Answer:
a) 0.0287 = 2.87% probability that three non-defective components in a batch of seven components.
b) 0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.
Step-by-step explanation:
A sequence of Bernoulli trials composes the binomial distribution.
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.
The probability that a selected component is non-defective is 0.8
This means that [tex]p = 0.8[/tex]
a) Three non-defective components in a batch of seven components.
This is P(X = 3) when n = 7. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{7,3}.(0.8)^{3}.(0.2)^{4} = 0.0287[/tex]
0.0287 = 2.87% probability that three non-defective components in a batch of seven components.
b) 8 non-defective components are drawn before the first defective component is chosen.
Now the order is important, so the we just multiply the probabilities.
8 non-defective, each with probability 0.8, and then a defective, with probability 0.2. So
[tex]p = (0.8)^8*0.2 = 0.0336[/tex]
0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.
Monica deposits $400 into a savings account that pays a simple interest rate of 4.3% .Paul deposits $500 into a savings account that pays a simple interest rate of %4.2 Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.
What is simple interest?
Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
[tex]A = P (1 + rt)\\\\A $ = final amount$\\P $ = initial principal balance$\\r $ = annual interest rate$\\t $ = time (in years)$[/tex]
Given that:
For Monica:
Principal (p) = $400
Rate (r) = 4.3% = 0.043
Year (t) = 1 year
Deposit Paul:
Principal = $500
Rate (r) = 4.2% = 0.042
Year (t) = 1 year
Now calculate the interest amount for Monica and Paul, we get
For Monica:
A = P(1 + rt)
A = 400(1 + (0.043 × 1))
A = 417.2
A = $417.20
Now for Monica, Interest will be
I = A - P
= 417.20 - 400
I = 17.20 dollars -----------(II)
For Paul:
A = P(1 + rt)
A = 500(1 + (0.042 × 1))
A = 521
A = $521 dollars
Now for Paul, Interest will be
I = A - P
= 521 - 500
I = 21 dollars ---------------(II)
From (I) and (II), we can say that Paul will earn more interest than Monica.
Hence, Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
P = 6000r = 0.059n = 4$10164.30Step-by-step explanation:
Given that $6000 is deposited into an account earning 5.9% compounded quarterly, you want the values of P, r, n used in the future-value formula, and you want the value after 9 years.
(A) Formula valuesThe problem statement tells you the values:
amount deposited = P = 6000
interest rate = r = 5.9% = 0.059
compounding periods in a year = n = 4
(B) Future valueUsing these numbers in the formula, you find (with t=9) ...
S(9) = 6000(1 +0.059/4)^(4·9) ≈ $10164.30
If no deposits or withdrawals
are made, money held in this
account may increase or
decrease.
This account may generate
income from a variety of
sources.
There is no risk of losing any
money put in this account.
Savings Account
Interest income is the only
way to earn money in this
type of account.
Investment Account
Answer:
Savings Account
There is no risk of losing any money put in this accountInterest income is the only way to earn money in this type of accountInvestment Account
If no deposit or withdrawals are made, money held in this account may increase or decreaseThis account may generate income from a variety of sources
Name a pair of overlapping congruent triangles in the diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.
Given: LM≅LK; LN≅LJ
ΔLMJ and ΔLKN are congruent by SAS congruence postulate.
What is SAS and ASA congruence rule for triangles?
SAS : If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
ASA : If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
According to the given question:
The pair of overlapping congruent triangles in the diagram are:
ΔLMJ and ΔLKN
Now,
LM ≅ LK (Given)
LN ≅ LJ (Given)
∠LJM = ∠LNK (Angles opposite to equal sides are equal)
∴ ΔLMJ ≅ ΔLKN by SAS congruence of triangles
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Determine how large the number aa has to be so that ∫a[infinity]1/(x^2+1)dx<0.001.
The number a has to be greater than or equal to 1000.
As per the given data we have to determine that how large the number a has to be so that [tex]$$\int_a^{\infty} \frac{1}{1+x^2} \cdot d x < 0.001$$[/tex]
[tex]$$\Rightarrow \quad\left[\tan ^{-1}(x)\right]_a^{\infty} < 0.001$$[/tex]
[tex]$\Rightarrow \quad \tan ^{-1}(x)-\tan ^{-1}(a) < 0.001$[/tex]
[tex]$$\begin{array}{ll}\Rightarrow & \frac{\pi}{2}-0.001 < \tan ^{-1}(a) \\\\\Rightarrow & 1.5698 < \tan ^{-1}(a)\end{array}$$[/tex]
[tex]$$\begin{aligned}& \Rightarrow \quad \tan ^{-1}(a) > 1.5698 \\& \Rightarrow \quad a > \tan (1.5698)\end{aligned}$$[/tex]
[tex]$$\begin{aligned}& \Rightarrow \quad a > 999.999 \\& \Rightarrow \quad a \geqslant 1000\end{aligned}$$[/tex]
Therefore the answer is [tex]\quad a \geqslant 1000[/tex]
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A librarian wants to check a sample of books from the library to get an idea of how many need replacing.
Why might simple random sampling be a good way to do this?
He will not need a list of all the books
He will take longer if he checks all the books instead of checking a few
He will have a more representative sample if he chooses randomly
He will be able to choose whichever books he likes because it is random
The reason why simple random sampling will be a good way to do the selection of bad books is; Option C: He will have a more representative sample if he chooses randomly
What is the importance of simple random sampling?A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.
The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.
Now, in this case, since the librarian wants to check a sample of books from the library to get an idea of how many need replacing, it means that a random sampling method is good because;
He will have a more representative sample if he selects randomly as the definition earlier stated makes clear.
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describe a procedure that you would use to localize the protein dynein in tissue sections of esophagus and trachea. indicate the results that you would expect from such an analysis.
Therefore, the five steps are taken to localize the protein dynein in tissue sections of the esophagus and trachea.
What is localization?Any procedure that involves moving, attaching to, or otherwise maintaining a cell, substance, or cellular entity in one place, like an organelle or protein complex. Substance localisation can also be accomplished through selective degradation.
In this case,
the steps that are done in order to localize the protein dynein in tissue sections of the esophagus and trachea are as follows:
1. Histoclear removes the medium to enable the labeling of the antibodies
2. to rehydrate the sample, add water.
3. Using BSA blocking solution after Triton X- 100, which ruptures membranes and makes antigens more accessible to antibodies
(4) Add the dynein antibody.
5. include a secondary antibody that is likewise peroxidase-active (adds specificity)
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f(x)=3x²+42-6
g(x)=62-5²-2
Find (f+g)(x).
O A. (f+g)(x) =-628+82 +42-4
O B. (f+g)(x) = 6r³-2r² +42-8
O c. (f+g)(x) = 9r³-2-8
OD. (f+g)(x) = 6x³+3x²-2-8
The composite function (f + g)(x) is (f + g)(x) = 9x² - x - 8
How to determine the composite functionFrom the question, we have the following parameters that can be used in our computation:
f(x)=3x²+42-6
g(x)=62-5²-2
Express properly
So, we have the following representation
f(x) = 3x² + 4x -6
g(x) = 6x² - 5x - 2
The composite function is then calculated as
(f + g)(x) = f(x) + g(x)
So, we have
(f + g)(x) = 3x² + 4x -6 + 6x² - 5x - 2
Evaluate
(f + g)(x) = 9x² - x - 8
Hence, the function is (f + g)(x) = 9x² - x - 8
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Suppose there are two types of tickets to a show: advance and same-day. Advance tickets cost $25, and same-day tickets cost $20. For one performance, there were 65 tickets sold in all, and the total amount paid for them was $1450. How many tickets of each type were sold?
The number of Advance tickets sold:
The number of same-day tickets sold:
By solving a system of equations we will see that they sold 35 advanced tickets and 30 same-day ones.
How to find the number of each ticket sold?Let's define the variables we will be using for this problem, these are:
x = number of same advance tickets.
y = number of same-day tickets.
With the given information we can write a system of equations:
x*$25 + y*$20 = $1,450
x + y = 65
To solve the system we can isolate x on the second equation:
x = 65 - y
Now let's replace that in the other equation:
(65 - y)*$25 + y*$20 = $1,450
$1,625 - y*$5 = $1,450
$1,625 - $1,450 = $5*y
$175/$5 = y
35 = y
Then the value of x is:
x = 65 - 35 = 30
So they sold 35 advanced tickets and 30 same-day ones.
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What is the product of the 4 x and the 3 x cubed y squared minus 2 x y cubed?
Answer: 170678
Step-by-step explanation:
try it and you'll see.
Alexandra and Maris are playing a game where they guess how many sides the regular polygon the other is holding has. Alexandra says her regular polygon has exactly 12 lines of symmetry. Maris says her regular polygon has an angle of rotational symmetry of 24°. How many sides does each regular polygon have?
The number of sides of Alexandra's regular polygon is 12.
The number of sides of Maris's regular polygon is 15.
What is a regulars polygon?
A regular polygon is denoted a area. The area bounded by equal length of arms. The angel between any two consecutive arms will same any other pair of consecutive arms.
The number of line of symmetry of a polygon is the same is the number of arm or sides of that polygon.
Thus the number of sides of a polygon that has 12 lines of symmetry is 12.
The angle of rotational symmetry of a polygon is 360°/n, where n is the number of arms.
Therefore,
Angle of rotational symmetry = 360°/n
Putting Angle of rotational symmetry = 24°:
24° = 360°/n
Multiply both sides by n
24n = 360
Divide both sides by 24:
n = 360/24
n = 15
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17. Which of the following statements about overhead expenses is true?
A. They contribute indirectly to the running of a business.
B. They contribute directly to the running of a business.
C. They're directly related to a specific department.
D. They're directly related to a specific product.
Thus ,the statement about overhead expenses which is true is option (B). .
What is overhead expenses?In the business world, an ongoing expense of operating a business is known as overhead or an overhead charge .In contrast to operating costs like raw material and labor, overheads are expenses that cannot easily be connected to or associated with any one revenue unit.
Here,
the statement about overhead expenses which is true is option (B).
Explanation :The costs of operating a firm that aren't directly connected to providing an item or service are referred to as overhead. These expenses might be either fixed, like rent, or variable, like transportation expenditures. Additionally, they may be semi-variable, like utilities. Thus contribute directly to the running of a business.
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If the 8th term of a sequence is 256, and the 5th term of the sequence is 32, the common ratio is:
The geometric sequence have a common ratio of 2
Geometric SequenceGeometric progression (GP) is a type of sequence where each next term is gotten by multiplying each previous term by a fixed number, which is called a common ratio.
In this problem, we must write out two equations to find the common ratio.
Let;
r = common ratioa = first termThe nth term of a GP is given as;
Tn = arⁿ⁻¹
T₈ = ar⁷
256 = ar⁷ ...eq(i)
T₅ = 32
32 = ar⁴ ...eq(ii)
Dividing equation (i) by equation (ii)
256 / 32 = ar⁷ / ar⁴
8 = r⁷⁻⁴
8 = r³
r = ∛8
r = 2
The common ratio of the geometric sequence is 2
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Question
There are two spinners. The first spinner has three equal sectors labeled 1, 2 and 3. The second spinner has four equal sectors labeled 3, 4, 5 and 6. The spinners are spun once.
What is the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner?
The number of possible outcomes that do not show 1 on the first spinner and 4 on the second spinner is 2.
What is sample space?It is the total number of possible outcomes from a given set.
We have,
The sample space for when both the spinners are spun once.
S = {(1, 2, 3) x (3, 4, 5, 6)}
S = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 4), (3, 5), (3, 6)}
Now,
The number of total outcomes = 12
The number of outcomes that do not show 1 on the first spinner and 4 on the second spinner.
= {(2, 4), (3, 4)}
= 2
Thus,
The number of required possible outcomes is 2.
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What is the y-value of the solution for this system of equations:
4x - y = 10
x - 4 = y
The required value of y is obtained as -2.
What are the types of a system of equations?The given system of equation can either have a unique solution, more than one solutions or no solution.
On this basis they are divided into two parts consistent and inconsistent.
A consistent system has one or more solutions while for an inconsistent system there are no solutions.
The given system of equations is as below,
4x - y = 10 (1)
x - 4 = y (2)
Substitute the value of y from equation (2) into equation (1) to get,
4x - (x - 4) = 10
=> 3x + 4 = 10
=> 3x = 6
=> x = 2
Then, substitute x = 2 in x - 4 = y to get,
y = 2 - 4 = -2
Hence, the value of y for the given system of equations is -2.
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may someone give me the answer
Answer:
x represents the number of hours.
(y) distance because the distance depends on the number of hours traveled.
H(x) = 50x
H(5) = 50(5)
H(5) - 250 miles
After 5 hours of driving at 50 miles per hour, the car has traveled 250 miles.
Step-by-step explanation:
Carl deposits $500 into the bank for 8 years with a 3% interest rate. After 8 years, how much will he have in the account?
After 8 years, the amount of money which Carl would have in the bank account is equal to $620.
How to calculate the future value?Mathematically, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P represents the principal or starting amount.R represents the interest rate.A represents the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have the following;
S.I = 500 × 3/100 × 8
S.I = $120.
Now, we can calculate the future value (A) as follows;
Future value (A) = P + S.1
Future value (A) = 500 + 120
Future value (A) = $620.
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Solve the formula c=pid for d
Answer:
d=c/pi
Step-by-step explanation
divide by pi then d=c/pi
Answer:
C / pi = d
Step-by-step explanation:
The formula for circumference is
C = pi * d
To solve for d, divide each side by pi
C / pi = d
i will mark brainliest determine the value of y for the inequality 4 times the quantity y plus one fifth end quantity is less than or equal to four fifths. y ≥ 0 y ≤ 0 y is greater than or equal to negative 1 over 40 y is less than or equal to negative 1 over 40
The value of y in the given inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.
How to Solve an Inequality?To solve any inequalities, apply the same knowledge used to solve a normal algebraic equation by isolating the value of the variable.
The given inequality is 4y + 1/5 ≤ 4/5. To solve for the value of y, follow the steps below:
4y + 1/5 ≤ 4/5 [given]
Subtract 1/5 from both sides of the inequality:
4y ≤ 4/5 - 1/5 [subtraction property of equality]
4y ≤ 3/5
Multiply both sides by 1/4:
4y × 1/4 ≤ 3/5 × 1/4
y ≤ (3 × 1) / (5 × 4)
y ≤ 3/20
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A food company sells its corn flakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length, width, and height of the box have all been increased by 25%.
If the regular box has dimensions l, w, and h, then the dimensions of the family value box would be 1.25l, 1.25w, and 1.25h. This means that the volume of the family value box would be 1.25 * 1.25 * 1.25 = 1.953125 times the volume of the regular box. Since the family value box is 25% larger in each dimension, its volume is nearly double the volume of the regular box.
which statement comparing the two functions is correct?
A .Function to has a small minimum value of -9.
B. Function to has a smaller minimum value of 4.
C. Function one has the smaller minimum value of -14.
D. Function one has the smaller minimum value of -2.
Answer:
it would be C
hope this helps
Step-by-step explanation:
what is the probability distribution that has a mean of 1 and a standard deviation of 0?
The required explanation of probability distribution that has a mean of 0 and a standard deviation of 1 is describe below.
What is probability distribution?Probability distributions help to show our reality, empowering us to get evaluations of the likelihood that a specific occasion might happen, or gauge the inconstancy of event. They are a typical method for depicting, and potentially foresee, the likelihood of an occasion
According to question:The mean of the z-scores is dependably 0. The standard deviation of the z-scores is dependably 1. The chart of the z-score dissemination generally has a similar shape as the first conveyance of test values. The amount of the squared z-scores is dependably equivalent to the quantity of z-score values.
Thus, it is dependable.
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Correct question:
A normal probability distribution can have any value of the mean or must have a standard deviation of 1 and a mean of 0?
Calculate each sum or difference.
a) 43.78 +21.05 +52.29
Answer:
117.12
Step-by-step explanation:
43.78+21.05 = 64.83
64.83+52.29 = 117.12
Find the area of the circle.
Use 3.14 for T. Do not round your answer.
Hint: A = πr²
18 inches
The area of circle when π is 3.14 is 1017.36 inches².
What is the area of circle?
It is obvious that one of the rectangle's sides will be the radius and the other will be half the circumference's length.Since we already know that a rectangle's area equals its length times its width, which is compounded by "r," As a result, r2 is the circle's area.Although a circle is not a square, the amount of internal space it encloses is measured in square units. Easy formula for calculating a square's area is length times width.However, a circle simply has a diameter, or width. Since a circle (by definition) is the collection of all points that are equally spaced apart from a particular point in the centre, it lacks a clearly discernible length and width.Area of the circle = πr²
= 3.14 * 18 * 18
= 3.14 * 324
= 1017.36 inches²
Hence, the area of circle when π is 3.14 is 1017.36 inches².
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someone mind helping me in the question......thank you :) ....
Answer:
NY: 4cm + 3cm = 7cm
XY: 8cm + 3cm = 11cm
Step-by-step explanation:
1. find the difference between XN and MN
2. use the difference to add to the value LN and LM
For the given probability distribution, what is P(X<4) ?
Step-by-step explanation:
5. the most significant challenge that small businesses face is financial problems.
PLEASE HELP!!!!
Jamal works as a valet and a waiter at a restaurant. As a valet, Jon made $10.25 an hour and an additional $50.10 in tips, while at the restaurant he made $6.75 an hour and an additional $125 in tips. He made the same amount of money at both jobs last week.
Part A: Select the equation that can be used to determine the number of hours Jamal worked last week.
Part B: The total amount of money that Jamal made when both paychecks were the same is $
Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9
What is equation?Equation: a claim that two expressions with variable- and/or number-filled expressions are equivalent. Mathematical development has been sparked by the desire to find solutions to equations, which are really just questions.
Here,
Part A:
Jamal works as a valet made $10.25 an hour and an additional $50.10 in tips,
Thus number of hours be x
equation : 10.25x + 50.10 =0
or
Jamal works as a waiter made $6.75 an hour and an additional $125 in tips
equation : 6.75x + 125 = 0
Part B:
The total amount he made when both paychecks are same
=> 6.75x + 125 = 10.25x + 50.10
=> 10.25x-6.75x = 125-50.10
=>3.5x = 74.9
=>x=74.9/3.5 =21.4
Thus the total amount he made
10.25(21.4) + 50.1 = 269.45
and
Total amount = 2* 269.45=538.9
Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9
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If 3(x+1)=4x-1, then x=
Answer:
X = 4Step-by-step explanation:
To solve the equation 3(x+1) = 4x-1, we need to use the rules of algebra to isolate the variable "x" on one side of the equation and simplify the other side.
First, we can distribute the 3 on the left side of the equation to obtain 3x + 31 = 4x-1. This gives us 3x + 3 = 4x-1.
Next, we can subtract 3x from both sides of the equation to obtain 3 + 3 = 4x-1-3x. This simplifies to 3 = x-1.
Now we can add 1 to both sides of the equation to obtain 3+1 = x. This gives us the final solution x = 4.
Therefore, the solution to the equation 3(x+1) = 4x-1 is x = 4.
evaluate f(x)=-25x^4+3x^2+2
f(x)=-25x^4+3x^2+2 = f'(x)=-100x^3+6x
Take derivation
f'(x)=d/dx(-25x^4+3x^2+2)
Formula
d/dx(f+ g)=d/dx(f) + d/dx(g)f'(x)=d/dx(-25x^4)+d/dx(3x^2)+d/dx(2)
Formula
d/dx(x^a)=ax^(a-1)f'(x)=-25(4x^3)+3(2x)+0
f'(x)=-100x^3+6x
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Answer the following questions.
1) Choose the equation of a line parallel to the given equation and passing through a point P.
x+2 y=5 ; P=(2,-5)
y=-1/2 x-1
y=2 x-4
y=-2 x-1
y=-1/2 x-4
2) Choose the equation of a line parallel to the given equation and passing through a point P.
-3 x-y=-4 ; P=(1,4)
y=-3 x+5
y=-3 x+7
$y=1/3 x-3
$y=1/3x+7
The linear functions in this problem are given as follows:
1. y = -x/2 - 4.
2. y = -3x + 7.
How to define the linear functions?Considering the options in these problems, the linear functions are defined in slope-intercept format, given as follows:
y = mx + b.
The coefficients of the function are given as follows:
m is the slope.b is the y-intercept.The slope-intercept definition of the two equations presented in this problem are given as follows:
y = -0.5x - 5.y = -3x + 4.When two linear functions are parallel, they have the same slope, hence the two functions will be given as follows:
y = -0.5x + b.y = -3x + b.For item 1, when x = 2, y = -5, hence the intercept b is calculated as follows:
-5 = -0.5(2) + b
b = -5 + 1
b = -4.
For item 2, when x = 1, y = 4, hence the intercept b is calculated as follows:
4 = -3(1) + b
b = 7.
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