Answer: C(t) = -475.5*cos(t*pi/6) + 475.5
Step-by-step explanation:
We know that we have a sinusoidal relation, with a minimum at 9:00 am and at 9:00 pm.
If we define the 9:00 am as our t = 0, we have that the maximum, at 3:00pm, is at t = 6 hours.
and the other minimum, at 9:00pm, is at t = 12 hours.
Then we need to find a trigonometric function that has the minimum at t = 0, we can do this as:
-Cos(c*t)
when t = 0
-cos(0) = - 1
then we have a function:
C(t) = -A*cos(c*t) + B
where A, c and B are constants.
We know that at t = 0 we have 0 customers, and that at t = 6h we have 875 customers, that is the maximum.
then:
C(0) = 0 = -A + B
this means that A = B, then our function is:
C(0) = -A*cos(c*t) + A.
now, at t = 6h we have a maximum, this means that -A*cos(c*6h) = A
then:
C(6h) = A + A = 875
2A = 875
A = 875/2 = 437.5
and we also have that, if -cos(c*6) = 1
then cos(c*6) = -1
and we know that cos(pi) = -1
then c*6 = pi
c = pi/6
Then our function is
C(t) = -475.5*cos(t*pi/6) + 475.5
Final answer:
On average, one customer arrives every two minutes at Somerset Mall on a Saturday, which means it takes six minutes on average for three customers to arrive. This question applies trigonometry, algebra, and statistical concepts.
Explanation:
A research firm finds that the average number of customers in Somerset Mall on a Saturday varies sinusoidally with time. The question involves understanding sinusoidal functions, their applications, and basic statistical concepts related to customer arrival rates. The sinusoidal nature of customer arrivals is a practical application of trigonometry and algebra in solving real-world problems.
Part a: Average Minutes Between Arrivals
Given that 30 customers arrive per hour, to find the average time between successive arrivals, we divide the number of minutes in an hour by the number of arrivals: 60 minutes / 30 customers = 2 minutes. Therefore, on average, one customer arrives every two minutes.
Part b: Time for Three Customers to Arrive
Since one customer arrives every two minutes on average, for three customers to arrive, it would take 3 * 2 minutes = 6 minutes on average.
The model's assumption that customers arrive one at a time and at a constant rate throughout the day simplifies the real-life complexity of customer behavior and peak shopping times. This is a critical consideration in the practical application of mathematical models in business.
Please help! in geo!
Answer:
pretty sure it would be 11 inches
Step-by-step explanation:
the rules of isosceles triangles is that two sides are the same and one is smaller.
Answer:
the missing side is 11 inches
Step-by-step explanation:
the missing angel is 37*
Please help ASAP and thank you sm!
What is the measure of each exterior angle of the right triangle?
x = _°
y = _°
z = _°
Answer:
X=90 degrees, Y=134 degrees, Z=136 degrees
Step-by-step explanation:
X=90 degrees. It is supplementary to the right angle or forms 180 degrees with it.
The triangle angles add up to 180 degrees. Therefore, the angle supplementary to Y is 180-(90+44)=46. Now, 180-46=134. You could also use the exterior angle theorem which states that the exterior angle is equal to the sum of the two remote interior angles. The 2 remote interior angle to y would be 90 and 44. 90+44=134=y.
Z is supplementary to 44 because it is also 180 degrees. Z=180-44=136 degrees.
Answer:
x = 90
y = 134
z = 136
Step-by-step explanation:
The right angle measures 90 degrees.
x + 90 = 180
x = 90
z + 44 = 180
z = 136
Theorem:
The measure of an exterior angles of a triangle equals the sum of the measure of the two remote interior angles.
Using the theorem, we get
y = 90 + 44
y = 134
Answer:
x = 90
y = 134
z = 136
Choose the number that is a solution of the inequality: a + 9 < 5
A) -2
B) 5
C) 0
D) -5
( i kept getting -4 am i wrong or are the choices wrong?)
Answer:
d: -5
Step-by-step explanation:
when you plug in all the answer choices -5 is the only true answer
Solve the equation using the distributive property and properties of equality.
5(a+ 3) = -55
Answer:
a = -14
Step-by-step explanation:
Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, divide 5 from both sides:
(5(a + 3))/5 = = (-55)/5
a + 3 = -55/5
a + 3 = -11
Next, fully isolate a by subtracting 3 from both sides:
a + 3 (-3) = -11 (-3)
a = -11 - 3
a = -14
a = -14 is your answer.
~
Final Answer:
a = -14In-depth explanation:
Hi! The question is asking us to solve the equation, which is:
[tex]\large\textbf{5(a + 3) = -55}[/tex]
Use the distributive property to simplify the left-hand side:
[tex]\large\textbf{5a + 15 = -55}[/tex]
Subtract 15 from each side:
[tex]\large\textbf{5a = -55 - 15}[/tex]
[tex]\large\textbf{5a = -70}[/tex]
Divide each side by 5:
[tex]\large\textbf{a = -14}[/tex]
∴ the answer is a = -14.[tex]\rule{350}{1}[/tex]
Solve the inequality: −2x > −6 Question 3 options: x < −3 x > 3 x > −3 x < 3
Answer:
divide both sides of the inequality by -2 and flip the inequality sign the you get (x < 3)
To solve the inequality -2x > -6, divide both sides by -2, remembering to reverse the inequality sign, to obtain x < 3 as the solution.
To solve the inequality -2x > -6, we start by isolating the variable x. To do this, we divide both sides of the inequality by -2. It's important to remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the direction of the inequality sign. Thus, dividing by -2, the inequality becomes x < 6/2. Simplifying further, we find that x < 3.
Others parts of the referenced information discuss concepts like absolute values, z-scores, and transitivity of numbers but are not directly relevant to solving this inequality.
Hence, the correct answer to the inequality is x < 3.
Is (1, 7) a solution to this system of inequalities? y < x + 8 y ≤ 6x + 1
Answer:
-8
Step-by-step explanation:
Final answer:
Upon checking both inequalities, the point (1, 7) satisfies y < x + 8 and y ≤ 6x + 1. Thus, (1, 7) is a solution to the system of inequalities.
Explanation:
To determine if the point (1, 7) is a solution to the given system of inequalities, we need to check if the point satisfies both inequalities. The system is:
y < x + 8
y ≤ 6x + 1
For the first inequality:
y < x + 8
7 < 1 + 8
7 < 9 ⇒ True
For the second inequality:
y ≤ 6x + 1
7 ≤ 6(1) + 1
7 ≤ 7 ⇒ True
Since the point (1, 7) satisfies both inequalities, it is indeed a solution to the system.
Describe the transformation f(x) = √x + 1 − 5 in words. The parent function f(x) = √x has been shifted 1 unit and 5 units.
We conclude that the parent function f(x) = √x has been shifted 1 unit to the left and 5 units downwards.
How was the parent function transformed?
For a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
If N is positive, the translation is upwards.If N is negative, the translation is downwards.For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x) + N
If N is positive, the translation is to the left.If N is negative, the translation is to the right.Here we have f(x) = √x, and g(x) = √(x + 1) - 5
Then:
g(x) = f(x + 1) - 5
From this, we conclude that the parent function f(x) = √x has been shifted 1 unit to the left and 5 units downwards.
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Which of the following best describes the volume of a prism? the product of the height and base the product of the height and base area the sum of the height and base area the sum of the height and base
your answer would be the product of the height and base
Answer:
the product of the height and base area
Step-by-step explanation:
The sum of a number and 14 is at least 18
The inequality fir the given phrase is x+14≥18, the solution for the obtained inequality is x≥4.
The given phrase is "The sum of a number and 14 is at least 18".
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Let the unknown number be x.
Here, the inequality is x+14≥18
Subtract 14 on both the sides of an inequality, we get
x+14-14≥18-14
x≥4
Therefore, the inequality fir the given phrase is x+14≥18, the solution for the obtained inequality is x≥4.
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Final answer:
The sum of a number and 14 is at least 18' can be expressed as the inequality x + 14 >= 18, indicating that the unknown number must be 4 or greater.
Explanation:
The student's question involves setting up an inequality to represent the situation described.
The problem statement, 'The sum of a number and 14 is at least 18,' translates to a mathematical inequality as follows:
Let 'x' represent the unknown number.
The problem states that when you add 14 to this number, the result should be at least 18. Therefore, the inequality would be:
x + 14 >= 18.
To solve this inequality, you would subtract 14 from both sides:
x = 18 - 14
x = 4
This means the unknown number must be 4 or any larger number. In other words, any number greater than or equal to 4, when added to 14, will be at least 18.
In January, Ben was charging $25 for individual hitting
lessons and in April started charging $30. What percent
did he increase his prices? _ _%
20% percentage increase in prices from $25 to $30.
To calculate the percentage increase:
Calculate the increase in price: $30 - $25 = $5
Calculate the percent increase: ($5 / $25) x 100% = 20%
Therefore, Ben increased his prices by 20%.
Help?!!?? I don’t get it??
Answer:
1/6
Step-by-step explanation:
1/2 (The probability that its tails) x 1/3(The probability that it lands on a green side)
n Pensacola, Florida, the average rainfall in the month of July is $7.40$ inches. By October, the average rainfall decreases by $35\%$ . By December, the average rainfall drops another $0.66$ inches.
Answer:
Olani???
Why are you here?
(East harlem scholars academy teacher)
Step-by-step explanation:
The average rainfall in December is 4.15 inches. Therefore option C is the answer.
Given that, in Pensacola, Florida, the average rainfall in the month of July is 7.40 inches. By October, the average rainfall decreases by 35%. By December, the average rainfall drops another 0.66 inches.
We need to find the average rainfall, in inches, in December.
What is average rainfall?The term "average annual rainfall" refers to the sum of the yearly precipitation totals for a location during a year as determined by the nearest National Weather Service station over the three decades prior.
In July, rainfall was 7.40 inches. By October, the average rainfall decreases by 35%.
That is, 7.40-35% of 7.40
=7.40-0.35 × 7.40
=7.40-2.59=4.81
By December, the average rainfall drops another 0.66 inches.
That is, 4.81-0.66=4.15
The average rainfall in December is 4.15 inches. Therefore option C is the answer.
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Your question is incomplete, probably the complete question/missing part is:
In Pensacola, Florida, the average rainfall
in the month of July is 7.40 inches. By
October, the average rainfall decreases by
35%. By December, the average rainfall
drops another 0.66 inches.
What is the average rainfall, in inches, in
December?
A. 1.64
B. 1.93
C. 4.15
D. 4.81
Henry can lay a brick walkway by himself in 12 hours. Roberts does the same job in 10 hours. Working together, how long will it take them to lay the brick walkway?
Please I need the answer right away!
Answer:
Henry = 12 hours
Robert = 10 hours
that 2 people
so 12/ divided by how many people
and 10/ divided by how many people
so 12/2
and 10/2
= 5 and 6
then find the (median) middle of both numbers one or more
which is 5 1/2
so they can finish working together in 5 1/2 hours
Ben wants to try a new restaurant for dinner. His online search
resulted in 7 new 3-star restaurants, 5 new 4-star restaurants, and 3
new 5-star restaurants. If he were to choose a restaurant at random,
what is the probability that he chooses a 5-star restaurant?
Select one:
33%
20%
47%
3%
A coin and a die is rolled. What is the probability of a head and a 3?
a. 1/4
b. 1/8
c. 1/12
d. 1/24
BRAINLIEST URGENTTT
Jackie's gross semimonthly pay is $3420.
To maintain her current way of life, how much should she have saved by the time she retires?
$812,600
$820,800
$889,200
$890,600
Answer:
$890,600
Step-by-step explanation:
Answer:
They say you should save 10%
So if you calculate her yearly income
3420 x 26 pay periods per year = 88,920
Multiply it by 10
$889,200
Step-by-step explanation:
The probability of a chance event is 0.05, it is
to happen
when compared to a chance event with a probability of 0.
Select one:
more likely
both more and less likely
less likely
equally likely
Answer:
less
Step-by-step explanation:
A plumber charges $130 2 hours of work and $235 for 5 hours of workWhat is the of change in dollars per hour
Final answer:
The plumber charges $35 per hour, calculated by dividing the change in total cost ($105) by the change in hours (3).
Explanation:
To find the rate of change in dollars per hour for the plumber's charges, we need to use the definition of rate of change, which is the change in cost divided by the change in time.
Here are the steps for calculation:
Determine the change in cost: $235 - $130 = $105.Determine the change in time: 5 hours - 2 hours = 3 hours.Calculate the rate of change: $105 ÷ 3 hours = $35 per hour.This means the plumber charges $35 per hour for their service.
BRAINLIEST !!!!!!for whoever gives me explanation and answer
Answer:
100 x 0.85 = 85
100 x 0.85 = 85
85 x 2 = 170
170/85=2 so divide 100 by 2 = 50
50 x 0.85 = 42.5
50 x 0.85 = 42.5
42.5 + 42.5 = 85
Your answer is 500 hope this helps.
Step-by-step explanation:
Can you help me with this question?
Answer: the first one
Step-by-step explanation: can i have brainlieist
The number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes) as a function of rainfall (in
centimeters) is modeled by:
m(x) = -(x - 5)2 + 25
How many centimeters of rainfall will produce the maximum number of mosquitoes?
Answer:
5 cm
Step-by-step explanation:
Given the function:
[tex]m(x)=-(x-5)^{2} +25[/tex]
As we know the above function is a quadratic equation (vertical parabola) open downward and the vertex is the maximum number of mosquitoes.
The vertex form of a quadratic function is:
[tex]y=a(x-h)^{2} +k[/tex] where (h,k) is the vertex
Our given function have the vertex form as well, so the
(h,k) = (5,25)
At the height of 5 cm the rainfall will produce the maximum number of mosquitoes
Final answer:
In the function modeling the number of mosquitoes by rainfall, 5 centimeters of rainfall will produce the maximum number of mosquitoes, corresponding to the vertex of the parabola.
Explanation:
To find the number of centimeters of rainfall that will produce the maximum number of mosquitoes in Minneapolis, Minnesota, we look at the vertex of the parabolic function m(x) = -(x - 5)2 + 25. The vertex form of a parabola is given by f(x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. In this equation, h represents the x-value that results in the maximum y-value for the parabola when a is negative, which corresponds to the maximum number of mosquitoes.
In this case, the vertex of the parabola is (5, 25), which tells us that 5 centimeters of rainfall will produce the maximum number, which is 25 million mosquitoes. This value is represented by h in the vertex form of the equation, indicating that the parabola opens downwards (since the coefficient of the (x - h)2 term is negative) and reaches its maximum at x = 5.
Write in if/Then form: A shape has 4 congruent sides, if it is a rhombus.
Answer: If a shape has 4 congruent sides, then it is a rhombus.
Step-by-step explanation: I just added the words in the appropriate places.
Alex needs to report his bowling average for the school newspaper. Here are his scores from the last 20 games: 132, 141, 110, 96, 154, 135, 111, 139, 102, 135, 133, 127, 99, 124, 129, 201, 131, 128, 134, and 135. Part A: What are the mean and median of this data? Part B: Which one of those two measures of central tendencies should he use for the newspaper and why? Part C: Are there any outliers? Please answer ASAP
Answer:
Part A:
Mean: 129.8
Median: 131.5
Step-by-step explanation:
The mean is the average so we add everything together and then divide it by however many numbers there are. 132 + 141 + 110 + 96 + 154 + 135 + 111 + 139 + 102 + 135 + 133 + 127 + 99 + 124 + 129 + 201 + 131 + 128 + 134 + 135 = 129.8
The median is the number in the middle. That is the number in between the rest from smallest to largest. 96, 99, 102, 110, 111, 124, 127, 128, 129, 131, 132, 133, 134, 135, 135, 135, 139, 141, 154, and 201
The medians are 131 and 132 so we add them together then divide by 2. That gives is 131.5 so that is our answer. I hope this helps and please mark me brainliest!
Help with mathematics
Answer:
ok
Step-by-step explanation:
Will give brainliest.
A candy company is designing the packaging for its new candy bar. the bars will be packed in cartons which are 1 foot long, 1 foot wide, and 1 foot high. how many of these cartons can they pack into the shipping crate which is 5 feet long, 12 feet wide, and 4 feet high?
Answer:
240 cartons
Step-by-step explanation:
First, I need to find the volume of the 2 objects.
If the measurements of the carton is 1 x 1 x 1, ultimately the volume of the carton is 1 cubic foot.
Then, to find the shipping crate volume, multiply 5 x 12 x 4. You will get 240 cubic feet.
Then, we need to find how many cartons can fit in the shipping crate. Divide 240 by 1, and obviously you get 240.
So, 240 cartons can be packed into the shipping crate.
can anyone help me with this question?
Answer:
I Believe its A
Step-by-step explanation:
IM so sorry if its wrong!!!!
but im pretty sure its right
You want to estimate the number of eighth-grade students in your school who find it relaxing to listen to music. You consider two samples. Which sample is unbiased?
fifteen randomly selected members of the band
every fifth student whose name appears on an alphabetical list of eighth-grade students
Question 2
Explain.
You want to estimate the number of twelfth-grade students in a high school who ride a bus to school. Which sample is unbiased?
A. 4 students in the hallway
B. all students on the soccer team
C. 50 twelfth-grade students at random
D. 100 students at random during lunch
explain
The graph represents this system of equations. A system of equations. y equals 4. y equals 3 minus StartFraction on-half EndFraction x. A coordinate grid with 2 lines. The first line passes through (negative 2, 4) and (0, 3). The second line passes through (negative 2, 4) and (0, 4). What is the solution to the system of equations? (–2, 4) (3, 4) (4, –2) (4, 3)
Answer:
b
Step-by-step explanation:
A coordinate grid with 2 lines. The first line passes through (negative 4, negative 3), (0, negative 3), and (4, negative 3). The second line passes through (0, negative 5) and (2, 4). The lines appear to intersect at about one-half, negative 3.
Solve the system of equations algebraically. Verify your answer using the graph.
y = 4x – 5
y = –3
What is the solution to the system of equations?
((StartFraction one-fourth EndFraction, negative 3), –3)
((StartFraction one-half EndFraction, negative 3), –3)
(–3, (negative 3, StartFraction 2 over 3 EndFraction))
The solution to the system of equations is (-2, 4).
The correct option is A.
We have,
y= 4
and, y= 3 - 1/2 x
To find the solution of Equation put y= 4 in equation 2 we get
4 = 3 - 1/2 x
4 - 3 = -1/2 x
1 = -1/2 x
x = -2
Thus, (-2, 4) is solution of Equation.
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At a carnival, you spin a spinner that has four equal-sized sections, each a different color: green, yellow, red, and blue. If you land on green, you win 2 points. If you land on yellow, red, or blue, you lose 1 point. Write the expected value equation. E (V) = StartFraction 1 Over a EndFraction (2) + StartFraction 1 Over b EndFraction (c) + StartFraction 1 OVer d EndFraction (e) + StartFraction 1 Over f EndFraction (g) a = b = c = d = e = f = g =
Answer:
a = 4
b = 4
c = -1
d = 4
e = -1
f = 4
g = -1
Step-by-step explanation:
To get the expected value equation you have to multiplicate the probability of each outcome by its reward and add them. The probability to get each color is 1/4 because the spinner has four equal-sized sections. If you win money, your reward is positive, but if you lost it, your reward is negative. Then:
expected value equation. E (V) = (1/4)*2 + (1/4)*(-1) + (1/4)*(-1) + (1/4)*(-1) = -0.25
Answer:
A 4
B 4
C -1
D 4
E -1
F 4
G -1
-0.25 points
lose 250 points
HELP!
What is the volume of the prism?
5.6 cm
4 cm
9 cm
7.8 cm
Answer:
Your answer
Step-by-step explanation:
Answer:140.4 is your answer!
Step-by-step explanation:hope this helped you!have an amazing rest of your night,afternoon or day!