Answer:
H1 : μ ≠ 20000
Step-by-step explanation:
Given that :
Population mean salary, μ = 20,000
To test if mean salary is more or less Than population mean salary, μ, this means we are testing if the mean salary is different from 20,000
Hence, the hypothesis :
Null, H0 : The mean salary is 20000
Alternative, H1 : The mean salary is not 20000
Using notation :
H0 : μ = 20000
H1 : μ ≠ 20000
Hence, alternative hypothesis is : H1 : μ ≠ 20000
Find the measure of the incanted angle to the nearest degree
Answer:
15.5⁰ or approximately 16⁰
Step-by-step explanation:
let unknown side be x
cos x= 53/55
cos x= 0.9636
x=cos inverse of 0.9636
x=15.5⁰
Answer:
[tex]cosx = \frac{53}{55} \\ x = {cos}^{ - 1} ( \frac{53}{55} ) \\ x = 15.4987[/tex]
The increase in length of an aluminum rod is twice the increase in length of an Invar rod with only a third of the temperature increase. Find the ratio of the lengths of the two rods.
Answer:
the ratio of lengths of the two rods, Aluminum to Invar is 11.27
Step-by-step explanation:
coefficient of linear expansion of aluminum, [tex]\alpha _{Al} = 23 \times 10^{-6} /K[/tex]
Coefficient of linear expansion of Invar, [tex]\alpha _{Iv} = 1.2 \times 10^{-6}/K[/tex]
Linear thermal expansion is given as;
[tex]\Delta L = L_0 \times \alpha\times \Delta T\\\\where;\\\\L_0 \ is \ the \ original \ length \ of \ the \ metal\\\\\Delta L \ is \ the \ increase \ in \ length[/tex]
The increase in length of Invar is given as;
[tex]\Delta L_{Iv} = L_0_{Iv} \times \alpha _{Iv}\times \Delta T_{Iv}[/tex]
The increase in length of the Aluminum;
[tex]\Delta L_{ Al} = L_0_{Al} \times \alpha _{Al} \times \Delta T_{Al}\\\\from \ the\ given \ question, \ the \ relationship \ between \ the \ rods \ is \ given \ as\\\\ L_0_{Al} \times \alpha _{Al} \times \frac{1}{3} \Delta T_{Iv}= 2( L_0_{Iv} \times \alpha _{Iv} \times \Delta T_{Iv})\\\\ L_0_{Al} \times \alpha _{Al} \times \Delta T_{Iv}= 6( L_0_{Iv} \times \alpha _{Iv} \times \Delta T_{Iv})\\\\ L_0_{Al} \times \alpha _{Al} \times \Delta T_{Iv} = 6L_0_{Iv} \times 6\alpha _{Iv} \times 6 \Delta T_{Iv}\\\\[/tex]
[tex]\frac{L_0_{Al}}{6L_0_{Iv} } = \frac{6\alpha _{Iv} \ \times \ 6 \Delta T_{Iv}}{\alpha _{Al} \ \times \ \Delta T_{Iv}} \\\\\frac{L_0_{Al}}{6L_0_{Iv} } = \frac{6\alpha _{Iv} \ \times \ 6}{\alpha _{Al} \ } \\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{\alpha _{Iv} }{\alpha _{Al} } )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{1.2 \times 10^{-6} }{23\times 10^{-6} } )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{1.2}{23} )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = \frac{259.2}{23} \\\\\frac{L_0_{Al}}{L_0_{Iv} } = 11.27[/tex]
Therefore, the ratio of lengths of the two rods, Aluminum to Invar is 11.27
The ratio of the lengths of the two rods which is length of aluminum to length of Invar rod is; 11.27
Formula for linear thermal expansion is;
ΔL = L × α × ΔT
Where;
ΔL is change in original length
L is original length
α is coefficient of linear expansion
ΔT is change in temperature
We are told that increase in length of aluminum rod is twice the increase in length of an Invar rod with only a third of the temperature increase.
Thus;
ΔL = 2ΔL
ΔT for the aluminum rod = ⅓ΔT for the Invar rod.
Thus, we have;
L_al × α_al × ⅓ΔT = 2L_in × 2α_in × 2ΔT
ΔT will cancel out to give;
⅓(L_al × α_al) = 2L_in × 2α_in × 2
Multiply both sides by 3 to get;
(L_al × α_al) = 6L_in × 6α_in × 6
From online tables, the linear coefficient of expansion of aluminum is 23 × 10^(-6) C¯¹
While the coefficient of thermal expansion for Invar rod is 1.2 × 10^(-6) K¯¹
Thus;
L_al × 23 × 10^(-6) = 6L_in × (6 × 1.2 × 10^(-6)) × 6
L_al/L_in = (6 × 6 × 1.2 × 10^(-6) × 6)/(23 × 10^(-6))
L_al/L_in = 11.27
Read more on coefficient of linear expansion at; https://brainly.com/question/6985348
What is the area of a trapezoid.. base 14in and 7in height is 5in?
if the formula is [tex]\frac{(B+b)}{2} .h[/tex] we just need to plug in the values
21/2 = 10.5 x 5 = 52.5
hope it helps :)
Answer:
A = 52.5 in^2
Step-by-step explanation:
The area of a trapezoid is
A = 1/2 (b1+b2)h
where b1 and b2 are the bases and h is the height
A = 1/2 ( 14+7)*5
A = 105/2
A = 52.5 in^2
Subtract the complex numbers: (–2 + 12i) – (–1 – 9i)
Question 18 options:
A)
–3 + 21i
B)
–1 + 21i
C)
–1 + 3i
D)
–3 + 3i
Answer:
B
Step-by-step explanation:
hope it is well understood
Ryanair provides cheap flights in Europe but prides itself on their on-time record. Ryanair quotes a flight time of 2 hours, 5 minutes. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.
What is the expected flight time in minutes?
Answer:
The expected flight time is 2 hours 10 minutes
Step-by-step explanation:
Given
[tex]a = 2\ hours[/tex]
[tex]b = 2\ hours\ 20\ mins[/tex]
Required
The expected flight time
To do this, we simply calculate the mean using:
[tex]Mean = \frac{a + b}{2}[/tex]
So, we have:
[tex]Mean = \frac{2\ hours + 2\ hours\ 20\ mins}{2}[/tex]
[tex]Mean = \frac{4\ hours\ 20\ mins}{2}[/tex]
[tex]Mean = 2\ hours\ 10\ mins[/tex]
a bus carry 53 passengar on a trif. how many passenger can 9 such carry if each dose 2 trif
Answer:
954 passengers
Step-by-step explanation:
(Assuming I read the question correctly)
1 bus can carry in 1 trip = 53 passengers
1 bus can carry in 2 trips : 106 passsengers
9 busses can carry in 2 trips = 106 x 9 = 954
Answred by Gauthmath
find the surface area of the triangular prism below.
Step-by-step explanation:
At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.
Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.
Then that's your answer.
9514 1404 393
Answer:
544 square units
Step-by-step explanation:
The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...
A = 1/2bh . . . . area of a triangle with base b and height h
A = LW . . . . . are of a rectangle of length L and width W
__
SA = 2(1/2)(12)(8) + (10 +10 +12)(14)
SA = 96 +448 = 544 . . . square units
I NEED HELP PLEASE ASAP!!
Answer:
Option B, 1
Step-by-step explanation:
tan 45° = 1/1 = 1
Factor this polynomial expression.
3x^2 - 12x+ 12
A. (3x - 2)(x-6)
B. 3(x-2)(x + 2)
C. 3(x-2)(x-2)
D. 3(x + 2)(x + 2)
hlo anyone free .... im bo r ed
d
Step-by-step explanation:
Excuse me! Who r u? where r u frm? tell me tht frst.
Answer:
Oop
Step-by-step explanation:
I’m bored
Which choice correctly shows the solution(s) of the equation x2 = 1442
A)
x= √144
B)
x=V12
X=-
-V144
D)
x = 1V144
Answer:
Step-by-step explanation:
If the 2s are exponents, you need to indicate this with "^":
x^2 = 144^2 means x² = 144²
x = ±√144² = ±144
Answer:
Step-by-step explanation:
f the 2s are exponents, you need to indicate this with "^":
x^2 = 144^2 means x² = 144²
x = ±√144² = ±144
Issac put $5 in a shoe box every day for the months of april, may, and june. He then spent 75% of the money on baseball cards. How much money is left in his shoe box.
Lấy ngẫu nhiên 25 lọ thuốc Vitamin tổng hợp do một máy tự động đóng chai ta thu được s'2 =0,012(l2).Máyđượcgọilàđạtchuẩnnếuđộphântántheoquyđịnhlà2 =0,005(l2). Với mức ý nghĩa 0,05 hãy kiểm định máy đóng chai có đạt chuẩn không? Biết lượng thuốc trong chai là biến ngẫu nhiên có phân phối chuẩn.
Answer:
I really can't read this
Step-by-step explanation:
I need help please can not figure out this problem
x^ 3 +x^ 2 +4x/x^ 2 +x-2
into partial
fractions
Answer:
x + (4/ x-2) + (2/ x-1)
Step-by-step explanation:
x + (6x/ x^2 + 2x - x -2)
x + (6x/ (x + 2) X (x - 1))
(6x/ (x + 2) X (x - 1))
(A/ x+2) + (B/ x-1)
(6x/ (x + 2) X (x - 1)) = (A/ x+2) + (B/ x-1)
6x = Ax + Bx - A + 2B
6x = (A+B)x + (-A+2b)
{0 = -A+2B
{6 = A+B
(A,B) = (4, 2)
(4/ x+2) + (2/ x-1)
x + (4/ x-2) + (2/ x-1)
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
VW ≈ 4.0
Step-by-step explanation:
Using the sine ratio in the right triangle
sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{VW}{VX}[/tex] = [tex]\frac{VW}{7}[/tex] ( multiply both sides by 7 )
7 × sin35° = VW , then
VW ≈ 4.0 ( to the nearest tenth )
Shortern this expression pls
Answer:
[tex]c =\frac{8}{3}[/tex]
Step-by-step explanation:
Given
[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]
Required
Shorten
We have:
[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]
Rationalize
[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}[/tex]
Expand
[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} + \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}[/tex]
[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} + \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}[/tex]
[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} + \sqrt{\frac{(4 - \sqrt 7)^2}{9}[/tex]
Take positive square roots
[tex]c =\frac{4 + \sqrt 7}{3} + \frac{4 - \sqrt 7}{3}[/tex]
Take LCM
[tex]c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}[/tex]
Collect like terms
[tex]c =\frac{4 + 4+ \sqrt 7 - \sqrt 7}{3}[/tex]
[tex]c =\frac{8}{3}[/tex]
find the area of the semi circle plss
Answer:
Step-by-step explanation:
A researcher wants to better understand the health benefits of eating vegetables. In a study he finds 300 adults aged 45-60 who eat at least 3 servings of vegetables a day on average. He finds another 200 adults who eat less than 3 servings of vegetables a day on average. The researcher looks at rates of cancer and heart disease in each group and compares both groups. In another study, the researcher finds 500 adults aged 45-60 who eat less than 3 servings of vegetables a day on average, and are willing to participate in a study. The researcher randomly assigns 250 of these adults to a diet which includes 4 servings of vegetables a day. The other 250 continue their usual habits. After 4 years, the rates of cancer and heart disease between the two groups are compared
Identify the statement that correctly states the reason for considering the first study as an observational study and second study as an experiment.
a. In the first study, the treatment is not imposed on the subjects, whereas in the second study the treatment is imposed on the subjects.
b. In the first study, the treatment is not imposed on every subject, whereas in the second study the treatment is imposed on every subject.
c. In the first study, the subjects were not randomly chosen, whereas in the second study the subjects were randomly assigned.
Answer:
a. In first study, the treatment is not imposed on the subjects, whereas in the second study the treatment is imposed on subjects.
Step-by-step explanation:
In the first study, observation are made on 300 adults who eat 3 servings of vegetables a day on average. The second study has further intensified the research which imposed treatment on the subjects. The random samples of adults are observed in both studies.
In what quadrant would the triangle be if rotated 90 degrees
I strongly believe the answer is 2, if it isnt that it must be 3.
"Rotated around the origin", as the question actually says, puts it in Quadrant-II (2).
But the way you put the question, just saying the triangle is rotated 90°, leaves it right where it is, in Quadrant-I, with vertex-H on the bottom.
I NEED HELP PLEASE!!!
The problem solving plan identifies steps to organize your information. Which of the following answer choices are included in the steps to organize your information?
A. Organize the problem and find the question.
B. Solve the problem and change your strategy if necessary.
C. Write the facts, organize your thoughts and define your strategy.
D. Organize the steps and underline the question.
c.write the fact,organize your thoughts and define your strategy.
Answer:
c
Step-by-step explanation:
Find the length of AB
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the given angle, we know the opposite side and want to know the hypotenuse. Therefore, we should use the sine function.
sin(54) = 16/AB
AB = 16/sin(54)
AB = 19.78 units
Hope this helps!
Suppose X has an exponential distribution with mean equal to 16. Determine the following:
(a) P(x >10) (Round your answer to 3 decimal places.)
(b) P( >20) (Round your answer to 3 decimal places.)
(c) P(x < 30) (Round your answer to 3 decimal places.)
(d) Find the value of x such that P(X 〈 x) = 0.95. (Round your answer to 2 decimal places.)
PLEASEEEE HELP
In the diagram, AABC-ADEC What is the value of x?
Similar triangles are proportional, meaning one will be a factor larger or smaller than the other. This factor will be the same for all of the sides. So, we can say that one corresponding pair of sides is equal to another corresponding pair of sides.
BA / ED = AC / CD
42 / 6 = (64 - x) / (x)
6(64 - x) = 42(x)
384 - 6x = 42x
384 = 48x
x = 8
Hope this helps!
Which equation has a graph that is a parabola with a vertex at (-2, 0)?
y= -2x^2
y = (x + 2)^2
y= (x – 2)^2
y= x^2 – 2
A survey asked 25 students about their favorite sport. A frequency table of their responses is below.
Basketball, 4; football, 7; lacrosse, 3; soccer, 8; volleyball, 3.
Which of the following is the correct relative frequency table for the students’ favorite sport?
Answer: The second one
Step-by-step explanation:
response/25=x/100 and then you solve for x
A percentage is a way to describe a part of a whole. The correct table is B.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given the number of students who play different sports as,
Basketball = 4
Football = 7
Lacrosse = 3
Soccer = 8
Volleyball = 3
Now, the percentage of students for each sport can be written as,
Basketball = 4/25 = 0.16
Football = 7/25 = 0.28
Lacrosse = 3/25 = 0.12
Soccer = 8/25 = 0.32
Volleyball = 3/25 = 0.12
Hence, the correct table is B.
Learn more about Percentages here:
https://brainly.com/question/6972121
#SPJ2
How many women must be randomly selected to estimate the mean weight of women in one age group? We want 90% confidence that the sample mean is within 3.7 lbs of the populations mean, and population standard deviation is known to be 28 lbs.
Answer:
155 women must be randomly selected.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The population standard deviation is known to be 28 lbs.
This means that [tex]\sigma = 28[/tex]
We want 90% confidence that the sample mean is within 3.7 lbs of the populations mean. How many women must be sampled?
This is n for which M = 3.7. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]3.7 = 1.645\frac{28}{\sqrt{n}}[/tex]
[tex]3.7\sqrt{n} = 1.645*28[/tex]
[tex]\sqrt{n} = \frac{1.645*28}{3.7}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*28}{3.7})^2[/tex]
[tex]n = 154.97[/tex]
Rounding up:
155 women must be randomly selected.
Diego made the shape on the left and Elena made the shape on the right. Each shape uses 5 circles.
Answer:
a
Step-by-step explanation:
(4x^5)^3 what is the equivalent?
[A] 4x^5+3
[B] 4x^5*3
[C] 4^3x^5+3
[D] 4^3x^5*3
Answer:
A
Step-by-step explanation:
They are different exponents but they have the same bas so you add them up.
4x^5+3 = 4x^8
[tex] \pink{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: as \: we \: know \: that \\ \\ \bf\: \: \rightarrow \: {(xy)}^{n} = {x}^{n} . {y}^{n} \\ \\ \bf \rightarrow \: {( {a}^{m} })^{n} = {a}^{m \times n} \\ \\ \bf \: now \\ \: \\ \blue{ {\boxed{\begin{array}{cc} \maltese \bf\: \: \: {(4 {x}^{5} })^{3} \\ \bf = {4}^{3} \times ({x}^{5} )^{3} \\ \bf = {4}^{3} \times {x}^{5 \times 3} \end{array}}}}\end{array}}}}[/tex]
So option D) is the correct answer
