Outside temperature over a day can be modeled as a sinusoidal function. suppose you know the temperature is 65 degrees at midnight and the high and low temperature during the day are 76 and 54 degrees, respectively. assuming t is the number of hours since midnight, the temperature, d, in terms of t. The Equation is :
D = - 11 sin(π/12) + 65
The range is 76 - 54 = 22
so, a = 11
we know that the period is 24 hours
So, 2π/k=24
⇒ 24k = 2π
⇒ k = π/12
So far we have:
D = 11 sin(π/12)(t) + 65
Giving us a range from 76 to 54
But obviously the temp after midnight would decrease, whereas our function has it increasing to 76 when t = 6 (6:00 am)
We could do a phase shift, or more simply, just flip the function to
D = -11sin(π/12)t + 76
Checking some values
t = 0 , D = -11sin0 + 65 = 65
t=6 , (6:00 am) D = -11 sin (π/2) + 65 = 54
t = 12 (noon), D = -11 sin π + 65 = 65
t = 18 , (6:00 pm) , D = -11sin 3π/2 + 65 = 76
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The length of a hadow of a building i 15 m. The ditance from the top of the building to the tip of the hadow i 25 m. Find the height of the building. If neceary, round your anwer to the nearet tenth
Answer:
The height of the building is 20 meters
Step-by-step explanation:
What is Pythagoras theorem ?The Pythagoras Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.
[tex]c^{2}=a^{2}+b^{2}[/tex]
Where c is the hypotenuse , a is perpendicular length , b is base
Length of the shadow of a building b = 15 m.
The distance from the top of the building to the tip of shadow c = 25 m
Let us assume the Height of the building to be = a
According to the pythagoras theorem
[tex]c^{2}=a^{2}+b^{2}[/tex]
[tex]25^{2}=a^{2}+15^{2}[/tex]
[tex]a^{2} = 25^{2}-15^{2}[/tex]
[tex]a^{2}[/tex] = 625-225
[tex]a^{2}[/tex] = 400
a = 20 meters
The height of the building is 20 meters
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Find x: 2x=1
X=1/2
X=1
X=2
X=-1
Answer: x = 1/2
Step-by-step explanation:
2(1/2)=1
1=1
What is the equation of the line that passes through the point (−3,4) and has a slope of −2?
Answer:
y=−2x−2
Step-by-step explanation:
What is the solution to this equation?
3(4x + 3) = 2x-5(3-X) + 2
Answer: The answer to this question is x= -22/5
what is the x-coordinate of the point that divides the directed line segment from k to j into a ratio 1:3 -1 3 7 11
The x-coordinate of the point that divides the directed line segment from k to j into a ratio 1:3 is given as follows:
x = 7.
How to obtain the x-coordinates?The direction of the segment is given as follows:
K to J.
The desired point divided the directed line segment from k to j into a ratio 1:3, hence the equation involving proportions is given as follows:
P - K = 1/4(J - K).
This equation is used to obtain both the x-coordinate and the y-coordinate of the point.
The x-coordinates of the points are given as follows:
Point P: x.Point K: 9.Point J: 1.Hence the x-coordinate of the segment is obtained as follows:
x - 9 = 1/4(1 - 9)
x - 9 = -2
x = -2 + 9
x = 7.
Missing InformationThe segment is given by the image shown at the end of the answer.
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Determine the smallest integer value of x in the solution of the following inequality.
5x7-1
The smallest integer value of x in the solution of the following inequality x is strictly less than 2 or x ∈ (-∞, 2)
What are inequalities?Inequalities are statements that are represented as comparison between two or more numbers or algebraic expressions.(strictly less, strictly great, greater, lesser)
Given that the inequality 5x - 7 < 2x - 1
Solving the given equation:
5x - 7 < 2x - 1
5x - 7 - 2x < 2x - 1 - 2x
3x - 7 < -1
3x - 7 + 7 < -1 + 7
3x < 6
x < 2
Therefore, We conclude that x is strictly less than 2.
Hence x ∈ (-∞, 2)
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find a set of scalar parametric equations for the line that passes through p(3, 4, 1) and q(4, -2, -1).
A set of scalar parametric equations for the line that passes through points p(3, 4, 1) and q(4, -2, -1) : x = 3 + 4t, y = 4 - 2t and z = 1 - t
In this question, we have been given two points p(3, 4, 1) and q(4, -2, -1).
We need to find a set of scalar parametric equations for the line that passes through points p and q.
We know that a set of scalar parametric equations is,
x = x0 + at, y = y0 + bt, z = z0 + ct
Let (x0, y0, z0) = (3, 4, 1)
and (a, b, c) = (4, -2, -1).
Therefore, scalar parametric equations as:
x = 3 + 4t,
y = 4 - 2t
and z = 1 - t
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in math, a statement that shows that two expressions are equal.
Answer:
= this is that two expression two equal numbers
If y varies inversely as x and x is 6 when y is 13, what is x when y is 8? a. 9.75 b. 3.69 c. 0.27 d. 6.5
If y fluctuates inversely as x as well as x is 6 if y is 13 then x is 9.75 when y is 8.
Define the term inverse proportion?When one variable declines, the others also decline in the same ratio. When two variables move in opposite directions, one variable reduces as another increases and the other increases as another variable lowers, the variables are said to be inversely proportional. Direct proportion is in opposition to it.Inverse variation is demonstrated by the following equation when two quantities, x and y, are in inverse proportion:-
x y = x1 y1
Now, if x is 6 when y is 13 and y varies inversely with x, then at y =8,
Thus,
x × 8 = 6× 13
x = (6×13)/8
x = 9.75
As a result, if y varies inversely as x as well as x is 6 if y is 13 then x is 9.75 when y is 8.
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Study the sequences (0, 6, 12, 18, 24, . . .) and (1, 6, 36, 216, 1,296, . . .), and answer these questions:
Which of the two sequences is an arithmetic sequence?
What is the common difference of the arithmetic sequence?
Can you think of any other mathematical relationship that exhibits a common difference between numbers?
Answer:
Step-by-step explanation:
In the first sequence, subtracting the previous term from each term starting from the second one gives these values: (0, 6, 12, 18, 24, . . .) is an arithmetic sequence.
How to find the common difference in the arithmetic sequence?
Common difference = second term - first term
The difference between the terms is constant. This sequence is an arithmetic one, with the common difference being 6.
Common difference = 6.
Just by looking at the terms in the second sequence,
(1, 6, 36, 216, 1,296, . . .), the difference between the consecutive terms is not common. This sequence is not an arithmetic sequence because it is based on the multiply by 6 rule.
Like arithmetic sequences, linear equations show a common difference between numbers.
Answer: In the first sequence, subtracting the previous term from each term starting from the second one gives these values:
6 – 0 = 6, 12 – 6 = 6, 18 – 12 = 6, and 24 – 18 = 6.
The difference of the terms is constant. This sequence is an arithmetic one, with the common difference being 6.
Just by looking at the terms in the second sequence, (1, 6, 36, 216, 1,296, . . .), it’s clear that the difference of the consecutive terms is not common. This sequence is not an arithmetic sequence because it is based on the multiply by 6 rule.
Like arithmetic sequences, linear equations show a common difference between numbers.
Step-by-step explanation: Edmentum Answer
PLEASE HELP, WILL GIVE BRAINLIEST! Help and explain, please! Thank you!
Answer:
56 cents
Step-by-step explanation:
cost/amount=price
4/2.24=0.56
5.6/10=0.56
6.72/12=0.56
Identify the slope of the function. Interpret its meaning in terms of the problem situation.
On a coordinate plane, a line goes through (negative 1, 1) and (0, negative 3). a point is at (negative 4, negative 3) and (0, negative 3). what is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, −3)? y 3 = −4(x 4) y 3 = –one-fourth(x 4) y 3 = one-fourth(x 4) y 3 = 4(x 4)
The equation of the required line would be x - 4y = 8.
What is the slope-point form of the line?
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).
A line goes through the point (-1, 1) and (0,-3)
so the slope of the given line would be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-3-1}{0-(-1)}\\\\m=-4[/tex]
And we have to find the line which passes through the point (-4, -3) and the required line is perpendicular to the given line.
As we know the product of slopes of perpendicular lines is -1.
So the slope of the required line would be = 1/4
By using a slope-point form of the line, we get
[tex]y - y_1=m(x-x_1)\\\\y-(-3)=\frac{1}{4}(x-(-4))\\\\4(y+3)=x+4\\\\4y+12=x+4\\\\x-4y=8[/tex]
Hence, the equation of the required line would be x - 4y = 8.
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Answer:
C
Step-by-step explanation:
A construction company is considering submitting bids for two contracts. The company estimates that it has a 20\%20%20, percent chance of winning any given bid. Here is the probability distribution of x=x=x, equals the number of bids the company wins:.
Where the variance is 0.32, the mean is 0.40, and there are provided sets of probabilities, the standard deviation will be 0.566.
What is standard deviation?The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. In general, values with a high standard deviation are spread out from the mean, whereas those with a low standard deviation are grouped together close to the mean.
Here,
mean=0.4
variance=(Xn-mean)².P(x)n
=(0-0.4)²*(0.64)+(1-0.4)²*(0.32)+(2-0.4)²*0.04
variance=0.32
Standard deviation=√(variance)
=√0.32
=0.566
The standard deviation will be 0.566 where variance in 0.32 and mean is 0.40 and given sets of probability.
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You plan to construct a brick wall measuring 14. 5 ft. In length, 5. 5 ft. High, and 0. 5 ft. In width. If a brick measures 6 in. X 4 in. X 2 in. , how many bricks will you need? (remember to round up. ) total volume (to the nearest tenth) = cubic feet. The number of bricks =.
Using simple mathematical operations, we know that we will require 1436 bricks to construct a brick wall.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.
In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
So, we know that:
A brick wall's measurements are provided by:
14.5 feet in length
Size: 0.5 feet wide
5.5 feet tall
Brick dimensions are provided by:
6 inches in length
4-inch width
2 inches tall
The number of bricks must be determined:
Thus, the number of bricks is provided by:
Number of bricks = Volume of brick wall/Volume of brick
Number of bricks = 14.5 * 5.5 * 0.5 * 12 * 12 * 12/6 * 4 * 2
Number of bricks = 1435.5
Number of bricks = 1436
Therefore, using simple mathematical operations, we know that we will require 1436 bricks to construct a brick wall.
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let x represent the full length of a certain species of newt. assume that x has a normal probability distribution with mean 110.6 inches and standard deviation 4.9 inches. you intend to measure a random sample of n
If x represents the full length of a certain species of newts then, the mean of the sampling distribution and standard deviation are 216, and 0.31 respectively.
Central Limit Theorem for mean: When a random sample of size n is taken from a population with a mean and standard deviation, the sample mean approaches the normal distribution with mean and standard deviation σ/sqrt (n) as the sample size increases.
Sampling distribution of the sample mean:
using, Central Limit Theorem, the mean of the sampling distribution is μ_{x-bar} = 216.
The standard deviation of the population is σ = 3.1 and the sample size is n =103, people
The standard deviation σ/√n= 3.1/√103 =0.31.
As a result, the sample mean for the 103 sample size, following normal distribution has a mean of μ_{x-bar} = 216 and a standard error of μ_{x-bar} = 0.31.
x-bar ≈ N (216, 0.31)
μ_{x-bar} = 216
σ_{x-bar} =0.31
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(complete question)
Let X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with a mean of 110.6 inches and a standard deviation of 4.9 inches. You intend to measure a random sample of n = 103. find the mean of the sampling distribution and standard deviation.
If 1 liter is approximately equal to 1.06 quarts, about how many quarts are in 28.5 liters
Answer:
About 30.21 quarts
Step-by-step explanation:
[tex]q=(28.5)(1.06)=30.21[/tex]
Hope this helps
on january 1 electro incorporated issued $740,000 of 7.5%, four-year bonds that pay interest semiannually on june 30 and december 31. they are issued at $680,186 and their market rate is 10% at the issue date. after recording the entry for the issuance of the bonds, bonds payable had a balance of $740,000 and discount on bonds payable had a balance of $59,814. electro uses the effective interest bond amortization method. the first semiannual interest payment was made on june 30. complete the necessary journal entry for the interest payment date of june 30 by selecting the account names from the drop-down menus and entering the dollar amounts in the debit or credit columns.
The interest payments is $27,750 and the Bond payable discount is $6,259
The electro incorporated issued $740,000 of 7.5%, four-year bonds that pay interest semiannually on june 30 and december 31.
They are issued at $680,186 and their market rate is 10% at the issue date
Interest payments = $740,000 x 7.5% x 1/2 = $27,750 (the credit to Cash).
bond interest expense = carrying value at 1/1/13 (the beginning of the period) of $680,186 x market rate of 10% x 1/2 = $34,009 (the debit to Bond interest expense).
Bond payable discount
The discount amortization $34,009 - $27,750 = $6,259
Therefore, the interest payments is $27,750 and the Bond payable discount is $6,259
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What is the value when the y intercept of f(x) is subtracted from the y intercept of g(x)? f(x) =3x-5 g(x) is shown in the graph below:
In the general form y = mx + c, c is the y-intercept of the line. The difference of y-intercepts is -5.2.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given that,
The equation for f(x) = 3x - 5
And, the value of y-intercept of g(x) from the graph is 0.2
The y-intercept of f(x) can be obtained by comparing it with y = mx + c, where c is the y-intercept as follows,
c = -5.
Thus, the difference of their y-intercepts as per the question is given as,
-5 - 0.2 = -5.2
Hence, the difference of the y-intercepts of f(x) and g(x) is given as -5.2.
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the ____ of a triangle is a segment that connects the midpoints of two side of the triangle called
Answer:
midsegment
Step-by-step explanation:
hope it helps!
The replacement set for an equation is {10, 24, 25, 36}.
The equation is represented by the sentence, "56 of a number is 30."
What is the solution set of the equation?
Responses
{10}
open curly bracket 10 close curly bracket,
{24}
open curly bracket 24 close curly bracket
{25}
open curly bracket 25 close curly bracket
{36}
The solution set of the equation is {26}
What is Set?Set is a collection of well defined objects.
Given,
The equation is represented by the sentence, "56 of a number is 30."
Replacement set for an equation is {10, 24, 25, 36}.
We need to find the solution set of the equation
"56 of a number is 30"
Fifty six of a number is thirty
56-30
26
Hence, the solution set of the equation is {26}
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10+\frac{3}{4}y=
10+
4
3
y=
\,\,43
43
Um, is there a possibility that you could clean this question up a bit? It is a little scrambled and hard to make out of the equation given. Thanks!
Some nations require their students to pass an exam before earning their primary school degrees or diplomas. A certain nation gives students an exam whose scores are normally distributed with a mean of 414141 points and a standard deviation of 999 points. Suppose we select 222 of these testers at random, and define the random variable ddd as the difference between their scores. We can assume that their scores are independent. Find the probability that their scores differ by more than 151515 points.
The required probability that their scores differ by more than 15 points is 0.99807.
As stated in the question, a specific country administers an exam to students with scores that are regularly distributed with a mean of 41 points and a standard deviation of 9 points. Assume we randomly select two of these testers and define the random variable d as the difference in their scores.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Z = x - μ / σ
Z = 15 - 41 / 9
Z = -2.88
Now,
P(x > 15) = P (z > -2.88)
= 0.99807
Thus, the needed chance is 0.99807 and their scores differ by more than 15 points.
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What are the products 4/9 X 6 and 6 X 4/9
HELP NOW PLEASE
Answer: Both products are 2.6 repeating
a quiz consists of 24 questions. each question has 4 answer choices with exactly one correct answer. a student is completely unprepared for the quiz, so he guesses on all 24 questions. how many questions should the student expect to answer correctly?'
According to the binomial distribution, there are 13 questions should the student expect to answer correctly.
Binomial distribution:
in statistics, binomial distribution refers the probability of getting a success must remain the same for the trials we are investigating.
Given,
A quiz consists of 24 questions. each question has 4 answer choices with exactly one correct answer. a student is completely unprepared for the quiz, so he guesses on all 24 questions.
Here we need to find how many questions should the student expect to answer correctly.
While we looking into the given question, we have identified that the total number of questions is 24.
Number of options = 4
So, the probability of getting correct answer = 1/4 = 0.25
The probability of getting incorrect answer is,
=> 1 - 1/4 = 3/4 = 0.75
So, based on the binomial distribution,
X ~ Binomial Distribution (m=25, p=0.25, q=0.75)
Then in probability it can be written as,
=> P (X=13) = (25C13)x ((0.25)¹³) x ((0.75)¹²)
=> P (X=13) = 0.00245461663
Therefore, the number of correct answers is 13.
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Does anyone know the answer or how to solve this please?
Answer: Choice (E) [tex]\displaystyle \text{xz} = \boldsymbol{\frac{\text{x}^3}{\text{zy}^2}}[/tex]
=========================================================
Explanation:
The goal is to find what xz is equal to (in terms of x, y, and z)
We are given [tex]\text{z}= \frac{\text{x}^2}{\text{zy}^2}[/tex]
The only thing we're missing on the left hand side is x.
Let's multiply both sides by x.
[tex]\text{z} = \frac{\text{x}^2}{\text{zy}^2}\\\\\text{xz} = \text{x}*\frac{\text{x}^2}{\text{zy}^2}\\\\\text{xz} = \frac{\text{x}*\text{x}^2}{\text{zy}^2}\\\\\displaystyle \text{xz} = \boldsymbol{\frac{\text{x}^3}{\text{zy}^2}}[/tex]
This points us to choice (E) as the final answer.
what is the ratio of the area of a square inscribed in a semicircle with radius $r$ to the area of a square inscribed in a circle with radius $r$? express your answer as a common fraction.
Ratio of the area of a square inscribed in a semicircle with radius 'r' to the area of a square inscribed in a circle with radius 'r' is equal to 2: 5.
As given in the question,
Let ABCD be the square with side 'a' inscribed in a semicircle with radius 'r'.
'O' be the center of the semicircle.
'M' be the midpoint of AB such that MB = a/2
Join OM, OB and OM ⊥ AB
OB = r
OM = BC = a
In ΔOMB.
OB² = OM² + MB²
⇒ r² = a² + (a/2)²
⇒r² = 5a²/4
⇒a² = 4r²/5
Area of the square inscribed in a semicircle = a²
= 4r²/5
Let PQRS be the inscribed in a circle with side 'x'
Diagonal of the square inscribed in a circle = 2r
In ΔPQR,
PR = diagonal
= 2r
PQ = QR = x
PR² = PQ² + QR²
⇒(2r)² = x² + x²
⇒x² = 4r² /2
⇒x² = 2r²
Area of the square inscribed in a circle = x²
= 2r²
Ratio of the area of the square inscribed in ( semicircle to the : circle )
= 4r²/5 / 2r²
= 2 / 5
= 2 : 5
Therefore, ratio of the area of the squares inscribed in a semicircle to the circle is 2 : 5.
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henry is organizing textbooks on his bookshelf. he has a spanish textbook, a math textbook, and a history textbook. how many different ways can he line the textbooks up on his bookshelf?
Answer:
6
Step-by-step explanation:
S = Spanish book
M = Math book
H = History book
These are the different ways in which he can organize the book on his bookshelf.
SMH
SHM
MSH
MHS
HSM
HMS
There are 6 ways.
you are interested in measuring the effects of a computer-assisted instruction program on the math scores of elementary school students; experimental and control students are matched on iq. group of answer choices within-subjects anova independent samples t test related samples t test between-subjects anova
you are interested in measuring the effects of a computer-assisted instruction program on the math scores of elementary school students within-subjects anova.
What is an ANOVA with within-subjects?
When there are identical participants in each group, a one-way repeated measures ANOVA, sometimes referred to as a within-subjects ANOVA, is used to assess whether three or more group means are different. The groups are sometimes referred to as "related" groups as a result.ANOVA within-subjects. Comparisons of the same individuals under various circumstances are included in within-subjects variables. For instance, each child's performance in the "ADHD Treatment" research was assessed four times, once after taking each of the four treatment doses for a week.A repeated measures ANOVA is another name for a within-subjects ANOVA. This kind of test is not just confined to two time periods; it is widely utilised when utilizing a pretest and posttest design.To know more about anova check the below link:
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Drag and drop the answer into the box to match each point to its coordinates.
The required Co-ordinates are A(-0.5, -0.25), B(-2.5, 1.5) and C(0.25, 0.5).
How to calculate points on the graph?To diagram a point, first find its situation on the x-axis, then track down its area on the y-hub, lastly plot where these meet. The middle place of the chart is known as the origin and is composed as the point (0, 0) since it's situated at the no point on the x-axis and the no point on the y-axis.
What are Co-ordinates ?The distance of a point from y-hub scaled with the x-hub is called abscissa or x direction of the point. The distance of a point from x-pivot scaled with the y-hub is called ordinate. The abscissa and ordinate all together are called organizes.
According to question:Now we find the co-ordinates of points on the graph,
Point A(-0.5, -0.25)
Point B(-2.5, 1.5)
And
Point C(0.25, 0.5)
Thus, required points are A(-0.5, -0.25), B(-2.5, 1.5) andC(0.25, 0.5).
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