Circle C has radius 8 ft with an arc AB intercepted by a central angle of pi/4 radians. What is the length of arc AB expressed in
terms of pi?
Answer:
b
Step-by-step explanation:
The arc length is, 720 ft.
How to find the relation between angle subtended by the arc, the radius and the arc length?[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
Length of an arc is given by:
l = r Ф .....[1]
where r is the radius of the circle and Ф is the angle in radian.
From the given information;
In a circle with a radius 8 ft with an arc AB intercepted by a central angle of pi/4 radians.
r = 8 ft and radian pi/4
Substitute these values in [1] we have;
l = r Ф
l = 8 x pi/4 ft.
l = 4 pi
l = 4 x 180
l = 720 ft
therefore, the arc length is, 720 ft.
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In ABC segment DC bisects /_C and divides AB into segment AD and BD. CD = 6 units and AC = 8.5, then which statement would
justify that ACD - BCD?
Answer:
ABC=BCD wtdf
Step-by-step explanation:
What is 5 times the quotient of 3 and 5?
Answer: 3
Step-by-step explanation:
5 X 3/5 = 3
9. Find the range, mean, median, and mode of the following data set. 5, 17, 21, 21, 7, 13, 1, 3 a. Range 20 Mean 11 Median 10 Mode 21 c. Range 20 Mean 10 Median 10 Mode 21 b. Range 24 Mean 11 Median 10 Mode 21 d. Range 20 Mean 11 Median 21 Mode 21
an open concrete tank is internally 1m wide, 2m long and 1.5m deep, the concrete being 10cm thick. Calculate the capacity of the tank in litres
The capacity of the tank is 3000 liters
Calculations and ParametersWe would first find the volume of concrete:
(0.1*1.5*1*2)+(0.1*1.5*2(0.1*2))*2)+(0.1*1.2*2.2)
=0.3+0.66+0.264
=[tex]1.224 m^3[/tex] of concrete
The capacity of the tank in liters:
1x2x1.5
=[tex]3m^3[/tex] or 3000 liters
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A tile is a square with an area of 64 cm square
Answer:
To find the perimeter, we will first find the side of the square tile.
Area - side ×side64 = side×side64=side² 8×8= side8=side Side = 8 cm.ㅤ
Now,let us find perimeter.
Perimeter - 4 ×side=4×8= 32cm Perimeter - 32cm.jaden makes 63% of the free throws he shoots. About how many shots do you predict he will have to take to make 15 free throws?
Answer:
I don't understand
Step-by-step explanation:
but hope u will understand
Answer:
3
Step-by-step explanation:
1. Find the focus of the parabola that has vertex (-7, 2), opens vertically, and passes through the point (-5,0).
A manufacturer produces safety jackets for competitive fencers. These jackets are rated by the minimum force, in newtons, that will allow a weapon to pierce the jacket. When the production process is operating correctly, it produces jackets that have ratings with an average of 840 newtons and a standard deviation of 14 newtons.FIE, the international governing body for fencing, requires jackets to be rated at a minimum of 825 newtons.To check if the process is operating correctly, a manager takes a random sample of 49 jackets from the process, rates them, and calculates the mean rating for jackets in the sample, which turns out to be 830 newtons. She is confident that the standard deviation of the process is at the specified value of 14 newtons.What is the p-value of the appropriate test if she wants to check if the production process currently meets the FIE standards
Answer:
0
Step-by-step explanation:
H0 : μ = 840
H1 : μ < 840
Sample size, n = 49
Standard deviation, s = 14
Test statistic = (xbar - μ) ÷ (s/√(n))
Test statistic = (830 - 840) ÷ (14/7)
Test statistic = - 10 / 2
Test statistic = - 5
The Pvalue ;
Pvalue = P(Z < - 5) = 0 (Z probability calculator)
The Pvalue = 0
Ms. Sharon bought 84 litre of cooking oil. She used 1/3 of it on Monday and another 20 litre
of it on Tuesday.
a) How much oil she used on Monday?
b) How much cooking oil did she use altogether?
c) How much cooking oil was left with her?
d) Write the fraction of cooking oil left with her
Find mZRTS.
R
112°
S
T
Answer:
RTS=(180-112)/2
=68/2
=34
P
Jimmy tried to solve the system of equations below, but he made an error
S 2.0
y=18
y= 40 +2
His work is shown. Find the error he made. Explain the error and show how to solve the sysm correctly.
1. 2.0 - 4.3 + 2 = 18
2.-2x = 16
3. = -8
4. y=4(-8) + 2
5. Y = -32 +2
6. y=-30
7. Check: 2 (-8) - (-30) = 18
8.
- 16 + 30 = 18
9 14 + 18
His mistake was on Line
because he should have
The correct solution is
Answer:
"His mistake was on line 1. He didn't distribute the negative sign (indicating a -1) to everything in the equation for y."
The correct solution is: x = -10, y = -38
Step-by-step explanation:
2x - y = 18
y = 4x + 2
Substitute the given value for y into the first equation:
2x - (4x + 2) = 18
2x - 4x - 2 = 18 ** here, he didn't distribute the (-) to everything in the parentheses that represents y
-2x -2 = 18
add 2 to both sides
-2x = 20
divide by -2
x = -10
-------------------
solve for y
y = 4x + 2
y = 4(-10) + 2
y = -40 + 2
y = -38
------------------
Check the math:
2x - y = 18
2(-10) - (-38) = - 20 + 38 = 18
Through (-2,-1) and perpendicular to the graph of F(x) - 1/5x + 1 ( function notation)
The equation of line that passes through (-2,-1) and is perpendicular to f(x) = (-1/5)x + 1 is f(x) = 5x + 9.
What is the equation of line that passes through the given point and is perpendicular to f(x) = (-1/5)x + 1?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the graph
f(x) = (-1/5)x + 1
Using the slope intercept, slope m is -1/5
The equation of a perpendicular line to f(x) = (-1/5)x + 1 must have a slope that is the negative reciprocal of the graph.
Slope of perpendicular line = -1 / (-1/5)
Slope of perpendicular line = 5
Plug the slope m = 5 and point (-2,-1) into point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
( y - (-1) ) = 5( x - (-2) )
( y + 1 ) = 5( x + 2 )
y + 1 = 5x + 10
y = 5x + 10 - 1
y = 5x + 9
f(x) = 5x + 9
Therefore, the equation of the perpendicular line is f(x) = 5x + 9.
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The perimeter of a rectangle is 408cm and the length is 134cm. Find the rectangle’s width.
Answer: 70 cm
Step-by-step explanation: perimeter = 2*width + 2*length
408 = 2*width + 2*134
408 = 2*width + 268
Subtract 268 from both sides.
140 = 2*width
DIvide both sides by 2
Width = 70 cm
Answer:
The width of the rectangle is 70 cm
Step-by-step explanation:
Given,
The perimeter of a rectangle is 408 cmThe length is given as 134 cmTo Find : The width of the rectangle
As we know, the formula to find the Perimeter of the rectangle is
[tex]P = 2(l+b)[/tex]
Now the Perimeter is given and the length
[tex]408 = 2(134 + b)[/tex]
Now using distributive property
[tex]408 = 268 + 2b[/tex]
[tex]408 - 268 = 2b[/tex]
[tex]140 = 2b[/tex]
[tex]\frac{140}{2} = b[/tex]
[tex]70cm = b[/tex]
Hence, the width of the rectangle is 70 cm
Two functions are shown below.
f(x) = 3x2 + 14x - 5
g(x) = 11x + 13
Select (click) the points at which the graphs of the two functions intersect.
(5,0)
(-3, -20)
(2, 35)
(6, 79)
Answer: (-3,20) (2,35)
Step-by-step explanation: well if the 2 is an exponent then this is the answer, I don’t know the step by step though sorry. <3
Please help no links look at picture ^^
Answer:
i cant see it
Step-by-step explanation:
g(x) = (2 (x+3))^3 + 4
.....................................
John made a kite with all four sides the same length, as shown below. What is the perimeter of the kite?
help ple
Answer:
A
Step-by-step explanation:
The formula to find the perimeter of a rhombus is p=4a
and 4 times 1 2/3= 4 2/3
Apskaičiuokite pavaizduoto kūgio tūrį. Laikykite, kad π≈3
Answer:
Say wahhhhh!
Step-by-step explanation:
A triangle has sides with lengths 8, 15, and 17. approximate the acute angles in this triangle to the nearest degree and list in ascending order
Answer:
28°, 62°
Step-by-step explanation:
As 8,15,17 is a Pythagorean Triple, the triangle must be a right triangle. Hence, we can use our common trig ratios to solve the problem. Let's assume our right triangle has a base of 8, a height of 15, and a hypotenuse of 17.
Here are all the acute angles in order:
[tex]\cos^{-1}(\frac{15}{17})\approx28^\circ[/tex]
[tex]\sin^{-1}(\frac{15}{17})\approx62^\circ[/tex]
Rosa Bought some place mats costing $17.16 and some napkin ring’s costing $10.36.If there were 4 place mats and 4 napkin ring’s what was the total cost for 1 place mat and 1 napkin ring?
Brian is trying to lose at least 2 pounds a week by eating less and walking 2 miles each day. For the past 3 weeks,he lost 2.4 pounds,1.9,and 3.2 pounds. what was the average number of pounds he lost?
Can someone answer these?
9514 1404 393
Answer:
$6.882.5 poundsStep-by-step explanation:
1. In this case, it appears that "some" means "4". The total cost of 4 place mats and 4 napkin rings is apparently ...
$17.16 +10.36 = $27.52
Then the total cost of 1 of each is 1/4 this amount, or ...
$27.52/4 = $6.88
__
2. The average of three numbers is their sum, divided by 3.
(2.4 + 1.9 + 3.2)/3 = 7.5/3 = 2.5
Brian lost an average of 2.5 pounds per week.
suppose 210 subjects are treated with a drug that is used to treat pain and 53 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20% of users develop nausea.
Find two Equivalent fractions of 4/2
Answer:
40/20 & 22/11
Step-by-step explanation:
To find an equivalent fraction to 4/2, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:By dividing the original fraction by 2, we get:4 ÷ 2 / 2 ÷ 2 = 21. By multiplying the original fraction by 2, we get:4 × 2 / 2 × 2 = 8/4. Here is the full list of equivalent fractions to 4/2. 2/1, 4/2, 6/3, 8/4, 10/5, 12/6, 14/7, 16/8, 18/9, 20/10, 22/11, 24/12, 26/13, 28/14, 30/15, 32/16, 34/17, 36/18, 38/19, 40/20...
Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa. how many dvds does marissa own?
The number of Dvds owned by Maarissa is 45
How to find the number of dvds?The given parameters that will guide us in finding the number of dvds owned by marissa are
Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa.
Let the number of dvds owned by Marissa be x
Nymber of dvds owned by Kyle be y
This implies that x+y = 66 ............................1
also, 2y + 3 = x ..................................................2
Substitute x = 2y + 3 in equation 1
= 2y + 3+y =66 Collecting like terms
⇒ 3y = 63
Making y the subject of the relation we have y=21
Recall that 2y + 3 = x
That means x = 2(21) + 3
x=45
Therefore Marrissa owns 45 dvds
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evaluate: a+b/c if a = -6,b = -4 and c= -2
Answer:
5
Step-by-step explanation:
-6+(-4)/-2
-6-4/-2
-10/-2
5
Solve for each variable.
Explain how as well please
I will give brainlist if you give me an answer and not a link or something weird
Answer:
a = 38⁰
b = 54⁰
c = 54⁰
Step-by-step explanation:
a + 142⁰ = 180⁰ because a straight line = 180⁰
b + 38⁰ + 88⁰ = 180⁰ because the angles of a triangle equal 180⁰, and the missing measurement = 38⁰ because it is a vertical angle to angle a
c + 88⁰ = 142⁰ because the angles are corresponding angles
60, 80, 100
Right traingle
Can someone help me with this? It's urgent.
The table is filled as described , shown below.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here, we have,
Rate per hour is $11.25
Number of regular hours is 40
Payment for regular hours:
time multiply with payment=
40*$11.25 = $450
Again, we have,
Rate per overtime hour:
$11.25*1.5 = $16.875 ≈ $16.88 (rounded up)
Number of overtime hours:
48.5 - 40 = 8.5
Payment for overtime hours:
$16.88*8.5 = $143.48
Now, we get ,
Gross payment is the sum of regular and overtime payments:
$450 + $143.48 = $593.48
Hence, he would get $593.48
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Identify the sequence that lists sides of STU in order from shortest to longest
ST, UT, SU
UT, SU, ST
SU, ST, UT
SU, UT, ST
On soloing the provided question we can say that - Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area. A = 210-123 = 87 sq unit
what is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
the sum of the areas of the circle, the triangle, and the square.
Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area.
A = 210-123 = 87 sq unit
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Find the value of each variable for each circle. Show your work
The values of the variables in the circles are
Circle 1: a = 34 degreesCircle 2: a = 58 degrees, b = 90 degrees and c = 61 degreesHow to determine the values of the variables in the circles?From the question, we have the following parameters that can be used in our computation:
Circles and missing angles (see attachment for the figures)
Circle 1
To determine the unknown variable (a), we make use of the following theorem
The angle subtended by an arc at the circumference is twice the angle subtended at the circumference
Mathematically, this means that
a = 2 * 17 degrees
Evaluate the product
a = 34 degrees
Circle 2
To determine the unknown variable (a), we make use of the following theorem
The angle at the circumference in a semicircle is 90 degrees.
Mathematically, this means that
b = 90 degrees
Also, we have
a + 122 degrees = 180 degrees
Evaluate
a = 58 degrees
Using the theorem in (a), we have
b + a/2 + c = 180
This gives
90 + 58/2 + c = 180
Evaluate the like terms
c = 61 degrees
Hence, the angle c is 61 degrees
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