The radioactive material has a half-life of roughly 11.8 days.
What exactly does half-life mean?The amount of time it takes for an active component of a medication to degrade by half in your body is referred to as the half-life.
Let's apply the exponential decay formula:
N(t) = N0 e(-kt)
Let's calculate the decay constant using the information provided:
At time t=0, the number of counts per minute is N0 = 16000.
At time t=13 days, the number of counts per minute is N(13) = 1000.
When we enter these numbers into the equation, we obtain:
N(13) = N0 e(-k*13)
1000 = 16000 e(-k*13)
e(-k*13) = 1000/16000
When we take the natural logarithm of both sides, we obtain:
ln(e(-k*13)) = ln(1000/16000)
-k*13 = ln(1000/16000)
k = -ln(1000/16000)/13
k ≈ 0.0585
We may use the half-life formula now that we know the decay constant:
t1/2 = ln(2)/k
Substituting k = 0.0585, we get:
t1/2 = ln(2)/0.0585
t1/2 ≈ 11.8
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Diane deposits $70,000 into an account that pays 3% interest per year, compounded annually. Henry deposits $70,000 into an account that also pays 3% per year. But it is simple interest. Find the interest Diane and Henry earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits.
Answer:
Step-by-step explanation:
For Diane's account:
Year 1: Interest = $70,000 x 0.03 = $2,100
Year 2: Interest = ($70,000 + $2,100) x 0.03 = $2,163
Year 3: Interest = ($70,000 + $2,100 + $2,163) x 0.03 = $2,227.89
For Henry's account:
Year 1: Interest = $70,000 x 0.03 = $2,100
Year 2: Interest = $70,000 x 0.03 = $2,100
Year 3: Interest = $70,000 x 0.03 = $2,100
For the first year, both Diane and Henry earn the same interest of $2,100. However, for the second and third years, Diane earns more interest than Henry. Therefore, Diane earns more interest for each year after the first year
how many eggs are in a half dozen
Answer:
6
Step-by-step explanation:
We know that a dozen is the value of 12 so to find half a dozen we simply need to half it!
12 ÷ 2 = 6This means that there are 6 eggs in a half dozen.
FUN FACT:
A baker's dozen is 13, one more than a regular dozen!
Hope this helps, have a lovely day!
how do you simplify 7/8 + 3/4?
Answer:
13/8
Step-by-step explanation:
You first find the lcm of 8 and 4 which is 8
Then make a dividing line (/) with the lcm as the numerator.
After which you start diviing the lcm by each denominator of the two terms, and then multiplying with their numerators:
8/8 x 7 + 8/4 x 3 all over the lcm which is 8
(1 x 7 + 2 x 3)/8
(7 + 6)/8
13/8
Find the standard normal area for each of the following(round your answers to 4 decimal places
With four decimal places added, we have P(2.04 Z 3.04) 0.0189.
Two decimal places are what?To round a decimal value to two decimal places, use the hundredths place, which is the second place to the right of the decimal point.
Subtracting the area to the left of 1.25 from the area to the left of 2.15 will give us the standard normal area between 1.25 and 2.15.
The area to the left of 1.25 is 0.8944, and the area to the left of 2.15 is 0.9842, according to a conventional normal distribution table or calculator.
So, the standard normal area between 1.25 and 2.15 is:
P(1.25 < Z < 2.15) = 0.9842 - 0.8944 = 0.0898
Rounding to four decimal places, we get:
P(1.25 < Z < 2.15) ≈ 0.0898
We follow the same procedure as before to determine the standard normal region between 2.04 and 3.04:
P(2.04 < Z < 3.04) = P(Z < 3.04) - P(Z < 2.04)\
The area to the left of 2.04 is 0.9798, and the area to the left of 3.04 is 0.9987, according to a conventional normal distribution table or calculator.
So, the standard normal area between 2.04 and 3.04 is:
P(2.04 < Z < 3.04) = 0.9987 - 0.9798 = 0.0189
Rounding to four decimal places, we get:
P(2.04 < Z < 3.04) ≈ 0.0189
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plssss helpppppp!!!!
Answer:
2.
a) log base 10 of 100
b) The expression means that 10 to the 2nd power equals 100.
c) 2
3.
4. It would make sense that the value is between 1 and 2 because 10 to the 1st power is 10, and 10 to the 2nd power is 100. 50 is between 10 and 100 so the value would have to be between 1 and 2. This works because logs are the inverse function to exponentiation.
a) 2.6021
b) 3 and the value is exact because the base 10 in the log expression is technically the exponent when you convert it to exponent form. This works because logs are the inverse function to exponentiation. So 10 to the 3rd power would give you exactly 1000.
THE FIRST ANSWER GETS BRAINLIEST AND FIVE STARS!
Parallelogram ABCD is a rhombus with measure EBC = 36. What is the measure of DAE?
picture below
Answer:
54°
Step-by-step explanation:
AB = BC = CD = AD (Because all sides of a rhombus are equal)
Let's consider the triangle DBC:
BC = DC => ∠DBC = 36°
The angle DCB is equal to:
180° - 36*2 = 180° - 72° = 108°
In a parallelogram, opposite angles are equal.
Then the angle DAB = DCB = 108°
Also, we know that the diagonals of a rhombus are the bisectors of the angles from which they come.
So, the angle DAE = EAB = 108° / 2 = 54°
5. Which of the graphs below illustrates water boiling in Denver, Colorado?
Your question is incomplete. The complete question is: Which of the graphs below illustrates water boiling in Denver, Colorado? (Altitude 1,600 meters.)
Answer:
The graphs that come with this question are in the picture attached.The answer is graph identified with the letter A.Explanation:
The normal boiling point of water is 100°C. That is the temperature at which water boils when the atmospheric pressure is 1 atm, i.e. at sea level.
The liquids boil when its vapor pressure equals the atmospheric pressure; so the higher the atmospheric pressure the higher the boiling point, and the lower the atmospheric pressure the lower the boiling point.
Since, it is stated that the altitude of Denver, Colorado is 1,600 m, the atmospheric pressure (the pressure exerted by the column of air above the place) is lower than 1 atm (atmospheric pressure at sea level).
Hence, water boiling point in Denver is lower than 100°C.
The graphs shown represent the temperature (T °C) as water is heated. Since when liquids boil their temperature remains constant during all the phase change, the flat portion of the graph represents the time during which the substance is boiling.
In the graph A, the flat portion is below 100°C; in the graph B, the flat portion is at 100 °C; in the graph C the flat part is above 100ªC, and, in graph D, there is not flat part. Then, the only graph that can illustrate water boiling in Denver, Colorado is the graph A.
it takes 6 painters 4 1/2 to paint these classroom. calculate how long 3 painters will take to complete the same job
Which function is represented by this graph?
A. ƒ(x) = −x² + x − 6
B. f(x) = x² – 5x +6
C. f(x) = -x² + 5x - 6
D. f(x)= x²-x+6
Answer:
Equation of B represents this graph
Let f(X)=x-8 and g(X) =4x^2. Perform the function operation and then find the domain of the result. (f-g)(x)
Answer:
(f - g)(x) = -4x² + x - 8
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
= x - 8 - (4x²)
= -4x² + x - 8
HELP ME I NEED HELP NOW THIS IS TIMED
Answer:
Step-by-step explanation:
If A B C are three matric such that AB=AC such that A=C then A is
Answer:
invertible
Step-by-step explanation:
If A is invertible then ∣A∣ =0
Label each of the following as Discrete Random Variable, Continuous Random Variable, Categorical Random Variable, or Not a Variable. 1. The Name of the people in the car that crosses the bridge Not a Variable 2. The time between each car crossing the bridge Continuous Random Variable 3. The type of cars that cross the bridge Categorical Random Variable 4. The number of cars that use the bridge in one hour Continuous Random Variable Question 2 3 pts Which of these are Continuous and which are Discrete Random Variables? 1. Type of coin Continuous Random Variable 2. Distance from a point in space to the moon Discrete Random Variable 3. Number of coins in a stack Continuous Random Variable
Distance from a point in space to the moon is a continuous random variable and Number of coins in a stack is a discrete random variable.
A discrete random variable is one that has a finite number of possible values or one that can be countably infinitely numerous. A discrete random variable is, for instance, the result of rolling a die because there are only six possible outcomes.
A continuous random variable, on the other hand, is one that is not discrete and "may take on uncountably infinitely many values," like a spectrum of real numbers.
1. The Name of the people in the car that crosses the bridge - Not a Variable
2. Continuous random variable measuring the interval between each car crossing the bridge.
3. The Categorical Random Variable for the type of vehicles crossing the bridge
4. The number of cars that use the bridge in one hour - Continuous Random Variable
For Question 2:
1. Type of coin - Categorical Random Variable
2. The distance from a given location in space to the moon - Continuous Random Variable
3. Number of coins in a stack - Discrete Random Variable
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Complete question is:
Label each of the following as Discrete Random Variable, Continuous Random Variable, Categorical Random Variable, or Not a Variable.
1. The Name of the people in the car that crosses the bridge Not a Variable
2. The time between each car crossing the bridge Continuous Random Variable
3. The type of cars that cross the bridge Categorical Random Variable
4. The number of cars that use the bridge in one hour Continuous Random Variable
Question 2: Which of these are Continuous and which are Discrete Random Variables?
1. Type of coin
2. Distance from a point in space to the moon
3. Number of coins in a stack
solve the quadratic equation 9×^2-15×-6=0
Answer:
To solve the quadratic equation 9×^2-15×-6=0, we can use the quadratic formula, which is given by:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, a = 9, b = -15, and c = -6, so we can substitute these values into the quadratic formula:
x = (-(-15) ± sqrt((-15)^2 - 4(9)(-6))) / 2(9)
Simplifying this expression gives:
x = (15 ± sqrt(225 + 216)) / 18
x = (15 ± sqrt(441)) / 18
x = (15 ± 21) / 18
So the two solutions to the quadratic equation are:
x = (15 + 21) / 18 = 2
x = (15 - 21) / 18 = -1/3
Therefore, the solutions to the quadratic equation 9×^2-15×-6=0 are x = 2 and x = -1/3.
Solve using the correct order of
operations.
P
E
MD
AS
15-(4-3) 2= [?]
Enter
Help
Using the correct order of operations, the value is 13
What is PEDMAS?PEDMAS is simply described as a mathematical acronym that represents the different arithmetic operations in order from least to greatest of application.
The alphabets represents;
P represents parentheses.E represents exponents.D represents division.M represents multiplication.A represents addition.S represents subtraction.From the information given, we have;
15-(4-3)2
solve the parentheses first
15 - (1)2
Multiply the values
15 - 2
Subtract the values
13
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The complete question:
Solve using the correct order of
operations of PEMDAS
15 - (4-3)2
Please help and explain what and why you did to get the answer.
For the equation complete the given ordered pairs.
x = -5
(,4), (, -3), (,0)
The ordered pairs of given equation are (3/2,4), (1/3, -3),(5/6,0)
What is ordered pairAn ordered pair is composed of the ordinate and the abscissa of the x coordinate, with two values supplied in parentheses in a specified sequence. Placing a point on the Cartesian plane could be beneficial for visual comprehension.
for example, the ordered pair (x, y) signifies an ordered pair in which 'x' is referred to as the first element and 'y' is referred to as the second element. These items, which can be either variables , have distinct names depending on the context in which they are used. In an ordered pair, the element order is quite significant.
Given Equation of Y=6x−5
First Ordered pair;(,4)
y=4
x=4+5/6
x=3/2
First Ordered pair;(, -3)
y=-3
x=-3+5/6
x=1/3
First Ordered pair; (,0)
y=0
x=5/6
The ordered pairs of given equation are
(3/2,4), (1/3, -3),(5/6,0)
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The complete question is:
For The Equation, Y=6x−5
Complete The Given Ordered Pairs (,4), (, -3), (,0)
choose 5 objects without replacement from 17 objects
Answer:
6188 ways
Step-by-step explanation:
there ate 5 objects to be choosen and there is no replacement of the object therefore you got
17 choices for the first selection of the object and 16 objects for the selection of the second object and so on until you get 13 objects for the last selection
totally you have 5 selections also arrangement does not matter there fore you have 17!/12!5! which is 6188
note we used 5! cause there are 5 placed objects and 12! are unplaced objects
note
that you have used one so you have to deduct one every time you use one
On the 1st January 2014 Carol invested some money in a bank account.
The total amount of money Carol originally invested is £22,000 in the bank account.
What is compound intrest?Compound interest is interest that is calculated not only on the initial amount of money invested or borrowed, but also on any accumulated interest from previous periods.
This results in exponential growth or accumulation of interest over time.
Let X be the amount that Carol originally invested in the account.
After 1 year, the amount of money in the account will be X(1+0.025) = X(1.025).
After Carol withdrew £1000, the amount of money in the account will be X(1.025) - £1000.
After 2 years (i.e. on 1st January 2016), the amount of money in the account will be (X(1.025) - £1000)(1+0.025) = (X(1.025) - £1000)(1.025).
We know that the amount of money in the account on 1st January 2016 was £23,517.60, so we can write the equation:
(X(1.025) - £1000)(1.025) = £23,517.60
Expanding the left-hand side and simplifying, we get:
X(1.025)² - £1000(1.025) = £23,517.60
X(1.025)² = £24,567.63
Dividing both sides by (1.025)², we get:
X = £22,000 (rounded to the nearest pound)
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The complete question is -
On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?
Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER RIGHT HELP EASY THANK UU
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment.
Answer:
going from left to right:
AA
BD
CB
DC
Hi please help will get max points + brainliest!
The perimeter of the given figures is: Triangle = 4x - 2. Rectangle = 8x - 8, and square = 12x - 8y.
What is perimeter?The whole distance encircling a form is referred to as its perimeter. It is the length of any two-dimensional geometric shape's border or outline. Depending on the size, the perimeter of several figures can be the same. Consider a triangle built of an L-length wire, for instance. If all the sides are the same length, the same wire can be used to create a square.
The perimeter of a figure is the sum of all the segments of the figure.
The perimeter of triangle is:
P = 2x - 5 + x + x + 3 = 4x - 2
The perimeter of rectangle is:
P = 2(l + b)
P = 2(3x + 1 + x - 5)
P = 2(4x - 4)
P = 8x - 8
The perimeter of square is:
P = 4(s)
P = 4(3x - 2y)
P= 12x - 8y
Hence, the perimeter of the given figures is: Triangle = 4x - 2. Rectangle = 8x - 8, and square = 12x - 8y.
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find the slope of a line parallel to the line whose equation is 5x - 6y = 30. fully simplify your answer 
By answering the presented questiοn, we may cοnclude that Since a line equatiοn parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.
What is equatiοn?When twο expressiοns are equal, a mathematical equatiοn is a statement stating that equality. Twο sides are jοined by the algebraic symbοl (=), and tοgether they make up an equatiοn. Fοr instance, the claim that "2x + 3 = 9" means that "2x plus 3" equals the number "9" is made in this argument. Finding the value(s) οf the variable(s) necessary fοr the equatiοn tο be true is the gοal οf sοlving equatiοns.
There are variοus types οf equatiοns, including regular and nοnlinear οnes with οne οr mοre elements. "x² + 2x - 3 = 0" is an equatiοn that raises the variable x tο the secοnd pοwer. Mathematical disciplines like algebra, calculus, and geοmetry all make use οf lines.
the given equatiοn:
[tex]$\begin{array}{c}{{5x-6y=30}}\\ {{-6y=-5x+30}}\\ {{y=(5/6)x-5}}\end{array}$[/tex]
Sο the slοpe οf the given line is 5/6.
Since a line parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.
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5. Based on the data in the table below, what is the probability that a driver aged 45 - 54 was involved in an accident? Express your answer as a percentage, rounded to 2 decimal places.
As a result, the probability of a 45-54-year-old motorist becoming involved in an accident is 5.38%, rounded to two decimal places.
What exactly is probability?Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.
To determine the likelihood that a driver aged 45-54 was involved in an accident, divide the number of drivers in that age group who were engaged in an accident by the total number of drivers in that age group:
Probability = Number of 45-54-year-old drivers involved in an accident / Total number of 45-54-year-old drivers
We can observe that 7 drivers aged 45 to 54 were engaged in an accident, with a total of 130 drivers in that age group:
The probability is 7/130 = 0.0538.
To convert this to a percentage, multiply by 100:
Probability = 0.0538 * 100 = 5.38 percent
As a result, the likelihood of a 45-54-year-old motorist becoming involved in an accident is 5.38%, rounded to two decimal places.
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An aquarium of height 1.5 feet is to have a volume of 12ft^3. Let x denote the length of the base and y the width.
a) Express y as a function of x.
b) Express the total number S of square feet of glass needed as a function of x.
The aquarium has six rectangular faces, four of which are identical (two sides and two ends), and two of which are identical to each other but different from the others (top and bottom).
What is the needed as a function?a) We can use the formula for the volume of a rectangular prism, which is given by V = lwh, where l is the length, w is the width, and h is the height. In this case, we have [tex]V = 12 ft^3 and h = 1.5 ft[/tex] . We want to express y as a function of x, so we need to eliminate w from the equation.
We can rearrange the equation for the volume to get [tex]w = V/(lh)[/tex] , and substitute in h [tex]= 1.5 ft[/tex] :
[tex]w = V/(1.5lx)[/tex]
Now we can substitute y for w to get:
[tex]y = V/(1.5lx)[/tex]
b) To find the total surface area, we need to find the area of each face and add them up.
The area of one of the identical sides or ends is lw, so the total area of these four faces is:
[tex]4lw = 4xy[/tex]
The area of the top and bottom faces is lx, so the total area of these two faces is:
[tex]2lx[/tex]
Therefore, the total surface area S is given by:
[tex]S = 4xy + 2lx[/tex]
We can express y in terms of x using the equation from part a):
[tex]y = V/(1.5lx)[/tex]
Substituting this into the expression for S, we get:
[tex]S = 4x(V/(1.5lx)) + 2lx[/tex]
Simplifying, we get:
[tex]S = (8/3)V/x + 2lx[/tex]
So the total surface area S is a function of x, and we can use this equation to find the value of S for any given value of x.
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Aubrey decides to estimate the volume of a coffee cup by modeling it as a right cylinder. She measures its height as 8.3 cm and its circumference as 14.9 cm. Find the volume of the cup in cubic centimeters
The estimated volume of the coffee cup is approximately 152.8 cubic centimeters.
What is circumference?It is the perimeter of the circle, which can be found by multiplying the diameter of the circle by pi (π), a mathematical constant that is approximately equal to 3.14.
According to question:The volume of a right cylinder is:
V = πr²h
We are given the height of the coffee cup as h = 8.3 cm. To find the radius,
C = 2πr
We are given the circumference of the coffee cup as C = 14.9 cm. Solving for r, we have:
14.9 = 2πr
r = 14.9 / (2π) ≈ 2.372 cm
Now we can substitute these values into the formula for the volume of a cylinder:
V = πr²h
V = π(2.372)²(8.3)
V ≈ 152.8 cubic centimeters
Therefore, the estimated volume of the coffee cup is approximately 152.8 cubic centimeters.
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What is the slope of a line that passes through the points (-2, 3) and (4, -12)?
A human head can be approximated as a sphere with a circumference of 60
centimeters. What is the approximate volume of a human head, rounded to the nearest 1,000
cubic centimeters?(GEOMETRY HELP)
The approximate volume of a human head is 4000 cubic centimeter.
What is the approximate volume of a human head?A sphere is simply a geometrical object that is a three-dimensional analogue to a two-dimensional circle.
The circumference of a sphere is given by the formula:
C = 2πr
Where r is the radius of the sphere. In this case, we are given that the circumference of the sphere (which approximates the human head) is 60 cm, so:
60 cm = 2πr
Solve for r
r = 60/2π
r = 30/π
The volume of a sphere is given by the formula:
V = (4/3)πr³.
Substituting the value we found for r, we get:
V = (4/3) × π × ( 30/π )³
V = (4/3) × π × ( 30/π )³
V = 3647.566 cm³
V = 4000 cm³
Therefore, the volume to the nearest 1,000 cubic cm is 4000 cm³.
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Can you guys help me?
Answer:
[tex]{ \sf{a = \frac{0.012}{0.633 -0.063 } }} \\ \\ { \sf{a = \frac{0.012}{0.57} }} \\ \\ { \sf{a = 0.021 \: (2 \: s.f)}}[/tex]
please help me 25 points
Answer:
7. 300 miles
8. 60 miles
9. 5 miles
10. 1000 meters
Step-by-step explanation:
7.
We Take
60 x 5 = 300 miles
So, Ruth drives 300 miles in 5 hours.
8.
5 miles = 10 minutes
1 mile = 2 minutes
2 hours = 120 minutes
We Take
120 / 2 = 60 miles
So, Carl drive 60 miles in 2 hours
9.
1 hour and 25 minutes = 85 minutes
We Take
85 / 17 = 5 miles
So, Nick travels 5 miles in an hour and 25 minutes.
10.
100 meters = 2 minutes
50 meters = 1 minute
We Take
50 x 20 = 1000 meters
So, Stan swims 1000 meters in 20 minutes.
Answer:
7. 300 miles/hours
8. 60 miles in 2 hours
9. 5 miles in 2 hours and 25 mins.
10. 1000 meters in 20 minutes.
Step-by-step explanation:
7. 60 x 5= 300 miles/hours
8. 5 miles in 10 minutes so in 2 hours it will be 5 x 12 = 60 miles in 2 hours
9. 5 miles in 2 hours and 25 mins.
10. 1000 meters in 20 minutes.
if the volume of a cube is 125 cm what is its surface area
Answer:
150
Step-by-step explanation:
Using the formulas
A=6a2
V=a3
Solving forA
A=6V⅔=6·125⅔ ≈150
Answer:
Step-by-step explanation:
If the volume of a cube is 125 cm³, it means that each side of the cube measures 5 cm (since 5 x 5 x 5 = 125).
To find the surface area of the cube, we need to calculate the area of each of the six faces and add them together.
The area of each face is simply the length of one side squared (or side x side).
So, the surface area of the cube would be:
6 x (5 cm x 5 cm) = 6 x 25 = 150 cm²
Therefore, the surface area of the cube is 150 cm².
Find the standard normal area for each of the following(round your answers to 4 decimal places)
Answer:
(a) 0.0955
(b) 0.0214
(c) 0.9545
(d) 0.3085
Step-by-step explanation:
You want the area under the standard normal PDF curve for intervals (1.22, 2.15), (2.00, 3.00), (-2.00, 2.00), and (0.50, ∞).
CalculatorThe probability functions of a suitable calculator or spreadsheet can find these values for you. The attachment shows one such calculator. Its "normalcdf" function takes as arguments the lower bound and upper bound.
We used 1E99 as a stand-in for "infinity" as recommended by the calculator's user manual. For the purpose here, any value greater than 10 will suffice.
