T(3) = - 50.59 is time period
What is Function using Radian ?A specific quantity is converted from degrees to radians using the RADIANS function. The supplied angle, which is in degrees, is translated into a roughly equivalent angle, which is in radians.
According to given information
Since maximum term is -50°C at 2 pm
So
We can start with cosine curve with maximum temperature -50°C at t = 0
Assuming 2 pm as starting point t = 0
Period = [tex]\frac{2\pi }{b}[/tex]
24 = [tex]\frac{2\pi }{b}[/tex]
b = [tex]\frac{\pi }{12}[/tex]
By using Formula
y = a cos(bx) + d
y = a cos([tex]\frac{\pi }{12}[/tex]t) - 52
At 5 pm , t = 3
T(3) = 2 cos([tex]\frac{\pi }{12}[/tex]×3) - 52
= 2 ×[tex]\frac{\sqrt{3} }{2}[/tex] - 52
T(3) = - 50.59 is time period
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Considerine line y=3/5x+4.
Find the equation of the line that is parallel to this line and passes through the point (-5, -1)
Answer:
y = 3/5x + 2
Step-by-step explanation:
Parallel lines have the same gradient, so
y = 3/5x + c
Put in your point (-5,-1):
(-1) = 3/5(-5) + c
-1 = -3 + c
-1 + 3 = c
2 = c
So
y = 3/5x + 2
a rancher wants to fence in an area of 1,500,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. what is the shortest length of fence that the rancher can use?
The shortest length of fence that the rancher can use is 6000ft
Given that
x = width of rectangle
y = length of rectangle
A = area of rectangle = x*y = 1500000 [tex]ft^{2}[/tex]
L = length of fencing needed = 2(x + y) + x = 3x + 2y
L = 3x + 2([tex]\frac{1500000}{x}[/tex]) = 3x + 3([tex]10^{6}[/tex])[tex]x^{-1}[/tex]
As x –> 0+, L –> +inf.
As x –> +inf, L –> (3x)+.
There will be a minimum in Quadrant I.
dL/dx = 3 - 3([tex]10^{6}[/tex])[tex]x^{-2}[/tex]
dL/dx = 0:
3 - 3([tex]10^{6}[/tex])[tex]x^{-2}[/tex] = 0
3([tex]10^{6}[/tex])[tex]x^{-2}[/tex]= 3
([tex]10^{6}[/tex])[tex]x^{-2}[/tex] = 1
[tex]x^{2}[/tex] = [tex]10^{6}[/tex]
x > 0, so x = 1000 feet for shortest length.
Shortest L = 3000 + 3([tex]10^{6}[/tex])([tex](10^{3} )^{-1}[/tex])= 6000 feet.
The shortest length of fence that the rancher can use is 6000ft
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The pheasant population on an island is declining at a rate of 1. 7% per year. The population was 4600 in the year 2009. Which answer is the best prediction of the population in the year 2015? responses 4010 4010 4080 4080 4120 4120 4150.
The best prediction of the population in the year 2015 will be 4150
rate of decrease involves The rate of reduction expressing a decrease as a percentage of the initial value.To compute a percentage drop, first determine the difference (decrease) between the two values being compared. Then, divide the reduction by the original number and multiply the result by 100.
Given that an island's peasant population is falling at a rate of 1.7% per year,
A 1.7% decrease means that 98.3% will remain.
as a result, decrease = 0.983/year
A(t) = A(original) multiplied by (0.983)^t
As a result, after 6 years, A(6) = 4600 x (0.983)6 = 4150
As a result, the population in 2009 will be 4150.
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we throw a fair die three times. if we observe the first throw is a 4, what is the probability that there is at least two 4s in the three throws?
The probability that there is at least two 4s in the three throws is [tex]\frac{2}{27}[/tex]
Permutations and combinations
permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor
given that
we throw a fair die three times
Due to the fact that each die has a 4 on it, the equation would be [tex]\frac{1}{6}[/tex]+ [tex]\frac{1}{6}[/tex]+ [tex]\frac{1}{6}[/tex]=[tex]\frac{1}{2}[/tex] if all the dice were added together.
(There are fifteen ways to get 2 fours: 441,414,144,442,424,244.. and so on until 446,464,644; another way to get the solution is using permutations and combinations:
=(1[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])(5[tex]C_{1}[/tex])+1[tex]C_{1}[/tex])(5[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])+(5[tex]C_{1}[/tex](1[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])/[tex](6C_{1} )^{3}[/tex]
= [tex]\frac{1+15}{216}[/tex]
=[tex]\frac{2}{27}[/tex]
The probability that there is at least two 4s in the three throws is [tex]\frac{2}{27}[/tex]
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why is an understanding of the central limit theorem essential to the concepts of estimation an hypothesis testing?
Because it permits one to assume that the sampling distribution of the mean would typically be normally distributed, the central limit theorem is helpful when examining big data sets. This makes statistical analysis and inference simpler.
Hypothesis :
In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.
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A publiher need to end many book to a local book retailer and will end the book in a combination of mall and large boxe. Each mall box can hold 20 book and each large box can hold 45 book. There were twice a many large boxe ent a mall boxe, which altogether can hold 440 book. Write a ytem of equation that could be ued to determine the number of mall boxe ent and the number of large boxe ent. Define the variable that you ue to write the ytem
The formula is = 7 and 3. It may be used to calculate the number regular mall boxes as well as the number of big boxes.
Which equation has ever been the hardest?What is the world's most difficult arithmetic problem? A mathematical conundrum that has baffled mathematicians over decades is finally solved earlier this week. Diophantine Equation, sometimes referred to as the "sum of three cubes," is what it is: Find x, y, & z such that, for any k between 1 and 100, x3+y3+z3=k.
Briefing:Let x= Number of small boxes , y = Number of large boxes.
As per given , 30x+55y=375 (i)
x+y=10 (ii)
Multiply (ii) by 30, we get
30x+30y=300 (iii)
Eliminate (iii) from (i), we get
25y=75
⇒ y= 3
Put y=3 in (ii), we get
x+3=10 ⇒ x=7
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What is a perpendicular line to Y =- 4x 7?
The original equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. A perpendicular line to Y = -4x + 7 would be Y = 4x + 7.
To find the equation of a line perpendicular to Y = -4x + 7, we need to switch the x and y variables and then change the sign of the slope.
The original equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Since the original equation has a slope of -4, the perpendicular line will have a slope of 4.
Therefore, the equation for the perpendicular line is y = 4x + b.
We can find the y-intercept by plugging in a point from the original equation.
For example, if we plug in (0,7), we get 7 = -4(0) + b, or b = 7.
Therefore, the equation for the perpendicular line is y = 4x + 7.
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find the value of x.
Answer: 7
Step-by-step explanation:
A student concluded that 8x−12=4(12x−6) has infinitely many solutions. Which statement best describes the student’s conclusion? Responses The conclusion is incorrect because the equation has no solution. The conclusion is incorrect because the equation has no solution. The conclusion is incorrect because there is exactly one solution to the equation. The conclusion is incorrect because there is exactly one solution to the equation. The conclusion is correct because there are exactly two solutions to the equation. The conclusion is correct because there are exactly two solutions to the equation. The conclusion is correct because when simplified, both sides of the equation are equivalent. The conclusion is correct because when simplified, both sides of the equation are equivalent.
Answer:
The conclusion is incorrect because there is exactly one solution to the equation.
Step-by-step explanation:
8x - 12 = 4(12x - 6)
4 x 12x = 48x 4 x -6 = -24
8x - 12 = 48x - 24
Move the terms
8x - 12 - 48x = -24
Move the constant to the right-hand side and change its sign
8x - 48x = -24 + 12
-40x = -24 + 12
-40x = -12
Divide both sides by -40
40x = -12
40 = 40
x = [tex]\frac{3}{10}[/tex] or, alternate form, x = 0.3
There are 8 squares and 10 triangles. What is the simplest ratio of squares to triangles?.
Answer: 4:5
Step-by-step explanation: The lowest form
Answer:
Step-by-step explanation:
4:5
[(8 x 10-3) x (0.0002)
Answer:
Step-by-step explanation:
0.0154, I think, I apologize if this is wrong.
What is closure under addition Give 2 example?
The closure property of addition states that the sum of two whole numbers will always be a whole number.
A whole number is a set of all positive integers from 0 to infinity. Now we all know that if we add two positive numbers up, the sum will either remain constant (if the number is 0) or be greater than both numbers. This means that the sum of two whole numbers has to be a whole number.
Example 1 If we add 0 and 45
0 + 45
= 45
We already know that 45 is a whole number.
Example 2- If we add 486 and 354
486 + 354
= 840
From the definition, we can say that 840 is a whole number.
This is the closure property.
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in a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the roman alphabet. how many different license plates can the country produce?
118,813,760 different combination license plates can the country produce
Permutations and combinations:
permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor. By considering the ratio of the number of desired subsets to the number of all possible subsets for many games of chance in the 17th century, the French mathematicians Blaise Pascal and Pierre de Fermat gave impetus to the development of combinatorics and probability theory.
Given that
In a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the roman alphabet
X = 10 × 26 × 26 × 26 × 26 × 26
= 10 × 11881376
= 118,813,760
118,813,760 different combinations license plates can the country produce
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help me with the question please
Answer:
Irrational
Step-by-step explanation:
An irrational number added to any other real numbers still keep its infinitely long and never repeating decimals, leaving it still irrational.
What is an equation of the line that passes through the points (8,-3) and (4,2)?
Answer:
y=-1.25x+7
Step-by-step explanation:
See the image
When three-digit telephone area codes were first put in place in the United States and Canada, the first number
could be any digit from 2 through 9, the second number could only be 0 or 1, and the third number could be any
digit from 0 through 9. How many possible area codes can be created with this format?
a. 24
b. 126
c. 140
d. 160
There are 160 possible area codes can be created with this format.
What is combination?A process determining the number of possible arrangements in a collection of items in which the order of the selection does not matter is called combination.
Given that, When three-digit telephone area codes were first put in place in the United States and Canada, the first number could be any digit from 2 through 9, the second number could only be 0 or 1, and the third number could be any digit from 0 through 9.
So, according to question,
The first digit has about 8 options
The second digit has about 2 options
The third digit has about 10 options
Therefore, the total possible code = 8×2×10=160.
Hence, 160 possible codes are there.
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Fill out the function table below f(x) = 3(2 – x) –2
The value of (x,y) on the given points of the function will be (-2,10),(-1,7),(0,4),(1,1), and (2,-2).
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given function,
f(x) = 3(2 – x) –2
Put x = -2
f(-2) = 3(2 + 2) - 2 = 10 thus, (-2,10)
Put x = -1
f(-1) = 3(2 + 1) - 2 = 7 thus, (-1,7)
Put x = 0
f(0) = 3(2 - 0) - 2 = 4 thus, (0,4)
Put x = 1
f(1) = 3(2 - 1) - 2 = 1 thus, (1,1)
Put x = 2
f(2) = 3(2 - 2) - 2 = -2 thus, (2,-2)
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Rewrite 2x2x2x2 as an exponent.
The required exponent form is obtained as 2 x 2 x 2 x 2 = 2⁴.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
The given expression is 2 x 2 x 2 x 2.
It can be written in exponent form as,
2 x 2 x 2 x 2
The number 2 is multiplied to itself by four times,.
Thus, the exponent form is given as 2⁴.
Hence, the exponent form of the given expression is 2⁴.
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What value of x makes the equation |7x|+4 = 2x + 5 true?
1/5 or -1/9 would both be correct
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer: nose
Step-by-step explanation:
An electrician need to run a cable from the top of a 68-foot tower to a tranmitter box located 51 feet away from the bae of the tower. Fidn how long he hould cut the cable
By using Pythagoras' theorem the required length of the cable is 85 feets.
What is Pythagoras' theorem?The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem. Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case because it is opposite the angle of 90°.
What is the name of Pythagoras' formula?The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of a right-angled triangle. Alternatively, the sum of the squares of a right triangle's two legs equals the square of its hypotenuse.
Given:
Height of the tower = 68 feet = perpendicular
distance of box form tower = 51 feet = base
Let's assume lenght of the cable = L = hypotenous
Acoording to the question by using Pythagoras' theorem,
[tex]hyp^{2}= perpendicular^{2} +base^{2} \\(L)^2 = (68)^2 + (51)^2\\L^2 = 4624 + 2601\\L^2 = 7225\\L =\sqrt{7225}\\L = 85 feet[/tex]
Hence by using Pythagoras' theorem the required length of the cable is 85 feets.
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What two rational expressions sum to 3x−4x2+x−12?
PLEASE HELP URGENTLY!!!!!!
Answer:
Step-by-step explanation:
g
Step-by-step explanation:
16. +. 5
__. ____
7(x+4). 7 (x-3)
Write the negation of each quantified tatement. 3. Everyone failed the quiz today
The negation of the given statement " Everyone failed the quiz today " is given by " No one failed the quiz today."
As given in the question,
Given statement is written as:
S : Everyone failed the quiz today.
Negation of the given statement represent the conversion of true statement into false statement or conversion of false statement into true statement.
Here given statement is true statement.
Convert the given statement into false statement.
So Negation of statement S is represented by ~ S.
~S : No one failed the quiz today.
Therefore, the negation of the given statement is equal to " No one failed the quiz today".
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a manufacturer wishes to set a standard time required by employees to complete a certain process. times from 21 employees have a mean of 6 hours and a standard deviation of 2 hours. test if the mean processing time exceeds 5.5 hours. what is the -value of the test (round off to second decimal place)? assume normal population.
The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process
The t-value will be equal to 1.39 for the given statistics.
How to calculate the t-value?To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.
The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:
H0: µ ≤ 5.5
The alternative hypothesis is that the mean processing time is greater than 5.5 hours:
Ha: µ > 5.5
We will use a significance level of 0.05.
The formula for the t-test statistic is:
t = (X - µ) / (s / √n)
Where:
X = sample mean
µ = hypothesized population mean
s = sample standard deviation
n = sample size
Substituting the given values, we get:
t = (6 - 5.5) / (2 / √21) = 1.386
The degree of freedom for the t-test is n-1 = 20.
Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.
Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.
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How do you find the remainder when a polynomial in x is divided by a binomial of the form XR?
There are two ways to find the remainder when a polynomial in x is divided by a binomial of the form x-r, the use of synthetic division or calculate P(r).
Synthetic division
The Synthetic division is a shortcut way of polynomial division, especially if we need to divide it by a linear factor. It is generally used to find out the zeroes or roots of polynomials and not for the division of factors.
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
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7w+6 i need help plese
Answer: 7w + 6
Step-by-step explanation:
Your question was "7w + 6". When we simplify this, we get 7w + 6. So your answer is 7w + 6.
531
x 47
Long multiplication :) please help
The sum of the measures of two exterior angles of a triangle is 264. What is the measure of the third exterior angle?
the patient/client has been measuring urine at home with a quart milk carton and states voiding 1 quarts 2 days ago and 2 quarts yesterday. how many liters is this?
The total urine patient/client has been measuring at home is 2.838 liters.
Given that,
the patient/client has been measuring urine at home with a quart milk carton and states voiding 1 quarts 2 days ago and 2 quarts yesterday.
We know that 1 quart = 0.946 litre
and 2 quarts = 1.892 litre
Therefore total amount = 0.946 + 1.892
= 2.838
Hence the total urine patient/client has been measuring at home is 2.828 litres.
What is Quart?
The quart is an English unit of volume equal to a quarter gallon. It is a quarter of a gallon. Measurement of volume, capacity. Its unit of measurement for liquids, equal to approximately 1.14 litres in the UK, or 0.95 litrs in the US.
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You own a small grocery store and want to start carrying Duracell AA batteries. You can purchase a 4-pack battery set for $3.99 from the wholesaler. You typically make products up 30%. What price should you charge for the batteries?
The Question is based on concept of Cost Price and selling Price is 5.2$
What is Cost PRice and Selling PRice?
Cost price is the actual price of an object where as selling price is the price in which seller sells it to customer
Solution
Cost Price of batteries = 4$
and shopkeeper can charge upto 30% interest
hence selling price will be 4$ + 30% of 4$
= 4 + 30/100(4)
= 4 + 1.2
5.2$
Hence answer to this Question is 5.2$
and this 5.2$ is the selling price of duracell batteries whereas 4$ was the cost price for the same
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