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The origin of the number zero is believed to be ancient India, where it was invented as a placeholder in the decimal system around the 5th century CE. The concept of zero as a number in its own right was a revolutionary idea that greatly advanced mathematical understanding and allowed for much more efficient mathematical calculation. From India, the use of zero spread to the Islamic world and eventually to the West. The modern representation of zero as a circle or a digit was introduced in the 13th century in India.
Perform the following operation
and express the answer in
scientific notation.
The solution of the expression in scientific notation is 1.5 * 10^-2
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
6.0 * 10^4 / 4.0 * 10^8
Divide 6 by 4
So, we have
6.0 * 10^4 / 4.0 * 10^8 = 1.5 * 10^4/10^8
Evaluate the final quotient
6.0 * 10^4 / 4.0 * 10^8 = 1.5 * 10^-2
Hence, the solution is 1.5 * 10^-2
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Raven just purchased a gumball machine. Each compartment has the
dimensions of 8 inches by 6 inches by 15 inches. Assuming the vending
machine uses Gumballs that are approximately spherical and 1 inch in
diameter, how many gumballs did she order if each machine has 3
compartments and she ordered 25 machines? (Hint: Packing spheres in a
rectangular prism usually take up 190% of the volume of the spheres.)
Round your answer to the nearest whole number.
O A. 2171
B. 10,856
C. 32,568
D. 54,280
*
10 points
Answer:
The answer is C. 32,568. Assuming that the gumballs are 1 inch in diameter and packed in a rectangular prism, each compartment can hold approximately 190% of the volume of the spheres. Therefore, each compartment can hold approximately 7,560 gumballs. Since there are 3 compartments per machine and 25 machines, the total number of gumballs that Raven ordered is 32,568.
Step-by-step explanation:
A right square pyramid has a volume of 12 cubic centimeters. If the height remains fixed but the sides of the base are multiplied by 3, what is the volume of the new pyramid?
A. 36 cm
B. 48 cm
C. 108 cm
D. 72 cm
If the height of a square pyramid remains fixed while its sides of the base is multiplied by 3, then the volume of the new pyramid is 108 cm³ (option C)
The volume of a square pyramid is given by:
V = A . h = a² . h
Where;
A = the area of the base = a²
h = height of the pyramid
a = sides of the base
In this problem,
V = 12 cm³
a² . h = 12 .... (equation 1)
Now, the sides of the base are multiplied by 3. Hence, the new volume will be:
V = (3a)² . h
= 9 a² . h
from equation 1 we know that a² . h = 12. Hence,
V = 9 x 12 = 108 cm³
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What advantage does the involvement of citizen scientists have in measuring biodiversity? Explain your answer.
Answer: citizen scientists are already providing large amounts of data for monitoring biodiversity, but they could do much more, according to a new study published in the journal Biological Conservation, which suggests that citizen science has the potential to contribute much more to regional and global assessments of biodiversity. Citizen scientists are regular people who provide data or input to science, for example by monitoring species in their community or examining satellite imagery for evidence of deforestation or land use change.
Step-by-step explanation:
Aya sells stuffed animals at a craft fair. She charges $13 for the small ones and $12 for the large ones. She sold $350 worth of animals. After the show, she noticed that she sold 27 stuffed animals. How many were small and how many were large?
Let's call the number of small stuffed animals sold "x" and the number of large stuffed animals sold "y".
We know that:
x + y = 27 (the total number of stuffed animals sold)
13x + 12y = 350 (the total amount of money Aya earned)
We can use these two equations to solve for x and y. To do this, we'll use substitution:
x + y = 27
x = 27 - y
Now, we'll substitute this expression for x into the second equation:
13(27 - y) + 12y = 350
351 - 13y + 12y = 350
351 = 350
This equation is true for all y, which means that we cannot solve for y using these two equations. We need more information to determine the number of small and large stuffed animals sold.
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x + y = 27 (the total amount of stuffed creatures sold) (the total number of stuffed animals sold)
These two formulae can be used to find the answers to x and y. We'll use replacement to accomplish this:
x + y = 27
x = 27 - y
We will now change x in the second equation to the following expression:
13(27 - y) + 12y = 350
351 - 13y + 12y = 350
351 = 350
A juice container haped like a cylinder ha a bae area of 100cm² and can hold 1500cm³ of juice. The height of the juice container id
The height of the juice container with a base area of 100cm² is 15 cm
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2
The base area of a cylinder is given by:
base area = π*r²
base area = 100 cm^2
100 = π * r^2
r^2 = 100 / π
r = √(100 / π)
The volume of a cylinder is given by:
volume = π*r²*h
1500 = π * [√(100 / π)]^2 * h
1500 = π* (100 / π) * h
1500 = 100h
Clearing the variable (h) height we have:
h = 1500 / 100
h = 15 cm
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East West Distributing is in the process of trying to determine where they should schedule next year's production of a popular line of kitchen utensils that they distribute. Manufacturers form in four different countries have submitted bids to East West. However, a pending trade in bill in Congress will greatly affect the cost to East West due to proposed tariffs, favorable trading status, etc. After a careful analysis, East West has determined the following cost breakdown for the four manufacturers (in $1,000's) on whether or not the trade bill passes: Bill Passes country A 260, country B 320, country C 240, country D 275 Bill Fails country A 210, country B 160, country C 240, country D 210 a. If East West estimates that there is a 40% chance of the bill passing, which country should they choose for manufacturing? b. Over what range of values for the "bill passing" will the solution in part (a) remain optimal?
Over the 0.33 and 0.375 range of values for the "bill passing" will country C remain optimal.
a. To calculate the estimated costs for each country, we must divide the cost by the likelihood of the bill being approved or rejected. Each country's expected cost is computed as follows:
Country A: 0.4 * 260 + 0.6 * 210 = 244
Country B: 0.4 * 320 + 0.6 * 160 = 256
Country C: 0.4 * 240 + 0.6 * 240 = 240
Country D: 0.4 * 275 + 0.6 * 210 = 250
Since country C has the lowest expected cost of $240,000, East West should choose this country for manufacturing.
b. Part a solution will continue to stay optimal as long as the estimated cost for country C is less than the estimated cost for the other countries. This means that if the "bill passing" range is such that country C still has the lowest estimated cost, the solution will remain optimal. To evaluate this range, we can find the "break-even points," which are the points at which the expected costs for country C equal the expected costs for countries A and D. The following is how these break-even points are calculated:
BE (country A) = (210 - 240) / (260 - 210) = 0.375
BE (country D) = (210 - 240) / (275 - 210) = 0.33
This means that as long as the probability of the bill passing is between 0.33 and 0.375, the solution of choosing country C will remain optimal.
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80 percent of students finished their assignment on time. if 30 turned theirs in late, how many total students were in the class?
Answer:
150
Step-by-step explanation:
80% on time so 20% late, 30 late
30/20% = 150
How heavy is 150 pounds? How much does 150 pounds weigh in kilograms? 150 lb to kg conversion.
The conversion of 150 pounds weight in kilograms 68.039.
What is meant by weight?
The gravitational force that pulls a body toward the earth or another celestial body; it is equal to the mass multiplied by the local gravitational acceleration.Weight, which is expressed in newtons, is a unit of measurement for the gravitational force acting on an object. The weight of a bird with a mass of 15 g changes with the strength of the gravitational force acting on it, and would differ significantly if it were measured, for instance, on the Moon rather than on Earth.On Earth compared to the Moon, an object would weigh differently as a result of gravity. The following is an explanation of the weight formula: Weight is calculated as mass multiplied by gravity. W = mg is the formula for this.To learn more about weight refer to
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Can someone PLEASE help me? I don’t understand. Could you please show work?
Answer:
Step-by-step explanation:
Angle ABD plus angle DBC = 90. That's what that little square in the corner there means...a right angle which is 90 degrees. Using substitution,
3x + 15 + 2x = 90 and
5x + 15 = 90 and
5x = 75 so
x = 15. Now we need to plug in 15 for x in 2x to get 2(15) which is 30. Second choice down.
consider the system of equations 2x −5y =1 4x −10y =3 how many solutions does this system have? explain.
Solutions for the system of equations 2x −5y =1 , 4x −10y =3 has no solution as ( 2 /4 ) = (-5/-10) ≠ (1/3) .
Simplify the system of equations to get the solution of the system :
2x - 5y = 1
⇒ 2x = 1 + 5y
⇒ x = ( 1+ 5y ) / 2 __(1)
4x -10y = 3
⇒ 2 ( 2x - 5y ) = 3
⇒2x - 5y = 3/2 ___(2)
Standard form of the system of equations are :
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Substitute the value of x from (1) into (2) we get,
2 ( 1 + 5y )/2 - 5y = 3/2
⇒1 + 5y -5y = 3/2
⇒1 = 3/2
⇒2 = 3 which is not true.
System of the equation has no solution.
Here, ( a₁ /a₂ ) = (b₁ /b₂) ≠ (c₁ /c₂ ) that is ( 2 /4 ) = (-5/-10) ≠ (1/3) .
Therefore, the system of equations has no solution.
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find the following limit or state that it does not exist. x-9
The limit of the function [tex]\lim_{x \to9}[/tex] [( x² - 81 ) / ( x - 9 ) ] is equal to 18.
[tex]\lim_{x \to9}[/tex] [( x² - 81 ) / ( x - 9 ) ]
Substitute the limit x tends to 9 in the function we have,
= ( 9² - 81 ) / ( 9 - 9 )
= ( 81 - 81 ) / 0
= 0 /0
0 /0 form is not defined term.
Simplify the function before substituting the limit we have,
[tex]\lim_{x \to9}[/tex] [( x² - 81 ) / ( x - 9 ) ]
= [tex]\lim_{x \to9}[/tex] [ ( x ² - 9² ) / ( x - 9 ) ]
= [tex]\lim_{x \to9}[/tex] [ ( x - 9 ) ( x + 9 ) / ( x - 9 ) ]
= [tex]\lim_{x \to9}[/tex] ( x + 9 )
= 9 + 9
= 18
Therefore, the value of the limit for the function [tex]\lim_{x \to9}[/tex] [( x² - 81 ) /( x - 9) ] is equal to 18.
The given question is incomplete, I answer the question in general according to my knowledge:
Find the following limit or state that it does not exist.
[tex]\lim_{x \to9} \frac{(x^{2} - 81)}{(x - 9)}[/tex].
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Question 5(Multiple Choice Worth 2 points)
(Translating Algebraic Inequalities MC)
Wyatt had to climb the stairs to ride the waterslide. The top of the waterslide was more than 56 feet from the ground. Which graph represents this inequalit
O
50
50
50
50
51
51
52
52
52
52
53
53
53
53
54
54
54
54
55
55
55
55
56
08
56
57
57
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45
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62
The graph representing the inequality x ≥ 12 is with a closed and shaded circle to the left.
What is inequality ?
An inequality is an expression that shows the non-equal comparison of the two or more numbers and variables. A number line can be used to represent numbers put on regular intervals. A number line is sometimes used to represent an inequality.
The height of the water slide is = 56 feet
The graph representing the inequality x ≥ 12 is shown on the number line begining from 12 with a closed and shaded circle.
Therefore, The graph representing the inequality x ≥ 12 is with a closed and shaded circle to the left.
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The value of the digit 2 in the number 25.381 is 10 times greater then the value of the digit 2 in which of the following numbers
The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in 52.
The correct option is A.
What is a place value?Place value, which is related to a digit's location in a number, is the amount that each digit is worth.
Given:
We have a decimal number 25.381.
From the given choices;
We have number 52.
In the number 52:
The place value of 2 is 2.
The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in 52.
Therefore, the number is 52.
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The complete question:
The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in which of the following numbers:
A) 52.
B) 25534.675
What conditions must be met for the results of an ANOVA test to be reliable?
The conditions that must be met for the results of an ANOVA test to be reliable are Independence , Random Sampling , Large Sample Size and Normality .
The ANOVA (Analysis of Variance) is defined as a statistical method that is used to determine if there are significant differences among the means of two or more groups.
For the results of an ANOVA test to be reliable, the conditions that must be met are :
(i) Independence: The observations within each group should be independent of each other.
(ii) Normality: The data within each group should be approximately normally distributed.
(iii) Random Sampling: The samples within each group should be selected randomly from the population.
(iv) Large Sample Size: The sample size within each group should be large enough to provide a robust estimate of the population mean.
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from largest to smallest, the correct order is:group of answer choicessample, sampling frame, population.
Population - - > Sampling Frame - - > Sample - - > Individual being surveyed is the order from largest to smallest.
The population is the largest as they include all units or subject of interest in a particular study or experiment.
Next is the sampling frame which is the list or compilation of all subjects which can form part of a sample. It is a compilation of all elements in the population from which the sample can be drawn.
The sample is a subset of the population of population, usually selected at random and it is representative of the population.
The individual surveyed represents a single subject or observation from the chosen sample.
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Classify the following triangle. Check all that apply. Angle 120
In the given triangle the length of the two sides of the triangle is equal hence the triangle is an isosceles triangle, and the angle is 120 degree hence the triangle is obtuse triangle.
What is an isosceles triangle?An isosceles triangle is one with two equally sized sides. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
If the sides AB and AC of a triangle ABC are equal, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent," states the theorem that characterizes the isosceles triangle.
In the given triangle the length of the two sides of the triangle is equal hence the triangle is an isosceles triangle, and the angle is 120 degree hence the triangle is obtuse triangle.
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Describe all solution of Ax = b, where A = [2 -5 3 -2 6 -5 -4 7 0] and b = [-3 4 3] Describe the general solution in parametric vector form.
The system has no solution, there is no particular solution x₀, and the general solution does not exist in this case.
The equation Ax = b, where A is a 3x3 matrix and b is a 3x1 column vector, represents a system of linear equations. To find all solutions of this system, we can either use Gaussian elimination or Cramer's rule.
In this case, A = [[2, -5, 3], [-2, 6, -5], [-4, 7, 0]] and b = [[-3], [4], [3]].
Using Gaussian elimination, we can transform the matrix A into its reduced row echelon form and then use back substitution to solve for the variables. The reduced row echelon form of A is:
[[1, 0, 1/2], [0, 1, -5/2], [0, 0, 0]]
Since the last row is all zeros except for the last entry, the system is inconsistent and has no solution.
Alternatively, we can use Cramer's rule to find the solution. The formula for Cramer's rule is:
x_i = det(A_i) / det(A), where A_i is the matrix A with the i th column replaced by the vector b.
In this case, det(A) = 0, so the system has no solution.
The general solution of this system of linear equations is the set of all linear combinations of the columns of A. If the system has a solution, the general solution can be expressed in the parametric vector form as:
x = x₀ + t₁ * v₁ + t₂ * v₂, where x₀ is a particular solution, v₁ and v₂ are the non-trivial solutions, and t₁ and t₂ are scalar parameters.
Since the system has no solution, there is no particular solution x_0, and the general solution does not exist in this case.
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Sales tax is __________ the price
Sales tax is added to the price.
How to complete the blanksFrom the question, we have the following parameters that can be used in our computation:
The statement is about sales tax
As a general rule
sales tax are added to the price of the item that is being bought
So, the complete statement is Sales tax is added to the price.
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A conical cup has a 10-cm diameter and is 12 cm deep. How much can this cup hold? (Continuation) Water in the cup is 6 cm deep. What percentage of the cup is filled? (Continuation)Dana takes a paper cone of the given dimensions,cuts it along a straight line from the rim to the vertex, then flattens the paper out on a table. Find the radius, the arc length, and the central angle of the resulting circular sector.
The radius, the arc length, and the central angle of the resulting circular sector is 13 cm
What is Radius?
A radius of a circle or sphere is any of the line segments connecting its center to its perimeter, and it is also their length in more recent usage. The term is derived from the Latin radius, which means both ray and spoke of a chariot wheel.
1) volume of the cone = 1/3[tex]\pi[/tex][tex]r^{2}[/tex]h
r = radius
h = height or depth
given, D = 10 cm
so r = 5 cm
v = 1/3*22/7*5*5*12
v = 100[tex]\pi[/tex]
2) for up to 6cm height
volume = ?
here in this triangle
triangle ΔAOC and ΔEDC are similar (have some shape as all three angle of both Δ are same
when two figure are similar the ratios of the length of their corresponding sides are equal
here, ΔAOC and ΔEDC
so r = 2.5cm
so volume when cup is 6cm deep
v1 = 1/3[tex]\pi r^{2} h[/tex]
v1 = 1/3 *[tex]\pi[/tex]*2.5*2.5*6
v1 = 12.5[tex]\pi[/tex]
length = [tex]r^{2}+h^{2}[/tex] pythogonus theorem
length = 13cm
arc length = angle (in radius)*radius
2*[tex]\pi[/tex]*5
=10[tex]\pi[/tex]
centre angle = 10[tex]\pi[/tex]/13 radiance
= 10 * 180 Degree/13
=138.46 degree
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9) Refer to the table which summarizes the results of testing for a certain disease.
Positive Test Negative Test
Result Result
Subject has the disease
Subject does not have the disease
111
11
4
172
one of the results is randomly selected, what is the probability that it is a false negative (test
indicates the person does not have the disease when in fact they do)? What does this probability
suggest about the accuracy of the test?
A) 0. 591, The probability of this error is high so the test is not very accurate.
B) 0. 0348, The probability of this error is low so the test is fairly accurate.
C) 0. 0134; The probability of this error is low so the test is fairly accurate.
D) 0. 0369; The probability of this error is low so the test is fairly accurate.
The probability that it is a false negative (test indicates the person does not have the disease when in fact they do) is 0.0348.
This probability indicates that the test's accuracy is 0. 0348; as the likelihood of this inaccuracy is minimal, the test is quite accurate.
The likelihood that a randomly chosen result will be a false negative, meaning that the test will show that the person does not have the condition while in fact they do:
[tex]P(NP|D) = \frac{4}{115} \\\\P(NP|D) = 0.0348[/tex]
We may infer that the occurrence is unlikely to occur and that the test is reasonably accurate because the probability is less than 0.0500.
Probability is simply the possibility that something will happen. When we don't know how something will turn out, we might talk about the possibility of one result or the likelihood of several. The study of occurrences that fit into a probability distribution is known as statistics.
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which of these statements do you think is true?
(a) Exactly one of these statements is false
(b) Exactly two of these statements are false
(c) Exactly three of these statements are false
(d) Exactly four of these statements are false
answer:
a. (a)
b. (b)
c. (c)
d. (d)
All the given options are paradoxical, and it's not possible to determine their truth value as they depend on their own veracity.
The statement "Exactly one of these statements is false" can be referred to as the liar paradox. It is a classic example of self-referential statements, where the truth of the statement depends on its own veracity.
In this paradox, if the statement is true, then it must be false, and if the statement is false, then it must be true. Hence, this statement creates a paradox and it's impossible to determine its truth value.
In the case of options (b), (c), and (d), it's also not possible to determine their truth value as they too depend on the truth value of the other statements, which are paradoxical.
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Cheese burgers= x
Hamburgers= y
y-x= 62
x+y = 588
add both equations
2y=650
y=650/2
y= 325 ---------- hamburgers
cheese burgers
The total number of Cheeseburgers will be 263.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
Cheese burgers= x
Hamburgers= y
y-x= 62
x+y = 588
we add both the equations we get 2y = 650
y=650/2
y= 325
x = 588-325= 263
Hence, The total number of Cheeseburgers will be 263.
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The dot plot represents the distribution of wages earned during a one-week period by 12 collage students.
From the line dot plot of 12 college students wages,
The Mean is $118.25
The Median is $118.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
From the dot plot.
Weekly wages = 112, 113, 116, 116, 116, 118, 118, 119, 119, 124, 124, 124.
Now,
Mean = Sum of all the values / Number of values
= (112 + 113 + 116 + 116 + 116 + 118 + 118 + 119 +119 + 124 +124 +124) / 12
= 118.25
Median = Mid value from the wages.
= 118
Thus,
The Mean is $118.25
The Median is $118.
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The diameter of a cone's circular base measures 10 inches, and the slant height of the cone is 8 inches.
What is the approximate surface area of the cone?
Responses
146.3 in²
146.3 in²
204.1 in²
204.1 in²
314.2 in²
314.2 in²
565.2 in²
The surface area of the cone with a slant height of 8in and diameter of 10in is 204.1 in².
What is the surface area of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The surface area of a cone is expressed as;
A = πrl + πr²
Given that;
Diameter d = 10inRadius = diameter/2 = 10/2 = 5inSlant height h = 8inSurface area A = ?Plug the given values into the above formula and simplify
A = πrl + πr²
A = ( 3.14 × 5 × 8 ) + ( 3.14 × 5² )
A = 125.6 + 78.5
A = 204.1 in²
Therefore, the surface area is 204.1 in²
Option B) 204.1 in² is the correct answer.
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The value of a certain car after t years is modeled by the expresslon 15,000(0. 7)^ What are the initial cost, and the rate of depreciation of this car?
The initial cost of the car was $15,000 and the rate of depreciation is 30%.
The equation [tex]15,000(0.7)^t[/tex] models the value of a car after t years. The value of the car after 0 years, or its initial cost, is [tex]15,000(0.7)^0[/tex] = 15,000. The rate of depreciation can be calculated as 1 - 0.7, which equals 0.3 or 30%. This means that each year, the value of the car decreases by 30% of its previous value. This model assumes a constant rate of depreciation, which may not always reflect real-world situations. However, it provides a simple estimate of the decline in value over time for this car.
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93 x 10 with the power of 3
Answer:93000
—————————————-
ASAP. Need the question soon—25 points given.
Answer:
s=8
Step-by-step explanation:
The two angles are vertical angles and vertical angles are equal.
110 = 8s-2
Add 2 to each side.
110+2 = 8s-2+2
112 = 8s
Divide each side by 8
112/8=8s/8
14=s
select the correct answer .
Which piecewise function is shown on the graph?
A piecewise function which is shown on the graph include the following: A. piecewise function A.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
Based on the graph shown above, we can evaluate the piecewise function based on the following domains (input values or independent values);
For the domain x ≤ -2, the value of y (y-value) is equal to 5. Additionally, for the domain -2 < x < 1,we can logically deduce that the function is a polynomial, which implies that it must have this ordered pair (0, -5):
For -2 < x < 1, when x is equal to 0 and y is equal to -5;
y = x² ± 5
For the domain x ≥ 1, we know that, when y is equal to 0, x would lie between 3 and 4;
y = 2^{x - 2} - 3
When y = 0, the value of x is given by:
0 = 2^{x - 2} - 3
2^{x - 2} = 3
x = 3.584.
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Let x stand for the number of minutes spent waiting in line for a rollercoaster at an amusement park. 81 people are sampled at a time. The sample mean is 18 minutes and the sample standard deviation is 0. 5 minutes.
The population mean (μ) is estimated to be: μ = 18 minutes
In this problem, we are given a sample of 81 people who waited in line for a rollercoaster at an amusement park. We are also given the sample mean (18 minutes) and the sample standard deviation (0.5 minutes).
To estimate the population mean (μ), we use the sample mean (18 minutes). Since the sample mean is a good estimate of the population mean, the estimated population mean (μ) is 18 minutes.
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The expected population mean () is: = 18 minutes.
Additionally, the sample mean (18 minutes) and sample standard variation are provided (0.5 minutes).
We use the sample mean to determine the population mean (). (18 minutes). The expected population mean () is 18 minutes because the sample mean is a reliable indicator of the population mean.