Answers
Answer:
13
Step-by-step explanation:
The box plot ends at 13.
Box plots show the average score of the data. It shows the minimum, median and maximum. The line inside the box is the median. The minimum, in this case is 0 and the max is 13.
Related Questions
A hose fills a hot tub at a rate of 3.49 gallons per minute. How many hours will it take to fill a 343-gallon hot tub? Question content area bottom Part 1 It will take enter your response here hours to fill the hot tub.
Answers
Answer:
answer = 98.2808022923 i think
A family rents a truck to move from Buffalo to Chicago. The rental has a base cost of $49.95, plus, an additional cost of $1.19 per mile driven. The family also pays for gas, which costs $3.89 per gallon. The truck’s average gas mileage is 18 miles per gallon. The family decided to take a rest in Cleveland, what would be the distance travelled from Buffalo to Cleveland if the total cost of the move is $724.85?
Answers
By solving a linear equation, we will see that the distance is 479.98 miles.
How to find the distance?We know:
The rental has a base cost of $49.95 plus $1.19 per mile.
There is also an extra cost of $3.89 per gallon of gas, and with one gallon they can travel 18 miles, then there is another extra cost of:
$3.89/18 per mile.
Then, if you travel x miles, the total cost is given by the linear equation:
C(x) = $49.95 + ($1.19 + $3.89/18)*x
We want to find the value of x, number of miles, such that the total cost is $724.85, then we need to solve:
$724.85 = $49.95 + ($1.19 + $3.89/18)*x
Let's solve that for x:
$724.85 - $49.95 = ($1.19 + $3.89/18)*x
$674.90 = ($1.19 + $3.89/18)*x
$674.90/($1.19 + $3.89/18) = x
479.98 = x
So the distance is 479.98 miles.
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Moussa sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
81 visitors purchased no costume.
6 visitors purchased exactly one costume.
3 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase more than one costume as a decimal to the nearest hundredth.
Answers
The probability that the next person will purchase more than one costume will be 1/30.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
As per the given,
Total visitors of a day = 81 + 6 + 3 = 90
The number of purchasing more than one costume = 3
Probability of purchasing more than one costume = 3/90 = 1/30
Hence"The probability that the next person will purchase more than one costume will be 1/30".
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Find the 11th term in the following
arithmetic sequence :
20, 18, 16, 14, . . .
Hint: Write a formula to help you.
Answers
Answer is 0
Given:- arithmetic sequence 20,18,16,14,....
To find:- 11th term of given arithmetic sequence
Arithmetic Progression (AP) is sequence of numbers in order, in which the difference between any two consecutive numbers is constant value. It is also known as Arithmetic Sequence.
The 11th term of the A.P. can be found by a formula, a(n)=a(1)+(n-1)d , where n is the number of terms, a(1) is teh first term of A.P and d is difference between any two continuously terms.
Number of terms to be found = 11
therefore, a(11) = a(1)+(n-1)d
d=a(2)-a(1)
d=18-20
d=-2
putting value of d in above equation,
a(11) = 20 + (11-1)(-2)
a(11) = 20 - 20
a(11) = 0
hence the 11th term of arithmetic sequence 20,18,16,14,.... is 0.
-5y^2+17y-84 / y^3+12y^2+36y partial fraction decompostion
Answers
[tex]5y^2+17y-84 / y^3+12y^2+36y[/tex] partial fraction decomposition is [tex]= -5y/(y² + 12y + 36) + 17/(y² + 12y + 36) - 84 (y³+12y²+36y)[/tex]
What is partial fraction decomposition?Partially decomposing a rational fraction, also known as partially expanding it, in algebra includes expressing the fraction as the sum of a polynomial and one or more fractions with a lower common denominator.
One technique for breaking down rational expressions into smaller partial fractions is partial fraction decomposition. This method serves the integration process better.
In order to integrate a rational function, it is condensed to a valid rational function. The integrand can be expressed as the sum of more elementary rational functions through the use of partial fraction decomposition.
Therefore, starting with the simplified solution and proceeding backwards, the final expression is “decomposed” into the original polynomial fractions.
[tex]= -5y²+ 17y-84 / y³+12y²+36y[/tex]
[tex]= -5y/(y² + 12y + 36) + 17/(y² + 12y + 36) - 84 (y³+12y²+36y)[/tex]
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
Answers
Answer:
Step-by-step explanation:
1) She can use the CUADRATIC FUNCTION for to solve
2) She can use factorization for to solve
3) She can use the ZERO method for to solve
Triangle ABC and DEF are similar what is the measure of side DF?
Answers
Answer:
15
Step-by-step explanation:
25 / 15 = 1.666...
9 x 1.666.... = 15
Answer:
Step-by-step explanation:
375
if they are simiar than 15 from abc would have been the same length
given an integer x and an array of numbers, find if two numbers in the array sum up to x. (or, find the pair of numbers whose sum is closest to x.)
Answers
The program for finding the two numbers in the array sum up to x is made.
Explain the term sorting?Sorting involves putting data into a meaningful order so how you can more efficiently evaluate it. For instance, if you want to plot a graph of sales performance, you could wish to sort the sales data per calendar month.Array A[n], x
Sort by the use of Mergesort ------- O(nlogn)Initialize 2 index variables to estimate candidit.Initialize 1st to that leftmost index: l = 0Initializ 2nd to that rightmost index: r = n - 1While l < r -----------O(n)if A[l] + A[r] == x; return trueelse if A[l] + A[r] < sum; increment lelse decrement rreturn falseTime Complexity:
As was covered in class, step one employs mergesort, which has an O(nlogn) complexity.
Since the worst-case scenario involves traversing through the full array, step three consumes O(n) time.
Total Running Time = O(nlogn + n) = O(nlogn)
Thus, the program for finding the two intergers in the array sum up to x is made.
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HELP NOW 50 POINTS IMPORTANT!
Using the image of the blank check below, match each item with what would go in that space.
Column A
1.
Date:
Date
2.
Who the check is being written to:
Who the check is being written to
3.
Amount of check, written in numeric format:
Amount of check, written in numeric format
4.
Amount of check, written in word format:
Amount of check, written in word format
5.
A description of what the check is for:
A description of what the check is for
6.
The checking account owner's signature:
The checking account owner's signature
Column B
a.Item 1
b.Item 4
c.Item 3
d.Item 5
e.Item 6
f.Item 2
Answers
Who the check is being written to is 1
Amount of check, written in numeric format is 3
Amount of check, written in word format is 4
A description of what the check is for is 5
And the checking account owners signature is 6.
Answer:
HOPE IT HELPED
Step-by-step explanation:
Date is item 2
Who the check is being written to is item 1
Amount of check, written in numeric format is item 3
Amount of check written in word format is item 4
A description of what the check is for is item 5
The checking account owner's signature is item 6
can someone help me with this thank you
Answers
Answer:
a, b, d: No
c: Yes
Step-by-step explanation:
You want to identify statements that are and are not the negation of "I am not drawing a rectangle."
NegationThe negation of a statement is a statement using the same subject and predicate, but with the opposite truth value.
The negation of ...
I am not drawing a rectangleis the statement ...
I am drawing a rectangleStatements about circles are irrelevant, as are statements about any action other than drawing (or not drawing).
3- =11 pls im scared to put 14 i over think
Answers
Answer: i believe it is 14 too
Step-by-step explanation:
The teacher is planning a party for the students. She needs to pick 2 of 6 dinners to offer and 3 to 5 desserts. How many different combinations can she pick?
Answers
She can choose from the various combinations of 6 of 2, 5 to 3.Permutation is the name given to the various techniques of putting a group of objects in a sequential sequence.
A permutation and a combination can be distinguished by how they are ordered.Permutation is the name given to the various techniques of putting a group of objects in a sequential sequence. Combination is one of the various methods for selecting elements from a huge collection of objects without taking the order into account.Permutations and combinations are the several ways that items from a set can be chosen, usually without replacement, to generate subsets.The order matters, for instance, if you have a lock that requires four digits to unlock. You cannot type the same numbers in any other order (for example, 6 8 2 3) and expect the lock to open if the right values are 8 3 6 2! That's a permutation, so.Explanation:
2 of 6 = 6 of 2
3 to 5 = 5 to 3.
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In a survey of 2926 adults, 1476 say they have started paying bills online in the last year.
Construct a 99% confidence interval for the population proportion. Interpret the results.
Answers
The confidence interval for the given equation will be: 0.504.
What is confidence interval?
In frequency statistics, the confidence interval (CI) is the range of estimated values for an unknown parameter. Confidence intervals are computed at the specified confidence level. A 95% confidence level is the most common, but other levels such as 90% and 99% are sometimes used. The confidence level represents the proportion of corresponding CIs over time that contain the true value of the parameter. For example, 95% of all intervals computed at the 95% level must contain the true value of the parameter.
Factors that affect the width of the CI include sample size, sample variability, and confidence level. All else being equal, a larger sample results in a narrower confidence interval, a more varied sample results in a wider confidence interval, and a higher confidence level results in a wider confidence interval.
Therefore, The confidence interval for the given equation will be: 0.504.
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Use point-slope form to write the equation of a line that passes through the point
(-11, -8) with slope -2/-3
Answers
Use the point-slope formula. The equation of a line of slope m
m
through (x0, y0)
(
x
0
,
y
0
)
is
y−y0=m(x−x0).
y
−
y
0
=
m
(
x
−
x
0
)
.
Let
(x0, y0)=(1, 3) and m=−2.
(
x
0
,
y
0
)
=
(
1
,
3
)
and
m
=
−
2
.
Then the equation of the required line is
y−3=−2(x−1).
y
−
3
=
−
2
(
x
−
1
)
.
Use the distributive rule and this is
y−3=−2x+2.
y
−
3
=
−
2
x
+
2
.
To get it In the slope-intercept form of
y=mx+b,
y
=
m
x
+
b
,
where b
b
is the second coordinate, that is, the ordinate of the y
y
intercept (0, b),
(
0
,
b
)
,
get y
y
by itself and
y=−2x+2+3.
y
=
−
2
x
+
2
+
3
.
Combine like terms and
y=−2x+5
y
=
−
2
x
+
5
and 5
5
is the ordinate of the y
y
intercept (0, 5).
(
0
,
5
)
.
In the standard form of
ax+by+c=0
a
x
+
b
y
+
c
=
0
it is
2x+y−5=0.
2
x
+
y
−
5
=
0
.
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Related questions (More answers below)
A mammogram is used to screen women for breast cancer. False positives are tests that incorrectly show a positive result. 85% of positive mammograms are actually false positives. If 1,000 women receive mammograms, and 200 are told there is an abnormal finding, how many women are likely to actually have breast cancer?
Answers
Answer:
30
Step-by-step explanation:
200 x .15 (1-.85 = .15)
30
Solve the triangle, if possible.
C=61° 50, c=31.2, b=23.6
Answers
a=34.697, only one triangle is formed.
And B=40°.7'
A≈77°.79'.So, option A is correct.
What is meant by triangle?Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one.
Any three points determine a distinct triangle and a distinct plane in Euclidean geometry when they are non-collinear (i.e. a two-dimensional Euclidean space). To put it another way, each triangle is contained in a plane, and there is only one plane that includes that particular triangle. All triangles are contained in one plane if and only if all geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except as otherwise specified, the subject of this article is triangles in Euclidean geometry, more specifically, the Euclidean plane.
Given,
C=61° 50, c=31.2, b=23.6
Sine rule:
sin B/b=Sin C/c
sin B=b sin C/c
=(23.6 sin 61° 50)/31.2
sin B=0.65219
sin B=139.3
A+B+C=180
A=180-B-C
A=180-139.3-61.50
A= -20.8 which is not possible.
Because the angle must be positive.
sin B=sin 40.70
A+B+C=180
A=180-40.70-61.50
A=77.79'
sin A/a=sin C/c
a=c sin A/sin C
So, a=34.697
Only one triangle is formed
And B=40°.7'
A≈77°.79'
Hence, option A is correct.
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Write the expression as a number in scientific notation.
quantity 8 times 10 squared end quantity times quantity 3.2 times 10 to the fifth power end quantity all divided by the quantity 4 times 10 cubed
7.2 x 107
7.2 x 104
6.4 x 107
6.4 x 104
Answers
The value of the expression in the scientific notation will be 6.4 × 10⁴. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ [(8 × 10²) × (3.2 × 10⁵)] / (4 × 10³)
Simplify the expression, then we have
⇒ [(8 × 10²) × (3.2 × 10⁵)] / (4 × 10³)
⇒ [(25.6 × 10⁷)] / (4 × 10³)
⇒ 6.4 × 10⁷⁻³
⇒ 6.4 × 10⁴
The value of the expression in the scientific notation will be 6.4 × 10⁴. Then the correct option is D.
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Answer for free9+10 =
Answers
Answer: 19
Step-by-step explanation:
Answer:19
Step-by-step explanation: 10 add the 9
The two red trapezoids have the same area.
Can you find the area of one of the blue triangles?
Answers
To find a trapezoid, add both bases and divide it by two (6+4)/2 giving 5
Now multiply by height to get 25 square units per trapezoid
Multiply by two for two trapezoids
Of the 60 square units of area our trapezoids take 50 square units.
Now we know in together the two triangles are 10 square units.
Divide by two and now we know each triangle is
5 square units each
Find the area of the shaded region, the graph to the right, depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
The area of the shaded region is ——?
Round to four decimal places as needed
Answers
Answer:
68%
Step-by-step explanation:
93 is 7 pts BELOW 100 this represents -7 /15 = -.4666 Z-score
From Z-score table this represents .3192 ..or 31.92 % to the LEFT of the 93 ...... to the RIGHT is 100% - 31.92 % = ~ 68%
How much money does Dana Jones have after 7 years if she invests $ 1100 at 5% interest compounded continuously?
Dana Jones has $__-after 7 years.
(Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.)
Answers
Dana Jones has amount after 7 years is $1560.97.
What is compounded continuously?
Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.
Given: Dana Jones invests $ 1100 at 5% interest compounded continuously for 7 years.
We have to find the amount after 7 years.
Consider, the formula
A = Pe^rt
where,
A is the amount after t years
P is the invested amount
r is the interest rate
t is the number of years
Plug P = 1100, r = 5% = 0.05, and t = 7 in the above equation.
[tex]A = 1100e^0^.^0^5^(^7^)\\A = 1560.9743\\A = 1560.97[/tex]
Hence, Dana Jones has amount after 7 years is $1560.97.
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What is the relationship between multiplying polynomials and factoring? How are these two concepts related? How can they be used to check your work? Give an example and work it out to explain your reasoning. Be sure to explain how your example shows the relationship you describe.
Things you MUST include:
- A verbal/written explanation that describes the relationship between the two concepts. (3 points)
- An example that shows how multiplying polynomials
Explain how your example shows the relationship. (2 points)
Answers
By spreading (by multiplying) that 3 back in, we may obtain our original expression 12.
What do you mean by Factoring of polynomial?
The process of multiplying polynomial factors is known as factoring polynomials. A polynomial of degree "n" in variable x is an equation of the form axn + bxn-1 + kcxn-2 +....+kx+ l, where each variable has a constant acting as its coefficient. A polynomial is an expression that has a constant and a variable together with an addition or a subtraction sign between them.
Factors of polynomials are zeros of polynomials that may be expressed as another linear polynomial. If we divide a given polynomial by any of its components after factorization, the residual will be zero.
Contingents: 1, 2, 5, and 7.variables: x, y, and hTerms: 3x, 8y, and 2h (terms are often separated by a + or a -).(Note that words can also include variables and constants)
Formulas: 3x+1, 4x +5, 2h + 2wEquations: P = 2h + 2w, x = 4, y = x + 2One of the variables or constants that is multiplied by another factor to create a phrase is called a factor. Factors 4 and x make up the phrase 4x. To factor is to divide the object of the multiplication. Therefore, factoring "disassembles" the result of multiplication.
We frequently need to factor a term in order to "solve" (that is, get the value of, say, x) an equation
For Example:
The operation of factoring falls in between multiplication and dividing. Let's examine the following statement:
3x + 12
We can factor out the third because 3x and 9 both share the number three:
3x ÷ 3 = x 12 ÷ 3 = 4
We set it aside what's left after factoring out 3:
3(x + 4)
By spreading (by multiplying) that 3 back in, we may obtain our original expression: x * 3 = 3x 4 * 3 = 12.
We now have: 3x + 12
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Find the absolute maximum and absolute minimum values of f on the given interval. (Round all answers to two decimal places.)f(t) = 2 cos t + sin 2t[0,pi/2]____min____max
Answers
The absolute minima of the function is at 12.85 and the absolute maxima is at 15.42.
Let the function be ,
f(t) = 5t + 5 cot( t/2 ).
first derivative of the function,
f'(t)
= d/dt ( 5t + 5 cot(t/2))
= d/dt(5t) + d/dt ( 5 cot (t/2))
= 5 - 5/2cos^2(t/2)
Taking the derivative equal to 0,
f'(t) = 0
t = pi/2 , 3pi/2 f
On evaluating the equation wrt to obtained critical value,
we will get ,
absolute minimum value 12.85
absolute maximum value 18.56.
The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.
The terms "local maxima" and "local minima" refer to additional maxima and minima of a function that are not its absolute maxima and minima.
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A sweater is priced at $60 normally. It is on sale for $45. By what percentage was the
sweater's price decreased?
Answers
i need to know the answer to this question
Answers
The function type is Linear function.
What is Linear function?
The terms "linear function" in mathematics refer to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
From the given figure it is easily noticed that the function is increasing in nature for [tex]$x < 0$[/tex] and the function is constant in nature for [tex]$x > 0$[/tex] because the value of [tex]$\mathrm{y}$[/tex] remains unchanged for any value of [tex]$\mathrm{x}$[/tex], where [tex]$x \geq 0$[/tex].
The value of function is 3 at x=0.
The value of the function is always 3 for all [tex]$x \geq 0$[/tex]. So, f(x)=3 for [tex]x \geq 0$.[/tex]
The function is a straight line with intercepts (-3,0) and (0,3).
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A cell phone manufacturer guarantees that the mean battery life for its latest cell phone model is at least 36 hours. You are asked to design a hypothesis test to challenge this claim.a. State the null and alternative hypotheses and identify which represents the claim.b. Describe type I and type II errors for a hypothesis test of the claim.c. Explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed.d. Explain how you should interpret a decision that rejects the null hypothesis. e. Explain how you should interpret a decision that fails to reject the null hypothesis.
Answers
Null hypothesis: H₀: population mean, μ ≥ 36hours
Alternate hypothesis: H₁: population mean, μ < 36hours
Given that,
A maker of cell phones promises that the average battery life of its most recent cell phone model is at least 36 hours. To refute this assertion, you are required to create a hypothesis test.
We have to find
a. Describe the null and alternative hypotheses, then choose the one that best supports the claim.
b. Explain type I and type II mistakes for the claim's hypothesis test.
c. Describe if the hypothesis test has left-, right-, or two-tailed distributions.
d. Describe how to read a conclusion that rejects the null hypothesis. a. Describe how you should evaluate a choice that does not rule out the null hypothesis.
We know that,
a. Null hypothesis: H₀: population mean, μ ≥36hours
Alternate hypothesis: H₁: population mean, μ < 36hours
b. Type 1 error: is an error made when we reject the null hypothesis, when the null hypothesis is true. This happens the significance level % of time. In our example, a type 1 error would be made when the population mean is actually greater than 36 hours, but we conclude that the population mean is less than 36 hours.
Type 2 error: is an error made when we fail to reject the null hypothesis, when the null hypothesis is false. This is represented by beta. In our example, a type 2 error would be made when the population mean is actually less than 36 hours, but we conclude that the population mean is not less than 36 hours.
c. The test is left tailed since the area of rejection is on the left side (less than side).
d. We would interpret that at x% confidence level (generally 95%), we reject the claim that the population mean is greater than 36 hours. We would conclude that we have enough evidence from the sample that the population mean is significantly less than 36, and hasn't happened as a matter of chance.
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A 0.60-kg basketball is dropped out of a window that is 6.1mabove the ground. The ball is caught by a person whose handsare 1.5m above the gound.1. How much work is done on e the ball by its weight?What is the gravitational potential energy of the basketball,relative to the ground, when it is ... 2. released and 3. caught?4. How is the change (PEf- PE0) in the ball'sgravitational potential energy related to the workdone by its weight?
Answers
The work that gravity does;
W = F.S = mgΔh
In light of the fact that gravity points downward and that displacement is also downward, their angle is 0 and their cosine 1, respectively.
W = mgΔh
g = 9.8 m/s²
Δh = 4.6 m
m = 0.60 kg
W = 0.60 x 9.80 x 4.6
W = 2.7 J
The source of gravitational potential energy in relation to the ground is;
U = mgh
The release point therefore
Ug = mgh(0)
U0 = 0.60 x 9.8 x 6.1
U0 = 35.87 J
At the point of release
U(gf) = mgh(f)
U(gf) = 0.60 x 9.80 x 1.5
U(gf) = 8.820 J
Gravitational potential energy changes are;
ΔU(g) = U(gf) - U0
ΔU(g) = 8.820 J - 35.87 J
ΔU(g) = -27.05 J
Result, we can see that the work done through gravity is the opposite of how the gravitational potential energy has changed.
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Given: Line m is parallel to line n
prove : <1 is supplementary to < 3 HELP PLEASE
Answers
Supplementary angles are two angles whose combined angle is 180 degrees. As shown below, the table of the proof that (1) is an addition to (3) can be completed.
What are Supplementary angles?Supplementary angles are two angles whose combined angle is 180 degrees. When a straight line crosses another line, two angles are created on either side of the initially imagined straight line. Two sets of additional angles make up those two-two angles. This implies that a straight line will be formed by the outside sides of any extra angles that are positioned next to one another.
For the demonstration that 1 is an addition to 3, the preceding table can be completed as shown below.
1) Line m in is parallel to line n;
2) ∠1 = ∠2 → Corresponding angles
3) m∠1 = m∠2 → Definition of Congruent angles
4) ∠2 and ∠3 for a linear pair → Adjacent angles on a straight line
5) ∠2 is supplementary to ∠3 → Definition of linear pair
6) m∠2 + m∠3 = 180° → Definition of supplementary angles
7) m∠1 + m∠3 = 180° → Substitution Property
8) ∠1 is supplementary to ∠3
As a result, the table containing the proof that item 1 is an addition to item 3 can be completed as displayed above.
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What is the value of y in the solution to the system of equations?
1/3*+1/4y=1
2x - 3y = -30
-8
-3
8
Answers
Answer:
(-3,6)
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{4}[/tex] y = 1 Divide all the way through by 12 to clear the fraction
4x + 3y = 12 Add this to the second equation
2x -3y = -30
6x = -18 Divide both sides by 6
x = -3
Substitute -3 into either of the original equations to solve for y
4x + 3y = 12
4(-3) + 4y = 12
-12 + 4y = 12 Add 12 to both sides
4y = 24 Divide both sides by 4
y = 6
If the hours of daylight in Miami can be
approximated using a sinusoidal wave, what is the
amplitude of the function if the shortest day in
Miami is 10 hours and 52 minutes long and the
longest day in Miami is 13 hours and 45 minutes
long?
Answers
Answer:
the sinusoidal function that approximates the hours of daylight in Miami has an amplitude of approximately 1.44 hours.
Step-by-step explanation:
The amplitude of a sinusoidal function is half the difference between the maximum and minimum values of the function. In this case, the shortest day in Miami is 10 hours and 52 minutes long, and the longest day is 13 hours and 45 minutes long, so the difference between the maximum and minimum values is 2 hours and 53 minutes, which is equal to 173 minutes. Half of this is 86.5 minutes, which is the amplitude of the function.
To express this in hours, divide the amplitude in minutes by 60. This gives an amplitude of 86.5 / 60 = 1.44 hours.
So, the sinusoidal function that approximates the hours of daylight in Miami has an amplitude of approximately 1.44 hours.