Answer:
184.85 square mm
Step-by-step explanation:
The area of a sector of a circle is [tex]\frac{1}{2} r^{2} \theta[/tex], where r is the radius and [tex]\theta[/tex] is the angle in radians subtended by the arc at the centre of the circle.
Since, diameter = 40.6 mm
So, radius(r)=20.3 mm and [tex]\theta[/tex]=[tex]\frac{2 \pi}{7}[/tex] radians
So, area of sector= [tex]\frac{1}{2} r^{2} \theta[/tex]
=[tex]\frac{1}{2} (20.3)^2 (\frac{2 \times 3.14}{7})[/tex]
=184.85 square mm
The area of the sector using given data is equal to 184.96 mm².
The area of a sector with a central angle of 2π7 radians and a diameter of 40.6 mm.
To solve this, we need to find the radius of the circle, which is half the diameter, and then use the formula for the area of a sector, which is ½ ×r² × θ, where θ is the angle in radians.
First, find the radius: r = ½ × diameter = 0.5 × 40.6 mm = 20.3 mm.
Then, substitute the values into the formula for the area of a sector:
Area = ½ × (20.3 mm)² × (2π7)
= 1/2 × (20.3)² × (2 × 3.14 /7)
= 1/2 × 412.09 × 0.89714
= 184.96 mm²
Rounded to the nearest hundredth, the area of the sector is 184.96 mm².
Write a solution in Interval Notation - (you don't have to help me on all, 1 or 2 is fine c: )
1) | m | -2 > 0
2) | x - 4 | - 3 > 5
3) | 6 + 9x | ≤ 24
4) | 1 - 5a | > 29
QUESTION 1
The given inequality is
[tex]|m|-2>0[/tex]
We group like terms to get,
[tex]|m|>2[/tex]
This implies that,
[tex]-m>2[/tex] or [tex]m>2[/tex].
We simplify the inequality to get,
[tex]m<-2[/tex] or [tex]m>2[/tex].
We can write this interval notation to get,
[tex](-\infty,-2)\cup (2,+\infty)[/tex].
QUESTION 2
[tex]|x-4|-3\:>\:5[/tex].
We group like terms to get,
[tex]|x-4|\:>\:5+3[/tex].
[tex]|x-4|\:>\:8[/tex]
We split the absolute value sign to get,
[tex]-(x-4)\:>\:8[/tex] or [tex]x-4\:>\:8[/tex]
This implies that,
[tex]x-4\:<\:-8[/tex] or [tex]x-4\:>\:8[/tex]
[tex]x\:<\:-8+4[/tex] or [tex]x\:>\:8+4[/tex]
[tex]x\:<\:-4[/tex] or [tex]x\:>\:12[/tex]
We can write this interval notation to get,
[tex](-\infty,-4)\cup (12,+\infty)[/tex].
QUESTION 3
The given inequality is
[tex]|6+9x|\leq 24[/tex]
We split the absolute value sign to obtain,
[tex]-(6+9x)\leq 24[/tex] or [tex](6+9x)\leq 24[/tex]
This simplifies to
[tex]6+9x\ge -24[/tex] and [tex]6+9x\leq 24[/tex]
[tex]9x\ge -24-6[/tex] and [tex]9x\leq 24-6[/tex]
[tex]9x\ge -30[/tex] and [tex]9x\leq 18[/tex]
[tex]x\ge -\frac{10}{3}[/tex] and [tex]x\leq 2[/tex]
[tex]-\frac{10}{3}\leq x\leq2[/tex]
We write this in interval form to get,
[tex][-\frac{10}{3},2][/tex]
QUESTION 4
The given inequality is
[tex]|1-5a|>29[/tex]
We split the absolute value sign to get,
[tex]-(1-5a)>29[/tex] or [tex]1-5a>29[/tex]
This simplifies to,
[tex]1-5a\:<\:-29[/tex] or [tex]1-5a\:>\:29[/tex]
This implies that,
[tex]-5a\:<\:-29-1[/tex] or [tex]-5a\:>\:29-1[/tex]
[tex]-5a\:<\:-30[/tex] or [tex]-5a\:>\:28[/tex]
[tex]a\:>\:6[/tex] or [tex]a\:<\:-\frac{28}{5}[/tex]
We write this in interval notation to get,
[tex](-\infty,-\frac{28}{5})\cup (6,+\infty)[/tex]
A building's basement is 15 feet below ground. The building is square shaped with side lengths of 60 feet. If the height of the building is 55 feet, what is the length of the building from basement to roof? A) 40 feet B) 45 feet Eliminate C) 70 feet D) 75 feet
ABC is reflected across x = 1 and y = -3. What are the coordinates of the reflection image of B after both reflections?A. (-7, -1)B. (-7, 1)C. (7, 1)D. (7, -1)
Answer:
The correct option is C.
Step-by-step explanation:
From the given figure it is noticed that the coordinates of B are (-5,-7).
If ABC is reflected across x = 1, then
[tex](x,y)\rightarrow(1-(x-1),y)[/tex]
[tex](x,y)\rightarrow(2-x,y)[/tex]
[tex](-5,-7)\rightarrow(2+5,-7)[/tex]
[tex](-5,-7)\rightarrow(7,-7)[/tex]
If ABC is reflected across y =-3.
[tex](x,y)\rightarrow(x,-3-(y-(-3)))[/tex]
[tex](x,y)\rightarrow(x,-6-y)[/tex]
[tex](7,-7)\rightarrow(7,-6-(-7))[/tex]
[tex](7,-7)\rightarrow(7,1)[/tex]
Therefore option C is correct.
A farm lets you pick 3 pints of raspberries for $12.00 how many pints do you get per dollar
Answer:
0.25 pints of raspberries do you get per dollar.
Step-by-step explanation:
Unit rate defined as the rates are expressed as as a quantity of 1, such as 3 feet per second or 4 miles per hour, they are called unit rates.
As per the given statement: A farm lets you pick 3 pints of raspberries for $12.00.
⇒ for $12 a farm lets you pick 3 pints of raspberries.
then by unit rate definition,
Unit rate per dollar = [tex]\frac{3}{12} = \frac{1}{4} = 0.25[/tex] pint
Therefore, 0.25 pints of raspberries do you get per dollar.
Answer:0.25
Step-by-step explanation: hope I helped !
Jocelyn estimates that a price of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of Jocelyn's estimate?
Answer:
The percent error of Jocelyn's estimate is 2.14 .
Step-by-step explanation:
Formula
[tex]Percentage\ error = \frac{Error\times 100}{exact\ value}[/tex]
Where
[tex]error = \left | approx\ value - exact\ value \right |[/tex]
As given
Jocelyn estimates that a price of wood measures 5.5 cm.
If it actually measures 5.62 cm.
approx value = 5.5 cm
exact value = 5.62 cm
Put in the error formula
[tex]error = \left | 5.5 - 5.62 \right |[/tex]
[tex]error = \left | -0.12\right |[/tex]
error = 0.12
Put in the formula
[tex]Percentage\ error = \frac{0.12\times 100}{5.62}[/tex]
[tex]Percentage\ error = \frac{12}{5.62}[/tex]
Percentage error = 2.14 (Approx)
Therefore the percent error of Jocelyn's estimate is 2.14 .
What would I write in the boxes? Geomtetry help!
c) definition of midpoint
f) definition of congruency
g) property of rectangle (opposite sides are congruent)
h) SAS
i) CPCTC
You earned $34,000 and your total tax due was $6,200. What was your average tax rate? a) 8% b) 10% c) 18% d) 20%
Answer is C 18%
Step-by-step explanation:
Tax returns filed manually have a 20% chance of containing errors, while tax returns filed electronically have a 0.05% chance of containing the same. If 2.7 million tax returns are filed each way, how many more erroneous manually filed returns will there be than erroneous electronically filed returns? a. 270,675 b. 538,650 c. 541,350 d. 269,325
Answer:
B) 538, 650
Step-by-step explanation:
Given:
Errors on tax returns filed manually = 20%
Errors on tax returns filed electronically = 0.05%
Tax return filled in each way = 2.7 million
Manual filing:
2,700,000 x 20% = 2,700,000*0.2 = 540,000
Electronic filing:
2,700,000 x 0.05% = 2, 700,000*0.0005 = 1,350
Error difference = 540,000 - 1,350 = 538,650
There will be 538,650 more erroneous tax returns filed manually than there are filed electronically.
Thank you.
The difference between manually filed return and the electronically filed return is [tex]\boxed{538650}[/tex]. Option (b) is correct.
Further Explanation:
Explanation:
The total tax return is 2.7 million.
The errors on the tax return for electronic filling are [tex]0.05\%.[/tex]
The errors on the tax return for manual filling are [tex]20\%.[/tex]
Number of errors in filing tax return manually can be calculated as follows,
[tex]\begin{aligned}{\text{Errors in manual filling}} &= 2700000 \times 20\%\\ &= 2700000 \times \frac{{20}}{{100}} \\&= 540000\\\end{alignd}[/tex]
Number of errors in filing tax return electronically can be calculated as follows,
[tex]\begin{aligned}{\text{Errors in electronically filling}} &= 2700000 \times 0.05\% \\&= 2700000 \times \frac{{0.05}}{{100}} \\&= 1350 \\\end{aligned}[/tex]
The difference in the errors can be calculated as follows,
[tex]\begin{aligned}{\text{Difference}} &= 540000 - 1350 \\&= 538650 \\\end{aligned}[/tex]
The difference between manually filed return and the electronically filed return is [tex]\boxed{538650}[/tex]. Option (b) is correct.
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Learn more about inverse of the function https://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497Answer details:
Grade: High School
Subject: Mathematics
Chapter: Tax and Returns
Keywords: Tax, returns, filed, tax return, 20%, chance, errors, electronically, 0.05%, containing errors, chance, same, 2.7 million, each way, manually, manually filed, erroneous, 270575, income tax, salary, tax on salary.
Kendyl is memorizing a piece of saxophone music to perform at a local festival. She currently has the first eight bars memorized and plans to memorize two more bars everyday until she has the whole piece memorized. Write a recursive formula to model Kendyl's progress.
Answer:
The recursive formula to model Kendyl's progress is:
Fourth option: an=an-1 + 2, a1=8
Step-by-step explanation:
She currently has the first eight bars memorized: The first value is 8:
a1=8
She plans to memorize two more bars everyday until she has the whole piece memorized:
The number of bars memorized is two more than the last day:
an=an-1 + 2
Then, the recursive formula is:
an=an-1 + 2, a1=8
Answer:
The correct choice is D hope that helps
Which expression represents a number that is four times as large as the sum of 8 and 160?
Solve this system of linear equations. Separate the x- and y- values with a coma. 3x=36-15y. 11x =-78+15y
Answer:
(-3,3)
Step-by-step explanation:
3x=36-15y and 11x =-78+15y
We move all x and y terms to the left hand side of the equation , so that we can apply elimination method
3x=36-15y , Add 15 y on both sides , 3x + 15y = 36
11x =-78+15y, subtract 15y on both sides, 11x -15y = -78
Now we add both equations
3x + 15y = 36
11x -15y = -78
------------------------
14x = -42
divide both sides by 14
x= -3
Now Plug in -3 for x in any one of the given equation
3x=36-15y
3(-3) = 36 - 15y
-9 = 36 - 15y
Subtract 36 on both sides
-45 = -15y
Divide both sides by -15
So y= 3
Answer is (-3,3)
The population of at a town has grown 2% each year. In 1998, the population of the town was about 10,000 people. What was the population in 1999?
Answer:
10200
Step-by-step explanation:
The population in 1999 was 10200.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the population of at a town has grown 2% each year. In 1998, the population of the town was about 10,000 people.
Let the population be in 1999 be {x}. Then, we can write -
{x} = 10000 + {2% of 10000}
{x} = 10000 + {2/100 x 10000}
{x} = 10000 + 200
{x} = 10200
Therefore, the population in 1999 was 10200.
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On a field trip, there was 5 girls for every 8 boys. How many girls attended the 130-student field trip
36?
Bc if you divied 130/5 (girls) you get 36? Im sorry this may not be right, I'm not for sure :P
You and your friend each start a car-washing service. You spend $25 $ 25 on supplies and charge $10 $ 10 per car. Your friend spends $55 $ 55 on supplies and charges $13 $ 13 per car. How many cars do you have to wash to earn the same amount of money as your friend?
Answer:
If this is from TTM the answer is 10 cars.
Step-by-step explanation:
Write an equation of a line perpendicular to the line y = -1/5x -3 and goes through the point (6,2), then use Point- Slope form to write the equation of the line. Then convert into Slope-Intercept Form.
Answer:
The equation of the line would be y = 5x - 28
Step-by-step explanation:
First, we need to know that perpendicular lines have opposite and reciprocal slopes. Give that information, we know that the new line will be the reciprocal and opposite of -1/5. This would be 5. Now that we have that information, we can use it along with a point to fill in the point-slope form of the equation.
y - y1 = m(x - x1)
y - 2 = 5(x - 6)
Then we must solve for y.
y - 2 = 5(x - 6)
y - 2 = 5x - 30
y = 5x - 28
The daily cost of hiring a plumber,y,to work x hours on a repair project can be modeled using the linear function y=55x +75. The plumber charges a fixed cost of $75 plus sn additional cost of 55 per hour.The plumber works a maximum of 50 hours per week. For one week of work what is the domain of the function for this situation
The domain of the function for one week of work is all values of x that are less than or equal to 50.
The domain of a function represents the set of all possible input values for that function. In this situation, the function represents the daily cost of hiring a plumber for x hours of work, and the maximum number of hours the plumber works per week is 50. Therefore, for one week of work, the domain of the function is the set of all values of x that are less than or equal to 50.
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Linda went to a store and bought 2 items .Each item cost $12. How much money did she spend?
Answer:
24 dollars
Step-by-step explanation:
Linda spends $24 for two items that bought from the store.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
Given that,
Cost price of one time = $12.
Also, number of items that Linda bought = 2.
To find the total amount that Linda spends.
Use mathematical operations,
cost of 1 item = $12
Cost of 2 items = 12 x 2 = 24.
Hence, Linda spends $24 for 2 items.
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Tickets for a basketball game cost $2 for students and $5 for adults. The number of students was 3 less than 10 times the number of adults. The total amount of money from ticket sales was $619. How many of each ticket were sold?
Answer:
The no. of adult's tickets sold is 25.
The no. of adult's tickets sold is 247
Step-by-step explanation:
Given :
Tickets for a basketball game cost $2 for students and $5 for adults.
The number of students was 3 less than 10 times the number of adults.
The total amount of money from ticket sales was $619.
To Find : No. of each ticket were sold
Solution :
Let x be the no. of the student's tickets sold
Let y be the no. of adult's tickets sold
Since we are given that The number of students was 3 less than 10 times the number of adults.
⇒ x = 10y -3 --(A)
Now cost of 1 student's ticket is $2
Thus, cost of x student's ticket is $2x
Now cost of 1 adult's ticket is $5
Thus,cost of y adult's ticket is $5y
Since we are given that the total amount of money from ticket sales was $619.
⇒2x +5y =619 ---(B)
Solving equation A and B by substitution method :
putting value of x from (A) in (B)
We get :
⇒2( 10y -3) +5y =619
⇒20y-6+5y= 619
⇒25y = 625
⇒y = 625/25
⇒y=25
Thus, the no. of adult's tickets sold is 25.
Putting value of y in equation A to get value of x .
⇒x = 10(25) -3
⇒x = 247
Thus the no. of adult's tickets sold is 247
WILL AWARD BRAINLIEST!!!
Trisha needs to make at least 50 gift bags for an event. Each gift bag will contain at least 1 thumb drive or 1
key chain. She wants to use at least 5 times as many key chains as thumb drives. She has 25 thumb drives and 200 key chains.
Let x represent the number of key chains. Let y represent the number of thumb drives.
Write an inequality for this situation and graph the inequality.
Answer:
[tex]\ y\geq 5\cdot x\\x+y\geq 50\\y\leq25\\x\leq200\\y\geq0\\x\geq0[/tex]
Step-by-step explanation:
STEP 1 : First we draw the graph for [tex]y\geq 5\cdot x[/tex] by letting [tex]y=5x[/tex]
it is denoted by red colour
STEP 2 : Now we draw the graph for [tex]x+y\geq 50[/tex] by letting [tex]x+y=50[/tex]
It is denoted by orange colour
STEP 3 : Now we draw for [tex]y\leq25[/tex] by letting [tex]y=25[/tex]
It is denoted by green colour.
STEP 4 : Now we draw for [tex]x\leq200[/tex] by letting [tex]x=200[/tex]
It is denoted by blue colour.
Tristan is building steps up to a deck that is 156 5 6 yards above the ground. The steps must all be the same height. If he wants to make 8 steps, how high should he make each step?
Answer:
8 1/4
Step-by-step explanation:
(: (: (: (: (: (: (: (: (: (: (: (: (:
Answer:
3
Step-by-step explanation:
I can see it in the demonstration graph
Answer:
3
Step-by-step explanation:
Male: 12
Female: 9
12 - 9 = 3
Hopes this helps
Jose has scored 562 points on his math test so far this this semester. To get an A for the semester, he must score at least 650 points. Write and solve an inequality to find the minimum number of points he must score on the remaining tests in order to get an A
Answer:
562 + x ≥ 650
x ≥ 88
Step-by-step explanation:
He has 562 points. He needs x points to get an A. He must get at least 60 points to get an A.
562 + x ≥ 650
To solve this, we subtract 562 from each side
562-562 + x ≥ 650-562
x ≥ 650-562
x ≥ 88
Help plz!! Will mark brainliest!
Answer: point Q is located in (3,4)
Step-by-step explanation: the ratio of SQ:QT is 5:2, and for every two units (up two, right two) it is one ratio. go up two, right two five times that leads a ratio between 5:2.
I need help on this. Please
Answer: choice C, y = 0.014x+0.85
==============================
Explanation:
Each column of the table represents an (x,y) pair of values
x = number of pages
y = cost
If we look at the first two columns, we see the two points (50,1.55) and (100,2.25). The x value is listed first. Let's compute the slope of the line through these two points
m = (y2-y1)/(x2-x1)
m = (2.25-1.55)/(100-50)
m = 0.7/50
m = 0.014
So far, we see the answer is between A,B or C as they have the slope of 0.014
Use this slope value, and one of the points -- say (x,y) = (50,1.55) -- to find the y intercept b
y = mx+b
y = 0.014x+b .... plug in the slope found earlier
1.55 = 0.014*50+b ... plug in the point (x,y) = (50,1.55)
1.55 = 0.7+b
1.55-0.7 = 0.7+b-0.7 ... subtract 0.7 from both sides
0.85 = b
b = 0.85
With m = 0.014 as the slope and b = 0.85 as the y intercept, we can say that y = mx+b turns into y = 0.014x+0.85. That narrows the answer down to choice C.
Andy Taylor and Ben share their team payment in the ratio 1:3:4. What percentage of the total does Andy recieve?
Answer:
12.5%
Step-by-step explanation:
sum the parts of the ratio 1 + 3 + 4 = 8 parts
8 parts represents 100%, hence
1 part = [tex]\frac{100}{8}[/tex] = 12.5% ← Andy's percentage of the total
Andy Taylor's share in the ratio of 1:3:4 results in him receiving 12.5% of the total team payment.
Explanation:The question is about the sharing of a total team payment between Andy Taylor and Ben in the ratio of 1:3:4. To find out what percentage Andy receives, we first need to establish the total parts in the ratio. The ratio 1:3:4 sums up to 8 parts in total. Andy's share is represented by 1 part out of these 8. To find the percentage, we divide Andy's 1 part by the total 8 parts, multiply by 100, giving us 12.5%. This means that Andy receives 12.5% of the total team payment.
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A jogger runs 91 yd in 10.00 seconds. What would be his time for a 449 m run at the same rate? Answer in units of s.
Answer:
4,910 seconds
Step-by-step explanation:
Please help!!
Which value of y is a solution of the inequality? 2y+9≤11
y = 1
y = 2
y = 11
y = 9
Answer:
y=1 for [tex]y\leq 1[/tex]
Step-by-step explanation:
We can solve an inequality much like we solve an equation. We will use inverse operations to isolate y. If we need to divide by a negative then we will need to flip the inequality.
[tex]2y+9\leq 11\\2y+9-9\leq 11-9\\2y\leq 2\\\frac{2y}{2}\leq \frac{2}{2} \\y\leq 1[/tex]
First, we moved 9 across the equal sign to combine it with 11 by subtracting by 9 from both sides.
Second, we divided both sides by 2.
[tex]y\leq 1[/tex] is the solution. All solutions equal to 1 and less than 1 will work.
1.)What number needs to be added to both sides of the equation in order to complete the square? x2+16x=18
answer is 64
x^2+16x+64=18+64
2.)Solve for x over the complex numbers.
x2+10x+41=0
answer is x=-5+4i and -5-4i
3.)What is the factored form of the expression over the complex numbers?
16x2+9y2
answer is (4x+3iy)(4x-3iy)
Answer:
all of your answers are correct
1.) 64
2.) x= -5+4i and x= -5-4i
3.) (4x+3iy)(4x-3iy)
Answer:
1.When we are completing squares, we need to divide by 2 the linear term and then find its square power, that's the term we need to add on both sides of the equality, as follows
[tex](\frac{16}{2})^{2} =(8)^{2}=64[/tex]
Basically, we need to add the number 64 both sides
[tex]x^{2} +16x+64=18+64[/tex]
2.The given equation is
[tex]x^{2} +10x+41=0[/tex]
We need to apply the quadratic formula to solve this equation
[tex]x_{1,2} =\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Where [tex]a=1[/tex], [tex]b=10[/tex] and [tex]c=41[/tex]. Replacing these values, we have
[tex]x_{1,2} =\frac{-10(+-)\sqrt{10^{2}-4(1)(41) } }{2(1)}\\x_{1,2} =\frac{-10(+-)\sqrt{100-164 } }{2}=\frac{-10(+-)\sqrt{-64} }{2}[/tex]
There we need to use complex number, to transform the subradical number in a positive number
[tex]x_{1,2}=\frac{-10(+-)\sqrt{64}i }{2}=\frac{-10(+-)8i}{2}\\ x_{1,2}=-5(+-)4i[/tex]
Therefore, the complex solutions are
[tex]x_{1}=-5+4i\\ x_{1}=-5-4i[/tex]
3.The given expression is
[tex]16x^{2} +9y^{2}[/tex]
To solve this expression, remember that [tex]i=\sqrt{-1}[/tex]
First, we expresse both squares uniformly,
[tex]16x^{2} +9y^{2}=(4x)^{2}+(3y)^{2}[/tex]
But, we know that [tex]-(-1)=1[/tex], so
[tex](4x)^{2}+(3y)^{2}=(4x)^{2}-(-1)(3y)^{2}[/tex]
Then,
[tex](4x)^{2}-(-1)(3y)^{2}=(4x)^{2}-(3y)^{2}i^{2}[/tex], because [tex]i^{2}=-1[/tex]
Therefore, the expression with complex numbers is
[tex](4x)^{2}-(3iy)^{2}\\\therefore (4x+3iy)(4x-3iy)[/tex]
In circle O, AE and FC are diameters. Arc ED measures 17°. What is the measure of ? °
Hey There!
The answer is going to be the answer is
mEFC=253°
To find the answer you must find the value of mEF which is
mEF,mFEC,mDC,mED
You subtract each of them and you should get 73.
Then add 180 and your final choice should be 253
Answer:
253
Step-by-step explanation:
Calculate the value of the exterior angle
10
95
3.57
1.4
Answer:
95
Step-by-step explanation:
We have been given a diagram triangle in which measurement of few angles in terms of x are given.
Using those we need to find the exterior angle but before that we need to find the value of x.
We know that exterior angle is equal to sum of two distant interior angles of that triangle so we can write:
(8x+15)=(3x+20)+(4x+5)
8x+15=3x+20+4x+5
8x+15=7x+25
8x-7x=25-15
x=10
Now plug x=10 into exterior angle 8x+15
8x+15=8*10+15=80+15=95
Hence final answer is 95.