Therefore , the solution of the given problem of trigonometry comes out to be cot(θ) = 9/5.
What does trigonometry actually mean?The link between the squares spline and trigonometric The field is thought to have been created with in late 1700s, however it probably got its start in the third century BC through the union of the astronomical & mathematical sciences. Precise mathematical approaches can be used to solve a wide variety of geometric equations or to calculate things that they might be used in. The six fundamental trigonometric operations are what trigonometry is all about.
Here,
Given : tan(θ) = y/x
Given that the termination side in this instance traverses (-9, -5), the tangent is as follows:
tan(θ) = -5/-9 = 5/9
The cotangent is hence the tangent's inverse:
=> cot(θ) = 1/tan(θ) = 9/5.
Therefore , the solution of the given problem of trigonometry comes out to be cot(θ) = 9/5.
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****************
The ratio of the three angles in a triangle are 1:2:6. Work out the size of each angle.
***********
Answer:
20° , 40° , 120°
Step-by-step explanation:
sum the parts of the ratio, 1 + 2 + 6 = 9 parts
divide the sum of the angles in a Δ , 180° by 9 to find the value of one part of the ratio.
180° ÷ 9 = 20° ← value of 1 part of the ratio, then
2 parts = 2 × 20° = 40°
6 parts = 6 × 20° = 120°
the 3 angles are 20° , 40° and 120°
The ratio of the distance around a circle to the distance across a circle through its center is represented by the number pi. the number pi is a decimal that does not repeat. the fraction 22/7 is sometimes used as an estimate for pi. is 22/7 a repeating decimal? explain.
No, 22/7 is not a repeating decimal. The fraction 22/7 is an estimate for pi, but since pi is an irrational number, it does not repeat and 22/7 is not an exact representation of pi.
1. The ratio of the distance around a circle to the distance across a circle through its center is represented by the number pi.
2. The number pi is a decimal that does not repeat.
3. The fraction 22/7 is sometimes used as an estimate for pi.
4. 22/7 is not a repeating decimal because pi is an irrational number, meaning it does not repeat and 22/7 is not an exact representation of pi.
No, 22/7 is not a repeating decimal. The fraction 22/7 is an estimate for pi, but since pi is an irrational number, it does not repeat and 22/7 is not an exact representation of pi.
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2
The probability distribution of the random variable X is shown in the following table.
0
3
1 2
0.12 0.16 9 0.22
-2
P(X=x) 0.08
X
-1
P
The mean of X is 1.05.
(i) Write down two equations involving p and q and hence find the values of p and q.
(ii) Find the variance of X.
[4]
[2]
Answer:
I don't know ooo y the same time that I can come get you if you want to
Ms. Jackson wants to rent a van for a week. It will cost the weekly fee plus $ 0. 50 per mile driven. Let m = the number of miles Ms. Jackson drives during the week. Use this information and the table to answer 13-15
The algebraic expression that shows the amount Ms. Jackson wants to rent a van for a week is T=320+0.50m
In order to calculate the total amount that Ms. Jackson will need to pay for renting we need to multiply the number of miles that she will drive by the price per mile driven.
Once we have that product we can simply add the weekly fee (w) to it which will give us the total (T) amount that Ms. Jackson will have to pay for her trip. This can all be combined into the following formula.
T = w + 0.50m
As per the mentioned table, a van containing ret for a week is 320, which is equal to the W value, then substitute the value in the equation we get:
T=320+0.50m
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students were surveyed on the number of siblings they have. the following probability model was created from the results. a 2-column table with 5 rows. column 1 is labeled number of siblings with entries 0, 1, 2, 3, 4 or more. column 2 is labeled probability with entries 0.223, 0.532, 0.121, 0.085, 0.039. what is the probability that a randomly selected student does not have 0 siblings? enter your answer as a decimal rounded to the thousandths place. p(not 0 siblings)
The likelihood that a student chosen at random has any siblings is 0.777. This is determined by deducting from 1 the probability of having no siblings (0.223).
1. Get the probability of 0 siblings : 0.223
2. Subtract the probability of 0 siblings from 1 :
1 - 0.223
= 0.777
3. Round the result to 3 decimal places :
0.777
The probability of a student not having 0 siblings can be calculated by subtracting the probability of having 0 siblings from 1. The probability model created from the survey results is a 2-column table with 5 rows. Column 1 is labeled number of siblings with entries 0, 1, 2, 3, 4 or more. Column 2 is labeled probability with entries
0.223, 0.532, 0.121, 0.085, 0.039.
The probability of having 0 siblings is 0.223. To calculate the probability of not having 0 siblings, we subtract 0.223 from 1. This gives us 0.777, which is the probability of not having 0 siblings. This result should be rounded to 3 decimal places, giving us 0.777 as the final answer.
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Identify the type of data (quantitative - discrete, quantitative - continuous, or qualitative) that would be used to describe a response. Number of Students Enrolled at Evergreen Valley College.
The type of data that would be used to describe the number of students enrolled at Evergreen Valley College is quantitative - discrete.
What is algebra ?
Algebra is a branch of mathematics in which arithmetic operations and other formal manipulations are applied to abstract symbols rather than specific numbers. Geometry is the branch of mathematics that deals with the shape of objects, their spatial relations, and the properties of the space the objects are in.
It's going to be quantitative because the number of students at a college can only take on certain numerical values, those that are into jurors continuous. All values can be taken by quantitative variables. Maybe 479.4, not just 479 or 480.
The type of data that would be used to describe the number of students enrolled at Evergreen Valley College is quantitative - discrete.
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Answer:
Quantitative discrete due to the fact that’s the current quantity
At nyu in 2013 the cost of the weekly meal options could be described as a function of the number of meals is the cost of the meal plan linear or non linear function
Correct option is A, the cost of the meal plan is non-linear.
How can a function's linearity or nonlinearity be determined?The simplest approach to tell if a function is linear is to look at its graph. A linear function produces a straight line on a graph. A nonlinear function is not straight and is curved in some way. A linear function results in a straight line on a graph. As a result, non-linear functions can be of any kind. Although determining a function's linearity from its input/output table or equation is the simplest method, it is also possible to do so.
Based on the given conditions, formulate:
The definition of linear function
8-10 meals = (135-123) = (10-8) =10/2=5
10-12 meals: (155-135) = (12-10)
=20/2
= 10
12-21 meals: (220-155) = (21-12)
= 65/9
=7 2/9
5 < 7 2/9 < 10
So the cost of the meal plan is non-linear.
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Complete question -
A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square with sides of length 2000. What is the length of each side of the octagon
A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square. To find the length of the side of the octagon, we can use the Pythagorean theorem to calculate the length of the hypotenuse of the isosceles right triangle.
In an isosceles right triangle, the two legs have the same length and the hypotenuse is the side opposite the right angle. Since the square has sides of length 2000, half of the side of the square is the leg of the isosceles right triangle.
So the leg of the isosceles right triangle is 2000/2 = 1000.
Applying the Pythagorean theorem to find the hypotenuse of the isosceles right triangle:
c^2 = a^2 + b^2
c = sqrt(a^2 + b^2)
c = sqrt(1000^2 + 1000^2)
c = sqrt(1000000)
c = 1000*sqrt(2)
So the length of each side of the octagon is 1000sqrt(2)
Noah has a coupon for 30% off at this favorite clothing store. he uses it to buy a hoodie and a pair of jeans.
a. noah paid $28 for the jeans after using the coupon. what is the regular price of the jeans?
b. the regular price of a hoodie is $27. what did noah pay for the hoodie?
c. if the regular price of an item is x dollars, what is the discount price in dollars?
Answer: ur mom
Step-by-step explanation: is so pretty
Answer two questions about Equations A and B:
2
−
1
=
5
.
−
1
=
3
A.
B.
2x−1
−1
=5x
=3x
1) How can we get Equation B from Equation A?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Add/subtract the same quantity to/from both sides
(Choice B)
B
Add/subtract a quantity to/from only one side
(Choice C)
C
Rewrite one side (or both) by combining like terms
(Choice D)
D
Rewrite one side (or both) using the distributive property
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes
(Choice B)
B
No
1. To get Equation B from Equation A, we add/subtract the same quantity to/from both sides.
2. Equation A is equivalent to Equation B
What is an equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.
Here, we have
1. We are given the equation :
2x - 1 = 5x .............(A)
To get Equation B from A, we would subtract 2x from both sides of the equation.
2x - 2x - 1 = 5x - 2x
- 1 = 3x...... (B)
Hence, to get Equation B from Equation A, we add/subtract the same quantity to/from both sides.
2. Based on the previous answer,
2x - 1 = 5x is equal to -1 = 3x.
Hence, both Equation A and Equation B are equivalent expressions.
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A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. -3x+2y - 3x-6y = 9
A) Subtract to eliminate y.
B) Add to eliminate x.
C) Subtract to eliminate x.
D) Add to eliminate y.
Answer:
B
Step-by-step explanation:
-3x + 2y = ? You forgot to put what this equals, but it does not matter.
3x + 6y = 9
9y = ?
When we add -3x and 3x the x's drop out.
do you need to multiply everything on one side of an equation if you are only multiplying a fractionating that's adding
Yes, we can multiply everything on one side of an equation if you are only multiplying a fractionating that's adding.
Multiplicative Property:
The multiplicative nature of the equation dictates that both sides of the equation can be multiplied or divided by the same nonzero fraction or Gebraic Equation without changing the solution.
if a, b, and c are any three fractions
if a = b and c ≠ 0
1. a × c = b × c
2. a ÷ c = b ÷ c
Multiplicative property for Fraction:
When multiplying two fractions, the numerator and denominator are multiplied separately. The first numerator is multiplied by his second numerator, and the first denominator is multiplied by his second denominator. Finally, reduce the fraction to its lowest term. A fraction has the smallest form if 1 is the only common divisor between the numerator and denominator.
Properties of Multiplying Fractions
1. Multiplying a non-zero fraction by 1 yields the exact fraction
Example: 38 × 1 = 38
2. Multiplying 0 by a non-zero fraction yields zero.
Example: 38 × 1 = 38
3. The product of a fraction and its reciprocal is always 1.
Example: 25×52 = 2×55×2 =1010 =1
(the reciprocal of 25 is 52)
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during the 2000 season, the home team won 138 of the 240 regular season national football league games. is this strong evidence of a home field advantage in professional football? test an appropriate hypothesis and state your conclusion. be sure the appropriate assumptions and conditions are satisfied before you proceed.
A) The 95% confidence interval is:
0.58 ± 0.062
B) At the 0.01 probability value, there is neither substantial evidence of a home-field advantage in professional football (they won and over half of the games).
Now, According to the question:
A) Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × [tex]\frac{\sqrt{pq} }{n}[/tex]
Where:
z = The z score corresponds to the amount of confidence.
p = sample proportion.
q = probability of failure
q = 1 - p
p = x/n
Where
n = the number of samples
x = the number of success
From the information given,
n = 240
x = 138
p = 138/240 = 0.58
q = 1 - 0.58 = 0.42
To determine the z score, The confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
Thus,
1 - 0.025 = 0.975
The z -score associated with the area just on z table approximately 1.96. Therefore, the z score with a 95% confidence level is 1.96.
As a result, the 95% confidence interval becomes
0.58 ± 1.96√(0.58)(0.42)/240
Confidence interval is
0.58 ± 0.062
B) Earning more than half of the games equates to winning 120 games or more.
p = 120/240 = 0.5
The hypothesis test will be
For the null hypothesis,
P ≥ 0.5
For the alternative hypothesis,
P < 0.5
Probability of success, p = 0.5
q = probability of failure = 1 - p
q = 1 - 0.5 = 0.5
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 138
n = number of samples = 240
P = 138/240 = 0.58
We need to find the values of the test statistic which will be the z score
z = (P - p)/√pq/n
z = (0.58 - 0.5)/√(0.5 × 0.5)/240 = 2.48
Remember that this is a two-tailed test. We would use the normal distribution table to calculate the probability potential of the property to the right of both the z score.
P value will be = 1 - 0.9934 = 0.0066
Since alpha, 0.01 > the p value, 0.0066, then we would reject the null hypothesis.
The given question is incomplete, The complete question is this:
__"During the 2000 season, the home team won 138 out of 240 regular season National Football League games. (15 points) a) Construct a 95% confidence interval for the winning proportion of the home team during this season. b) At the 0.01 significance level, is there strong evidence of a home field advantage (they win more than half of the games) in professional football? State hypotheses, calculate the test statistic and p-value, and make a conclusion in context"__
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The following set of ordered pairs, represents a power inverse variation. Find the value of r given that k=5. ( 1/2,20)(1,5)(2,5/4) : a. r=5 b. r=2 c. r=-5 d. r=2
The correct value of r is 2.
What is the power inverse variation?
Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.
The equation for a power inverse variation is y = kx^r,
where k is a constant, x is the independent variable, y is the dependent variable, and r is the power.
We have given the set of ordered pairs,
we can find the value of r by substituting in the known values of x and y and solving for r.
(1/2,20) => 20 = 5 * (1/2)^r => r = log(20)/log(1/2) = -2
So the answer is:
r = 2
Hence, the correct value of r is 2.
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her budget is still $50 a month. to find out how many gigabytes of data she could use if she chose this plan, she writes c(x)
The function that represents the total cost for the number of gigabytes is; C(x) = 50x
How to express linear equation word problems?Some of the steps to writing a system of linear equations from word problems are;
1) Understand the problem like the words used in stating the problem and what exactly you are trying to find.
2) Translate the problem to an equation by assigning a variable (or variables) to represent the unknown.
3) Carry out the plan and solve the problem.
We are told that her budget is $50 a month. Therefore this is like the rate for each gigabyte and if the number of gigabytes is denoted as x, then the function of the total cost is;
C(x) = 50x
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Coins are placed into a treasure chest, and each coin has a radius of 1.4 inches and a height of 0.0625 inches. If there are 230 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
0.38 in3
126.39 in3
353.88 in3
88.47 in3
Answer:
D. 88.47 in3
Step-by-step explanation:
The volume of a single coin would be the volume of a cylinder with a radius of 1.4 inches and a height of 0.0625 inches. The formula for the volume of a cylinder is V = πr^2h. So, V = 3.14 * (1.4^2) * 0.0625 = 0.38 in^3
Since there are 230 coins, the total volume of the coins would be 230* 0.38 = 87.40 in^3
So, the answer would be 87.40, which is closest to D. 88.47 in3
Answer: D: 88.47 in³
Step-by-step explanation:
So what you want to do is first find the individual volume of the coins. Use the volume formula: V = πr^2h
Take 1.4 and times it by itself
1.4 x 1.4 = 1.96
Now multiply 1.96 by 0.0625
1.96 x 0.0625 = 0.1225
And times 0.1225 by pi, or in this case, 3.14
0.1225 x 3.14 = 0.38465
Now you have found the individual volume of each coin. You are trying to find how much space all of the coins take up together. The question says that there is 230 coins in total. So times 0.38465 by 230 to find how much space all the coins take up.
0.38465 x 230 = 88.4695 in³
Now round it to the nearest hundredth: 88.47 in³
That is your answer.
Also I took the same test and I picked 88.47 inches cubed and got it right.
Proof:
Have a good day :)))
8th grade Mathematics
What is the solution to the system of equations below?
Y=2/5x-3 and x = -10
A. (-10, -7)
B. (-10, -1)
C. (-7, -10)
D. (-1, -10)
⚠️ WARNING ⚠️
Any SCAM answers like “well I don’t know” are immature and irritating , if you answer like that your “answer” will be reported!!!
Reporting results in a ban!!!
Thank you to those who are sincere have a great day :)
Answer:
A) ( -10, -7)
Step-by-step explanation:
x = -10 is a vertical line going through x = -10
No matter what y is, x will be -10
Plug -10 into the first equation to find the y value
y = 2/5(-10) - 3
y = -4 - 3
y = -7
for breakfast bob has three options: cereal, eggs or fruit. he hasto choose exactly two items out of the three available.(a) describe the sample space of this experiment
According to the concept of probability, the sample space for the experiment is explained below.
The term probability in math is called as the occurrence of a random event and the sample space is defined as a collection or a set of possible outcomes of a random experiment.
Here we have know that the same space of this experiment is the possible outcomes of selecting two out of the three breakfast.
Here let us consider that the sample space is B
And the the sample space is written as.
=> {(cereal and egg), (cereal and fruit), (fruit and egg), (fruit and cereal), (egg and fruit), (egg and cereal)}
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a bag contains:5 red marbles 6 blue marbles 3 green marbles 4 black marbles2 yellow marble a marble will be drawn from the bag and replaced 180 times. what is a reasonable prediction for the number of times a red or yellow marble will be drawn?
A reasonable prediction for the number of times a Red or Yellow Marble Draws = (7/20) x 180 = 126.
The total number of marbles in the bag is 20 (5 red, 6 blue, 3 green, 4 black, and 2 yellow). Therefore, the probability of drawing a red or yellow marble is 7/20. Applying this probability to the 180 times a marble is drawn and replaced, we can calculate that the number of times a red or yellow marble is likely to be drawn is 126 (7/20 x 180). This can be expressed as a formula as follows: Red or Yellow Marble Draws = (Number of Red and Yellow Marbles / Total Number of Marbles) x Number of Draws. In this case, Red or Yellow Marble Draws = (7/20) x 180 = 126.
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Suppose you are asked to find the amount of time ttt , in seconds, it takes for the turntable to reach its final rotational speed. Which of the following equations could you use to directly solve for the numerical value of ttt
An answer is- More information is needed before t can be found. So, option(D) is the correct answer.
Here initial rotation speed is given, the final rotation speed is given, and the asking for time( in a sec) is.
If we use,
A) θ=θ0+ω0t+(1/2)αt2
For this equation, we don't have any details about the value of angular displacement and angular acceleration, so it is not useful.
B) We use,
ω=ω0+αt
For this equation, we don't have any details about angular acceleration, so it is not useful.
C) We know that,
ω2=ω02+2α(θ−θ0)
In this equation, time is not included, hence it is not useful.
D) So, more information is needed.
Thus, option (D) is the correct answer.
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The complete question is:
Suppose you are asked to find the amount of time t, in seconds, it takes for the turntable to reach its final rotational speed. Which of the following equations could you use to directly solve for the numerical value of t?
A) θ=θ0+ω0t+(1/2)αt2
B) ω=ω0+αt
C) ω2=ω02+2α(θ−θ0)
D) More information is needed before t can be found.
Hannah has two bags of sweets.
In the first bag there are 5 red sweets and 7 green sweets.
In the second bag there are 7 red sweets and 4 green sweets.
Harmah takes at random a sweet from the first bag.
She then takes at random a sweet from the second bag.
(a) Complete the probability tree diagram.
first bag
red
green
11
second bag
red
(b) Work out the probability that Hannah takes two green sweets.
green
. red.
green
(2)
28
The size of each interior angle of an
Work out how many sides the poly
Answer:
(a) Refer below for the Probability tree diagram
(b) [tex]\frac{7}{33}[/tex]
Step-by-step explanation:
(a) Probability tree diagram:
First bag: Second bag
Red: [tex]\frac{7}{7 + 4}[/tex] = [tex]\frac{7}{11}[/tex]
Red: [tex]\frac{5}{12}[/tex]
Green:[tex]\frac{4}{7 + 4}[/tex] = [tex]\frac{4}{11}[/tex]
Red: [tex]\frac{7}{11}[/tex]
Green [tex]\frac{7}{12}[/tex]
Green: [tex]\frac{4}{11}[/tex]
(b) Probability that Hannah takes two green sweets:
Green sweet from first bag AND green sweet from second bag
= [tex](\frac{7}{12}).(\frac{4}{11} )[/tex]
= [tex](\frac{28}{132})[/tex]
Divide the numerator and denominator by the highest common factor (i.e 4)
= [tex]\frac{7}{33}[/tex]
Find the value of each card and put them in order, from lowest to highest.
2-7+6
1 +4-6
4-8 +2
6-3-7
Answer:
Hope This Helps <3
Step-by-step explanation:
4-8 +2 = -11
6-3-7 = -4
1 +4-6 = -1
2-7+6 = 1
Find the slope of the line graphed below.
Answer:
Step-by-step explanation:
Hello, I am the same guy that told you that your previous question had no image.
Ok, so slope formula is m = (y₂ - y₁)/(x₂ - x₁)
Two coordinates on the given line is (-2 , 1) and (3, 5)
Just substitute the values there.
m = (5 - 1)/(3 + 2)
= 4/5
slope/m = 4/5
Pls mark as brainliest. I really need for no apparent reason. Cheers
How to tell if a system of 3 equations has no solution or infinitely many?
Answer:A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.
Step-by-step explanation:
Evaluate the line integral, whereCis the given curve.∫ xyds,C:x=t^2 ,y=2t,0≤t≤2C
According to the given information the line integral is [tex]=\frac{8}{15}(1+125.\sqrt{10})[/tex].
What distinguishes a line integral from a definite integral?Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.
[tex]\int_C\hairsp xyds,C:x=t^2,y=2t,0\le t\le3\\x^\prime=2t\\y^\prime=2\\ds=\sqrt{\left(x^\prime\right)^2+\left(y^\prime\right)^2}\\\sqrt{{4\left(t\right)}^2+4}\\\int C\ xy\ ds\ =\int_0^3\hairspt^2\cdot2t\cdot2\cdot\sqrt{1+t^2}\mathrm{\ }dt\\t=\ \ tan\ \theta\\dt=(1+{tan}^2\theta)d\theta=({Sec}^2\theta)d\theta\ \\{=\int}_0^3\hairsp4t^3\sqrt{1+t^2}\mathrm{\ }dt\\=\frac{8}{15}(1+125.\sqrt{10})[/tex]
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Find the slope of the line that passes through these two points
Step-by-step explanation:
your teacher gave you even the formula. so, what is still not clear ?
in regular words, the slope of a line is the ratio
y coordinate difference / x coordinate difference
when going from one point on the line to another.
so, we have here (-2, 1) and (3, 2).
x changes by +5 (from -2 to 3).
y changes by +1 (from 1 to 2).
so, the slope is +1/+5 = 1/5
Mrs. Ramirez is planning a family reunion and deciding where to buy food and drinks. She considers the information below. She expects 96 family members to attend. How much would it cost to buy 96 hotdogs purchased from Value Market? Show your work.
b) How much would 96 hotdogs cost from Sammy's Bulk Store? Show your work. Which store offers the better buy for bottled water? Explain your reasoning HELP ME PLEASE<3
a) The cost for 96 hotdogs from Value Market = $94.04.
b) The cost for 96 hotdogs from Sammy's Bulk Store = $75.84.
How did we get the values?a) The cost for 96 hotdogs from Value Market would be $96 x $0.99/hotdog = $94.04.
b) The cost for 96 hotdogs from Sammy's Bulk Store would be $96 x $0.79/hotdog = $75.84.
For bottled water, Sammy's Bulk Store offers the better buy, with $0.69/bottle, compared to Value Market's $0.99/bottle. The reasoning is that Sammy's Bulk Store has a lower price per bottle of water.
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Helpppp - due tomorrow
Answer:
9.68
Step-by-step explanation:
x*(x-4)=55; x approximately equals 9.68
I need the answer to this problem asap
Answer: well you need to divid
Step-by-step explanation: well by dividing you get a answer so like you compare if the answer you got is for all of them and if it is not you say it is not proportional
Volume: 655
4. a square pyramid has a base that
measures 8 inches on each side. the height
of the pyramid is 11.5 inches. determine the
volume of the pyramid.
y
