2 * 4 - (k+5) = 0
15 k - 45 = 0
k = 3
The value of k if 4 is one of the zeros of the quadratic polynomial is 3.
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Complete question:
If one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k.
6x -3=-18 + 2х what doe that equal !!!!!
Pat has 8 flowerpots, and she wants to plant a different type of flower in each one. There are 10 types of flowers available at the garden shop. In how many different ways can she choose the flowers?
A. 45
B. 90
C. 80
D. 1,814,400
Answer:
A
Step-by-step explanation:
Determine the null and alternative hypotheses. The principal of a middle school claims that the seventh grade test scores at her school vary less than the test scores of seventh-graders at neighboring schools, which have variation described by σ=14.7
.
A.H0:σ=14.7;Ha:σ<14.7
B.H0:σ=14.7;Ha:σ>14.7
C.H0:σ=14.7;Ha:σ≤14.7
D.H0:σ=14.7;Ha:σ≠14.7
E.H0:σ=14.7;Ha:σ≥14.7
The null and alternative hypotheses for the given scenario are:
H0: σ = 14.7
Ha: σ < 14.7
The given scenario involves testing a claim made by the principal of a middle school that the test scores of seventh-graders in her school vary less than the test scores of seventh-graders in neighboring schools, which have a variation of σ = 14.7. The null hypothesis (H0) in this case is that the standard deviation of test scores in the principal's school is equal to the standard deviation of test scores in neighboring schools, which is 14.7. The alternative hypothesis (Ha) is that the standard deviation of test scores in the principal's school is less than 14.7.
To test these hypotheses, one could conduct a one-tailed z-test for the population standard deviation. The test statistic would be calculated as:
z = (s - σ) / (σ / √(n))
Where s is the sample standard deviation, σ is the hypothesized population standard deviation, and n is the sample size. The p-value for this test would be calculated based on the z-score and the directionality of the alternative hypothesis. If the p-value is less than the significance level (α), the null hypothesis would be rejected in favor of the alternative hypothesis.
Therefore, in conclusion, the correct answer is option A, and the null and alternative hypotheses for this scenario are H0: σ = 14.7 and Ha: σ < 14.7.
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what factor is equivalent to -3/2
Multiplying the numerator and the denominator by the same constant, we get an equivalent fraction, as follows:
\(-\frac{3}{2}=-\frac{3}{2}\cdot\frac{2}{2}=-\frac{3\cdot2}{2\cdot2}=-\frac{6}{4}\)Then, -6/4 is equivalent to -3/2
Please answer all 5 questions in order.
You will be marked as Brainliest.
Answer:
1 - b 2-c 3-d 4-5 6-C 7-A 8-B
Step-by-step explanation:
A sequence is defined recursively using the formula. If the first term of the sequence is 120, what is f(5)? −15 −7. 5 7. 5 15.
A sequence is defined recursively using the formula. If the first term of the sequence is 120 and the sequence is defined recursively, the value of f(5) is 7.5.
To determine the value of f(5), we need to apply the recursive formula to calculate each term of the sequence. The formula provided is not specified in the question, so we cannot provide a specific explanation of the formula. However, based on the given answer choices, we can determine the value of f(5).
Given that the answer choices are -15, -7.5, 7.5, 15, we can see that the sequence is increasing. Since the first term is 120, and f(5) is greater than 120, the answer must be a positive value. Therefore, the only option that satisfies this condition is 7.5.
It's important to note that without the specific recursive formula, we cannot provide a detailed explanation of how the terms of the sequence are calculated. The recursive formula would be required to generate the sequence and find the exact value of f(5).
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6. Marilyn collects old dolls. She purchases a doll for $450. Research shows this doll's value will
increase by 2.5% each year. Write an equation that determines the value, V, of the doll tyears after
purchase. Assuming the doll's rate of appreciation remains the same, will the doll's value be doubled in
20 years? Justify your reasoning.
[4 points]
The equation that determines the value, V, of the doll years after purchase will be V=450(1.025)²⁰. The value of the V will be $ 737.35.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
The fact that the exponential growth function's equation is provided by;
y=a(1+r)ˣ
Y represents the doll's worth.
The number of years is x=20
a is the starting point = $450
The rate of change is r= 2.5% = 0.025
Put the given values;
y=a(1+r)ˣ
y=450(1+0.025)²⁰
y= $ 737.35
Hence, the equation that determines the value, V, of the doll years after purchase will be V=450(1.025)²⁰. The value of the V will be $ 737.35.
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1. An AP has a common difference of 3. Given that the nth term is 32, and the sum of the first n terms is 185, calculate the value of n.
Answer:
The value of n is 10
Step-by-step explanation:
The formula of the nth term of the arithmetic progression is a\(_{n}\) = a + (n - 1)d
a is the first termd is the common difference between each 2 consecutive termsn is the position of the termThe formula of the sum of nth terms is S\(_{n}\) = \(\frac{n}{2}\) [2a + (n - 1)d]
∵ An AP has a common difference of 3
∴ d = 3
∵ The nth term is 32
∴ a\(_{n}\) = 32
→ Substitute them in the 1st rule above
∵ 32 = a + (n - 1)3
∴ 32 = a + 3(n) - 3(1)
∴ 32 = a + 3n - 3
→ Add 3 to both sides
∴ 35 = a + 3n
→ Switch the two sides
∴ a + 3n = 35
→ Subtract 3n from both sides
∴ a = 35 - 3n ⇒ (1)
∵ The sum of the first n terms is 185
∴ S\(_{n}\) = 185
→ Substitute the value of S\(_{n}\) and d in the 2nd rule above
∵ 185 = \(\frac{n}{2}\) [ 2a + (n - 1)3]
∴ 185 = \(\frac{n}{2}\) [2a + 3(n) - 3(1)]
∴ 185 = \(\frac{n}{2}\) [2a + 3n - 3]
→ Multiply both sides by 2
∴ 370 = n(2a + 3n - 3)
∴ 370 = 2an + 3n² - 3n
→ Substitute a by equation (1)
∴ 370 = 2n(35 - 3n) + 3n² - 3n
∴ 370 = 70n - 6n²+ 3n² - 3n
→ Add the like terms in the right side
∵ 370 = -3n² + 67n
→ Add 3n² to both sides
∴ 3n² + 370 = 67n
→ Subtract 67 from both sides
∴ 3n² - 67n + 370 = 0
→ Use your calculator to find n
∴ n = 10 and n = 37/3
∵ n must be a positive integer ⇒ 37/3 neglecting
∴ n = 10
∴ The value of n is 10
If g(x) = x2 + 2, find g(3). (2 points)
Оа
9
Ob
8
Ос
11
Od
6