Answers
The equation 2 and 3 would not present linear functions.
What is linear function?
A linear function is one in which the maximum power of the variables is one.
A linear function is a function that has the form f(x) = mx + b, where m and b are constants. In other words, a linear function is a straight line when plotted on a graph.
Out of the given relationships, the following do not represent a linear function:
2) The ant population for a colony that begins with 5 ants and doubles in number every two weeks.
This relationship is not linear because the rate of change (the number of ants per unit time) is not constant. The number of ants increases exponentially, which results in a curve rather than a straight line when plotted on a graph.
3) A history student's grade on a test that begins at 100 but decreases by 4 points for each question answered incorrectly.
This relationship is not linear because the rate of change (the decrease in points per incorrect question) is not constant. The decrease in points results in a curve rather than a straight line when plotted on a graph.
The other two relationships do represent linear functions.
Therefore, The equation 2 and 3 would not present linear functions.
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Related Questions
32 Ounces of Juice for $7.04. How much per ounce
Answers
Answer:
$0.22.
Step-by-step explanation:
To find the cost per ounce of juice, divide the total cost of 32 ounces of juice by the number of ounces:
7.04 ÷ 32 ounces = 0.22 per ounce
So, the cost per ounce of juice is approximately $0.22.
Answer:
0.22
Step-by-step explanation:
Two factory plants are making TV panels. Yesterday, Plant A produced 4000 fewer panels than Plant B did. Four percent of the panels from Plant A and 2% of
the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 500 defective panels?
14
Answers
The number of panels that Plant B produced is; 11000 panels
How to solve algebra word problems?We are told that Plant A produced 4000 fewer panels than Plant B did.
Thus;
A = B - 4000 -----(1)
Four percent of the panels from Plant A and 2% of the panels from Plant B were defective. Thus;
0.04A + 0.02B = 500 ------(2)
Put eq 1 in eq 2 to get;
0.04(B - 4000) + 0.02B = 500
0.04B - 160 + 0.02B = 500
0.06B = 660
B = 660/0.06
B = 11000 panels
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Pls help can u please answer 4 and 5
Answers
4A. The number of whole pie shaded are 2
4B . The number of partial pie shaded is 3
4C. The mixed number formed is 2 3/5
5A. The whole number part which is 2 is the quotient
5B. The remainder is 3
What are fractions in math?
In mathematics, a fraction is a number that represents a part of a whole. It consists of two parts: a numerator, which is the part of the fraction that represents the number of parts being considered, and a denominator, which is the number that represents the total number of parts in the whole.
A mixed number is a combination of a whole number and a fraction. It represents a quantity that is greater than the fraction but less than the next whole number.
For example, In the division problem, the dividend is 13 and and the divisor is 5. the division results to mixed number of value 2 3/5.
The mixed number 2 3/5 represents a quantity that is equal to
two whole and three fifths.
converting to improper fractions gives 13/5
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53. The cutting tool on a lathe moves 3/128 in. along the piece being turned for each revolution of work. The piece revolves at 45 revolutions per minute. How long will it take to turn a length of 9 9/64-in. Find in one operation?
Answers
Using the concept of rates, the machine will complete 9 9/64 inches in 8.67 minutes
How long will it take to turn a particular length
To determine how long it will take to turn a particular length of iron, we can calculate the rate at which it works and it must be in a definite proportion.
If the lathe moves 3/128 in one revolution.
And the machine completes 45 revolutions in 1 minutes, we can determine how many inches in moves in that minute.
3/128 in = 1 rev
x in = 45
45 * (3/128) = 45 revolutions = 1 minute
1.054 inches in 1 minute.
We can further use this to determine the time it takes to move 9 9/64 inches
1.054 inches = 1 minute
9 9/64 inches = x minute
cross multiply both sides and solve
x = 8.67 minutes
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3. Find the height of the tree below to the nearest foot.
Answers
The height of the tree to the nearest foot is 27 feet.
How to find the height of a tree?The height of the tree can be found as follows:
The height of the tree can be found using trigonometric ratios. Therefore,
let
tan ∅ = opposite / adjacent
Therefore,
opposite side = adjacent tan ∅
Hence,
height of the tree = 20 + x tan 45° = x tan 75°
20 + x tan 45° = x tan 75°
20 tan 45 + x tan 45° = x tan 75°
20 tan 45 = x tan 75° - x tan 45°
20 tan 45 = x(tan 75 - tan 45)
20 tan 45 = x(3.73205080757 - 1)
2.73205x = 20
x = 20 / 2.73
x = 7.32600732601
x = 7.34
Therefore,
height of the tree = x tan 75°
height of the tree = 7.34 × tan 75°
height of the tree = 27.3186119114
height of the tree = 27 ft
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A group consisting of 32 aggressive zombies quadruples in size every hour. Which equation matches the number of zombies after 6 hours?
Answers
Answer:
131,072 Zombies:
the equation: 32 x 4^6 = 131,072
the equation in scientific notation form: 3.2 x 4^7 = 131,072
Step-by-step explanation:
The amount of zombies starts at 32. It quadruples per hour, so we need to multiply the amount by 4 six times(once for every hour).
We can use an exponent to represent this in an equation:
32 x 4^6 = 131,072
Or, if we put it in scientific notation,
3.2 X 4^7 = 131,072.
The equation which represents the number of zombies is;
= [tex]1.31072[/tex]×[tex]10^{5}[/tex]
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
Given that
The amount of zombies = 32.
And It quadruples per hour,
Therefore,
Multiply the amount by 4 six times (as it occurs once for every hour).
The the exponent form to represent this equation:
32 x 4^6 = 131,072
Hence, in scientific notation the equation is,
= [tex]1.31072[/tex]×[tex]10^{5}[/tex]
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−4x+7=2y−3 how do i solve for x
Answers
get rid of y. that's all you have to do.
To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes
had the extra donut, and the shop owner claimed that one in seven boxes had an extra donut. Nine customers each bought one box
of donuts at the shop. Let X = the number of customers that bought a box containing an extra donut. What are the mean and
standard deviation of X? Provide an interpretation for each value in context.
Opx = 1.143 and ox= 0.990; If the shop were to sell many boxes of donuts, the average number of boxes with an extra
donut is 1.143 out of 9, and they will typically sell between 0.153 and 2.133 boxes out of 9 with extra donuts.
O μx = 1.286 and ox= 1.050; If the shop were to sell many boxes of donuts, the average number of boxes with an extra
donut is 1.286 out of 9, and they will typically sell between 0.236 and 2.336 boxes out of 9 with extra donuts.
Opx 1.286 and ox= 1.050; If the shop were to sell many boxes of donuts, the average number of extra donuts is 1.286
out of 9, and they will typically sell between 0.236 and 2.336 extra donuts.
Opx 1.143 and ox=0.990; If the shop were to sell many boxes of donuts, the average number of extra donuts is 1.143
out of 9, and they will typically sell between 0.153 and 2.133 extra donuts.
Answers
The answer is given below:
What is binomial distribution?Binomial distribution is a discrete probability distribution in which it gives two values that is either success or failure.
A local donut shop began putting an extra donut in some of the boxes.
The shop owner claimed that one in seven boxes had an extra donut.
Nine customers each bought one box of donuts at the shop.
Probability of success fixed is, [tex]p=\frac{1}{7}[/tex]
A value of n fixed, n=9.
We can use binomial distribution to solve this problem,
The probability mass function for the Binomial distribution is given as:
Assume X is a binomial distribution, [tex]B(n=9,p=\frac{1}{7}=1.143)[/tex].
[tex]P(X)=(nCx)(p)^{x} (1-p)^{n-x}[/tex]
The mean is given by:
[tex]E(X)=np=9*\frac{1}{7}=1.29\\[/tex]
The variance is given by,
[tex]Var(X)=np(1-p)=9*\frac{1}{7}(1-\frac{1}{7} )[/tex]=1.1094
From variance, the standard deviation is given by, [tex]std(X)=\sqrt{1.1094}[/tex]=1.05.
Two of the nine customers buy a box of donuts with an extra donut. Compute P(X ≥ 2) and use the result to justify your answer.
[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)][/tex]
And if we find the individual probabilities we got,
[tex]P(X=0)=(9C0)(0.143)^{0} (1-0.143)^{9-0}=0.249\\P(X=1)= (9C1)(0.143)^{1} (1-0.143)^{9-1}=0.374[/tex]
[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)]\\[/tex]
= 1-[0.249+0.374]
= 0.377
Hence, [tex]P(X\ge2)=[/tex] 0.377.
This case makes sense the claim since the probability is higher or equal than the expected with the claim.
Corrected question:
To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes had the extra donut and the shop owner claimed that one in seven boxes had an extra donut. Nine customers each bought one box of donuts at the shop. Let X = the number of customers that bought a box containing an extra donut.A. Is X a binomial random variable? Explain.B. What is the mean and standard deviation of X? Provide an interpretation for each value in context.C. Two of the nine customers buy a box of donuts with an extra donut. Is the shop's claim accurate? Compute P(X ≥ 2) and use the result to justify your answer.
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Problem
Aurelia has a coin that she suspects is unfair. She wants to test
H
0
:
p
=
0.5
H
0
:p=0.5H, start subscript, 0, end subscript, colon, p, equals, 0, point, 5 versus
H
a
:
p
≠
0.5
H
a
:p
=0.5H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 5, where
p
pp is the proportion of flips that this coin lands showing heads.
She flipped the coin
100
100100 times and it landed showing heads
43
4343 of those times.
Which of the following represents the P-value for Aurelia's test?
Answers
The correct option is C, P - value is 0.0718.
Describe sample percentageA sample proportion in statistics is a measurement of the proportion or percentage of a sample that demonstrates an important characteristic or quality. It is computed by dividing the sample's overall population by the proportion of participants who exhibit the characteristic.
For instance, if a sample of 100 individuals is chosen to estimate the percentage of people who love chocolate ice cream, and 30 of those individuals state that they do, the sample proportion would be 0.3 or 30%, as 30 out of 100 individuals state that they do.
We must first compute the test statistic in order to determine the P-value for Aurelia's test. The test statistic has a typical normal distribution when the null hypothesis is true.
The sample proportion of heads is:
p' = 43/100 = 0.43
The test statistic is:
[tex]z = \frac{(p' - p)}{ \sqrt{(p(1-p) / n)}}[/tex]
where p is the hypothesized proportion under the null hypothesis, and n is the sample size.
Substituting the given values, we get:
[tex]z = \frac{(0.43 - 0.5)}{/ {sqrt(0.5 \times 0.5 / 100)}} = -1.8[/tex]
Since this is a two-sided test, we need to find the area under the standard normal distribution curve in both tails of the distribution that is more extreme than the observed test statistic.
Using a standard normal distribution table, we find that the area to the left of -1.8 is 0.0359. Therefore, the area in both tails is:
P-value = 2 × 0.0359 = 0.0718
So, the correct answer is:
c) 0.0718
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Answer:C
Step-by-step explanation: Kahn Academy
please help im kinda failing in math
Answers
Answer:
Step-by-step explanation:
c
a
LB =
Round your answer to the nearest hundredth.
B
?
CT
5
4
A
C
3
Answers
Measure of angle B is 36.87°.
What are Trigonometric Functions?Trigonometric functions are defined as the real functions or the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
Given is a right angled triangle.
We have to find measure of angle B.
Cosine of an angle in a right angled triangle is equal to the ratio of it's adjacent side to the hypotenuse.
Hypotenuse = AB = 5
Adjacent side to B = CB = 4
Cos B = 4/5
∠B = Cos⁻¹ (4/5)
= 0.6435 radians
= 36.87°
Hence the measure of the angle B is 36.87°.
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You buy 1 box of dog food and 2 cans of cat food for $23. Your friend buys 2 boxes of dog food and 1 can of cat food for $22. What is the cost of each box of dog food?
Answers
One box of dog food costs $7, while one can of cat food costs $8.
What is an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It illustrates that the expressions printed on the left and right sides have an equal relationship.
Some of the components of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. When expressing an equation, the "=" symbol and terms on both sides are a need.
Given data ,
Let the price of a single box of dog food at x.
Let's say the price of one can of cat food is y.
The cost of 1 box of dog food and 2 cans of cat food is = $ 23
One can of cat food and two boxes of dog food cost $22, total.
So , the equation will be
1x + 2y = 23 ....... (1)
2x + 1y = 22 ....... (2)
Equation (1) is multiplied by 2 to get
2x + 4y = 46 ....... (3)
When equation (2) is subtracted from equation (3), we obtain
3y = 24
value of y is obtained by dividing both sides by 3,
y = $ 8
Equation (1) can be solved by substituting the value of y.
x + [tex]2*8[/tex] = 23
x + 16 = 23
16 is subtracted from both sides, giving us
x = $ 7
Therefore , the value of x is $ 7 and value of y is $ 8
Thus, one package of dog food costs $7, while one can of cat food costs $8.
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Write a quadratic function in standard form whose graph satisfies the given condition(s). 13. vertex: (-9, -4)
Answers
Answer:
Tech 9 rock and no answer
Step-by-step explanation:
Consider the following three events for college students:
A={A student is female.}
B={A student has financial aid.}
C={A student finishes his/her undergraduate degree in four years.}
Use symbols to describe the event that a college student is female or has financial aid.
Answers
The probability of a college student being either female or having financial aid can be expressed as P(A ∪ B) = P(A) + P(B).
What is Probability?
Probability is a mathematical concept used to measure the likelihood of a particular event occurring. It is a way of expressing the chance or possibility of an event happening, ranging from 0 (impossible) to 1 (certain).
In probability theory, an event is a subset of the possible outcomes of an experiment or a random process. Probability can be expressed in terms of fractions, percentages, or decimals.
The symbol for the event that a college student is female is A, as given in the statement. The symbol for the event that a college student has financial aid is B, as given in the statement.
So, A={A student is female} and B={A student has financial aid}.
These events are mutually exclusive because one does not necessarily affect the other. For example, a male student can have financial aid and a female student may not have financial aid. Hence, the occurrence of one event does not influence the occurrence of the other event.
Therefore, the probability of a college student being either female or having financial aid can be represented as the union of the events A and B. It can be denoted as P(A ∪ B) and is calculated as:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Where P(A ∩ B) represents the probability of a student having both characteristics, i.e., being female and having financial aid.
However, as these events are mutually exclusive, P(A ∩ B) = 0. So the probability of a college student being either female or having financial aid is simply the sum of their individual probabilities:
P(A ∪ B) = P(A) + P(B) - 0
P(A ∪ B) = P(A) + P(B)
Hence, the probability of a college student being either female or having financial aid can be expressed as P(A ∪ B) = P(A) + P(B).
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The planet Neptune orbits the Sun. Its orbital radius is 30.1 (AU)
Assuming Neptune's orbit is circular, what is the distance it travels in a single orbit around the Sun?
Give your answer in terms of π
Answers
Step-by-step explanation:To calculate the distance that Neptune travels in a single orbit around the Sun, we can use the formula for the circumference of a circle, which is given by 2 * π * r, where r is the radius of the circle.
In this case, the radius of Neptune's orbit is 30.1 AU, so the circumference of the circle can be calculated as follows:
2 * π * 30.1 = 188.49
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A sports club has 140 junior members, 695 adult members, and 210 senior members. What is the probability that the first member selected at random will not be a senior member?
Answers
Answer: The total number of members in the club is 140 + 695 + 210 = 1,045.
The number of non-senior members is 140 + 695 = 835.
The probability that the first member selected at random will not be a senior member is 835 / 1,045 = 0.798 or 79.8%.
So, the answer is 0.798 or 79.8%.
Step-by-step explanation:
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.
Answers
The average rate of change of f(x) over the interval 3≤x≤4 is 15
What is the average rate of change of f(x) over the intervalFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have
f(3) = -4
f(4) = 11
The average rate is then calculated as
Average rate = [f(4) - f(3)]/[4 - 3]
Substitute the known values in the above equation, so, we have the following representation
Average rate = (11 + 4)/(4 - 3)
Evaluate
Average rate = 15
Hence, the average rate is 15
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Complete question
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.
X f(x)
3 -4
4 11
5 8
6 10
7 11
8 14
who has a better chance of winning the super bowl 2023
Answers
The Kansas City Chiefs has a better chance of winning the super bowl 2023.
In 1967's Super Bowl I, Las Vegas sportsbooks gave the Green Bay Packers a 14-point advantage against the Kansas City Chiefs. Nevada was the only state up until 2018 to allow legal Super Bowl sports betting.
The reigning champion Kansas City Chiefs are the early favorited in the Super Bowl 58 odds, according to the top NFL betting companies. At BetMGM, the Super Bowl 58 odds for the Kansas City Chiefs are +600. You can evaluate the odds on a team you prefer to discover the best price because competing sportsbooks provide different odds for each team to win the Super Bowl.
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Colton is flying a kite, holding his hands a distance of 3 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 32 . If the string from the kite to his hand is 90 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Answer:
The height of the kite above the ground is; approximately 50.69 feet.
What are trigonometric identities?
Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
The height of his hands above the ground, h is given by 3 feet
Angle of elevation of the string (above the horizontal), θ = 32°
Length of the string, l is given as 90 feet
The height of the kite above the ground is given by trigonometric ratios as ;
Sin∅ =h /90
Sin 32°= h/90
0.52 =h /90 (Sin32°= 0.52)
so h= 47.69 feet
Then height from ground is (H) = 3 +47.69
H = 50.69 feet
The height of the kite above the ground , ≈ 50.69 feet
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Step-by-step explanation:
Factor the polynomial.
3x³-300x
Answers
The result to the factorization of the polynomial is 3x (x + 10) (x - 10).
Polynomial FactorizationFactoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.
Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.
= 3x³ - 300x
= 3x(x²) - 300x
= 3x(x²) - 3x(100)
= 3x(x² - 100)
= 3x(x² - 10²)
Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );
where
a = x and b = 10= 3x (x+10) (x−10)
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HELP AAHHHHHHH FFASDF
Answers
Answer:
Step-by-step explanation:
Need help with geometry please help
Answers
Answer:31.42 sq.
Step-by-step explanation:
A=2πrh+2πr2a knitted hat pattern comes in styles with stitch options and sizes, and there are yarns appropriate for the hat. disregarding size, how many different hats can be made?
Answers
A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. There are 112 different hats that can be made using the knitted hat pattern, disregarding size.
To find the total number of different hats that can be made using the knitted hat pattern, we need to multiply the number of choices for each feature.
There are 4 styles to choose from and 4 stitch options, so there are 4 x 4 = 16 different combinations of style and stitch.
For each of these style and stitch combinations, there are 7 yarns that can be used, so the number of possible yarn choices is 7.
Therefore, the total number of different hats that can be made, disregarding size, is:
16 (style and stitch combinations) x 7 (yarn choices) = 112
This calculation shows how the multiplication principle of counting can be used to find the total number of outcomes in a multi-stage process where the number of choices at each stage is known. In this case, we multiplied the number of style and stitch combinations by the number of yarn choices to find the total number of different hats that can be made.
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Complete question is:
A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. Disregarding size, how many different hats can be made?
f(x)=x^2-4x+3 find the quadratic function
Answers
Answer:
Step-by-step explanation:
Find the area of the polygon in square units.
Answers
The area of the figure is solved to be
10 square unitsWhat is the area of ta kite?The area of a kite is solved using the formula
= P * q / 2
Where
p = length of long diagonal
q = length of short diagonal
Using the figure the length can be traced to be
p = 3 - -5 = 3 + 5 = 5
q = 6 - 2 = 4
Area of the figure
= 5 * 4 / 2
= 20 / 2
= 10 square units
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Which of the following is equal to the square root of the cube root of 5?
Group of answer choices
5 to the power of one third
5 to the power of one sixth
5 to the power of two thirds
5 to the power of three halves
Answers
5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.
What is the definition of square root?
The square root of a number is a value that, when multiplied by itself, yields the original number. The square root is the opposite of squaring a number. As a result, squares and square roots are ideas that are connected.
If x is the square root of y, it is denoted as x=√y, or the same equation may be expressed as x² = y. √" is the radical symbol used to symbolise the numerical root here. When a positive number is multiplied by itself, it represents the number's square. The square root of a positive number yields the original value.
Now,
Given that square root of the cube root of 5 i.e. √∛5=?
=√5¹÷³
=5¹/²*¹/³
=5¹/⁶
hence,
5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.
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Kelly is reading a 456- page book. During the past 7 days she has read 168 pages. If she continues reading at the same rate, how many more days will it take her to complete the book?
Answers
Answer:
12 Days
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
To find the ratio of the problem (days: pages) we can use this equation:
pages read ÷ days it took = pages read each day
Fitting the numbers into the equation:
168 ÷ 7 = 24
So, everyday Kelly reads 24 pages.
To find out how many more days Kelly needs to read, if she reads at the same rate, we can use this equation:
(456 - 168) ÷ 24 = days left
We can use this to check our work:
168 + (24 ×?) = 456
Solving for the first equation:
(456 - 168) ÷ 24 = days left
288 ÷ 24 = 12
Now, we can check our work.
168 + (24 ×?) = 456
Inserting 12 into the equation:
168 + (24 × 12) = 456
168 + 288 = 456
Therefore, to complete the book it will take Kelly 12 more days.
It says its wrong is it?
Answers
Answer: Yes, it's wrong.
Step-by-step explanation:
In the equation, it was [tex]A=\pi r^{2}[/tex]3 ft is the circle's diameter, and d is not the r.
r = d/2 = 3/2 = 1.5 ft
[tex]A=\pi r^{2}\\[/tex]
≈ 3.14 x 1.5
= 4.71
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 80 degrees occurs at 5 PM and the average temperature for the day is 60 degrees. Find the temperature, to the nearest degree, at 3 AM.
Answers
The temperature at 3 AM is about 53 degrees Fahrenheit.
How would you define temperature?The average kinetic energy of the particles in a medium, such as a gas, liquid, or solid, is measured by its temperature. It is a basic physical characteristic that governs the rate and amount of heat transmission between two bodies that are in thermal contact.
A thermometer is commonly used to measure temperature. It does this by detecting changes in a substance's physical characteristics that change with temperature, such as the expansion or contraction of a liquid or the resistance of a wire.
We are aware that a sinusoidal function models temperature, and the following information is crucial:
A high of 80 degrees is reached at 5 PM, or 17:00 in a 24-hour period.
The day's average temperature is 60 degrees.
We're looking for the temperature at three in the morning, or three in 24-hour time.
We can utilize the fact that the temperature moves through one full cycle in a 24-hour day to determine the frequency. As the time frame is 24 hours, the frequency is:
B = 2π/24 = π/12
To find the phase shift, we can use the fact that the high temperature occurs at 5 PM, which is 8 hours after noon (when the temperature starts to rise). So the phase shift is:
C = (8/24) * 2π = (1/3)π
To find the amplitude, we can use the fact that the temperature swings 10 degrees above and below the average. So the amplitude is:
A = 10
Finally, we can use the formula to find the temperature at 3 AM:
f(x) = A sin(B(x - C)) + D
f(3) = 10 sin(π/12(3 - (1/3)π)) + 60
f(3) ≈ 53.4
So the temperature at 3 AM is about 53 degrees Fahrenheit.
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what is 3 1/2x - 5 1/2x,x=2/5
Answers
Answer:
[tex]-\dfrac{4}{5}[/tex]
Step-by-step explanation:
We have the following expression
[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x[/tex]
and asked to evaluate this expression at [tex]\[x = {2\over\displaystyle 5\][/tex]
First convert [tex]3 \; \dfrac{1}{2}[/tex] and [tex]5 \; \dfrac{1}{2}[/tex] to mixed fractions
[tex]3 \; \dfrac{1}{2} = \dfrac{3 \times 2 + 1}{2} = \dfrac{7}{2}\\[/tex]
[tex]5 \; \dfrac{1}{2} = \dfrac{5 \times 2 + 1}{2} = \dfrac{11}{2}[/tex]
Therefore
[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x\\\\= \dfrac{7}{2}x - \dfrac{11}{2}x\\\\= \dfrac{7 - 11}{2} x\\\\= -\dfrac{4}{2}x \\\\= -2x\\\\[/tex]
[tex]\mathrm{For \;x =\dfrac{2}{5}},\\\\= -2x \\= - 2 \times \dfrac{2}{5}\\\\= -\dfrac{4}{5}[/tex]
