Answer:
We are given:
[tex]SSx = 4[/tex]
[tex]SSy=25[/tex]
[tex]Sp=6[/tex]
We know that the Pearson's correlation coefficient is:
[tex]r=\frac{S_{p}}{\sqrt{SS_{x} \times SS_{y}} }[/tex]
[tex]=\frac{6}{\sqrt{4 \times 25} }[/tex]
[tex]=\frac{6}{\sqrt{100} }[/tex]
[tex]=\frac{6}{10}[/tex]
Therefore, the option 6/10 is correct
Which is closest to the value of x
Answer:
11
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that
... Cos = Adjacent/Hypotenuse
so you know ...
... cos(41°) = x / 14
Multiplying by 14 gives the value of x.
... x = 14·cos(41°) ≈ 10.566 ≈ 11
_____
Comment on answer choices
The visible answers are 10, 40, 12. The best choice of those is 10. If there is no choice offering 11 as the answer, then I'd choose 10.
Answer:
11
Step-by-step explanation:
Here we are given a right angled triangle with a known angle of 41°, length of the hypotenuse to be 14 and we are to find the length of the base x.
For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.
[tex]cos \alpha =\frac{base}{hypotenuse}[/tex]
So putting in the given values to get:
[tex]cos 41=\frac{x}{14} \\\\x= cos 41*14\\\\x=10.56[/tex]
Therefore, the value of x is the closest to 11.
Prove that u(n) is a group under the operation of multiplication modulo n.
Answer:
The answer is the proof so it is long.
The question doesn't define u(n), but it's not hard to guess.
Group G with operation ∘
For all a and b and c in G:
1) identity: e ∈ G, e∘a = a∘e = a,
2) inverse: a' ∈ G, a∘a' = a'∘a = e,
3) closed: a∘b ∈ G,
4) associative: (a∘b)∘c = a∘(b∘c),
5) (optional) commutative: a∘b = b∘a.
Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.
If n isn't prime, we exclude from the group all integers which share factors with n.
Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).
Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).
Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.
Associative and Commutative:
(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)
a∘b = b∘a because ab = ba.
Answer:
The answer is the proof so it is long.
The question doesn't define u(n), but it's not hard to guess.
Group G with operation ∘
For all a and b and c in G:
1) identity: e ∈ G, e∘a = a∘e = a,
2) inverse: a' ∈ G, a∘a' = a'∘a = e,
3) closed: a∘b ∈ G,
4) associative: (a∘b)∘c = a∘(b∘c),
5) (optional) commutative: a∘b = b∘a.
Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.
If n isn't prime, we exclude from the group all integers which share factors with n.
Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).
Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).
Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.
Associative and Commutative:
(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)
a∘b = b∘a because ab = ba.
At a basketball game, a vender sold a combined total of 165 sodas and hot dogs. The number of sodas sold was 39 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
102 sodas63 hot dogsStep-by-step explanation:
Let s and h represent the numbers of sodas and hotdogs sold, respectively. The problem statement tells you ...
... s + h = 165
... s - h = 39
Add these two equations to get ...
... 2s = 204
... s = 102 . . . . . divide by w
... h = 165 - 102 = 63 . . . . use the first equation to find h from s
The vendor sold 102 sodas and 63 hot dogs at the basketball game.
Write an equation that gives the proportional relationship of the graph.
A)
y = 1/6x
B)
y = 2x
C)
y = 6x
D)
y = 12x
C) y = 6x
Step-by-step explanation:Pick any point. It is often convenient to use x = 1 (no marked point) or x = 10 (where y = 60).
Use these values to see which equation agrees.
A: 60 ≠ (1/6)·10
B: 60 ≠ 2·20
C: 60 = 6·10
D: 60 ≠ 12·10
____
Or, you can solve ...
... y = kx
for k, using the point values you found on the graph.
... 60 = k·10
... 60/10 = k = 6 . . . . . divide by 10
This makes the equation be ...
... y = 6x . . . . . . matches selection C
find the area of a triangle with the given base and height
7ft, 2in
Answer:
A = 84 inches^2
Step-by-step explanation:
We know that the formula for the area of a triangle is given by
A = 1/2 b*h
Let's substitute what we know
We need the units to be the same
Convert 7 ft to inches
1 ft = 12 inches
Multiply both sides by 7
7 ft = 84 inches
A = 1/2 *84*2
A = 84 inches^2
Write a sentence to represent the equation 4 m = -8.
Answer:
The product of 4 and m is -8.
Without numbers: The product of four and the variable m is negative eight.
Step-by-step explanation:
4m means m is multiplied by 4. The result of the multiplication operation is called a "product." The equal sign translates to "is".
The sentence 'Four times a certain number equals negative eight' corresponds to the equation 4m = -8, indicating that multiplying a number by four yields negative eight.
The sentence to represent the equation 4 m = -8 might be: "Four times a certain number equals negative eight." This sentence encapsulates the equation by specifying that the product of the number m and four is equivalent to negative eight, implying that m will have a negative value since it is equal to a negative number when multiplied by a positive.
Can anyone help me with THIS and the other TWO‼️PLEASE I’m really need HELP
Answer:
y = 3x +2
Step-by-step explanation:
It is helpful to be acquainted with the parts of at least a couple of different forms of the equation for a line.
You are given the equation of a line in "slope-intercept" form. It looks like ...
... y = mx + b . . . . . . . where m=-1/3 and b=-1
The coefficient of x, which is m, is the slope of the line. That is -1/3 for the given line.
The relationship between the slopes of perpendicular lines is that they multiply to give -1. We say each is the opposite reciprocal of the other. If we let "m" stand for the slope of the perpendicular line, it satisfies the equation ...
...(m)(-1/3) = -1
... m = -1/(-1/3) = 3 . . . . . the slope of the perpendicular line is 3.
____
Here's where another form of the equation for a line is useful. We can write the "point-slope" form* as ...
... y = m(x -h) +k . . . . . . for a line of slope m through point (h, k)
We want our line of slope = 3 to go through the point (1, 5), so its equation can be ...
... y = 3(x -1) +5 . . . . . . . variation of "point-slope" form
The given equation is in slope-intercept form, and the question asks for "the" equation of the line, so we probably should write our answer in the same form as the given equation. We can do this by eliminating the parentheses and simplifying the equation we have.
... y = 3x -3 +5 . . . . eliminate parentheses using the distributive property
... y = 3x +2 . . . . . . collect terms
The graph shows our result is at least plausible: it looks like it is perpendicular, and it goes through the given point.
___
*Comment on point-slope form
Usually, you will see "point-slope" form written as ...
... y -k = m(x -h) . . . . . . . . standard version of "point-slope" form
When our intent is to use this form to get to slope-intercept form, it is more convenient to add k to this equation to get ...
... y = m(x -h) +k . . . . . . . occasionally useful version