Immediately, by definition of cotangent, we find
tan(α) = 1/cot(α) = 1/(-√3)
⇒ tan(α) = -√3
Given that π/2 < α < π, we know that cos(α) < 0 and sin(α) > 0. In turn, sec(α) < 0 and csc(α) > 0.
Recall the Pythagorean identity,
cos²(α) + sin²(α) = 1
Multiplying both sides by 1/sin²(α) recovers another form of the identity,
cot²(α) + 1 = csc²(α)
Solving for csc(α) above yields
csc(α) = + √(cot²(α) + 1) = √((-√3)² + 1) = √4
⇒ csc(α) = 2
⇒ sin(α) = 1/2
Solve for cos(α) using the first form of the Pythagorean identity:
cos(α) = - √(1 - sin²(α)) = - √(1 - (1/2)²) = - √(3/4)
⇒ cos(α) = -√3/2
⇒ sec(α) = -2/√3
Hey guys please help me please and thank you
Answer:
B
Step-by-step explanation:
No matter how many times you multiply 1 by itself, it will always be 1 which makes A and D incorrect.
x is a power. The question is 1/4 * 1/4 * 1/4 which is 1/64
Answer: B
Step-by-step explanation:
[tex]f(x)=(\frac{1}{4})^x\\f(3)=(\frac{1}{4})^3\\f(3)=(\frac{1}{4})(\frac{1}{4})(\frac{1}{4})\\f(3)=\frac{1}{64}[/tex]
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find y.
A. 16
B. 6
C. 18
D. 32
9514 1404 393
Answer:
B. 6
Step-by-step explanation:
The diagonals of a parallelogram intersect at their midpoints, so ...
DE = BE
4y -8 = y +10
3y = 18 . . . . . . . add 8-y
y = 6 . . . . . . . . divide by 3
__
Additional comment
The value of x is found the same way:
2x = x+2 ⇒ x = 2
please help ill mark brainliest
Answer:
x=3
Step-by-step explanation:
6(x+5)=4(x+9)
6x+30=4x+36
2x+30=36
2x=6
x=3
Can you please help me
Answer: 1/6
Step-by-step explanation:
Given:
4/9 and 11/18
Solve:
STEP ONE: Make the denominators equal by determining the LCM
LCM = Least Common Multiple
First Five multiples of 9 = 9, 18, 27, 36, 45
First FIve multiples of 18 = 18, 36, 54, 72, 90
As we can see from the list above, both 18 and 36 overlap, however, 18 is less than 36. Therefore, 18 is the LCM.
STEP TWO: Compare the size and determine the greater one.
4/9 = (4 × 2) / (9 × 2) = 8/18
11/18 = 11/18
Since 11 > 8, therefore, 11/18 is greater than 8/18
STEP THREE: Find the difference between the two fractions.
11/18 - 4/9
=11/18 - 8/18
=(11 - 8) / 18
= 3 / 18
= 1/6
Hope this helps!! :)
Please let me know if you have any questions
Find an equation in slope-intercept form of the line satisfying the specified conditions.
Through (8,-3), perpendicular to -6x + 7y=-62.
Answer:
[tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex]
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
-6x +7y= -62
Rewriting this equation into the slope-intercept form:
7y= 6x -62
[tex]y = \frac{6}{7} x - \frac{62}{7} [/tex]
The product of the slope of 2 perpendicular lines is -1.
Let the slope of the unknown line be m.
[tex]m( \frac{6}{7} ) = - 1[/tex]
[tex]m = - 1 \div \frac{6}{7} [/tex]
[tex]m = - \frac{7}{6} [/tex]
Substitute the value of m into the equation:
[tex]y = - \frac{7}{6} x + c[/tex]
To find the value of c, substitute a pair of coordinates into the equation.
When x= 8, y= -3,
[tex] - 3 = - \frac{ 7}{6} (8) + c[/tex]
[tex] - 3 = - \frac{28}{3} + c[/tex]
[tex]c = \frac{28}{3} - 3[/tex]
[tex]c = \frac{19}{3} [/tex]
[tex]c = 6 \frac{1}{3} [/tex]
Thus, the equation of the line is [tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex].
Solve for x. 2^4x-7=16
Answer:
23/16
Step-by-step explanation:
2*4 x x-7 = 16
16x - 7 = 16
16x = 16 + 7
16x = 23
x = 23/16
Give me a rating XD <3
Given the function f(x) = -5x + 2, find the range ofly for x = -1, 0, 1.
O 7, 2, -3
O 7, 2, 3
O-7, -2, 3
0-7, -2, -3
Answer:
A
Step-by-step explanation:
f(-1)=7, f(0)=2, f(1)=-3
Find the midpoint of the line segment defined by the points: (5, 4) and (−2, 1) (2.5, 1.5) (3.5, 2.5) (1.5, 2.5) (3.5, 1.5)
Answer:
[tex]\boxed {\boxed {\sf (1.5 , 2.5)}}[/tex]
Step-by-step explanation:
The midpoint is the point that bisects a line segment or divides it into 2 equal halves. The formula is essentially finding the average of the 2 points.
[tex](\frac {x_1+x_2}{2}, \frac {y_1+ y_2}{2})[/tex]
In this formula, (x₁, y₁) and (x₂, y₂) are the 2 endpoints of the line segment. For this problem, these are (5,4 ) and (-2, 1).
x₁= 5 y₁= 4 x₂= -2 y₂= 1Substitute these values into the formula.
[tex]( \frac {5+ -2}{2}, \frac {4+1}{2})[/tex]
Solve the numerators.
5+ -2 = 5-2 = 3 4+1 = 5[tex]( \frac {3}{2}, \frac{5}{2})[/tex]
Convert the fractions to decimals.
[tex](1.5, 2.5)[/tex]
The midpoint of the line segment is (1.5 , 2.5)
Three yellow balls, two red balls and five orange balls are placed in a bag. Mark draws a
ball out, and replaces it. He then picks another ball.
Draw a tree diagram to represent this information.
What is the probability that he gets at least one yellow ball?
Give your answer as a fraction in its simplest form
i think this could be the answer
3-8(1+8x)=-133
Solve for x
Answer:
x=2
Step-by-step explanation:
Expanding, we have 3 - 8-64x=-133.
Combining like terms, we have -5 - 64x=-133
Adding 5 to both sides, we have -64x= -128
Dividing by -64, we have x = 2
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 421 gram setting. It is believed that the machine is underfilling the bags. A 43 bag sample had a mean of 414 grams. Assume the population standard deviation is known to be 19.
Required:
a. Is there sufficient evidence at the 0.1 level that the bags are underfilled?
b. Find the P-value of the test statistic.
Answer:
a) The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.
b) 0.0078.
Step-by-step explanation:
Question a:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 421 gram setting.
At the null hypothesis, it is tested if the mean is of 421, that is:
[tex]H_0: \mu = 421[/tex]
It is believed that the machine is underfilling the bags.
At the alternative hypothesis, it is tested if the mean is of less than 421, that is:
[tex]H_a: \mu < 421[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
421 is tested at the null hypothesis:
This means that [tex]\mu = 421[/tex]
A 43 bag sample had a mean of 414 grams. Assume the population standard deviation is known to be 19.
This means that [tex]n = 43, X = 414, \sigma = 19[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{414 - 421}{\frac{19}{\sqrt{43}}}[/tex]
[tex]z = -2.42[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean below 414, which is the p-value of z = -2.42.
Looking at the z-table, z = -2.42 has a p-value of 0.0078.
The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.
b. Find the P-value of the test statistic.
As found above, the p-value of the test statistic is 0.0078.
A large bag contains 29 balls of different colors. The balls are of the same size, weight, surface, such that besides the color they cannot be differentiated. Among the 29 balls, 8 are green, 4 are yellow, 6 are red, 5 are blue, and 6 are black.
(a) What is the probability of getting exactly 1 green, 1 yellow and 2 red when pulling 8 balls? number (rtol=0.01, atol=0,0001)
(b) What is the probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls? number (rtol=0.01. atol=0.0001)
(c) What is the probability of getting first and last a green, and then in any order 2 yellow and 2 red when pulling 8 balls? (Note: If there are remaining balls, they need to be either blue or black) number (rtol=0.01, atol=0.0001)
(d) What is the probability of getting 2 blue and 2 non-blue when pulling 4 balls? number (rtol=0.01, atol=0.0001)
(e) Recalculate part (d) using a binomial distribution. number (rtol=0.01, atol=0.0001)
Answer:
White
6
Red
9
Green
Total number of balls =5+6+9
=20
(i) Probability =
Total cases
favourable cases
P(Green) =
20
9
(ii) P(White or red) =
20
5+6
=
20
11
(iii) P(neither green nor white) = P(Red)
=
20
6
=
10
3
The probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.
The probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.
(a) Probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls:
Total number of balls = 29
Total number of balls to be pulled = 8
Number of ways to choose 1 green out of 8 = C(8, 1) = 8
Number of ways to choose 1 yellow out of the remaining 7 = C(7, 1) = 7
Number of ways to choose 2 red out of the remaining 6 = C(6, 2) = 15
Total favorable outcomes = 8 x 7 x 15 = 840
Total possible outcomes = C(29, 8) = 2,765,905
Probability
= favorable outcomes / possible outcomes
= 840 / 2,765,905
= 0.000303
Therefore, the probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.
(b) Total number of balls = 29
Total number of balls to be pulled = 6
Number of ways to choose 1 green out of 8 = C(8, 1) = 8
Number of ways to choose another green out of the remaining 7 = C(7, 1) = 7
Number of ways to choose 2 yellow out of the remaining 5 = C(5, 2) = 10
Number of ways to choose 2 red out of the remaining 3 = C(3, 2) = 3
Total favorable outcomes = 8 x 7 x 10 x 3 = 1,680
Total possible outcomes = C(29, 6) = 593,775
Probability
= favorable outcomes / possible outcomes
= 1,680 / 593,775
= 0.00283
Therefore, the probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.
(c) Probability of getting first and last a green, and then in any order 2 yellow and 2 red when pulling 8 balls:
Total number of balls = 29
Total number of balls to be pulled = 8
Number of ways to choose the first green = C(8, 1) = 8
Number of ways to choose the last green = C(7, 1) = 7
Number of ways to choose 2 yellow out of the remaining 6 = C(6, 2) = 15
Number of ways to choose 2 red out of the remaining 4 = C(4, 2) = 6
Number of ways to choose the remaining 2 balls (either blue or black) = C(5, 2) = 10
Total favorable outcomes = 8 x 7 x 15 x 6x 10 = 50,400
Total possible outcomes = C(29, 8) = 2,765,905
Probability
= 50,400 / 2,765,905 ≈ 0.0182
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What fraction must be subtracted from the sum of 1/4 and 1/6 to have an average of 1/12 of all the two fractions
Answer:
so 1/3 must be subtracted from the sum of 1/4 and 1/6 to have an average of 1/12 of all the two fractions.
Step-by-step explanation:
let the fraction be x
(1/4 + 1/6)-x = 1/12
or, 10/24 - x = 1/12
or, 5/12-1/12 = x
so, x = 4/12 = 1/3
The perimeter of a rectangle is 202 the length is 26 more than 4 times the width find the dimensions
Answer:
Width = xLength = 26 + 4xPerimeter
[tex]202 = x + x + 26 + 4x + 26 + 4x\\202-26-26=10x\\150=10x\\x=15[/tex]
Therefore, the dimensions are
Width = x = 15Length = 26 + 4x = 26 + 4(15) = 86A $300 bike is marked down to $175. Find the percent markdown to the nearest whole percent.
Answer:
58
Step-by-step explanation:
58 because you divide 200 by 100 then getting that answer (3) then divide 175 by 3 which equals one percent and you get 58.333 you round it to the nearest whole and u get 58
Given f (t )equals 3 minus 2 t squared. Find and simplify fraction numerator f (2 plus h )minus f (2 )over denominator h end fraction.
Answer:
ushshdbs the 7th century there where the gall bladder and merchants Bank Ltd bank in the 7th
I’m failing pls help I’ll brainlest ASAP
Find the equation of the line
Answer:
Y = 4x - 9
Step-by-step explanation:
Hope this helps! If it’s wrong I’m really sorry.
Pls give brainliest!
Answer:
...
Step-by-step explanation:
180 °
35 °
X °
X = ? °
Answer:
x=145°
Step-by-step explanation:
180 = 35 + x
x = 180-35
x= 145°
Q: Solve for x: 8x-2-5x=8
A. OX=13
B. OX=2 1/2
C. OX=3 1/3
D. OX=7
Answer:
c. 3 1/3
Step-by-step explanation:
8x-2-5x=8
3x=10
x=10/3=3 1/3
Answer:
x=[tex]3\frac{1}{3}[/tex]
Step-by-step explanation:
Hi there!
We want to find the value of x in this expression:
8x-2-5x=8
Our goal is to isolate x on one side
Combine like terms on the left side (add the terms with x together)
3x-2=8
Add 2 to both sides (-2+2=0)
3x-2=8
+2 +2
__________
3x=10
Divide both sides by 3
x=[tex]\frac{10}{3}[/tex]
Simplify the improper fraction
x=[tex]3\frac{1}{3}[/tex]
Hope this helps!
I NEED HELP ASAP!!! convert 0.252525 to a fraction and convert 2.454545 to a fraction
Answer:
1. What is 0.252525 as a fraction?
0.252525 as a fraction equals 252525/1000000
2. 2.454545 as a fraction equals 2454545/1000000
Step-by-step explanation:
To write 0.252525 as a fraction you have to write 0.252525 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.252525 = 0.252525/1 = 2.52525/10 = 25.2525/100 = 252.525/1000 = 2525.25/10000 = 25252.5/100000 = 252525/1000000
And finally we have:
0.252525 as a fraction equals 252525/1000000
2. What is 2.454545 as a fraction?
To write 2.454545 as a fraction you have to write 2.454545 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
2.454545 = 2.454545/1 = 24.54545/10 = 245.4545/100 = 2454.545/1000 = 24545.45/10000 = 245454.5/100000 = 2454545/1000000
And finally we have:
2.454545 as a fraction equals 2454545/1000000
Thanks
11)
Given the function, f(x) = x2 + 5x - 3 evaluate f(-2).
Answer:
f(- 2) = - 9
Step-by-step explanation:
Substitute x = - 2 into f(x) , that is
f(- 2) = (- 2)² + 5(- 2) - 3 = 4 - 10 - 3 = 4 - 13 = - 9
PLZ HELP ME WITH MY MATH HOMEWORK!!!!!! SHOW WORK
Answer:
Step-by-step explanation:
-(4q+8) + 6q = 12q - 5/6(18q + 6)
Open brackets:
<=> - 4q - 8 + 6q = 12q - 5/6*18q - 5/6*6
<=> - 4q - 8 + 6q = 12q - 15q - 5
Put q in one side and non q in one side:
<=> - 4q + 6q - 12q + 15q = 8 - 5
<=> 5q = 3
<=> q = 3/5
Solve forx.
(2x - 1) (5x+3) = 0
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{(2x - 1)(5x + 3) = 0}\\\rightarrow\large\textsf{10x}\mathsf{^2}\large\textsf{ + x - 3 = 0}[/tex]
[tex]\huge\text{FACTOR the LEFT SIDE of the equation}[/tex]
[tex]\large\textsf{(5x + 3)(2x - 1) = 0}[/tex]
[tex]\huge\text{SET the FACTORS to equal to 0}[/tex]
[tex]\large\textsf{5x + 3 = 0 or 2x - 1 = 0}[/tex]
[tex]\huge\text{SIMPLIFY \& YOU HAVE YOUR RESULT}\\\\\huge\text{to your question if you solved correctly.}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: \boxed{\mathsf{x = - \dfrac{3}{5}\ or \ x = \dfrac{1}{2}}}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
if a,b,c,d,e are in continued proportion then a/c is equal to what ?
Answer:
huh
Step-by-step explanation:
that don't make no sense
If a,b,c,d,e are in continued proportion then a/c = a²/b²
What is Ratio?Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
It is given that
a,b,c,d,e are in continued proportion
We can write it as
a/b = b/c = c/d = d/e = k
d=ek, c=ek², b=ek³ and a=ek⁴
Here a/c
Substitute the values of a and c
⇒ ek⁴/ek²
⇒ k² [ k = a/b ]
⇒ a²/b²
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What is the value of 40 1/2÷3 1/2
Answer:
81/7 (11.57, 11 4/7)
Step-by-step explanation:
Lets rewrite these mixed fractions
[tex]40\frac{1}{2}=\frac{81}{2}[/tex]
[tex]3\frac{1}{2} =\frac{7}{2}[/tex]
Here we can do divide these two numbers:
[tex]\frac{\frac{81}{2} }{\frac{7}{2} }=\frac{81}{7}[/tex]
The answer therefore is 81/7, or 11.571 (11 4/7)
if 24 bags of sugar with equal weight weigh 21 kg, how many bags of sugar would weigh 122kg?
Answer:
24 bags = 21 kg
1.142 bag = 1 kg
About 139 bags = 122 kg
You start off with 24 bags that equal the same amount as 21 kg. You need to find out how many bags of sugar equal the same amount as 122 kg. The first line is a ratio and to find your answer you need to figure out what is 1 kilogram equal to in the amount of bags. You divide both sides by 21 leaving 1.142 bag equal to 1 kilogram. In order to find 122 kilograms, you have to multiply both sides by 122 kilograms which would give you about 139 bags = 122 kilograms.
Your final answer: 139 bags
I hope this helped!
Find a12 for the geometric sequence -4, -2, -1, -1/2, ...
9514 1404 393
Answer:
-1/512
Step-by-step explanation:
The first term is -4, and the common ratio is -2/-4 = 1/2. Then the n-th term is ...
an = -4·(1/2)^(n-1)
and the 12th term is ...
a12 = -4(1/2)^(12 -1) = -4/2048
a12 = -1/512
Fill in the blanks to solve 900 x 6
Answer:
The answer is 900 ×6= 5,400 u can use a calculator
The total cost, C, for running an advertisement in a local newspaper, The Free Press, is made up of an initial cost of $12 plus a charge of $5 per day. A rival newspaper, The Banner, is currently running a special on advertisements at $8 per day with no initial cost.
a) Write an equation representing the cost in The Free Press.
b) Write an equation representing the cost in The Banner.
c) For each newspaper, create a table of values.
d) Use Rapid Tables (will need to select 2 lines from the drop down - see example in relation to the Jason's Trip graph below) to graph each cost on the same set of coordinate axis. Your two lines will represent The Free Press and The Banner. You are also able to create the graph on other technology or a piece of paper.
e) Which newspaper would you use for an ad that ran 1 day?
f) Which newspaper would you use for an ad that ran 12 days?
Answer:
(a) [tex]C(x) = 12 + 5x[/tex]
(b) [tex]C(x) = 8x[/tex]
(c) Tables
(d) See attachment for graph
(e) Banner newspaper
(f) Free press newspaper
Free Press
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}[/tex]
Banner
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}[/tex]
Step-by-step explanation:
Given
Free Press
[tex]Initial = 12[/tex]
[tex]Rate =5[/tex]
Banner
[tex]Initial=0[/tex]
[tex]Rate =8[/tex]
Solving (a): Free Press Equation
This is calculated as:
[tex]C(x) = Initial + Rate * x[/tex]
Where
[tex]x \to[/tex] days
So, we have:
[tex]C(x) = 12 + 5x[/tex]
Solving (b): Banner Equation
This is calculated as:
[tex]C(x) = Initial + Rate * x[/tex]
Where
[tex]x \to[/tex] days
So, we have:
[tex]C(x) = 0 + 8x[/tex]
[tex]C(x) = 8x[/tex]
Solving (c): Table of values
For free press, we have:
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}[/tex]
C(x) is calculated as:
[tex]x = 1;\ C(1) = 12 + 5* 1 =17[/tex]
[tex]x = 2;\ C(2) = 12 + 5* 2 =22[/tex]
..
[tex]x = 5;\ C(5) = 12 + 5* 5 =37[/tex]
For banner, we have:
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}[/tex]
C(x) is calculated as:
[tex]x = 1;\ C(1) = 8* 1 =8[/tex]
[tex]x = 2;\ C(2) = 8* 2 =16[/tex]
..
[tex]x = 5;\ C(5) = 8* 5 =40[/tex]
Solving (d): Graph of both using rapidtable
See attachment
Solving (e) Newspaper to use for 1 day
From the graph, when [tex]x = 1[/tex]
[tex]Free\ press = 17[/tex]
[tex]Banner = 8[/tex]
So, we use Banner newspaper because it is cheaper
Solving (f) Newspaper to use for 12 days
From the graph, when [tex]x = 12[/tex]
[tex]Free\ press = 72[/tex]
[tex]Banner = 96[/tex]
So, we use free press newspaper because it is cheaper
