Because of high tuition costs at state and private universities, enrollments at community colleges have increased dramatically in recent years. The following data show the enrollment (in thousands) for Jefferson Community College for the nine most recent years.
Year Period (t) Enrollment (1,000s)
2001 1 6.5
2002 2 8.1
2003 3 8.4
2004 4 10.2
2005 5 12.5
2006 6 13.3
2007 7 13.7
2008 8 17.2
2009 9 18.1
Required:
a. What type of pattern exists in the data?
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
c. What is the forecast for year 10?
Answer:
a. A linear pattern exists in the data.
b. The parameters for the line that minimizes MSE for this time series are as folows:
ß1 = Estimated slope = 1.4567
ß0 = Estimated intercept = 4.7165
Also, we have:
MSE = Mean squared error = 0.4896
c. Forecast for year 10 is 19,280.
Step-by-step explanation:
a. What type of pattern exists in the data?
Note: See Sheet1 of the attached excel file for the line graph.
From the line graph, it can be observed that a linear pattern exists in the data.
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
Note: See Sheet2 of the attached excel file for all the calculations to obtain the following:
Sample size = 9
Total of X = 45
Total of Y = 108
Mean of X = Total of X / Sample size = 45 / 9 = 5
Mean of Y = Total of X / Sample size = 108 / 9 = 12
SSxx = Total of (X - Mean of X)^2 = 60
SSyy = Total of (Y - Mean of Y)^2 = 130.74
SSxy = Total of (X - Mean of X) * (Y - Mean of Y) = 87.40
Therefore, we have:
ß1 = Estimated slope = SSxy/SSxx = 87.4 / 60 = 1.4567
ß0 = Estimated intercept = Mean of Y – (ß1 * Mean of X) = 12 - (5 * 1.4567) = 4.7165
Therefore, the parameters for the line that minimizes MSE for this time series are as folows:
ß1 = Estimated slope = 1.4567
ß0 = Estimated intercept = 4.7165
Regression equation which also used in the attached excel is as follows:
Y = ß0 + ß1X =
Y = 4.7165 + 1.4567X …………………. (1)
SSE = Sum of squared error = Total of (Y - Y*)^2 = 3.4273
Therefore, we have:
MSE = Mean squared error = (SSE/(n-2)) = (3.4273 / (9 - 2)) = 0.4896
c. What is the forecast for year 10?
This implies that X = 10
Substitute X = 10 into equation (1), we have:
Y = 4.7165 + (1.4567 * 10) = 19.28
Since it is 1,000s, we have:
Y = 19.28 * 1,000 = 19,280
Therefore, forecast for year 10 is 19,280.
4ab-3a+3bx-2ab anyone know the answer to this problem?
Answer:
-3a+3bx+2ab
Step-by-step explanation:
Find the equation and check answer of (−8x=−2x−8)
Answer:
x = 4/3
Step-by-step explanation:
you need to move -8x to the right side.0=6x-8then, you need to move -8 to the left side.8=6xyou can get answer!x = 4/3
can someone tell me if why these triangles are similar
Answer:
Step-by-step explanation:
If the triangles given in the picture are similar,
ΔVUT ~ ΔVLM
By the property of similarity of two triangles, their corresponding sides will be proportional.
[tex]\frac{TV}{VM}= \frac{VL}{VU}[/tex]
[tex]\frac{49}{14}=\frac{28}{8}[/tex]
[tex]\frac{7}{2}=\frac{7}{2}[/tex]
True.
Therefore, ΔVUT and ΔVLM will be similar.
SOMEONE PLS HELP ME I WILL MAKE U BRAINLIST ! In a survey sample of 83 respondents, about 30.1 percent of the samplework less than 40 hours per week. What is the estimated standard error for the group of respondents who work 40 hours or more per week?
(*round to two decimal places)
Answer:
Answer = √(0.301 × 0.699 / 83) ≈ 0.050
A 68 percent confidence interval for the proportion of persons who work less than 40 hours per week is (0.251, 0.351), or equivalently (25.1%, 35.1%)
Step-by-step explanation:
√(0.301 × 0.699 / 83) ≈ 0.050
We have a large sample size of n = 83 respondents. Let p be the true proportion of persons who work less than 40 hours per week. A point estimate of p is because about 30.1 percent of the sample work less than 40 hours per week. We can estimate the standard deviation of as . A confidence interval is given by , then, a 68% confidence interval is , i.e., , i.e., (0.251, 0.351). is the value that satisfies that there is an area of 0.16 above this and under the standard normal curve.The standard error for a proportion is √(pq/n), where q=1−p.
Hope this answer helps you :)
Have a great day
Mark brainliest
Cathy is planning to take the Certified Public Accountant Examination (CPA exam). Records kept by the college of business from which she graduated indicate that 73% of students who graduated pass the CPA exam. Assume that the exam is changed each time it is given. Let n = 1, 2, 3, ... represent the number of times a person takes the CPA test until the first pass. (Assume the trials are independent).
(a) What is the probability that Cathy passes the CPA test on the first try?
(b) What is the probability that Cathy passes the CPA test on the second or third try?
Answer:
The responses to these question can be defined as follows:
Step-by-step explanation:
For point a:
[tex]\to P(1) = 0.73[/tex]
For point b:
[tex]\to P(2\ or\ 3) = P(2) + P(3)[/tex]
[tex]= 0.27 \times 0.73 + 0.27\times 0.27\times0.73\\\\=0.1971+0.1971\times 0.27\\\\=0.1971+0.053217\\\\=0.250317[/tex]
If 5x = 3x+12 then x = …..
↦ [tex]\huge\underline{ \underline{Answer:-}}[/tex]
[tex]5x = 3x + 12 \\ 5x - 3x = 12 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Step-by-step explanation:
Explanation is in the attachmenthope it is h helpful to you
determine the general solution of cos2X -7cosX -3=0
Answer:
x=2pi/3 +2pi n, 4pi/3 +2pi n for all integar of n.
Step-by-step explanation:
If the domain of a function that is reflected over the x-axis is (1, 5), (2, 1), (-1, -7), what is the range?
A. (1, -5), (2, -1), (-1, 7)
B. (5, 1), (1, 2), (-7, -1)
C. (-5, -1), (-1, -2), (7, 1)
D. (-1, 5), (-2, 1), (1, -7)
Answer:
A. (1, -5), (2, -1), (-1, 7)
Step-by-step explanation:
Reflecting a function over the x-axis:
When a function is reflected over the x-axis, the x-value stays the same, while y changes the signal, so the transformation rule is:
[tex](x,y) \rightarrow (x,-y)[/tex]
To find the range:
We apply the transformation to the points in the domain. Thus:
[tex](1,5) \rightarrow (1,-5)[/tex]
[tex](2,1) \rightarrow (2,-1)[/tex]
[tex](-1,-7) \rightarrow (-1,-(-7)) = (-1, 7)[/tex]
Thus the correct answer is given by option a.
Answer:
It is letter A and please give me brainliest
Step-by-step explanation:
2.According to www.city-data, the mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000. Check the three assumptions associated with the Central Limit Theorem. What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009
Answer:
0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000.
This means that [tex]\mu = 192723, \sigma = 42000[/tex]
Sample of 75:
This means that [tex]n = 75, s = \frac{42000}{\sqrt{75}}[/tex]
What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009?
1 subtracted by the p-value of Z when X = 190000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{190000 - 192723}{\frac{42000}{\sqrt{75}}}[/tex]
[tex]Z = -0.56[/tex]
[tex]Z = -0.56[/tex] has a p-value of 0.2877
1 - 0.2877 = 0.7123
0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.
Young invested GH150,000 and 2.5% per annum simple interest. how long will it take this amount to. yield an interest of GH11,250,00
Answer: 3 years
Step-by-step explanation:
Interest is calculated as:
= (P × R × T) / 100
where
P = principal = 150,000
R = rate = 2.5%.
I = interest = 11250
T = time = unknown.
I = (P × R × T) / 100
11250 = (150000 × 2.5 × T)/100
Cross multiply
1125000 = 375000T
T = 1125000/375000
T = 3
The time taken will be 3 years
A student takes an exam containing 16 true or false questions. If the student guesses, what is the probability that he will get exactly 14 questions right
Answer:
0.001831055
Step-by-step explanation:
Here, n = 16, p = 0.5, (1 - p) = 0.5 and x = 14
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)
We need to calculate P(X = 14)
P(x =14) = 16C14 * 0.5^14 *(1-0.5)^2
= 120 * 0.5^14 *(1-0.5)^2
= 0.001831055
Identify the quantities that are equivalent to 250 meters.
Ratio Conversion Table
kilometer (km) : meter (m) 1 : 1,000
meter (m) : centimeter (cm) 1 : 100
centimeter (cm) : millimeter (mm) 1 : 10
Answer:
1. Convert all measurements to meters:
2.5km * 1,000 = 2,500m;.250km * 1,000 = 250m; 2,500cm / 100 = 25m
25,000cm / 100 = 250m; 250mm / 1,000 =.25m
2.) Compare the converted measurements. Therefore, the quantities that are equivalent to 250m are:
.250km; 25,000cm
Step-by-step explanation:
A sample of 100 is drawn from a population with a proportion equal to 0.50. Determine the probability of observing between 43 and 64 successes.
Answer:
The probability of observing between 43 and 64 successes=0.93132
Step-by-step explanation:
We are given that
n=100
p=0.50
We have to find the probability of observing between 43 and 64 successes.
Let X be the random variable which represent the success of population.
It follows binomial distribution .
Therefore,
Mean,[tex]\mu=np=100\times 0.50=50[/tex]
Standard deviation , [tex]\sigma=\sqrt{np(1-p)}[/tex]
[tex]\sigma=\sqrt{100\times 0.50(1-0.50)][/tex]
[tex]\sigma=5[/tex]
Now,
[tex]P(43\leq x\leq 64)=P(42.5\leq x\leq 64.5)[/tex]
[tex]P(42.5\leq x\leq 64.5)=P(\frac{42.5-50}{5}\leq Z\leq \frac{64.5-50}{5})[/tex]
[tex]=P(-1.5\leq Z\leq 2.9)[/tex]
[tex]P(42.5\leq x\leq 64.5)=P(Z\leq 2.9)-P(Z\leq- 1.5)[/tex]
[tex]P(42.5\leq x\leq 64.5)=0.99813-0.06681[/tex]
[tex]P(43\leq x\leq 64)=0.93132[/tex]
Hence, the probability of observing between 43 and 64 successes=0.93132
Can you help me figure out this question I’ve been stuck on this for 20 minutes
Step-by-step explanation:
[tex]\dfrac{2x^2+x-6}{x+x-6} = \dfrac{(2x-3)(x+2)}{2(x-3)}[/tex]
Solve the inequality. |X-15|>9
Answer:
X<6 or X>24
Step-by-step explanation:
A(n) _____ is an expression that uses variables to state a rule.
plz help asap
Answer:
A FORMULA is an expression that uses variables to state a rule.
A 17 feet ladder is placed against a building. The bottom of the ladder is 15 feet away from the building. How many feet high is the top of the ladder?
7 feet
12 feet
8 feet
15 feet
Answer:
[tex]8 \ feet[/tex]
Step-by-step explanation:
In this situation, one is given the following information. A ladder is leaning against a wall and has a measure of (17) feet. The bottom of the ladder is (15) feet away from the wall. One can infer that the wall forms a right angle with the ground. Thus, the triangle formed between the ground, ladder, and wall is a right triangle. Therefore, one can use the Pythagorean theorem. The Pythagorean theorem states the following,
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the right angle of the right triangle. The parameter (c) represents the hypotenuse or the side opposite the right angle. In this case, the legs are the ground and wall, and the hypotenuse is the ladder. Substitute this into the formula a solve for the height of the wall.
[tex]a^2+b^2=c^2[/tex]
Substitute,
[tex](ground)^2+(wall)^2=(ladder)^2\\\\(15)^2+(wall)^2=(17)^2\\[/tex]
Simplify,
[tex](15)^2+(wall)^2=(17)^2\\\\225+(wall)^2=289[/tex]
Inverse operations,
[tex]225+(wall)^2=289\\\\(wall)^2=64\\\\wall=8[/tex]
In a box of chocolates, 12 of the chocolates are wrapped in red foil. That is 30% of the chocolates in the box. How many chocolates are there?
Answer:
The answer is 40 chocolates in the box in total
find the equation of the line shown
Answer:
y=1/2x+1/2
Step-by-step explanation:
In order to find the slope, you can use rise/run, in this case, the slope is 1/2 and the y-intercept is at (0, 0.5)
Please help!! How do I solve for x?
The line in the middle is half the length of the line on the outside. Multiply the middle line by 2 and set it equal to the outside line.
2(x-3) = x + 6
Simplify:
2x -6 p x + 6
Add 6 to both sides
2x = x + 12
Subtract x from both sides:
X = 12
The answer is B) 12
Ben starts walking along a path at 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 7 mi/h. How long (in hours) will it be before Amanda catches up to Ben?
Enter the exact answer.
Hint: The distance formula is that distance = rate * time, so for example in one and a half hours, Ben has walked 3 * 1.5 miles.
Amanda catches up to Ben in ____________ hours.
Answer:
1.125 hours
Step-by-step explanation:
Given :
Ben's speed = 3 mi/hr
Time before Amanda starts = 1.5 hours
Amanda's speed = 7 mi/hr
Time before Amanda catches up with Ben
Recall :
Distance = speed * time
Distance already covered by Ben before Amanda starts :
(3 * 1.5) = 4.5
Hence, we can setup the equation :
Ben's distance = Amanda's distance
Let time taken = x
4.5 + 3x = 7x
4.5 = 7x - 3x
4.5 = 4x
x = 4.5 / 4
x = 1.125 hours
1.125 * 60 = 67. 5 minutes
Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.
(a) f (x, y) = x^2 - y^2; x^2 + y^2 = 1
Max of 1 at (plusminus 1, 0), min of - 1 at (0, plusminus l)
(b) f (x, y) = 3x + y; x^2 + y^2 = 10
Max of 10 at (3, 1), min of - 10 at (- 3, - 1)
(c) f (x, y) = xy; 4x^2 + y^2 = 8
Max of 2 at plusminus (1, 2), min of - 2 at plusminus (l, - 2)
Answer:
a) f(x,y) = - 1 minimum at P ( 0 ; -1 )
b) f (x,y) = 10 maximum at P ( 3 , 1 ) and f (x,y) = - 10 minimum at Q ( - 3 , - 1 )
c) Max f ( x , y ) = 2 for points P ( 1, 2 ) and T ( -1 , -2 )
Min f ( x , y ) = -2 for points Q ( 1 , - 2 ) and R ( -1 , 2 )
Step-by-step explanation:
A) f(x,y) = x² - y² subject to x² + y² = 1 g(x,y) = x² + y²- 1
δf(x,y)/ δx = 2*x δg(x,y)/ δx = 2*x
δf(x,y)/ δy = - 2*y δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ* δg(x,y)/ δx
2*x = λ*2*x
δf(x,y)/ δy = λ* δg(x,y)/ δy
- 2*y = λ*2*y
Then, solving
2*x = λ*2*x x = λ*x λ = 1
- 2*y = λ*2*y y = - 1
x² + y²- 1 = 0 x² + ( -1)² - 1 = 0 x = 0
Point P ( 0 ; -1 ) ; then at that point
f(x,y) = x² - y² f(x,y) = 0 - ( -1)² f(x,y) = - 1 minimum
b) f( x, y ) = 3*x + y g ( x , y ) = x² + y² = 10
δf(x,y)/ δx = 3 δg(x,y)/ δx = 2*x
δf(x,y)/ δy = 1 δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ * δg(x,y)/ δx ⇒ 3 = 2* λ *x (1)
δf(x,y)/ δy = λ * δg(x,y)/ δy ⇒ 1 = 2*λ * y (2)
x² + y² - 10 = 0 (3)
Solving that system
From ec (1) λ = 3/2*x From ec (2) λ = 1/2*y
Then (3/2*x ) = 1/2*y 3*y = x
x² + y² = 10 ⇒ 9y² + y² = 10 10*y² = 10
y² = 1 y ± 1 and
y = 1 x = 3 P ( 3 , 1 ) y = - 1 x = -3 Q ( - 3 , - 1 )
Value of f( x , y ) at P f (x,y) = 3*x + y f (x,y) = 3*(3) +1
f (x,y) = 10 maximum at P ( 3 , 1 )
Value of f( x , y ) at Q f (x,y) = 3*x + y f (x,y) = 3*(- 3) + ( - 1 )
f (x,y) = - 10 minimum at Q ( - 3 , - 1 )
c) f( x, y ) = xy g ( x , y ) = 4*x² + y² - 8
δf(x,y)/ δx = y δg(x,y)/ δx = 8*x
δf(x,y)/ δy = x δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ * δg(x,y)/ δx ⇒ y = λ *8*x (1)
δf(x,y)/ δy = λ * δg(x,y)/ δy ⇒ x = λ *2*y (2)
4*x² + y² - 8 = 0 (3)
Solving the system
From ec (1) λ = y/8*x and From ec (2) λ = x/2*y Then y/8*x = x/2*y
2*y² = 8*x² y² = 4*x²
Plugging that value in ec (3)
4*x² + 4*x² - 8 = 0
8*x² = 8 x² = 1 x ± 1 And y² = 4*x²
Then:
for x = 1 y² = 4 y = ± 2
for x = -1 y² = 4 y = ± 2
Then we get P ( 1 ; 2 ) Q ( 1 ; - 2)
R ( - 1 ; 2 ) T ( -1 ; -2)
Plugging that values in f( x , y ) = xy
P ( 1 ; 2 ) f( x , y ) = 2 R ( - 1 ; 2 ) f( x , y ) = - 2
Q ( 1 ; - 2) f( x , y ) = -2 T ( -1 ; -2 ) f( x , y ) = 2
Max f ( x , y ) = 2 for points P and T
Min f ( x , y ) = -2 for points Q and R
F(x)=-x^2-4 for x= -3
Answer:
5Step-by-step explanation:
Given:
f(x)=-x²-4Substitute x= -3:
f(-3) = (-3)² - 4 = 9 - 4 = 5please try this for answer my question please
Answer:
1. +30
2. +64
3. 0
4. -3
5. +24
6. +18
7. -48
8. -64
9. +21
10. -30
11. +12
12. 0
13. -4
14. +56
15. +2
Step-by-step explanation:
When multiplying integers:
two negatives = positive
two positives = positive
one negative x one positive = negative
So, if the signs are the same, the answer is positive.
If you have two different signs, the answer is negative.
You multiply the integers like normal.
Anything multiplied by zero = 0.
Anything multiplied by one = itself (just be careful of the sign).
what is the difference between the products of the digits in 425 and the sum of the digits in the numeral 92784
Answer: 10
Step-by-step explanation:
4 x 2 x 5 = 40
9 + 2 + 7 + 8 + 4 = 30
40 - 30 = 10
= 10
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 12 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 11.5.
Answer:
we conclude that population mean is not 11.5
Step-by-step explanation:
The hypothesis :
H0 : μ = 11.5
H1 : μ ≠ 11.5
The test statistic :
(xbar - μ) ÷ (s/√(n))
Test statistic = (12 - 11.5) ÷ (2/√(16))
Test statistic = (0.5) ÷ (2 ÷ 4)
Test statistic = 0.5 / 0.5
Test statistic = 1
The Pvalue from test statistic value, df = n - 1 = 16 - 1 = 15
Pvalue = 0.333
Pvalue > α ; we fail to reject the null ; Hence, we conclude that population mean is not 11.5
PLEASE HELLPP!!! Choose the best graph that represents the linear equation:
-x = 2y + 1
Graph A
On a coordinate plane, a line goes through (negative 1, 0) and (1, negative 1).
Graph B
On a coordinate plane, a line goes through (negative 3, negative 1) and (1, 1).
Graph C
On a coordinate plane, a line goes through (1, 0) and (5, negative 2).
Graph D
On a coordinate plane, a line goes through (negative 3, negative 2) and (1, 0).
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D
Please select the best answer from the choices provided
A
B
C
D
Answer:
C
Step-by-step explanation: just C-
Answer: Its not c
Step-by-step explanation: It is A
In May 2010, the Pew Research Center for the People & the Press carried out a national survey to gauge opinion on the Arizona Immigration Law. Responses (Favor, Oppose, Don’t Know) were examined according to groups defined by political party affiliation (Democrat, Republican, Independent). Which of the following would be appropriate for displaying these data?
a. Pie charts
b. Segmented bar chart.
c. Side by side bar chart.
d. Contigency table
Explanation:
It's most effective to use a contingency table because we have two variables here: 1) the responses, and 2) the party affiliation.
We can have the responses along the rows and the party affiliation along the columns, or vice versa.
See the example below. The values are completely random simply for the purpose of the example (and not drawn from any real life data source).
As per the given options, the appropriate for the displaying these data will be contingency table. Hence, option D is correct.
What is a Pie chart?A pie chart is a visual depiction of information in the shape of a pie, where the pieces of the pie represent the magnitude of the data. To depict data as a pie chart, you need a list of quantitative variables as well as categorical variables.
As per the given information in the question,
A contingency table in statistics is a particular kind of matrix-style table that shows the frequency of the variables. They are extensively utilized in scientific, engineering, business intelligence, and survey research.
To know more about Pie charts:
https://brainly.com/question/24207368
#SPJ5
Question 5 Multiple Choice Worth 1 points)
(01.03 MC)
Bunny Hill Ski Resort charges $35 for ski rental and $10 an hour to ski. Black Diamond Ski Resort charges $40 for ski rental and $5 an hour to ski. Create an equation to determine at what point
the cost of both ski slopes is the same.
Answer:
Bunny Hill Ski Resort:
y = 10x + 35
Diamond Ski Resort:
y = 5x + 40
Point where the cost is the same:
(1, 45)
Step-by-step explanation:
The question tells us that:
$35 and $40 are initial fees
$10 and $5 are hourly fees
This means that x and y will equal:
x = number of hours
y = total cost of ski rental after a number of hours
So we can form these 2 equations:
y = 10x + 35
y = 5x + 40
Now we are going to use System of Equations to find what point the cost of both ski slopes is the same.
Because they both equal y, we can set the equations equal to each other:
10x + 35 = 5x + 40
And we use basic algebra to solve for x:
10x + 35 = 5x + 40
(subtract 5x from both sides)
5x + 35 = 40
(subtract 35 from both sides)
5x = 5
(divide both sides by 5)
x = 1
Remember, x equals the number of hours.
That means when your rent out the skis for 1 hour, you will get the same price of $45 (you find the price by plugging in 1 into both of the equations)
Hope it helps (●'◡'●)
