The probability of the 6th order being the order with the free appetizer is 0.0417 (approx).
The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.
The probability of getting a free appetizer is 1/18.
The probability of not getting a free appetizer is 17/18.
If the restaurant gives away an appetizer on the 6th order, then there must have been 5 orders before the 6th one that had no free appetizer, followed by the one with the free appetizer.
[tex]P (X = 6) = P(N N N N N F)[/tex]
= 17/18 x 17/18 x 17/18 x 17/18 x 17/18 x 1/18
[tex]= \frac{17^4}{18^5}[/tex] ≈ 0.0417
Thus, the probability of the 6th order being the order with the free appetizer is 0.0417 (approx).
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jerry is trying to figure out how much pizza remains after his party last night. he finds six whole pizzas, as well as 5/8 of another pizza. if he finds one more slice in the fridge (1/8 of a whole pizza), then how many pizzas does jerry have?
On solving the provided question we can say that by equation we have
remain = x+y = 5/8 + 1/8 = 6/8 3/4
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
six whole pizzas, as well as = 5/8 of another pizza
another one = 1/8 of a whole pizza
Remain -by forming equation
let x = 5/8 of another pizza
and y = 1/8 of a whole pizza
remain = x+y = 5/8 + 1/8 = 6/8 3/4
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Otis wants to borrow 10000 to buy a used car. he examined his budget and decided that he can afford a payment of $200 a month. if his bank offers him a rate of 7.5%, how long should he borrow the money so he can afford his monthly payment?
Answer: Otis should borrow the money for 60 months (5 years) so he can afford his monthly payment of $200.
Step-by-step explanation: To calculate the duration of the loan, we can use the formula:
Duration (in months) = Loan amount / Monthly payment
In this case, the loan amount is $10,000, and the monthly payment is $200. So by substituting the values, we get:
Duration (in months) = 10000 / 200 = 50
The duration of the loan is 50 months, however, the bank offers him a rate of 7.5%.
To calculate the total interest, we can use the formula:
Total Interest = Loan amount * Interest Rate * Duration (in months) / 12
The total interest is = 100007.5/10050/12 = 3750
So the Otis will have to pay an additional $3750 in interest over the course of the loan.
So, the total amount he will have to pay is 10000+3750 = 13750
And the time duration to pay this amount is 60 months ( 5 years)
Note: As per the information provided, the interest rate is not annual, it is monthly. So, it is not necessary to divide it by 12 in the interest formula. The equation should be Total Interest = Loan amount * Interest Rate * Duration (in months)
the size of a television screen is given by the length of diagonal of the screen. What size is a tv screen the is 21.6 inches wide and 16.2 inches high
The size of a television screen that is 21.6 inches wide and 16.2 inches high is approximately 27 inches (measured diagonally).
What is the Pythagorean theorem?
It's a relation in Euclidean geometry among the three sides of a right triangle. In it, the square of the hypotenuse is equal to the sum of the squares of the other 2 sides.
The size of a television screen can be found by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the length of the diagonal of the screen is the hypotenuse, the width is 21.6 inches, and the height is 16.2 inches. We can use the theorem to find the length of the diagonal:
diagonal²= width² + height²
diagonal² = 21.6² + 16.2²
diagonal² = 467.76 + 262.44
diagonal² = 730.2
diagonal = √730.2
diagonal ≈ 27 inches
Hence, the size of a television screen that is 21.6 inches wide and 16.2 inches high is approximately 27 inches (measured diagonally).
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which of the changes would keep then hanger in balance? select all that apply
the answer is just D
2. Togetherness Are good grades in high school associated with family togetherness? A random sample of 142 high school students was asked how many meals per week their families ate together. Their responses produced a mean of 3.78 meals per week, with a standard deviation of 2.2. Researchers then matched these responses against the students' grade point aver- ages (GPAs). The scatterplot appeared to be reasonably linear, so they created a line of regression. No apparent pattern emerged in the residuals plot. The equation of the line was GPA = 2.73 + 0.11 Meals. a) Interpret the y-intercept in this context. b) Interpret the slope in this context. c) What was the mean GPA for these students? d) If a student in this study had a negative residual, what did that mean? e) Upon hearing of this study, a counselor recommended that parents who want to improve the grades their children get should get the family to eat together more often. Do you agree with this interpretation? Explain.
As per the given standard deviation, the y intercept of the equation is 2.78 and the slope of the equation is 0.11 and the mean of the equation is 24.08
The term standard deviation in math is known as a quantity expressing by how much the members of a group differ from the mean value for the group
Here we have random sample of 142 high school students was asked how many meals per week their families ate together. And their responses produced a mean of 3.78 meals per week, with a standard deviation of 2.2.
And the equation of the line was written as,
=> GPA = 2.73 + 0.11 Meals.
Here let us consider that x meals and y refers the GPA.
Then the equation is rewritten as,
=> y = 0.11x + 2.73
While we compare this one with the standard form of the equation, then we get
the value of the slope as 0.11 and the intercept as 2.73
Then the value of the mean is calculated as,
=> 144/ (3.78 + 2.2)
=.> 24.08
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the length of each side of a square is 3 inches more than the length of each side of a smaller square. the sum of the areas of the squares is 149 inches squared. find the length of the side of the smaller square.
The length of the side of the smaller square is 7 inches.
Let x be the length of the side of the smaller square.
The length of each side of a square is 3 inches more than the length of each side of a smaller square. Thus the length of the side of the larger square is
(x + 3) inches.
The area of the smaller square is
x^2 square inches.
The area of the larger square is
(x + 3)^2 square inches.
We can set up the equation:
x^2 + (x + 3)^2 = 149
Expanding and simplifying the equation gives:
x^2 + x^2 + 6x + 9 = 149
Combining like terms:
2x^2 + 6x - 140 = 0
Using the quadratic formula, we can solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-6 ± √(6^2 - 4 * 2 * (-140))) / 2 * 2
x = (-6 ± √(36 + 1120)) / 4
x = (-6 ± √(1156)) / 4
x = (-6 ± √(596)) / 4
x = (-6 ± 34) / 4
x = -10 or x = 7
The side length of the smaller square can't be negative, so x = 7 inches.
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A group of researchers investigated the effect of media usage (whether or not subjects watch television or use the Internet) in the bedroom on ""Tiredness"" during the day (measured on a 50 point scale a. Identify each of the variables, state whether the variables are quantitative or categorical, and identify each variable as either explanatory or response variables. nterviewed b. To collect these data, the researchers randomly selected homes to visit and i the adult member of the household whose birthday was nearest. Is this an experiment or an observational study? Briefly explain.
a. Media usage is categorical and Tiredness is quantitative. The effect of media is the explanatory variable and Tiredness is the response variable.
b. Yes, this is an observational study.
What is an Observational Study?In fields including epidemiology, social sciences, psychology, and statistics, observational studies draw conclusions from a sample of the population when the independent variable is not under the researcher's control due to ethical issues or practical constraints.In a normal observational study, participants are assigned to either the treated group or the control group, and the researcher observes how the therapy may influence them.This does not occur in experiments such as randomized controlled trials when each subject is randomly assigned to either a treated group or a control group. Observational studies by their very nature provide difficulties for inferential analysis due to the absence of an assignment process.This research was done via observation. The researchers are not modifying or controlling any variables; instead, they are watching and assessing the correlation between media use and fatigue. By visiting randomly chosen households and interviewing the adult household member with the closest birthday, they are gathering data.
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do you need to multiply everything on one side of an equation if you are only multiplying a fractionating that's adding
Yes, we can multiply everything on one side of an equation if you are only multiplying a fractionating that's adding.
Multiplicative Property:
The multiplicative nature of the equation dictates that both sides of the equation can be multiplied or divided by the same nonzero fraction or Gebraic Equation without changing the solution.
if a, b, and c are any three fractions
if a = b and c ≠ 0
1. a × c = b × c
2. a ÷ c = b ÷ c
Multiplicative property for Fraction:
When multiplying two fractions, the numerator and denominator are multiplied separately. The first numerator is multiplied by his second numerator, and the first denominator is multiplied by his second denominator. Finally, reduce the fraction to its lowest term. A fraction has the smallest form if 1 is the only common divisor between the numerator and denominator.
Properties of Multiplying Fractions
1. Multiplying a non-zero fraction by 1 yields the exact fraction
Example: 38 × 1 = 38
2. Multiplying 0 by a non-zero fraction yields zero.
Example: 38 × 1 = 38
3. The product of a fraction and its reciprocal is always 1.
Example: 25×52 = 2×55×2 =1010 =1
(the reciprocal of 25 is 52)
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The measure of angle JKL is 145°.
The measure of angle MKL is 60°.
The measure of angle JKM is x°.
Find the value of x.
X=
0
X
5
Xº
K
145°
M
60°
D
1.2m divided by 40 cm
Answer:3
Step-by-step explanation:
Answer: the answer is 3
Step-by-step explanation:I did the dividing on paper and the answer is 3
←
▲
of 1
Suppose that a new employee starts working at $7.54 per hour
and receives a 3% raise each year. After time t, in years, his
hourly wage is given by the equation y = $7.54(1.03). Find the
amount of time after which he will be earning $10.00 per hour.
www
After what amount of time will the employee be earning $10.00
per hour?
years (Round to the nearest tenth of a year as needed.)
Qu
The amount of time after which the employee will be earning $10 is 9 years.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
The raise per year = 3%
The amount received per hour = $7.54
The equation for the hourly wage after t years.
y = 7.54 x [tex]1.03^t[/tex]
Now,
For t = 9,
y = 7.54 x [tex]1.03^9[/tex]
y = 7.54 x 1.326
y = $10
Thus,
After 9 years the hourly earning is $10.
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The wood you are using for the floor costs 3.50 per square foot. how much will it cost to buy the material assuming you can buy a piece exactly the right size
On solving the provided question, we can say that by equation it cost to buy the material assuming you can buy a piece exactly the right size = $350.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
the floor costs = 3.50 per square foot
assuming we can buy a piece exactly the right size = x
then cost =
x * 3.50
let x be 100
cost = $350
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the dominican republic has 10.7 million people and a national population growth rate of 1.5 percent. paraguay has 6.8 million people and a national population growth rate of 1.5 percent. in how many years will each country double in size?
The population of each country will become double in 47 years.
Given that,
The population of the Dominican republic is, n = 10.7 million.
The growth rate of the Dominican republic is, p = 1.5 %.
The population of Paraguay is, n' = 6.0 million.
The growth rate of Paraguay is p' = 1.5 %.
The doubling time of population growth depends on the rate of population growth.
Here,
n is the final population and n0 is the initial population and doubling the value in the future, n= 2*n0.
Solving this, we get:
t= ln (2*n0/n0)/(1.5/100) = 47 years.
Thus, we can conclude the population of each country will become double in 47 years.
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