Answer:
P(M < 0.917 g) = 0.1611.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 0.974 g and a standard deviation of 0.325 g.
This means that [tex]\mu = 0.974, \sigma = 0.325[/tex]
Sample of 32:
This means that [tex]n = 32, s = \frac{0.325}{\sqrt{32}}[/tex]
Fnd the probability of randomly selecting 32 cigarettes with a mean of 0.917 g or less.
This is the p-value of Z when X = 0.917. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.917 - 0.974}{\frac{0.325}{\sqrt{32}}}[/tex]
[tex]Z = -0.99[/tex]
[tex]Z = -0.99[/tex] has a p-value of 0.1611.
So
P(M < 0.917 g) = 0.1611.
Choose the equation of the line that is parallel to the x-axis.
x = 4
x + y = 0
x = y
y = 4
1. Determine the length and perimeter of Laura's property.
(5)
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Answer:
length: 40 mperimeter: 136 marea: 653 m²volume: 6.52 m³Step-by-step explanation:
1.The outer dimensions of the property are 20 squares (length) by 14 squares. Each square is 2 m on a side, so the overall length of the property is ...
(20 squares)×(2 m/square) = 40 m . . . . length
The overall width of the property is ...
(14 squares)×(2 m/square) = 28 m . . . . width
Then the perimeter is ...
P = 2(length + width) = 2(40 +28) m = 136 m . . . . perimeter
__
Additional comment
We have computed the perimeter as though the plot were a rectangle. If you carefully consider the total length of horizontal edges and the total length of vertical edges, you see that those totals are the same as they would be for a 20×14 square (40×28 m) rectangle.
_____
2.The area of open ground is perhaps most easily computed by finding the area that must be subtracted from the overall 20×14 square rectangle. Those exclusions will be (in dimensions of squares) ...
lower right corner: 8 wide by 3 high = 24 squaresfish pond: 2 wide by 3 high = 6 squaresveranda: 4 wide by 4 high = 16 squareshouse: 9 wide by 7 high = 63 squarespavement: 4 wide by 2 high = 8 squaresThe total area of exclusions is 24+6+16+63+8 = 117 squares. The bounding rectangle is 20 by 14 = 280 squares, so the open ground is ...
280 squares - 117 squares = 163 squares
At (2 m)(2 m) = 4 m² per grid square, that's an area of ...
(163 squares)(4 m²/square) = 652 m²
The surface area of the open ground is 652 m².
_____
3.The volume is given by the formula ...
V = Bh
where B is the base area and h is the height.
1 cm = 1/100 m = 0.01 m thickness. That means the total volume is ...
V = (652 m²)(0.01 m) = 6.52 m³
6.52 cubic meters of topsoil are needed to cover the open ground to a depth of 1 cm.
What is the y-intercept of this quadratic function? f(x)= -x^2
Answer:
x-intercept(s):
( 0 , 0 )
y-intercept(s):
( 0 , 0 )
Step-by-step explanation:
Answer:
(0,0)
Step-by-step explanation:
This has no real starting point. The x-intercept as well as the y-intercept is (0,0).
\left(a+b\right)^2 hihihihihiihihihihihih
Consider, we need to find the expanded form of the given expression.
Given:
The expression is:
[tex]\left(a+b\right)^2[/tex]
To find:
The expanded form of the given expression.
Solution:
We have,
[tex]\left(a+b\right)^2[/tex]
It can be written as:
[tex]\left(a+b\right)^2=(a+b)(a+b)[/tex]
Using distributive property of multiplication over addition, we get
[tex]\left(a+b\right)^2=a(a+b)+b(a+b)[/tex]
[tex]\left(a+b\right)^2=a(a)+a(b)+b(a)+b(b)[/tex]
[tex]\left(a+b\right)^2=a^2+ab+ab+b^2[/tex]
[tex]\left(a+b\right)^2=a^2+2ab+b^2[/tex]
Therefore, the expanded form of the given expression is [tex]a^2+2ab+b^2[/tex].
6. a semicircle has as its diameter the hypotenuse of a right triangle shown below. determine the area of the semicircle to the nearest tenth of a square centimeter. show how you arrived at your answer.
Answer:
[tex]A = 137.3cm^2[/tex]
Step-by-step explanation:
Given
See attachment
Required
The area of the semicircle
First, we calculate the hypotenuse (h) of the triangle
Considering only the triangle, we have:
[tex]\cos(68) = \frac{7}{h}[/tex] --- cosine formula
Make h the subject
[tex]h = \frac{7}{\cos(68)}[/tex]
[tex]h = \frac{7}{0.3746}[/tex]
[tex]h = 18.7[/tex]
The area of the semicircle is then calculated as:
[tex]A = \frac{\pi h^2}{8}[/tex]
This gives:
[tex]A = \frac{3.14 * 18.7^2}{8}[/tex]
[tex]A = \frac{1098.03}{8}[/tex]
[tex]A = 137.3cm^2[/tex]
Which statement is true.?
Answer:
B
Step-by-step explanation:
can someone help me with this?
Answer: 22
Step-by-step explanation: 44:2=22
Let x be a real number such that x + (1/x) is an integer. Prove that (x^n) + 1/(x^n) is an integer for every positive integer n.
Answer:
sim eu também preciso desta respota
khalil has a circular cake that he plans to share equally betweeb himself and 5 friends. if tge cake is 8 inched in a diameter, what will be the length of the arc of each slice of cake.
Answer:
4.2
Step-by-step explanation:
The length of the arc of each slice of cake will be 4.18 inches if Khali shares the cake between him and 5 friends equally.
What is the circumference of a circle?
The circumference is the length of the outer boundary of the circle. It can be calculated as under:
Circumference=2πr
How to find length of arc?
We have been given that the diameter of the cake is 8 inches So, the radius becomes 4 inches. We have to calculate the circumference of the cake. so the circumference becomes:
Circumference=2π(4)=8π
=8*22/7
=25.1
Then we have to divide it into 6 people so it will be 25.1/6=4.18 inches.
Hence the length of the arc will be 4.8 inches.
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4n-6 in as a undistributed expression
Answer:
2( 2n-3)
Step-by-step explanation:
4n-6
2*2 n - 2*3
Factor out the greatest common factor
2( 2n-3)
Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes. For a randomly received emergency call, find the following probabilities. (For each answer, enter a number. Round your answers to four decimal places.)
a. between 5 and 10 min
b. less than 5 min
c. more than 10 min
Answer:
a) 0.5447
b) 0.0228
c) 0.4325
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes.
This means that [tex]\mu = 9.6, \sigma = 2.3[/tex]
a. between 5 and 10 min
This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5. So
X = 10
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 9.6}{2.3}[/tex]
[tex]Z = 0.17[/tex]
[tex]Z = 0.17[/tex] has a p-value of 0.5675
X = 5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 9.6}{2.3}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228
0.5675 - 0.0228 = 0.5447 probability that a randomly received emergency call is between 5 and 10 minutes.
b. less than 5 min
p-value of Z when X = 5, which from item a), is 0.0228, so 0.0228 probability that a randomly received emergency call is of less than 5 minutes.
c. more than 10 min
1 subtracted by the p-value of Z when X = 10, which, from item a), is of 0.5675.
1 - 0.5675 = 0.4325
0.4325 probability that a randomly received emergency call is of more than 10 minutes.
A particular fruit's weights are normally distributed, with a mean of 275 grams and a standard deviation of 19 grams. If you pick one fruit at random, what is the probability that it will weigh between 244 grams and 305 grams?
Answer:
0.8913 = 89.13% probability that it will weigh between 244 grams and 305 grams.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 275 grams and a standard deviation of 19 grams
This means that [tex]\mu = 275, \sigma = 19[/tex]
What is the probability that it will weigh between 244 grams and 305 grams?
This is the p-value of Z when X = 305 subtracted by the p-value of Z when X = 244.
X = 305
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{305 - 275}{19}[/tex]
[tex]Z = 1.58[/tex]
[tex]Z = 1.58[/tex] has a p-value of 0.9429.
X = 244
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{244 - 275}{19}[/tex]
[tex]Z = -1.63[/tex]
[tex]Z = -1.63[/tex] has a p-value of 0.0516
0.9429 - 0.0516 = 0.8913
0.8913 = 89.13% probability that it will weigh between 244 grams and 305 grams.
reflectiion across y=x
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Answer:
see attached
Step-by-step explanation:
The reflection across y=-x swaps the coordinates and negates both of them. The first-quadrant figure becomes a third-quadrant figure.
(x, y) ⇒ (-y, -x)
PLEASE HELP ME WITH THIS ONE QUESTION
How many combinations without repetition are possible if n = 4 and r = 3?
A) 16
B) 12
C) 3
D) 4
Given:
[tex]n=4[/tex] and [tex]r=3[/tex].
To find:
The combinations without repetition are possible if [tex]n=4[/tex] and [tex]r=3[/tex].
Solution:
Combination of selecting r item from total n items is:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
We have [tex]n=4[/tex] and [tex]r=3[/tex]. By using the above formula, we get
[tex]^4C_3=\dfrac{4!}{3!(4-3)!}[/tex]
[tex]^4C_3=\dfrac{4\times 3!}{3!1!}[/tex]
[tex]^4C_3=4[/tex]
Therefore, the correct option is D.
Answer:
Step-by-step explanation:
the sum of 1+2-3-4+5+6-7-8+9+10-...+1378
Answer:
1389
Step-by-step explanation:
hope this helps?
Noah is ordering a taxi from an online taxi service. The taxi charges $2.50 just for the pickup and then an additional $2 per mile driven. How much would a taxi ride cost if Noah is riding for 4 miles? How much would a taxi ride cost that is mm miles long?
Answer:
$10.50
Step-by-step explanation:
We can make an equation
2.50+2x=?
x=4 because we are riding 4 miles.
so it's 2.5+2*4=?
let's solve
2.5+8=$10.50
The Cost of the taxi ride for 4 miles is $10.50 and Charge for m miles is 2.50 + 2m
Given:
Pick up charge = $2.50
Charge per mile = $2
Number of miles = 4
Cost of the taxi ride for 4 miles = Pick up charge + (Charge per mile + Number of miles)
= 2.50 + (2 × 4)
= 2.50 + 8
= $10.50
Charge for m miles = Pick up charge + (Charge per mile + Number of miles)
= 2.50 + (2 × m)
= 2.50 + 2m
Therefore, Cost of the taxi ride for 4 miles is $10.50 and Charge for m miles is 2.50 + 2m
Read more:
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I don't understand plz help
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Answer:
x = 2
Step-by-step explanation:
Triangles QST and QSR are congruent, so angle QST is congruent to angle QSR.
(3x +24)° = 30°
3x = 6 . . . . . . . . . divide by °, subtract 24
x = 2 . . . . . . . . . . divide by 3
__
Additional comment
What matters here is the relationship between the two marked acute angles. The fact that point Q is equidistant from the sides of angle TSR tells you that QS is an angle bisector and the two angles have equal measures. (The definition of an angle bisector is that it is equidistant from the sides of the angle.)
Recognition that the two triangles are congruent is another way to see that the marked acute angles have the same measure. The triangle congruence can be claimed on the basis of the HL theorem, since both are right triangles, have the same hypotenuse (QS), and have legs (QT, QR) with the same measure.
6. A company builds a model of its earning, and finds that its profit fits the linear model()=5―2500 Where p is the profit in dollars and q is the quantity of its product sold. a) Explain what the slope and y-intercept mean in the context of the problem. Be specific and answer in complete sentence. (2 points)
Answer:
The slope of 5 means that for each product sold, the profit increases by 5, and the intercept of -2500 means that if no products are sold, the company loses 2500.
Step-by-step explanation:
Linear function:
A linear function has the following format:
[tex]y = mx + b[/tex]
In which m is the slope, that is, by how much y changes for each unit of x, and b is the y-intercept, which is the values of y when x = 0.
In this question:
[tex]p(q) = 5q - 2500[/tex]
p is the profit in dollars and q is the quantity of its product sold.
a) Explain what the slope and y-intercept mean in the context of the problem.
The slope of 5 means that for each product sold, the profit increases by 5, and the intercept of -2500 means that if no products are sold, the company loses 2500.
A, B, and C are collinear points:
B is between A and C.
If AB = 3x + 4, BC = 4x - 1, and AC = 6x + 5,
find AC.
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Answer:
AC = 17
Step-by-step explanation:
The segment sum theorem tells you ...
AB +BC = AC
Substituting the given expressions, we have ...
(3x +4) +(4x -1) = (6x +5)
x = 2 . . . . . . . . . . . . . . . . . . subtract 3+6x from both sides
AC = 6x +5 = 6(2) +5
AC = 17
_____
AB = 10, BC = 7
Find the sine of ZF.
H
2/2
3/3
F
Write your answer in simplified, rationalized form. Do not round.
sin (F) =
Answer:
1/9 √57
Step-by-step explanation:
the length of HG = √(3√3² - 2√2²)
= √(27-8) = √19
sin L F = HG/GF = √19/ 3√3
= 1/9 √57
Please solve this equation
Answer:
fggggg hasdnkuw
Step-by-step explanation:
Please help me solve this. I keep getting the answer weong
Answer:
21 is the answer I think sike I lied ik its not im just trying get this over with
You can use this formula to work out the area of a triangle when you know two sides and the angle inbwtween them :
1/2 x a x b x sin(C)
where a and b are the two sides you know and C is the angle in between them.
So here a = 7, b = 14, C = 125.
Area = 1/2 x 7 x 14 x sin(125) = 40.138...
= 40.1 (nearest 10th)
A road has a scale of 1:50 000 The length of a road on the map is 8.5cm.Work out the length of the real road in kilometres
Answer:
ok so
8.5*150000
1275000 cm into kilometers is
12.75 kilometers
Hope This Helps!!!
A zoo is designing a giant bird cage consisting of a cylinder of radius rr feet and height hh feet with a hemisphere on top (no bottom). The material for the hemisphere costs 2020 per square foot and the material for the cylindrical sides costs 1010 per square foot; the zoo has a budget of 45004500. Find the values of rr and hh giving the birds the greatest space inside assuming the zoo stays within its budget. Note: surface of a cylinder's side 2πrh2πrh, surface of a sphere 4πr24πr2, volume of a cylinder's side πr2hπr2h, volume of a sphere 43πr343πr3
Answer:
r = 42,32 ft
h = 84.8 ft
Step-by-step explanation:
We are going to apply Lagrange multipliers method
The greatest space means maximum volume
V(cage) = Vol. of the cylinder + volume of the hemisphere
V(cylinder ) = π*r²*h
V(sphere) = (4/3)*π*r² ⇒ V(hemisphere) = (2/3)*π*r³
V(cage) = π*r²*h + (2/3)*π*r³
Associated costs:
Costs = cost of cylinder + cost of hemisphere
Area of the cylinder = Lateral area ( no bottom no top)
Area of the cylinder = 2*π*r*h
Area of hemisphere = 2*π*r²
A(r,h) = 2*π*r*h + 2*π*r²
C(r , h ) = 10* 2*π*r*h + 20* 2*π*r² C(r , h ) = 20*π*r*h + 40*π*r²
4500 = 20*π*r*h + 40*π*r²
20*π*r*h + 40*π*r² - 4500 = 0 20*π*r*h + 40*π*r² - 4500 = g(r,h)
V(cage) = π*r²*h + (2/3)*π*r³
δV/δr = 2*r*π*h + 2*π*r² δg(r,h)/δr = 20*π*h + 80*π*r
δV/δh = π*r² δg(r,h)/δh = 20*π*r
δV/δr = λ* δg(r,h)/δr
2*r*π*h + 2*π*r² = λ* 20*π*h + 80*π*r
2*r*π* ( h + r ) = 20*π* λ* ( h + 4*r)
r* ( h + r ) = 10*λ* ( h + 4*r) (1)
δV/δh = λ* δg(r,h)/δh
π*r² = 20*λ*π*r r = 20*λ (2)
20*π*r*h + 40*π*r² - 4500 = 0 (3)
We need to sole the system of equation 1 ; 2 ; 3
r = 20*λ plugging that value in equation 1
20*λ ( h + 20*λ ) = 10*λ* ( h + 4*r)
2( h + 20*λ ) = ( h + 4*20*λ)
2*h + 40*λ = h + 80*λ
h = 40*λ
20*π*r*h + 40*π*r² - 4500 = 0
20*π*20*λ*40*λ + 40*π+400λ² - 4500 = 0
16000*π*λ² + 16000*π*λ² = 4500
32000*π*λ² = 4500
320*π*λ² = 4500
λ² = 4500/1004,8 λ² = 4.48 λ = 2.12
Then
r = 20* λ r = 42,32 ft
h = 40* λ h = 84.8 ft
There are 9 students in a class: 7 boys and 2 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?
Answer: 9/7
Step-by-step explanation:
if a line intersect x axis at a point (6,0) and y axis at a point (0,-8). then what is equation of a line?
Answer: y = 4/3x -8
Step-by-step explanation:
(6,0) (0,-8)
0-(-8)/6-0 = 8/6 = 4/3
y intercept is given already
find the value of x if 3x over 2 equals to 3
Answer:
x = 2
Step-by-step explanation:
3x/2 = 3/1
cross-multiply to get:
3x = 6
divide each side by 2 to get:
x = 2
Find the percent of decrease from 46 songs to 41 songs. Round to the nearest tenth of a percent if necessary.
percent of decrease
%
Answer:
10.9 %
Step-by-step explanation:
46 - 41 = 5
5/46 * 100% = 10.8695652174%
Rounded
10.9 %
Joe drives for 3 hours and covers 201 miles. In miles per hour, how fast was he driving?
Answer:
50
Step-by-step explanation:
A local hamburger shop sold a combined total of 393 hamburgers and cheeseburgers on Thursday. There were 57 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Thursday?
Answer:
H+C = 393
H - 57 = C
~~~~~~~~~~~~~~~~
H + H - 57 = 393
2H = 450
H = 225
C = 168
Step-by-step explanation: