The required expressions are both equations 1 and 2 as shown:
[tex]s + t = 90 ......... 1[/tex]
[tex]t<2s[/tex] .... 2
Complementary angles are angles that sum up to 90 degrees. For instance, and A and B are complementary if A + B = 90.
According to the question, if two complementary angles have measures of s and t then:
[tex]s + t = 90 ......... 1[/tex]
Twice of 's' is expressed as [tex]2s[/tex]
If t is less than twice s, this can be expressed as [tex]t<2s[/tex] .... 2
The required expressions are both equations 1 and 2 as shown:
[tex]s + t = 90 ......... 1[/tex]
[tex]t<2s[/tex] .... 2
Learn more on word problems leading to simultaneous equations here: https://brainly.com/question/14294864
help with q25 please. Thanks.
First, I'll make f(x) = sin(px) + cos(px) because this expression shows up quite a lot, and such a substitution makes life a bit easier for us.
Let's apply the first derivative of this f(x) function.
[tex]f(x) = \sin(px)+\cos(px)\\\\f'(x) = \frac{d}{dx}[f(x)]\\\\f'(x) = \frac{d}{dx}[\sin(px)+\cos(px)]\\\\f'(x) = \frac{d}{dx}[\sin(px)]+\frac{d}{dx}[\cos(px)]\\\\f'(x) = p\cos(px)-p\sin(px)\\\\ f'(x) = p(\cos(px)-\sin(px))\\\\[/tex]
Now apply the derivative to that to get the second derivative
[tex]f''(x) = \frac{d}{dx}[f'(x)]\\\\f''(x) = \frac{d}{dx}[p(\cos(px)-\sin(px))]\\\\ f''(x) = p*\left(\frac{d}{dx}[\cos(px)]-\frac{d}{dx}[\sin(px)]\right)\\\\ f''(x) = p*\left(-p\sin(px)-p\cos(px)\right)\\\\ f''(x) = -p^2*\left(\sin(px)+\cos(px)\right)\\\\ f''(x) = -p^2*f(x)\\\\[/tex]
We can see that f '' (x) is just a scalar multiple of f(x). That multiple of course being -p^2.
Keep in mind that we haven't actually found dy/dx yet, or its second derivative counterpart either.
-----------------------------------
Let's compute dy/dx. We'll use f(x) as defined earlier.
[tex]y = \ln\left(\sin(px)+\cos(px)\right)\\\\y = \ln\left(f(x)\right)\\\\\frac{dy}{dx} = \frac{d}{dx}\left[y\right]\\\\\frac{dy}{dx} = \frac{d}{dx}\left[\ln\left(f(x)\right)\right]\\\\\frac{dy}{dx} = \frac{1}{f(x)}*\frac{d}{dx}\left[f(x)\right]\\\\\frac{dy}{dx} = \frac{f'(x)}{f(x)}\\\\[/tex]
Use the chain rule here.
There's no need to plug in the expressions f(x) or f ' (x) as you'll see in the last section below.
Now use the quotient rule to find the second derivative of y
[tex]\frac{d^2y}{dx^2} = \frac{d}{dx}\left[\frac{dy}{dx}\right]\\\\\frac{d^2y}{dx^2} = \frac{d}{dx}\left[\frac{f'(x)}{f(x)}\right]\\\\\frac{d^2y}{dx^2} = \frac{f''(x)*f(x)-f'(x)*f'(x)}{(f(x))^2}\\\\\frac{d^2y}{dx^2} = \frac{f''(x)*f(x)-(f'(x))^2}{(f(x))^2}\\\\[/tex]
If you need a refresher on the quotient rule, then
[tex]\frac{d}{dx}\left[\frac{P}{Q}\right] = \frac{P'*Q - P*Q'}{Q^2}\\\\[/tex]
where P and Q are functions of x.
-----------------------------------
This then means
[tex]\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 + p^2\\\\\frac{f''(x)*f(x)-(f'(x))^2}{(f(x))^2} + \left(\frac{f'(x)}{f(x)}\right)^2 + p^2\\\\\frac{f''(x)*f(x)-(f'(x))^2}{(f(x))^2} +\frac{(f'(x))^2}{(f(x))^2} + p^2\\\\\frac{f''(x)*f(x)-(f'(x))^2+(f'(x))^2}{(f(x))^2} + p^2\\\\\frac{f''(x)*f(x)}{(f(x))^2} + p^2\\\\[/tex]
Note the cancellation of -(f ' (x))^2 with (f ' (x))^2
------------------------------------
Let's then replace f '' (x) with -p^2*f(x)
This allows us to form ( f(x) )^2 in the numerator to cancel out with the denominator.
[tex]\frac{f''(x)*f(x)}{(f(x))^2} + p^2\\\\\frac{-p^2*f(x)*f(x)}{(f(x))^2} + p^2\\\\\frac{-p^2*(f(x))^2}{(f(x))^2} + p^2\\\\-p^2 + p^2\\\\0\\\\[/tex]
So this concludes the proof that [tex]\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 + p^2 = 0\\\\[/tex] when [tex]y = \ln\left(\sin(px)+\cos(px)\right)\\\\[/tex]
Side note: This is an example of showing that the given y function is a solution to the given second order linear differential equation.
What is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is thirty five degrees and the other is unknown.
Answer:
145
Step-by-step explanation:
Angles in a straight line = 180
So,
Let unkown angle be x,
x+35=180
x=180-35
x=145
Heather, a sociology major is interested in studying mass media topics. She is particularly interested in the percentage of mass media topics that relate to entertainment. Based on previous research, 72% of mass media topics relate to entertainment. She suspects this percent is different. During the process of hypothesis testing, she calculates a probability using the test statistic. What is the probability associated with the test statistic called
Answer:
Pvalue
Step-by-step explanation:
The Pvalue measure which takes up a value in the range 0 - 1 is a statistical measure used on hypothesis testing to measure the likelihood of obtaining result atleast as extreme as the outcome of the statistical hypothesis test, The Pvalue is used in hypothesis testing to make a case for the alternative hypothesis, which involves being compared with the α - value.
Lower p values favors the adoption of alternative depending on how extreme th α-value is. The Pvalue is dependent on the value if the test statistic.
Can u please help I got 1 minnnn lefttttt
Answer:
26 cm
Step-by-step explanation:
P = 2a + 2b
a = side
b = base
Answer:
The area=base×height
=10×4
=40cm^2
perimeter=2(length+breadth)
I think to find the height Dc you use the pythagoras theorem of
Dc^2=de^2+ce^2
=√16+9
=5
therefore the perimeter will be
p=2(5+10)
=20cm
I hope this helps and sorry if it's wrong
Find the 5 data points needed for a box plot of the given data set: { 8, 19, 11, 20, 2, 14, 17, 9, 15}
Give the answers in order from least to greatest.
Data Point 1:
Data Point 2:
Data Point 3:
Data Point 4:
Data Point 5:
Answers:
Data Point 1: 2 Data Point 2: 8.5 Data Point 3: 14 Data Point 4: 18 Data Point 5: 20The boxplot is shown below.
=========================================
Explanation:
What your teacher wants is the five number summary.
This consists of:
MinQ1MedianQ3MaxGiven in that exact order.
The given data set is { 8, 19, 11, 20, 2, 14, 17, 9, 15}
This sorts to {2, 8, 9, 11, 14, 15, 17, 19, 20}
From this sorted set, we see that 2 is the smallest item. So this is the min value. This is data point 1.
The max is the largest item, which in this case is 20, so this value goes in the box for data point 5.
---------------------
Count out the number of values in the sorted set. You should count out n = 9 items.
Because n is odd, this means the median is in slot n/2 = 9/2 = 4.5 = 5
The value in the 5th slot is 14 which is the median (data point 3).
-----------------------
Once you determine the median, break the sorted set up like so
L = {2, 8, 9, 11}
U = {15, 17, 19, 20}
L is the lower set of values smaller than the median
U is the upper set of values larger than the median
The median itself is not part of set L and not part of set U either. It's ignored entirely from this point on.
From here, we find the middle values of L and U
You should find that the middle value of L is (8+9)/2 = 17/2 = 8.5 which is the value of Q1 (data point 2)
And also, the middle value of set U is (17+19)/2 = 36/2 = 18 which is the value of Q3 (data point 4)
-----------------------
To wrap everything up, we have this five number summary
Min = 2Q1 = 8.5Median = 14Q3 = 18Max = 20These will determine the features of the boxplot as shown below.
In this case, there are no outliers.
Jorge plans to paint a bedroom wall that is shaped like a trapezoid. The bottom edge of the wall is 22.5 feet long, and the top edge of the wall is 9.5 feet long. If the wall is 8 feet tall, what is the area of the wall? Round your answer to the nearest hundredth if necessary.
You play a game where you roll a single die. You pay $1 to play, and the payouts are $0.50 if you roll an
even number, $2 if you roll a 1, and $1 if you roll a 3 or 5. What are the odds for winning money if you play this game? Show your work and Explain.
Let W be the random variable representing your winnings from playing the game. Then
[tex]P(W=w)=\begin{cases}\text{prob. of rolling an even number}=\frac12&\text{if }w=\$0.50-\$1=-\$0.50\\\text{prob. of rolling a 1}=\frac16&\text{if }w=\$2-\$1=\$1\\\text{prob. of rolling 3 or 5}=\frac13&\text{if }w=\$1-\$1=\$0\\0&\text{otherwise}\end{cases}[/tex]
In short, you have a 1/6 chance of profiting from the game, and a 5/6 chance of losing money. So the odds of winning are (1/6)/(5/6) = 1/5 or 1 to 5.
Lines of symmetry give e the answer
Answer:
4
Step-by-step explanation:
There are 4 reflectional symmetry
A pole that is 3 m tall casts a shadow that is 1.23 m long. At the same time, a nearby building casts a shadow that is 42.75 m long. How tall is the building? round your answer to the nearest meter.
Answer:
Hello,
Just using the theorem of Thalès,
Step-by-step explanation:
Let say h the hight of the building
[tex]\dfrac{h}{3} =\dfrac{42.75}{1.23}\\\\h=104.268296...\approx{104(m)}[/tex]
Twenty-seven minus 3/2 of a number (x) os not mpre than 36. What is the number?
Answer:
-6
Step-by-step explanation:
27-3/2x=36
53-3x=72
3x=-18
x=-6
If you were asked to measure the success of a campaign to fight for human rights, what criteria would you use?
Step-by-step explanation:
Many factors would be used to assess the effectiveness of a human rights campaign, including the following:
Social Influence. Direct Interpersonal Reach. Participant Observation. Reputation. Volume of Search & Interest. Website Traffic.
National Research.
An ice cream store determines the cost of its sundaes by using the formula C = 0.50s + 0.35n + 0.25t, where C is the total cost in dollars, s is the number of scoops of ice cream, n is the number of scoops of nuts, and t is the number of liquid toppings. A Nutty Sundae costs $3.55. It has 3 scoops of nuts and 2 different liquid toppings. How many scoops of ice cream are in this sundae?
Answer:
4 scoops of ice cream
Step-by-step explanation:
Plug in the total cost, number of scoops of nuts, and number of liquid toppings into the formula. Then, solve for s:
C = 0.50s + 0.35n + 0.25t
3.55 = 0.50s + 0.35(3) + 0.25(2)
3.55 = 0.50s + 1.05 + 0.5
3.55 = 0.50s + 1.55
2 = 0.50s
4 = s
So, the sundae had 4 scoops of ice cream.
What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right and four units upward?
A)
K′ = (–2,0), L′ = (1,0), M′ = (1,–3), N′ = (–2,–3)
B)
K′ = (–2,2), L′ = (1,2), M′ = (1,–1), N′ = (–2,–1)
C)
K′ = (–0,0), L′ = (3,0), M′ = (3,–1), N′ = (0,–1)
D)
K′ = (–2,–2), L′ = (1,–2), M′ = (1,–5), N′ = (–2,–5)
9514 1404 393
Answer:
B) K′ = (–2,2), L′ = (1,2), M′ = (1,–1), N′ = (–2,–1)
Step-by-step explanation:
Translation 2 units right adds 2 to the x-coordinate.
Translation 4 units upward adds 4 to the y-coordinate.
The translation can be represented by the relation ...
(x, y) ⇒ (x +2, y +4)
__
You can choose the correct answer by looking at the translation of K.
K(-4, -2) ⇒ K'(-4+2, -2+4) = K'(-2, 2) . . . . . matches choice B
Find an equation of the line through the given pair of points. (-7,-5) and (-1,-9) The equation of the line is (Simplify your answer. Type an equation using x and y as the variables. Use integers or fractions for any numbers in the equation.) please help
Answer:
The equation of the line is y = -2/3x - 29/3
Step-by-step explanation:
The slope of these points (-7,-5) and (-1,-9) is m = -2/3
Once you plug that into the y = mx + b equation, you can see that the y-intercept is -29/3.
Put all of that into the y = mx + b equation and you'll get --> y = -2/3x - 29/3
Been stuck for 30 mins now please help !!!
Answer:
D) y = 2x + 1
Step-by-step explanation:
Thank you guys fir the help
Find f′ in terms of g′
f(x)=x2g(x)
Select one:
f′(x)=2xf′(x)+2xg′(x)
f′(x)=2xg′(x)
f′(x)=2x+g′(x)
f′(x)=x2g(x)+2x2g′(x)
f′(x)=2xg(x)+x2g′(x)
9514 1404 393
Answer:
(e) f′(x)=2xg(x)+x²g′(x)
Step-by-step explanation:
The product rule applies.
(uv)' = u'v +uv'
__
Here, we have u=x² and v=g(x). Then u'=2x and v'=g'(x).
f(x) = x²·g(x)
f'(x) = 2x·g(x) +x²·g'(x)
Please help this is due at 11:59 and im really stuck.
9514 1404 393
Answer:
B B C C A A
Step-by-step explanation:
If we number the equations 1 to 6 left to right, then we have ...
B - can be put (y = 2x)B - can be put (y = (1/9)x)C - other, not a proportional relationshipC - other, y = 5/x, an inversely proportional relationshipA - has the form, k = 0.04A - has the form, k = -118. Add.
445,976 + 37,415 =
A physical trainer decides to collect data to see if people are actually weight changing weight during the shelter in place. He believes there will not be a meaningful change in weight due to the shelter in place order. He randomly chooses a sample of 30 of his clients. From each client, he records their weight before the shelter in place order, and again 10 days after the order. A summary of the data is below.
The trainer claims, "on average, there is no difference in my clients' weights before and after the shelter in place order." Select the pair of hypotheses that are appropriate for testing this claim.
H0: µd = 0
H1: µd < 0 (claim)
H0: µd = 0 (claim)
H1: µd ≠ 0
H0: µd ≠ 0 (claim)
H1: µd = 0
H0: µd = 0 (claim)
H1: µd > 0
H0: µd = 0
H1: µd > 0 (claim)
H0: µd = 0
H1: µd ≠ 0 (claim)
H0: µd = 0 (claim)
H1: µd < 0
H0: µd ≠ 0
H1: µd = 0 (claim)
b) Select the choice that best describes the nature and direction of a hypothesis test for this claim.
This is a right-tail t-test for µd.
This is a right-tail z-test for µd.
This is a two-tail t-test for µd.
This is a two-tail z-test for µd.
This is a left-tail t-test for µd.
This is a left-tail z-test for µd.
c) Find the standardized test statistic for this hypothesis test. Round your answer to 2 decimal places.
d) Find the P-value for this hypothesis test. Round your answer to 4 decimal places.
e) Using your previous calculations, select the correct decision for this hypothesis test.
Fail to reject the alternative hypothesis.
Reject the alternative hypothesis.
Fail to reject the claim.
Reject the claim.
Fail to reject the null hypothesis.
Reject the null hypothesis.
f) Consider the following statements related to the trainer's claim. Interpret your decision in the context of the problem (ignoring the claim) and interpret them in the context of the claim.
Answer:
H0: µd = 0 (claim)
H1: µd ≠ 0
This is a two-tail t-test for µd
Step-by-step explanation:
This is a paired (dependent) sample test, with its hypothesis is written as :
H0: µd = 0
H1: µd ≠ 0
From the equality sign used in the hypothesis declaration, a not equal to ≠ sign in the alternative hypothesis is used for a two tailed t test
The data isn't attached, however bce the test statistic cannot be obtained. However, the test statistic formular for a paired sample is given as :
T = dbar / (Sd/√n)
dbar = mean of the difference ; Sd = standard deviation of the difference.
Hot-dog buns come in packages of 10. Wieners come in
packages of 12. Barry would like to buy the smallest
number of hot-dog buns and wieners so that he will have
exactly 1 wiener per bun. How many packages of hot-dog
buns and wieners must he buy?
A 6 packages of buns, 5 packages of wieners
B 5 packages of buns, 5 packages of wieners
C 8 packages of buns, 7 packages of wieners
05 packages of buns, 4 packages of wieners
Answer:
A 6 Packages of buns and 5 packages of wieners.
Step-by-step explanation:
Because if you multiply 6x10 you get 60 and if you multiply 5x12 you get 60 exactly 1 wieners per bun
Q-21: The regions of inequalities are also called:
A) Planes B) Lines C) Half planes D) None of these
Answer:
D ) none of these .. i think this help you
(b) If 124n= 232 five, find n.
Answer:[tex]n=\frac{58}{31}[/tex]
Step-by-step explanation:
[tex]124n=232\\\frac{124n}{124}=\frac{232}{124}\\n=\frac{232}{124}=\frac{58}{31}[/tex]
The value of n is 18.75. To find the value of n, we need to solve the equation: 124n = 232 five
Let's first convert "232 five" into a numerical value:
"232 five" means 2325 (since five is in the units place).
Now, the equation becomes:
124n = 2325
To solve for n, divide both sides of the equation by 124:
n = 2325 / 124
Now, perform the division:
n = 18.75
So, the value of n is 18.75.
To know more about equation:
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Question
Five people, each working 8 hours a day, can assemble 400 toys in a 5-day work week. What is the average
number of toys assembled per hour, per person?
Find the length of AC on this triangle
Answer:
A
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan12° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{44}[/tex] ( multiply both sides by 44 )
44 × tan12° = AC , then
AC ≈ 9.35 ( to 2 dec. places )
help please! I need the answer quickly! thank you!
Answer:
B) 1 unit to the left
Step-by-step explanation:
Stuck on this one!!
Shelly believes the honor roll students at her school have an unfair advantage in being assigned to the math class they request. She asked 500 students at her school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are shown in the table below:
Honor roll Not on honor roll Total
Received math class requested 125 215 340
Did not get math class requested 80 80 160
Total 205 295 500
Help Shelly determine if all students at her school have an equal opportunity to get into the math class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.
Answer: No, there isn't equal opportunity
======================================================
Explanation:
Let's define the two events
A = person is on the honor rollB = person got the math class they requestedFrom the table, we see that
P(B) = 340/500 = 0.68
meaning that there's a 68% chance of picking someone who got the class they wanted (i.e. 68% of the people got the class they wanted)
------------
Now let's assume that the person is on the honor roll. This means we only focus on the "honor roll" column. There are 125 people here that got the class they wanted out of 205 honor roll students total.
So,
P(B given A) = 125/205 = 0.609756
which rounds to 0.61
This says that if a person is on the honor roll, then they have roughly a 61% chance of getting the class they want.
The chances have gone down from 68% to 61% roughly.
------------
It appears that being on the honor roll does affect your chances of getting into the class you want.
Therefore, all students do not have the same equal opportunity.
We would need to have P(B) and P(A given B) to be the same exact value for true equal opportunity to happen.
All students do not have equal opportunity.
From the table, we have the following parameters:
205 people are on honor roll call340 people got the math class requested500 people were surveyedThe above means that:
The probability that a person is on honor roll call is:
p1 = 205/500
p1 = 0.41
The probability that a person got the math class requested
p2 = 340/500
p2 = 0.68
Both probabilities are not equal.
Hence, it is true that all students do not have equal opportunity.
Read more about probability at:
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a principal of $1500 is invested at 5.5 interest compounded annually. how much will the investment be worth after 7 years
Answer:
Step-by-step explanation:
1500(1.055)^7= 2182.02
There is only 3/4 cup of ice cream left. If 3 friends share the ice cream equally, how much ice cream will they each get?
Answer:
1/4 cup each
Step-by-step explanation:
Take the amount of ice cream and divide by 3
3/4÷ 3
Copy dot flip
3/4 * 1/3
Rewriting
3/3 * 1/4
1/4 cup each
1.8 times 15.42 please this question has me stuck
Answer:
27.756
Step-by-step explanation:
1) Move all the decimal points to the right and do the multiplication
18 * 1524 = 27756
1.8 to 19 = one move
15.42 to 1542 = two moves
total three decimal point shifts
2) count the number (total) that you moved the decimal points
3) starting from the right move the decimal point that many times to the LEFT in for the answer
27.756
