Answer:
a) 1,518,000
b) 2,284,880
c) 60,720
Step-by-step explanation:
a) a. if the first letter must be Upper C comma Upper X comma Upper T comma or Upper M and no letter may be repeated?
We draw 5 boxes, and based on that we will see the total possible cases. There are 26 alphabets
The first box should have C or X or T or M .No letter may be repeated.
Any Any Any Any Any
5 alphabets of the of the of the of the
C,X , T , M remaining remaining remaining remaining
25 alphabets 24 alphabets 23 alphabets 22 alphabets
Therefore; total possible call letters = 5 × 25 × 24 × 23 × 22 = 1,518,000
b)
The first box should have C or X or T or M Repeats as allowed
Any Any Any Any Any
5 alphabets of the of the of the of the
C,X , T , M remaining remaining remaining remaining
26 alphabets 26 alphabets 26 alphabets 26 alphabets
Therefore Total possible call letters = 5 × 26 × 26 × 26 × 26 = 2,284,880
c) The first box should have C,X , T , M and end with S
So the last place if fixed, and we now have 25 alphabets. The first box can go in 5 ways. The next box then will have only 24 letters to choose from, as the first box has taken a letter and the last box already has S in it. Repetition not allowed
Any Any Any Any S
5 alphabets of the of the of the is fixed
C,X , T , M remaining remaining remaining here
24 alphabets 23 alphabets 22 alphabets
Therefore Total possible call letters = 5 × 24 × 23 × 22 × 1 = 60,720
a. 30,240 different call letters can be made if the first letter must be C, X, T, or M and no letter may be repeated. b. 11,881,376 different call letters can be made if repeats are allowed. c. 22,464 different call letters can be made if the call letters start with C, X, T, or M, have no repeats, and end with S.
Explanation:a. If the first letter must be C, X, T, or M, and no letter may be repeated, the options for the first letter are 4. For the remaining 4 positions, we can choose from 25 letters (all except the first letter chosen). Therefore, the total number of different 5-letter radio station call letters is 4 * 25 * 24 * 23 * 22 = 30,240.
b. If repeats are allowed, including the first letter being C, X, T, or M, we still have 26 options for each position (including the possibility of repeating the first letter chosen). Therefore, the total number of different 5-letter radio station call letters is 26 * 26 * 26 * 26 * 26 = 26^5 = 11,881,376.
c. To have no repeats and end with the letter S, we have 24 options for the first position (all letters except C, X, T, or M) and 1 option for the last position (the letter S). For the remaining 3 positions, we can choose from 24 letters (all except the first and last position chosen). Therefore, the total number of different 5-letter radio station call letters starting with C, X, T, or M and ending with S is 4 * 24 * 24 * 24 * 1 = 22,464.
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45 is blank times as many as 9 and is blank times as many as 5
Answer:
45 is 5 times as many as 9 and 9 times as many as 5 :)
Step-by-step explanation:
45 is 5 times as many as 9 and is 9 times as many as 5.
We have the following statement -
45 is x times as many as 9 and is y times as many as 5
We have to find x and y.
A number 'n' is 'a' times as many as 'b'. Then n equals to ?n will be equal to -
n = ab
According to the question -
45 is x times as many as 9 and is y times as many as 5. Using the method shown above we can write two equations -
45 = [tex]x[/tex] x 9 ---(1)
and
45 = y x 5 ---(2)
Now -
Solving both, we get -
x = 5 and y = 9
Hence, 45 is 5 times as many as 9 and is 9 times as many as 5.
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What is 15 divided 1/3
Answer: 45
Explanation: Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of that fraction or that fraction flipped.
Also, think of the 15 in this problem as 15/1.
So we can rewrite 15/1 ÷ 1/3 as 15/1 · 3/1.
Multiplying across the numerators and the denominators,
we find that our answer is 45/1 or just 45.
15 divided by 1/3 is equal to 45.
To divide 15 by 1/3, we can interpret it as finding how many groups of 1/3 can be made from 15.
To begin, we can convert the division of 15 by 1/3 into a multiplication problem by taking the reciprocal of 1/3, which is 3/1 or simply 3.
So, we have:
15 ÷ (1/3) = 15 x 3
Multiplying 15 by 3, we get:
15 x 3 = 45
Therefore, 15 divided by 1/3 is equal to 45.
In other words, 15 can be divided into 45 equal parts of size 1/3. Each of these parts represents the quotient when dividing 15 by 1/3.
When we multiply 1/3 by 45, we get 15. This confirms that 15 divided by 1/3 is indeed equal to 45.
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5. Solve the equation.
6i - 10 = - 82
Equation:
Answer:
i=-12
Step-by-step explanation:
1.) Add 10 to -82 to get the equation 6i=-72
2.) Divide -72 by 6 to get the answer i=-12
Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the sample mean for x and for y. Round your answer to the nearest tenth. x: 11 0 36 22 34 24 25 -11 -11 -22 y: 9 -3 28 14 23 16 14 -3 -4 -9
Answer:
(a). Σx= 108, Σx^2 = 4984, Σy^2 = 2,157.
(b). 10.8, 0.1.
(C) and (d) => check explanation.
Step-by-step explanation:
To Calculate for Σx we will have to add all the values for x that is the summation of x-values.
Σx = 11 + 0 + 36 + 22 + 34 + 24 + 25 + -11 + -11 + -22 = 108.
Σx^2 = 11 × 11 + 0 × 0 + 36 × 36 + 22 × 22 + 34 × 34 + 24 ×24 + 25 × 25 + -11 × -11 + -11 × -11 + -22 × -22 = 4984.
Σy^2 = 9× 9 + -3 × -3 + 28 ×28 + 14 × 14 + 23 × 23 + 16 × 16 + 14× 14 + -3 ×-3 + -4 × -4 + -9 × -9= 2,157.
(b). Sample mean for x = 108/10 = 10.8.
Variance for x:
11 - 10.8 = 0.3
0 - 10.8 = -10.8
36 - 10.8 =25.2.
22 - 10.8=11.2.
34 - 10.8 = 23.2
24 -10.8 = 13.2.
25 - 10.8= 14.2
-11 - 10.8 = -21.8.
-11 - 10.8 = - 21.8
-22 -10.8 = -32.8.
Total=0.1
Standard deviation for x = √ s^2 = 0.3162
This can be done for y too
(c). 75% Chebyshev interval around the mean for x values = 10.8 + 2 (0.3162); 10.8 - 2(0.3162).
=> (11.4324, 10.1676).
(d). The coefficient of variation= (0.3162)/10.8 × 100 = 2.92%.
The sample means for annual returns of the Vanguard Total Stock Index (x) and Vanguard Balanced Index (y) have been computed as 10.8 and 8.5 respectively. The inclusion of bonds in a portfolio can lower overall return slightly while also reducing the risk.
Explanation:The student's task revolves around the subject of statistical analysis, here applied to investment portfolio management. Their goal is to compute the sample mean (average) for two variables - x and y - which each represent annual returns for certain types of portfolios.
Portfolio x represents a 100% stock holding in the Vanguard Total Stock Index, while y represents a 60% stock and 40% bond holding in the Vanguard Balanced Index. Such portfolios carry varying degrees of risk, with all-stock portfolios generally accepted to be more volatile, yet offering higher potential returns than mixed portfolios.
In order to calculate the sample means for x and y, you simply add together all the annual returns for each, then divide by the number of years.
For x: (11 + 0 + 36 + 22 + 34 + 24 + 25 - 11 - 11 - 22)/10 = 10.8 (rounded to the nearest tenth)
For y: (9 - 3 + 28 + 14 + 23 + 16 + 14 - 3 - 4 - 9)/10 = 8.5 (rounded to the nearest tenth)
As seen, stocks did yield a higher average return over the period in consideration, though the range of returns was also much wider. By adding bonds to the portfolio (shown by y), the overall return reduced slightly, but so did the risk (variability) of returns.
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what is the area of a triangle with 9mi and 20 mi
Answer:
Area=90mi
Step-by-step explanation:
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles.
If Hank shoots from inside the three-point line, what can be said about his distance from the center of the basket?
Answer:
If Hank shoots from inside the three-point line we can say that he has to shoot 246 inches to make the ball into the hoop.
Hank's distance from the center of the basket, if he is shooting from inside the three-point line, would be less than the distance of the three-point line from the basket. This distance varies between 6.75 metres (NBA, FIBA) or 6.1 metres (college games).
Explanation:When a player stands inside the three-point line in basketball, it can be said that they are less than 6.75 metres (for NBA and FIBA) or 6.1 metres (for college games) from the centre of the basket. This distance varies because different basketball associations have different guidelines for the distance of the three-point line from the center of the basket. For instance, the NBA has its line located 7.24 metres from the basket, FIBA has it at 6.75 metres, and in college games, it's 6.1 metres away. As such, if Hank is shooting inside the three-point line, he is definitely standing closer than these distances to the basket's center.
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Of the five quadratics listed below, four of them have two distinct roots. The fifth quadratic has a repeated root. Find the value of the repeated root.
-x^2 + 18x + 81
3x^2 - 3x - 168
x^2 - 4x - 4
25x^2 - 30x + 9
x^2 - 14x + 24
Answer: 3/5
Step-by-step explanation: The fourth quadratic in the list is the square of a binomial:
25x^2 - 30x + 9 = (5x - 3)^2
Therefore, the repeated root of this quadratic is the solution to 5x - 3=0, which is 3/5
the mean weight of 9 players and 3 reserve players is 188 pounds what is the mean weight of the 3 reserve players
Answer:
83.56/p
Step-by-step explanation:
Let the weight of the players = p
Let the weight of the reserve players = r
Since there 9 players, there weight = 9p
And since there 3 reserve players, there weight = 3r
(9p + 3r) / 12 = 188
9p + 3r = 12 * 188
9p + 3r = 2256
Solve for r
r = 2256 / 27p
r = 83.56/p
The scatter plot shows the number of tickets sold and the price of the tickets.
Using the trend in the scatter plot, about how much will people pay for a ticket if 50 tickets are sold?
Answer: People will pay about $5 for a ticket if 50 are sold.
Step-by-step explanation:
What we can deduce from this graph is the more expensive the tickets are, the less tickets are sold.
So far, the greatest number of tickets sold are 40 with a price of around $10.
Now, if people were to sell 50 tickets, following with the graph, it
would mean that the price would have to be less than 10.
Only one of the options is less than 10, and that is 5, so therefore, the answer is 5.
The answer is 168 but what is it cm2 cm3 or just cm?
Answer:
if its length then its cm
if its area then its cm²
if its volume then its cm³
Step-by-step explanation:
Melissa ran 6 2/5 miles north 2 3/4 west and 2 1/3 south how far did she run
Answer:11.5
Step-by-step explanation:
distance=6 2/5 + 2 3/4 + 2 1/3
d=(5x6+2)/5 + (4x2+3)/4 + (3x2+1)/3
d=32/5 + 11/4 + 7/3
d=(12x32+15x11+20x7) ➗ 60
d=(384+165+140) ➗ 60
d=689 ➗ 60
d=11.5
The total distance did she run is 11.5 miles.
It is required to find the total distance.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
Melissa ran 6 2/5 miles north ,2 3/4 west and 2 1/3 south.
According to given question we have,
Total distance=6 2/5 + 2 3/4 + 2 1/3
d=(5x6+2)/5 + (4x2+3)/4 + (3x2+1)/3
d=32/5 + 11/4 + 7/3
d=(12x32+15x11+20x7) /60
d=(384+165+140) / 60
d=689 / 60
d=11.5 miles.
Therefore, the total distance did she run is 11.5 miles.
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If f(x) is the slope of a trail at a distance of x miles from the start of the trail, what does 7 f(x)dx 5 represent? The change in the elevation between x = 5 miles and x = 7 miles from the start of the trail. The elevation at x = 5 miles from the start of the trail. The elevation at x = 7 miles from the end of the trail. The elevation at x = 7 miles from the start of the trail. The change in the elevation between x = 5 miles and x = 7 miles from the end of the trail.
Answer:
The answer is option A
Step-by-step explanation:
[tex]\int\limits^7_5 {f(x)} \, dx[/tex]
From the question given, the limit is between 5 and 7, the differentiation starts from the beginning of the trail
In this exercise we have to solve the integral and classify the correct alternative:
The answer is option A.
In this case we will have to solve the integral:
[tex]\int\limits^7_5 {f(x)} \, dx[/tex]
From the question given, the limit is between 5 and 7 the differentiation starts from the beginning of the trail.
The answer is option A.
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In circle G with m angle of FGH = 90 and FG = 9 units find area of sector FGH. Round
to the nearest hundredth.
Answer:63.6 units
Step-by-step explanation:
Theta=90°
Radius =9
area of sector=(theta)/360 x π x r x r
area of sector=90/360 x 3.14 x 9 x 9
area of sector=(90x3.14x9x9)➗360
area of sector=22890.6 ➗ 360
area of sector=63.535
area of sector=63.6 approximately
Answer:
It's 63.62
Step-by-step explanation:
Jerome solved the equation below by graphing. log Subscript 2 Baseline x + log Subscript 2 Baseline (x minus 2) = 3 Which of the following shows the correct system of equations and solution? y 1 = StartFraction log x Over log 2 EndFraction + StartFraction log (x minus 2) Over log 2 EndFraction, y 2 = 3; x = 3 y 1 = StartFraction log x Over log 2 EndFraction + StartFraction log (x minus 2) Over log 2 EndFraction, y 2 = 4; x = 4 y 1 = log x + log (x minus 2), y 2 = 3; x = 33 y 1 = log x + log (x minus 2), y 2 = 3; x = 44
Answer:
x=4
Step-by-step explanation:
The solution for the logarithmic equation is x = 4 and it is graphically shown in the figure.
What is graphing a logarithmic function?Every logarithmic function is the inverse function of an exponential function, we can think of every output on a logarithmic graph as the input for the corresponding inverse exponential equation.
For the given situation,
The equation is
[tex]log_{2}x+log_{2}(x-2) =3[/tex]
⇒ [tex]log_{2} (x)(x-2)=3[/tex]
⇒ [tex]log_{2}(x^{2} -2x)=3[/tex]
we know that [tex]y=log_{b} x[/tex] can be written as [tex]x=b^{y}[/tex]
⇒ [tex]x^{2} -2x=2^{3}[/tex]
⇒ [tex]x^{2} -2x-8=0[/tex]
⇒ [tex](x-4)(x+2)[/tex]
⇒ [tex]x=4[/tex] or [tex]x=-2[/tex]
The solution for the logarithmic function is shown in the graph below.
Hence we can conclude that the solution for the logarithmic function is x = 4.
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Evaluate this exponential expression. 9/2 4/3 81/16
Answer:
81/16
Step-by-step explanation:
The simplification of the provided exponential expression is 81/16 option (C) 81/16 is correct.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
The complete question is:
Evaluate this exponential expression:
[tex]\dfrac{27}{8}^ {\dfrac{4}{3}}[/tex]
A. 9/2 B. 4/3 C. 81/16We have an exponential expression:
[tex]= \dfrac{27}{8}^ {\dfrac{4}{3}}[/tex]
[tex]\rm =\dfrac{27^{\dfrac{4}{3}}}{8^{\dfrac{4}{3}}}[/tex]
[tex]=\dfrac{81}{8^{\dfrac{4}{3}}}[/tex]
= 81/16
Thus, the simplification of the provided exponential expression is 81/16 option (C) 81/16 is correct.
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Please help me find the Area
Answer:
8 x 17 x 15 = 2040 that's your area
Step-by-step explanation:
good day and be safe
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⊕ΘΞΠΤ⊕
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Answer:
60 units squared
Step-by-step explanation:
The formula for the area of the triangle is: [tex]\frac{base*height}{2}[/tex]
To work this out you would first have to multiply 8 by 15, which gives 120. Then you would divide 120 by 2, Which gives you 60. This is because the formula is the same for the area of a square however the triangle is half of a square that has the same dimensions.
1) Multiply 8 by 15.
[tex]8*15=120[/tex]
2) Divide 120 by 2.
[tex]120/2=60^{2}[/tex]
Define interest rate
Answer:
In my own words interest rate is the proportion of a loan that is charged as interest to the borower, typically expressed as an annual percentage of the loan outstanding. :D Hope this help and do you like brownies
Step-by-step explanation:
Final answer:
The interest rate is the cost of borrowing money or the return on investment deposited in financial institutions. It's influenced by financial regulations like usury laws, which cap the maximum interest rate to prevent excessive charges.
Explanation:
The interest rate is often referred to as the "price" of borrowing money in the financial market, and it's also the rate of return on an investment. When you deposit money into a savings account at a bank, the bank will pay you interest, which is a percentage of your deposits. This is the interest rate. Conversely, when you take out a loan, you will pay interest to the lender, which is the cost of borrowing the funds you need to purchase something, like a car or a computer.
There are also regulations like usury laws that set maximum limits on the interest rates that can be charged, ensuring that lenders do not exceed legal thresholds. The concept is similar to the idea of minimum wage, which sets a 'price floor' for hourly wages, below which it is illegal for employers to pay employees.
Jordan has $5.37, which he is using to buy ingredients to make salsa. He is buying one red pepper for $1.29 and
three pounds of tomatoes. If Jordan has exactly the right amount of money he needs, what is the price per pound of
the tomatoes?
Choose the correct equation to represent this real-world problem.
Solve the equation and verify the reasonableness of your answer.
A pound of tomatoes costs
Answer:
The price of tomato per pound is $1.36
Step-by-step explanation:
Jordan has $5.37.
He is buying one red pepper for $1.29
He is also buying three pounds of tomatoes.
If he has exactly the right amount of money he needs, then
5.37 = 1.29 + 3x
Where x is the price of tomato per pound
And( 5.37 = 1.29 + 3x) is the equation to solve for x
5.37 = 1.29 + 3x
5.37-1.29 = 3x
4.08 = 3x
4.08/3 = x
1.36 = x
The price of tomato per pound is $1.36
To verify it again..
3*1.36 + 1.29
= 4.08 +1.29
= 5.37 ( which is the initial total amount)
Answer:
Jordan has $5.37, which he is using to buy ingredients to make salsa. He is buying one red pepper for $1.29 and three pounds of tomatoes. If Jordan has exactly the right amount of money he needs, what is the price per pound of the tomatoes?
Choose the correct equation to represent this real-world problem.
✔ 5.37 = 3x + 1.29
Solve the equation and verify the reasonableness of your answer.
A pound of tomatoes costs
✔ $1.36
.
Step-by-step explanation:
The mean number of sick days per employee taken last year by all employees of a large city was 10.6 days. A city administrator is investigating whether the mean number of sick days this year is different from the mean number of sick days last year. The administrator takes a random sample of 40 employees and finds the mean of the sample to be 12.9. A hypothesis test will be conducted as part of the investigation. Which of the following is the correct set of hypotheses?
H0:μ=10.6Ha:μ>10.6 A
H0:μ=10.6Ha:μ≠10.6 B
H0:μ=10.6Ha:μ<10.6 C
H0:μ=12.9Ha:μ≠12.9 D
H0:μ=12.9Ha:μ<12.9 E
Answer:
For this case we are trying to proof if the mean number of sick days this year is different from the mean number of sick days last year (10.6 days). And that would represent the alternative hypothesis. And the complement would represent the null hypothesis.
Then the system of hypothesis are:
Null hypothesis: [tex]\mu =10.6[/tex]
Alternative hypothesis: [tex]\mu \neq 10.6[/tex]
And the best option would be:
H0:μ=10.6Ha:μ≠10.6 B
Step-by-step explanation:
For this case we are trying to proof if the mean number of sick days this year is different from the mean number of sick days last year (10.6 days). And that would represent the alternative hypothesis. And the complement would represent the null hypothesis.
Then the system of hypothesis are:
Null hypothesis: [tex]\mu =10.6[/tex]
Alternative hypothesis: [tex]\mu \neq 10.6[/tex]
And the best option would be:
H0:μ=10.6Ha:μ≠10.6 B
And the data from the sample is:
[tex]\bar X = 12.9[/tex] represent the sample mean
[tex]n =40[/tex] the sample size
A rabbit eats turnips and radishes. The number of turnips is four more then twice the number of radishes. Let n represent the number of radishes. Write the expression that gives the number of turnips
Answer:
2n+4
Step-by-step explanation:
To represent the number of turnips based on the number of radishes (n), the correct expression is 2n + 4, which means twice the number of radishes plus four.
Explanation:The student is asking to write an expression for the number of turnips a rabbit eats, given that the number of turnips is four more than twice the number of radishes. If n represents the number of radishes, the expression for the number of turnips is 2n + 4.
Here's the step-by-step explanation:
Let n be the number of radishes.
According to the question, the number of turnips is twice the number of radishes, plus four. This is written mathematically as 2n (twice the number of radishes) plus 4 (four more).
So, the expression for computing the number of turnips is 2n + 4.
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Martha, A statistician wishes to analyze teachers’ salaries in the state of California. She determines that teacher’s salaries in California are normally distributed with a mean salary of $37,764 and a standard deviation of $5,100. Answer the following questions. a) What is the probability that a randomly selected teacher’s salary in California is greater than $45,000?
Answer:
0.078 or 7.8%
Step-by-step explanation:
Mean salary (μ) = $37,764
Standard deviation (σ) = $5,100
The z-score for any given teacher's salary in California, X, is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = $45,000:
[tex]z=\frac{45,000-37,764}{5,100}\\ z=1.419[/tex]
A z-score of 1.419 corresponds to the 92.20th percentile of a normal distribution. Therefore, the probability that a salary is greater than $45,000 is:
[tex]P(X>\$45,000) = 1-0.9220\\P(X>\$45,000) = 0.078=7.8\%[/tex]
The probability is 0.078 or 7.8%.
To find the probability of a teacher's salary being more than $45,000 in California, calculate the Z-score using the formula given and find the corresponding probability. This calculation reveals there's a 7.78% chance of a randomly selected teacher's salary exceeding $45,000.
Explanation:To find the probability that a randomly selected teacher’s salary in California is greater than $45,000 when the salaries are normally distributed with a mean of $37,764 and a standard deviation of $5,100, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. In this case, X = $45,000, μ = $37,764, and σ = $5,100.
Calculating the Z-score gives us: Z = ($45,000 - $37,764) / $5,100 ≈ 1.42. Using the Z-table or a calculator with normal distribution functions, we find that the area to the right of Z = 1.42 corresponds to the probability we are looking for.
This area represents the probability that a teacher’s salary is greater than $45,000. Since we know the total area under the normal curve equals 1 (or 100%), the area to the right of Z = 1.42 is approximately 0.0778, which means there is a 7.78% chance that a randomly selected teacher’s salary in California is greater than $45,000.
What is the solution of the equation s=-4s+30
Answer:
6
Step-by-step explanation:
What is another word of magnitude
Answer:
largeness
Step-by-step explanation:
look up in dictionary
Please help me with this.
Answer:
3.5, three-and-a-half, 7/2
A restaurant offers three courses, appetizers, main dishes and desserts. It has 6 choices of appetizers, 10 choices of main dishes and 8 choices of desserts. How many different meals are there if a customer can order only one dish from each course and can have a meal consisting of one course only, two different courses or a meal with all three courses.
Answer:
692 different meals are possible.
Step-by-step explanation:
- There are 3 courses, appetizers, main dishes and desserts.
- There are 6 choices of appetizers, 10 choices of main dishes and 8 choices of desserts.
- A customer can order only one dish from each course and can have a meal consisting of one course only, two different courses or a meal with all three courses.
To find the number of different meals possible, we take the choice of number of courses one by one.
- If a customer decides to take a meal with only one course.
The customer can take only 1 choice out of 6 choices of appetizers or 1 choice out of 10 choices of main dishes or 1 choice out of 8 choices of desserts.
6C1 + 10C1 + 8C1 = 6 + 10 + 8
= 24 different meals
- If a customer decides on a two course meal
The customer can combine a choice of appetizer with a choice of main dish or a choice of appetizer with desert or a choice of main dish with dessert with order unimportant.
(6C1 × 10C1) + (6C1 × 8C1) + (10C1 × 8C1)
= (6 × 10) + (6 × 8) + (10 × 8)
= 60 + 48 + 80
= 188 different meals
- If a customer decides to take a combination of all the 3 courses.
This means a combination of a choice from each of the courses for the 3 courses.
6C1 × 8C1 × 10C1
= 6 × 8 × 10
= 480 different meals.
Total number of different meals possible
= 24 + 188 + 480
= 692 different meals.
Hope this Helps!!!
Answer:
692
Step-by-step explanation:
Which of the following figures does not have a line of symmetry?
Answer:
b
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
C cannot be folded upon any axis and lay upon itself.
A coin is tossed 18 times. It lands on heads 12 times. What is the experimental probability
of the coin landing on tails? reduce the fraction!
1/2
2/3
1/3
Answer:
The experimental probability of the coin landing on tails is 1/3
Step-by-step explanation:
Total no. of times coin tossed = 18
No. of times lands on head = 12
No. of times lands on tail = 18-12
No. of times lands on tail = 6
We are supposed to find the experimental probability of the coin landing on tails
So, the experimental probability of the coin landing on tails =[tex]\frac{\text{favorable outcome}}{\text{Total outcome}}[/tex]
So, the experimental probability of the coin landing on tails =[tex]\frac{6}{18}[/tex]
So, the experimental probability of the coin landing on tails =[tex]\frac{1}{3}[/tex]
Hence the experimental probability of the coin landing on tails is 1/3
Garrett works for a company that builds parking lots the graph shows the area of a parking lot based on the length of one side.
which equation best models the graph
A. A= -0.5x^2 -69.9x + 3,263
B. A= x^2 -69.9x + 3,263
C. A= x^2 -78x + 2,258
D. A= 0.5x^2 -69.9x + 3,263
Answer: Option D.
Step-by-step explanation:
this is a quadratic equation of the form:
y = ax^2 + bx + c
First, things you must see.
The graph opens up, so we must have thata a is greater than zero, so we can discard the first option.
Second, we can see that the vertex is located in x ≈ 70
The vertex of a quadratic equation is: x = -b/2a
so we have:
70 = -b/2a
let's try our options and see if we can discard other:
B:
-b/2a = 69.9/2 = 34.95
we can discard this option.
C:
-b/2a = 78/2 = 39 we can discard this option.
D:
-b/2a = 69.9/2*0.5 = 69.9
This is the only one that fits, so this is the correct option.
Answer:
Its D!!
Step-by-step explanation:
(-8) . (-8) . (-8) . (-8) . (-8) . (-8) . (-8)
Answer:
-2097152
Step-by-step explanation:
(-8)(-8)(-8)(-8)(-8)(-8)(-8) =
-2097152
Answer: -2097152
Step-by-step explanation:
(-8)(-8)(-8)(-8)(-8)(-8)(-8)=
(-8)^7
=-2097152
There are 50 students in a calculus class. The amount of time needed for the instructor to grade a randomly chosen midterm exam paper is a random variable with a mean of 6 minutes and a standard deviation of 4 minutes. If grading times are independent, what is the probability that the instructor can finish grading in 4 and a half hours (round off to second decimal place)
Answer:
14.46% probability that the instructor can finish grading in 4 and a half hours
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For sums of n values from a distribution, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sqrt{n}\sigma[/tex]
In this problem, we have that:
[tex]\mu = 6*50 = 300, s = \sqrt{50}*4 = 28.2843[/tex]
What is the probability that the instructor can finish grading in 4 and a half hours
Four and half hours is 4.5*60 = 270.
So this probability is the pvalue of Z when X = 270.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{270 - 300}{28.2843}[/tex]
[tex]Z = -1.06[/tex]
[tex]Z = -1.06[/tex] has a pvalue of 0.1446
14.46% probability that the instructor can finish grading in 4 and a half hours