Using the binomial distribution, it is found that there is a:
0.2965 = 29.65% probability that exactly 2 out of 8 randomly selected Americans own a cat.0.4482 = 44.82% probability that more than 3 own a cat.What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, we have that:
30% of Americans own a cat, hence p = 0.3.A sample of 8 Americans is taken, hence n = 8.The probability that exactly 2 out of 8 randomly selected Americans own a cat is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.3)^{2}.(0.7)^{6} = 0.2965[/tex]
0.2965 = 29.65% probability that exactly 2 out of 8 randomly selected Americans own a cat.
The probability that more than 3 own a cat is given by:
[tex]P(X > 3) = 1 - P(X \leq 2)[/tex]
In which:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.3)^{0}.(0.7)^{8} = 0.0576[/tex]
[tex]P(X = 1) = C_{8,1}.(0.3)^{1}.(0.7)^{7} = 0.1977[/tex]
[tex]P(X = 2) = C_{8,2}.(0.3)^{2}.(0.7)^{6} = 0.2965[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0576 + 0.1977 + 0.2965 = 0.5518[/tex]
[tex]P(X > 3) = 1 - P(X \leq 2) = 1 - 0.5518 = 0.4482[/tex]
0.4482 = 44.82% probability that more than 3 own a cat.
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n/52 = 180/120 = n
18/n = 21/28 =n
n/4 = 24/6 =n
10/16 = n/56=n
solve each propotion
Answer:
1. n/52 = 180/120
180/120 = 1.5
n/52 = 1.5
Multiply 52 on both sides to simplify:
n=78
2. 18/n = 21/28
21/28 = 0.75
18/n = 0.75
Multiply n on both sides to remove
fraction: 18 = 0.75n and divide both sides
by 0.75 to simplify again.
n=24
3. n/4 = 24/6
24/6 = 4
n/4 = 4
Multiply 4 by both sides to simplify:
n=16
4. n/56 = 10/16
10/16 = 0.625
n/56 = 0.625
Multiply 56 on both sides to simplify:
n=35
Step-by-step explanation:
find the area bounded by the Curves y=4-x² and y
The area bounded by the Curves y=4-x² and y = 2x + 1 is 10 1/3 units.
What is area?Area is the amount of space occupied by a two dimensional shape or object.
y = 4 - x² and y = 2x + 1
4 - x² = 2x + 1
x² + 2x - 3 = 0
(x + 3)(x - 1) = 0
x = -3; or x = 1
The area (A) is given by:
[tex]A=\int\limits^1_{-3} {x^2+2x-3} \, dx \\\\A=10\frac{1}{3}[/tex]
The area bounded by the Curves y=4-x² and y = 2x + 1 is 10 1/3 units.
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First try was incorrect
A bag has 5 green rocks, 6 speckled rocks, and 7 yellow rocks. You
randomly pull a rock from the bag, put it back, and then pull out
another one
What is the probability of not getting a speckled and then not getting a
green? Write your answer as a percent rounded to the nearest whole
number.
Symbol required
Answer:
48%
Step-by-step explanation:
P (not getting a speckled rock) = 12/18 = 2/3
P (not getting a green rock) = 13/18
2/3 * 13/18 = 26/54 = 13/27 ≈ 48%
Rhombus J K L M is shown. The length of J K is 2 x + 4 and the length of J M is 3 x.
What is the length of a side of rhombus JKLM?
4 units
8 units
12 units
16 units
Answer:
12 units
Step-by-step explanation:
Properties of Rhombus:
1. length of all sides are equal.
2. Diagonals bisect each other at right angles
As the length of all sides are equal,
JM = JK
3x = 2x + 4
Subtract 2x from both sides,
3x - 2x = 4
x = 4
JM = 3*4 = 12 units
What is 1 + 1 x 3 Whoever answers it to
Answer:
It equals 4
Step-by-step explanation:
1 + 1 x 3=4
Answer:
I think it equals 4
Step-by-step explanation:
1 + 1 x 3=4
What will be the angle A?
Answer: 30 degrees
Step-by-step explanation:
Each of two computers can process bills at 160/min a newer model can process bills at 200/min after the first two computers have worked 1.5 min they are joined by the third computer how long will it take fromthe time the first two computers are turned on to process 1780
7*8/10 product lies between what numbers
Answer:
5 and 6.
Step-by-step explanation:
7*8 is 56. 56 divided by 10 is 5 6/10
Huntington Medical Center purchased a used low-field MRI scanner 2 years ago for $445,000. Its operating cost is $350,000 per year and it can be sold for $150,000 anytime in the next 3 years. The Center’s director is considering replacing the presently owned MRI scanner with a state-of-the-art 3 Tesla machine that will cost $2 million.The operating cost of the new machine will be $280,000 per year, but it will generate extra revenue that is expected to amount to $550,000 per year. The new unit can probably be sold for $875,000 3 years from now. You have been asked to determine how much the presently owned scanner would have to be worth on the open market for the AW values of the two machines to be the same over a 3-year planning period. The Center’s MARR is 10% per year.
The worth of the old scanner machine in the open market will be $86601.60.
How to calculate the worth on open market?To calculate the worth of the scanner on the open market, it's important to compare the values of the machines.
The calculation of the worth of the scanner goes thus:
Let the worth be represented by x.
x(A/P,10%, 3) - 350000 + 150000(A/F, 10%, 3) = 2000000(A/P, 10%, 3) + 270000 + 875000(A/F, 10%, 3)
= 0.4021x - 350000 + 45315 = -804200 + 270000 + 264337.50
0.4021x = 34822.50
Divide by 0.4021
x = 34822.60/0.4021
x = 86601.60
Therefore, the worth is $86601.60.
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Which graph represents an exponential function?
Answer:
the linear graph man
please why ask ezzy questions
A second-degree polynomial is a quadratic polynomial. O A. True O B. False
Answer:
True
Step-by-step explanation:
In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree
Answer:
Step-by-step explanation:
the answer isis truetrue
how many roots does y=x2-6x+9 have
Answer:
One root ; x = 3
Step-by-step explanation:
( a ± b )² = a² ± 2ab + b²
~~~~~~~~~
y = x² - 6x + 9
x² - 6x + 9 = x² - 2(x)(3) + 3² = ( x - 3 )²
( x - 3 )² = 0 ⇒ x - 3 = 0 ⇒ x = 3
Compared with the graph of the parent function,
which equation shows a vertical stretch by a factor
of 6, a shift of 7 units right, and a reflection over the
X-axis?
Step-by-step explanation:
as I don't see any equations or graphs here I can only answer in general :
f(x) is the patent function.
g(x) is the transformed function.
g(x) = -6f(x-7)
the "-" reflects the curve over the x-axis (what was positive is now negative and vice versa).
the factor 6 stretches the curve up and down by the factor 6 (everything is now 6 times larger or smaller).
and the argument "x-7" relates x (for the new function) with "x-7", meaning that now things are happening at x, that were originally happening at x-7, so they happen now "later" (more to the right on the x-axis) than before - hence a shift to the right.
Answer:
its D
Step-by-step explanation:
took the test :)
Write a formula that only works if the angle in the formula is given in radians.
Triangle ABC is similar to triangle WYZ.
Select all angles whose cosine equals 3/5.
Angle A
Angle C
Angle Z
Angle B
Angle W
Angle Y
Answer:
Angles A and W.
Explanation:
Cosine = Adjacent side/Hypotenuse
Determine the value of x if the mode is 18
Simplify the expression. (x)^2(2xy^3)^5
Answer:
32x^7y^15
Step-by-step explanation:
x^2(2xy^3)^5
can be simplified by adding up the x and y values.
23 10. Construct a quadratic equation whose roots are 1 and 2.A 3X-3x + 2-0 B. 3 + 3x - 2-0 C 22 + 3x - 2.0 D 2 - 3x +2=0 E.2x - 3x - 2 =0
Answer:
Step-by-step explanation:
Basic quadratic equation has this following form:
[tex](x-x_{1})(x-x_{2})=0[/tex]
where x1 and x2 are the roots.
For [tex]x_{1}=1[/tex] and [tex]x_{2}=2[/tex], we can find:
[tex](x-1)(x-2)=0 \rightarrow x^{2}-2x-x+2=0 \rightarrow x^{2}-3x+2=0[/tex]
Raul is drawing a plan for his bedroom. He needs to determine
the material costs for his flooring. The blueprint of the bedroom
uses a scale of 1 inch = 4 feet. If the flooring material costs
$2.55 per square foot, how much will it cost to buy the flooring
for Raul's bedroom?
The length on the blueprint is 3.25 inches. The width is 2.75 in.
The cost to buy the flooring for Raul's bedroom is $364.65.
What is the cost to buy the flooring for Raul's bedroom?A scale drawing is a reduced form in terms of dimensions of an original image / building / object
Actual length of the bedroom = 4 x 3.25 = 13 feet
Actual length of the bedroom = 4 x 2.75 = 11 feet
Area = 143 square feet
Cost = 143 x 2.55 = $364.65
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Help picture below problem 16
Answer:
40
Step-by-step explanation:
A straight angle is basically just a straight line, and it equals 180 degrees. Angle FPG is a straight angle.
To find the measure of angle DPE, we have to add together the other angles in the straight angle (which would be Angle FPD and Angle EPG) and then subtract that from 180 (measure of a straight angle).
Let's add Angle FPD and Angle EPG.
105 + 35 = 140
Now, let's subtract that from 180.
180 - 140 = 40
So, the measure of Angle DPE is 40. I hope this helps! Have a lovely day! (i basically just copy-and-pasted my answer to problem 17 because it was the same answer as this lol)
there are 374 students at a school. Each table in the cafeteria hold 16 students. What is the MINIMUM number of tables needed for all of the students to eat lunch at the same time
Answer: There should at least be 23 tables
Step-by-step explanation:
If there is 23 tables there will still be six students with nowhere to sit :)
Winston-Salem is halfway between Boone and Raleigh. Burlington is halfway between Winston- Salem and Raleigh. If Boone is located at the coordinates (-1,3) and Raleigh is at (-5, 9), what are the coordinates of Burlington?
Answer:
The answer is (-4, 15/2)
Step-by-step explanation:
Let the Boone be x, Winston-Salem be y, Raleigh be z and Burlington be m.
We are given that Winston-Salem is halfway between Boone and Raleigh. Burlington is halfway between Winston- Salem and Raleigh.
If Boone is located at the coordinates (-1,3) and Raleigh is at (-5, 9).
We will use Midpoint Formula
[tex]( \frac{x _{1} + x _{2}}{2} , \frac{y _{1} + y _{2}}{2} ) \\ [/tex]
Where,
x₁ = (-1) and x₂ = (-5)
y₁ = 3 and y₂ = 9
Now, We will find Co-ordinates of y i.e., Winston-Salem.
So,
[tex] ( \frac{( - 1) + ( - 5)}{2} , \frac{3 + 9}{2} ) \\ [/tex]
[tex]( \frac{( - 1 - 5)}{2} , \frac{12}{2} ) \\ [/tex]
[tex]( \frac{ - 6}{2} , \frac{12}{2} ) \\ [/tex]
[tex]( - 3,6)[/tex]
Here, The coordinates of y i.e., Winston-Salem is (-3, 6).
Now, We will find Co-ordinates of m i.e., Burlington.
So,
Again, Using of Midpoint Formula;
Where,
x₁ = (-3) and x₂ = (-5)
y₁ = 6 and y₂ = 9
So,
[tex]( \frac{( - 3) + ( - 5)}{2} , \frac{6 + 9}{2} ) \\ [/tex]
[tex]( \frac{( - 3 - 5)}{2} , \frac{15}{2} ) \\ [/tex]
[tex]( \frac{( -8)}{2} , \frac{15}{2} ) \\ [/tex]
[tex]( - 4 , \frac{15}{2} ) \\ [/tex]
Thus, The coordinates of Burlington is (-4, 15/2).
least to greatest 52, 63, 55, 56, 62, 54, 59, 60, 53, 61, 88
Answer:
52, 53, 54, 55, 56, 59, 60, 61, 62, 88
Step-by-step explanation:
You need to start from 52 to 88 (least to greatest) and then you will get answer.
00:23:04
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Product A sells 2.5 times more than Product B. Product B sells 60% less than Product C. Product C sold 25,000 units this month.
How many units of Product A were sold?
10,000
15,000
25,000 37,500 62,500
Answer:37,500
Step-by-step explanation: Find 60% of 25000 which is 15000 then multiply by 2.5
Find the equation of the line passing through the given point and
PARALLEL to the given equation. Write your answer in slope intercep
form. (xX_PARALLEL_Xx) *
(5,3) and y = x + 4
Answer:
y= x -2
Step-by-step explanation:
Slope-intercept form:
y= mx +c, where m is the slope and c is the y-intercept
Given equation: y= x +4
This equation is already in the slope-intercept form, thus its slope can be found from the coefficient of x.
Slope= 1
[tex]\textcolor{steelblue}{\text{Parallel lines have the same slope.}}[/tex]
Slope of unknown line= 1
Substitute the m= 1 into y= mx +c:
y= x +c
To find the value of c, substitute a pair of coordinates the line passes through into the equation.
When x= 5, y= 3,
3= 5 +c
c +5= 3
c= 3 -5
c= -2
Thus, the equation of the line is y= x -2.
Please help, has t toy cars. Zachary has 3 times as many toy cars as Oliver. Write an expression
that shows how many toy cars Zachary has.
Answer:
z=3t
Step-by-step explanation:
multiply it by 3
If two chords are the same distance from the center of a circle, then they are ______.
Answer:
1 is the answer to have the distance same
-0.5(14a - 22) = ? this for my work, please help me.
Answer:
-7a+11
Step-by-step explanation:
Which of the following number sentences is an example of the associative property? Select all that apply.
[tex](1\frac{2}{5}*3\frac{1}{2} )*4=1\frac{2}{5} (3\frac{1}{2} *4)[/tex]
[tex]2.5*(1.8+6.3)=(2.5*1.8)+(2.5*6.3)[/tex]
10(4.6 × 3) = (10 × 4.6) × 3
6.3 × 1 = 6.3
Associative property:-
a+(b+c)=(a+b)+cLets check one by one
#1
Here the rule is
(ab)c=a(bc)Hence Yes associative property
#2
Here the rule is
a(b+c)=ab+acHence no it's distributive property
#3
a(bc)=(ab)cYes
#4
ab=baNo
Associative property meaning rearranging the parentheses in an expression which will not change the result.
✔A)
[tex]\rightarrow \sf (1\dfrac{2}{5} \ x \ 3\dfrac{1}{2} ) \ x \ 4 = 1\dfrac{2}{5} (3\dfrac{1}{2} \ x \ 4 )[/tex]
[tex]\rightarrow \sf \dfrac{98}{5} = \dfrac{98}{5}[/tex]
This uses associate property as it is rearranged in a different way and result same.
B)
[tex]\rightarrow \sf 2.5 \ x \ (1.8 +6.3) = (2.5 \ x \ 1.8)+(2.5 \ x \ 6.3 )[/tex]
This property is called distributive property. a(b + c) = a(b) + a(c)
✔C)
[tex]\sf \rightarrow 10(4.6 \ x \ 3) = (10 \ x \ 4.6) \ x \ 3[/tex]
[tex]\sf \rightarrow 138 = 138[/tex]
associate property as the following is rearranged inside the parentheses
D)
[tex]\rightarrow \sf 6.3 \ x \ 1 = 6.3[/tex]
This does not fall under any method or else multiplicative identity property.
How does finding a pattern for a rule change if you subtract instead of add?
Answer:
When you subtract, the numbers decrease however when you add the numbers increase.
Step-by-step explanation: Theres the answer but is it multiple choice? if so than you can give me the choices and ill tell you the answer. But i hope this helped and if u need anything u can ask!