Answer:
k = -10/9 and k = 10/9
Step-by-step explanation:
given y = cos(kt) and the differential equation 81y'' = -100y
y' = -ksin(kt)
y'' = -k²cos(kt)
Substituting the value of y and y'' in the differential equation we have;
81 (-k²cos(kt))= -100 (cos(kt))
-81k²cos(kt)) = -100cos(kt))
-81k² = -100
k² = 100/81
k = ±[tex]\sqrt{\frac{100}{81} }[/tex]
k = ±10/9
k = -10/9 and k = 10/9
Want Brainliest get this correct What is the sum of the fractions below?
In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $112. The population standard deviation is known to be $16.
a. Which form of the hypotheses should be used to test whether or not the average room price is significantly different from $108.50?
H0:
-mu is greater than or equal to $108.50
mu is greater than $108.50
mu is less than $108.50mu is less than or equal to $108.50
mu is equal to $108.50mu is not equal to $108.50
Ha: -
-mu is greater than or equal to $108.50
mu is greater than $108.50mu is less than $108.50
mu is less than or equal to $108.50
mu is equal to $108.50mu is not equal to $108.50
b. Test to determine if whether or not the average room price is significantly different from $108.50, using an alpha level of .05.
Reject H0
or
Fail to reject H0
Answer:
Step-by-step explanation:
H0: mu is equal to $108.50
Ha: mu is not equal to $108.50
This test is a two tailed test and using the z tat formula, we can ascertain if there is a difference.
z = x-u / sd/√n
Where x is $112, u is $108.50 sd is $16 and n is 64
z = 112-108.50 / 16/√64
z = 3.5/(16/8)
z = 3.5/2
z = 1.75
To help us arrive at a conclusion, we need to find the p value using alpha id = 0.05. The p value is 0.08. Since the p value is great than 0.05, we fail to reject the null and conclude that there is not enough statistical evidence to prove that the average room price is significantly different from $108.50
Using the following conversions between the metric and U.S. systems, convert the measurement. Round your answer to 6 decimal places as needed
1 meter ≈ 3.28 feet
1 Liter ≈ 0.26 gallons
1 kilogram ≈ 2.20 pounds
33.777 yd ≈ __________ km
Answer:
33.777 yd = 0.030886 km
Step-by-step explanation:
==>Given:
33.777 yd
==>Required:
Convert 33.777 yd to km to 6 decimal places, using the metric and U.S systems.
==>Solution:
To convert, note that 1 km = 1093.6133 yd.
Thus,
1 km = 1093.6133 yd
x km = 33.777 yd
Cross multiply
1 × 33.777 = 1093.6133 × x
33.777 = 1093.6133x
Divide both sides by 1093.6133, to solve for x
33.777/1093.6133 = x
0.03088569 = x
x ≈ 0.030886 (to 6 decimal places)
Therefore, 33.777 yd = 0.030886 km
Which number is greatest? 6.23 times 10 Superscript 12 6.23 times 10 Superscript 8 6.23 times 10 Superscript negative 6 6.23 times 10 Superscript 3
The greatest number is 6.23 times 10 superscript 12.
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
We are given that the number so;
A.6.23 x 10^12 is equivalent to rolling the decimal 12 times to the right.
B.6.23 x 10^8 is equivalent to rolling the decimal 8 times to the right.
C.6.23 x 10^-6 is equivalent to rolling the decimal 6 times to the left.
D.6.23 x 10^3 is equivalent to rolling the decimal 3 times to the right.
This shows the 10 has been multiplied by itself thrice.
Learn more about scientific notation here:
https://brainly.com/question/3112062
#SPJ6
How do you write 416.7 in scientific notation? ___× 10^____
Answer:
4.167(10²)
Step-by-step explanation:
Step 1: Put number into proper decimal form
416.7 = 4.167
Step 2: Figure out exponent
Since we are moving the decimal places 2 places to the right, our exponent is 2
Answer:
4.167 × 10^2
Step-by-step explanation:
= 4.167 × 10^2
(scientific notation)
= 4.167e2
(scientific e notation)
= 416.7 × 10^0
(engineering notation)
(one)
= 416.7
(real number)
the lines given by the equations y=2x and y=4x+1 are
Answer:
A
Step-by-step explanation:
For lines to be parallel, their slopes need to be the same.
For lines to be perpendicular, the product of their slopes needs to be -1.
None of these conditions are met since the slopes are 2 and 4 respectively.
Sooo.... The answer must be A! :)
Answer:
The lines given are neither perpendicular nor are they parallel.
Step-by-step explanation:
In order for two lines to be be parallel, they must have the same slope but different y-intercepts. In order for two lines to be perpendicular, one line has to have a slope that is the negative reciprocal of the other line.
We are given two line equations.
y = 2x
y = 4x + 1
These lines do not represent a perpendicular situation nor do they represent a parallel situation.
Question
Drag each description to the correct location on the table.
Examine the equation to determine if the descriptions listed are key features of the function or not.
Answer:
Key Feature: - decreasing, As x approaches -(infinite), y approaches (infinite), As x approaches (infinite), y approaches a constant.
Not a Key feature: increasing, As x approaches (infinite) y approaches (infinite), As x approaches -(infinite) y approaches -(infinite), & As x approaches -(infinite) y approaches a constant.
Step-by-step explanation:
3.A man answers 10 maths problems, one after the other. He answers the first problem correctly and the second problem incorrectly, for each of the remaining 8 problems the probability that he answers the problem correctly equals to the ratio of the number of problems that he has already answered correctly to the total number of problems that he has already answered. What is the probability that he answers exactly 5 out of 10 problems correctly
Answer:
Probability of answering 5out of 10 correctly= 0.246
Step-by-step explanation:
Total question answered= 2
Question answered correctly= 1
Probability of answered correctly= 1/2
Probability of answered correctly= 0.5
Probability of answered incorrectly = 0.5
Probability of answering 5out of 10 correctly= 10C5(0.5)^5(0.5)^5
Probability of answering 5out of 10 correctly = 10!/5!5!(0.5)^5(0.5)^5
Probability of answering 5out of 10 correctly = 252(0.03125)(0.03125)
Probability of answering 5out of 10 correctly= 0.246
2) Find the diameter.
4) If the diameter is equal to 3 inches ,d=
Answer:
d = 3 in
Step-by-step explanation:
Since we are trying to find the diameter, and the diameter is given to us as 3 in, our diameter is 3 in.
Determine the best answer
6 points
MULTIPLE CHOICE Find the length of BC. (Lesson 10-2)
B
21 cm
C
168°
A 18°
C 168°
B 2.20 cm
D 30.79 cm
A
Answer:
angle of bc= 180-168= 12°
length of bc= 12/360 × π × diameter
= 12/360 × 22/7 × 21
= 12/360 × 66
= 2,20 cm (b)
If you average your costs over your total production, you get the average cost, written C: C(x, y) = C(x, y) x + y . Find the average cost for the cost function C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−0.01(x + y).
Answer:
Average cost
= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)
Step-by-step explanation:
Average cost is the cost per unit of production. It is expressed mathematically as the total cost divided by the total number of units produced.
If total cost = C(x, y)
Average cost = C(x, y) ÷ (x+y)
For this question, total cost function is
C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾
The average cost is simply this total cost function divided by the total number of units produced.
Average cost
= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)
If numerical values are then provided, this can then be worked around. But as the numerical values are absent, the average cost function just remains in this its raw form.
Hope this Helps!!!
A geometric series has second term
375 and fifth term 81. The nth term
of the series is Un. Find the value of
un
n = 6
Answer: 243/5 = 48.6
Step-by-step explanation:
a₁, 375, a₃, a₄, 81 , a₆
First, let's find the ratio (r). There are three multiple from 375 to 81.
[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]
Next, let's find a₆ which is one multiple from 81.
[tex]a_6=81\bigg(\dfrac{3}{5}\bigg)^1\\\\\\.\quad =\large\boxed{\dfrac{243}{5}}[/tex]
Which of the following is not a congruence theorem or postulate? A. SSS B. SAS C. SSA D. AAS
Answer:
SSA the only other right one missing is ASA
3a. Write an equation in slope-intercept form of a
line that passes through (2,1) and (6,-5).
Answer:
[tex]y = -3/2x + 4[/tex]
Step-by-step explanation:
[tex](2,1) and (6,-5).\\x_1 = 2\\x_2 = 6\\y_1 =1\\y_2 =-5\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-1}{x-2} = \frac{-5-1}{6-2}\\\\\frac{y-1}{x-2} = \frac{-6}{4} \\Cross-Multiply\\4(y-1) = -6(x-2)\\4y-4=-6x+12\\4y =-6x+12+4\\4y = -6x+16\\Divide through-by ; 4\\\frac{4y = -6x+16}{4} \\\\y = -\frac{3}{2} x +4[/tex]
A circle is shown. Angles 3 and 4 intersect an arc with a measure of 106 degrees. Angles 1 and 2 intersect an arc with measure 58 degrees. Is the measure of ∠1 equal to the measure of ∠2? Why?
Answer:
yes, because they intercept the same arc
Step-by-step explanation:
Answer:
yes, because they intercept the same arc
Step-by-step explanation:
To dilute a solution that is 40% saline, a chemist combines it with a solution that is 15% saline. How much of each solution should she use if she needs 150 mL of a solution that is 25% saline? Hint: solve by using system of equations
Answer:
60 ml of 40% saline and 90 ml of 15% saline
Step-by-step explanation:
We can call the amount of 40% solution x and the amount of 15% solution y.
x + y = 150 -- (1)
0.40x + 0.15y = 150 * 0.25 -- (2) --- 150 * 0.25 = 37.5
40x + 15y = 3750 (Multiply (2) by 100 to get rid of decimals)
15x + 15y = 2250 -- (3) (Multiply (1) by 15)
25x = 1500 (Subtract (3) from (1)
x = 60
y = 150 - 60 = 90
Answer:
[tex] 37.5= 0.4 x +0.15 y[/tex]
We can solve for x and we got:
[tex] x= \frac{37.5-0.15y}{0.4}= 93.75-0.375 y[/tex]
And replacing into the water condition we have:
[tex] 112.5 = (93.75-0.375 y)*0.6 +0.85y[/tex]
Solving for y we got:
[tex] 112.5= 56.25 -0.225 y+0.85 y[/tex]
[tex] y = \frac{112.5-56.25}{0.625}= 90[/tex]
And then solving for x we got:
[tex] x=\frac{37.5- 0.15*90}{0.4}= 60[/tex]
So we need 60 ml for the solution of 40% saline and 90 ml for the 15% saline solution
Step-by-step explanation:
We can solve this problem with the following system of equations:
[tex] 150*0.25 = x*0.4 + y *0.15[/tex] salt
[tex] 150*(1-0.25)= x(1-0.4) +y(1-0.15)[/tex] water
With x the ml of solution for 40% concentration and y the ml of solution at 15% of concentration
From the salt condition we have:
[tex] 37.5= 0.4 x +0.15 y[/tex]
We can solve for x and we got:
[tex] x= \frac{37.5-0.15y}{0.4}= 93.75-0.375 y[/tex]
And replacing into the water condition we have:
[tex] 112.5 = (93.75-0.375 y)*0.6 +0.85y[/tex]
Solving for y we got:
[tex] 112.5= 56.25 -0.225 y+0.85 y[/tex]
[tex] y = \frac{112.5-56.25}{0.625}= 90[/tex]
And then solving for x we got:
[tex] x=\frac{37.5- 0.15*90}{0.4}= 60[/tex]
So we need 60 ml for the solution of 40% saline and 90 ml for the 15% saline solution
The mass of each candy in a box is 5g. The mass of the empty box is 20g let T grams represent the total mass of the box and candies. Let n represent the number of candies, so that t= 5n + 20 Using the information create a table of values. And graph the relation. Please help asap!! Thanks
Answer:
[tex]\begin{center}\begin{tabular}{ c c } n & T\\ 0 & 20 \\ 1 & 25 \\ 2 & 30 \\ 3 & 35 \\ 4 & 40 \\ \end{tabular}\end{center}[/tex]
Please refer to graph attached.
Step-by-step explanation:
Given that mass of each candy in the box is 5 gm.
Mass of empty box is 20 gm.
Total grams, [tex]T = 5n + 20[/tex]
To find: A table of values and graph of the relation.
Solution:
The given equation is nothing but a Linear equation in two variables.
Let us try to create a table of values by putting some values of 'n' and then finding the values for Total grams 'T'.
Let us put [tex]n = 0 \Rightarrow T =5\times 0 +20 = 20[/tex]
Let us put [tex]n = 1 \Rightarrow T =5\times 1 +20 = 25[/tex]
Let us put [tex]n = 2 \Rightarrow T =5\times 2 +20 = 30[/tex]
Let us put [tex]n = 3 \Rightarrow T =5\times 3 +20 = 35[/tex]
Let us put [tex]n = 4 \Rightarrow T =5\times 4 +20 = 40[/tex]
So, the table of values becomes:
[tex]\begin{center}\begin{tabular}{ c c } n & T\\ 0 & 20 \\ 1 & 25 \\ 2 & 30 \\ 3 & 35 \\ 4 & 40 \\ \end{tabular}\end{center}[/tex]
We can see that the value of T is increasing with increasing values of 'n'.
Please refer to the attached image for the graph of given equation.
As it is a linear equation in two variables, it will be a straight line. It will be an increasing positive slope graph.
how do you solve this problem
Answer:
more info is needed
Step-by-step explanation:
What is the value of X in equation? 1/3 X - 2/3 = - 18
Answer:
x=-52
Step-by-step explanation:
1/3x=-17 1/3
x=-52
evaluate 25.1 * 2.51 in two decimal places
Answer:
63.00
Step-by-step explanation:
25.1 × 2.51
Multiply.
= 63.001
Round to two decimal places.
63.00
Answer:
63.00
Step-by-step explanation:
when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00
Which of the following is the missing side length that completes the
Pythagorean triple below?
5, 12,
Answer:
13
Step-by-step explanation:
We can find the missing side length by using the pythagorean theorem
a² + b² = c²
5² + 12² = c²
25 + 144 = c²
169 = c²
13 = c
So, 13 is the missing side length.
Shrinivas deposited $1300 in an account which pays 8% annual interest, compounded continuously. How long will it take to reach $3500?
Select one:
O a. 12.4 years
O b. 9.2 years
O c. 176 years
O d. 1.2 years
Answer: a. 12.4 years
Step-by-step explanation:
Function to represent exponential growth continuously:
[tex]A=A_0e^{rt}[/tex] ...(i)
, where [tex]A_0[/tex] = initial amount, r= rate of interest ( in decimal) , A = Amount after t years.
As per given , we have
[tex]A_0=\$1300\\\\r=8\%=0.08\\\\ A=\$3500[/tex]
To find : t
Put all values in (i) ,
[tex]3500=(1300)e^{0.08t}\\\\\Rightarrow\ 2.6923077=e^{0.08t}[/tex]
Taking natural log on both sides
[tex]\ln(2.6923076)= 0.08t\\\\\Rightarrow\ 0.99039867=0.08t\\\\\Rightarrow\ t=\dfrac{0.99039866}{0.08}=12.37998325\approx12.4[/tex]
Hence, it would take 12.4 years.
so, the correct option is a. 12.4 years .
Which function has an inverse that is also a function?
A: (-1,-2),(0,4),(1,3),(5,14),7,4)
B: (-1,2),(0,4),(1,5),(5,4),(7,2)
C: (-1,3),(0,4),(1,14),(5,6),(7,2)
D: (-1,4),(0,4),(1,2),(5,3),(7,1)
Answer:
Option (C)
Step-by-step explanation:
Option (A):
(-1, -2),(0, 4), (1, 3), (5, 14), (7, 4)
In these ordered pairs (4, 4) and (7, 4) have the same y-value.
This function is not a one-to-one function.
Therefore, this function will have no inverse function.
Option (B):
(-1, 2), (0,4), (1, 5), (5, 4), (7, 2)
(-1, 2) and (7, 2) have the same output values for input values -1 and 7.
This function is not a one-to-one function.
Therefore, this function will have no inverse function.
Option (C).
(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)
For every input value there is a different output value in these pairs.
So the function is one-to-one function.
Therefore, inverse of this function will be a function.
Option (D).
(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)
Here (-1, 4) and (0, 4) show the same y-value which shows, the given function is not a one-to-one function.
Therefore, inverse of this function will not be a function.
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2-4n/3
Answer:
(n- 2/3)²
Step-by-step explanation:
Perfect square trinomial is: a²+2ab+b²= (a+b)²We have:
n² - 4n/3It can be put as:
n² -2×n×2/3Here we consider n = a and -2/3 = b, then
b²= (-2/3)²= 4/9Now we add 4/9 to a given binomial to make it perfect square:
n² - 2×n×3/2 + 4/9= (n- 2/3)²So, added 4/9 and got a perfect square (n- 2/3)²
In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. Dedicated statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips. Some of their data are given below. 1219 1214 1087 1200 1419 1121 1325 1345 1244 1258 1356 1132 1191 1270 1295 1135 Find a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies.
Answer:
A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].
Step-by-step explanation:
We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.
Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 94.3
n = sample of car drivers = 16
[tex]\mu[/tex] = population mean number of chips in a bag
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95 {As the critical value of t at 15 degrees of
freedom are -2.131 & 2.131 with P = 2.5%}
P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95
P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]
= [1187.96, 1288.44]
Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].
I’m Confused On The Question
Round 2826 to the nearest hundred.
Answer:
2800
Step-by-step explanation:
2826 to the nearest hundred is 2800
What is the height, X, of the equilateral triangle ? (Help)
Answer:
A. 7√3 in
Step-by-step explanation:
We first have to draw out the altitude on the triangle. When we do so, we should see that we will get 2 congruent 30-60-90 triangles. From there, our h height is x and we use tan∅ to solve:
tan60° = x/7
x = 7tan60°
x = 7√3
Answer:
It's A
Step-by-step explanation:
Victor always runs out of money by the end of the month, so he wants to start keeping a budget. Last month, he spent a total of $176.47 on groceries, $78.66 for phone, and $62.37 on gas. Estimate his monthly total for groceries, phone, and gas by first rounding to the nearest $10.
Answer:
Yearly budget= $3840
Monthly budget= $320
Step-by-step explanation:
His budget will be calculated first by rounding off to the nearest$10 all his monthly spending.
For groceries= $176.47
Round off=$ 180.00
For phone =$ 78.66
Round off = $80.00
For gas = $62.37
Round off= $60.00
His total round off = $180+$80+$60
His total round off = $320
Before the round off, his total spending was $176.47+$78.66+$62.37
= $317.5
So his monthly budget should be $320
And yearly budget =$ 320*12
Yearly budget= $3840
A simple random sample of 44 adults is obtained from a normally distributed population, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is 5.31 and the sample standard deviation is 0.51 . Use a 0.05 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5.4 comma which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample group?
Answer:
There is not enough evidence to support the claim that the population mean is significantly less than 5.4.
This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.
If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the population mean is significantly less than 5.4.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=5.4\\\\H_a:\mu< 5.4[/tex]
The significance level is 0.05.
The sample has a size n=44.
The sample mean is M=5.31.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.51.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.51}{\sqrt{44}}=0.077[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{5.31-5.4}{0.077}=\dfrac{-0.09}{0.077}=-1.171[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=44-1=43[/tex]
This test is a left-tailed test, with 43 degrees of freedom and t=-1.171, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.171)=0.124[/tex]
As the P-value (0.124) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the population mean is significantly less than 5.4.
This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.
If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.