Answer:
Similarities: All the trigonometric functions are periodic functions. All these trigonometric function values can be found by using special right triangles from the unit circle. Diffferences: The tangent has different domain and range values from sine and cosine. The tangent function is not a continuous function, unlike sine and cosine.
Step-by-step explanation:
The similarities and differences between the sine, cosine, and tangent ratios are given.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The sine, cosine, and tangent are three trigonometric ratios used in geometry to relate the angles of a right triangle to the lengths of its sides.
Similarities:
All three ratios involve comparing two sides of a right triangle to each other.
They are all functions of an angle and are dependent on the measure of the angle and not the size of the triangle.
They are all defined as ratios of two sides of a right triangle, and the values of these ratios depend on the angle in question.
Differences:
The sine and cosine ratios are periodic functions with a period of 2π, while the tangent ratio is not periodic, and its graph has vertical asymptotes.
The sine and cosine ratios are always between -1 and 1, while the tangent ratio can take any value, positive or negative.
The cosine of an angle is equal to the sine of its complement, while the tangent of an angle is equal to the sine of the angle divided by the cosine of the angle.
Hence, the similarities and differences between the sine, cosine, and tangent ratios are given.
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If angle a measures 67 degrees ,how much does angle b measure ?
Answer:
∠ b = 23°
Step-by-step explanation:
Complementary angles sum to 90°, thus
∠ a + ∠ b = 90°, that is
67° + ∠ b = 90° ( subtract 67° from both sides )
∠ b = 23°
Simplify this power raised to a power: (54)4 1. Expand using four factors of 54: 54 ∙ 54 ∙ 54 ∙ 54 2. Apply the product of powers rule: 54+ 4+ 4+ 4 3. Simplify: 5x What is the value of x in the simplified power? x =
Answer:
x=16
Step-by-step explanation:
you add all the 4s from the second step and get a product of 16.
The question simplifies a power raised to a power, (5^4)^4. Whereby, the rule is to multiply the exponents. Therefore, x in our simplified expression 5^x, equals 16.
Explanation:Let's simplify this (power raised to a power): (54)4.
First, we recognize it as a case of exponents raised to another exponent, where the rule is: if you have an exponent raised to another exponent, you should multiply the exponents. In this case, it's 4 * 4.We multiply the exponents: 4 * 4 = 16So, the simplified form is: 516
Therefore, the value of x in the simplified power is 16.
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Simplify the rational expression. State any restrictions on the variable.
Answer:
Step-by-step explanation:
The value of t must not be one that makes the denominator zero, hence must not be 8.
***EASY***** HELP!!!!!! i have been crying over this problem for an hour. please help
Answer:
UT = 15
Step-by-step explanation:
Its okay this was a hard one to know. since its a 90 degrees angle you can use the Pythagorean theorem.
A^2 + B^2 =C^2
but in this case they give you c and as for b
so it be C^2 - A^2 = B^2
17^2 - 8^2 = B^2
289 - 64 = B^2
225 = B^2
now you square both sides getting B = [tex]\sqrt{225}[/tex]
A baseball player had 4 hits in 8 games. At this rate, how many hits will the baseball player have in the next 28
Answer:
The answer is 14 hits!
Step-by-step explanation:
This is because of dividing 28 by 8: so you get 3.5. Use the 3.5 and times it by the amount of hits: which is 4. Then BOOM, you got yourself 14 hits!
Three moons are in the same circular orbit around a planet. The moons are ach 125,000 km from the surface of the planet, llocated at points a, b, and c. The planet is 15,000 km in diameter and angle abc= 90 degrees. How far is point a from point c?
Answer:
AC = 215,000 km
Step-by-step explanation:
I've attached a diagram that depicts this 3 moons and the planet in regards to their positions.
We need to find the distance AC as shown in the image.
We are given that AM and NC = 100,000 km
And diameter; MN = 15,000km
Thus,AC = MN + NC
AC = 15000 + 100,000 + 100000 = 215,000 km
A família Oliveira consiste no pai, na mãe e em alguns filhos. A idade média da família é de 18 anos. Sem contar com o pai, que tem 38 anos, a idade média familiar diminui para 14 anos. Quantos filhos tem a família Oliveira? a) 2 b) 3 c) 4 d) 5 e) 6
Answer: e) 6
Step-by-step explanation:
Let x be mother + children = 18
Father's age = 38
Average age of the family = 14
38 + 18x /( x + 1 )= 14
Opening the bracket
38 + 18x = 14x + 14
Collecting like terms
24 = 4x
x = 6
no of children in the family is 6.
I need help asap :&/$/$/
Answer:
A
Step-by-step explanation:
The equation must equal 50 and the 4 should be added not multiplied
Solve each equation -3(n+5)=27
Answer:
n = − 14
Step-by-step explanation:
-3(n+5)=27
-(3n+3·5)=27
-(3n+15)=27
Please mark me brainliset if this helped (I need it)
Answer: n=4
Step-by-step explanation:
Lou has a solid clay brick in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches. If the clay weighs 1.055 oz/in^3, how much does Lou's brick weigh, to the nearest ounce?
Answer:
The weight of the brick is 60 ounce to the nearest ounce
Step-by-step explanation:
In this question, we are asked to calculate the weigh of Lou’s brick given the dimensions of the shape of the brick and the weight of the clay.
To answer this question quite aptly, we need to know exactly the volume of the rectangular prism given the dimensions we have in the question.
To calculate this volume , we simply use the measurements we have to get it.
mathematically the volume of a rectangular prism is simply V = w * h * l
where w , h and l are width, height and length respectively.
now let’s calculate!
V = 3.5 * 2.25 * 8 = 63 inches^3
Now we need to know what the brick weigh in ounce. We already have the weight of the clay. now this is equal to the volume of the brick divided by the weight of the clay.
Mathematically this is = 63/1.055 = 59.72 ounce which is 60 ounce to the nearest ounce
Answer:
60 ounce
Step-by-step explanations:
The volume of a rectangular prism is length multiplied by width and the height.
And if the width is 3.5 inches
Length is 8 inches
Height of 2.25 inches
V = 2.25 × 8 × 3.5
= 63 in³
And since the clay weighs 1.055 oz/in³,the total weight of the clay brick will be derived by dividing the volume of the brick by its weight per in³
63/1.055
= 59.7 and to the nearest whole number = 60 ounce
What is the change in elevation from 8,500 m to 3,400 m?
Should be 5,100 from the information that is given.
Answer: 5,100 meters
A weather forecast during September says that it will likely rain two out of the next five days. If the weather does not change, how many days will it likely rain in the month of September (30 days)?
A. 2/30
B. 5/30
C. 12/30
D. 75/30
Answer:
C. 12/30
Step-by-step explanation: 2/5 for every 5 days and there are 30 days in September so there is already 2/5 so 5 days are already in place so add 2 to the 2/5 and 5 to the 2/5 on their corresponding numbers until the five reaches thirty then the 2 will reach 12. Happy to Help.
A circle with area \blue{81\pi}81πstart color #6495ed, 81, pi, end color #6495ed has a sector with a central angle of \purple{120^\circ}120 ∘ start color #9d38bd, 120, degrees, end color #9d38bd. What is the area of the sector?
Answer:
27π
Step-by-step explanation:
trust me, it's right lol
at a fall festival,the student council sold 149 drinks and collected $223.50. The total amount collected is proportional to the number of drinks sold. What is the constant of proportionality in terms of dollars per drink ?
Answer:
1 drink/$1.50
Step-by-step explanation:
you have to find the cost of each drink by dividing the money raised by the number of drinks sold
223.50/149=
1.50
Answer:
Step-by-step explanation:
Find the unit cost:
$223.50
------------------ = $1.50/drink
149 drinks
Then y = revenue from sales of drinks = ($1.50/drink)(number of drinks).
The constant of proportionality is $1.50/drink.
Would you rather buy 18 eggs at this price 2/$8.00 or 18 eggs at this price? $.97 buy 2 get one free
Answer:
you should by 18 eggs at the second price.
Step-by-step explanation:
my reason being is that if you buy it for the second price you will get two for the price of one which will be $0.97cents.
Answer:
Answer: you should by 18 eggs at the second price. Step-by-step explanation: my reason being is that if you buy it for the second price you will get two for the price of one which will be $0.97cents.
Step-by-step explanation:
Answer: you should by 18 eggs at the second price. Step-by-step explanation: my reason being is that if you buy it for the second price you will get two for the price of one which will be $0.97cents.
What's 0.11 as a fraction?
Answer:
11/100
Step-by-step explanation:
Translate this sentence into an equation.
72 is the sum of 20 and Chau's age.
Use the variable c to represent Chau's age.
Answer:
c+20=72
Step-by-step explanation:
If KM is drawn on this quadrilateral, what will be its length?
18
45M
16 units
18 units
40 units
45 units
The length of KM on the quadrilateral would be 18 units .
Using the following Information from the quadrilateral;
The sides JM and KL are parallel , This means that :
KL||JM.The length of the diagonals of the quadrilateral would be the same .
JL = KM (diagonals of Isosceles trapezoid are equal)From the question ;
JL = 18
JL = KM = 18 (diagonals of isosceles trapezoid are equal)Then ;
KM = 18
Hence, the length of KM would be ; 18 units .
5
y=2x+5y, equals, 2, x, plus, 5
Complete the missing value in the solution to the equation.
Answer:
(2,9)
Step-by-step explanation:
It's on khan
The missing value is 9 in the solution to the given equation y = 2x + 5.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given in the question
y = 2x + 5 ....(i)
The one value is 2 in the solution to the equation
To determine the missing value, we have to substitute the value of x = 2 in the given equation.
As per the question, we have
⇒ y = 2x + 5
⇒ y = 2(2) + 5
Apply the multiplication operation,
⇒ y = 4 + 5
Apply the addition operation,
⇒ y = 9
Therefore, the missing value is 9 in the solution to the given equation.
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The question seems to be incomplete the correct question would be
y = 2x + 5 Complete the missing value in the solution to the equation. (2, [] )
Suppose 20% of the population are 65 or over, 26% of those 65 or over have loans, and 53% of those under 65 have loans. Find the probabilities that a person fits into the following categories. (a) 65 or over and has a loan (b) Has a loan (c) Are the events that a person is 65 or over and that the person has a loan independent? Explain.
Answer:
(a)The probability that a person 65 or over and has a loan is 0.052.
(b)The probability that a person 65 or over and has a loan is 0.476
(c) The probability that a person is 65 or over and has a loan independent is 0.0952
Step-by-step explanation:
Conditional probability:
Let A and B any two event is connected to a given random experiment E. The conditional probability of the event A on the hypothesis that the event B is occurred, denoted by P(A|B), is defined as,
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
So, P(A∩B) = P(B).P(A|B)
Given that,
The age of 20% of population are 65 years or over.
26% of those whose age 65 years or more have loans.
53% of those whose age under 65 years have loans.
E= the person is 65 or more.
F= the person has loan.
P(E)= 20%=0.2
P(F|E)=26%=0.26
P(F|E')=53%=0.53
So,
P(E')=1-0.2=0.8
P(F'|E)= 1-0.26=0.74
P(F'|E')= 1-0.53=0.47
(a)
The probability that a person 65 or over and has a loan is
=P(E∩F)
=P(F|E).P(E)
=0.26×0.2
=0.052
(b)
A person who has a loan either 65 or more , or under 65.
P(F)= P(F∩E)+P(F∩E')
=P(F∩E)+P(E').P(F|E')
= 0.052+ (0.8).(0.53)
=0.476
(c)
Independent event:
If A and B are two independent event,
Then,P(A∩B)=P(A).P(B)
The probability that a person is 65 or over and has a loan independent is
=P(E∩F)
=P(E).P(F)
=(0.2)×(0.476)
=0.0952
The probability that a person is 65 or over and has a loan is 0.052, the probability that a person has a loan is 0.476, and the probability that a person is 65 or over and that the person has a loan independent is 0.0952.
Given :
Suppose 20% of the population are 65 or over, 26% of those 65 or over have loans, and 53% of those under 65 have loans.
Let A represent the person who is 65 or more and B represents the person who has a loan.
If (P(A) = 20% = 0.2) then (P(A') = 1 - 0.2 = 0.8)
If (P(B|A) = 26% = 0.26) then (P(B'|A) = 1 - 0.26 = 0.74)
If (P(B|A') = 53% = 0.53) then (P(B'|A') = 1 - 0.53 = 0.47)
a) The probability that a person is 65 or over and has a loan is:
[tex]\rm = P(A\cap B)[/tex]
[tex]\rm = P(B|A)\times P(A)[/tex]
[tex]=0.26\times 0.2[/tex]
= 0.052
b) The probability that a person has a loan is:
[tex]\rm P(B) = P(A\cap B)+P(B\cap A')[/tex]
[tex]\rm = P(B \cap A)+P(A')\times P(B|A')[/tex]
[tex]=0.52+0.8\times 0.53[/tex]
= 0.476
c) The probability that a person is 65 or over and that the person has a loan independent is:
[tex]= \rm P(A\cap B)[/tex]
= P(A).P(B)
= (0.2)[tex]\times[/tex](0.476)
= 0.0952
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The blueprints of a house show that a wall is 3.5 inches long. If the blueprints have a map scale of 1.5 inches = 3 feet, how long is the actual wall?
Step-by-step explanation:
Given the blueprints of a house show that a wall is 3.5 inches long.
Length of the wall = 3.5 inches
Mpa scale used in blue print is,
1.5 inches = 3 feet
Such that 1 inch = 2 feet
Length of the wall = 3.5 inches = 3.5 * 2 = 7 feet
The length of the actual wall = 7 feet
In ΔCDE, the measure of ∠E=90°, the measure of ∠D=38°, and DE = 12 feet. Find the length of CD to the nearest tenth of a foot.
Given:
Given that the triangle CDE is a right triangle.
The measure of ∠E is 90° and ∠D is 38°
The length of DE is 12 feet.
We need to determine the length of CD.
Length of CD:
The length of CD can be determined using the trigonometric ratio.
Thus, we have;
[tex]cos \ \theta=\frac{adj}{hyp}[/tex]
where [tex]\theta=D[/tex] and the side adjacent to angle D is ED and hypotenuse is CD.
Substituting these values, we get;
[tex]cos \ D=\frac{ED}{CD}[/tex]
where ∠D = 38°, ED = 12 feet.
Substituting, we get;
[tex]cos \ 38^{\circ}=\frac{12}{CD}[/tex]
Simplifying, we have;
[tex]CD=\frac{12}{cos \ 38^{\circ}}[/tex]
[tex]CD=\frac{12}{0.788}[/tex]
Dividing, we get;
[tex]CD=15.2[/tex]
Thus, the length of CD is 15.2 feet.
Answer:
51.6
Step-by-step explanation:
its because you have to use cos toh and all of the calculator functions
Given a linear function y =23x+2, which two points make the line?
(0, -2) and (3, 4)
(0, 2) and (3, 4)
(0, 0) and (2, 3)
(2, 3) and (0, 0)
Answer:
(0, 2) and (3, 4)
Step-by-step explanation:
The equation is in slope-intercept form:
y = mx +b . . . . . a line with slope m and y-intercept b
So, you know immediately that the y-intercept is (0, 2). This matches only one answer choice.
(0, 2) and (3, 4)
3 friends split the cost of renting a boat. Each person rented a life preserver. The cost of the boat was $120. The total cost for the boat and life preservers was $135. Write and solve an equation to find the cost of renting a life preserver?
Answer:
boat rent: $40/per person
Life preserver: $5/per person
Step-by-step explanation:
120 ÷ 3 = 40
135 ÷ 3 = 45
45 - 40 = 5
Suppose that 35% of all voters voted for a recall. Find the mean of the sampling distribution of the proportion of the 3150 people sampled in an exit poll who voted for the recall.
Answer:
0.35 is the mean of the sampling distribution of the proportion.
Step-by-step explanation:
We are given the following in the question:
Percentage of voters who voted for recall = 35%
[tex]p = 35\% = 0.35[/tex]
Sample size, n = 3150
We have to find the mean of the sampling distribution.
Formula for mean of sampling distribution:
[tex]\mu = p[/tex]
Putting values, we get,
[tex]\mu = 0.35[/tex]
Thus, 0.35 is the mean of the sampling distribution of people sampled in an exit poll who voted for the recall.
What is the answer to this question
The relationship between the distance run and the time for Amy can be represented by the equation Y equals 17.45X, where she ran Y meters in X seconds. which two equations could be used to represent the relationship for Brandon and Ruben
Question;
Assumption:
Let us assume Brandon's running speed is = 18.30 and
Ruben's running speed is = 16.50 and
Answer:
The two equations that can represent the relationship between the meters and second for Brandon and Ruben are;
Brandon → Y₁ = 18.3·X₁ and
Ruben → Y₂ = 16.5·X₂
Step-by-step explanation:
The equation is of the form
Y = 17.45·X
That is Amy ran Y meters in X seconds
Therefore we have
[tex]17.45 = \frac{Y}{X}[/tex] or the value 17.45 is the running speed of Amy
Therefore, where the running speed of Brandon is 18.30 and the running speed of Ruben is 16.50 we have
Y meters ran by Brandon in X seconds given by
Y₁ = 18.3·X₁ and
For Ruben we have Y meters ran in X seconds given by
Y₂ = 16.5·X₂.
Answer:
Brandon : Y = BX, where B is the speed (positive integer) and X is the time in seconds.
Ruben : Y = RX, where R is the speed (positive integer) and X is the time in seconds.
Step-by-step explanation:
For Amy, the relationship between the distance run and the time taken is represented by the equation Y equals 17.45X, where she ran Y meters in X seconds.
Therefore we have,
Y = 17.45X
Y/X = 17.45 m/s, where m/s is meter per second.
Let us assume that the speed for Brandon is represented by B and that of Ruben is represented by R.
For Brandon, we obtain Y/X = B m/s
Y = BX
For Ruben, we obtain Y/X = R m/s
Y = RX
High School Mathematics 5+3 pts
The relationship between the distance run and the time for Amy can be represented by the equation Y equals 17.45X, where she ran Y meters in X seconds.
The monthly salary of workers in the public works department is $1,500, $3,000, $3,500, $3,500, $4,000, $4,500, $5,000, $6,000, $6,500, $6,500, and $9,000. Explain the impact of the outlier(s) on the measure of central tendency for this data set.
1.There is a minimal increase to the mean because there is a low outlier and a high outlier in the data set.
2.There is a minimal decrease to the mean because there is a low outlier and a high outlier in the data set.
3.There is a large increase to the mean because of the $9,000 outlier.
4.There is a large decrease to the mean because of the $1,500 outlier.
Answer:
(B) median because there is an outlier
Step-by-step explanation:
The given data is as follows:
{1, 4, 9, 4, 10, 8, 42}
We can see from the given data that 42 is a data point which differ greatly from the other data points, and from the definition of OUTLIER that is a data point that differ greatly from the trend expressed by the other values in the data set.
Thus, 42 is an outlier.
Now, We have to find the center for the given data set, thus we will use the median as the definition of median states that median is the middle value of the data set.
Therefore, the best measure to find the center of the given data will be median because there is an outlier 42 present in it.
Thus, option B is correct.
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Step-by-step explanation:
You are comparing phone plans. Q company charges a one time fee of $25 and then $3 per month. W company charges a one time fee of $60 and then $1 per month. How many months until the two companies have the same cost
Answer:
17 1/2 months or rounded up to 18
Step-by-step explanation:
so first you need to set up an equation,
lets do company Q first..
because the monthly fee is 3 bucks thats gonna be the number that goes hand in hand with x so lets put that down
Q - 3x
now we have to add our one time fee of 25 dollars
Q - 3x + 25 .. bam thats our first equation
lets do the same thing for our next company
W - x + 60
( because the fee is one dollar, theres no reason to put 1x, its not mathematically correct, so we just leave it as x )
so now we have to set up the equation together, and because we are trying to find when the two will meet and have an EQUAL cost we make them equal to each other
so
3x + 25 = x + 60
if you solve it...
2x + 25 = 60
2x + 35
x = 17.5
What percent of Coach passengers did not check bags
Answer:B is the Answer
Step-by-step explanation: