The Area of Hexagon can be calculated by using the formula [tex]\frac{3\sqrt{3}s^{2} }{2}[/tex] , where the length of side of the hexagon is "s" .
What is a Hexagon ?
A hexagon is defined as a two dimensional closed figure made up of 6 sides .
A Regular hexagon has : 6 equal sides and 6 equal angles and 6 vertices.
Sum of interior angles is equal to 720° ;
A regular hexagon is made by combination of 6 equilateral triangles.
So , formula to find area of Hexagon is given as : [tex]\frac{3\sqrt{3}s^{2} }{2}[/tex] , where "s" is side length of the hexagon .
Another formula to calculate the Area of hexagon is :
Area = [tex]\frac{1}{2}[/tex] × Apothem × (Perimeter of hexagon) .
The given question is incomplete , the complete question is
How do you find the area of a Hexagon ?
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At the Planetarium, tickets cost $13.50 for adults and $5.50 for kids under 12. How many total tickets would someone get if they purchased 4 adult tickets and 14 kids tickets? How many total tickets would someone get if they purchased aa adult tickets and kk kids tickets?
If someone bought 4 adult tickets and 14 child tickets, they would get a total of 18 tickets.
If a customer buys aa adult tickets and kk child tickets, they will get a total of aa + kk tickets.
What are tickets?Generally, A ticket is a piece of paper or electronic document that gives you permission to enter an event, travel by a particular mode of transportation, or participate in an activity.
There are many different types of tickets, including tickets to concerts, sporting events, plays, and other performances, airline tickets, train tickets, and tickets to theme parks or other attractions.
Some tickets are sold in advance, while others are available at the door or at a ticket booth.
The number of total tickets someone would get if they purchased 4 adult tickets and 14 kids tickets are
18.
If someone purchases aa adult tickets and kk kids tickets, the total number of tickets they would get is
aa + kk.
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Find the radius of convergence R of the series.
[infinity] n
bn (x − a)n, b > 0
n = 1
R =
Find the interval of convergence of the series. (Enter your answer using interval notation.)
The interval of convergence is from (a - b) to (a + b), where b is a positive number.
1. The radius of convergence R is given by the formula R = 1/|b|.
2. The interval of convergence is given by the formula (a - b, a + b).
The radius of convergence R of a series is a measure of how quickly the series converges. It is calculated by taking the inverse of the coefficient of the term with the highest power of the variable in the series. In this case, the coefficient of the highest power of the variable is b, so the radius of convergence is 1/|b|.
The interval of convergence is the region in which the series converges. It is determined by the coefficient of the term with the highest power of the variable in the series. In this case, the coefficient of the highest power of the variable is b, so the interval of convergence is (a - b, a + b). This means that the series converges for values of x in the range from (a - b) to (a + b).
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Use technology to convert (4, –2) into approximate polar coordinates. r = 3.46; θ = –0.46 r = 3.46; θ = 0.46 r = 4.47; θ = –0.46 r = 4.47; θ = 0.46
Using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $73,025?.
The maximum mortgage payment allowed for someone with an annual salary of $73.025 would be $2,190.75 per month.
The correct answer is an option A.
In this question we need to find the maximum mortgage payment allowed for someone with an annual salary of $73,025 using the standard 28/36 guidelines.
We know that the standard 28/36 rule used to calculate the amount of debt an individual or household should assume.
This rule says that a household should spend a maximum of 28% of its gross monthly income on total housing expenses and no more than 36% on total debt service.
Let the maximum mortgage payment allowed be x dollars
So, x = ((73025 x 36) / 100) / 12
x = (2,628,900 / 100) / 12
x = $2,190.75
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A complete question is:
Using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $73,025?
a. $2,190. 75
b. $2,044. 70
c. $1,703. 92
d. $1,217. 8.
Answer:
a
Step-by-step explanation:
Alexander is taking part in a race. For the first 180 m he runs at 3 m/s. The remaining 240 m of the race takes him 100 seconds. What is Alexander's average speed, in m/s, over the whole race? If your answer is a decimal, give it to 2 d.p.
A slice of chocolate fudge cake contains 7.25 grams of sugar. How many grams of sugar are in of a 2/3 slice of chocolate? Write your answer as a mixed fraction in simplest form.
Answer:
4 2/3
Step-by-step explanation:
7.25 ÷ 3 = 2 5/12 × 2 = 4 2/3
If a building that is 6 stories tall has a shadow that is 24 meters long, how many stories tall is a building with a shadow that is 40 meters long?
To make 40 meters long shadow, building should have 10 stories.
What is multiplication?In arithmetic, the multiplication of two numbers represents the repeated addition of one number with respect to another. These numbers can be whole numbers, natural numbers, integers, fractions, etc. If m is multiplied by n, then it means either m is added to itself ‘n’ number of times or vice versa.
Given,
Stories of building 24 meters long shadow = 6
Stories making 1 meter long shadow = 6/24
Stories in building making 40 meters long shadow = 6/24 × 40
= 240 / 24
Stories in 40 meters long building = 10
Hence, 10 stories tall building will make shadow length of 40 meters.
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Every day, the Mercer Pet Store uses 5 bags of dog food to feed the dogs. How many
days will 5 5/8 bags of dog food last?
Task 9: Cookie Jar Problem There was a jar of cookies on the table. Latoya was hungry because she hadn't had breakfast, so she took half of the cookies. Then Mark came along and noticed the cookies. He thought they looked good, so he ate a third of what was left in the jar. Kandi came by and decided to take a fourth of the remaining cookies with her to her next class. Then Shannon came dashing up and took a cookie to munch on. When Michelle looked at the cookie jar, she saw that there were two cookies left. "How many cookies were there in the jar, to begin with?" she asked Kira.
Extension: If there were 2/3 of a cookie left over, how many cookies were there before Latoya came?
Can you please explain the work too, please!
The number of cookies in the jar initially was 42
To find out how many cookies were in the jar initially, we can use algebra to represent the problem. Let x be the number of cookies in the jar initially. After Latoya took half of the cookies, Mark took 1/3 of the remaining cookies, Kandi took 1/4 of the remaining cookies, and Shannon took 1 cookie, there are 2 cookies left in the jar.
We can use this information to set up the equation:
x/2 - (x/2)/3 - (x/2)/4 - 1 - 2 = 0.
By solving this equation, we get x = 42. This means there were 42 cookies in the jar initially. To find out how many cookies were there before Latoya came, we just add the 2/3 of a cookie that was left over to the 2 whole cookies we know of.
So, 42+2/3 = 42.67 which means 42 cookies were there before Latoya came.
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The corners of triangle pqr lie on a circle. pq = 3i 4j and pr = -8i 6j. by showing that the triangle is right-angled, or otherwise, find the area of the circle. [8]
The area of the circle is [tex]\pi r^2 = \pi \cdot \left(\frac{10}{2}\right)^2 = \boxed{25 \pi}$[/tex].
Since pq and pr are both vectors, we can find the length of the hypotenuse qr by taking the square root of the sum of the squares of the magnitudes of pq and pr. This is given by the Pythagorean Theorem:
[tex]$$qr = \sqrt{|pq|^2 + |pr|^2} = \sqrt{3^2 + 4^2 + (-8)^2 + 6^2} = 10$$[/tex]
Therefore, the area of the circle is [tex]\pi r^2 = \pi \cdot \left(\frac{10}{2}\right)^2 = \boxed{25 \pi}$[/tex].
The Pythagorean Theorem is a mathematical equation used to calculate the length of the sides of a right triangle. It states that the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse. In other words, a2 + b2 = c2, where a and b are the lengths of the two legs and c is the length of the hypotenuse.
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A triangle PQR is a right triangle and the area of the circle is 98.17 square units.
In this question we have been given the corners of triangle PQR lie on a circle.
We need to show that the triangle is right-angled otherwise we need to find the area of the circle.
Given that [tex]\vec{PQ}= 3\hat{i} + 4\hat{j}[/tex] and [tex]\vec{PR}= -8\hat{i} + 6\hat{j}[/tex]
Consider the product of PQ and PR.
[tex]\vec{PQ} . \vec{PR}=(3\hat{i} + 4\hat{ij}) . (-8\hat{i} + 6\hat{j})\\\\\vec{PQ} . \vec{PR}=-24|i|^2 + 18ij - 32ij + 24|j|^2\\\\\vec{PQ} . \vec{PR}= -14ij -24 + 24\\\\\vec{PQ} . \vec{PR}= -14ij\\\\\vec{PQ} . \vec{PR}= -14 |i| |j| cos < i, j > \\\\\vec{PQ} . \vec{PR}= 0[/tex]
This means, PQ and PR are perpendicular to each other.
[tex]\Rightarrow \angle QPR=90^{\circ}[/tex]
Thus, the triangle PQR is a right triangle.
|PQ| = 5 units
|PR| = 10 units
Using Pythagoras theorem,
[tex]|QR| = \sqrt{|PQ|^2+ |PR|^2} \\\\|QR| = \sqrt{5^2 + 10^2}\\\\|QR| = \sqrt{25+100} \\\\|QR| = \sqrt{125} \\\\|QR| = 5\sqrt{5} ~~units[/tex]
We know that the hypotenuse is the alrgest side of right triangle.
So, hypotenuse of right triangle PQR = diameter of circle
So, the radius r of circle would be,
[tex]r = \frac{5\sqrt{5} }{2}[/tex]
Now we need to find the area of circle.
[tex]A = \pi\times r^2\\\\A = \pi \times (\frac{5\sqrt{5} √5}{2})^2\\\\A = \pi \times (\frac{125}{4})[/tex]
A = 98.17 square units
Therefore, the area is 98.17 square units
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A complete question is:
The corners of triangle PQR lie on a circle. PQ = 3i + 4j and PR = -8i + 6j. By showing that the triangle is right-angled, or otherwise, find the area of the circle.
Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was
110 ft from camera 2, which was 137 ft from camera 3. Cameras 1 and 3 were 158 ft apart.
Which camera had to cover the greatest angle?
Can anyone tell me if I answered that correctly? Because it was sort of confusing:)
The camera had to cover the greatest angle will be camera 2. Then the correct option is D
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Degrees and sides in relation to one another The biggest side and angle of any triangle are in opposition to one another. The smallest side and angle in every triangle are on opposing sides. The middle side and middle angle are always in opposition to one another in triangles.
Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 110 ft from camera 2, which was 137 ft from camera 3. Cameras 1 and 3 were 158 ft apart.
The distance between Camera 1 and Camera 3 is the largest one. Then the camera had to cover the greatest angle will be camera 2. Then the correct option is D
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How do you find the surface area and volume of a hexagonal prism?
For a Hexagonal Prism , the Surface Area can be calculated by using the formula [tex]3sh+3\sqrt{3}s^{2}[/tex] , and the volume can be calculated by using the formula [tex]\frac{3\sqrt{3}s^{2}}{2} \times s^{2} h[/tex] .
What is a Hexagonal Prism ?
The hexagonal prism is defined as the prism that has a hexagonal base and top. hexagonal prism is a 3D shape and that has 8 faces, 18 edges, and 12 vertices. As it has 8 faces it can also called as Octahedron.
The formula to calculate the Surface Area of the hexagonal prism is written as : [tex]3sh+3\sqrt{3}s^{2}[/tex] ;
The formula to calculate the Volume of hexagonal prism is written as : [tex]\frac{3\sqrt{3}s^{2}}{2} \times s^{2} h[/tex] ;
where h = is the height of hexagonal prism , and
s = is the side of the hexagonal base .
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Please help me pls I need help if you do thank you so much
The solution is
a) The total area of the rectangular grass area is 9600 feet²
b) The number of bags required is 9.6 bags
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangular grass area be = A
Now , the equation will be
The length of the rectangular grass portion = 120 feet
The width of the rectangular grass portion = 80 feet
The area of the rectangular grass portion = Length x Width
Substituting the values in the equation , we get
The area of the rectangular grass portion A = 80 x 120
The area of the rectangular grass portion A = 9600 feet²
Now , each bag of the grass seed covers 1000 feet²
So , the number of bags required for the entire area = area of the rectangular grass portion A / each bag of the grass seed covers 1000 feet²
On simplifying the equation , we get
The number of bags required for the entire area = 9600 / 1000
The number of bags required for the entire area = 9.6 bags
Therefore , the number of bags required is 9.6 bags
Hence , the total area of the rectangular grass area is 9600 feet²
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Eating at all you can eat buffet at your favorite restaurant cost $18.50, and increases its cost by 6% each year .
1. Write a function that correctly depicts the scenario.
2. How much will the buffet cost 10 years from now round your answer to the nearest cent
3. How much did the buffet cost 15 years ago ?round your answer to the nearest cent
The function that correctly depicts the scenario is f(x) = 18.50 * (1.06)^x
The cost of the buffet in 10 years is $33.13The cost of the buffet 15 years ago is $7.71How to write a function that correctly depicts the scenario.From the question, we have the following parameters that can be used in our computation:
Value of buffet = $18.50
Rate of increment = 6%
The function that correctly depicts the scenario is represented as
f(x) = Value of buffet * (1 + Rate of increment)^x
Substitute the known values in the above equation, so, we have the following representation
f(x) = 18.50 * (1 + 6%)^x
So, we have
f(x) = 18.50 * (1.06)^x
How much will the buffet cost 10 years from nowThis means that
x = 10
Substitute the known values in the above equation, so, we have the following representation
f(10) = 18.50 * (1.06)^10
Evaluate
f(10) = 33.13
How much did the buffet cost 15 years ago?This means that
x = -15
Substitute the known values in the above equation, so, we have the following representation
f(-15) = 18.50 * (1.06)^(-15)
Evaluate
f(-15) = 7.71
Hence, the amount 15 years ago is $7.71
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-4x+5y=17
4x+6y= - 16
use elimination to solve system of equations .
The solution to the simultaneous equation using elimination method is x = -4 4/11 and y = -1/11
How to solve equation using elimination method?Elimination method of solving simultaneous equation is by completing removing or eliminating a variable in order to solve for the other variable.
-4x+5y=17
4x+6y= - 16
Add both equations to eliminate x
5y + 6y = 17 + (-16)
11y = 17 - 16
11y = -1
divide both sides by 11
y = -1/11
Substitute into equation (1)
-4x+5y=17
-4x + 5(-1/11) = 17
-4x -5/11 = 17
-4x = 17 + 5/11
-4x = (187 + 5) /11
-4x = 192/11
divide both sides by -4
x = 192/11 ÷ -4
= 192/11 × -1/4
= -192/44
= - 4 16/44
x = -4 4/11
Therefore, x = -4 4/11 and y = -1/11 is the solution to the simultaneous equation -4x+5y=17; 4x+6y= - 16
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If there are 30 dogs and 40 cats at a pet daycare, fill out all of the possible ratios of dogs to cats that could be made.
Answer:75%or0.75.
Step-by-step explanation: Based on the given conditions formulate:: 30 / 40Cross out the common factor: 3/4 3/4: 75% or 0.75.
9. Select each equation that the decimal
0.29 makes true.
10² x
= 29
10⁰ x
X
= 0.29
☐ 10² x
= 290
104 ×
= 2,900
= 29
en
3
10¹ ×
X
97
TIC
The required equations are 10⁴x = 2900 and 10²x = 29
What are equations?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, which equation is making, 0.29.
Considering 10⁴x = 2900 and 10²x = 29
1) 10²x = 29
100x = 29
x = 29 /100
x = 0.29
2) 10⁴x = 2900
10000x = 2900
x = 2900 / 10000
x = 0.29
Hence, the equations making 0.29 are 10⁴x = 2900 and 10²x = 29
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In fifteen days it will be the first of the month. Fifteen days ago it
was the first of the month. It is also summer time in Canada. Give
today's date (month and day). (Hint: what is the first day of summe
in Canada?)
To solve this we must be knowing each and every concept related to month. Therefore, today's date is June 21st. It is also summer time in Canada.
What is month?A month is a measure of time used with calendars that is about the length of the Moon's natural orbital period; the phrases moon and Month are cognates. The conventional definition evolved from the lunar phase cycle; such lunar month ("lunations") comprise synodic months that last around 29.53 days.
In fifteen days it will be the first of the month. Fifteen days ago it was the first of the month. It is also summer time in Canada, then today's date is June 21st.
Therefore, today's date is June 2st.
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Simplify the given expression using the order of operations and exponent rules. Write the answer without negative exponents(assume no division by zero)
The simplification of the Indices ((7c⁶d³)/(8c⁴d³))^-2 is 64c²/49
What is Indices?An index is a small number that tells us how many times a term has been multiplied by itself. The plural of index is indices. Below is an example of a term written in index form: 43. 4 is the base and 3 is the index.
Simplifying (7c⁶d³)/(8c⁴d³))^-2
Firstly we open the parentheses
(7^-2c^6-2d^3-2 ) ÷ 8^-2c^4-2d^3-2
= 7^-2c⁴d ÷ 8^-2c²d
= 7^-2/8^-2(c^4-2d^1-1)
= 7^-2/8^-2(c²)
= 1/49÷ 1/64(c²)
= 1/49× 64(c²)
= 64c²/49
Therefore the simplification of (7c⁶d³)/(8c⁴d³))^-2 is 64c²/49
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The floor of a gazebo is in the shape of a regular octagon. The perimeter of the floor is 72 feet. The distance from the center of the octagon to one of the vertices is 11.8 feet. What is the approximate length of the apothem
The approximate length of the apothem is 10.86 feet.
For a regular polygon, the apothem is the perpendicular line drawn from the center to the midpoint of any of its sides.
The formula to find the apothem given its perimeter is:
a = P / (2n tan (180 / n))
where a = length of the apothem
P = perimeter
n = number of sides of the polygon
Plug in the values and solve for the apothem.
a = P / (2n tan (180 / n))
a = 72 feet / (2)(8)(tan (180 / 8))
a = 10.86 feet
Therefore, the approximate length of the apothem is 10.86 feet.
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Can someone help me with this please
Answer: get smart bro
you would know it if you was smart
Step-by-step explanation:
you wont do your work, you always cheat, and you don't listen to the teacher
you need to find the answer out on your own.
P.S. i hope you have a good day :)
log(3x² + 4x) = log(2x²+12)
To solve this equation, you would need to isolate the logarithm on one side of the equation.
What is a logarithm in simple terms?
A logarithm is the power to which a number must be increased in order to get some other number (see Section 3 of this Math Review for more about exponents) (see Section 3 of this Math Review for more about exponents). For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2, or log 100 = 2.
You can start by using the property of logarithms that states that log(a*b) = log(a) + log(b).
So, you can split the left side of the equation into two logarithms: log(3x²) + log(1 + 4/3x) = log(2x²) + log(1 + 6/x)
Now, you could use the property log(a^b) = b*log(a) to simplify the equation further.
So, you will have: 2log(x) + log(1 + 4/3x) = 2log(x) + log(1 + 6/x)
Then by using log(1+x) ≈ x, you can simplify the equation further to 2log(x) + 4/3x ≈ 2log(x) + 6/x.
Now it's clear that the equation is not true and can't be solved.
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let f(x) = x3 − 2x2. find the point(s) on the graph of f where the tangent line is horizontal.
Answer:
x=0 and x=4/3
Step-by-step explanation:
The tangent line will be horizontal at the points where [tex]f'(x)=0[/tex]:
[tex]f(x)=x^3-2x^2\\f'(x)=3x^2-4x\\0=3x^2-4x\\0=x(3x-4)\\x=0,\frac{4}{3}[/tex]
Thus, at x=0 and x=4/3, the tangent line will be horizontal at those points.
What is the perimeter of △lmn? 8 units 9 units 6 startroot 10 endroot units 8 startroot 10 endroot units
After solving, the perimeter of △lmn is 8 + √10.
In the given question, we have to find the perimeter of △lmn.
The graph of the given question is given below:
From the graph we can see that N(-1, 4), L(2, 4) and M(-2, 1)
Before finding the perimeter we have to find the length of the line.
We can find the length of the line using the formula
L = √[{x(2)-x(1)}^2+{y(2)-y(1)}^2]
We firstly find the length of line NL.
x(1) = -1, y(1) = 4, x(2) = 2 and y(2) = 4
L(NL) = √[(2-(-1))^2+(4-4)^2]
L(NL) = √[(2+1)^2+0^2]
L(NL) = √[(3)^2+0]
L(NL) = 3
Now we find the length of line LM.
x(1) = 2, y(1) = 4, x(2) = -2 and y(2) = 1
L(LM) = √[(-2-2)^2+(1-4)^2]
L(LM) = √[(-4)^2+(-3)^2]
L(LM) = √[16+9]
L(LM) = √25
L(LM) = 5
Now we find the length of line MN.
x(1) = -2, y(1) = 1, x(2) = -1 and y(2) = 4
L(MN) = √[(-1-(-2))^2+(4-1)^2]
L(MN) = √[(-1+2)^2+(3)^2]
L(MN) = √[(1)^2+9]
L(MN) = √[1+9]
L(MN) = √10
Now we finding the perimeter of △lmn
Perimeter of △lmn = length of NL + length of LM + length of MN
Perimeter of △lmn = 3 + 5 + √10
Perimeter of △lmn = 8 + √10
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The perimeter is equal to the sum of the lengths of its three sides. We added 8 units, 9 units, and 10 units to get a total of 27 units, which is the perimeter of △lmn.
The perimeter of a triangle is the sum of the lengths of its three sides. To calculate the perimeter of △lmn, we must first identify the lengths of the three sides. Let's say the length of side lm is 8 units, side mn is 9 units, and side ln is 10 units. We can now use the formula for the perimeter of a triangle to calculate the perimeter of △lmn:
Perimeter of △lmn = 8 + 9 + 10
Perimeter of △lmn = 27 units
To calculate the perimeter of △lmn, we first identified the lengths of its three sides. Then, we used the formula for the perimeter of a triangle, which states that the perimeter is equal to the sum of the lengths of its three sides. We added 8 units, 9 units, and 10 units to get a total of 27 units, which is the perimeter of △lmn.
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Emma took a taxi from the airport to her house. She paid a flat fee of $$55 plus $$3. 703. 70 per mile. The fare came to $$4242. Complete the equation that can be used to find the correct distance dd in miles and then solve it to determine distance.
Emma traveled 1127.2 miles from the airport to her house.
The equation to calculate the distance traveled by Emma is:
55 + 3.703 * d = 4242
To solve the equation, we need to subtract 55 from both sides of the equation.
4242 - 55 = 4187
Then, we will divide both sides of the equation by 3.703
4187 / 3.703 = 1127.2
Finally, we can calculate the distance traveled by Emma in miles.
d = 1127.2 miles
Therefore, Emma traveled 1127.2 miles from the airport to her house.
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Emma traveled 10 from the airport to her house.
In this question we have been given that Emma took a taxi from the airport to her house.
She paid a flat fee of $5 plus $3. 70 per mile.
The fare came to $42.
We need to find an equation that can be used to find the correct distance d in miles and then solve it to determine distance.
Let c be the total traveling cost.
So, from given information an equation to calculate the distance traveled by Emma would be,
c = 5 + (3.70)d
The fare came to $42.
c = $42
Substiting this value in above equation we get,
42 = 5 + 3.70d
We solve this equation for d
42 - 5 = 3.70d
37 = 3.70d
d = 37 / 3.7
d = 10 miles
Therefore, the distance in miles covered by Emma is 10 miles.
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Please answer MCQ 10
VII) (-i)^19 = -i. Option C
VIII) The imaginary part of i/1 + i = 1/2. Option C
IX) The modulus of 3 - 4i is 5. Option C
X) For Z = a + ib, sin θ = a/b. Option A
XI) There are 3 elements in the set. Option A
What are the imaginary numbers?We know that the imaginary numbers has to do with the numbers that we can be not be able to find on the number line. These are not real numbers but they are very important in the process of computation. There are two parts of a complex number. We have the imaginary part and we have the real part.
It is sometimes possible that we can be able to represent the complex number by the use of an Argand diagram which shows the complex number in the polar form.
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q11 ANSWER FOR 20 POINTS
Answer: 15+0.65x=80
Step-by-step explanation:
Two-thirds of the members of Highland Church attended the International Dinner during their annual missions conference. When seven of the members were not able to attend, the total number of attendees was Seventy-one. How many members does Highland Church have?
The total number of members Highland Church have, 113
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
Two-thirds of the members of Highland Church attended the International Dinner
The members were not able to attend = 7
The total number of attendees = 71
Suppose the total members of Highland Church = x
So, 2/3x = 71
⇒ x = 106.5 ≈ 106
The total number in church = attendees + non attendees
= 106 + 7
= 113
So, 113 members lives in Highland Church
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PLEASE HELP!
Suppose the mean height for women is 64 inches with a standard deviation of 2 inches. The World Health Organization wants to post a range of heights that include 95% of the world's population of women. What would the range be?
From [blank] to [blank] inches.
The range for 95% of the population would be from 60 inches to 68 inches.
What is the standard deviation?The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.
The mean height for women is 64 inches with a standard deviation of 2 inches.
As we know that the range for 95% of the population would be as:
μ - σ < x < μ + σ
(64 - 2 × 2) < x < (64 + 2 × 2)
60 < x < 68
Thus, the range would be from 60 inches to 68 inches.
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A number has the digits 8 and 4. To the nearest 10 the number rounds to 50. What is the number.
A number has the digits 8 and 4. To the nearest 10 the number rounds to 50. The value of the number will be 48.
The general equation for writing a two-digit number is 10x+y,
Where, x = number placed at ten's digit, while y = number placed at unit's digit.
Here, numbers have two digits 8 and 4.
We can assume two different cases:
Case 1
When 8 is at ten's digit and 4 is at unit's digit
So, the value of the number will be =(10*8) +4 = 80+4 = 84
As the number is rounds to 50, but here in this case 84 can only be rounds to either 80, or 100 (when we round it to nearest 100)
So, this will not be the required number.
Case 2:
When, 8 is at unit digit and 4 it at ten's digit.
So, the value of the number will be (10*4)+8 = 40+8 = 48
As the number is rounds to 50, so in that case 48 can be rounds to 50.
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The number is 48.
The number 8 and 4 can be combined to make 84. The nearest 10 to 84 is 80. To get to 50, you must add 8 more, making the number 48.
The number 8 and 4 can be combined to create a two-digit number, 84. When rounding to the nearest 10, the number 84 rounds to 80. To get to 50, 8 more must be added, making the number 48. Therefore, the number that is composed of 8 and 4 and rounds to 50 is 48.
The two-digit number 8 and 4 combine to form 84. Rounding to the nearest 10 gives 80. To reach 50, 8 must be added, resulting in 48. Therefore, 8 and 4 together round to 50 and equal 48.
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