Using the Fundamental Counting Theorem, it is found that for each case, the total number of outcomes is:
a) 60,466,176.
b) 5,961,600.
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with n1, n2, ... ways to be done, each thing independent of the other, the number of ways they can be done is N=n1*n2*n3*....
Item a:
No restrictions, hence, for each of the five characters, there are 36 outcomes, hence n1=n5=36.
Then, the possible number of passwords is:
N=36^5=60,466,176
Item b:
The letters and the digits have to be alternated, hence:
Starting with a letter n1=n3=n5=36, n2=n4=10.
Starting with a digit n1=n3=n5=10, n2=n4=36.
Then, the possible number of passwords is:
N=36^3*10^2+10^3*36^2=5,961,600.
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18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89
The requried, Multiplies(with switching factors.) area given below,
a.
693 x 83 = 57489
83 x 693 = 57489
The answer is 57489.
b.
910 x 45 = 40950
45 x 910 = 40950
The answer is 40950.
c.
38 x 84 = 3192
84 x 38 = 3192
The answer is 3192.
d.
409 x 89 = 36401
89 x 409 = 36401
The answer is 36401.
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Donna is thinking about buying a house that costs $125,000. If she puts down $25,000 and is able to get a 5 percent mortgage, she wants an estimate of her total monthly housing expenses. The average annual cost for owning a house, beyond the 5% cost of mortgage interest, is 4.09 percent of the value of the house. Not including the opportunity cost of the down payment, amortization on the loan, or any tax benefits from homeownership, what will be her monthly cost the first month?
A. $206.25
B. $279.60
C. $842.71
D. $746.43
Donna can expect her total monthly housing expenses to be approximately $842.71 for the first month after purchasing the house, assuming no tax benefits or amortization on the loan.
To calculate Donna's monthly housing expenses, we first need to determine the total amount of the mortgage. Since she puts down $25,000 on a $125,000 house, she will need to take out a mortgage for $100,000.
Next, we can calculate the annual cost of owning the house beyond the 5% cost of mortgage interest, which is given as 4.09% of the value of the house. So, 4.09% of $125,000 is:
0.0409 x $125,000 = $5,112.50
This means that Donna can expect to pay approximately $5,112.50 per year in additional expenses associated with owning the house.
To calculate the monthly cost, we simply divide this by 12:
$5,112.50 / 12 = $426.04
So, Donna can expect to pay approximately $426.04 per month in additional expenses associated with owning the house.
Adding the cost of the mortgage interest, we can calculate her total monthly housing expenses as follows:
Total monthly housing expenses = Mortgage interest + Additional annual costs / 12
Mortgage interest = 5% of $100,000 = $5,000 per year or $416.67 per month
Total monthly housing expenses = $416.67 + ($5,112.50 / 12) = $416.67 + $426.04 = $842.71
Hence, Donna can expect her total monthly housing expenses to be approximately $842.71
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please help me with this!
4 glue sticks cost $7.76.
which equation would help determine the cost of 13 glue sticks
choose 1 answer
A x/13 = 4/$7.76
B 13/x = $7.76/4
C 4/$7.76 = 13/x
D 13/4 = $7.76/x
E None of the above
Answer:
13 glue sticks cost $25.22.
Step-by-step explanation:
4 blue sticks cost $7.76, this means that one glue stick costs
$7.76/4 = $1.94.
Let be the cost of the glue sticks, and be the number of glue sticks; then
We can use this equation to find the cost of 13 glue sticks; we just put into our equation and it gives:
So 13 glue sticks cost $25.22.
Angel works at a small shop that sells candy
bars. She oversees ordering more boxes of
candy bars. A box of candy bars (p) costs
$64 and Angel has no more than $230 to
spend on the order. What inequality
represents her situation?
Op 64 >= 230
Op 64 <= 230
O p/64 <= 230
O p/64 >= 230
Answer:
p/64 <= 230
Step-by-step explanation:
The inequality that represents Angel's situation is:
p/64 <= 230
This inequality states that the number of boxes of candy bars, represented by p, divided by 64 (the cost of each box), is less than or equal to 230 (the maximum amount Angel has to spend on the order).
Using the image below, answer the following question: you are asked to pick 2
marbles out of the bag, what is the probability of picking a blue marble and then a
green marble, without replacing the blue one?
PLEASE URGENT
The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.
We have,
We see that there are 10 marbles.
Now,
Number of blue marbles = 2
Number of green marbles = 4
Now,
The probability of picking a blue marble first is 2/10, as there are 2 blue marbles out of 10 in total.
After picking a blue marble, there will be 9 marbles left in the bag.
The probability of picking a green marble second, without replacing the blue one, is 4/9, as there are 4 green marbles remaining out of the 9 marbles in total.
Now,
P(blue marble and green marble) = P(blue marble) x P(green marble)
= (2/10) x (4/9)
= 8/90
= 4/45.
Therefore,
The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.
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Please help due soon
Stmt of cash flows problem
Balance Sheet for Stand Corp Dec 31st:
Cash
Accounts Receivable
Inventory
Total Current Assets
2022
$177,000
$180,000
$100,000
$457,000
2021
$78.000
$185.000
$100.000
$363,000
Investments
Equipment
Accumulated Deprec
Total Non-Current Liabs
$52,000
$298,000
($106,000)
$244.000
$74,000
$240,000
($89.000)
$225,000
Total Assets
$701.000
$588.000
Current Liabilities
$134.000
$151.000
Common Stock
Retained Earnings
$260.000
$307,000
$260,000
$177,000
Total Liabs & Equity
$701.000
$588,000
OTHER INFORMATION:
-Investments were sold in 2022 at a loss of $10.000
-No equipment was sold in 2022
-Cash dividends were paid in 2022
-Net Income for 2022 was $160,000
REQUIRED:Prepare the Statement of Cash Flows:
1. Prepare the Statement of Cash Flows
2. Calculate Free Cash Flow
The Free Cash Flow based on the information given will be $115,000
How to explain the cash flowStatement of Cash Flows for Stand Corp for the year ended December 31, 2022
Cash flows from operating activities:
Net income $160,000
Adjustments to reconcile net income to net cash provided by operating activities:
Depreciation expense $17,000
Loss on sale of investments $10,000
Changes in current assets and liabilities:
Increase in accounts receivable ($5,000)
Increase in inventory ($20,000)
Increase in accounts payable $17,000
Increase in accrued expenses $11,000
Net cash provided by operating activities $190,000
Cash flows from investing activities:
Sale of investments $52,000
Purchase of equipment ($75,000)
Net cash used in investing activities ($23,000)
Cash flows from financing activities:
Payment of cash dividends ($25,000)
Net cash used in financing activities ($25,000)
Net increase in cash $142,000
Cash at beginning of year $78,000
Cash at end of year $220,000
Free Cash Flow = Net cash provided by operating activities - Purchase of equipment
Free Cash Flow = $190,000 - $75,000
Free Cash Flow = $115,000
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What is the surface area of a cone with radius 8 in. and slant height 9 in.?
The total surface area of the cone is 427.04 square inches.
What is the surface area of the cone?For a cone of radius R and slant height L, the total surface area is given by the formula:
S = π*R*L + π*R²
Where π = 3.14
In this case, we know that the radius of the cone is 8 inches, and the slant height of the cone is 9 inches.
Then the total surface area of the cone is:
S = 3.14*8in*9in + 3.14*(8in)²
S = 427.04 in²
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evaluate xy-y when x = 2 and y = 5
Answer:
5
Step-by-step explanation:
Just do as the problem says:
xy-y = (2)(5)-(5) = 10-5 = 5
Answer: 5
Step-by-step explanation: All you have to do is substitute x & y for their respective numbers. In this case, change x for 2 & y for 5, So xy-y becomes 2(5)-5, which equals 10-5, which is 5.
Part A: Jan INCORRECTLY finds the surface area of the cone using the following work. Explain Jan's error and find the
correct volume AND surface area of the cone.
Therefore, Jan has taken the wrong slant height, he has taken height, h is a place of slant height, l. That's why he has got the wrong answer.
How to solveGiven:,
r= d/2
22/2= 11m
Using the Pythagorean theorem, we can find the length:
l =[tex]11\sqrt{5}\\ = 24.6m[/tex]
Therefore, to find the surface area:
SA= 3.14(270.56 + 121)
=[tex]1229.5m^2[/tex]
Therefore, to find the volume:
V= [tex]1/3 \pi.r^2h[/tex]
V= [tex]2786.23m^3[/tex]
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The Complete Question
Jan INCORRECTLY finds the surface area of the cone using the following work. Explain Jan's error and find the correct volume AND surface area of the cone. 22 m SA = = url + ar?
Maxine's credit card has an APR of 27.99%. If her current monthly balance, before interest, is $1,834.50, what will her monthly interest charge be? (4 points) $42.78 $42.79 $51.67 $65.54
Answer:
(b) $42.79
Step-by-step explanation:
You want the monthly interest charge on a balance of $1834.50 when the annual rate is 27.99%.
Monthly rateThe monthly interest rate is the annual rate divided by 12. This means the interest charge is ...
I = Prt . . . . . interest on P at annual rate r for t years
I = $1834.50 × 0.2799 × 1/12 ≈ $42.79
Her monthly interest charge will be $42.79.
a quadratic function is defined by f(x) = x*2 - 8x - 4.
Which expression also defines f and best reveals the max and mini of the function?
a) (x-4)*2 - 20
B) (x-4)*2 + 12
c) x(x-8) -4
d) (x-4)*2 + 20
The expression that best reveals the maximum and minimum of the function[tex]f(x) = x^2 - 8x - 4 is (x - 4)^2 - 20.[/tex] Option A
How to find the expressionThe vertex form of a quadratic function is given by[tex]f(x) = a(x - h)^2 + k[/tex] where (h, k) represents the coordinates of the vertex.
In the given quadratic function [tex]f(x) = x^2 - 8x - 4[/tex], we can rewrite it in the vertex form by completing the square:
[tex]f(x) = (x - 4)^2 - 16 - 4\\f(x) = (x - 4)^2 - 20[/tex]
From this expression, we can see that the vertex of the quadratic function is at the point (4, -20).
The term[tex](x - 4)^2[/tex] tells us that the vertex is at x = 4, and the constant term -20 indicates the y-coordinate of the vertex.
The expression that best reveals the maximum and minimum of the function[tex]f(x) = x^2 - 8x - 4[/tex] is [tex](x - 4)^2 - 20.[/tex]
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100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!
Answer:
[tex]3 {cos}^{2} x - {sin}^{2} x = 0[/tex]
[tex]3 - 3 {sin}^{2} x - {sin}^{2} x = 0[/tex]
[tex]3 - 4 {sin}^{2} x = 0[/tex]
[tex]4 {sin}^{2} x = 3[/tex]
[tex] {sin}^{2} x = \frac{3}{4} [/tex]
sin(x) = +(1/2)√3
x = π/3 + 2kπ or x = 2π/3 + 2kπ
x = -π/3 + 2kπ or x = -2π/3 + 2kπ
(k is an integer)
Solve: log 3 (3x) + log 3 (3) = 5
Answer: x=27
Step-by-step explanation:
Assumption the 3's are the bases
[tex]log_{3} 3x +log_{3} 3=5[/tex] >combine using multiplication log rule (logs with
same base, that are being added can be
combined with multiplication)
[tex]log_{3}( 3x)(3) =5\\[/tex] >simplify
[tex]log_{3}( 9x) =5\\[/tex] >rewrite into exponent form
[tex]3^{5} = 9x[/tex] >simplify
243 = 9x
x=27
Answer:
x = 27
Step-by-step explanation:
using the rules of logarithms
• [tex]log_{b}[/tex] b = 1
• [tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
then
[tex]log_{3}[/tex] (3x) + [tex]log_{3}[/tex] 3 = 5
[tex]log_{3}[/tex] (3x) + 1 = 5 ( subtract 1 from both sides )
[tex]log_{3}[/tex] (3x) = 4
3x = [tex]3^{4}[/tex] = 81 ( divide both sides by 3 )
x = 27
The graph of a sine function has an amplitude of 4, a midline of y=2, and a period of 10.
There is no phase shift. The graph is reflected over the x-axis.
What is the equation of this function?
The equation of the given sine function is y = 4 × sin((π/5)x) + 2.
The equation of the given sine function can be determined based on the given information. We know that the general form of a sine function is:
y = A × sin(Bx - C) + D,
where A represents the amplitude, B represents the frequency, C represents the phase shift, and D represents the vertical shift.
In this case, we are given the following information:
Amplitude (A) = 4: The amplitude is the distance between the maximum and minimum values of the function. Since the function is reflected over the x-axis, the amplitude is positive 4.
Midline (D) = 2: The midline is the horizontal line around which the graph oscillates. In this case, it is y = 2, indicating a vertical shift of 2 units upwards.
Period = 10: The period is the distance between two consecutive peaks (or troughs) of the function.
Given that there is no phase shift, the phase shift (C) is 0.
From the given information, we can deduce the values of A, B, C, and D to construct the equation.
A = 4 (amplitude)
D = 2 (vertical shift)
C = 0 (no phase shift)
To determine B, we use the formula:
B = 2π / Period
Plugging in the value for Period (10), we can calculate B:
B = 2π / 10 = π / 5
Therefore, the equation of the given sine function is:
y = 4 × sin((π/5)x) + 2.
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Show that the points (2, 5), (5 , 2) and (6,6) are composites of a triangle
The slopes of the lines connecting all the points are distinct. Hence, they form a triangle.
Proof that 3 points form a triangleTo show that the points (2, 5), (5, 2), and (6, 6) form a triangle, we can calculate the slopes of the lines connecting these points. If the slopes are all distinct, then the points form a triangle.
Let's calculate the slopes:
The slope between (2, 5) and (5, 2):
m₁ = (y₂ - y₁) / (x₂ - x₁)
= (2 - 5) / (5 - 2)
= -3/3
= -1
The slope between (2, 5) and (6, 6):
m₂ = (y₂ - y₁) / (x₂ - x₁)
= (6 - 5) / (6 - 2)
= 1/4
The slope between (5, 2) and (6, 6):
m₃ = (y₂ - y₁) / (x₂ - x₁)
= (6 - 2) / (6 - 5)
= 4/1
= 4
Since the slopes of the lines connecting these points are all distinct (-1, 1/4, and 4), the points (2, 5), (5, 2), and (6, 6) form a triangle.
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Find the distance from point X to line p.
Answer:
[tex]\sf 2\sqrt{17}[/tex]
Step-by-step explanation:
To find the distance of a line using distance formula:
The line from point X intersect the line p at (0 , -3).
( -2 , 5) ⇒ x₁ = -2 & y₁ = 5
(0 , -3) ⇒ x₂ = 0 & y₂ = -3
[tex]\boxed{\bf Distance = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}}[/tex]
[tex]\sf = \sqrt{-2-0)^2+(5-[-3])^2}\\\\=\sqrt{(-2-0)^2 + (5+3)^2}\\\\=\sqrt{(-2)^2+(8)^2}\\\\=\sqrt{4+64}\\\\=\sqrt{68}\\\\=\sqrt{2*2*17}\\\\=2\sqrt{17}[/tex]
What is the domain of f(x)? {x | 1 < x < 5} {x | 1 < x < 5} {y | −4 < y < 1} {y | −4 < y < 1}
The domain of function f(x) is given as follows:
{x | 1 ≤ x < 5}.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.The values of x of the function given at the end of the answer are as follows:
Starts at x = 1(closed interval).Ends at x = 5 (open interval).Hence the domain is given as follows:
{x | 1 ≤ x < 5}.
Missing InformationThe function is given by the image presented at the end of the answer.
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Answer:
A - {x | 1 < x < 5}
Step-by-step explanation:
took the Quiz
How many 1/3 inch cubes does it take to fill a box with a width of 2 2/3 inches, length of 3 1/3 inches with a height 2 1/3
The number of 1/3 inch cubes required to fill the box is 62.
Volume of boxVolume = length × width × height
Height = 7/3
Length = 10/3
width = 8/3
Hence ,
Volume = 7/3 × 10/3 × 8/3 = 560/27
Size of cube = 1/3
Number of cubes required = Volume of box / size of cube
Number of cubes = 560/27 × 3/1
Number of cubes = 1680/27 = 62.22
Therefore, it will take 62 1/3 cubes to fill the box
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D
(x+2)(x+6)=0
In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:
O zero product property
O division property
O transitive property
O multiplication property
H
OI
The property used to calculate x in (x + 2)(x + 6) = 0 is (a) the zero product property
How to determine the property used to calculate xFrom the question, we have the following parameters that can be used in our computation:
(x + 2)(x + 6) = 0
The equation when expanded becomes
x + 2 = 0 or x + 6 = 0
In algebra, the zero product property states that
if ab = 0, then a = 0 or b = 0
using the above as a guide, we have the following:
The property used to calculate x is (a) the zero product property
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We mixed 5l of 45% alcohol, 4l of 82% and 1l of 92% alcohol. How many percent alcohol does the resulting mixture contain? I got 58.6% and im wondering IF that's correct.
The resulting mixture contains approximately 64.5% alcohol, not 58.6% as you mentioned.
To solve this problemWe can calculate the weighted average of the alcohol percentages based on the volumes of each component.
Let's figure out how much alcohol there is overall in the mixture:
Total alcohol is calculated as follows: (Volume of 45% alcohol) * (Property of 45% alcohol) + (Volume of 82% alcohol) * (Property of 82% alcohol) + (Volume of 92% alcohol) * (Property of 92% alcohol).
Total alcohol = (5 liters) * (45%) + (4 liters) * (82%) + (1 liter) * (92%)
Total alcohol = 2.25 liters + 3.28 liters + 0.92 liters
Total alcohol = 6.45 liters
Let's now determine the amount of alcohol included in the final mixture:
Alcohol content is calculated as (total alcohol / total mixture volume) * 100.
The mixture's total volume is = 5 liters + 4 liters + 1 liter = 10 liters
Alcohol content: (6.45 liters / 10 liters) x 100 = 64.5%
Therefore, the resulting mixture contains approximately 64.5% alcohol, not 58.6% as you mentioned.
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What do they mean and why please
Si 10 obreros construyen un consultorio médico en 12 dias.¿Con cuántos obreros se hará la misma obra en 15 dias?
A total of 8 workers are required for a building time of 15 days.
How many workers are needed to complete a building?
In this problem we find a case of inverse relationship, in which the number of workers (n) is inversely proportional to building time (t), in hours. The situation is represented by following formulas:
n ∝ 1 / t
n = k / t
Where k is the proportionality ratio, which can be eliminated by building the following formula:
n₁ · t₁ = n₂ · t₂
If we know that n₁ = 10, t₁ = 12 and t₂ = 15, then the required number of workers is:
n₂ = n₁ · (t₁ / t₂)
n₂ = 10 · (12 / 15)
n₂ = 10 · (4 / 5)
n₂ = 8
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When Grace opens and lays a shipping box out flat, she sees that the top and the bottom of the box
both measure 10 inches by 14 Inches, the sides of the box both measure 14 inches by 8 inches, and
the front and back of the box both measure 8 inches by 10 inches. What is the surface area of Grace's
strooing box?
The surface area of Grace's shipping box is 664 square inches.
We have,
The box can be divided into six rectangles, each of which represents the face of the box.
To find the surface area of the box, we need to find the area of each face and then add them all up.
The top and bottom of the box are both 10 inches by 14 inches, so the area of each of these faces is:
= 10 x 14
= 140 square inches
The sides of the box are both 14 inches by 8 inches, so the area of each of these faces is:
= 14 x 8
= 112 square inches
The front and back of the box are both 8 inches by 10 inches, so the area of each of these faces is:
8 x 10
= 80 square inches
To find the surface area of the whole box, we add up the areas of all six faces:
= 2(140) + 2(112) + 2(80)
= 280 + 224 + 160
= 664 square inches
Therefore,
The surface area of Grace's shipping box is 664 square inches.
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NO LINKS!! URGENT HELP PLEASE!!
O is the center of the regular dodecagon below. Find its area. Round to the nearest tenth.
Answer:
80.4 square units.
Step-by-step explanation:
solution Given:
apothem(a)=5
no of side(n)= 12
Area(A)-?
The area of a regular polygon can be found using the following formula:
[tex]\boxed{\bold{Area =\frac{1}{2}* n * s * a}}[/tex]
where:
n is the number of sidess is the length of one sidea is the apothemIn this case, we have:
n = 12s = ?a = 5First, we need to find S.
We can find the length of one side using the following formula:
[tex]\boxed{\bold{s = 2 * a * tan(\frac{\pi}{n})}}[/tex]
substituting value:
[tex]\bold{s = 2 * 5 * tan(\frac{\pi}{12})=2.679}[/tex] here π is 180°
To find the area substituting value in the above area's formula:
[tex]\bold{Area = \frac{1}{2}* 12 * 2.679 * 5=80.37\: sqaure\: units}[/tex]
in nearest tenth 80.4 square units.
Therefore, the area of the regular polygon is 80.4 square units.
Answer:
80.4 square units (nearest tenth)
Step-by-step explanation:
The given diagram shows a regular dodecagon (12-sided polygon) with an apothem of 5 units.
The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.
We can calculate the side length of a regular polygon given its apothem using the following formula:
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
Substitute n = 12 and a = 5 into the equation to create an expression for s:
[tex]5=\dfrac{s}{2 \tan \left(\dfrac{180^{\circ}}{12}\right)}[/tex]
[tex]s=10\tan \left(15^{\circ}\right)[/tex]
Now we can use the standard formula for an area of a regular polygon:
[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]
Substitute the found expression for s, n = 12 and a = 5 into the formula and solve for A:
[tex]A=\dfrac{12 \cdot 10\tan \left(15^{\circ}\right) \cdot 5}{2}[/tex]
[tex]A=\dfrac{600\tan \left(15^{\circ}\right)}{2}[/tex]
[tex]A=300\tan \left(15^{\circ}\right)[/tex]
[tex]A=80.3847577...[/tex]
[tex]A=80.4\; \sf square\;units\;(nearest\;tenth)[/tex]
Therefore, the area of a regular dodecagon with an apothem of 5 units is 80.4 square units, rounded to the nearest tenth.
the third term of an arithmetic sequence is 7 and the twelfth term in 106. what is the one hundredth term of the sequence
Answer:
a₁₀₀ = 1074
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₃ = 7 and a₁₂ = 106 , then
a₁ + 2d = 7 → (1)
a₁ + 11d = 106 → (2)
solve the equations simultaneously to find a₁ and d
subtract (1) from (2) term by term to eliminate a₁
(a₁ - a₁) + (11d - 2d) = 106 - 7
0 + 9d = 99
9d = 99 ( divide both sides by 9 )
d = 11
substitute d = 11 into (1) and solve for a₁
a₁ + 2(11) = 7
a₁ + 22 = 7 ( subtract 22 from both sides )
a₁ = - 15
Then
a₁₀₀ = - 15 + (99 × 11) = - 15 + 1089 = 1074
NO LINKS!!! URGENT HELP PLEASE!!!
The distance between Miami, Florida and Bermuda is about 1042 miles. The distance from Bermuda to San Juan. Puerto Rico is about 965 miles, and the distance from San Juan to Miami is about 1038 miles. Find the area of the triangle formed by the three locations.
Answer:
444523.45 square miles
Step-by-step explanation:
By using Heron's formula, we can easily find the area of the triangle formed by Miami, Bermuda, and San Juan, we need to use the lengths of the three sides of the triangle.
Let,
Side a: Distance from Miami to Bermuda = 1042 miles
Side b: Distance from Bermuda to San Juan = 965 miles
Side c: Distance from San Juan to Miami = 1038 miles
Now we can use Heron's formula to find the area of the triangle:
s =[tex]\frac{a+b+c}{2}[/tex]
s = [tex]\frac{1042 + 965 + 1038}{2}=1522.5[/tex] miles
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
A = [tex]\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}=444523.45[/tex]
Therefore, the area of the triangle formed by Miami, Bermuda, and San Juan is approximately 444523.45 square miles.
Answer:
444,523.45 square miles (2 d.p.)
Step-by-step explanation:
To find the area of a triangle formed by the locations of Miami, Bermuda, and San Juan, use Heron's formula.
[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]
Label the three sides of the triangle as 'a', 'b', and 'c', where 'a' is the distance from Miami to Bermuda (1042 miles), 'b' is the distance from Bermuda to San Juan (965 miles), and 'c' is the distance from San Juan to Miami (1038 miles):
a = 1042 milesb = 965 milesc = 1038 milesTo find the half perimeter, s, half the sum of the three side lengths:
[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{1042+965+1038}{2}=1522.5[/tex]
Substitute the values of a, b, c and s into Heron's formula and solve for area, A:
[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}\\&=\sqrt{1522.5(480.5)(557.5)(484.5)}\\&=444523.4468348...\\&=444523.45\; \sf miles^2\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the area of the triangle formed by the three locations is 444,523.45 square miles, to two decimal places.
If Shawn rides his bike ¾ mile every ½ hour, how many miles does he bike per hour?
Answer:
1 1/2 miles per hour
Step-by-step explanation:
We can use a ratio to solve
3/4 mile
--------------
1/2 hour
Double the top and the bottom to get to 1 hour
3/4 * 2 miles
--------------
1/2 *2 hours
1 1/2 miles
-------------------
1 hours
1 1/2 miles per hour
Answer:1 1/2 mile or 6/4 mile
Step-by-step explanation:
Every half hour he rides 3/4Just multiply 3/4 by 2 which equals 6/4 or 1 1/2.
Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?
possible answers -
By the cross product property, AB2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by AD.
By the cross product property, AB2 = BC multiplied by AD.
The correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:
By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].
To prove that [tex]BC^2 = AB^2 + AC^2[/tex], we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:
Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.
By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).
Using the proportionality of similar triangles, we can write the following ratio:
[tex]$\frac{AB}{BC} = \frac{AD}{AB}$[/tex]
Cross-multiplying, we get:
[tex]$AB^2 = BC \cdot AD$[/tex]
Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:
[tex]$\frac{AC}{BC} = \frac{AD}{AC}$[/tex]
Cross-multiplying, we have:
[tex]$AC^2 = BC \cdot AD$[/tex]
Now, we can substitute the derived expressions into the original equation:
[tex]$BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$[/tex]
It was made possible by cross-product property.
Therefore, the correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:
By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].
For more questions on cross-product property:
https://brainly.com/question/14542172
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A spinner has 3 equal sections: red, white, and blue. John spins the spinner and tosses a coin. Which shows the sample space for spinning the spinner and tossing the coin?
The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}. Thus, the correct option is D.
Given that:
A coin is tossed.
A spinner has 3 equal sections: Red, White, and Blue.
The samples are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
The total number of samples is calculated as,
Total samples = 2 x 3
Total samples = 6
The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}.
Thus, the correct option is D.
More about the sample link is given below.
https://brainly.com/question/8053622
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Use the figure to answer the following.
a. What is the surface area of the cylinder? Leave your answer in terms of x.
b. Suppose the diameter and the height of the cylinder are cut in half. How does this affect the surface area of the cylinder? Explain
The diameter of the cylinder is 8 and the height is 11
a. The surface area of the cylinder is 120π square units.
b. Assuming the diameter and the height of the cylinder are cut in half, the surface area of the cylinder would be reduced by a scale factor of 1/4.
How to calculate surface area of a cylinder?In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.Note: Radius = diameter/2 = 8/2 = 4 m.
By substituting the side lengths into the formula for the surface area (SA) of a cylinder, we have the following;
Surface area = 2πrh + 2πr²
Surface area = 2(π)(4)(11) + 2(π)(4²)
Surface area = 120π square units.
Part b.
Assuming the diameter and the height of the cylinder are cut in half, we have:
Surface area = 2(π)(4/2)(11/2) + 2(π)((4/2)²)
Surface area = 2(π)(2)(5.5) + 2(π)(2²)
Surface area = (π)(2)(11) + 2(π)(4)
Surface area = 22π + 8π
Surface area = 30π square units.
Scale factor = 30π/120π
Scale factor = 1/4.
Read more on surface area here: brainly.com/question/27118100
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Note: "The diameter of the cylinder is 8 and the height is 11"