Answer:
a) There are 3,628,800 different strings.
b) There are 28,800 different strings if the letters ad digits must alternate.
c)There are 86,400 different string if all five letters must be adjacent in each string.
Step-by-step explanation:
There are 10 digits.
Our strings have the following format:
C1 - C2 - C3 - C4 - C5 - C6 - C7 - C8 - C9 - C10
repitition of letters is not allowed.
a) How many different strings are there?
C1 can be any of the 10, C2 can be 9, C3 can be 8, ...
So in total there are:
[tex]T = 10*9*8*7*6*5*4*3*2*1 = 3,628,800[/tex]
There are 3,628,800 different strings.
b) How many different strings are there if the letters, i.e. A, E, I, O, U and the digits, i.e. 1,3, 5, 7, 9 must alternate?
There are the following possiblities:
5(l) - 5(d) - 4(l) - (4d) - ...
Or
5(d) - 5(l) - 4(d) - 4(l) - ...
So:
[tex]T = 2*(5*5*4*4*3*3*2*2*1*1) = 28,800[/tex]
There are 28,800 different strings if the letters ad digits must alternate.
c) How many different strings are there if all five letters must be adjacent in each string?
L - L - L - L - L - D - D - D - D - D
D - L - L - L - L - L - D - D - D - D
D - D - L - L - L - L - L - D - D - D
D - D - D - L - L - L - L - L - D - D
D - D - D - D - L - L - L - L - L - D
D - D - D - D - D - L - L - L - L - L
There are [tex]T = 6*(5*5*4*4*3*3*2*2*1*1) = 86,400[/tex]
There are 86,400 different string if all five letters must be adjacent in each string.
If an albuterol inhaler contains 18 mg of albuterol, how many inhalation-doses can be delivered if each inhalation-dose contains 90 μg?
Answer:
Hello, Your question is already answered but I wanted to add something else if you dont mind :) Inhalants can cause sudden death.
Step-by-step explanation:
Inhalants can kill you instantly. Inhalant users can die by suffocation, choking on their vomit, or having a heart attack. Most teenagers also consider Inhalants as relaxation, like when your stressed or if you've seen in most movies, people panic and then breath in paper bag. I'm not sure if those are the inhalers your talking about but It said 10 points so why not? Thank you, have a great day :)
The albuterol inhaler can deliver 200 inhalation-doses.
How many inhalation-doses in 18 mg albuterol?1 mg = 1000 μg
So, 18 mg = 18 * 1000 μg = 18000 μg
Number of inhalation-doses = Total albuterol / Amount per dose
Number of inhalation-doses = 18000 μg / 90 μg/dose
Number of inhalation-doses = 200 inhalation-doses
Therefore, the albuterol inhaler can deliver 200 inhalation-doses.
Read more about inhaler
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What is the cost of constructing a fence 6 feet, 6 inches, high around a lot measuring 90 feet by 175 feet, if the cost of erecting the fence is $1.25 per linear foot and the cost of materials is $0.825 per square foot of fence? Round your answer to the nearest cent.
A. $1,752.62 B. $2,054.63 C. $2,084.62 D. $3,504.63
Answer:
The total cost is $3504.625
Step-by-step explanation:
1 inch = 0.0833333 feet
Height = 6 feet 6 inches =[tex]6+6 \times 0.0833333=6.5 feet[/tex]
Length = 90 feet
Breadth = 175 feet
Perimeter = [tex]2(l+b)=2(90+175) = 530 feet[/tex]
Cost of erecting the fence is $1.25 per linear foot .
So, Cost of erecting the fence of 530 feet = [tex]530 \times 1.25[/tex]
Cost of erecting the fence of 530 feet = [tex]662.5[/tex]
Area of fence = [tex]2(l+b)h=530 \times 6.5=3445 feet^2[/tex]
Cost of materials is $0.825 per square foot of fence
Cost of materials of 3445 square foot of fence = [tex]3445 \times 0.825[/tex]
= [tex]2842.125[/tex]
Total cost = $2842.125+$662.5
Total cost = $3504.625
Hence the total cost is $3504.625
What is the relationship between rational numbers and Integers?
Rational Numbers are a subset of Integers because all Rational Numbers are Integers.
There is some overlap between Rational Numbers and Integers, but there are numbers that are just Rational and numbers that are just Integers but not both.
There is no relationship as there are no overlapping numbers.
Integers are a subset of Rational Numbers because all Integers are Rational Numbers.
Answer:
Integers are a subset of Rational Numbers because all Integers are Rational Numbers.
Step-by-step explanation:
A rational number such as 4/2 is also an integer: 2. A rational number such as 4/3 is not an integer. Hence, integers are a subset of rational numbers.
Answer:
Integers are a subset of Rational Numbers because all Integers are Rational Numbers.
Step-by-step explanation:
3 is integer but it can be written as [tex]\frac{3}{1} \ or \ \frac{6}{2},.. etc.[/tex] which is rational form. Hence every integer can be express as Rational Number.
Thus the last option is correct.
Further, Integers can be defined as the whole numbers including zero and positive whole numbers. i.e. ......,-3, -2, -1, 0, 1, 2, 3,.....
Example: -546, 87855889, 0, etc.
Rational Number is the number in the form [tex]\frac{p}{q}[/tex], where q≠0.
Example: [tex]\frac{2}{9}, \frac{-1}{267}, \frac{875}{2}, 3, etc.[/tex]
If aſc and a +b = C, prove that a|b.
Answer:
Assuming a being a divisor of c and [tex]a,b,c \in \mathbb{Z}[/tex]
Step-by-step explanation:
We are told that [tex]a \mid c[/tex]
and that [tex]a+b =c[/tex]
which means that
[tex]\exists k \in \mathbb{N}[/tex] so that [tex]c = k.a[/tex]
so we can rewrite [tex]a+b[/tex] as
[tex]a+b = c = k.a[/tex]
[tex]b = k.a-a = (k-1).a[/tex]
and as [tex]k \in \mathbb{N}[/tex]
We have that either
Showing that [tex]a \mid c[/tex]
How many grams of digoxin (Lanoxin) would be required to make 25,000 tablets each containing 250 mcg of digoxin?
Answer:
6.25 grams would be required
Step-by-step explanation:
This problem can be solved as a rule of three problem.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
Unit conversion problems, like this one, is an example of a direct relationship between measures.
First step: The first step is determining how many mcg are used to make 25,000 tablets.
The problem states that each tablet contains 250 mcg of digoxin. So:
1 tablet - 250mcg
25,000 tables - x mcg
x = 25,000*250
x = 6,250,000 mcg
25,000 tables have 6,250,000mcg
Final step: Conversion of 6,250,000mcg to g
Each g has 1,000,000 mcg. How many g are in 6,250,000mcg? So:
1g - 1,000,000 mcg
xg - 6,250,000 mcg
1,000,000x = 6,250,000
[tex]x = \frac{6,250,000}{1,000,000}[/tex]
x = 6.25g
6.25 grams would be required
Using the digits 0 through 9, find out how many 4-digit numbers can be configured based on the stated conditions: a. [1 pt] The number cannot start with zero and no digits can be repeated. b. [1 pt] The number must begin and end with an odd digit. (Repeated digits are okay.) c. [1 pt] The number must be at least 5000 and be divisible by 10. (Repeated digits are okay.) d. [2 pt] The number must be less than 3000 and must be even. No digits may be repeated in the last 3 digits. (That is, 2234 would be okay, but 2334 would not be okay.)
Answer:
a. 4536, b. 2500, c. 500, d. 1080
Step-by-step explanation:
for every question we can use the numbers 0 - 9, this is 10 numbers in total (0, 1, 2, ,3 , 4, 5, 6, 7, 8, and 9).
Fore every case we have to check how many numbers we are allow to use in each digit.
a."The number cannot start with zero" this left us with 9 options of numers for the first digit.
"no digits can be repeated." So if we already use one numer for the first, we can't repeat this in the second, and so on. So for the second numer we have 9 numbers as option (now we can use 0), for the third, since we already use 2 digits, we have 8 options, and for the last, we have 7
that results in: 9*9*8*7 = 4536
b"The number must begin and end with an odd digit. " for odd digits we have 1, 3, 5, 7, 9 --> 5 options for the fist and last digit, and for the two middle digits, we have 10 options for each since it is allowed to repeat numbers
that results in: 5*10*10*5=2500
c"The number must be at least 5000" So the first digit can use 5, 6, 7, 8, or 9 -->5 options for the fist digit
"and be divisible by 10." so it has to end in a 0, --> 1 option fot the last numer
and for the middle digits there are no restrictions, so we use the 10 options for each.
that results in: 5*10*10*1=500
d"The number must be less than 3000 and must be even" for it to be less than 3000 it has to start with 0, 1 or 2 -> 3 options for the first digit
"and must be even" so the number has to end in 0, 2, 4, 6 or 8 --> 5 options for the last number
"No digits may be repeated in the last 3 digits." So we can't repeat in the middle number the one we put in the last digit, this gives us 9 options for the fist middle number and 8 for the second middle number
that results in: 3*8*9*5 = 1080
Final answer:
A step-by-step calculation is conducted for each condition to find the number of 4-digit numbers that can be formed using the digits 0-9 without repetition with conditions such as starting digit restrictions, parity, and divisibility. In total, there are 4536, 2500, 500, and 900 possible numbers for each condition respectively.
Explanation:
To calculate the number of 4-digit numbers meeting various conditions using the digits 0 through 9, we must consider each condition separately.
For a 4-digit number that cannot start with zero and with no repeated digits, we have 9 options for the first digit (1-9), 9 options for the second digit (0-9 except the first digit), 8 options for the third digit, and 7 options for the fourth, resulting in 9 × 9 × 8 × 7 = 4536 possible numbers.For a 4-digit number that must begin and end with an odd digit, there are 5 options for the first and last digit (1, 3, 5, 7, 9), and 10 options for each middle digit, leading to 5 × 10 × 10 × 5 = 2500 possible numbers.For a 4-digit number that must be at least 5000 and divisible by 10, we can pick any number between 5000 and 9990 that ends in '0'. We have 5 options for the first digit (5-9), 10 options each for the second and third digits, and only one option for the last digit ('0'). There are thus 5 × 10 × 10 = 500 possibilities.For a 4-digit number that must be less than 3000 and must be even, there are 2 options for the first digit (1 or 2), 10 options for the second digit, 9 options for the third digit (all except the second digit), and 5 options for the last even digit (0, 2, 4, 6, 8 excluding the one used as the first digit). This gives us 2 × 10 × 9 × 5 = 900 possible numbers.The average summer vacation costs $2252. If 82% of this amount is charged on credit cards, then what amount of the vacation cost is charged?
Answer: $1846.64
Step-by-step explanation:
Given : The average summer vacation costs $2252.
If 82% of this amount is charged on credit cards, then the amount of the vacation cost is charged will be :-
[tex]82\%\text{ of }\$2252\\\\\text{Convert percent into fraction by dividing it by 100, we get}\\\\=\$[\dfrac{82}{100}\times2252]\\\\=\$[\dfrac{184664}{100}]\\\\=\$1846.64[/tex]
Therefore the amount of the vacation cost is charged= $1846.64
Find the critical value from the Studentized range distribution for H0: μ1 = μ2 = μ3 = μ4 = μ5, with n = 35 at α = 0.01. Provide answer to three decimal places (example, 3.254).
Answer:
t-value = 2.441
Step-by-step explanation:
Let's assume that this is a one-tailed test to calculate the critical value, the process is this:
Calculate alpha (α): α = 1 - (confidence level / 100) , but we already have this α=0.01Find the critical probability (p*): p* = 1 - α/2 = 1-0.005=0.995Then, the critical value would be shown as a t statistic, but for this we need:degrees of freedom (df)= n-1=35-1=34
The critical t statistic (t*) or critical value is the t-value having degrees of freedom equal to 34 and a cumulative probability equal to 0.995.From the attached table we can see:
t-value = 2.441
Final answer:
The critical value from the Studentized range distribution for the given hypothesis test can be found using the qtukey() function in R or by looking it up in the table. For n=35 and α=0.01, the critical value is approximately 4.116.
Explanation:
To find the critical value from the Studentized range distribution, we need to use the qtukey() function in R or look up the value in the Studentized range distribution table.
Since n=35 and α=0.01, we have k=5 (number of groups) and df=5*(n-1)=170.
Using R, the critical value for a 5% significance level (α=0.05) is approximately 4.116.
NetSell, a the TV remote control supplier for Lumyn Electronics, has a weekly production cost of q TV remote controls that is given by
C(q) = 0.000004q^3 - 0.03q^2 + 100q + 75,000
where q is in the interval [0, 10,000].
The demand function for this product is given by
p(q) = -0.005q + 200.
Based on this information, find the following:
a) The marginal cost for the company.
b) The marginal revenue for the company.
c) The marginal profit for the company when 2,000 and 7,000 TV remote controls are manufactured.
Answer:
a. [tex]\frac{dC(q)}{dq} = 0.000012q^2 -0.06q + 100[/tex]
b. [tex]\frac{dR(q)}{dq}=-0.01q+200[/tex]
c.
[tex]U'(2000)=-0.000012(2000)^2+0.05(2000)+100 = 152[/tex]
[tex]U'(7000)=-0.000012(7000)^2+0.05(7000)+100 = -138[/tex]
Step-by-step explanation:
a) The marginal cost function is given by the derivative of the total cost function, in this way the marginal cost function for this company is:
[tex]\frac{dC(q)}{dq} = \frac{dC(q)}{dq} (0.000004q^ 3 - 0.03q ^ 2 + 100q + 75000) = 0.000012q^2 -0.06q + 100[/tex]
b) The income function is given by the relation [tex]R (q) = P (q) q = -0.005q^2 + 200q[/tex].
The marginal revenue function for the company is given by the derivative of the revenue function, in this way the marginal revenue function is:
[tex]\frac{dR(q)}{dq}= -0.01q+200[/tex]
(c) The profit function of the company is given by the relation [tex]U (q) = R (q) - C (q)[/tex], and the marginal utility function is given by the derivative of the utility function, in this way , the marginal utility function is:
[tex]\dfrac{dU(q)}{dq}=R'(q) - C'(q) = -0.01q+200 - (0.000012q^2-0.06q+100) = -0.000012q^2+0.05q+100[/tex]
When q = 2000, the marginal utility is:
[tex]U'(2000)=-0.000012(2000)^2+0.05(2000)+100 = 152[/tex]
When q = 7000, the marginal utility is:
[tex]U'(7000)=-0.000012(7000)^2+0.05(7000)+100 = -138[/tex]
The slopeof a linear function h(x) is 2. Suppose the function is translated 8 units up to get d(x). How can h(x) be translated to the left or right to represent the same function d(x)?
Answer:
4 units to the right
Step-by-step explanation:
Since all we know about function h(x) is that it has slope 2, we don't know its y intercept, so let's call it b and write the equation of that first line as:
[tex]h(x) = 2x + b[/tex]
Now, we translated that function up 8 units to get function d(x). This vertical displacement is expressed by adding 8 units to function h(x):
[tex]d(x) = h(x) + 8 = 2x+b+8[/tex]
We want to translate this last function d(x) either to the right or to the left in order to get the same expression as for function h(x).
Recall that translations to the right or left a fix number of units "c" affects the "x" coordinate of the function (by adding "c", we move to the left c units the graph of the function, and by subtracting "c" we move to the right the graph of the function).
So represent a generic shift for d(x) for example to the right in c units:
[tex]d(x) = 2(x-c)+x^{2} +b+8= 2x-2c+b+8[/tex]
Now we want this new shifted function to be EXACTLY as h(x) so we write the equality:
[tex]2x-2c+8+b=h(x)=2x+b\\2x-2c+8+b = 2x+b[/tex]
We can solve in the equation for the value "c" we need for the translation:
[tex]2x-2c+8+b = 2x+b\\-2c+8=0\\2c=8\\c=\frac{8}{2} = 4[/tex]
subtracting 2x from both sides, and also subtracting "b" from both sides.
This means that the translation to the right by 4 units will result on the exact same graph as for function h(x)
14 of 16 (12 complete) In a baseball league consisting of 7 teams, each team plays each of the other teams twice. How many games will be played? There will be games played.
Answer: There will be 42 games played.
Step-by-step explanation:
The number of combination to arrange n things if r things are taken at a time:-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Similarly, the number of combination to arrange 7 teams if 2 teams are taken at a time:-
[tex]^7C_2=\dfrac{7!}{2!(7-2)!}\\\\=\dfrac{7\times6\times5!}{2\times5!}=21[/tex]
∴ Number of combination to arrange 7 teams if 2 teams are taken at a time=21
Also, each team plays each of the other teams twice.
Then, the number of games will be played: [tex]21\times2=42[/tex]
Hence, There will be 42 games played.
Final answer:
To calculate the total number of games played in a league with 7 teams where each team plays the others twice, use the formula n(n - 1) × 2, which results in 7 * 6 * 2 = 84 games.
Explanation:
To find out the total number of games played in a baseball league with 7 teams where each team plays each of the other teams twice, we can use the formula for the number of games in a round-robin tournament: n(n - 1), where n is the number of teams. Since each team plays each other twice, the formula modifies to n(n - 1) × 2.
Substituting the number of teams (7) into the formula gives us: 7 * (7 - 1) × 2 = 7 * 6 × 2 = 42 × 2 = 84 games in total.
Assume that a customer shops at a local grocery store spending ak average if $200 a week, resulting in the retailer earning a $25 profit each week from this customer. Assuming the shopper visits the store all 52 weeks of the year, calculate the customer lifetime value if this shopper remains logal over a 10-year life-span.
Answer:
$13,000
Step-by-step explanation:
We have been given that the retailer earns a $25 profit each week from a customer.
The shopper visits the store all 52 weeks of the year, so number of weeks in 10 years would be 10 times 52 that is 520 weeks.
We know that the customer lifetime value stands for a prediction of the net profit attributed to the entire future relationship with a customer.
The customer lifetime value would be profit made per week times number of weeks the customer will shop.
[tex]\text{The customer lifetime value}=\$25\times 520[/tex]
[tex]\text{The customer lifetime value}=\$13,000[/tex]
Therefore, the customer lifetime value would be $13,000.
What are the odds of winning a game, if the probability of winning the game is 9/10?
Remember:
The probability of an event happening is the fraction: favorable outcomes/total outcomes.
The odds of an event happening treats the event as a win. The odds are given by the ratio: wins: losses
9:1
9:10
1:10
1:9
Final answer:
The odds of winning the game with a probability of 9/10 are 9:1, which means there are 9 chances of winning for every 1 chance of losing.
Explanation:
The question asks for the odds of winning a game given a probability of winning is 9/10. To find the odds in favor of winning, we calculate the ratio of the probability of winning to the probability of not winning. There are 9 chances to win for every 10 chances, so there is 1 chance out of 10 of not winning. Therefore, the odds in favor of winning are 9:1 (9 chances to win versus 1 chance to lose).
The odds of winning the game are 9:1, meaning for every 9 times one wins, one can expect to lose approximately 1 time.
The odds of winning a game, given the probability of winning is 9/10, can be calculated by considering the definition of odds. The odds in favor of an event are given by the ratio of the number of favorable outcomes to the number of unfavorable outcomes.
In this case, the probability of winning is 9/10, which means there are 9 favorable outcomes for every 10 total outcomes (including both wins and losses).
To find the odds, we subtract the probability of winning from 1 to get the probability of losing, which is 1 - 9/10 = 1/10. Now, we have 9 favorable outcomes (wins) and 1 unfavorable outcome (loss) since the total outcomes are 10.
Therefore, the odds of winning the game are 9 favorable outcomes to 1 unfavorable outcome, which is 9:1.
The correct answer is 9:1.
The probability of winning is given as 9/10.
- The probability of losing is the complement of the probability of winning, which is 1 - 9/10 = 1/10.
- Odds are calculated by comparing the number of favorable outcomes to the number of unfavorable outcomes.
- Here, there are 9 favorable outcomes (wins) and 1 unfavorable outcome (loss), so the odds of winning are 9:1.
- The odds format does not consider the total number of outcomes but rather the ratio of wins to losses. Hence, we do not include the total outcomes in the odds ratio.
combinatorics: what is the coefficient of (a^2)(b^3)(c) in (2a - b + 3c)^6?
Hence, the coefficient of a²b³c = -720.
Step-by-step explanation:
As from the question,
The general formula to find the coefficient is given by Binomial theorem:
That is, the coefficient of [tex]x^{\alpha}\cdot y^{\beta}\cdot z^{\gamma}[/tex] in (x + y + z)ⁿ is given by:
[tex]\frac{n!}{\alpha ! \cdot \beta ! \cdot \gamma !} (x)^{\alpha} \cdot (y)^{\beta} \cdot (z)^{\gamma}[/tex]
Now,
From the question we have
[tex](2a-b+3c)^{6}[/tex] having n = 6
∴ x = 2a
y = -b
z = 3c
Now,
The coefficient of a²b³c, that is
α = 2
β = 3
γ = 1
Therefore the coefficient of a²b³c =
[tex]= \frac{6!}{2 ! \cdot 3 ! \cdot 1 !} (2a)^{2} \cdot (-b)^{3} \cdot (3c)^{1}[/tex]
[tex]= \frac{6!}{2 ! \cdot 3 ! \cdot 1 !} 4(a)^{2} \cdot (-b)^{3} \cdot (3c)[/tex]
= -720 a²b³c
Hence, the coefficient of a²b³c = -720.
Is the statement given below true or false? Give
ajustification if true or a counterexample if false
ALL ISOSCELES TRIANGLES WITH CONGRUENT VERTEX ANGLES
ARESIMILAR.
Answer:
Yes, "All isosceles triangles with congruent vertex angles are similar".
Step-by-step explanation:
Consider the provided statement.
All isosceles triangles with congruent vertex angles are similar.
As we know that the two sides of an isosceles triangle are same.
It is given that the isosceles triangles with congruent vertex angles.
If vertex angles are congruent it means the opposite side of those angles are congruent. Also the sums of the base angles are the same,
As we know the base angles of an isosceles triangle are congruent, so by the AAA similarity we can say "All isosceles triangles with congruent vertex angles are similar".
Or
let say ΔABC and ΔDEF are isosceles triangles where AB=DE and AC=DF
It means ∠B=∠E and ∠C=∠F also it is given that ∠A=∠D
Thus. from AAA similarity we can say "All isosceles triangles with congruent vertex angles are similar".
Is the set \mathbb{Z} a group under the operation a*b = a - b + ab ? Justify your answer.
Answer:
Step-by-step explanation:
Given that *is the binary operation in the sets of integers.
[tex]a*b = a - b + ab[/tex]
closure: a-b+ab is again an integer belongs to Z. Hence closure is true.
Associativity: [tex]a*(b*c) = a*(b+c-bc)\\= a-b-c+bc+ab+ac-abc\\= a-b-c +ab+bc+ca-abc[/tex]
[tex](a*b)*c=(a+b-ab)*c\\=a+b-ab-c+ac+bc-abc\\[/tex]
The two are not equal. Hence this cannot be a group as associtiavity does not hold good.
The rules of the game are as following: a player draws one card from a standard 52-card deck. If the player picks a heart, they win $10. If they pick a face card that is not a heart, the player wins $8. Picking a face card heart counts the same as picking a heart. If a player picks another card, they lose $6. Is this gambling game a good way to make money for someone or not?
Let's suppose "good" here means that the amount a player can expect to win is positive.
The probability of drawing a heart from the deck is 13/52 = 1/4.
The probability of drawing a face card that is not a heart is 9/52.
The probability of drawing anything else is 30/52 = 15/26.
The expected winnings are then 10(1/4) + 8(9/52) - 6(15/26) = 11/26, meaning on average the player can expect to win about $0.42 per game, so by our definition this game is a "good" way to make money.
Statistically speaking, a player would gain 42 cents per game in the long run, making this gambling game potentially profitable.
This is determined by computing expected value, which takes into account the gains or losses for each possible outcome and the probability of each outcome.
Explanation:The subject of this question is probability with reference to a game of cards. To evaluate whether or not the game is a good idea, we need to determine the expected value of the game, which is calculated by multiplying the value of each outcome by their probability and then summing these products. Here's how finances from the game might play out statistically:
There are 13 hearts in the deck (which includes 3 face cards), so the probability of drawing a heart is 13/52 = 0.25, or 25%. When a player draws a heart, they gain $10.There are 12 face cards in the deck overall, and 3 of those are hearts and are already accounted for. So, only 9 face cards count for this category. The probability of drawing a face card that is not a heart is then 9/52 = 0.173 (17.3%). In this case, the player would win $8.There are 52 - 13 - 9 = 30 other cards. The chance of drawing one of these is 30/52 = 0.577 (57.7%). Drawing one of these cards means the player loses $6.The expected value of one round of the game is thus (0.25 x $10) + (0.173 x $8) + (0.577 x -$6) = $2.5 + $1.38 - $3.46 = $0.42. Therefore, statistically speaking, a player would gain 42 cents per game in the long run, making this gambling game potentially profitable.
Learn more about Expected Value here:https://brainly.com/question/37190983
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Which of the following is the best example of a business economic decision.
Answer:
C. Hiring part-time employees to save on costs
Step-by-step explanation:
It is good economically to not have to pay the employee full time but still have someone to help the business so they are there a shorter period of time
Though this question is not mathematics, the best example of a business economic decision is C) Hiring part-time employees to save on costs.
What is an economic decision?Economic decisions revolve around the following economic activities in the use of economic resources:
SavingExchangeInvestmentProductionDistributionConsumption.Business economic decisions are made to achieve business goals, including savings, efficiency, and effectiveness.
Thus, the best example is of a business economic decision is Option C because it involves the achievement of a business goal, savings.
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Use the Euclidean algorithm to determine the greatest common divisor of 2288 and 4875
Answer:
13
Step-by-step explanation:
We have to find greatest common divisor of two number 2288 and 4875.
Now, greatest common divisor of two number is defined as the highest common factor that divides both the number.
We can use the Euclidean algorithm to do so.
Since 4875 is the larger of the two number
4875 ÷ 2288: Quotient = 2, Remainder = 299
2288 ÷ 299: Quotient = 7, Remainder = 195
299 ÷ 195: Quotient = 1, Remainder = 104
195 ÷ 104: Quotient = 1, Remainder = 91
104 ÷ 91: Quotient = 1, Remainder = 13
91 ÷ 13: Quotient =7, Remainder = 0
Hence, we stop here and the greatest common divisor = 13
Final answer:
The greatest common divisor of 2288 and 4875 is 1.
Explanation:
The Euclidean algorithm is used to determine the greatest common divisor (GCD) of two numbers. To find the GCD of 2288 and 4875, we will use the Euclidean algorithm as follows:
Divide 4875 by 2288, giving a quotient of 2 and a remainder of 299.
Divide 2288 by 299, giving a quotient of 7 and a remainder of 35.
Divide 299 by 35, giving a quotient of 8 and a remainder of 19.
Divide 35 by 19, giving a quotient of 1 and a remainder of 16.
Divide 19 by 16, giving a quotient of 1 and a remainder of 3.
Divide 16 by 3, giving a quotient of 5 and a remainder of 1.
The Euclidean algorithm ends when we reach a remainder of 1. The GCD of 2288 and 4875 is the previous remainder, which is 1.
So, the greatest common divisor of 2288 and 4875 is 1.
assume that the number of production defects is 28 and that 14 of these are classified as major defects, 8 are classified as design defects, and 11 were neither major defects nor design defects. How many of the design defects were major?
Answer: 5
Step-by-step explanation:
Let A denotes the number of major defects and B denotes the number of design defect.
By considering the given information, we have
[tex]U=28\ ;\ n(A)=14\ ;\ n(B)=8\ \ ;\ n(A^c\cap B^c)=1[/tex]
Now, the number of major defects or design defects:
[tex]n(A\cup B)=U-n(A^c\cap B^c)=28-11=17[/tex]
Also,
[tex]n(A\cap B)=n(A)+n(B)-n(A\cup B)\\\\\Rightarrow\ n(A\cap B)=14+8-17=5[/tex]
Hence, the number of design defects were major=5
There are 5 design defects that are also classified as major defects.
To solve this problem, let's break down the information given and organize it in a systematic way using a Venn diagram and algebra.
Given data:
Total number of defects: 28Number of major defects: 14Number of design defects: 8Number of defects that are neither major nor design: 11We need to find out how many of the design defects are also major defects.
Let's denote:
A: Major defectsB: Design defectsA ∩ B: Major design defects (defects that are both major and design)First, note that the defects that are neither major nor design are given as 11.
Therefore, the defects that are either major or design or both are:
[tex]28 - 11 = 17[/tex]
This tells us the total number of defects in sets A or B or both is 17.
Using the principle of inclusion-exclusion, the number of defects that are either major or design can be represented as:
[tex]|A \cup B| = |A| + |B| - |A \cap B|[/tex]
Where:
[tex]|A \cup B| = 17[/tex]
[tex]|A| = 14[/tex]
[tex]|B| = 8[/tex]
Now, substituting the values, we get:
[tex]17 = 14 + 8 - |A \cap B|[/tex]
Solving for [tex]|A \cap B|[/tex]:
[tex]17 = 22 - |A \cap B|[/tex]
[tex]|A \cap B| = 22 - 17 = 5[/tex]
So, the number of defects that are both design defects and major defects is 5.
pleases help im stuck on both
A physician prescribed mometasone furoate monohydrate (NASONEX) nasal spray for a patient, with directions to
administer two sprays into each nostril once daily. If each spray contains 50 μg of drug and the container can deliver a
total of 120 sprays, how many micrograms of drug would the patient receive daily, and how many days of use will the
prescription last the patient?
Answer: The patient receives [tex]200\ \mu g[/tex] daily.
The prescription will last 30 days .
Step-by-step explanation:
Given : Prescription= Two sprays into each nostril once daily.
That means total sprays for both nostrils = [tex]2\times2=4[/tex] [∵ 1 nostrils in each nose.]
If each spray contains [tex]50 \mu g[/tex] of drug, then the amount of drug received by patient daily :-
[tex]4\times50=200\ \mu g[/tex]
Thus , the patient receives [tex]200\ \mu g[/tex] daily.
Also, the container can deliver a total of 120 sprays.
Then, the number of days of use will the prescription last the patient will be:_
[tex]\dfrac{120}{4}=30[/tex]
Hence, the prescription will last 30 days of use .
Final answer:
The patient will receive 200 micrograms of mometasone furoate monohydrate daily, and the prescription will last for 30 days.
Explanation:
The question involves calculating the total dosage of mometasone furoate monohydrate received daily by a patient and determining how many days the prescription will last, based on the dose and the number of sprays available.
To find the daily dose, we can multiply the number of sprays per nostril by the dosage per spray and the number of nostrils:
2 sprays/nostril × 50 μg/spray × 2 nostrils = 200 μg/day
The patient receives 200 micrograms daily.
To find out how many days the prescription will last:
120 sprays/container ÷ (2 sprays/nostril × 2 nostrils) = 120 sprays/container ÷ 4 sprays/day = 30 days
The prescription will last the patient for 30 days.
The number of species n found on islands typically increases with the area of the island A. Suppose that this relationship is such that the rate of increase with island area is always proportional to the density of species (that is, number of species per unit area) with a proportionality constant k between 0 and 1. Find the function that describes the species-area relationship. (Let n(1) = n1.)
Answer:
[tex]n(A) = n_1A^k[/tex]
Step-by-step explanation:
Taking into account that the growth rate of the number of species on the island is proportional to the density of species (number of species between area of the island), a model based on a differential equation is proposed:
[tex]\frac{dn}{dA} = k\frac{n}{A}[/tex]
This differential equation can be solved by the method of separable variables like this:
[tex]\frac{dn}{n} = k\frac{dA}{A}[/tex] with what you get:
[tex]\int\ {\frac{dn}{n}}\ = k\int\ {\frac{dA}{A}}[/tex]
[tex]ln|n| = kln|A|+C[/tex]. Taking exponentials on both sides of the equation:
[tex]e^{ln|n|} = e^{ln|A|^{k}+C}[/tex]
[tex]n(A) = e^{C}A^{k}[/tex]
how do you have to [tex]n (1) = n_1[/tex], then
[tex]n(A) = n_1A^k[/tex]
a box of 100 nails weighs 1 5/8 pounds. mark used 3 1/3 boxes of naila to build a 2 story tree house. how many pounds of nails did he use?
Answer:
5 5/12 pounds of nails
Step-by-step explanation:
(3 1/3 boxes) × (1 5/8 pounds/box) = (10/3)(13/8) pounds = 65/12 pounds
= 5 5/12 pounds
Mark used approximately 5.41 pounds of nails to build the tree house. This is found by converting the given fractions to decimal and then multiplying the weight of one box of nails by the number of boxes use
Explanation:In the problem, we know that a box of 100 nails weighs 1 5/8 pounds. We are also told that Mark used 3 1/3 boxes of nails. Therefore, we first need to find out how much one box of nails weighs, and then multiply that weight by the number of boxes Mark used.
To convert 1 5/8 to a decimal, we know that 5/8 = 0.625, so 1 5/8 = 1.625 pounds. Mark used 3 1/3 boxes, and 1/3 converted to a decimal is approximately 0.33, so Mark used approximately 3.33 boxes. By multiplying 1.625 pounds by 3.33, we find that he used approximately 5.41 pounds of nails to build the tree house.
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Recent studies indicate that the average surface temperature of the earth has been rising steadily. Some scientists have modeled the temperature by the linear function T − 0.02t 1 8.50, where T is temperature in °C and t represents years since 1900. (a) What do the slope and T-intercept represent? (b) Use the equation to predict the average global surface temperature in 2100.
Answer:
a) The slope represents the change per year in the earth's surface temperature (0.02 ºC) and the T-intercept represents the average earth's surface temperature in 1900 (18.5ºC)
b) The average global surface temperature will be 22.5ºC in 2100.
Step-by-step explanation:
I think there's a "+" sign missing in the function you wrote, and that you meant to write T= 0.02t + 18.50 and I'll solve the problem for this function.
If I am wrong with the values or the + you can always substitute the values you have in your function based on the procedure I'll write down.
So, this function is T= 0.02t + 18.50.
A linear function is expressed as y = f(x) = mx + b where m is the slope of the function and b is the interception with the y-axis.
a) In this particular function, we would have that the slope of the function is 0.02 and it represents the change per year in the earth's surface temperature, since T is temperature in ºC, the change per year would be of 0.02ºC.
On the other hand, the T-intercept would be the value of the function when t=0
T(0) = 0.02(0) +18.50
T(0) = 18.50
This 18.50 represents the average surface temperature of the earth when measures started, meaning, the average surface temperature of the earth in 1900 was 18.50
b) To predict the average global surface temperature in 2100, we are going to substitute 200 in the function (since 2100 - 1900 = 200)
T(200) = 0.02 (200) + 18.50 = 4 + 18.50 = 22.5
Therefore, the average global surface temperature in 2100 will be 22.5ºC
Final answer:
The slope of the linear function represents the rate of temperature increase per year while the T-intercept represents the estimated global surface temperature in 1900. Substituting t=200 into the equation predicts an average global surface temperature of 12.50°C in 2100.
Explanation:
Understanding the Linear Model of Earth's Temperature Rise
The linear function given is T = 0.02t + 8.50, where T is the temperature in degrees Celsius and t represents the years since 1900. The slope of this function is 0.02, which indicates the average rate at which the average global surface temperature is increasing per year. The T-intercept is 8.50°C, which can be interpreted as the estimated global surface temperature in the base year, 1900.
To project the average global surface temperature in 2100, we simply substitute t = 200 into the equation (since 2100 is 200 years after 1900) and calculate:
T = 0.02(200) + 8.50 = 4 + 8.50 = 12.50°CTherefore, using this model, the predicted average global surface temperature in 2100 is 12.50°C.
A town's population has been growing linearly. In 2003, the population was 59.000 and the population has been growing by 1,700 people each year. a. Write a formula for the population x years after 2003. b. What will the town's population be in 2007? c. In what year will the population be 77,700 people?
Answer:
In 2003, the population was 59000 and the population has been growing by 1,700 people each year.
A.
The equation will be:
59000+1700x = (population 'x' years after 2003)
For x, you plug in the amount of years after 2003.
Like if it is the year 2003, the population is [tex]59000+1700(0)[/tex]
= 59000
when it is year 2005, the population is [tex]59000+1700(2)[/tex]
= 62400
B.
The town's population in 2007 will be :
[tex](2007-2003=4)[/tex]
[tex]59000+1700(4)[/tex]
Population = 65800
C.
[tex]59000+1700x=77700[/tex]
=> [tex]1700x=18700[/tex]
x = 11
Means [tex]2003+11=2014[/tex]
Hence, by year 2014 the population will be 77700.
The data below represents the number of T-shirts sold per week by a student who started his own online t-shirt business. Find the weighted mean of the number of t-shirts sold per week. (Round your answer to the nearest tenth if necessary.)
T-Shirts Sold per Week Frequency
2 1
4 4
6 7
8 3
Answer:
The weighted mean of the number of t-shirts sold per week is 5.6.
Step-by-step explanation:
Given : The data below represents the number of T-shirts sold per week by a student who started his own online t-shirt business.
T-Shirt Sold per Week([tex]x_i[/tex]) Frequency([tex]w_i[/tex])
2 1
4 4
6 7
8 3
To find : The weighted mean of the number of t-shirts sold per week ?
Solution :
The formula of weighted mean is
[tex]\text{Weighted mean}=\frac{\sum (x_i\times w_i)}{\sum w_i}[/tex]
Substituting the values in the formula,
[tex]\text{Weighted mean}=\frac{2(1)+4(4)+6(7)+8(3)}{1+4+7+3}[/tex]
[tex]\text{Weighted mean}=\frac{2+16+42+24}{15}[/tex]
[tex]\text{Weighted mean}=\frac{84}{15}[/tex]
[tex]\text{Weighted mean}=5.6[/tex]
Therefore, The weighted mean of the number of t-shirts sold per week is 5.6.
Final answer:
To find the weighted mean of T-shirts sold per week, you multiply each amount by its frequency, sum these products, and then divide by the total frequency. For this data, the weighted mean is 5.6 T-shirts per week.
Explanation:
To calculate the weighted mean of the number of T-shirts sold per week, we must multiply each number of T-shirts sold by its respective frequency and then divide the sum by the total number of observations.
We have the following data:
6 * 7 = 42
Add these products together:
2 + 16 + 42 + 24 = 84
Next, calculate the total frequency (total number of weeks):
1 + 4 + 7 + 3 = 15
Now, divide the sum of products by the total frequency to get the weighted mean:
84 / 15 = 5.6
Therefore, the weighted mean number of T-shirts sold per week is 5.6.
Rita Crudwell was the appointed comptroller and treasurer of the town of Dixon, Illinois (population 15,700 in 2010) for 29 years. Despite her busy, dual job, she was able to establish and run a world renowned quarter horse breeding operation, amassing 52 world championships. I do now know how she found the time and energy to do this but I do know where she got the money: over the course of her last 22 years in office, she embezzled $53,740,394 million dollars from the town (caught in 2012, she is currently serving a 19 year prison term) What would be the "hourly wage"
dollars from the town (caught in 2012, she is currently serving a 19 year prison term) What would be the "hourly wage" for a person that wants to make $53,740,394 million over exactly 22 years? (NOTE: assume 1 year 365.256 days) 1-2 If a certain physics professor gets $65,000/year, how many years would it take for such a person to make $53,740,394 million?
Answer:
a) $278.65 million per hour
b) 826.77 million years
Step-by-step explanation:
Given:
Total money = $53,740,394 million
Time taken to earn the money = 22 years
Now,
1 year = 365.256 days
and 1 day = 24 hours
thus,
22 years = 22 × 365.256 × 24 = 192855.168 hours
Therefore,
for a person that wants to make $53,740,394 million over exactly 22 years, will have hourly wage
= [tex]\frac{\textup{money to be earned}}{\textup{Time taken in hours}}[/tex]
= [tex]\frac{\textup{53,740,394 million}}{\textup{192855.168 hours}}[/tex]
= $278.65 million per hour
Now,
Salary of a physics professor = 65000 /year
Thus,
for physics professor to earn $53,740,394 million number of years taken will be
= [tex]\frac{\textup{$53,740,394 million}}{\textup{65000 /year}}[/tex]
= 826.77 million years
Final answer:
To earn $53,740,394 through embezzlement over 22 years equates to an "hourly wage" of $1,174.60, assuming a 40-hour workweek. It would take a physics professor making $65,000 a year approximately 827 years to earn the same amount.
Explanation:
Calculating the "hourly wage" for embezzling $53,740,394 over 22 years requires us to first determine the total hours worked over those years, assuming a standard full-time job framework of 40 hours per week. Also, to calculate how many years it would take a physics professor earning $65,000 a year to amass the same amount of money embezzled requires straightforward division.
Step 1: Calculate the Total Number of Hours Worked Over 22 years
Number of weeks in a year = 52
Hours worked per week = 40
Total hours worked in a year = 52 weeks * 40 hours/week = 2,080 hours
Total hours worked over 22 years = 2,080 hours/year * 22 years = 45,760 hours
Step 2: Calculate the Hourly "Wage" from Embezzlement
Total embezzled = $53,740,394
Hourly "wage" = Total embezzled / Total hours worked over 22 years = $53,740,394 / 45,760 hours = $1,174.60 per hour
Step 3: Calculate the Years for a Physics Professor to Earn $53,740,394
Annual salary = $65,000
Years required = Total embezzled / Annual salary = $53,740,394 / $65,000 ≈ 826.78 years
The score on a trivia game is obtained by subtracting number of incorrect answers from twice the number of correct answers. If a player answered 40 questions and obtained a score of 50, how mary questions did the player answer correctly?
Answer:
30
Step-by-step explanation:
I solved this question algebraically. First a variable (I used 'c') is introduced into the equation (for the number of correct answers). Thus we get the equation;
2c - (40 - c) = 50
solving this...
2c - 40 + c = 50
3c = 90
c = 30
So the number of correct answers is 30. (30*2-10=50)
[Alternatively we can use a variable for the number of incorrect answers and get; 2* (40 - a) - a = 50, and solve this equation but this method is longer as you'll need to subtract this answer from 40 to get the number of correct responses.]
250 ml of a liquid medication contains 125 mg of Drug Z. If the patient gets an injection of 50 ml of this medication, how much drug Z is in that injection
Final answer:
To find the amount of Drug Z in the 50 ml injection, set up a proportion based on the known concentration (125 mg in 250 ml). Solving for the unknown quantity gives 25 mg of Drug Z in the injection.
Explanation:
To determine how much of Drug Z is in a 50 ml injection when 250 ml of the medication contains 125 mg of Drug Z, you can use a proportion. The proportion can be set up as follows:
(125 mg of Drug Z) / (250 ml of medication) = (X mg of Drug Z) / (50 ml of medication)
To solve for X, which represents the amount of Drug Z in the 50 ml injection, you cross-multiply and divide:
(125 mg) × (50 ml) = (250 ml) × (X mg)
6250 mg·ml = 250 ml·X mg
Divide both sides by 250 ml to isolate X:
X = (6250 mg·ml) / (250 ml)
X = 25 mg of Drug Z
Therefore, the 50 ml injection contains 25 mg of Drug Z.