Answer:
\(\mu=473.2\)
Step-by-step explanation:
Binomial Distribution
The binomial distribution is commonly used to model the number of successes in a sample of size n drawn with replacement from a population of size N.
The mean value of a binomial distribution is given by:
\(\mu=np\)
Where b is the number of trials and p is the success probability for each trial.
We need to find the mean value with parameters n=676 and p=0.7, thus:
\(\mu=676\cdot 0.7\)
\(\boxed{\mu=473.2}\)
Suppose that the demand of a certain item is x=-0.7p+10.
Evaluate the elasticity at 6.
The item is an inelastic good at a price of 6 because it is negative and have a demand of -0.71.
What is the item's demand if elasticity is at 6?The formula for elasticity of demand is Elasticity of demand = (% change in quantity demanded) / (% change in price)
The initial quantity demanded at a price of 6 and the quantity demanded at a slightly different price must be know.
Let say Initial quantity demanded is:
x = -0.7(6) + 10
x = 5.8
Assume price changes slightly to 6.01, which gives us a new quantity demanded of x:
= -0.7(6.01) + 10
= 5.793
The % change in quantity demanded will be:
= [(new quantity demanded - initial quantity demanded) / initial quantity demanded] x 100%
= [(5.793 - 5.8) / 5.8] x 100%
= -0.12%
As price has changed from 6 to 6.01, we can calculate the percentage change as follows:
% change in price = [(new price - initial price) / initial price] x 100%
= [(6.01 - 6) / 6] x 100%
= 0.17%
Elasticity of demand = (% change in quantity demanded) / (% change in price)
= (-0.12% / 0.17%)
= -0.71
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Tính tích phân sau bằng cách dùng tọa độ cực I=∫∫ \(\frac{1}{\sqrt{x^{2} +y^{2} } }\)dxdy R là miền nằm trọg góc phần tư thứ nhất thỏa mãn 4\(\leq x^{2} +y^{2} \leq 9\)
It sounds like R is the region (in polar coordinates)
R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}
Then the integral is
\(\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}\)
rina is climbing a mountain. she has not yet reached base camp write an iequality to show the reaming distance d in feet she must climb to reach the peak
Answer:
Let b be the distance in feet to base camp and p be the distance in feet to the peak. Then, the remaining distance Rina must climb to reach the peak is:
Rina's distance = p - b
Since Rina has not yet reached base camp, we know that b > 0. Thus, the inequality to show the remaining distance d in feet she must climb to reach the peak is:
p - b > 0
Step-by-step explanation:
A vehicle can travel 132 km with 12 litres of petrol. What is the petrol consumption in km/litre?
Answer:
The amount of kilometers per liter is in terms on fuel consumption, the range in kilometers that a vehicle can travel while consuming one liter of gas
Step-by-step explanation:
help pleaseee geometryyy
Step-by-step explanation:
angle ABE=angle EBC
2x+20=4x-620+6=4x-2xx=26/2X=13stay safe healthy and happy.HELP ME!!!!!
Solve. −n/2 + 3/8 = −6 7/8 Enter your answer as a mixed number in simplest form in the box.
If f(x) = -x³ + x² + x, find f(-3).
Answer:
33
Step-by-step explanation:
Substitute f(-3) in the problem and you'll get f(-3) = -x³ + x² + x.
Substitute the given value into the function and evaluate.
Answer:
33.
Step-by-step explanation:
f(x) = -x³ + x² + x.
f(-3) = -(-3)³ + (-3)² + (-3)
= -(-27) + (9) - 3
= 27 + 9 - 3
= 36 - 3
= 33.
Hope this helps!
The width of a rectangle is 4 cm and its perimeter is 26 cm. What is the perimeter of a square has the same area as the rectangle
Answer:
length = 9 cm
Step-by-step explanation:
perimeter = p =26 cm
width = w= 4 cm
perimeter of a rectangle= 2*w+2*L
L= length
so we have:
26 = 2*(4) +2*L
26= 8 +2L
26-8 = 2L
18 = 2L
L= 18/2
L =9 cm = length
Mika taught her sister the steps for dividing a decimal by a decimal. Which instructions are correct? 1. Multiply the divisor by a multiple of 10 to create an integer divisor. 2. Multiply the dividend by the same multiple of 10 as step 1. 3. Divide, and apply the rules for dividing signed numbers. 1. Multiply the dividend by a multiple of 10 to create an integer. 2. Multiply the divisor by the same multiple of 10 as step 1. 3. Divide, and apply the rules for dividing signed numbers. 1. Divide the divisor by a multiple of 10 to create an integer divisor. 2. Divide the dividend by the same multiple of 10 as step 1. 3. Divide, and apply the rules for dividing signed numbers. 1. Divide the dividend by a multiple of 10 to create an integer. 2. Divide the divisor by the same multiple of 10 as step 1. 3. Divide, and apply the rules for dividing signed numbers.
Answer: its A
1. Multiply the divisor by a multiple of 10 to create an integer divisor.
2. Multiply the dividend by the same multiple of 10 as step 1.
3. Divide, and apply the rules for dividing signed numbers.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Two digits are selected with replacement from the digits 1, 2, 3, 4, 5, and 6.
How many possibilities are there for the first digit?
There are six possibilities for the first digit, as any of the six digits can be selected with replacement.
What is principle of counting?A fundamental combinatorial rule called the principle of counting, sometimes referred to as the counting principle or multiplication principle, enables us to determine the total number of outcomes in a series of occurrences. According to the principle, there are m n methods to perform both events sequentially if we have m ways to perform one event and n ways to perform another.
Consider that the numbers 1, 2, 3, 4, 5, and 6 are all distinct and equally likely to be chosen in order to understand why. When we choose a digit with replacement, it indicates that, regardless of the digits that were previously chosen, we can choose any of the six digits on the initial draw. Thus, the first digit has six potential values.
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What is the solution to |x − 4| ≥ 7? PLEASE HELP ME I NEED TO GRADUATE
A.
-3 ≤ x ≤ 11
B.
-11 ≤ x ≤ 3
C.
x ≥ 11 or x ≤ -3
D.
x ≥ 3 or x ≤ -11
Answer:
C. x ≥ 11 or x ≤ -3
Step-by-step explanation:
This inequality can be resolved into two:
-7 ≥ x -4 or x -4 ≥ 7
Adding 4 to the first one of these gives ...
-3 ≥ x ⇔ x ≤ -3
Adding 4 to the second of the inequalities above gives ...
x ≥ 11
The full solution is then ...
x ≥ 11 or x ≤ -3 . . . . . matches choice C
______
Additional comment
You can see in the attachment that when the value of the absolute value expression is supposed to be greater than some number, the solution set will have two disjoint parts. That means the answer expression must include "or", eliminating choices A and B.
__
When you are given the inequality in the form ...
|f(x)| ≤ c . . . . . note "less than ..."
It can be resolved to the compound inequality ...
-c ≤ f(x) ≤ c
When the inequality symbol points the other way ("greater than ..."), this sort of resolution doesn't really make sense. (You can do it, but you need to recognize the nonsense involved. Your teacher may not appreciate this "work".) In the present case, that would look like ...
-7 ≥ x -4 ≥ 7
When you add 4 to all parts of this, it becomes ...
-3 ≥ x ≥ 11
Recognizing the nonsense in this expression, you can rewrite it in two parts the way it should be written:
-3 ≥ x OR x ≥ 11
PLSsssssssssssssssssssssssssssssss need help
Answer:
yr question is not here!!!!!!!!!!
Find the total area of the irregular polygon shown? * m 11 m 36 sqm 84 sq.m 88 sqm
Answer:
100
Step-by-step explanation:
Split it into 3 different rectangles, find the area of each, and add them together.
Rectangle 1: length=11 width=4 11×4=44
Rectangle 2: length=11-9=2 width=6 2×6=12
Rectangle 3: length=11 width=4 11×4=44
44+12+44=100
Picture included!!! Please help! Suppose a = 10 and b = 24. Give the value of each of the following. Give answers as integers or rounded to 2 decimal places as appropriate.
Answer:
A = 22.62°
B = 67.38°
c = 26
Step-by-step explanation:
\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)
\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios
\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)
There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.
A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 90 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.1 m3/min, how fast (in m/min) is the water level rising when the water is 10 cm deep?
Answer:
Let's start by finding the volume of water in the trough as a function of its depth.
At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:
V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm
Simplifying this expression, we get:
V(h) = (13/2000) h^2 m^3
Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:
dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)
At the moment when the water is 10 cm deep, we have:
h = 10 cm
dV/dt = 0.1 m^3/min
Plugging in these values, we get:
0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)
Solving for dh/dt, we get:
dh/dt = 0.1 m^3/min / (26/2000) / 10 cm
dh/dt ≈ 0.192 m/min
Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.
Arrange and Write the Integers in Increasing Order
-13 9 -17 64 -20 -82
Answer:
-82, -20, -17, -13, 9, 64
Step-by-step explanation:
With positive numbers, larger numbers are greater than smaller numbers.
For example, 64 is greater than 9.
With negative numbers, ignore the negative sign. Then to compare numbers; the smaller numbers are greater.
For example, -20 is greater than -82.
Answer: -82, -20, -17, -13, 9, 64
Answer:
greatest to least: 64, 9, -13, -17, -20, -82
Least to greatest: -82, -20, -17, -13, 9, 64
Was this the way you wanted me to do it?
Step-by-step explanation:
The answer would be “Yes” right? Just double checking :)
Answer:
yes
Step-by-step explanation:
its correct because opposite sides are parallel
Answer:
yes
Step-by-step explanation:
Solve the system using elimination or substitution. Please help
The values of the system using elimination method is,
x = 4, y = 3 and z = -1.
Elimination method:
The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.
Given,
The given system of equations,
-4x + 6y - 2z = 4 -----------------(1)
-2x - 6y - 2z = -24 --------------(2)
x + 6y + z = 21 --------------------(3)
Here we need to solve this one by using elimination or substitution method.
Here we use the elimination method to solve this,
For that, first we have to add the equations (1) and (2),
Then we get,
=> (-4x + 6y - 2z) + (-2x - 6y -2z) = 4 + (-24)
=> -6x - 4z = -20 -------------------(4)
Now we have to add the equation (2) and (3),
Then we get,
=> ( -2x - 6y - 2z) + ( x + 6y + z) = -24 + 21
=> -x -z = -3 -------------------(5)
Now we have to multiply 6 with equation(5),
Then,
=> 6 x (-x - z) = 6 x -3
=> -6x -6z = -18 --------------------(6)
Now subtract equation (6) from equation (4),
Then,
=> (-6x - 6z) - (-6x - 4z) = -18 - (-20)
=> -6x -6z + 6x + 4z = -18 + 20
=> -2z = 2
=> z = -1
Apply the value of z on the equation (5),
=> -x - (-1) = -3
=> -x + 1 = -3
=> -x = -4
=> x = 4
Now apply the value of x and z on the equation (3),
Then we get,
=> 4 + 6y + (-1) = 21
=> 4 - 1 + 6y = 21
=> 3 + 6y = 21
=> 6y = 18
=> y = 3
Therefore, the solutions are x = 4 , y = 3 and z = -1.
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Line A has a slope of −3 . Line B has a slope of 4. Line C has a slope of 2.
Which line is closest to being horizontal?
Line A
Line B
Line C
I don't know.
Line C is closest to being horizontal.
Given,
Line A has a slope of −3.
Line B has a slope of 4.
Line C has a slope of 2.
To find the which line is closest to being horizontal?
Now, According to the question:
Slope of line A (m1) = -3
Slope of line B (m2) = 4
Slope of line C (m3) = 2
Slope of horizontal line = 0
Closest to being horizontal is given by l m l
For line A = l-3 l = 3
For line B = l4l = 4
For line C = l2l = 2
As 2 is smaller it is closest to horizontal
Hence, Line C is closest to being horizontal.
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how to solve this separable differential equation?
The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,
\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).
What is a differential equation?Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.
The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).
Now, multiplying both sides by dx we,
\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).
Dividing both sides by \(2^{\sqrt{x}}\) we have,
\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).
\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).
\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).
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A fence with 2 gates in it surrounds a lion enclosure.
Each gate is 4 m wide.
an image
What is the length of the fence around the enclosure not including the gates?
The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.
Let's assume the length of the rectangle is 'l' and the width is 'w'.
From the given data, we know that each gate is 4 m wide.
Therefore, the width of the rectangle is:
Width = w + (4 m + 4 m) = w + 8 m
The perimeter of the rectangle is:
P = 2l + 2(w + 8 m) = 2l + 2w + 16 m
Now, we need to subtract the combined length of the two gates from the perimeter:
P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m
So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
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a situation for Y=5x+4
Four racers are racing on a track.
Raheem covers 26%
of the track, Lila covers 38
of the track, Khalid covers 0.3
of the track, and Juanita covers 0.24
of the track.
List the people in order by the distance on the track each person covers from least to greatest.
The rank of the proportions covered on the track, from least to greatest, are given as follows:
Juanita, Raheem, Khalid, Lila.
How to rank the proportions?The proportions for each person are given as follows:
Raheem: 26% = 0.26.Lila: 3/8 = 0.375. (fraction to decimal, divide the numerator by the denominator).Khalid: 0.3.Juanita: 0.24.Considering that 0.24 is the lowest proportion and 0.375 is the highest proportion, the rank is given as follows:
Juanita, Raheem, Khalid, Lila.
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answer the following questions in the picture
a. The chart is prepared below.
b. At the end of 4 years, Ross still owes his parents $1,576.92.
How to calculate interest ?To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.
The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.
The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.
Here are the steps for calculating the balance for each year:
Year 1:
Beginning balance = $2,500.00
Interest for the year = $2,500.00 x 0.032 = $80.00
Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00
Year 2:
Beginning balance = $2,280.00
Interest for the year = $2,280.00 x 0.032 = $72.96
Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96
Year 3:
Beginning balance = $2,052.96
Interest for the year = $2,052.96 x 0.032 = $65.76
Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72
Year 4:
Beginning balance = $1,818.72
Interest for the year = $1,818.72 x 0.032 = $58.20
Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92
Here's a table that shows the details:
Year ,principal ,Interest rate, interest, Payment ,annual owing
1 $2,500.00 $80.00 $300.00 $2,280.00
2 $2,280.00 $72.96 $300.00 $2,052.96
3 $2,052.96 $65.76 $300.00 $1,818.72
4 $1,818.72 $58.20 $300.00 $1,576.92
b. At the end of 4 years, Ross still owes his parents $1,576.92.
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write 7298 to nearest thousand?
Answer:
Rounds down to 7000.
Step-by-step explanation:
What the meaning of statement this?
This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.
The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:
∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))
The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.
The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.
The statement can be interpreted as follows:
"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."
In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.
It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.
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Simplify:
2
(
3
x
)
+
(
x
+
10
)
2(3x)+(x+10)
Answer:
7x+10
Step-by-step explanation:
2x(3x)+1x(x+10)
6x+1x+10
7x+10
Scott equipment produces high-quality soccer balls if the fixed cost per ball is three dollars when the company produces $15,000 what is the fixed cost per ball went to produce 22,500 boss assume that both volumes are in the same relevant
The fixed cost per ball went to $4.5 when the company produce 22,500.
what is the fixed cost per ball went to produce?fixed cost per ball is three dollars when the company produces 15,000
fixed cost per ball went x to produce 22,500
So,
3 : 15000 = x : 22,500
3/15,000 = x/22,0/500
cross product
3 × 22,500 = 15,000 × x
67,500 = 15,000x
divide both sides by 15,000
x = 67,500 /15,000
x = 4.5
Therefore, the fixed cost per ball to produce 22,500 is $4.5
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If a car moves 12 km North,19 km east, and 12 km south, what is its displacement
Answer:
19 km east
Step-by-step explanation:
By going North 12 then south 12 the two cancel eachother out leaving only the eastern movement
Answer:
19 km, East
Step-by-step explanation:
I hope you get it right
Find the length of side AB. Round to the nearest hundredth inch.
The value of length of side AB is,
⇒ AB = 5 units
We have to given that;
The figure is shown a trapezoid.
Hence, By using Pythagoras theorem we get;
⇒ AB² = 4² + (5.25 - 2.25)²
⇒ AB² = 16 + 3²
⇒ AB² = 16 + 9
⇒ AB² = 25
⇒ AB = √25
⇒ AB = 5 units
Therefore, The value of length of AB is,
⇒ AB = 5 units
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