Answer:
Step-by-step explanation:
Since the side lengths are proportional, the ratio of the width to length in the old phone will be equal to the ratio of the width to length in the new phone. That is:
(width of old phone) / (length of old phone) = (width of new phone) / (length of new phone)
We know the length of the old phone is 1.41.4 inches, and the width is 2.82.8 inches, so we can use that information to solve for the width of the new phone:
(2.82.8 inches) / (1.41.4 inches) = (width of new phone) / (1.611.61 inches)
Cross multiplying, we get:
(width of new phone) = (2.82.8 inches) * (1.611.61 inches) / (1.41.4 inches)
Using a calculator, we can find that the width of the new phone is approximately 3.23.2 inches.
Fatina uses 7.8 pints of white paint and blue paint to paint her bedroom walls 3/5 of this amount is white paint and the rest is blue paint how many pints of blue paint did she use to paint her bedroom walls
Using the fractional value of blue paint to white paint, the number of pints of blue paint Fatina used to paint her bedroom walls is 3.12 pints.
What is a fractional value?A fractional value is a proportional quantity of the whole value.
Fractional values are depicted in decimals, fractions, or percentages.
The total quantity of white and blue paints used on the bedroom walls = 7.8 pints
The fraction of the white paint = 3/5
The fraction of the blue paint = 2/5 (1- 3/5)
2/5 of 7.8 = 3.12 pints
Thus, proportionately, we can conclude that the blue paint Fatina used was 3.12 pints.
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Kathy uses 3.12 pint of white paint to paint her bedroom walls
How many pints of blue paint did she use?Total amount of paint ( Blue and white paint)= 7.8 pints
Amount of blue paint=3/5 x 7.8 = 4.68Pints
amount of white paint = Total amount of paint - amount of blue paint
= 7.6 pints - 4.68 pints
=3.12 pint of white paint
In conclusion, she uses 3.12 pint of white paint to paint her bedroom walls
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\Plot the point (4, −3).
Start at the origin.
Move 4 units
Move 3 units
The point is at ___
Model |
^
On a coordinate plane, point A is 4 units to the left and 3 units up. Point B is 3 units to the left and 4 units up. Point C is 4 units to the right and 3 units up. Pound D is 4 units to the right and 3 units down.
The points A(-4,3) ; B(-3,4) ; C(4,3) ; D(4,-3) are plotted on the graph.
What is meant by a coordinate plane?
Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line which is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.
The given points are
A is 4 units to the left and 3 units up which means A is (-4,3).
B is 3 units to the left and 4 units up which means B is (-3,4).
C is 4 units to the right and 3 units up which means C is (4,3).
D is 4 units to the right and 3 units down which means D is (4,-3).
All these 4 points are plotted on the coordinate plane and the graph is attached below.
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An account earns simple annual interest. $600 at 5% for 2 years
The total amount of interest earned at the end of 2 years is $60.
1. Calculate the interest earned in one year:
Interest = Principal × Rate × Time
Interest = 600 × 0.05 × 1
Interest = $30
2. Multiply the interest earned in one year by the number of years:
Total interest = 30 × 2
Total interest = $60
The total amount of interest earned at the end of 2 years is $60. This amount was earned by taking the principal amount of $600 and multiplying it by the rate of 5%, and then multiplying that product by the number of years, which in this case is 2. This calculation can be expressed as:
Total interest = Principal × Rate × Time
Total interest = 600 × 0.05 × 2
Total interest = $60
the complete question is :
An account earns simple annual interest. $600 at 5% for 2 years. How much interest will be earned on $600 invested at 5% simple annual interest for 2 years?
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HELP FOR 15 Points I SUCK AT MATH
The sum Given it can seen that according to the closure property of Rational numbers the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x.
What is Closure Property of Integers ?
Closure Property of Integers states the sum or subtraction of two integers always gives an integer.
Rational number is defined as a number that can be made by dividing two integers.
Using the definition of rational and expanding the property, we can conclude that the sum of two rational numbers will result in a rational number.
using the closure property and based on the sum given, the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x
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15
Determine if lines a and b are parallel, perpendicular or neither.
(1 Point)
Line a: 2x + y = 10
Line b:
- 6x – 3y = 3
O parallel, they have the same slope
perpendicular, their slopes are opposite reciprocal
neither
parallel, their slopes are opposite reciprocal
perpendicular, their slopes are the same
Both slope are equal so we can say that both lines are parallel
slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").
Line a: 2x + y = 10
Line b:
- 6x – 3y = 3
and line
Line a: 2x + y = 10
= slope of line A is
2x + y = 10
y = -2x+10
slope = -2
- 6x – 3y = 3
-3y = 6x +3
x = -2y -1
slope = -2
in this case both slope are equal so we can say that both lines are parallel
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Indicate the method you would use to prove the two 's . If no method applies, enter "none".
SSS
ASA
SAS
AAS
None
As a result, no particular postulate can be used to demonstrate their congruence due to a lack of adequate data. So "None" is the correct response.
What in mathematics is a similarity?If two figures share the same form, congruent corresponding angles (which means the angles in the same locations of each shape are the same), and identical scale factors, they are said to be "similar figures." Equal scale factors signify a matched ratio between the lengths of their respective sides.
Two triangles can be seen in the illustration, and their corresponding angles are both equal.As a result, they match the AAA similarity requirement. However, no more details are provided to demonstrate their consistency.Although comparable triangles may not be congruent, congruent triangles are known to be similar.To know more about similarity visit:
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Answer: None
Step-by-step explanation: I Just did it
1. suppose a point is to be selected at random from the unit square. write the sample space associated with this random experiment.
a) The x-range of a unit square is from o to 1 and y-range is also from 0 to 1
Sample space = {(x, y)} , 0≤x≤1, 0≤y≤1.
So, sample space associated with this random experiment is
{(x, y)} , 0≤x≤1, 0≤y≤1.
b) From the given data,
Sample space for A : {1, 3, 5, 7, 9, 11,...}
Sample space for B: {5, 10, 15, 20, 25,...}
Therefore, the sample space for A∩B will be the set of all odd natural numbers divisible by 5 which is
{5, 15, 25, 35,....}
c) First letter is the capital letter = 26 Possibilities
then four digits = 9*10*10*10
two lower case letters = 26*26
Total possible ways = 26*9*10*10*10*26*26
= 15,81,84,000 ways.
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Complete question:
Suppose a point is to be selected at random from the unit square. Write the sample space associated with this random experiment. 2. Let S = {0, 1, 2, 3, 4, ...), A = the set of odd natural numbers, and B = the set of natural numbers divisible by 5. What is the set An B? 3. A computer password consists of two lowercase letters followed by a capital letter and four digits. Find the total number of possible passwords.
Cool Down: Bacteria Population
The graph shows the bacteria population on a petri dish as a function of the days d since an
antibiotic is introduced.
number of bacteria
1,000,000
Interpreting Exponential Functions
500,000
(0, 1000000)
(1, 900000)
2
(2, 810000)
4
time in days
6
8
00
10
The approximate value of f(4.5) is 550000.
What is the exponential function?Exponents are used in exponential functions, as the name suggests. But take note that an exponential function does not have a constant as its base and a variable as its exponent (A function is a power function rather than an exponential function if its base is a variable and its exponent is a constant).
From the given graph, the coordinate points are (0, 1000000), (1, 900000) and (2, 810000)
We know that, f(x)=mx+c
Here, (0, 1000000) and (1, 900000)
Now, m=(900000-1000000)/(1-0)
m=-100000/(1-0)
m=-100000
Substitute b=-100000 and (x, y)=(0, 1000000) in y=mx+c
1000000=-100000(0)+c
c=1000000
Substitute m=-100000 and c=1000000 in y=mx+c, we get
y=-100000x+1000000
The approximate value of f(4.5)
Now, y=-100000(4.5)+1000000
y=550000
Therefore, the approximate value of f(4.5) is 550000.
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Anna ate 5/8 of an orange and gave the other 3/8 to her brother.
The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.
5/8 - 3/8 = x
5/8 = 5 ÷ 8
= 0.625
3/8 = 3 ÷ 8
= 0.375
0.625 - 0.375 = x
= 0.25
Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.
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The complete question is
Anna ate 5 8 of an orange and gave the other 3 8 to her brother. Which equation can be used to find the difference between the amount Anna ate and the amount she gave her brother?
A school ordered `3` large boxes of markers. After giving `15` markers to each of `3` teachers, there were `90` markers left
How many markers were originally in each box?
Answer:
135 markers
Step-by-step explanation:
Let's call the number of markers in each large box "x."
After giving away 15 markers to each of 3 teachers, there were 90 markers left, so:
x - (15 * 3) = 90
Expanding the expression on the right side:
x - 45 = 90
Adding 45 to both sides:
x = 135
So, each large box originally contained 135 markers.
the ratio of 9 minutes and 600 seconds in its simplest form
Answer:
Step-by-step explanation:
600 secs=600/60 mins=10 mins
9 mins= 9 mins
Therefore, 9 mins : 600 secs
=9 mins : 10 mins
=9:10
The average daily balance is the mean of the balance in an account at the end of each day in a month. The following table gives the dates and amounts of the transactions in Elliott's account in June.
Day of June Transaction type Transaction amount (in dollars)
1 Starting balance 1223
10 Deposit 615
15 Withdrawal -63
22 Withdrawal -120
There are 30 days in June.
What is the average daily balance of Elliott's account for the month of June?
Answer: 1583.90
In June it’s 1583.90$
the average daily balance of Elliott's account for the month of June is $902.
calculate the average daily balance for Elliott's account in June. To calculate the average daily balance, we need to determine the balance at the end of each day in June. Starting with a balance of $1223 on June 1st, we can calculate the balance at the end of each day by adding or subtracting the amount of each transaction. The table below shows the daily balances: Day of June - Transaction type - Transaction amount -Balance
1 - Starting balance - 1223 - 1223
5 - Deposit - 615 - 1838
8 - Withdrawal - -632 - 1206
9 - Withdrawal - -120- 1086
10 - 30 - No transactions - 0 1086
The sum of the daily balances is: 01086 × 30 = 32580
The average daily balance is the sum of the daily balances divided by the number of days in June:
average daily balance = 32580 / 30 = 902
Therefore, the average daily balance of Elliott's account for the month of June is $902.
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I increased a number by 5% twice how much id it increase by in percent.
Answer:
10%
Explanation:
You increased it by 5% twice, which is basically 5+5 or 5x2 which equals 10
Please help me with this question real quick I didn't understand it if anyone can help please try to
you forgot to put the question
You attempt an obstacle course five times. The table shows the amounts of time that it takes you to complete the course on your first four attempts. For what values of x will you have a mean time no greater than 120 seconds?
Time (seconds)
118 129 120 114 x
The values of x which have a mean time no greater than 120 seconds is 1
What is mean?The mean (means the arithmetic mean, different from the geometric mean) of a data value is the sum of all values divided by the total number of values.
The most commonly used measure of central tendency and referred to as the “average.”
We are given that;
Time =120sec
Table
118 129 120 114 x
Now,
The mean value of the table entry;
Mean=(118+ 129+ 120+ 114+ x)/5
Mean= 481+x/5
481+x/5<120
481+x<600
x<119
Therefore, the values by the mean will not be grater than 120 will be 1
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IM BEING TIMED PLS HURRRYYY
Use factoring to write an expression equivalent to
100x^2-49y^2
SHOW UR WORKKK
The equivalent expression is (10x - 7y)²
What are algebraic expressions?They are defined as expressions that are composed of variables, terms, coefficients, factors and constants.
They are also made up of arithmetic operations.
It is important to note that equivalent expressions are defined as expressions having the same solution but usually differ in the mood of their arrangement.
From the information given, we have that;'
100x^2-49y^2
Find the perfect squares of the values, we have;
(10x - 7y)²
Hence, the expression is (10x - 7y)²
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The quadratic expression 100x² - 49y² is equivalent to (10x - 7y)(10x + 7y)
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
Given the quadratic equation:
100x² - 49y²
Factorizing the polynomial:
100x² + 70xy - 70xy - 49y²
= 10x(10x + 7y) - 7y(10x + 7y)
= (10x - 7y)(10x + 7y)
The expression is equivalent to (10x - 7y)(10x + 7y)
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a rectangular pyramid is sliced so the cross section is perpendicular to its base but does not pass through its vertex. what is the shape of the cross section?
When a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid.
To understand why this is the case, it is helpful to visualize a rectangular pyramid. A rectangular pyramid is a three-dimensional figure with a rectangular base and four triangular faces that meet at a single point at the top, known as the vertex.
If a plane is passed through the pyramid perpendicular to the base but not through the vertex, it will intersect each of the four triangular faces of the pyramid at a different angle, resulting in a cross section that has four sides.
Since the base of the rectangular pyramid is a rectangle, the two opposite sides of the trapezoid cross section will be parallel, and the other two sides will be non-parallel. The shape and size of the trapezoid cross section will depend on the orientation of the plane with respect to the rectangular pyramid.
In summary, when a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid with two parallel sides and two non-parallel sides.
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the general rule of thumb is that it takes a driver 3/4 of a second to percieve the need to stop her car. it then takes another 3/4 of a second to react and move her foot from the accelerator to the brake and begin streeing out of the way. how far will a car traveling at 60 miles per hour travel (in feet) before the driver reacts to an obstacle?
A car traveling at 60 miles per hour will travel distance of 66 feet before the driver reacts to an obstacle.
To convert miles per hour to feet per second, we need to multiply by the conversion factor of 1.4667 (since 1 mile = 5280 feet and 1 hour = 3600 seconds, 5280/3600 = 1.4667).
Therefore, a car traveling at 60 miles per hour is traveling at 88 feet per second.
Using the given reaction time of 3/4 of a second, the distance traveled before the driver reacts is:
distance = rate x time = 88 feet/second x 3/4 second = 66 feet
Hence,
A car traveling at 60 miles per hour will travel a distance of 66 feet before the driver reacts to an obstacle.
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Simplify. -8/9 - (-2/9)
- 8/9 - (-2/9)
The answer I have gotten is -6/9
Zera has a credit limit of $2,000 on her credit card. Each month, she charges about $200 and makes a payment of $125. Estimate the number of months that Zera can continue this pattern until she reaches her limit?
Answer: 80/3 months
Step-by-step explanation:
Let x be the number of months until Zera reaches her limit.
Then on month x, her charges are 200x, and her payments are 125x.
This leaves her with 200x - 125x = 75x dollars owed.
we need to see when this equals 2000, so she hits her limit:
2000 = 75x
.: x = 2000/75 = 80/3
She can continue her pattern for 80/3 months, (≈26.666667)
the coordinates of the endpoints of no are n(5,16) and o(19,9). point p is on no and divides it such that np:op is 4:3. what are the coordinates of p?
The coordinates of point P are (12, 12.5).
to put different elements or individuals in a coordinated effort.
To find the coordinates of point P, we can use the fact that P divides NO into two segments in the ratio of 4:3.
First, we can find the distance between points N and O using the distance formula:
d(NO) = sqrt((19-5)^2 + (9-16)^2) = sqrt(196 + 49) = sqrt(245)
Next, we can use the ratio of 4:3 to determine the distance between P and O:
d(OP) = (3/7) * d(NO) = (3/7) * sqrt(245)
Similarly, we can find the distance between P and N:
d(NP) = (4/7) * d(NO) = (4/7) * sqrt(245)
Now, we can use the midpoint formula to find the coordinates of P:
x-coordinate of P = (x-coordinate of N + x-coordinate of O) / 2 = (5 + 19) / 2 = 12
y-coordinate of P = (y-coordinate of N + y-coordinate of O) / 2 = (16 + 9) / 2 = 12.5
So the coordinates of point P are (12, 12.5).
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What is the standard function of f? F(x)=4(x+6)2+5
The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.
What is the definition of a function?
A function is defined as a connection between a set of inputs and a single output. A function is a link between inputs that corresponds to exactly one output. Every function has a domain, a co-domain, and a range. A function is often denoted as f(x), where x represents the input. The general representation of a function is y = f(x).
There are several types of functions in mathematics. Here are a few examples:
An injective function or a one to one function exists when there is a mapping for a range for each domain between two sets.
Surjective functions, also known as Onto functions, are employed for transferring more than one element from domain to range.
A polynomial function is a function composed of polynomials.
Functions that may be used to inverse another function are known as inverse functions.
Now,
Given function is F(x)=4(x+6)2+5
=(4x+24)2+5
=8x+48+5
=8x+53
hence,
The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.
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pls help me
pls homework
I need help in both questions
The complete question:
A carpet is laid on a rectangular floor of length 12m and breadth 8m. This leaves a margin of width 1m round the carpet. What is the area of the carpet?
Solution:
The area of the carpet laid on a rectangular floor of length 12m and breadth 8m is, 56 meter²
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
The area of the carpet can be calculated by subtracting the area of the margin from the total area of the rectangular floor.
The total area of the floor is:
= 12m x 8m
= 96 square meters.
The area of the margin is:
= 2 x (12m + 8m) x 1m
= 40m.
Therefore, the area of the carpet is:
= 96m² - 40m²
= 56 meter²
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Scatter Plot 8 grades, help please!!!
The of association represented in the graph is positive linear association.
option C
What is a positive correlation?
A positive correlation is a statistical relationship between two variables such that as one variable increases, the other variable also increases, and as one variable decreases, the other variable decreases as well.
In other words, positive correlation means that as the value of one variable goes up, the value of the other variable also goes up, and vice versa. The correlation is said to be positive because both variables move in the same direction.
The strength of the correlation can be measured using a correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation, while a correlation coefficient of 0 indicates no correlation.
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If these two shapes are similar, what is the measure of the missing length h?
In similar triangles, 15.07 miles is the measure of the missing length h .
What does "similarity" for triangles mean?
Triangles are said to be comparable if two of their angles have measurements that are the same as those of two other triangles' angles. In proportion, and with the same measure, are the equivalent sides and angles of identical polygons.
To test whether two triangles are similar, use one of the three triangle similarity theorems, Angle-Angle (AA), Side-Angle-Side (SAS), or Side-Side-Side (SSS).
35/65 = 28/h
h = 35 * 28/65
h = 15.07 miles
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An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle?
(A) 30√2 m
(B) 45 m
(C)30√3 m
(D)60√3 m.
The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.
We have,
In an equilateral triangle,
- all three sides are of equal length
- the altitude drawn from any vertex bisects the opposite side into two equal segments, forming a right triangle.
Let's denote the side length of the equilateral triangle as "s."
When an altitude is drawn, it bisects the base into two equal segments, each measuring "s/2."
The altitude forms a right triangle with the base, where one leg is the altitude (15 m) and the other leg is half of the base (s/2).
So,
Using the Pythagorean theorem, the value of "s":
s² = (s/2)² + 15²
s² = s²/4 + 225
4s² = s² + 900
3s² = 900
s² = 300
s = √300 = 10√3
Now,
Perimeter = 3 * side length
Perimeter = 3 * 10√3
Perimeter = 30√3 meters
Thus,
The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.
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10-1/2x<-18 which inequality represents the solution to this inequality?
The solution for inequality 10 - 1/2x < -18 is 0 < x < 1/56.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The given inequality is -
10 - 1/2x < -18
Solve the inequality to get the value for x.
First collect all the like terms -
-1/2x < -18 + (-10)
Then use arithmetic operation of addition -
-1/2x < -28
Multiply (-1) to both the sides -
-1/2x × (-1) < -28 × (-1)
1/2x < 28
Then move the coefficient of variable to right hand side of the equation -
x < -1 / (2 × (-28))
Then use arithmetic operation of multiplication and division-
x < 1/56
Therefore, the inequality is 0 < x < 1/56.
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Farmer Quect started with 110 rews on his farm. Every hour, he destoryed 6 more of them. Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them?
Write a systems of equations in slope intercept form. Farmer's rews (y), hours (x)
The systems of equations in slope intercept form is
y = -6x + 110
y = 9x + 54
What is Slope- intercept form?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
As, We know Slope-intercept form is
y = mx + b
where b is the starting value and m is the change per day.
Farmer Quect started with 110 rews on his farm. Every hour he destroyed 6 more of them.
So, the Equation to show the Situation
y = -6x + 110
and, Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them.
So, the Equation to show the Situation
y = 9x + 54
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Clinton borrows a certain amount of money and pays the principle amount and the interest back after 5 years. Calculate the simple interest rate if Clinton pays back double the amount he borrowed
Answer: The simple interest will be 20%.
Step-by-step explanation:
we know the simple interest of borrowed amount is:
S.I.= (P x R x T)/100 ..... (i)
where P⇒ Principal amount
R⇒ rate of interest
T⇒ time
and
total Pays Back amount = Principal amount + S.I.
Hence S.I. = Pays Back amount - Principal amount
Now, as per the question: Clinton pays back Double of the amount hi borrowed. Means
if Principal amount = P
then Pays Back amount = 2P ⇒ S.I.= P
Rate of Interest = R
and Time = 5 years
P= (P x R x 5)/100
R= 100/5
R = 20%
Therefore, the simple interest is 20% annually.
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the weight distribution of packages sent in a certain manner is normal with mean value 12 lb and standard deviation 3.5 lb. the package service wishes to establish a weight value c beyond which there will be a surcharge. what value of c is such that 99% of all packages are at least 1.0 lb under the surcharge weight?
The surcharge weight should be set at 12.25 lb, since 99% of all packages are at least 1.0 lb under this weight.
In this problem, we are given that the weight distribution of packages sent in a certain manner is normal, with a mean value of 12 lb and a standard deviation of 3.5 lb. The standard deviation is a measure of how much the data varies from the mean.
Now, the package service wishes to establish a weight value c, beyond which there will be a surcharge. We want to find the value of c such that 99% of all packages are at least 1.0 lb under the surcharge weight. This means that we are looking for a weight value that is exceeded by only 1% of all packages.
To find this weight value, we can use the properties of the normal distribution. We know that the area under the normal curve represents the probability of an event occurring. In this case, we want to find the weight value c that corresponds to the 1% probability.
To do this, we first need to standardize our normal distribution by converting it to the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can do this by subtracting the mean (12 lb) from our target weight value c, and then dividing by the standard deviation (3.5 lb). This gives us a z-score, which represents the number of standard deviations away from the mean our target weight value is.
Next, we can use a standard normal distribution table or calculator to find the z-score that corresponds to the 1% probability. This is approximately -2.33.
Finally, we can solve for c by reversing the standardization process. We multiply the z-score (-2.33) by the standard deviation (3.5 lb) and add the mean (12 lb) to get our target weight value c.
Therefore, c = -2.33 x 3.5 + 12 ≈ 0.25 lb.
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