Answer is - 2 [tex]\sqrt{3}[/tex] / 13
Cosecant Given a point P(x, y) on the terminal side of an angle θ in standard position
cosθ = cos (π + d) (d is the inner angle of the tringle)
= - cos 2
= - 4 / - [tex]\sqrt{(- 6^{2} + (- 4^{2} )[/tex]
= - 4 / - [tex]\sqrt{36 + 16 }[/tex]
= - 4 / -[tex]\sqrt{52}[/tex]
= - 4 / 2[tex]\sqrt{13}[/tex]
= - 2 / [tex]\sqrt{13}[/tex]
multiply by [tex]\sqrt{13}[/tex]
we get,
= - [tex]\frac{2 \sqrt{13} }{13}[/tex]
Formulae :
Arc cosecant y = arcs(x) = csc-1(x). Another way to write x = csc(y).
Arccosine y = arcos(x) = cos-1(x). Another way to write x = cos(y).
Arc cotangent y = arcos(x) = cot-1(x). Another way to write x = cot(y).
Arc secant y = arcsec(x) = sec-1(x). Another way to write x = sec(y).
Arcsine y = arcsine(x) = sin-1(x). Another way to write x = sin(y).
Arctangent y = arctan(x) = tan-1(x). Another way to write x = tan(y).
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A swimming pool measures 30 ft by 25 ft and is 6 feet deep.
a) How much fencing is needed if the fence is to be 7 ft from each side of the
pool?
______________________
b) How much material is needed to make a cover for the pool. (the pool only)
_______________________
c) How many cubic feet of water are needed to fill the pool?
Answer:
Step-by-step explanation:
Colin is borrowing money from his parents to purchase a $700
computer. He will pay them $35 per month for two years. Determine the
simple interest rate on Colin's loan.
Colin paid the loan at a ten percent annual interest rate.
Simple interest is the form of interest calculation in which the principal amount remains the same for the entire duration for which the loan is taken.
It is also assumed that Colin will repay $35 per month for the next two years.
We must calculate a simple interest rate on Colin's borrowings.
As a result, Colin's total payment to his parents for two years is $35.
We are required to find simple interest rate on Colin's borrowings
Therefore, total amount paid by Colin to his parents= 35$ for 2 years
=35*24=840
The amount paid by Colin is principal + interest
Thus, the simple interest amount= 840-700=140$
We know that the simple interest formula is principal*rate*time/100.
We know that the simple interest is 140, the principal is 700, the time is two years, and we need to find the rate of interest.
SI= P*R*T/100
140= 700*R*2/100
140/7*2=R
R=140/14=10
Therefore, The Rate of interest on which Colin paid the loan is 10 per cent per annum
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FACT or FIB?
-3-4-(-12)
-19
use 22/7 to calculate the pelmeter of the rectangle 3cm 5cm
The Perimeter of rectangle 3cm 5cm is 16 cm.
What is rectangle ?In geometry, a rectangle is a plane figure of four sides having four angles of 90 degree. A rectangle has different length and breadth.
Some important formulas for rectangle :
Area of rectangle = Length × BreadthPerimeter of rectangle =2 * ( length + breadth ) Diagonal of rectangle = √(length^2 + breadth^2)What is perimeter of rectangle?Perimeter is define as the distance around all the edges of a shape. In case of rectangle perimeter is the distance of all 4 edges i.e. 2 lengths and 2 breadth .
Thus , perimeter of rectangle = ( 2 × length ) + (2 × breadth)
= 2 ( length + breadth )
In the given question,
length of rectangle = 3cm
breadth of rectangle = 5cm
therefore, perimeter of rectangle = 2(3+5) = 16cm
Hence, The Perimeter of rectangle is 16 cm.
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Help !!! Evaluate -3 5
-7 7
Which of the following real numbers should be subtracted from -5 to get a difference of 0?
A.
-10
B.
-5
C.
0
D.
5
The real number that should be subtracted from - 5 to get 0 is -5 (option b).
What is the real number?A real number is a quantity that can be written as an infinite decimal expansion. A real number is made up of both rational numbers and irrational numbers.
Rational numbers are numbers that can be expressed as a fraction of two integers. An example is 5, -5. Irrational numbers cannot be expressed as a fraction of two integers. An example is 22/7, 1/3.
In mathematics, the following rules exist:
a negative number multiplied by a negative number yields a positive number. a negative number multiplied by a positive number, yields a negative number. a positive number multiplied by a positive number yields a positive number.-5 - (-5)
= -5 + 5
= 0
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A car uses 3.75 gallons of gas to travel 100.5 miles. How much gas will they use after 20 miles?
Please helpppp!!! I suck at simplifying
In a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. If one sweater and four shirts cost $47, while four sweaters and three shirts cost $84, find the price of one sweater and the price of one shirt.
Answer:
Step-by-step explanation:
Let x be the sweater
Let y be the shirt
Equation1: x+4y=47
Equation2: 4x+3y=84
Now solve for x in the first equation:
x+4y=47
x=47-4y
Now that we've solved for x, substitute the value for x which is 47-4y into Equation2 as follows:
4x+3y=84
4(47-4y)+3y= 84
188-16y+3y= 84
188-13y= 84
-13y= 84-188
-13y= -104
y= -104/-13
y= 8
Now plug in the value for y which is 8 into Equation 1 and solve for x:
x+4y=47
x+4(8)=47
x+32=47
x=47-32
x=15
You can perform a check by plugging in the x and y values into equations 1 and 2 which should yield true statements.
The answer is: 1 sweater costs $15 and 1 shirt costs $8
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Only 1 try remaining for this problem or else I get a zero. Please help if you know the answer or how to solve.
Using the shell method, the volume is
[tex]\displaystyle 2\pi \int_0^1 (2-x) \cdot 8x^3 \, dx = 16\pi \int_0^1 (2x^3 - x^4) \, dx[/tex]
Each cylindrical shell has radius [tex]2-x[/tex] (the horizontal distance from the axis of revolution to the curve [tex]y=8x^3[/tex]); has height [tex]8x^3[/tex] (the vertical distance between a point on the [tex]x[/tex]-axis in [tex]0\le x\le1[/tex] and the curve [tex]y=8x^3[/tex]).
Compute the integral.
[tex]\displaystyle 16 \pi \int_0^1 (2x^3 - x^4) \, dx = 16\pi \left(\frac{x^4}2 - \frac{x^5}5\right) \bigg|_{x=0}^{x=1} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 16\pi \left(\frac12 - \frac15\right) \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{24}5\pi = \boxed{4.8\pi}[/tex]
=
How many gallons of a 50% antifreeze solution must be mixed with 70 gallons of Strength
25% antifreeze to get a mixture that is 40% antifreeze? Use the six-step method.
The number of gallons that must be needed to antifreeze 50% solution is 105.
Given that 50% antifreeze solution must be mixed with 70 gallons of Strength 25% antifreeze to get a mixture that is 40% antifreeze.
The six-step method involves a few steps that need to perform. These are defining the problem, determining the root cause, finding the alternative solution to solve the problem, selecting the solution, implementing the solution, and finally evaluating the outcome.
Let's consider x be the number of gallons of a 50% antifreeze solution.
As we know we need to make an antifreeze solution by adding the given quantities.
Hence,
x×50%+70×25%=40%×(x+70)
x×0.5+70×0.25=0.4×(x+70)
Now, we will multiply the numbers, we get
0.5x+17.5=0.4(x+70)
Now, we will multiply both sides by 10, we get
0.5x×10+17.5×10=0.4(x+70)×10
5x+175=4(x+70)
5x+175=4x+280
Further, we will subtract 175 from both sides, we get
5x+175-175=4x+280-175
5x=4x+105
Furthermore we will subtract 4x from both sides, we get
5x-4x=4x+105-4x
x=105
Hence, 105 gallons of 50% antifreeze solution must be needed.
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Solve the formula for the specified variable.
F
[tex]D=\frac{1}{5}kf \\ \\ 5D=kf \\ \\ \boxed{f=\frac{5D}{k}}[/tex]
5. Daunte's favorite video game store is running a clearance sale. Every week until
everything is sold, the store's owner is going to reduce the price of the remaining
merchandise by 25%. Duante figures that he should wait 4 weeks to go to the
store because then the merchandise will be 100% off! Construct a mathematical
argument involving an exponential function to explain whether Daunte is correct
or incorrect.
Daunte is incorrect. After 4 weeks, the price would be 68.5 percent off.
Is Daunte correct?An exponential function is a mathematical function that has the form : f(x) = a^x
Where:
a = constant x = variableAn exponential function indicates that the quantity is either increasing at a faster rate or reducing at a faster rate. This is true because an exponential increase or decrease is faster than a linear increase or decrease. In a linear increase or decrease, the function is either increasing or decreasing at a constant value.
The price of the video games would reduce by 25% of the previous weeks' price. Thus, the function that would represent this is an exponential function.
The form of the exponential equation would be:
Price after 4 weeks = Initial price x (1 - percentage decrease)^number of years
Let's assume that the initial price is 100
100 x (1 - 0.25)^4
100 x (0.75)^4 = 31.64
The total percentage decrease in the price of the good: (current price initial price) - 1
(31.64 / 100) - 1 = 0.684 = 68.4%
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EXERCISE 5.3
1. Find the values of the letters:
(a) 2 B C
(b)
+C 7 A
6 AB
ABC 3
5 D
BD 9 C
8 AA 50
87 BD C
X
(c)
A 2 BC
1 D 6
2 CA 10
BBDD 00
A 2 B C 0 0
7 D 7 7 10
X
2. Write five 2-digit numbers the product of whose digits is even.
3. Write three 4-digit even numbers divisible by 9.
4. Write four 5-digit numbers divisible by 3.
5. Write a 3-digit number divisible by 3 whose digits are consecutively
decreasing.
Answer:
a
Step-bye-step explanation:
that's the correct answer
C
Using a Number Line to Add Fractions
Slide the green dot from 0 to plot the number at the correct
location.
Plot
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0
0.5 1
Use the number line to find
O
19
4
O
19
8
O-2
21
¹()+(-3¹)
8
21
8
Answer:
c
Step-by-step explanation:
C
Using a Number Line to Add Fractions
Slide the green dot from 0 to plot the number at the correct
location.
Plot
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0
0.5 1
Use the number line to find
O
19
4
O
19
8
O-2
21
¹()+(-3¹)
8
21
8
Find each of the following sums by first deciding if the answer is positive or negative and then using subtraction to help find the final answer (a) -237+359 (b) 87+-163 (c)-35.7+22.9 (d)8.79+6.41
Given the given task content, the answer to the sums are:
The answer is positiveThe answer is negativeThe answer is negativeThe answer is positiveSubtraction of numbersThe subtraction of numbers is difference between two or more numbers
(a) -237 + 359
= 122
The answer is positive(b) 87 + (-163)
= 87 - 163
= -76
The answer is negative(c) - 35.7 + 22.9
= -12.8
The answer is negative(d) 8.79 + 6.41
= 15.20
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Which rule describes the translation ABCD → A′B′C′D′?
Answer:
translation
all the points are in the same orientation, and all the lengths are the same.
all that has changed are the coordinates.
A box of candy weighs 4 and 7/10 pounds. 2/5 get dumps out of the box. What is the weight of the candy left in the box?
2/5 get dumps out of the box from 4 and 7/10 pounds of candy then weight of the candy left in the box is 2 and [tex]\frac{41}{50}[/tex] pounds.
As given,
Total weight of the candy = 4 and 7/10 pounds = [tex]\frac{47}{10\\}[/tex] pounds
pound is the imperial unit of weight generally written as lb.
one pound = 0.4535 kilograms = 453.5 gm.
[tex]\frac{2}{5}[/tex] th of candy is dumps out of the box.
1- [tex]\frac{2}{5}[/tex] = [tex]\frac{3}{5}[/tex] th of the total candy is left in the box.
weight of the candy left in the box = [tex]\frac{3}{5}[/tex] * [tex]\frac{47}{10}[/tex] = [tex]\frac{141}{50}[/tex] pounds.
now 141= 50*2 + 41
[tex]\frac{141}{50}[/tex] pound = 2 and [tex]\frac{41}{50}[/tex] pounds
Hence, weight of the candy left in the box= 2 and [tex]\frac{41}{50}[/tex] pounds.
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MP Attend to Precision Trent writes 10 x 6 = 60 to find
the number of muffins in 10 boxes. Describe what each of
the factors represents in the multiplication equation.
Trent writes 10×6=60, then in multiplication equation 10 represents the number of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the total numbers of muffins.
Given,
Trent writes 10×6=60,
Here,
10 represents the number of muffin boxes
6 represents the numbers of muffins in each box
60 represents the total numbers of muffins
Hence, Trent writes 10×6=60, then in the multiplication equation 10 represents the number of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the total numbers of muffins.
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Use the information below to answer all parts of the question.
Kylle is going to play laser tag with some friends. To rent the laser tag gear, the initial fee is $3, and each game costs $2 to play.
PART A
Fill in the table for the amount of money (cost) to play laser tag.
Number
of Games
Cost
In linear equation , $8 the amount of money (cost) to play laser tag.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable.It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value.One such linear equation in one variable is 9x + 78 = 18.let x = number of games, let y = cost of tag
then Total cost = x•$3 + y
In this case, TC = 3•$2 + $2
TC = $8
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A customer paid a total of $6.00 for 68 copies at a print shop. Some of the copies were black-and-white copies, and the rest were color copies.
• Each black-and-white copy cost $0.08.
• Each color copy cost $0.15.
How many copies of b, the number of black-and-white, and c, the number of color did the customer pay for?
The number of black-and-white is 60 and the number of color copies is 8.
How to calculate the value?Let b = the number of black-and-white.
Let c = the number of color copies.
The equation will be:
b + c = 68
0.08b + 0.15c = 6
Multiply equation I by 0.08
Multiply equation ii by 1.
0.08c + 0.08c = 5.44
0.08b + 0.15c = 6
Subtract
0.07c = 0.56
c = 0.56/0.07
c = 8
Since b + c =68
b= 68 - 8 = 60
Therefore, the number of black-and-white is 60 and the number of color copies is 8.
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Salaries for teachers in a particular elementary school district are normally distributed
with a mean of $44,000 and a standard deviation of $6,500.
Thus standard daviation is x~N(4400,6500)
Let X denote the salaries for all the teachers in a particular alimentary school.
As per the generation X is commonly distinguished with a mean of u=44,000
standard daviation of €=$6500
The answer is x~N(44000,6500)
Since the 10 teachers are survived randomly from the district
The site of n=10
Variable€x present salary of all 10 teachers in a particular alimentary sel.
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PLS HELP!!!
Solve.
2x-y+2z=-6
-3y+z=-2
2x-3z+4
The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7
How to solve the system of equations?The system of equations is given as
2x - y + 2z = -6
-3y + z = -2
2x - 3z = -4
Subtract 2x - 3z = -4 from 2x - y + 2z = -6
This is represented as
(2x - y + 2z = -6) - (2x - 3z = -4)
This gives
- y + 5z = -2
Multiply - y + 5z = -2 by 3
-3y + 15z = -6
Subtract -3y + 15z = -6 from -3y + z = -2
This is represented as
(-3y + z = -2) - (-3y + 15z = -6)
This gives
-14z = 4
Divide by -14
z = -2/7
Substitute z = -2/7 in - y + 5z = -2
- y - 5 * 2/7 = -2
This gives
- y - 10/7 = -2
Rewrite as:
y = 2 - 10/7
Evaluate
y = 4/7
Substitute z = -2/7 in 2x - 3z = -4
2x - 3 * 4/7 = -4
This gives
2x - 12/7 = -4
So, we have:
2x = 12/7 - 4
Evaluate
2x = -16/7
Divide by 2
x = -8/7
Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7
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A musician kept track of the concert arenas on this year's tour and found that 60% of the arenas were sold out. Of those that were not sold out, 25% had been on the previous tour schedule from last year, while 90% of those that were sold out were on the previous tour schedule. Which of the following represents the joint relative frequency of arenas that were sold out and not on the previous tour schedule?
75%
54%
30%
6%
Answer:
6%
Step-by-step explanation:
First, let's break this down:
60% of arenas sold out
90% had been on previous tourOut of those arenas that did NOT sell out
25% had been on previous tourWe want to know the joint relative frequency of area that were sold out AND NOT on the previous tour schedule, therefore all the information about areas that did NOT sell out is irrelevant.
Because 90% of the areas that were sold out had been on the previous tour, 10% had NOT been on the previous tour.
Therefore, considering all the arenas, 10% of 60% of the arenas were sold out and not on the previous tour.
Let x equal the total number of arenas:
[tex](.10)(.60)x=0.06x[/tex]
Convert to percent
6%
Therefore, the joint relative frequency of sold out arenas that were not on the previous tour is 6%.
Please solve the Quadratic Equation
2z^2 +13z +15 = 0
Please show steps for Brainliest!
A homesteaded A homesteaded property is located in Jupiter, Florida, in Palm Beach County. The property has been assessed at $185,000. The city tax rate is 8.8 mills, the county tax rate is 9.3 mills, and the school board levy is 6.5 mills. The owner is a widow and has qualified for and received homestead tax exemption. How much will the owner pay in property taxes?property is located in Jupiter, Florida, in Palm Beach County. The property has been assessed at $185,000. The city tax rate is 8.8 mills, the county tax rate is 9.3 mills, and the school board levy is 6.5 mills. The owner is a widow and has qualified for and received homestead tax exemption. How much will the owner pay in property taxes
Based on the fact that the widow got an exemption on homestead tax, the amount that the owner would pay in property taxes is $3,471.20.
What is the property tax?The widow received a homestead tax exemption of $25,000 on the property.
The amount to be paid in property tax is:
= (8.8 + 9.3 + 6.5) / 1,000 x (185,000 - 25,000)
= 21.7/1,000 x 160,000
= $3,471.20
In conclusion, the property tax to be paid is $3,471.20.
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Which of the following is equivalent to (5y + 3x) + 9x?
15xy + 9y
9x(5y + 3x)
5y + 12x
5y + 27x
Answer:
5y + 12x
Step-by-step explanation:
Let's simplify step-by-step.
5y+3x+9x
Combine Like Terms:
=5y+3x+9x
=(3x+9x)+(5y)
=12x+5y
Answer:
5y + 12x
Step-by-step explanation
Simplify step-by-step.
5y+3x+9x
Combine like terms:
=5y+3x+9x
=(3x+9x)+(5y)
=12x+5y
Vectors u and v are shown on the graph.
Which of the following vectors represents v – u?
Answer:
see attached
Step-by-step explanation:
The vector difference u -v can be represented on a vector diagram by the sum u +(-v), where -v is a vector the same length as v, but in the opposite direction.
__
Nathan earns $78.75 for working 5 hours. Calculate the unit rate. How much money does he earn in 1 hour?
Answer: $15.75
Step-by-step explanation:
$78.75/5 hr=$15.75/hr
Answer:
He earns $15.75 an hour
Step-by-step explanation:
You have to divide $78.75 by 5 to get the unit rate(earnings for 1 hour).
11 ft
7 ft 8 ft
20 ft What is the area of the shape?
Answer:
Area = 192.5 ft.²
Step-by-step explanation:
By splitting the shape in 2, we can find the area much simpler.
Starting with the parallelogram (on the left), the area formula is A = b × h.
b (base) = 11 ft.
h (height) = 7 ft.
A (area) = (11 ft.)(7 ft.)
A = 77 ft.² (save this for later)
Then, the trapezoid's (on the right) area formula is A = [(a + b) ÷ 2] × h.
a (first base) = 8 ft.
b (second base) = (20 - 7) = 13 ft.
h (height) = 11 ft.
A = [(8 ft. + 13 ft.) ÷ 2] × 11 ft.
A = [(21 ft.) ÷ 2] × 11 ft.
A = (10.5 ft.) × 11 ft.
A = 115.5 ft.²
Now, bringing back the first area, we can add them together to find the total:
A = 77 ft.² + 115.5 ft.²
A = 192.5 ft.²
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