Answer:
[tex]P(X = x) = C_{5,x}.(0.3)^{x}.(0.7)^{5-x}[/tex]
Possible values of x: Any from 0 to 5.
[tex]P(X = 0) = C_{5,0}.(0.3)^{0}.(0.7)^{5-0} = 0.16807[/tex]
[tex]P(X = 1) = C_{5,1}.(0.3)^{1}.(0.7)^{5-1} = 0.36015[/tex]
[tex]P(X = 2) = C_{5,2}.(0.3)^{2}.(0.7)^{5-2} = 0.3087[/tex]
[tex]P(X = 3) = C_{5,3}.(0.3)^{3}.(0.7)^{5-3} = 0.1323[/tex]
[tex]P(X = 4) = C_{5,4}.(0.3)^{4}.(0.7)^{5-4} = 0.02835[/tex]
[tex]P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{5-5} = 0.00243[/tex]
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this question:
[tex]n = 5, p = 0.3, q = 1 - p = 0.7[/tex]
So
[tex]P(X = x) = C_{5,x}.(0.3)^{x}.(0.7)^{5-x}[/tex]
Possible values of x: 5 trials, so any value from 0 to 5.
For each value of x calculate p(☓ =x)
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.3)^{0}.(0.7)^{5-0} = 0.16807[/tex]
[tex]P(X = 1) = C_{5,1}.(0.3)^{1}.(0.7)^{5-1} = 0.36015[/tex]
[tex]P(X = 2) = C_{5,2}.(0.3)^{2}.(0.7)^{5-2} = 0.3087[/tex]
[tex]P(X = 3) = C_{5,3}.(0.3)^{3}.(0.7)^{5-3} = 0.1323[/tex]
[tex]P(X = 4) = C_{5,4}.(0.3)^{4}.(0.7)^{5-4} = 0.02835[/tex]
[tex]P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{5-5} = 0.00243[/tex]
Points $A(-1, -2)$ and $B(3, 2)$ are the endpoints of a diameter of a circle graphed in a coordinate plane. How many square units are in the area of the circle? Express your answer in terms of $\pi$.
Answer:
8 pi square units
Step-by-step explanation:
AB=V[3-(-1)]^2+[2-(-2)]^2=V16+16=V4^2*2=4V2
radius =4V2/2=2V2
Area=pi*(2V2)^2=8pi square units
Given the diagram below, what is cos(45") ?
A. 22
B.
C.
V2
D. 4,2
Graph the solution set for the inequality
y > 2x - 5 by following these steps:
Step 1: Identify the slope and y-intercept.
slope = y-intercept =
-4
Answer:
Salutations!
The slope is (2)
And the y-intercept is (-5)
Hope you're having a good day, and may god bless :)
Slope of the given inequality is 2 and the y-intercept of the given inequality is (0, - 5).
What is an inequality?"An inequality is the relationship between two values that are not equal is defined by inequalities. Inequality means not equal."
The given inequality is:
y > 2x - 5
By plotting this inequality, we get:
Slope of the given inequality is 2.
The y-intercept of the given inequality is (0, - 5)
Learn more about an inequality here: https://brainly.com/question/20708985
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Identify the equation that translates y = l n (x) five units down. y = l n (x minus 5) y = l n (x) + 5 y = l n (x + 5) y = l n (x) minus 5
Answer:
y=ln(x) minus five
Step-by-step explanation:
y=ln(x) five units down
Five units down could mean minus five(-5)
The expression can be written as
y=ln(x)-5
That is,
y=ln(x) minus five
The equation that translates y = ln(x) 5 units down is y' = ln(x) - 5
How to determine the equation?The function is given as:
y = ln(x)
When translated down by 5 units, the rule of translation is:
(x, y) => (x, y - 5)
So, we have:
y' = ln(x) - 5
Hence, the equation that translates y = ln(x) 5 units down is y' = ln(x) - 5
Read more about transformation at:
https://brainly.com/question/4289712
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Which ordered pair is a solution to the system of linear equations 1/2x-3/4y=11/60 and 2/5x+1/6y=3/10
Answer:
([tex]\frac{2}{3} , \frac{1}{5}[/tex])
Step-by-step explanation:
The fastest way to do this is to convert both equations into slope-intercept form and graph it to find the solution point. If you wanted to do this algebraically, you might want to start out by getting rid of the fractions and using either substitution or elimination to find x and y.
In a rectangular coordinate system, what is the number of units in the distance from the origin to the point (7, -24)?
Answer:
25 units
Step-by-step explanation:
Distance Formula: [tex]d = \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
Our points: (0, 0) and (7, -24)
[tex]d = \sqrt{7^2+(-24)^2}[/tex]
d = √(49+576)
d = √625
d = 25
Answer:
25
Step-by-step explanation:
You can also use the pythagorean theorem.
From (0, 0) to (7, -24), one of the side lengths of the triangle is 24, and the other is 7.
Now we can use the pythagorean theorem with these numbers
[tex]7^2 +24^2=x^2[/tex], and now we can solve these squares to get
[tex]49+576=x^2\\625=x^2\\\sqrt{625} = x\\[/tex], So x = 25
Una casa de ropa tiene todos sus artículos en liquidación por cambio de temporada. El cartel de la puerta dice: 20% de descuento. Cuánto tendrá que pagar una persona que gastó $3500? Y alguien que gastó $8000
Answer:
$2,800 and $6,400
Step-by-step explanation:
Aquí, sabemos que hay un 20% de descuento en compras.
Entonces, para una persona que compró cosas por valor de $ 3,500, el monto que debe pagar será; 20/100 * 3500 = $ 700
Entonces, la cantidad a pagar = 3500-700 = $ 2,800
Para la persona que compró $ 8000, monto a pagar = 20/100 * 8,000 = $ 1,600
Cantidad a pagar = 8000-1600 = 6400
Plllllllllllease heeeeelp
Answer:
SA = 967.6 cm²
Step-by-step explanation:
Surface Area of cylinder = [tex]2\pi r h + 2\pi r^2[/tex]
Where r = 7 cm, h = 15 cm
=> SA = 2(3.14)(7)(15)+2(3.14)(7)²
=> SA = 659.7 + 2(3.14)(49)
=> SA = 659.7 + 307.9
=> SA = 967.6 cm²
Answer:
967.12 cm^2
Step-by-step explanation:
To find surface area of cylinder:
Find area of cross section x 2 = pi x r ^2 = 153.86 x 2 = 307.72cm^2
Area of curved surface = 3.14 x 14 x 15 = 659.4 cm^2
Total Surface Area = 659.4 + 307.72 = 967.12cm^2
Hope this helps
3 quarts but in cups
Answer:
12 cups
Step-by-step explanation:
there are 4 cups in 1 quart. You multiply both of them by 3 so there are 12 cups in 3 quarts
Answer:
12 cups
Step-by-step explanation:
1 quart = 4 cups
4*3 = 12
12 cups
brainliest??
The polynomial x^2+3x-1 is a factor of x^4+3x^3-2x^2-3x+1 true or false?
Answer:
Yes, it is true that [tex]x^2+3x-1[/tex] is a factor of [tex]x^4+3x^3-2x^2-3x+1[/tex].
Step-by-step explanation:
Let us try to factorize [tex]x^4+3x^3-2x^2-3x+1[/tex]
[tex]x^4+3x^3-2x^2-3x+1\\\Rightarrow x^4-2x^2+1-3x+3x^3[/tex]
Let us try to make a whole square of the given terms:
[tex]\Rightarrow (x^2)^2-2\times x^2 \times 1+1^2+3x^3-3x\\\Rightarrow (x^2-1)^2+3x^3-3x\\[/tex]
--------------
Formula used above:
[tex]a^{2} -2 \times a \times b +b^{2} = (a-b)^2[/tex]
In the above equation, we had [tex]a = x, b = 1[/tex].
--------------
Further solving the above equation, taking [tex]3x[/tex] common out of [tex]3x^3-3x[/tex]
[tex]\Rightarrow (x^2-1)^2+3x(x^2-1)\\[/tex]
Taking [tex](x^{2} -1)[/tex] common out of the above term:
[tex]\Rightarrow (x^2-1)((x^2-1)+3x)\\\Rightarrow (x^2-1)(x^2+3x-1)[/tex]
So, the two factors are [tex](x^2-1)\ and\ (x^2+3x-1)[/tex].
[tex]\therefore[/tex] The statement that [tex]x^2+3x-1[/tex] is a factor of [tex]x^4+3x^3-2x^2-3x+1[/tex] is True.
Find the perimeter of the figure?
Answer:
36
Step-by-step explanation:
9+9+9+9=36
Answer: 36 cm
Step-by-step explanation:
The perimeter is the sum of all side lengths of the figure. Since this is a square, all sides have the same length.
9 * 4 = 36
the diagram shows a scale drawing of a playground. The scale of the drawing is 1:500. Work out the perimeter. Give answer in metres
Answer:
The perimeter of the playground is 65 metres
Step-by-step explanation:
Questions like this requires attachment; See attachment for diagram.
From the diagram, we have the following parameters
[tex]Length = 2cm[/tex]
[tex]Width = 4.5cm[/tex]
Required
Calculate the parameter of the actual diagram
First, the actual length and width has to be calculated;
Given that the scale drawing is 1:500
[tex]Actual\ Length = 500 * 2cm = 1000cm[/tex]
[tex]Actual\ Width = 500 * 4.5cm = 2250cm[/tex]
Now, the perimeter can be calculated;
[tex]Perimeter\ of\ a\ Rectangle = 2(Length + Width)[/tex]
[tex]Perimeter = 2(1000cm + 2250cm)[/tex]
[tex]Perimeter = 2(3250cm)[/tex]
[tex]Perimeter = 6500cm[/tex]
However, the question requires answer to be in meters
If 100 cm = 1 m, then
[tex]6500cm = \frac{6500m}{100}[/tex]
[tex]6500cm = 65m[/tex]
Hence, the perimeter of the playground is 65 metres
Which point is in Quadrant IV?
Answer:
1,1 or -1,3
Step-by-step explanation:
Answer:
h
Step-by-step explanation:
bottom right quadrant is IV
Which ordered pair is a solution of the equation y-4=7(x-6)
Only (5,4)
Only (6,5)
Both
Neither
Answer:
first we will check if the coordinate (5,4) is a solution:
you fill in only the X-coordinate (or the y-coordinate). I fill in 5 for X:
y-4 = 7(5-6)
now we have to work this out like:
y-4 = 7 • -1
y -4 = -7
y = -3 if the coordinate was the solution for the y-coordinate the answer should be 4 but it isn't so coordinate (5,4) isn't a solution.
the same goes for coordinate (6,5):
y-4 = 7 (6-6)
y-4 = 0
y = 4 if the coordinate was the solution for the y-coordinate the answer should be 5 but it isn't so coordinate (6,5) isn't a solution.
so the answer is neither
Answer:
Neither
Step-by-step explanation:
Simplify the given equation.
y - 4 = 7(x - 6)
y - 4 = 7x - 42
y = 7x - 38
Now, take the point (5, 4) and test to see if this is a solution.
y = 7x - 38
4 = 7(5) - 38
4 = 35 - 38
4 ≠ -3
Since that point did not prove to be true, answer choices A and C are cancelled out. Take point (6, 5) and test it.
y = 7x - 38
5 = 7(6) - 38
5 = 42 - 38
5 ≠ 4
Neither points provide a solution so D is the answer.
Lizbeth has 38 coins consisting of nickels, dimes, and quarters. The total value of the coins is $6.40. The number of quarters if three more than three times the number of dimes. How many of each type of coin does Lizbeth have? PLEASE EASY 25 POINTS.
Answer:
21 quarters, 6 dimes, and 11 nickels
Step-by-step explanation:
# of Quarters = x.
# of Dimes = y.
# of Nickels = z.
(i)x = 3y+3.
(ii) 0.25x + 0.1y + 0.05z = 6.4
(iii) x + y + z = 38.
Multiplying (iii) by -0.05, and adding it to (ii),
we then get:
0.2x + 0.05y = 4.5.
Now plug in (i) into this.
0.65y + 0.6 = 4.5.
0.65y = 3.9
y = 6.
Since y = 6, we can subsitute this into our equation.
0.2x + 0.3 = 4.5
0.2x = 4.2
x = 21.
Since x = 21, y =6, then z = 11.
Solve 6x - 11 = x + 14
Answer:
x=5
Step-by-step explanation:
(the goal is to get x by itself)
subtract x on both sides
5x-11=14
add 11 on both sides
5x=25
divide 5 on both sides
x=5
and check your work by plugging x back in to see if the two sides equal each other.
Step-by-step explanation:
6x-11=x+14
[tex]6x - x - 11 - 14 = 0 \\ 5x - 25 = 0 \\5x = 25 \\ x = 5[/tex]
Can i get some help please??? Thanks!!!!
Answer:
The length is 40 units.
Step-by-step explanation:
You need to use a triangle for the base then use the hypotenuse of the base as the base of the diagonal shown in the prism.
[tex]0.5*8*2=\\4*2=\\16[/tex]
The hypotenuse of the triangle of the base is 16.
[tex]0.5*16*5=\\8*5=\\40[/tex]
The diagonal shown in the prism is 40 units.
Which is the graph of the function f(x) = -√x
Answer:
1st Graph
Step-by-step explanation:
Easiest and quickest way is to graph the function in a graphing calc and then choosing the best answer.
Which graph represents the function (x) = - 21 - 1
Answer:
the one with a vertical line at the x value of -22
Step-by-step explanation:
subtract negative 21 to 1 to get -22
Then x=-22
Graph.
kissa brought an item at Tsh 250,000/= she sold it by a certain price and got loss of 1/4 of the buying price. find the percentage loss.
Answer:
Loss %age = 25%
Step-by-step explanation:
Cost Price of Item = 250,000/-
Loss = 1/4 = 0.25 of 250,000
=> 62,500 /-
%age Loss = [tex]Loss*100/Cost Price[/tex]
=> 62,500 * 100 / 250,000
=> 6,250,000/250,000
=> 25 %
what is( 7^4 * 9^-3 +7^5 * 9^-4) / 7^4 * 9^-4
Answer:
3.7168917E-7
Step-by-step explanation:
Answer:
3.7168917E-7
Step-by-step explanation:
On Monday, Crisitan groomed 15 dogs in 10 hours and Kenneth groomed 10 dogs in 8 hours. If they each make $12.75 per dog, how much did they each make on Monday?
Answer:
Christian made $191.25 and Kenneth made $127.50 each.
Step-by-step explanation:
With each dog, you multiply how many dogs with the amount of cash they get each dog.
Christian: 15x12.75= $191.25
Kenneth: 10x12.75= $127.50
So you just multiply the amount of dogs with money :)
Help If anyones awake
Last option is the correct answer
Answer:
ASA Postulate
Step-by-step explanation:
[tex] In\: \triangle TKS\: \& \: \triangle TLR\\
\angle 1 \cong \angle 2....(given) \\
TK \cong TL... (given) \\
\angle 3 \cong \angle 4....(given) \\
\therefore \triangle TKS\: \cong \: \triangle TLR.. (ASA \: Postulate) \\[/tex]
Answer:
First option is the correct choice.
Step-by-step explanation:
AAS theorem applies here to prove the claim.
Best Regards!
A steam engine for pulling trains has wheels of diameter 1.5 metres.
The steam engine travels 1000 metres along a test track.
Work out the number of complete turns of a wheel.
Answer:
The wheel completed a total of 212 turns.
Step-by-step explanation:
A wheel has a circular form, therefore its length is given by the following formula:
[tex]length = 2*\pi*radius[/tex]
Where radius is half the diameter. Applying the data from the problem to calculate the length of the wheel gives us:
[tex]length = 2*\pi*(\frac{1.5}{2})\\length = 1.5*\pi = 4.7124[/tex]
Since the engine traveled a distance of 1000 metres and each turn of the wheel has 4.7124 metres, in order to calculate the number of turns the wheel made in that course we need to divide both numbers as shown below:
[tex]turns = \frac{1000}{4.7124} = 212.21[/tex]
The wheel completed a total of 212 turns.
Election Three candidates run for an office in a local election. In all, 12,936 votes
are cast, and the breakdown of votes for the three candidates is in the extended ra
3:4:5. Find the actual numbers of votes cast for the three candidates.
Answer:
3234
4312
5390
Step-by-step explanation:
3x +4x + 5x = 12936
12x = 12936
PLEASE HELP MEEEEEEE THANK YOU
Choose the best answer: The solution of ? includes the entire line y = 2x + 1.
y 2x + 2
y 2x + 1
y < 2x
y 2
Answer:
the correct one is y < 2x
Step-by-step explanation:
Answer:
y 2x + 1 or B
Step-by-step explanation:
thats whats right on edge
Use the term 3xy + 2 to answer the following questions.
Answer:
5. 2 terms; 3xy, 2
6. 3
7. 0, can't be factored
Step-by-step explanation:
What is the product of 6x – y and 2x – y + 2?
Answer:
12x^2 - 8xy + y^2 + 12x - 2y
Step-by-step explanation:
Find the sum (the question is in the photo)
x3+3x2−4
________
9x4−12x2
Algebra isn't fun. Hope that helps though!
Mandana is ordering new tile for her kitchen floor. The area of the floor is 111.8 square feet, and she wants to order between 15%
and 20% extra of the materials. Which of the following is a reasonable amount of tile for Mandana to order?
OA. 135 square feet
OB. 125 square feet
OC. 127 square feet
OD. 133 square feet
Answer:
127
Step-by-step explanation