Answer:
A) μ = 91.2; σ = 9.3
B) No
Step-by-step explanation:
To find the mean, μ, we use the formula
μ = np, where n is the sample size and p is the probability of success (percentage of times the letter is used).
This gives us
μ = 0.057(1600) = 91.2
To find the standard deviation, we use the formula
σ = √(np(1-p)
This gives us
σ = √(1600×0.057×(1-0.057))
= √(1600×0.057×0.943) = √86.0016 = 9.2737 ≈ 9.3≈
Any value that is more than two standard deviations from the mean is considered unusual. The value 102 is
(102-91.2)/9.3 = 10.8/9.3 = 1.16 standard deviations from the mean. This is not statistically unusual.
Calculations were made based on standard English language letter frequencies to establish a mean and a standard deviation for a set number of letters. In this example, an occurrence was not considered unusual as it was within one standard deviation of the mean.
Explanation:The subject revolves around probability and statistics and involves the calculation of the mean and standard deviation, and understanding of what might be considered an unusual result in a statistical sense.
In standard English text, a particular letter is used at a rate of 5.7%. This means on average, the letter will appear approximately 5.7% of the time. If each page consists of 1600 characters, then the mean (Μ) number of times that this letter will appear on a page can be calculated by multiplying the total characters by the usage rate (1600 * 0.057 = 91.2).
The standard deviation (sigma) is given as 9.3. This measure shows the dispersion or how spread out the numbers are from the mean.
In the intercepted message, the letter occurred 102 times. To determine if this is unusual, we look at how many standard deviations away from the mean this number falls. If it falls within 2 standard deviations (2 * 9.3 = 18.6) of the mean, it is not unusual. 102 is approximately one standard deviation above the mean (102 - 91.2 = 10.8), therefore, it is not considered an unusual occurrence.
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Use the x-intercept method to find all real solutions of the equation.
x^3-8x^2+9x+18=0
Answer:
a. [tex]x=-1,3,\:or\:6[/tex]
Step-by-step explanation:
The given equation is;
[tex]x^3-8x^2+9x+18=0[/tex]
To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator or software.
The corresponding function is
[tex]f(x)=x^3-8x^2+9x+18[/tex]
The solution to [tex]x^3-8x^2+9x+18=0[/tex] is where the graph touches the x-axis.
We can see from the graph that; the x-intercepts are;
(-1,0),(3,0) and (6,0).
Therefore the real solutions are:
[tex]x=-1,3,\:or\:6[/tex]
Answer:
Use a graphing utility or a graphing calculator.
x = -1, 3, 6. (3 real solutions).
Step-by-step explanation:
The points of intersection on the x axis are the 3 solutions to the equation.
Identify the area of the trapezoid. Please help!
Answer:
[tex]\large\boxed{A=46x\ m^2}[/tex]
Step-by-step explanation:
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]
b₁, b₂ - bases
h - height
We have
b₁ = 12m , b₂ = 6.4 m, h = 5x m.
Substitute:
[tex]A=\dfrac{12+6.4}{2}\cdot5x=\dfrac{18.4}{2}\cdot5x=9.2\cdot5x=46x[/tex]
The correct option is a) [tex]\large\boxed{A=46x\ m^2}[/tex]
The formula of an area of a trapezoid:
[tex]A=(b_1+b_2)/(2)\cdot h[/tex]
b₁, b₂ - bases
h - height
We have
b₁ = 12m , b₂ = 6.4 m, h = 5x m.
Substitute:
[tex]A=(12+6.4)/(2)\cdot5x=(18.4)/(2)\cdot5x=9.2\cdot5x=46x[/tex]
Jon makes a map of his neighborhood for a presentation. The scale of his map is 1 inch:125 feet. How many feet do 4 inches
represent on the map? Answer-500 feet ( I just need help on the problem below)
From the problem above Jon lives 250 feet away from Max. How many inches separate Jon’s home from Max’s on the map? Show your work.
Answer:
Part A) [tex]500\ ft[/tex]
Part B) [tex]2\ in[/tex]
Step-by-step explanation:
we know that
The scale of the map is [tex]\frac{1}{125} \frac{in}{ft}[/tex]
That means
1 in on the map represent 125 ft in the real
Part A) How many feet do 4 inches
using proportion
[tex]\frac{1}{125} \frac{in}{ft}=\frac{4}{x} \frac{in}{ft}\\ \\x=125*4\\ \\x=500\ ft[/tex]
Part B) Jon lives 250 feet away from Max. How many inches separate Jon’s home from Max’s on the map?
using proportion
[tex]\frac{1}{125} \frac{in}{ft}=\frac{x}{250} \frac{in}{ft}\\ \\x=250/125\\ \\x=2\ in[/tex]
Jon's home is 2 inches from Max's on the map, according to the scale of 1 inch:125 feet, considering Jon lives 250 feet from Max.
Explanation:To find out how many inches separate Jon's home from Max's on the map, we need to apply the given scale of the map which is 1 inch:125 feet. Since Jon lives 250 feet away from Max, we can set up a proportion to solve for the distance on the map as follows:
1 inch / 125 feet = x inches / 250 feet
Cross-multiply to solve for x:
125x = 1 * 250
125x = 250
Now, divide both sides by 125 to isolate x:
x = 250 / 125
x = 2
So, Jon's home is 2 inches from Max's on the map.
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 4x − y = −5 12x − 3y = 15 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Answer:
NO SOLUTION.
Step-by-step explanation:
4x - y = -5
12x - 3y = 15
Multiply the first equation by 3:
12x - 3y = -15
Note that the left side of this equation is the same as the left side of the second one, but the right sides are different. The left side cannot be equal to 2 different values. Therefore there is NO SOLUTION.
Note if we subtract the last 2 equations we get:
0 = 30 which is, of course, absurd.
If you double a number and then add 8, you get fourteen more than the original number. What is the original number?
Answer: 6
Step-by-step explanation: The formula to solve this is 2x + 8 = x + 14
First, you need to subtract x from each side:
X + 8 = 14
Next, subtract 8 from each side:
X = 6
Final answer:
To find the original number, we can solve the equation 2x + 8 = 14 + x.
Explanation:
To solve this problem, let's represent the original number as 'x'.
If you double the number, it becomes 2x. If you then add 8 to it, the equation becomes: 2x + 8 = 14 + x.
To isolate 'x' on one side of the equation, we subtract 'x' from both sides: 2x - x = 14 - 8.
This simplifies to: x = 6.
So, the original number is 6.
Find the following measure for this figure.
Slant height =
15.6 units
13 units
2√(11) units
Answer: second option.
Step-by-step explanation:
Let's represent the slant height of the figure with: [tex]l[/tex]
Then, to find the value of the slant height you must apply the Pythagorean Theorem, where:
[tex]l[/tex] is the hypotenuse and the other legs are 12 units and 5 units ([tex]\frac{10units}{2}=5units[/tex])
Therefore, you obtain that the slant height of the figure is the shown below:
[tex]l=\sqrt{(5units)^2+(12units)^2}\\l=13units[/tex]
Answer:
The correct answer is Slant height =13 units
Step-by-step explanation:
From the figure we can see a square pyramid
Points to remember
Hypotenuse² = Base² + Height²
To find the slant height
Fro figure we can see a right angles triangle with,
Base = 10/2 = 5 units and Height = 12 units
We have to find Hypotenuse (Slant height)
Hypotenuse² = Base² + Height²
Slant height² = 5² + 12² = 25 + 144 = 169
Slant height = √169 = 13 units
Therefore the slant height = 13 units
Identify the area of the kite. Please help!!
Answer:
[tex]\large\boxed{A=480\ m^2}[/tex]
Step-by-step explanation:
The formula of an area of a kite:
[tex]A=\dfrac{d_1d_2}{2}[/tex]
d₁, d₂ - diagonal
Look at the picture.
Use the Pythagorean theorem.
[tex]x^2+5^2=13^2[/tex]
[tex]x^2+25=169[/tex] subtract 25 from both sides
[tex]x^2=144\to x=\sqrt{144}\\\\x=12\ m[/tex]
Therefore d₁ = (2)(12 m) = 24 m.
[tex]y^2+12^2=37^2[/tex]
[tex]y^2+144=1369[/tex] subtract 144 from both sides
[tex]y^2=1225\to y=\sqrt{1225}\\\\y=35\ m[/tex]
Therefore d₂ = 5 + 35 = 40 m.
Substitute:
[tex]A=\dfrac{(24)(40)}{2}=(24)(20)=480\ m^2[/tex]
Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 15. Find the probability that a randomly selected adult has an IQ less than 130.
Answer:
The probability would be 97.8%
Step-by-step explanation:
In order to find that, lets look at the amount of standard deviations away the amount given is. Since the number is 30 away from the mean, and the standard deviation is 15, we can find the total number of deviations it is away.
30/15 = 2
Now that we have that, we can look at the probability curve for standard deviations. Outside of 2 standard deviations above is only a 2.2% likelihood. Since that is the case, we can find the amount that would be under that as 100% minus the amount we just found.
100% - 2.2% = 97.8%
Please help me with thesw question i will give 10 points
A is the answer to that question
What is the width of a rectangular room with an are 90 square feet and a length of 9 feet
[tex]A=lw\Rightarrow w=\frac{A}{l}=\frac{90}{9}=10\: ft[/tex]
Answer:
10 ft
Step-by-step explanation:
Area of a rectangular room is
A = l*w
We know the area and the length
90 = 9*w
Divide by 9
90/9 = 9w/9
10 =w
The width is 10 feet
The quadrilateral is inscribed in a circle with opposite angles measuring 3x + 2 and 3x – 32. Find the value of x.
Question 5 options:
35
22
25
30
Answer:
[tex]x=35\°[/tex]
Step-by-step explanation:
we know that
In a quadrilateral inscribed in a circle , the opposite angles are supplementary
so
In this problem
[tex](3x+2)\°+(3x-32)\°=180\°[/tex]
Solve for x
[tex]6x-30\°=180\°[/tex]
[tex]6x=210\°[/tex]
[tex]x=210\°/6=35\°[/tex]
Answer:
A. 35
Step-by-step explanation:
I did this question earlier and A. 35 was the answer that was right for me. Hope this helps!
How do I find the equation of a line parallel to y=-1/2x +3 passing through (3,1/2) please help I’ve been here for a hour
➷ If a line is parallel to the line, then the slope will remain the same
Now, you just need to substitute the values of that coordinate into the equation
1/2 = -1/2(3) + c
Simplify:
1/2 = -1.5 + c
Add 1.5 to both sides
c = 2
Therefore, the equation of the line would be:
y = -1/2x + 2
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x + 3 is in this form
with m = - [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes, hence
slope of parallel line = - [tex]\frac{1}{2}[/tex], thus
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (3, [tex]\frac{1}{2}[/tex]) into the partial equation
[tex]\frac{1}{2}[/tex] = - [tex]\frac{3}{2}[/tex] + c ⇒ c = 2
y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation of parallel line
What is the slope of the line passing through points A and B?
Answer:
1/3
Step-by-step explanation:
you go up 1 and down 3
Answer:
1/3
Step-by-step explanation:
The way to find slop is find the RISE/RUN between the two points.
NEED HELP !!!!! WILL GIVE BRAINLIEST AND 99 PTS!!!!order from least to greatest. 0.81, 4/5, 90%
In order from least to greatest, it goes 4/5, 0.81, 90%
Answer:
4/5, 0.81, 90% is the answer from least to greatest.
Hope this helps :)
Solve for x. Write the smaller solution first, and the larger solution second. 3x^2?9x?12=0
the operation functions are shown as question marks, please replace accordingly
Please help!
Given the following: mED=mDB=mBC
In circle F, what is the measure of EFD?
A. 17.5°
B. 35°
C. 60°
D. 70°
Answer: Option D.
Step-by-step explanation:
To solve this exercise you must keep on mind the Angle at the Center Theorem.
According to the Angle at the Center Theorem, an inscribed angle is half of the central angle.
Therefore, given in the inscribed angle m∠BAC=35°, you can calculate the central angle m∠EFD as following:
[tex]BAC=\frac{EFD}{2}[/tex]
- Solve for EFD.
[tex]EFD=2*BAC[/tex]
- When you substitute values. you obtain:
[tex]EFD=2(35\°)\\EFD=70\°[/tex]
Answer:
Option B. ∠EFD = 35°
Step-by-step explanation:
In a circle F, it has been given mED = mDB = mBC
We have to find the measure of ∠EFD
We should always remember the inscribed angle theorem which states that the measure of an inscribed angle is always half the measure of intercepted arc.
m(arc BC) = 2×∠CAB = 2×35 = 70°
Now it has been given in the question
mED = mBC
Therefore m(arc ED) = 70°
Again applying the same theorem
m(arc ED) = 2×∠EFD
70° = 2×∠EFD
m∠EFD = [tex]\frac{70}{2}=35[/tex]
Option B. 35° is the answer.
Point a (-7 -2) is rotated 270 clockwise rotation and shifted 3 units downs what is the coordinate of K'
To find the coordinate of K', we first rotate point a (-7,-2) 270 degrees clockwise. Then, we shift the resulting coordinates 3 units down. The coordinate of K' is (-7, -5).
Explanation:To find the coordinate of K', we first need to rotate point a (-7,-2) 270 degrees clockwise. To do this, we can use the rotation matrix:
[cos(theta) -sin(theta)] [x]
[sin(theta) cos(theta)] [y]
Plugging in the values, we get:
[cos(270) -sin(270)] [-7]
[sin(270) cos(270)] [-2]
Simplifying, we have:
[-0 -1] [-7]
[1 0]] [-2]
Multiplying, we get:
[0 -7]
[1 0]]
Now, we shift the resulting coordinates 3 units down. Adding -3 to the y-coordinate, the coordinate of K' is (-7, -5).
Approximate the change in the lateral surface area (excluding the area of the base) of a right circular cone of fixed height of h=6 m when its radius decreases from r= 10m to r= 9.9 m
Answer:
The change in the lateral surface area is approximate [tex]6.32\ m^{2}[/tex]
Step-by-step explanation:
we know that
The lateral surface area of the cone is equal to
[tex]LA=\pi r l[/tex]
where
r is the radius of the base
l is the slant height
Part 1
we have
[tex]r=10\ m, h=6\ m[/tex]
Calculate the slant height l (applying the Pythagoras Theorem)
[tex]l^{2}=r^{2}+h^{2}[/tex]
substitute the values
[tex]l^{2}=10^{2}+6^{2}[/tex]
[tex]l^{2}=136[/tex]
[tex]l=\sqrt{136}\ m[/tex]
Find the lateral area of the cone
[tex]LA=\pi (10)(\sqrt{136})[/tex]
[tex]LA=10\pi \sqrt{136}\ m^{2}[/tex]
Part 2
we have
[tex]r=9.9\ m, h=6\ m[/tex]
Calculate the slant height l (applying the Pythagoras Theorem)
[tex]l^{2}=r^{2}+h^{2}[/tex]
substitute the values
[tex]l^{2}=9.9^{2}+6^{2}[/tex]
[tex]l^{2}=134.01[/tex]
[tex]l=\sqrt{134.01}\ m[/tex]
Find the lateral area of the cone
[tex]LA=\pi (9.9)(\sqrt{134.01})[/tex]
[tex]LA=9.9\pi \sqrt{134.01}\ m^{2}[/tex]
Part 3
Find the change in the lateral surface area
[tex]10\pi \sqrt{136}-9.9\pi \sqrt{134.01}[/tex]
assume [tex]\pi =3.14[/tex]
[tex]10(3.14)\sqrt{136}-9.9(3.14)\sqrt{134.01}=6.32\ m^{2}[/tex]
To approximate the change in the lateral surface area of a right circular cone with a fixed height of 6m, we can use the formula √A = 2πrL, where A is the cross-sectional area, r is the radius, and L is the slant height. By calculating the slant height for both radii and using the formula, we find that the change in the lateral surface area is 15.36m².
Explanation:To approximate the change in the lateral surface area of a cone, we can use the formula √A = 2πrL, where A is the cross-sectional area, r is the radius, and L is the slant height. In this case, the height (h) is fixed at 6m. So, we need to find the slant height for both radii, using the formula L = √(r² + h²).
Step 1: Find the slant height for the first radius, r1 = 10m:
L1 = √(10² + 6²) = √136 = 11.66m
Step 2: Find the slant height for the second radius, r2 = 9.9m:
L2 = √(9.9² + 6²) = √135.20 = 11.61m
Step 3: Calculate the change in the lateral surface area, using the formula √A1 - √A2:
√A1 = 2π x 10m x 11.66m = 732.94m²
√A2 = 2π x 9.9m x 11.61m = 717.58m²
Change in Lateral Surface Area = √A1 - √A2 = 732.94m² - 717.58m² = 15.36m²
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Kim and her 2 brothers each use 1 1/2 cups of milk for breakfast.How many fluid ounces of milk do they use in 4 day's
The amount of fluid used in 4 days will be 18 ounces
Step-by-step explanation:Since each of them use 1 1/2 cups and they are 3
so the collective amount in 1 day will be
3 * 1 1/2 = 9/2
Now
The amount in 4 days will be
4 * 9/2 = 18
Therefore they will collectively use 18 ounces in 4 days
Find the lateral area of the cone in terms of π.
Answer:
[tex]15\pi\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of the cone is equal to
[tex]LA=\pi rl[/tex]
where
r is the radius of the base
l is the slant height
we have
[tex]r=3\ cm[/tex]
Applying the Pythagoras Theorem find the slant height
[tex]l^{2}=3^{2} +4^{2}\\ \\l^{2}=25\\ \\l=5\ cm[/tex]
substitute in the formula
[tex]LA=\pi (3)(5)=15\pi\ cm^{2}[/tex]
The domain of f(x) is the set of all numbers greater than or equal to 0 and then less than or equal to 2
It means f(x) has a set of numbers from 0-2
i.e, 0,1,2
manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Round your answer to the nearest hundredth. Predict the number of computers with defects in a shipment of 15,000 computers. Round your answer to the nearest whole number.
Answer:
0.01.
113.
Step-by-step explanation:
Probability of a defect = 9/1200
= 0.0075
= 0.01 to the nearest hundredth.
Prediction of number of defects in 15,000 computers
= 15,000 * 0.0075
= 113.
The probability of choosing defective computers is 0.01 and the number of predictions is 113.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of samples
Given that manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect.
The probability will be calculated as,
Probability of a defect = 9/1200
= 0.0075
= 0.01 to the nearest hundredth.
Prediction of the number of defects in 15,000 computers
= 15,000 * 0.0075
= 113.
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Based on the dartboard shown below, what is the probability of a random throw hitting a section that is pink or 1?
Answer:
Step-by-step explanation:
5 out of 8 because there are four one spaces and one pink space so that equals 5 and there are a total of 8 spaces to hit
Answer:
5/8.
Step-by-step explanation:
There are a total of 8 sectors of which 4 are 1 and 1 is pink.
So Prob (hitting a 1) = 4/8 = 1/2.
Prob (hitting a pink) = 1 /8.
So the probability of hitting a pink or a 1 = 1/2 + 1/8
= 5/8.
How much would it cost to ship a package weighing 3.2 lbs at a cost of $2.69 per pound. Explain how you arrived at your answer.
Answer:
$8.608
Step-by-step explanation:
We are given that it costs $2.69 per pound to ship a package and we are to find how much would it cost to ship a package weighing 3.2 lbs.
To find this, we simply need to multiply the unit cost per pound with the weight of the package that is to be shipped.
Total cost to ship 3.2 lbs package = [tex] 3.2 \times 2.69 [/tex] = $8.608
Help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 48°
Step-by-step explanation: The Answer is 48° this is because a triangle is equal to 180° and to find the missing side, add the two sides you do know and subtract them from 180 and you will get 48°
Have an awesome day,
Eric
On a number line, what is the distance between ?17 and 9? A) -26 B) -8 C) 8 D) 26 Submit
Answer:
c) 8
Step-by-step explanation:
its C. because 17-9=8.
Find the area of a triangle when A=22 B=105 and B=14
Answer:
a.30.4 units²
Step-by-step explanation:
Using the triangle attached, we can find the angle at C which is 180-(22+105)=53°
Then we use the sine rule to find the value of side c.
14/sin105=c/sin53
c=(14/sin105)× sin53
c=11.575
We can now use the sine formula to find the area of the triangle. A=(1/2)absin∅
A= (1/2)×14×11.575sin22
A=30.4
Answer:
30.4
Step-by-step explanation:
Correct on edg2020
Find the limit , picture provided
Answer:
d. does not exist
Step-by-step explanation:
The given limits are;
[tex]\lim_{x \to 4} f(x) =5[/tex], [tex]\lim_{x \to 4} g(x) =0[/tex] and [tex]\lim_{x \to 4} h(x) =-2[/tex]
We want to find
[tex]\lim_{x \to 4} \frac{f}{g}(x)= \lim_{x \to 4} \frac{f(x)}{g(x)}[/tex]
By the properties of limits, we have;
[tex]\lim_{x \to 4} \frac{f}{g}(x)= \frac{\lim_{x \to 4} f(x)}{\lim_{x \to 4} g(x)}[/tex]
This gives us;
[tex]\lim_{x \to 4} \frac{f}{g}(x)= \frac{5}{0}[/tex]
Division by zero is not possible. Therefore the limit does not exist.
Identify the domain of the function shown in the graph.
For this case, we find the equation of the line, for this we look for points where the line passes:
[tex](x1, y1) = (- 2,0)\\(x2, y2) = (- 10, -4)[/tex]
We found the slope:
[tex]m = \frac {y2-y1} {x2-x1} = \frac {-4-0} {- 10 - (- 2)} = \frac {-4} {- 10 + 2} = \frac {- 4} {- 8} = \frac {1} {2}[/tex]
Thus, the equation of the line is:
[tex]y = \frac {1} {2} x + b[/tex]
We substitute a point to find "b":
[tex]0 = \frac {1} {2} (- 2) + b\\0 = -1 + b\\b = 1[/tex]
Finally:
[tex]y = \frac {1} {2} x + 1[/tex]
Now, the domain is given by all the values for which the function is defined.
It is observed that "x" can take any value, that is, it is defined for all real numbers.
Answer:
Option A
Tobias’s closet has 1 red hat and 1 black hat; 1 white shirt, 1 black shirt, and 1 black-and-white-striped shirt; and 1 pair of black pants and 1 pair of blue pants. He is picking an outfit by reaching into his closet and randomly choosing a hat, a shirt, and a pair of pants. How many possible outfit combinations are there?
Answer: C) 12
Answer:
12
Step-by-step explanation:
Let's calculate how many possible outfits does Tobias has.
Hats: 2, Shirts: 3, Pants: 2
If he's picking everything at random blindly from his closet, he could pick any of the hats, any of the shirts and any of the pants. That makes a total of:
2 x 3 x 2 = 12 possible combinations.
That doesn't mean the arrangement will look pretty :-)
Tobias has 12 possible outfit combinations from his closet. This is calculated by multiplying the choices he has for each item of clothing: 2 hats, 3 shirts, and 2 pairs of pants.
Explanation:In this mathematics problem, Tobias has 2 hats, 3 shirts, and 2 pairs of pants. In such problems, an easy rule to remember is that for independent choices you multiply your options. So, for his hats, he has 2 options. For shirts, he has 3 options and for pants, he has 2 options. To find the total number of outfit combinations, just multiply these options: 2 (hats) * 3 (shirts) * 2 (pants) = 12 possible outfit combinations. Therefore, Tobias can mix and match his clothing items to make 12 different outfits.
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