Answer:
3. A matched-pairs t-test with H0 : μd = 0, HA : μd ≠ 0
Step-by-step explanation:
An investigator wants to asses the difference in mean pulses rates between sitting and standing persons in population.
The matched paired t-test is appropriate choice because the observations in the data are paired. The observations in the data are the calculated pulse rates of 50 persons while sitting and standing. For each person. sitting and standing pulse rates are measured and this indicates the before and after effect is measured. The before and after effect is measured through matched paired t test.
Also, an investigator wants to determine whether there is difference in mean pulse rates between sitting and standing in population. This indicates two tailed test. so, the hypotheses would be
Null hypotheses : μd = 0
Alternative hypotheses: μd ≠ 0.
Thus, situation indicates a matched-pairs t-test with H0 : μd = 0, HA : μd ≠ 0.
The option that represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population is: Option C: A matched-pairs t-test with [tex]H_0 : \mu_d = 0\\H_A : \mu_d \neq 0[/tex]
When do we use two-sample t-test?The two-sample t-test is used to determine if two population means are equal.
When there has to be done comparison between means of two sets of paired data, then we use matched pair t test.
How to form the hypotheses?There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.
Null hypothesis is the one which researchers try to disprove.
For this case, we want to determine if there is a difference in mean pulse rates between sitting and standing in the population.
That is the reason why we will use matched pair t-test.
Where paired data is the pair of data obtained from each of those 50 people, the pair of data being sitting pulse rate and standing pulse rate.
Now, since we want to determine if there's any difference, so the null hypothesis will nullify the presence of any difference.
Thus, we get:
Null hypothesis = [tex]H_0: \mu_d = 0[/tex] (the difference between mean of sitting pulse rate and that of standing pulse rate is 0, therefore no difference).
This can be rewritten as: [tex]H_0: \mu_{\text{sitting}} = \mu_{\text{standing}}[/tex]
Alternate hypothesis = [tex]H_A: \mu_d \neq 0[/tex] or [tex]H_A: \mu_{\text{sitting}} \neq \mu_{\text{standing}}[/tex]
Thus, the option that represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population is: Option C: A matched-pairs t-test with [tex]H_0 : \mu_d = 0\\H_A : \mu_d \neq 0[/tex]
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I WILL GIVE BRAINLIEST! 30 POINTS!
Koji is installing a rectangular window in an office building. The window is 823 feet wide and 534 feet high.
The formula for the area of a rectangle is A=bh.
What is the area of the window?
Enter your answer as a mixed number in simplest form in the box.
$$
ft2 ( ? ) ( ? )
-------
( ? )
Answer:
Area = 823 * 534 = 439,482 ft^2
Step-by-step explanation:
I need ASAP!!
Find CU. If necessary, round answers to 4 decimal places
Answer:
The correct answer for this equational ratio is x = 5
Step-by-step explanation:
In order to calculate for x, we must create the necessary ratios
[tex]\frac{16}{20} = \frac{45-5x}{5x}[/tex]
Cross multiply to get
900 - 100x = 80x
900 = 180x
x = 5
WHAT IS (13X6)+89 WITH HE SECOND POWER? PLEASE HELP WILL MAKE BRAINLIEST
(13x6)+89 with the power of 2 is 7999
in massaschusetts a team of scientists studying great white sharks estimate that a population of 15000 seals support fewer than 100 sharks. why are there so few top level consumers in this system?
Answer:
The higher you go in the good chain the lower the population.
Explanation:
In the food web, there are only a few sharks since in the food chain they are higher. Just 10% energy is retained in the tissues once the energy is moved from one trophic level to another, and the leftover power is emitted as metabolic energy.
If an animal is high up the energy ladder, the individual has less resources; thus, a few of the highest predators are present in an ecosystem.
Answer:
because there are more sharks than seals in the area
Step-by-step explanation:
A large group of people is to be checked for two common symptoms of a certain disease. Itis thought that 20% of the people possess symptomAalone, 30% posseess symptomBalone,10% possess both symptoms, and the remainder have neither symptom. For one person chosen atrandom from this group, Ønd these probabilities:
a. (2 points) that the person has neither symptom
P(A\πB)=0:20
P(πA\B)=0:30
P(A\B)=0:10
P(πA\πB)=1°P(A[B)
P(πA\πB)=1°[P(A\πB)+P(πA\B)+P(A\B)]
=1°(0:20+0:30 + 0:10)
=1°0:60
=0:40
b. (2 points) that the person has at least one symptom
P(A[B)=P(A\πB)+P(πA\B)+P(A\B)
=0:20 + 0:30+10
=0:60
or
P(A[B)=1°P(πA\πB)
=1°0:40
=0:60
c. (2 points) that the person has both symptoms, given that he has symptom
BP(AjB)=P(A\B)/P(B)
=P(A\B)P(A\B)+P(πA\B)
=0:100:10+0:30
=0:100:40
=0:25
Answer:
(a) and (b) are correct but (c) is not correct
Step-by-step explanation: (c) P(nA)*P(nB) + P(nA/nB)
0.20*0.30 + 0.10 = 0.060 + 0.10 = 0.160
Issa jogged two-thirds of the way home from school. Then he was tired, so he walked the remaining 3{,}200\text{ m}3,200 m3, comma, 200, start text, space, m, end text. How many kilometers did Issa travel from school to his house? kilometers
Answer:
9.6
Step-by-step explanation:
The question is :
Solution;
Let total distance from school to home = 'x' meters
Issa jogged 2/3rd of 'x'= [tex]\frac{2x}{3}[/tex]
So total distance from school to home = [tex]\frac{2x}{3} +3200[/tex]
But total distance from school to home = [tex]x[/tex]
[tex]==> \frac{2x}{3} + 3200 = x[/tex]
[tex]==> 3200= \frac{x}{3}[/tex]
[tex]==> 9600=x[/tex]
So total distance from school to home is 9600 meters
We convert it into km now
we know 1000 meters = 1km
==> 9600 meters = 1/100 x 9600= 9.6 km
Answer:
9.6 or (48\5
Step-by-step explanation:
Maria and Katy each have a piece of string. When they put the two pieces of string together end to end, the total length is 84inches. Maria's string is 6 inches longer than Katy's. How long is Maria's piece of string? How long is Katy's piece of string
Answer: the length of Maria's piece of string is 45 inches.
the length of Katy's piece of string is 39 inches
Step-by-step explanation:
Let x represent the length of Maria's piece of string.
Let y represent the length of Katy's piece of string.
When they put the two pieces of string together end to end, the total length is 84inches. This means that
x + y = 84 - - - - - - - - - - - -1
Maria's string is 6 inches longer than Katy's. This means that
x = y + 6
Substituting x = y + 6 into equation 1, it becomes
y + 6 + y = 84
2y + 6 = 84
2y = 84 - 6 = 78
y = 78/2 = 39
x = y + 6 = 39 + 6
x = 45
Find the least common denominator please
Answer:
(n -4)(n +1)^2 = n^3 -2n^2 -7n -4
Step-by-step explanation:
The least common denominator is the smallest denominator that lets you write the sum as a single fraction.
[tex]\dfrac{n^5}{n^2+2n+1}+\dfrac{-4}{n^2-3n-4}=\dfrac{n^5}{(n+1)^2}+\dfrac{-4}{(n+1)(n-4)}\\\\=\dfrac{n^5}{(n+1)^2}\cdot\dfrac{n-4}{n-4}+\dfrac{-4}{(n+1)(n-4)}\cdot\dfrac{n+1}{n+1}=\dfrac{n^5(n-4)-4(n+1)}{(n+1)^2(n-4)}\\\\=\dfrac{n^6-4n^5-4n-4}{n^3-2n^2-7n-4}[/tex]
The least common denominator is ...
(n-4)(n+1)^2 = n^3 -2n^2 -7n -4
How high is a tree that casts a 2222-ftft shadow at the same time a 44-ftft postpost casts a shadow which is 77-ftft long?
Answer: The height of the tree is 12.57 ft.
Step-by-step explanation:
The height of a thing is proportional to the its shadow.
Let H = Height and S = length of shadow
Then by equation direct proportion , [tex]\dfrac{H_1}{S_1}=\dfrac{H_2}{S_2}[/tex] (i)
Given : A tree that casts a 22 ft shadow at the same time a 4 ft postpost casts a shadow which is 7-ft long.
Put [tex]S_1=22 ,\ H_2= 4,\ \ S_2=7[/tex] in (i), we get
[tex]\dfrac{H_1}{22}=\dfrac{4}{7}\\\\ H_1=\dfrac{4}{7}\times22\approx12.57[/tex]
Hence, the height of the tree is 12.57 ft.
What the user said above!
Write a polynomial expression that represents the area of the trapezoid. (A=1/2h(b1+b2))
Answer:
[tex]A = 5 {x}^{2} + 6x + 1[/tex]
Step-by-step explanation:
[tex]A = \frac{(a + b)h}{2} = \frac{(6x - 5 + 4x + 7)(x + 1)}{2} = \frac{(10x + 2)(x + 1)}{2} = \frac{2(5x + 1)(x + 1)}{2} = 5 {x}^{2} + 6x + 1[/tex]
I'm need help a question and I'm confuse.
Answer:
Step-by-step explanation:
Since angle ABD is 133 degrees and the sum of the angles in a triangle is 180 degrees, it means that
m∠ DAB + 133 + 22 = 180
m∠ DAB = 180 - 155 = 25 degrees
Also, ∆ ADC is an isosceles triangle because two of its sides are equal. It also means that the base angles are equal. Thus,
m∠ A = m∠ B
Therefore,
m∠ A + m∠ B + angle D = 180
m∠ A + m∠ B = 180 - 22 × 2
m∠ A + m∠ B = 180 - 44 = 136
m∠ A = m∠ B = 136/2 = 68 degrees
m∠ CAB + m∠ DAB = m∠ A
Therefore,
m∠ CAB = 68 - 25 = 43 degrees
Since ∆ ABC is isosceles, then
m∠ CAB = m∠ ACB
m∠ ACB = 43 degrees
m∠ ABC = 180 - (43 × 2) = 180 - 86
m∠ ABC = 94 degrees
m∠ BCD = 68 - m∠ ACB
m∠ BCD = 68 - 43 = 25 degrees
The shark are fed three times a day during the morning feeding 2/15 of a ton. During the afternoon feeding the weight of fish fed will be 1/15 of a ton more than the fish fed during the morning if the total fish fed in a day is 1/2 of Aton how much is fed during the feeding in the night
Answer:
The shark are fed [tex]\frac16 \ ton[/tex] of fish during the night.
Step-by-step explanation:
Given:
Weight of fish fed in the morning = [tex]\frac{2}{15}\ ton[/tex]
Also Given:
During the afternoon feeding the weight of fish fed will be 1/15 of a ton more than the fish fed during the morning.
Weight of fish fed in the afternoon = [tex]\frac{2}{15}+\frac{1}{15}=\frac{2+1}{15}=\frac{3}{15}\ ton[/tex]
Total fish fed in whole day = [tex]\frac12 \ ton[/tex]
We need to find the Weight of fish fed in the night.
Solution:
Now we can say that;
Weight of fish fed in the night can be calculated by by subtracting Weight of fish fed in the morning and Weight of fish fed in the afternoon from Total fish fed in whole day .
framing in equation form we get;
Weight of fish fed in the night = [tex]\frac{1}{2}-\frac{2}{15}-\frac{3}{15}= \frac{1}{2}-(\frac{2}{15}+\frac{3}{15})=\frac{1}{2}-\frac{2+3}{15}= \frac{1}{2}-\frac{5}{15} = \frac{1}{2}-\frac{1}{3}[/tex]
Now we will use LCM for making the denominator common we get;
Weight of fish fed in the night = [tex]\frac{1\times3}{2\times3}-\frac{1\times2}{3\times2} = \frac{3}{6}-\frac{2}{6}[/tex]
Now denominator are common so we will solve the numerators.
Weight of fish fed in the night = [tex]\frac{3-2}{6}=\frac16 \ ton[/tex]
Hence The shark are fed [tex]\frac16 \ ton[/tex] of fish during the night.
If the eyepiece of a compound microscope has a magnification power of 10X and the objective lense has a magnification power of 4X, what is the total magnification of the microscope at this setting?
Answer:
Total magnification of microscope at this setting is 40X
Step-by-step explanation:
Total magnification of microscope is determined by multiplying the magnification power of individual lenses.
So if eyepiece has magnification power of 10X and objective lense has magnification power of 4X , the total magnification of microscope would be
10 × 4 = 40
which means the object will appear 40 times larger than actual object.
The total magnification of the microscope at this setting is 40X.
To determine the total magnification of a compound microscope, one needs to multiply the magnification power of the eyepiece by the magnification power of the objective lens. In this case, the eyepiece has a magnification power of 10X and the objective lens has a magnification power of 4X.
The formula for the total magnification [tex]\( M_{total} \)[/tex] is given by:
[tex]\[ M_{total} = M_{eyepiece} \times M_{objective} \][/tex]
Substituting the given values:
[tex]\[ M_{total} = 10X \times 4X \][/tex]
[tex]\[ M_{total} = 40X \][/tex]
Therefore, the total magnification of the microscope when using the 10X eyepiece and the 4X objective lens is 40X. This means that the image seen through the microscope will appear 40 times larger than its actual size.
A survey conducted by Black Flag asked whether the action of a certain type of roach disk would be effective in killing roaches. Seventy-nine percent of the respondents agreed that the roach disk would be effective. The number 79% is a(n) ________.a. population. b. statistic. c. parameter. d. sample.
Consider the matrices A = 2 1 2 2 2 −2 3 1 1 and x = x1 x2 x3
(a) Show that the equation Ax = x can be rewritten as (A − I)x = 0 and use this result to solve Ax = x for x.
(b) Solve Ax = 4
Answer:
94
Step-by-step explanation:
Jen has
25 Points.
The function f(x) = 4x + 3 represents the length of a rectangle. The function g(x) = 2x − 5 represents the width of the rectangle. Use (f • g)(4) to determine the area of the rectangle.
57
19
16
3
Answer:
57
Step-by-step explanation:
(f•g)(x) = f(x)•g(x)
= (4x+3)(2x-5)
= 8x²-20x+6x-15
= 8x²-14x-15
(f•g)(4) = [4(4)+3] [2(4)-5]
= (16+3)(8-5)
= 19 • 3
= 57
Answer:
57
Step-by-step explanation:
got it correct on test. :)
Does the graph represent a function ? Why or Why Not
This does NOT represent a function.
There should only be one pair per input and output, but this graph has multiple.
A windshield wiper blade turns through an angle of 135°. The bottom of the blade traces an arc with a 8-inch radius. The top of the blade traces an arc with a 24-inch radius. To the nearest inch, how much longer is the top arc than the bottom arc? Round to the nearest whole number.
Answer:142
2
+2
Step-by-step explanation:
For which function does f(14)=23?
A. (x)=12x−20
B. f(x)=14x+23
C. f(x)=3x−7
D. f(x)=x+9
Final answer:
By substituting x with 14 in each option, it is determined that option D, which is f(x) = x + 9, is the correct function where f(14) equals 23.
Explanation:
The student is asking to find the function for which f(14)=23. To answer this, we substitute x with 14 in each of the given options and see which one results in f(x) being equal to 23.
Substitute x=14 in f(x)=12x−20: f(14)=12(14)−20=168−20=148, which is not 23.
Substitute x=14 in f(x)=14x+23: f(14)=14(14)+23=196+23=219, which is not 23.
Substitute x=14 in f(x)=3x−7: f(14)=3(14)−7=42−7=35, which is not 23.
Substitute x=14 in f(x)=x+9: f(14)=14+9=23, which is the correct answer.
The correct function is D. f(x)=x+9.
Do you expect δhsoln to be a large positive number, a large negative number, or close to zero? do you expect to be a large positive number, a large negative number, or close to zero? δhsoln is a large positive number. δhsoln is a large negative number. δhsoln is close to zero.
Answer:
δhsoln will be close to zero.
Step-by-step explanation:
In calculus, the symbol d represents a large or significant increment in a value. For example, say the change in the volume of a liquid in a tank depends upon the change of the height h.
The above statement can be written like this:
dV/dh
This means that the volume of the tank (V) depends with a significant change in the height of the liquid (h).
It is also possible to compute small changes in physical quantities. The symbol δ simply presents a small increment or small change. Using the same expression above, if a very large tank was to have a very very small leak, the change would be: δV/δh
In other words, the change in the volume will be almost negligible and will be close to zero.
what is -5x -10= -20
a.2
b.3
c.7
d.6
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{-5x -10= -20}\\\\\large\text{ADD 10 to BOTH SIDES}\\\mathsf{-5x - 10 + 10 = -20 + 10}\\\\\large\text{SIMPLIFY IT!}\\\mathsf{-5x = -20 + 10}\\\mathsf{-5x = -10}\\\\\large\text{DIVIDE -5 to BOTH SIDES}\\\mathsf{\dfrac{-5x}{-5}= \dfrac{-10}{-5}}\\\\\large\text{SIMPLIFY IT!}\\\mathsf{x = \dfrac{-10}{-5}}\\\\\mathsf{x = 2}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{Option \ A. \ 2}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
Option a ( 2 ) is the answerStep-by-step explanation:
In this question we are given with an equation that is -5x - 10 = -20 . And we are asked to find it's solution ( value of x ).
Solution : -
[tex] \longmapsto \qquad \: - 5x - 10 = - 20[/tex]
Step 1 : Adding 10 to both sides :
[tex] \longmapsto \qquad \: - 5x - \cancel{10 }+ \cancel{10} = - \bold{20 }+ \bold{10}[/tex]
On further calculations , We get :
[tex] \longmapsto \qquad \: - 5x = - 10[/tex]
Step 2 : Dividing with -5 on both sides :
[tex] \longmapsto \qquad \: \dfrac{ \cancel{- 5}x}{ \cancel{- 5}} = \cancel{ \dfrac{ - 10}{ - 5} }[/tex]
On further calculations , we get :
[tex] \longmapsto \qquad \: \ \: \pink{\underline{ \boxed{\frak{x = 2}}}}[/tex]
Henceforth , value of x is 2 that means option a is correct .Verifying : -
Now we're verifying our answer by substituting value of x in given equation. So ,
-5x - 10 = -20-5 ( 2 ) - 10 = -20-10 - 10 = -20-20 = -20L.H.S = R.H.SHence , Verified .Therefore , our answer is correct .
#Keep LearningA baker has 15 cups of flour. He sets aside 4 cups, and uses the rest for a cookie recipe that calls for 1/2 cup of flour. How many batches of cookies can the baker make?
Answer:
So, 22 batches of cookies can the baker make.
Step-by-step explanation:
A baker has 15 cups of flour.
He sets aside 4 cups.
So, the remaining cups = 15 - 4 = 11
A cookie recipe that calls for 1/2 cup of flour.
So, x batches of cookies can the baker make with 11 cups
Use the ratio and proportional
1 : 1/2 = x : 11 ⇒ multiply both sides by 2
2 : 1 = 2x : 22
solve for x
2x = 2 * 22
x = 22
So, 22 batches of cookies can the baker make.
She can make 22 batches of cookies.
Given that there are 15 cups of flour. The baker sets aside 4 cups.
So remaining (15 - 4) = 11 cups.
Let she can make x batches.
Given each batch takes 1/2 cup.
That means she will need [tex]x\cdot\frac{1}{2}=\frac{x}{2}[/tex] cups.
According to the question:
[tex]\frac{x}{2}=11\\x=22[/tex]
So she can make 22 batches of cookies.
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Mr. Davis buys 5 packages of the package a glue sticks. Ms. Wilson buys 8 package of the package b glue sticks. Use your equations to find the difference in the total number of glue sticks that each person purchased.
To find the difference in the total number of glue sticks that Mr. Davis and Ms. Wilson purchased, subtract the number of glue sticks each person bought from one another.
Explanation:To find the difference in the total number of glue sticks that Mr. Davis and Ms. Wilson purchased, we can subtract the number of glue sticks each person bought from one another.
Mr. Davis bought 5 packages of glue sticks, and each package has a certain number of glue sticks in it.
Ms. Wilson bought 8 packages of glue sticks, and each package also has a certain number of glue sticks in it.
To find the difference, subtract the total number of glue sticks from Mr. Davis from the total number of glue sticks from Ms. Wilson.
For example, if each package of glue sticks contains 4 glue sticks, Mr. Davis purchased 5 x 4 = 20 glue sticks. Ms. Wilson purchased 8 x 4 = 32 glue sticks. The difference is 32 - 20 = 12 glue sticks.
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#SPJ12
Please help!! I don't know what to do :(
Find the value of x. Show all your work for full credit.
Yo sup??
This question can be solved by applying the properties of similar triangles
the triangle with sides 5x and 20 is similar to the triangle with sides 45 and 36
therefore we can say
5x/45=20/36
x=5 units
Hope this helps
The latest online craze is a new game, Khan on Seven. You get 100100100 points for playing the game. In addition, you get 505050 points for each seven-letter word you make with the ten letters you receive. Sal wants to break the record, and he needs 18{,}00018,00018, comma, 000 or more points to do so. Write an inequality to determine the number of seven-letter words, www, Sal could make to break the record.
Answer:
[tex]50w+100 \ge 18000[/tex]
Step-by-step explanation:
Each seven-letter word is worth 50 points. [tex]w[/tex] words are then worth [tex]w\times50=50w[/tex].
Since Sal gets 100 points for playing the game, his points total after [tex]w[/tex] words is [tex]50w +100[/tex]. If he wants to break the record, he must get, at least, 18000 points. "At least" in inequality means [tex]\ge[/tex] (just as "at most" means [tex]\le[/tex]). Then the required inequality is
[tex]50w+100 \ge 18000[/tex].
Note that the question says "18000 or more", which is why we used the [tex]\ge[/tex] symbol. If the phrase had been "more than 18000", we would have used [tex]>[/tex].
Jake shows that △ △ C B A is congruent to △ △ A D C by rotating △ 180° △ C B A 180 ° around point C so it matches up with △ △ A D C exactly. Which conclusion can be drawn from Jake's transformations?
Answer:
Reflection about either the x- axis or y- axis.
Step-by-step explanation:
It is likely that the triangle shows a mirror image when it has been rotated at point C so that it matches ΔADC.
The triangles are congruent if the sides and angles are equal. The only way to effect the change is through a rotation.
In fact, two objects are said to be congruent if they can be transformed into another shape by translation, rotation, and reflection.
The resulting image is a distinct figure that can fit and match the other completely.
In this case, the triangle is rotated through 180⁰ so the resulting image is a reflection or mirror image.
Answer:
If two pairs of angles and the included side are congruent, the triangles are congruent.
Step-by-step explanation:
itsLearning
WHAT IS 5/12 X - 1/2= 1/3
A. -1/72
B. 5/72
C. 2
D. 2/5
Answer:
C. 2
Step-by-step explanation:
Given:
[tex]\frac{5}{12}x-\frac12=\frac13[/tex]
We need to solve the equation to find the value of x.
Solution:
[tex]\frac{5}{12}x-\frac12=\frac13[/tex]
Combining like terms we get;
[tex]\frac{5}{12}x=\frac13+\frac12[/tex]
Now Using LCM for making the denominators same we get;
[tex]\frac{5}{12}x=\frac{1\times2}{3\times2}+\frac{1\times3}{2\times3}\\\\\frac{5}{12x}=\frac{2}{6}+\frac{3}{6}[/tex]
Now Denominators are common so we solve the number we get;
[tex]\frac{5}{12}x=\frac{2+3}{6}\\\\\frac{5}{12}x=\frac{5}{6}[/tex]
Now Dividing both side by [tex]\frac{12}{5}[/tex] we get;
[tex]\frac{5}{12}x\times \frac{12}{5}=\frac{5}{6}\times \frac{12}{5}\\\\x=2[/tex]
Hence the value of x is 2.
Joe traveled against the wind in a small plane for 3hours. The return trip with the wind took 2.8 hours. Find the speed of the wind to the nearest tenth if the speed of the plane in still air is 180 mph.
Answer: the rate of the wind is 6.2 mph
Step-by-step explanation:
Let x represent the rate of the wind.
Joe traveled against the wind in a small plane for 3hours. If the speed of the plane in still air is 180 mph, then the total speed with which the plane flew is
(180 - x) mph
Distance = speed × time
Therefore, distance travelled against the wind is
3(180 - x)
= 540 - 3x - - - - - - - - - - - - - -1
The return trip with the wind took 2.8 hours.
the total speed with which the plane flew is
(180 + x) mph
Therefore, distance travelled with the wind is
2.8(180 + x)
= 504 + 2.8x - - - - - - - - - - - - - -2
Since the distance is the same, then
540 - 3x = 504 + 2.8x
540 - 504 = 2.8x + 3x
5.8x = 36
x = 36/5.8 = 6.2
A shipping conpany is loading cube shaped crates into larger cube shaped container. The smaller cubes have side lenghts of 2 1/2 feet. And the larger shipping container has side lengths of 10 feet. How many crates will it feet in the large shipping container
Answer:
64
Step-by-step explanation:
10 ft is 4 times 2 1/2 ft, so the larger container has dimensions of 4 crates in every direction. That is, it will hold 4^3 crates, or 64 crates.
The graph shows how many meters above a stream, y, that a bucket on a water wheel is rotating for a given number of seconds x.
How many degrees is the bucket rotating in 10 s?
After 10 s, the bucket has rotated [tex]180^{\circ}[/tex]
Step-by-step explanation:
The motion of the bucket on the water wheel is a periodic motion, which means that it repeats itself periodically. The period of the motion is the time it takes for the bucket to returns to its original position: it can be found from the graph by looking at after how much time the graph has again the same shape.
We see that if we start from x = 0 seconds, then the graph has the same shape again (=it has completed one full cycle) at x = 20 seconds, so the period is
T = 20 s
This also means that in a time of 20 seconds, the bucket has covered a full revolution, so an angle of
[tex]\theta=360^{\circ}[/tex]
Therefore, in order to find how many degrees x the bucket has rotated in
t = 10 s
We can use the rule of three:
[tex]\frac{\theta}{T}=\frac{x}{t}[/tex]
And solving for x, we find
[tex]x=\frac{\theta t}{T}=\frac{(360)(10)}{20}=180^{\circ}[/tex]
Learn more about periodic motions:
brainly.com/question/5438962
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