Answer:
[tex]\lim_{x \to\frac{\pi }{4} } (3x-tanx)[/tex] = [tex]3(\frac{\pi }{4} )[/tex]
Step-by-step explanation:
Explanation:-
Given that
[tex]\lim_{x \to\frac{\pi }{4} } (3x-tanx)[/tex]
= [tex]\lim_{x \to\frac{\pi }{4} } (3x) - \lim_{x \to\frac{\pi }{4} } tanx)[/tex]
= [tex]3(\frac{\pi }{4} )+tan(\frac{\pi }{4} )[/tex]
= [tex]3(\frac{\pi }{4} )+ 1 )[/tex]
= [tex]3(\frac{\pi }{4} )[/tex]
Evaluate 2x − 2 for x = 0, x = 1, and x = 2. Question 1 options: A) −1, 0, 2 B) −1, 1, 2 C) 0, 1, 2 D) 1, 2, 4
The value of x in 2^x - 2 when x = 0, x = 1 and x = 2 are -1, 0 and 2 respectively. option A
Algebra2^x - 2
when x = 0
2^x - 2
= 2^0 - 2
= 1 - 2
= -1
when x = 1
2^x - 2
=2^1 - 2
= 2 - 2
= 0
when x = 2
2^x - 2
= 2^2 - 2
= 4 - 2
= 2
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What is the equation,in point-slope from ,of the line that is perpendicular to given line and passes through the point (-4,-3)?
The equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is y + 3 = 1/4(x + 4)
How to determine the equation of the line?The complete question is added as an attachment
The points on the line are given as:
(-1, 1) and (0, -3)
Start by calculating the slope of the line using
m = (y2 - y1)/(x2 - x1)
The slope of the perpendicular line is
m2 = -(x2 - x1)/(y2 - y1)
So, we have:
m2 = -(0 + 1)/(-3 - 1)
This gives:
m2 = 1/4
The equation of the line is then calculated as
y - y1 = m(x - x1)
This gives
y + 3 = 1/4(x + 4)
Hence, the equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is y + 3 = 1/4(x + 4)
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help me pleaseeeee (20 points)
what is the volume of this solid?
Answer:
A) 39
Step-by-step explanation:
If you calculate the volume of the cube which is the V=a^3 you get 27, then calculating the pyramid, the Length is 3, and the Width is also 3. Then the height is 4. so you put that into the formula to calculate the volume which is V=L*W*H
--------
3
you get 12. Now its simple, you just add the 2 volumes, so you do 27+12 and its 39.
39 is the answer by calculating the volume using formula!
43 POINTS!!,!,!!,!,!!
Alex went to a furniture shop to buy chairs and tables for his cafe. Find the maximum numbers of chairs he can buy if, he spent $300 for 3 tables cost of 1 chair is $30 and, he cannot spend more than $800 on the furniture.
Answer:
16 chairs
Step-by-step explanation:
800 - 300 = 500
500/30 = 16.6 since it's money you can only afford 16
Integral of
11-3x/
x²+2x-3
dx
Answer:
2x+2
Step-by-step explanation:
x²+2x-3
=2(x^2-1)+2*1(2x^1-1)
A washer and a dryer cost $737 combined. The washer costs $37 more than the dryer. What is the cost of the dryer
Answer: $350
Step-by-step explanation:
$700 divided by 2 is 350
If A is a 2 × 2 matrix, then A × I =
and I × A =
Since the multiplication between two matrices is not commutative, then [tex]\vec A\, \times\,\vec I \ne \vec I \,\times \,\vec A[/tex], regardless of the dimensions of [tex]\vec A[/tex].
Is the product of two matrices commutative?
In linear algebra, we define the product of two matrices as follows:
[tex]\vec C = \vec A \,\times \vec B[/tex], where [tex]\vec A \in \mathbb{R}_{m\times p}[/tex], [tex]\vec B \in \mathbb{R}_{p\times n}[/tex] and [tex]\vec C \in \mathbb{R}_{m \times n}[/tex] (1)
Where each element of the matrix is equal to the following dot product:
[tex]c_{ij} = \left[\begin{array}{cccc}a_{i1}&a_{i2}&\ldots&a_{ip}\end{array}\right]\,\bullet\,\left[\begin{array}{ccc}b_{1j}\\b_{2j}\\\vdots\\b_{pj}\end{array}\right][/tex], where 1 ≤ i ≤ m and 1 ≤ j ≤ n. (2)
Because of (2), we can infer that the product of two matrices, no matter what dimensions each matrix may have, is not commutative because of the nature and characteristics of the definition itself, which implies operating on a row of the former matrix and a column of the latter matrix.
Such "arbitrariness" means that resulting value for [tex]c_{ij}[/tex] will be different if the order between [tex]\vec A[/tex] and [tex]\vec B[/tex] is changed and even the dimensions of [tex]\vec C[/tex] may be different. Therefore, the proposition is false.
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During a flu epidemic a company with 200 employees had 1/3 on Monday and another 3/10 call in sick on Tuesday.
Part (a)
[tex]\frac{1}{10}+\frac{3}{10}=\frac{4}{10}=\boxed{\frac{2}{5}}[/tex]
Part (b)
[tex]200\left(\frac{2}{5} \right)=\boxed{80}[/tex]
Evaluate functions from their graph g(−9)=
See the Correct Answer Attached!
Evaluating the function from the given graph, g(-9) = 1.
How to Evaluate a Function?To find the value of a function for a given x-value using a given graph, trace the x-value against the corresponding y-value on the y-axis.
To evaluate the function from the graph given, for g(-9), find the y-value that corresponds to the x-value of -9.
The graph shows that when x = -9, the corresponding y-value is 1.
Therefore, g(-9) = 1.
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A trapezoid has an area given by A =1-2(b1-b2)h,where b1,is the length of one base, b2 is the length of the other
base, and h is the height. If the trapezoid has an area of 14 square units, solve for b in terms of the other variables.
The value of [tex]b_{1}[/tex] is 69/4h and value of [tex]b_{2}[/tex] is 43/4h if the area of trapezoid is 14 square units.
Given that area is equal to 1-2([tex]b_{1} -b_{2}[/tex])h and area is 14 square units.
We know that area of trapezoid is equal to (a+b)h/2.
We have to put the given equation equal to 14 to get our first equation.
14=1-2([tex]b_{1} -b_{2}[/tex])h
14=1-2[tex]b_{1}[/tex]h+2[tex]b_{2}[/tex]h
2[tex]b_{1}[/tex]h-2[tex]b_{2}[/tex]h=-13------------1
Now put the value of area in the formula of area of trapezoid.
14=[tex](b_{1} +b_{2})h/2[/tex]
[tex]b_{1}[/tex]h+[tex]b_{2}h[/tex]=28-----------------2
Multiply equation 2 by 2 and then subtract 2 from 1
[tex]2b_{1}h -2b_{2}h -2b_{1}h-2b_{2}h[/tex]=-13-56
-4[tex]b_{2}h[/tex]=-43
[tex]b_{2}[/tex]=43/4h
Put the value of [tex]b_{2}[/tex] in 2 to get the value of [tex]b_{1}[/tex].
[tex]b_{1} h+43/4h*h=28[/tex]
[tex]b_{1}[/tex]=69/4h
Hence The value of [tex]b_{1}[/tex] is 69/4h and value of [tex]b_{2}[/tex] is 51/4h if the area of trapezoid is 14 square units.
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Find the value of 2a + 3b
Answer: 19
Step-by-step explanation:
Using the sum of an arithmetic series formula,
[tex]\sum^{30}_{n=2} (an+b)=2407 \implies 29(16a+b)=2407 \implies 16a+b=83\\\\\sum^{40}_{n=1} (an+b)=4220 \implies 20(41a+2b)=4220 \implies 41a+2b=211[/tex]
Multiplying the second equation by 2 gives us [tex]32a+2b=166[/tex].
Subtracting this from the second equation, we get that [tex]9a=45 \implies a=5[/tex].
Substituting this back into the first equation, we get that [tex]b=3[/tex].
Therefore, [tex]2a+3b=2(5)+3(3)=19[/tex]
You have customers of the following ages, what is the median age of your customer base? 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70
The median age of your customer base = 45
What is median?The median is the value that divides a data sample, a population, or even a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set. The fundamental difference between the mean and the median when describing data is that the median is more representative of the "typical" value because it is not skewed by the a small proportion of extremely large or small values. Due to the fact that income distribution can be highly skewed, the median income, for instance, might be a better indicator of what is considered a "typical" income.
Mean = middle term
= 6th term
= 45
Hence, Median of age = 45.
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Rationalize the denominator and simplify
√a+1-2/√a+1+2
5+a-4√(a+1)/(a-3) is the simplified form of the number. This can be obtained by multiplying numerator and denominator with conjugate of the denominator.
Simplify the number:Given the number,
√a+1-2/√a+1+2
Denominator = √a+1+2
Conjugate of the denominator = √a+1 - 2
Now, (√a+1-2)(√a+1 - 2 )/√(a+1+2)(√a+1 - 2 )
=(√a+1 - 2 )²/(√a+1)² - 4
=(a+1 -4√a+1+5)/(a+1-4)
=5+a-4√(a+1)/(a-3)
Hence 5+a-4√(a+1)/(a-3) is the simplified form of the number.
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find an angle measure of angle A and B
A (5y-3)
C (3y+27)
The measure of angle A and C will be 94.5° and 85.5°.
How to calculate the angle?(5y - 3) + (3y + 27) = 180
Collect like terms
5y + 3y - 3 + 27 = 180
8y = 180 - 27 + 3
8y = 156
y = 156/8 = 19.5
(5y - 3) = (5 × 19.5) - 3 = 94.5
(3y + 27) = (3 × 19.5) + 27 = 85.5
Therefore, the measure of angle A and C will be 94.5° and 85.5°.
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• If a doctor orders 60mg of Benadryl, and each tablet contains 7 mg, how many tablets should
be given to the patient?
• Also, if the patient is only to take 1 tablet per day, how many days should the patient stay on the
medication?
A patient should be given 8 and a half tablets and Approx. 8 days should the patient stay on the medication.
How many tablets should be given to the patient and how many days should the patient stay on the medication?Given:
A doctor orders 60mg of Benadryl.Each tablet contains 7 mg.To find:
How many tablets should be given to the patient?If the patient is only to take 1 tablet per day, how many days should the patient stay on the medication?Solution:
If each tablet contains 7 mg and the doctor orders 60 mg of Benadryl.
Then the patient should be given 60/7 tablets i.e., 8 and a half tablets.
If the patient is only to take 1 tablet per day, then approx 8 days the patient we stay on the medication.
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What is the distance between point (3, 2) and line
1
y=-x-9
4
Select the best answer from the cholces provided.
OA.
OB. 41
√5
O C.
41
√17
O D.
13
2
2
√17
The distance between the coordinate point (3, 2) and line y = ¹/₄x - 9 is; 10.25 units
How to find the distance between a line coordinate?
We want to find the distance between the coordinate point (3, 2) and line y = ¹/₄x - 9.
Thus, we will plug in 3 for x in the line equation given to get;
y = ¹/₄(3) - 9
y = 0.75 - 9
y = -8.25
Thus, we can say that point on the line is (3, -8.25)
The difference in y-values would give us the required distance;
Required distance = -8.25 - 2
Required distance = -10.25
However distance cannot be negative and so we will take the absolute value as 10.25 units.
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PLS HELP OR I WILL FAIL I BEG U HELP
Answer:
The first one, you cannot factor because the two values do not share any common factors. Hence, the answer would just be:
a. 51x-25
The other one, we can factorise to:
b. 3x(4-x)
Step-by-step explanation:
For the second option:
Common factor between 12x and 3x^2 is 3x.
Take this out to the front, we are left with:
3x(4-x)
A website I recommend you use (math calculator with some instructions) is Symbolab.
https://www.symbolab.com/solver/factor-calculator/factor%2012x-3x%5E%7B2%7D?or=input
The function P=48∙e^((.045t)) gives the number of bacteria in a population as a function of time in hours.
a) How many bacteria are there in t = 8 hours? *Accurate to four decimal.
b) How fast is this population growing in t = 8 hours? *Accurate to four decimals.
The number of bacteria when t = 8 is approximately 66 bacterias
Exponential functionsGiven the function that gives the number of bacteria in a population as a function of time in hour expressed as:
P=48∙e^((0.045t))
If the value of t is 8, hence;
P=48∙e^((0.045(8))
P = 48e^0.36
P = 65.933
Hence the number of bacteria when t = 8 is approximately 66 bacterias
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if Jill's age is 84 and johns age is 21 how many years ago was Jill 10 times older than john
Between permanent life insurance and term life insurance, which typically has the lower premium and why?
a.
Term life insurance has the lower premium because term life insurance pays the face value to your beneficiary if you die within a certain set period of time, whereas whole life insurance covers you your entire life.
b.
Term life insurance has the lower premium because you cannot renew the insurance after your term has ended.
c.
Permanent life insurance has the lower premium because you are making more premium payments (your whole life versus a set period of time), so the amount per premium payment is less.
d.
Permanent life insurance has the lower premium because the amount you contribute is then invested and makes interest for the life insurance company.
Please select the best answer from the choices provided
A
B
C
D
Term life insurance has the lower premium because term life insurance pays the face value to your beneficiary if you die within a certain set period of time, whereas whole life insurance covers you your entire life. (Option A)
What is insurance?Insurance is when a third-party (the insurer) promises to indemnify another party (the insured) for losses they might suffer in the future in exchange for agreed upon payments.
Permanent life insurance is a type of insurance that provides a coverage that never expires. The person with a permanent life insurance is covered until he or she passes on. Whole life insurance is a type of permanent life insurance that has a fixed and guaranteed premium and a fixed death benefit.
Term life insurance is a type of insurance that provides coverage to a person only for a scheduled period of time. For example, a person who buys a 10 year term life insurance, the person's insurance only lasts for 10 years. If the person passes on within the 10 years, his beneficiary receives payments. If the person passes on after 10 years, his beneficiary does not receive any payments.
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Factor the greatest common binomial factor from each polynomial
6x^2(5x-1) +5x-1
The factored polynomial is given as follows:
(5x - 1)(6x² + 1)
How are polynomials factored?Polynomials are factored placing the common factor in evidence, then dividing all terms by the common factor.
The polynomial is:
6x²(5x - 1) + (5x - 1).
The common factor is (5x - 1), hence:
[tex](5x - 1)\left(\frac{6x^2(5x - 1)}{5x - 1} + \frac{5x - 1}{5x - 1}\right) = (5x - 1)(6x^2 + 1)[/tex]
Hence the factored polynomial is given as follows:
(5x - 1)(6x² + 1)
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Write down the 2×2 matrices representing the following transformations of the plane. (i) Reflection in the y-axis, (ii) Reflection in the line y = x (iii) Rotation through 180◦ about the origin (iv) Enlargement from the origin with scale factor λ.
The 2 x 2 matrices of the transformations are
[tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex], [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex], [tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right][/tex] and [tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right][/tex]
(i) Reflection in the y-axisThe rule of reflection in the y-axis is
(x, y) ⇒ (-x, y)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex]
(ii) Reflection in the line y = xThe rule of reflection in the line y = x is
(x, y) ⇒ (y, x)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}y&x\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}y&x\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]
(iii) Rotation through 180◦ about the originThe rule of rotation through 180◦ about the origin is
(x, y) ⇒ (-x, -y)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&-y\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right][/tex]
(iv) Enlargement from the origin with scale factor λ.The rule of the enlargement from the origin with scale factor λ.
(x, y) ⇒ (λx, λy)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}\lambda x&\lambda y\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}\lambda x&\lambda y\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right][/tex]
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Consider these two functions:
F(x) = 2cos(πx)
G(x) = 1/2cos(2x)
What are the amplitudes and periods of the two functions?
Answer:
[tex]\mathrm{pK}_{\mathrm{a}}+\mathrm{pK}_{\mathrm{b}}=\mathrm{pK}_{\mathrm{w}}[/tex] for [tex]\mathrm{HCl}[/tex] \& [tex]\mathrm{ClOH}[/tex]
Answer:
f(x): Amplitude = 2, Period = 2
g(x): Amplitude = ¹/₂, Period = π
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
f(x) = A cos(B(x + C)) + D
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftFunction f(x)
[tex]f(x)=2 \cos (\pi x)[/tex]
Comparing this with the standard form of a cosine function:
Amplitude = 2[tex]\sf Period = \dfrac{2 \pi}{\pi}=2[/tex]Function g(x)
[tex]g(x)=\dfrac{1}{2} \cos (2x)[/tex]
Comparing this with the standard form of a cosine function:
[tex]\sf Amplitude=\dfrac{1}{2}[/tex][tex]\sf Period = \dfrac{2 \pi}{2}=\pi[/tex]Learn more about the cosine graph here:
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Joy wants to invest $3000 in a savings account. Determine the interest rate (simple interest) required for Joy 's investment to double in value in 18 years. Round your answer to the nearest tenth of a percent.
The interest rate needed to double the investment in 18 years is 6%.
What is the interest rate?Interest earned is a function of the amount invested, interest rate and time. The future value of the investment is to be $6000 (3000 x 2). Interest earned would be $3000 (6000 - 3000)
Interest rate = interest earned / (amount invested x time )
$3000 / ($3000 x 18) = 6%
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I’m confused in the exponential
Answer:
this mean in case of multiplying exponents with same base you should add the exponent and keep base same.
example:
[tex] {6}^{4} \times {6}^{5 } = {6}^{4 + 5} \\ = {6}^{9} [/tex]
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 12 pieces and costs \$8 dollar sign, 8.
Let R represent the number of additional rolls that Sofia orders.
Sofia will order 7 more rolls of sushi (84 pieces) and pay $56St
Step-by-step explanation: im right
The soil samples for the next field indicate that fertilizer
In order to have a greater fertilizer coverage, you need to increase flow rate and: A. increase speed to approximately 7.1 mph so that you cover the field more quickly.
What is a flow rate?A flow rate is an average rate and it can be defined as the number of flow units that are created per unit time such as fertilizer coverage on a farm.
In this context, we can infer and logically deduce that you have to increase flow rate and your increase speed to approximately 7.1 mph, so that you can cover the field more quickly and have a greater fertilizer coverage.
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Complete Question:
The soil samples for the next field indicate that fertilizer coverage needs to be greater. To achieve this, you need to increase flow rate. How would you achieve this?
A. Increase speed to approximately 7.1 mph so that you cover the field more quickly
B. Increase the engine speed to approximately 2,000 rpm
C. Decrease speed to approximately 6.0 mph so that you cover the field more slowly
D. Shift to second gear so that the engine speed slows
solve 4/7- (-4/7)
A. 8/7
B.-8/7
C.-4/7
D.4/7
Answer:
A. 8/7
Step-by-step explanation:
Step 14/7 - (-4/7) --> 4/7 + 4/7
The two minutes turn into a plus, removing the bracket.
Step 24/7 + 4/7 = 8/7
Add the two fractions together.
Answer:
A. 8/7
Step-by-step explanation:
Find the slope of a line parallel to a line that contains the points (8, -3) and (2, 5).
Select the best answer from the choices provided.
OA
413
OB. 4
O D.
413
3
OC 3
3|4
314
Answer:
[tex]-\frac{4}{3}[/tex](Your answer choices were really confusing, so I just put the plain answer)
Step-by-step explanation:
To find the slope of a line with just two points, we can use the formula [tex]\frac{y2-y1}{x2-x1}[/tex]. In this case, [tex]\frac{5-(-3)}{2-8}[/tex]. This is [tex]\frac{8}{-6}[/tex]. This reduces to [tex]-\frac{4}{3}[/tex]
a coin is flipped 10 times and the result is recorded. How many outcomes are in the event n(A)?
There are 1024 outcomes in the event
How to determine the number of outcomes?The given parameters are:
Device = coin
Number of flips = 10
A coin has 2 faces.
So, the number of outcomes is
Outcome = Faces^Flip
This gives
Outcome = 2^10
Evaluate
Outcome = 1024
Hence, there are 1024 outcomes in the event
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Answer:
[tex]1024[/tex]
Step-by-step explanation:
Each and every flip of our coin has two possible outcomes on the whole: it is either the heads or the tails. Besides, it resembles the bit in computing, right? Indeed, it has two options likewise: it can be either [tex]0[/tex] or [tex]1[/tex]. For now on I suggest thinking neither in heads nor in tails, but in bits. Suppose the heads is [tex]0[/tex], the tails is [tex]1[/tex]. Let us slightly simplify the condition, namely: suppose that the number of flips is [tex]3[/tex]. Then, our possible outcomes:
[tex]000 \\ 001 \\ 010 \\ 011 \\ 100 \\ 101 \\ 110\\ 111[/tex]
Take a look at the first number. In case it is [tex]0[/tex], we have [tex]4[/tex] outcomes because we can put either [tex]0[/tex] or [tex]1[/tex] not only on the second place, yet also on the third one. Abiding by the same logic, we also have [tex]4[/tex] outcomes when the first one is [tex]1[/tex]. In mathematics: [tex]2 * 2 * 2 = 2^3 = 8[/tex] outcomes.
As for the initial condition, it does not globally differ from our simplification, it just has more flips, hence it is not just a walk in the park to list all the possible outcomes anymore in this case, it is time-consuming otherwise. Even though, it is still not a big deal to count it: [tex]2 * ... * 2 = 2^{10} = 1024[/tex] outcomes.