Answer:
[tex]-\frac{3 \cdot cos^2x}{(1+sinx)^3}[/tex]
Step-by-step explanation:
[tex]y = (\frac{cosx}{1+sinx})^3\\\\\frac{dy}{dx} = 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{dy}{dx}(\frac{cosx}{1+sinx})[/tex] [tex][ y = x^n\ \ \ => \ \ \ \frac{dy}{dx} = b \cdot x^{n-1} \ ][/tex]
[tex]= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{(1+sin x(-sinx) - cosx(cosx)}{(1+sinx)^2}\\\\[/tex] [tex][\ \frac{u}{v} = \frac{v \dcot u'- u \cdot v'}{v^2}\ ][/tex]
[tex]= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-sin x-sin^2x- cos^2x}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-sin x- (sin^2x+ cos^2x)}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-sin x-1}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-1 \cdot(sin x+1)}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-1}{(1+sinx)}\\\\[/tex]
[tex]= -3 \cdot \frac{cos^2x}{(1+sinx)^3}[/tex]
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.12 and the probability that the flight will be delayed is 0.08. The probability that it will not rain and the flight will leave on time is 0.82. What is the probability that it is raining if the flight leaves on time? Round your answer to the nearest thousandth.
Answer:
0.109 = 10.9% probability that it is raining if the flight leaves on time.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Conditional probability:
Event A: Leaves on time
Event B: Raining
Probability that the flight will be delayed is 0.08.
So 1 - 0.08 = 0.92 probability that it leaves on time, that is, [tex]P(A) = 0.92[/tex]
The probability that it will not rain and the flight will leave on time is 0.82.
0.92 - 0.82 = 0.1 probability it is raining and the flight leaves on time, so:
[tex]P(A \cap B) = 0.1[/tex]
What is the probability that it is raining if the flight leaves on time?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1}{0.92} = 0.109[/tex]
0.109 = 10.9% probability that it is raining if the flight leaves on time.
PLEASE HELP!! WILL MARK BRAINLIEST TO WHOEVER GETS IT RIGHT
Answer:
perpendicular, negative reciprocal
Step-by-step explanation:
a negative and a positive slope. 1/5 is the opposite of 5
the perimeter of a rectangle is 40 feet. if the lenght is 15 feet, 6 inches, what is the width
Need help with this question please <<><>>
9514 1404 393
Answer:
√7
Step-by-step explanation:
The Pythagorean theorem tells you the square of the hypotenuse is equal to the sum of the squares of the sides. Let x represent the unknown side. Then we have ...
x² +9² = (√88)²
x² +81 = 88
x² = 7 . . . subtract 81; next, take the (positive) square root
x = √7 . . . . the third side
In recent years, business failures in the United States numbered 63509. The chemical industry accounted for 9499 of these business failures. The Mid-West states accounted for 7900 of the business failures. Suppose that 1270 of all business failures were chemical businesses located in the Mid-West. A failed business is randomly selected from this list of business failures. What is the probability that the business is in the chemical industry if it is known that the business is located in the Mid-West
Answer:
0.1608 = 16.08% probability that the business is in the chemical industry if it is known that the business is located in the Mid-West.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Failed business in the Midwest.
Event B: Chemical industry.
Probability of failed business being in the Mid-West:
7900 out of 63509. So
[tex]P(A) = \frac{7900}{63509}[/tex]
Probability of a failed business being a chemical industry in the Mid-West.
1270 out of 63509. So
[tex]P(A \cap B) = \frac{1270}{63509}[/tex]
What is the probability that the business is in the chemical industry if it is known that the business is located in the Mid-West?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{1270}{63509}}{\frac{7900}{63509}} = \frac{1270}{7900} = 0.1608[/tex]
0.1608 = 16.08% probability that the business is in the chemical industry if it is known that the business is located in the Mid-West.
Classify the following as discrete or continuous random variables.
1. The weight of bags of apples, with 10 apples in each bag.
2. The number of times required for a modem to dial an internet provider before connecting.
3. Out of 10 times connecting to an internet provider, the average number of attempts necessary before connecting.
4. A pair of dice is rolled, and the sum to appear on the dice is recorded.
Answer:
A discrete variable is a variable that can only take some selected given values from a given set, like x ∈ {x₁, x₂, ..., xₙ}
While a continuous variable can take any value in the range, like x ∈ {x₁, xₙ}.
1) The weight of bags of apples, with 10 apples in each bag.
Here the weight depends on the number of apples in the bag, and we can have only whole numbers of apples in the bag, so this is clearly a discrete variable.
2) The number of times required for a modem to dial an internet provider before connecting.
Same as before, here we can have only a whole number of attempts, so this set is discrete.
3) Out of 10 times connecting to an internet provider, the average number of attempts necessary before connecting.
Here we will have an average of 10 integer numbers:
[tex]M = \frac{x_1 + x_2 + ... + x_{10}}{10}[/tex]
so here we have a kinda dense set of possible values, so we can think of this as a continuous variable.
4) A pair of dice is rolled, and the sum to appear on the dice is recorded.
Here the possible values are whole numbers again, so we can not have values like 3.5, so again, this is a discrete variable.
The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.55 oz. Suppose we take a random sample of 56 bottles filled by this machine. So, 75% of the sample means will be less than what value
Answer:
0.9836
Step-by-step explanation:
How many inches are there in 3 yards?
A. 108 in.
B. 96 in.
C. 72 in.
D. 48 in.
Answer:
108
Step-by-step explanation:
3 yards equal 9 feet and 1 foot equals 12 inches so that means do 12 x 9 and you get 108
The correct option is A.
How to convert feet to yards?Feet ÷ 3 = 1 yards. yard is 3 feet long, so all you have to do is divide the number of feet by 3 to get the number of yards for your measurement
We know that,
1 feet is equal to 12 inches.
1 feet = 12 inches.
1 yard = 36 inches.
3 yards = 36 × 3 = 108 inches.
3 yards = 108 inches.
Therefore, 108 inches are there in 3 yards.
Learn more about yard and inches here:
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According to recent reports, Apple Inc. holds 27.6% of the Tablet Computer market. Suppose a consumer research company believes that 27.6% is too high and undertakes a survey to see if their suspicion is supported by the sample data. A random sample was taken of tablet computer purchases and find that of 200 purchases, 52 are Apple tablet computers. The P-value is 0.3064 and the hypothesis is : H:P = 0.276 H:P < 0.276 You would conclude at a significance level of 5%.
There is statistically significant evidence that Apple Inc. holds less than 27.6% of the tablet computer market.
there is a 30.36% chance that Apple Inc. holds at least 27.6% of the Tablet computer market.
we don't have sufficient evidence to support the claim
We have sufficient evidence to suppot the claim, that Apple holds less than 27.6%
Answer:
We don't have sufficient evidence to support the claim
Step-by-step explanation:
Null hypothesis:
[tex]H_0: p = 0.276[/tex]
Alternate hypothesis:
[tex]H_1: p < 0.276[/tex]
The P-value is 0.3064
0.3064 probability of finding a sample proportion lower than the one found.
The p-value is higher than the significance level of 0.05, which means that there is no sufficient evidence to support the claim.
I need help??????????????
Answer:
f(n) = 4n + 16
Step-by-step explanation:
n is the nth number in the sequence
plug in the first 3 to check the rule:
4(1) + 16 = 4 + 16 = 20
4(2) + 16 = 8 + 16 = 24
4(3) + 16 = 12 + 16 = 28
it works
PLS HELP ASAP !!! PLSSS !!
Answer:
74
Step-by-step explanation:
the lines r parallel and the angle on the same side
Answer:
74°
Step-by-step explanation:
..........................
Substitute the isolated variable into the second equation. I need help with this, i don’t understand.
Answer:
Step-by-step explanation:
Substitute the value for y or x into the equation thats listed with it.
For the first one, substitute 3 in place of y.
3x + 6 y = 60 turns into
3x + 6 * 3 = 60
3x + 18 = 60
3x = 60-18
3x = 42
x = 42/3
x = 14
Apply the same to the other equations
10x + 4y = 70 turns into
10 * 5 + 4y = 70
Then solve for y
the premeter of a rectangle is 326cm and its lenght is 98cm find its breath and area
Perimeter = 2(length+breadth)
326= 2(98+b),
breadth= 65 cm
Area of rectangle = l×b = 98×65= 6370cm²
What is the same as 4/8
Answer:
1/2 or 2/4 or 8/16 or 16/32....
Step-by-step explanation:
If X + Y means X is the brother of Y, X - Y means X is the sister of Y, and X * Y means X is the father of Y, then which of the following means that C is the son of M?
(1) M-N * C + F
(2) F-C + N * M
(3) N +M-F * C
(4) M * N-C + F
(5) M-N+F * C
Answer:
4
Step-by-step explanation:
Based on this question, addition means the first number is the brother of the other, subtract means the first number is the sister of the other and multiplying means the first number is the father of the other.
We see 4 is literally multiplying M by N-C, meaning N is the sister of C and M is the father of N and C.
product of x+3 and x-9
Answer:
Step-by-step explanation:
(x+3)(x-9)
multiply x with whole (x-9) and 3 with (x-9)
=x(x-9)+3(x-9)
multiply the brackets
=x^2-9x+3x-27
add or subtract like terms
=x^2-6x-277 is a required answer
Answer:
[tex] {x}^{2} - 6x - 27[/tex]
Step-by-step explanation:
[tex](x + 3) \times (x - 9)[/tex]
[tex]x(x−9)+3(x−9)[/tex]
[tex]x \times x+x(−9)+3(x−9)[/tex]
[tex] {x}^{2} +x(−9)+3x+3(−9)[/tex]
[tex] {x}^{2} −9x+3x−27[/tex]
[tex] {x}^{2} - 6x - 27[/tex]
Hope it is helpful...what is the mean mark of 847 ÷ 30?
Answer:
Step-by-step explanation:
What is the relationship between Riemann Sum and definite integral?
If A and B are two independent events with P(A)=2÷3 and P(B) =1÷5, find P(AUB).
Answer:
[tex]for \: independent \: events : \\ P(AUB) = P(A) + P(B) \\ P(AUB) = \frac{2}{3} + \frac{1}{5} \\ = \frac{13}{15} [/tex]
Step-by-step explanation:
P(AUB) is P(A) + P(B) because P(AnB) is zero.
[tex]P(AUB) = P(A) + P(B) - P(A{ \huge{n} }B) \\ P(AUB) = P(A) + P(B) + 0[/tex]
Instructions: Find the area of the sector. Round your answer to the nearest tenth.
Can some one help please.
Answer:
[tex]area = \frac{30}{360} \times \pi(17)^{2} \\ =75.66002307395 \\ = 76in ^{2} [/tex]
What is the answer?
Answer:
2.- 8.0 in.
Step-by-step explanation:
8.1 in
Step-by-step explanation:
A^2+B^2=C^2
49+16= 65
square root of 65≈8.06
round up to 8.1
Max has 4/5 qt of apple juice. He drinks 1/2 qt of it. How many apple juice does he have left? (Give your answer in quarts)
Find the point-slope equation for the line that passes through the points (2, 1) and (-2, 5). Use the first point in your equation.
Answer:
y = -x +3
Step-by-step explanation:
first find the slope
m = (y2-y1) / (x2-x1)
m = (5-1) / (2--2) = -1
note that it does not matter which points you chose to be second or first
use point-slope equation
y - y1 = m ( x - x1 )
y - 1 = -1 ( x - 2)
y = -x +2 + 1
y = -x +3
please if you find my answer helpful mark it brainiest
Answer:
y=-x+3
Step-by-step explanation:
Gradient(m)= y1-y2÷x1-x2
=1-5÷2-(-2)
=-4÷4
=-1
therefore m= -1
y-y1=m(x-x1)
y-1=-1(x-2)
y=-x+2+1
y=-x+3
A six-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test at the 5% level to determine if the die is fair. The data below are the result of the 120 rolls. (Enter exact numbers as integers, fractions, or decimals.)
Face Value Frequency Expected Frequency
1 14 ?
2 33 ?
3 15 ?
4 14 ?
5 30 ?
6 14 ?
Required:
a. State the null hypothesis.
b. State the alternative hypothesis.
c. What are the degrees of freedom?
Answer:
Die is not fair given that Pvalue< 0.05, hence we reject Null hypothesis
a) H0: Die = fair
b) Ha : Die ≠ fair
c) df = 5
Step-by-step explanation:
The expected frequency of every face values = 20
a) state Null hypothesis
H0: Die = fair
b) Alternate Hypothesis
Ha : Die ≠ fair
c) degree of freedom
df = ( n - 1 )
= ( 6 - 1 ) = 5
n = sample size ( number of faces a die has )
Note : After conducting hypothesis test
Pvalue ≈ 0.0026
test statistic ≈ 18.30
Hence we can conclude that die is not fair given that Pvalue < 0.05, hence we reject Null hypothesis
Please help and explain
9514 1404 393
Answer:
d. f(2) < g(2)
Step-by-step explanation:
The attached table and graph shows how the functions relate for the various x-values of interest. The true statement is ...
f(2) < g(2)
-3 < 0
If x-12y=-210and x-6y=90 then x =
Answer:
90
Step-by-step explanation:
x
−
12
y
=
−
210
=
=
−
210
x
−
6
y
=
90
=
=
90
x
=
=
90
I NEED HELP QIUCK PLZ HELP ME
You might need: Calculator
What is the area of the following circle?
Either enter an exact answer in terms of IT or use 3.14 for I and enter your answer as a decimal.
r = 5
units?
Answer:
A = 25pi
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi (5)^2
A = 25pi
Answer:
Area of circle is 25 π Or 78.5 .
Step-by-step explanation:
We know that
Area of circle = π × r ²
Here,
π = 3.14
r = 5
Substituting the given values in this formula
Area of circle = π × ( 5 ) ²
Area of circle = π × 25
multiplying the values, we get
Area of circle = 25 π Or 78.5
What is the area of triangle in centimeters squared?
what’s the answerrr..........
Answer:
D.90
the answer is 90 because it only flips once
please answer this , like ASAP
Answer:
let total be U and strawberry be S and.apple be A .
now
n[U]=200
n[S]=56% 0f 200=112
n[A]=44%of 200=88
n[A n S]=30%of 200=60
now
[tex] \bar {A U S}=?[/tex]
we have
n[U]=n[A] +n[B]-n[ A n B]+[tex] \bar{A U S}[/tex]
[tex] \bar{A U S}[/tex]=200-112-88+60=60
option C. 60 is a required answer.
Hope this help!!!
Have a nice day!!!