a. Sin (θ) = √35 / 6
b. Tan (θ) = Tan θ = √35
c. Sec (θ) = 6
d. Csc (90° -θ) = 6
Explanations:Note that according to trigonometric identities:
cos θ = Adjacent / Hypotenuse
From the question:
cos θ = 1/6
Comparing this with the given trigonometric identity:
Adjacent, A = 1
Hypotenuse, H = 6
Let us look for the opposite, O
Using the pythagora's theorem
H² = A² + O²
6² = 1² + O²
36 = 1 + O²
36 - 1 = O²
O² = 35
O = √35
Therefore, Opposite = √35
a) Sin θ = Opposite / Hypotenuse
Sin θ = √35 / 6
b) Tan θ = Opposite / Adjacent
Tan θ = √35 / 1
Tan θ = √35
c) Sec θ = 1 / cos θ
Sec θ = 1 ÷ 1/6
Sec θ = 1 x 6
Sec θ = 6
d) Csc ( 90 - θ) = Sec θ
Since Sec θ = 6
Csc ( 90 - θ) = 6
The first aircraft has 65 more seats than the second aircraft. The third aircraft has 41 fewer seat than the second aircraft. If their total number of seats is 402, find the number of seats for each aircraft.
Solution:
Let A be the first aircraft
Let B be the second aircraft
Let C be the third aircraft
Here is the information that is given in the question:
The first aircraft has 65 more seats than the second aircraft:
A = B + 65
The third aircraft has 41 fewer seats than the second aircraft
C = B - 41
their total number of seats is 402
A + B + C = 402
Now substitute the values in the 1st and 2nd equations into the 3rd.
(B+65) + B + (B-41) = 402
this is equivalent to:
3B + (65-41) = 402
this is equivalent to:
3B + 24 = 402
this is equivalent to:
3B = 402 - 24 = 378
solving for B, we get:
[tex]B\text{ = }\frac{378}{3}=126[/tex]We can conclude that the correct answer is:
first aircraft A:
A = B + 65 = 126 + 65 = 191
that is:
A = 191
second aircraft:
B = 126
third aircraft:
C = B - 41 = 126 - 41 = 85
that is:
C = 85
Whats 5 and 6/4 ×8 and 9/6
Given that 5 6/4 x 8 9/6
Firstly, we need to convert the mixed fraction into improper fractions
[tex]undefined[/tex]How many pounds of N are in 2 tons of manure (4.8% N)?
Answer: 192 lbs
Total weight of manure = 2 tons
Step1: we need to converts tons to pounds
1 ton = 2000 lb
2 tons = x lb
Cross multiply
2 x 2000 = 1 * x
x = 2 x 2000
x = 4000 lbs
Therefore, 2 ton of manure = 4000 lbs of manure
We have 4.8% of N in the manure
Pounds of N = 4.8/100 x 4000
Pounds of N = 0.048 x 4000
Pounds of N = 192 lbs
The pounds of N in 2 tons of manure is 192 lbs
A local Pet Shelter has 4 orange cats and 7 black cats. What is probability of selecting a black cat? Please enter your answer as a fraction.
The Solution:
Given:
We are asked to find the probability of selecting a black cat.
By formula,
[tex]Probability=\frac{number\text{ of required outcomes}}{total\text{ possible outcomes}}[/tex]Thus,
[tex]P(B)=\frac{number\text{ of black cats}}{total\text{ number of cats}}=\frac{7}{11}[/tex]Therefore, the correct answer is 7/11
5. Write the division problem as a
multiplication equation with a
missing factor. The find the quotient.
2.1 /0.7
The quotient in this division problem is 3,4.
What is division problem?
There are three main parts to a division problem that are -the dividend, the divisor, and the quotient. The dividend is the number that will be the divided. The division is the number of (people )that the the number is being divided by among And The quotient is the answer.
a division is a process of a splitting a specific of amount into the equal parts.
Sol-
The formula is -
a/b=?
b×?=a
We can write a division statement as a multiplication statment
12/4=3
4×3=12
Thus
The quotients in this division problem are 3 and 4.
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1/6 of a number r decreased by 24 what is the algebraic expression
Explain how to undo pemdas with this equation and find answer
Given that Sarah spent half of her weekly allowance.
She earns $4.70 for washing dogs.
The final amount is $ 13.50.
Let x be the weekly allowance.
She spent half of her allowance so she has half of the allowance.
[tex]\frac{x}{2}[/tex]She earns $ 4.70, add this to her half of the allowance.
[tex]\frac{x}{2}+4.70[/tex]This is equal to 13.50.
[tex]\frac{x}{2}+4.70=13.50[/tex]Subtracting 4.70 from both sides, we get
[tex]\frac{x}{2}+4.70-4.70=13.50-4.70[/tex][tex]\frac{x}{2}=8.80[/tex]Multiplying 2 on both sides, we get
[tex]\frac{x}{2}\times2=8.80\times2[/tex][tex]x=17.60[/tex]Hence Sarah's weekly allowance is $ 17.60.
There are eight turtles 15 fish and 17 pelicans what percent of the animals are pelicans
The number of animals are given as;
[tex]\begin{gathered} \text{Turtles}=8 \\ \text{Fish}=15 \\ \text{Pelicans}=17 \\ \text{Total animals}=40 \end{gathered}[/tex]The percentage that are pelicans would be calculated as follows;
[tex]\begin{gathered} \text{Percentage Pelicans}=\frac{17}{40}\times\frac{100}{1} \\ \text{Percentage Pelicans}=\frac{1700}{40} \\ P\text{ercentage Pelicans}=42.5\text{ } \end{gathered}[/tex]ANSWER:
The percentage of the animals that are Pelicans is 42.5%
Write the equation of the function shown below. Identify domain and range.
The function can be split in 2 straight lines: the first one from x = 2 to the left, and the other one from the same point to the right.
Now, a straight line equation is of the form
[tex]ax+m[/tex]Where a is the slope and m is the y-intercept.
"Left" line:
- m (y-intercept):
To find it we need to see where the line cross (intercepts) the y-axis. From the figure we can see that m = -2.
- a (slope):
To calculate the slope, we can use the following equation:
[tex]a=\frac{\Delta y}{\Delta x}[/tex]Where, chossing 2 points in the line, we have:
[tex]\begin{gathered} \Delta y=how\text{ much do we move up or down between the 2 points} \\ \Delta x=\text{ how much do we move to the right betw}en\text{ the 2 points} \end{gathered}[/tex]Look that for x we have to move to the right. Let's see a drawing:
In our case, we can take the points (0, -2) and (2, 4), so, we have:
[tex]a=\frac{\Delta y}{\Delta x}=\frac{4-(-2)}{2-0}=\frac{6}{2}=3[/tex]So, we have the equation for the "left" line:
[tex]3x-2[/tex]-"Right" line:
- m (y-intercept):
In this case we can not see where the line cross (intercepts) the y-axis. Let's leave this for latter.
- a (slope):
As we did before, we can pick to points on the line, like (3, 1) and (2, 4).
[tex]a=\frac{\Delta y}{\Delta x}=\frac{1-4}{3-2}=\frac{-3}{1}=-3[/tex]- m (y-intercept) continues:
We now know that the equation for this line is:
[tex]-3x+m[/tex]To find m, we can pick one single point and solve for that variable. For example, taking the point (2,4), we have:
[tex]\begin{gathered} y=ax+m \\ y=-3x+m \\ 4=-3\cdot(2)+m \\ 4=-6+m \\ 4+6=m \\ 10=m \end{gathered}[/tex]And so, for the right line, we have:
[tex]-3x+10[/tex]Finally, the equation of the function can be written as:
[tex]f(x)=\begin{cases}3x-2\text{ if x }\leq\text{ 2} \\ -3x+10\text{ if x }\ge\text{ 2}\end{cases}[/tex]Now, the domain of the function is the set of points (or numbers) for which the function has values. The set of departure. In this case, all the numbers can be "trasnformed" or mapped with this function, so the domain is all the numbers, the set of real numbers, R:
[tex]\begin{gathered} -\inftyLastly, the range of the function is the complete set of all possible resulting values after aplying the function. We can see that the function can takes, as maximum, a value of 4, then the range is:[tex]\begin{gathered} (\infty;\text{ 4}\rbrack \\ or \\ y\leq4 \end{gathered}[/tex]Between which steps does Morgan use the subtraction property of equality to justify her work?
Morgan uses the subtraction property of equality in step 5.
What is the subtraction property of equality?The subtraction property of equality describes the balancing of an equation by subtracting the same value on both sides of the equality.
There is also the addition property of equality which states adding the same number to both sides of the equality also balances an equation.
Given Morgan's work Step 1 - 6(x+5) = 25.
Step 2 - 6(x) + 6(5) = 25 . (Distributive property).
Step 3 - 6x + 30 = 25.
Step 4 - 6x + 30 - 30 = 25 - 30 (Subtraction property of equality)
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david borrowed $4 from his mother each of the last tree months how much money does he owe his mother?
Answer:
12$
Step-by-step explanation:
He borrowed 4$ for three months.
4 x 3 = 12.
Answer = 12.
Hope this helps!
(Brainliest would mean a lot to me, thanks!)
Let f(-1)=16 and f(5) = -8Write the equation of the line in slope intercept form that passes throughthese two points
going to send u a pic of the q
we have the phrase
fifteen occupant or less
[tex]\begin{gathered} n\leq15 \\ n\ge0 \end{gathered}[/tex]Remember that the occupants can not be negative numbers
so
n=0,1,2,3,.....,15we have
seventy stadiums or more
the algebraic expression is
[tex]n\ge70[/tex]so
n=70,71,72,73,...
option Abecause the number of stadiums must be a whole number be a"How can an understanding of thenumber properties help you to solveequations that represent real-worldsituations?"
Undersatanding number properties helps you to solve equation because we can transfom ans simplify any equation in a way we just have to add or rest numbers. for example when you go shopping and there is a sale or a promotion, knowing this properties would help you to get the best price.
=MATHEMATICAL READINESSSummation of indexed dataThe following is a list of 14 measurements.38. -82. 19. 84. -37.93.-31, -73, -50.-65.-31. -85, -48Suppose that these 14 measurements are respectively laSum of Xi/ 50 with i going from 1 to 14Round your answer to at least two decimal places.
In order to calculate the sum we need to iterate over the "xi" variable going from 1 to 14 and adding all the data.
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop=1}\frac{x_i}{50}\text{ = }\frac{38\text{ - 82}+19+84-37.93-31-73-50-65-31-85-48}{50} \\ \sum ^{\infty}_{n\mathop{=}1}\frac{x_i}{50}\text{ = }\frac{-361.93}{50}\text{ = -7}.2386 \end{gathered}[/tex]The answer is approximately -7.24.
a cooler at picnic contain
we know that
the total cans are 100
number of cans of root beer=24
number of cans of orange soda=12
number of cans of cola=16
therefore
the probability is equal to
P=(24+12+16)/100
P=52/100
P=0.52 or P=52%
as fraction is 52/100=26/50=13/25
answer is 13/256. A grocery store sells bags of oranges in two different sizes.
The 3-pound bags of oranges cost $4.
The 8-pound bags of oranges for $9.
Which oranges cost less per pound? Explain or show your reasoning.
(From Unit 2, Lesson 10.).
Help! Help! 9261 divided by 57
162.4736842 is 9261 divided by 57
The rectangular floor of a classroom is 36 feet in length and 30 feet in width. A scale drawing of the floor has a length of 12 inches. What is the area, in square inches, of the floor in the scale drawing?
Answer:
120 square inches
Step-by-step explanation:
L = 36 feet
W = 30 feet
Scale:
l = 12 inches (1 foot)
w = 10 inches because 30/36 = 10/12..
10x12 inches = 120 square inches
3z - 8xyz + 4x^2y^2z please solve this
Answer:
z(3-8xy+4x^2y^2)
1. Brian's math test scorés: 86, 90, 93, 85, 79, 92, 20, 84Mean:Median:
Answer:
[tex]\begin{gathered} \text{ Mean=78.625} \\ \text{Median}=84 \end{gathered}[/tex]Step-by-step explanation:
The mean is the sum of all the values in a set of data, divided by the number of values on the list.
Hence, the mean of Brian's math test scores:
[tex]\begin{gathered} \text{ Mean= }\frac{86+90+93+85+79+92+20+84}{8} \\ \text{ Mean=}\frac{629}{8} \\ \text{ Mean=78.625} \end{gathered}[/tex]The median is the middle number in a sorted, ascending or descending, list of numbers:
Arrange the data set from smallest to largest, if the number of data set is even, the median is the average of the two middle data points in the list.
[tex]20,79,84,82,86,90,92,93[/tex]Hence, the median is the average of 82 and 86:
[tex]\begin{gathered} \text{Median}=\frac{82+86}{2} \\ \text{Median}=84 \end{gathered}[/tex]Calculate the population growth rate for Brazil:
r = (CBR + Immi) - (CDR + Emigr)
CBR = 2.6%, Immi = 2%, CDR = 2.3%,
Emig = 2%
(Portions of the numeric data are factual.)
0.3% is the population growth rate for Brazil.
How to find the population growth rate?CBR = 2.6%
Immi = 2%
CDR = 2.3%
Emig = 2%
Solution:
r = (CBR + Immi) - (CDR + Emigr)
r = (2.6 + 2) - (2.3 + 2)
r = 4.6 - 4.3
r = 0.3%
0.3% is the population growth rate for Brazil.
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ASAP PLEASE HURRY
What is the value of q − 8 if q = −18?
A. 26
B. -26
C. 10
D. -10
Answer:
-26
Step-by-step explanation:
Q = -18
-18 - 8
-26
Hope this helps! :)
Which represents the equation 6x+3y= 12 whO y=-2x+4O y = 2x+4Oy=-2x-4O y=2x-4
Given the equation:
6x + 3y = 12
We need to solve for y. Dividing by 3:
2x + y = 4
Subtracting 2x:
y = -2x + 4
First choice
what is the volume of the object in cubic centimeters? i think its 20, but i just want to double check to see if im right.
Given,
The measure of edge of the cube is 4 cm.
The total number of cubes are 5.
Required
The volume of the soid.
The volume of the solid is calculated as,
[tex]volume\text{ = side}\times side\times side[/tex]Substituting the values then,
[tex]\begin{gathered} Volume\text{ =4}\times4\times4 \\ =64\text{ cm}^3 \end{gathered}[/tex]The volume of the solid is,
[tex]\begin{gathered} Volume=5\times64 \\ =320\text{ cm}^3 \end{gathered}[/tex]Hence, the volume of the solid is 320 cm^3.
6 3 2 1 -6 -5 4 22 10 2 3 6 13 What kind of transformation does the graph show? A) flip B) rotation 9 slide D) translation
Student did not provided any picture and became unresponsive.
HELP ASP show your work!!
The minimum number of friends for which Jump it Up is 7
A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on each other (often y and x) (usually x).
Sky high pricing:
$50 for <=10 people and $5 per person after that
Jump it Up pricing:
Set up charges = $70
Per person charges = $2
Let p be the number of people
Formulating the equation we get:
50 + 5p = 70 + 2p
3p = 20
p = 6.66
or p =7
So, Jump it up will be less expensive for 7 friends
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HELPPPPPPPPPPDIDEOEOEKEKMEMENDNDNDNDND
Does this work show that 8 is a solution to the equation s-3=11 and how?
Given -
s - 3 = 11
To Find -
Is s = 8 a solution or not?
Step-by-Step Explanation -
on Putting s = 8 in the above equation
8 - 3 = 11
5 = 11
Which is not true as 5 ≠ 11
Final Answer -
Option (D)
No, Because the last line of the work is not true. 5 and 11 are not equal
Cody's rent is increasing by $51 per month starting next year. That is an increase of 15% from his current rent. Let r represent Cody's current rent. Set up an equation and solve it to fibd the value of r.
Given :
Cody's rent is increasing by $51 per month starting next year.
That is an increase of 15% from his current rent.
Let the current rent = r
so, the increase = 15% of r = 0.15r
So, the equation that represent the situation is :
[tex]0.15\cdot r=51[/tex]Solve for r :
[tex]r=\frac{51}{0.15}=340[/tex]So, the current rent = $340
The rent for the next year = 340 + 51 = $391