The range of the cigarette tax (in cents) for 50 selected states is 62.
What is range?The range of a function is defined as the set of all the possible output values that are valid for the given function.
The range of a given set of data is the difference between the largest value and the smallest value.
Given the data shown represent the cigarette tax (in cents) for 50 selected states
70,12,42,45,50,51,60,69,8,40,18
Required; The range
This is calculated as:
Range = highest - lowest
Range = 70 - 8
Range = 62
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You are given a coin. You do not know if it is a fair coin or not.
You want to figure out a way so that you can make a sound statement about the fairness of the coin.
One way to figure out the fairness of the coin is to conduct a large number of coin flips and record the number of heads and tails.
Describe probability in coin sample?Probability is a measure of the likelihood of an event occurring. In the context of a coin flip, the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.
For a fair coin, the two possible outcomes are heads (H) and tails (T). The probability of getting heads or tails in a single coin flip is equal to 1/2, or 50%. This means that if you flip a fair coin 100 times, you would expect to get approximately 50 heads and 50 tails.
It's important to note that probability is a theoretical concept, and the actual outcome of a coin flip can never be predicted with 100% certainty. However, the law of large numbers states that as the number of coin flips increases, the ratio of heads to tails will approach the theoretical probability.
The concept of probability can also be applied to more complex events involving multiple coin flips. For example, the probability of getting two heads in a row is (1/2) * (1/2) = 1/4, or 25%. The probability of any specific sequence of heads and tails can be calculated using the same method.
One way to figure out the fairness of the coin is to conduct a large number of coin flips and record the number of heads and tails. Then, calculate the proportion of heads and compare it to 0.5, which is the expected proportion for a fair coin. The larger the sample size, the more confident you can be in your conclusion about the fairness of the coin. If the proportion of heads is close to 0.5, it is likely that the coin is fair. If the proportion deviates significantly from 0.5, it is likely that the coin is not fair. It's also important to use a rigorous statistical method to test the hypothesis of fairness, such as a one-sample proportion test, to account for random fluctuations in the results.
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=
Use the Percentiles flow chart interactive to answer the following question.
When finding the 35th percentile from a sample of 200 IQ scores, the locator L is found to be 80. What is the value of the 35th percentile?
Choose the correct answer below.
OA. The 80th IQ score in the sorted list
OB. The IQ score that is midway between the 35th and 36th scores in the sorted list.
OC. The IQ score that is midway between the 80th and 81st scores in the sorted list.
OD. The 35th IQ score in the sorted list
Next
C. An IQ score of 80 is more unusual than an IQ score of 120
is the false answer
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
Firstly we need to find the probability of the test score to be less than 90(P<90) then we will continue finding the probability of the IQ score to be between 90 and 110(90<P<110) then we find the probability of the IQ score being more than 110 (P>110).
For P<90
Firstly we compute this using a scientific calculator where we choose the stat option and enter the mean of 100 and a standard deviation of 10, so we check if we make the normal random variable(X) to be 90 the outcome or answer for that is 0.16 so now we know the probability of the IQ score to be less than 90 is 16% chances.
For 90<P<110
then we check with the same method what will be the probability for an IQ score to be between 90 and 110 for a mean of 100 and a standard deviation of 10 we again check a normal random variable(X) of 110 to see what will be the probability of P<110 which we find an answer of 0.84 which is 84% chances so now therefore the probability of an IQ score to be more than 110 is 0.
therefore this tells us an IQ score of 120 is more unusual than an IQ score of 120.
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HEEELP MEE!!
The population of a colony started with 1,120 grows at an annual rate of 4.98%. How much more would you have, at the same time if you used continuous growth, compared to a growth rate when the continuous reaches 3,480?
The time that is taken by the colony is 23 years.
What is the time taken for the growth?The exponential growth function can be used to account for the exponential increase in the number of the organisms that are to be found in the colony.
Given that we have that;
P=Poe^rt
P = Number at time t
Po = Number initially present
r = rate of growth
t = time taken
Thus;
3480 = 1120e^0.0498t
3480/1120 = e^0.0498t
3.1 = e^0.0498t
ln(3.1) = 0.0498t
t = ln3.1/0.0498
t = 23 years
There are 23 years
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HELP PLEASE.
Write the following sentence as an equation. Use x to represent "a number."
A number subtracted from 18 amounts to 107.
The equation is
-
*** HELP
Answer:
-18 - x = 107
Step-by-step explanation:
Find f(x) if f is a linear function such that f(6)=4 and f(−5)=−6 .
Answer:
f(x) =[tex]\frac{10}{11}[/tex]x [tex]-\frac{16}{11}[/tex]
Step-by-step explanation:
The format of the linear function f(x) is ax + b. Thus, we can list the following equations:
4 = 6a + b .... (1)
-6 = -5a + b .... (2)
We can use the first equation to subtract the second equation getting: 10 = 11a. This means a = [tex]\frac{10}{11}[/tex]. From that, if we plug in the value of a into the first equation, we get 4 = [tex]\frac{60}{11}[/tex] + b, so b = [tex]-\frac{16}{11}[/tex]. Thus, f(x) =[tex]\frac{10}{11}[/tex]x [tex]-\frac{16}{11}[/tex]
Evaluate −2x+17 when x=−8.
9.03 divided by 0.15
9.03 divided by 0.15 is equal to 60.2.
What do you know about division?The opposite of multiplication in arithmetic is called division. It's used to determine how many times one quantity is contained inside another. Division is done by dividing the dividend by the divisor, which can be done visually by using the division sign () or a fraction bar (/). The quotient, which shows how many times the dividend can be divided by the divisor, is the operation's output. For instance, if you split up eight apples into four equally sized pieces, each piece would contain two apples. This division is denoted by the equation 8/4 = 2, where 8 is the dividend, 4 is the divisor, and 2 is the quotient.
The division of 9.03 by 0.15 can be calculated as follows:
9.03 ÷ 0.15 = 9.03 / 0.15
= 60.2
So, 9.03 divided by 0.15 is equal to 60.2.
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Let G be an abelian group and let H be the subset of G consisting of all elements of G of finite order. That is,
H={α∈G∣the order of a is finite}.
Prove that H is a subgroup of G.
H is a subgroup of G since it is closed under the group operation, contains the identity element and inverses of its elements.
A subset H of a group G is a subgroup of G if it satisfies the following three properties:
1. Closure: H is closed under the group operation, that is, if α, β∈H then αβ∈H.
2. Identity element: H contains the identity element e of G.
3. Inverses: For each element α∈H, its inverse (or reciprocal) α−1 is also an element of H.
In this case, the subset of G consisting of elements of finite order (H) satisfies all of these three properties. Since H is closed under the group operation, if α, β∈H then αβ∈H. The identity element of G, e, is also an element of H since the order of the identity element is always 1, which is finite. Finally, for each element α∈H, its inverse α−1 is also an element of H since the inverse of a finite order element is also of finite order. Therefore, by satisfying all of the three properties of a subgroup, H is indeed a subgroup of G.
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Ernie scores 50 points in Level 1 of a video game.
In each subsequent level, he scores twice as many
points as he did in the previous level.
The Formula is [tex]a_n[/tex]= 50 ([tex]2^{n-1[/tex] ).
What is Sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite).
Given:
Ernie scores 50 points in Level 1 of a video game.
After II level the points would be
50 x 2 = 100
Then, after III level the points would be
100 x 2 = 200
So, the Recursive formula for the situation is
[tex]a_n[/tex]= a [tex]r^{n-1[/tex] where r is common ratio = 100/50 = 2
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4r^2+3s^2-rs r=-1 S=3
Need help with steps because everyone keeps saying it’s 26 but I get 28
Answer:
34
Step-by-step explanation:
4r² + 3s² - rs ← substitute r = - 1, s = 3 into the expression
= 4(- 1)² + 3(3)² - (- 1)(3)
= 4(1) + 3(9) - (- 3)
= 4 + 27 + 3
= 34
Andrea is making a sandbox for her children. She has made a wooden frame for her backyard that is 8 feet long, 5 feet wide, and 4 feet deep. She can purchase sand for the sandbox for $20 per cubic meter. How much will it cost Andrea to purchase sand? (Hint: 1 foot = 0.3048 meters.)
(Round your answer to the nearest dollar.)
Answer:
Step-by-step explanation:
The wooden frame is a cuboid
and the volume of a cuboid = Length x Width x Depth
Therefore,
The volume of this wooden frame = (8 feet) x (5 feet) x (4 feet)
= 160 cubic feet
The purchasing rate for the sand is $20 per cubic meter (which is NOT the same as cubic feet)
Unit conversion has to be applied then:
1 foot = 0.3048 meters
1 cubic feet = (0.3048 meters) x (0.3048 meters) x (0.3048 meters)
1 cubic feet = [tex]0.3048^{3}[/tex] cubic meters
Therefore: 160 cubic feet = (160)([tex]0.3048^{3}[/tex]) cubic meters
Cost of sand:
1 cubic meter = $20
Therefore: (160)([tex]0.3048^{3}[/tex]) cubic meters = $(20)(160)([tex]0.3048^{3}[/tex])
= $90.61
= $91 (Rounded to the nearest dollar)
It will cost Andrea $91 to purchase sand for the sandbox
2. The mean incubation time of fertilized chicken eggs kept in an incubator is 21.3 days. Suppose that the incubation times are normally distributed and the standard deviation is 1.1 days. (4 pts)
Mean = 21.3
Sd= 1.1
a. What is the 22nd percentile for incubation times of chicken eggs? (2 pts)
b. Determine the two incubation times that mark off the middle (center) 95% of fertilized chicken eggs. (2 pts)
a) The 22nd percentile for incubation times of chicken eggs is of: 20.5 days.
b) The middle 95% of incubation times is in this following interval: (19.1, 23.5) days.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The parameters for this problem are given as follows:
[tex]\mu = 21.3, \sigma = 1.1[/tex]
The 22nd percentile is the value of X when Z has a p-value of 0.22, hence X when Z = -0.77, thus:
-0.77 = (X - 21.3)/1.1
X - 21.3 = -0.77 x 1.1
X = 20.5 days.
The middle 95% of incubation times is obtained from X when Z = -1.96(2.5th percentile) to X when Z = 1.96(97.5th percentile), hence:
-1.96 = (X - 21.3)/1.1
X - 21.3 = -1.96 x 1.1
X = 19.1 days.
1.96 = (X - 21.3)/1.1
X - 21.3 = 1.96 x 1.1
X = 23.5 days.
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Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Volume = 10,000π in.3
h ≈
in.
r ≈
cm
The Height is 10 inch and radius is 10 inch.
What is Volume?Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. While capacity can be measured in virtually any other unit, such as litres, gallons, pounds, etc., volume is measured in cubic units.
Given:
Volume = 10,000π in³
Volume of b= π r² h
So, 10,000π= π r² h
10,000 = r² h
r² h = 10 x 10 x 10
r² h = 10² x 10
Now, comparing the values
r= 10 inch and h= 10 inch
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uppose the number of goals scored per game in an under 14 boys indoor soccer league follows a Poisson distribution with 3.3 goals per game. Define x as the number of goals scored in a game. You will answer questions concerning the probabilities of different values of x in this sample Excel spreadsheet: A B 1 P(x = 2) =POISSON.DIST(2,3.3, FALSE) 2 P(x = 5) 3 P(x > 3)
A excel spreadsheet computes likelihood of various upsides of objectives scored in a game utilizing the POISSON.DIST capability. The equation for x=2, 5 and x>3 objectives is given.
In the Succeed calculation sheet, Segment A rundowns the various upsides of x that we need to track down the probabilities for.
Segment B contains the relating equation to ascertain the likelihood utilizing the POISSON.DIST capability.
The recipe in cell B1 works out the likelihood of scoring 2 objectives in a game, P(x = 2), utilizing the POISSON.DIST capability with the contentions 2, 3.3, and Misleading.
The equation in cell B2 computes the likelihood of scoring 5 objectives in a game, P(x = 5), utilizing the POISSON.DIST capability with the contentions 5, 3.3, and Misleading.
The recipe in cell B3 works out the likelihood of scoring multiple objectives in a game, P(x > 3), utilizing the POISSON.DIST capability with the contentions 3, 3.3, and Valid. The Genuine contention works out the combined conveyance capability, which gives the likelihood of getting a worth not exactly or equivalent to the contention. To track down the likelihood of getting a worth more prominent than the contention, deduct the combined dissemination capability from 1.
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What is the surface area of a sphere with radius 8? Use 3.14 for pi and round your answer to the nearest hundredth if necessary.
Answer:
The formula for the surface area of a sphere with radius r is 4πr^2. Plugging in the given radius of 8, we get:
Surface area = 4π * 8^2 = 4π * 64 = 256π
Using an approximate value of π = 3.14, the surface area of the sphere is approximately:
256 * 3.14 = 803.84
Rounding to the nearest hundredth, the surface area of the sphere is approximately 803.84 square units.
Answer:
803.84cm²
SolutionArea of a sphere = 4πr²
When we put the given values we get
Area of a sphere = 4x3.14x8²
Area of a sphere = 4x3.14X16
= 804.25cm²
Rounding to the nearest hundredth we get,
803.84cm²
what is (-5,-3) reflected over the Y axis
The point (-5,-3) reflected over the y-axis is (5, -3).
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
(-5, -3)
Along y-axis:
(x, y) → (-x, y)
So,
(-5, -3) → (-(-5), -3) = (5, -3)
Thus,
(5, -3) is the reflected point.
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Tony, Hans, and Dante made flyers last Wednesday. The table below shows the number of flyers each person made and how much time each person spent.
Write the time spent per flyer for each person. Then determine who worked the fastest.
Among Tony, Hans and Dante, Dante made flyers the fastest and he took least time to do the work of making flyers.
What do we mean by time and work?Time and work deals with the time it takes an individual or group to complete a task and the efficiency of the work they do.
According to the information given in the question:
Tony made 8 flyers in 64 minutes
Hans made 3 flyers in 21 minutes
Dante made 6 flyers in 30 minutes
By observing, it says
Tony took 8 minutes to make 1 flyer
Hans took 7 minutes to make 1 flyer
Dante took 5 minutes to make 1 flyer
Hence, it can be concluded by time and work relationship that Dante was the fastest among the three competitors.
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Step by step please, need help. Good luck and thank you for your help
Angle of triangle AFC is 37°
What is an angle?An angle is the formed when two lines meet at the same vertex. It is measured is degrees. There are three types of angles based on their measurements.
From the given figure consider ABCF as trapezium,
Given that angle of triangle BCF is 37°
Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non-parallel side, add up to 180°
Therefore, ∠BCF + ∠CBF = 180°
⇒∠B = 180° - 37°⇒143°
Similarly ∠A = ∠B = 143°
⇒∠A+∠F=180°
⇒∠F=180°-143° ⇒ 37°
Hence, m∠AFC = 37°.
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according to the histogram, which range of length (in inches) contains the longest sampled eastern diamondback rattlesnake?
According to the histogram 87.5 - 90.5 range of length (in inches) contains the longest sampled eastern diamondback rattlesnake.
In statistics, a histogram is a graphic representation of data distribution. Each bar in the histogram represents a different type of data, and the histogram is displayed as a group of adjacent rectangles. Statistics is a discipline of mathematics that is used in many different fields.
Frequency, which may be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data. One type of graph that can be used to illustrate a frequency distribution visually is a histogram.
The range of a histogram is the x-axis breadth that the bars cover. Since histograms show bin values rather than actual data values, these numbers are approximations.
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Complete question:
Question According to the histogram, which range of length (in inches) contains the longest sampled Eastern diamondback rattlesnake? Provide your answer below: greater than but less than
The fraction 9/21 is in lowest terms? A. True B. False
Answer:
B) False
Step-by-step explanation:
It can be simplified to 3/7 as they both have the common factor 3.
Please help me. A cone has a volume of 350 cubic meters. The area base is 70 square meters. What is the height of the cone?
On solving the provided question we can say that Area of the base = [tex]pi*r^2 = 70[/tex] => 350 (3/70) = h = 15 m
What is area?The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.
[tex]pi * r^2 * h / 3[/tex]
Area of the base = [tex]pi*r^2 = 70[/tex]
350 = 70 * h / 3
350 = (70/3) * h
350 (3/70) = h = 15 m
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A sweater is on sale for a 20% discount. The amount of the discount is $12. What is the original cost of the sweater?
The original cost of the sweater is $60.
What is Percentage?Percentage is simply defined as the parts of a number per fraction of 100.
Percentage is usually denoted by the symbol '%'.
Percentage of a number in a whole can be calculated by dividing the number by the whole and then multiply with 100.
Given that,
A sweater is on sale for a 20% discount. The amount of the discount is $12.
Percentage of discount = 20%
Amount of the discount = $12
Let x be the original cost of the sweater.
20% of x = 12
0.2x = 12
x = 60
Hence the original price of the sweater was $60.
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CAN SOMEONE HELP WITH THESE QUESTIONS?
Answer:
Graphed line is shown below
Step-by-step explanation:
m = 1/3, (-3, 3)
y - y1 = m (x - x1)
y - 3 = 1/3 (x + 3)
y - 3 = (1/3)x + 1
y = (1/3)x + 4
x^2-6x-3=(x-a)^2-b, where a and b are constants
Answer:
Below
Step-by-step explanation:
This is an exercise in 'completing the square'
x^2 - 6x -3
take 1/2 of the x coefficient (6) square it and add it and subtract it
x^2 - 6x + 9 - 9 - 3 Now you can reduce the underlined portion
(x-3)^2 - 12 a = 3 b= -12 Done
. The x-intercepts of y = f(x) are -1, 3, and 6. Find the x-intercepts of
(a)y = f(2x)
(b) y = 2f(x)
(c) y = f(x + 2)
Compare the appearance of each graph to the appearance of the graph y = f(x).
(d)y = f(mx)
(A) the x-intercepts of y = f(2x) are (-1)/2, 3/2, and 6/2.
(B) the x-intercepts of y = 2f(x) are 1, 3, and 6.
(C) the x-intercepts of y = f(x + 2) are (-1 - 2), (3 - 2), and (6 - 2), which are -3, 1, and 4.
How did we get the values?(a) To find the x-intercepts of y = f(2x), we need to find the values of x for which f(2x) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the corresponding x-intercepts of y = f(2x) are (-1)/2, 3/2, and 6/2.
(b) To find the x-intercepts of y = 2f(x), we need to find the values of x for which 2f(x) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the x-intercepts of y = 2f(x) are the same: -1, 3, and 6.
(c) To find the x-intercepts of y = f(x + 2), we need to find the values of x for which f(x + 2) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the corresponding x-intercepts of y = f(x + 2) are (-1 - 2), (3 - 2), and (6 - 2), which are -3, 1, and 4.
(d) The appearance of y = f(mx) will be a compression or expansion of the graph of y = f(x), depending on the value of m. If m < 1, the graph of y = f(mx) will be a compression of the graph of y = f(x) along the x-axis. If m > 1, the graph of y = f(mx) will be an expansion of the graph of y = f(x) along the x-axis. The x-intercepts of y = f(mx) can be found by finding the values of x for which f(mx) = 0.
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A quadratic equation whose roots are -2 and 5, and whose leading coefficient is 2.
[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -5 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{since the leading coefficient is 2, let's a = 2}}{2(x+2)(x-5)=y} \\\\\\ 2\stackrel{\textit{F O I L}}{(x^2-3x-10)=y}\implies \boxed{2x^2-6x-20=y}[/tex]
For what value of n is the polynomial x^3 - 9x^2 + nx - 12 divisible by x - 3? Show work.
Answer:
B
Step-by-step explanation:
if a polynomial f(x) is divisible by (x - a) , then f(a) = 0
for the polynomial to be divisible by (x - 3) then the polynomial will equal zero when x = 3 , that is
3³ - 9(3)² + 3n - 12 = 0
27 - 9(9) + 3n - 12 = 0
27 - 81 + 3n - 12 = 0
3n - 66 = 0 ( add 66 to both sides )
3n = 66 ( divide both sides by 3 )
n = 22
Required information Consider the following diagrams: Diagram 1 Diagram 2 7 7 6- 6 5 5 4 4 3 3 2 2 1 1 - 0 0 0 0 1 2 3 4 5 6 7 1 2 3 4 -10 8 7 Diagram 3 Diagram 4 7 7 9 6 5 40 st 4- 3 3 FZ 2 - 1 - 1 - 2 3 4 6 0 0 O O 1 3 2 4 5 6 2 4 7 3 6 5 7 c. Research shows that organic produce sales are higher among more educated consumers. Correct diagram: (Click to select) Slope: (Click to select)
To better understand the relationship between education level and organic produce sales, we need to have data on these variables.
The data would typically be in the form of a table or a graph, with education level on one axis and organic produce sales on the other. Once we have the data, we can look at the pattern of the points to determine the relationship between education level and organic produce sales. If there is a positive relationship between the two variables, then as the education level increases, we would expect to see an increase in organic produce sales. This positive relationship could be represented by a line that slopes upward from left to right on a graph.
The slope of the line represents the rate of change of organic produce sales with respect to education level. A steep slope would indicate that even small changes in education level lead to significant changes in organic produce sales, while a shallow slope would suggest that changes in education level have little effect on organic produce sales.
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The table below displays the adult literacy rate in Bolivia for several different years. The adult literacy rate is the percentage of people ages 15 and above who can both read and write with understanding a short simple statement about their everyday life.
Data downloaded on 2/19/2020 from https://ourworldindata.org/grapher/literacy-rate-adults?tab=chart&time=1973..2016.
Year 1976 2001 2012
Literacy Rate 63.2% 86.7% 94.5%
When answering the questions below, round to four decimal places in your intermediate computations.
Use interpolation or extrapolation (whichever is appropriate) to predict the literacy rate in Bolivia in 1992. Round your answer to one decimal place. You only get one submission for the unit.
Use interpolation or extrapolation (whichever is appropriate) to predict the literacy rate in Bolivia in 2050. Round your answer to one decimal place. You only get one submission for the unit.
Is your 2050 prediction realistic? You must select all correct responses at the same time to receive credit for this problem. You get two submissions.
Yes, the 2050 prediction is realistic because it is possible for a literacy rate to exceed 100%.
No, the 2050 prediction is not realistic because the literacy rate will not grow at the exact same rate for more than 40 years.
Yes, the 2050 prediction is realistic because it was made using a mathematical formula.
No, the 2050 prediction is not realistic because the literacy rate cannot exceed 100%.
Is your 2050 prediction realistic?
No, the 2050 prediction is not realistic because the literacy rate cannot exceed 100%
How to solveGiven data is
x0=1976, y0=63.2
x1=2001, y1=86.7
x2=2012, y2=94.5
Then the Lagrange interpolation formula is
[tex]y - y_1 = \frac{y_2 - y_1}{x_2 -x_1} (x - x_1)[/tex]
Here we have to interpolate to predict the literacy rate in 1992.
i.e. x=1992.
It lies between 1976 and 2001.
Then
x1=1976, y1=63.2
x2=2001, y2=86.7
Then interpolation function become
[tex]63.2 + \frac{23.5}{25}(16)[/tex]
= 63.2 + 15.04 = 78.24
i.e. The predicted literacy rate in 1992 is 78.24%.
Now, to find the literacy rate in 2050, we have to use extrapolation.
Since, 2050 is not in between any of the given data, we will have to take last two datas.
i.e.
x1=2001, y1=86.7
x2=2012, y2=94.5
And x=2050.
Then our extrapolation formula become
[tex]86.7 + \frac{7.8}{11} (49)[/tex]
= 86.7 + 34.75
=121.45
i.e. The literacy rate in 2050 is 121.45%.
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8. Write a new function, N(t), that represents the amount of money in Jennifer’s new account after t years. Be sure to use correct notation
The new function of Jennifers's investment is f(t) = 50000 * (1.15)^t
How to determine the new functionFrom the question, we have the following parameters that can be used in our computation:
Initial investment, a = 50000
Rate of growth, r = 15%
Using the above as a guide, we have the following:
f(t) = a * (1 + r)^t
Substitute the known values in the above equation, so, we have the following representation
f(t) = 50000 * (1 + 15%)^t
So, we have
f(t) = 50000 * (1.15)^t
Hence, the function is f(t) = 50000 * (1.15)^t
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Complete question
ennifer starts a new investment account that grows exponentially. Her financial advisor tells her the initial investment of $50,000 grows at a rate of about 15% annually.
Write a new function, N(t), that represents the amount of money in Jennifer’s new account after t years. Be sure to use correct notation