We may state with confidence that the exponential function y = [tex]3(3^{x} )[/tex]models the provided data because both of these values agree with the data.
How is exponential function determined?
Since the output values (y) increase by a factor of three every time the input value (x) increases by one, the data demonstrate exponential growth. As a result, we can use an exponential function of the form y = a(b)x to represent this data.
We can utilise the first two data points to determine the values of a and b.
With y = 3 and x = 0, we get:
3 = [tex]a(b^{0} )[/tex]
3 = a
With x=1 and y=9, we get:
9 = [tex]a(b^{x} )[/tex]
b = 3
Hence, y = [tex]3(3^{x} )[/tex] is the exponential function that represents the data.
We may substitute the other input values and compare them to the appropriate output values to validate this model:
If x = 2, then y = [tex]3(3^{2} )[/tex] = 27.
If x = 3, then y = [tex]3(3^{3} )[/tex] = 81.
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Select all the expressions that equal 6^{-10}6 −10.
a. 6^{-5} \times 6^{2}6 −5 ×6 2
b. (\frac{1}{6^{2}})^{5}( 6 21 ) 5
c. (6^{-5})^{2}(6 −5 )2
d. \frac{6^{-3}}{6^7}676−3
e. \frac{6^{5} \times 6^{-3}}{6^{-8}}6−865 ×6 −3
Any given expressions in the οptions that simplifies tο -9.9999 are equal tο [tex]6^{-10}\times6 -10[/tex] ( since the expressiοns in the οptiοns are nοt clear, mentiοning the value)
What is Expressiοn?An expressiοn in math is a sentence with a minimum οf twο numbers/variables and at least οne math οperatiοn in it.
An expressiοn that includes variables, cοnstants, and algebraic οperatiοns is knοwn as an algebraic expressiοn in mathematics (additiοn, subtractiοn, etc.). Terms cοmbine tο fοrm expressiοns.
Given expressiοn :
[tex]6^{-10}\times6 -10[/tex]
This simplifies tο -9.9999
Any given expressiοns in the options that simplifies to -9.9999 are equal to [tex]6^{-10}\times6 -10[/tex] ( since the expressions in the οptions are not clear, mentiοning the value)
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For the following Graph, select the answer for the
following questions.
What is the Domain?
What is the Range?
Is it a Function?
-6 -5 -4 -8 -2
O [-2,2]
O(-5,5)
O (-∞0,00)
O(-00, 4]
[-4,3)
No
[0,00)
Yes
20 40 D N +
5+
4+
3
+ N O 40 60
-2
-3
-4--
-5
-61
Domain: [-6,-2], Range: [-4,3) and Function: Yes, this graph can be expressed as a function as it passes the vertical line test.
What is Function?A function is a set of instructions used to perform a specific task. It is a fundamental building block of computer programming, and it is used to create programs that can perform specific tasks. A function is a named block of code that performs a specific task. It can take one or more arguments as input and return a value as output. Functions can be used to divide a large program into smaller, more manageable pieces. Functions are also useful for code reuse, since the same code can be used multiple times within a program. In addition, functions can help improve program efficiency since code does not need to be written multiple times.
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The domain of the original function is [-1, 0) and the range of the original function is [-3, ∞), the domain of the inverse function is [-3, ∞).
What is function?Function is an operation that takes one or more input values and produces one or more output values. It is a mathematical concept that is used in programming to create programs that can be used to solve problems. Functions can be used to organize code blocks into reusable pieces, making it easier to debug and maintain the code. A good example of a function is the mathematical function f(x) = x2, which takes an input value x and produces an output value of x2.
The domain of the inverse of a function is the range of the original function, and the range of the inverse is the domain of the original function. Therefore, since the domain of the original function is [-1, 0) and the range of the original function is [-3, ∞), the domain of the inverse function is [-3, ∞).
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Complete Question is attached below:
Keisha will spend more than 27$ on gifts. So far, she has spent 16$. What are the possible additional amounts she will spend?
Use C for the additional amount (in dollars) Keisha will spend.
Write your answer as an inequality solved for C.
pls give me the answer and how to write it
Keisha will likely spend any sums over $11 as potential extra money. The response is as follows:
C > 11
what is addiction?One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, in addition. This operator is used to combine two or more objects or numbers. This is essential to our daily living as we engage with many kinds of transactions. Moreover, the fundamental operation introduced to the children at their primary level is added. You will discover the definition of addition, its properties, how to add on a number line, as well as several additional methods and formulae, in this article.
from the question:
Let C represent the extra money Keisha will spend (in dollars).
We are aware that Keisha will purchase gifts for more than $27. This can be written as follows:
16 + C > 27
We can take 16 away from both sides of the inequality to solve for C:
C > 27 - 16
C > 11
Hence, all sums over $11 represent potential extra expenditures by Keisha. The response is as follows:
C > 11
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Write the polynomial in factored form. x 3 − 3 x 2 − 10 x show work
Answer:
x(x - 5)(x + 2)
Step-by-step explanation:
[tex]x^3 - 3x^2 - 10x = x(x^2 - 3x - 10)[/tex]
x² - 3x - 10
Now, we look for two integers which when added give (-3) and when multiplied give (-10). The factors are 2 and (-5).
Sum = -3
Product = -10
Factors = 2 , (-5) {2*(-5) = -10 and 2 + (-5) = -3}
x² - 3x - 10 = x² - 5x + 2x - 10 {Rewrite the middle term using the factors}
From the first and second term, take out the common factor 'x' & take out the common factor 2 from the third and fourth term.
= x(x - 5) + 2(x - 5)
= (x -5)(x + 2)
[tex]x^3 - 3x^2 - 10x = x(x -5)(x + 2)[/tex]
8. Calculate the area of the triangle below. A. 25cm² B. D. 16cm² E. - 12cm 24cm² 15cm² 8cm 30⁰ C. 20cm²
The area of the triangle is given as follows:
22.8 ft².
How to obtain the area of a triangle?The area of a triangle of base b and height h is given by half the multiplication of these two dimensions, according to the equation presented as follows:
A = 0.5bh.
From the image given at the end of the answer, the dimensions of the triangle are given as follows:
b = 8 ft.h = 5.7 ft.Hence the area of the triangle is given as follows:
A = 0.5 x 8 x 5.7 = 22.8 ft².
Missing InformationThe triangle from which we are going to calculate the area is given by the image presented at the end of the answer.
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Mr. Golv is practicing his jiu-jitsu drill where he does
5
55 guard passes and
2
22 kimura arm locks. A guard pass takes
G
GG seconds, and a kimura arm lock takes
K
KK seconds
Mr. Golv's total time to complete the jiu-jitsu drill is 7GG + 2KK seconds, where GG is the time taken for guard passes and KK is the time taken for kimura arm locks.
Mr. Golv's total time to complete the jiu-jitsu drill can be calculated as follows:
Guard passes: 5 x GG = 5GG seconds
Kimura arm locks: 2 x KK = 2KK seconds
Total time: 5GG + 2KK = (5 x GG) + (2 x KK) = 7GG + 2KK seconds
Therefore, the total time required by Mr. Golv to complete the jiu-jitsu drill is 7GG + 2KK seconds.
For example, if GG = 10 and KK = 6, then the total time required by Mr. Golv to complete the jiu-jitsu drill is (5 x 10) + (2 x 6) = 50 + 12 = 62 seconds.
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complete question
How much time will Mr. Golv take to complete his jiu-jitsu drill which includes 5 guard passes and 2 kimura arm locks, where a guard pass takes GG seconds and a kimura arm lock takes KK seconds?
In a 3-4-5 right triangle which of the following is closest to the measure of the larger acute angle in the triangle
According to the given information, the measure of the larger acute angle in the 3-4-5 right triangle is approximately 36.87 degrees.
What is 3-4-5 right angle triangle?
A 3-4-5 right triangle is a right triangle where the lengths of the three sides are in the ratio of 3:4:5. In other words, the length of the longest side (the hypotenuse) is 5 times the length of the shortest side, and the length of the remaining side is 4 times the length of the shortest side. This special right triangle has angles of 30 degrees, 60 degrees, and 90 degrees, which are the angles of a 30-60-90 triangle. The sides of a 3-4-5 right triangle can be scaled up or down by any common factor (e.g. 6-8-10, 9-12-15, etc.) and will still form a right triangle with the same angles.
In a 3-4-5 right triangle, the larger acute angle is opposite to the longer leg, which has a length of 4. To find the measure of this angle, we can use the inverse tangent function:
tan(theta) = opposite / adjacent = 3/4
[tex]theta = tan^{-1} (3/4)[/tex]
Using a calculator, we can find that:
theta ≈ 36.87 degrees
Therefore, the measure of the larger acute angle in the 3-4-5 right triangle is approximately 36.87 degrees.
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Type your answer in to the boxes. The three points marked on the graph are the vertices (corners) of a parallelogram Y 10 q 8 5 B 3 2 2 3 5 6 7 8 9 10 X What are the coordinates of the fourth vertex?
The cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).
What is cοοrdinate?A spherical οr elliptical cοοrdinate system knοwn as the geοgraphic cοοrdinate system is used tο measure and transmit pοsitiοns οn Earth as latitude and lοngitude.
First, we can find the distance between pοints Y and q, which will be the same as the distance between pοints 5 and B since they are οppοsite sides οf the parallelοgram:
Distance Yq = [tex]\sqrt{[(10-8)^2 + (5-10)^2] }[/tex]
Distance Yq = [tex]\sqrt{8 + 25 }[/tex]
Distance Yq =[tex]\sqrt{ 33}[/tex]
Distance 5B = [tex]\sqrt{[(3-2)^2 + (2-3)^2] }[/tex]
Distance 5B = [tex]\sqrt{2}[/tex]
Since οppοsite sides are cοngruent, √33 = √2x, where x is the length οf the missing side οf the parallelοgram. Sοlving fοr x, we get:
x = (33/2)
Next, we can find the slοpe οf the line passing thrοugh pοints Y and q,
Slοpe Yq = (10-5)/(8-10) = -5/2
Slοpe B-missing vertex = -5/2
write the equatiοn οf the line passing thrοugh B and the missing vertex:
y - 2 = (-5/2)(x - 3)
Simplifying, we get:
y = (-5/2)x + (19/2)
Therefοre, the cοοrdinates οf the missing vertex are (19/2, x), where x = 2 + (33/2) = 19.5.
Sο the cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).
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PLEASE HELP!!! Using technology, graph these functions and find the solution to the system.
f(x) = x²+x-4
g(x) = -2x2-2x+14
(-2.5, 5) and (1.5, 5)
(-4, 14)
(-3, 2) and (2, 2)
No solution: They do not intersect.
The solution of the functions given will be (-3, 2) and (2, 2) as we can see in graph.
What is the definition of a function?
In mathematics, a function is a rule that associates each element in one set, called the domain, with a unique element in another set, called the range. In other words, a function is a relation between two sets such that each element in the domain is paired with exactly one element in the range.
A function can be represented by an equation, a graph, a table, or a verbal description. The notation f(x) is often used to represent a function, where f is the name of the function and x is the input (or independent variable). The output (or dependent variable) is then given by f(x).
Now,
For functions f(x) = x²+x-4
g(x) = -2x²-2x+14
the graph will be made as shown in image
and their intersection points will be the solution of the given functions
Hence,
The solution of the functions given will be (-3, 2) and (2, 2) as shown in graph.
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whats the missing side lengths !
Answer:
x = 6
y = 3√2
Step-by-step explanation:
tan45 = y / (3√2)
y = (3√2)(tan45) = 3√2
x = (3√2) / cos45 = 6
this is a 45-45-90 isosceles triangle
the graph shows that you are traveling at a constant rate three of the statements are true, which is not
Step-by-step explanation:
Find unit rate :
90 miles in 1.5 hrs
90 /1.5 = 60 miles/hr
that is one mile per minute 20 miles takes 20 minutes
120 miles takes 120 minutes = 2 hours
A project has 4,416 apartments, each apartment has an average of 4 persons what is the total number of residents in the project
The total number of residents in the project is 17,664.
The total number of residents in the project can be calculated by using the following formula:
Number of residents = Number of apartments x Average number of persons per apartment
In this case, the calculation would be:
Number of residents = 4,416 x 4
Number of residents = 17,664
Therefore, the total number of residents in the project is 17,664.
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Determine whether given the coordinates of the vertices. Explain.
P(0,3), Q(0,-1), R(-2,-1), S(1,2), T(1,-2) U(-1,-2)
Question 10 options:
No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU.
Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU.
Yes; Both triangles have an obtuse angle.
No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU
The correct option is No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU.
What is Side-Angle-Side (SAS) criterion?
The Side-Angle-Side (SAS) criterion is a rule used in geometry to determine whether two triangles are congruent, which means they have the same size and shape. The SAS criterion states that if two sides and the angle between them in one triangle are equal to two corresponding sides and the angle between them in another triangle, then the two triangles are congruent. This means that all corresponding angles and sides of the two triangles are equal in length and measure.
To determine whether the two triangles are congruent, we can use the side-angle-side (SAS) congruence criterion. We can see that triangle PQR has sides PQ, QR, and RP, and angle QPR, while triangle STU has sides ST, TU, and US, and angle TSU. We can compare the corresponding sides and angles:
PQ is of length 4, and ST is of length 4.
QR is of length 1, and TU is of length 4.
RP is of length 2, and US is of length 2.
Angle QPR is a right angle, while angle TSU is an acute angle.
Therefore, the two triangles do not have the same corresponding sides and angles, and we cannot conclude that they are congruent.
The correct option is:
No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU.
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In the system shown below, how might multiplying each term in the second equation by 2 help us use elimination to solve the system of equations?
4d + 200m = 450
2d + 400m = 300
The solution to the system of equations is d = 100 and m = 1/4. Multiplying each term in the second equation by 2 helped us to eliminate the variable d and solve for m.
How to Solve a System of Equations by Elimination?To solve the system of equations, we can use the elimination method, which involves adding or subtracting the two equations to eliminate one of the variables.
In this case, if we add the two equations as they are, we won't be able to eliminate one of the variables.
Multiply each term in the second equation by 2, we will get:
4d + 200m = 450
4d + 800m = 600
Now, we can subtract the first equation from the second equation to eliminate d:
(4d + 800m) - (4d + 200m) = 600 - 450
600m = 150
m = 1/4
Substituting this value of m back into either of the original equations, we can solve for d:
4d + 200(1/4) = 450
4d + 50 = 450
4d = 400
d = 100
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If X equals seven what is X times by 7÷2
Answer:
24.5
Step-by-step explanation:
we know that x=7
so 7x/2 (just a fancy way of saying x multiplied by 7/2)=
7*7/2= 24.5
Hope this helps! :)
PLEASE I NEED HELP BADLY
Answer:
Given as steps.
Step-by-step explanation:
Step 2: Transitive Property of Equality
Step 3: SSS Congruency Therom
Step 5: If alt. Interior angles are congruent when two lines are cut by a transversal then the lines are parallel
Step 6: Quadrilateral with opposite sides parallel and congruent is a parallelogram
hope it helps.
A small company has five employees. Let X denote the number of employees absent during a
given week. Suppose the pmf of X is as follows:
X 0 1 2 3 4 5
___________________________________________________
P(x) 0.12 0.15 0.20 0.25 0.19 0.09
Find the probability of the following events.
a) Exactly 3 employees are absent during a given week.
b) At least 3 employees are absent during a given week.
c) At most 3 employees are absent during a given week.
d) At most 2 employees are absent during a given week.
e) Between 2 and 4 employees inclusive are absent during a given week.
f) Strictly between 2 and 4 employees are absent during a given week.
g) More than 3 employees are not absent during a given week.
The probability that exactly 3 employees are absent during a given week is 0.25.
The probability that at least 3 employees are absent during a given week is 0.19 + 0.09 + 0.25 = 0.53.
The probability that at most 3 employees are absent during a given week is P(X ≤ 3) = 0.12 + 0.15 + 0.20 + 0.25 = 0.72.
The probability that at most 2 employees are absent during a given week is P(X ≤ 2) = 0.12 + 0.15 + 0.20 = 0.47.
The probability that between 2 and 4 employees inclusive are absent during a given week is P(2 ≤ X ≤ 4) = 0.20 + 0.25 + 0.19 = 0.64.
The probability that strictly between 2 and 4 employees are absent during a given week is P(2 < X < 4) = 0.25 + 0.19 = 0.44.
The probability that more than 3 employees are not absent during a given week is P(X ≤ 3) = 0.12 + 0.15 + 0.20 = 0.47, and the probability that more than 3 employees are absent during a given week is P(X > 3) = 0.19 + 0.09 = 0.28. The probability that more than 3 employees are not absent is the complement of the probability that more than 3 employees are absent. Therefore, the probability that more than 3 employees are not absent during a given week is 1 - 0.28 = 0.72.
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Consider the random variable X such that X ∼ B(7, p), p < 0. 5, and P(X = 4) = 0. 9724. Find P(X = 2)
The probability of X = 2 can be found using the binomial probability formula, with p ≈ 0.119 obtained by solving for p using the equation P(X = 4) = 0.9724. The resulting probability is approximately 0.193.
We can use the binomial probability formula to find P(X = 2):
P(X = 2) = (7 choose 2) * p² * (1-p)⁽⁷⁻²⁾
We know that P(X = 4) = (7 choose 4) * p⁴ * (1-p)⁽⁷⁻⁴⁾ = 0.9724
Solving for p in this equation, we get p ≈ 0.119
Substituting this value of p in the formula for P(X = 2), we get:
P(X = 2) = (7 choose 2) * 0.119² * 0.881⁽⁷⁻²⁾ ≈ 0.193
Therefore, the probability that X = 2 is approximately 0.193.
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A piano teacher schedules either 30-minute lessons or 60-minute lessons with her students. Last week, the teacher gave 9 lessons which lasted for a total of 7 hours. How many 30-minute lessons did the teacher give last week?
Let's use algebra to solve this problem. Let x be the number of 30-minute lessons that the teacher gave last week, and let y be the number of 60-minute lessons. We know that the teacher gave a total of 9 lessons, so we can write:
x + y = 9
We also know that the total time spent on lessons was 7 hours, which we can convert to minutes:
30x + 60y = 420
Now we have two equations with two unknowns, which we can solve using substitution or elimination. Let's use substitution:
x + y = 9 -> y = 9 - x
30x + 60y = 420 -> 30x + 60(9 - x) = 420
Simplifying and solving for x:
30x + 540 - 60x = 420
-30x = -120
x = 4
Therefore, the teacher gave 4 30-minute lessons last week. To find the number of 60-minute lessons, we can substitute x = 4 into either equation:
x + y = 9 -> y = 9 - x -> y = 9 - 4 -> y = 5
So the teacher gave 5 60-minute lessons last week.
Data are drawn from a bell-shaped distribution with a mean of 120 and a standard deviation of 5. There are 900 observations in the data set. a. Approximately what percentage of the observations are less than 130? (Round your answer to 1 decimal place.) Percentage of observations 0 b. Approximately how many observations are less than 130? (Round your answer to the nearest whole number.) Number of observations
The percentage of observations less than 130 is 97.7%, and the number of observations less than 130 = 879
The question asks about the percentage and number of observations that are less than 130 in a data set that follows a bell-shaped distribution with a mean of 120 and a standard deviation of 5.
a. To find the percentage of observations that are less than 130, we can use the z-score formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
Plugging in the given values, we get:
z = (130 - 120) / 5
z = 10 / 5
z = 2
Using a standard normal table or calculator, we can find that the probability of a z-score being less than 2 is approximately 0.9772. This means that approximately 97.7% of the observations are less than 130.
b. To find the number of observations that are less than 130, we can multiply the percentage by the total number of observations:
Number of observations = 0.9772 * 900
Number of observations = 879.48
Rounding to the nearest whole number, we get that approximately 879 observations are less than 130.
Therefore, the answers are:
a. Percentage of observations less than 130 = 97.7%
b. Number of observations less than 130 = 879
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Consider a Newsvendor problem with a single product that sells at a price of p and costs $3 per item.
Assume that the store holds 5 products and that the demand is a Poison random variable with rate
10€-(P-3)
(a) (6 points) Compute the expected profit if the price if $4.
(b) (10 points) Find the price $p that maximizes the profit.
Type in the answers in the following way: a= ..., b=..; use 2 significant figures when plugging the answers. You can also answer "a=. or "b=..." and get partial grades if the answer is correct.
Based on the given scenario, the expected profit if the price is $4 is $11.91, while the price that maximizes the profit is $5.47.
What is the Newsvendor problem?
The Newsvendor problem is a problem in inventory theory that tries to answer the question of how much inventory should be ordered to maximize profit, given limited shelf space or warehouse space, uncertain product demand, and a fixed order quantity. This problem is often encountered in newspaper, magazine, and perishable food industries, and the answer lies in balancing the risk of stocking out (not having enough inventory to meet demand) with the cost of holding excess inventory.
Newsvendor problem with a single product that sells at a price of p and costs $3 per item. Assuming that the store holds 5 products and that the demand is a Poison random variable with rate 10€-(P-3), let’s answer the two questions.
a. Compute the expected profit if the price is $4.The expected profit (EP) is given by:
EP = Revenue - Cost =
EP = (p*min{Demand, Quantity}) - (3*Quantity)
For the given problem, Quantity is 5, and Demand is a Poison random variable with rate 10€-(P-3). Therefore:
EP(p) = (p*min{Demand, 5}) - (3*5)EP(p)
EP(p) = {p*(1 - exp[-10€-(p-3)] + (5*(1 - exp[-10€-(p-3)]))} - 15.
Using p = $4:
EP(4) = {(4*(1 - exp[-7])) + (5*(1 - exp[-7]))} - 15EP(4)
EP(4) = $11.91
Therefore, the expected profit is $11.91 when the price is $4.
b. Find the price $p that maximizes the profit.The profit function is given by:
P(p) = (p*(1 - exp[-10€-(p-3)] + (5*(1 - exp[-10€-(p-3)]))} - 15
To maximize the profit, we need to take the derivative of the profit function with respect to p, set it equal to zero, and solve for p:
P'(p) = {1 - exp[-10€-(p-3)]} + p*{10€-(p-3)}*exp[-10€-(p-3)] - 5*{10€-(p-3)}*exp[-10€-(p-3)] = 0
Rearranging and using numerical methods to solve for p, we find:
p = $5.47
Therefore, the price that maximizes the profit is $5.47.
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what is the measure of angle DEB?
30,60,120,150 explanation
Answer:30
Step-by-step explanation:
6. Last month, Lucie had total expenditures of $900. The pie chart below breaks down these
expenditures by category. The category in which Lucie's expenditures were greatest is what
percent of her total expenditures, to the nearest 1%?
a. 24%
b. 28%
c. 32%
d. 34%
e. 39%
gas- $120
insurance- $182
clothes- $254
entertainment- $125
food- $219
Answer:
There is no pie chart to answer it
Step-by-step explanation:
the ricoffy tin container no dimensions that container is 2,5 times smaller then what it is in reality the actual weight of coffees 750g , measure the diameter of the diameter of the tin in mm and write down the real diameter in mm
The required diameter of the actual Ricoffy tin container is approximately 92 mm.
Explain about Container.By enclosing units in containers—that is, by circling, boxing, or otherwise enclosing units—container numbers indicate magnitude. The worth of each container's contents is multiplied by the number system's fundamental unit. Typically, the basis is either 2 or 10 (the decimal system) (the binary system).
According to question:Let the diameter of the actual Ricoffy tin container be d mm.
Since the volume of the tin container is proportional to the cube of its dimensions, and the tin container is 2.5 times smaller than its actual size, we have:
[tex]$(\frac{d}{2.5})^3 = \frac{1}{2.5} \times d^3 = \frac{3}{4} \times 750\text{ g} = 562.5\text{ g}$$[/tex]
where we have used the fact that the actual weight of the coffee is 750g.
Solving for d, we get:
[tex]$$d = \sqrt[3]{\frac{562.5\text{ g}}{\frac{1}{2.5}}} \approx 91.98\text{ mm}$$[/tex]
Therefore, the diameter of the actual Ricoffy tin container is approximately 92 mm.
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A restaurant customer left $1.05 as a tip. The tax was 8% and the tip was 15% of the cost including tax.
What was the total bill?
well, the total bill doesn't include the tip, so the total bill is the cost plus the tax.
so assuming the total bill means before tax, let's call it "x", now if we apply the tax to "x", hmmm how much is 8% of "x"?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of x}}{\left( \cfrac{8}{100} \right)x}\implies 0.08x[/tex]
so "x" plus the tax will just be x + 0.08x = 1.08x.
The tip was 15% of that 1.08x, and we happen to know that was $1.05.
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1.08x & 100\\ 1.05& 15 \end{array} \implies \cfrac{1.08x}{1.05}~~=~~\cfrac{100}{15} \\\\\\ 16.2x=105\implies x=\cfrac{105}{16.2}\implies x\approx 6.48[/tex]
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Answer:hello
Step-by-step explanation:
Question 10
Which equation represents the line parallel to the line whose equation is 4x+2) = 14 and
passing through the point (2, 2)?
03²=-2x+6
0y=-2x
Oy-x+1
2 pts
Oy-x
Answer:
First choice, y = -2x+6
Step-by-step explanation:
Convert the original equation to slope-intercept form, where y = mx + b.
We are looking for a parallel line so keep x, y, and the slope. turn the 7 into an intercept variable. Plug in (2,2) for (x,y). Solve for b. b = 6. Rewrite the equation with the same slope and the new y-intercept.
y = -2x + 6
When the mortgage is completely paid off for Mark and Lynne's house, it will be 5 times as old as it is now. If they have 28 years left on the mortgage, how old
is the house right now?
The house is now
years old
Mark and Lynne have 28 years left on their mortgage. To figure out how old their house is right now, we need to divide the remaining years on the mortgage by 5.
This is because when the mortgage is paid off, their house will be 5 times as old. Therefore, 28 divided by 5 is equal to 5.6 years old. This means that the house is currently 5.6 years old. After 28 years, the house will be 33.6 years old.
Mark and Lynne have a mortgage on their house that still has 28 years remaining on it. To figure out the age of the house currently, we need to do a simple calculation. When the mortgage is paid off, their house will be 5 times as old as it is now. Therefore, if we divide the remaining years on the mortgage by 5, we will get the current age of the house. 28 divided by 5 is equal to 5.6 years old. This means that the house is currently 5.6 years old. In 28 years, when the mortgage is paid off, the house will be 33.6 years old. It is important to pay off the mortgage in a timely manner, as this will save Mark and Lynne a lot of money in the long run.
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If A = and B = , find BA
The average amount of time until a car accident on a particular 60 mile stretch of road is 60 minutes. Assume (unreasonably) that car accidents are independent, and that two accidents cannot occur at the same time.
(a) What is the probability of a car accident occurring in the two hours?
(b) What is the probability of a car accident occurring between 45 and 75 minutes?
(c) What is the variance of the time until a car accident occurs?
(d) If a car accident has not happened in 3 hours, what is the probability it will happen in the next two hours?
(a) The probability of a car accident occurring in the two hours is 0.3679.(b) The probability of a car accident occurring between 45 and 75 minutes is 0.3935 (c) The variance of the time until a car accident occurs is 0.0167 d) If a car accident has not happened in 3 hours, the probability it will happen in the next two hours is 0.7385
Since the average rate of car accidents is 1/60 accidents per minute, we can use the Poisson distribution to find the probability:
[tex]P(X = 1) = (e^(-120/60) * (120/60)^1) / 1! = 0.3679[/tex]
So the probability of a car accident occurring in the two hours is 0.3679.
Since the average rate of car accidents is 1/60 accidents per minute, we can use the Poisson distribution to find the probability:
[tex]P(X = 1) = (e^(-30/60) * (30/60)^1) / 1! = 0.3935[/tex], So the probability of a car accident occurring between 45 and 75 minutes is 0.3935.
The variance of a Poisson distribution is equal to the average rate, so the variance of the time until a car accident occurs is: [tex]Var(X) = 1/60 = 0.0167[/tex]Given that no car accident has occurred in the previous 180 minutes. We can use the conditional probability formula to find this probability:
[tex]P(X = 1 | X = 0) = P(X = 1 and X = 0) / P(X = 0) = (e^(-120/60) * (120/60)^1) / (e^(-180/60) * (180/60)^0) = 0.3679 / 0.0498 = 0.7385[/tex]
So the probability of a car accident occurring in the next two hours, given that no car accident has occurred in the previous 3 hours, is 0.7385.
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