Answer:
first, arrange the numbers from least to greatest order. (Actually this is a longer step, if you also want to find the median. But since you are only asking for range and standard deviation, I won't do that here.) So, just find the lowest number and the highest number. Subtract the lowest from the highest. That is your range.
Your problem:
lowest: 98.6
highest: 131.9
subtract: 131.9 - 98.6 = 33.3 ← this is your range
Now, standard deviation.
Standard deviation is the amount of variety you have in your data sample.
Step 1: Find the mean
Add up all your numbers and divide by how many numbers you have.
You have 10 numbers in your sample.
115.6 + 109.3 + 126 + 104.9 + 131.9 + 113.7 + 119.8 + 98.6 + 131.9 + 131.9
total = 1,183.6
now divide this by 10. (n is the variable used here, so n = 10. This is because you have ten numbers. )
so n = 10
and 1,183.6/10 = 118.3
Now subtract each number by 118.3.
115.6 - 118.3 = -2.7
109.3 - 118.3 = -9
126 - 118.3 = 7.7
104.9 - 118.3 = -13.4
131.9 -118.3 = 13.6
113.7 - 118.3 = -4.6
119.8 - 118.3 = 1.5
98.6 - 118.3 = -19.7
131.9 - 118.3 = 13.6
131.9 - 118.3 = 13.6
now square all these numbers
7.29
81
59.29
179.56
184.96
21.16
0.75
388.09
184.96
184.96
Find the sum of these squares now. (We're almost done!)
sum = 1,292.02
remember our n?
it was n=10
now the formula for this is,
sum of squares ÷ n-1
substitute all this in.
1,292.02 ÷ 9 = 143.55
Remember. This is the VARIANCE. NOT the standard deviation.
The last step to find the standard deviation is, to find the square root of what we got. (143.55)
√143.55
= 11.9812353286 this is the number, but rounded two more decimal places is..
11.98 is the standard deviation.
Hope this helped!
You were assigned to make souvenirs. You have 4m
20cm of ribbon which you plan to use. You want to
cut the ribbon equally into 70cm long pieces. How
many smaller ribbons can you make?
First, we need to convert the length of the ribbon to centimeters to match the length of the ribbon pieces we plan to cut:
4m 20cm = (4 x 100)cm + 20cm = 420cm
Next, we can divide the total length of the ribbon by the length of each piece to find how many pieces we can cut:
420cm ÷ 70cm = 6
Therefore, we can cut 6 smaller ribbons, each 70cm long, from the 4m 20cm length of ribbon we have.
Here are ten numbers:
3 7 2 4 7 5 7 18 8
a) Write down the mode.
b) Work out the median.
c) Calculate the mean.
d) What is the range?
Step-by-step explanation:
a) The mode is 7, because it appears three times, which is more than any other number in the list.
b) To find the median, we need to arrange the numbers in order from smallest to largest:
2 3 4 5 7 7 7 8 18
The median is the middle number, which in this case is 7, since there are an equal number of values on either side of it.
c) To calculate the mean, we add up all the numbers and then divide by the total number of values:
(3 + 7 + 2 + 4 + 7 + 5 + 7 + 18 + 8) / 9 = 61 / 9 ≈ 6.78
So the mean is approximately 6.78.
d) The range is the difference between the largest and smallest numbers in the list:
18 - 2 = 16
So the range is 16.
Answer:
The numbers are 9 in total
Step-by-step explanation:
a) Mode 7
7 is the most occuring number.
b) Rearrange the numbers to find median
2, 3, 4, 5, 7, 7, 7, 8, 18
median=7
middle number is the median
c) Mean=2+3+4+5+7+7+7+8+18/9
mean=6.7
d) Range= Highest number - lowest number
18-2=16
I hope this helps a lot!
An English teacher counted the number of misspelled words in a 1000-word essay he assigned to his students. From a group of 49 students, the mean number of misspelled words was 9.1. The distribution of the student population is normal with a variance of 12.25. What is a confidence interval for the mean number of misspelled words in the student population, considering a confidence level of 99.7%? (Use 3 for the Z value in the formula below)
Answer:
C. [7.6, 10.6]
Step-by-step explanation:
To calculate the confidence interval for the mean number of misspelled words in the student population, we can use the confidence interval formula:
[tex]\boxed{CI=\overline{x}\pm z\left(\dfrac{s}{\sqrt{n}}\right)}[/tex]
where:
[tex]\overline{x}[/tex] is the sample mean.z is the confidence level value.s is the sample standard deviation.n is the sample size.Given values:
[tex]\text{Mean}\;\overline{x} = 9.1[/tex][tex]\text{Variance}\;s^2=12.25[/tex][tex]\text{Sample size}\;n=49[/tex]The standard deviation is the square root of the variance:
[tex]s=\sqrt{s^2}=\sqrt{12.25}=3.5[/tex]
The empirical rule states that approximately 99.7% of the data points will fall within three standard deviations of the mean.
Therefore, z-value for a 99.7% confidence level is z = 3.
Substituting these values into the formula, we get:
[tex]CI=9.1\pm 3\left(\dfrac{3.5}{\sqrt{49}}\right)[/tex]
[tex]CI=9.1\pm 3\left(\dfrac{3.5}{7}\right)[/tex]
[tex]CI=9.1\pm 3\left(0.5\right)[/tex]
[tex]CI=9.1\pm 1.5[/tex]
Therefore, the 99.7% confidence limits are:
[tex]CI=9.1-1.5=7.6[/tex]
[tex]CI=9.1+1.5=10.6[/tex]
Therefore, the confidence interval for the mean number of misspelled words in the student population is [7.6, 10.6].
what percent of 41.12 is 10.28 ?
5
x
−
2
−
(
x
−
2
)
4
x
Answer:
Step-by-step explanation:
To simplify the expression (5x - 2) / (x - 2) - (4x), we can follow these steps:
First, let's simplify the numerator:
5x - 2
Now, let's distribute the negative sign to the term (4x):
-4x
Next, let's combine the terms in the numerator:
(5x - 2) - 4x = 5x - 2 - 4x = x - 2
Now, let's rewrite the expression:
(x - 2) / (x - 2) - 4x
Since we have (x - 2) as both the numerator and denominator, we can simplify further by canceling out the common factor:
1 - 4x
Therefore, the simplified form of the expression (5x - 2) / (x - 2) - (4x) is 1 - 4x.
amar is a unmarried newly secondary class joint secretary of minister of finance. his monthly salary with dearness allowance is Rs 58,786. he gets one month salary for expense of festival at once. 10% of his monthly salary deposited in employee's provident fund (EPF) and Rs 3,300 in life insurance in each month.the government deposits the same EPF amount in the fund
1) find his yearly income assessable income
2) find taxable income of amar
3) how much income tax does he pay in total? find it
The correct answer is Yearly income assessable income: Rs 7,75,974
Taxable income of Amar: Rs 7,66,796
To find Amar's yearly income, we'll consider his monthly salary and additional benefits:
Yearly Income:
Monthly salary = Rs 58,786
Yearly salary = Monthly salary * 12 = Rs 58,786 * 12 = Rs 7,05,432
Additional benefits:
One month salary for festival expense = Rs 58,786
EPF contribution per month (deducted from salary) = 10% of monthly salary = 0.10 * Rs 58,786 = Rs 5,878
Government's EPF contribution = Rs 5,878
Total additional benefits per year = One month salary + EPF contribution + Government's EPF contribution = Rs 58,786 + Rs 5,878 + Rs 5,878 = Rs 70,542
Yearly income assessable income = Yearly salary + Total additional benefits = Rs 7,05,432 + Rs 70,542 = Rs 7,75,974
Taxable Income:
To calculate the taxable income, we deduct certain deductions from the assessable income.
Deductions:
EPF contribution per month (deducted from salary) = Rs 5,878
Life insurance per month = Rs 3,300
Total deductions per year = EPF contribution + Life insurance = Rs 5,878 + Rs 3,300 = Rs 9,178
Taxable income = Assessable income - Total deductions = Rs 7,75,974 - Rs 9,178 = Rs 7,66,796
Income Tax:
To determine the income tax paid, we need to apply the applicable tax rate to the taxable income. Since tax rates can vary based on the country and specific rules, I am unable to provide the exact income tax amount without additional information.
Learn more about statistics here;
https://brainly.com/question/12805356
#SPJ8
HELP I WILL MARK BRAINLIEST AND GIVE 30 POINTS
Construct a difference table to predict the next term of the sequence.
-1, 6, 24, 56, 105, 174, 266, ...
The difference table for the sequence (-1, 6, 24, 56, 105, 174, 266) reveals a cubic pattern, where the third differences are constant at 3. Based on this pattern, the next term in the sequence is predicted to be 289.
The difference table for the given sequence (-1, 6, 24, 56, 105, 174, 266):
Term | First Difference | Second Difference | Third Difference
----------------------------------------------------------------------------------------------------------
-1
6 7
24 18 11
56 32 14 3
105 49 17 3
174 69 20 3
266 92
To construct the difference table, we start by writing down the given sequence. Then, in the first column, we calculate the differences between consecutive terms. In the second column, we calculate the differences between the values in the first difference column. Similarly, in the third column, we calculate the differences between the values in the second difference column.
Analyzing the difference table, we observe that the third differences are constant at 3. This indicates a cubic pattern in the sequence, where the difference between consecutive terms is increasing by a constant amount each time.
To predict the next term, we take the last term of the sequence (266) and add the next difference (23) to it:
Next term = 266 + 23 = 289
Therefore, based on the pattern observed in the difference table, the next term in the sequence is predicted to be 289.
For more such information on: difference table
https://brainly.com/question/14457908
#SPJ8
pleasee help so disssicult
When going from left to right, the item goes up, it increases, and when it goes down, it decreases
please help!!!!!!!!!!!!!!!
The third option best describes a stratified sample of customers. The Option C.
How does the analyst form a stratified sample of customers based on mortgage amounts?To form a stratified sample, the analyst divides the customers into six groups based on their mortgage amounts. This ensures that customers from different mortgage amount ranges are represented in the sample.
Then, the analyst randomly selects 13 customers from each group. By stratifying the sample based on mortgage amounts and selecting customers at random within each group, the analyst ensures that the sample is representative of the overall population of mortgage customers.
Read more about stratified sample
brainly.com/question/20544692
#SPJ1
Consider the equation: 0=x^(2)+4x+1 Rewrite the equation by completing the square. Your equation should look like (x+c)^(2)=d or (x-c)^(2)=d.
The equation after completing the square is (x+2)²=3. Consider the equation: 0=x²+4x+1. To rewrite the equation by completing the square, we need to complete the square by adding and subtracting the square of half of the coefficient of the x.
Let's see how to complete the square: 0 = x² + 4x + 1(1)
We'll take the constant term (1) to the right-hand side of the equation, so it becomes negative. 0 = x² + 4x - 1(2)
To complete the square, we add and subtract the square of half of the coefficient of x. (a) Half of the coefficient of x is 4/2 = 2.
(b) We'll add and subtract 2² = 4. 0 = x² + 4x + 4 - 4 - 1(3)
The first three terms can be expressed as the square of the quantity x+2: (x+2)² = 0 + 4 - 1(4)This simplifies to: (x+2)² = 3
Thus, the equation after completing the square is (x+2)²=3.
For more question on equation
https://brainly.com/question/17145398
#SPJ8
Will give Branliest Hurry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which linear graph represents a proportional relationship? a graph of a line that passes through the points 0 comma 0 and 2 comma negative 1 a graph of a line that passes through the points 0 comma 1 and 1 comma 3 a graph of a line that passes through the points 0 comma 3 and 1 comma 3 a graph of a line that passes through the points 0 comma negative 1 and negative 1 comma 2
Answer:On a coordinate plane, a straight line with positive slope goes through points (3, 3) and (4, 4).
Step-by-step explanation:
Cual es la velocidad de un auto que recorre 10800m en 560s?
25 shaded squares 13 used what percentage used
Answer:
52% used.
Step-by-step explanation:
13/25=52/100=52%
How do I interpret residuals and just this entire page? I slacked off for my statistics class and I need all of this and all the terms on this page explained so I can do my other assignments. Also are my previous answers correct?
a. The interval of time between eruptions if the previous eruption lasted 4 minutes is 86.51 minutes.
b. The residual for this cycle is 2.07 minutes.
c. The interval of time between eruptions lasted for 2.07 minutes than the regression line equation predicted.
d. The slope of the regression line means that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.
e. No, the value of the y-intercept doesn't have meaning in the context of the problem.
How to determine the interval of time between eruptions?Based on the information provided above, the relationship between the duration of the previous eruption (x in minutes) and the interval of time between eruptions (y in minutes) is modeled by this regression line equation:
ÿ = 33.35 + 13.29x
Part a.
When x = 4 minutes, the value of is given by:
ÿ = 33.35 + 13.29(4)
ÿ = 86.51 minutes.
Part b.
The residual for the given cycle can be calculated as follows;
Residual = y - ÿ
Residual = 62 - (33.35 + 13.29(2))
Residual = 62 - 59.93
Residual = 2.07 minutes.
Part c.
Based on the calculation above, we can logically deduce that the interval of time between eruptions lasted for 2.07 minutes than the equation of regression line predicted.
Part d.
The slope of the regression line is equal to 13.29 and it implies that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.
Part e.
In the context of the problem, we can logically deduce that the value of the y-intercept doesn't have any meaning because the duration of the previous eruption cannot be equal to 0 minutes.
Read more on regression here: brainly.com/question/16793283
#SPJ1
Adults are encouraged to visit the dentist at least once a year. In the 2019 National College Health
Assessment, 28,021 out of a random sample of 38,433 college students said they had a dental exam in
the last 12 months.
¹American College Health Association-National College Health Assessment (2020). Undergraduate student
reference group data report, Fall 2019. https://www.acha.org/NCHA/ACHA-
NCHA Data/Publications and Reports/NCHA/Data/Reports ACHA-NCHAIIl.aspx
Use the appropriate data analysis tool to construct a 99% confidence interval to estimate the
population proportion of college students who said they had a dental exam in the last 12 months.
Lower Bound
Upper Bound
The boundaries of the 99% confidence interval are
Lower bound = 0.7232Upper bound = 0.7348Constructing the 99% confidence intervalFrom the question, we have the following parameters that can be used in our computation:
Selected, x = 28021
Sample, n = 38433
This means that the proportion, p is
p = 28021/38433
p = 0.729
The 99% confidence interval is then calculated as
CI = p ± z * √(p * (1 - p)/n)
Where
z = 2.576 i.e. the z-score at 99% confidence interval
So, we have
CI = 0.729 ± 2.576 * √(0.729 * (1 - 0.729)/38433)
Evaluate
CI = 0.729 ± 0.0058
Evaluate
CI = (0.7232, 0.7348)
Hence, the confidence interval is (0.7232, 0.7348)
Read more about confidence interval at
https://brainly.com/question/32801070
#SPJ1
The height h(x), of an object is given by the function h(x) = -16x + 176x + 65
where x is time in seconds and h(x) is height in feet. When does the object reach its maximum height? Round your answer to two decimal places.
To find an object's maximum height, we need to find the vertex of this quadratic equation.
Answer: 5.50 seconds
Terms to know:
Quadratic function: A quadratic function is a polynomial function of degree 2, which means the highest power of the variable in the equation is 2.
Vertex: The vertex of a quadratic function is the point on the graph where the function reaches its highest or lowest point. In the case of a quadratic function in the form f(x) = ax^2 + bx + c, the vertex is given by the coordinates (x, f(x)).
Step-by-step explanation:
The vertex of a quadratic equation can be represented as [tex](\frac{-b}{2a}, f(\frac{-b}{2a})[/tex]
Since we only are looking at the time it takes to reach maximum height we will only look at the x value.
[tex]x= \frac{-176}{2(-16)}[/tex]
[tex]x= 5.50[/tex]
Find the perimeter of the following square and the area of the shaded part if the radius of the
circle is 12 cm.
The perimeter of the square and the area of the shaded part are 48cm and 454.16cm² respectively²
How to determine the valueThe formula for calculating the area of a circle is expressed as;
Area = πr²
Now, substitute the value, we have;
Area = 3.14 × 12²
Find the square and multiply the values, we have;
Area = 3.14(144)
Multiply the values
Area = 452. 16 cm²
Perimeter of a square take the formula;
Perimeter = 4a
Substitute the value
Perimeter = 4(12) = 48 cm
Learn more about area at: https://brainly.com/question/25292087
#SPJ1
You give up a full time salary of $45,000 a year to go to school for 2 years. The total cost of going to school is $30,000. If you want to be able to recover your investment in 5 years or less, what is the minimum salary you would need to earn upon earning your degree?
Answer:
Step-by-step explanation:
To recover your investment in 5 years or less, you would need to earn enough to cover the cost of going to school ($30,000) as well as make up for the lost salary over the 2 years of schooling ($45,000/year * 2 years = $90,000).
Therefore, the minimum salary you would need to earn upon earning your degree is the sum of the cost of going to school and the lost salary:
Minimum salary = $30,000 + $90,000 = $120,000.
In order to recover your investment in 5 years or less, you would need to earn a minimum salary of $120,000 per year.
To recuperate the total cost of $120,000 ($30,000 tuition + $90,000 forgone salary) over 5 years, you would need to earn $24,000 more per year on top of your original $45,000 salary. This implies that the minimum salary you need to earn after graduating is $69,000 per annum.
Explanation:To determine the minimum salary, we first need to calculate your total forfeiture over the 2 years of school, which equates to real costs and opportunity costs. Firstly, the real cost is the tuition of $30,000. Secondly, the opportunity costs are the 2 years of salary you're forgoing, best understood as the wages you would've made if you hadn't gone to school. Assuming the salary of $45,000 per year, the total opportunity cost for the 2 years would be $90,000.
Therefore, the total investment is calculated as the sum costs of tuition and forgone salary i.e. $30,000 (tuition) + $90,000 (forgone salary) = $120,000. So to recover this investment in 5 years, you would need to earn an addition of $120,000 above your original salary. Meaning, you will have to recover $120,000 / 5 years = $24,000 per year on top of your initial salary to recover your total costs in the stated timeframe.
Therefore, the minimum salary you need to earn after earning your degree is equal to your original salary plus recovered investment per year: $45,000 (original salary) + $24,000 (increase) = $69,000. Hence, upon completion of your degree, you will have to earn at least $69,000 per year to recover your total investment within 5 years.
Learn more about Calculating Return On Investment here:
https://brainly.com/question/33935269
#SPJ11
What is the least common denominator of the equation Three-fourths (x minus 3) minus one-half = two-thirds? 2 9 12 36
Answer:
12
Step-by-step explanation:
[tex]\frac{3}{4}[/tex](x - 3) - [tex]\frac{1}{2}[/tex] = [tex]\frac{2}{3}[/tex]
We are looking at the denominators of 4, 2 and 3. We are looking for the least common multiple. If we listed out the multiples of the 3 numbers, we are looking for the lowest number that is in all three lists.
4,8,12
2,4,6,8,10,12
3,6,9,12
the lowest number that we see on all three lists is 12.
The better definition of Intersection is:
OA system that has at least one solution.
O Where lines cross over each other. The lines have a common point.
OA value we can put in place of a variable (such as x) that makes the equation true.
OA system that has no solutions.
Answer:
Where lines cross over each other. The lines have a common point.
Josephine can correct her students’ test papers in 5 hours, but if her teacher’s assistant helps, it would take them 3 hours. How long would it take the assistant to do it alone?
Step-by-step explanation:
1 job divided by the sum of the rates = 3 hours
1 / ( 1/5 + 1/x ) = 3
x = 7.5 hrs for assistant alone
the sum of five consecutive even numbers is 220. find the smallest of these numbers.
Answer:
The smallest number is 40.
Step-by-step explanation:
Let the number be x. Then the next 4 number will be x+2, x+4, x+6, x+8
.°. x+x+2+x+4+x+6+x+8 = 220
5x + 20 = 220
5x = 200
x = 40
Therefore the smallest of the five consecutive numbers is 40
Mark me as brainliest if you find my answer''Mark-worthy'' :)
So i'm doing this Equation and it told me to use the values below, bit I'm so confused on how to do it can some of y'all help me out?
Part A: solve the equation---
5+x-12=2x-7
x-7=2x-7
x-7+7=2x-7+7
x=2x
x-2x=2x-2x
-x=0
--- ---
-1 -1
x=0
--
-1
x=0
Part B: use the values
x= -0.5, 0, 1
Answer:
when substituting x = -0.5, 0, and 1 into the equation, we get the results -8, -7, and -5, respectively.
Step-by-step explanation:
Part A:
To solve the equation 5 + x - 12 = 2x - 7, follow these steps:
Combine like terms on each side of the equation:
-7 + 5 + x - 12 = 2x - 7
-14 + x = 2x - 7
Simplify the equation by moving all terms containing x to one side:
x - 2x = -7 + 14
-x = 7
To isolate x, multiply both sides of the equation by -1:
(-1)(-x) = (-1)(7)
x = -7
Therefore, the solution to the equation is x = -7.
Part B:
Now let's substitute the given values of x and evaluate the equation:
For x = -0.5:
5 + (-0.5) - 12 = 2(-0.5) - 7
4.5 = -1 - 7
4.5 = -8
For x = 0:
5 + 0 - 12 = 2(0) - 7
-7 = -7
For x = 1:
5 + 1 - 12 = 2(1) - 7
-6 = -5
A group of adults were asked how many children they have in their families. The bar graph below shows the number of adults who indicated each number of children. 4+ 3.5+ 3- 2.5 2- 1.5- 1 0.5- 0 1 2 Number of Children How many adults were questioned? m St 4 5 What percentage of the adults questioned had 2 children? Round answer to 1 decimal place. %
Answer:
Step-by-step explanation:
To determine the percentage of adults who had 2 children, we need to first find the total number of adults questioned.
Looking at the bar graph, we can see that the bar representing 2 children has a height of 2.5. This means that 2.5 adults indicated having 2 children.
Let's assume the total number of adults questioned is "m". According to the bar graph, the sum of the heights of all the bars represents the total number of adults questioned.
From the bar graph, we can see the following:
The bar representing 4+ children has a height of 4.
The bar representing 3- children has a height of 3.5.
The bar representing 2- children has a height of 2.5.
The bar representing 1- children has a height of 1.5.
The bar representing 1 child has a height of 1.
The bar representing 0.5- children has a height of 0.5.
The bar representing 0 children has a height of 0.
To find the total number of adults questioned (m), we sum up the heights of all the bars:
m = 4 + 3.5 + 3 + 2.5 + 2 + 1.5 + 1 + 0.5 + 0
m = 18
Therefore, the total number of adults questioned is 18.
To find the percentage of adults who had 2 children, we divide the number of adults with 2 children (2.5) by the total number of adults questioned (18) and multiply by 100:
Percentage = (2.5 / 18) * 100
Percentage ≈ 13.9 (rounded to 1 decimal place)
Therefore, approximately 13.9% of the adults questioned had 2 children.
Evaluate leaving your answer in a standard form 0.0048*0.81 /0.027*0.04
Step-by-step explanation:
When we simplify the expression, we get:
0.0048 * 0.81 / 0.027 * 0.04 = (0.0048 / 0.027) * (0.81 / 0.04)
Using a calculator to evaluate the two fractions separately, we get:
0.0048 / 0.027 ≈ 0.1778
0.81 / 0.04 = 20.25
Substituting these values back into the original expression, we get:
(0.0048 / 0.027) * (0.81 / 0.04) ≈ 0.1778 * 20.25
Multiplying these two values together, we get:
0.1778 * 20.25 ≈ 3.59715
To express the answer in standard form, we need to write it as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point three places to the left, since there are three digits to the right of the decimal point:
3.59715 ≈ 3.59715 × 10^(-3)
Therefore, the final answer in standard form is approximately 3.59715 × 10^(-3).
The ratio of the length to the width of a rectangle is 3:2. If the perimeter of the rectangle is 40, what is the length of the rectangle?
Answer:
Step-by-step explanation:
Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.
The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:
P = 2(3x + 2x)
40 = 2(5x)
Now, let's solve for x:
40 = 10x
x = 40/10
x = 4
Now that we have the value of x, we can find the length of the rectangle:
Length = 3x = 3(4) = 12
Therefore, the length of the rectangle is 12.
Solve the system of equations using elimination.
5x + 3y = 8
4x + y = 12
O (1, 1)
O (2.4)
O (3,0)
O (4,-4)
Answer: O (4, -4)
Step-by-step explanation:
To solve the system of equations using elimination, we can multiply the second equation by -3 to eliminate the y term:
Original equations:
5x + 3y = 8 (Equation 1)
4x + y = 12 (Equation 2)
Multiply Equation 2 by -3:
-3(4x + y) = -3(12)
-12x - 3y = -36 (Equation 3)
Now we can add Equation 1 and Equation 3 to eliminate the y term:
(5x + 3y) + (-12x - 3y) = 8 + (-36)
Simplifying:
5x - 12x + 3y - 3y = 8 - 36
-7x = -28
Divide both sides by -7:
x = -28 / -7
x = 4
Now substitute the value of x back into either of the original equations, let's use Equation 2:
4(4) + y = 12
16 + y = 12
y = 12 - 16
y = -4
Therefore, the solution to the system of equations is x = 4 and y = -4.
Given that P(A)=0.450 and P(B)=0.680 and P( A U B)=0.824. Find the probability
The probability of the union of events A and B, P(A U B), is 0.824.
To find the probability, we can use the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
Given that P(A) = 0.450, P(B) = 0.680, and P(A U B) = 0.824, we can substitute these values into the formula:
0.824 = 0.450 + 0.680 - P(A ∩ B)
To find the probability of the intersection of events A and B (P(A ∩ B)), we rearrange the equation:
P(A ∩ B) = 0.450 + 0.680 - 0.824
P(A ∩ B) = 1.130 - 0.824
P(A ∩ B) = 0.306
Therefore, the probability of the intersection of events A and B, P(A ∩ B), is 0.306.
We can also calculate the probability of the union of events A and B, P(A U B), by substituting the given values into the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A U B) = 0.450 + 0.680 - 0.306
P(A U B) = 0.824
Therefore, the probability of the union of events A and B, P(A U B), is 0.824.
In summary, we have found that the probability of the intersection of events A and B, P(A ∩ B), is 0.306, and the probability of the union of events A and B, P(A U B), is 0.824, based on the given probabilities.
for more such question on probability visit
https://brainly.com/question/251701
#SPJ8
On days when the temperature was less than 58
These are general considerations, and specific experiences may vary depending on geographical location, cultural practices, and individual preferences.
On days when the temperature was less than 58 degrees, it indicates that the weather was relatively cool. This could imply various conditions and experiences depending on the context and location. In general, some possible scenarios on such days may include:
Cooler outdoor activities: People might engage in activities such as hiking, jogging, or outdoor sports that are more enjoyable in cooler temperatures.
Layered clothing: Individuals may choose to wear warmer clothing, including jackets, sweaters, or scarves, to stay comfortable in the cooler weather.
Indoor activities: Cooler temperatures may encourage people to spend more time indoors, engaging in activities such as reading, watching movies, or pursuing hobbies.
Increased energy consumption: Cold weather often leads to an increased need for heating systems, resulting in higher energy consumption to maintain indoor comfort.
Changes in vegetation: Cooler temperatures can affect plant growth and flowering patterns. Certain plants may thrive in cooler conditions, while others may enter a dormant phase.
Changes in animal behavior: Some animals may adapt to cooler temperatures by seeking shelter or adjusting their activities and migration patterns.
Possible health effects: Cooler temperatures may impact individuals with certain health conditions, such as respiratory issues or joint pain, requiring them to take appropriate measures to stay comfortable.
These are general considerations, and specific experiences may vary depending on geographical location, cultural practices, and individual preferences.
for such more question on temperature
https://brainly.com/question/14820864
#SPJ8
