What is the area of the shaded region? Round to the nearest tenth of a centimeter.
Answers
The area of the shaded region found using trigonometric ratios is about 86.6 square centimeters
What are trigonometric ratios?Trigonometric ratios are expressions of the relationship between the interior angle of a right triangle and the ratio of two of the sides of the triangle.
Whereby, the inscribing figure of the quadrilateral is a regular hexagon, we get;
Interior angle of a regular hexagon = 120°
The 10 cm segment bisects the top vertex angle of the regular hexagon, which together with the 5·√3 cm side and trigonometric ratios, indicates that we get;
sin(60) = s/(5·√3) = (√3)/2
Where;
s = The side length of the regular hexagon
(5·√3)/s = (√3)/2
s = (5·√3)/((√3)/2) = 10
The side length of the regular hexagon, s = 10
The area of the regular hexagon, A = ((3·√3)/2) × s² = (1/2)×6 ×s ×a
Where;
a = The apothem = 5·√3
Therefore; A = ((3·√3)/2) × 10² = 150·√3
A = (1/2)×6 ×10 × 5·√3 = 150·√3
Area of the quadrilateral = 4 × (1/2) × 5·√3 × 10 = 100·√3
Area of the shaded region = Area of the hexagon - Area of the quadrilateral
Therefore;
Area of the shaded region = 150·√3 - 100·√3 = 50·√3 ≈ 86.6
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Related Questions
1/2of 2/3 =1/2 of _ Third(s)= _third(s)
Answers
Answer: 1/2of 2/3 = 1/2 of 2 Third(s)= 1 third
similarity help for math please
Answers
The triangles that do not follow the similarity statement and therefore are not similar triangle are ACT and CAR
What is similar triangleSimilar triangles are triangles that have the same shape, but may have different sizes. Their corresponding angles are congruent, and the corresponding sides are proportional. In other words, if you were to enlarge or shrink one triangle uniformly, it would overlap exactly with the other triangle.
In this problem, we can find two triangles that are similar and that implies that they must be equal to one another.
In this case, we have
1. ART ≈ CAT
2. CAR ≈ CTA
Only ACT ≠ CAR
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$200 invested at 5% compounded quarterly after a period of 3 years
Answers
Given:-
[tex] \rm{Principal= \bold{200}}[/tex][tex] \rm{Time = \bold 3}[/tex][tex] \rm{Intrest \: Rate = \bold 5}[/tex]By using formula:-
[tex]\boxed { \color{green}\rm{Simple \: interest= \frac{Principal×Time×Rate}{100}}}[/tex]Solution:-
[tex] \rm{SI = \frac{PTR}{100} }[/tex][tex] \: [/tex]
[tex] \rm{SI = \frac{2\cancel{00}×3×5}{1\cancel{00}} }[/tex][tex] \: [/tex]
[tex] \rm{SI=2×3×5}[/tex][tex] \: [/tex]
[tex] \boxed { \rm \red{ SI = 30}}[/tex][tex] \: [/tex]
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How many digits of the form x15y is di ivsble by 15
Answers
There are a total of 8 + 7 = 15 digits of the form x15y that are divisible by 15.
A number is divisible by 15 if and only if it is divisible by both 3 and 5.For a number of the form x15y to be divisible by 5, y must be either 0 or 5.
For a number of the form x15y to be divisible by 3, the sum of its digits must be divisible by 3. Since the sum of the digits is x + 1 + 5 + y = x + y + 6, x + y must be either 0, 3, 6, 9, 12, or 15.
So, we need to find all possible values of x and y such that x + y is one of these six values, and y is either 0 or 5.
If y = 0, then x must be one of the numbers 0, 3, 6, 9, 12, 15, 18, or 21, for a total of 8 possibilities.
If y = 5, then x must be one of the numbers 2, 5, 8, 11, 14, 17, or 20, for a total of 7 possibilities.
Therefore, there are a total of 8 + 7 = 15 digits of the form x15y that are divisible by 15.
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MODELING REAL LIFE Scientists rope off two excavation sites. Site A is rectangular with a length of $60$ meters and a width of $40$ meters. Site B is similar in shape to Site A but has a length of $45$ meters. How much rope is needed for both sites?
m=
Answers
By using unitary methods, the amount of rope is needed for both sites is 350 meters.
Unitary method is a mathematical problem-solving technique that involves finding the value of one unit and using it to calculate the value of other units.
Let's start by looking at Site A, which is a rectangular area with a length of 60 meters and a width of 40 meters. To surround this area with rope, we need to measure the perimeter, which is the distance around the site.
=> Perimeter = 2 (length + width)
=> 2(60 + 40)
=> 2 x 100
=> 200 meters
Therefore, we need 200 meters of rope to surround Site A.
Now let's move on to Site B, which is also rectangular but has a length of 45 meters. To find the width of Site B, we can use the fact that it is similar in shape to Site A. Similar shapes have the same angles and proportional sides, so we can use a unitary method to find the missing dimension.
The length ratio of Site B to Site A is
=> 45/60 = 3/4
Since the shapes are similar, the width of Site B must also be 3/4 of the width of Site A.
Width of Site B = 3/4 x 40 = 30 meters
Now we can use the same formula as before to find the perimeter of Site B:
Perimeter = 2 (length + width)
=> 2(45 + 30)
=> 2 x 75
=> 150 meters
Therefore, we need 150 meters of rope to surround Site B.
To find the total amount of rope needed for both sites, we simply add the two perimeters:
Total rope needed = 200 + 150 = 350 meters
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The diameter of each of the three circular lights in a traffic signal is 7 inches. In this activity, you will find the total area of the three lights.Part C What is the total area of all three circular lights?
Answers
Answer:
The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. If the diameter of each circular light is 7 inches, the radius would be half of that, or 3.5 inches.
Therefore, the area of one circular light would be:
A = π * 3.5^2 = 3.5^2 * π = 12.25 * π square inches.
Since there are three circular lights, the total area of all three would be:
3 * 12.25 * π = 36.75 * π square inches.
Step-by-step explanation:
pls mark brainlist
The balance in an account after several transaction is shown in the table. Is the relationship between the balance and the number of withdrawals of linear? Blank If so, find the constant rate of change. Write the slope as a unit rate and explain your reasoning.
Answers
It should be noted that the relationship between the balance and the number of withdrawals is linear, because there is a constant amount of $10 per withdrawal.
How to express the relationshipTo confirm this, we can calculate the differences in balance for each pair of withdrawals:
Between withdrawals 3 and 2: 170 - 140 = 30
Based on the information, the starting amount is $200.
The equation to illustrate the withdrawal will be:
= 200 - 10w
where w = withdrawal.
These differences are constant, which means the rate of change of the balance is constant too.
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Find the image of (2,3) under a dilation with center at the origin and a scale factor of −3.
Answers
The image of (2, 3) under a dilation with center at the origin and a scale factor of −3 will be (-6, -9).
What is Image of a point ?
Dilation is the process of resizing or altering an object. With the aid of the specified scale factor, it is a transformation that reduces or enlarges the objects. The initial figure is referred to as the pre-image, while the new figure acquired after dilatation is known as the image.
Given point : (2,3)
the scale factor is -3 which means the point should be enlarged by -3 times to get the desired image.
So, we can write as : (a, b) where,
a = 2 × -3 = -6
and, b = 3 × -3 = -9
Hence, the coordinates of the image will be (-6, -9).
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A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34. 5-foot shadow. How tall is the building (Round your answer to the nearest tenth. )
Answers
A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34. 5-foot shadow then the building is approximately 95.2 feet tall.
What is similar triangles ?
Similar triangles are useful in geometry and other fields because they allow us to solve problems involving unknown distances or heights. We can use the known lengths and angles of one triangle to find the lengths and angles of the other triangle, as long as we know that the two triangles are similar. This can be done using the properties of proportional relationships and the rules of similar figures.
Let's use similar triangles to solve this problem. The height of the building and the height of the flagpole are proportional to the lengths of their shadows. We can set up the following equation:
height of building / length of building's shadow = height of flagpole / length of flagpole's shadow
Let x be the height of the building. Then we have:
x / 103 = 32 / 34.5
Simplifying this equation, we get:
x = 103 * (32 / 34.5) ≈ 95.23
Therefore, the building is approximately 95.2 feet tall.
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Given that 4ax² + 9x + c is always negative, what conditions must apply to the constants a and c?
Answers
Answer:
Step-by-step explanation:
According to question
[tex]4ax^{2} +9x+c < 0[/tex]
This means that the coefficient of the highest degree term
([tex]4ax^{2}[/tex]) must be positive
And the constant term (c) must be negative
So, the according to condition
4a must be positive,
which means a must be positive
And, c must be negative
[tex]a > 0\\c < 0[/tex]
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12. Tickets to a school play cost $5.00 for general
admission (g) and $3.50 with a student ID (s). On
opening night, 400 tickets were sold for a total of
$1580. How many of each kind of ticket were sold?
Answers
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Answer:
120 general admission
280 with student with a student ID
Step-by-step explanation:
x is tickets for general admission
y is tickets with a student ID
5x+3.5y=1580
x+y=400
y=400-x
5x+3.5(400-x)=1580
5x+1400-3.5x=1580
1.5x=180
x=120
120+y=400
y=280
A group of students atten a math club. Half of them students are boys 4/9 of them boys have brown eyes
Answers
The fraction of the group are boys with brown eyes with total group of students who attend the math club is equals to the 2/9.
Let us assume that total number of students who attend the math club be 'x'. Now, according to problem, half of students who attend the math are boys. So, boys students out of total students who attend the math club, B = ( 1/2)x --(1)
Also, 4/9 of them boys have brown eyes. That is the boys students have brown eyes out of boys students who attend the math club, E = 4/9 of B
=> (4/9)B --(2)
We have to determine the relationship between boys with brown eyes (E) and the group of students (x). so, let's replace B in second equation with the expression present in eqution (1).
=> E = (4/9)(x/2)
For simplification, multiply the two fractions, that denominator with denominator and numerator with numerator.
=> E = 4x/18
For further simplification, simply dividing both the numerator and denominator by their common factor, ( 4, 18 ) = 2,
=> E = 2x/9
so, the required relationship between E and x is 2/9. Hence, required value is 2/9.
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Complete question :
a group of students attend a math club half the students are boys and 4/9 of the boys have brown eyes what fraction of the group are boys with brown eyes.
A bus leaves the station every 12 minutes
A train leaves the station every 18 minutes
At 8am a bus and a train leave their stations at the same time.
a) when is the next time that a bus and a train leave at the same time?
b) Between 8am and 11am, on how many occasions does a bus and a train leave at the same time?
thank you so much for the help
Answers
Answer:
a) 8:32 am
b) 5 occasions
What is the scale factor?
6
3
1/3
1/6
Answers
Answer:
3
Step-by-step explanation:
You multiply the pre-image by 3 to get the image numbers.
Answer:
B.3
Step-by-step explanation:
The scale factor is 3 because all of the images are dilated 3 times larger than the preimage.
is the answer to this not 225000???
Answers
2.25 km on the ground is represented by 9cm on the map.
What is the actual distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Here, we have
Given: The scale on the map is 1:25000
We have to find the actual distance of 9 cm on the map.
First, we have to find the actual distance of 1 cm on the map:
1cm = 25000cm
1cm = 250m
1cm = 0.25km
Now Find the actual distance of 9 cm on the map:
1cm = 0.25km
9cm = 9(0.25) = 2.25km
Hence, 2.25 km on the ground is represented by 9cm on the map.
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Q9.
Gavin bought 3 pairs of jeans in the USA.
He paid a total of $72
Gavin sold the 3 pairs of jeans in England,
He sold each pair of jeans for £34.50
£1 = $1.34
Work out Gavin's percentage profit.
Give your answer correct to the nearest whole number.
Answers
Answer:
Gavin made a Profit of $66.69 that is 93% Profit
Step-by-step explanation:
First, we calculate the Selling Price of Jeans after converting from GBP to USD on the given rate:
Rate: £1 = $1.34
Quantity: 3
Price in USD = Selling Price per pair * Rate in USD
£34.50 * 1.34 = $46.23 per pair of jeans.
Total Selling Price = Price Per Pair * Quantity
= 46.23 * 3
= $138.69
Total Profit = Total Selling Price - Total Cost Price
= $138.69-$72
= $66.69
Percentage of Profit = Total Profit / Total Cost Price
=66.69 / 72
=92.65
Therefore, the Profit Percentage is 92.65 % the nearest whole number would be 93%
To calculate Gavin's percentage profit, find the difference between the selling price and the buying price, and calculate the percentage of the buying price that the profit represents.
Explanation:To calculate Gavin's percentage profit, we need to find the difference between the selling price and the buying price, and then calculate the percentage of the buying price that the profit represents.
First, convert the selling price of each pair of jeans from pounds to dollars. Since £1 = $1.34, each pair of jeans sold for $34.50 x 1.34 = $46.23.Next, calculate the total selling price by multiplying the selling price of each pair by the number of pairs: $46.23 x 3 = $138.69.Then, calculate the profit by subtracting the total buying price from the total selling price: $138.69 - $72 = $66.69.Finally, calculate the percentage profit by dividing the profit by the total buying price and multiplying by 100: ($66.69 / $72) x 100 ≈ 92.6%.Gavin's percentage profit is approximately 92.6%.
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Write a similarity transformation that maps ∆ABC to ∆DEF
Answers
Answer:
Reflect ABC over the y axis. Translate ABC 1 unit to the right. C is the center, dilate ABC with a scale factor of 2.
Step-by-step explanation:
On a test that has a normal distribution, a score of 34 falls two standard deviations above the mean, and a score of 22 falls one standard deviation below the mean. Determine the mean of this test.
Answers
The mean of this data set is 65.
What is the mean absolute deviation?The average distance between each data item and the mean is known as the mean absolute deviation.
The gap between each data value and the mean in absolute terms is represented by this average.
Let the mean be 'x' and the standard deviation be 'y'
3 standard deviations the mean means that we are taking away 3 standard deviations from the mean
Mathematically, we have that as;
x - 3y = 41...(i)
73 is 1 standard deviation above the mean
Mathematically;
x + y = 73...(ii)
So let us solve both equations simultaneously
Simply multiply equation (ii) by 3 then add to (i)
x - 3y = 41
3x + 3y =219
4x = 41 + 219
4x = 260
x = 260/4
x = 65.
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Answer: 26
Step-by-step explanation:
If A = {3,5,9} and B
{2,4,5,6,9,12}, what is AU B?
Answers
For the given sets A = { 3, 5, 9 } and set B = { 2, 4, 5, 6, 9, 12 } then the value of AU B is equal to { 2, 3, 4, 5, 6, 9, 12 }.
Two different sets A and set B are equal to :
Set A = { 3, 5, 9 }
Set B = { 2, 4, 5, 6, 9, 12 }
Union of two different set A and B is defined as set having all the elements of set A and set B .
Union of two sets A and B is represented by AU B .
AU B
= { 3, 5, 9 } ∪ { 2, 4, 5, 6, 9, 12 }
= { 2, 3, 4, 5, 6, 9, 12 }
Therefore, the union of two given sets A and set B is given by :
AU B = { 2, 3, 4, 5, 6, 9, 12 }.
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Howard's pencil is 75 cm long. How many millimeters long is Howard's pencil?
Answers
Answer:
Howard's pencil is 750 millimeters
Step-by-step explanation:
[tex]\begin{array}{|l}\underline{km~}\\~~~~~\underline{|hm~}\\~~~~~~~~~~~\underline{|dam}~~~~~~~~\nwarrow~\div10\\~~~~~~~~~~~~~~~~~\underline{|m~~}\\~~~~~~~~~~\searrow~~~~~~~\underline{|dm~}\\~~~\times10~~~~~~~~~~~~~~~~~~\underline{|cm~}\\\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|mm~}\end{array}\\~~~~~~~~~~~\rm Converting ~Length ~ Unit[/tex][tex]~[/tex]
Step-by-step:
75 cm = 75 × 10 mm
75 cm = 750 mm
FIND THE PERIMETER AND AREA OF THE TRIANGLE BELOW
Answers
Answer:
perimeter = 8a³b + 4ab
area = 4a^4b²
Step-by-step explanation:
perimeter = 2a³b + 6a³b + 4ab
perimeter = 8a³b + 4ab
area = bh/2
area = 4ab × 2a³b / 2
area = 4a^4b²
Perimeter :- 4ab(2a+1)
Detailed explanation:-
Klaus is cycling at a speed of -8 miles per hour. If he starts at the same position as Rachel (zero) , what will his position be after 60 minutes?
Klaus will be ____ miles be hind where he started, and ___ miles away from Rachel.
Answers
Klaus wil be behind where he started with a distance of 8miles
What is distance?Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
Distance can also be defined as the space or gap between two points.
Velocity = distance/time
distance = velocity × time
time = 60minutes = 1hr
therefore the distance made by Klaus in 60 minutes =
= 8 ×1
= 8miles
therefore within 60 minutes Klaus will cover a distance of 8miles from where he started.
Klaus and Rachel will be at same position with the same speed
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The United States Postal Service has an online guide to make life easy for people using their
postal service. This is an extract.
First Class Mail
First class mail must be used for handwritten or personal correspondence.
First Class Mail Rates - single piece rates
$0.44
First ounce (oz.) Letter size mail
Each additional oz. or fraction
First ounce Flat size mail **
Each additional oz. or fraction
First ounce Parcel ***
Each additional oz. or fraction
Standard Postcard ****
$0.17 per oz. up to 3.5 oz.
$0.88
$0.17 per oz. up to 13 oz.
$1.22
$0.17 per oz. up to 13 oz.
$0.28
* Letters: (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W,
max. weight 3.5 oz). Letter size mai over 3.5 ounces, see Flat size prices.
**Flats: (min. dimension: 11.5 L, 6.125" H, 0.25"W; max. dimension: 15 L, 12 H, 0.75 W).
*** Parcels: Anything larger.
**** Postcards: (min. dimension: 5L, 3.5" H, 0.007"W; max. dimension: 61, 4.25 H, 0.016 W).
I want to send two items through the post using first class mail.
One fts into an envelope 20 L, 10°H and 4"W and weighs 10oz.
The other fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz.
How much are the items going to cost me to send?
Answers
Answer:
The first item that fits into an envelope 20 L, 10°H and 4"W and weighs 10oz is a "Flat size mail." According to the rate chart, the first ounce of Flat size mail costs $0.88 and each additional ounce costs $0.17. The cost for the 10 ounces of this item will be $0.88 + 9 x $0.17 = $1.83.
The second item that fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz is a "Letter size mail." According to the rate chart, the first ounce of Letter size mail costs $0.44 and each additional ounce costs $0.17. The cost for the 2.5 ounces of this item will be $0.44 + 1.5 x $0.17 = $0.75.
So, the total cost for both items will be $1.83 + $0.75 = $2.58.
one of my factors are 4, when you pair me with 32 we have an lcm of 32, i am greater than 4 and less the 15. what is the mystery number?
Answers
The mystery number is 8. It is the number that is greater than 4 and less than 15 which when paired with 32 has an LCM of 32.
The mystery number is 8. To find this number, we first need to determine the Least Common Multiple (LCM) of two numbers. The two given numbers are 4 and 32. To find the LCM, we can list out the multiples of each number until we find a common multiple. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, and so on. The multiples of 32 are 32, 64, 96, 128, and so on. We can see that 32 is the first common multiple of 4 and 32. Therefore, the LCM of 4 and 32 is 32. We are then told that the mystery number is greater than 4 and less than 15. This means the mystery number must be 8, since it is the only number between 4 and 15 that when paired with 32, has an LCM of 32.
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What value represents the number of ways in which the expected classes are free to vary in the chi-square goodness-of-fit test?Degrees of Freedom.
Answers
Answer The formula df = (c – 1) (r – 1) is used to find the degree of freedom – The degree of freedom of the chi-square test is calculated by the formula df = (c – 1) (r – 1), where c represents the column number of cell and r represents the row number of the cell.
Please help thank you
Answers
The ocean current has a bearing of 19.1°E and travels at a speed of about 16.9 knots.
Why is math speed important?Math is made more fascinating and enjoyable using Speed Maths (Vedic Maths). by assisting the child in quickly performing some improbable computations. By combining the correct amount of enjoyment, memory, skills, memory recall, and formula application, your child will become a superstar performer.
Let's use the letters "c" for OC magnitude and "" for the angle between OC and OD (the present bearing). Next, we have:
c² = 28² + 20² - 2(28)(20)cos(106°)
c ≈ 16.9 knots
Using the law of sines, we can find the angle θ:
sin(53°) / c = sin(θ) / 20
sin(θ) = (20/c) sin(53°)
θ ≈ 19.1°
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A probability model is a list of outcomes and the probability of each outcome. According to the following probability model, what is P(2)?
Answers
The value of the probability P(2) is 0.11
How to determine the value of the probabilityFrom the question, we have the following parameters that can be used in our computation:
The table of values
As a general rule:
The sum of probabilities must equal to 1
Using the above as a guide, we have the following:
0.1 + P(2) + 0.35 + 0.1 + 0.3 + 0.04 = 1
Evaluate the like terms
This gives
P(2) + 0.89 = 1
So, we have
P(2) = 0.11
Hence, the solution is 0.11
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Suppose p and q vary inversely and p = 14 when a = 4 Find p when q = 8 please show work
Answers
If p and q vary inversely and p = 14 when a = 4, then the work is q = 8, p = 7.
What is inverse proportionality?
Inverse proportionality occurs when x increases and y decreases, and when x decreases and y increases.
If p and q vary inversely, this means that their product is constant:
p * q = k
where k is a constant. We can use this relationship to solve the problem.
We are given that when a = 4, p = 14. This means that:
p * a = k
14 * 4 = k
56 = k
So we know that the product of p and a is 56.
To find p when q = 8, we can use the fact that p and q vary inversely. This means that:
p * q = k
We know that k = 56, so we can substitute:
p * q = 56
We are given that q = 8, so we can substitute this as well:
p * 8 = 56
Solving for p, we get:
p = 56 / 8 = 7
Therefore, when q = 8, p = 7.
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Some girl needs to earn R500 in interest so she will have enough to buy a used bicycle. She puts R2000 into an account that earns 5% per year simple interest. How long will she need to leave her money in the account to have enough money for the bicycle?
Answers
The money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.
What is simple interest?The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.
Let us suppose the time period as x.
The simple interest is given as:
SI = PRT/100
Where,
SI = Simple Interest = 500
P = Principal = 2000
R = Rate = 5%
T = x
Substituting the values:
500 = (2000)(5)(x) / 100
500 = 100x
x = 5 years
Hence, the money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.
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how many decimeters are in 3.6 millimeters
Answers
Final Answer:
There are 0.036 decimeters in 3.6 millimeters.
Explanation:
To convert from millimeters to decimeters, we can use the following measurement conversion:
1 millimeter = 0.01 decimeters
So, to find out how many decimeters are in 3.6 millimeters, we can multiply 3.6 by 0.01:
3.6 * 0.01 = 0.036
Therefore, there are 0.036 decimeters in 3.6 millimeters.
