Answer:
Total weight of blades = ~134gm
Step-by-step explanation:
Radius of circle, [tex]r[/tex] = 4 inches
Central angle of sector = [tex]20^\circ[/tex]
For finding the weight of blades, we need to find the area of blades.
Area of circle, A = [tex]\pi r^{2}[/tex]
We know that circle has a central angle of [tex]360^\circ[/tex].
We can use unitary method to find the area of sector with angle [tex]20^\circ[/tex].
Area of [tex]360^\circ[/tex] central angle = [tex]\pi r^{2}[/tex]
Area of [tex]1^\circ[/tex] central angle = [tex]\dfrac{\pi}{360} r^{2}[/tex]
Area of [tex]20^\circ[/tex] central angle = [tex]\dfrac{\pi}{360} r^{2} \times 20[/tex]
Putting value of r = 4 inches
Area of blade:
[tex]\dfrac{\pi}{360} \times 4^{2} \times 20\\\Rightarrow 2.79\ in^{2}[/tex]
We have 3 blades here, so area of 3 blades =
[tex]2.79 \times 3\\\Rightarrow 8.38\ in^{2}[/tex]
Weight of steel = 16 grams per square inch
Total weight of all 3 blades = 16 [tex]\times[/tex] 8.38 = ~ 134gm
4
Find the arc length of the partial circle.
Either enter an exact answer in terms of or
use 3.14 for and enter your answer as a
decimal.
units
Answer:
12.56
Step-by-step explanation:
The arc length of the partial circle is L = 18.849 units
What is Central Angle?The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.
The central angle of a circle formula is as follows.
Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
r is the radius of the circle
Central Angle = 2 x Angle in other segment
Given data ,
Let the radius of the circle be r = 4 units
Let the arc length of the circle be L
Let the central angle be = 270°
So , Central Angle = ( s x 360° ) / 2πr
On simplifying , we get
L = ( 270° / 360° ) x 2πr
L = ( 3/4 ) ( 8π )
L = 18.849 units
Hence , the arc length of the circle is 18.849 units
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An architect is designing a house. He wants the bedroom to have the dimensions of 8 ft by 4 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume of the bedroom. Solve on paper. Then check your work on Zearn. The bedroom will be ft3.
Answer:
No. The den will have 8 times the volume of the bedroom.
Step-by-step explanation:
The architect wants the bedroom to have the dimensions of 8 ft by 4 ft by 7 ft. Let's find the volume of the bedroom:
8 * 4 * 7 = 224 cubic feet
The architect doubles all three dimensions to create the den. This means that the den has dimensions as 16 ft by 8 ft by 14 ft.
The volume of the den is:
16 * 8 * 14 = 1792 cubic feet
Double of 224 cubic feet is 448 cubic feet.
Hence, the den will not have double the volume of the bedroom instead it will have a volume 8 times the that of the bedroom.
Doubling the initial dimensions of 8 ft. by 4 ft. by 7 ft. means that the
volume will 8 times the initial volume or 1,792 ft.
What is the scale factor of volume be used?
The dimensions of the room = 8 ft. by 4 ft. by 7 ft.
The amount by which the architect increases the dimension = Double the dimensions
Solution;
The volume of the room, V = 8 ft. × 4 ft. × 7 ft. = 224 ft.³
When the dimensions are doubled, we have;
Length = 2 × 8 ft. = 16 ft.
Width = 2 × 4 ft. = 8 ft.
Height = 2 × 7 ft. = 14 ft.
The new volume of the bedroom = 16 ft. × 8 ft. × 14 ft. = 1792 ft.³
Therefore;
The volume of the bedroom after doubling the dimension will be 1,792 ft.³Scale factor of volume = (Scale factor of length)³
Therefore;
Doubling the dimensions means that the volume of he room will be
multiplied by 2³ = 8 rather doubling the initial volume.
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Which represents the solution(s) of the system of equations, y = –x2 + 6x + 16 and y = –4x + 37? Determine the solution set algebraically.
Answer:
The equations had 2 solutions:
x = 3, y = 25 or x = 7, y = 9
Step-by-step explanation:
(x - 6) x + y = 16, 4 x + y = 37
y = 37 - 4 x
x2-6x+37-4x-16=0
x2-10x+21=0
(x - 7) (x - 3) = 0 -> x =3 or x = 7
Answer:
C. is right on edg.
for the Black Panther trip 420 students were scheduled to go. After selecting more parents surveys 15% more students are going on the trip each Administration ticket cost 22.75 dollars what was the total amount pay for all the tickets purchased
Answer: $10988.25
Step-by-step explanation:
From the question, we are told that for the Black Panther trip 420 students were scheduled to go and 15% more students were selected. This means that the total number of students that are going will be:
= 420 + (15% × 420)
= 420 + (0.15 × 420)
= 420 + 63
= 483 students
Since each administration ticket cost 22.75 dollars. The total amount paid for all tickets purchased will be:
= 483 × $22.75
= $10988.25
Joey is building a frame for a sandbox. The sandbox is going to be a quadrilateral that has the lengths shown. A rectangle is shown. The length of the top and bottom sides are 8 feet, and the length of the left and right sides are 12 feet. A diagonal that is 14 feet long is drawn from the bottom one corner of the rectangle to the other corner of the rectangle. Points X and C are opposite to the diagonal. If the diagonal of the sandbox measures 14 feet, which best describes the shape of the sandbox? a rectangle, because angle C is a right angle a rectangle, because angle C and angle X are congruent a quadrilateral, because angle C and angle X are acute a quadrilateral, because angle C and angle X are obtuse
Answer:
C) a quadrilateral, because angle C and angle X are acute
Step-by-step explanation:
It is a quadrilateral because angle C and angle X are acute angles and not right angles option third is correct.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners. It has two pairs of congruent sides and one pair of opposite congruent angles.
From the Pythagoras theorem:
[tex]14^2=12^2+8^2[/tex]
196 ≠ 208
The angles C and X are not right angles since angles C and X are congruent and acute angles.
Thus, it is a quadrilateral because angle C and angle X are acute angles and not right angles option third is correct.
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Work out m and c for the line: y = x − 6
Answer:
As y = mx + c (standard form)
Thus relating the equation , we get
m = 1
c = -6
Answer:
m = 1
c = -6
Step-by-step explanation:
m is the gradient of the line.
c is the intercept of the line.
The formula for it is : y = mx+c
so m = 1
c = -6
Hope this helps
Suppose you physically simulate the random process of rolling a single die. (a) After 1010 rolls of the die, you observe a "one" 44 times. What proportion of the rolls resulted in a "one"? (b) After 2020 rolls of the die, you observe a "one" 22 times. What proportion of the rolls resulted in a "one"?
Answer:
(a) 0.4 or 40%
(b) 0.1 or 10%
Step-by-step explanation:
(a) If you get 4 "ones" after 10 rolls of the die, the proportion of the rolls that resulted in "ones" is:
[tex]p=\frac{4}{10}\\ p=0.4[/tex]
(b) If you get 2 "ones" after 20 rolls of the die, the proportion of the rolls that resulted in "ones" is:
[tex]p=\frac{2}{20}\\ p=0.1[/tex]
Can someone please help me it’s geometry
Answer:
No, the triangles are not congruent.
Step-by-step explanation:
Triangle HOT has AAS, whilst triangle CLD has ASA. Therefore, the triangles are not congruent. There is also no way to prove that HOT and CLD are isoscles triangles, which means we cannot use ASA or AAS.
Which pair of polygons are congruent?
A) pairs 1,2,3,and 4
B) pairs 1 and 4
C) pairs 1,2,and 3
D) pairs 2 and 4
Pair 2 shows one figure rotated 180 degrees compared to the other, and translated as well. So they are congruent (ie the same).
Pair 4 shows one triangle reflected over the vertical line x = 22 to get the other triangle; which shows they are the same triangle.
The other pairs are not congruent. You can show that the areas of each figure being different is enough to prove they aren't the same figure.
Identify the vertex of the function, fx) = 3(x - 1)2 + 5.
Answer:
fx) = [tex]3x+4[/tex]
Step-by-step explanation:
1. step:
solve the bracket
fx) = 3([tex]x[/tex] - 1) 2 + 5
[tex]fx) = 3x-1+2+5[/tex]
2. step:
use the BEDMAS form.
fx) = [tex]3x-3+7[/tex]
fx) = [tex]3x+4[/tex]
Liner equation Melissa and Jane are planting trees Melissa plants 10 tree in 1 hour Jane plants 17 trees in 2 hours enter an equation that can be used to find the number of hours t t takes Melissa and Jane to plant 111 trees together
Answer:
6 hours
Step-by-step explanation:
What we must do is calculate the speed of each one,
Melissa in one hour plants 10 trees, that is 10/1 is her speed.
Jane in two hours plants 17 trees, that is 17/2 is her speed.
Now, we want to know the time it takes to plant 11 trees, so the sum of the previous speeds is equal to 111 / x
10/1 + 17/2 = 111 / x
18.5 = 111 / x
x = 111 / 18.5
x = 6
Which means that in 6 hours between the two they can plant 111 trees
which choice is equivalent to the expression below ? sqrt -12
The expression that is equivalent to √-12 is √12i
What are complex numbers?In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation[tex]i^{2}=-1}[/tex] every complex number can be expressed in the forma + bi, where a and b are real numbers.
Given here, √-12= √12×√-1
= √12i
Hence, The expression that is equivalent to √-12 is √12i
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this graph shows the solution to which inequality?
Answer:
the answer is B
Step-by-step explanation:
based on coordinate (3,2) :
y ≥ 4/3(3) - 2
2 ≥ 2
based on coordinate (-3,-6)
y ≥ 4/3(-3) -2
-6 ≥ -6
* the symbol is ≥ because the shaded region is above the line
Jack, Davis, Faiza, and Marry want to take a picture together. In how many ways can they are arranged?
Answer:
16
Step-by-step explanation:
Solve for r.
–7r = –8r − 20
r =
Answer:
r = -20
Step-by-step explanation:
–7r= –8r−20
Add 8r to both sides
r = -20
Answer:
[tex] \boxed{r = -20} [/tex]
Step-by-step explanation:
[tex] = > - 7r = - 8r - 20 \\ \\ = > - 7r + 8r = - 20 \\ \\ = > 8r - 7r = - 20 \\ \\ = > r = - 20[/tex]
A 32cm long string just fits round the perimeter of a square board. The area of the board is
Answer:
64cm2
Step-by-step explanation:
(32÷4)=8
8×8=64cm2
Answer:
64cm²
Step-by-step explanation:
perimeter of a square= 4 x side of the square
perimeter= 32cm
i.e side of the square= 32/4
side= 8cm.
Area of square = side of the square ²
=8²
therefore, area of square = 64cm²
What is the complementary angle of an angle that measures 30 degrees?
A. 90 degrees
B. 20 degrees
C. 150 degrees
D. 60 degress
Answer:
Step-by-step explanation:
If 2 angles are complementary, that means that they add up to 90 degrees.
The angle complementary to a 30-degree angle has to measure 60 degrees. D is your choice.
A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of
64 square meters. What is the length of the other base?
The length of the other base is 4 meters.
What is a trapezium?It is a quadrilateral that has one pair of parallel sides and a height.
The area is calculated as 1/2 x the sum of the parallel sides x height.
Examples:
Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.
Area = 1/2 x (3 + 4) x 5
Area = 1/2 x 7 x 5
Area = 35/2 = 17.5 cm^2
We have,
The area of a trapezoid.
A = (1/2) h (b1 + b2)
where A is the area, h is the height, b1, and b2 are the lengths of the two bases.
We are given,
h = 8, b1 = 12, and A = 64.
We can substitute these values into the formula and solve for b2:
64 = (1/2)(8)(12 + b2)
Simplifying:
64 = 4(12 + b2)
16 = 12 + b2
b2 = 4
Therefore,
The length of the other base is 4 meters.
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In ΔIJK, the measure of ∠K=90°, IK = 9, JI = 41, and KJ = 40. What ratio represents the sine of ∠I?
Answer:
The ratio is 40/41
Step-by-step explanation:
In this question, we are to find the ratio that represents sine of angle I
Firstly, let’s consider the diagram of the triangle attached.
When we talk of sine, what we mean is the trigonometric identity which measures the ratio of the opposite to the hypotenuse.
Since the angle we are considering is I, the opposite is 40, while the hypotenuse is 41 ( the longest side of the triangle and the side that faces the angle 90, which is the length JI)
Thus,
mathematically sine I = 40/41
Answer:
Step-by-step explanation:
Find the slope and y-intercept: (4,2) (8,4)
Answer:
Slope: 1/2
Y-Intercept: 0
Step-by-step explanation:
Use the slope formula and the slope-intercept form to find the slope (m) and y-intercept (b ).
Brett has a $30 online gift voucher. He plans to buy as many books as he can. The cost of each book is $4. There is also a single shipping charge of $2. How many books can he afford without spending more than his gift voucher amount
How would i put that as a inequality i really need the answer quickly!
Answer:
Brett can afford 5 books.
Step-by-step explanation:
each book is $4 and an additional charge of $2 for shipping.
4 + 2 = 6
6 x 5 = 30
brett will spend exactly $30
There are 12 horses competing in a show. In how many ways can the blue, red, and yellow ribbons be awarded?
Answer
Answer:
There are 12 choices for the blue ribbon, 11 choices for the red and 10 choices for yellow so the answer is 12 * 11 * 10 = 1320.
WOULD LOVE IF SOMEONE CAN ANSWER THIS FOR ME, NEED HELP ASAP
Answer:
B
Step-by-step explanation: If you look at the graph, the only graph with (0,0) is B
Answer:
B
Step-by-step explanation:
Which statements about experimental probability are true?
Experimental probability is written as a ratio.
Experimental probability includes the number of possible outcomes.
Experimental probability is found by conducting trials of an experiment.
Experimental probability includes the number of times an event occurs in the numerator, and the total number of trials in the denominator.
Experimental probability includes the number of times an event occurs in the denominator, and the total number of trials in the numerator.
Answer:
free points
Step-by-step explanation:
first, third, and fourth options
Answer:
1,3,4
Step-by-step explanation:
e2020
a square whose sides are 12 inches long has been shaded and then overlaid with two quarter circles, each of which having a radius of 6 incches. What percent of the total area is shaded
Answer:
71.8%Step-by-step explanation:
The shape described in question is a square overlaid with two quarter circles(a semi circle)
Area of the figure = Area of the square + area of the semi circle
Area of the figure = [tex]L^{2}+\frac{\pi r^{2} }{2}[/tex]
L = length of a side of the square = 12in
r is the radius of the semi circle = 6in
Area of the figure = [tex]12^{2} + \frac{36\pi }{2} }\\[/tex]
Area of the figure = [tex]144+18\pi[/tex] = 200.55in²
Since the shaded portion is a square;
percent of the total area is shaded = area of the square/total area * 100%
percent of the total area is shaded = 144/200.55* 100
percent of the total area is shaded= 71.8%
Simplify, using the distributive property and then combining like terms.
4m−3(2m+1)
Answer:
4m−3(2m + 1)
= 4m - 3*2m - 3*1
= 4m - 6m - 3
= -2m - 3
Hope this helps!
:)
Answer:
-2m - 3
Step-by-step explanation:
Remember to follow PEMDAS. First, distribute -3 to all terms within the parenthesis:
-3(2m + 1) = (-3 * 2m) + (-3 * 1) = -6m + (-3)
4m - 6m - 3
Simplify. Combine like terms:
(4m - 6m) - 3
(-2m) - 3
-2m - 3 is your answer.
~
Some of the steps in the derivation of the quadratic formula are shown. Step 3: –c + b^2/4a=a(x^2+b/ax+b^2/4a^2 step4a: -c+b^2/4a=a(x+b/2a)^2 step4b: -4ac/4a+b^2/4a=a(x+b/2a)^2 Which best explains or justifies Step 4b? factoring a polynomial multiplication property of equality converting to a common denominator addition property of equality
Answer:
(C)Converting to a common denominator
Step-by-step explanation:
Given some of the steps in the derivation of the quadratic formula below:
[tex]\text{Step 3:} -c + \dfrac{b^2}{4a}=a(x^2+ \dfrac{b}{a}x+ \dfrac{b^2}{4a^2})\\\\\text{Step 4a:} -c + \dfrac{b^2}{4a}=a(x+\dfrac{b}{2a})^2\\\\\text{Step 4b:} \dfrac{-4ac}{4a}+ \dfrac{b^2}{4a}=a(x+\dfrac{b}{2a})^2[/tex]
Step 4b is derived from Step 4a by converting the left-hand side to a common denominator 4a.
Therefore, that which best explains or justifies Step 4b is:
(C)Converting to a common denominator
Answer:
C
Step-by-step explanation:
lol
What is the length of the hypotense,c?
26 m
29 m
34 m
36 m
Answer:
Choice C
Step-by-step explanation:
Using the Pythagorean theorem, you can find that the length of the hypotenuse is:
[tex]\sqrt{3^2+5^2}=\\\\\sqrt{9+25}=\\\\\boxed{\sqrt{34}}[/tex]
Hope this helps!
Answer:
[tex]c=\sqrt{34}[/tex]
Step-by-step explanation:
Using the Pythagorean theorem (a^2 + b^2 = c^2), you can find the hypotenuse
Begin by plugging in 3 into a and 5 into b.
3^2 + 5^2 = c^2
9 + 25 = c^2
34 = c^2
Then, take the square root of both sides.
[tex]\sqrt{34} =\sqrt{c^{2} }[/tex]
[tex]c=\sqrt{34}[/tex]
A bag contain 6 red and 5 green identical balls.
Two ball are draw at random one after the
other without replacement. What is the
probability that both balls are of the same
colour
Answer:
3/11 for two red balls
2/11 for two green balls
Step-by-step explanation:
6 red and 5 green balls
first ball - red= 6/11, green= 5/11second red ball- 5/10=1/2, second green ball- 4/10= 2/5Two red balls = 6/11*1/2= 3/11Two green balls= 5/11*2/5= 2/11Answer:
3/11
2/11
Step-by-step explanation:
is 3/8 squared irratonal
the correct answer is yes. 3/8 is the irrational.
step by step explaination: Assuming you meant, then it's irrational. The square root of any Natural Number which is not a perfect square is irrational. 8 is not a perfect square so is irrational.
I am glad to help you!!!!!!!!!!!!
