[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{-8}-\underset{x_1}{(-6)}}} \implies \cfrac{-4 +3}{-8 +6} \implies \cfrac{ -1 }{ -2 } \implies \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{(-6)}) \implies y +3 = \cfrac{ 1 }{ 2 } ( x +6) \\\\\\ y+3=\cfrac{ 1 }{ 2 }x+3\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 2 }x \end{array}}[/tex]
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than -2.74°C. Round your answer to 4 decimal places
Answer:
Step-by-step explanation:
We are given that the temperature readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Let X be the temperature reading of a single thermometer selected at random. Then, X ~ N(0, 1).
We need to find the probability of obtaining a reading less than -2.74°C, which can be expressed mathematically as P(X < -2.74).
Using standard normal distribution tables or a calculator, we can find that the z-score corresponding to -2.74°C is:
z = (x - μ) / σ = (-2.74 - 0) / 1 = -2.74
The probability can be calculated as:
P(X < -2.74) = P(Z < -2.74) ≈ 0.0030 (rounded to 4 decimal places)
Therefore, the probability of obtaining a reading less than -2.74°C is approximately 0.0030.
Answer:
We need to find the probability of obtaining a reading less than -2.74°C from a normal distribution with a mean of 0°C and a standard deviation of 1.00°C.
Using the standard normal distribution, we have:
z = (x - μ) / σ
where:
x = -2.74°C (the reading we want)
μ = 0°C (the mean)
σ = 1.00°C (the standard deviation)
Substituting the values, we get:
z = (-2.74 - 0) / 1.00 = -2.74
Using a standard normal distribution table or calculator, we find that the probability of obtaining a z-score less than -2.74 is approximately 0.0030.
Therefore, the probability of obtaining a reading less than -2.74°C from the batch of thermometers is approximately 0.0030.
Walmart was having a sale on video games. They offered a 15% discount on a game that was originally priced at $30. After the sale, the discounted price of the game was increased by 10%. What is the new price of the game after this increase?
Answer:
28.05$
Step-by-step explanation:
The game got a discount of 15%.
New price is (30$) ( 0.85 ) = 25.5$ (since the discount is 15% you only pay for the 85% of the original price)
Then an increase of 10%. this is:
New price: 25.5$ (1.10) = 28.05
New price is 28$ with 5 cents
Find the derivative of f(x) = -2x^3 by the limit process…
Answer:
f'(x) = -6x^2
f'(-5) = -150
f'(0) = 0
f'(√17) = -102
ection A-Classwork Let's make mathematical sentences of each of the following stateme Statements Mathematical sentences a) The sum of x and 4 is 7. b) The difference of y and 5 is 4. c) Two times x is 10. d) Two times y added to 3 is 9. e) f) x is more than 2 by 1. 3 is less than y by 2.
a) The sum of x and 4 equals 7: x + 4 = 7
b) The difference of y and 5 equals 4: y - 5 = 4
c) Two times x equals 10: 2x = 10
d) Two times y added to 3 equals 9: 2y + 3 = 9
f) If y > 3 + 2 or if 3 = y - 2 then y is smaller than y by 2
Define equationAn equation is a statement in mathematics that two expressions are equivalent. It has two sides that are divided by the equals sign (=). One or more terms, such as integers, variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation, may be included on each side of the equation.
a) The sum of x and 4 equals 7:
x + 4 = 7
b) The difference of y and 5 equals 4:
y - 5 = 4
c) Two times x equals 10:
2x = 10
d) Two times y added to 3 equals 9:
2y + 3 = 9
e) If x exceeds 2 by 1, then either x = 3 or x > 2 + 1.
f) If 3 is smaller than y by 2 then either y > 3 + 2 or 3 = y - 2
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Please help I-readyyyyyy
Select the correct answer.
Consider the function f(x) = 3° and the function g, which is shown below.
g(x) = f(x) - 2 = 3° _ 2
How will the graph of g differ from the graph of f?
O A.
The graph of g is the graph of fshifted 2 units down.
О B.
The graph of g is the graph of f shifted 2 units up.
O c.
The graph of g is the graph of f shifted 2 units to the left.
O D.
The graph of g is the graph of f shifted 2 units to the right.
Therefore , the solution of the given problem of function comes out to be option A is right response the graph of g is a 2 unit downshifted version of the graph of f.
Explain function.The midterm exam will include questions in variable design, mathematics, each topic, and both actual and hypothetical locations. a catalog of the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input. Additionally, each mailbox has a unique address, which could be an enclave.
Here,
The graph of f is an increasing curve that passes through the point because the exponential growth function f(x) = 3x depicts growth where the base 3 is higher than 1. (0,1).
The curve of f is shifted down by 2 units to yield the function g(x) = f(x) - 2 = 3x - 2. This indicates that to acquire the corresponding y-coordinates of the graph of g, all the y-coordinates of the graph of f must be decreased by 2.
As a result, choice A—the graph of g is the graph of f moved down by two units—is correct.
So, A is the right response. The graph of g is a 2 unit downshifted version of the graph of f.
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Let X be a random variable whose probability density function is given by else (a) Write down the moment generating function for X (b) Compute the first and second moments.
a) The moment generating function of X is
M(t) =
{ (1/(2-t)) e^(-2t) + (1/(2-t)) (1/(1+t)) if t<1
{ infinity if t>=1
b) The first moment (mean) of X is 3/4.
The second moment (expected value of X^2) of X is 7/8
(a) The moment generating function (MGF) of a random variable X with probability density function f(x) is defined as M(t) = E(e^(tX)), where E(.) denotes the expected value operator. Therefore, the MGF of X is
M(t) = E(e^(tX)) = ∫[0,∞) e^(tx) f(x) dx
Substituting the given probability density function f(x), we get
M(t) = ∫[0,∞) e^(tx) (e^(-2x) + (e^-x)/2) dx
Simplifying and integrating by parts, we get
M(t) = [(1/(2-t)) e^(-2t) + (1/(2-t)) (1/(1+t))] for t<1, and
M(t) = infinity for t>=1
Therefore, the MGF of X is
M(t) =
{ (1/(2-t)) e^(-2t) + (1/(2-t)) (1/(1+t)) if t<1
{ infinity if t>=1
(b) To compute the first moment (i.e., the mean or expected value) of X, we take the first derivative of the MGF at t=0
E(X) = M'(0) = d(M(t))/dt | t=0
Differentiating the MGF and simplifying, we get
E(X) = 3/4
To compute the second moment (i.e., the expected value of X^2), we take the second derivative of the MGF at t=0
E(X^2) = M''(0) = d^2(M(t))/dt^2 | t=0
Differentiating the MGF again and simplifying, we get
E(X^2) = 7/8
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The given question is incomplete, the complete question is:
Let x be a random variable whose probability density function is given by f(x) = e^(-2x) + (e^-x)/2 when x>0 f(x) = 0 when else, a) write down the moment generating function X (b) Compute the first and second moments
? Answer the question below. Type your response in the space provided. What do you call the materials that help you achieve your goals?
Answer:
Acquired resources
Step-by-step explanation:
Acquired resources
for populations that are not known to be normally distributed which of the following is true within the central limit theorem
The sampling distribution of the sample mean is approximately normal for large sample sizes, regardless of the distribution of the population is the best definition of the Central Limit Theorem. So the option e is correct.
The Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases. This means that the sample mean will be normally distributed, even if the population from which the sample is drawn is not normally distributed. This is useful because it can be used to make inferences and predictions about the population based on the sample data. So the option e is correct.
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The complete question is:
Which one of the following statements is the best definition of the Central Limit Theorem?
(a) In large populations, the distribution of the population mean is approximately normal.
(b) For non-normally distributed populations, the sampling distribution of the sample mean will be approximately normal, regardless of the sample size.
(c) If the distribution of the population is non-normal, it can be normalized by taking a large sample size.
(d) For large sample sizes, the sampling distribution of the population mean is approximately normal, regardless of the distribution of the population.
(e) The sampling distribution of the sample mean is approximately normal for large sample sizes, regardless of the distribution of the population.
PLEASE HELP, 30 POINTS!
Answer:
1097.28 centimeters
Step-by-step explanation:
You have to multiply length given by 91.44
Answer:
1097.28 cm
Step-by-step explanation:
1 yd = 36 in
=> 12 yrd = 12 x 36 = 432 in
1 in = 2.54 cm
=> 432 in = 432 x 2.54 = 1097.28 cm
solve using systems answer in a ordered pair
y = –x + 3
y = 4x – 2
Answer:
(1,2)
Step-by-step explanation:
Pre-SolvingWe are given the following system of equations:
y = -x + 3
y = 4x - 2
And we want to solve it, with the answer in an ordered pair.
SolvingBecause both systems are equal to y, we can set both of the equations equal to each other, and solve for x in that way.
This is possible due to transitivity, which states that if a=b, and b=c, then a=c.
Hence,
-x + 3 = 4x - 2 (same as y=y)
We can add x to both sides.
3 = 5x - 2
Add 2 to both sides.
5 = 5x
Divide both sides by 5.
1 = x
Now, we can use this value to find y.
Substitute 1 as x in either y = -x + 3 or y = 4x - 2
Taking y = -x + 3 for instance:
y = -1 + 3 = 2
So, we now that x=1, y=2.
As an ordered pair, that is (1,2).
Suppose we want to choose 5 letters, without replacement, from 15 distinct letters
[tex]\text{order does not matter}[/tex]
[tex]\text{sample space}= \text{15 letters}[/tex]
[tex]\text{no repetition}[/tex]
[tex]\text{P(A)}= \text{15C5}= \text{3003 ways}[/tex]
Find the 6th term of the geometric sequence described below.
m₁ = -3(-5)-1
Show your work here
Hint: To add an exponent (z"), type "exponent" or press "A"
Answer:
m₆ = 9375
Step-by-step explanation:
Given sequence is
[tex]m,_i = -3(-5)^{i - 1}[/tex]
To find the 6th term, all you have to do is substitute i = 6 and compute
For i = 6 we get
[tex]m_6 = -3(-5)^{6 - 1}\\= -3(-5)^5\\\\= -3(-3125) \\\\= 9375[/tex]
A negative number raised to an odd number is negative that is why (-5)⁵ is negative
if the slope of the line joining the points (2,4) and (5,k) is 2. find the value of k
10 is the value of k of the slope of the line .
What are slopes called?
Slope, usually referred to as rise over run, is a line's perceived steepness. By dividing the difference between the y-values at two places by the difference between the x-values, we can determine slope.
You may determine a line's slope by looking at how steep it is or how much y grows as x grows. slope categories. When lines are inclined from left to right, they are said to have a positive slope, a negative slope, or a zero slope (when lines are horizontal).
the points (2,4) and (5,k)
formula from slope of two points
slope = y₂ - y₁/x₂ - x₁
substitute the values in formula
slope = 2
slope = k - 4/5- 2
2 =k - 4/3
6 = k - 4
k = 6 + 4
k = 10
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please help me 60 points
Answer:
Matt would walk 8 miles in to hours.
Step-by-step explanation:
15 minutes is 1/4 of an hour, meaning it would be 1/8 of 2 hours.
1 mile times 8 = 8 miles
Hope that helps!
A cylindrical room is rotating fast enough that two small blocks stacked against the wall do not drop. The mass of block A is 4 kg and that of block B is 3 kg. Draw a diagram of the wall and of blocks A and B. Indicate the direction of the acceleration of block B. If it is zero, state that explicitly. Draw separate free-body diagrams for blocks A and B and label the forces as described on page 89. Identify any Third Law companion forces on your diagrams using tick marks like those used in Example 6.1. Rank the magnitudes of all the horizontal forces that you identified above in order from largest to smallest. Explain your reasoning. Determine the magnitude of each of the vertical forces on block A. (Use the g 10 m/s^2. ) If it is not possible to determine one of these, explain why not.
The vertical forces on block A are: the force of gravity acting downwards with a magnitude of 40 N, and the normal force of the wall acting upwards with a magnitude of 40 N. It is not possible to determine the magnitude of the frictional force between block A and block B without knowing the coefficient of static friction.
The force of gravity on block A is equal to its mass (4 kg) times the acceleration due to gravity (10 m/s^2), which gives a magnitude of 40 N. Since block A is in contact with the wall, there must be a normal force acting on it from the wall to counteract the force of gravity. This normal force has the same magnitude as the force of gravity on block A. Therefore, the magnitude of the normal force of the wall on block A is also 40 N.
The frictional force between block A and block B depends on the coefficient of static friction between the two surfaces in contact and the normal force of block A on block B. Since we are not given the coefficient of static friction, we cannot determine the magnitude of the frictional force.
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Sarah is a psychologist at an practise. she earns a basic salary of R3000 per month as well as 20% commission on income up to R 5000. She receives an additional 10% bonus on top of the normal commission rate on earning above R 5000. If Sarah did work to the value of R 12000 ,how much did she earn in total???
Answer:
Sarah earns R6 100 in total for her work to the value of R12 000.
Step-by-step explanation:
To calculate Sarah's earnings, we need to break down her income into two parts: the commission she earns on income up to R5 000, and the bonus commission she earns on income above R5 000.
Commission on income up to R5 000:
Sarah's basic salary is R3 000 per month, and she earns 20% commission on income up to R5 000. So for the first R5 000 of income, Sarah's commission is:
[tex]\text{Commission on income up to} \ R5, 000 = 20\% \ \text{of} \ R5, 000 = R1 ,000[/tex]
Bonus commission on income above R5 000:
Sarah also receives a 10% bonus on top of the normal commission rate on earning above R5 000. So for the amount earned above R5 000, her commission is:
[tex]\text{Commission on income above} \ R5, 000 = (20\% + 10\%) of (R12, 000 - R5, 000) = 30\% \ \text{of} \ R7, 000 = R2 ,100[/tex]
Total earnings:
Sarah's total earnings are the sum of her basic salary and the commission she earns:
Total earnings = Basic salary + Commission on income up to R5 000 + Commission on income above R5 000
[tex]\text{Total earnings} = R3, 000 + R1 ,000 + R2 ,100[/tex]
[tex]\text{Total earnings} = 6,100[/tex]
Therefore, Sarah earns R6 100 in total for her work to the value of R12 000.
for positive integers n. which elements of this sequence are divisible by 5? what about 13? are any elements of this sequence divisible by 65
No element in this sequence can be divided by 5, 13, or 65.
This sequence's elements are not all divisible by 5, 13, or 65.
For positive integers n, we define the sequence a1 = 2n - 3.
We must determine if 2n - 3 is divisible by 5 for various values of n in order to determine whether members of this sequence are divisible by 5.
2ⁿ mod 5 equals 2ⁿ mod 1 = 2ⁿ mod 2 = 4ⁿ mod 3 = 3ⁿ mod 4 = 1, etc.
None of the items in this sequence can be divided by 5, as we can see from the fact that 2ⁿ mod 5 is not necessarily 0.
When divided by 13, 2ⁿ mod 13 equals 2ⁿ mod 1 mod 13 = 2, 2n mod 2 mod 4 mod 8 mod 3 mod 13 = 3, etc.
Since 2ⁿ mod 13 is not necessarily 0, none of the sequence's elements are divisible by 13 as a result.
When 65 is divided by 5*13, 2n mod 65 equals 2n mod 65 times 2, 2ⁿ
mod 65 times 4, 2ⁿ mod 65 times 8, 2ⁿ mod 65 times 3, etc.
None of the items in this sequence are divisible by 65 since 2ⁿ mod 65 is not necessarily 0.
Hence, No element in this sequence can be divided by 5, 13, or 65.
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The complete question is:
Consider the sequence a₁ = = 2¹-3=-1₁ -2²-3=1, 0₂= 03 =2³-3=5, 04-2¹-3=13, ⠀ a₁ = 2" - 3, defined for positive integers n. Which elements of this sequence are divisible by 5?
What about 13? Are any elements of this sequence divisible by 65= 5. 13? Why or why not?
What is 0.1 in exponent form
Answer:
pretty-pretty sure its 1/10
Step-by-step explanation:
Convert to a mixed number by placing the numbers to the right of the decimal over
10
. Reduce the fraction.
1
10
Hence, determine the circumstances of the base base of a coffee tin
Answer:
We can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
Step-by-step explanation:
What is function?
A function is a relation between a dependent and independent variable.
Mathematically, we can write → y = f(x) = ax + b.
Given is to find the diameter and height of the tin can.
Assume the density of coffee as {ρ}. We can write the volume of the tin can as -
Volume = mass x density
Volume = 750ρ
We can write -
πr²h = 750ρ
r = √(750ρ/πh)
D = 2r
D = 2√(750ρ/πh)
Now, we can write the circumferance as -
C = 2πr
C = 2π√(750ρ/πh)
Therefore, we can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
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How many functions are there from the set {1, 2, . . . , n}, where n is a positive integer, to the set {0, 1} a) that are one-to-one? b) that assign 0 to both 1 and n? c) that assign 1 to exactly one of the positive integers less than n?
The number of functions ,
(a) that are one-to-one are 0.
(b) that assign 0 to both 1 and n are 2ⁿ⁻²,
(c) that assign "1" to exactly one of positive-integers less than n are 2.(n-1).
Part(a) : We have to find total number of "one-to-one" functions from the set {1,2,......,n} to {0,1}.
⇒ If n=1 then there are 2 possible functions depending whether 1 is mapped to "0" or "1" ,So there are 2 such functions.
⇒ If n=2 then domain is {1,2} then there are 2 choices for first element in domain.
Then, since one choice is taken there is one choice for second element in the domain. So, if n=2 we have 2×1 = 2 functions.
⇒ If value of n is greater than 2 then domain will be {1,2,....n} then only two value of this domain will be mapped to codomain {0,1} to provide a one-to-one function and
So, domain will not be used fully so there does not exist any one-to-one function.
Part(b) : Every element in the domain {1, 2, . . . , n} has two options in codomain {0, 1},
So, there are total of "2n" functions from domain to co-domain.
Since, the function assigns 0 to both 1 and n.
There are "n-2" elements left in domain which can be assigned 0 or 1.
So, for "n-2" elements in domain and there are "2ⁿ⁻²" functions from domain to codomain.
Part(c) : The domain set has "n" elements and codomain set has "2" elements.
So, each of "n" elements from domain has 2 choices in function and thus we get "2n" total functions.
There are "n-1" elements less than "n" in domain.
Now, by the condition that exactly "1" positive-integer less than "n" maps to "1".
So, all other remaining less than n (i.e. n-2) must be map to 0.
We find this number in ⁿ⁻²C₁ ways = n-2;
So, total number of ways in which elements less than "n" can be mapped is = n-2(mapped to 0) +1(mapped to 1) = n-1
Also, "n" can be mapped to either "0" or "1" which means., nth element have two-choices.
So, there are 2.(n-1) possible functions.
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Where i = sqrt(- 1) which of the following complex numbers is equal to (6 - 5i) - (4 - 3i) + (2 - 7i) ? A (4 - 9i)/25 B 4 - i C 9i - 4 D 4 - 9i E 4 + 9i
Answer: A) 4 - 9i/25
Step-by-step explanation:
We can simplify the expression (6 - 5i) - (4 - 3i) + (2 - 7i) by combining the real and imaginary parts separately:
Real part: (6 - 5i) - (4 - 3i) + (2 - 7i) = 6 - 4 + 2 - (-5i + 3i + 7i) = 4 - 5i
Imaginary part: 0
Therefore, the complex number equal to (6 - 5i) - (4 - 3i) + (2 - 7i) is 4 - 5i.
None of the answer choices matches this result exactly, but we can simplify 4 - 5i further:
(4 - 5i)/1 = (4 - 5i)/sqrt(1*1) [multiply the numerator and denominator by 1]
= (4/sqrt(1)) - (5/sqrt(1))i [divide the real and imaginary parts by 1]
= 4 - 5i
Therefore, the answer is A) (4 - 9i)/25. We can verify this by multiplying the numerator and denominator of this fraction by 25:
(4 - 9i)/25 = (4/25) - (9/25)i
Now, we can see that this is equivalent to 4 - 5i, which is the simplified form of the original expression.
A baker baked 124 more chocolate cookies than almond cookies. He sold 3/4 of his chocolate cookies and 2/3 of almond cookies and had a total of 66 cookies left. How many cookies were sold altogether?
Answer:
792
Step-by-step explanation:
so first we need find out how many fraction of cookie is left
[tex]\frac{3}{4} -\frac{2}{3} =\frac{1}{12}[/tex] this had been equal to 66
which we use this to time 66
12•66=792 in total
if you want to know chocolate that will be 458
and almond will be 334
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which purchased paint for an upcoming project. She purchased three different colors,
which come in different sized containers. How much paint does she have altogether?
Color
White
Black
Yellow
Amount
0,4 L
0.75 L
0.3 L
Answer:
1.45 L
Step-by-step explanation:
Suppose that an individual has a body fat percentage of 16.3% and weighs 163 pounds. How many pounds of his weight is made up of fat? Round your answer
to the nearest tenth.
pounds
X
Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).
what is unitary method ?By determining the value of a single unit or quantity and then scaling that value up or down to determine the value of another quantity, the unitary method is a mathematical strategy used to solve problems. According to the unitary method's guiding concept, if one quantity or unit has a certain value, then a predetermined number of those same quantities or units will have a proportionate value. For instance, 5 apples would cost $5 if 1 fruit cost $1.
given
We can use the person's weight and body fat proportion to determine how many pounds of body fat they have. We can commence by calculating the decimal weight of the body fat:
weight of body fat Equals body fat percentage * weight
= 0.163% * 163 lbs.
= 26.509 lbs.
Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).
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Please help me on this geometry question. Use a trig function to find the missing side to the nearest 10. Please show step by step
Answer:
x = 42.9
Step-by-step explanation:
We can let 34 represent the reference angle. Using this angle, we see that the side measuring 24 units is the opposite side and the side measuring x is the hypotenuse.
Thus, we can use the sine trig function which is
[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]
We plug in what we have into the equation above and solve for x:
[tex]sin(34)=\frac{24}{x}\\ x*sin(34)=24\\x=\frac{24}{sin(34)}\\ x=42.9189996\\x=42.9[/tex]
Elizabeth works as a server in coffee shop, where she can earn a tip (extra money) from each customer she serves. The histogram below shows the distribution of her 60 tip amounts for one day of work. 25 g 20 15 10 6 0 0 l0 15 20 Tip Amounts (dollars a. Write a few sentences to describe the distribution of tip amounts for the day shown. b. One of the tip amounts was S8. If the S8 tip had been S18, what effect would the increase have had on the following statistics? Justify your answers. i. The mean: ii. The median:
a. Histogram shows tip amounts ranging between $6 and $25, skewed to the right with a longer tail of higher tips.
b. Increasing the $8 tip to $18 would increase the mean since total tip amount increases by $10 spread out over 60 customers. Median won't be affected since changing one value does not alter the middle value.
a. The histogram shows that Elizabeth received a range of tip amounts, with the majority of tips falling between $6 and $25. The distribution is skewed to the right, with a longer tail of higher tip amounts.
b. i. The mean would increase because the total tip amount would increase by $10, and this increase would be spread out over the 60 customers.
ii. The median would not be affected because it is the middle value when the data is ordered, and changing one value does not change the middle value.
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According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.† Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800.
(a) What is the probability that a household in Maryland has an annual income of $90,000 or more? (Round your answer to four decimal places.)
(b) What is the probability that a household in Maryland has an annual income of $50,000 or less? (Round your answer to four decimal places.)
The required probability that a household in Maryland with annual income of ,
$90,000 or more is equal to 0.3377.
$50,000 or less is equal to 0.2218.
Annual household income in Maryland follows a normal distribution ,
Median = $75,847
Standard deviation = $33,800
Probability of household in Maryland has an annual income of $90,000 or more.
Let X be the random variable representing the annual household income in Maryland.
Then,
find P(X ≥ $90,000).
Standardize the variable X using the formula,
Z = (X - μ) / σ
where μ is the mean (or median, in this case)
And σ is the standard deviation.
Substituting the given values, we get,
Z = (90,000 - 75,847) / 33,800
⇒ Z = 0.4187
Using a standard normal distribution table
greater than 0.4187 as 0.3377.
P(X ≥ $90,000)
= P(Z ≥ 0.4187)
= 0.3377
Probability that a household in Maryland has an annual income of $90,000 or more is 0.3377(rounded to four decimal places).
Probability that a household in Maryland has an annual income of $50,000 or less.
P(X ≤ $50,000).
Standardizing X, we get,
Z = (50,000 - 75,847) / 33,800
⇒ Z = -0.7674
Using a standard normal distribution table
Probability that a standard normal variable is less than -0.7674 as 0.2218. This implies,
P(X ≤ $50,000)
= P(Z ≤ -0.7674)
= 0.2218
Probability that a household in Maryland has an annual income of $50,000 or less is 0.2218.
Therefore, the probability with annual income of $90,000 or more and $50,000 or less is equal to 0.3377 and 0.2218 respectively.
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4.5. Using Linear Scale
Solve the following scenarios.
8. You have a map that is missing a scale. The distance from Point A to Point B is
five inches on the map, and after driving it, you know it is 250 miles in reality.
The scale of the map is 1 inch to 50 miles, or 1:50.
What is distance?
Distance is defined as the space between two points in space.
To find the scale of the map in inches per mile, we can use the ratio of the distance on the map to the actual distance:
5 inches on the map / 250 miles in reality
Simplifying this ratio gives:
1 inch on the map / 50 miles in reality
Therefore, the scale of the map is 1 inch to 50 miles, or 1:50.
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Please order the following fractions from least to greatest: 5/6, 2/3, 5/9, 5/12, 6/5
Answer:
5/12, 5/9, 2/3, 5/6, 6/5
Step-by-step explanation:
5/12= 0.41666667, 5/9= 0.55555556, 2/3= 0.66666667, 5/6= 0.83333333, 6/5= 1.2