An engineering firm designs a custom hexagonal screw for a computer board. A sketch of the top of the screw is below. To the nearest tenth,
what is the area of the screw head?
Answers
Given that the screw is a regular hexagon with side length 6 mm, the area of the screw is 93.5 mm^2
How can the area of the screw be found?The area of an hexagon can be found using the following equation;
[tex]A = \mathbf{ \frac{3 \cdot \sqrt{3} }{2} \times {a}^{2}} [/tex]
Where a = The side length
However the side lengths are not equal, and the figure is a composite figure with two triangles and one rectangle;
Base length of the triangles = 12
Height of the triangles = 3
Area of each triangle = 0.5 × 12 × 3 = 18
Width of the rectangle = 12
Height of the rectangle = 6
Area of the rectangle = 12 × 6 = 72
Area of the screw = 18 + 18 + 72 = 108
However taking the screw as a regular hexagon, with side length a = 6, we have;
[tex]A = \frac{3 \cdot \sqrt{3} }{2} \times {6 \: mm}^{2} = 93.5 \: mm^2 [/tex]
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Related Questions
In the figure below AOD is a diameter of the circle cetre O. BC is a chord parallel to AD. FE is a tangent to the circle. OF bisects angle COD. Angle BCE = angle COE = 20° BC cuts OE at X
Calculate;
(a) angle BOE
(b) angle BEC
(c) angle CEF
(d) angle OXC
(e) angle OFE
Answers
Step-by-step explanation:
∠ACB=90∘
[∠ from diameter]
In ΔACB
∠A+∠ACB+∠CBA=180∘
∠CBA=180∘
−(90+30)
∠CBA=60∘ (1)
In △OCB
OC=OB
So, ∠OCB=∠OBC
[The sides are equal]
∠OCB=60∘
∠OCD=90∘
∠OCB+∠BCD=90°
∠BCD=30∘ (2)
∠CBO=∠BCO+∠CDB
[external ∠ bisectors]
60=30+∠CDB
∠CDB=30° (3)
from (2) & (3)
BC=BD
[The ∠.S are equal]
What does it mean for an event to be unusual? why should the cutoff for identifying unusual events not always be 0. 05?.
Answers
An unusual event is an occurrence that has a low probability of happening. The cutoff for identifying unusual events not always be 0.05, because it is not always a good idea to utilize the same cutoff to spot unexpected occurrences.
What is an unusual event?An unusual event is an occurrence that has a low probability of happening.
If an event is improbable, its likelihood is zero. If an occurrence is unavoidable, its probability is one.
The probability of an event happening increases as it gets closer to 1. An occurrence that has a probability of 0.375, for instance, is more likely to happen than one with a probability of 0.125.
The less likely an event is to occur, the closer the probability is to 0. An unusual event is what this kind of event falls under. A probability of 5%, or 0.05, is typically regarded as unusual event.
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the question is on the image.
Answers
Answer:
18+[tex]6\sqrt{5}[/tex]
Step-by-step explanation:
Since the helicopter flies east for six miles and north for 12 miles, it flies 18 miles. Then on the way back, it flies an unknown amount of miles. the path the helicopter takes is in the form of a triangle, and the path back is the hypotenuse of the triangle. To find the hypotenuse, we can do [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse. We do
[tex]6^2+12^2=c^2\\36+144=c^2\\180=c^2\\\sqrt{180}=c\\ 6\sqrt{5}=c[/tex]Therefore, the total distance flown by the helicopter is 18+[tex]6\sqrt{5}[/tex].
Nathan received $1,500 dollars for his birthday. He saves 3/5 of his money. 6/20 of his money was used to buy a new game. How much money does he have left?
Answers
Answer:
$150
Step-by-step explanation:
→ Find 3/5 of 1500
( 1500 ÷ 5 ) × 3 = 900
→ Find 6/20 of 1500
( 1500 ÷ 20 ) × 6 = 450
→ Find the sum of the 2 numbers
900 + 450 = 1350
→ Minus it from the original 1500
1500 - 1350 = $150
How tall is the tower?
Answers
Answer:
x=33ft
height of tower=33+6=39ft
Can someone help me. What number is it can anyone help?
Answers
Step-by-step explanation:
2k=3×4
2k=12
2k/2=12/2
k=6
Answer:
k = 6
Step-by-step explanation:
In Ratio Questions , The Denominator takes the same Ratio as the Numerator and vice versa
so for Question , 4 is double 2
Then k must be double of 3
Then k=2*3 = 6
A boy had a packet of 320 candies with 2 different flavours. 7/16 were orange flavour and the rest were lemon. He gave his friend 30 orange candies and some lemon ones. As a result, the ratio of the number of orange candies to that of lemon became 11:15. How many lemon candies did he give his friend
Answers
30 lemon candies he give his friend.
It is given that a boy had 320 candies. There were 2 flavors. 7/16 were orange flavor and the rest were lemon. He gave his friend 30 orange candies and some lemon ones.
320 (7/16) = 140 were orange
320 - 140 = 180 were lemon
Let x be the number of lemon ones he gave away
So,
[ 140 - 30 ] / [ 180 - x ] = 11/15
110 = (11/15) ( 180 - x )
(15/11) (110) = 180 - x
150 = 180 - x
x = 180 - 150 = 30
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Triangle GHI is rotated 90Degrees clockwise and then reflected over the y-axis. Which congruency statement is true?
On a coordinate plane, triangle G H I is rotated 90 degrees clockwise and then is reflected over the y-axis.
Angle G is congruent to angle H is congruent to angle I
Angle G double-prime is congruent to angle H double-prime is congruent to angle I double-prime
Triangle G H I is congruent to triangle G double-prime H double-prime I double-prime
Triangle G H I is congruent to triangle I H G
Answers
The congruency statement which is true among the answer choices is;
On a coordinate plane, triangle G H I is rotated 90 degrees clockwise and then is reflected over the y-axis.Triangle G H I is congruent to triangle G double-prime H double-prime I double-prime.Which congruency statement is true?According to the task content, the initial transformation is; Triangle GHI is rotated 90Degrees clockwise and then reflected over the y-axis.
On this note, the congruency which are true regarding the transformation are;
On a coordinate plane, triangle G H I is rotated 90 degrees clockwise and then is reflected over the y-axis.Triangle G H I is congruent to triangle G double-prime H double-prime I double-prime.This follows from the fact that the transformation.does not involved dilation by means of a scale factor and hence, size remains equal and all angle measures remain the same.
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Box of 24 chocolate contains 6 cream-filled. What is the probability of randomly selecting a cream filled
Chocolate
Answers
The probability of randomly selecting a cream filled
Chocolate is 1/4
Probability is the likelihood of an event will occur Probability of an event is find out by divide the number of favorable outcomes by the total number of possible outcomes. The simplest example is flipping of a coin. There are only two possible outcomes when you flip a coin. It wiil be either heads or tails.Total probability is always lie between 0 and 1Let E be the event of selecting cream filled chocolate.
Number of favourable outcome = 6
Total number of possible outcome = 24
Probability if selecting a cream filled chocolate = 6/24
= 1 / 4
Hence, the probability of randomly selecting a cream filled chocolate is 1/4
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use coordinate notation to write the rule that maps each preimage to its image. The identify the transformation and confirm that it preserves length and angle measure. Number 5
Answers
The rigid transformations used for each figure:
Figure 5 - Reflection around x and y axes: (x, y) → (- x, - y)Figure 6 - Horizontal and vertical translations: (x, y) → (x + 1, y - 2)What transformation rules do create the resulting images?
In this question we must determine what kind of rigid transformations generates each image. Rigid transformations are transformations applied on geometric loci such that Euclidean distance is conserved. Now we proceed to determine the transformation rule for each case:
Figure 5 - Reflection around the x-axis followed by reflection around the y-axis.
(x, y) → (- x, - y)
Figure 6 - Translation one unit in the +x direction and two units in the -y direction.
(x, y) → (x + 1, y - 2)
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subtracting polynomial expressions
Answers
Answer:7m^5 - 3m^3 + 9
Step-by-step explanation: You’d have to remove the brackets, but remember that the second has to have everything multiplied by -1, because there’s a minus sign in front of the second bracket. Then you’d group like terms, then add or subtract. Here’s the step by step
6m^5 + 3 - m^3 - 4m + m^5 - 2m^3 + 4m + 6
2. 6m^5 + m^5 - 2m^3 - m^3 + 4m - 4m + 6 + 3
Subtract or add what’s needed, which would be figures with the same variable and coefficient.
3. 7m^5 - 3m^3 + 9
After this, there’s nothing you can add, since the remaining figures don’t have the same variable.
Hope it’s clear and this wasn’t that long
Writing an Equation from a Graph
10
8
*
x
-10 8 6 4
2 4 6 8 10
-2
-6
-8
-10-
Intro
6
Yo
2469 9
Study the graph of the line. Use the drop-down menu
to find its equation.
The equation of the line is
Done
Answers
Answer:
y = x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 2) ← 2 points on the line
m = [tex]\frac{2-0}{0-(-2)}[/tex] = [tex]\frac{2}{0+2}[/tex] = [tex]\frac{2}{2}[/tex] = 1
the line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = x + 2 ← equation of line
What is thirty six times thirty eight divided by three
Answers
Answer:
456Step-by-step explanation:
What is thirty six times thirty eight divided by three
36 * 38 : 3 =
1368 : 3 =
456
PLEASE HELP!!! FINDING PROBABILITY MATH!!!
i need the answer to question 2, 3, and 4. question 1's answer is 9/28 & 32.1%.
Answers
The probability that a person wins the game is 32.1%
How to illustrate the probability?Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.
Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:
= 24 + 4 = 28
The frequency table will be such that 28 or more have a relative frequency of 9. Therefore, the probability that a person wins the game will be:
= 9/28 = 32.1%
When you win 25% of the time, this illustrates that the number of products picked will be:
= 25% × 28
= 7 products.
The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:
= 1/6⁴ = 1/1296
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A bag contains 14 good eggs and 7 bad ones. if one egg is picked at random fr the bag what is the probability that it is goods
Answers
Answer:
2/3
Step-by-step explanation:
expected over total
14/14+7 = 14/21 = 2/3
[tex]bad \: eggies = 7 \\ good \: eggies = 14 \\ total \: number \: of \: eggs = 21[/tex]
[tex]let \: event \: a = getting \: a \: good \: egg[/tex]
[tex]p(a) = \frac{number \: of \: good \: eggs}{total \: number \: of \: eggs} = \frac{14}{21} = \frac{2}{3} [/tex]
Find the remainder of the division. 2001 • 2002 • 2003 + 2004^3 by 7.
Show steps.
Answers
Answer:
[tex]1[/tex]
Step-by-step explanation:
The gist of modular arithmetic in a nutshell: the numbers [tex]a[/tex] and [tex]b[/tex] are considered to be congruent by their modulus [tex]m[/tex] if [tex]m[/tex] is a divisor of their difference.
In mathematics: [tex]a \equiv_{m} b \Leftrightarrow (a - b) \vdots m[/tex]
Exemplifying this: [tex]6 \equiv_{7} -1[/tex] because [tex]6 - (-1) = 6 + 1 = 7[/tex], [tex]7 \vdots 7[/tex].
Let us have following equivalences: [tex]a \equiv_{m} b[/tex] and [tex]c \equiv_{m} d[/tex], then: [tex](a - b) \vdots m[/tex] and [tex](c - d) \vdots m[/tex] by definition.
Properties:
1. [tex]a + c \equiv_{m} b + d \Leftrightarrow ((a + c) - (b + d)) \vdots m \Leftrightarrow (a + c - b - d) \vdots m \Leftrightarrow ((a - b) + (c - d)) \vdots m[/tex].
2. [tex]a - c \equiv_{m} b - d \Leftrightarrow ((a - c) - (b - d)) \vdots m \Leftrightarrow (a - c - b + d) \vdots m \Leftrightarrow ((a - b) - (c - d)) \vdots m[/tex].
3. [tex]ac \equiv_{m} bd \Leftrightarrow (ac - bd) \vdots m \Leftrightarrow (ac - bc - bd + bc) \vdots m \Leftrightarrow (c(a - b) + b(c - d)) \vdots m[/tex].
4. What if we have [tex]a \equiv_{m} b[/tex] twice? If we abide by property 3, we can come to the conclusion that [tex]a^2 \equiv_m b^2[/tex]. It is fair enough that there is room for the equivalence [tex]a^n \equiv_{m} b^n[/tex].
[tex]2001 * 2002 * 2003 + 2004^3 = 2002 * (2001 * 2003) + 2004^3 \equiv_{7} 0 * (2001 * 2003) + 2^3 \equiv_{7} 0 + 8 \equiv_{7} 8 \equiv_{7} 1[/tex]
Notice that [tex]2002 \vdots 7[/tex] already. There is no need to consider the rest multipliers because the product is [tex]0[/tex] anyways, we can cut corners in this regard.
We used property 4.
Recapitulating this: our remainder is [tex]1[/tex].
does 3:3 or any full ratio equal 1:1?
Answers
Answer:
yes
_____________________________
you can look at 3:3 as 3/3 which is 1
and 1:1 = 1/1 which is also 1
the ratio sign also means divide.
_____________________________
hope this helps :)
Question 9 of 25
Which of the sequences is an arithmetic sequence?
OA. -3, -10,-17, -24, -31, ...
OB. 3, 6, 9, 15, 24,...
OC. 1, -2, 3, 4, 5, ...
OD. 1, 8, 16, 24, 32, ...
Answers
Answer:
B.
Step-by-step explanation:
an arithmetic sequence is B
Answer:0c
Step-by-step explanation:
The diagram shows MNP. Which term describes point Q?
M
OA. Incenter
OB. Orthocenter
C. Centroid
OD. Circumcenter
N
P
Answers
Answer:
answer is A - incenter just did it
Step-by-step explanation:
To use the two sample t procedure to perform a significance test on the difference of two means, we assume:
Answers
We assume that the population standard deviation are known, the samples from each population are independent, the population is normally distributed if we use t test of two samples.
Given T test of significance has been used.
T test is a statistical test that is like z test. Z test is used when n>30 and t test is used when n<30. It is used in hypothesis testing.
We know that there are many test which can be used to test a hypothesis.
The requirements to perform a two sample t procedure are as follows:
1)The two samples have equal variance. Hence the variance should be known.
2) The samples for which the two sample t procedure is performed must be independent.
3) The data are in alignment with the normal distribution probability.
4) The sample are random samples taken from different respective population.
Hence when two sample t procedure is performed we have to assume population standard deviation is known and population is normally distributed.
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Find the surface area of the composite solid.
Answers
The area of the composite solid in the image given is: 399.6 m².
What is the Surface Area of a Composite Solid?The surface are of the composite solid = area of the 3 triangular face of the top solid + area of the triangular base of the bottom solid + 3(area of rectangular face of the bottom solid).
Area of the 3 triangular face of the top solid = 3(1/2bh) = 3(1/2 × 8 × 7) = 84 m²
Area of the triangular base of the bottom solid = 1/2bh = 1/2 × 8 × 6.9 = 27.6 m²
3(area of rectangular face of the bottom solid) = 3(length × width) = 3(12 × 8) = 288 m²
Surface area of the solid = 84 + 27.6 + 288 = 399.6 m²
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Samarium-146 has a half-life of 103.5 million years. after 1.035 billion years, how much samarium-146 will remain from a 205-g sample?
Answers
Answer: 0.200 g
Given: Half life of Sm-146 = t1/2 = 103.5 million years
Time period, t = 1.035 billion years = 1035 million years
The original mass of the sample, [A]₀ = 205 g
To determine:
Amount of sample after t = 1035 million years
Explanation:
The rate of radioactive decay is given as:
Answer:
A: 0.200 g.
Step-by-step explanation:
Question 4(Multiple Choice Worth 1 points)
(08.03 LC)
What are the exact solutions of x2 − 3x − 5 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a?
x = the quantity of negative 3 plus or minus the square root of 29 all over 2
x = the quantity of 3 plus or minus the square root of 29 all over 2
x = the quantity of 3 plus or minus the square root of 11 all over 2
x = the quantity of negative 3 plus or minus the square root of 11 all over 2
Answers
i know its the frist or second one i did the test i am also in flvs :)
Wen is factoring the polynomial, which has four terms. 6x3 – 12x2 7x – 14 6x2 (x – 2) 7(x – 2) which is the completely factored form of his polynomial?
Answers
Completely factored form of Wen's polynomial is (6x² + 7) (x-2).
What is a polynomial?
An algebraic expression called a polynomial includes coefficients and variables. Indeterminates are another name for variables. For a polynomial expression, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents, but division by variable is not possible. Although a polynomial can have multiple number of terms, it can't be infinite.
Factorizing the polynomial
Complete factorization of a polynomial results in products-of-sums
Given polynomial is,
6x³ - 12x² + 7x - 14
This polynomial can be factorized as follows,
6x² (x - 2) + 7(x - 2)
Now, we can factor out the common term (x-2) form each term on either side of the plus operator. thus, we get the following factors,
(6x² + 7) (x-2)
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Answer:
Answer is A :)
Step-by-step explanation:
A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio of the area of the larger hexagon to the area of the smaller hexagon
Answers
4/3 of the area of the larger hexagon to the area of the smaller hexagon
Let the sides of the interior hexagon be 2 cm long, then this hexagon is made up of 6 equilateral triangles of side = 2.
The area of this hexagon = 6 * 1 * sqrt3 = 6 sqrt3 ( as the triangle is made up of 2 60-30-90 triangles)
The exterior hexagon is made up of 6 equilateral triangles with altitude 2 and the area = 6 * 2 * (2 / sqrt3 ) = 24 / sqrt3
area exterior hex / interior hex = 24 / sqrt3 * 1 / 6sqrt3 = 24/18
= 4/3
Required ratio = 4/3 answer
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Trigonometry Problem, please help and explain
Answers
The bottom triangle is a 30°-60°-90° triangle that has the special property that its hypotenuse is twice the length of the shortest leg, 20√3.
The upper triangle is a 45°-45°-90° triangle, in which the hypotenuse is longer than one of its legs by a factor of √2.
All this to say x = √2 × 20√3 = 20√6 (A).
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 99% of the time
Answers
The manufacturer should advertise 13811 pages for each cartridge if it wants to be correct 99% of the time
z-score is the number of standard deviations from the mean value of the reference population
99%=0.99
The z-value associate with 0.99 is 2.33:
2.33 = (X - 12425) / 595:
X - 12425 = 2.33 * 595
X = (2.33 * 595) + 12425
X = 138111
Therefore, The manufacturer should advertise 13811 pages for each cartridge if it wants to be correct 99% of the time
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A right cylinder has a radius of 2 units and a height of 5 units. a right cylinder has a radius of 2 units and a height of 5 units. what is the volume of the cylinder? round to the nearest tenth.
Answers
The volume of the cylinder given the radius and the height is 562.2 cubic units
Volume of cylinderRadius, r = 2 unitsHeight, h = 5 unitsVolume of a cylinder = πr²h
= 3.14 × 2² × 5
= 3.14 × 4 × 5
= 562.2 cubic units
Therefore, the volume of the cylinder is 562.2 cubic units.
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Answer:62.8
Step-by-step explanation:
just took the test
Question 6 of 10
If a student had homework 67 days out of 100, what fraction and what
percentage of days did the student not have homework? Choose two
answers.
Answers
Answer: 33/100, 33%
Step-by-step explanation:
I can't choose two answers if you don't give me the possible answers
67 days of homework = 100-67 or 33 days without homework.
33/100 or 33%
Step-by-step explanation:
100% = 100 days
1% = 100%/100 = 100/100 = 1 day
the student does NOT have homework on 100-67 = 33 days.
that is 33 out of 100 days or on 33/100 of days.
33 days are 33×1% = 33%
△TUS∼△CBS
Two similar triangles. Triangle TUS is similar to triangle CBS. Segment BU and segment CT pass through point S. Side TU and side BC are horizontal. Side BS has a length of 8 point 5. Side CS has a length of 7 point 5. Side US has a length of 42 point 5. The length of side TS is unknown, and is labeled x.
What is the value of x?
Enter your answer as a decimal in the box.
x
=
Answers
The value of x from the diagram is 42. 5
How to determine the valueSince we have that △TUS∼△CBS
Line BS = 8. 5
Line CS = 7. 5
Line US = 42. 5
TS = x
To find TS, we can see that line US is equivalent in length to line TS
If line US = 42. 5, then line TS = 42. 5
TS = x = 42. 5
Thus, the value of x from the diagram is 42. 5
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