If the bottom of the ladder slides away from the wall, then x changes by 12cosθ with respect to theta and when θ = π/6, x changes by 6[tex]\sqrt{3}[/tex] inches with respect to θ.
Here, we are given that a ladder 16 ft long rests against a vertical wall and theta is the angle between the top of the ladder and the wall.
We know that, sin of an angle = opposite / hypotenuse
Thus, sinθ = x/16
⇒ x = 16 sinθ
The rate of change of x with respect to θ will be given by dx/dθ
dx/dθ = d/dθ (12sinθ)
= 12 d/dθ (sinθ)
= 12cosθ
Now, we need to find the value of dx/dθ when θ = π/6,
= 12 cosπ/6
= 12 ([tex]\sqrt{3}[/tex]/2)
= 6[tex]\sqrt{3}[/tex]
Thus, when θ = π/6, x changes by 6[tex]\sqrt{3}[/tex] inches with respect to θ.
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Your question was incomplete. Check for full content below-
A ladder 12 feet long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall, and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π/6?
6+5m<1 how do I do this this is to hard
Answer: m < -1
Step-by-step explanation:
Step 1: 6 + 5m < 1. Step 2: 5m/5 < -5/5 m = -1
-6. -6
Answer: m < −1
Step-by-step explanation:
1. Rearange: 5m+6<1
2. 5 + 6−6 < 1−6
3. 5m < -5
4. 5m/5 < -5/5
5. Cancel terms that are in both the numerator and denominator then divide the numbers.
6. answer: m < -1
I need help with 1-4 please and thanks
Estimate intercepts of the graph of the functions
1. [tex]y=\frac{1}{3} x+1[/tex]
=>At x axis
x = 0
y= 0+ 1
y = 1
=>At y axis
y= 0
1/3x = -1
x= -3
The x intercepts:( -3, 0)
The y intercepts : (0,1)
2. [tex]y= x^{2} -3x-4[/tex]
=> At x axis
x=0
y= - 4
=> At y axis
y= 0
[tex]x^{2} -3x-4= 0[/tex]
(x-4)(x+1) = 0
x= 4,-1
The x intercepts: (4,0) ( -1, 0)
The y intercepts : (0,-4)
3. y= -2 |x-5|
=> At x axis
x=0
y= -2(5)
y= -10
=> At y axis
y= 0
-2|x-5|=0
Divide both sides by -2
|x - 5|= 0
x- 5 = 0
x = 5
The x intercepts: (5,0)
The y intercepts : (0,-10)
4. [tex]y= -4x^{3} -13x^{2} -10x[/tex]
=> At x axis
x= 0
y = 0
=>At y axis
y=0
[tex]0=-4x^{3} -13x^{2} -10x \\\\4x^{3} +13x^{2} +10x =0[/tex]
By factorization ,
x( 4x+5 )( x+2)= 0
x= 0, -2, -5/4
The x intercepts: (0,0) (-2,0) ,(-5/4,0)
The y intercepts: (0,0)
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Premises:
If I'm a student, then I go to school. If I go to school, then I learn.
Conclusion:
If I'm a student, then I learn.
This is an example of the Law of
The given statement is an example of the law of detachment.
Given that,
Premises:
If I'm a student, then I go to school. If I go to school, then I learn.
Conclusion:
If I'm a student, then I learn.
This is an example of the Law of which is to be determined.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Following the statement given in the premises gives a certain conclusion which shows the detachment behavior.
Thus, the given statement is an example of the law of detachment.
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kusa rode his bike for 10 miles /hour for 0.75 hours chaman rode his bike for 12 mile/hour for 0.6 hours
need please asap will give brainlyies
who rode farthur and how far did trhat person ride?
A. kusa he rode 10 miles
B. kusa he rode 7.5 miles
C. charman he rode 6 miles
D. charman he rode 7.2 miles
Answer:
B
Step-by-step explanation:
Kusa=10x0.75=7.5
Chaman=12x0.6=7.2
7.5>7.2
so kusa rode further than chaman.
Answer:
b
Step-by-step explanation:
Hong has 16 one-dollar bills. he wants to give each of his 6 children the same number of bills. how many bills can he give each child? how many bills will hong have remaining?
Hong has 16 one-dollar bills. he wants to give each of his 6 children the same number of bills. Then Hong will give 12 bills to his 6 children and 4 bills Hong have remained
Hong has 16 one-dollar bills.
he wants to give each of his 6 children the same number of bills.
how many bills can he give each child?
how many bills will Hong have remaining?
since Hong has 16 one dollar bills and he wants 6 children the same number of bills
then he give 6 children two bills to each
then the total number of bills he give to 6 children is 12
and he has 16 bills and 12 bills give to his children
the remaining bills left = 16 bills - 12 bills = 4 bills
Hence , Hong will give 12 bills to his 6 children and 4 bills Hong have remained
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Shanika is thinking of a rational number, but tells you its opposite. What is true about the number she is thinking of?
a- it is located at zero on the number line
b-it is to the right of zero on the number line
c- it is twice as far from zero as the number she tells you
d-it is the same distance from zero as the number she tells you
Answer:
d. It is the same distance from zero as the number she tells you.
Step-by-step explanation:
Case 1: Let Shanika thought a positive rational
number
Let the number that Shanika thought be c.
Then, the distance of it from zero = lc - Ol = c.
But, the number she told = -c
The distance of -c from zero = 10--(-c)| = c
Case 2: Let Shanika thought a negative rational number
Let the number that Shanika thought be -c (c>0).
Then, the distance of it from zero = 10--(-c)| = c.
But, the number she told = c
The distance of -c from zero = Ic-01 = c
In both cases, the number she thought is the same distance from zero as the number she tells us.
A researcher is testing the effect of a new cold and flu medication on reaction time. A sample of n=16 students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each student’s reaction time is measured. The scores for the sample averaged 220 milliseconds with a standard deviation of 20. Assuming that reaction time for students in the regular population averages 200 milliseconds, are the data sufficient to conclude that the medication has a significant effect on reaction time? Use a two-tailed single-sample (one-group) t-test with alpha = .05.
What are the null and alternative hypotheses?
The null hypothesis is that the reaction time for students in the regular population averages 200 milliseconds.
The alternate hypothesis is that the reaction time for students in not the regular population averages 200 milliseconds.
What is null hypothesis?In statistical hypothesis testing, null and alternate hypotheses are utilized. The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.
With the aid of a statistical test, researchers weigh the evidence in favor of and against the null and alternative hypotheses, which are two opposing claims:
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find the distance between the parallel lines. if necessary, round your answer to the nearest tenth. coordinate plane shows two lines. line y equals negative 3 x plus 1 and line y equals negative 3 x plus 4.
By taking the difference between the y-intercepts, we conclude that the distance between the lines is 3 units.
How to find the distance between the parallel lines?A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two linear equations are parallel if and only if both lines have the same slope and different y-intercepts.
And the distance is given by the difference between the y-intercepts.
Here the lines are:
y = -3*x + 1
y = -3*x + 4
The difference between the y-intercepts gives:
4 - 1 = 3
That is the distance between the lines.
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can someone help pls????
detail for me as well
Step-by-step explanation:
the easy straight forward method is to simply sum up the 5 terms.
you know that this symbol just means "sum", right ?
and that the index variable is "running" from 1 to 5.
so, you have to sum up
3×1 + 3×2 + 3×3 + 3×4 + 3×5 = 3 + 6 + 9 + 12 + 15 = 45
now, if you want it done via a summary formula to add the first n terms of an arithmetic sequence, like in this case
a1 = 3
an = an-1 + 3 = a1×n = 3n
then
the sum of the first n terms in an arithmetic sequence is (n/2)⋅(a₁+aₙ).
it simply means : first plus last term added up n/2 times.
why ?
because a1 + an = a2 + an-1 = a3 + an-2 = ...
we get n/2 times such part sums.
so, in our case, n = 5, and we get
(3 + 3×5)×5/2 = (3 + 15)×5/2 = 18×5/2 = 9×5 = 45
Answer:
∑ (i = 1 to 5) (3·i)
= 3·∑ (i = 1 to 5) (i)
= 3·(1 + 2 + 3 + 4 + 5)
= 3·15
= 45
BRAINLIEST!! Find the arc length on a circle of radius 10 cm intercepted by a central angle of 6 rad
The length of the arc intercepted by a central angle of
6 radians is 60.34 cm.
What is an Arc?
An arc is any smooth curve joining two points.
Given is an circle of radius 10 cm intercepted by a central angle of
6 radians.
We can calculate the length of the arc using the formula -
L[arc] = (Ф/360°) x 2πr
Ф = 6 radians = 343.78 degrees
L[arc] = (343.78/360) x 2π x 10
L[arc] = 0.96 x 2π x 10
L[arc] = 60.34 cm
Therefore, the length of the arc intercepted by a central angle of
6 radians is 60.34 cm.
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Find the slope that passes through the points
(3, 5) and (7, 17)
Answer:
y=3x-4
Step-by-step explanation:
n proof testing of circuit boards, the probability that any particular diode will fail is 0.030.03. suppose a circuit board contains 150 diodes and that each one performs or fails independently of all others. how many diodes would you expect to fail, and what is the standard deviation of the number that are expected to fail? 5 points
You would expect 4.5 diodes to fail. The standard deviation of the number that are expected to fail is 2.089.
The number of diodes failing, E(X), can be calculated by multiplying the population, n, with the probability, p.
n = 150
p = 0.03
E(X) = n × p
E(X) = 150(0.03)
E(X) = 4.5
Standard deviation, denoted by σ, is defined as the measure that indicates the average distance of observations from the mean of the data set.
σ = √(n x p x (1 - p))
σ = √(150 x 0.03 x (1 - 0.03))
σ = √150 x 0.03 x 0.97
σ = √4.365
σ = 2.089
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If I were to roll 2 dice looking for a 1 and anything but a 3, or 4. What is the probability I will get the result I'm looking for.
The prοbability οf getting the desired οutcοme is 1/9 οr apprοximately 0.1111 (rοunded tο fοur decimal places)
What is Prοbability?In mathematics, prοbability is a measure οf the likelihοοd οr chance οf an event οccurring, expressed as a number between 0 and 1, where 0 represents an impοssible event and 1 represents a certain event. It is a fundamental cοncept in statistics and is used tο mοdel and analyze a wide range οf real-wοrld phenοmena.
The prοbability οf getting a 1 οn a single die is 1/6, and the prοbability οf getting anything but a 3 οr 4 οn a single die is 4/6 (since there are 6 pοssible οutcοmes and 3 οf them result in a 3 οr a 4).
Tο find the prοbability οf getting the desired οutcοme when rοlling twο dice, we can use the multiplicatiοn rule οf prοbability, which states that the prοbability οf twο independent events οccurring tοgether is the prοduct οf their individual prοbabilities.
Sο the prοbability οf getting a 1 οn οne die and anything but a 3 οr 4 οn the οther die is:
(1/6) x (4/6) = 4/36 = 1/9
Since there are 36 pοssible οutcοmes when rοlling twο dice, the prοbability οf getting the desired οutcοme is 1/9 οr apprοximately 0.1111 (rοunded tο fοur decimal places).
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the non-engineer wants 600 pounds of total initial thrust from the 20 rockets. what is the probability that his/her scheme will produce the minimum required thrust?
The exit mass flow rate times the exit velocity less the free stream mass flow rate times the free stream velocity equals the force (thrust).
If we take into account the factors mentioned above, we will see that if the aircraft can fly at full thrust in cruise, this fits nicely with a static sea level thrust force equivalent to one third of its weight force. The thrust required to sustain flight is approximately 1/18 of the aircraft weight. It takes classroom teaching, ground training, and flying training from a certified instructor to obtain a high-altitude endorsement. we will learn about the warning signs and symptoms of altitude sickness, when to use supplemental oxygen, how long you can use that oxygen safely, and more during ground school.
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Holland added three decimals that made a sum of 2. One of the decimals was 0.34.
What are two other decimals Holland could have used to make a sum of 2? Explain how you know.
Two decimals are 0.34, 0.83, and 0.83 and Holland could have used it to make a sum of 2.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
We get x + x = 2x by using x to signify our missing values and the assumption that there are two missing values. We obtain the equation 2x + 0.34 since it is the product of these integers and 0.34; after setting it equal to 2, 2x + 0.34 equals 2.
First, take 0.34 off both sides to get 2x = 1.66. To get x = 0.83, divide both sides by 2 now.
Therefore, the decimals are 0.34, 0.83, and 0.83.
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Mikey is conducting a science experiment about the rate at which different materials will burn. In his hypothesis, he states that a pencil and a lemon will burn at the same rate because they are both yellow. Which logical fallacy has Mikey used? False analogy Hasty generalization Red herring Slippery slope
The logical fallacy which Mikey has used is referred to as: A. False analogy.
What is a fallacy?A fallacy can be defined as a mistaken or false belief (assumption) that are based on illogical arguments or reasoning.
The types of fallacy.In Science, there are different types of fallacy and these include the following:
Red herringAppeal to authoritySlippery slopeHasty generalization.Ad HominemAppeal to Popularity (Ad populum)Fallacy of exclusionFalse analogyAdditionally, a false analogy simply refers to a type of informal fallacy which states that since quantity A and quantity B both share the same quality X (color yellow), then, they must also share quality Y in common (burning rate).
In this context, we can reasonably infer and logically deduce that Mikey's hypothesis is a false analogy.
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Answer: hey sis! the answer is a
Step-by-step explanation: A.) false analogy
(btw this language arts not math)
(50 POINTS) and will give BRAINLIEST to BEST ANSWER!
200 divided by 5 x 32 + 12 -101=______?
Answer:
–87.75
Step-by-step explanation:
Write the equation:
200 ÷ 5 • 32 + 12 – 101 = ?
PEMDAS
200 ÷ (5 • 32) + 12 – 101 = ?
(200 ÷ 160) + 12 – 101 = ?
(1.25 + 12) – 101 = ?
(13.25 – 101) = ?
–87.75 = ?
–87.75
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Solve for all values of y in simplest form.
10 = |y/9|
Answer: y = -90, 90
Step-by-step explanation:
To solve this, we will isolate the variable.
Given:
10 = |[tex]\frac{y}{9}[/tex]|
Absolute value:
10 = [tex]\frac{y}{9}[/tex] & -10 = [tex]\frac{y}{9}[/tex]
Multiply both sides of both equations by 9:
90 = y & -90 = y
Answer:
y = -90, 90
Please help I will give brainliest
Answer:
y=1/2x+2
Step-by-step explanation:
y=mx+b
m = slope = rise/run
b = y-intercept
Look at the graph, and find the slope.
m= slope = rise/run = 1/2
b = y-intercept = 2
Therefore, the correct answer is option y=1/2x+2
M- (-7)<5
-helpppp please
Answer: M + 7
Step-by-step explanation:
Well, it doesn’t show the variable’s number correct?
So, since we don’t have the number, we are going to multiply -1 by -7, getting 7 from this. Now, change it to addition. You should have m + 7.
I hope this helps!
help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
I need help asap!!!!
Answer: -1 and 5
Step-by-step explanation:
In a company's first year in operation, it made an annual profit of $111, 000. The
profit of the company increased at a constant 24% per year each year. How much
total profit would the company make over the course of its first 24 years of operation,
to the nearest whole number?
The total profit made by the company over the course of its first 24 years of operation is $10,016,640
Given,
The annual profit made by a company in first year = $111,000
The increase in profit per year = 24% = $26640
We have to find the total profit made by the company over the course of its first 24 years of operation
Lets take this as an arithmetic progression.
First term, a = 111,000
Common difference, d = 26640
nth term = 24
Sum of nth term,
Sₙ = n/2 [2a + (n - 1) d]
S₂₄ = 24/2 [2 × 111,000 + (24 -1) 26640]
S₂₄ = 12 [222,000 + 23 × 26640]
S₂₄ = 12 [222,000 + 612,720]
S₂₄ = 12 × 834,720
S₂₄ = 10,016,640
That is,
The total profit made by the company over the course of its first 24 years of operation is $10,016,640
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Which following conditions are necessary to use the binomial distribution
The conditions necessary for binomial distribution is option C that is I and III only "There is a series of N trials." and "The outcomes are mutually exclusive."
What is binomial distribution?In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.
What are the conditions of binomial distribution?If the following circumstances hold true, the binomial distribution describes the behavior of a count variable X: 1: There will always be n observations. 2: Every observation stands alone. Three: Each observation corresponds to one of two results ("success" or "failure").
Option C, which consists solely of I and III, meets the requirements for the binomial distribution. "The results are mutually exclusive" and "There is a series of N trials."
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ASAP PLEASE HELP !!!!
Evaluate.
4^4+400÷(4+6^2)−2^4
Which answer is correct?
250
244
18
10
Answer:
250
Step-by-step explanation:
4^4+400÷(4+6^2)−2^4
256 + (400 ÷(4+36) ) -16
256 + (400÷40) -16
256+ (400 (1/40) ) -16
256 + (400/40) -16
256 + (2 · 6) -16
256 + 10 =16
250
A Ferris wheel is designed in such a way that the height (h), in feet, of the
seat above the ground at any time, t, is modeled by the function h(t) = 49cos
(π/15+T) + 50. What is the maximum height of the wheel?
what unit would you use to measure the length of Supermarket
The length of the building should be measured in meters, as that is the most appropriate unit.
What are units?A unit of measurement is a specific magnitude of a quantity that has been established and adopted by law or convention and is used as a benchmark for measuring other quantities of the same kind. A multiple of the unit of measurement can be used to express any other quantity of that type. A length, for instance, is a physical quantity.The most suitable unit to measure the length of the building will be measuring the length of the building in meters.
Therefore, the length of the building should be measured in meters, as that is the most appropriate unit.
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Enter the value for n for the equation 3^5 x 3^n = 3^8
Hope this will be helpful.
A college has 19 engineering students for every 81 students enrolled. if the college has 750 students, approximately haw many are engineering students
The number of engineering students for 750 college students will be 176 students
Number of engineering students: 19
The number of total students for 19 engineering students = 81 students
Percentage: A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Percentage of engineering students in relation to the total students = Number of engineering students/ Total students*100
= 19/81*100
= 23.45%
So, for 750 students the number of engineering students will be
= 23.45% of 750
= 23.45/100*750
= 175.87 or 176 students
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Find the equation of the linear function represented by the table below in slope-intercept form X 0,1,2,3,4 Y -2,5,12,19,26
The equation of the linear function represented in the table in slope intercept form is y = 7x -2
How to represent linear equation in slope intercept form?A linear function can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the table follows a linear pattern.
Hence, using (0, -2)(1, 5) we can find the slope and the y-intercept of the linear function.
Therefore,
m = 5 - (-2) / 1 - 0
m = 5 + 2 / 1
m = 7
Therefore, let's find the y-intercept using (0, - 2).
y = mx + b
-2 = 7(0) + b
hence,
b = -2
Therefore, the slope intercept form of the table is y = 7x - 2
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