Answer:
0.7208 = 72.08% probability that this whole shipment will be accepted.
Step-by-step explanation:
For each tablet, there are only two possible outcomes. Either it meets the required specifications, or it does not. The probability of a tablet meeting the required specifications is independent of any other tablet, which means that the binomial probability distribution is used to solve this question.
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.
4% rate of defects
This means that [tex]p = 0.04[/tex]
26 tablets
This means that [tex]n = 26[/tex]
What is the probability that this whole shipment will be accepted?
Probability that at most one tablet does not meet the specifications, which is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Thus
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{26,0}.(0.04)^{0}.(0.96)^{26} = 0.3460[/tex]
[tex]P(X = 1) = C_{26,1}.(0.04)^{1}.(0.96)^{25} = 0.3748[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.3460 + 0.3748 = 0.7208[/tex]
0.7208 = 72.08% probability that this whole shipment will be accepted.
How do I solve for x?
In the diagram below of triangle MNO, P is the midpoint of MO and Q is the midpoint of NO. If PQ = 5x + 62, and MN = 6x-4, what is the measure of PQ?
Answer:
29
Step-by-step explanation:
There is a triangle embedded in triangle MNO, which is triangle PQO, and these are similar triangles in that their corresponding sides are always in the same ratio, which in this case is 2:1, as MP = MO due to the midpoint definition, and therefore MO is twice as long as MP. Same for NO and QO.
Now that we know the ratio, we can set 6x-4 = 2(-5x+64)
6x-4 = -10x +108
16x = 112
x = 7
Plug x back in for PQ, -5(7)+64 = 29
The measure of PQ is 22 units.
What is mid point theorem?A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.
Given:
PQ = 5x + 62, and MN = 6x-4
Now, using Mid- Point Theorem
PQ= 1/2 MN
-5x+ 62 = 1/2( 6x - 4)
-5x+ 62 = 3x - 2
-5x- 3x = -2 - 62
-8x = -64
x= 8
and, PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22
Hence, the measure of PQ is 22 units.
Learn more about mid point theorem here:
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What is the equation of the following line written in slope-Intercept form?
Answer:
Step-by-step explanation:
(-5,-1) & (-2, -3)
[tex]Slope= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\= \frac{-3-[-1]}{-2-[-5]}\\\\= \frac{-3+1}{-2+5}\\\\= \frac{-2}{3}[/tex]
m= -2/3 ; (-5,-1)
[tex]y-y_{1}=m(x-x_{1})\\\\y-[-1]= \frac{-2}{3}(x-[-5])\\\\y+1= \frac{-2}{3}(x+5)\\\\y+1=\frac{-2}{3}x+5*\frac{-2}{3}\\\\y+1=\frac{-2}{3}x+\frac{-10}{3}\\\\y=\frac{-2}{3}x+\frac{-10}{3}-1\\\\y=\frac{-2}{3}x+\frac{-10}{3}-\frac{3}{3}\\\\y=\frac{-2}{3}x-\frac{13}{3}[/tex]
John is twice as old as Mary. The sum of thelr ages is 21. How old Is Mary?
Answer: 7 years
Step-by-step explanation:
let x be the age of Mary
so John's age will be 2x
the equation becomes
2x+x=21
3x=21
x=21/3
x=7
Answer:
Step-by-step explanation:
Let Mary's age = x years
John's age = 2 * x = 2x
The sum of their ages = 21
x + 2x = 21
3x = 21
Divide both sides by 3
x = 21/3
x = 7
Mary's age = 7 years
Of the $77.84 direct-deposited from Problem 3, you have 50% placed into a savings account. How much is deposited in the saving account each month?
Answer:
38.92 dollars
Step-by-step explanation:
What is the factorization of 49b2 − 81?
(7b – 9)(7b – 9)
(7b – 9)(7b + 9)
(7b2 – 9)(7b2 – 9)
(7b2 – 9)(7b2 + 9)
Answer:
B. (7b – 9)(7b + 9)
Step-by-step explanation:
got 100% on my quiz
pleaae help me solve this 61/2×(8/9÷13/18)+(3/4) of 31/5
Answer:
[tex]10 \frac{2}{5}[/tex]
Step-by-step explanation:
Using BODMAS
[tex]6\frac{1}{2} \times (\frac{8}{9} \div\frac{13}{18}) + ( \frac{3}{4} )\ of \ 3\frac{1}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ solving \ expression \ inside \ bracket \ ]\\\\\frac{13}{2} \times (\frac{8}{9} \times \frac{18}{13}) + (\frac{3}{4}) \ of \ \frac{16}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \ ]\\\\\frac{13}{2} \times (\frac{16}{13}) + (\frac{3}{4}) \ of \frac{16}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ solving \ of \ ] \\\\[/tex]
[tex]\frac{13}{2} \times (\frac{16}{13} ) + (\frac{3}{4} \times \frac{16}{5} )\\\\\frac{13}{2} \times (\frac{16}{13} ) + \frac{12}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ solving \ \times \ expressions \ ] \\\\(\frac{13}{2} \times \frac{16}{13}) + \frac{12}{5}\\\\8 + \frac{12}{5}\\\\\frac{40 + 12}{5}\\\\\frac{52}{5}\\\\10\frac{2}{5}[/tex]
xy + x3 ( That 3 is cube )
s the following relation a function?
x y
−1 −2
2 3
3 1
6 −2
Answer:
can u plz rewrite the question
Trong k gian vecto R^3 , cho hệ B={u(2,1,-1),v=(3,2,5) , w=(1,-1,m)} a)xác định giá trị m để B là một cơ sở k gian R^3
Answer:
Dhhdhdhgdgdgd djjdhdhdhfh dbdjhdhfv djjdhfhhb is a hdhdh yhvggfff tghrh9
what is the percent of decrease from 300 to 50?
URGENT!!!!!!!!!
The percentage reduction can be written as 16.6667% of 300. 83.3333 percent decrease (%↓) or reduction from 300 is 50.
Answer:
83.33%
Step-by-step explanation:
300-50=250
250/300=83.33%
Prove that A - B = A-(A n B) using a Venn diagram
Step-by-step explanation:
my answer is an image above
Determine the numerical length of JK.
Answer:
30
So the two sectors add to the full length:
JK + IJ = IK
x+6 + 9 = 2x
Rearrange:
x=15
So the numerical length:
2x
2*15
30
The drama club is running a lemonade stand to raise money for its new production. A local grocery store
donated cans of lemonade and bottles of water. Cans of lemonade sell for $2.50 each and bottles of water
sell for $1.25 each. The club needs to raise at least $600 to cover the cost of renting costumes. The students
can accept a maximum of 460 cans and bottles.
Write a system of inequalities that can be used to represent this situation.
The club sells 144 cans of lemonade. What is the least number of bottles of water that must be sold to cover
the cost of renting costumes? Justify your answer.
Answer:
Part A
x + y ≤ 460...(1)
2.5·x + 1.25·y ≥ 600...(2)
Part B
The number of bottles of water the student must sell ≥ 192 bottles of water
Step-by-step explanation:
The given parameters are;
The selling price of each can of lemonade = $2.50
The selling price of each bottle of water = $1.25
The amount of money the club needs to raise = $600
The maximum number of cans and bottles the students can accept = 460
Part A
Let 'x' represent the number of cans of lemonade the students accept, and let 'y' represent the number of bottles the student accept, the system of inequalities that can be used to represent the situation can be presented as follows;
x + y ≤ 460...(1)
2.5·x + 1.25·y ≥ 600...(2)
Part B
The number of cans of lemonade the club sells, x = 144
The number of bottles of water the student must sell to cover the cost of costumes, 'y', is given from the second inequality as follows;
2.5 × 144 + 1.25·y ≥ 600
1.25·y ≥ 600 - 2.5 × 144 = 240
1.25·y ≥ 240
y ≥ 240/1.25 = 192
y ≥ 192
The number of bottles of water the student must sell = 192 bottles of water
Please hurry i want the answer of this question please
[tex]\displaystyle\bf 1200=12*100=3*4*(2*5)^2=3*2^2*2^2*5^2=2^4*3^1*5^2 \\\\Answer: \boxed{ A)\quad a=4 \quad ; \quad b=1 \quad ; \quad c=2}[/tex]
Un león, al ver correr un grupo de venados ¡exclamó!: "Adiós, mis cien venados", a lo cual los venados contestaron: "Estás equivocado, señor león. Con nosotros, otros tantos, la mitad de nosotros, la cuarta parte de nosotros y tú, señor león, somos 100". Cuántos venados van en el grupo? ( Utilice una ecuación de primer grado)
Answer:
Hay 56 venados en el grupo.
Step-by-step explanation:
En primer lugar, debemos traducir la proposición (oración) en una expresión matemática:
"Estás equivocado, señor león. Con nosotros, otros tantos, la mitad de nosotros, la cuarta parte de nosotros y tú, señor león, somos 100"
[tex]x + \frac{x}{2} + \frac{x}{4} + 1 = 100[/tex]
[tex]\frac{3\cdot x}{2} + \frac{x}{4} = 99[/tex]
[tex]\frac{7\cdot x}{4} = 99[/tex]
Donde [tex]x[/tex] es el número de venados.
[tex]x = 56.571[/tex]
Puesto que la cantidad de venados es un número entero, debemos truncar al entero más cercano. Es decir:
[tex]x = 56[/tex]
Hay 56 venados en el grupo.
Students are asked to estimate the number of gumballs in a jar. Sam says there are 228 gumballs. In actuality, there are 240 gumballs. What is the percent error
Answer:
5%
Step-by-step explanation:
Percent error = (actual - estimated) / actual x 100
(240 - 228) / 240 x 100 = 5%
NEED AN ANSWER ASAP
a linear piecewise function is represented by the graph. use the graph to evaluate the function.
when x = -5, y = ___
a) -5
b) 3
c) 5
when x = –1, y = ___
a) -2
b) 1
c) 3
When x = 3, y = ___
a) -4
b) 1
c) 3
Step-by-step explanation:
When X is - 5 then y is 3
When X is-1 then y is - 2
When X is 3 then y is -4
From the graph we get, when x is - 5 then y is 3, when x is -1 then y is - 2, and when x is 3 then y is -4.
What is a point?A point is a dot in space used to indicate an exact location in space.
Consider the first line, which has constant y values. its x value ranges from -1 to negative infinity.
The second line is starts from (-1,-2) point and tend towards positive infinity but its y values and x values are varying.
Hence, when x = -5 y is 3 and at x = -1 the y values is -2. Similarly, when x = 3 then y = -4.
To learn more about point, use the link given below:
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Topic: Modeling exponential functions
Kathy plans to purchase a car that depreciates
(loses value) at a rate of 14% per year. The initial
cost of the car is $21,000. Which equation
represents the value, v, of the car after 3 years?
1) v = 21,000(0.14)
2) v = 21,000(0.86)
3) v= 21,000(1.14)
4) v= 21,000(0.86)(3)
Answer:
Step-by-step explanation:
The standard form equation for this type of problem is
[tex]y=a(b)^x[/tex] where a is the initial value, b is the rate of depreciation, and x is the number of years in question. Because the value of the car is going down, b can also be written as (1 - r) where r is the rate of depreciation. For us, then, the equation will look like this:
[tex]y=a(1-r)^x[/tex] and filling in:
[tex]y=21000(1-.14)^3[/tex] which in simplified form is
[tex]y=21000(.86)^3[/tex] which I'm assuming is how choice 4 should look.
Solve (x + 9)2 = 25.
Answer:
x=3.5
Step-by-step explanation:
25÷2=12.5
12.5-9=3.5
Answer:
7/5 or 3.5
Step-by-step explanation:
2 (x+9) =25
x+9 = 25/2
x = (25/2) - 9
x = 7/2 in decimal = 3.5
Order the list of numbers from least to greatest.
Answer:
0, 0.5, 8/3, root 5, 3.1
PLEASE ANSWER ASAP :"( I need to submit the homework and i dont understand how to do the solution
p/s PLEASE READ THIS pls ignore the another language just read the english one..
Answer:
x -2 -1 0 1
y -1 2 5 8
Step-by-step explanation:
y=3x+5
When x=-2
y=3(-2)+5
y=-6+5
y=-1
when x=-1
y=3(-1)+5
y=-3+5
y=2
whenx=0
y=3(0)+5
y=5
When x=1
y=3(1)+5
y=3+5
y=8
Surf Shack rents boards to beach goers. Each boogie board, b, rents for $5 per day and each surfboard, s, rents for $10 per day. On Tuesday, they rent out a total of 14 boards and have an income of $80. Write two equations relating boogie boards, b, and surfboards, s.
Answer:
b + s = 14
5b + 10s = 80
Step-by-step explanation:
Answer:
b + s = 14
$5b + $10s = $80
Step-by-step explanation:
the sum of boogie board and surfboard rented is 14
boogie board rented + surfboard rented = 14
b + s = 14 equation 1
total income derived from renting the two types of boards is $80
total income derived = total income derived from renting boogie boards + total income derived from renting surfboards
total income derived from renting boogie boards = cost of renting one boogie board x number of boogie boards rented
= $5 x b = 5b
total income derived from renting surfboards = cost of renting one surfboard x number of surfboards rented
= $10 x s = 10s
80 = 5b + 10s equation 2
Solve this please!!,!,!
Answer:
z = -74
Step-by-step explanation:
12 = (2+z) / -6
Multiply each side by -6
-6 * 12 = (2+z)/ -6 * -6
-72 = 2+z
Subtract 2 from each side
-72-2 = 2+z-2
-74 =z
What fraction of 40 kg is 16 kg?
Write your answer to part a as a percentage.
Answer:
I hope it helps u..........
HELP!!!
f(x) =x^2. What is g(x)?
Answer:
C. g(x) = 4x²
Step-by-step explanation:
we have one specific point on g(x) : (1,4)
so, for x=1 the functional value (y) has to be 4.
A. (4×1)² = 4² = 16 and not 4. => wrong
B. 1/4 × 1² = 1/4 and not 4. => wrong
C. 4×1² = 4 and that IS 4 => correct
D. 16×1² = 16 and not 4 => wrong
Susana has a budget for school stationery of $33, but has already spent 19.10 on books and folders. Let p represent the amount that Susana can spend on other stationery. Write an inequality that shows how much she can spend on other stationery, and solve for p.
Answer: $13.90
Step-by-step explanation:
Since Susana has a budget for school stationery of $33, but has already spent $19.10 on books and folders, the inequality that shows how much she can spend on other stationery, will be represented by:
p + $19.10 = $33
p = $33 - $19.10
The inequality is p = $33 - $19.10
Then, the amount that she can spend on other stationery will be:
P = $33 - $19.10
P = $13.90
She can spend $13.90 on other stationary
If the first three Fibonacci numbers are given as x, = 1, X2 = 1 and x3 = 2,
what is the value of n for which X, + Xp = 55?
Answer:
n=8
Step-by-step explanation:
The sum of 10 and twice Mai’s age
Answer:
Can I get the full question please
Step-by-step explanation:
x + y = 10 - - - 1
x=2y - - - - - 2
Putting the value of x in eqn 1,
2y+y=10
y=10/3
=3.33 yrs
Which i feel is incorrect
Does this graph show a function? Explain how you know.
Answer:
Option C, functions can only have one y-value at any given x-place
