Answer:
monomial
Step-by-step explanation:
1. What are foci? 2. What is the first step to take to write the equation of a hyperbola? 3. How do you represent parts of a hyperbola algebraically?
Answer: see below
Step-by-step explanation:
1) Foci is plural for Focus. Since a hyperbola has two focus points, they are referred to as foci. The foci is where the sum of the distances from any point on the curve to the foci is constant.
2) When determining the equation of a hyperbola you need the following:
a) does the hyperbola open up or to the right?
b) what is the center (h, k) of the hyperbola?
c) What is the slope of the asymptotes of the hyperbola?
3) The equation of a hyperbola is:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]
(h, k) is the center of the hyperbola± b/a is the slope of the line of the asymptotesThe equation starts with the "x" if it opens to the right and "y" if it opens upcan someone EXPLAIN this to me? you don't have to answer the questions. They are for my college class. Last assignment! thank you..
The population mean annual salary for environmental compliance specialists is about $63 comma 500. A random sample of 31 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $60 comma 500? Assume sigmaequals$6 comma 200.4
Answer:
0.0035289
Step-by-step explanation:
From the question;
mean annual salary = $63,500
n = sample size = 31
Standard deviation = $6,200
Firstly, we calculate the z-score of $60,500
Mathematically;
z-score = x-mean/SD/√n = (60500-63500)/6200/√(31) = -2.6941
So we want to find the probability that P(z < -2.6941)
We can get this from the standard normal table
P( z < -2.6941) = 0.0035289
A sample of bacteria is growing at an hourly rate of 10% compounded continuously. The sample began with 4 bacteria. How many bacteria will be in the sample after 18 hours?
Answer:
24
Step-by-step explanation:
The computation of the number of bacteria in the sample after 18 hours is shown below:
We assume the following things
P = 4 = beginning number of bacteria
rate = r = 0.1
Now
We applied the following formula
[tex]A = Pe^{rt}[/tex]
[tex]= 4\times e^{18\times0.1}[/tex]
[tex]=4e^{1.8}[/tex]
[tex]= 4\times6.049647464[/tex]
= 24
We simply applied the above formula to determine the number of bacteria after the 18 hours
magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. What values do , , n, E, and p represent? If the confidence level is %, what is the value of ?
Complete Question
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12 % chose chocolate pie, and the margin of error was given as plus or minus 5 percentage points.What values do [tex]\r p , \ \r q[/tex], n, E, and p represent? If the confidence level is 90%, what is the value of [tex]\alpha[/tex] ?
Answer:
a
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e [tex]\r q = 1- \r p[/tex]
b
[tex]\alpha = 10\%[/tex]
Step-by-step explanation:
Here
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e
[tex]\r q = 1- \r p[/tex]
[tex]\r q = 1- 0.12[/tex]
[tex]\r q = 0.88[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as
[tex]\alpha = ( 100 - C )\%[/tex]
Where [tex]C[/tex] is the confidence level which is given in this question as [tex]C = 90 \%[/tex]
So
[tex]\alpha = ( 100 - 90 )\%[/tex]
[tex]\alpha = 10\%[/tex]
Find the minimum sample size necessary to be 99% confident that the population mean is within 3 units of the sample mean given that the population standard deviation is 29. (a) What is the critical value that corresponds to the given level of confidence? Round your answer to two decimals, and remember that critical values are always positive.
Answer:
623
Step-by-step explanation:
Given that margin of error (E) = 3 unit, standard deviation (σ) = 29, sample size (n) = ?
a) The confidence (C) = 99% = 0.99
α = 1 - C = 1 - 0.99 = 0.01
α/2 = 0.01 / 2 = 0.005
From the normal distribution table, The z score of α/2 (0.005) is the critical value and it corresponds to the z score 0.495 (0.5 - 0.005) which is 2.58.
[tex]critical\ value = z_{\frac{\alpha}{2} }=z_{0.005}=2.58\\[/tex]
b) The margin of error (E) is given as:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\\\\sqrt{n}= z_{\frac{\alpha}{2} }*\frac{\sigma}{E }\\ \\n=( z_{\frac{\alpha}{2} }*\frac{\sigma}{E })^2\\\\Substituting:\\\\n=(2.58*\frac{29}{3} )^2=622.0036\\\\\\n=623(to\ the \ next\ whole\ number)[/tex]The minimum sample size (n) is 623
evaluate the following when x=3
[tex]y = - 3 \times 4^{x} [/tex]
evaluate the following when x=-2
[tex]f(x) = 6 \times ( \frac{1}{3} )^{x} [/tex]
evaluate the following when x=4
[tex]f(x) = \frac{1}{4}\times {2}^{x} [/tex]
(help me with this please)
Answer:
y=-192
Step-by-step explanation:
Rounded to the nearest tenth what is the perimeter of the triangle
Answer:
D. 11.8 cm.
Step-by-step explanation:
This is a 30-60-90 triangle, which means that the hypotenuse is 2x, the short leg is x, and the long leg is x[tex]\sqrt{3}[/tex].
In this case, the hypotenuse is 5.
5 / 2 = 2.5. That is the short leg.
The long leg is 2.5 * [tex]\sqrt{3}[/tex] = 4.330127019.
5 + 2.5 + 4.330127019 = 7.5 + 4.330127019 = 11.83012702, which is about D. 11.8 cm.
Hope this helps!
An equation is shown below: 4x + 2(x – 3) = 4x + 2x – 11 Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points) Part B: Name one property you used to solve this equation. (4 points)
Answer:
Part A: no solution
Part B: Distributive property of multiplication over addition.
Step-by-step explanation:
Part A:
4x + 2(x – 3) = 4x + 2x – 11
4x + 2x - 6 = 6x - 11
6x - 6 = 6x - 11
-6 = -11
Since -6 = -11 is a false statement, there is no solution.
Number of solutions: 0
Part B:
Property used: Distributive property of multiplication over addition.
Part A: Here are the steps I used to solve this equation-
4x + 2(x – 3) = 4x + 2x – 11
4x + 2x - 6 = 6x - 11
6x - 6 = 6x - 11
-6 = -11
Since -6 = -11 is a false statement, there is no solution.
The final number of solutions: 0
Part B: I used the distributive property of multiplication over addition.
Express the following as an expression: subtract y form 5 A 5y B 5-y C y-5 D y / 5
Answer:
5 - yStep-by-step explanation:
Given the statement "subtract y from 5", we are to express the statement mathematically. Expressing mathematically is as shown;
5 - y
Since we are removing the value of a variable y from 5, the variable we are subtracting will come last in the expression. For example say, we want to subtract 5 from 10, since we are taking out 5 from 10, the value of 5 will come last in the expression i.e 10 - 5 not 5 - 10.
According to the statement in question, we can see that we are to subtract y from 5, therefore y will come last in our expression and will be expressed as 5 - y
5-(m-4)= 2m+ 3 (m-1)
Answer: m= 2
Step-by-step explanation: First Expand the brackets! 5-m+4=2m+3m-3
Then Do the addition and subtraction in both sides!
9-m=5m-3
Then bring m to one side and the constants the other!
6m=12
Then solve for m where m=2
If you want you can check your answer bu substituting m as 2. 5-(2-4)=7 and 2(2) + 3(2-1) which also = 7.
The vertices of a triangle are given in the columns of the matrix T= [0,4,0,0,0,5] If [-1,0,0,-1] is found to preform a transformation, what are the coordinates of the transformed triangle?
Answer:
(0,0), (-4,0), (0,-5).
Step-by-step explanation:
Note: Matrices are not in proper format.
Consider the given matrix is
[tex]T=\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]
It means vertices are (0,0), (4,0) and (0,5).
Transformation matrix is
[tex]A=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}[/tex]
To find the coordinates of the transformed triangle multiply both matrices and calculate matrix AT.
[tex]AT=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]
[tex]AT=\begin{bmatrix}\left(-1\right)\cdot \:0+0\cdot \:0&\left(-1\right)\cdot \:4+0\cdot \:0&\left(-1\right)\cdot \:0+0\cdot \:5\\ 0\cdot \:0+\left(-1\right)\cdot \:0&0\cdot \:4+\left(-1\right)\cdot \:0&0\cdot \:0+\left(-1\right)\cdot \:5\end{bmatrix}[/tex]
[tex]AT=\begin{bmatrix}0&-4&0\\ 0&0&-5\end{bmatrix}[/tex]
It means coordinates of the transformed triangle are (0,0), (-4,0), (0,-5).
Answer:
A
Step-by-step explanation:
E2020
For what value of k are the roots of the quadratic equation kx (x-2)+6=0 equal?
Answer:
[tex]\boxed{\sf k=6}[/tex]
Step-by-step explanation:
[tex]\sf kx (x-2)+6=0[/tex]
Expand brackets.
[tex]\sf kx^2 -2kx+6=0[/tex]
This is in quadratic form.
[tex]\sf ax^2 +bx+c=0[/tex]
Since this is for equal roots:
[tex]\sf b^2 -4ac=0[/tex]
[tex]\sf a=k\\b=-2k\\c=6[/tex]
[tex]\sf (-2k)^2 -4(k)(6)=0[/tex]
[tex]\sf 4k^2-24k=0[/tex]
[tex]\sf 4k(k-6)=0[/tex]
[tex]\sf 4k=0\\k=0[/tex]
[tex]\sf k-6=0\\k=6[/tex]
Plug k as 0 to check.
[tex]\sf \sf 0x^2 -2(0)x+6=0\\6=0[/tex]
False.
So that means k must equal 6.
One positive number is 4 more than twice another. Their product is 198
Answer:
[tex]\large \boxed{\sf \ \ 9 \text{ and } 22 \ \ }[/tex]
Step-by-step explanation:
Hello,
We can write that, x being the second number
(4 + 2*x) *x = 198
Let's solve this equation.
[tex](4+2x)x=198\\\\4x+2x^2=198 \\\\\text{*** subtract 198 from both sides ***}\\\\2x^2+4x-198 = 0\\\\\text{*** The product of the zeroes is -198/2=-99=-11*9 and their sum is -4/2=-2 ***}\\\\2x^2+4x-198=2(x-9)(x+11)=0\\\\x=9 \ \ or \ \ x=-11[/tex]
We are looking for positive number so the solution is 9.
And the first number is 4 + 2 * 9 = 4 + 18 = 22
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
22 and 9
Step-by-step explanation:
Let the positive number be x.
Let the other number be y.
x = 2y + 4
xy = 198
Substitute x as 2y + 4 in the second equation.
(2y+4)y = 198
2y² + 4y = 198
2y² + 4y - 198 = 0
2(y-9)(y+11) = 0
y-9=0 or y+11=0
y=9
y=-11
The product is 198, so y is positive.
x(9)=198
x=22
You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 245 yards due west from your position and takes a bearing on the cabin of N 22.6°E. How far are you from the cabin? answer asap and ill give you a pat on the back
Answer:
101.98 yards.
Step-by-step explanation:
Please refer to the diagram that I drew (sorry for the messiness; I do not own a stylus and so I was using my mouse to try to draw it).
Since the triangle is a right triangle, you can use SOH CAH TOA. In this case, you are trying to figure out the opposite length, but you are given the adjacent. So, we will use tangent to solve this (TOA = Tangent, Opposite over Adjacent).
The angle is 22.6 degrees, and the tangent of the angle is equivalent to the opposite length, x, divided by the adjacent length, 245 yards.
tan(22.6) = x / 245
x / 245 = tan(22.6)
x = tan(22.6) * 245
x = 0.4162598242 * 245
x = 101.9836569
So, you are about 101.98 yards from the cabin.
Hope this helps!
The ratio of the legs of a trapezoid is 1:2, and the sum of the angles adjacent to the bigger base is 120°. Find the angle measures of the given trapezoid.
Answer:
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Step-by-step explanation:
A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.
Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:
[tex]2\cdot \alpha = 120^{\circ}[/tex]
[tex]\alpha = 60^{\circ}[/tex]
The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])
[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]
[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]
[tex]\beta = 180^{\circ}-\alpha[/tex]
[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]
[tex]\beta = 120^{\circ}[/tex]
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
What is the five-number summary for this data set?
12, 15, 17, 20, 22, 25, 27, 30, 33, 37
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max.
Answer: min = 12, Q1 =17, median =23.5 , Q3 = 30, max = 37 .
Step-by-step explanation:
The five-number summary for this data set consists of min, Q1,
median, Q3, max.
Given data: 12, 15, 17, 20, 22, 25, 27, 30, 33, 37, which is already arranged in a order.
Minimum value = 12
Maximum value = 37
since , number of observations = 10 (even)
So , Median = Mean of middle most terms
Middle most terms = 22, 25
Median =[tex]\dfrac{22+25}{2}=23.5[/tex]
First quartile ([tex]Q_1[/tex])= Median of first half ( 12, 15, 17, 20, 22)
= middle most term
= 17
Third quartile ([tex]Q_3[/tex]) = Median of second half (25, 27, 30, 33, 37)
= middle most term
= 30
Hence, five-number summary for this data set :
min = 12, Q1 =17, median =23.5 , Q3 = 30, max = 37 .
What is the measure of x?
Answer:
9 in.
Step-by-step explanation:
Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.
As such, the ratio of the sides would give the same results.
Hence,
4/6 = 10/(6 + x)
cross multiplying
4(6 + x) = 60
Dividing both sides by 4
6 + x = 15
collecting like terms
x = 15 - 6
= 9
We want to estimate the population mean within 5, with a 99% level of confidence. The population standard deviation is estimated to be 15. How large a sample is required? (Round up your answer to the next whole number.)
Answer: 60
Step-by-step explanation:
Formula to calculate sample size (n):
[tex]n=(\dfrac{\sigma\times z^*}{E})^2[/tex]
, where [tex]\sigma[/tex] = population standard deviation, E Margin of error , z* = critical value for the confidence interval.
As per given , we have
E =5
[tex]\sigma=15[/tex]
Critical value for 99% confidence = 2.576
Then,
[tex]n=(\dfrac{15\times2.576}{5})^2\\\\\Rightarrow\ n=59.721984\approx60[/tex]
So, Required sample size = 60 .
Write an equation of the line that passes through the point (5, -8) with slope 5
Answer:
y=5x-33
Step-by-step explanation:
We are given a point and a slope. Use the slope-intercept formula.
[tex]y-y_{1} =m(x-x_{1} )[/tex]
where (x1, y1) is a point on the line and m is the slope.
The slope is 5 and the point is (5,-8).
x1=5
y1= -8
m=5
[tex]y--8 =5(x-5 )[/tex]
We want to find the equation of the line, which is y=mx+b (m is the slope and b is the y-intercept). Therefore, we must get y by itself on one side of the equation.
[tex]y+8=5(x-5)[/tex]
First, distribute the 5 on the right side of the equation. Multiply each term inside the parentheses by 5.
[tex]y+8=(5*x)+(5*-5)[/tex]
[tex]y+8=5x-25[/tex]
Next, subtract 8 from both sides since it is being added on to y.
[tex]y+8-8=5x-25-8[/tex]
[tex]y=5x-25-8[/tex]
[tex]y=5x-33[/tex]
The equation of the line is: y=5x-33
If possible, find A − B.
Answer:
-2 7
-1 -6
Step-by-step explanation:
I used a calculator.
A bus company has contracted with a local high school to carry 450 students on a field trip. The company has 18 large buses which can carry up to 30 students and 19 small buses which can carry up to 15 students. There are only 20 drivers available on the day of the field trip.
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.
Answer:
The answer is below
Step-by-step explanation:
Let x represent the big buses and y represent small buses. The large buses can carry 30 students and the small buses can carry 15 students. The total number of students are 450, this can be represented by the inequality:
30x + 15y ≤ 450
They are only 20 drivers, therefore only 20 buses can be used. It is represented by:
x + y ≤ 20
They are only 19 small buses and 18 large buses:
x ≤ 18
y ≤ 19
After plotting the graph, the minimum solution to the graph are at:
A (15,0), B(18,0), C(10, 10), D(18, 2).
The cost function is given as:
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.
F(x, y) = 225x + 100y
At point A:
F(x, y) = 225(15) + 100(0) = $3375
At point B:
F(x, y) = 225(18) + 100(0) = $4050
At point C:
F(x, y) = 225(10) + 100(10) = $3250
At point D:
F(x, y) = 225(18) + 100(2) = $4250
The minimum cost is at point C(10, 10) which is $3250
Fake Question: Should Ujalakhan01 be a moderator? (If you could answer I'd appreciate it haha.)
Real Question: Simplify [tex](a^5*a^4)+(b^2*b^3)-(c^7*c^6)[/tex]
Answer:
[tex]a^9 + b^ 5 + c^{13}[/tex]
Step-by-step explanation:
[tex](a^5 \times a^4)+(b^2 \times b^3) + (c^7 \times c^6)[/tex]
When bases are same and it is multiplication, then add the exponents.
[tex](a^{5+4})+(b^{2+3})+(c^{7+6})[/tex]
[tex](a^9)+(b^ 5) + (c^{13})[/tex]
Apply rule : [tex](a^b)=a^b[/tex]
[tex]a^9 + b^ 5 + c^{13}[/tex]
Answer:
[tex]a^9+b^5-c^{13[/tex]
Step-by-step explanation:
[tex](a^5*a^4) + (b^2*b^3)-(c^7*c^6)[/tex]
When bases are same, powers are to be added.
=> [tex](a^{5+4})+(b^{2+3})-(c^{7+6})[/tex]
=> [tex]a^9+b^5-c^{13[/tex]
Pls help!! Thank you sooooo much if you help me on this, pls show proof
Answer:
√468 = 6√13
Step-by-step explanation:
ABCDEF is a regular hexagon of side length 6.
A'B'C'D'E'F' is the reflection of ABCDEF across BC.
The line FE' is the line from F to E'. It is also the hypotenuse of the right triangle FEE'. FE = 6, and EE' = 4a, where a is the apothem of the hexagon.
To find the apothem, draw the 30-60-90 triangle formed by the apothem and the radius (essentially 1/12th of the hexagon).
Using properties of a 30-60-90 triangle:
a = (6/2)√3
a = 3√3
4a = 12√3
Using Pythagorean theorem:
x² = (6)² + (12√3)²
x² = 36 + 432
x = √468
x = 6√13
Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1
Answer:
5
Step-by-step explanation:
The limit of f(x) at x=-1 is 5 when approached from the left or right. Since those limits are the same, the limit exists and is ...
[tex]\boxed{\lim\limits_{x\to-1}f(x)=5}[/tex]
What is the measure of XYZ, given that yz and xy are tangent to ?
A.
212
B.
127
C.
106
D.
53
Answer:
D) 53 Degrees.
Step-by-step explanation:
Things we need to establish beforehand: We know that Lines OZ and OX are equal because they are both radii of the circle. We can make an Iscoceles traingle by drawing a line between ZX. We know angle YZO and angle YXO is a right angle because YZ and XY are tangent to the circle. The Arc angle is the same angle as angle ZOX.
1) Find angles OZX and OXZ. these will be 26.5, because 180-127 is 53, which is the sum of the two angles. the two angles are the same, so divide 53 by 2.
2) Find Angles XZY and ZXY. We know that YZO is a right angle, and both XZY and OZX make up this right angle so XZY + OZX = 90. OZX is 26.5, so 90-26.5=XZY. XZY = ZXY, so both angles equal 63.5.
3) Now that we have two angles of triangle XYZ, we can find angle XYZ. 180-(XZY+ZXY)=XYZ, so (180-(63.5+63.5)=53. Angle XYZ=53.
A funeral director in Kumasi must assign 15 mourners to three limousines: 6 in the first limousine, 5 in the second limousine and 4 in the third. In how many ways can this be done?
Answer:
For me, ill say there are many ways it can be done.
First, u can pick at random. Or u can decide to do it boys and girls
Step-by-step explanation:
The product of 2 numbers is 918 one number is 37 less than the other what are the numbers
¿Cuál es la fórmula para calcular el área de cualquier triangulo?
¡Hola! ¡Ojalá esto ayude!
--------------------------------------------------------------------------------------------------------
La fórmula para calcular el área de cualquier triángulo es:
base multiplicada por la altura y dividida por dos.
||
||
||
\/
Bh / 2.
A statistical program is recommended.
The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.
32.1 30.9 31.6 30.4 31.0 31.9
The report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed.
Required:
a. Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using α= 0.01.
b. Calculate the test statistic and determine the P-value.
c. What can you conclude?
Answer:
We conclude that the true average stopping distance exceeds this maximum value.
Step-by-step explanation:
We are given the following observations that are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.;
X = 32.1, 30.9, 31.6, 30.4, 31.0, 31.9.
Let [tex]\mu[/tex] = true average stopping distance
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 30 {means that the true average stopping distance exceeds this maximum value}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30 {means that the true average stopping distance exceeds this maximum value}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean stopping distance = [tex]\frac{\sum X}{n}[/tex] = 31.32 ft
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 0.66 ft
n = sample size = 6
So, the test statistics = [tex]\frac{31.32-30}{\frac{0.66}{\sqrt{6} } }[/tex] ~ [tex]t_5[/tex]
= 4.898
The value of t-test statistics is 4.898.
Now, at 0.01 level of significance, the t table gives a critical value of 3.365 at 5 degrees of freedom for the right-tailed test.
Since the value of our test statistics is more than the critical value of t as 4.898 > 3.365, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average stopping distance exceeds this maximum value.