The sin(x) = 0.88 and sin(y) = 32/68=0.47 in the Trigonometric Functions
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
The given triangle is a right-angled triangle
As Z² = X²+Y²
So sin (x) = 60/68=0.88
and sin(y) = 32/68=0.47
Hence the sin(x) = 0.88 and sin(y) = 32/68=0.47.
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Please help me I NEED HELP
Answer:
A= 6n
B= 9n
C= 15n
Step-by-step explanation:
It's just adding.
A= 6n
B= 9n
C= 15n
15:45 in its simplest form
1:3
Step-by-step explanation:= 15:45
= 15/45
= 15/45 {can be divided by 15}
= 15/15 = 1 ; 45/15 = 3
Therefore, 15/45 is 1/3
15:45 is 1:3
Find sin 2x, cos 2x, and tan 2x from the given information.
tan x=-1/5
sin 2x =
cos 2x =
tan 2x =
The values of the different trigonometric functions are as follows:
2x = -5/13Cos 2x = 12/13Tan 2x = -5/12.What is trigonometry?The study of relationships between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations.Now, solve using trigonometry as follows:
tan x=-1/5Now, we have:
sin 2x= (2tan x)/(1 + tan²x)=2*-1/5/(1+(-1/5)²)=-2/5(1+1/25)=-2/5/(26/25)=-2/5*25/26=-10/26=-5/13Then, calculate as follows:
cos 2x= (1 - tan²x)/(1 + tan²x)=(1-(-1/5)²)/(1+(-1/5)²)=(1-1/25)/(1+1/25)=24/25/26/25=24/25*25/26=24/26=12/13Now, we obtain:
tan 2x= 2tan x/(1-tan² x)=2*-1/5/(1-(-1/5)²)=-2/5/(1-1/25)=-2/5/24/25=-2/5*25/24=-10/24=-5/12Therefore, the values of the different trigonometric functions are as follows:
2x = -5/13Cos 2x = 12/13Tan 2x = -5/12.Know more about trigonometry here:
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Fewer than %97 of adults have a cell phone. In a reputable poll of 1160 adults, % 88
said that they have a cell phone. Find the value of the test statistic
The value of the test statistic of the given problem is; -17.969
How to find the test statistic?
In statistics, hypothesis testing is simply a method used to test a claim about a population.
We are given;
Sample size; n = 1160
Sample proportion; p^ = 88% = 0.88
The percentage of 97% represents the proportion of a population and this tells us that we are making a claim about the population proportion (p) in the hypotheses.
We claim "fewer then 97%", which indicates less than 97% or 0.97:
p<0.97
The null hypothesis states that the population proportion is equal to the value mentioned in the claim.
H₀: p = 0.97
The claim is either the null hypothesis or the alternative hypothesis. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.
Hₐ: p < 0.97
The value of the test-statistic is gotten from the formula;
z = (p^ - p)/(√(p(1 - p)/n))
z = (0.88 - 0.97)/(√(0.97(1 - 0.97)/1160))
z = -17.969
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If [tex]y = \frac{(1 + x)u}{(1 + x)v} [/tex]
Find dy/dx
The value of dy/dx is ( v du/dx - u dv/dx)/v²
From the question, we have
y = (1+x)u/(1+x)v
y = u/v
dy/dx = d/dx(u/v)
d/dx(u/v) = ( v du/dx - u dv/dx)/v²
Derivatives:
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial. In calculus, a function's derivative measures how sensitively its output value changes in response to changes in its input value.
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the dimensions of a rectangle are 5x-7 and 2x-1. what is the perimeter?
please help fast!
The formula for the perimeter of the rectangle is:
P(x) = 14x - 16
What is the perimeter?We know that for a rectangle of length L and width W the perimeter is given by the formula:
P = 2*(W + L)
In this case we know that:
W = 2x - 1
L = 5x - 7
Replacing that in the perimeter formula we get:
P(x) = 2*(2x - 1 + 5x - 7)
Now we can simplify this so we get:
P(x) = 2*(2x + 5x - 1 - 7)
P(x) = 2*(7x - 8)
P(x) = 14x - 16
That is the perimeter of the rectangle in terms of x.
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find the equation of a line parallel to 3x +2y=14 that passes through the point (8,8)
The equation of the parallel line is y = (-3/2)x + 20
What does the term Slope of a Straight Line means?
A line's slope is defined as the change in y coordinate with respect to the change in x coordinate. The net y coordinate change is y, while the net x coordinate change is x.
Solution:
Firstly we need to find the slope of the given line 3x+2y = 14
Since, the equation is in the form ax + by = c
Therefore, by comparing we can say a = 3 and b = 2
Slope = -(b/a) = -3/2
Since we need to find the equation of the parallel line
So, the slope of the parallel line will be -3/2
y = mx + b
we know that the line passes through the point (8,8)
putting x,y = 8 and m = -3/2
8 = (-3/2)*8 + b
8 = -12 + b
b = 20
So, the equation of the parallel line is y = (-3/2)x + 20
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Rewrite polynomial in standard form
The standard form of polynomial is x^2 + 9x - 1/10
To write the equation in standard form, look at the degree of highest term and then rewrite the equation in decreasing order of degree i.e. from highest to lowest.
The given polynomial is
⇒ x^2 + 9x - 1/10
The standard form of the polynomial is
⇒ x^2 + 9x - 1/10
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Ralph wants to join a travel soccer team, a discretionary expense. His parents tell him he must get a job to earn the money to cover the costs. Ralph now views this discretionary expense as an
essential expense since he must pay his parents back. The costs of the travel team are listed below.
Find the total cost of being on the team.
If Ralph takes a summer job and works 10 weeks over the summer, how much must be average each week to cover the travel team expenses?
If Ralph is paid at a flat rate of exactly q dollars each week, what is the standard deviation of the distribution of his 10 weekly paychecks?
The total cost to be in the team will be $1192. He must earn an average of $119.2 per week for 10 weeks. If Ralph is paid at a flat rate of exactly q dollars each week, so the standard deviation will $0.
What is total cost?Total cost is the sum of all expenditures made to produce a certain level of output; when this total cost is divided by the quantity produced, average or unit cost is discovered. The sum of the fixed and variable costs is the total cost. For instance, if a company has a fixed cost per unit of $30 and a variable cost per unit of $5 that increases as output increases, the total cost will be $35. Total cost is equal to the sum of all fixed and variable costs. Total Cost = (Average Fixed Cost + Average Variable Cost) x Number of Units is another way to express it. All of this had to do with the total cost formula, which is a crucial idea for figuring out the total cost of production.
Here,
The expenses of team is,
Uniform=$67.00
Registration=$50.00
Tournaments=$775.00
Travel =$300.00
Total cost=sum of all expense
=67+50+775+300
=$1192
Average cost=Total cost/number of weeks he worked
=1192/10
=$119.2
Deviation of distribution cost,
If Ralph is paid at a flat rate of exactly q dollars each week then there will be $0 deviation.
It will cost $1192 in total to join the team. For ten weeks, he must make an average of $119.2 per week. If Ralph receives a fixed weekly salary of exactly q dollars, the standard deviation will be zero.
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A rectangle has an area of 20 square centimeters.
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
A
B
1 cm and 20 cm
2 cm and 10 cm
3 cm and 8 cm
4 cm and 5 cm
Answer:
Most likely 4cm and 5cm
Step-by-step explanation:
Where 5cm=length
And 4cm=width
Evaluate (6x+3y)-z2 divided by (2x) when X = -3 , y=4 , z=-6
The evaluated expression of (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6 is 5.3
How to evaluate an expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators.
Therefore, let's evaluate the expression, (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6.
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
In other words, to evaluate the expression, we have to substitute the given value of the variable and simplify the expression.
Therefore,
(6x+3y) - z² = (6(-3)+3(4)) - (-6)² = (-18 + 12) - 36 = -32
2x = 2(-3) = -6
Hence,
- 32 / -6 = 5.3
Therefore,
(6x+3y) - z² / 2x when x = -3, y = 4 and z = -6 is 5.3
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How many bit strings are there of length eight?
There are 28 which is 256. That means there are 256 different values you can store in a byte, since a byte is eight bits. There are 256 eight-bit ASCII codes, for instance.
1 byte = 8 bits
Number of bits = [tex]2^{8}[/tex]
= 2*2*2*2*2*2*2*2
= 4*2*2*2*2*2*2
= 8*2*2*2*2*2
= 16*2*2*2*2
= 32*2*2*2
= 64*2*2
= 128*2
= 256 bits.
Therefore that means there are 256 different values you can store in a byte, since a byte is eight bits.
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5. Mary wants to make several aluminum cups like the one below. She is going to cut them from a sheet of aluminum that has an area of 3,750 in². How many complete cups will she be able to make?
Answer:
50 aluminium cups maybe win 3750
Complete (assume $50,000 of overhead to be distributed): (Round your Ratio answers to the nearest hundredth.) Sq. Ft. Ratio Amount of Overhead Allocated Dept. A 20,000 A B Dept. B 80,000 C D
The calculation of the ratios, resulting from the square feet occupied by both departments, and the amounts of overhead allocated to the two departments are as follows:
Ratio Amount
Department A 1/5 $10,000
Department B 4/5 $40,000
What is the ratio?The ratio is the numerical relationship shared by two or more values.
Ratios are fractional values and are depicted using fractions, decimals, and percentages.
Ratios, like proportions, show how much a value or variable is contained in another.
Total overhead = $50,000
Department Square Feet Ratio Amount of Overhead Allocated
Dept. A 20,000 A = 1 B = $10,000 ($50,000 x 1/5)
Dept. B 80,000 C = 4 D = $40,000 ($50,000 x 4/5)
Ratios = 20,000:80,000
= 1:4
Sum of Ratios = 5
Thus, based on the cost driver allocation ratios, Department A will bear $10,000, while Department B will be allocated $40,000.
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5. Describe a relationship between the two variables shown in this graph. Be
sure to include a description that includes the whole pattern of what happens
to the money during the tone shown.
Time please help asap
The relationship between the variables is that an increase in the degree of slope cause an increase in the loss of soil
How to describe the relationship between the variables?The possible graph that completes the question is added as an attachment
From the attached graph, we have the variables represented to be
Degree of slope - on the x-axisLoss of soil - on the y-axisNext, we determine the relationship
To start with:
The relationship between the variables on a graph is simply the end bahavior of the graph
In this case, we can see that:
As the degree of the slope increases, the loss of soil also increase
However, the increase in the slope does not cause a constant increase in the loss of soil
The loss of soi starts by increasing slowly as the degree of slope increases, then the loss of soil increases sharply as the degree increases further
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Find point C on the x-axis so that AC + BC is a minimum.
A(-8,4), B(-1,3)
The point C on the x-axis when A(-8,4), B(-1,3) so that AC + BC is a minimum is (36,0).
A(x₁,y₁) = (-8,4)
B(x₂,y₂) = (-1,3)
C(x, y ) = (x ,0)
equation of a line is given as:
y - y₁ = (y₂ - y₁)/ (x₂ - y₁) (x - x₁)
y - 4 = (3 - 4)/(-1 + 8)(x + 8)
y - 4 = -1/7(x + 8)
7(y - 4) = -1(x + 8)
7y - 28 = -x + 8
x + 7y - 36 = 0
when y = 0 then the value of x is given as:
x + 7y- 36 = 0
x + 7(0) - 36 = 0
x = 36
point C on the x-axis (x , 0) = (36,0)
The point C on the x-axis when A(-8,4), B(-1,3) so that AC + BC is a minimum is (36,0).
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8x-4=2(4x-4)
for how many games is the total cost of bowling equal for the two bowling establishments??
Answer: x= 0.5
Step-by-step explanation:
8x-4=2(4x-4)
You would want to take away the smaller x which is (4x)
4x-4=2-4
+4 +4
4x-4=2
+4 +4
4x=2
daddy ;)
b) How many more squares need to be shaded so that 70% of the grid is shaded?
The percentage of shaded grid is 45% and the number of squares is 5.
How to find the percentage of shaded grid?a. Percentage of shaded grid
The total number of shaded and unshaded grid is 20 while the total number of shaded area is 9 now let find the percentage of the shaded grid.
Percentage of shaded grid = Shaded grid /Total grid
Percentage of shaded grid = 9/20 × 100
Percentage of shaded grid = 45%
b. Number of squares to be shaded
Number of squares = 20 grid × (70% - 45%)
Number of squares = 20 grid × 25%
Number of squares = 5 squares
Therefore the percentage is 45% .
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Expand and simplify 5(x + 7) + 3(x–2)
Answer:
8x + 29
Step-by-step explanation:
[tex]5(x + 7) + 3(x–2) \\ 5 \times x + 5 \times 7 + 3 \times x - 3 \times 2 \\ 5x + 35 + 3x - 6 \\ 5x + 3x + 35 - 6 \\ 8x + 29[/tex]
i’m stuck on c and e
The adult daily dosage for a certain medicine is 260 mg (milligrams) of medicine for every 40 pounds of body weight. a. At this rate, find the daily dose for a man who weighs 195 pounds. b. If the man is to receive 600 mg of this medicine every 8 hours, is he receiving the proper dosage? a. The daily dose for a man who weighs 195 pounds is (Round to the nearest tenth as needed.) mg.
a) Daily dose for a man who weighs 195 pounds is 30 mg.
b)Here 422.5 mg is less than 600mg. Then, He doesn't receive proper dosage.
What is proportional ?
Any relationship that always has the same ratio is referred to be proportionality. For instance, the average number of apples per tree determines the proportionality between the quantity of apples in a crop and the number of trees in the orchard.
Here , The adult daily dosage for a certain medicine is 260 mg
=> [tex]\frac{40}{260} = \frac{195}{x}[/tex]
=> x = [tex]\frac{260*195}{40}[/tex]
=> x =1267.5 mg.
a) Daily dose for a man who weighs 195 pounds is 30 mg.
b) Here for 24 hours = 1267.5 then,
=> 8 hours = x
=> x = [tex]\frac{1267.5*8}{24}[/tex]
=> x = 422.5 mg.
Here 422.5 mg is less than 600mg. Then, He does'nt receive proper dosage.
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Please help, i dont understand
The equation of lines are (a) x - 2y + 6 = 0
(b) 2x - y - 4 = 0
(c) x - y + 1 = 0
(d) 4x + 3y + 4 = 0
Slope-intercept form of the equation -> y = mx + c
Slope = m = [tex]\frac{y2-y1}{x2-x1}[/tex]
(a) A(0,3) and B(6,6)
m = [tex]\frac{6-3}{6-0}[/tex]
= 3/6
= 1/2
Putting the value in equation,
3 = (1/2)*0 + c
c = 3
Equation -> y = (1/2)x + 3
2y = x + 6
x - 2y + 6 = 0
(b) A(0,-4) and B(5,6)
m = [tex]\frac{6+4}{5-0}[/tex]
= 10/5
= 2
Putting the value in equation,
-4 = (2)*0 + c
c = -4
Equation -> y = (2)x - 4
2x - y - 4 = 0
(c) A(-4,-3) and B(2,3)
m = [tex]\frac{3+3}{2+4}[/tex]
= 6/6
= 1
Putting the value in equation,
3 = (1)*2 + c
3 = 2 + c
c = 3 - 2
c = 1
Equation -> y = (1)x + 1
y = x + 1
x - y + 1 = 0
(d) A(-6,4) and B(3,-8)
m = [tex]\frac{-8-4}{3+6}[/tex]
= -12/9
= -4/3
Putting the value in equation,
-8 = (-4/3)*3 + c
-8 = -4 + c
c = -8 + 4
c = -4
Equation -> y = (-4/3)x - 4
3y = -4x - 4
4x + 3y + 4 = 0
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Given that (x - 5) is a factor of
x³ - 7x² + 2x + a, find the value of a
check your textbook for the remainder theorem, where it states that for a factor (x-5) of f(x) then the remainder will be 0, thus f(5) = 0, what the heck all that means?
well, it means that if we evaluate f(5) our result should be 0, so
[tex]\stackrel{factor}{(x-5)}\hspace{5em}f(5)=(5)^3-7(5)^2+(5)+a=0 \\\\\\ 0=(5)^3-7(5)^2+(5)+a\implies 0=125-175+10+a \\\\\\ 0=-40+a\implies \boxed{40=a}[/tex]
Which function is positive for the entire interval [–3, –2]?
Graph 2 represents that the function is positive for the entire interval [-3,-2].
What is a function?Every possible input value results in exactly one output value in a function. "The output is a function of the input," we state. The domain is made up of the input values, while the range is made up of the output values.
Four different graphs for various functions are provided. We must identify the graph that is positive throughout the range [-3,-2].
We make the following observation from the given graphs.
1. The function in graph 1 has a value of 0 at -3 and decreases in value from -3 to -2. As a result, in the provided interval, the function is negative.
2. Graph 2 makes it abundantly evident that the function has a positive value for the entire specified interval.
3. In graph 3, the function shows a negative value entirely in the given interval.
4. In graph 4, the function exhibits both positive and negative values in the given interval and is not positive in the entire interval.
Thus, the function in graph 2 is positive for the entire interval [-3,-2].
The missing image is attached with the answer below,
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Answer the questions
(1) 150 cola cans and 260 fruit juice cans need to be stacked in a school canteen. If each stack is
to be of the same height and is to contain cans of the same type, what would be the greatest
number of cans each stack can have?
The greatest number of cans each stack can have is 10.
What is Greatest Common Divisor (GCD)?
The number that divides two or more numbers most precisely by itself is said to be the greatest common divisor (GCD) of those numbers. It is also defined as the highest common factor (HCF).
If a and b are two numbers then the greatest common divisor of both numbers is denoted by GCD(a, b).
Given, Total number of cola cans = 150
Total number of fruit juice cans = 260
According to the question condition, we need to find GCD (150,260)
Now, the prime factorization of 150 and 260 are:
150= 2 x 3 x 5 x 5
260 = 2 x 2 x 5 x 13
So, common factor = 2 x 5 = 10
Then, GCD (150,260) = 10
Hence, the greatest number of cans in each stack can have 10.
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A dictionary costs $15.00 and a map costs $5.00. If you want to
spend exactly $60.00 and you need to buy 3 dictionaries, how
many maps can you buy? Write an equation in standard form
modeling this situation then see how many maps you can buy.
Let a represent the number of dictionaries you buy and b
represent the number of maps you buy.
maps
Answer:
15.00x +5.00y = 60.00
Step-by-step explanation:
answer is to the equation is 3 because u plug in 3 to x given information provided to get 45.00 dollars. u then subtract 60 and 45 to see how much money u have left for maps. each map is 5.00 dollars and with 15.00 dollars remaining, u can get three maps and three dictionaries to equal 60.00 dollars!! Hope this helps!
Answer:
You can buy 3 maps. Equation: 15a + 5b = 60 ⇒ 15(3) + 5(3) = 60
Step-by-step explanation:
15 multiplied by 3 equals 45. Now you have $15 left. 15 divided by 5 equals 3. Therefore, you can buy 3 maps. Hope that helped! :)
PLEASE HELP!!!! "CLEVERLY CONICS Portfolio"
Choose one of your conic examples to study in greater detail. Complete the table to create the graph and equation for your chosen example.
1. If possible, use a photo of the structure or item. Otherwise, draw a detailed sketch.
2. Measure and label the key dimensions of the shape in order to duplicate them in a to-scale graph. Be sure to label your units of measure to reflect the actual measurements.
3. Draw the underlying conic section on a coordinate grid.
4. Identify the coordinates of the appropriate key parts of the conic section.
5. Determine the closest approximation of the equation in standard form for the conic section.
Answer:
Hello there! While I didn't have this assignment, I found the assignment on Coursehero and took the liberty of downloading the pdf.
BE SURE TO USE QUILLBOT FOR PARAPHRASING AND PREPOSTSEO FOR PLAGIARISM CHECKING
Step-by-step explanation:
Miriam bought a barbecue grill on sale for 25% off the original price. Including an 8% sales tax, the final cost was $79.95. If Miriam wants to determine the original cost of the grill, what is an equation that she can use to solve the problem if x represents the original price?
The Original price of barbecue grill is 96.325.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The final cost barbecue grill is $79.95.
Discount = 25%
and Tax = 8%
let the original price be x
x- 0.25x + 0.08x = 79.95
0.83x = 79.95
x= 79.95/0.83
x = $96.325
Hence, the Original price of barbecue grill is 96.325.
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Classify the triangle by the side lengths and what the angle measures appear to be. Then find the perimeter and area of the triangle.
Answer:
Classification - Right Scalene
Perimeter - 30ft
Area - 30ft
Step-by-step explanation:
Classification - There's a right angle, and 3 unequal sides.
Perimeter - 5 + 13 + 12 = 30
Area = 5*12=60, 60/2 = 30
which is the correct answer ?????
Explanation:
Technically you could isolate any variable you wanted, from either equation. However, convention is to pick the variable in which isolating it is easiest, and most efficient.
The key thing to look for is if there's a coefficient of 1. This is found in the second equation for the y term. Think of -4x+y = -13 as -4x+1y = -13. Due to the coefficient of 1, when solving for y we won't involve messy fractions.
If you were to solve for y, then you'd get y = 4x-13, which is then plugged in (aka substituted) into the first equation. That allows you to solve for x. Once you know x, you can determine y.