Select the correct answer.
Consider the arithmetic sequence.
-9, -2, 5, 12,...
Given that the sequence is represented by the function f(n), what are the values of f1) and the common difference?
O A. f(1) = -9
Common difference: -7
OB. f(1) = -2
Common difference: -7
OC. f(1) = -9
Common difference : 7
O D.
f(1) = -2
Common difference : 7
Answers
The correct answer among the answer choices is; Choice C; f(1) = -9, Common difference : 7.
What are the values of the first term and the common difference?From the task content; it follows that the arithmetic sequence is given by f(n) and hence, the term f(1) is the first term and is = -9 .
The common difference is given as;
-2-(-9) = 5-(-2) = 7.
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Related Questions
Can someone help me on this??!??
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the equation is y=27x
How many cards does each friend have? See image below
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Nina loves peanut butter she can either buy a 64 ounce jar for $$8.96 or a 40 ounce jar for $5.60 which is a better buy?
Answers
I need help fast smart people I need your answer
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Answer:
The angle D is 64 degrees.
Step-by-step explanation:
This is because they are vertical
Answer:
i think its the yellow square
Step-by-step explanation:
There are 20 children at a library. Six of the children have a averahe age of 5 years. The remaining children have a sverage age of 8 years. What is the average age of the children at the library?
Answers
Answer: The average age of the children at the library is 7.1 years.
Step-by-step explanation:
Given,
Out of 20 children, six of the children have an average age of 5 years,
Thus, the sum of the ages of 6 students = 5 × 6 = 30
( Total sum of observations = Their Average × Total numbers of the observations )
Now, remaining students = 20 - 6 = 14,
Since, the remaining children have an average age of 8 years.
Thus, the sum of the ages of 14 students = 14 × 8 = 112,
Total sum of the ages of 20 students = 30 + 112 = 142
=142/20
= 7.1 years
Answer:
The average is 7.1 years!
Step-by-step explanation:
6 children = average of 5 years
14 children = average of 8 years
P=x-2 ÷ x+1 for what value of x is P undefined
Answers
Answer:
x = - 1
Step-by-step explanation:
P = \(\frac{x-2}{x+1}\)
the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.
x + 1 = 0 ( subtract 1 from both sides )
x = - 1
P is undefined when x = - 1
What is the cos A?Will give 15 points.
Answers
Answer:
Step-by-step explanation:
cos A = \(\frac{\sqrt{8} }{3}\)
Answer the question please
Answers
Answer:
x = 45°
Step-by-step explanation:
Quadrilaterals:Sum of all the angles of quadrilateral = 360
2x + 2x + 30 + 2x - 10 + x + 25 = 360
2x + 2x + 2x + x + 30 - 10 + 25 = 360
Combine like terms,
7x + 45 = 360
Subtract 45 from both sides,
7x = 360 - 45
7x = 315
Divide both sides by 7,
x = 315 ÷ 7
\(\boxed{\bf x = 45^\circ}\)
Answer:
x = 45
Step-by-step explanation:
The sum of the interior angles of any quadrilateral is 360°so 2x+2x+30+2x-10+x+25 = 360°
we solve the equation
2x+2x+30+2x-10+x+25 = 360
7x = 360 - 30 + 10 - 25
7x = 315
x = 315 : 7
x = 45
Which rules of exponents will be used to evallate this expression? Select three options.
Answers
The owner of a large fast food chain is considering whether to re-open the dining rooms of his restaurants now that it is legal in the state of Georgia. He is interested to know what percentage of his employees support the re-opening, so he decides to conduct a survey. (a) Which of the following plans would be more likely to produce a sample statistic very close to the true percentage who support re-opening? A simple random sample of 34 employees A simple random sample of 340 employees Both plans are equally likely to get this result, since they are both random samples. (b) He thinks it would be easier to sample employees by randomly selecting franchise locations (individual restaurants) and asking managers to administer surveys to all the workers at the selected restaurants, what kind of sampling method should he use? a) Cluster sample b) Systematic sample c) Convenience sample d) Stratified sample
Answers
Answer:
a) A simple random sample of 340 employees
b) a) Cluster sample
Step-by-step explanation:
a) Remember, the sample size of most research work is a factor to consider in other to determine if the data collected represents the true percentage of the entire population.
Hence, a small random sample of 34 employees will not give more precise information than a larger sample of 340 employees because the larger sample contains more representation of the population.
b) A cluster sample is best used in this case because it involves dividing the population into several clusters or groups, then the researcher randomly selects a particular cluster or group in other collect research data for analysis.
Whereas in this case, the randomly selected clusters are the different (individual restaurant) franchise locations.
Suppose that 21 people are competing in an Olympic event, where first place earns Gold, second place earns Silver, and third place earns Bronze. How many different possible outcomes are there for this Olympic event
Answers
Answer:
Step-by-step explanation:
This is a combination problem. Combination has to do with selection
Total people competing in the event = 21people
Prizes to be won = 3(Gold, silver and bronze)
Using the formula
nCr = n!/(n-r)!r!
21C3 = 21!/(21-3)!3!
21C3 = 21!/18!3!
21C3 = 21×20×19×18!/18!3!
21C3 = 21×20×19/3!
21C3 = 21×20×19/6
21C3 = 1330
Hence 1330 possible outcome are there for the event.
what type of data would best be displayed in a box plot
Answers
Answer:(2x+7)+(2x+7)
Step-by-step explanation:
what you do is put 2x on the top and on the side and then seven on the top and on the side and then you got your answer
f(x)=\(\sqrt{x^2-4}\), x\(\leq \}\)0
find \((f^-^1)'(1)\)
I keep getting the wrong answer. The correct answer is\(\frac{1}{\sqrt{5} }\)
Answers
Solve for x when √(x ² - 4) = 1 :
√(x ² - 4) = 1
x ² - 4 = 1
x ² = 5
x = ±√5
We're looking at x ≤ 0, so we take the negative square root, x = -√5.
This means f (-√5) = 1, or in terms of the inverse of f, we have f ⁻¹(1) = -√5.
Now apply the inverse function theorem:
If f(a) = b, then (f ⁻¹)'(b) = 1 / f '(a).
We have
f(x) = √(x ² - 4) → f '(x) = x / √(x ² - 4)
So if a = -√5 and b = 1, we get
(f ⁻¹)'(1) = 1 / f ' (-√5)
(f ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5
The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of f at x = 1.
![f(x)=[tex]\sqrt{x^2-4}[/tex], x[tex]\leq \}[/tex]0 find [tex](f^-^1)'(1)[/tex]I keep getting the wrong](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/1IpU6DnzImnhCDH9fwMUERtbNvnJ5Fb9.png)
3. A large tank is partially filled with a solution. The tank has a faucet that allows solution to enter the tank at a rate of 16 3/4 liters per minute. The tank also has a drain that allows solution to leave the tank at a rate of 19 4/5 liters per minute.
(a) What expression represents the change in volume of solution in the tank in 1 minute?
(b) What is the change in volume of the solution after 15 seconds? Show necessary work.
(c) What does the change in volume after 15 seconds mean in the real world? Answer in complete sentences.
Answers
Answer:a) 16 3/4 - 19 4/5 liters/min
b) (16 3/4 - 19 4/5) / 4 liters
c) The level of water will drop.
Step-by-step explanation:
Find the LCM of 16,25 and 35 using the prime factorization method
Answers
Answer:
it's 2800
Step-by-step explanation:
2×2×2×2×5×5×7
please answer it’s due!!
Answers
Answer:
42
Step-by-step explanation:
TOPIC 3: Finding Possible Values of a Random Variable
A. Two cards are drawn from a deck. How many possible values can each of
the following variables take?
1. sum of the numbers on the cards ___________
2. number of times both cards are black ________
3. Number of times both cards are 7s ___________
4. Number of times the first card is six and the second card is red _____
5. Number of times the first card is face card and the second card is not
a face card
Answers
there are 19 possible values, there are 2 possible values, there are 3 possible values, there are 13 possible values. the probability of getting a face card followed by a non-face card is much higher than the probability of getting a face card followed by another face card .
The sum of the numbers on the cards can take values from 2 (when both cards are Aces) to 20 (when both cards are Kings). Therefore, there are 19 possible values.
The number of times both cards are black can take values from 0 (when both cards are red) to 1 (when both cards are black). Therefore, there are 2 possible values.
The number of times both cards are 7s can take values from 0 (when neither card is a 7) to 1 (when both cards are 7s). Therefore, there are 2 possible values.
The number of times the first card is six and the second card is red can take values from 0 (when the first card is not a six or the second card is not red) to 2 (when both cards are sixes and both are red). Therefore, there are 3 possible values.
The number of times the first card is a face card and the second card is not a face card can take values from 0 (when both cards are not face cards) to 12 (when the first card is a King and the second card is an Ace, two, three, four, five, six, seven, eight, nine, or ten). Therefore, there are 13 possible values.
It is important to note that these values are not equally likely. For example, the probability of getting a sum of 2 is much lower than the probability of getting a sum of 7, since there is only one way to get a sum of 2 (both cards are Aces) but there are several ways to get a sum of 7 (one card is a 4 and the other card is a 3, or one card is a 5 and the other card is a 2, or both cards are 7s). Similarly, the probability of getting a face card followed by a non-face card is much higher than the probability of getting a face card followed by another face card, since there are more non-face cards in the deck than face cards.
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CALC
PLEASE HELP!!
A chemical substance has a decay rate of 8.8% per day. The rate of change of an
dN
amount N of the chemical after t days is given by = -0.088N
dt
(i) Let No represent the amount of the substance present at to. Find the exponential function
that models the decay.
(ii) Suppose that 400g of the substance is present at to. How much will remain after 3 days?
(iii) What is the rate of change of the amount of the substance after 3 days?
(iv) After how many days will half of the original 400 g of the substance remain?
Answers
A function is a relationship between a few different inputs and an output, where each input can only lead to one possible outcome.
What is the chemical substance has a decay rate?(i) The exponential function that models the decay of the substance is given by:
\(N(t) = Noe^(-0.088t)\)
(ii) If \(400g\) of the substance is present at to, then \(No = 400g\) . Therefore, the amount of the substance remaining after 3 days is:
\(N(3) = 400e^(-0.0883) = 309.21g\) (rounded to two decimal places)
(iii) The rate of change of the amount of the substance after 3 days is given by:
\(dN/dt = -0.088N(3) = -0.088309.21 = -27.21 g/day\) (rounded to two decimal places)
(iv) To find the number of days it takes for half of the original \(400g\) of the substance to remain, we need to solve the equation:
\(N(t) = 0.5No\)
\(0.5No = Noe^(-0.088t)\)
\(0.5 = e^(-0.088t)\)
\(ln(0.5) = -0.088t\)
\(t = ln(0.5)/(-0.088) = 7.89 days\) (rounded to two decimal places)
Therefore, after \(7.89\) days, half of the original \(400g\) of the substance will remain.
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2. Quadrilateral PQRS with P(-5,1). Q(-2,6), R(3, 7), and S(6, 4); dilate by a scale factor of 4 12 0. Is this an enlargement or reduction? How do you know? 14 b. What are the vertices of the image after the transformation?
Answers
Enlargement since k > 1
P'(-20, 4)
Q'(-8, 24)
R'(12, 28)
S'(24, 16)
1) Since the Quadrilateral PQRS has been enlarged by a scale factor greater than 1, in this case, 4. Then we can state that this was an enlargement
2) To find out the vertices of that image, since no other information has been given we assume that dilation was centered at the origin. Therefore, we can write:
Pre-image Scale Factor Image
P(-5,1) k=4 P'(-20, 4)
Q(-2,6) Q'(-8, 24)
R(3, 7) R'(12, 28)
S(6, 4) S'(24, 16)
3) Hence the answers are:
Enlargement since k > 1
P'(-20, 4)
Q'(-8, 24)
R'(12, 28)
S'(24, 16)
4(7x+3)=-3(2-9x) Please I need it quickly. It for school
Answers
Answer: x=-18
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
\( \huge{ \fbox{ \sf{x = - 18}}}\)
Step-by-step explanation:
\( \text{4(7x + 3) = - 3(2 - 9x)}\)
\( \text{Step \: 1 \: : Distribute \: 4 \: through \: the \: parentheses}\)
\( \hookrightarrow{ \sf{28x + 12 = - 3(2 - 9x)}}\)
\( \text{Step \: 2 \: : Distribute \: - 3 \: through \: the \: parentheses}\)
\(\hookrightarrow{ \sf{28x + 12 = - 6 + 27x}}\)
\( \text{Step \: 3 \: : Move \: 27x \: to \: left \: hand \: side \: and \: change \: its \: sign}\)
\( \hookrightarrow{ \sf{28x - 27x + 12 = - 6}}\)
\( \text{Step \: 4 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}\)
\( \hookrightarrow{ \sf{28x - 27x = - 6 - 12}}\)
\( \text{step \: 5 \: : Collect \: like \: terms}\)
\( \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}\)
\( \hookrightarrow{ \sf{x = - 6 - 12}}\)
\( \text{step \: 6 \: : Calculate}\)
\( \text{ \underline{ Remember!}} : \sf{ \: The \: negative \: integers \: are \: always \: added \: but \: posses \: the \: negative \: ( - ) \: sign.}\)
\( \hookrightarrow{ \boxed{ \sf{x = - 18}}}\)
Hope I helped!
Best wishes ! :D
~\( \text{TheAnimeGirl}\)
3. In triangle ABC, 4A is a right angle, and m<B = 45°. What is the length of BC? If your answer is not an integer, leave it in simplest radical form.
A. 18 ft.
B. 18√2
C. 18√3
D. 36
what is the answer? thank you
Answers
What is the value of sin-1(1)?
Answers
The value of sin^(-1) 1 is; π/2
We want to find the value of sin^(-1) 1Now, when using trigonometric functions, we know that; If sin θ = x Then; θ = sin^(-1) xNow, we want to find the angle.We know that in radians the value of θ at which sin θ = 1 is; π/2 radians
Thus; sin^(-1) 1 = π/2
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The following data points represent how many goals Hank scored each season. 45 , 43 , 45 , 44 , 44 , 44 , 47
Answers
Answer:
so if you are looking for Mean, Range, and Median:
Median:44
Range:44
Mean: estimated: 44.6
Step-by-step explanation:
Answer:
If your looking for the M.A.D here
Step-by-step explanation:
Step 1. 45+43+45+44+44+44+47 =312
Step 2. 312/7 =44.57
Step 3.
45 - 44.57=0.43
43 - 44.57=1.57
45 - 44.57=0.43
44 - 44.57=0.57
44 - 44.57=0.57
44 - 44.57=0.57
47 - 44.57=2.43
Step 4.
0.43+1.57+0.43+0.57+0.57+0.57+2.43=6.57
Step 5.
6.57/7 = 0.93
You are going shopping for some new sweaters, t-shirts, and pants. Sweaters (s) cost $29, t-shirts (t) cost $16, and pants (p)
cost $25. What algebraic expression models the total cost of clothes that you buy?
Suppose you bought 28 sweaters, 7 t-shirts, and 17 pairs of pants. How much did you spend?
Answers
Answer:
You spent $1349
Step-by-step explanation:
sweaters s = $29
t-shirts t = $16
pants p = $25
Cost = C
28s + 7t + 17p = C
28 ($29) + 7 ($16) + 17 ($25) = C
$812 + $112 + $425 = C
$1349 = C
Help Quickly! A truck needs 7 gallons of fuel to travel 56 miles. Can the truck travel 48 miles with 6 gallons of fuel? Explain.
Giving brainliest
Answers
The correct answer is:
O Yes; 7/56 and 48/6 are proportional because 7 * 6 = 48 * 56.
How to find the correct optionTo determine if the truck can travel 48 miles with 6 gallons of fuel, we can compare the ratios of fuel consumption to distance traveled.
Given that the truck needs 7 gallons of fuel to travel 56 miles, we can express this as the ratio 7/56 (gallons/miles).
If we compare it to the second scenario where the truck is traveling 48 miles, we can express it as the ratio 6/48 (gallons/miles).
To check if they are proportional, we can cross-multiply: 7 * 48 = 6 * 56. If the cross-multiplication results in equal values, then the ratios are proportional.
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EASY POINTS!
Jess is playing the newest video game. The object of the game is to collect as many
points as you can in the shortest time. The amount of points Jess collects is directly
proportional to the number of hours she plays. This relationship is represented in the
graph shown here:
Meanwhile, her friend Kira has also been playing the game. At the end of each day, she
recorded the number of points she collected. It turns out, she is collecting points in
direct proportion to the number of days she plays. This relationship is represented by
the equation: y = 440x.
Who is collecting points faster in this new game, Jess or Kira?
Answers
According to the information, it can be inferred that Jess scores more points than Kira in the new video game.
How to find who scores the most points in the new video game?To find who scores the most points in the new video game we must perform the following operation:
We know that Kira gets 440 points for each day, so we need to calculate how many points Jess gets each day. Therefore, we must multiply the points Jess earns each hour by the 24 hours she has in a day to find how many points she earns in a day.
20 points / hour * 24 = 480 points / day
According to the above, Jess will make more points in a day than Kira. However, she would have to play the full 24 hours of the day without a break.
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The graph compares the weights in pounds of 100 dogs and cats that are brought in
to a veterinarian's office. Using the medians, how much more does a typical dog weigh than a typical cat?
Answers
Answer:20
Step-by-step explanation:this is wrong
Answer:
40
Step-by-step explanation:
subtract median of dogs and median of cats
Suppose c(p) gives the number of calories burned doing p push-ups, and
p(t) gives the number of push-ups a person can do in t seconds.what is the meaning of the composite function c(p(45)).
Answers
The meaning of the composite function c(p(45)) is the number of calories burned doing push-ups in 45 seconds
How to interpret the meaning of the composite function c(p(45))?The functions are given as:
c(p) gives the number of calories burned doing p push-upsp(t) gives the number of push-ups a person can do in t secondsSo, the interpretation of the function c(p(t)) is
The number of calories burned doing push-ups in t seconds
In c(p(45)), the value of t is 45
Hence, the meaning of the composite function c(p(45)) is the number of calories burned doing push-ups in 45 seconds
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Joe caught a one year old flounder whose length had a z score of 1.2. How long was this fish.
Answers
The fish with a z-score of 1.2 is 154.60 millimeters.
A Z-score is a metric that quantifies how closely and accurately a value relates to the measure of central tendency or mean of a set of values. the values of standard deviation from the mean are used to calculate Z-score. A Z-score of zero means the data for which the score is zero is equivalent to the mean score.
The formula for calculating a z-score is :
z = (x-μ)/σ ,
where x is the data value at a that z-score , μ is the mean of all the data and σ is the standard deviation.
Here the z-score is given as 1.2 , mean is 127 and standard deviation is 23 . Using these values we find the value of x , the length of the flounder.
So x = zσ + μ
or, x = 1.2 × 23 + 127
or, x = 27.6 + 127
or, x = 154.60 mm
Therefore the length of the 1 year old flounder is 154.60 mm .
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Disclaimer: The complete question is :
The mean length of a 1 year old flounder is 127 mm and the standard deviation is 23 mm. Joe caught a one year old flounder whose length had a z score of 1.2. How long was this fish?
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Solve for f.
3<
f
–
1
+7
Answers
Answer:
F will be +5
Step-by-step explanation: