We can conduct a hypothesis test to determine the scale 1's mean weight is less than the weight of scale 2.
H0: μ1 ≥ μ2 (the mean weight on Scale 1 is greater than or equal to the mean weight on Scale 2)
Ha: μ1 < μ2 (the mean weight on Scale 1 is less than the mean weight on Scale 2)
We will use a significance level of α = 0.10.
First, we calculate the sample means and the difference between the means:
Sample mean weight on Scale 1, μ1 = (12.35 + 15.08 + 9.00 + 11.55 + 24.36 + 9.88 + 15.36 + 7.05 + 13.39)/10 = 12.43
Sample mean weight on Scale 2, μ2 = (12.51 + 14.99 + 9.10 + 11.47 + 24.35 + 10.00 + 15.55 + 7.04 + 13.57)/10 = 13.15
Difference between the means, ud = μ1 - μ2 = -0.72
s.d.(ud) = sqrt((s1^2/n1) + (s2^2/n2))
s1 and s2 are sample standard deviations n1 n1 and n 2
s1 = sqrt(((12.35 - 12.43)^2 + (15.08 - 12.43)^2 + ... + (13.39 - 12.43)^2)/9) = 3.153
s2 = sqrt(((12.51 - 13.15)^2 + (14.99 - 13.15)^2 + ... + (13.57 - 13.15)^2)/9) = 2.114
n1 = n2 = 10
The test statistic can now be calculated as:
t = (ud - 0) / (s.d.(ud)/sqrt(n)) = (-0.72 - 0) / (1.109/sqrt(10)) = -2.05
Using a t-distribution table with 9 degrees of freedom and a one-sided test at α = 0.10, we find the critical value to be -1.383. As the calculated value so we will not consider null hypothesis.
The mean weight of scale 1 can be less than the scale 2 mean weight at 0.10 level.
To know more about comparing scales
brainly.com/question/29586646
#SPJ4
Using a calculator, work out
(3.5 × 107)
107) + (7.1 × 10⁹)
Give your answer in standard form.
The addition of the two numbers in scientific notation is given as follows:
[tex](3.5 \times 10^7) + (7.1 \times 10^9) = 7.135 x 10^9[/tex]
What is scientific notation?A number in scientific notation is given by the notation presented as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.
The addition operation for this problem is given as follows:
[tex](3.5 \times 10^7) + (7.1 \times 10^9)[/tex]
To add two terms, they must have the same exponent, hence I am going to convert 3.5 x 10^7 to exponent 9, as follows:
[tex]3.5 \times 10^7 = 0.35 \times 10^8 = 0.035 \times 10^9[/tex]
Two add two terms, we add the bases and keep the exponents, hence:
[tex](0.035 \times 10^9) + (7.1 \times 10^9) = 7.135 \times 10^9[/tex]
More can be learned about scientific notation at https://brainly.com/question/5756316
#SPJ1
Dani spends 1520 total to create
2 treat bags. How much more
would she have to spend to make
5 more similar bags?
Answer: 2280 more
Step-by-step explanation:
We need to first find out how much Dani spends to make one treat bag:
1520/2 = 760
Now we can find out how much it would cost to make 5 more bags:
760 x 5 = 3800
Therefore, Dani would have to spend 3800 - 1520 = 2280 more to make 5 more similar bags.
y is inversely proportional to x.
When y = 6, x = 8
a) Work out an equation connecting y and x.
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{y varies inversely with x}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=8\\ y=6 \end{cases} \\\\\\ 6=\cfrac{k}{8}\implies 48=k\hspace{10em}\boxed{y=\cfrac{48}{x}}[/tex]
Maxine wants to bake and needs to buy flour. She will need 1 3/4
cups of flour to make a chocolate cake. She will also need 2 1/3
cups of flour for chocolate chip cookies. Finally, Maxine will need
1 2/3 cups of flour for brownies. Maxine wants to buy enough
flour to bake with and only wants to have less than two cups left
over.
Based on the information provided, Maxine needs to buy a total of 6 cups of flour.
How to calculate the amount of flour Maxina needs to buy?The total of flour can be calculated by adding the numbers provided; however, to make it easier let's simplify the numbers:
Chocolate cake: 1 3/4 = 1.75
Chocolate chip cookies: 2 1/3 = 2.33
Brownies: 1 2/3 = 1.66
Now, let's add the amounts given:
1.75 + 2.33 + 1.66 = 5.74 which can be rounded as 6 cups, which means she will need to buy a 6 or 7-cup bag.
Learn more about fractions in: https://brainly.com/question/10354322
#SPJ1
In one to two sentences, describe an impact that division of labor had on the economic growth of the United States. (2 points)
The division of labor, or specialization of tasks, has boosted efficiency and productivity in the United States, thereby stimulating economic growth. It also facilitates the growth of factories and mass production, which further contributes to the overall economic growth of the country.
Division of labor:
Division of labor is the process of dividing the work of producing goods and services into separate tasks performed by different people or groups of people. Division of labor is an economic concept that states that dividing a production process into stages allows workers to focus on specific tasks. If workers can concentrate on a small aspect of production, as long as sufficient quantities and quantities are produced, overall efficiency will increase.
This division is generally based on the skills, expertise and resources of the worker, as well as the wants and needs of the market.
The purpose of division of labor is to increase efficiency and productivity by allowing workers to specialize in specific tasks and develop expertise in those tasks. This can lead to better quality products and services and lower costs. The division of labor is a key concept in economics and an important factor in the development and growth of societies.
Learn more about Division:
https://brainly.com/question/23941896
#SPJ4
please help thanks !!!
Answer:
boron
particle 1
Step-by-step explanation:
boron is number 5 on the periodic table of elements.
mass - protons= neutrons
11(rounded up) - 5 = 6 neutrons
ions are when an atom is positively or negatively charged. for example electrons are higher than protons or vice versa.
I need help, please!!!!!!!
After answering the provided question, we can conclude that As a result, probability the correct answer is C) A• The expected point value is 0.13, so guessing is advantageous.
What is probability?Probability of how likely an event is to occur. It is represented by a number is for both 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Shifting a fair coin and coin flips has a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a mathematical discipline that investigates random events instead than their properties. It is applied in many fields, including facts and figures, finance, scientific knowledge, and engineering.
After eliminating one of the six possible answers, the remaining five options are equally likely to be correct, so the probability of correctly guessing is now 1/5 and the probability of incorrectly guessing is 4/5.
Point value expected = (probability of gaining points x point value) - (probability of losing points x point value)
(1/5 x 1) is the expected point value. - (4/5 x 1/6)
1/5 - 1/30 = expected point value
5/30 - 1/30 = expected point value
4/30 is the expected point value.
The expected point value is 0.13. (rounded to two decimal places)
It is advantageous to guess because the expected point value is positive.
As a result, the correct answer is C) A• The expected point value is 0.13, so guessing is advantageous.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
4.02 Lesson check ! (7)
100 is the common difference of the given sequence
Determining the common difference of a sequenceAn ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is the number of elements.
Given the sequence below
8, 108, 208, 308...
The nth term of an arithmetic sequence is given as Tn = a + (n-1)d
The common difference is the difference between the preceding and the succeeding term.
First term = 12
Second term = 20
Common difference = 108 -8 = 208 - 108
Common difference = 100
Hence the common difference of the sequence is 100
Learn more on common difference here: https://brainly.com/question/23601373
#SPJ1
Tom wishes to purchase a property that has been valued at $300,000. He has 25% of this amount available as a cash deposit, and will require a mortgage for the remaining amount. The bank offers him a 25-year mortgage at 2% interest. Calculate his monthly payments
Tom's monthly mortgage payment will be $984.84 As Tom has a cash deposit of 25% of $300,000 which is $75,000.
Therefore, he needs to borrow $225,000 from the bank to purchase the property.
Using the formula for calculating the monthly payment for a mortgage, we get:
M = [tex]P [ i(1 + i)^n ] / [ (1 + i)^{n-1}][/tex]
Where:
P = Principal amount borrowed = $225,000
i = monthly interest rate = 2%/12 = 0.001667
n = total number of monthly payments = 25 years x 12 months/year = 300
Plugging in these values, we get:
M = $225,000 [0.001667[tex](1 + 0.001667)^{300[/tex]] / [[tex](1 + 0.001667)^{300[/tex] – 1] = $984.84
Therefore, Tom's monthly mortgage payment will be $984.84.
Learn more about Interest Rates:
https://brainly.com/question/25720319
#SPJ4
I need help with these problems , please and thank you
Therefore, the value of x that satisfies the equation √x = 14i√3 is -588. The answer is (a). The only value of x that satisfies this equation is option (b): which is -2i.
What is the value of xWe can start by squaring both sides of the equation to eliminate the square root:
We have to apply the knowledge of multiplying or squaring a complex number will give us a negative value.
(√x)^2 = (14i√3)^2
x = (14i)^2 x (√3)^2
We have to take the square of the complex number and the square root of 3.
x = -196 x 3
Multiply the value
x = -588
The value of x in the equation is -588.
2. We can factor out x from the expression as follows:
x(x^4 + 6x^2 + 8)
Now, we need to find the value(s) of x that make the expression equal to 0.
We can see that one solution is x = 0, since anything multiplied by 0 is 0.
To find the other solution(s), we can solve the quadratic equation inside the parentheses:
x^4 + 6x^2 + 8 = 0
Substitute y = x^2:
y^2 + 6y + 8 = 0
Factor the quadratic equation:
(y + 4)(y + 2) = 0
Therefore, the possible values of y are -4 and -2. Substituting back y = x^2, we get:
x^2 = -4 or x^2 = -2
Since x^2 cannot be negative for real numbers, there are no real solutions to this equation. However, if we allow complex numbers, we can find the solutions by taking the square roots of -4 and -2:
x = ±2i or x = ±sqrt(2)i
Learn more on complex number here;
https://brainly.com/question/10662770
#SPJ1
The Good Fruit stand sells baskets of cherries for $4 and baskets of blueberries for $3.
Its daily sales goal is $720
The Good Fruit stand needs to sell 180 baskets of cherries and 240 baskets of blueberries to reach their daily sales goal of $720.
1 cherry = $4
1 blueberry = $3
60 cherry basket:
60 × 4
= 240
Goal amount = $720
Bw day selling blueberry basket
Money:
= 720 - 240
= 480
Blueberry basket = 480 ÷ 3
Cherry = 60
Blueberry = 160
Sales goals are measurable objectives that sales reps and teams use to guide them through their day-to-day sales activities and help them make big-picture strategic decisions. Sales goals are usually based on KPIs and specific sales metrics.They are data-driven and are meant to provide a blueprint for sellers and organizations on how to achieve new levels of success. Sales goals bring clarity and control to the sales process while also mitigating risk.
For such more questions on sales goal :
brainly.com/question/5059809
#SPJ4
Question:
The Good Fruit stand sells baskets of cherries for $4 and baskets of blueberries for $3. Its daily sales goal is $720. Write and graph the linear equation that describes the problem. Use the graph to find how many baskets of blueberries it must sell to reach its goal if 60 baskets of cherries are sold.
Which is more economical: purchasing the economy size of a detergent at 2 kilograms for $3. 15 or purchasing the regular size at 920 grams for 60?
The economy size is more economical, as you will get 2kg for $3.15, which comes out to be $1.58 per kg, while the regular size will cost you $0.65 per gram.
To determine which option is more economical, we need to calculate the cost per unit of weight for each detergent.
For the economy size, the cost per kilogram is:
Cost = $3.15
Weight = 2 kg
Cost per kilogram = Cost / Weight = $3.15 / 2 kg = $1.575/kg
For the regular size, the cost per kilogram is:
Cost = $0.60
Weight = 920 g = 0.92 kg
Cost per kilogram = Cost / Weight = $0.60 / 0.92 kg = $0.652/kg
Therefore, the regular-size detergent is more economical as it has a lower cost per kilogram.
To learn more about Economy :
https://brainly.com/question/29254379
#SPJ4
find the surface area to the nearest tenth of a cylinder 61.7 ft tall that has a diameter of 38 ft
The surface area of the cylinder to the nearest tenth is approximately 9617.9 [tex]ft^{2}[/tex].
The surface area of a cylinder is given by the formula:
Surface area = 2π[tex]r^{2}[/tex] + 2πrh
where r is the radius of the cylinder, h is its height, and π is a constant equal to approximately 3.14159.
To solve this problem, we first need to find the radius of the cylinder. The diameter of the cylinder is given as 38 ft, so the radius is half of that:
radius = diameter / 2 = 38 ft / 2 = 19 ft
The height of the cylinder is given as 61.7 ft.
Now, we can plug in these values into the surface area formula:
Surface area = 2π[tex]r^{2}[/tex] + 2πrh
Surface area = 2π[tex](19ft)^{2}[/tex]+ 2π(19 ft)(61.7 ft)
Surface area = 2π(361[tex]ft^{2}[/tex]) + 2π(1168.3 [tex]ft^{2}[/tex])
Surface area = 722π [tex]ft^{2}[/tex] + 2336.6π [tex]ft^{2}[/tex]
Surface area = 3058.6π[tex]ft^{2}[/tex]
We can approximate π to 3.14159 and evaluate the expression:
Surface area ≈ 3058.6 × 3.14159
Surface area ≈ 9617.9 [tex]ft^{2}[/tex]
Therefore, the surface area of the cylinder to the nearest tenth is approximately 9617.9 [tex]ft^{2}[/tex].
To learn more about surface area:
https://brainly.com/question/29101132
#SPJ4
A puppy weighed 4 kg. Later, he weighed 5 kg. What is the percentage increase?
Mathematically, this can be expressed as follows: Percentage Increase = (15 - 10) / 10 x 100= 5 / 10 x 100= 50%.
The percentage increase can be calculated by taking the difference between the two weights and dividing it by the original weight. In this case, the percentage increase is 25%. Mathematically, this can be expressed as follows: Percentage Increase = (5 kg - 4 kg) / 4 kg x 100= 1 kg / 4 kg x 100= 25%In a broader sense, the formula for calculating the percentage increase of any quantity is given by: Percentage Increase = (Final Value - Initial Value) / Initial Value x 100This formula can be used to determine the percentage increase of any quantity, not just weight. For example, if the price of a product increases from $10 to $15, then the percentage increase in the price can be calculated using the same formula. In this case, the percentage increase would be 50%. Mathematically, this can be expressed as follows: Percentage Increase = (15 - 10) / 10 x 100= 5 / 10 x 100= 50%.
Step 1: Calculate the difference between the two weights:
5 kg - 4 kg = 1 kg
Step 2: Calculate the percentage increase:
(1 kg / 4 kg) x 100 = 25%
Learn more about percentage here:
https://brainly.com/question/16797504
#SPJ4
factirise fully.
[tex]2x + 4x { \\ }^{2} [/tex]
7) Given: the sequence 4, 8, 16, 32,. . . When using the geometric sequence formula an
determine the 15th term, which variable would be replaced with the number 27
1) a1
2) n
3) an
4) r
Answer:
The correct answer is 3) an.
In a geometric sequence, the term can be calculated by the formula an = a1 × r^(n–1).
In this case, the first term (a1) is 4, the common ratio (r) is 2, and the 15th term (n) is 15. Therefore, replacing an with 27, we get 27 = 4 × 2^(15–1). Solving for the 15th term (n), we get n = 27/4 × 2^(-14). The 15th term is 27.
Question is down below
Answer:
C is the answer.
Step-by-step explanation:
Answer:
The answer is A and C
Step-by-step explanation:
The answer is A and C because as you can see the angles of the triangles are both the same. If you took the smaller triangle or triangle A and enlarged it, it would be the same triangle.
Sam spent $23.00 to buy 12 flowers for his mother.
Answer:
$1.92
Step-by-step explanation:
We take
23 / 12 = $1.92 per flower
So, it costs $1.92 per flower.
Can someone help me out?
Answer:
rar
Step-by-step explanation:
rar
Answer: 666
Step-by-step explanation:
someone help me please
Answer:
Step-by-step explanation:
Knowing that we have a Right triangle find the third angle first, 53 + 90 =180 which the answer will be 37 degrees then add that answer to 41 to get you the second degree of your whole triangle, which will be 78 degrees. Then you can find the last angle by adding 78 + 53 = 180, the answer is 49 degrees. Now you have enough information to find the second triangles hypotenuse, using the law of sines which will end up being 12 inches approximately then you can use law of sines again but this time for the 1st triangle on the left. Giving you an answer of 15 inches for the whole side on the top of the triangle, but then you must subtract 8 inches, giving you the FINAL answer of 7 inches.
Alfonzo works for a lean service company. It takes him 3/4 hour to mow a lawn. If he works more than 8 hours, he gets 1/2 lunch break. Write and solve an inequality to find the number of lawns he can mow if he works at least 14 hours.
Alfonzo can mow at most 4 lawns if he works at least 14 hours. And we used the "less than or equal to" symbol because Alfonzo may not be able to mow a fraction of a lawn.
What is an Inequality ?
An inequality is a mathematical statement that describes a relationship between two values or expressions that are not necessarily equal.
Let's start by determining how many lawns Alfonzo can mow in 1 hour:
1 hour = 4/4 hours
Lawns mowed in 1 hour = 1 / (3/4) = 4/3
Now, let L be the number of lawns Alfonzo can mow if he works at least 14 hours. Since he works 8 hours without a lunch break, he has (14 - 8 - 1/2) = 5.5 hours left to work after his lunch break. Therefore, we can set up the following inequality to find L:
4/3(L) ≤ 5.5
Multiplying on both sides by 3/4, we get:
L ≤ 5.5 x 3/4
L ≤ 4.125
Therefore, Alfonzo can mow at most 4 lawns if he works at least 14 hours. Note that we used the "less than or equal to" symbol because Alfonzo may not be able to mow a fraction of a lawn.
To learn more about Inequality from given link.
https://brainly.com/question/30797813
#SPJ1
Use the order of operations to simplify 19×33−2(16+23) .
Answer:
549
Step-by-step explanation:
What is the order of operations?The order of operations is a sequence in which operations should be performed to evaluate a mathematical expression correctly. A common way to remember is PEMDAS:
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionTo simplify the expression 19×33−2(16+23) using the order of operations, first solve the operations inside the parentheses:
16 + 23 = 39Now we multiply:
2 × 39 = 78The expression now looks like this:
19 × 33 − 78.Perform the multiplication before the subtraction:
19 × 33 = 627Now that we have done the multiplication, we can subtract:
627 - 78 = 549Therefore, the expression simplified is 549.
Answer:
b
Step-by-step explanation:
Which sequence is represented by the equation a n =4(3)^ n-1
The sequence represented by means of the equation a n =4(3)^ n-1 is an exponential sequence with a commonplace ratio of 3 and an preliminary term of 4.
To see this, we can plug within the values of n and study the pattern:
Whilst n = 1:
a 1 = 4(3)^0 = 4(1) = 4
Whilst n = 2:
a 2 = 4(3)^1 = 4(3) = 12
Whilst n = 3:
a three = 4(3)^2 = 4(9) = 36
While n = 4:
a 4 = 4(3)^3 = 4(27) = 108
And so on.
We can see that every time period in the sequence is received by way of multiplying the previous term by using 3, and that the first term is 4.
Thus, the sequence is an exponential sequence with a commonplace ratio of 3 and an preliminary term of 4.
Learn more about Exponential sequence:-
https://brainly.com/question/30127597
#SPJ4
Brian is 2 years older than Bod who is 7 years older than Mark. If their combined age is 61 years, find the age of each person. (4)
Bod is 22 years old, Brian is 24 years old, and Mark is therefore 15 years old.
what is variables ?A variable in mathematics is a symbol or letter that denotes a possible number or quantity. It frequently serves as a placeholder for an unknowable number that needs to be calculated or solved for in mathematical expressions or equations. For instance, the factors x and y are used in the equation y = 3x + 5. The value of x, which can be any integer, determines the value of y. If we know the number of x, we can find a solution for y.
given
Let's indicate their ages with variables:
Mark's age: M
Body Age: B Equals M + 7
Br = B + 2 = (M + 7) + 2 = M + 9 is Brian's age.
Their total age is 61, so we can create the following equation:
M + (M + 7) + (M + 9) = 61
M is simplified to 3M Plus 16 and the answer is 61.
3M = 45
M = 15
Bod is 22 years old (15 + 7), Mark is 15 years old (15 + 7), and Brian is 24 years old (22 + 2).
Bod is 22 years old, Brian is 24 years old, and Mark is therefore 15 years old.
To know more about variable visit :-
https://brainly.com/question/2466865
#SPJ1
A block exerts a force of 9 N on the ground. Calculate the pressure the block exerts on the ground, in N/m², when it is a) flat on the ground, so that the area of its base is 0.04 m². b) standing up on its side, so that the area of its base is 0.015 m². a) base area = 0.04 m² b) base area = 0.015 m² Not drawn accurately
The pressure exerted by the block on the ground is 225 N/m² and 600 N/m² respectively.
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
The equation for pressure is:
Pressure = Force / Area
A block exerts a force of 9 N on the ground
a) If the area of its base is 0.04 m², hence:
Pressure = Force / Area = 9 N / 0.04 m² = 225 N/m²
a) If the area of its base is 0.015 m², hence:
Pressure = Force / Area = 9 N / 0.015 m² = 600 N/m²
The pressure exerted on the ground is 225 N/m² and 600 N/m² respectively.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
-3y 2 + 4x when x =-4 and y = 2
Answer: -22
Step-by-step explanation:
replace the variables with their given values and calculate
-3(2) + 4(-4)
Leah invests in an account paying a simple interest of 8% per year. If no money will be added or removed from the investment, what should she multiply her current balance by to find her total balance in a year in one step
Leah should multiply her current balance by 1.08 to find her total balance in one year.
To find Leah's total balance in one year, we can use the simple interest formula:
Simple Interest = Principal x Rate x Time
where:
Principal is the amount of money invested
Rate is the interest rate per year
Time is the time period in years
In this case, we know that Leah's account pays a simple interest rate of 8% per year, and no money will be added or removed from the account during the year. Hence, we may condense the formula to:
Total Balance = Principal + Simple Interest
Total Balance = Principal + (Principal x Rate x Time)
Total Balance = Principal x (1 + Rate x Time)
So to find Leah's total balance in one year, she should multiply her current balance by (1 + 0.08 x 1), which simplifies to 1.08:
Total Balance = Current Balance x 1.08
For example, if Leah currently has 1,000 in her account, her total balance in one year would be:
Total Balance = 1,000 x 1.08
Total Balance = 1,080
So Leah should multiply her current balance by 1.08 to find her total balance in one year.
for such more question on investment
https://brainly.com/question/24703884
#SPJ4
Interquartile range for 1 1 1 3 4 5
Answer:
3
Step-by-step explanation:
Of the top 10 cars and trucks based on gas mileage, 4 are Hondas, 3 are Toyotas, and 3 are Volkswagens. If you choose one at random, what is the probability that the car is Japanese or German?
Of the top 10 cars and trucks based on gas mileage, 4 are Hondas, 3 are Toyotas, and 3 are Volkswagens. Therefore, The probability that the car is Japanese or German is 01.
Probability:
The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of an event that will definitely occur is 1. The probabilities of two complementary events A and B (A or B) add up to 1.
A simple example is tossing a fair (fair) coin. If a coin is fair, both possible outcomes ("heads" and "heads") are equally likely; since the two outcomes are complementary and the probability of "heads" is equal to the probability of "heads" Probability, so the probability of each of the two outcomes is equal to 1/2 (which can also be written as 0, 5 or 50%).
According to the Question:
Given that:
Total cars = 10
Honda cars = 04
Toyota Cars = 03
and, Volkswagens cars = 03
From the above list the Japanese cars are : Toyota
German cars are: Honda and Volkswagens.
(a) Let P(J or G) = probability of getting Both Japanese and German car.
Probability of Getting Japanese or German car :
P(J or G) = Total number of Japanese and German car / Total number of cars.
⇒ P(J or G) = 4 + 3 + 3/ 10
⇒ P(J or G) = 10/10
⇒ P(J or G) = 1
Learn more about Probability:
https://brainly.com/question/11234923
#SPJ4
D
Question 15
Which of the following lines is parallel to the line graphed below?
O
y=x+3
O4x+3y=6
Oy=-3x+2
O-4x+y=7
B
-4x + y = 7 is the line parallel tο the line graphed. Optiοn D is cοrrect.
What is parallel?Parallelism is a writing style that uses similar grammatical structures, phrases, οr wοrds tο make a pοint. It is used tο emphasize a pοint and make the writing mοre interesting and easier tο understand. Parallelism is used in different types οf writing such as persuasive writing, pοetry, stοries, and legal dοcuments.
Parallelism can alsο be used in speech, allοwing the speaker tο emphasize their pοint. It creates balance and structure in the writing, making it mοre οrganized and easier tο read. Parallelism can alsο be used tο create rhythm in the writing. By creating rhythm, the writing becοmes mοre memοrable and easier tο understand.
The line parallel will have a same slοpe
Lets find the slοpe
Any two pοints form the graph are, (1, 1) and (0, -3)
Slope m = [tex]$ \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Slope m = [tex]$ \frac{-3 -1}{0 - 1}[/tex]
m = 4
Nοw, frοm the given οptiοns,
a. y=x+3 is nοt parallel as it have a οppοsite slοpe.
b. 4x + 3y = 6, write in y-intercept fοrm
y = (-4x + 6)/y. Nοt parallel
c. y =- 3x+2 is nοt parallel as it have a οppοsite slοpe.
d. -4x + y = 7, write in y-intercept fοrm
y = 4x + 7, That is parallel as the slοpe is same.
Therefοre, -4x + y = 7 is the line parallel tο the line graphed.
To learn mοre about parallel
brainly.com/question/30195834
#SPJ1
Complete question: