Answer:
The sample size necessary is of 168.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Based on a previous study, arrival delay times have a standard deviation of 39.6 minutes.
This means that [tex]\sigma = 39.6[/tex]
Find the sample size necessary to estimate the mean arrival delay time for all American Airlines flights from Dallas to Sacramento to within 6 minutes with 95% confidence.
This is n for which M = 6. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]6 = 1.96\frac{39.6}{\sqrt{n}}[/tex]
[tex]6\sqrt{n} = 1.96*39.6[/tex]
[tex]\sqrt{n} = \frac{1.96*39.6}{6}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*39.6}{6})^2[/tex]
[tex]n = 167.34[/tex]
Rounding up:
The sample size necessary is of 168.
Find two consecutive even numbers whose sum is 758.
Answer:
378 and 380
Step-by-step explanation:
The two even consecutive numbers that add up to 758 are going to be very close to half of 758. This is because two half of 758 are going to be the most similar addends of 758. This is important because the answers will be consecutive and therefore, must also be very similar. To solve, first, divide 758 by 2. This is 379, which is not an even number. So, to find the needed addends subtract and add 1 to 379. Both of these will be even and consecutive. These two numbers are 378 and 380. Then, to check you, can add them and see that they do sum 758.
Answer:
Step-by-step explanation:
Let the first number = x
Let the second number = x + 2
x + x + 2 = 758 Collect like terms
2x + 2 = 758 Subtract 2
2x = 758 - 2 Combine
2x = 756 Divide by 2
2x/2 = 756/2
x = 378
The first number is 378
The second number 380
If your teacher is really fussy, you can do it this way.
Let the first number = 2x
Let the second number = 2x + 2
The reason for this is to guarantee that both numbers were even to start with.
2x + 2x+2 = 758 Combine like terms
4x + 2 = 758 Subtract 2
4x = 756 Divide by 4
x = 756/4
x = 189
Therefore 2x = 378
2x + 2 = 380 Just as before.
1. Đường kính của một loại trục máy là một đại lượng ngẫu nhiên có phân phối chuẩn N (μ = 250mm, σ2 = 25mm2). Trục máy được gọi là hợp quy cách nếu đường kính từ 245mm đến 255mm. Cho máy sản xuất 100 trục. Tính xác suất để:
a. Có 50 trục hợp quy cách.
b. Có không quá 80 trục hợp quy cách
Answer:
please ask in English
Step-by-step explanation:
then I can help
Test scores are normally distributed with a mean of 68 and a standard deviation of 12. Find the z – score for a grade of 74. Round your answer to two numbers after the decimal.
Answer:
gang nem
Step-by-step explanation:
The hypotenuse of a right triangle is two more than the length of one of its legs. Find the side lengths of the right triangle given the perimeter= 60 and it's area= 120
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Answer:
10 and 24
Step-by-step explanation:
We know that some of the Pythagorean triples that appear in math problems are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17).
These have (perimeter, area) values of (12, 6), (30, 30), (56, 84), (40, 60).
For some scale factor n, we want (p·n, a·n²) = (60, 120). Of the triangles listed, we see that the (5, 12, 13) triangle scaled by n=2 will satisfy the problem requirements. (30·2, 30·2²) = (60, 120)
The side lengths are 10 and 24.
__
Check
For the side lengths we found, the perimeter is 10+24+26 = 60; the area is 1/2(10)(24) = 120. The hypotenuse is 2×13 = 26 = 24+2.
__
In the attached, one side is x, the other is y. The hypotenuse is (x+2). The square root equation comes from ...
x² +y² = (x+2)² ⇒ y² = (x² +4x +4) -x² ⇒ y² = 4x +4 = 4(x +1)
_____
Additional comment
The graph shows the solution of the various constraints. At least, the combination of constraints will give a quadratic equation in x. They can be combined in a way that gives a cubic equation in x. Either way, we prefer the graphical or "guess and check" approach (above) as being easier to do.
Using the third equation in the attachment to write an expression for y, we have ...
y = 58 -2x
Substituting that into the second equation gives ...
(x(58 -2x)/2 = 120
29x -x² = 120
x² -29x +120 = 0
(x -5)(x -24) = 0 . . . . x = 5 or 24.
The root x=5 is a legitimate solution to the pair of equations we chose to solve. The line y=58-2x intersects the hyperbola xy/2 = 120 in two places. However, (x, y) = (5, 48) does not satisfy the hypotenuse requirement that x+2 > y.
22. The ratio in which (4, 5) divides the join of (2, 3)
and (7, 8) is :
(a) 4 : 3
(c) 3 : 2
(b) 5:2
(d) 2:3
Let the ratio be m:n
(x,y)=(4,5)Points be (x1,y1)=(2,3)(x2,y2)=(7,8)We know
[tex]\boxed{\sf (x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]
[tex]\\ \sf\longmapsto (4,5)=\left(\dfrac{7m+2n}{m+n},\dfrac{8m+3n}{m+n}\right)[/tex]
Now
.[tex]\\ \sf\longmapsto \dfrac{7m+2n}{m+n}=4\dots(1)[/tex]
[tex]\\ \sf\longmapsto \dfrac{8m+3n}{m+n}=5\dots(2)[/tex]
Adding both
[tex]\\ \sf\longmapsto \dfrac{7m+2n+8m+3n}{m+n}=4+5[/tex]
[tex]\\ \sf\longmapsto \dfrac{7m+8m+2n+3n}{m+n}=9[/tex]
[tex]\\ \sf\longmapsto \dfrac{15m+5n}{m+n}=9[/tex]
[tex]\\ \sf\longmapsto 15m+5n=9(m+n)[/tex]
[tex]\\ \sf\longmapsto 15m+5n=9m+9n[/tex]
[tex]\\ \sf\longmapsto 15m-9m=9n-5n[/tex]
[tex]\\ \sf\longmapsto 6m=4n[/tex]
[tex]\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{6}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{3}{2}[/tex]
[tex]\\ \sf\longmapsto m:n=3:2[/tex]
Option B is correct
Write the ratio 4 L : 5.6 L as a fraction in the simplest form with whole numbers in the numerator and denominator
Answer:
Step-by-step explanation:
It's 5/7
You get that by having a calculator that does that. If you don't then the way to do it is multiply the numerator and denominator by 1.25
4 * 1.25 = 5
5.6 * 1.25 = 7
In 10 words or fewer, what is the square root of -9?
Type answer here...
What is the square root of -9
Answer:
no solution
Step-by-step explanation:
a negative number cannot be square rooted
Answer:
"not possible". no such thing as a negative squared number
what is the simple definition of realnumbers
Answer:
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion).
Find the length of side
x
x in simplest radical form with a rational denominator.
Thanks In advance.
Answer:
Sorry I dont really understand wish I could help:(
Step-by-step explanation:
Answer:
[tex]\sqrt{10}[/tex]
[tex]\sqrt{5 } ^{2} + \sqrt{5 } ^{2} = x^{2}[/tex]
[tex]x^{2} =10[/tex]
Step-by-step explanation:
What effect will replacing x with (x−4) have on the graph of the equation y=(x−3)2 y = ( x − 3 ) 2 ?
Answer:
y"= 2 wich is positive
Step-by-step explanation:
Step-by-step explanation:
Our equation is: y=(x-3)²
x should be replaced by x-4
y=(x-3)²
y=[(x-4)-3]²
y=(x-4-3)²
y=(x-7)²
The graph is still a parabola but with a different vertex
The vertex here is :
y= (x-7)²
y= x²-14x-49
y'= 2x-14
solve y'=0
2x-14=0
2x=14
x=7
You can easily find it without derivating by dividing -14 by -2
since: x²-14x-49
a=1 b= -14 c=-49
-b/2a = 14/2 = 7
the image of 7 is:
y=(7-7)² = 0
so the coordinates of the new vertex are (7,0) and it's a maximum
since y">0
y'= 2x-14
y"= 2 wich is positive
I need to know how to find the area and to simplify it
Area of parallelogram = b × h
Base = x + 7
Height = x + 3
ATQ
Area = (x + 7) ( x + 3)
x² + 3x + 7x + 21
x² + 10x + 21
Answered by Gauthmath must click thanks and mark brainliest
Find the degree of each polynomial and indicate whether the
polynomial is a monomial, binomial, trinomial, or none of these.
Answer:
1. Degree = 1, monomial
2. Degree = 2, monomial
3. degree = 2, trinomial
4. Degree = 2, binomial
5. Degree = 2, binomial
Step-by-step explanation:
An equal number of juniors and seniors are trying out for six spots in this year's decathlon
team. If the team must consist of four seniors and two juniors, then how many different
possible decathlon teams could result if five juniors try out?
50
55
75
100
There are 50 different possible debating teams that could be selected as obtained using COMBINATION.
Since there are EQUAL number of juniors and seniors ;
Then we have 5 of each.
Here, the order of arrangement DOES NOT matter, Hence, we use COMBINATION
since the team MUST contain 4 SENIORS and 2 JUNIORS
4 Seniors from 5 = 5C4 = 5
2 Juniors from 5 = 5C2 = 10
Hence, (5C4 * 5C2) = 5 * 10 = 50
Hence, there are 50 different possible debating teams that could be selected.
Learn more about COMBINATION :
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ANSWER PLS!! :DD
Which of the following is not a property of a regular pyramid?
A. lateral faces that are parallel
B. lateral faces that are congruent isosceles triangles
C. lateral edges that are congruent
D. volume of the pyramid is equal to one-third the product of the area of its base and its altitude
Answer:
a
Step-by-step explanation:
Lateral faces that are parallel is not a property of a regular pyramid. The correct option is A.
What is a regular pyramid?Any pyramid whose base is a regular polygon and whose lateral edges are all of the same lengths is said to be regular.
The properties of a regular pyramid are:-
Lateral faces that are congruent isosceles triangles. Lateral edges that are congruent and the volume of the pyramid is equal to one-third the product of the area of its base and its altitude.
Hence, option A is correct.
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What is the slope of the line that passes through the points (-7, -4) and
(-11, -2)? Write your answer in simplest form.
Answer:
-1/2
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -2 - -4)/( -11 - -7)
=( -2+4)/( -11+7)
= 2 / -4
= -1/2
The king and queen spent $1500 on decorations for the ball +8 dollars per guest for party favors. The king and queen are charging each guest $12 to enter the dance. How many guests must come to the ball for the king and queen to break even? (you must write an equation and then solve)
Answer:
375 guests
Step-by-step explanation:
costs: 1500 + 8g
income: 12g
They must be equal
1500+8g = 12g
Subtract 8g from each side
1500 +8g-8g =12g-8g
1500= 4g
Divide by 4
1500/4 = 4g/4
375 = g
If f(x)=-4x-5 and g(x)=3-x whats is g(-4)+f(1)
Answer: -2
Step-by-step explanation:
g(-4) = 3 - (-4) = 3 + 4 = 7f(1) = -4(1) - 5 = -4 - 5 = -9g(-4) + f(1) = 7 + (-9) = 7 - 9 = -2
Chris is buying new wood flooring for his house. The cost depends on the area of the floors.
Which is the dependent variable, and which is the independent variable?
Answer:
strong and fexible .
variable
How tall is the table?
Answer:
too complex:<
Step-by-step explanation:
120cm+120cm=240cm (2 squirrels + 2 air spaces)
90cm+90cm=180cm (2 rats + 2 air spaces)
240cm-180cm=(2 squirrels + 2 air spaces) - (2 rats + 2 air spaces)
=2 squirrels + 2 air spaces - 2 rats - 2 air spaces
=2 squirrels - 2 rats
=60cm
1 squirrel - 1 rat = 60cm divided by 2
= 30cm
120cm + 90cm = squirrel + air space + rat + air space
= 210cm
I've no idea!! This qn is too challenging!!
But i hope the above workings might help you in a way or another:>
The table is 105cm tall.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let the table is x
Squirrel is y
Rat is z
From 1st diagram
x+y-z=120...(1)
From 2nd diagram
x+z-y=90...(2)
Add 1 and 2
x+y-z+x+z-y=120+90
2x=210
Divide both sides by 2
x=105
Hence, the table is 105cm tall.
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Jared works at a clothing store and is listening to a customer complain about a shirt he purchased that's damaged. Which behavior can Jared exhibit to show good communication skills with the customer? O a) Stopping the customer to quickly explain the store's return policy b) Repeating back what he has heard once the customer is done speaking Od Asking the customer how the shirt was damaged O d) Promising the customer a full refund even though it's against policy
Answer:
C
Step-by-step explanation:
in my point of view, my choice is C (asking the customer how the shirt was damaged) because when he finds out the reason why the shirt was damaged, he will explain whether or not that fault is in the store's return policy
another reason:
A) stopping the customers when they are talking, it's impolite behavior and i ensure that that customer will feel disatified.
B) i guess that customer doesnt waste of time because it
D) a full refund without finding the reason, i dont think it's a good idea
Find f(2) given f(x) = -3x^2 + 2x+11
Answer:
Answer:f(2)=-3(2)^2+2*2+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11 =3
hence, f(2)=3
answer this now please :)
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Answer:
E. 384 cu ft
Step-by-step explanation:
The sum of length and width is half the perimeter, so the width is ...
(40/2) -12 = 8 . . . feet
The depth is half that, so is 8/2 = 4 feet.
The volume is ...
V = LWH = (12 ft)(8 ft)(4 ft) = 384 ft³
write each of the following fraction as equivalent fractions with a denominator of 10 a. 1/2 b. 1/4 c. 3/30 d. 12/30
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Answer:
a. 5/10
b. 2.5/10
c. 1/10
d. 4/10
Step-by-step explanation:
To find the numerator, multiply each fraction by 10.
a. (1/2)(10) = 5, so 1/2 = 5/10
b. (1/4)(10) = 2.5, so 1/4 = (2.5)/10 or (5/2)/10
c. (3/30)(10) = 1, so 3/30 = 1/10
d. (12/30)(10) = 4, so 12/30 = 4/10
I need help guys thanks so much
Answer:
A. 243
Step-by-step explanation:
[tex] 81^\frac{5}{4} = (3^4)^\frac{5}{4} = 3^{4 \times \frac{5}{4}} = 3^5 = 243 [/tex]
Answer: A
I just simplified it to 3^5, and that is also 243.
I really need help with this one
To make sky blue Sam uses two drops of blue paint for every eight drops of white paint. He wants to
make a large amount of sky blue paint. If he uses sixteen drops of blue, how many drops of white will he
need?
Answer:
64
Step-by-step explanation:
The Ratio of Blue to White drops is 2:8
16*4=64,... 16:64 Have a nice day!
in triangle JKL, angle JKL is a right angle, line KM is an altitude, JL=20, ML=4. Find KM
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Answer:
KM = 8
Step-by-step explanation:
The ratio of long side to short side is the same for all of the triangles in this geometry:
KM/ML = JM/KM
KM² = ML·JM = 4(20-4) = 64
KM = √64 = 8
The length of KM is 8 units.
t 0 2 4 6 8 10
P(t) 0 36 43 47 52 60
Kunyu's family has an above ground swimming pool in the shape of a cylinder, with a radius of 10 feet and a height of 5 feet. The pool contains 1000 cubic feet of water at time t=0. During the time interval 0≤t≤10 hours, water is pumped into the pool at the rate () cubic feet per hour. The table above gives values of () for selected values of . During the same time interval, water is leaking from the pool at the rate of () cubic feet per hour, where ()=18−0.04.
(Note: The volume V of a cylinder with radius r and height h is given by =2ℎ .)
Find the rate at which the volume of water in the pool is increasing at time t=6 hours. How fast is the water level in the pool rising at t=6 hours? Indicate units of measure in both answers.
Answer:
a. 24.12 ft³/hr b. 0.0768 ft/hr
Step-by-step explanation:
a. Find the rate at which the volume of water in the pool is increasing at time t=6 hours.
The net rate of change of volume of the cylinder dV/dt = volume flow rate in - volume flow rate out
Since volume flow rate in = P(t) and volume flow rate out = R(t),
dV/dt = P(t) - R(t)
[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]
We need to find the rate of change of volume when t = 6.
From the table when t = 6, P(6) = 47 ft³/hr
Also, substituting t = 6 into R(t), we have R(6)
[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]
[tex]\frac{dV}{dt} = 47 - 18e^{0.04X6}\\\frac{dV}{dt} = 47 - 18e^{0.24}\\\frac{dV}{dt} = 47 - 18 X 1.27125\\\frac{dV}{dt} = 47 - 22.882\\\frac{dV}{dt} = 24.118 ft^{3}/hr[/tex]
dV/dt ≅ 24.12 ft³/hr
So, the rate at which the water level in the pool is increasing at t = 6 hours is 24.12 ft³/hr
b. How fast is the water level in the pool rising at t=6 hours?
Since the a rate at which the water level is rising is dV/dt and the volume of the cylinder is V = πr²h where r = radius of cylinder = 10 ft and h = height of cylinder = 5 feet
dV/dt = d(πr²h)/dt = πr²dh/dt since the radius is constant and dh/dt is the rate at which the water level is rising.
So, dV/dt = πr²dh/dt
dh/dt = dV/dt ÷ πr²
Since dV/dt = 24.12 ft³/hr and r = 10 ft,
Substituting the values of the variables into the equation, we have that
dh/dt = dV/dt ÷ πr²
dh/dt = 24.12 ft³/hr ÷ π(10 ft)²
dh/dt = 24.12 ft³/hr ÷ 100π ft²
dh/dt = 0.2412 ft³/hr ÷ π ft²
dh/dt = 0.2412 ft³/hr
dh/dt = 0.0768 ft/hr
So, the arate at which the water level is rising at t = 6 hours is 0.0768 ft/hr
The graph of [tex]y = ax^2 + bx + c[/tex] is a parabola. The axis of symmetry is [tex]x = -b/2a[/tex]. What are the coordinates of the vertex?
The vertex can be written as:
(-b/2a, b^2/(4*a) - b^2/2a + c)
For a general parabola:
y = a*x^2 + b*x + c
We can write the vertex as:
(h, k)
The x-value of the vertex is the value of the axis of symmetry.
Then we have:
h = x = -b/2a
Now we need to find the y-value of the vertex.
To do that, we just replace the variable "x" by the x-value of the vertex in our equation, so we get:
k = y = a*(-b/2a)^2 + b*(-b/2a) + c
k = b^2/(4*a) - b^2/2a + c
Then the coordinates of the vertex are:
(h, k) = (-b/2a, b^2/(4*a) - b^2/2a + c)
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Find the distance between the points (-4, -2) and (-8, 6)
Answer:
distance=√[(x2-x1)²+(y2-y1)²]
√[{6-(-2)}²+ (-8-(-4))²]
√(64+16)
√[100]
10
Points given
(-4,-2)(-8,-6)Distance:-
[tex]\\ \sf \longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{(-8+4)^2+(6+2)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{(-4)^2+(8)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{64+16}[/tex]
[tex]\\ \sf \longmapsto \sqrt{80}[/tex]
[tex]\\ \sf \longmapsto 8.4[/tex]
