The integers are -47, -11, -6, 12, 20 in order of least to greatest.
Explain about the integers?A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.
Positive numbers, negative numbers, and zero make up integers. Thus, integers include 0 through 3, as well as -1, -2, and -3. No further parts, such as fractions or decimals, are allowed in integers. Therefore, fractional and decimal numbers like 3 1/2 and -7.5 are NOT integers.
Integer is derived from the Latin integer, which means whole or untouched, from the prefix in (for "not") with tangere ("to touch"). The words "entire" and "integer" are both derived from the same root, which is the French word entire.
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y = 2x - 2 please help me
Answer: x = − [tex]\frac{y}{2}[/tex] - 1
Steps for solving linear equation.
y = − 2x − 2
Swap sides so that all variable terms are on the left-hand side.
−2x − 2 = y
Add 2 to both sides.
−2x = y + 2
Divide both sides by −2.
[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{y + 2}{-2}[/tex]
Dividing by −2 undoes the multiplication by −2.
x = [tex]\frac{y+2}{-2}[/tex]
Divide y + 2 by −2.
x = -[tex]\frac{y}{2}[/tex] - 1
Graph:
1) ASTU~ASEF
U
39
?
S
12
13
F
E
Answer:
The value of SU is 36
Step-by-step explanation:
Given;∆STU ~ ∆SEFSo,
ST/SE = SU/SF
Here,
ST = 39SF = 12SE = 13SU = ?Let us take SU as x
Now,
ST/SE = SU/SF
39/13 = x/12
3 = x/12
Multiply 12 from both sides we get,
3 × 12 = x/12 × 12
36 = x
x = SU = 36
Thus, The value of SU is 36
ST/SE = SU/SF
39/13 = 36/12 = 3
Answer for ten points!
The simplified expression of 3y + 6x - 2x - 2y is y + 4x.
How to simplify an expression?An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations like addition and subtraction.
To simplify an expression means to write an equivalent expression which contains no similar terms or rewriting the same algebraic expression with no like terms.
Therefore, let's simplify the expression with no like terms as follows;
3y + 6x - 2x - 2y
combine like terms
3y - 2y + 6x - 2x
Therefore, the simplified expression is y + 4x
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a teacher has a grading policy for a group assignment such that each team can earn up to 100 points, which will then be divided between four team members based on the quality of each team member's contribution to the group. this situation would be what type of game for team members?
This situation would be known as a positive-sum game for team members.
In game theory, a scenario is said to as a positive-sum game if the sum of the profits and losses is more than zero. When resources are somehow expanded and a strategy is developed that satisfies the wants and requirements of everyone involved, a positive sum results. One instance would be when two parties engage in a competition and, regardless of the outcome, both sides stand to profit financially. In situations of distributive bargaining, where various interests are discussed in order to satisfy everyone's wants, positive-sum outcomes take place.
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Elevation (meters) -2 , 2 , -4 which is higher ???
Answer:
2
Step-by-step explanation:
-2 and -4 are less than 0
2 is greater than
If you write down in descending order ===> 2, -2 , -4
Determine whether the distribution represents a probability distribution. If not, identify any requirements that are not satisfied.
x P(x)
10.49
20.05
30.32
40.07
50.07
Answer: This is a valid probability distribution.
The P(x) values add to 1; each P(x) is between 0 and 1 inclusive.
============================================================
Further Explanation:
A valid probability distribution is when,
The P(x) values add to 1.Each P(x) value is between 0 and 1 inclusive; i.e. [tex]0 \le P(\text{x}) \le 1[/tex]The given data table is:
[tex]\begin{array}{|c|c|} \cline{1-2}\text{x} & \text{P(x)}\\\cline{1-2}1 & 0.49\\\cline{1-2}2 & 0.05\\\cline{1-2}3 & 0.32\\\cline{1-2}4 & 0.07\\\cline{1-2}5 & 0.07\\\cline{1-2}\end{array}[/tex]
It's fairly clear that rule 2 has been satisfied. Something like [tex]0 \le 0.49 \le 1[/tex] is indeed a true statement. It's like saying 49% is between 0% and 100%. The other P(x) values are similar in nature.
---------
Let's see what the P(x) probability values add to:
0.49+0.05+0.32+0.07+0.07 = 1
We see that rule 1 has been met as well.
Since both rules have been satisfied, this means we have a valid probability distribution.
Solve for the shaded region
The Area of the Shaded Region is 184.61 sq. mm
What is Area?
The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Solution:
Area of the Shaded Region = Area of Rectangle - 2 * Area of Circles
Area of Recatangle = Length * Breadth = 21 * 13 = 273 sq. mm
2 * Area of Circle = 2* πr² = 2 * 22/7 * 7.5/2 * 7.5/2
= 88.39 sq. mm
Area of the Shaded Region = 273 - 88.39 = 184.61 sq. mm
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the manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a variance equal to 1,456. based on this information, what are the chances that the revenue on the first show will exceed $800?
The chances that the revenue on the first show will exceed $800 when mean revenue is $336.25 and standard deviation is $38.16 is essentially zero. i.e. 0
A normal distribution is a type of continuous probability distribution in which the majority of data points cluster in the middle of the range, while the remainder taper off symmetrically toward either extreme. The mean of the distribution is also known as the middle of the range.
The normal distribution is primarily used to calculate the likelihood of an observation in a distribution falling above or below a given value.
Given,
Mean, [tex]\mu[/tex] = 336.25
variance, [tex]\sigma^2[/tex]= 1456
then,
standard deviation, [tex]\sigma = \sqrt{1456}[/tex] = 38.16
To determine the chances that the revenue on the first show will exceed 800 is1:
[tex]1-p(z=\frac{x-\mu}{\sigma})\\\\=1-p(z=\frac{800-336.25}{38.16})\\\\=1-p(z=\frac{436.75}{38.16})\\\\=1-p(z=12.15)\\\\=1-1=0[/tex]
Hence, there is no chance that the revenue will exceed $800 on the first show.
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You are planning a trip to an amusement park with a new water slide. It costs $25
for admittance to the park, plus $5 each time you ride the new water slide. Let w
represent the number of times you go down the slide and c represent the total cost
in dollars.
Write the amount that you will spend as a function of the number of times you
ride the new water slide. What is the total cost if you go down the slide 6 times?
Answer
55
Step-by-step explanation:
5w+25= c
5(6)+25=55
Need help with this equation and graphing table asap!! Look at the image
first 2;
a) 7(2) + 8 = 22 > 16, 7(4) + 8 = 36>32
36 - 22 = 14/2 = 7
32 - 16 = 16/2 = 8
7<8
the table has a greater rate of change
y intercept
equation; 8
table; 0
8> 0
the equation has a greater y intercept
Write the expression as a number in scientific notation.
the quantity 3.6 times ten to the fifth power end quantity times the quantity 1.5 times ten to the negative eighth power end quantity all divided by the quantity 2.5 times ten to the negative fourth power end quantity
2.6 × 107
2.16 × 101
2.16 × 10−1
2.6 × 10−7
The expression is written as a number in scientific notation as 2.16 × 10^1. Option B
What is scientific notation?Scientific notation can be described as a form of expressing or representing large numbers or very small numbers in a more simpler form.
It is also called index form or standard form.
From the information given, we have;
3.6 times ten to the fifth power = 3. 6 × 10^51.5 times ten to the negative eighth power = 1. 5 × 10^82.5 times ten to the negative fourth power = 2. 5 × 10^4Now, let's substitute the values
3. 6 × 10^5 × 1. 5 × 10^8/2. 5 × 10^4
Multiply the decimals and add the powers
5. 4 × 10^5/2. 5 × 10^4
Divide the values and subtract the powers, we get
2. 16 × 10^5-4
2. 16 × 10^1
Hence, the value is 2. 16 × 10^1
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Answer:
The expression is written as a number in scientific notation as 2.16 × 10^1. Option B
Step-by-step explanation:
Jason bought a football for $24. The sales tax rate is 7.5%. What was the price for the football including tax?
Answer:
25.80$
Step-by-step explanation:
Original Price for Football:$24
Rate of Tax:7.5%
[tex]Formula for Tax[/tex]
[tex]\frac{Taxpercent}{100} x 24[/tex]
[tex]\frac{7.5}{100} x24\\=1.80[/tex]
[tex]Tax \\Applied:[/tex]24+1.80=25.80$
Domain:1,2,3,4,5 range:68,71,74,77,80 what is a reasonable domain for this
The reasonable domain for the range: 68,71,74,77,80 is { 1,2,3,4,5 } .
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The collection of all feasible independent variable values is known as the mathematical domain. The set of all independent variable values that are conceivable yet make sense in the context at hand is known as the reasonable domain.
Given:
range: 68,71,74,77,80
Domain:1,2,3,4,5
Here, the situation is not given.
So, the reasonable domain is { 1,2,3,4,5 }
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Find the minimum value of the function f ( x ) = x 2 + 8 x + 9.6 f(x)=x 2 +8x+9.6 to the nearest hundredth.
The maximum and minimum values of the given function will be equal to -1.47 and -6.52.
What is the quadratic equation?The 2nd equation in x is known as a quadratic function. ax² + bx + c = 0 is the quadratic equation in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.
As per the equation given in the question,
f(x) = x² + 8x + 9.6
D = b² - 4ac
= 8² - 4(1)(9.6)
D = 25.6
Now, find the roots,
-(b ± √D)/2a
-(8 ± 5.05)/2
So, the roots are,
-(8 + 5.05)/2 = -1.47, (x + 1.47)
-(8 - 5.05)/2 = -6.52, (x + 6.52)
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13. If f(x)=x² + 3x-2, find f(-2).
By using the substitution property, the value of f(-2) is -4.
What is the substitution property of equality?
In an expression or equation, one value can be substituted for another and the result will still be the same. This is known as the substitution property of equality. If the values of x and y are the same, then x and y can be substituted for one another.
Given, f(x) = x² + 3x - 2
To find the value of f(-2), apply substitution property
f(-2) = (-2)² + 3(-2) - 2 = 4 - 6 - 2 = -2-2 = -4
Hence, the value of f(-2) is -4.
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Question
If a car travels at an average speed of x miles per hour, how far would the car travel in 90 minutes?
Omiles
3 miles
O 2x miles
02 miles
The distance travelled by car in 90 minutes will be 1.5x miles. The correct option is B.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Given that If a car travels at an average speed of x miles per hour. The distance travelled by car in 90 minutes will be calculated as,
x miles ⇒ 1 hours
x miles ⇒ 60 minutes
1 minute ⇒ x / 60 miles
90 minutes ⇒ ( 90x) / 60
90 minues ⇒ 1.5x miles
The missing options are given below.
A. 1.5x miles
B. 3x miles
C. 2x miles
D. 4x miles
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Simplify −2r(−16r + 3r − 18).
Answer: 26r^2 + 36r
Step-by-step explanation:
−2r(−16r + 3r − 18)
32r^2 - 6r^2 + 36r
26r^2 + 36r
Answer:
26[tex]r^2[/tex] + 36r
Step-by-step explanation:
Combine like terms:
-2r(-13r - 18)
Use the distributive property:
-2r(-13r) + (-2r)(- 18)
26[tex]r^2[/tex] + 36r
Jill made a popcorn container that is shaped like a cone. The diameter of the opening is 8 inches and the height is 9 inches. What is the volume of the popcorn container? Leave answer alone, do not round.
Aniyah invests $2300 in one account and $1400 in an account paying 4 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest
The rate of interest in one account whose investment is $2300 will be 3.21%.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Aniyah puts $2300 in one record and $1400 in a record paying 4 % higher interest. Toward the finish of one year, she had procured $130 in interest.
Let 'x' be the interest. Then the equation is given as,
(2300 × x × 1)/100 + (1400 × 4 × 1) / 100 = 130
Simplify the equation, then we have
23x + 56 = 130
23x = 74
x = 3.21%
The pace of revenue in one record whose speculation is $2300 will be 3.21%.
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The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation h = 15 cosine (startfraction pi over 20 endfraction t). How long does it take for the waterwheel to complete one turn?.
The waterwheel takes 40 seconds to make one turn.
To find the period of the function, we need to find the time it takes for the function to repeat itself. In this case, we want to find the time it takes for the waterwheel to complete one turn.
The function h = 15 cos (π/20) t models the height of the cloth in relation to sea level as a function of time.
The cosine function has a period of 2π, so the period of the function h = 15 cos (π/20) t will be 2π divided by (π/20) which simplifies to 40 seconds.
Therefore, it takes 40 seconds for the waterwheel to complete one turn.
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find an equation for a line perpendicular to y=2x-3, passing through the origin.
Billy pulled a number of colored marbles from a large bag. green 1 orange 4 red 1 yellow 9 white 3 Based on experimental probability, how many of the next 20 marbles selected should you expect to be yellow marbles?
The likelihood that the next 20 marbles picked will be yellow marbles is 9/20.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
The probability that of the next 20 marbles selected it is expect to be yellow marbles,
=9/20
The probability that of the next 20 marbles selected it is expect to be yellow marbles will be 9/20.
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Answer:
the answer is 10
Step-by-step explanation:
ixl says its ten
Write the equation of the line that passes through the points (-7,7)(−7,7) and (-2,-6)(−2,−6).
The equation of the line y = - (13 / 5) · x - 56 / 5 passes through the points (x₁, y₁) = (- 7, 7) and (x₂, y₂) = (- 2, - 6).
What is the equation of a line that passes through two points?In this question we must derive the equation for a line that passes through two points on Cartesian plane. This can be done by means of the following two formulas:
Secant line formula
m = Δy / Δx
Equation of the line in slope-intercept form
y = m · x + b
Where:
Δx - Change in the independent variable.Δy - Change in the dependent variable.m - Slope of the lineb - Intercept of the lineFirst, write the given points:
(x₁, y₁) = (- 7, 7), (x₂, y₂) = (- 2, - 6)
Second, determine the slope of the line:
m = (- 6 - 7) / [- 2 - (- 7)]
m = - 13 / 5
Third, calculate the intercept of the equation of the line:
b = y - m · x
b = - 6 - (- 13 / 5) · (- 2)
b = - 6 - 26 / 5
b = - 30 / 5 - 26 / 5
b = - 56 / 5
Fourth, write the resulting equation of the line:
y = - (13 / 5) · x - 56 / 5
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Help me with this question please !!
Answer:
∠1 = 33°∠2 = 47°Step-by-step explanation:
You want to know the measure of angle 1 given that angle 2 is 14° more and their total is 80°.
Angle sum theoremThe angle sum theorem tells you the whole is equal to the sum of the parts.
∠1 +∠2 = ∠ABD
Using the given values, we have ...
∠1 +(∠1 +14°) = 80°
2×∠1 = 66° . . . . . . . . . subtract 14°
∠1 = 33° . . . . . . . . divide by 2
∠2 = 33° +14°
∠2 = 47°
Which of the following is the solution to the following system of inequalities?
x+2y<=4
3x-y>=2
See the picture for the graphs. Any help is appreciated!! This is honors algebra 2 on Apex learning.
Answer: B.
Step-by-step explanation:
x+2y≤4
3x-y≥2
Grace has 2 quartera . Jen have 4 dimesss were ans 1 nickels. Keesha has 3 dimes and 3 nickels. Terry has 1 quarters , 1 dime who has the most money
Answer: grace has the most money
Step-by-step explanation:
Because
Grace has 2 quarters = 50 cents
Jen has 4 dimes and 1 nickel = 45 cents
Keesha has 3 dimes and 3 nickels = 33 cents
Terry has 1 quarter and 1 dime = 26 cents
so as you can see grace has the most money
you are dealt a hand of three cards, one at a time. find the probability that your cards are all face cards.
The probability that your cards are all face cards are,
The first club you get is the third card dealt P = 0.145Your cards are all black [tex]P_{all are black}[/tex] = 0.116You get no hearts [tex]P_{no heart}[/tex] = 0.413You have at least one red card [tex]P_{at least one red}[/tex] = 0.884We know that Total number of cars is 52 .
26 red and 26 is black.
13 are hearts ,
13 are diamonds,
13 are clubs,
13 are spades.
(a) The first club you get is the third card dealt,
Probability P (first club get is the third card dealt) = P(Non-club x Non club x club)
So,
P = [tex]\frac{39}{52} * \frac{38}{51} * \frac{13}{50}[/tex]
P = 0.145
(b) Your cards are all black,
[tex]P_{all are black}[/tex] = [tex]\frac{26}{52} *\frac{25}{51} *\frac{24}{50}[/tex]
[tex]P_{all are black}[/tex] = 0.116
(c) You get no hearts,
[tex]P_{no heart}[/tex] = [tex]\frac{39}{52} *\frac{38}{51} *\frac{37}{50}[/tex]
[tex]P_{no heart}[/tex] = 0.413
(d) You have at least one red card,
[tex]P_{at least one red}[/tex] = 1 - [tex]P_{no red}[/tex]
[tex]P_{no red}[/tex] = [tex]\frac{26}{52} *\frac{25}{51} *\frac{24}{50}[/tex]
[tex]P_{no red}[/tex] = 0.116
[tex]P_{at least one red}[/tex] = 1 - 0.116
[tex]P_{at least one red}[/tex] = 0.884
Therefore,
The probability that your cards are all face cards are,
The first club you get is the third card dealt P = 0.145Your cards are all black [tex]P_{all are black}[/tex] = 0.116You get no hearts [tex]P_{no heart}[/tex] = 0.413You have at least one red card [tex]P_{at least one red}[/tex] = 0.884To learn more about Probability visit :
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Use the tax table below to answer the following question.
A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.
Consider cases where the number of withholding allowances is less than 6. Which will cause the amount of federal income tax withheld to increase?
a.
Gross pay stays the same and withholding allowances increase.
b.
Gross pay increases by more than $20 and withholding allowances stay the same.
c.
Gross pay increases by more than $20 and withholding allowances increase.
d.
Gross pay decreases by more than $20 and withholding allowances stay the same.
Using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.
What is the Percentage?A percentage is a relative figure that has the ability to represent 1/100th of any quantity.
Since 1% denotes one percent, 100 percent and 200 percent indicate the full amount and double the quantity, respectively.
By multiplying by 100 and inserting the "percentage sign"%, a ratio and fraction can be transformed into a percentage.
So, Luce is single and makes $763 twice weekly.
She does not request any compensation from federal withholding.
The value of this amount ranges from $760 to $780.
If we look at the table in the issue, the federal tax for this slab is $86.
Federal taxes now make up 19% of all state taxes.
Hence, the $86 in federal tax at a rate of 19% is:
Tax = 86 * 19/100
Tax = 16.34
Therefore, using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.
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Correct question:
Use the tax table to help answer the following question.
A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.
Luce is single and makes $763 biweekly. She claims no federal withholding allowances. If the state tax is 19% of the federal tax, how much in state tax does Luce contribute?
a. $12.92
b. $15.13
c. $15.77
d. $16.34
Type the correct answer in each box. Use numerals instead of words. If necessary, round to the nearest hundredth.
The relationship between the values of two different currencies is modeled by a linear function that varies depending on the current value of each currency. The table shows the relationship between an amount in U.S. dollars, x, and the equivalent amount in euros, f(x), where f(x) = x/1.06.
The inverse function is given by f⁻¹(x) = 1.06x. 2 euros is equivalent to 2.12 U.S. dollars. 4 euros is equivalent to 4.24 U.S. dollars
How to find the inverse function?Given that: the two different currencies is modeled by a linear function f(x) = x/1.06
where, x = an amount in U.S. dollars and f(x) = the equivalent amount in euros
To find the inverse function f⁻¹(x). Let y = f(x):
y = x/1.06
x = 1.06y
Since x = f⁻¹(y) = 1.06y
Thus, f⁻¹(x) = 1.06x
Note: f⁻¹(x) will help you convert from euros to dollar
2 euros to dollars will be:
f⁻¹(x) = 1.06x
f⁻¹(2) = 1.06(2) = 2.12
Thus, 2 euros is equivalent to 2.12 U.S. dollars
4 euros to dollars will be:
f⁻¹(x) = 1.06x
f⁻¹(4) = 1.06(4) = 4.24
Thus, 4 euros is equivalent to 4.24U.S. dollars
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it has been estimated that about 30% of frozen chickens are contaminated with enough salmonella bacteria to cause illness if improperly cooked. chickens are delivered to grocery stores in crates of 24. assume the chickens are chosen for inclusion in a crate at random. what is the probability that a randomly selected crate has more than 4 contaminated chickens?
Using the binomial distribution, it is found that there is a 0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.
For each chicken, there are only two possible outcomes, either they are contaminated, or they are not. The chickens are independently selected, hence, the binomial distribution is used.
What is the binomial probability distribution formula?
The formula is:
P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ
Cₙ,ₓ = n!/x!(n-x)!
The parameters are:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
In this problem:
About 30% of frozen chickens are contaminated, hence p=0.3.
Chickens are delivered to grocery stores in crates of 24, hence n=24
The probability that a certain crate has more than 4 contaminated chickens is:
P(X>4)=1-P(X≤4)
In which:
P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
Then
P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ
P(X=0) = C₂₄,₀.(0.3)⁰.(0.7)²⁴ = 0.0002
P(X=1) = C₂₄,₁.(0.3)¹.(0.7)²³ = 0.0020
P(X=2) = C₂₄,₂.(0.3)².(0.7)²² = 0.0097
P(X=3) = C₂₄,₃.(0.3)³.(0.7)²¹ = 0.0305
P(X=4) = C₂₄,₄.(0.3)⁴.(0.7)²° = 0.0687
Hence
P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
= 0.0002+0.0020+0.0097+0.0305+0.0687
= 0.1111
0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.
You can learn more about the binomial distribution at brainly.com/question/24863377
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