The combination of the letters will be 60.
When an order or sequence of arrangement is required, permutations are used. Combinations are used when there are only a limited number of possible groups to find and there is no requirement for the order or sequence of arrangements. For different kinds of things, permutations are used. Combinations are employed for similar items.
Given that the passcode for a smartphone consists of 3 letters followed by 3 digits.
The number of the vowels is:-
Vowels = { A, E, I, O, U} = 5
Number of letters = 3
The arrangements of the vowels will be:-
Number = ⁵C₃
Number = ( 5 x 4 x 3 )
Number = 60
Hence, the vowels can be arranged in 60 ways.
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A solution contains furosemide (frusemide) 10 mg/mL. How many milligrams of frusemide are in 3 mL of solution?
Answer:
30mg
Step-by-step explanation:
10 mg/mL x 3 mL
Celine purchased a ball of red yarn costing $2.33. She gave the cashier $7.19. How much change did the cashier give back to Celine?
Answer:
$ 4.86
Step-by-step explanation:
Subtract 7.19 and 2.33
7.19-2.33=4.86
A garbage incinerator charges $30, plus $15 per ton, to incinerate a truckload of garbage. The average cost per ton (in dollars) for incinerating n tons of garbage is
given by A(n) =
15n+30
n
a. Use the accompanying graph to determine whether the average cost per ton is increasing or decreasing as the size of the load increases.
b. A company uses trucks with capacities of 9, 16, and 18 tons. What is the average cost per ton for each truck?
erage costq
a. The average cost per ton is increasing as the size of the load increases.
b. For a 9-ton truck, the average cost per ton is $45. For a 16-ton truck, the average cost per ton is $60. For an 18-ton truck, the average cost per ton is $65.
Determine the average cost.This question uses the concept of linear functions.
The equation A(n) = 15n+30 is an example of a linear function, as it is a function of the form f(x) = mx + b, where m is the slope and b is the y-intercept.
The graph of this equation is a straight line, which shows that the average cost per ton is increasing as the size of the load increases.
a. To determine whether the average cost per ton is increasing or decreasing as the size of the load increases, we can look at the graph provided.
The graph shows that as the size of the load increases, the average cost per ton increases.
Therefore, the average cost per ton is increasing as the size of the load increases.
b. To calculate the average cost per ton for each truck, we can use the equation A(n) = 15n+30. For a 9-ton truck, we plug in n = 9 and calculate A(9) = 15(9) + 30 = 135 + 30 = 165. Therefore, the average cost per ton for a 9-ton truck is $45.
For a 16-ton truck, we plug in n = 16 to calculate A(16) = 15(16) + 30 = 240 + 30 = 270.
Therefore, the average cost per ton for a 16-ton truck is $60.
For an 18-ton truck, we plug in n = 18 to calculate A(18) = 15(18) + 30 = 270 + 30 = 300.
Therefore, the average cost per ton for an 18-ton truck is $65.
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The probability that a passenger is chosen for customs inspection is 10 %. Emma and Michael go through customs. What is the probability that neither of them is chosen for inspection? The probability of one passenger being chosen is independent of that of other passengers.
a) 81 %
b) 90 %
c) 99 %
d) other
The probability that neither of them is chosen for inspection is given as follows:
a) 81 %
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[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 given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 2, p = 0.1.
The probability of neither is P(X = 0), hence:
P(X = 0) = (1 - 0.1)² = 0.81.
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solve the given initial-value problem. Dy dx + y = f(x), y(0) = 1, where f(x) = 1, 0 ≤ x ≤ 1; -1 , x ≥ 1
The general solution of the ODE is:
y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1
y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1
How did we get the values?This is a first-order linear ordinary differential equation (ODE) with constant coefficients. It can be solved using the method of integrating factors.
Let's multiply both sides by the integrating factor e^(∫p(x)dx), where p(x) = 1.
e^(∫p(x)dx) * Dy/dx + e^(∫p(x)dx) * y = e^(∫p(x)dx) * f(x)
D/dx (e^(∫p(x)dx) * y) = e^(∫p(x)dx) * f(x)
Integrating both sides, we get:
e^(∫p(x)dx) * y = ∫ e^(∫p(x)dx) * f(x) dx + C
where C is an arbitrary constant of integration.
Using the initial condition y(0) = 1, we can find the value of the constant C.
y(0) = 1 = e^(∫p(x)dx) * y(0) = e^(∫p(x)dx) * 1 = ∫ e^(∫p(x)dx) * f(x) dx + C
So, C = 1 - ∫ e^(∫p(x)dx) * f(x) dx
For 0 ≤ x ≤ 1, we have f(x) = 1 and:
∫ e^(∫p(x)dx) * f(x) dx = ∫ e^x dx = (e^x - 1) / 1
For x ≥ 1, we have f(x) = -1 and:
∫ e^(∫p(x)dx) * f(x) dx = ∫ -e^x dx = -(e^x - 1) / 1
Therefore, the general solution of the ODE is:
y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1
y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1
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A dinner was held to raise money for a children's museum. A ticket for one person cost $200 and a ticket for a couple (two people) cost $350. A total of 130 people attended the dinner, and the ticket sales total was $24,000. What is the total number of tickets that were sold?
Using simultaneous equations, during the dinner to raise money for a children's museum, 90 tickets were sold.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently or at the same time.
Simultaneous equations are also called a system of equations.
The cost of one-person ticket = $200
The cost of two-people ticket = $350
The total number of attendees at the dinner = 130
The total ticket sales = $24,000
Let number of one-person ticket = x
Let number of two-people ticket = 2y
Equations:x + 2y = 130... Equation 1
200x + 250y = 24000... Equation 2
Multiply Equation 1 by 200:
200x + 400y = 26000... Equation 3
Subtract Equation 2 from Equation 3:
200x + 400y = 26000
-
200x + 350y = 24000
50y = 2000
y = 40
x = 130 - 2y
= 130 - 80
= 50
Thus, the number of tickets sold at the dinner was 90.
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Rewrite in simplest terms: 0.8 ( − 5 � − 0.8 ) − 0.3 ( 0.5 � − 1 ) 0.8(−5w−0.8)−0.3(0.5w−1)
The expression 0.8(−5w − 0.8) − 0.3(0.5w − 1) in the simplified form will be −4.15w + 0.36.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 0.8(−5w − 0.8) − 0.3(0.5w − 1)
Simplify the equation, then we have
⇒ 0.8(−5w − 0.8) − 0.3(0.5w − 1)
⇒ −4w − 0.64 − 0.15w + 0.30
⇒ −4.15w + 0.36
The expression 0.8(−5w − 0.8) − 0.3(0.5w − 1) in the simplified form will be −4.15w + 0.36.
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Integrate 1/(1+x2) for limit [0,1].
Answer:
Step-by-step explanation:
in 2010 an earthquake below the ocean floor initiated a devastating tsunami in Samatra. scientists can approximate the velocity V in feet per second of a tsunami in water of depth d feet with the formula [tex]\sqrt{16} \\[/tex] [tex]\sqrt{d}[/tex]. Determine the velocity of a tsunami in 300 feet of water. Write your answer in simplified radical form.
Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
here, we have,
Since the depth of the water 'd' (in feet) and the velocity of the wave 'v' (in feet per second) are related by the equation
v = √(16d)
a wave forms in water with a depth of 300 feet,
therefore d = 300 ft
so, we get,
velocity = √(16*300)
= 4√300
=4*17.32
=69.28
Hence, Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.
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Mr.Ramirez 24 cookies. 3 fourths were oatmeal. How many oatmeal cookies did Mr.Ramirez bake
The amount of oatmeal cookies with Mr. Ramirez is 18
How to find the amount to oatmeal cookiesThe problem is dealing with multiplication of fractions
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split.
In the problem saying that 3 fourths were oatmeal means that 3/4 of the cookies where oatmeal hence
number of cookies = 3/4 * 24
number of cookies = 18
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Which inequality does the graph represent? The graph with X-coordinate marks -2, 0, and 2; Y-coordinate marks -2, 0, and 2. There is a line which passes through the points (3, 3), and (2, 3.5). There is shaded region which is above the line. A. y > (–13 )x + 4 B. y ≥ (–13 )x + 4 C. y < (–13 )x + 4 D. y ≤ (–13 )x + 4
The values of {x} are given above upto 2³.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the graph with x - coordinate marks (-2, 0, and 2) and y -coordinate marks (-2, 0, and 2). There is a line which passes through the points (3, 3) and (2, 3.5).
The inequality line representing the shaded region as -
y ≥ - 13x + 4
Therefore, the inequality line representing the shaded region is y ≥ - 13x + 4.
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number 5 only please help
The series 1/2 + 1/5 + 1/10 + 1/17 + 1/26 + ... converges
How to determine the test of convergenceFrom the question, we have the following parameters that can be used in our computation:
1/2 + 1/5 + 1/10 + 1/17 + 1/26.....
To apply the Integral test to given series, we can compare it to the area under the function 1/x.
As a general rule, the function 1/x is a decreasing function on the interval (1, ∞),
This means that the series converges.
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Is this no solution?
Answer: 0=0
Step-by-step explanation:
4(2x-15) = 2(4x-30)
Simplify
8x-60=8x-60
Add 60 to both sides
8x=8x
Answer: 0=0
So the answer is infinite. Theres an infinite about of answers for x.
Answer:
The result of your question would equal: 0 = 0
Step-by-step explanation:
First lets distribute them!
4(2x - 15) = 2(4x - 30)
8x - 60 = 2(4x - 30)
8x - 60 = 2(4x - 30)
8x - 60 = 8x - 60. :
4(2x - 15 = (4x - 30)
8x - 60 = 8x - 60.
Add:
8x - 60 = 8x - 60
8x - 60 + 60 = 8x - 60 + 60
Simplifying:
8x - 60 + 60 = 8x - 60 + 60
8x = 8x - 60 + 60
Again:
8x = 8x - 60 + 60
8x = 8x =
8x - 60 + 60 = 8x - 60 + 60
8x = 86
Subtracting:
8x = 8x
8x - 8x = 8x - 8x
Simplifying again...
Combining like terms
8x - 8x = 8x - 8x
0 = 8x - 8x
0 = 8x - 8x
0 = 0
The answer equals:
0 = 0
You have been answered by one of many helper robots.
The student used the gift card to spend the same amount of money at the coffee shop every day until the remaining value of the card was $0. This function represents f(n), the value, in dollars, of the gift card after n days.f(n) = −2.5n + 75A. Based on the function, what was the original value, in dollars, of the giftcard? Show or explain how you got your answer.B. Based on the function, how much money, in dollars, did the student spend each day at the coffee shop? Show or explain how you got your answer.C. What was the remaining value, in dollars, of the gift card after 20 days? Show or explain how you got your answer.D. How many days in total did it take until the remaining value of the gift
Answer:
A. The original value of the gift card is 75 dollars, which is the y-intercept of the function.
B. The student spent 2.5 dollars each day at the coffee shop, which is the coefficient of n in the function.
C. After 20 days, the remaining value of the gift card is -2.5 * 20 + 75 = 25 dollars.
D. To find the total number of days until the gift card was used up, we need to find when f(n) = 0. Setting the function equal to 0 and solving for n, we get: 0 = -2.5n + 75, so n = (75)/(-2.5) = 30 days.
URGENT!!!
Sharon invested $5,000 in a bond for 2 years. The total interest earned on the investment was $600. What was the interest rate on the investment?
The interest rate required to pay a simple interest of $600 from an investment of $5000 in 2 years is 6%.
What is the interest rate on the investment?Simple interest is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $5,000Interest I = $600Elapsed time t = 2 yearsInterest rate r = ?Plug the given values into the above formula and solve for r.
I = P × r × t
r = I / Pt
r = 600 / ( 5,000 × 2 )
r = 600 / ( 10,000 )
r = 0.06
Interest rate = r × 100%
Interest rate = 0.06 × 100%
Interest rate = 6%
Therefore, the interest rate is 6%.
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Find p and q , if X1 = 17, n1 = 25, X2 = 28, and n2 = 80
The solutions are given below:-
Part (a),
X₁ + X₂ have distribution Bi(n₁+n₂, p)
Part (b),
P(X ₁+ X₂ = 1 | X₂ = 0) = np(1-p)ⁿ¹⁻¹
P(X₁+X₂ = 1| X₂ = 1) = (1-p)ⁿ¹
P(X₁ + X₂ = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
What is binomial distribution?Since both variables are independent but they have the same probability parameter, you can interpret that as if the experiment that models each try in both variables is the same.
When you sum both random variables together, what you obtain as a result is the total amount of success in n₁+n₂ tries of the same experiment, thus X₁+X₂have distribution Bi(n₁ + n₂, p).
b)
Note that, if X₂ = k, then X₁ +X₂ = 1 is equivalent to X₁ = 1-k. Since X1 and X₂ are independent, then P(X₁ +X₂ = 1| X₂ = K) = P(X1=1-k|X₂=k) = P(X₁ = 1-k).
If k = 0, then this probability is equal to P(X₁ = 1) = np(1-p)ⁿ¹⁻¹
If k = 1, then it is equal to P(X₁ = 0) = (1-p)ⁿ¹
Thus,
P(X₁+X₂ = 1) = P(X₁+X₂ = 1| X₂ = 1) * P(X₂=1) + P(X₁+X₂ = 1| X₂ = 0) * P(X₂ = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹.
The complete question is given below.
Let X1 and X2 be two random variables following Binomial distribution Bin(n1,p) and Bin(n2,p), respectively. Assume that X1 and X2 are independent.
(a) The mgf of binomial distribution Bin(n, p) is (1 − p + pet)n. Use this fact to obtain the distribution of X1 + X2.
(b) Find the probability P(X1 + X2 = 1|X2 = k) for k = 0 and 1. Then use the law of total probability to find P (X1 + X2 = 1)
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Priya says the sum of 1 2/5 and 4/5 is 1 6/5. Kiran says the sum is 11/5. Elena says it is 1 6/10. Tyler says it is 2 1/5. Do you agree with any of them? Use this space to solve the addition problem. Then Justify whether each person's answer is right or wrong using full sentences. You may use drawings if it helps.
The sum of the numbers 1 ²/₅ and ⁴/₅ in different form will be 1 + ⁶/₅, 11 / 5, and 2 ¹/₅. So, Priya, Kiran, and Tyler are correct.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The sum of the numbers 1 ²/₅ and ⁴/₅ is given as,
⇒ 1 ²/₅ + ⁴/₅
⇒ 1 + ²/₅ + ⁴/₅
⇒ 1 + ⁶/₅
⇒ 11 / 5
⇒ 2 ¹/₅
The sum of the numbers 1 ²/₅ and ⁴/₅ in different form will be 1 + ⁶/₅, 11 / 5, and 2 ¹/₅. So, Priya, Kiran, and Tyler are correct.
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Express it in mathematical phrases:
The quotient of a number by eight
The mathematical expression, for the given phrase is n / 8
What is an expression?A mathematical statement, containing variables and numbers related by a mathematical operator, is called an expression.
Given that, a mathematical phrase: The quotient of a number by eight, we are asked to convert it into a mathematical expression,
Let n be the unknown number,
The quotient shows a result of division of two numbers,
Therefore,
The quotient of a number, n by eight, can be written as,
n / 8
Hence, the mathematical expression, for the given phrase is n / 8
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what is 4z−(−3z) in combining like terms
Answer:
7z because 4z-(-3)=4z+3z
Answer:
The answer would be 7z
Step-by-step explanation:
a negative and a negative make a positive so therefore you would just add 4 and 3 together
.42 is 1 tenth of what number
Answer: 4.2
Multiply both sides by 10
0.42 (10) = 0.1 (10)
4.2 = 1
Answer:
4.2
Step-by-step explanation:
What is the surface area of the polyhedron
Answer: equal to the sum of the area of all of its faces
Step-by-step explanation:
A basketball team had a 60% decrease in the number of victories it had this season compared to last season. If the team had 48 fewer victories, how many victories did they have this season?
66
32
80
28
please help ASAP
The number of victories that the team had this season is given as follows:
32.
How to obtain the number of victories?The number of victories is obtained applying the proportions in the context of this problem.
A decrease of 48 represents a decrease of 60% of the amount, that is, 60% of the total amount is of 48, hence the amount x is obtained as follows:
0.6x = 48
x = 48/0.6
x = 80.
The amount x represents the number of victories in the previous season, hence the number of victories in the current season is given as follows:
80 - 48 = 32.
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Given the following table of values for f(x), find f(7)
What is the area of the parallelogram
Answer:
40 units^2
Step-by-step explanation:
The parallelogram shown is basically made of two triangles divided by the x-axis. The bases go from 3 to 13 on the axis, so they have a length of 10. The height of one triangle is from a 0 to 4, which is a height of 4.
The area of a triangle is [tex]\frac{bh}{2}[/tex], so plugging those numbers in gets:
[tex]\frac{4*10}{2}[/tex] = 20
Since there are two triangles it would be double the area: 40 units^2
(x+2)^2=4(x+5)+y standard form
The standard form of the equation (x + 2)² = 4 (x + 5) + y is:
x² + y - 16 = 0
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The standard form of an equation is Ax + By = c.
Now,
(x + 2)² = 4 (x + 5) + y
x² + 4x + 4 = 4x + 20 + y
x² + 4 = 20 + y
x² + y = 20 - 4
x² + y = 16
x² + y - 16 = 0
Thus,
x² + y - 16 = 0 is the standard form of an equation.
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Write an expression equivalent to 2(x+5).
Answer: 2x+10
same expression, just simplified
ed buys a vase for £24 and adds 25% onto the price before putting it into his shop window
What price does the price-tag say in the window
Write the phrase as an expression. a number x divided by 2
Answer: x/2
Step-by-step explanation: Good morning. I am not sure what you mean by "A number x", so I suppose that is a typo.
Answer: x/2 IS CORRECT
Step-by-step explanation:
I TRIED IT :)
If the purchase price for a house is $210,600, what is the monthly payment if you put 20% down for a 30-year loan with a fixed rate of 5%?
The monthly payment for a 30-year loan with a fixed rate of 5% is $702.
How is the monthly payment for a 30-year loan determined?Divide the number of payments you make annually by 30, the length of the loan. For instance, 30 x 12 equals 360. Over the course of the loan, you will make 360 payments.
The following equation is used to determine the down payment: down payment = down payment percentage times purchase price. For the sake of this calculation, the down payment percentage must be converted to a decimal.
Purchase price for a house is $210,600
Down payment is 20%.
remaining payment 80% of total price = $210,600*80/100= $168480.
$168480 payment for a 30-year loan with a fixed rate of 5%
then interest will be
interest = 168480 *5*30/100= $84240
total amount to be paid 30 yr= 168480+ 84240= $252720
amount to be paid per month= $252720/(30*12) = $702.
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if u help me for this its basically free brainliest
The required 3/4 is 11/3 and 26/3 times in fractions 11/4 and 6 1/2 respectively.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Given ration 3/4
(1)
Fraction 3/4 in 11/4
= 11/4 / 3/4
= 11/3
Although, 3/4 is 11/3 times in the value 11/4
Similarly
(2)
Fraction 3/4 in 6 1/2
= 13 / 2 / [3/4]
= 26/3
Although, 3/4 is 26/3 times the value of 6 1/2.
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