Answer:
1.) very large sample size
2.) 0.11326
3.) np and n(1-p) should be ≥ 10
4.) 0.010809
Step-by-step explanation:
Given :
p = 0.65 ; n = 500
2.)
P(x ≤ 300)
P(x =x) = nCx * p^x * (1 - p)^(n - x)
Using a binomial probability calculator :
P(x ≤ 300) = 0.11326
To justify why if it can be approximated using a normal distributon :
np and n(1-p) should be ≥ 10
np = 500 * 0.65 = 325
n(1-p) = 500(1 - 0.65) = 175
4.) probability using normal distribution estimate:
Mean, m = np = 500 * 0.65 = 325
Standard deviation, s = sqrt(n*p*(1-p)) = sqrt(500*0.65*(1 - 0.65)) = sqrt(113.75) = 10.665
x ≤ 300
Correction:
x = x + 0.5 = 300 - 0.5 = 300.5
P(x ≤ 300.5)
Zscore = (x - m) / s
Zscore = (300.5 - 325) / 10.665
Zscore = - 24.5 / 10.665
Zscore = - 2.297
P(Z ≤ - 2.297) = 0.010809
X can be modeled by a binomial distribution even though the sample was selected without replacement because the sample size is too large, and the probability that 300 or fewer high school students in the sample eat breakfast before going to school is 0.010809.
Given :
Suppose that 65% of high school students eat breakfast before going to school. A random sample of 500 high school students was surveyed. Let X = the number of high school students in a random sample of size 500 who eat breakfast before going to school.1) X can be modeled by a binomial distribution even though the sample was selected without replacement because the sample size is too large.
2) The formula for the binomial distribution is given by:
[tex]\rm P (x=x)= \; ^nC_x \times p^x \times (1-p)^{n-x}[/tex]
Now, substitute the known terms in the above formula.
[tex]\rm P (x\leq 300)= \; ^{500}C_x \times (0.65)^x \times (1-0.65)^{500-x}[/tex]
Simplify the above expression.
[tex]\rm P(x \leq 300)=0.11326[/tex]
3) Now, the value of np and n(1 - p) is given below:
np = 500 [tex]\times[/tex] 0.65 = 325
n(1 - p) = 500 [tex]\times[/tex] (1 - 0.65) = 175
X can be approximated by a Normal distribution because the value of np and n(1 - p) is greater than or equal to 10.
4)
First, determine the standard deviation.
[tex]\rm \sigma = \sqrt{np(1-p)}[/tex]
[tex]\rm \sigma = \sqrt{500\times 0.65 \times (1-0.65)}[/tex]
[tex]\rm \sigma = 10.665[/tex]
Now, the z-score can be calculated by using the formula:
[tex]\rm z =\dfrac{X-\mu}{\sigma}[/tex]
[tex]\rm z =\dfrac{300.5-325}{10.665}[/tex]
z = -2.297
So, the probability that 300 or fewer high school students in the sample eat breakfast before going to school is given by:
[tex]\rm P(Z\leq -2.297) = 0.010809[/tex]
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The sum of two numbers is 37 and the difference is 9. What are the numbers
Answer:
23 and 14
Step-by-step explanation:
Slope =3/2 y-intercept =0
Answer:
The equation is y=3/2x
Step-by-step explanation:
What is the y-intercept of the graph of the line given by the equation 3y + 4x = 15
A. 5
B. 4
C. 3
D. -4/3
Answer:
It would be 5
Step-by-step explanation:
*when a very low mental stability and exhaustion makes you forget to put the question
Answer:
5
Step-by-step explanation:
Think of 5 positive things and 9 negative things.
O O O O O
P P P P P P P P P
5 of the positive things will cancel out 5 of the negative things, leaving behind 4 negative things.
#teamtrees #WAP (Water And Plant)
[tex]\large\mathcal{\red {\underline {\overline {\mid {\purple {Answer}}\mid}}}}[/tex]
[tex] - 4 = 5 - 9[/tex]
Lupita y Fernando y Andrés quieren comprar entre los tres una bicicleta que ven todos los días en el aparador de la tienda todo para todos para sus vacaciones le han deseado tanto que decidieron comprarla cada uno sacó cuentas de lo que debería pagar por la bicicleta
Answer:
el precio de la biciclete entre 3 es lo que van a pagar cada quien.
Step-by-step explanation:
Help plz I need answe
your Answers are:
1. 0
2. 128
Pls help me pls and thank you
Answer:
10
Step-by-step explanation:
2/3 of 15 is 10
At a store closing, a universal discount rate is applied to all items. the table shows the price for three items.
Part B: To the nearest penny, what is the value of x?
A. $17.17
B. $28.62
C. $0.97
D. $10.80
Answer:
Step-by-step explanation:
the anser to this will b e c
Answer:
c
Step-by-step explanation:
The answer is c
Help me please many thanks :)
Answer:
(a) median = 6
(b) median = 14
(c) median = 37
(d) median = 19
(e) median = 4.5
(f) median = 15
(g) median = 126
(h) median = 345
(i) median = 50
(j) median = 75
Step-by-step explanation:
The median of the ungrouped data is obtained by arranging the numbers from the lowest to the highest number, then select the middle number. If you have two numbers in the middle, sum the two numbers and divide it by 2.
(a) in order: 3 4 4 6 7 8 8
median = 6
(b) in order: 11 11 12 14 15 16 17
median = 14
(c) in order: 31 31 34 37 38 41 42
median = 37
(d) in order: 17 17 18 19 19 21 23
median = 19
(e) in order: 3 3 3 4 5 6 7 9
median = (4 + 5) / 2 = 4.5
(f) in order: 12 14 14 14 16 18 19 20
median = (14 + 16)/2 = 15
(g) in order: 120 121 124 128 129 131
median = (124 + 128)/2 = 126
(h) in order: 321 339 342 345 352 358 362
median = 345
(i) in order: 43 46 49 49 51 51 51 52
median = (49 + 51)/2 = 50
(j) in order: 68 70 73 74 76 77 77 81
median = (74 + 76)/2 = 75
ok so this is an exaple of the question before this last question
Answer:
the expression is 3 + ( - 4) so as you can tell there are more
negative than positive as you can see in the table you first add 3 than you add -4 which you get -1
Step-by-step explanation:
hope it helps!
x/7-1=1-2/3y
HELPPPPP
Answer:
-14/3y+ 14
Step-by-step explanation:
hope this helps
What is the approximate radius of a sphere with a volume of 1436 cm3?
A. 41 cm
B. 14 cm
c. 7 cm
D. 69 cm
Answer:
r≈7cm
Step-by-step explanation:
Using the formula
V=4
--------= πr^3
3
r=(3V
-------------
4π)⅓=(3·1436
4·π)⅓≈6.99877cm
the answer is 7cm
Answer:
C. 7 cm
Step-by-step explanation:
Took the quiz. Trust
Work out the area of a rectangle with base, b = 20mm and perimeter, P = 42mm.
Answer:
20mm
Step-by-step explanation:
base=20mm
base x 2 because there are two long lines
20 x 2 = 40
42-40=2
amount needed on either side to balance
height=1mm
20 x 1 = 20mm
area = 20mm
Answer:
Let the length of the rectangle be 'l'
We have,
Perimeter of rectangle, P = 42mm.
[tex]or, 2(l+b) = 42\\or, l +b = \frac{42}{2} = 21\\or, l + 20 = 21\\or, l = 1mm\\[/tex]
Area of rectangle = [tex]lb = 1(20) = 20mm^{2}[/tex]
What is the value of y=5x+3 when x = 3
Answer:
y = 5(3)+3
= 15 +3
= 18
y = 18
hope it's helpful ❤❤❤❤
THANK YOU.
Hope you can see this
Answer:
I can see it, sorry
Step-by-step explanation:
Factor 2x2 - 6x + 4 completely.
Answer:
2(x - 1)(x - 2)
Step-by-step explanation:
2x^2 - 6x + 4
= 2(x^2 - 3x + 2)
= 2(x - 1)(x - 2)
Find the geometric mean of sqrt 77 and sqrt 343.
Answer:
12.75
Step-by-step explanation:
The computation of the geometric mean of sqrt 77 and sqrt 343 is given below:
As we know that
Geometric mean = [tex]\sqrt{ab}[/tex]
where
a is the first number = [tex]\sqrt{77}[/tex]
And, the b is the second number = [tex]\sqrt{343}[/tex]
Now first we have to convert into a number
For a it, is = 8.78
And, for b, it is = 18.52
Now the geometric mean is
[tex]= \sqrt{8.78 \times 18.52}[/tex]
= 12.75
Cost of a tie: $35.50
Markup: 30%
Discount: 20%
Tax: 5%
Answer:
40.25 i believe
Step-by-step explanation:
NEED HELPP CORRECTT ANSWERS AND WILL GIVE THANKS AND MARK BRAINLIST ONLY FOR CORRECT ANSWER
4,20
i think that the answer
Omar is setting up a proof of the Pythagorean theorem. He draws a scalene right triangle and plans to use similar triangles in his proof. What else should he draw?
Answer:
The altitude to the triangles hypotenuse
Step-by-step explanation:
HELP PLS I am failing!! Will mark brainiest show your work!
Answer:
Step-by-step explanation:
1.)
7 - 3i - 6 - 4i
Combine like terms
1 - 7i
Cant do anything else
__________________________________________________________
2.)
5 + 4i - 9 - i
Combine like terms
- 4 + 3i
Can't do anything else
__________________________________________________________
3.)
5i - 3 - 7 + 2i
7i - 10
Can't do anything else
__________________________________________________________
4.)
9i + 3 - 4 + 3i
12i - 1
Cant do anything else
__________________________________________________________
Hope this helped!
Have a supercalifragilisticexpialidocious day!
Answer:
1. is 7-3i-(6-4i)= 1+i
2. is 5 + (4 * i) - (9 - i) = -4+5i
3. is (5 * i) - 3 - (7 + (2 * i)) = -10+3i
4. is (9 * i) + 3 - (4 + (3 * i)) = -1+6i
trust me guys Im in 11 grade i did this all ready
Step-by-step explanation:
-An internatinal call costs $9.35 for 32 minutes. What is the cost per minute?
Simplify the expression:
2(1 + 2v) =
a. Identify the series of transformations that would map Circle A onto Circle B.
b. Identify the series of transformations that would map Circle C onto Circle A.
Answer:
Step-by-step explanation:
Assumed Knowledge
Motivation
Content
Radii and chords
Angles in a semicircle
Angles at the centre and circumference
Cyclic quadrilaterals
The alternate segment theorem
Similarity and Circles
Links Forward
Converse of the circle theorems
Coordinate geometry
Calculus
History and Applications
The Euler line
The nine-point circle
Morley’s trisector theorem
Appendix − Converses to the Circle Theorems
Answers to Exercises
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ASSUMED KNOWLEDGE
Introductory plane geometry involving points and lines, parallel lines and transversals, angle sums of triangles and quadrilaterals, and general angle-chasing.
Experience with a logical argument in geometry written as a sequence of steps, each justified by a reason.
Ruler-and-compasses constructions.
The four standard congruence tests and their application to proving properties of and tests for special triangles and quadrilaterals.
The four standard similarity tests and their application.
Trigonometry with triangles.
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MOTIVATION
Most geometry so far has involved triangles and quadrilaterals, which are formed by intervals on lines, and we turn now to the geometry of circles. Lines and circles are the most elementary figures of geometry − a line is the locus of a point moving in a constant direction, and a circle is the locus of a point moving at a constant distance from some fixed point − and all our constructions are done by drawing lines with a straight edge and circles with compasses. Tangents are introduced in this module, and later tangents become the basis of differentiation in calculus.
The theorems of circle geometry are not intuitively obvious to the student, in fact most people are quite surprised by the results when they first see them. They clearly need to be proven carefully, and the cleverness of the methods of proof developed in earlier modules is clearly displayed in this module. The logic becomes more involved − division into cases is often required, and results from different parts of previous geometry modules are often brought together within the one proof. Students traditionally learn a greater respect and appreciation of the methods of mathematics from their study of this imaginative geometric material.
The theoretical importance of circles is reflected in the amazing number and variety of situations in science where circles are used to model physical phenomena. Circles are the first approximation to the orbits of planets and of their moons, to the movement of electrons in an atom, to the motion of a vehicle around a curve in the road, and to the shapes of cyclones and galaxies. Spheres and cylinders are the first approximation of the shape of planets and stars, of the trunks of trees, of an exploding fireball, and of a drop of water, and of manufactured objects such as wires, pipes, ball-bearings, balloons, pies and wheels.
a) The series of transformations to map Circle A onto Circle B is likely a translation. b) The series of transformations to map Circle C onto Circle A is a translation, rotation, and scaling.
a. To map Circle A onto Circle B, we must determine the transformation sequence. We can scale, rotate, and translate.
Translation: An object is translated horizontally or vertically without affecting shape or orientation. To match Circle B, Circle A appears to need to be shifted right and up.
Rotation: An object rotates around a fixed point. Rotation may not be needed since Circle A and Circle B appear to be aligned.
Scaling: An object is resized by scaling. Since Circle A and Circle B are the same size, scaling doesn't seem necessary.
Thus, Circle A-to-Circle B transformations are likely translations.
b. Again, we must determine the transformation sequence to transfer Circle C onto Circle A. Translation: Based on their relative positions, Circle C needs to be shifted left and down to match Circle A.
Rotation: To align Circles A and C, they must be rotated.
Scaling: Circle A is larger than Circle C, hence Circle C should be scaled down.
Thus, translating, rotating, and scaling map Circle C onto Circle A.
To know more about transformations
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18. Find the measure of angle STP.
Answer:
x=7
Step-by-step explanation:
∠STP=∠SWT+∠TSW(exterrior ∠ of Δ)
15x=7x+1+7x+6
x=7
Which shows only a vertical translation? A triangle is translated to the right. A triangle is translated upwards. A triangle is translated diagonally.
Answer:
b
Step-by-step explanation:
A triangle being translated upwards shows only a vertical translation. Option A is correct.
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
When a shape is translated vertically, it moves up or down along the y-axis, maintaining its shape and size. In the case of a triangle being translated upwards, the y-coordinates of its vertices are increased, resulting in a vertical shift of the entire triangle.
When a shape is translated horizontally, it moves left or right along the x-axis, maintaining its shape and size.
When a shape is translated diagonally, it moves in both the horizontal and vertical direction, changing its position but maintaining its shape and size.
Learn more about transformation here:
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Can someone help me on this? Quite lost
answer:
2. 3/2
1. y=-7
Step-by-step explanation:
You and a friend join a gym. The registration fee is $30 and the monthly membership is $20. If the total bill for you and your friend is $420, how many months did you pay for?
Answer:
You payed for 18 months.
Step-by-step explanation:
420-60=360
360÷20=18
A group of 12 adults and 26 children go to a theme park.
The total cost of tickets was £1804.80
And adults ticket costs £51.60
Find the cost for a child
Answer:
45.56923076923077
Step-by-step explanation:
Work out 51.6 x 12 which is 619.2 and subtract that from 1804.80 then x your answer which is 1,184.8 and divide by 26 to get your answer which is 45.569....
5 (y + 6) + 2y < 4 (y+2) - 5
Answer:
I think the answer is Y < -9
Answer:
i think the answer is 7y + 30 < 4y + 3