Answer:
[tex]cos\alpha =\frac{7}{25}; \ tan\alpha =-\frac{7}{24}.[/tex]
Step-by-step explanation:
if π<α<2π and cotα<0, then 1.5π<α<2π. It means, that cosα>0 and tanα<0.
1) tanα=1/cotα; ⇒tanα= -7/24;
2) [tex]cos\alpha =\frac{1}{\sqrt{1+cot^2\alpha }}}; \ cos\alpha =\frac{7}{25}.[/tex]
The shaded area in the distribution below represents approximately 95% of the data. Use the diagram to find the mean and the standard deviation.
Answer:
mean = 85, standard deviation = 3.5
Step-by-step explanation:
The empirical rule states that for a normal distribution, 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviation of the mean and 99.7% falls within three standard deviation of the mean.
From the diagram since the shaded are is approximately 95% of the data. Hence 95% falls within two standard deviations of the mean.
σ = standard deviation, μ = mean
Hence; μ ± 2σ = (78, 92)
μ - 2σ = 78 (1);
μ + 2σ = 92 (2)
Adding equation 1 and 2, gives 2μ = 170
μ = 85
μ - 2σ = 78
85- 2σ = 78
2σ = 7
σ = 3.5
Problem 6
Let T, be the nth triangular number, Qn be the nth square number and
Pn be the nth pentagonal number.
(a) Show that 3Pn = T3n-1.
(b) Show that Pn - Qn = Tn-1 and hence that Pyn - 3Pn = Qan.
Answer:
The given symbol for the nth triangular number = Tₙ
The given symbol for the nth square number = Qₙ
The given symbol for the nth pentagonal number = Pₙ
The mathematical formula for the nth triangular number, Tₙ = n·(n + 1)/2
The nth square number is given by Qₙ = n²
The nth pentagonal number is given by Pₙ = n·(3·n - 1)/2
(a) T₃.ₙ₋₁ = (3·n - 1)·(3·n - 1 + 1)/2 = (3·n - 1)·(3·n)/2 = 3·(3·n - 1)·(n)/2 = 3·Pₙ
Therefore;
T₍₃.ₙ ₋ ₁₎ = 3·Pₙ
(b) Pₙ - Qₙ = n·(3·n - 1)/2 - n²
Expanding the above equation gives;
n·(3·n - 1)/2 - n² = (3·n² - n - 2·n²)/2 = (n² - n)/2 = n·(n - 1)/2
T₍ₙ ₋ ₁₎ = ((n - 1)· ((n - 1) + 1))/2 = ((n - 1)· n)/2 = n·(n - 1)/2
∴ Pₙ - Qₙ = n·(3·n - 1)/2 - n² = n·(n - 1)/2 = T₍ₙ ₋ ₁₎
∴ Pₙ - Qₙ = T₍ₙ ₋ ₁₎
Therefore, we get;
P₃.ₙ - Q₃.ₙ = T₍₃.ₙ ₋ ₁₎
Where, T₍₃.ₙ ₋ ₁₎ = 3·Pₙ from (a) above, gives;
P₃.ₙ - Q₃.ₙ = 3·Pₙ
∴ P₃.ₙ - 3·Pₙ = Q₃.ₙ
Plugging in the values, gives;
P₃.ₙ = (3·n)·(3·(3·n) - 1)/2 = (3·n)·((9·n) - 1)/2
3·Pₙ = 3·n·(3·n - 1)/2
P₃.ₙ - 3·Pₙ = (3·n)·((9·n) - 1)/2 - 3·n·(3·n - 1)/2 = (3·n)·(((9·n) - 1) - (3·n - 1))/2
(3·n)·(((9·n) - 1) - (3·n - 1))/2 = (3·n)·(9·n - 1 - 3·n + 1)/2 = (3·n)·(6·n )/2 = 9·n²
Q₃.ₙ = (3·n)² = 9·n²
∴ P₃.ₙ - 3·Pₙ = P₃.ₙ - 3·Pₙ
Step-by-step explanation:
5. Make a conjecture about the line that contains the diagonal from the tip of the vertex of the tail of a dart and the diagonal that joins the fin angles.
Answer:
A conjecture that can be made is that the line that contains the diagonal from the tip to the vertex of the tail of a dart and the diagonal that joins the fin angles are perpendicular to each other
Step-by-step explanation:
Question; Make a conjecture about the line that contains the diagonal from the tip to the vertex of the tail of a dart and the diagonal that joins the fin angles
Explanation;
We note that a diagonal is a straight line that joins one corner of a polygon with another corner of the polygon from the vertex points of the connected corners
The diagonal that joins the fin angles forms an isosceles triangle at the tail of the dart, and the locus of the line that forms the diagonal from the tip to the tail is a equidistant from the vertex of the fin angles
Therefore, the diagonal from the tip bisects the diagonal that joins the fin angles bisects the base of the formed isosceles triangle while passing through the vertex of the isosceles triangle, it is therefore, perpendicular to the base of the isosceles triangle which is the diagonal that joins the fin angles
A conjecture that can be made is that the line that contains the diagonal from the tip to the vertex of the tail of a dart and the diagonal that joins the fin angles is therefore, that they are perpendicular to each other
Find four fractions between 1/10 and 1/8
9514 1404 393
Answer:
5/48, 5/46, 5/44, 5/42
Step-by-step explanation:
We can choose unit fractions with denominators between 8 and 10, separated by (10-8)/5 = 0.4 units:
1/8.4 = 5/42
1/8.8 = 5/44
1/9.2 = 5/46
1/9.6 = 5/48
__
Check
1/8 = 0.1255/42 ≈ 0.1195/44 ≈ 0.1145/46 ≈ 0.1095/48 ≈ 0.1041/10 = 0.100_____
Additional comment
There are an infinite number of such fractions. We are given unit fractions with different denominators, so it works reasonably well to choose denominators between those given. Then the trick is to convert the fraction to a ratio of integers. In this case, multiplying by (5/5) does the trick.
__
Another approach is to write the fractions with a common denominator, then choose numerators between the ones given. For example, 1/10 = 4/40, and 1/8 = 5/40, so you could write some fractions with numerators between 4 and 5. Possibilities are 4.1/40 = 41/400, 4.3/40 = 43/400, 4.7/40 = 47/400, 4.9/40 = 49/400.
Anyone know the answer ?? Please, appreciate it
Answer:
D
Step-by-step explanation:
1. If the value of a number in decimal system is 955, find its value in quinary system and in binary system.
Answer:
Quinary - 12310
Binary - 1110111011
Answer:
Quinary= (12310)5
Binary=(1110111011)2
Find the value of x in the equation below.
Answer:
Here is your answer....
Hope it helps.....
Answer:
-3
Step-by-step explanation:
expand the bracket by multiplying everything
inside by 3
after that collect like terms
then solve to come up with -3 as ur answer
Which expression is equivalent to 5(w+4) when w= 9?
519)
9(5)
5(9)+4
O 5(9)+20
Answer:
D
Step-by-step explanation:
[tex]5(9 + 4) \\ 5(13) \\ 65 \\ prove \: it \: d \: answer \\ 5(9) + 20 \\ 45 + 20 \\ = 65[/tex]
I would really appreciate some help on this! 30 points and I will give brainliest!!
Match the following graph with its proper equation.
Answer:
D: it is the only equation that has strictly positive exponents...
the function is "always going up"
if a function has a negative exponent 2^-x the curve will "decay"
[tex]2^{x^{2} }[/tex] the [tex]x^{2}[/tex] is always positive
Step-by-step explanation:
Line K has a slope of -3/4. If the slope of of lines that are perpendicular to each other are opposite reciprocals, what is the slope of a line perpendicular to line k?
Answer:
+4/3
Step-by-step explanation:
-3/4 * -1 = 3/4 then flip it to 4/3
Answer:
4/3
Step-by-step explanation:
the slope of a perpedicular line is the inverse times negative one.
1)the inverse of -3/4 is -4/3
2)-4/3*-1 is 4/3
In 12 years, M will be thrice as old as N was 12 years ago. If M is now 8 years older than N, the present age of N is (in years)?
Answer:
M = 36 year old
N = 28 years old
Step-by-step explanation:
here,
let the present age of M and N be 'x' and 'y' respectively.
By the first condition,
(x+12) = 3( y - 12)
x+12 = 3y - 36
x = 3y-48 ........ eqn (i)
and
By the second condition,
x= y+8 ........ eqn (ii)
now,
combining both the equations...
x = x
3y-48 = y+8 ( from i and ii )
2y= 56
y = 28
then , if y = 28
soo.. x= y+8
= 28+8
= 36
Anybody help me with this question please? ;D
9514 1404 393
Answer:
35 cm²
Step-by-step explanation:
You can count the squares, or ...
you can multiply the number in each row by the number of rows, or ...you can multiply the number in each column by the number of columns.Any way you do this, there are 35 square, so the area is 35 square centimeters.
Based on the graph, how many calories will Colin burn if he walks 3 mi.?
A. 300 calories
B. 550 calories
C. 750 calories
D. 900 calories
Look at the figure. Which surface of the figure is represented by plane EFHG?
the right side
the back
the top
the bottom
The following dot plot represents two data sets, A and B.
The mean of set B is about ______ (40, 50, 30) higher than the means of set A, which is about _______ (half, twice, the same as) the mean absolute deviation of either set.
Answer:
30, half
Step-by-step explanation:
mean of A = (10*5+7*20+2*30+40+4*50+80)/20 = 28.5
mean of B = (2*20+40+5*50+3*60+8*70+80)/20 =57.5
difference =57.5-28.5 =29
mean absolute deviation = (the sum of every data point - mean)/total number
in this case,
MAD = 304/20 = 15.2
Answer:
30 , twice
Step-by-step explanation:
i just did the lesson and got it right
t
i need help in this plz!!!!
Step-by-step explanation:
1) = {5(x+y)} - 2x
= 5x + 5y - 2x
= 3x + 5y
2)= {2(p×q)} + (p×q)
= (2p×2q)+ p×q
= 4pq + pq
= 5pq
3)= 6a + (8b + 2a)
= 8a + 8b
= 8(a+b)
4)= 3x² + ( x²+7x)
= 4x² + 7x
= x(4x+7)
Answer:
Step-by-step explanation:
72) 5*(x +y) - 2x
= 5x + 5y - 2x {Distributive property}
= (5x - 2x) + 5y {Combine like terms}
= 3x + 5y
73) 2*(pq) + pq
= 2pq + pq {Combine like terms}
= 3pq
74) 6a + (8b + 2a)
= 6a + 2a + 8b {Combine like terms}
= 8a + 8b
75) 3*x² + (x² + 7x)
= 3x² + x² + 7x {Combine like terms}
= 4x² + 7x
Given m|n, find the value of x.
t
(x-1)
(8x-14)
Answer:
Submit Answer
attempt 1 out of 2
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Plssssss help
Answer:
x=13
Step-by-step explanation:
These are corresponding angle and corresponding angles are equal
7x-1 = 8x-14
Subtract 7x from each side
7x-1-7x = 8x-14-7x
-1 = x-14
Add 14 to each side
-1+14 = x-14+14
13 =x
Which expression is equivalent to ?
Answer:
Option 4 .
Step-by-step explanation:
We need to simplify out the given expression . The given expression is ,
[tex]\rm\implies \dfrac{ 12x^4 ( x -3)(x+5)}{30x(x+3)(x+5)}[/tex]
Now see that the term ( x +5) is common in both numerator and denominator . Therefore we can cancel it out . The expression becomes ,
[tex]\rm\implies \dfrac{ 12x^4 ( x -3)\cancel{(x+5)}}{30x(x+3)\cancel{(x+5)}} =\dfrac{ 12x^4(x-3)}{30x(x+3)}[/tex]
Now x⁴ and x can again be cancelled out in numerator and denominator . Similarly we can cancel 12 and 30 by 6 . We have ,
[tex]\rm\implies \dfrac{ 2x^3(x-3)}{5(x+3)}[/tex]
On looking at the provided options , 4th option is correct .
The original price of a mountain bike was reduced by $125.
If p = the mountain bike's original price in dollars, which algebraic expression represents the reduced price?
Answer:
p-$125= reduced price
Step-by-step explanation:
reduced implies that the $125 was SUBTRACTED from the original price.
Sara had 97 dollars to spend on 6 books. After
buying them she had 13 dollars. How much did each book cost ?
A local store sells oranges at a price for 6 fo $9.00. If Alley wants to buy 10 oranges what would the total price be?
Answer:
15$
Step-by-step explanation:
you need to check how much of e costs and you do that by dividing the price by the amount and than comes up to 1.5 that's for 1 and for 10 it's 15 hope that helps
factor 4a^2-b^2-2a+b
Answer:
lo emos aprendido mucho chicas y chicos xporfor cuidense mucho porque les quiero x xd
Answer:
[tex](2a-b)(2a+b -1 )[/tex]
Step-by-step explanation:
[tex]4a^2-b^2-2a+b[/tex]
[tex](2a+b)(2a-b) -1(2a-b)[/tex]
[tex](2a-b)(2a+b -1 )[/tex]
247 divided by 7
[tex]247 \div 7[/tex]
Answer:
247/7 = 35 2/7
247/7 = 35 reminder 2
247/7 = 35.2857142857...
Step-by-step explanation:
35
----------------------------------
7 | 247
21
-----------
37
35
---------
2
247/7 = 35 2/7
247/7 = 35 reminder 2
247/7 = 35.2857142857...
-8/5+-4/7 is equal to
Answer:
-36/35 or -1 1/35
Step-by-step explanation:
-8/5 + 4/7
Get a common denominator of 35
-8/5 * 7/7 + 4/7 *5/5
-56/35 + 20/35
-36/35
-35/35 - 1/35
-1 1/35
Answer:
-36/35
Step-by-step explanation:
First, we need to find the LCM of 5 and 7 (the denominators) which is 35.
-8*7/35 + 4*5/35 = -56/35 + 20/35 = -36/35
Your answer is -36/35, or if it asks for a mixed number it's -1 1/35.
Hope this helps
In a GEOMETRIC sequence, the first term is 21 and
the common ratio is 2. Find the 15th term.
Answer:
344064
Step-by-step explanation:
hope it is well understood
Distribute and simplify the radicals below
Answer:
i think A is answer you should to do
What is the justification for step 2 in the solution process? 10x − 25 − 3x = 4x − 1 Step 1: 7x − 25 = 4x − 1 Step 2: 7x = 4x + 24
Answer:
Add 25 to each side using the addition property of equality
Step-by-step explanation:
10x − 25 − 3x = 4x − 1
Step 1: 7x − 25 = 4x − 1 Combine like terms
Step 2: 7x = 4x + 24 Add 25 to each side using the addition property of equality
A group of students is arranging squares into layers to create a project. The first layer has 6 squares. The second layer has 12 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?
f(1) = 6; f(n) = 6 + d(n − 1), n > 0
f(1) = 6; f(n) = 6 ⋅ d(n − 1), n > 0
f(1) = 6; f(n) = 6 ⋅ d(n + 1), n > 0
f(1) = 6; f(n) = 6 + d(n + 1), n > 0
Answer:
a.
f(1)=6; f(n)=6+d(n-1), n>0
Step-by-step explanation:
We are given that
First layer has squares, a=6
Second layer has squares, a2=12
We have to find an arithmetic explicit formula to determine the number of squares in each layer.
[tex]d=a_2-a_1=12-6[/tex]
nth term of an A.P
[tex]a_n=a+(n-1)d[/tex]
Substitute the value of a
Now, we get
[tex]a_n=6+(n-1)d[/tex]
f(1)=a=6
[tex]a_n=f(n)=6+d(n-1)[/tex]
Hence, option a is correct.
a.
f(1)=6; f(n)=6+d(n-1), n>0
Answer:
f(1) = 6; f(n) = 6 + d(n − 1), n > 0
Step-by-step explanation:
I took the test on flvs and got it right.
100% Guaranteed Correct :)
, Hope this helps
Have a great day!!
What is the length of bc
Express the following as ONE fraction:
(( b - c )/ b ) + (b / ( b + c ))
Answer:
Step-by-step explanation:
(b - c)/b * (b+c)/b Notice how the second fraction is inverted and multiplied. That's how you handle a 4 tier fraction. Here's a simpler example
[tex]\frac{\frac{2}{3} }{\frac{4}{5} } = \frac{2}{3} * \frac{5}{4}[/tex]
What you get with your problem is
(b^2 - c^2)/b^2