Answer: f(f(f(x)) = 8x - 7
Step-by-step explanation:
f(f(x)) means that we are evaluating f(x) with itself, then if f(x) = 2x - 1
f(f(x)) = 2*f(x) - 1 = 2*(2x - 1) - 1 = 4x - 2 - 1 = 4x - 3
f(f(x)) = 4x - 3
Then, we have f(f(f(x)) = 4*f(x) - 3
= 4*(2x - 1) - 3 = 8x - 4 - 3 = 8x - 7
Applying the Segment Addition Postulate
Point B lies between points A and C on AC. Let x
represent the length of segment AB in inches.
A
B
3x
Use the segment to complete the statements.
The value of x is v.
The length of AR in inches is
✓x
C
The length of BC in inches is
20 inches
Intro
Answer:
x = 5, AB=5, BC = 15
Step-by-step explanation:
AC = AB + BC (Segment Addition)
AC= 20, AB =x Bc = 3x,
20= x+3x 20=4x
x=5
AB=x, AB =5
BC=3x BC= 15
The segment addition postulate states gives the value of x as 5, given
that the sum of x and 3·x is 20.
Responses:
The value of x is 5The length of [tex]\overline{AB}[/tex] is 5 inchesThe length of [tex]\overline{BC}[/tex] is 15 inchesHow does segment addition postulate give the value of x?From the given diagram, we have;
[tex]\overline{AB}[/tex] = x
[tex]\overline{BC}[/tex] = 3·x
According to segment addition postulate we have;
[tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{AC}[/tex] = 20 inches
Which gives;
x + 3·x = 20
Therefore;
4·x = 20
[tex]x = \dfrac{20}{4} = 5[/tex]
The value of x is 5The length of [tex]\overline{AB}[/tex] is 5 inches[tex]\mathbf{\overline{BC}}[/tex] = 3·x
[tex]\mathbf{\overline{BC}}[/tex] = 3 × 5 = 15
The length of [tex]\overline{BC}[/tex] is 15 inchesLearn more about segment addition postulate here:
https://brainly.com/question/1397818
PLEASE ANSWER How many liters of a 35% salt solution must be mixed with 20 liters of 70% salt solution to obtain a solution that is 45% salt?
Answer:
50 liters
Step-by-step explanation:
Amount of salt in the 35% solution + amount of salt in the 70% solution = amount of salt in the 45% solution
0.35 x + 0.70 (20) = 0.45 (x + 20)
0.35 x + 14 = 0.45 x + 9
5 = 0.1 x
x = 50
The volume of the 35% solution is 50 L
Known parameter;
The percentage concentration of the salt solution with unknown volume = 35%
The percentage concentration of the 20 liters salt solution = 70%
The percentage concentration of the resulting solution = 45%
Unknown parameter;
The volume of the 35% salt solution
Strategy;
Let x represent the volume of the 35% salt solution that must be mixed to obtain the 45% salt solution
Balance the masses of the salts before and after mixing
The mass of the salts before mixing = 70% × 20 L + 35% × x
The mass of the salt solution mixture after mixing = 45% × (20 L + x)
By conservation principles, we get;
70% × 20 L + 35% × x = 45% × (20 L + x)
0.7 × 20 L + 0.35 × x = 0.45 × (20 L + x)
14 L + 0.35·x = 9 L + 0.45·x
14 L - 9 L = 0.45·x - 0.35·x = 0.1·x
5 L = 0.1·x
x = 5 L/(0.1) = 5 L × 10 = 50 L
The volume of the 35% solution that must be mixed with the 70% salt solution x = 50 L
Learn more about calculations of concentration of mixtures here;
https://brainly.com/question/11866299
solve the eqauation 76a^3+19a^2+16a=-4
Answer:
The solutions are a₁ = -4/19 i, a₂ = 4/19 i and a₃ = -1/4
Step-by-step explanation:
Given the equation 76a³+19a²+16a=-4, for us to solve the equation, we need to find all the factors of the polynomial function. Since the highest degree of the polynomial is 3, the polynomial will have 3 roots.
The equation can also be written as (76a³+19a²)+(16a+4) = 0
On factorizing out the common terms from each parenthesis, we will have;
19a²(4a+1)+4(4a+1) = 0
(19a²+4)(4a+1) = 0
19a²+4 = 0 and 4a+1 = 0
From the first equation;
19a²+4 = 0
19a² = -4
a² = -4/19
a = ±√-4/19
a₁ = -4/19 i, a₂ = 4/19 i (√-1 = i)
From the second equation 4a+1 = 0
4a = -1
a₃ = -1/4
find the local and/or absolute extrema for the function over the specified domain. (Order your answers from smallest to largest x.) f(x)
Answer:
Minimum 8 at x=0, Maximum value: 24 at x=4
Step-by-step explanation:
Retrieving data from the original question:
[tex]f(x)=x^{2}+8\:over\:[-1,4][/tex]
1) Calculating the first derivative
[tex]f'(x)=2x[/tex]
2) Now, let's work to find the critical points
Set this
[tex]2x=0\\x=0[/tex]
0, belongs to the interval. Plug it in the original function
[tex]f(0)=(0)^2+8\\f(0)=8[/tex]
3) Making a table x, f(x) then compare
x| f(x)
-1 | f(-1)=9
0 | f(0)=8 Minimum
4 | f(4)=24 Maximum
4) The absolute maximum value is 24 at x=4 and the absolute minimum value is 8 at x=0.
find the sum (12p +9) +(4p-3)
Hey there! :)
Answer:
16p + 6.
Step-by-step explanation:
Add the two binomials together by combining like terms:
12p + 9 + 4p - 3
12p + 4p + 9 - 3
16p + 6.
Answer:
16p+6
Step-by-step explanation:
You combine like terms you do not multiply.
Rewrite 100⋅(200⋅300) using the Associative Law of Multiplication.
Answer:
6 x 10⁶ or 6,000,000
Step-by-step explanation:
100 × (200 × 300)
100 x 60,000 → 6,000,000
6,000,000 → 6 x 10⁶
Hope this helps! :)
If a varies inversely with b, and a=12 when b=1/3, find the equation that relates a and b
Answer:
a = 4 /b
or ab = 4
Step-by-step explanation:
An inverse relation is given by
a = k/b where k is the constant
Rewriting
ab = k
12 * 1/3 = k
4 = k
a = 4 /b
or ab = 4
Please help me the venn diagram is wrong too im confused on how to do this :(((
Answer:
probability of chosing a student that has a cat and a dog is 9/25
Step-by-step explanation:
And yes the Venn diagram is wrong because you forgot to subtract 9 from 15 and 16
This makes it
[ 3 ( 6 ( 9 ) 7 ) ]
3 + 6 + 9 + 7 = 25
The net price equivalent rate of 9 / 15 / 18 is
Answer:
f so final percentage
= .91(.85)(.82) = .63427
or 63.427% of the original price
Step-by-step explanation:
Shaun's tent (shown below) is a triangular prism. Find the surface area, including the floor, of his tent.
Answer: 52.8
Step-by-step explanation: it’s on khan ,
Ok, so. I know It’s -27 + 23x and X = 7 right?? Or am I doing something wrong.
Answer:
134 degrees
Step-by-step explanation:
Right so far. To find the numerical measure of the angle, you need to use x=7 in your expression for the angle measure:
m∠STU = -27 +23(7) = 134 . . . degrees
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 290 babies were born, and 261 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?
Answer:
The 99% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.
Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.
Step-by-step explanation:
Confidence interval for the proportion:
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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 290, \pi = \frac{261}{290} = 0.9[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.8546[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 + 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.9454[/tex]
Percentage:
Proportion multplied by 100.
0.8546*100 = 85.46%
0.9454*100 = 94.54%
The 99% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.
Based on the result, does the method appear to be effective?
Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.
The houses on a city block were valued at $172,000, $164,000, $142,000,
$159,000, $191,000, $124,000, and $146,000, respectively. But a public
assessor has determined that the value of each house is actually $13,000
higher than previously thought. According to the public assessor, what is the
median value of the houses?
A. $159,000
B. $165,000
C. $172,000
D. $177,000
Answer:
C. $172,000
Step-by-step explanation:
Calculation for the median value of the houses
The following data was given in the question:$172,000, $164,000, $142,000,
$159,000, $191,000, $124,000, and $146,000
The first step is to Arrange the above data in ascending order
$124,000,$142,000,$146,000,$159,000,
$164,000,$172,000,$191,000
Second step is to find the Median
The Median will be the mid value, which means that $159,000 is the mid value
Based on the information given in the question we were given that a public
assessor has determined that the value of each house is actually $13,000 higher than previously thought
Hence, the Median will be = $159,000+$13,000=$172,000
Therefore the median value of the houses will be $172,000
When (81x^2/7) (2/9x^3/7) is simplified, it can be written in the form ax^b where a and b are real numbers. Find ab.
Answer:
In improper form your solution will be [tex]\frac{90}{7}[/tex]. As a mixed fraction it will be [tex]12\frac{6}{7}[/tex].
Step-by-step explanation:
The first thing we want to do here is to simplify this expression. After doing so, " a " and " b " should be multiplied to result in a possible improper fraction,
[tex]\left(81x^{\frac{2}{7}}\right)\:\left(2/9x^{\frac{3}{7}}\right)\:[/tex] - Apply exponential rule " [tex]\:a^b\cdot \:a^c=a^{b+c}[/tex] "
= [tex]81\cdot \frac{2}{9}x^{\frac{2}{7}+\frac{3}{7}}[/tex] - Combine fractions [tex]\frac{2}{7}[/tex] and [tex]\frac{3}{7}[/tex]
= [tex]81\cdot \frac{2}{9}x^{\frac{5}{7}}[/tex] - Multiply the fractions, and simplify further
= [tex]\frac{162x^{\frac{5}{7}}}{9}[/tex] = [tex]18x^{\frac{5}{7}}[/tex] - This is out simplified expression
Now that we have this simplified expression, we can see that a = [tex]18[/tex], and b = [tex]\frac{5}{7}[/tex]. Therefore, multiplying the two we should receive the improper fraction as follows,
[tex]18 * \frac{5}{7}[/tex] = [tex]\frac{90}{7}[/tex] - Note that this is in improper form. If you want your solution in a mixed fraction, it will be [tex]12\frac{6}{7}[/tex].
John didnt have money for a game system, so he bought it with his credit card. he paid for it monthly over the course of a year. The $350.00 game system ended up costing $429, What percentage of the game system price did he pay in interest?
Answer:
percentage of interest = 22.6% (to one decimal place)
Step-by-step explanation:
actual price paid (including interest) = 429, out of which
interest = 429-350 = 79
Percentage of interest out of actual price paid
= 79/429* 100%
= 22.6%
Please help ?!!! Solve the three equations in the table using any method of your choice. List the method you used.
Equation
x^2-4=-12
-9x^2+4x-10=0
x^2+8x=-17
With solutions and method
Step-by-step explanation:
[tex]x = \frac{ - b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
The quadratic formula is honestly the most straightforward way of solving here.
Your other options are completing the square (which is the same thing as the quadratic formula but it's good to know that method if you have to take Integral Calculus at some point) or maybe factoring by grouping if it's appropriate. But the quadratic formula will work for you in all three equations:
1) a=1, b=0, c=8
This reduces pretty quickly into x=8i,-8i due to the negative under the radical. (Actually we didn't even really need the formula here.)
2) a=-9, b=4, c=-10
This reduces into x=(-4+i√(344))/-18, (-4-i√(344))/-18 and doesn't go any further because 344 isn't a perfect square.
3) a=1, b=8, c=17
This reduces to x=(-4+i), (-4-i)
So those are the answers for each.
Please Refer to the screenshot. Hope this helps!
Assume that a sample is used to estimate a population proportion p. Find the 99% confidence interval for a sample of size 315 with 37% successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.
Answer:
The 99% confidence interval is = 0.37 +/- 0.070
= (0.300, 0.440)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
p+/-z√(p(1-p)/n)
Given that;
Proportion p = 37% = 0.37
Number of samples n = 315
Confidence interval = 99%
z value(at 99% confidence) = 2.58
Substituting the values we have;
0.37 +/- 2.58√(0.37(1-0.37)/315)
0.37 +/- 2.58√(0.00074)
0.37 +/- 2.58(0.027202941017)
0.37 +/- 0.070183587825
0.37 +/- 0.070
= (0.300, 0.440)
The 99% confidence interval is = 0.37 +/- 0.070
= (0.300, 0.440)
PLEASE HELP!! Find the missing side and round answer to the nearest tenth.
Answer:
Step-by-step explanation:
opp=x,hyp=16
sin 51°=[tex]\frac{x}{16}[/tex]
cross multiply
sin 51° x 16 =x
0.7771 x 16=x
12.4=x
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The table gives the boiling point of water at different altitudes.
Altitude (1,000 feet) Boiling Point of Water (°F)
0 212.0
0.5 211.1
1.0 210.2
2.0 208.4
2.5 207.5
3.0 206.6
4.0 204.8
4.5 203.9
Based on the table, the linear equation that represents the change in water’s boiling point for every 1,000-foot change in altitude has a slope of
units.
Answer:
[tex]\large \boxed{\text{-1.8$^{\circ}$F/1000 ft}}[/tex]
Step-by-step explanation:
Identify the changes (Δ) in each consecutive pair of x-values and y-values, then calculate the corresponding values of Δy/Δx
Your working table should look like the one below.
[tex]\begin{array}{cccc}\textbf{Alt/1000 ft} & \textbf{B.p.$/^{\circ}$F} & \Delta\textbf{B. p}& \Delta\textbf{B.p/1000 ft}\\0 & 212.0 & & \\& &-0.9 & -1.8\\0.5 & 211.1 & & \\& &-0.9 & -1.8\\1.0 & 210.2 & & \\& &-1.8 & -1.8\\2.0 & 208.4 & & \\& &-1.8 & -1.8\\3.0 & 206.6 & & \\& &-1.8 & -1.8\\4.0 & 204.8 & & \\& &-0.9 & -1.8\\4.5 & 203.9 & & \\\end{array}[/tex]
[tex]\text{ The change in boiling point per thousand feet of altitude is $\large \boxed{\textbf{-1.8$^{\circ}$F/1000 ft}}$}[/tex]
Answer:
Answer:
Step-by-step explanation:
Identify the changes (Δ) in each consecutive pair of x-values and y-values, then calculate the corresponding values of Δy/Δx
Your working table should look like the one below.
Step-by-step explanation:
Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?
Hey there! I'm happy to help!
The domain is all of the possible x-values and the range is all of the possible y-values.
Let's quickly rearrange our equation so we can plug in x to see what y is.
12x+6y=24
We subtract 12x from both sides.
6y=-12x+24
We divide both sides by six.
y= -2x+4
Since there are three domains we can plug into this equation that can give us one output, we will have three numbers in our range! Let's plug in our x-values to get our three y-values.
y=-2(-4)+4
y=12
y=-2(0)+4
y=4
y=-2(5)+4
y= -6
When writing your range, you order the numbers from least to greatest. We can write this range as {-6,4,12}
Have a wonderful day!
06:Pretest 06:Quadrilaterals
27. Which statement is true?
O All squares are quadrilaterals,
O All quadrilaterals are parallelograms,
All rectangles are squares,
O All quadrilaterals are squares,
Answer:
all squares are quadrilaterals
I NEED HELP PLEASE, THANKS! :)
Write 18(cos169° + isin169°) in rectangular form. Round numerical entries in the answer to two decimal places. (Show work)
Answer:
z = -17.67 + i3.43
Step-by-step explanation:
Let us apply the formula z = r(cos Ф + i sin Ф), given 18(cos169° + isin169°) -
z = 18( cos169 + isin169 ),
z = r(cos Ф + i sin Ф)
Now we can solve this question in the form z = a + bi, in this case where a = 18 cos169, and b = 18 sin169. This is as a = r cos Ф and b = r sin Ф -
sin169 is positive, while cos169 is negative, thus -
a = -17.6692893021...,
b = 3.43456191678...
Rectangular Form, z = -17.67 + i3.43
Hope that helps!
Which linear inequality is represented by the graph?
ysx-1
yzx-1
3 4 5
y< 3x - 1
y > 3x - 1
Answer:
y>3x -1 is the right answer
Determine whether the sequence is arithmetic, geometric, or neither:
-2, -4,-8, -16,...
a) arithmetic b)geometric
c) neither
Answer:
b) geometric
Step-by-step explanation:
Notice that each new term is derived by multiplying the previous term by 2. Thus: the first term is -2 and the common ratio is 2. This is a geometric sequence.
Suppose that the function g is defined, for all real numbers, as follows.
Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles.
A) List all outcomes in the event A that all three vehicles go in the same direction.
B) List all outcomes in the event B that all three vehicles take different directions.C) List all outcomes in the event C that exactly two of the three vehicles turn right.D) List all outcomes in the event D that exactly two vehicles go in the same direction.E) List outcomes in D'.F) List outcomes in C ∪ D.G) List outcomes in C ∩ D.
Answer:
A) A = {RRR, LLL, SSS}
B) B = {LRS. LSR, RLS, RSL, SLR, SRL}
C) C = {RRL, RRS, RSR, RLR, LRR, SRR}
D) D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}
E) D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}
F) C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}
G) C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}
Step-by-step explanation:
A) All vehicles must go right, left or straight ahead (three possibilities):
A = {RRR, LLL, SSS}
B) One vehicle must go right, one must go left, and the remaining one must go straight ahead (six possibilities):
B = {LRS. LSR, RLS, RSL, SLR, SRL}
C) There are three ways that exactly two vehicles go right (1 and 3, 2 and 3, 1 and 2), there are then two options for the remaining vehicle (left and straight) for a total of six possibilities:
C = {RRL, RRS, RSR, RLR, LRR, SRR}
D) Follow the same reasoning from the previous item, but multiply the number of possibilities by 3 (for each direction in which both cars can go: right, left or straight):
D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}
E) D' is the set containing all possibilities not present in set D. D' is comprised by the possibilities of all vehicles going in the same direction, or each vehicle in a different direction:
D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}
F) The outcomes in C ∪ D is the union of elements from set C and D (neglecting repeated values), which happens to be all values in set D.
C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}
G) The outcomes in C ∩ D is the list of values present in both sets C and D, which happens to be all values in set C:
C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}
A survey of 128 DeVry statistics students found that 83% read the announcements each week. What is the population and what is the sample
Answer:
-Population is DeVry statistics students - Sample is 128 DeVry statistics students.
Step-by-step explanation:
First of all, population is defined as a set of all elements while sample includes some or all those of elements, whereas, sample never includes more elements when compared to population.
Hence, we select sample from the population.
Now, in this question, the survey include 128 DeVry statistics students. Thus, these 128 statistics students would be a sample while total number of Devry statistics students will be the population.
83% is the sample statistic because it gives us numerical information about the sample.
Thus, we can conclude that;
-Population is DeVry statistics students - Sample is 128 DeVry statistics students.
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) −3, 2, − 4 3 , 8 9 , − 16 27 , ...
Answer:
The general term is
Sn = -(-2)ⁿ.3¹⁻ⁿ
step by step Explanation:
we were told to find a general term of the above sequence, what should come to mind is that the terms will follow an order....
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
a city grid of Anytown, USA is shown on the grid below the fire department is represented by the quadrilateral RSTU. Another fire department is opening in a different part of the city to maximize fire protection. The size of the new department's property must be congruent to the older department. Vertices A and B are plotted on the grid below to represent two vertices of the new?fire Department quadrilateral ABCD:
What could be the ordered pairs of representing vertices C and D of quadrilateral ABCD so that the new fire department to congruent to the old fire department?
Answer:
C(1, 1)D(4, 1)Step-by-step explanation:
The fire department property is 2 units in height. 2 units from the line y=3 can be on the line y=5, or on the line y=1.
There are no answer choices with y=5, so the appropriate choices are those with C and D having the x-coordinates of B and A, respectively, and y=1.
C(1, 1), D(4, 1)
Tensile strength tests were carried out on two different grades of wire rod, resulting in the accompanying data.
Grade Sample Size sample mean(kg/mm^2) Sample S
AISI 1064 m = 126 x = 102.8 s1 = 1.2
AISI 1078 n = 126 y = 121.3 s2 = 2.0
a. Does the data provide compelling evidence for concluding that true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.
b. Test the appropriate hypotheses using the P-value approach.
c. Calculate the test statistic and p-value.
d. State the conclusion in the problem context.
Answer:
The null hypothesis is rejected.
There is enough evidence to support the claim that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.
Test statistic t=-40.91
P-value = 0
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=-10\\\\H_a:\mu_1-\mu_2< -10[/tex]
The significance level is 0.05.
The sample 1 (AISI 1064), of size n1=126 has a mean of 102.8 and a standard deviation of 1.2.
The sample 2 (AISI 1078), of size n2=126 has a mean of 121.3 and a standard deviation of 2.
The difference between sample means is Md=-18.5.
[tex]M_d=M_1-M_2=102.8-121.3=-18.5[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1.2^2}{126}+\dfrac{2^2}{126}}\\\\\\s_{M_d}=\sqrt{0.011+0.032}=\sqrt{0.043}=0.2078[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-18.5-(-10)}{0.2078}=\dfrac{-8.5}{0.2078}=-40.91[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-2=126+126-2=250[/tex]
This test is a left-tailed test, with 250 degrees of freedom and t=-40.91, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-40.91)=0[/tex]
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.