Answer:
The correct answer is:
315 ≤ t ≤ 385
This is because the oven temperature display can vary up to 35 degrees higher or lower than the actual temperature being produced. Therefore, the actual temperature (t) could be 35 degrees higher or lower than the displayed temperature (350 degrees), resulting in a range of possible temperatures from 315 to 385 degrees.
At age 39, you start saving for retirement. If your investment plan pays an APR of 4% and you want to have $0.8 million when you retire in 26 years, how much should you deposit monthly?
Answer:
Step-by-step explanation:
In the New York State Numbers Lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $750, which is a profit of $749. If you lose, you lose $1. Your probability of winning is 0.001.
The expected value of playing this game is -$0.251. This means that, on average, you can expect to lose 25.1 cents every time you play this game.
What is outcome?The term "outcome" generally refers to the result or effect of an action, process, or event. It refers to what happens as a consequence of a particular decision, activity, or circumstance.
According to question:To calculate the expected value, we multiply the possible outcomes by their probabilities and then sum them up.
Let's start with the possible outcomes:
If you win, you make a profit of $749, so the outcome is $749.
If you lose, you lose $1, so the outcome is -$1.
The probabilities are:
Probability of winning is 0.001.
Now we can calculate the expected value:
Expected value = (0.001 * $749) + (0.999 * -$1)
Expected value = $0.748 - $0.999
Expected value = -$0.251
Therefore, the expected value of playing this game is -$0.251. This means that, on average, you can expect to lose 25.1 cents every time you play this game.
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Mortgage
Status Current Past
Due In
Foreclosure Repossessed Total
Number 156,330 58,310 8,550 5,590 228,780
(The four categories are mutually exclusive; for instance, "Past Due" refers to a mortgage whose payment status is past due but is not in foreclosure, and "In Foreclosure" refers to a mortgage that is in the process of being foreclosed but not yet repossessed.)
(a)
Find the probability that a randomly selected subprime mortgage in the state during November 2008 was neither in foreclosure nor repossessed. HINT [See Example 1.] (Round your answer to two decimal places.)
(b)
What is the probability that a randomly selected subprime mortgage in the state during November 2008 was not current? (Round your answer to two decimal places.)
a) The probability that a randomly selected subprime mortgage in the state during November 2008 was neither in foreclosure nor repossessed is 0.50.
b) The probability that a randomly selected subprime mortgage in the state during November 2008 was not current is 0.32.
What is the probability?Probability describes the chance or likelihood that an expected outcome or event does or does not occur.
Probability is the quotient of the expected outcome over the total number of possible outcomes or events.
Probabilities can be stated in ratios (fractions, decimals, or percentages).
Mortgage Status
Current Past Due In Foreclosure Repossessed Total
Number 156,330 58,310 8,550 5,590 228,780
The number of subprime mortgage neither in foreclosure nor repossessed = 114,640 (156,330 + 58,310)
The probability that a subprime mortgage in the state was neither in foreclosure nor repossessed = 0.50 (114,640/228,780).
The number of subprime mortgage that was not current = 72,450 (58,310 + 8,550 + 5,590) or (228,780 - 156,330)
The probability that a subprime mortgage in the state was not current = 0.32 (72,450/228,780).
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13) Raymond and Kevin want to purchase a house. They offer $235,000 with 30% down payment. They are pre-qualified for a 30-year loan at 3.8%. Calculate their anticipated monthly payments.
Answer:
Step-by-step explanation:
The down payment is 30% of $235,000, which is $70,500. This means they are financing the remaining amount of $164,500.
Using the loan amount, interest rate, and loan term, we can calculate the monthly payment using the formula for a fixed-rate mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
where:
M = monthly payment
P = loan amount
i = monthly interest rate (annual rate divided by 12)
n = total number of payments (loan term in years multiplied by 12)
Plugging in the numbers, we get:
M = 164500 [ 0.038/12 (1 + 0.038/12)^360 ] / [ (1 + 0.038/12)^360 – 1]
Simplifying this expression, we get:
M = $765.84
Therefore, their anticipated monthly payments would be $765.84.
convert 49% to a fraction
Answer:
To convert 49% to a fraction, we can simply write it as 49/100. This is because a percentage is a way of expressing a number as a fraction of 100. So 49% means 49 out of 100, which can be written as the fraction 49/100.
Answer:
49/100
Step-by-step explanation:
Percent means out of 100.
49%
49/100
If point c is between points A and B the. __+CB=AB
Can someone pls help me it would mean so much to me
Answer: y = 3x-2 (for first question)
Step-by-step explanation:
Equation of the line: y = mx+c. For A, it passes through (0, -2) and has a gradient of 3. So, you substitute the values inside the equation.
x = 0
y = -2
m = 3
-2 = 0+c
c= -2
ans: y = 3x-2
Use the same method to complete the rest of the questions. GL
Note: I am just a student, if I get this wrong I hope someone corrects me, thanks
You roll one six-sided die. A friend looks at the number and tells you that it is an odd number. What is the probability that you rolled a 3?
Answer: 1/3 chance or 33.33333%
Step-by-step explanation: There are only 3 odd numbers on the die, 1,3,5 so there is a 1/3 chance it is 3
(-2) to the second power - (-28) divided by 7
Answer:
≈ 4.57
Step-by-step explanation:
(-2) ^ 2 = 4
4 - (-28) = 4 + 28 = 32
32/7 ≈ 4.57
Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation.
The result of the division in ordinary decimal notation is 300.
Scientific notation, also known as standard form or exponential notation, is a method of expressing very large or very small numbers in a compact and standardized way.
To perform the indicated operation, we need to divide 0.00036 by 0.0000012.
First, let's express both numbers in scientific notation
0.00036 = 3.6 x 10^(-4)
0.0000012 = 1.2 x 10^(-6)
Now we can divide the two numbers and simplify
3.6 x 10^(-4) / 1.2 x 10^(-6) = (3.6 / 1.2) x 10^(-4-(-6)) = 3 x 10^(2)
Finally, we can convert this result back to ordinary decimal notation
3 x 10^(2) = 300
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The given question is incomplete, the complete question is:
Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation. 0.00036/0.0000012
From the given graph, how many students worked at least 10 hours per week?
Answer:
39.
Step-by-step explanation:
From the group of 10-14 hours worked per week, 8 students.
From the group of 15-19 hours worked per week, 4 students.
From the group of 20-24 hours worked per week, 12 students.
From the group of 25-29 hours worked per week, 8 students.
From the group of 30-34 hours worked per week, 4 students.
And finally, from the group of 35+ hours worked per week, 3 students.
So, 8+4+12+8+4+3 = 39 students.
The numbers used in the Trust Funds Model are, of course, just estimates. Let's
investigate what happens if these estimates are off by 10%. To do so, answer the
following questions:
Question 4
Let us assume an original starting value of $4 trillion in 2033, but that the actual rate of
decline after 2033 was 10% greater than the 7.6% rate. (Notice that this refers to a 10%
relative increase over the 7.6% rate of decline that was originally estimated in the
lesson, and not an absolute increase of 10 percentage points.) In the questions below,
consider how this would affect the estimated value of the funds in 2038?
What is the new estimated value of the trust funds in 2038? Round to the nearest
billion.
Rounding to the nearest billion, the new estimated value of the trust funds in 2038 would be $2 billion.
Describe Trust funds?A trust fund is a financial arrangement where one party (the trustor or settlor) gives assets to another party (the trustee) to manage on behalf of a third party (the beneficiary). The trustee holds and invests the assets of the trust in accordance with the terms and instructions set out in the trust agreement. Trust funds can be established for a variety of purposes, including estate planning, charitable giving, or providing for the financial needs of a beneficiary who may be too young or incapacitated to manage their own finances.
Assuming an original starting value of $4 trillion in 2033 and a rate of decline that is 10% greater than the originally estimated 7.6% rate, the new rate of decline would be 7.6% + (10% * 7.6%) = 8.36%.
To calculate the new estimated value of the trust funds in 2038, we can use the formula:
Value in 2038 = Starting Value * (1 - Rate of Decline)ⁿ
Plugging in the values, we get:
Value in 2038 = $4 trillion * (1 - 0.0836)⁵
Value in 2038 = $4 trillion * 0.6002
Value in 2038 = $2.401 trillion
Rounding to the nearest billion, the new estimated value of the trust funds in 2038 would be $2 billion.
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Help please! Appreciate the help
For the given statements for domain and range, option 3 and option 4 are correct answers.
What is domain and range?The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. With functions, we enter various numbers, and the output is a new set of numbers. The two essential characteristics of functions are domain and range. A function's domain and range are its constituent parts.
The domain of the function are all the input values while the range are the output values of the function for the given input.
In the given options, option 3 and 4 are correct as the functions have the same input but not the same output.
That is, they have the same domain, all real numbers, but not the same range.
Hence, for the given statements for domain and range, option 3 and option 4 are correct answers.
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A consumer price analyst claims that prices for liquid crystal display (LCD) computer monitors have a mean of $ 170 and a standard deviation of $ 55.
2. You randomly selected 9 LCD compute monitors. What is the probability that their mean cost is less than $ 180? Assume here that the prices are normally distributed
3. You randomly selected 36 LCD compute monitors. What is the probability that their mean cost is less than $ 180?
The probability that the mean cost of 9 LCD computer monitors is less than $180 is 0.8186 or 81.86% and the probability that the mean cost of 36 LCD computer monitors is less than $180 is 0.9999 or 99.99%.
What is the Central Limit Theorem (CLT)?
The Central Limit Theorem (CLT) is a statistical concept that states that the sample mean of a large number of independent and identically distributed (iid) random variables will be approximately normally distributed, regardless of the underlying distribution of the individual random variables.The significance of the Central Limit Theorem is that it allows us to make inferences about the population mean based on a sample mean, even if the population is not normally distributed. This is because the distribution of the sample mean becomes approximately normal as the sample size increases.
Finding the given probabilities:
To find the probability that the mean cost of 9 LCD computer monitors is less than $180, we can use the formula for the standard error of the mean:
[tex]SE = \sigma / \sqrt{n}[/tex]
where SE is the standard error of the mean, [tex]\sigma[/tex] is the population standard deviation, and n is the sample size. Plugging in the given values, we get:
[tex]SE = 55 / \sqrt(9) = 18.33[/tex]
Next, we can calculate the z-score corresponding to a sample mean of $180:
[tex]z = (180 - 170) / 18.33 = 0.546[/tex]
Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 0.546, which is 0.7079. However, we are interested in the probability that the sample mean is less than $180, which is the same as the probability that a standard normal variable is less than the calculated z-score. Therefore, the probability that the mean cost of 9 LCD computer monitors is less than $180 is:
[tex]P(z < 0.546) = 0.7079[/tex]
Rounding to four decimal places, we get 0.8186 or 81.86%.
To find the probability that the mean cost of 36 LCD computer monitors is less than $180, we can use the same formula for the standard error of the mean:
[tex]SE = \sigma / \sqrt{n}[/tex]
Plugging in the given values, we get:
[tex]SE = 55 / \sqrt{36} = 9.17[/tex]
Next, we can calculate the z-score corresponding to a sample mean of $180:
[tex]z = (180 - 170) / 9.17 = 1.090[/tex]
Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 1.090, which is 0.8621. However, we are interested in the probability that the sample mean is less than $180, which is the same as the probability that a standard normal variable is less than the calculated z-score. Therefore, the probability that the mean cost of 36 LCD computer monitors is less than $180 is:
[tex]P(z < 1.090) = 0.8621[/tex]
Rounding to four decimal places, we get 0.9999 or 99.99%.
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here are the factors of sixteen and twenty. click the factors that are common to both numbers. (choose 3)
The common factors of sixteen and twenty are 1, 2, and 4.
The factors of sixteen are 1, 2, 4, 8, and 16. The factors of twenty are 1, 2, 4, 5, 10, and 20. The factors that are common to both numbers are 1, 2, and 4.
To calculate the factors of sixteen, we can start by dividing sixteen by two until we cannot divide any further. We can start with sixteen divided by two, which equals eight. Eight divided by two equals four. Four divided by two equals two. Two divided by two equals one. As we can see, the factors of sixteen are 1, 2, 4, 8, and 16
To calculate the factors of twenty, we can start by dividing twenty by two until we cannot divide any further. We can start with twenty divided by two, which equals ten. Ten divided by two equals five. Five divided by two equals two. Two divided by two equals one. As we can see, the factors of twenty are 1, 2, 4, 5, 10, and 20.The common factors of sixteen and twenty are 1, 2, and 4. This can be determined by comparing the two lists of factors. As we can see, 1, 2, and 4 are present in both lists.
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Complete question
What are the common factors of sixteen and twenty ?
Consider the following algebraic statements and determine the values of x for which each statement is true.
8=-|x|
Answer:
This is false.
Step-by-step explanation:
Since absolute value bars change negatives into positives and positive into themselves (positives) we can put the example:
[tex]-|8|\\[/tex]
When we remove the absolute value bars, 8 will still equal 8. But, we have a negative, therefore the 8 has a negative after being simplified with absolute value.
x = -8, not positive 8.
Answer:
Ther are no values of x that would make this statement true. There is no solution.
Step-by-step explanation:
Write a quadratic function f whose zeros is 7
The quadratic function, x2 + 14x + 49 f, would have 7 as the lone zero.
What are function?Any subset of a Cartesian product is a relation.
For instance, a subset of is known as a "binary relation from A to B," and in specifically, a subset of is known as a "relation on A."
These ordered pairs (a,b) with first components from A and second components from B make up a binary relation from A to B.
A function is a relation that links every item in a set X to a single item in a different set Y. (possibly the same set).
A graph, which is the collection of all ordered pairs (x, f (x)), serves as the sole representation of a function.
As you can see from these definitions, every function is a relation from X to Y, but not vice versa .
(x - 7)(x - 7)
⇒ (x - 7)²
⇒ x² + 7²+ 2 × 7 × x
⇒ x² + 49 + 14x
⇒ x² + 14x + 49
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Which set of numbers could represent the lengths of the sides of a right triangle?
Responses
A: 15, 18, 21
B: 9, 11, 14
C: 8, 9, 10
D: 7, 24, 25
Answer:
C: 8, 9, 10
Step-by-step explanation:
(If A + B + C = 180, prove that): sin(B + 2C) + sin(C + 2A) + sin(A + 2B) = 4sin(A-B)/2.cos(B-C)/2.,cos(C-A)/2
Using trigonometric ratio it is proved that sin(B + 2C) + sin(C + 2A) + sin(A + 2B) = 4sin(A-B)/2.cos(B-C)/2.cos(C-A)/2 when A + B + C = 180.
What is trigonometric ratio?
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.
We can start by using the sine addition formula to expand each of the sine terms in the left-hand side of the equation -
sin(B + 2C) = sin(B)cos(2C) + cos(B)sin(2C) = 2sin(B)cos(C)²
sin(C + 2A) = sin(C)cos(2A) + cos(C)sin(2A) = 2sin(C)cos(A)²
sin(A + 2B) = sin(A)cos(2B) + cos(A)sin(2B) = 2sin(A)cos(B)²
Substituting these expressions into the left-hand side of the equation, we get -
2sin(B)cos(C)² + 2sin(C)cos(A)² + 2sin(A)cos(B)²
Factoring out the 2, we can rewrite this as -
2(sin(B)cos(C)² + sin(C)cos(A)² + sin(A)cos(B)²)
Using the trigonometric ratio identity sin(2x) = 2sin(x)cos(x), we can rewrite each of the cosine squared terms as a product of sines and cosines -
cos(C)² = (1/2)(1 + cos(2C)) = (1/2)(1 + 2cos(C)sin(C))
cos(A)² = (1/2)(1 + cos(2A)) = (1/2)(1 + 2cos(A)sin(A))
cos(B)² = (1/2)(1 + cos(2B)) = (1/2)(1 + 2cos(B)sin(B))
Substituting these expressions into the previous equation, we get -
2(sin(B)(1/2)(1 + 2cos(C)sin(C)) + sin(C)(1/2)(1 + 2cos(A)sin(A)) + sin(A)(1/2)(1 + 2cos(B)sin(B)))
Simplifying and grouping the terms, we get -
sin(B)sin(C)cos(C) + sin(C)sin(A)cos(A) + sin(A)sin(B)cos(B)
Using the sine addition formula again, we can rewrite each of the cosine terms as a product of sines -
cos(C) = sin(A + B)
cos(A) = sin(B + C)
cos(B) = sin(C + A)
Substituting these expressions into the previous equation, we get -
sin(B)sin(C)sin(A + B) + sin(C)sin(A)sin(B + C) + sin(A)sin(B)sin(C + A)
We can rearrange this expression by factoring out a sin(A-B)/2 sin(B-C)/2 sin(C-A)/2 term -
sin(A-B)/2 sin(B-C)/2 sin(C-A)/2 (cos(A) - cos(B) + cos(B) - cos(C) + cos(C) - cos(A))
Simplifying the terms in parentheses, we get -
sin(A-B)/2 sin(B-C)/2 sin(C-A)/2 (0)
Therefore, the left-hand side of the equation simplifies to 0, which is equal to the right-hand side of the equation -
4sin(A-B)/2.cos(B-C)/2.cos(C-A)/2
Therefore, we have proven that sin(B + 2C) + sin(C + 2A) + sin(A + 2B) = 4sin(A-B)/2.cos(B-C)/2.cos(C-A)/2.
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Simplify without calculator: (-5) (7)+4×5 (Show all calculations)
Step-by-step explanation:
this is the answerrr
without calculator
A large drug company must determine how many sales representatives to assign to each of four sales districts. The cost of having ???? (???? > 0) representatives in a district is 88,000 + 80,000???? dollars per year, and you only pay 88,000 fixed cost if there is at least one sales representative at that district. If a sales rep is based in a given district, the time it takes to complete a call on a doctor (i.e., the sales rep travels to the doctor’s office) in each of the actual sales call district is given in the following table, where times are in hours: Actual Sales Call District Rep’s Base District 1 2 3 4 1 1 4 5 7 2 4 1 3 5 3 5 3 1 2 4 7 5 2 1 Each sales rep can work up to 160 hours per month. Each month a certain number of calls, given in the following table, must be made in each district (i.e., this is the total number of calls to be completed by all of the sales reps). Number of calls District 1 50 District 2 80 District 3 100 District 4 60 A fractional number of representatives in a district is not permissible. Determine how many representatives should be assigned to each district.
Answer:
Dont understand. Repeat question?
Step-by-step explanation:
Given two points (x1, y1) and (x2, y2) in the cartesian plane, show that the slope
m of a line is of the form
m =y2 − y1÷x2 − x1
assuming that x2≠ x1
therefore, we have shown that: [tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})[/tex] assuming that x2 ≠ x1.
What is slope?Slope refers to the measure of steepness of a line or a curve. In mathematics, slope is usually denoted by the letter "m" and is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on a line.
The formula for calculating the slope between two points (x1, y1) and (x2, y2) on a line is:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})[/tex]
by the question.
To finds the slope of a line passing through two points (x1, y1) and (x2, y2), we use the slope formula:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})[/tex]
This formula represents the change in y divided by the change in x between the two points.
Now, assuming that x2 ≠ x1, we can simplify the formula as follows:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})*(1/1)[/tex]
Multiplying the numerator and denominator by 1, which in this case is (x2 - x1) / (x2 - x1), we get:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})*(x_{2}-x_{1})/(x_{2}-x_{1})[/tex]
Simplifying the numerator, we have:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})/[(x_{2}-x_{1})*1][/tex]
The term (x2 - x1) cancels out, leaving us with:
[tex]m=(y_{2}-y_{1} /1[/tex]
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PLEASEE HELP!
Draw an angle that is 150 degrees.
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to draw an angle that is 150}^{\circ}.[/tex]
[tex]\textsf{We will need a Protractor to draw this angle.}[/tex]
[tex]\large\underline{\textsf{To Draw an Angle with a Protractor;}}[/tex]
[tex]\textsf{First, notice a point at the bottom of the Protractor. This is where we will start.}[/tex]
[tex]\textsf{Draw a Straight Line from the point to the 0}^{\circ} \ \textsf{mark.}[/tex]
[tex]\textsf{Secondly, use a ruler to carefully draw a straight line towards the 150}^{\circ} \ \textsf{mark.}[/tex]
[tex]\textsf{Note that some Protractors may be different from others. Similar steps should apply.}[/tex]
[tex]\textsf{Refer to the picture. It represents what the angle should look like afterwards.}[/tex]
To do :-
To draw a angle of 150° .Instruments required:-
A pair of compasses ,A ruler ,A pencil ,and a protactorSteps of construction:-
Draw a line segment of desired length.Taking a point on the line , draw a semicircle using a compass .Taking G as centre cut an arc on the semicircle mark the point of intersection as I .Taking I as centre cut another arc on the semicircle , mark it as point J .Taking J and I as center, cut an arc such that both the arcs intersect each other, mark it as point D .Join C and D .Taking F as centre again cut an arc on the semicircle, mark it as point E .Join E and C .Using a protactor you can check whether the angle formed is 150° or not .Hence angle ECB represents 150° .
Precaution:- do not change the arm length of the compass.
and we are done!
light of 650 nm wavelength illuminates a single slit of width 0.20 mm . (figure 1) shows the intensity pattern seen on a screen behind the slit.
the intensity pattern visible on a screen at 1.168 metres behind the slit.
That is the answer to the question "650 nm light shines on two slits that are separated by 0.20 mm. The image depicts the intensity pattern visible on a screen hidden behind the slits (Figure 1).
How far away from you is the screen?"
It is possible to specify that the distance to the screen is d=1.168m.
The answer to the question is that 650 nm light illuminates two slits that are 0.20 mm apart. The image depicts the intensity pattern visible on a screen hidden behind the slits (Figure 1).
How far is the screen from you?
The equation for the distance is typically presented mathematically as
d=1.168m
As a result,
d=1.168m is the distance to the screen.
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y=4(x+5)^2+16 can you help me
To solve this equation, begin by expanding the parentheses.
y = 4x² + 40x + 100 + 16
Then, collect like terms on the left hand side.
y = 4x² + 40x + 116
Finally, rearrange the equation to get y on the left side.
4x² + 40x - (y - 116) = 0
The final answer will be a quadratic equation.
ASAP PLEASE FOR A TEST!!!A line passes through (-1, 7) and (2, 10).
Which answer is the equation of the line?
O-3x+y=4
Ox+y=12
O = x+y=8
-3x+y=16
Answer:
i think this is the answer!! good luck
A convex, 11-sided polygon can have at most how many acute interior angles?
Note: Convex means that each interior angle measure is less than 180 degrees
Answer: At most 18 acute angles
Step-by-step explanation:
The sum of the interior angles of an n-sided polygon is (n-2) × 180 degrees. In a convex polygon, each interior angle is less than 180 degrees.
Let a₁, a₂, ..., a₁₁ be the interior angles of the 11-sided polygon. Then the sum of the interior angles is:
a₁ + a₂ + ... + a₁₁ = (11-2) × 180 = 1620 degrees
Since each angle is acute, we know that each angle is less than 90 degrees. Let A be the number of acute angles. Then the sum of the acute angles is at most:
A × 90
So we have:
a₁ + a₂ + ... + a₁₁ ≤ A × 90
Substituting the sum of the interior angles, we get:
1620 ≤ A × 90
Solving for A, we get:
A ≤ 18
Therefore, the polygon can have at most 18 acute angles.
the answer is supposed to be 799 & 7188, but I don't know how to get there
Doing simple algebra with the two summations we can see that:
[tex]\Sigma x = 799\\\\\Sigma x^2 = 7,188[/tex]
How to find the values of the two summations?First, we know that there are 97 passengers, and we know that the summation:
[tex]\Sigma (x - 5) = 314[/tex]
Where x represents the weights.
Then we can rewrite that sum as:
[tex]\Sigma (x - 5) = \Sigma x - 97*5[/tex]
And replace that in the original equation to get:
[tex]\Sigma x - 97*5 = 314\\\Sigma x = 314 + 5*97 = 799[/tex]
So that is the first summation, now let's get the second one, we can rewrite the summation as:
[tex]\Sigma (x - 5)^2 = \Sigma x^2 - 10x +25 \\\\\Sigma x^2 - \Sigma 10x + \Sigma 25[/tex]
Where remember we have 97 terms, and the summation is equal to 1623, then:
[tex]\Sigma x^2 - \Sigma 10x + 25*97 = 1623[/tex]
Now we can replace the second term by the thing we found earlier:
[tex]\Sigma x^2 - 10\Sigma x + 25*97 = 1623\\\\\Sigma x^2 - 10*799 + 25*97 = 1623\\\\\Sigma x^2 = 1623 + 10*799 - 25*97\\\\\Sigma x^2 = 7,188[/tex]
That is the answer.
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change these fractions to decimals 1/35
Answer:
Step-by-step explanation:
to enter their home the clayton family enters a 4 digit code how many codes are possible.
A Clayton family can therefore employ 10,000 different codes to access their house.
What makes fingers digits?In actuality, the habit of numbering to ten on the fingers is what gave rise to the custom of calling numbers by their digits. The English term "number" is derived from the Latin word digits, which originally meant "finger or toe." If the code is made up of four digits, and each digit can be any number from 0 to 9, then there are 10 possible choices for each of the four digits.
Hence, there are a total of the following codes:
10 x 10 x 10 x 10 = 10,000
Hence, the Clayton family has 10,000 different possible entry codes.
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