The data in the table represents the average number of daylight hours each month in Springfield in 2015, rounded to the nearest quarter.

Jan 9.5
Feb 10.5
March 12
April 13.25
May 14.5
June 15
July 14.75
Aug 13.75
Sept 12.5
Oct 11
Nov 9.75
Dec 9.25

Write the equation that best models the data.

What is the expected number of daylight hours in March 2020? Explain.

Answers

Answer 1

For a better understanding of the solution provided here please go through the graph in the attachment. Please note that the solution provided here will be an approximate solution.

In the graph, the x axis is the number of months. 1 is January, 2 is February, so on and so forth.

The y axis is the expected number of daylight hours in those months. Each point has been depicted in the graph as shown.

Now, when we look at the graph we notice a pattern. The graph is nearly a cosine graph. Thus the equation that will best model the data will be an equation of the cosine form and will look like:

[tex] y=A cos(\omega t)+B [/tex]

where symbols have their usual meanings.

Let us find each term now:

We know that in December, the expected number of daylight hours is 9.25 hours. Thus, let us assume that the expected number of daylight hours in previous December was 9.25 hours too.

With this assumption let us proceed.

Amplitude=[tex] \frac{Highest - Lowest}{2} =\frac{15-9.25}{2} =2.875 [/tex]

The Vertical Shift Up is B=[tex] \frac{9.25+15}{2} = 12.125[/tex]

Also, the frequency can be calculated as: [tex] \omega=\frac{2\pi}{Period}= \frac{2\pi}{12}=\frac{\pi}{6} [/tex]

Thus, plugging in all the values, the final equation will be:

[tex] y=-2.875cos(\frac{\pi}{6}t)+12.125 [/tex]....(Equation 1)

The negative value of A suggests that the function starts below the horizontal y=12.125 line.

The above is the (Equation 1) that best models the given data.

Now, to find the expected number of daylight hours in March 2020, we just have to find the value of the time, t from January 2015 to March 2020.

Now, we know that each year has 12 months. So, 5 years from start of 2015 to end of 2019 will have 12 x 5=60 months. We need to add to this the first three months of the year 2020 to take us till March 2020. Thus, the value of t from January 2015 to March 2020 is 63.

Now, let us use the (Equation 1) to find the value of expected number of daylight in March 2020 by plugging in t=63 in it.

Thus,

Expected number of daylight in March 2020 is:

[tex] y=-2.875cos(\frac{\pi}{6}\times 63)+12.125 [/tex]

[tex] \therefore y=12.125 [/tex] hours.

The Data In The Table Represents The Average Number Of Daylight Hours Each Month In Springfield In 2015,

Related Questions

Someone Please Help!!!
Find the radian measure of an angle of -280 degrees

Answers

Answer: -4.88691778Solution:1.Write down the number of degrees you want to convert to radians Given Degree = -280° The formula to convert degrees to radian measure is:Radian = degree x π/180 2. Multiply the number of degrees by π/180. Think of it like multiplying two fractions: the first fraction has the number of degrees in the numerator and "1" in the denominator, and the second fraction has π in the numerator and 180 in the denominator. -280 x π/180 = -280π/1803. Find the largest number that can evenly divide into the numerator and denominator of each fraction and use it to simplify each fraction. The largest number for 280 is 20.-280 x π/180 = -280π/180 ÷ 20/20 = -14π /9 4. Then multiply the numerator by 3.14159 because pi or π is equivalent to 3.14159, -14x 3.14159= -43.982265. To get the radian measure, we will divide -43.98226 by 9. -43.98226/9= -4.88691778

Answer:-14pi/9

Step-by-step explanation:

The graph shows the cost for renting a post hole digger from a local hardware store. Determine the rate of change or cost per day.
A) $60 per day
B) $30 per day
C) $90 per day
D) $15 per day

Answers

It increases by $30 per day.

The given graph shows the cost for renting a post hole digger from a local hardware store. We have to determine the rate of change or cost per day.

Let us consider any two points.

Let us consider (1,30) and (2,60)

We have to determine the rate of change which is basically termed as "slope".

Rate of change is expressed as a ratio between a change in one variable relative to a corresponding change in another variable.

Therefore, rate of change or cost per day =

Change in y [tex] \div [/tex] Change in x

= [tex] \frac{60-30}{2-1} [/tex]

= 30

Therefore, the rate of change or cost per day is $30 per day.

If PQRS is a parallelogram, what is the value of Y

Answers

To find the value of y all you have to do is set side RQ and SP equal to each other because opposite sides of a parallelogram are congruent.

RQ = SP
1/4 y = 13

Now you will multiply the reciprocal of 1/4 on both sides.

4(1/4 y) = (13)4
y = 52.

So the answer is option C.

The value of y is equal to 52. The correct option is C.

What is a parallelogram?

A parallelogram is a quadrilateral having four sides and the two opposite sides are equal and parallel to each other.

To find the value of y all you have to do is set side RQ and SP equal to each other because opposite sides of a parallelogram are congruent.

RQ = SP

1/4 y = 13

Now you will multiply the reciprocal of 1/4 on both sides.

4(1/4 y) = (13)4

y = 52.

Hence, the answer is option C.

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Which of the following pairs of organisms compete with each other for food?

A. squirrels and owls

B. mice and owls

C. rabbits and green plants

D. mice and rabbits

Answers

The answer would be D. Mice and Rabbits. Hope it helps! :)

its gotta be D. mice and rabbits, hope this helps. :))

What is the second term when 3+2x^2-3x^4+x3

Answers

x^3

I can explain if you want.

PLEASE HELP ME OUT PLEASE!!
EXPLAIN IT PLEASE SO I CAN UNDERSTAND IT BETTER
THX

Answers

The answer is -47-10w=-9w-40-3w bc the equation above equals 7/2 and this equation does too first combine like terms -47-10w=(-9w+3w)+40 which gives you -10w-47=-12w-40 then Add 12w to both sides which gives you 2w-47=-40 and then Add 47 to both sides and gives you 2w=7 and then divide 2 in both sides and gives you 7/2

PLEASE HELP MATH WILL MARK BRAINLY ASAP PICTURE ATTACHED

Answers

The sum of all angles of a pentagon is 540°, because you can draw interior lines to divide it into 3 triangles which each have angles that sum to 180, and 3 times 180 is 540.

So for x we have 540 - 83 - 89 - 119 - 90 = 159° left

A coin is tossed and a number cube is rolled. What is the probability that the coin shows heads and the number cube shows 5? A. start fraction 1 over 6 end fraction B. start fraction 1 over 12 end fraction C. start fraction 2 over 3 end fraction D. one-fourth

Answers

Answer:

i got 1/4

Step-by-step explanation:

me sorry in wrong

Khan academy how to solve equations with fractions and mixed numbers

Answers

Generally, you are told to approach these by "clearing fractions". That is, you generally multiply the equations by the least common denominator so all fractions and mixed numbers become integers.

Alternatively, you can simply do the arithmetic using the numbers given. You learned a long time ago how to add, subtract, multiply, and divide mixed numbers and fractions. Do these operations as necessary to solve the equations.

Carlos has $690,000 he wants to save. If the FDIC insurance limit per depositor, per banks will guarantee that all of his money is insured?

Answers

question incomplete. If the limit is 250k. The Answer is 230k bank A, 240K bank b and 220k bank c.

Answer:

D. $230,000 in bank A, $240,000 in bank B, $220,000 in bank C

Step-by-step explanation:

Carlos has $690,000 he wants to save. If the FDIC insurance limit per depositor, per banks will guarantee that all of his money is insured?

A. $200,000 in bank A, $200,000 in bank B, $290,000 in bank C

B. $200,000 in bank A, $220,000 in bank B, $270,000 in bank C

C. $230,000 in bank A, $260,000 in bank B, $200,000 in bank C

D. $230,000 in bank A, $240,000 in bank B, $220,000 in bank C

By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?
AND NO, it is not 33, 33.3, 66, or 66.6 percent.

Answers

Let N be the numerator, D be the denominator
[tex] \frac{N}{D} [/tex]

if its numerator is decreased by 50%
[tex] N - \frac{50}{100}N [/tex] ==> (this will be the numerator part)

if its denominator is decreased by 25%
[tex] D - \frac{25}{100}D [/tex] ==> (this will be the denominator part)

I try to separate them out, so it's easier to see the problem.

[tex] N - \frac{50}{100}N = \frac{100N}{100} - \frac{50N}{100} = \frac{50N}{100} [/tex]

[tex] D - \frac{25}{100}D = \frac{100D}{100} - \frac{25D}{100} = \frac{75D}{100}[/tex]

[tex] \frac{\frac{50N}{100}}{\frac{75D}{100}} = \frac{50N}{100} * \frac{100}{75D}[/tex]

[tex] \frac{50N}{75D} = \frac{2}{3}(\frac{N}{D})[/tex] by this, you can understand that
[tex] \frac{2}{3}(\frac{N}{D})[/tex] as 66.6% of N/D because 2/3 is 0.666666.... The answer should be 66.7% if you round them up.

4x^3+2x^2+3x+4 divided by x+4

Answers

By synthetic division
= 4x^2 -14x +59 -232/(x+4)

The remainder is f(-4) = -232.

Divide: 4x^3+2x^2+3x+4/x+4

Simplify: 4x^4+2x^3+3x^2+4x+4/x

The points (15, 10), (25, 20), (30, 22), (40, 32), (55, 53), (60, 55) represent the time, x, it takes 6 people to travel y miles. The scatterplot below represents the situation.

(Graph Below)

A. 32 miles
B. 42 miles
C. 48 miles
D. 54 miles

Answers

Answer:IT IS B

Step-by-step explanation:

I GOT A 100 ON MY TEST YOUR WELCOME :D

PLEASE HELP ASAP!!!!!!!!!

Answers

[tex]\begin{cases}y=-3x+8\\y=-5x-2\end{cases}\\\\\\-5x-2=-3x+8\\\\-5x+3x=8+2\\\\-2x=10\qquad|:(-2)\\\\\boxed{x=-5}\\\\\\y=-3x+8\\\\y=-3\cdot(-5)+8\\\\y=15+8\\\\\boxed{y=23}\\\\\\ \begin{cases}x=-5\\y=23\end{cases}[/tex]

Answer C)

Can someone help me?

Answers

check the picture below.

make sure your calculator is in Degree mode.

I need to write these description into the new function but I keep getting the wrong thing -.-

1.The function f(x)=(1/2)^x is translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5

2.The function f(x)=ln x is translated 3 units left, horizontally compressed by a factor of 1/4 and translated 0.5 units down.

3. The function f(x)=e^x is horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right.

Answers

Since you're studying this stuff, you know that
.. translation right by k units: f(x) ⇒ f(x-k)
.. translation up by k units: f(x) ⇒ f(x) +k
.. horizontal stretch by a factor of k: f(x) ⇒ f(x/k) . . . . same as compressed by 1/k
.. vertical stretch by a factor of k: f(x) ⇒ k*f(x)
.. reflection across the x-axis: f(x) ⇒ -f(x)
.. reflection across the y-axis: f(x) ⇒ f(-x)
The sequence in which these are done is important.

1. f(x) = (1/2)^x
.. translated 4 units right: f(x) = (1/2)^(x -4)
.. reflected across the x-axis: f(x) = -(1/2)^(x -4)
.. vertically stretched by a factor of 1.5: f(x = -1.5(1/2)^(x -4)

2. f(x) = ln(x)
.. translated 3 units left: f(x) = ln(x +3)
.. horizontally compressed by a factor of 1/4: f(x) = ln(x/4 +3)
.. translated down 0.5 units: f(x) = -0.5 +ln(x/4 +3)

3. f(x) = e^x
.. horizontally stretched by a factor of 3: f(x) = e^(x/3)
.. reflected across the y-axis: f(x) = e^(-x/3)
.. translated 1 unit right: f(x) = e^(-(x -1)/3)

Final answer:

The transformed equations for each of your base functions according to given changes are f(x) = -1.5*(1/2)ˣ⁻⁴, f(x) = ln(4×(x+3))-0.5, and f(x)=e⁻³×(x-1) respectively.

Explanation:

1. The transformed function for your first one, namely f(x)= (1/2)ˣ, after being translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5 would be f(x) = -1.5×(1/2)⁽ˣ⁻⁴⁾.

2. Your second function, f(x) = ln(x), after being translated 3 units left, horizontally compressed by a factor of 1/4, and translated 0.5 units down becomes:
f(x) = ln(4×(x+3))-0.5.

3. Your final function, f(x)=e^x, when it's horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right, would transform into: f(x)=e⁻³×(x-1).

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The. system shown is ____.
consistent
equivalent
inconsistent

Answers

Answer:

inconsistant mi boii

Step-by-step explanation:

The given system of equations is inconsistent.

What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.

Given is the graph of three lines as shown.

A system of equations is called an inconsistent system of equations if there is no solution. Since, the given lines do not intersect at one common point, hence the given system of equations is inconsistent.

Therefore, the given system of equations is inconsistent.

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Point D is on segment BC. Segment BC measures 8x units in length.What is the length of segment BC?units

Answers

144 this is the answer im taking the test now

What is the median of the data set?

42 55 27 31 17 24 65 47 39 18

A. 21

B. 35

C. 17

D. 24

Answers

first we need to arrange the numbers in this number set from smallest to biggest:17,18,24,27,31,39,42,47,55,65. Then there are 10 numbers in this number set. So when we calculate the median, we need to find the middle two numbers and calculate their average. So the median is (31+39)/2=35. SO the answer is B

B᷉᷈. 35

Y᷉᷈o᷉᷈u᷉᷈ p᷉᷈l᷉᷈a᷉᷈c᷉᷈e᷉᷈ t᷉᷈h᷉᷈e᷉᷈m᷉᷈ i᷉᷈n᷉᷈ n᷉᷈u᷉᷈m᷉᷈e᷉᷈r᷉᷈i᷉᷈c᷉᷈a᷉᷈l᷉᷈ o᷉᷈r᷉᷈d᷉᷈e᷉᷈r᷉᷈
T᷉᷈h᷉᷈e᷉᷈n᷉᷈ f᷉᷈i᷉᷈n᷉᷈d᷉᷈ t᷉᷈h᷉᷈e᷉᷈ m᷉᷈i᷉᷈d᷉᷈d᷉᷈l᷉᷈e᷉᷈ n᷉᷈u᷉᷈m᷉᷈b᷉᷈e᷉᷈r᷉᷈

Which step will get you closest to the solution of this equation? 5⋅(x−2)=7

Answers

Distribute the 5 with all everything In the parenthesis and It should be: 5x-10=7. i will hope this help

Please help and show work. 15 points.

Answers

the answer is D
the x satys the same, the Y reverses positive/negative

(Please help, urgent).

What is the value of r?

Round your final answer to the nearest whole number.

Answers

◆ APPLICATIONS OF TRIGONOMETRY ◆

[tex] Heya \: ! \: \\ \\ We \: know \: that \\ \\ \: \sin( \alpha ) = \frac{perpendicular}{hypotenuse} \\ \\ \sin(67.4) = \frac{12}{r} \\ \\ \\ also \: , \\ \\ \sin(67.4) = 0.9231 \\ \\ comparing \: both \: ,\\ \\ \frac{12}{r} = 0.9231 \\ \\ r = \frac{12}{0.9231} \\ \\ r = 13 \: \: \: \: \: ans.[/tex]

helppppppppppppppppppppppppppppppppppppp

Answers

Answer:
a < -2

Explanation:
To solve the inequality, we will need to isolate the a on one side of the inequality as follows:
3 - 2a > 7

1- subtract 3 from both sides:
3 - 2a - 3 > 7 - 3
-2a > 4

2- divide both sides by -2. Remember that when dividing by a negative number, we flip the inequality sign.
-2a / -2 > 4 / -2
a < -2

Hope this helps :)

jesse uses 19 beads to decorate each picture frame. In all, Jesse used 133 beads. How many picture frames did Jesse make?

Answers

use division: 133/19 = 7 picutre frames

Answer:

use division: 133/19 = 7 picutre frames

Step-by-step explanation:

I Will Mark it the brainiest

A bouncy ball is dropped such that the height of its first bounce is 3.5 feet and each successive bounce is 75% of the previous bounce's height. What would be the height of the 9th bounce of the ball? Round to the nearest tenth (if necessary).

Answers

For this case, what we should do is write an equation of the potential type:
y = A * (b) ^ x
Where,
A: initial height
b: decrease rate of initial height
x: number of bounces.
We have then:
y = 3.5 * (0.75) ^ x
For the ninth bounce:
y = 3.5 * (0.75) ^ x
y = 0.26
Answer:
The height of the 9th bounce of the ball is:
y = 0.26 feet.

Factor completely.

y^2+6y+8

Answers

This is a quadratic expression, meaning it can be factored into two binomials each with the variable to the power of one. Knowing this, we can already deduce that the factorization would look something like this:

(y + ____)(y + ______)

The blanks equal the factors of the last term. The last term may have multiple pairs of factors, but you need to look at the middle term to find the correct pair. The sum of the pair of factors should equal the middle term. For instance, in this example 8 + 1 does not equal 6, even though it is a factor pair of 8. It is easier to grasp the answer if you name all the factor pairs and work from them. With practice, factor pairs will come easier. In this case, the factor pair is 4 and 2.

4x2 = 8 and 4 + 2 = 8.

Therefore, (y + 2)(y + 4) = y^2 + 6y + 8

Final answer:

To factor the expression [tex]y^2+6y+8[/tex] completely, we use the method of factoring binomials. The expression can be factored as (y + 2)(y + 4).

Explanation:

To factor the expression y2 + 6y + 8 completely, we need to find two binomials that multiply together to give us the original expression. Since the coefficient of the y2 term is 1, we know that the binomials will take the form (y + a)(y + b). To find the values of a and b, we need to find two numbers that add up to 6 (the coefficient of the y term) and multiply to give 8 (the constant term).

The numbers that satisfy these conditions are 2 and 4, because 2 + 4 = 6 and 2 × 4 = 8. So, we can factor the expression as (y + 2)(y + 4).

True or false the fraction 9/21 is in lowest terms

Answers

This is false.

9/12 in it's lowest terms is 3/7.

very simple false becuse the lowest form is 3\7

3\7 in decimal is 0.42857142 or 0.43

3\7 in percent 42.857143% or 43 %

use math way . c o m

please help I will mark brainlist if correct

Answers

The admission fee at a fair is $2.00 for children and $4.00 for adults.

On Saturday 2,500 people entered the fair and $7,000.00 were collected.

How many children and how many adults attended? Give your answer, using x for children, y for adults.

Form of: x =, and y =

Let K = no. of children

Let A = no. of adults

2500 people mean

Kids + Adults

K + A = 2500

K = 2500 – A

2K + 4A = 7000

K + 2A = 3500

(2500 – A) + 2A = 3500

A = 3500 – 2500

(A = 1000, adults)

K = 2500 – A

K = 2500 -1000

(K = 1500, Kids)

CHECK:

1500*2 = $3000

1000*4 = $4000

(Total = $7000, people.).

Hope this helps:

Factor completely 2x3 + x2 - 18x - 9

A. (x2-9)(2x+1)
B. (x-3)(x+3)(2x-1)
C. (x-3)(x+3)(2x+1)
D. (2x-3)(2x+3)(x-1)

Answers

Factor the following:
2 x^3 + x^2 - 18 x - 9

Factor terms by grouping. 2 x^3 + x^2 - 18 x - 9 = (2 x^3 + x^2) + (-18 x - 9) = x^2 (2 x + 1) - 9 (2 x + 1):
x^2 (2 x + 1) - 9 (2 x + 1)

Factor 2 x + 1 from x^2 (2 x + 1) - 9 (2 x + 1):
(2 x + 1) (x^2 - 9)

x^2 - 9 = x^2 - 3^2:
(2 x + 1) (x^2 - 3^2)

Factor the difference of two squares. x^2 - 3^2 = (x - 3) (x + 3):

Answer: (x - 3) (x + 3) (2 x + 1) thus the Answer is C.

Final answer:

The factorization of the given polynomial 2x3 + x2 - 18x - 9 is (x-3)(x+3)(2x+1) and we achieve this by factoring common terms and applying the formula for difference of squares.

Explanation:

To factor the polynomial 2x3 + x2 - 18x - 9, you would first tie together similar terms (if any), then check for any common factors in all the terms. In this case, we can factor this expression in two steps:

First step: Looking for common factors, we can rewrite the expression as x2(2x) - 9(2x) + x2 - 9.Second step: Then, factor using the formula for the difference of squares and you will find that the fully factored expression is (x-3)(x+3)(2x+1).

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Jesse wants to write a function to represent the graph. He says that the period of the graph is triple that of sin x and that the equation of the graph is f(x)=3sin x. Why is he incorrect?
a. The period of the graph is twice that of sin x.
b. The frequency of the graph is triple that of sin x.
c. The equation of the graph should be f(x)=sin x/3.
d. The equation of the graph should be f(x)=3sin x.

Answers

Answer C

the value of sin(pi/2) =1

the value of sin(pi) = 0

according to the graph sin(3pi/2) = 1 and sin(3pi) =0

so the correct equation for the graph must be f(x) = sin(x/3)

Jesse is incorrect, because the equation of the graph should be [tex]f(x) = \sin(\frac{x}{3})[/tex]

From the question, we understand that the period is 3 times sin x.

The above claim is wrong.

Given that, the period (B) is 3.

i.e B = 3

The function is represented as:

[tex]f(x) = \sin(\frac{2\pi}{B})[/tex]

So, we have:

[tex]f(x) = \sin(\frac{2\pi}{3})[/tex]

Represent [tex]2\pi[/tex] with x

[tex]f(x) = \sin(\frac{x}{3})[/tex]

Hence, the equation of the graph should be [tex]f(x) = \sin(\frac{x}{3})[/tex]