The maximum number of elements in $s$ is $\boxed{7}$, which we can achieve by choosing one element from each of the residue classes modulo $7$.
To find the maximum number of elements in $s$, we need to consider the elements of $\{1,2,3,...,50\}$ that are congruent to each residue class modulo $7$. There are seven residue classes modulo $7$, namely $\{0,1,2,3,4,5,6\}$. Since the sum of two elements from the same residue class modulo $7$ will also be in the same residue class modulo $7$, we cannot include more than one element from each residue class in $s$.
We can include one element from the residue class $0$, which gives us one element. For the other six residue classes, we can choose at most one element from each of them without violating the condition that no pair of distinct elements in $s$ has a sum divisible by $7$. This gives us a total of $1+6=7$ elements in $s$.
Therefore, the maximum number of elements in $s$ is $\boxed{7}$, which we can achieve by choosing one element from each of the residue classes modulo $7$.
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Compute the zeroes of the polynomial 4x2 – 4x – 8. Also, establish a
relationship between the zeroes and coefficients.
The zero's of the polynomial 4x² - 4x - 8 are as follows:
x = 2 or x = -1
How to find zeros of a polynomial?Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole. In other words, the zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.
Therefore, let's find the zero's of the polynomial.
4x² - 4x - 8 = 0
divide through by 4
x² - x - 2 = 0
x² + x - 2x - 2 = 0
x(x + 1) -2(x + 1) = 0
(x - 2)(x + 1) = 0
Therefore,
x = 2 or x = -1
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The zeros of polynomial 4x² - 4x - 8, are 2 and -1. The relationship between the zeros and coefficients are 1 and -2.
Let the given polynomial be p(x) = 4x² - 4x - 8
To find zeros, take p(x) = 0
Factorizing the equation,
4x² - 4x - 8 = 0
4(x² - x - 4) = 0
x² - 2x + x- 2 = 0
x(x-2) + 1(x-2) = 0
(x-2) (x+1) = 0
∴ x=2 and x=-1
The roots of 4x² - 4x- 8 are 2 and -1
Relationship between the sum of zeros and coefficients:
-Coefficient of x/ coefficient of x²
(-1) + 2 = -(-4)/4 = 1
Relation between the product of zeros and coefficients:
Constant/ coefficient of x²
(-1) × 2 = -8/4 = -2
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The exchange rates between pounds, Singapore dollars and Hong Kong dollars are shown below. 1 Singapore dollar = £0.58 £1 = 10.50 Hong Kong dollars Tsion bought a watch in Singapore for 72 Singapore dollars. Ibrahim bought the same model of watch in Hong Kong for 399 Hong Kong dollars. What is the difference between the amounts that Tsion and Ibrahim paid for their watches? Give your answer in pounds.
The Difference in the amounts that Tsion and Ibrahim paid for their watches is £3.85.
To find the difference in the amounts that Tsion and Ibrahim paid for their watches, we need to convert the prices to the same currency. We can use the exchange rates given to convert both prices to pounds.
1 Singapore dollar = £0.58
72 Singapore dollars = 72 x £0.58 = £41.76
1 Hong Kong dollar = £0.09
399 Hong Kong dollars = 399 x £0.095 = £37.91
Therefore, Tsion paid £41.76 for the watch and Ibrahim paid £37.91 for the same model of watch.
To find the difference in the amounts paid, we can subtract the smaller amount from the larger amount:
£41.76 - £37.91 = £3.85
Therefore, the difference in the amounts that Tsion and Ibrahim paid for their watches is £3.85.
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PLEASE ANSWER THIS QUICKLY RIGHT ANSWERS ONLY 50 POINTS!!!
Determine this period
Answer:a
Step-by-step explanation:s
Lesson 118 5. The first roll knocked down 3 of the 10 bowling pins. (107) What percent of the pins were still standing?
Answer: 70%
Step-by-step explanation:
obviously 7/10 gives you 70%
Answer:
70%
Step-by-step explanation:
If 3 of the pins were knocked down, that means 7 pins were still standing.
Next, to find what percent 7 is of 10, divide 10 by 100 to get 0.1.
0.1 is 1% of 10, so we need to divide 7 by 0.1 to find the percentage, which is 70.
Halp me this the question
Answer:
Step-by-step explanation:
if 32 was originally there now some left and 21 are left we can pit it into a subtraction equation.
32-?=21
we can also make an addition equation
21+?=32
we know that ?= 11 because of commen scene.
Answer: 32-(__)=21
Step-by-step explanation:
I like to think of what I'm given to be the left side, and what's after to be the right side. If there are 32 originally, then you take some away (since 21 is fewer than 32), that's subtracting by some number. Then, we have 21 left so put 21 on the right side. To solve, subtract the 21 from the 32 and add the unknown over to get (__)=9
The one-to-one functions g and h are defined as follows.
g={(-8, -3), (-3, 2), (3, 0), (5, 6)}
h(x) = -2x+13
Find the following.
g^-1(-3)
h^-1(x)=
(h^-1•h)(3)
By finding the inverses we can see that:
g⁻¹(-3) = -8h⁻¹(x) = (x - 13)/-2(h⁻¹*h)(3) = 35How to find the inverses?Two functions g(x) and g⁻¹(x) are inverses if:
g⁻¹(g(x)) = x
Here we know that the function g is defined by:
g={(-8, -3), (-3, 2), (3, 0), (5, 6)}
And we want to find:
g⁻¹(-3)
On the table we can see that g(-8) = -3, then:
g⁻¹(-3) = -8
And we have:
h(x) = -2x + 13
Evaluating on the inverse we should get:
h(h⁻¹(x)) = x
= -2*h⁻¹(x) + 13 = x
Solving for the inverse:
h⁻¹(x) = (x - 13)/-2
Now we can get the product:
(h⁻¹*h)(3) = (-2*3 + 13)(3 - 13)/-2
= 7*5 = 35
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What do tips and markups have in common?
Suppose you are conducting a study of reaction times for a group of 10 depressed individuals and 10 non-depressed individuals. You want to compare mean reaction times but in order to use a pooled t test you need to make sure the variances for the two groups are not significantly different. Let var1=8 and var2=25. Are the variances similar enough so you can use the pooled t test to evaluate differences in the means?
Yes or no?
No, the variances are not similar enough to use the pooled t test. The ratio of the two variances (25/8) is greater than 3, which is the typical cutoff for determining similarity of variances. Therefore, an alternative method such as the Welch's t-test or a non-parametric test should be used to compare the means.
To determine if the variances are similar enough to use a pooled t-test, you can perform an F-test for equality of variances. Follow these steps:
1. Calculate the F statistic by dividing the larger variance by the smaller variance: F = var2 / var1 = 25 / 8 = 3.125.
2. Determine the degrees of freedom for each group: df1 = 10 - 1 = 9 and df2 = 10 - 1 = 9.
3. Check the F critical value for the given degrees of freedom and chosen significance level (e.g., 0.05) using an F-distribution table or a calculator. For df1 = 9 and df2 = 9 at a 0.05 significance level, the F critical value is approximately 3.18.
4. Compare the calculated F statistic to the F critical value: 3.125 < 3.18.
Since the F statistic is less than the F critical value, we fail to reject the null hypothesis that the variances are equal. Therefore, the variances are similar enough to use the pooled t-test to evaluate differences in the means. The answer is yes.
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i need the full breakdown
Step-by-step explanation:
The triangles are similar. Writing a proportion:
(3x − 5 + 10) / 28 = (3x − 5) / 20
Cross multiply:
20 (3x − 5 + 10) = 28 (3x − 5)
Simplify and solve:
20 (3x + 5) = 28 (3x − 5)
5 (3x + 5) = 7 (3x − 5)
15x + 25 = 21x − 35
60 = 6x
x = 10
The symbol x¯ represents the population mean of all possible sample means of size n.
False
True
False. The symbol x¯ represents the population mean of all possible sample means of size n.
The symbol x¯ (x-bar) represents the sample mean, not the population mean of all possible sample means of size n. The population mean of all possible sample means of size n is denoted by μ (mu). The sample mean, x¯, is calculated by taking the average of the observations in a specific sample.
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in a sequence, each term after the second is the sum of the two preceding terms. the first and fifth terms are each 3. what is the second term in the sequence?
The second term in the sequence is 0.
To solve the problem, we can use the fact that each term after the second is the sum of the two preceding terms. Let's call the first term a and the second term b. Then, according to the problem, we have:
a = 3 (the first term is 3)
b = ?
c = a + b = 3 + b
d = b + c = b + (3 + b) = 2b + 3
e = c + d = (3 + b) + (2b + 3) = 3b + 6
We also know that the fifth term is 3, so we can set e equal to 3 and solve for b:
3b + 6 = 3
3b = -3
b = -1
Therefore, the second term in the sequence is 0, since each term after the second is the sum of the two preceding terms and the first term is 3.
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pollster wishes to estimate the true proportion of u.s. voters who oppose capitalpunishment. how many voters should be surveyed in order to be 95% confident thatthe true proportion is estimated to within 2%?
The pollster should survey approximately 2,401 U.S. voters to estimate the true proportion of voters who oppose capital punishment with 95% confidence and a margin of error of 2%.
In order to estimate the true proportion of U.S. voters who oppose capital punishment with a 95% confidence level and a margin of error of 2%, the pollster should survey approximately 2,401 voters.
To calculate the sample size needed for this estimation, we can use the formula:
n = (Z² * p * q) / E²
where n is the sample size, Z is the z-score corresponding to the confidence level (in this case, 1.96 for 95% confidence), p is the estimated proportion of voters who oppose capital punishment, q is the estimated proportion of voters who support capital punishment (which is 1-p), and E is the desired margin of error (in this case, 0.02).
Assuming a conservative estimate of p = q = 0.5, we can plug in the values and solve for n:
n = (1.96² * 0.5 * 0.5) / 0.02² ≈ 2,401
Therefore, the pollster should survey approximately 2,401 U.S. voters to estimate the true proportion of voters who oppose capital punishment with 95% confidence and a margin of error of 2%.
In conclusion, to estimate the true proportion of U.S. voters who oppose capital punishment with a 95% confidence level and a margin of error of 2%, the pollster should survey approximately 2,401 voters. This sample size calculation is based on the formula for calculating sample size using the z-score, estimated proportions, and desired margin of error
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5. Which of the following statements is FALSE about the function f(x) = cos x? Explain your reasoning.
A) f(x) = f(-x)
B) f(x) has a y-intercept of 1.
C) The x-axis represents the cosine ratio.
D) f(146π) = 1
Trig please I’ll kiss you on the lips if you can help me out
Answer:
Step-by-step explanation:
The tables represent hat sizes measured in inches for two baseball teams. Cougars 21.5 24.5 22 21 22 23 22.5 24 21 22 23.5 22 23.5 22 24 Panthers 22.5 20 23.5 21 24 22 20.5 21.5 23 23 22.5 21 24 22 24.5 Which team has the largest overall size hat for their players? Determine the best measure of center to compare and explain your answer.
The Panthers have the largest overall size hat for their players based on the mean calculation. The mean is the best measure of center to compare the two teams because it takes into account all the data and provides a representative value of the central tendency.
To determine which team has the largest overall size hat for their players, we need to find the team with the highest average hat size. The best measure of center to compare the two teams would be the mean, as it provides a representative value of the central tendency of the data.
To calculate the mean for each team, we need to add up all the hat sizes and divide by the number of players on the team. For the Cougars, the sum of the hat sizes is 308.5 and there are 14 players, so the mean hat size is 22.04 inches. For the Panthers, the sum of the hat sizes is 333 and there are also 14 players, so the mean hat size is 23.79 inches.
Based on these calculations, we can see that the Panthers have the largest overall size hat for their players, with an average hat size of 23.79 inches compared to the Cougars' average hat size of 22.04 inches.
In conclusion, the Panthers have the largest overall size hat for their players based on the mean calculation. The mean is the best measure of center to compare the two teams because it takes into account all the data and provides a representative value of the central tendency.
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The terminal ray of an angle passes through the point
[tex](\stackrel{\stackrel{ adjacent }{x}}{-3}~~,~~\stackrel{\stackrel{ opposite }{y}}{-\sqrt{7}})\hspace{5em}\textit{let's find the \underline{hypotenuse}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{-3}\\ o=\stackrel{opposite}{-\sqrt{7}} \end{cases}[/tex]
[tex]c=\sqrt{ (-3)^2 + (-\sqrt{7})^2}\implies c=\sqrt{ 9 + 7 } \implies c=\sqrt{ 16 }\implies c=4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cos(\theta )=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{4}}~\hfill[/tex]
Alice Fox and Basil Cat are searching for treasure. They start at the old oak tree in the Field of Wonders and walk 240 m, each counting their own steps. Basil Cat takes 100 fewer steps than Alice Fox. Find the length of Alice’s step and the length of Basil’s step if Basil’s step is 20 cm longer than Alice’s step.
The length of Alice’s step is 0.6 m.
The length of Basil’s step is 0.8 m.
What is the length of Alice’s step?Let's A to represent the length of Alice's step in meters.Since Basil takes 100 fewer steps than Alice to walk 240 m;
the number of steps Basil takes = (240/A) - 100.
Let's B to represent the length of Basil's step in meters.Basil's step is 20 cm longer than Alice's step;
B = A + 0.2
The distance each person walks is calculated as;
A(240/A) = (A + 0.2) [(240/A) - 100]
240 = 240 - 100A + 48/A - 20
0 = - 100A + 48/A - 20
100A - 48/A = -20
100A² - 48 = -20A
100A² + 20A - 48 = 0
Solve for A using formula method;
A = 0.6 m
Basil's step length:
B = 0.6 + 0.2
B = 0.8 m
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Find the coordinates of point P that represents the weighted average of the set of points if point A weighs 3 times as much as point C
A is -5
C is 7
The coordinates of point P that represents the weighted average of the set of points are (-8/5, y).
Given that point A weighs 3 times as much as point C. This implies that the weight of point C is 1, and the weight of point A is 3.
To find the weighted average of the points, we can use the formula:
[tex]P = \dfrac{(w_1 \times A + w_2 \times B + w_3 \times C)}{(w_1 + w_2 + w_3)}[/tex]
where P is the weighted average point, w₁, w₂, and w₃ are the weights of points A, B, and C, respectively, and A, B, and C are the coordinates of the points.
Substituting the given values, we have:
P = (3 × (-5) + 0 + 1 × 7) / (3 + 1 + 1)
P = (-15 + 7) / 5
P = -8/5
Therefore, the coordinates of point P that represents the weighted average of the set of points are (-8/5, y).
The y-coordinate cannot be determined without additional information.
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please answer completely with work
The dimensions of the deck are 26 meters by 16 meters and 84 meters of fencing will need to be purchased for the deck and pool area.
Let's denote the width of the deck as 'x'.
The length of the pool is 20 meters, and the width is 10 meters.
The combined area of the pool and the deck is 264 square meters.
The area of the pool is length times width: 20 × 10 = 200 square meters.
The area of the deck is (20 + 2x)(10 + 2x) - 200 square meters. We subtract 200 square meters to account for the area of the pool.
Therefore, the polynomial equation representing the given information is:
(20 + 2x)(10 + 2x) - 200 = 264
(200 + 40x + 20x + 4x^2) - 200 = 264
4x²+ 60x = 264
4x² + 60x - 264 = 0
Factoring out a common factor of 4:
4(x² + 15x - 66) = 0
Factoring the quadratic equation:
(x + 18)(x - 3) = 0
The width of the deck is x = 3 meters.
The dimensions of the deck can be found by adding twice the width to the length and width of the pool:
Length of the deck = 20 + 2x = 20 + 2(3) = 26 meters
Width of the deck = 10 + 2x = 10 + 2(3) = 16 meters
Therefore, the dimensions of the deck are 26 meters by 16 meters.
To calculate the length of fencing required, we need to consider the perimeter of the deck.
Perimeter of the deck = 2×(Length of the deck + Width of the deck)
Perimeter of the deck = 2 × (26 + 16)
Perimeter of the deck = 2 × 42
Perimeter of the deck = 84 meters
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find the area of the surface. the part of the plane 2x + 5y + z = 10 that lies in the first octant
The area of the part of the plane 2x + 5y + z = 10 that lies in the first octant is 8√6/5 square units.
The first octant is the region of space where x, y and z are all positive. We need to find the area of the surface of the part of the plane 2x + 5y + z = 10 that lies in the first octant.
To find the surface area, we need to first parameterize the surface. We can do this by fixing one variable and expressing the other two in terms of it. Let's fix x:
2x + 5y + z = 10
Solving for z, we get:
z = 10 - 2x - 5y
Now, we can express y in terms of a parameter t:
y = t
And we can express z in terms of x and t:
z = 10 - 2x - 5t
So the parameterization of the surface is:
r(x, t) = (x, t, 10 - 2x - 5t)
To find the surface area, we need to compute the magnitude of the cross product of the partial derivatives of r with respect to x and t:
|∂r/∂x x ∂r/∂t| = |<1, 0, -2>| x |<0, 1, -5>| = |<2, 1, 1>|
= √(2^2 + 1^2 + 1^2) = √6
So the surface area is:
∫∫ √6 dA
where the double integral is over the region in the first octant where 2x + 5y + z = 10. We can express this region as:
0 ≤ x ≤ 5
0 ≤ y ≤ (10 - 2x)/5
0 ≤ z ≤ 10 - 2x - 5y
So the integral becomes:
∫₀^₅ ∫₀^(10-2x)/5 √6 dz dy dx
Evaluating this integral, we get:
∫₀^₅ ∫₀^(10-2x)/5 √6 dz dy dx = √6 ∫₀^₅ ∫₀^(10-2x)/5 dz dy dx
= √6 ∫₀^₅ (10-2x)/5 dy dx
= √6 ∫₀^₅ 2 - (2/5)x dx
= √6 [2x - (1/5)x²] from 0 to 5
= √6 [10 - (1/5)(25)]
= √6 (8/5)
= 8√6/5
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Write the numbers 50 to 75 on
a sheet of paper.
How many of these numbers
are divisible by 9?
Answer: 54, 63, 72
Step-by-step explanation: Well let's multiply 9 till 75 so 9(1), 18(2), 27(3), 36(4), 45(5), 54(6), 63(7), 72(8). The underlined numbers are ones that are divisible by 3. Hope this helps! :)
The Doppler formula for the frequency detected can be written f = f’ (v - vD) / (v - vS), where f’ is the frequency emitted, v is the speed of sound, vD and vs are suitable components of the detector and source velocities. (vD and vs can be of either sign depending on the direction of the motion relative to the S-D axis.) Suppose the source is traveling at 5 m/s away from the detector, the detector is traveling at 7 m/s toward the source, and there is a 3 m/s wind blowing from the source toward the detector. The values that should be substituted into the Doppler shift equation are (in m/s):
a. vD = 10 vs = 2 b. vD = -7 vs = -5 c. vD = -7 vs = 5 d. vD = 4 vs = 2 e. vD = -10 vs = -8
Answer:
he correct answer is c. vD = -7 vs = 5.
The Doppler shift equation is:
f = f' (v - vD) / (v - vS)
Where:
f is the frequency detected
f' is the frequency emitted
v is the speed of sound
vD is the velocity of the detector
vs is the velocity of the source
In this case, the source is traveling at 5 m/s away from the detector, the detector is traveling at 7 m/s toward the source, and there is a 3 m/s wind blowing from the source toward the detector.
The velocity of the detector is negative because it is moving towards the source. The velocity of the source is positive because it is moving away from the detector.
Therefore, the values that should be substituted into the Doppler shift equation are:
vD = -7
vs = 5
Step-by-step explanation:
according to census 2000, how did the overall american indian and alaska native population compare to the national median age?
According to the Census 2000, the overall American Indian and Alaska Native population had a younger median age compared to the national median age. The national median age in 2000 was 35.3 years, whereas the median age for the American Indian and Alaska Native population was 26.3 years.
This can be attributed to several factors, including higher fertility rates and lower life expectancies in some American Indian and Alaska Native communities. Additionally, many Native American tribes have a strong cultural emphasis on family and community, which can contribute to larger family sizes and a younger overall population. It is important to note that these demographic trends may have shifted in the years since the Census 2000, and that there is significant diversity within the American Indian and Alaska Native population in terms of age, geography, and culture.
it is clear that the American Indian and Alaska Native population had a younger median age in 2000 compared to the national median age.
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The price of two tickets and one coke is $11.00 The price of three tickets and two cokes is $17.00. How much is one ticket?
Answer:5$
Step-by-step explanation:
The unit rate of change of y with respect to x is the amount y changes for a change of one unit in x. Is the unit rate of change of y with respect to x greater in the equation y =0.32 or in the graph below?
answers:
a. the equation
b. the graph
c. the unit rates are the sam
Note that the unit rate of change of the equation is 0.32, and the one of the graph is 1, so the correct option is B.
Which one has a greater unit rate of change?We define the unit rate of change as the slope or constant of proportionality.
y = 0.32 * x
The unit rate of change is 0.32
In the graph we can see that for each unit moved in horizontally, the line moves one unit vertically, then the unit rate of change is just 1.
y = x
Then we can conclude that the graph has the greater unit rate of change.
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what does ctrl or command z stand for
Answer: It means Undo
Step-by-step explanation:
or harper divides a package of 12 baby carrots evenly among her 3 pet hamsters, harvey, hammy, and flo. flo eats 2 baby carrots right away. how many baby carrots does flo have left?
If Harper divides 12 baby carrots evenly among her 3 pet hamsters, Harvey, Hammy, and Flo, then each hamster would get 4 baby carrots. However, since Flo ate 2 baby carrots right away, she would only have 2 baby carrots left.
When Harper divides a package of 12 baby carrots among her 3 pet hamsters, each hamster gets 4 baby carrots. But since Flo eats 2 baby carrots right away, she is left with only 2 baby carrots. This means that Harvey and Hammy also have 4 baby carrots each, as they did not eat any carrots. It's important to divide food equally among pets, as it ensures that every pet gets an equal share of nutrients.
In conclusion, Harper divided 12 baby carrots among her 3 pet hamsters equally, but Flo ate 2 baby carrots right away. Therefore, Flo was left with only 2 baby carrots, while Harvey and Hammy had 4 baby carrots each. Dividing food equally among pets is important to ensure that every pet gets a fair share of nutrients.
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Suppose Aaron is going to build a playlist that contains 13 songs. In how many ways can Aaron arrange the 13 songs on the​ playlist?
There are 6,227,020,800 ways in which Aaron can arrange the 13 songs on the playlist.
To determine the number of ways Aaron can arrange the 13 songs on the playlist, we can use the concept of permutations. Since the order of the songs matters (i.e., each arrangement is different), we can use the formula for permutations.
The number of ways to arrange n items in a specific order is given by n factorial, denoted as n!. The factorial of a number n is the product of all positive integers less than or equal to n.
In this case, Aaron has 13 songs to arrange on the playlist, so the number of arrangements can be calculated as:
13! = 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Calculating this expression, we find:
13! = 6,227,020,800
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part c requires you to match 6 questions with 6 different answers. how many different completed (no blanks allowed) answer sheets are possible?
There are 720 different completed answer sheets possible, where no blanks are allowed.
In this problem, we have 6 questions and 6 different answers to match with each question. We need to determine how many different completed answer sheets are possible, where no blanks are allowed. To solve this, we'll use combinatorics and permutations.
To find the number of different completed answer sheets, we can consider each question as a distinct entity. Let's label the questions as Q1, Q2, Q3, Q4, Q5, and Q6. Similarly, let's label the answers as A1, A2, A3, A4, A5, and A6.
Since each question needs to be matched with a different answer, we can think of this as a one-to-one mapping between the questions and answers. In other words, we want to find the number of permutations of the answers that satisfy the matching condition.
The first question (Q1) can be matched with any of the 6 answers (A1, A2, A3, A4, A5, or A6). Once Q1 is matched, the second question (Q2) can be matched with any of the remaining 5 answers. Similarly, the third question (Q3) can be matched with any of the remaining 4 answers, and so on.
Using the fundamental principle of counting, we can multiply the number of choices available for each question.
The number of possible completed answer sheets is given by:
Number of completed answer sheets = 6 * 5 * 4 * 3 * 2 * 1 = 720.
So, there are 720 different completed answer sheets possible, where no blanks are allowed.
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1a. Write a polynomial that represents the length of the north side of the house
1b. Simplify the expression. Show all work.
2- 32. 2. Your cousin said the length of the north side of the house is 9y+2y"
a. Is he correct?
b. Explain in detail how you know if your cousin is correct or not correct?
Answer:
1a. Let’s assume that the length of the north side of the house is represented by ‘x’. Then the polynomial that represents the length of the north side of the house is x.
1b. There is no expression to simplify.
2a. Your cousin is not correct.
2b. The length of the north side of the house is represented by ‘x’ and not by ‘9y+2y’. Therefore, your cousin is not correct.
The polynomial stated by the cousin as the length of the north side of the house, 9y + 2y, simplifies to 11y. Thus, the cousin is not correct. Polynomials and simplifying expressions are part of basic algebra skills.
Explanation:Based on your cousin's statement, the polynomial representing the length of the north side of the house is 9y + 2y. To determine the correctness of this polynomial, we must first simplify the expression. By combining like terms (terms with the same variable and exponent), the expression simplifies to 11y. So, the length of the north side is represented by 11y, not 9y + 2y. Hence, your cousin's statement is not correct.
Understanding how to combine like terms, simplify expressions, and handle polynomials is an important part of basic algebra skills. Polynomials can be used to represent many real world quantities such as the length of a side of a house as in this problem. Remember that it is crucial to perform all calculations accurately to avoid errors.
Learn more about Simplifying Polynomialshttps://brainly.com/question/32120657
