Answer:
True
Step-by-step explanation:
What is the range of g(x)=-1/2|x-6|+1
Answer:
The answer is A: ( - ∞, 1 )
Step-by-step explanation:
. A certain coin is a circle with diameter 18 mm. What is the exact area of either face of the coin in terms of p?
Answer:
[tex] r =\frac{D}{2}=\frac{18mm}{2}= 9mm[/tex]
The area is given by:
[tex]A= \pi r^2[/tex]
And replacing we got:
[tex] A=\pi (9mm)^2 =81\pi mm^2[/tex]
So then we can conclude that the area of the coin is [tex] 81\pi[/tex] mm^2
Step-by-step explanation:
For this case we know that we have a coin with a diamter of [tex] D =18mm[/tex], and by definition the radius is given by:
[tex] r =\frac{D}{2}=\frac{18mm}{2}= 9mm[/tex]
The area is given by:
[tex]A= \pi r^2[/tex]
And replacing we got:
[tex] A=\pi (9mm)^2 =81\pi mm^2[/tex]
So then we can conclude that the area of the coin is [tex] 81\pi[/tex] mm^2
Do You Understand?
D
4.
1. Essential Question How does an equation
show the relationship between variables and
other quantities in a situation?
Answer:
An equation is basically a way to show a relationship of variables (x,y,a,b, etc) and numbers.
Step-by-step explanation:
Answer:
Shown by explanation.
Step-by-step explanation:
An equation shows a relationship between variables and other factors by defining the variables that are dependent and independent and how these dependent variables are related to the independent variables, this is usually as a result of a prescribed experiment where the relationship of this variables are investigated.
Also remember conditions that favour this experiment must be taken into consideration. And the experiment must always be performed under such conditions.
A bag contains some number of marbles. It is known that 20 of them are red. When 15 marbles are drawn, without replacement, we get 6 red. Assuming E(X)=6 red, what is the total number of marbles in the bag?
Answer:
The total number of marbles in the bag is 50.
Step-by-step explanation:
Here, we have n trials, without replacement. So the hypergeometric distribution is used.
The mean of the hypergeometric distribution is:
[tex]E(X) = \frac{n*k}{N}[/tex]
In which n is the number of items in the sample, k is the number of items in the population that are classified a success and N is the size of the population.
15 marbles are drawn:
This means that [tex]n = 15[/tex]
A bag contains some number of marbles. It is known that 20 of them are red.
This means that [tex]k = 20[/tex], since a success is drawing a red marble.
Assuming E(X)=6 red, what is the total number of marbles in the bag?
We have to find N when [tex]E(X) = 6[/tex]
So
[tex]E(X) = \frac{n*k}{N}[/tex]
[tex]6 = \frac{15*20}{N}[/tex]
[tex]6N = 300[/tex]
[tex]N = \frac{300}{6}[/tex]
[tex]N = 50[/tex]
The total number of marbles in the bag is 50.
6th grade math help me. :D.....
Answer:
(1) 4x + 28 (2) 18x- 27
Step-by-step explanation:
the first question 4(x + 7) can be simplified by multiplying the number outside the parenthesis (4) by both of the values inside:
4x + 28 or the last answer choice
in the second question you can use the same method:
9 (2x) = 18x
9 ( -3) = -27
therefore the correct answer choice is 18x - 27
hope this helps :)
The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.
You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why?
1. No. The events cannot occur together. 2. Yes. The events can occur together. 3. No. The probability of drawing a specific second card depends on the identity of the first card. 4. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.
(b) Find P(ace on 1st card and jack on 2nd). (Enter your answer as a fraction.)
(c) Find P(jack on 1st card and ace on 2nd). (Enter your answer as a fraction.)
(d) Find the probability of drawing an ace and a jack in either order. (Enter your answer as a fraction.)
Answer:
(a)No. The probability of drawing a specific second card depends on the identity of the first card.
(b)4/663
(c) 4/663
(d) 8/663
Step-by-step explanation:
(a)The events are not independent because we are drawing cards without replacement and the probability of drawing a specific second card depends on the identity of the first card.
(b) P(ace on 1st card and jack on 2nd).
[tex]P$(Ace on 1st card) =\dfrac{4}{52}\\ P$(Jack on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(ace on 1st card and jack on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]
(c)P(jack on 1st card and ace on 2nd)
[tex]P$(Jack on 1st card) =\dfrac{4}{52}\\ P$(Ace on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(jack on 1st card and ace on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]
(d)Probability of drawing an ace and a jack in either order.
We can either draw an ace first, jack second or jack first, ace second.
Therefore:
P(drawing an ace and a jack in either order) =P(AJ)+(JA)
From parts (b) and (c) above:
[tex]P$(jack on 1st card and ace on 2nd) =\dfrac{4}{663}\\P$(ace on 1st card and jack on 2nd) =\dfrac{4}{663}\\$Therefore:\\P(drawing an ace and a jack in either order)=\dfrac{4}{663}+\dfrac{4}{663}\\=\dfrac{8}{663}[/tex]
How far from zero would you move on the x-axis to reach the point (10, 8)?
Answer:
You would move 10 units to the right from zero on the x-axis.
The given point is 10 units from zero, when you move on the x-axis to reach the point (10, 8).
What is coordinate plane?A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
The given coordinate point (10, 8).
The distance of any point from the x-axis is called the x-coordinate.
In the point (10, 8), 10 units from the x-axis
Therefore, the given point is 10 units from zero, when you move on the x-axis to reach the point (10, 8).
Learn more about the coordinate plane here:
https://brainly.com/question/24134413.
#SPJ6
The relationship of variance and mean informs researchers about the spread of data. If a researcher calculates the mean abundance per unit area of a species, and then calculates the variance, the relationship between mean and variance will reflect the distribution pattern.
Which distribution pattern pictured below will have variance greater than the mean?
Answer:
The distribution pattern that will have variance greater than mean is one where the population of species is clustered and thus far from the mean abundance of species per unit area.
This distribution pattern can be found, using the POISSON distribution.
Step-by-step explanation:
Variance is a measure of dispersion while Mean is a measure of central tendency.
The mean is the average of all values (in this case, the abundance or concentration of species per unit area). It is the sum total of all values, divided by the number of values there are.
The variance of a given set of data, on the other hand, is a measure of the spread or distance or dispersal of the data from the mean. It measures the spread between each datum/value and the mean value.
The relationship between mean and variance surely reflects the pattern that the distribution will take. The kind of distribution pattern that will have a greater variance than mean is a Poisson distribution. Sample size is usually large here. Since the variance is greater than the mean, the population is a clustered or clumped distribution.
Kyle is making a frame for a rectangular piece of art. The length of the frame is 3 times the width, as shown below.
TIME REMAINING
54:06
3x
x
If Kyle uses 10 feet of wood to make the frame, what is the length of the frame? Write the answer in decimal form,
0.75
4.60
0.00
Answer:
3.75 feet
Step-by-step explanation:
The length of the frame is 3 times the width.
Let the width be x.
The length will be 3x.
Kyle uses 10 feet of wood to make the frame. This means that the perimeter is 10 feet.
The perimeter of a rectangle is:
P = 2(L + W)
=> 10 = 2(3x + x)
=> 10/2 = 4x
5 = 4x
=> x = 5/4 = 1.25 feet
The width is 1.25 feet. The length is therefore:
1.25 * 3 = 3.75 feet
Real Estate One conducted a recent survey of house prices for properties located on the shores of Tawas Bay. Data on 26 recent sales, including the number of bathroom, square feet and bedrooms are below.
Selling Price Baths Sq Ft Beds
160000 1.5 1776 3
170000 2 1768 3
178000 1 1219 3
182500 1 1568 2
195100 1.5 1125 3
212500 2 1196 2
245900 2 2128 3
250000 3 1280 3
255000 2 1596 3
258000 3.5 2374 4
267000 2.5 2439 3
268000 2 1470 4
275000 2 1678 4
295000 2.5 1860 3
325000 3 2056 4
325000 3.5 2776 4
328400 2 1408 4
331000 1.5 1972 3
344500 2.5 1736 3
365000 2.5 1990 4
385000 2.5 3640 4
395000 2.5 1918 4
399000 2 2108 3
430000 2 2462 4
430000 2 2615 4
454000 3.5 3700 4
Action:
Use the data above and multiple regression to produce a model to predict the average sale price from other variables. Comment on the following:
a. Regression equation
b. R, R2 and 1-R2, adjusted R2
c. Standard error of estimate
d. Report the t's for each value and the corresponding p-values
e. Overall test of hypothesis and decision
f. Use a .05 level of significance. Cite which variables are significant and which are not significant, based on the t values and p values for each independent variable.
Answer:
Step-by-step explanation:
Hello!
Given the data for the variables:
Y: Selling price of a house on the shore of Tawas Bay
X₁: Number of bathrooms of a house on the shore of Tawas Bay.
X₂: Square feet of a house on the shore of Tawas Bay.
X₃: Number of bedrooms of a house on the shore of Tawas Bay.
The multiple regression model is Y= α + β₁X₁ + β₂X₂ + β₃X₃ + εi
a. Using software I've entered the raw data and estimated the regression coefficients:
^α= a= -5531.01
Represents the mean selling price of the houses when 0 bathrooms, 0 square feet and 0 bedrooms.
^β₁= b₁= -1386.21
Represents the modification of the mean selling price of the houses when the number of bathrooms increases in one unit and the square feet and number of bedrooms remain unchanged.
^β₂= b₂= 60.28
Represents the modification of the mean selling price of the houses when the square feet increase in one unit and the number of bathrooms and bedrooms remain unchanged.
^ β₃= b₃= 54797.08
Represents the modification of the mean selling price of the houses when the number of bedrooms increase in one unit and the number of bathrooms and square feet of the houses remain unchanged.
^Y= -5531.01 -1386.21X₁ + 60.28X₂ + 54797.08X₃
b)
R²= 0.55
R²Aj= 0.49
The coefficient of determination gives you an idea of how much of the variability of the dependent variable (Y) is due to the explanatory variables. Each time you add another explanatory variable to the regression the coefficient increases regarding of real contribution of the new variable. This could lead to thinking (wrongly) that the new variables are good to explain the dependent variable.
The adjusted coefficient of determination is a correction made to the raw coefficient of determination to have a more unbiased estimation of the effect the independent variables have over the dependent variable.
⇒ As you can see both coefficient are around 50%, which means that these explanatory variables
c)
The standard error estimate, this is the estimate of the population variance of the errors. In the ANOVA is represented by the Mean Square of the errors (MME)
Se²= MME= 3837640577.01
Se= 61948.6931
d) and f)
For the hypotheses tests for each slope the t- and p-values are:
α: 0.05
β₁: [tex]t_{H_0}= \frac{b_1-\beta_1 }{Sb_1}[/tex] t= -0.06; p-value: 0.9528 ⇒ Do not reject H₀, the test is not significant.
β₂: [tex]t_{H_0}= \frac{b_2-\beta_2 }{Sb_2}[/tex] t= 2.56; p-value: 0.0180 ⇒ Reject H₀, the test is significant.
β₃: [tex]t_{H_0}= \frac{b_3-\beta_3 }{Sb_3}[/tex] t= 2.28; p-value: 0.0326 ⇒ Reject H₀, the test is significant.
e)
H₀: β₁= β₂= β₃
H₁: At least one βi is different from the others ∀ i=1, 2, 3
α: 0.05
F= 9.03
p-value: 0.0004
⇒ Reject H₀, the test is significant.
I hope it helps!
Classify the triangle by its sides, and then by its angles.
128 degrees
26 degrees
26 degrees
16 cm
16 cm
28 cm
Classified by its sides, the triangle is a(n)
▼
isosceles
scalene
equilateral
triangle.
Classified by its angles, the triangle is a(n)
▼
obtuse
acute
right
triangle.
Really easy math question!
the answer is A: 146 ≤ 9c + 10
6th grade math :) ........
Answer:
Step-by-step explanation:
1) d
2) c
1) 3 hearts, 7 other shapes that isn't hearts
2) 2 triangs, 5 circles
Answer:
1) d
2) c
Step-by-step explanation:
looks like i was wrong last time lol, this is right for sure tho, i see what i did wrong, sorry
Which of the following is a radical equation?
X3 - 13
X+ 15 - 13
√x+3-13
x+3 - 13
Answer:
√x+3-13
Step-by-step explanation:
This answer is a radical equation because a square root is used in the equation. This makes the equation radical. The other choices have no square roots so they can't be the answers.
Determine whether the underlined number is a statistic or a parameter. In a study of all 1700 professors at a college, it is found that 35% own a computer Choose the correct statement below. O Parameter because the value is a numerical measurement describing a characteristic of a sample. Statistic because the value is a numerical measurement describing a characteristic of a population. O Statistic because the value is a numerical measurement describing a characteristic of a sample. Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits minimum = 21, maximum = 120, 8 classes (Type a whole number.) Choose the correct lower class limits below .
A. 21, 33, 47, 59, 72, 86, 98, 112
B. 21.34, 47, 60, 73, 86, 99. 112
Answer:
The first option is correct.
Parameter because the value is a numerical measurement describing a characteristic of population.
Class width = 12.375
B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit
Step-by-step explanation:
The first option is correct.
Parameter because the value is a numerical measurement describing a characteristic of population.
Parameter is a measure that describes the entire population.
Statistic basically describes a sample of the population.
From the given information , the entire 1700 professors at a college is the population and only 35 % own a television is a characteristic, called parameter, of population.
Another objective we are to find here is:
Use the given minimum and maximum data entries, and the number of classes, to find the class width, .
Class width = Maximum - Minimum /No of classes
Given that :
Maximum = 120
Minimum = 21
number of classes = 8
Then;
Class width = 120 - 21 /8
Class width = 12.375
From the given information :
B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit
A supermarket is redesigning it’s checkout lanes. Design A has a sample size of 50, sample mean of 4.1 minutes, and sample standard deviation of 2.2 minutes. Design B has a sample size of 50, sample mean of 3.5 minutes, and sample standard deviation of 1.5 minutes. At the 0.05 level of significance, determine if their is evidence that the checkout times of the two systems differ.
Answer:
The calculated value t = 1.57736 < 1.9845 at 5 % level of significance
Null hypothesis is accepted at 5 % level of significance
There is no significance difference between Design A and Design B
Step-by-step explanation:
Given sample size of design A
n₁ = 50
sample mean of design A x⁻₁ = 4.1 minutes
Sample standard deviation S₁ = 2.2 minutes
Given sample size of design B
n₂ = 50
sample mean of design A x⁻₂ = 3.5 minutes
Sample standard deviation S₂ = 1.5 minutes
Null Hypothesis : H₀ : There is no significance difference between Design A and Design B
Alternative Hypothesis : H₁:There is significance difference between Design A and Design B
Level of significance ∝ = 0.05
Test statistic
[tex]t = \frac{x^{-} _{1}- x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} }) } }[/tex]
where
[tex]S^{2} = \frac{n_{1} S_{1} ^{2} +n_{2} S^2_{2} }{n_{1} +n_{2} -2}[/tex]
[tex]S^{2} = \frac{50 (2.2)^{2} +50(1.5)^2}{50+50-2}[/tex]
On calculation , we get
S² = 3.6173
Test statistic
[tex]t = \frac{4.1-3.5}{\sqrt{3.617(\frac{1}{50} +\frac{1}{50} }) }[/tex]
On calculation , we get
t = 1.57736
Degrees of freedom
ν = n₁ + n₂ -2 = 50 +50 -2 =98
t₀.₀₂₅ ,₉₈ = 1.9845
The calculated value t = 1.57736 < 1.9845 at 5 % level of significance
null hypothesis is accepted
please help, limited on time!!
Answer:
D. 5/13
Step-by-step explanation:
Cosin is adjacent/hypotenuse so, the adjacent would be 5 and the hypotenuse is 13 since it is the longest side. This is viewed from angle B.
Answer:
5/13 (answer D)
Step-by-step explanation:
cos beta = adjacent side / hypotenuse = 5 / 13 (answer D)
If P(-2, 1) is rotated 90°, its image is
The image of P(-2,1) after it is rotated 90° is (-1,-2).
7. Tyson obtained a loan from the bank at 7.5% simple interest for 2. 5 years. If the simple interest was
N$347.50, how much did he borrow?
8. Hilma invested N$20 000 on 01/01/2018 at 9.5 % interest p.a compounded semi-annually.
How much will she receive by 01/01/2022?
Answer:
7.He borrowed $1853.33
8.She received $28990.936
Step-by-step explanation:
7.Let x be the amount borrowed by Tyson
Rate of interest = 7.5%
Time = 2.5 years
Simple Interest = 347.50
Formula : [tex]Si = \frac{P \times T \times R}{100}[/tex]
Where SI = simple interest
P = Principal
T = Time
R = Rate of interest
Substitute the values in the formula :
[tex]347.50=\frac{x \times 2.5 \times 7.5}{100}\\\frac{347.50 \times 100}{2.5 \times 7.5}=x\\1853.33=x[/tex]
Hence he borrowed $1853.33
8) Principal = 20000
Rate of interest = 9.5%
No. of compounds per year = 2
Time = 4 years
Formula : [tex]A=P(1+\frac{r}{n})z^{nt}[/tex]
Where A= amount
r = Rate of interest
n = no. of compounds
t = time
Substitute the values in the formula :
So, [tex]A=20000(1+\frac{9.5}{200})^{2(4)}[/tex]
A=28990.936
Hence she received $28990.936
BP Under 30 30-49 Over 50 Total Low 27 38 31 96 Normal 48 90 92 230 High 23 59 72 154 Total 98 187 195 480 What is the percentage of employees who are 30 and over and have normal or low blood pressure? Group of answer choices 67.9% 52.3% 41.7% 75.4%
Answer:
The correct answer to the following question will be Option A (67.9%).
Step-by-step explanation:
As we know,
The number of total employees will be:
= 480
The number of employees having normal or low BP will be:
= 96 + 230
= 326
Hence, the percentage of low or normal BP workers will be:
= [tex](\frac{326}{480} )\times 100 \ percent[/tex]
= [tex]67.9 \ percent[/tex]
Note:- % (percent)
We know that if the probability of an event happening is 100%, then the event is a certainty. Can it be concluded that if there is a 50% chance of contracting a communicable disease through contact with an infected person, there would be a 100% chance of contracting the disease if 2 contacts were made with the infected person
Answer:
The correct answer to the following question will be "No". The further explanation is given below.
Step-by-step explanation:
Probability (Keeping the disease out of 1 contact)
= [tex]0.5[/tex]
Probability (not keeping the disease out of 1 contact)
= [tex]1-0.5[/tex]
= [tex]0.5[/tex]
Now,
Probability (not keeping the disease out of 2 contact)
= Keeping the disease out of 1 contact × not keeping the disease out of 1 contact
On putting the estimated values, we get
= [tex]0.5\times 0.5[/tex]
= [tex]0.25[/tex]
So that,
Probability (Keeping the disease out of 2 contact)
= [tex]1-0.25[/tex]
= [tex]0.75 \ i.e., 75 \ percent[/tex]
∴ Not 100%
Calculate the length of the apothem of a regular polygon. A
regular hexagon is shown. What is the length of the apothem,
rounded to the nearest inch? Recall that in a regular hexagon,
the length of the radius is equal to the length of each side of the
hexagon
10 in.
a
5 in
9 in
11 in
4 in
Answer:
9 in
Step-by-step explanation:
For an n-sided polygon, the length of the apothem is ...
a = r·cos(180°/n)
We assume your problem statement is saying the radius is 10 inches. For a hexagon, n=6 and we have ...
a = (10 in)cos(30°) ≈ 8.66 in
Rounded to the nearest inch, the apothem is 9 in.
Suppose your total taxable income this year is $75,000 you are taxed a rate of 10 percent on the first 25,000 20 percent on the next 25,000 and 30 percent on the final 25,000 what is your total income tax
What’s the correct answer for this?
Answer:
34°
Step-by-step explanation:
According to the theorem, "any two angles in the same segmant are congruent"
<BED = <BCD
So
<BED = 34°
What is the main issue with plugging values into a function and then graphing it?
Too hard to calculate.
Takes too much time.
Never sure of exact data points.
Does not provide accurate results.
Answer:
B: It takes too much time
Step-by-step explanation:
Once the points have been calculated and then graphed, the solutions to y = 0 can be found. Look for y = 0 and the solutions are -5 and -1. But that takes a lot of time. There must be an easier way, and fortunately, there is.
A can of beans has surface area 320cm squared . Its height is 14 cm. What is the radius of the circular top?
Steps:
All cans take on the shape of a cylinder, unless you have seen interesting shape of cans like a starfish.
The formula for surface area of a cylinder is
SA = 2πr2 + 2πrh
where:
r = radius
h = height
Since we know the surface area and height, we can plug them in. Note that we can factor out the 2π. You will see why we factor out 2π rather than 2πr.
2π(r2 + (20)r) = 396
2π(r2 + 20r) = 396
Divide both sides of the equation by 2π to isolate the r terms.
r2 + 20r = 63.025
Subtract 63.025 on both sides of the equation.
r2 + 20r - 63.025 = 0
Use the quadratic formula to solve for r:
r = (-b ± √(b2 - 4ac)) / 2a
where:
a = 1
b = 20
c = -63.025
Plug in these values into the formula. You should get two solutions because of the plus/minus sign. Accept the positive value of r.
Please mark brainliest
Hope this helps.
Jankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 10 percent are returned. If eight rings are sold today, what is the probability that fewer than three will be returned
Answer:
[tex]P(X<3) =[/tex] [tex]0.9619[/tex]
Step-by-step explanation:
From the given information;
the probability of getting returned p = 0.1
If eight rings are sold today, what is the probability that fewer than three will be returned;
According to binomial distribution
Binomial distribution is the probability of success or failure of an outcome of an experiment under observation which is usually repeated several trials. Binomial experiments are random experiment with fixed number of repeated experiment. If we cannot predict before head, the outcome of an experiment , the experiment is called a random experiment.
So , using binomial distribution to determine the probability that fewer than three will be returned;
i.e
[tex]P(X<3) =[/tex] [tex]\sum_{x=0}^{2}\binom{8}{x}(0.1)^{x}(1-0.1)^{8-x}[/tex]
[tex]P(X<3) =[/tex] [tex]0.9619[/tex]
A pair of shoes usually sells for $70. If the shoes are 30% off, and sales tax is 5%, what is the total price of the shoes, including tax?
Answer:
The total price of the shoes including tax is 51.45
Step-by-step explanation:
You could go about this 2 ways.
One way is if the shoes originally cost $70 and they are now 30% off, it basically means that the discounted price of the shoes is 70% of the original cost, which is $49. Then to find the total price including tax, you need to find 105% of 49, because you are adding 5% to the discounted price(100). When you do the math, you should get the answer 51.45.
The other way to do it is by first finding 30% of 70, which is 21, and then subtracting that from the original price(70) to get the discounted price, $49. Then you need to find 5% of 49 and then add that to 49 to find the total cost w/ tax, which is 51.45.
What is the y coordinate of the point that divides the directed line segment from j to k into a ratio of 2 to 3
Answer:
y = [tex]y_{1}[/tex] + rise * 2/5
Step-by-step explanation:
Adam earns $45,000 in his first year as an accountant and earns a 3% increase in each
successive year.
(a) Write a geometric series formula,
n S
, for Adam’s total earnings over
n
years.
(b) Use this formula to find Adam’s total earnings for her first 12 years of his job, to the nearest
cent.
Answer:
$638641.33
Step-by-step explanation:
Adam earns $45,000 in his first year.
His salary increases by 3% each successive year. Therefore, his salary the next year is 103% of his previous year.
This is a geometric sequence where the:
First Term, a= $45,000Common ratio, r =103%=1.03(a)
Sum of geometric series[tex]=\dfrac{a(r^n-1)}{r-1}[/tex]
Substituting the given values, Adam's total earnings over n years
[tex]=\dfrac{45000(1.03^n-1)}{1.03-1}\\\\$Adam's Total Earnings=\dfrac{45000(1.03^n-1)}{0,03}[/tex]
(b)When n=12 years
[tex]\text{Adam's Total Earnings for the first 12 years=}\dfrac{45000(1.03^{12}-1)}{0.03}\\=\$638641.33$ (correct to the nearest cent)[/tex]
