Solution :
Given information :
A sample of n = 10 adults
The mean failure was 24 and the standard deviation was 3.2
a). The formula to calculate the 95% confidence interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]
Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]
= 2.145
Substitute the values
[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]
(26.17, 21.83)
When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]
b). The formula to calculate 95% prediction interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]
[tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]
(31.13, 16.87)
Can someone help me? I am struggling and I would be so happy if any of you helped me. Thank you for your help!
Answer:
Mean = 52
Standard Deviation = 13.64
Step-by-step explanation:
mean = 260/5
= 52
Standard Deviation = [tex]\sqrt{\frac{930}{5} }[/tex] = 13.64
I wasn't sure about my answer so used the Gauthmath app
Find the area of the sector round your answer to the nearest 10th
Answer:
63.4
Step-by-step explanation:
Area of sector=pi*r^2*(theta/360)
Area of sector=pi*121*(60/360)
Area of sector=63.4
Jaqueline used 2.5 pounds of ground beef to make 25 tacos for a family gathering. Peter wants to use the same recipe using 1 pound of ground beef.
How many tacos will Peter be able to make?
Answer:
Peter can make 10 tacos.
Step-by-step explanation:
Jaqueline's recipe calls for .1 pounds of beef per taco.
Given only 1 pound, multiply by, taking the reciprocal of .1 gives us 10 tacos.
How many edges are there?
A. not enough information
B. 15
C. 7
D. 10
The number of edges in the given figure is 15. The correct option is B.
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
The shape is made up of the triangular prism and the trapezoidal prism the total number of edges in the shape will be 15.
Therefore, the number of edges in the given figure is 15. The correct option is B.
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Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on their knowledge. The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the .05 level, evaluate the researcher's hypothesis that the instructional program affects students' knowledge. What is the correct cutoff score(s)
Answer:
The solution according to the problem given is provided below in the explanation segment.
Step-by-step explanation:
According to the question,
[tex]H_o: \mu_1=\mu_2[/tex]
[tex]H_a: \mu_1 \neq \mu_2[/tex]
Level of significance,
[tex]\alpha = .05[/tex]
The test statistics will be:
⇒ [tex]Z = \frac{(\bar x_1 - \bar x_2)}{\sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2} } }[/tex]
[tex]=\frac{(38-35)}{\sqrt{\frac{(3)^2}{30} +\frac{(5)^2}{30} } }[/tex]
[tex]=2.82[/tex]
The p-value will be:
= [tex]0.0024[/tex]
Find the slope of a line parallel to a line with a slope of m = 1/3
Answer:
1/3
Step-by-step explanation:
Parallel lines have the same slope. Thus, a line parallel to one with a slope of 1/3 is just 1/3.
Help? Please!?
ASAP if you can
Answer:
tan A = 1.375
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan A = CB/ AC
tan A = 11/8
tan A = 1.375
consider the differential equation x3y ''' + 8x2y '' + 9xy ' − 9y = 0; x, x−3, x−3 ln(x), (0, [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(x, x−3, x−3 ln(x)) = ≠ 0 for 0 < x < [infinity].
Verifying that a given expression is a solution to the equation is just a matter of plugging in the expression and its derivatives, and making sure that the given expressions are indeed linearly independent.
For example, if y = x, then y' = 1 and the other derivatives vanish. So the DE after substitution reduces to
9x - 9x = 0
which is true for all 0 < x < ∞.
To check for linear independence, you compute the Wronskian, which, judging by what you wrote, you've already done...
A factory makes twenty-three million, five hundred fifty candies each month. This number in standard form is
Answer:
23,000,550
Step-by-step explanation:
A million has six zeroes, so twenty three million is
23,000,000
Since five hundred fifty is not in the thousands, it replaces the last trio of zeroes.
We have the number in standard form as
23,000,550
Answer:
23000550
Step-by-step explanation:
An article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively. Suppose these are the population average lifetimes.
Required:
Let x̄ be the sample average lifetime of 64 Duracell and ȳ be the sample average lifetime of 64 Eveready Energizer batteries. What is the mean value of x̄- ȳ(i.e., where is the distribution of -centered)?
Answer:
The mean is of -0.4 hours.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem and subtraction of normal variables.
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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Mean of the sample of 64 Duracell:
By the Central Limit Theorem, 4.1 hours.
Mean of the sample of 64 Eveready:
By the Central Limit Theorem, 4.5 hours.
Mean of the difference?
Subtraction of normal variables, so we subtract the means.
4.1 - 4.5 = -0.4
The mean is of -0.4 hours.
the probability of a thunderstorm on memorial day 0.72 and the probability of a thunderstorm on independance day is 0.14. assuming that these two events are independent, what is the probability of thunderstorms on both memorial day and independence day
Answer:
0.1008 = 10.08% probability of thunderstorms on both memorial day and independence day.
Step-by-step explanation:
Probability of independent events:
If two events are independent, the probability of both happening is the multiplication of the probabilities of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this question:
Event A: Thunderstorm on memorial day.
Event B: Thunderstorm on memorial day
The probability of a thunderstorm on memorial day 0.72
This means that [tex]P(A) = 0.72[/tex]
The probability of a thunderstorm on independance day is 0.14.
This means that [tex]P(B) = 0.14[/tex]
What is the probability of thunderstorms on both memorial day and independence day?
[tex]P(A \cap B) = P(A)P(B) = 0.72*0.14 = 0.1008[/tex]
0.1008 = 10.08% probability of thunderstorms on both memorial day and independence day.
Probabilities are used to determine the chances of events
The probability of thunderstorm on both days is 0.1008
Represent the event that there is thunderstorm on Memorial Day with A, and the event that there is thunderstorm on Independence Day with B
So, we have:
P(A) = 0.72
P(B) = 0.14
The probability of thunderstorm on both days is then calculated as;
P(Both) = P(A) * P(B) - P(A or B)
Given that the events are independent, the equation becomes
P(Both) = P(A) * P(B)
So, we have:
P(Both) = 0.72 * 0.14
Multiply
P(Both) = 0.1008
Hence, the probability of thunderstorm on both days is 0.1008
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In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student who has a cat also has a dog?
Has a cat Does not have a cat
Has a dog 7 6
Does not have a dog 8 2
Seven and one-half foot-pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional 3 inch.
Answer:
Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:
W = int_a^b kx dx
W = k * int_a^b x dx
Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)
W = k * x^(1+1)/(1+1)|_a^b
W = k * x^2/2|_a^b
From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches. To be consistent, apply the conversion factor: 12 inches = 1 foot then:
2 inches = 1/6 ft
1/2 or 0.5 inches =1/24 ft
To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring 2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.
Applying W = k * x^2/2|_a^b , we get:
7.5= k * x^2/2|_0^(1/6)
Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .
7.5 =k [(1/6)^2/2-(0)^2/2]
7.5 = k * [(1/36)/2 -0]
7.5= k *[1/72]
k =7.5*72
k =540
To solve for the work needed to compress the spring with additional 1/24 ft, we plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .
Note that compressing "additional one-half inches" from its 2 inches compression is the same as to compress a spring 2.5 inches or 5/24 ft from its natural length.
W= 540 * x^2/2|_((1/6))^((5/24))
W = 540 [ (5/24)^2/2-(1/6)^2/2 ]
W =540 [25/1152- 1/72 ]
W =540[1/128]
W=135/32 or 4.21875 ft-lbs
Step-by-step explanation:
Plane P is a cross-section of the solid below. What shape is the cross section?
A. rectangle
B. not enough information
C. hexagon
D. pentagon
Answer:
C. Hexagon
Step-by-step explanation:
The answer is clearly C. Hexagon. This is because the question is referring to the shape shown on Plane P as if it were 2D. Therefore, the shape with 6 sides is a hexagon and cannot be anything else.
The shape is the cross-section is a hexagon.
What is a hexagon?In geometry, a hexagon may be described as a closed two-dimensional polygon with six aspects. The hexagon has 6 vertices and 6 angles also. Hexa means six and gonia approach angles.
All hexagons have six facets, regardless of the sort of hexagon it is. which means that normal hexagons, irregular hexagons, concave hexagons, and convex hexagons all have six facets.
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ko dung may tinh hay so sanh
3√7 vs 7√3
Answer:
what this makes bi sense haha
Step-by-step explanation:
but ok
commission received
Answer:
Commission Received refers to a percentage amount received by the company (or) an individual on the total sales incurred. It is an indirect income/revenue recorded on the credit side of profit and loss account.
Step-by-step explanation:
mark me brainliest if my answer is correct
2/5 + 1/10= In simplest form
A. 3/15
B. 5/10
C. 1/4
D. 1/2
Answer:
1/2
Step-by-step explanation:
2/5 + 1/10
Get a common denominator of 10
2/5 * 2/2 + 1/10
4/10 + 1/10
5/10
simplify
Divide the top and bottom by 5
1/2
Answer:
[tex] \frac{1}{2} [/tex]
Answer D is correctStep-by-step explanation:
[tex] \frac{2}{5} + \frac{1}{10} \\ \frac{2 \times 2}{5 \times 2} + \frac{1}{10} \\ \frac{4}{10} + \frac{1}{10} \\ \frac{5}{10} \\ \frac{5 \div 5}{10 \div 5} \\ = \frac{1}{2} [/tex]
If the slope of a wheelchair ramp is 1/11 then what is the angle of inclination to the nearest tenth of a degree?
Answer
4.8 degrees to the nearest tenth.
Step-by-step explanation:
The slope = rise / run = opposite side / adjacent side.
So the angle of inclination is the angle whose tangent is 1/12.
To the nearest tenth of a degree it is 4.8 degrees.
Differentiate the following Functions
5x^2-2xy + 4y^3= 5
Answer:
[tex]\displaystyle y' = \frac{y - 5x}{x + 6y^2}[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringCalculus
Differentiation
DerivativesDerivative NotationImplicit DifferentiationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 5x^2 - 2xy + 4y^3 = 5[/tex]
Step 2: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[5x^2 - 2xy + 4y^3] = \frac{dy}{dx}[5][/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{dy}{dx}[5x^2] - \frac{dy}{dx}[2xy] + \frac{dy}{dx}[4y^3] = \frac{dy}{dx}[5][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle 5\frac{dy}{dx}[x^2] - 2\frac{dy}{dx}[xy] + 4\frac{dy}{dx}[y^3] = \frac{dy}{dx}[5][/tex]Basic Power Rule [Chain Rule]: [tex]\displaystyle 10x - 2\frac{dy}{dx}[xy] + 12y^2y' = 0[/tex]Product Rule: [tex]\displaystyle 10x - 2\bigg[ \frac{dy}{dx}[x]y + x\frac{dy}{dx}[y] \bigg] + 12y^2y' = 0[/tex]Basic Power Rule [Chain Rule]: [tex]\displaystyle 10x - 2\bigg[ y + xy' \bigg] + 12y^2y' = 0[/tex]Simplify: [tex]\displaystyle 10x - 2y + 2xy' + 12y^2y' = 0[/tex]Isolate y' terms: [tex]\displaystyle 2xy' + 12y^2y' = 2y - 10x[/tex]Factor: [tex]\displaystyle y'(2x + 12y^2) = 2y - 10x[/tex]Isolate y': [tex]\displaystyle y' = \frac{2y - 10x}{2x + 12y^2}[/tex]Factor: [tex]\displaystyle y' = \frac{2(y - 5x)}{2(x + 6y^2)}[/tex]Simplify: [tex]\displaystyle y' = \frac{y - 5x}{x + 6y^2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Find the measure of angle x in the figure below:
A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 57 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 61 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 67 degrees. The interior angle on the left is labeled as x.
35°
47°
51°
62°
Your answer iss...
It is 51º
Becca tried to evaluate the expression
45−(8×3+15
Answer:
Step-by-step explanation:
45 - (8 x 3 + 15)
45 - (24 + 15) ---> do parentheses first
45 - ( 39 )
45 - 39
6
The value of the expression Becca should get after simplification is 6.
Given is an expression 45 - (8 × 3 + 15), Becca is trying to solve the same,
To evaluate the expression 45 - (8 × 3 + 15), Becca should follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):
First, calculate the value inside the parentheses: 8 × 3 + 15
= 24 + 15
= 39.
Now, substitute this value back into the original expression: 45 - 39.
Finally, perform the subtraction: 45 - 39 = 6.
So, the value of the expression is 6.
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According to an independent research, a point estimate of the proportion of U.S. consumers of black tea is p = 0.76. Calculate the sample size needed to be 95% confident that the error in estimating the true value of p is less than 0.015? Use the z-value rounded to two decimal places to obtain the answer. 4072.69
Answer:
The sample size needed is 3115.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Point estimate:
[tex]\pi = 0.76[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Calculate the sample size needed to be 95% confident that the error in estimating the true value of p is less than 0.015?
This is n for which M = 0.015. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.015 = 1.96\sqrt{\frac{0.76*0.24}{n}}[/tex]
[tex]0.015\sqrt{n} = 1.96\sqrt{0.76*0.24}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.76*0.24}}{0.015}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.76*0.24}}{0.015})^2[/tex]
[tex]n = 3114.26[/tex]
Rounding up:
The sample size needed is 3115.
For an avid bird watcher, the probability of spotting a California Condor while birdwatching in the Grand Canyon area is 0.3. The probability of being able to take a clear picture of the bird suppose one is able to spot it is 0.8. What is the probability that the bird watcher is able to take a clear picture of a California Condor
Answer:
the probability of taking a clear picture of a California candor is .24
Figure
А A
Figure B
How many squar
w many square are in
tigne
this
Answer:
7 square are 0resent on aaaaaa
What type of line is PQ?
A. altitude
B. angle bisector
C. side bisector
D. median
The line PQ of the triangle is an altitude. The correct option is A.
What is the altitude of the triangle?
A line segment passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.
The extended base of the altitude is the name given to this line that contains the opposing side. The foot of the altitude is the point at where, the extended base and the height converge.
In the given triangle the line segment PQ is passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.
Therefore, the line PQ of the triangle is an altitude. The correct option is A.
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Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives less than 159 miles in a day. Round your answer to four decimal places.
Answer:
the probability that a truck drives less than 159 miles in a day = 0.9374
Step-by-step explanation:
Given;
mean of the truck's speed, (m) = 120 miles per day
standard deviation, d = 23 miles per day
If the mileage per day is normally distributed, we use the following conceptual method to determine the probability of less than 159 miles per day;
1 standard deviation above the mean = m + d, = 120 + 23 = 143
2 standard deviation above the mean = m + 2d, = 120 + 46 = 166
159 is below 2 standard deviation above the mean but greater than 1 standard deviation above the mean.
For normal districution, 1 standard deviation above the mean = 84 percentile
Also, 2 standard deviation above the mean = 98 percentile
143 --------> 84%
159 ---------> x
166 --------- 98%
[tex]\frac{159-143}{166-143} = \frac{x-84}{98-84} \\\\\frac{16}{23} = \frac{x-84}{14} \\\\23(x-84) = 224\\\\x-84 = 9.7391\\\\x = 93.7391\ \%[/tex]
Therefore, the probability that a truck drives less than 159 miles in a day = 0.9374
What is the sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4? The answer is 1, but how is it solved?
Answer: -1
Step-by-step explanation:
sum of 2 and 3 subtracted from the product of 2 difference of 7 and 4
(2+3) - 2 ( 7 - 4 ) = -1
(2+3)-2(7-4) =
5 - 2(3) =
5-6 = -1
The sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4 is equivalent to 1.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4
From the question, we can model the equation as -
x = 2 × (7 - 4) - (2 + 3)
x = 2(3) - 5
x = 6 - 5
x = 1
Therefore, the sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4 is equivalent to 1.
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Determine which type of error is most likely to arise from the following situations. a 1. the time in which individuals are contacted to take a survey occurs during work hours f 2. the last part of a newspaper article asks readers to mail or email the newspaper their opinion about universal health coverage 3. subjects are asked to recall how often they snacked between meals in the past 30 days 4. a survey to assess teachers' opinions about Common Core uses a member list for the largest teachers' union as the sampling frame a. question wording b. undercoverage c. processing error d. bad sampling method e. response error f. nonresponse g. random sampling error
Answer:
Determination of type of error arising from the situations
Situation Type of Error
1. Nonresponse
2. Bad sampling method
3. Question wording
4. Undercoverage
Step-by-step explanation:
Types of errors:
a. question wording means that the manner a question is worded elicits some particular responses, which may not accurately reflect reality.
b. undercoverage occurs when some elements of the target population is not represented on the survey frame.
c. processing error arises from data processing
d. bad sampling method is caused by the voluntariness of those who choose to respond.
e. response error is caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements.
f. nonresponse error arises as a result of incomplete information or partial response.
g. random sampling error arises from the limited sample size when compared with the population size.
A company pays $20 per hour for up to 8 hours of work, and $30 per hour for overtime hours (hours beyond 8 hours). For up to 8 hours worked, the equation for total pay (y) for hours worked (x) is y = 20x. For over 8 hours worked, what is the equation for total pay (y) as a function of total hours worked (x)?
Answer: y = 30x
Step-by-step explanation:
Because we are talking about over 8 hours. The question states that you get 30$ per hour for overtime hours. That means if you work over 8 hours your dollars per hour increases to 30. So because the amount of dollars increases to 30 you can infer that all you have to do is make the same equation as the 20 dollar's per hour equation. Except you put 30 making it y = 30x.
For the following function, one zero is given. Find all other zeros.
f(x)=x3-7x2+17x-15; 2-i
Answer:
1,-3,-5
Step-by-step explanation:
Given:
f(x)=x^3+7x^2+7x-15
Finding all the possible rational zeros of f(x)
p= ±1,±3,±5,±15 (factors of coefficient of last term)
q=±1(factors of coefficient of leading term)
p/q=±1,±3,±5,±15
Now finding the rational zeros using rational root theorem
f(p/q)
f(1)=1+7+7-15
=0
f(-1)= -1 +7-7-15
= -16
f(3)=27+7(9)+21-15
=96
f(-3)= (-3)^3+7(-3)^2+7(-3)-15
= 0
f(5)=5^3+7(5)^2+7(5)-15
=320
f(-5)=(-5)^3+7(-5)^2+7(-5)-15
=0
f(15)=(15)^3+7(15)^2+7(15)-15
=5040
f(-15)=(-15)^3+7(-15)^2+7(-15)-15
=-1920
Hence the rational roots are 1,-3,-5 !
