The half-life of an element in the periodic table measured over a period of time, , is modeled by the function . What is the initial amount of the element?
The initial amount of the element is 16
Since, The function is given as:
f(t) = 16(1/2)^t
Now, Set t = 0, to determine the initial amount.
f(0) = 16(1/2)⁰
This gives
f(0) = 16 x 1
Evaluate as
f(0) = 16
Hence, the initial amount of the element is 16
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The management of lamda corporation has received the following forecast for the next year Sales revenue 600,000 Fixed cost 275,000 Variable cost 270,000 Total cost 545,000 Net income 55,000 Capacity is a sales volume of $800,000. (a) Compute (i) The contribution margin (ii) The contribution rate (b) Compute the break-even point (i) In dollars (ii) As a percent of capacity (c) Determine the break-even volume in dollars if fixed cost is increased by $40,000 while variable cost is held to 40% of sales
A. I) The contribution margin of Lamda Corporation, given the forecast for the next year, is $330,000.
A. II) Based on the forecast, the contribution rate is 55%.
B. I) The break-even point in dollars is $500,000.
B. II) The break-even point as a percent of capacity is 62.5%.
C) The break-even volume in dollars if fixed cost is increased by $40,000 while variable cost is held to 40% of sales is $525,000.
How the break-even points and contribution margins are computed:Sales revenue = $600,000
Fixed cost = $275,000
Variable cost = $270,000
Total cost = $545,000
Net income = $55,000
a) Contribution margin = $330,000 ($600,000 - $270,000)
Contribution rate = 55% ($330,000 ÷ $600,000)
b) Break-even point in dollars = Fixed Cost/Contribution rate
= $275,000 ÷ 0.55
= $500,000
Break-even point as a percent of capacity = 62.5% ($500,000/$800,000 x 100)
c) Break-even point in dollars when fixed cost is increased by $40,000 and variable cost held to 40% of sales
Fixed cost = $315,000 ($275,000 + $40,000)
Contribution margin rate = 60% (100 - 40%)
= $315,000÷60%
= $525,000
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Use DeMoivre's Theorem to find the indicated power of the complex number. rectangular form. [2(cos 40 deg + i * sin 40 deg)] ^ 3
The answer is -17.984 + 20.569i in rectangular form using DeMoivre's Theorem with the given complex number.
DeMoivre's Hypothesis is a recipe used to track down the force of a complicated number in polar structure. The hypothesis expresses that for any complicated number z = r(cosθ + I sinθ) and any sure whole number n, we have:
[tex]z^n = r^n(cos(nθ) + I sin(nθ))[/tex]
Utilizing this hypothesis, we can find the demonstrated force of the perplexing number [tex][2(cos 40° + I sin 40°)]^3[/tex] in rectangular structure.
In the first place, we can change the complicated number over completely to polar structure by utilizing the personality:
[tex]cosθ + I sinθ = e^(iθ)[/tex]
In this way, we have:
[tex]2(cos 40° + I sin 40°) = 2e^(i40°)[/tex]
Presently, we can raise this intricate number to the third power utilizing DeMoivre's Hypothesis:
[tex][2(cos 40° + I sin 40°)]^3 = [2e^(i40°)]^3[/tex]
[tex]= 2^3 e^(3i40°)[/tex]
[tex]= 8(cos 120° + I sin 120°)[/tex]
We can now change over this outcome back to rectangular structure:
8(cos 120° + I sin 120°) = 8(-0.5+0.866i)
= -4 + 6.928i
In this way, the showed force of the mind boggling number [tex][2(cos 40° + I sin 40°)]^3[/tex] in rectangular structure is -4+6.928i.
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There is a square with line segments drawn inside it. The line segments are drawn
either from the vertices or the midpoints of other line segments. We colored 1/8 of the
large square. Which one is our coloring?
Find the exact value of sin V in simplest radical form.
The exact value of sin V, in simplest radical form, is √17 / 17.
Since we know the lengths of XV and VW, we can use the Pythagorean theorem to find the length of VX:
[tex]VX^{2}[/tex] = [tex]XV^{2}[/tex] + [tex]VW^{2}[/tex]
[tex]VX^{2}[/tex] = 6^2 + (√32)^2
[tex]VX^{2}[/tex] = 36 + 32
[tex]VX^{2}[/tex] = 68
VX = √68 = 2√17
Now, we can use the definition of sine to find sin V:
sin V = opposite / hypotenuse
In this case, the opposite side is WX, which has length 2. So:
sin V = WX / VX
sin V = 2 / (2√17)
sin V = 1 / √17
To simplify this further, we can rationalize the denominator by multiplying both the numerator and the denominator by √17:
sin V = (1 / √17) * (√17 / √17)
sin V = √17 / 17
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please help algebra homework
Answer: a=9, b=1
Step-by-step explanation:
Let's assume the two numbers as number a, and number b.
a+b= 10
b-a= -8
a= b+8
a= 10-b
a=a
b+8= 10-b
b+b=10-8
2b= 2
b= 1
b= a-8
b= 10-a
b=b
a-8=10-a
a+a=10+8
2a= 18
a= 9
h(x)=-x-3
Complete the function table.
X H(x)
-1
0
1
3
4
The value of the function H(X) is,
H(-1) = -2
H(0) = -3
H(1) = -4
H(3) = -6
H(4) = -7
To complete the function table, we need to evaluate the function H(x) for each value of x:
A function is a mathematical object that takes an input (or inputs) and produces a corresponding output (or outputs) based on a set of rules or instructions. In other words, a function is a relationship between two sets of numbers, where each input corresponds to exactly one output.
The value of the function at different input values are,
H(-1) = -1 -(-1) - 3 = -2
H(0) = 0 -(0) - 3 = -3
H(1) = 1 -(1) - 3 = -4
H(3) = 3 -(3) - 3 = -6
H(4) = 4 -(4) - 3 = -7
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cassie wants to buy a pair of shoes for 16.50 and a shirt for 8.50. If the tax rate is 8% what will be the total amount of cassie's purchase
In the figure below, Z is the center of the circle. Suppose that QR= 13, ST=3x+ 1, ZU=6, and ZV=6. Find the following.
The value of 'x' will be 4. Then the length of QU will be 6.5 units.
Given that:
Chords, QR = 13 and ST = 3x + 1
Perpendicular length, ZU = 6 and ZV = 6
It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The perpendicular length ZU and ZV are the same. Then the length of the chords will be the same. Then we have
QR = ST
13 = 3x + 1
3x = 13 - 1
3x = 12
x = 4
The value of QU is half of QR, then we have
QU = QR / 2
QU = 13 / 2
QU = 6.5
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We spent a lot of time in class focusing on how trigonometric functions combined with different angles produce ratios. Taking all of our conversations from class into consideration, your goal in this question to find the greatest possible ratio possible when finding sine of an angle.
There are two rules you must follow when trying to obtain the largest possible ratio:
O You can only use the digits 1 through 9.
O You can only use each digit once in each of the boxes above.
a. In at least two complete sentences, state your first thought and/or strategy that you are going to use for your first attempt to obtain the largest possible ratio.
b. Now, show all of your work and thought processes in an organized manner that led you to your final answer of what you believe is the largest possible ratio when you find sine of an angle. Your work must include all answers you knew were not the largest possible ratio along with briefly explaining, in words, what guided your next idea(s) to an even larger possible ratio. The use of Desmos is highly encouraged in this problem.
To understand this problem:
a. My first thought is to try to maximize the numerator while minimizing the denominator.
To do this, I can try to use the largest digits (9, 8, 7) in the numerator and the smallest digits (1, 2, 3) in the denominator.
b. To find the largest possible ratio for the sine of an angle, I will start by trying to use the digits 9, 8, and 7 in the numerator and digits 1, 2, and 3 in the denominator.
I will try different combinations until I find the largest possible ratio.
First, I will try 987/321. Using a calculator, I find that sin(987/321) ≈ 0.9984.
Next, I will try swapping the digits in the numerator to see if I can get a larger ratio. I will try 987/231. Using a calculator, I find that sin(987/231) ≈ 0.9999, which is larger than the previous ratio.
Finally, I will try using the digit 6 in the denominator instead of 3, since 6 is closer in value to 7 and 8 than 3. I will try 987/216. Using a calculator, I find that sin(987/216) ≈ 0.9999999955, which is even larger than the previous ratio.
Therefore, I believe that the largest possible ratio for the sine of an angle using the digits 1 through 9, each used once, is approximately 0.9999999955, and it can be obtained with the ratio 987/216.
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From the following table, calculate the correlation coefficient by Karl Pearson's method.
Correlation analysis is meant to determine the strength of a linear
relationship between variables.
A true statement of correlation analysis is that; The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero.
Here, we have,
Reasons:
Correlation analysis is a test to determine the presence and or amount of relationship that exists between variables.
During an hypothesis test aimed at determining the existence of a correlation between variables, the null and alternative hypothesis are as follows;
Null hypothesis, H₀: There are no relationships between the variables
H₀: r = 0
Alternative hypothesis, Hₐ: The variables have an association
Hₐ: r ≠ 0
Therefore, the true statement of the correlation analysis is; The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero.
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How does the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325? Be sure to include what you know about place value in your answer.
The solution is, the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325 is 2700.
Here, we have,
given that,
the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325.
we have,
The value of the digit 3 in the number 63,297 is 3,000 while the value of the digit 3 in the number 60,325 is 300.
we know,
the value of the digit 3 in the number 63,297 = 3000
the value of the digit 3 in the number 60,325 = 300
so, we get,
The difference between value of the digit 3 in the number 63,297 and the value of the digit 3 in the number 60,325 will be:
= 3000 - 300
= 2700
Hence, the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325 is 2700.
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Use the marginal tax rate chart to answer the question.
Marginal Tax Rate Chart
Tax Bracket Marginal Tax Rate
$0–$10,275
10%
$10,276–$41,175
12%
$41,176–$89,075
22%
$89,076–$170,050
24%
$170,051–$215,950
32%
$215,951–$539,900
35%
> $539,901
37%
Determine the amount of taxes owed on a taxable income of $38,520.
$3,852.00
$4,416.90
$4,622.40
$8,474.40
$4,416.90 is the amount of taxes owed on a taxable income of $38,520.
To determine the amount of taxes owed on a taxable income of $38,520, we need to use the marginal tax rate chart to determine the tax owed for each tax bracket, and then add them up.
The first $10,275 of income is taxed at a rate of 10%, which results in a tax of:
$10,275 x 0.10 = $1,027.50
The next $28,245 of income ($38,520 - $10,275) is taxed at a rate of 12%, which results in a tax of:
$28,245 x 0.12 = $3,389.40
Therefore, the total amount of taxes owed on a taxable income of $38,520 is:
$1,027.50 + $3,389.40 = $4,416.90
Therefore, the correct answer is $4,416.90.
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What will be the result of substituting 2 for x in both expressions below?
1/2x+4
x+6-3x-2
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
Both expressions equal 6 when substituting 2 for x because the expressions are equivalent.
One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
The result when substituting 2 for x is: C. one expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
How to Evaluate an Expression?In order to find out the value of the expressions, we have to substitute 2 for x in each of the given expressions, the evaluate it to determine if they are equivalent.
If two expressions have the same value when evaluated, then both are said to be equivalent.
1/2x + 4 = 1/2(2) + 4
= 1 + 4
= 5
x + 6 / 3x - 2
2 + 6 / 3(2) - 2
8 / 4
= 2
Therefore, we can conclude that: C. one expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
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Please help will mark brainiest
Use the red point in your equation. Write your answer using integers, proper fractions, and improper fractions in simplest form.
An equation of the line in point-slope form is y - 7 = 6(x - 4).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.4 7 3 1
First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 7)/(3 - 4)
Slope (m) = -6/-1
Slope (m) = 6
At point (4, 7) and a slope of 6, an equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 7 = 6(x - 4)
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For the set C = {4, 6, 8, 10, 13), determine n(C).
n(C) =
For the set C = {4, 6, 8, 10, 13), the Cardinality or size of the set C is :n(C) =5.
How to find the Cardinality or size of the set C?The cardinality or size of a set C is denoted by the notation n(C). It shows the total number of elements in set C, where each element is distinct and does not occur more than once.
In set C = {4, 6, 8, 10, 13}, there are five distinct elements in which each of this element tend to occur once in the set.
Hence,
Cardinality or size of the set C = 5
OR
n(C) = 5
Therefore n(C) is 5.
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Which is more, 48 ounces or 3 pounds?
Answer:
3 pounds equals 48 ounces because 3x16=48.Apr 29, 2020
PLS MARK BRAINLIEST
Step-by-step explanation:
Answer:
They're the same amount
Step-by-step explanation:
16 oz = 1 pound
48/16 = 3
So 48 oz is 3 pounds
The _______________ states that the distribution of the sample means tend to be approximately normal as sample sizes increase.
Answer:
The Central Limit Theorem states that the distribution of the sample means tend to be approximately normal as sample sizes increase.
Step-by-step explanation:
Which of the following transformations will produce a figure that is similar, but not congruent, to the original figure? (someone help me! Ill give 100 points!)
The transformation that produces a similar figure that is not congruent to the orginal figure would be: A. dilation.
We know that Dilation is a formm of transformation which involves the enlargement or reduction of an image to create a new image that is similar to the original image.
By implication, the new image has becomes different size but the same shape with the original image.
However Dilation produces a figure that is similar but not congruent to the original figure.
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How many monthly payments will it take to pay off the loan?
It will take the college student 14 months to retire the loan. It will take 293 monthly payments to pay off the home loan.
1) It will take him 14 months to retire the loan.
2) It will take 293 monthly payments to pay off the home loan.
The information given in first scenario is
P = $250
A = $3000
r = 2%
Using the formula,
n = - log( 1 - Ar/12P) / log(1+ r/12)
Substituting the values,
n = - log( 1 - (0.02/12)*3000/250) / log(1+ 0.02/12)
n = 13.96
Rounding to the nearest month,
It will take him 14 months to retire the loan.
The information given in second scenario is,
P = $585.80
A = $133000
r = 5%
Using the formula,
n = - log( 1 - Ar/12P) / log(1+ r/12)
Substituting the values,
n = - log( 1 - (0.05/12)*133000/585.80) / log(1+ 0.05/12)
n = 292.43
Rounding to the nearest month,
It will take 293 monthly payments to pay off the home loan.
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what is the volume in cubic feet?
Answer:
120 cubic inches
Step-by-step explanation:
One of the formulas for volume (V) of a triangular prism is V = 1/2bhl, where, where b is the base, h is the height, and l is the length (distance between triangular faces)
Since we know that the base is 6 in., the height is 5 in., and the length is 10 in., we can now find the volume:
V = 1/2(6)(4)(10)
V = 3 * 40
V = 120 cubic inches
Mrs Newton is moving grade levels, she wants to make sure the reading level of her classroom library is
appropriate for her new students. She pulls fifteen books off her old shelf and flips to a random page.
From the page she records the number of upper level of vocabulary words. She repeats this method
after cleaning out her library and adding new books. The results are shown below.
Old Library
New Library
Median: 5
Median: 9
Range: 10
Range: 18
Which of the following statements is MOST LIKELY TRUE?
There is too much variability in Mrs. Newton's new library to draw any inferences from this data.
O Mrs. Newton is likely moving to a higher grade level.
O Mrs. Newton is likely moving to a lower grade level.
O There is no difference between the libraries, so Mrs. Newton needs to continue to update her library.
Based on the given data, it is MOST LIKELY TRUE that Mrs. Newton is likely moving to a higher grade level. This can be inferred because the median number of upper-level vocabulary words in her new library (9) is higher than the median in her old library (5), and the range of the number of upper-level vocabulary words is also greater in her new library (18) compared to her old library (10). These findings suggest that the books in her new library have a higher level of vocabulary and may be more appropriate for older or more advanced readers.
Which of the expressions are equivalent to the one below check all the apply (12 + 3) ÷ 5
The expression is equivalent to the expression (12 + 3) ÷ 5 is (3 + 12) ÷ 5
Which of the expressions are equivalent to the expressionFrom the question, we have the following parameters that can be used in our computation:
(12 + 3) ÷ 5
The above expression is a quotient expression
However, we can apply some algebraic properties
Take for instance;
12 + 3 can be expressed as 3 + 12
So, we have
(12 + 3) ÷ 5 = (3 + 12) ÷ 5
Hence, the expression is equivalent to the expression is (3 + 12) ÷ 5
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What is the linear correlation coefficient and determine if there is a linear relationship between x and y
The linear correlation coefficient is 0.99.
Yes, there is a linear relationship between x and y.
How to determine the linear regression equation and correlation coefficient?In this scenario, the hours worked (x) would be plotted on the x-axis of the scatter plot while the final grade (y) would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the relationship between the hours worked (x) and final grade (y), an equation for the linear regression is given by:
y = 96.49860724 - 2.682451253x
Correlation coefficient, r = -0.9922898032 ≈ 0.99.
In conclusion, there is a strong correlation between the data because the correlation coefficient (r) approximately equals to 1;
0.7＜|r| ≤ 1 (strong correlation)
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the temperature on Monday morning was -2 Fahrenheit it Rose 10° by noon by Tuesday morning the temperature has dropped 14 degrees. What is the temperature on Tuesday morning?
The temperature on Tuesday morning -6 degree Fahrenheit.
We have,
Temperature on Monday = -2 F
At noon on Monday the temperature rose by 10 F
= -2 + 10
= 8 F
Now, on Tuesday the Temperature dropped 14 degrees
= 8 F - 14 F
= - 6 F
Thus, the temperature on Tuesday is -6 degree Fahrenheit.
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Here's another technology that's approaching a critical price. This is a fascinating research from WHO that shows the effect of generic drugs on anti-retroviral drug compounds and cocktails. In January 2000, the price was 10,000 dollars, or 27 dollars a day. The generics came in, first in Brazil and elsewhere, and the effect was just dramatic on pricing. Today it's less than 50 cents a day. And what's interesting is if you look at the price elasticity, if you look at the correlation between these two, as the anti-retrovirals come down, the number of people you can treat goes radically up. And the Clinton Foundation and WHO believe that they can treat three million people worldwide by 2005 -- two million in sub-Saharan Africa. And the falling price of drugs has a lot to do with that. What does the graph show?
What values are on the y- and x-axis?
What is the overall pattern displayed on the graph?
Approximate two points on the graph and write these as ordered pairs. Determine the slope between these two points. Be sure to show the math you used to compute the slope value. Interpret what this slope means as a rate of change between the two variables. Be sure to mention all key points on the graph as presented.
The graph represents the price of anti-retroviral drugs over time. The x-axis likely represents time, while the y-axis represents the price of the drugs.
The overall pattern displayed on the graph is likely a downward trend, showing a decrease in the price of anti-retroviral drugs over time.
Two approximate points on the graph could be (January 2000, $10,000) and (present day, less than $0.50). To find the slope between these two points, we can use the formula:
slope = (change in y) / (change in x)
change in y = (less than $0.50 - $10,000) = -9999.5
change in x = (present day - January 2000) = some positive value
Without knowing the actual values of present day and January 2000, we cannot calculate the exact slope. However, we can see that the slope will be a very large negative value. This means that the price of anti-retroviral drugs is decreasing rapidly over time.
The key point on the graph is the downward trend, which indicates that the price of anti-retroviral drugs is decreasing significantly. This has led to an increase in the number of people who can be treated with these drugs, particularly in sub-Saharan Africa.
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Type the correct answer in the box. Spell all words correctly.
Linda is discussing her interior design ideas for a children’s playroom with her client. What type of drawing will be useful to express her ideas to her client?
Linda can represent the different kinds of spaces she has planned for the playroom through a ________ diagram.
Linda can represent the different kinds of spaces she has planned for the playroom through a floor plan diagram.
What is a floor plan ?The purpose and function of a floor plan, which is an illustration of a room or building's layout viewed from above, and includes walls, windows, doors, furniture, and other objects in the space.
When designing a children's playroom, a floor plan can be useful to indicate various designated areas such as storage, seating, and play spaces, along with the arrangement of fixtures like tables, shelves, and chairs relative to those zones. By utilizing visual references for planning purposes, creating a functional and visually-pleasing play area that caters to the needs of its young inhabitants becomes much more achievable.
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Select all the correct answers.
Which statements are true about function f?
f(x)={1/3x, -x^2+2x-1,
As x approaches positive infinity, f (x) approaches positive infinity.
Function f is continuous.
The value of f (1) is 2.
The domain of function f is all real numbers.
Function f is decreasing over the entire domain.
The correct statement of function is the function is continuous.
We have,
In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
As, functions approach the same value as x approaches 0.
Now, -x² +4x +1 at x= 2 we get
= -4 + 8 +1 = 5
and, 1/2x + 3 = 1+3= 4
So, we reject the statement.
Now, as x increases without bound,
1/2x +3 increases with bound.
Therefore the statement B is true statement.
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complete question:
Which statement is true about function f?
A. The function is increasing over its entire domain
B. The function is continuous
C. As x approaches positive Infinity, f(x) approaches positive infinity
D. The domain is all real numbers
find the variance with the mean score of 161.2 n=5
The variance with a mean score of 161.2 and n=5, assuming scores of 160, 162, 165, 159, and 163, is 4.12.
To work out the difference with a mean score of 161.2 and an example size of 5, we really want to involve the equation for fluctuation:
Difference =[tex](Σ (X - μ)^2)/n[/tex]
Where [tex]Σ (X - μ)^2[/tex] is the amount of squared deviations of each score from the mean, and n is the example size. How about we accept that the scores are as per the following: 160, 162, 165, 159, and 163. In the first place, we work out the deviation of each score from the mean:
160-161.2=-1.2
162-161.2=0.8
165-161.2=3.8
159-161.2=-2.2
163-161.2=1.8
Then, we square every deviation:
[tex](-1.2)^2[/tex] = 1.44
[tex](0.8)^2[/tex] = 0.64
[tex](3.8)^2[/tex] = 14.44
[tex](-2.2)^2[/tex] = 4.84
[tex](1.8)^2[/tex] = 3.24
Then, we total the squared deviations:
1.44 + 0.64 + 14.44 + 4.84 + 3.24 = 24.6
At last, we partition the amount of squared deviations by the example size to acquire the difference:
Change = 24.6/5 = 4.92
In this way, the fluctuation with a mean score of 161.2 and an example size of 5, expecting the scores are 160, 162, 165, 159, and 163, is 4.92.
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The complete question is:
Calculate the mean, variance and standard deviation of final exam scores of 6 students in MAT150.5 course. There are total 25 students. 90 85 74 91 89 (?) (?) = Last two digits of your CUNYFirst ID Number. (05 = 5,00 = 0) X-X (x-x)2.
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Assume that adults have IQ scores that are normally distributed with a mean of μ = 105 and a standard
deviation = 20. Find the probability that a randomly selected adult has an IQ between 90 and 120.
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The probability that a randomly selected adult has an IQ between 90 and 120 is
(Type an integer or decimal rounded to four decimal places as needed.)
The probability that a randomly selected adult has an IQ between 90 and 120 is 0.6554 or 65.54%.
We need to find the probability of an adult having an IQ between 90 and 120.
Using the formula for standardizing a normal distribution:
z = (x - μ) / σ
where x is the IQ score, μ is the mean IQ, and σ is the standard deviation.
For x = 90:
z = (90 - 105) / 20 = -0.75
For x = 120:
z = (120 - 105) / 20 = 0.75
Using a standard normal distribution table or calculator
we can find the area under the curve between z = -0.75 and z = 0.75 to be approximately 0.6554.
Therefore, the probability that a randomly selected adult has an IQ between 90 and 120 is approximately 0.6554 or 65.54%.
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