The sin function can be model as N(t) = 0.5sin(πt/6) + 1.5 if the attendance ranges from a low of approximately 1,000,000 visitors in September to a high of approximately 2,000,000 visitors in March.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
The attendance ranges from a low of approximately 1,000,000 visitors in September to a high of approximately 2,000,000 visitors in March.
We know the sine function is:
y = Asin(w + c) + s
Here:
A is amplitude
w is angular velocity,
s is vertical Displacement,
c = phase angle
A = (2000000 - 1000000) /2 = 500,000
w = 2π/T
T = 12
w = 2π/12 = π/6
s = (1000000 +2000000) /2 = 3,000,000/2 = 1,500,000
500,000sin(π/6 + 0) + 1500000
500000sin(π/6)+1500000
or
0.5sin(πt/6) + 1.5
Thus, the sin function can be model as N(t) = 0.5sin(πt/6) + 1.5 if the attendance ranges from a low of approximately 1,000,000 visitors in September to a high of approximately 2,000,000 visitors in March.
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Four friends are planning a party at a skating rink. The friends must pay $3 for
each person attending the party. They will also spend $36 on snacks. If each
friend contributes $21 to the party, what is the maximum number of people that
can attend the party?
16
19
28
48
Answer:
The answer is 28. It is easy.
3. Which of the following is an exponential function?
O f(x)= 2/x
O f(x)= 5x-6
O f(x) = 3^x
O f(x) = 3x^3
Answer:
B is correct I hope this helps.
Et $a_1, a_2, a_3,\dots$ be an arithmetic sequence.
if $a_1 + a_3 + a_5 = -12$ and $a_1a_3a_5 = 80$, find all possible values of $a_{10}$.
Since it's an arithmetic sequence,
[tex]a_2 = a_1 + d[/tex]
[tex]a_3 = a_2 + d = a_1 + 2d[/tex]
[tex]a_4 = a_3 + d = a_1 + 3d[/tex]
and so on, up to
[tex]a_n = a_1 + (n-1)d[/tex]
Now, by substitution,
[tex]a_1 + a_3 + a_5 = -12[/tex]
[tex]a_1 + (a_1+2d) + (a_1+4d) = -12[/tex]
[tex]3a_1 + 6d = -12[/tex]
[tex]a_1 + 2d = -4[/tex]
[tex]\implies a_1 = -4-2d, a_3 = -4, a_5 = -4+2d[/tex]
Then the product [tex]a_1a_3a_5=80[/tex] depends only on d, so that
[tex](-4-2d) \times (-4) \times (-4+2d) = 80[/tex]
Solve for d :
[tex](4+2d) (4-2d) = -20[/tex]
[tex]16 - 4d^2 = -20[/tex]
[tex]4d^2 = 36[/tex]
[tex]d^2 = 9[/tex]
[tex]d = \pm3[/tex]
If d = 3, then the first term in the sequence is [tex]a_1 = -10[/tex], and the tenth term would be [tex]a_{10} = \boxed{17}[/tex].
If d = -3, then the first term would instead by [tex]a_1 = 2[/tex], and the tenth term would be [tex]a_{10} = \boxed{-25}[/tex].
Susie needs to cover her triangular garden with new top soil. Her garden has a base of 7 ft and a height of 10 ft. A bag of soil will cover 5 square feet. How many bags will she need?
Question 7 options:
70 bags of soil
35 bags of soil
12 bags of soil
7 bags of soil
If 1 bag of soil will covers 5 square feet, the number of bags of soil that will cover Susie's 35 square feet triangular garden is 7 bags.
Option D) is the correct answer.
How many bags will Susie need?Area of a triangle is expressed as half base multiply by height.
A = (1/2)base × height
Given that;
Base of the triangular garden = 7ftHeight = 10ftArea of the triangular garden A = ?A = (1/2)base × height
A = (1/2) × 7ft × 10ft
Area of the triangular garden A = 35ft²
Now, if 1 bag of soil covers 5 square feet. how many will cover 35 square feet?
1 bag covers 5ft²
x bags covers 35ft²
x = 35 / 5
x = 7 bags
Therefore, if 1 bag of soil will covers 5 square feet, the number of bags of soil that will cover Susie's 35 square feet triangular garden is 7 bags.
Option D) is the correct answer.
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Find the distance between the two points rounding to the nearest tenth (if necessary). (-6, 7) and (-3, 0)
Answer: [tex]the[/tex] [tex]answer[/tex] [tex]is[/tex] [tex]7.6[/tex] or [tex]\sqrt{58}[/tex]
Step-by-step explanation:
[tex](-6-(-3))^2 + (7-0)^2[/tex]
[tex](-6, 7) and (-3, 0)[/tex]
[tex]the[/tex] [tex]distance[/tex] [tex]between[/tex] [tex]the[/tex] [tex]two-points[/tex] [tex]rounding[/tex] [tex]to[/tex] [tex]the[/tex] [tex]nearest[/tex] [tex]tenth[/tex].
[tex](-6,7)=(-6=[/tex]
[tex]7=)[/tex]
[tex](-3,0)=(-3=[/tex]
[tex]0=)[/tex]
[tex]Exact Form:\sqrt{58}[/tex]
The answer is [tex]7.2[/tex] [tex](7.61577310)[/tex] and [tex]\sqrt{58}[/tex]
Answer: [tex]\sqrt{58}[/tex] and [tex]7.6[/tex]
Find the length of the arc AB in the circle with radius 3 meters shown below. (Round your answer to the nearest tenth.) 60 3 meters چارے
Considering the circumference of the circle, it is found that the length of arc AB is of 3.1 meters.
What is the circumference of a circle?
The circumference of a circle of radius r is given by:
[tex]C = 2\pi r[/tex].
This measure is equivalent to the length of an arc of 360º.
In this problem, we have that the radius is of r = 3m, hence the circumference is given by:
C = 6 pi m.
Arc AB has an angle of 60º, hence it's length is 1/6 of the circumference, which will then be of pi m = 3.1 meters.
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A point T divides a line AB internally in the ratio5:2 .Given that A is (-4,10) and B is (10,3) , find the coordinates of T
Answer:
T(6,5)
Step-by-step explanation:
Solution,
Let the coordinate of T be T(a,b), where T divides a line AB internally in the ratio 5:2. Given that A is (-4,10) and B is (10,3).
From the section formula,
[tex]x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}[/tex]
Let,
(x,y)=(a,b)
(x₁,y₁)=(-4,10)
(x₂,y₂)=(10,3)
m₁:m₂=5:2
Now substitute the values.
[tex]\hookrightarrow x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}\\\\\hookrightarrow a=\frac{5\times10+2\times(-4)}{5+2},b=\frac{5\times3+2\times10}{5+2}\\\\\hookrightarrow a=\frac{42}{7},\: b=\frac{35}{7}\\\\\hookrightarrow a=6, \:b=5[/tex]
Brendan's original plan was to visit stuttgart, dresden, weisbaden, and berlin. however, he would like to keep his costs under €860. which change to brendan’s travel plans would result in his staying under, but closest, to his original budget? a. replace dresden with potsdam. b. replace stuttgart with kiel. c. replace berlin with munich. d. replace weisbaden with hanover.
Brendan's trip plans could be changed to keep him under, but near to, his original budget if he replaces Stuttgart with Kiel. Therefore, it is B.
What exactly is a budget?A budget is basically a financial forecast of revenue and spending for a given period.
The substitution of Kiel for Stuttgart in Brendan's trip plans would result in him keeping under, but near to, his original budget. This will help save money.
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17 students and 15 teachers went on a field trip to an art museum. student tickets cost $10 each, and adult tickets cost $12 each. How much did the museum tickets cost in all?
Answer:
350 dollars
Step-by-step explanation:
We're given:
17 students15 teachersStudent ticket = 10 dollarsAdult ticket = 12 dollarsFirst, find the total cost for student tickets:
17 students × 10 dollars = 170 dollarsTherefore, the total cost for student tickets was 170 dollars.
Now, find the total cost for adult tickets:
15 teachers × 12 dollars = 180 dollarsTherefore, the total cost for adult tickets was 180 dollars
To find the total cost for the museum tickets, find the sum:
180 + 170 = 350 dollars
Therefore, the museum tickets cost 350 dollars in total.
Find the circumference of a circle whose area is 25π. Leave the answer in terms of π.
[tex]\text{Given that,}\\\\~~~~~~~\text{Area} = 25\pi\\\\\implies \pi r^2 = 25 \pi\\\\\implies r^2 = 25\\\\\implies r= 5\\\\\text{Now,}\\\\\text{Circumference}= 2\pi r\\\\~~~~~~~~~~~~~~~~~~~~=2\pi \cdot 5\\ \\~~~~~~~~~~~~~~~~~~~~=10\pi[/tex]
Anna is 12, she is 5'3, 107 pounds, and her shoe size is 6 (girls, USA shoe size). however, she is trying to buy womens shoes and doesn't know which shoe size would fit her good. What size would fit her feet?
Answer:
Size 8
Step-by-step explanation:
A woman's size 8 in kids is a 6 or 6.5 youth shoe size.
check whether (x-1) is a factor of 2x²-3x+1 or not ................
Answer:
(x - 1) is a factor of 2x² - 3x + 1
Step-by-step explanation:
Method 1
If (x - 1) is a factor of f(x) = 2x² - 3x + 1 then f(1) = 0
Substitute x = 1 into the equations:
f(1) = 2(1)² - 3(1) + 1
= 2 - 3 + 1
= 0
Therefore, (x - 1) is a factor of 2x² - 3x + 1
Method 2
Factor 2x² - 3x + 1
Find 2 two numbers that multiply to 2 and sum to -3: -2 and -1
Rewrite the coefficient of the middle term as the sum of these 2 numbers:
⇒ 2x² - 2x - x + 1
Factorize the first two terms and the last two terms separately:
⇒ 2x(x - 1) - 1(x - 1)
Factor out the common term (x - 1):
⇒ (2x - 1)(x - 1)
Thus proving that (x - 1) is a product of 2x² - 3x + 1
Determine the solution for the following equation: x = 3 x = 5 x = 13 x = 65
Answer:
x = 3
Step-by-step explanation:
[tex](8x - 8)^{3/2} = 64\\(8x - 8)^{3} = 4096\\x = 3[/tex]
Answer:
A on edge 23
Step-by-step explanation:
because math
5. 7/8 = 2/48
O
A. 42
O B. 1
O C. 13
OD. 6
Answer: A. 42
7/8 = ?/48
8 * 6 = 48
7 * 6 = 42
? = 42
30 POINTS
Packaging of a product can cost a lot of money. Can you design
the cheapest package?
• Your task is to decide on the most cost effective and efficient
way to pack 12 golf balls. The radius of each golf ball is 1,8 cm.
All 12 golf balls fit side by side and you must design a box that
will hold the 12 golf balls with the minimum amount of wasted
card. The cost of cardboard is going to 0,01€ per cm squared.
In the design of a package, things to take into consideration are:
The sizeIts safetyIts durabilityIts storage space, etc.What is cost effectiveness?The most cost effective and efficient to pack 12 golf balls is through the use of a small golf bag or a small box that is made specially for that purpose.
The design of the box will be in a rectangle shape where there will be two rows of which the ball is made to fit in till the 12 balls are completely inside the box. The lock is automatic and it is one that can be easily closed and opened easily when one wants to take a ball.
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What are the measures of the numbered angles?
Answer:
Angle 1 = 78 degrees
Angle 2= 90 degrees.
Angle 3= 12 degrees
Step-by-step explanation:
For angle 1,
Since all opposite angles of a kite is congruent, if the opposite half of the angle is 78 degrees, then the other opposite half is also 78 degrees.
For angle 2,
Diagonals of a kite will ALWAYS form right angles, this since angle 2 is formed by intersecting diagonals, it would be 90 degrees.
For angle 3,
Opposite angles of a kite are supplementary, meaning that the two angles will form a straight line, or 180 degrees.
We know that 78 degrees is half of one opposite angle, so the opposite angle can be concluded as 156 degrees.
The other set of two angles is unknown, so we take it as this formula:
156+2x=180
We subtract 156 from 180 to cancel out the coefficient.
2x=24
Now we use the division property of equality.
2x/2=24/2
x=12.
Angle 3= 12.
Rick went on a hike with his family in Big Bend National Park. During the hike, he saw 6 lizards, 1 scorpion, 2 foxes, 3 jackrabbits, 6 deer, and 2 snakes.
Rick has a pet snake, so he was most excited to see the snakes. What percent of the animals were snakes?
During the hike, Rick saw 20 animals and 10% of the animals were snakes.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
During the hike, he saw 6 lizards, 1 scorpion, 2 foxes, 3 jackrabbits, 6 deer, and 2 snakes.
Total number of animals = 6 + 1 + 2 + 3 + 6 + 2 = 20 animals
Percentage of animals that were snakes = (2 / 20) * 100% = 10%
During the hike, Rick saw 20 animals and 10% of the animals were snakes.
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Using the image above, what is the measure of side EG? Round to nearest hundredth
Answer:
is 3.5
Step-by-step explanation:
you need to use SOH CAH TOA
Answer:
this is how I solve it....
PLEASE HELP WILL GIVE BRAINLEST!
Answer:
2[tex]\pi[/tex]
Step-by-step explanation:
Answer:
option 1
Step-by-step explanation:
The radius of a unit circle is 1 and its diameter is 2 . π can be defined as the ratio of the circumference of a circle to its diameter, hence the circumference of the unit circle is 2π . In general the circumference of a circle of radius r is 2πr
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When Abigail had one cat, she needed to serve 2 cans of cat food each day. Now that Abigail
has adopted a second cat, she needs to serve a total of 3 1/2 cans each day. How much extra
food is needed to feed the second cat?
Write your answer as a fraction or as a whole or mixed number.
cans
Based on the information provided, to feed the second cat it is necessary 1 1/2 extra cans or 1.5 cans.
How much extra food is needed to feed the second cat?This difference can be found by substracting the total cans fed with only one cat to the total fed with two cats:
3 1/2 cans - 2 cans = 1 1/2 cans, which can also be expressed as 1.5 cans.Based on this, to have a second cat implies 1.5 extra cans.
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What are the measures of the numbered angles?
Answer:
m<1 = 94
m<2 = 132
Step-by-step explanation:
This is a right trapezoid
Since the base lines are parallel, the facing angles would be supplementary and their sum is equal to 180 which means:
m<1 + 86 = 180 so m<1 = 94
and
m<2 + 48 = 180 so m<2 = 132
Quadrilateral ABCD is dilated at center (0.0) with scale factor 1/2 to form quadrilateral A’B’C’D’. What is the length of A’B’?
Answer:
Step-by-step explanation:
Factor 2x^2+x-3
(PLEASE INCLUDE STEP BY STEP)
The unit is "Factoring trinomials by grouping" so please use that method
Answer:
[tex]2x^2+x-3=(2x+3)(x-1)[/tex]
Step-by-step explanation:
Rewrite the middle term as a sum of two terms so that the coefficients add up to the coefficient of the middle term, and group the entire polynomial into two binomials in which they have the same factor:
[tex]2x^2+x-3\\2x^2-2x+3x-3\\(2x^2-2x)+(3x-3)\\2x(x-1)+3(x-1)\\(2x+3)(x-1)[/tex]
Hope this helps! Let me know if you are still confused.
HELP PLEASE!!!!!!! not Hubby097 tho
Answer:
729.
Step-by-step explanation:
-3 /1 =-3
9 / -3= -3
-27/9 = -3
So this is a geometric sequence with common ratio r = -3.
First term a = 1 so
nth term = ar^(n-1)
= 1(-3)^(n-1)
7th term = 1(-3)^(7-1)
= (-3)^6
= 729.
Help me on this pls.
Answer:
f - 65 pages per hour
Step-by-step explanation:
420 - 160 = 260
6 - 2 = 4
260 divided by 4 is 65 on average per hour
Answer:
F. 65.
Step-by-step explanation:
The number of pages he has left to read = 420 - 160
= 260.
So mean number per hour 260/4
= 65.
Simplify the expression: 4(n - 3) - 2(-3 + n)
Answer:
[tex]2(n-3)=2n-6[/tex]
Step-by-step explanation:
[tex]4(n-3)-2(-3+n)\\\\4(n-3)-2(n-3)\\\\(4-2)(n-3)\\\\2(n-3)[/tex]
can someone help me with the first 6
Answer & Step-by-step explanation:
These questions are wanting you to find the sequence and solve for the nth term in said sequence.
The easiest way to do this is to just see the difference between each number, and continue adding or subtracting to the nth term the question is asking for.
For example, the first one is decreasing by 3 every time, so the 7th term will be -4, (the 4th term), subtracted by 3, three more times.
5, 2, -1, -4, -7, -10, -13
The other way to do this is to find the rule, and subsitute in what term is required.
For letter c (the second c), the sequence is 30, 24, 18, 12
The rule is to subtract 6 every time, so -6 n
Since we start our 1st sequence from 30, our rule must start from 30 + 6, the opposite of our rule, which gives us 36.
Our rule is 36 - 6n
So since we are looking for the 11th term, we substutute in 11 into our equation.
36 - 6 n
36 - 6 (11)
36 - 66
-30
This way of thinking will work for the whole set of questions you have here
170 over 360 simplify
Answer:
17/36
Step-by-step explanation:
Finding a probability a movie complex is showing three action films and three comedy films. you randomly select two
different films to watch. find the probability that you select a comedy to watchsecond given that you randomly selected a
comedy to watch first
The probability that you select a comedy to watch second given that you randomly selected a comedy to watch first will be,[tex]\rm \frac{1}{5}[/tex].
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.
Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
No of action films = 3
No of comedy films=3
The probability that you select a comedy to watch second given that you randomly selected a comedy to watch first is found as;
[tex]\rm P = \frac{C_3'}{C_6'} \times \frac{C_2'}{C_5'} \\\\\ P=\frac{3}{6} \times \frac{2}{5} \\\\ P=\frac{1}{5}[/tex]
Hence, the probability that you select a comedy to watch second given that you randomly selected a comedy to watch first will be,[tex]\rm \frac{1}{5}[/tex].
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Find its Surface Area 5 m 7 m 3 m 4 m
Answer:
D. 96 m²
Step-by-step explanation:
The surface area of a triangular prism is the sum of the areas of all of the faces. A triangular prism has two triangular faces (bases) and three rectangular faces.
__
rectangular facesThe dimensions of the rectangular faces are such that they can be considered together as a rectangle whose width is the distance between the triangular faces, and whose length is the perimeter of the triangle. For this prism, that is a 7 m width and a (3+4+5) = 12 m length.
triangular facesThe two triangular faces together have an area that is equal to that of a rectangle with the same base and height as the triangular face. For this prism, that is a 3 m base and a 4 m height.
totalThe total surface area is ...
lateral area + base area = (7 m)(12 m) +(3 m)(4 m) = (84 +12) m²
surface area = 96 m²
_____
Additional comment
The formula for the area of a triangle is ...
A = 1/2bh
A triangular prism has two congruent triangular faces, so their total area is ...
A = 2(1/2bh) = bh
We elected to skip the halving and doubling, and go straight to the total base area.