In this exercise we have to use the knowledge of cosine quadrants, like this:
Letter B
We have that the quadrant of the cosine is given by:
The two quadrants on the right are positive.The two quadrants on the left are negative.So we know that:
[tex]cos (2\pi/3)[/tex] If it's in quadrant three, that's negative.
[tex]cos(5\pi/3)[/tex] If you're in quadrant four, that's positive.
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The correct answer is option B. Cosine is negative in the second quadrant and positive in the fourth quadrant.
To determine why [tex]cos(\frac{2\pi }{3})[/tex] is not equal to [tex]cos(\frac{5\pi }{3})[/tex], we can analyze the properties of cosine in different quadrants.
Reference Angles: The reference angle for both [tex]\frac{2\pi }{3}[/tex] and [tex]\frac{5\pi }{3}[/tex] is [tex]\frac{\pi }{3}[/tex].Quadrants: [tex]\frac{2\pi }{3}[/tex] is in the second quadrant, while [tex]\frac{5\pi }{3}[/tex] is in the fourth quadrant.Sign of Cosine: In the second quadrant, cosine is negative. In the fourth quadrant, cosine is positive.Thus, because cosine is negative in the second quadrant and positive in the fourth quadrant, [tex]cos(\frac{2\pi }{3})[/tex] is not equal to [tex]cos(\frac{5\pi }{3})[/tex]. Therefore, the best explanation is: Cosine is negative in the second quadrant and positive in the fourth quadrant.
Joe flips the disc shown below 15 times:
A disc with two layers is shown. The top layer is shaded in a darker shade of gray, and the lower section of the disc is white.
What is the probability that the 16th flip will result in the disc landing white side up?
Juana can use the expression 64 divided by 4 to determine
A. 4% of 64.
B. 10% of 64.
C. 25% of 64.
D. 50% of 64.
Answer:
it is a 4% of 64
Step-by-step explanation:
Which of these is a simplified form of the equation 6y + 4 = 8 + 2y + 2y? 6y = 8 10y = 12 2y = 4 4y = 12
A website has 826,140 hits what is the value of the 8 in 826,140
Which type of angle is ∠ABC?
x y
0 3
1 1
2 -1
Which equation represents the data in the table shown?
A) y = -2x
B) y = 2x + 3
C) y = -2x + 3
D) y = -2x - 3
Answer:
Option C - [tex]y=-2x+3[/tex]
Step-by-step explanation:
Given : Table of data
x y
0 3
1 1
2 -1
To find : Which equation represents the data in the table shown?
Solution :
To find the equation we need to check all the points satisfying the equation or not.
A) [tex]y=-2x[/tex]
Put x=0
[tex]y=-2(0)=0[/tex]
Not satisfied
B) [tex]y=2x+3[/tex]
Put x=0
[tex]y=2(0)+3=3[/tex]
Put x=1
[tex]y=2(1)+3=5[/tex]
Not satisfied
C) [tex]y=-2x+3[/tex]
Put x=0
[tex]y=-2(0)+3=3[/tex]
Put x=1
[tex]y=-2(1)+3=1[/tex]
Put x=2
[tex]y=-2(2)+3=-1[/tex]
All points satisfied.
D) [tex]y=-2x-3[/tex]
Put x=0
[tex]y=-2(0)-3=-3[/tex]
Not satisfied
Therefore, The required equation satisfying all the points of the table is [tex]y=-2x+3[/tex]
So, Option C is correct.
Write the equation y=-3/5x+3 in standard form using integer coefficients
Final answer:
To convert the equation y = -3/5x + 3 into standard form with integer coefficients, multiply both sides by 5 to get rid of the fraction, resulting in 5y = -3x + 15. Then, rearrange the terms to obtain the standard form, which is 3x + 5y = 15.
Explanation:
The equation y = -3/5x + 3 is given in slope-intercept form. To convert it into standard form using integer coefficients, we need to rearrange the terms so that all variables and constants are on one side of the equation and the constant is on the other side. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.
First, multiply both sides of the equation by 5 to clear the fraction:
5y = -3x + 15
Next, move the x-term to the left side of the equation:
3x + 5y = 15
Now, the equation is in standard form with integer coefficients.
Which product is less than 99 (look at pic) please answer
Answer: 10 / 11 × 99
Step-by-step explanation:
The first one is; 16/15 × 99 = 1584/15 = 105.6
Its greater than 99
The second one is; 12/7 × 99 = 1188/7 = 169.71
The value is greater than 99
The fourth one is; 20/20 × 99 = 1980/20 = 99
The value is equal 99
The third one is; 10/11 × 99 = 990/11 =90
The value is less than 99
Therefore the product of 10/11 ×99 is less than 99
Fifty students in the fourth grade class listed their hair and eye colors in the table below: Brown hair Blonde hair Total Green eyes 16 12 28 Brown eyes 14 8 22 30 20 50 Are the events "green eyes" and "brown hair" independent?
The events "green eyes" and "brown hair" are not independent because the probability of a student having both green eyes and brown hair is not equal to the product of their individual probabilities.
Explanation:To determine whether the events "green eyes" and "brown hair" are independent, we need to look at the probabilities of each event occurring separately and together.
The probability of having green eyes (P(Green Eyes)) is the total number of students with green eyes divided by the total number of students, which is 28/50.
The probability of having brown hair (P(Brown Hair)) is the total number of students with brown hair divided by the total number of students, which is 30/50.
The probability of having both green eyes and brown hair (P(Green Eyes AND Brown Hair)) is the number of students with both green eyes and brown hair divided by the total number of students, which is 16/50.
Events A and B are independent if P(A and B) = P(A) * P(B). Using this formula, we can determine if the events are independent:
P(Green Eyes AND Brown Hair) = P(Green Eyes) * P(Brown Hair)
16/50 ≠ (28/50) * (30/50)
Since the probability of having both green eyes and brown hair does not equal the product of the probabilities of having green eyes and having brown hair, these events are not independent.
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Find each product or quotient. Use significant digits. 11ft *825ft a. 9,080 ft2 b. 9,100 ft2 c. 9,000 ft2 d. 9,075 ft2
Bernard works as a courier delivering and picking up packages for a shipping company. Three of the communities on his route form an isosceles right triangle as shown in the figure. There are approximately 68 miles between Old Mill and Clarksville and between Clarksville and Hamilton. Approximately how many miles are there between Old Mill and Hamilton? Round your answer to the nearest mile if necessary.
If s = 1/3 unit and A = 54s2, what is the value of A, in square units? ____ square unit(s). (Input whole number only.)
Answer:
Plus in s.
A=54(1/3)^2
First, apply exponents.
1/3 x 1/3= 1/9
A=54(1/9)
1/9 x 54= 6
Final answer: 6 square units
Step-by-step explanation:
The tongue of a chameleon is one and a half times it's body length. Write this as a decimal
The tongue of a chameleon is 1.5 times its body length when expressed as a decimal.
If the tongue of a chameleon is one and a half times its body length, we express this as a decimal by multiplying the body length by 1.5. For example, if the body length is represented by 1 unit, then the tongue length would be 1 imes 1.5, which equals 1.5. Therefore, the length of the tongue as a decimal is 1.5 times the body length.
True or false. A figure that has opposite sides with equal lengths and equal slopes and diagonals with slopes that are negative reciprocals must be a rhombus.
Answer:
The statement is false, it describes all parallelogram.
Step-by-step explanation:
The figure that has opposite sides with equal lengths and equal slopes and diagonals with slopes that are negative reciprocals must be a rhombus. This is a true statement
What is a rhombus?A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
Given:
A figure that has opposite sides with equal lengths and equal slopes and diagonals with slopes that are negative reciprocals must be a rhombus,
Given that it possesses all the characteristics of a parallelogram, a rhombus is regarded as one of the exceptional parallelograms. The two lines of symmetry for a rhombus are its two diagonals. A line that splits an object into two equally sized halves is referred to as the axis of symmetry.
Thus, it is a Rhombus, As the opposite sides are parallel and equal and the diagonal of the rhombus is perpendicular.
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Sonya wants to know how much her annual take-home pay will be after she pays FICA taxes totaling 7.65% on an annual salary of $36,590.
Final answer:
Sonya's annual take-home pay, after FICA taxes of 7.65% on her annual salary of $36,590, would be $33,790.86.
Explanation:
To calculate Sonya’s annual take-home pay after FICA taxes, we first need to understand that FICA consists of two separate taxes: Social Security and Medicare. The total rate for these combined is 7.65% of the gross income. Sonya’s annual salary is $36,590.
First, we calculate the total FICA tax Sonya has to pay:
Social Security tax (6.2% of $36,590) = $2,268.58Medicare tax (1.45% of $36,590) = $530.56Add these two amounts to get the total FICA tax:
$2,268.58 (Social Security) + $530.56 (Medicare) = $2,799.14
Finally, subtract this total FICA tax from the annual salary to find Sonya’s take-home pay:
$36,590 (annual salary) - $2,799.14 (FICA taxes) = $33,790.86
John is choosing a password for his access to the internet. He decided not to use the digit 0 or the letter M. Each letter or number may be used more than once. How many passwords of 2 letters followed by 4 digits are possible?
a.)4,200,625
b.)3,100,625
c.)4,100,625
d.)3,100,500
There are 4100625 possible passwords of 2 letters followed by 4 digits
How to determine the number of passwords?The usable characters are:
Digits 1 - 9 i.e. 9 digitsAll alphabets except M i.e. 25 lettersGiven that the characters can be repeated, and the password uses 2 letters and 4 digits.
The number of password is:
Password = 25* 25 * 9*9*9*9
Evaluate
Password = 4100625
Hence, there are 4100625 possible passwords
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Which expression is equivalent to 5(2+7)?
Answer
b
Step-by-step explanation:
i got it on eduenity
i have no clue what to do please help
a child find 29 nickels and dimes. how many dimes are there if the total value of the coins are $2.10?
in the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with 80 degrees angle and the 60 degree angle. write and solve the equation to determine the measure of angle x
What number best completes both questions 5/7 ÷ 1/3=? ? ×1/3= 5/7
answer please!!!!!!!!!!!!!!!!!!
For 6 consecutive days, Alejandro studied for 5 minutes more each day than he did the previous day. Which best represents the change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day?
The change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day is given by -30 minutes, the correct option is A.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
Alejandro studied for 6 consecutive days.
Let he studied for x minutes on the first day
Next day he studies (x + 5) minutes.
Each day the time is increasing by 5 minutes.
The equation for time he studied each day = x + 5 t
On last day he studied,
= x + 5 * 6
= x +30
The change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day is given by
x - x -30
= -30 minutes
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Answer:
A
Step-by-step explanation:
two million, four hundred and two dollars overdrawn; write this using a negative number.
John draws a straight line in his notebook. What is the minimum number of points through which the line is drawn?
Final answer:
A straight line is determined by a minimum of two points. This is a fundamental concept in geometry and algebra, necessary for defining lines on any two-dimensional path or graph.
Explanation:
To determine the minimum number of points through which a straight line is drawn, we need to understand that a straight line is defined by only two points.
The minimum number of points through which a straight line is drawn is two. In geometry, a line extends infinitely in both directions but is determined by just two points. The concept of a line is fundamental in understanding various subjects such as algebra and geometry.
Marina can bicycle 19.5 miles in the same time it takes her to run 6 miles. She bikes 9 miles per hour faster than she runs. At what speed does Marina run? Distance Rate Time Bicycling 19.5 mc016-1.jpg mc016-2.jpg Running 6 r mc016-3.jpg
Running Speed = x
Cycling Speed = x + 9
19.5/x + 9 = 6/x
Cross multiply
19.5x = 6x + 54
19.5x - 6x = 54
13.5x = 54
x = 4
she runs 4 mph
Answer:
4 mph
Step-by-step explanation:
Plz Help me with this math problem
evaluate 5x^2-3x+2 for x=-3
For February, sales revenue is $900,000; sales commissions are 5% of sales; the sales manager's salary is $96,000; advertising expenses are $80,000; shipping expenses total 2% of sales; and miscellaneous selling expenses are $2,100 plus 1/2 of 1% of sales. Total selling expenses for the month of February are:
Final answer:
The total selling expenses for February amount to $245,600, calculated by adding the sales commissions, sales manager's salary, advertising expenses, shipping expenses, and miscellaneous selling expenses together.
Explanation:
To calculate the total selling expenses for the month of February, each component of the selling expenses will be computed based on the provided sales revenue, and then all these components will be summed up.
Sales commissions: 5% of $900,000 = $45,000
Sales manager's salary: $96,000 (fixed cost)
Advertising expenses: $80,000 (fixed cost)
Shipping expenses: 2% of $900,000 = $18,000
Miscellaneous selling expenses: $2,100 + 0.5% of $900,000 = $2,100 + $4,500 = $6,600
Adding all these expenses together:
$45,000 + $96,000 + $80,000 + $18,000 + $6,600 = $245,600
Therefore, the total selling expenses for the month of February are $245,600.
Write a algebraic expression for 8 more than 5 times a number.
Algebraic expression for 8 more than 5 times a number is 5x+8
What is Algebraic expression?In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations
Given,
8 more than 5 times a number
Consider the number is x
Then, 8 more than 5 times a number is
5x+8
Hence, Algebraic expression for 8 more than 5 times a number is 5x+8
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