Using the binomial distribution, the probabilities are given as follows:
a. 0.2637 = 26.37%.
b. 0.8965 = 89.65%.
c. 0.0148 = 1.48%.
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.The values of the parameters for this problem are:
n = 5, p = 0.25.
Item a:
The probability is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637[/tex]
Item b:
The probability is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]
[tex]P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955[/tex]
[tex]P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965[/tex]
Item c:
The probability is:
[tex]P(X \geq 4) = P(X = 4) + P(X = 5)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0147[/tex]
[tex]P(X = 5) = C_{5,1}.(0.25)^{5}.(0.75)^{0} = 0.0001[/tex]
Then:
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0147 + 0.0001 = 0.0148[/tex]
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Select the correct answer.
Which function is the inverse of function f if the domain of f is ?
The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6
How to determine the inverse function?The function is given as:
f(x) = x^2 + 6
Rewrite as:
y = x^2 + 6
Swap x and y
x = y^2 + 6
Subtract 6 from both sides
y^2 = x - 6
Take the square root
[tex]y = \sqrt{x - 6}[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt{x - 6}[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6
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Simplify the following expression
Answer:
-ab^2
Step-by-step explanation:
7b^2a - 5b^2a - 3ab^2
= 2b^2a - 3ab^2
= (2 × b^2 × a) - (3 × a × b^2)
= -ab^2
b^2a and ab^2 is the same thing. hope it helps!
A pole that is 2.8 tall casts a shadow that is 1.79 long. At the same time, a nearby building casts a shadow that is 42.25 long. How tall is the building? Round your answer to the nearest meter.
Answer:
The building is around 47 meters tall
Step-by-step explanation:
Pole:
tall/long
2.8/1.79
Building:
tall/long
x/42.25
Solve for x:
2.8/1.79 = x/42.25
1.79x = 84.5
x ≈ 47
Which statement about the function represented by this graph is true? A curve rises from (0, 2), (2, 3 point 9), (4, 4), (5, 4 point 1), (6, 4 point 9), (8, 5), (9, 5), and (10, 5) on the x y coordinate plane. A. The function has an inverse because it passes the vertical line test. B. The function does not have an inverse because it does not pass the horizontal line test. C. The function does not have an inverse because it never crosses the x-axis. D. The function has an inverse because it passes the horizontal line test.
The true statement about the function which is represented by this graph is: D. the function has an inverse because it passes the horizontal line test.
What is the horizontal line test?The horizontal line test states that if the graph of function (f) is intersected by any horizontal line more than once, then, the function (f) doesn't have an inverse.
Conversely, if the graph of function (f) isn't intersected by any horizontal line more than once, then, the function (f) has an inverse.
By critically observing the graph of the given function (f) shown in the image attached below, we can logically deduce that it has an inverse because it passed the horizontal line test.
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Answer: D. The function has an inverse because it passes the horizontal line test.
Step-by-step explanation:
Got it right on test.
For the following exercises, solve the equations below and express the answer using set notation.
11. | 6 − x | = 5
Answer: 0,11
Step-by-step explanation:
to solve this absolute value equation, you can remove the absolute value symbols and set 2 separate equations:
6-x=5
6-x=-5
solve them and you get the answers
write the equations after translating the graph of y = | 1/2 x -2 | + 3 one unit to the right
Using translation concepts, the equation of the graph is:
y = |0.5x - 2.5| + 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The function is:
y = |0.5x - 2| + 3.
When it is shifted one unit to the right, we have that x -> x - 1, hence:
y = |0.5(x - 1) - 2| + 3
y = |0.5x - 2.5| + 3.
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alison, beatrice and chole each had some books. alison gave beatrice and chole some books that doubled the number of books they had, lastly chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end. how many books did each of them have at first?
alison, beatrice and chole each of them have at first 56, 8, 32 books.
alison, beatrice and chole each had some books. alison gave beatrice and chole some books that doubled the number of books they had, lastly chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end.
What is Working backward?Working backward is process in which calculation done in reverse direction.
let alison, beatrice and chole has x,y and z books initially,
alison gave beatrice and chole some books that doubled the number of books they had
alison, beatrice and chole has (96-2y-2z), (2y) , (2z)
chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end.
alison, beatrice and chole has 2(96-2y-2z), 2(2y) , (96-2(96-2y-2z)-4y)
at the end,
beatrice = 32
4y=32
y = 8
chole =32
96-2(96-2y-2z)-4y)=32
z=32
alison = 96-y-z
x=96-8-32
x=56
Thus the required alison, beatrice and chole each of them have at first 56, 8, 32 books.
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What value of k makes the statement true?
x² (2x³ + 7x²yª) = 2xªyª + 7x³y8?
By apply the distributive property of multiplication, the value of k which makes the statement true is 1.
What is the distribution property?Mathematically, the distributive property of multiplication is given by tis expression:
x(y + z) = xy + xz.
Next, we would apply the distributive property of multiplication to the given equation by distributing to the left-hand side using xy⁴:
k(2x⁴y⁴ + 7x³y⁸) = 2x⁴y⁴ + 7x³y⁸
Dividing both sides by the common factor, we have:
k = (2x⁴y⁴ + 7x³y⁸)/(2x⁴y⁴ + 7x³y⁸)
k = 1.
In conclusion, the value of k which makes the statement true is 1.
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Complete Question:
What value of k makes the statement true?
[tex]x^k[/tex]y⁴(2x³ + 7x²y⁴) = 2x⁴y⁴ + 7x³y⁸
The length of a rectangle is increased by 25% , but the width of the rectangle is decreased by 25%. By what percent was the rectangle's area decreased
The rectangle's area decreased by 19%.
Length = L
Breadth = B
Original area = L x B
New area = A = L x (1 + 25%) x B x (1 - 25%)
A = L x B x 0.25 x 0.75 = L x B x 1.05
Therefore the area of the rectangle has decreased by 19%.
To find the location of a rectangle, multiply its width by means of its height. If we understand the sides of the rectangle which are different lengths, then we have each the height and the width.
The perimeter P of a rectangle is given through the system, P=2l+2w, wherein l is the period and w is the width of the rectangle. The area A of a rectangle is given by means of the method, A=lw, in which l is the duration and w is the width.
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HELP HELP HELP HELP
HELP HELP HELP
Answer: The base should be 4.
Step-by-step explanation:
1. We draw a triangle shape like the image.
(The steps was showed in the image).
(b) Figure 2 below is made up of 4 identical rectangles of length 4 cm and breadth 2 cm. What is the perimeter of Figure 2?
ASAP!!
Answer:
48 cm is the answer
Step-by-step explanation:
Using Perimeter of rectangle = 2(l+b)
=> 2(4+2)
=> 2(6)
=> 12
As 4 rectangles multiply by 4
so, 12 × 4
= 48
Any questions you may ask.
A coordinate plane with a line drawn passing through the points (0, 3) and (1,1). which equation represents the graphed function? y = –2x 3 y = 2x 3 y = x 3 y = –x 3
Answer:
y = - 2x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 3 ) and (x₂, y₂ ) = (1, 1 )
m = [tex]\frac{1-3}{1-0}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = - 2x + 3 ← equation of line
One evening 1500 concert tickets were sold for the fair mount jazz festival. tickets cost 20 for covered pavilion seats and $10 for lawn seats total receipts were 23,000 how many tickets of each were sold
A total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.
We assume the number of covered pavilion tickets sold to be x and the number of lawn seat tickets sold to be y.
As a total of 1500 tickets were sold, we can form an equation:
x + y = 1500 ... (i),
as we had only those two types of tickets.
The cost of each covered pavilion ticket = $20.
Hence, the total revenue from covered pavilion tickets = $20x.
The cost of each lawn seat ticket = $10.
Hence, the total revenue from lawn seat tickets = $10y.
The total receipts were said to be $23,000.
Thus, we can represent this as an equation:
20x + 10y = 23000 ...(ii).
Combining (i) and (ii), we get a system of equations:
x + y = 1500 ... (i).
20x + 10y = 23000 ... (ii).
Dividing equation (ii) by 10, we get:
2x + y = 2300 ... (iii).
Subtracting (i) from (iii), we get:
2x + y = 2300.
x + y = 1500.
(-) (-) (-)
____________
x = 800.
Substituting x = 800 in (i), we get:
x + y = 1500,
or, 800 + y = 1500,
or, y = 1500 - 800,
or, y = 700.
Thus, a total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.
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Raj was friends with his waitress so he left her a 90 percent tip.
Percents
Total
90%
10%
100%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
x
If his tip was $27.54, what is the value of x in the table above?
The value on the table above will be $30.6. Then the correct option is D.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
Raj was friends with his waitress, so he left her a 90 percent tip.
If his tip was $27.54.
Then the value in the table above will be
⇒ $27.54 / 0.90
⇒ $30.6
Then the correct option is D.
The complete question is given below.
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HELP ASAP
The lengths of two sides of a parallelogram are 5x + 4 and 2x + 3y. Identify an expression for the perimeter of the parallelogram.
Answer: 2(7x + 3y + 4) [unsimplified] or 14x + 6y + 8 [simplified]
Step-by-step explanation: The perimeter of a parallelogram is 2 * (the two sides.)
Adding 5x + 4 and 2x + 3y, we get 7x + 3y + 4 by combining like terms in the x terms.
Now, we multiply by 2. This is 2(7x + 3y + 4) or 14x + 6y + 8
Select the correct answer. Which inequality is equivalent to the given inequality? -4(4+7) <3 ) x-2)
Answer:
x>-42
Step-by-step explanation:
I dont have time to explain de but thats the answer
Given: x is the midpoint of MN¯¯¯¯¯¯¯¯¯¯ and MX=RX
Prove: XN=RX
A midpoint of a line segment implies a point on the line that is equidistant to its two ends. So that the required proof is shown below:
Given: line segment MN
x, the midpoint of MN
MX = RX
Then;
MX = XN (midpoint property of a line)
So that,
MN = MX + XN
= MX + MX (since XN = MX)
MN = 2MX
Thus,
MX = XN = RX (given that MX = RX)
Therefore, it can be concluded that;
XN = RX
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Which statements are correct? Check all that apply.
One-halfQP = UT
One-halfTS = RQ
SU = PR
SU ∥ RP
UT ⊥ RP
By applying the triangle midpoint theorem to the two triangles (see attachment), the correct statements are:
A. One-halfQP = UT
D. SU ∥ RP
What is triangle midpoint theorem?Triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.
By applying the triangle midpoint theorem to the two triangles (see attachment), we can infer and logically deduce that one-half of side QP is equal to side UT and side SU is parallel to side RP (SU ∥ RP).
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Complete Question:
Points S, U, and T are the midpoints of the sides of ΔPQR. ΔSUT is inside of ΔPQR. Points S, U, and T are the midpoints of ΔPQR. Which statements are correct? Check all that apply.
A. One-half QP = UT
B. One-half TS = RQ
C. SU = PR
D. SU ∥ RP
E. UT ⊥ RP
Answer: a and d
Step-by-step explanation:
24. A pizzeria sells a medium pizza for $5.99 plus $0.75 for each topping.
They also sell a large pizza for $6.99 plus an additional $0.50 per topping.
After how many toppings will the medium and large pizzas cost the same
amount?
The pizzas will cost the same at 4 toppings.
The pizzas will cost the same at 5 toppings.
The pizzas will cost the same at 6 toppings.
The pizzas will never cost the same amount.
Answer:
a.) The pizzas will cost the same at 4 toppings
Step-by-step explanation:
Medium Pizza:
$5.99 + $0.75x
Large Pizza:
$6.99 + $0.50x
Find x
$5.99 + $0.75x = $6.99 + $0.50x
0.25x = 1
x = 4
I need help pls WILL GIVE BRAINLIEST
Answer: (1, -3)
Step-by-step explanation:
[tex]8x+4y=-4\\-4x-5y=11[/tex]
[tex]2(-4x-5y)=11(2)\\-8x-10y=22[/tex]
new system:
[tex]8x+4y=-4\\-8x-10y=22[/tex]
add.
[tex]-6y=18\\y=-3[/tex]
plug in -3 for y
[tex]8x+4(-3)=-4\\8x-12=-4\\8x=8\\x=1[/tex]
system:
[tex](1,-3)[/tex]
Answer:
Make one of the variable in one of the equations the subject of the formular first.[tex]4y = - 4 - 8x[/tex]to leave y independent divide the whole equation by the coefficient of y at this point it is 4.Then divided the whole equation by 4.[tex] \frac{4y}{4} = \frac{ - 4}{4} - \frac{8x}{4} [/tex]therefore the new equation will be[tex]y = - 1 - 2x....(3)[/tex]substitute the new equation in the other equation N.B not the one you extracted the new equation from.you will use -4x-5y=11 in substituting y=-1-2y[tex] - 4x - 5( - 1 - 2x) = 11 \\ - 4x + 5 + 10x= 11 \\ \\ - 4x + 10x = 11 - 5 \\ 6x = 6 \\ \frac{6x}{6} = \frac{6}{6} \\ x = 1[/tex][tex]y = - 1 - 2(1) \\ y = - 1 - 2 \\ y = - 3[/tex]HOPE THIS HELPS!4 cm
A
C
If BX = 2 cm, XA = 3 cm, and BY = 3, find the value of YC.
O 5.5 cm
5 cm
B
O 45 cm
Y
4
Answer:
Step-by-step explanation:
Comment and answer
ABC is similar to XBY The triangles are similar because
B is a common angle to both<A = <BXY AB is a transversal cutting 2 parallel lines<C = <BYX BC is a transversal cutting 2 parallel linesBX = 2 Given
XA = 3 Given
BY = 3 Given
YC = x Object of question
BX/(BX + XA) = BY / (BY + YC) Parts of two similar triangles
2/(2 + 3) = 3/(3+ x) Combine the left
2/5 = 3/(3 + x) Cross Multiply
2*(3 + x) = 3*5 Remove the brackets
6 + 2x = 15 Subtract 6 from both sides
6-6+2x = 15 - 6 Combine
2x = 9 Divide by 2
2x/2 = 9/2
x = 4.5
Answer
x = 4.5 or D
Categorize the graph as linear increasing, linear decreasing, exponential
growth, or exponential decay.
A. Exponential decay
B. Linear increasing
C. Linear decreasing
D. Exponential growth
Answer:
B. Linear increasing
Step-by-step explanation:
decay means decreasing
exponential graph would have a curve
PLEASE HELPPPPP
For the first picture determine the equation of the parabola shown in the diagram in vertex form and for the second picture determine the equation of the parabola shown in the diagram in factored form.
Answer:
see explanation
Step-by-step explanation:
the equation of parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier.
here (h, k ) = (3, 1 ) , then
y = a(x - 3)² + 1
to find a substitute any other point on the graph into the equation.
using (0, 7 )
7 = a(0 - 3)² + 1 ( subtract 1 from both sides )
6 = a(- 3)² = 9a ( divide both sides by 9 )
[tex]\frac{6}{9}[/tex] = [tex]\frac{2}{3}[/tex] = a
y = [tex]\frac{2}{3}[/tex] (x - 3)² + 1 ← in vertex form
------------------------------------------------------
the equation of a parabola in factored form is
y = a(x - a)(x - b)
where a, b are the zeros and a is a multiplier
here zeros are - 1 and 3 , the factors are
(x - (- 1) ) and (x - 3), that is (x + 1) and (x - 3)
y = a(x + 1)(x - 3)
to find a substitute any other point that lies on the graph into the equation.
using (0, - 3 )
- 3 = a(0 + 1)(0 - 3) = a(1)(- 3) = - 3a ( divide both sides by - 3 )
1 = a
y = (x + 1)(x - 3) ← in factored form
Solve the following proportion by cross multiplying:
x / 8 = 28 / 32
Answer: x = 7
Step-by-step explanation:
[tex]\frac{x}{8} =\frac{28}{32}[/tex]
We cross multiply, and we get:
32x = 8(28)
32x = 224
x = 7
Solve for x : log(3x) + log(x + 4) = log(15).
Please explain it to me.
Answer:
x = 1
Explanation:
[tex]\sf \rightarrow log(3x) + log(x + 4) = log(15)[/tex]
Rule: log(a) + log(b) = log(ab)
[tex]\sf \rightarrow log(3x(x + 4)) = log(15)[/tex]
cancel out log on both sides
[tex]\sf \rightarrow 3x(x + 4) = 15[/tex]
relocate constant variable
[tex]\sf \rightarrow 3x^2 + 12x -15 = 0[/tex]
take 3 as a common factor
[tex]\sf \rightarrow 3(x^2 + 4x -5) = 0[/tex]
divide both sides by 3
[tex]\sf \rightarrow x^2 + 4x -5 = 0[/tex]
middle term split
[tex]\sf \rightarrow x^2 + 5x -x-5 = 0[/tex]
factor common terms
[tex]\sf \rightarrow x(x + 5) -1(x+5)= 0[/tex]
collect into groups
[tex]\sf \rightarrow (x-1)(x+5)= 0[/tex]
set to zero
[tex]\sf \rightarrow x-1 = 0 , \ x+5= 0[/tex]
relocate variables
[tex]\sf \rightarrow x = 1, \ x = -5[/tex]
There must be a positive solution for log, so the solution is only x = 1
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Given:
[tex]\log (3x)+\log(x+4)=\log (15)[/tex]
As the logs have no base, assume that the base is 10.
[tex]\textsf{Apply log Product law}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\implies \log_{10} (3x)+\log_{10}(x+4)=\log_{10} (15)[/tex]
[tex]\implies \log_{10} \left(3x(x+4)\right)=\log_{10} (15)[/tex]
Expand the brackets:
[tex]\implies \log_{10} \left(3x^2+12x\right)=\log_{10} (15)[/tex]
[tex]\textsf{Apply the log Equality law}: \quad \textsf{if }\: \log_ax=\log_ay\:\textsf{ then }\:x=y[/tex]
[tex]\implies 3x^2+12x=15[/tex]
Subtract 15 from both sides:
[tex]\implies 3x^2+12x-15=0[/tex]
Factor out the common term 3:
[tex]\implies 3(x^2+4x-5)=0[/tex]
Divide both sides by 3:
[tex]\implies x^2+4x-5=0[/tex]
Split the middle term:
[tex]\implies x^2+5x-x-5=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies x(x+5)-1(x+5)=0[/tex]
Factor out the common term (x + 5):
[tex]\implies (x-1)(x+5)=0[/tex]
Therefore:
[tex]x-1=0 \implies x=1[/tex]
[tex]x+5=0 \implies x=-5[/tex]
As logs cannot be taken of negative numbers, [tex]x=-5[/tex] is an extraneous solution. Therefore, the only valid solution is: [tex]x=1[/tex]
Geometry question need help with it ASAP
Answer:-
DIY(do it yourself)
If a soccer team made 28 penalty shots out of 100, what fraction and what
percentage of penalty shots did the team miss? Choose two answers.
_____+29 ÷4 = 16
Fill in the blank, Please
Answer:
8.75 + 29 ÷ 4 = 16or8 3/4 + 29 : 4 = 16or 35/4 + 29 : 4 = 16Step-by-step explanation:
_____+29 ÷4 = 16
Fill in the blank, Please
we can solve with an equation
x + 29 : 4 = 16
x + 7.25 = 16
x = 16 - 7.25
x = 8.75
--------------------
check
8.75 + 29 : 4 = 16
8.75 + 7.25 = 16
16 = 16
the answer is good
Answer:
35
Step-by-step explanation:
first u multiply by 4 to get 64
then subtract 29 to get
Rsm Ch. 3 71...........................
Geoffrey is evaluating the expression
(-3)³(26) (2)
(-3) 5 (2²) (-3)*
C
-99
What are the values of a, b, c, and d?
O a=4, b=2, c= 16, d=9
O a=4, b= -2, c=16, d=9
O a=8, b= 8, c= 256, d=6,561
O a=8, b=8, c= 256, d=-6,561
(-3)³ (26)
(-3) (2²)
as shown below.
Answer: The values are a = 4, b = 2, c = 16, d = 9
simplified further
c = 16
d = 9