Answer:
8.8
Step-by-step explanation:
10. Use the diagram below to find the value of x.
Answer:
x=20
Step-by-step explanation:
Hello There!
Remember the exterior angle of a triangle rule:
An exterior angle of a triangle is equal to the sum of the opposite interior angles
Knowing this, we can create an equation to solve for x
exterior angle (100) = sum of opposite interior angles (3x+2x)
100 = 2x+3x
now we solve for x
step 1 combine like terms
2x+3x=5x
now we have 100=5x
step 2 divide each side by 5
5x/5=x
100/5=20
we're left with x = 20
Answer:
With their steel hoofs, their long legs, their stag-like muscles, their thick skins, their powerful horns, they could walk the roughest ground, cross the widest deserts, climb the highest mountains, swim the widest rivers, fight off the fiercest bands of wolves, endure hunger, cold, thirst and punishment as few beasts of the earth have ever shown themselves capable of enduring.
i need help with this i will mark you as brainliest
Answer:
The answer is 7 (A)
Step-by-step explanation:
Answer:
D. The length is the same as line MN.
Step-by-step explanation:
Even if the line is moved any one bit, the length of the line will not change. So as a result, A, B & C are already out. That leaves D as our answer.
what is the measure of angle A?
Answer:
122
Step-by-step explanation:
180 - (43 + 15)
Answer:
The answer is 2.86
Step-by-step explanation:
you just have to divide 43 by 15
Chris makes $25 an hour and is getting a 10% raise. What is her new
earning per hour?
Answer:
$27.50
Step-by-step explanation:
Hope this helps and have a great day!!!!
Step-by-step explanation:
Since his pay is increased by 10 percent, then you multiply 10% by 25 and then add that to 25.
25+10/100(25)=55/2
27.5
Hope that helps :)
16. Suppose that 7₁, 72 are linear dependent in a vector space V. Show that V₁ + V2, V₂ - V₁ are also linearly dependent.
By supposing that 7₁, 72 are linearly dependent in a vector space V. The coefficient of 7₁ is 1 and the coefficient of 72 is 0, while in the second linear combination, the coefficient of 7₁ is 0 and the coefficient of 72 is 1. Therefore, we can conclude that V₁ + V2, V₂ - V₁ is also linearly dependent.
To show that V₁ + V2, V₂ - V₁ is also linearly dependent, we will begin by using the given linear combination of vectors to determine whether they are linearly dependent or independent. Suppose that 7₁, and 72 are linearly dependent in a vector space V.
Let us recall that a set of vectors is linearly dependent if it can be represented as a linear combination of other vectors in the vector space. This implies that if 7₁, 72 are linearly dependent, then there exist scalars α and β, not all zero, such that α7₁ + β72 = 0. To show that V₁ + V2, V₂ - V₁ is also linearly dependent, we need to use the definitions of vector addition and subtraction to writing each of these vectors as a linear combination of 7₁ and 72. Let's begin with V₁ + V2.
Using the definition of vector addition, we have
V₁ + V2 = 1 · 7₁ + 1 · 72 = 7₁ + 72.
Similarly, using the definition of vector subtraction, we have
V₂ - V₁ = -1 · 7₁ + 1 · 72 = -7₁ + 72.
Now we can write V₁ + V2, V₂ - V₁ as linear combinations of 7₁ and 72:
V₁ + V2 = 1 · (7₁ + 72) + 0 · (-7₁ + 72)V₂ - V₁
= 0 · (7₁ + 72) + 1 · (-7₁ + 72)
Notice that the coefficients in each linear combination are not all zero. We can say that V₁ + V2, V₂ - V₁ is linearly dependent.
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Kaylee deposited $1,450 in an account that earns 2.596 interest compounded annually. Which function represents the situation, where tis
the time in years?
fit) = 1450(2.5)
f(t) = 1450(1.25)
FO) = 1450(.025)
f(t) = 1450(1,025)
Answer:
[tex]f(t) = 1450(1.025)^{t}[/tex]
Step-by-step explanation:
Given
[tex]P =1450[/tex] -- principal
[tex]r = 2.5\%[/tex] --- rate
[tex]n = 1[/tex] --- compounded once a year
Required
Determine the function for compound interest
Compound interest f(t) is calculated as:
[tex]f(t) =P(1 + r/n)^{nt[/tex]
So, we have:
[tex]f(t) = 1450(1 + 2.5\%/1)^{1 * t}[/tex]
[tex]f(t) = 1450(1 + 2.5\%)^{t}[/tex]
[tex]f(t) = 1450(1 + 0.025)^{t}[/tex]
[tex]f(t) = 1450(1.025)^{t}[/tex]
Select the correct answer.
Which value in this data set is an outlier?
4,5, 1, 7, 4, 5, 8, 9, 6, 5, 4, 9,7
O A. 1
OB.
N
O C.
3
D. 9
Answer:
answer is 1
Step-by-step explanation:
Calculate the following limits using the limit laws and limx→2f(x)=−3, limx→2g(x)=4, limx→2h(x)=7 (a) limx→2(f(x)−2g(x))= (b) limx→2(h(x)2)= (c) limx→2h(x)⋅g(x)f(x)=
The value of limits after using limit laws is [tex]$\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} = -\frac{28}{3}$.[/tex]
What are Limit Laws?
Limit laws, also known as limit properties or limit theorems, are a set of rules and principles that allow us to simplify and evaluate limits of functions. These laws provide a systematic approach to finding the limit of a more complex expression by breaking it down into simpler parts.
Given:
[tex]\lim_{x \to 2} f(x) &= -3 \\\lim_{x \to 2} g(x) &= 4 \\\lim_{x \to 2} h(x) &= 7\end{align*}\textbf{(a) Calculate} $\lim_{x \to 2} (f(x) - 2g(x))$:[/tex]
Using the limit laws, we can split the expression and apply the limit laws individually:
[tex]\lim_{x \to 2} (f(x) - 2g(x)) &= \lim_{x \to 2} f(x) - \lim_{x \to 2} (2g(x)) \\&= \lim_{x \to 2} f(x) - 2 \lim_{x \to 2} g(x) \\&= (-3) - 2(4) \\&= -3 - 8 \\&= -11[/tex]
Therefore,[tex]$\lim_{x \to 2} (f(x) - 2g(x)) = -11$.[/tex]
[tex]\textbf{(b) Calculate} $\lim_{x \to 2} (h(x))^2$:[/tex]
Again, using the limit laws, we can apply the limit to the expression:
[tex]\lim_{x \to 2} (h(x))^2 &= \left(\lim_{x \to 2} h(x)\right)^2 \\&= (7)^2 \\&= 49[/tex]
Therefore,
[tex]\lim_{x \to 2} (h(x))^2 = 49$.\textbf{\\\\(c) Calculate} $\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)}$:[/tex]
Applying the limit laws, we can evaluate the limit as follows:
[tex]\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} &= \frac{\lim_{x \to 2} h(x) \cdot \lim_{x \to 2} g(x)}{\lim_{x \to 2} f(x)} \\\\&= \frac{7 \cdot 4}{-3}\\ \\&= \frac{28}{-3}[/tex]
Therefore,[tex]$\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} = -\frac{28}{3}$.[/tex]
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At an electronics store, DVDs are on sale. Some DVDs cost $15.00 each and some cost $12.00 each. Bart purchased 8 DVDs and spent a total
of $105.00. Write a system of equations and solve by using substitution to determine how many $12.00 DVDs Bart purchased.
$105
15*3=45
12*5=60
60+45=105
(12*5)+(15*3)=105
Can i get brainliest
The number of $15 DVDs and $12 DVDs at an electronics store will be 3 and 5, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
At a hardware store, DVDs are at a bargain. A few DVDs cost $15.00 each and some expenses $12.00 each. Bart bought 8 DVDs and spent a sum of $105.00.
Let 'x' be the number of $15 DVDs and 'y' be the number of $12 DVDs. Then the equations are given as,
x + y = 8 ...1
15x + 12y = 105 ...2
From equations 1 and 2, then we have
15x + 12(8 - x) = 105
15x + 96 - 12x = 105
3x = 9
x = 3
Then the value of y is given as,
y = 8 - 3
y = 5
The number of $15 DVDs and $12 DVDs at an electronics store will be 3 and 5, respectively.
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The average car decreases in value by about 15% per year. If a car's original value is $28,000, which function best represents its value, y, after t years?
A. y=28,000(1+15)^t
B. y=28,000(1+0.15)^t
C. y=28,000(1-15)^t
D. y=28,000(1-0.15)^t
Answer:
D
Step-by-step explanation:
D
please help find What is AB?
Answer:
oblique
Step-by-step explanation:
PLEASE ANSWER ALL
What is the equation of the axis of symmetry of the function?
What are the coordinates of the vertex of the function?
What are the coordinates of the x¬-intercepts of the function?
What are the coordinates of the y-intercept of the function?
Step-by-step explanation:
The axis of symmetry: is the line that makes the parabola split in exactly half and lines up with the vertex. For that parabola x=1 is the line of symetry.
The vertex is where the minimum of the graph is, on this graph you can eyeball it to be (1,-9)
The x-intercept is where y is 0 so that's where the lines intersex with the x-axis. (-2,0) and (4,0)
The y-intercept of the function is where x is 0 and where the parabola intersects with the y-axis. On this graph it would be (0,-8)
Hope that helps :)
You have 35 plants. You want to split them equally between 4 sections of your garden. You use as many as you can in each section. How many plants do you have left?
answer:
3 plants are left !
step-by-step explanation:
hi there!
first lets use our times table to see which number gets use closest to 35 when it is multiplied by 4
4, 8, 12, 16, 20, 24, 28, 32,
4 * 8
= 32
then you can just subtract 35 by 32 to get you final answer of
35 - 32
= 3 plants are left over
( i hope i did the problem right since the wording of it was kinda hard to understand it )
________________________________________________________
| | | | |
| 1 | 2 | 3 | 4 |
| | | | |
________________________________________________________
| | | | |
| 5 | 6 | 7 | 8 |
| | | | |
________________________________________________________
| | | | |
| 9 | 10 | 11 | 12 |
| | | | |
________________________________________________________
| | | | |
| 13 | 14 | 15 | 16 |
| | | | |
________________________________________________________
| | | | |
| 17 | 18 | 19 | 20 |
| | | | |
________________________________________________________
| | | | |
| 21 | 22 | 23 | 24 |
| | | | |
________________________________________________________
| | | | |
| 25 | 26 | 27 | 28 |
| | | | |
________________________________________________________
| | | | |
| 29 | 30 | 31 | 32 |
| | | | |
________________________________________________________
i made a table with each number being the plant! just in case your a visual learner like me!
but i hope this help you and if i made anything confusing or if i made a mistake please let me know! but other then that i hope you have a good rest of your day :)
There are 3 plants left.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Total number of plants = 35
And, You want to split them equally between 4 sections of your garden.
Now,
To find the left plants after splitting into 4 sections, we can divide and find the remainder as;
The number of left plants = 35 ÷ 4
4 ) 35 ( 8
- 32
-------
3
Clearly, The remainder = 3
Thus, There are 3 plants left.
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In ΔGHI, h = 650 cm, i = 130 cm and ∠G=72°. Find the area of ΔGHI, to the nearest square centimeter.
Answer:
84500 is the correct answer
Answer:
40182 delta math
Step-by-step explanation:
A thermometer is taken from a room where the temperature is 21 degrees Celsius to the outdoors, where the temperature is 5 degrees Celsius. After one minute the thermometer reads 15 degrees Celsius.
(a) What will the reading on the thermometer be after 3 more minutes?
(b) When will the thermometer read 6 degrees Celsius?
degrees Celsius
a) the reading on the thermometer after 3 more minutes will be -3 degrees Celsius.
b) the thermometer will read 6 degrees Celsius after 1.5 minutes.
To solve the given problem, we can assume that the temperature change follows a linear pattern based on the given information.
(a) To find the reading on the thermometer after 3 more minutes, we need to determine the rate of temperature change per minute. From the initial reading of 21 degrees Celsius to the reading after one minute of 15 degrees Celsius, there was a temperature decrease of 6 degrees Celsius in one minute.
Therefore, the rate of temperature decrease is 6 degrees Celsius per minute. If this rate remains constant, after 3 more minutes, the thermometer will show a further temperature decrease of:
3 minutes * 6 degrees Celsius per minute = 18 degrees Celsius
Thus, the reading on the thermometer after 3 more minutes will be 15 degrees Celsius - 18 degrees Celsius = -3 degrees Celsius.
(b) To find when the thermometer will read 6 degrees Celsius, we need to determine the time it takes for the temperature to decrease from 15 degrees Celsius to 6 degrees Celsius.
The initial reading is 15 degrees Celsius, and the final desired reading is 6 degrees Celsius. Therefore, we need to calculate the time it takes for a temperature decrease of:
15 degrees Celsius - 6 degrees Celsius = 9 degrees Celsius
Since the rate of temperature decrease is 6 degrees Celsius per minute, we can set up the equation:
9 degrees Celsius = 6 degrees Celsius per minute * t minutes
Solving for t (the time it takes to reach 6 degrees Celsius):
t = 9 degrees Celsius / 6 degrees Celsius per minute = 1.5 minutes
Therefore, the thermometer will read 6 degrees Celsius after 1.5 minutes.
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What level of measurement is used in the operationalization of extracurricular participation?
Measures Extracurricular Participation Students listed the university-based clubs they participated in during the academic year. Based on these lists, we created a variable reflecting whether they were involved in at least one activity (37% were involved). Of the activities listed, 28% were sports/ recreation (i.e., intercollegiate athletics, club sports, intramural sports, or campus recreation), 18% fraternities/sororities, 15% cultural, 13% departmental/professional, 9% campus programs, 8% special interest, 7% service, and 3% religious.
The level of measurement used in the operationalization of extracurricular participation is categorical/nominal.
In the operationalization of extracurricular participation, the measurement of students' involvement in university-based clubs is done using categorical/nominal level of measurement.
This is evident from the variable created to reflect whether students were involved in at least one activity, indicating a binary (yes/no) response. The subsequent breakdown of the activities listed into different categories, such as sports/recreation, fraternities/sororities, cultural, departmental/professional, campus programs, special interest, service, and religious, further supports the use of categorical measurement.
Each activity falls into a distinct category, and the percentages represent the proportions of students engaged in each category. Categorical/nominal measurement allows for classifying and organizing data into mutually exclusive categories, without any inherent order or numerical value associated with the category.
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what are all possible values for x in the equation x^3=375?
Answer:
Select all possible values for x in the equation.
x cubed=375.
5*the cubed root of 3
the cubed root of 375
75*the cubed root of 5
125*the cubed root of 3
I am trying to do a practice test to prepare for my real test tomorrow and I don't understand the question. Can anyone help explain it plz any help would be great.
Step-by-step explanation:
Daily question: what is 5 to the 3rd power?
Answer:
125
Step-by-step explanation:
5 to the 3rd power means 5³
5³ = 5x5x5
= 125
An insurance company crashed four cars in succession at 5 miles per hour. The cost of repair for each of the four crashes was $421. 5452.5415, $232 Compute the range, sample variance, and sample standard deviation cost of repair, The range is 2-dollars? (Round to the nearest whole number as needed.) (Round to two decimal places as needed)
The range of the repair costs for the four car crashes is $5452.54 - $232 = $5220.54. The sample variance of the repair costs is $4,898,414.69, and the sample standard deviation is $2,214.17.
What are the range, sample variance, and sample standard deviation of the repair costs?The range of the repair costs for the four car crashes is the difference between the highest and lowest cost, resulting in a range of $5220.54. This indicates the variability in the repair costs. The sample variance is a measure of the average squared deviation from the mean, calculated to be $4,898,414.69. It shows the dispersion of the repair costs from the average. The sample standard deviation is the square root of the variance, amounting to $2,214.17. It provides a measure of how spread out the repair costs are, with a higher value indicating greater variability.
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Codification and Decodification let F = Z2. Consider the code
C = {000000, 001111, 110011, 111100, 101010}.
(a) Show that C is not a linear code.
b) Add words to C to form a new code C' that is linear.
c) Find a base of C'
Main Answer: The base of C' is {0110, 1001, 1100, 0011}.
Supporting Explanation: In a communication system, codification and decodification are used to encode and decode messages. C is the code for the message, where C={0000, 1100, 1010, 0110, 0101, 0011, 1001, 1111}. The code is a binary code since F=Z2. C' is the dual code of C. The codewords in C' are orthogonal to those in C. A basis for C' can be determined by finding a generator matrix for C'. Thus, the generator matrix for C is the parity check matrix for C'. A generator matrix for C is given as, G = [I | P] where P is the parity check matrix. The parity check matrix for C can be determined as, P = [-AT | Im-k]. Therefore, P = [0101; 1010; 1111].The rows of C' correspond to the columns of P. Thus, a basis for C' is {0110, 1001, 1100, 0011}.
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3. Michael surveyed a random sample of students in his school about
the number of sports they play. There are 300 students in Michael's
school. Use the results of the survey to estimate the number of
students in Michael's school who play exactly one sport. Explain
your answer. PLEASE HELP ILL ALSO MARK IT THE MOST BRAINLY ANSWER I didn’t spell that right but oh well
Answer:
Micheal surveyed 60 students.
Answer: Look at the explanation please.
Step-by-step explanation:
Please note that I am using what is in the Mathematics textbook.
So we need to know for the students who play Exactly 1 sport.
So you have to make an equation. It will look like this...
15/60 = x/300
Note that we get the 15 from the table of the number of students. We get 60 from adding 13+15+32 which is all the students Michael has surveyed. Lastly we get 300 from the question There are 300 students in his school.
x = 75 when you do the math. Cross multiply and divide.
Hope this helps :)
A car worth $14,000 depreciates at a rate of 4% per month. How long until it is worth $10,000?
please help with this ?!?
A beam of light in air strikes a slab of crown glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.
The angle of incidence for a beam of light in air striking a slab of crown glass, where the angle of reflection is twice the angle of refraction, can be determined using the laws of reflection and refraction. The angle of incidence is approximately 39.2 degrees.
we can apply the laws of reflection and refraction to find the relationship between the angles. Let's denote the angle of incidence as θ, the angle of reflection as θ_r, and the angle of refraction as θ_t.
According to the law of reflection, the angle of reflection is equal to the angle of incidence: θ_r = θ.
According to Snell's law of refraction, the relationship between the angles of incidence and refraction is given by: n_1 × sin(θ) = n_2 × sin(θ_t), where n_1 and n_2 are the refractive indices of the two media.
In this case, the light travels from air (with a refractive index of approximately 1) to crown glass (with a refractive index of 1.52). Substituting the values, we have: sin(θ) = (1.52 / 1) × sin(θ_t).
Since the angle of reflection is twice the angle of refraction, we can write: θ = 2θ_t.
Substituting this relation into the previous equation, we get: sin(2θ_t) = (1.52 / 1) × sin(θ_t).
Using the double-angle trigonometric identity, sin(2θ_t) = 2sin(θ_t)cos(θ_t), we have: 2sin(θ_t)cos(θ_t) = 1.52sin(θ_t).
Dividing both sides by sin(θ_t), we obtain: 2cos(θ_t) = 1.52.
Solving for cos(θ_t), we have: cos(θ_t) = 1.52 / 2.
Taking the inverse cosine, we find: θ_t = cos^(-1)(1.52 / 2) ≈ 26.8 degrees.
Finally, substituting this value into θ = 2θ_t, we get: θ ≈ 2 × 26.8 degrees ≈ 53.6 degrees.
Hence, the angle of incidence is approximately 39.2 degrees.
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Find the measure of C to the nearest tenth of a degree
Determine whether the following functions are injective, or surjective, or neither injective nor surjective.
a) f ∶ {a, b, c, d} → {1, 2, 3, 4, 5} given by f (a) = 2, f (b) = 1, f (c) = 3, f (d) = 5. Is f injective? Is f surjective?
b) f ∶ R → R by f (x) = x + 1. Is f injective? Is f surjective?
c) f ∶ Z × Z → Z by f (m, n) = m + n. Is f injective? Is f surjective?
d) f ∶ Z × Z → Z by f (m, n) = m2 + n 2 . Is f injective? Is f surjective?
a) The function f is not injective but is surjective.
b) The function f is injective and surjective.
c) The function f is not injective but is surjective.
d) The function f is not injective and not surjective.
a) The function f maps four elements from the domain {a, b, c, d} to five elements in the codomain {1, 2, 3, 4, 5}. Since there are more elements in the codomain than the domain, f cannot be injective. However, since every element in the codomain is mapped to by at least one element in the domain, f is surjective.
b) The function f(x) = x + 1 is a linear function that maps every real number to a unique real number. Hence, f is injective. Additionally, for every real number y, there exists x = y - 1 such that f(x) = y, meaning f is surjective.
c) The function f(m, n) = m + n maps pairs of integers from the domain Z × Z to integers in the codomain Z. Since there are infinitely many pairs that can result in the same sum, f cannot be injective. However, for every integer in the codomain, there exists at least one pair of integers in the domain whose sum is equal to it, making f surjective.
d) The function f(m, n) = m^2 + n^2 maps pairs of integers from the domain Z × Z to integers in the codomain Z. Since different pairs of integers can have the same sum of squares, f is not injective. Furthermore, there are integers in the codomain that cannot be obtained as a sum of squares, making f not surjective.
In summary, the injectivity and surjectivity of the given functions are as follows: a) not injective, surjective; b) injective, surjective; c) not injective, surjective; d) not injective, not surjective.
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1) Suppose a random variable X can only take the six values (1,2,3,4,5, and 6 ). If each value has equal probability, what is its pmf? b) Suppose the probabilities of X(0,1,2, and 3) are 1/9,2/9,2/9, and 4/9. show its pmf?
Answer : a) a random variable X can only take the six values (1,2,3,4,5, and 6 ). If each value has equal probability, then p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = 1/6
b) The pmf of the random variable X is:p(0) = 1/9p(1) = 2/9p(2) = 2/9p(3) = 4/9
Explanation :
A probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value.[1] Sometimes it is also known as the discrete density function.
The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.
a) If each value has equal probability, the pmf of the random variable X which can only take the six values (1,2,3,4,5, and 6) is : p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = 1/6
b)If the probabilities of X(0,1,2, and 3) are 1/9,2/9,2/9, and 4/9. The pmf of the random variable X is:p(0) = 1/9p(1) = 2/9p(2) = 2/9p(3) = 4/9
The sum of these probabilities is:p(0) + p(1) + p(2) + p(3) = 1/9 + 2/9 + 2/9 + 4/9 = 9/9 = 1
So, the pmf is defined for all X.
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Answer number two please please
Answer: 11
Step-by-step explanation:
Sooooo all I did was take the formula for the area of a triangle ( A= 1/2(b)(h) 0 and plug In the values. So 'b' would be 4 and 'h' would be 5.5. I assumed this rectangle had equal widths and equal heights.
The distribution of actual weights of wedges of cheddar cheese produced at a dairy is normal with a mean of 10.2 ounces and a standard deviation of 0.2 ounces. (Round all answers to 4 decimal places, if needed.)
(a) The probability that a randomly chosen wedge of cheddar cheese is greater than 10.14 is .
(b) If a sample of 16 is randomly chosen, then the distribution of the sample mean weight is approximately normal not normal left-skewed right-skewed with a mean of ? and a standard deviation of .
(c) The probability that the sample mean weight of this sample of 16 is less than 10.14 is .
(d) The probability that the sample mean weight of this sample of 16 is greater than 10.14 is .
(e) The probability that the sample mean weight of this sample of 16 is between 10.14 and 10.3 is .
(f) There is only a 7% chance that the average weight of a sample of these 16 cheese wedges will be below .
(a) The probability that a randomly chosen wedge of cheddar cheese is greater than 10.14 is found using the standard normal distribution as follows:
P(Z > z) = P(Z > (10.14 - µ)/σ)
= P(Z > (10.14 - 10.2)/0.2)
≈ 0.3085.
Therefore, the probability is approximately 0.3085.
(b) If a sample of 16 is randomly chosen, then the distribution of the sample mean weight is approximately normal with a mean of 10.2 ounces and a standard deviation of σ/√n,
Where n = 16.
The sample standard deviation is given by σ = 0.2, so the standard deviation of the sample mean weight is:
σ/√n = 0.2/√16
= 0.05.
Therefore, the distribution of the sample mean weight is approximately normal with a mean of 10.2 ounces and a standard deviation of 0.05 ounces.
(c) The probability that the sample mean weight of this sample of 16 is less than 10.14 is found using the standard normal distribution as follows:
P(Z < z) = P(Z < (10.14 - µ)/(σ/√n))
= P(Z < (10.14 - 10.2)/(0.2/√16))
≈ P(Z < -1.6)
≈ 0.0548.
Therefore, the probability is approximately 0.0548.
(d) The probability that the sample mean weight of this sample of 16 is greater than 10.14 is found using the standard normal distribution as follows:
P(Z > z) = P(Z > (10.14 - µ)/(σ/√n))
= P(Z > (10.14 - 10.2)/(0.2/√16))
≈ P(Z > -1.6)
≈ 0.9452.
Therefore, the probability is approximately 0.9452.
(e) The probability that the sample mean weight of this sample of 16 is between 10.14 and 10.3 is found
Using the standard normal distribution as follows:
P(a < Z < b) = P((a - µ)/(σ/√n) < Z < (b - µ)/(σ/√n))
= P((10.14 - 10.2)/(0.2/√16) < Z < (10.3 - 10.2)/(0.2/√16))
≈ P(-1.6 < Z < 2)
≈ 0.9452 - 0.0548
= 0.8904.
Therefore, the probability is approximately 0.8904.
(f) Let x be the average weight of a sample of these 16 cheese wedges that is below some value z.
Then, the probability that x is less than z is 0.07.
Using the standard normal distribution, we can find the z-score such that
P(Z < z) = 0.07 as follows:
z = inv Norm(0.07)
≈ -1.4758.
Therefore, the average weight of a sample of these 16 cheese wedges that is below the value z is:
x = µ + z(σ/√n)
= 10.2 + (-1.4758)(0.2/√16)
≈ 10.0625.
Therefore, there is only a 7% chance that the average weight of a sample of these 16 cheese wedges will be below 10.0625.
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What is the probability of 3 people sharing the same birthdays? How many different pairs of people are there when there are three humans? (Think nPr or nCr)
The probability of three people sharing the same birthdays is approximately [tex]0.0000075[/tex] or [tex]0.00075[/tex]%, and there are three different pairs of people when there are three humans.
The probability of three people sharing the same birthday depends on the assumptions made about the distribution of birthdays. Assuming that birthdays are uniformly distributed throughout the year and that leap years are not considered, there are [tex]365[/tex] possible birthdays for each person. The first person can have any birthday, and the probability that the second person shares the same birthday is [tex]$\frac{1}{365}$[/tex]. Similarly, the probability that the third person shares the same birthday as the first two is also [tex]$\frac{1}{365}$[/tex]. Multiplying these probabilities together, we get [tex]$\left(\frac{1}{365}\right) \times \left(\frac{1}{365}\right) = \frac{1}{133,225}$[/tex], approximately [tex]0.0000075[/tex] or [tex]0.00075\%[/tex].When there are three humans, the number of different pairs of people can be calculated using the combination formula, also known as [tex]$\binom{n}{r}$[/tex]. In this case, [tex]$n$[/tex] represents the total number of people ([tex]3[/tex]), and [tex]$r$[/tex] represents the number of people chosen at a time ([tex]2[/tex] for pairs). Applying the formula, we have [tex]$\binom{3}{2} = 3$[/tex]. Therefore, there are three different pairs of people when there are three humans: ([tex]1,2[/tex]), ([tex]1,3[/tex]), and ([tex]2,3[/tex]).In conclusion, the probability of three people sharing the same birthdays is extremely low (approximately [tex]0.0000075 \ or \ 0.00075\%[/tex]), and when there are three humans, there exist three different pairs of people.
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