The apothem of the hexagon is 8√3 cm.
We are given that;
The area of a regular hexagon= 384√3Cm²
Now,
To find the side length, radius, and apothem of a regular hexagon given its area, we can use the following formulas:
Area = (3√3 s^2) / 2 Area = (1/2) a P Area = (3/2) r a
where s is the side length, a is the apothem, P is the perimeter, and r is the radius of the hexagon. We can solve for any of these variables by rearranging the formulas and plugging in the given area.
A. To find the side length, we can use the first formula and solve for s:
s^2 = (2 Area) / (3√3) s = sqrt((2 Area) / (3√3))
Plugging in Area = 384√3, we get:
s = sqrt((2 * 384√3) / (3√3)) s = sqrt(256) s = 16
Therefore, the side length of the hexagon is 16 cm.
B. To find the radius, we can use any of the formulas and solve for r. For example, using the third formula, we get:
r = (2 Area) / (3 a)
To find a, we can use the second formula and solve for a:
a = (2 Area) / P
To find P, we can use the fact that P = 6s and plug in s = 16:
P = 6 * 16 P = 96
Plugging in P and Area into the formula for a, we get:
a = (2 * 384√3) / 96 a = 8√3
Plugging in a and Area into the formula for r, we get:
r = (2 * 384√3) / (3 * 8√3) r = 32
Therefore, the radius of the hexagon is 32 cm.
C. To find the apothem, we can use any of the formulas and solve for a. For example, using the second formula, we get;
a = (2 Area) / P
Plugging in Area = 384√3 and P = 96, we get:
a = (2 * 384√3) / 96 a = 8√3
Therefore, by polygon the answer will be 8√3 cm.
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100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function. Then graph the function. Thank you!
The amplitude and the period of the function f(x) = 2cos[3(θ + 45)] + 2 are 2 and 2π/3
The Phase shift is 45 and the vertical shift is 2
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2cos[3(θ + 45)] + 2
A sinusoidal function is represented as
f(x) = Acos(B(x + C)) + D
Where
Amplitude = A
Period = 2π/B
Phase shift = C
vertical shift = D
Using the above as a guide, we have the following:
Amplitude = 2
Period = 2π/2
Next, we have
Phase shift = 45
vertical shift = 2
Hence, the amplitude is 2 and the period is 2π/3
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Find an angle in each quadrant with a common reference angle with 311°, from 0°≤θ<360°
Angles in each quadrant with common reference angle as 311° are :
First quadrant = 49°, second quadrant = 131°, third quadrant = 229° and fourth quadrant = 311°.
Given that,
Reference angle = 311°
We have to find an angle in each quadrant with this reference angle.
311° is in the fourth quadrant.
The equivalent angle on the first quadrant is,
360° - 311° = 49°
Equivalent angle on second quadrant is,
180° - 49° = 131°
Equivalent angle on third quadrant is,
360° - 131° = 229°
Hence the angles are found.
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What is the strength of the association between the two
variables in the scatter plot?
Select from the drop-down menu to correctly complete the
statement.
The strength of association is Choose...
Strong or weak
Simplify the expression 5x2+6x+4+x2+x
.
Thank You!
The simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.
The given expression is 5x²+6x+4+x²+x
Simplifying the given expression
5x²+6x+4+x²+x
Firstly, put the similar terms together
5x²+x²+6x+x+4
Adding the similar terms
6x²+7x+4
∵ The expression cannot be solved further, 6x²+7x+4 is the final solution.
Therefore, the simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.
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A baseball player earns $3 million in 2015. During the next 15 years, the earning increase 4% each year.
Write an exponential growth model giving the earning y (in millions of dollars) t years after 2015. Write the base of the model as a decimal
The exponential growth model for the baseball player's earnings, in millions of dollars, t years after 2015 is[tex]y = 3 \times (1.04)^t,[/tex] with a base of 1.04.
To model the exponential growth of the baseball player's earnings, we can use the formula:
[tex]y = a \times (1 + r)^t[/tex]
where:
y represents the earning in millions of dollars
a represents the initial earning in millions of dollars (in this case, $3 million)
r represents the growth rate per year (4%, which can be expressed as 0.04)
t represents the number of years after 2015
In this case, we want to find the earning y (in millions of dollars) t years after 2015.
Since the initial earning in 2015 is $3 million, we can substitute a = 3.
Therefore, the exponential growth model for the player's earnings is:
[tex]y = 3 \times (1 + 0.04)^t[/tex]
Simplifying the expression further, we have:
[tex]y = 3 \times 1.04^t[/tex]
The base of the model is 1.04, which is the decimal representation of the growth rate (4%).
Using this model, we can calculate the player's earnings for any year after 2015 by plugging in the value of t.
For example, if we want to find the earnings 5 years after 2015, we substitute t = 5 into the equation:
[tex]y = 3 \times 1.04^5[/tex]
This will give us the projected earnings in millions of dollars for that particular year.
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Which statements is true and justify your answer
Answer:
Step-by-step explanation:
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21. If AXYZ ≈ AJKL, which segment corresponds to KJ?
If triangles ΔXYZ is congruent to ΔJKL, then the segment which corresponds to KJ is YX.
Given that, two triangles ΔXYZ and ΔJKL are congruent to each other.
So the corresponding vertices are,
Vertex X of ΔXYZ corresponds to vertex J of ΔJKL
Vertex Y of ΔXYZ corresponds to vertex K of ΔJKL
Vertex Z of ΔXYZ corresponds to vertex L of ΔJKL
Now, the segment which corresponds to KJ in ΔXYZ will be the segment formed by joining the vertices that corresponds to K and J.
We already have,
K corresponds to Y and J corresponds to X.
So the equivalent segment is YX.
Hence the segment required is YX.
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The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that exactly 10 flights arrive on time.
Probability that exactly 10 flights arrive on time is 53.33%.
Given that,
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation.
Recently, Southwest Air had the best rate with 80% of its flights arriving on time.
Total number flights in sample = 15
Probability that exactly 10 flights arrive on time is,
P = 10/15 × 80%
= 0.5333
= 53.33%
Hence the required probability is 53.33%.
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sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2
Answer:
sin( 3pi/4 ) = -√2/2
So, B.
please answer this question correctly.
The inequality representing the dollar amount, n, that Zack must be paid for each room in order to make a profit of more than $300 is n > $107.50.
Option C is the correct answer.
We have,
Profit = Amount Paid - Cost of Supplies
Given that the cost of supplies for each room is $32.50, we can represent the profit for each room as:
Profit per room = Amount Paid per room - $32.50
Zack wants to make a profit of more than $300 for painting 4 identical rooms.
The total profit for the 4 rooms should be greater than $300.
We can write this inequality as:
4 x (Profit per room) > $300
Substituting the expression for profit per room, we have:
4 x (Amount Paid per room - $32.50) > $300
Now, let's solve the inequality to find the dollar amount that Zack must be paid for each room:
4 x (Amount Paid per room - $32.50) > $300
4 x Amount Paid per room - 4 x $32.50 > $300
4 x Amount Paid per room - $130 > $300
4 x Amount Paid per room > $300 + $130
4 x Amount Paid per room > $430
Amount Paid per room > $430 / 4
Amount Paid per room > $107.50
Therefore,
The inequality representing the dollar amount, n, that Zack must be paid for each room in order to make a profit of more than $300 is n > $107.50.
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Susan borrows $1000 for 8 months at 7 1/8% per annum simple interest. What is the amount due?
Answer:
$1047.50-------------------------
Given:
principal (P) = $1000, time (t) = 8 months, and interest rate (r) = 7 1/8% per annum.Convert the interest rate to a decimal:
7 1/8% = 7.125% = 0.07125Convert the time from months to years:
8 months / 12 months per year = 2/3 years.Now, we can calculate the simple interest using the formula:
I = P * r * tI = $1000 * 0.07125 * (2/3) = $47.50Finally, add the interest to the principal to find the amount due:
Amount due = $1000 + $47.50 = $1047.50Susan's amount due for the loan is $1047.50.
The simple interest amount of Susan for time of 8 months is A = $ 1047.50
Given data ,
To calculate the amount due, we need to consider the principal amount borrowed, the interest rate, and the time period.
Principal (P) = $1000
Time (t) = 8 months
Interest rate (r) = 7 1/8% per annum
First, we need to convert the interest rate from a percentage to a decimal. To do this, we divide the given rate by 100:
r = 7 1/8% = 7.125% = 7.125/100 = 0.07125 (decimal)
Next, we can calculate the simple interest using the formula:
Simple Interest (I) = Prt
I = $1000 x 0.07125 x (8/12)
I = $1000 x 0.07125 x (2/3)
I = $47.50
Finally, to find the amount due, we add the principal amount to the simple interest:
Amount Due = Principal + Simple Interest
Amount Due = $1000 + $47.50
Amount Due = $ 1047.50
Hence , the amount is A = $ 1047.50
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Explain each step and answer 50 points
1 Yes the set of rational expressions is closed under subtraction
2. Yes the set of rational expressions is closed under multiplication
3. No the set of rational expressions is not closed under division
How to determine if the expression is closed
1. The subtraction of two rational expressions results in another rational expression.
= p(x)/q(x) - r(x)/s(x)= ((p(x)s(x) - r(x)q(x))/(q(x)s(x)))
this is also a rational expression.
2. The multiplication of two rational expressions results in another rational expression.
=(p(x)/q(x)) * (r(x)/s(x)) = ((p(x)r(x))/(q(x)s(x)))
this is a rational expression.
3. Division of two rational expressions may result in an expression that is not a rational expression.
= (p(x)/q(x)) / (r(x)/s(x)))
= ((p(x)s(x)) / (q(x)r(x)))
this may not be a rational expression if q(x)r(x) equals zero at some point, causing division by zero
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25. Solve for the missing variables.
The missing angles in the cyclic quadrilateral are as follows:
a = 101°
b = 67°
c = 84°
d = 80°
How to find the angles in a cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.
Opposite angles of a cyclic quadrilateral is supplementary.
c = 180 - 96
c = 84 degrees
d = 180 - 100
d = 80 degrees
100 = 1 / 2 (a + 99)
100 = 0.5a + 49.5
0.5a = 50.5
divide both sides by 0.5
a = 50.5 / 0.5
a = 101 degrees
84 = 1 / 2 (101 + b)
84 = 50.5 + 0.5b
84 - 50.5 = 0.5b
0.5b = 33.5
b = 33.5 / 0.5
b = 67 degrees
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100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
The values of the trigonometry functions are sin(θ) = 3/√13, cos(θ) = 2/√13, tan(θ) = 3/2, csc(θ) = √13/3, sec(θ) = √13/2 and cot(θ) = 2/3
Finding the values of the trigonometry functionsfrom the question, we have the following parameters that can be used in our computation:
The right triangle
The hypotenuse of the right triangle is calculated as
h² = 2² + 3²
When evaluated, we have
h = √13
The values of the trigonometry functions are then evaluated as
sin(θ) = 3/√13
cos(θ) = 2/√13
tan(θ) = 3/2
csc(θ) = √13/3
sec(θ) = √13/2
cot(θ) = 2/3
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The felt cover on this pool table needs to be replaced. How much material is needed if the pool table is 86” long by 48” wide?
4,128 sq. in.
4,256 sq. in.
3,284 sq. in.
3,298 sq. in.
The correct answer is 4,128 square inches.
To determine the amount of material needed to replace the felt cover on the pool table, we need to calculate the surface area of the table.
The pool table has dimensions of 86 inches in length and 48 inches in width.
Surface area is the measure of the total area of the external or exposed surfaces of a three-dimensional object.
It represents the sum of the areas of all the faces or surfaces of an object, including its top, bottom, and sides.
Surface area is typically measured in square units such as square inches, square centimeters, or square meters.
To find the surface area, we multiply these two dimensions together:
Surface area = Length [tex]\times[/tex] Width
Surface area = 86 inches [tex]\times[/tex] 48 inches
Surface area = 4,128 square inches.
Therefore, the correct answer is 4,128 square inches.
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The shaded square has an area of 55 square units.
Enter the exact value of the side length of the square
and press "Try it."
I
units
Try It
The exact value of the side length of the square is √55 unit.
Given that the shaded square has an area of 55 square units.
We need to determine the exact value of the side length of the square,
To determine the exact value of the side length of the square, we can use the formula for the area of a square, which is given by the equation:
Area = side length²
In this case, the area is given as 55 square units. Therefore, we can set up the equation as follows:
55 = side length²
To solve for the side length, we need to find the square root of both sides of the equation:
√55 = √(side length)²
Simplifying further:
√55 = side length
Thus, the exact value of the side length of the square is √55 unit.
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A small square has length y cm
A large square has length 40 cm
The area of the small square is of
the area of the large square.
25
Work out the value of y.
Your final line must say, y = ...
y cm
40 cm
Total marks: 3
Answer:
Step-by-step explanation:
The area of a square is given by the formula A = s^2, where A is the area and s is the length of a side of the square.
Let y be the length of the side of the small square.
Then, the area of the small square is y^2 cm^2.
According to the question, the area of the small square is 1/25 of the area of the large square.
Thus, the area of the large square is (25)(y^2) cm^2.
The length of a side of the large square is given by the formula s = √A.
Therefore, the length of a side of the large square is √(25y^2) = 5y cm.
Since the length of a side of a cube is equal to its height, width, and length, the dimensions of the cube are 5y cm x 5y cm x 5y cm = (5y)^3 cm^3.
Therefore, y = 40/5 = 8.
Thus, the dimensions of the cube are 40 cm x 40 cm x 40 cm.
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40. What is mzWXY? How do you know?
W
X
69°
Z
Y
The value of the angle m<WXY is 69 degrees
How to determine angleWe need to know that the shape given is a parallelogram.
The properties of a parallelogram are given as;
Opposite sides of the shape are parallel.Opposite sides of the shape are congruent.Opposite angles of a parallelogram are equal.Same-Side interior angles are supplementary, that is sum up to 180 degrees.Each diagonal of a parallelogram separates it into two equal trianglesThe diagonals of a parallelogram bisect each other.From the information given, we have that;
Angel WZY and Angle WXY are opposite angles of the parallelogram
Then,
m<WXY = 69 degrees
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Given f(x)=(1/4)^-x, Evaluate f(-2), f(1), and f(2).
When we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16.
To evaluate f(x)=(1/4)^-x for specific values of x, we can substitute the given values into the function expression and simplify the calculations.
Evaluating f(-2):
Substitute x = -2 into the function f(x):
f(-2) = (1/4)^-(-2) = (1/4)^2 = 1/16
Evaluating f(1):
Substitute x = 1 into the function f(x):
f(1) = (1/4)^-1 = 4^1 = 4
Evaluating f(2):
Substitute x = 2 into the function f(x):
f(2) = (1/4)^-2 = (1/4)^2 = 1/16
Therefore, the evaluations of f(-2), f(1), and f(2) are:
f(-2) = 1/16
f(1) = 4
f(2) = 1/16
In conclusion, when we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16. These values represent the corresponding outputs of the function for the given inputs.
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Which inequality is graphed below
Answer:
wheres it at?
Step-by-step explanation:
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Tara looks up hotel room prices for a holiday.
A hotel has a 25% off sale on its prices.
A VAT charge of 20% must be added on at the end of the transaction after any discount.
If the regular price of a room is £80 per night, how much will Tara pay for 5 nights?
Answer:
360
Step-by-step explanation:
80*5=400 and .25*400=100 so it costs 300 for five nights without tax, and adding on the tax raises the cost to 60 (300+(.2*300)=360)
Find 3 ways the equation f(x)=3x^{2}+4x+3 can be used in the real world.
Answer:
Step-by-step explanation:
The equation f(x) = 3x^2 + 4x + 3 is a quadratic function. Here are three ways this equation can be used in the real world:
In physics, this equation can be used to model the height of an object thrown into the air. The equation f(x) = 3x^2 + 4x + 3 can be used to calculate the height of the object at any given time x, where x is the time elapsed since the object was thrown. The coefficient 3 in the equation represents the acceleration due to gravity, and the other terms represent the initial height and velocity of the object.
In economics, this equation can be used to model the profit of a company. If x represents the number of units sold, then f(x) = 3x^2 + 4x + 3 can be used to calculate the profit made by the company at any level of sales. The coefficient 3 in the equation represents the fixed costs of the company, while the other terms represent the variable costs and revenue.
In engineering, this equation can be used to model the trajectory of a projectile. The equation f(x) = 3x^2 + 4x + 3 can be used to calculate the distance traveled by a projectile at any given time x, where x is the time elapsed since the projectile was launched. The coefficient 3 in the equation represents the initial velocity of the projectile, and the other terms represent the effects of air resistance and gravity.
Find the ordered pair solutions for the
system of equations.
f(x)=x²-3x - 10
f(x) = -x-2
([ ? ],
) and (
Enter the smallest x first.
Answer:
[tex]( - 2, 0 )\; and \; ( 4, - 6)[/tex]
Step-by-step explanation:
To find the ordered pairs set the right side expressions equal to each other and solve for x, then use those values for x to evaluate f(x) values
We get
x² - 3x - 10 = -x - 2
Moving -x - 2 to the left side gives
x² -3x - 10 + x + 2 = 0
(moving an expression from one side to another changes the signs of the terms)
Grouping like terms:
x² - 3x + x -10 +2 = 0
x² -2x -8 = 0
Expression on the left can be factored as (x + 2)(x-4)
This results in
(x + 2)(x - 4) = 0 giving
(x + 2) = 0 ==> x = -2 as one solution for x
(x - 4) =0 ==> x = 4 as the second solution
Plug in x = -2 into the second expression -x - 2 to get
f(-2) = -(-2) -2 = 2 - 2 = 0
So one ordered pair is (-2, 0)
Plug in x = 4 into -x - 2 to get
f(4) = - 4 -2 = -6
So (4, -6) is another ordered pair
Simplify.
√n/18.
Answer choices:
A 1/6n √2.
B √1/9
C 1/6 √2n
Please explain the answer my radical calculator doesn't work on anything with letters in it.
Answer: C 1/6*√2n
Step-by-step explanation:
• Simplify √n/18 as (1/3)^2*n/2
• Multiply them under the radical so the squares 1/3 cancels out to 1/3*√n/2
• Multiply the √n/2 on both sides as √2*n/√2*√2 so it comes out to √2n/2
• Multiply √2n/2 with 1/3 to make √2n/6
√2n/6 is equal to 1/6*√2n
The radical expression √n/18 when simplified is 1/3√n/2
Simplifying the radical expressionFrom the question, we have the following parameters that can be used in our computation:
√n/18
Express 18 as 9 * 2
So, we have the following representation
√n/18 = √n/(9 * 2)
Rewrite as
√n/18 = √n/(2 * 9)
Take the square root of 9
This gives
√n/18 = 1/3 * √n/2
Evaluate the products
√n/18 = 1/3√n/2
Hence, the expression when simplified is 1/3√n/2
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Suppose you're making a soup that uses 5 cups of chicken broth for 8 servings. You need to make 12 servings of the soup. How much broth do you need?
A) 7.5 cups
B) 2.5 cups
C) 8.7 cups
D) 10 cups
There are 40 students trying out for a soccer team. After tryouts, 16 of these
students will make the soccer team and 4 of those who make the team will be
captains. What is the probability that Julie will be captain, given that she makes
the team?
The probability that Julie will be a captain, given that she makes the team is 1/3.
Given,
Number of students trying out for a soccer team = 40
Case of probability,
P(A) = n(A)/n(S)
n(A) = number of favourable outcomes, n(S) is the total number of events in the sample space.
Given ,
18 of 40 students will make the soccer team.
⇒ n(S) = 18
Let event A: Julie will be a captain, given that she makes the team
⇒ n(A) = 3
So, the probability that Julie will be a captain, given that she makes the team,
= P(A) = n(A)/n(S)
= P(A) = 3/18
= P(A) = 1/6
Therefore, the probability that Julie will be a captain, given that she makes the team is 1/3.
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Subtract (8n-5)-(-2n-3)
Answer:
Step-by-step explanation:
( 8n - 5 ) - ( -2n - 3 )
( 8n - 5 ) + ( 2n + 3 )
8n - 5 + 2n + 3
10n - 2
The following data are an example of what type of regression?
13.000
12.000
11,000
10,000-
9.000-
8.000-
7,000
6,000
5.000
4,000
3.000
2.000-
1,000
H
3-2-1
1234567
Model
Linear
Quadratic
Exponential
O A. Exponential
OB. Quadratic
O C. Linear
1²
0.808
0.997
0.813
D. None of the above
The data given is an example of a B. Quadratic regression.
How to determine the data ?The r-squared ( r ²) value is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.
The r² values are highest for the quadratic model (r ² = 0. 997), meaning this model explains the most variance in your data compared to the linear (r² = 0. 808) and exponential models (r ² = 0. 813). Thus, the data are best modeled with a quadratic regression.
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The time (t) required to do a job varies inversely as the number of people (p) working on the job.
It takes 9 hours for 4 roofers to complete a certain job. How long would it take 6 roofers to complete the same job?
hours
Answer:
6 hours
Step-by-step explanation:
Varying inversely simply means using the "inverse proportion" methodSo therefore,
4 roofers= 1 hour
1 roofer= 9 * 4
= 36 hours
Why? Because the lesser amount of workers you have, the more time will be needed so as to complete the work.6 roofers= 36/6=6 hours
The more people you have, the lesser amount of time will be spent on completing the work.a cube with a surface area of 6 square inches is removed from the corner of a cube with a surface area of of 96 square inches.
questions
a. what do you think removing the smaller cube from largers cubes has on its surface area? explain your answer
b. find the surface area of the new solid.
a. The surface area of the cube is reduced .
b . The new surface area of the new solid is 90 in²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
a. The surface area of the original cube is 96 in² and a cube of another 6 in² is removed from the old cube.
This means that the surface area of the cube is reduced.
The surface area of a cube is expressed as;
SA = 6l²
where l is the side length of the cube.
b. The surface area of the new solid = surface area of big cube - surface area of old cube = 96-6
= 90 in²
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