The equation of a straight line given two points (4, -1) and (-8, -7) can be found using the formula:
\(\begin{gathered} \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \text{where the points are:} \\ (x_1,y_1)=(4,-1) \\ (x_2,y_2)=(-8,-7) \end{gathered}\)Put the coordinate points into the formula,
\(\begin{gathered} \frac{-7-(-1)}{-8-4}=\frac{y-(-1)}{x-4} \\ \frac{-7+1}{-12}=\frac{y+1}{x-4} \\ \frac{-6}{-12}=\frac{y+1}{x-4} \\ \text{simplify the fraction} \\ \frac{1}{2}=\frac{y+1}{x-4} \\ \text{cross multiply,} \\ 2(y+1)=x-4 \\ \text{divide through by 2,} \\ \frac{2(y+1)}{2}=\frac{x-4}{2} \\ y+1=\frac{x}{2}-\frac{4}{2} \\ \text{simplify the fraction} \\ y+1=\frac{1}{2}x-2 \\ \text{collect like terms} \\ y=\frac{1}{2}x-3 \end{gathered}\)Comparing the equation of the line obtained with the formula y = mx + b:
\(\begin{gathered} y=mx+c \\ y=\frac{1}{2}x-3 \\ On\text{ comparing,} \\ m=\frac{1}{2} \\ c=-3 \end{gathered}\)Therefore, m= 1/2, c = -3
3. A one-tailed hypothesis test with the t statistic
Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions.
Suppose you have a sample of 40 12-year-old children with antisocial tendencies and you are particularly interested in the emotion of surprise. The average 12-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed.
You believe that children with antisocial tendencies will have a harder time recognizing the emotion of surprise (in other words, they will have higher scores on the emotion recognition test).
What is your null hypothesis stated using symbols?
What is your alternative hypothesis stated using symbols?
This is a tailed test. Given what you know, you will evaluate this hypothesis using a statistic.
Using the Distributions tool, locate the critical region for α = 0.05.
In order to use the t distribution, you will first need to determine the degrees of freedom (df) for α = 0.05. The degrees of freedom (df) is . The critical value of t is .
Your sample of 12-year-old children with antisocial tendencies has an average score of 12.55 with a standard deviation of 3.28.
Calculate the t statistic. To do this, you will first have to calculate the estimated standard error. The estimated standard error is . The t statistic is . (Hint: For the most precise results, retain four significant figures from your calculation of the standard error to calculate the t statistic. Round your final answer to four decimal places, and then round it again to two decimal places for your answer selection.)
The t statistic lie in the critical region. Therefore, you reject the null hypothesis.
Based on the results of this test, there enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies.
Based on the results of this test, there is not enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies.
Is there is enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies?The null hypothesis stated using symbols is: H0: μ ≤ 11.80 (where μ represents the population mean score on the emotion recognition scale for 12-year-old children with antisocial tendencies)
The alternative hypothesis stated using symbols is: H1: μ > 11.80
This is a one-tailed test, as the alternative hypothesis is only looking for an increase in the population mean score for recognizing the emotion of surprise among children with antisocial tendencies.
Using the Distributions tool with a one-tailed test and α = 0.05, the critical region is in the right tail of the distribution and the critical value of t is 1.684.
The degrees of freedom (df) for α = 0.05 and n = 40-1 = 39 is 39.
The estimated standard error is the standard deviation of the sample divided by the square root of the sample size, which is 3.28/√40 = 0.518. The t statistic is (12.55 - 11.80) / 0.518 = 1.45 (rounded to four decimal places), which is not greater than the critical value of t. Therefore, we fail to reject the null hypothesis.
Based on the results of this test, there is not enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies.
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show that the volume of the unit cube is one
Check the picture below.
At the local Theatre of the Arts, tickets cost $4 for children and $5 for adults. In the opening Saturday night of a play, the theater made $540. The second day was a matinee and the prices were lower for children at $3 and the same price as Saturday for adults. They made $440 at the matinee.
A) Write a system of equations in standard form that represents the prices at the Theatre on Saturday and the second day.
B) Rewrite the system of equations in slope-intercept form. What are the y-intercepts of both equations?
A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.
B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.
A) Let's define the variables:
Let x represent the number of children attending.
Let y represent the number of adults attending.
On Saturday night:
The equation for the revenue generated on Saturday night is:
4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).
Matinee on the second day:
The equation for the revenue generated at the matinee is:
3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).
Therefore, the system of equations in standard form is:
4x + 5y = 540
3x + 5y = 440
B) Let's rewrite the system of equations in slope-intercept form:
On Saturday night:
4x + 5y = 540
Rearranging the equation, we get:
5y = -4x + 540
Dividing both sides by 5, we get:
y = (-4/5)x + 108
The y-intercept of this equation is 108.
Matinee on the second day:
3x + 5y = 440
Rearranging the equation, we get:
5y = -3x + 440
Dividing both sides by 5, we get:
y = (-3/5)x + 88
The y-intercept of this equation is 88.
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The total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x. If the initial total attendance (that is, the total attendance when x=0) was measured January 1, 2013, what was the initial total attendance?
The initial total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x will be 17371.
How to calculate the value?It should be noted that from the information, the total attendance at a science museum is modeled by the function
In this case, the total attendance when x=0 will be:
f(x) = 17,371(1.041)x.
f(x) = 17,371(1.041^0)
= 17371 × 1
= 17371
Therefore, the total attendance when x = 0 will be 17371.
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Question 4 of 10
What is 7C4?
O A. 35
O B. 14
O c. 10
O D. 28
Answer:
d
Step-by-step explanation:
i just took the test.
Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year. She finds that the proportion of people taking extended vacations nationally is 15%. z equals fraction numerator p with hat on top minus p over denominator square root of begin display style fraction numerator p q over denominator n end fraction end style end root end fraction The z statistic for this data is __________. -0.56 0.45 -0.45 0.56
Answer:
0.56
Step-by-step explanation:
RATIONALE
To make things a little easier, let's first note the denominator
We can now note that
Finally, subbing all in we find
Answer:
0.56
Step-by-step explanation:
What is a reasonable estimate for the limit of hhh at x=3x=3x, equals, 3?
Answer:
Limit does not exist.
Step-by-step explanation:
From the graph, notice that the limit does not exist, when you move to the right the limit tend to -3 and when you approach from the left your limit approaches 4, therefore since the right and left limit are not equal the limit does not exist.
You deposit $5000 in an account earning 5% interest compounded continuously. How much will you have in the account in 5 years? Round to the nearest cent.
100 Points!!! Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Photo attached
The 2nd graph is consistent as it does follow consistency condition and 3rd one in is inconsistent.
What is the condition of consistent equations?
Consistency condition:
a1/a2=b1/b2=c1/c2
Now,in the 2nd Given equations are y=x-5=>x-y-5=0
-2x+2y+10=0
Substituting for consistency checking: 1/-2=-1/2=5/-10
=>-1/2=- 1/2=-1/2
The 2nd graph is consistent.
While considering different values of 2nd graph and putting them we are not getting same line so it is dependent.
A consistent independent system of equations will have one solution.
The 3rd graph is not consitent as the condition is not satisfied.
Given equations : 2x-5y-10=0
3x+y-15=0
So here consistency condition is not satisfied.
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5/6 having denominator 35
Answer:( 175/6)
Step-by-step explanation: 5*35/6=175/6 sour our numerator is 175/6. So sour answer is (175/6)/35
What is the value of x? Round to the nearest thousandth.
Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.
How to Find the Value of x Using the Tangent Ratio?The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:
tan (∅) = opposite/adjacent
We have the following:
Reference angle (∅) = 53 degrees
Length of opposite side = 21
Length of adjacent side = x
Plug in the values:
tan 53 = 21/x
x * tan 53 = 21
x = 21 / tan 53
x = 15.824
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5,10,15,20,25 what is the common difference
Answer:
The common difference in the given sequence is 5.
Step-by-step explanation:
The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15
The mean weight from a sample of 256 computer parts created by a computer manufacturer was 274.3 grams, with a standard deviation of 25.9 grams. Can this company claim that the mean weight of its manufactured computer parts will be less than 275 grams? Test this hypothesis using a 1% level of significance.
Since -1.7 > -2.33, we faiI tο reject the nuII hypοthesis. Therefοre, we cannοt cIaim with 99% cοnfidence that the mean weight οf the manufacturer's cοmputer parts is Iess than 275 grams
What is Standard Deviatiοn?Standard deviatiοn is a statisticaI measure that shοws hοw much variatiοn οr dispersiοn there is frοm the mean οf a set οf data. It is caIcuIated by finding the square rοοt οf the variance.
Tο test this hypοthesis, we need tο perfοrm a οne-sampIe t-test with the fοIIοwing hypοtheses:
NuII hypοthesis: The mean weight οf the cοmputer parts prοduced by the manufacturer is greater than οr equaI tο 275 grams.
AIternative hypοthesis: The mean weight οf the cοmputer parts prοduced by the manufacturer is Iess than 275 grams.
We wiII use a οne-taiIed test with a IeveI οf significance οf 1%, which cοrrespοnds tο a t-scοre οf -2.33 (frοm the t-distributiοn tabIe with 255 degrees οf freedοm).
The test statistic fοr this sampIe is:
t = (sampIe mean - hypοthesized mean) / (sampIe standard deviatiοn / √(sampIe size))
t = (274.3 - 275) / (25.9 / √(256))
t = -1.7
Since -1.7 > -2.33, we faiI tο reject the nuII hypοthesis. Therefοre, we cannοt cIaim with 99% cοnfidence that the mean weight οf the manufacturer's cοmputer parts is Iess than 275 grams
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Answer:Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
Step-by-step explanation:The mean weight from a sample of 256 computer parts created by a computer manufacturer was 274.3 grams, with a standard deviation of 25.9 grams. Can this company claim that the mean weight of its manufactured computer parts will be less than 275 grams? Test this hypothesis using a 1% level of significance.
Reject the null hypothesis. There is not enough evidence to oppose the company's claim.
Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
Reject the null hypothesis. There is enough evidence to oppose the company's claim.
Fail to reject the null hypothesis. There is enough evidence to oppose the company's claim.
The test statistic needs to fall within the rejection regions that are above and below the critical z-score associated with a 1% level of significance in order to reject the null hypothesis. Otherwise, we will fail to reject the null hypothesis.
1
Points
/ 1
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
C
Step-by-step explanation:
Step-by-step explanation:
Hi tag brainliest ❣️
Thanks
Since the shaded area equal 4
our answer is A
that is the number of shaded area ÷ the total number of points
-
A quarterback completes 44% of his passes. Show all work.
a. Construct a probability distribution table (out to n = 6) for the number of passes attempted before the quarterback has a completion?
b. What is the probability that the quarterback throws 3 incomplete passes before he has a completion?
c. How many passes can the quarterback expect to throw before he completes a pass?
d. Determine the probability that it takes more than 5 attempts before he completes a pass.
e. If he throws 8 passes on the opening drive, what is the probability that he made at least half of them?
a.The probability distribution table for the first six attempts is shown below:
X P(X=k)
1 0.44
2 0.56 ×0.44
3 0.56²×0.44
4 0.56³ × 0.44
5 0.56⁴ ×0.44
6 0.56⁵×0.44
b. the probability is 0.1399.
c. the quarterback can expect to throw about 2.27 passes before completing one.
d. the probability is 0.1865.
e. the probability is 0.7349.
what is probability?The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.
a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:
P(X=k) = \((1-p)^{k-1}\)×p
where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.
The probability distribution table for the first six attempts is shown below:
X P(X=k)
1 0.44
2 0.56 ×0.44
3 0.56²×0.44
4 0.56³ × 0.44
5 0.56⁴ ×0.44
6 0.56⁵×0.44
b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:
P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰
= 0.56²×0.44
= 0.1399
Therefore, the probability is 0.1399.
c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:
E(X) = 1/p
where p is the probability of completion on each attempt.
In this case, p = 0.44, so the expected number of passes is:
E(X) = 1/0.44
= 2.27
Therefore, the quarterback can expect to throw about 2.27 passes before completing one.
d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:
P(X > 5) = 1 - P(X <= 5)
= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]
= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]
= 0.1865
Therefore, the probability is 0.1865.
e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:
P(X ≥ 4) = 1 - P(X < 4)
where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.
Using the binomial probability distribution table or calculator, we can find:
P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]
= 0.7349
Therefore, the probability is 0.7349.
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Shaniqua brings home $250 per week working 25 hours. She is able to save $30 of her earnings each week.
Shaniqua wants to have $750 saved at the end of 15 weeks. She is allowed to work up to 30 hours per week if she
wants. She can save all the money earned working extra hours. How many hours (as a whole number) each week
must Shaniqua work to save $750 at the end of 15 weeks? Show your work.
Answer: She'd have to work 27 hours a Week because by her working 2 more hours shed be able to save up 50 a week.
Explanation: 750 divided by 15 (the weeks) is 50. Shed need to save 50 a week instead of 30 to reach her goal and the amount 50 divided by the number of hours she works (25) is 2. Add the 2 to 25 and you get 27 weeks.
Phillip is looking at two different jobs. One has a higher hourly pay rate while the other has more benefits. The first job pays $25 an hour while the second job pays $20 an hour. Benefit’s from the second job are equivalent to $100 per pay period. How many hours per pay period will Phillip have to work in the first job to make the same as the second job, including benefits?
Answer:
One has a higher hourly pay rate, while the other offers benefits. The first job pays $25 an hour, while the second job pays $20 an hour.
Step-by-step explanation:
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The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. A measuring device is calibrated to give V=253.5 in^3 when T=390 degrees and P= 20 lb/in^2. What is the volume on this device when the temperature is 400 degrees and the pressure is 10 lb/in^2?
(Scroll Down for Answer!)
the volume on this device when the temperature is 400 degrees and the pressure is 10 lb/in^2 is V = 253.5 * (400/390) * (20/10) = 263.0 in^3
V = 253.5 * (T/390) * (20/P)
V = 253.5 * (400/390) * (20/10)
V = 263.0 in^3
The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. Knowing this, we can calculate the volume for any given temperature and pressure by using the formula V = 253.5 * (T/390) * (20/P). In this problem, the device was calibrated to give V=253.5 in^3 when T=390 degrees and P= 20 lb/in^2. To find the volume on this device when the temperature is 400 degrees and the pressure is 10 lb/in^2, we plug these values into the formula, which gives us V = 253.5 * (400/390) * (20/10) = 263.0 in^3.
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Which answer choice best represents 3/15?
Select the Hint button to view a hint. You will get 14 points.
A: 5/6 5
B: 5/1 5
C: 6/1 5
D: 6/6 5
The equivalent fraction for the given fraction is 1/5.
What is an equivalent fraction?Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.
The given fraction is 3/15.
The equivalent fraction is 3/15 =1/5
Therefore, the equivalent fraction for the given fraction is 1/5.
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Question 9
Use algebra to show that 4.57 (5 and 7 recurring) equal 4 and 19/33
o show that 4.57 (5 and 7 recurring) is equal to 4 and 19/33, we can use algebraic equations. First, let x = 4.57 (5 and 7 recurring), then we multiply both sides by 100 to get 100x = 457.5757... Next, we subtract x from 100x to get 99x = 453. Thus, x = 453/99. We can simplify this fraction by dividing both the numerator and denominator by 3, giving us 151/33. Finally, we can write 151/33 as a mixed number, which is 4 and 19/33. Therefore, we have shown that 4.57 (5 and 7 recurring) is equal to 4 and 19/33 using algebraic equations.
The radius of a circle is 19 cm. Find the area
Answer: 1134.11
A=3.14*r^2
Step-by-step explanation:
Answer:
a ≈ 1134.11 cm2
Step-by-step explanation:
The formula:
\(a=\pi r^{2}\)
\(a=\pi (19)^{2} =361\pi\)
\(a=1134.11cm^{2}\)
Hope this helps
Just help me please anyone
Answer: Volume = 179.4 inches cubed
Step-by-step explanation:
Volume = 1/3 * height * length * width
V = (1/3) * 11.5 * 6 * 7.8
V = 179.4
help please, correct answers only
The solution to the quadratic equation 3x² + 5x + 4 = 0 is -5 ±√23/6
How to determine the solutionUsing the quadratic formula, we have the general equation;
ax + bx + c = 0
The general formula is given as;
= (-b±√(b²-4ac))/(2a)
Now, substitute the values, we get;
= -(5) ± √(-5)² - 4 × 3 × 4)/2(3)
find the square value and multiply
= -5± √25- 48/6
Then, we have;
= -5 ±√23/6
Hence, the solutions is -5 ±√23/6
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Atlanta's population is two million, eight hundred thirty-three thousand, five hundred
eleven. Write this number in standard form (using numbers).
??
Answer:
2,833,500
Step-by-step explanation:
3 step equations, I really need help on these with all the work:
1.
4x+y+5z=-9
x-4y-2z=-2
2x+3y-2z=21
2.
x-7y+3z=17
5x+2y-2z=-57
3x-10y-z=-11
Answer:
fdsfskdfdsjg,dgkdfjkgjkdfgjkfjkdghdkj
Step-by-step explanation:
You are given the first four terms of an arithmetic sequence. Under what
conditions might a recursive formula be preferred over the explicit formula?
Under what conditions might an explicit formula be preferred over the
recursive formula?
How many ways can we arrange five of the seven Harry Potter books on a shelf if Harry Potter and The Chamber of Secrets must be one of them?
There are 7 Harry potter books and 5 books needs to be arranged.
One of the five place is filled by book "Harry Potter and The Chamber of Secrets" and remaining 4 places must be filled by remaining 6 books.
So number of ways are,
\(\begin{gathered} 1\cdot^6P_4=1\cdot\frac{6!}{(6-4)!} \\ =1\cdot\frac{6\cdot5\cdot4\cdot3\cdot2\cdot1}{2\cdot1} \\ =1\cdot6\cdot5\cdot4\cdot3 \\ =360 \end{gathered}\)So there are 360 ways in which 5 of 7 Harry pooter book can be arranges such that " Harry Potter and The Chamber of Secrets" must included.
Dos horas y media ¿A cuántos minutos equivale?
Answer:
90 minutos
Step-by-step explanation:
una hora es 60 minutos y media es 30 minutos.
Please i need help right now Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)
Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work.
Part A:
This data appears to be modeling a geometric sequence because the time to complete each station is increasing by a constant factor. For example, the time to complete station 2 is 4 minutes, which is double the time it took to complete station 1. Similarly, the time to complete station 3 is 8 minutes, which is double the time it took to complete station 2, and so on.
Part B:
To find the time Aurora will take to complete station 5 using a recursive formula, we can use the formula:
a_n = a_1 * r^(n-1)
where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).
We are given that a_1 = 2 and a_2 = 4, so we can solve for r:
r = a_2 / a_1
= 4 / 2
= 2
Then we can use this value of r to find the time it takes to complete station 5:
a_5 = a_1 * r^(5-1)
= 2 * 2^4
= 2 * 16
= 32
Therefore, Aurora will take 32 minutes to complete station 5.
Part C:
To find the time Aurora will take to complete station 9 using an explicit formula, we can use the formula:
a_n = a_1 * r^(n-1)
where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).
We are given that a_1 = 2 and a_2 = 4, so we can solve for r:
r = a_2 / a_1
= 4 / 2
= 2
Then we can use this value of r to find the time it takes to complete station 9:
a_9 = a_1 * r^(9-1)
= 2 * 2^8
= 2 * 256
= 512
Therefore, Aurora will take 512 minutes to complete station 9.
say no more
Pls help with this problem. This is due today!
Answer:
2.8 > 2.8< i think
Step-by-step explanation: