Answer:
The difference is 60.
Step-by-step explanation:
Since no more than 5 people can stay in each of the 15 rooms, we can multiply these numbers to get the largest amount of guests.
5 x 15 = 75
We assume the smallest amount can be 1 person in each of the 15 rooms.
1 x 15 = 15
We then subtract the smallest from the largest to find the difference.
75 - 15 = 60
A bank offers a saving account with an introductory interest rate of 7% for the first year,
and a follow-on rate of 5%, compounded annually.
If £500 is invested in the account for 3 years, how much interest will be earned?
Answer:
=£5898.38
Step-by-step explanation:
5000×1.07×1.05^(2)
=£5898.38
61 Développer et réduire l'expression suivante.
B(x)=(x-1)² + x² + (x + 1)²
b. Déterminer trois entiers naturels consécutifs dont
la somme des carrés est 4 802.
Pour les
à l'aide
68 a.
c. 422-
69
Answer:
Step-by-step explanation:
iven, the equation is (x - 1)² + 2(x + 1) = 0. We have to determine if the equation has a real root. By using algebraic identity, (a - b)² = a² - 2ab + b² (x - 1)² = x² - 2x + 1.
Find the measure of each angle indicated.
A. 111 degree
B. 69 degree
Help!!!
Answer: A. 111 degree
Step-by-step explanation:
Because they are Alternate Interior angles! Which means the two angles are congruent and have the same degree!
You pay $54 of interet on a loan of $1600 that had a 4. 5% interet rate. How long did it take you to pay off the loan?
The time required to pay off the loan at 4.5% interest rate 0.75 years.
The equation of simple interest will be used for calculation of time. The formula will be -
S. I. = Principal × Rate × Time/100
Keep the values in formula to find the value of time -
54 = 1600 × 4.5 × time/100
Rewriting the equation -
Time = (54 × 100)/(1600 × 4.5)
Performing multiplication on Right Hand Side of the equation
Time = 5400/7200
Performing division on Right Hand Side of the equation
Time = 0.75 years
I will need to take 0.75 years time to pay off the loan.
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Suppose that 6 < x < 7 and 10 < y < 12. Find all possible values of each expression.
y - x
The set of all possible y-x values is between 3 and 6, excluding both endpoints.
===================================================
Explanation:
The y-x value is smallest when:
The y value is as small as possibleThe x value is as large as possibleI recommend to draw out a number line. The idea is to place x and y as close as possible to each other.
Based on those two conditions, we use y = 10 and x = 7 respectively. That gives y-x = 10-7 = 3 as the smallest possible difference. Keep in mind we can't actually reach this value so we would write y-x > 3 which is the same as 3 < y-x.
--------------------
Similarly, y-x is largest when:
The y value is largestThe x value is smallestLike earlier, use a number line to see why this would be the case. We're trying to space x and y out as far as possible.
The largest y value and smallest x value are y = 12 and x = 6 in that order. So the upper bound is y-x = 12-6 = 6. Like before, we can't actually reach this number which means we write y-x < 6.
--------------------
Recap:
In the 1st section, we found that 3 < y-xIn the 2nd section, we found that y-x < 6Put those two results together in a tidy compound inequality to get the final answer 3 < y-x < 6
It says: The expression y-x is between 3 and 6, excluding both endpoints.
The time spent (in days) waiting for a heart transplant for people ages 35-49 in a recent year follows a normal distribution with a mean wait time of 204 days and standard deviation 25. 7 days. The 12% of people who wait the shortest for a heart transplant wait no more than how many days?.
Using the table of Z-normal distribution and with the value of mean, standard deviation and the 12% who wait the shortest, The answer is
173.80 days.
What do you mean by probability distributions?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions. The probability distribution of X is defined as the function f(x) p(x)= P(X=x) for any x falling within the range of X. The probability mass function for the discrete random variable X is another name for it.
What is a Z-normal distribution?A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it. Z scores provide the number of standard deviations from the mean that each value falls within.
[tex]P(x < Z) = 0.12\\Z = -1.175[/tex](From Z-normal table)
[tex]\frac{x-204}{25.7} = -1.175\\x= -1.175*25.7 +204\\x=173.80\\[/tex]
Days = 173.80 days .
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Describe the Vertex Form of a Quadratic
equation in words.
The vertex form of a quadratic equation is a standard form of a quadratic equation that is written in the form:
y = a(x-h)^2 + k
where a, h, and k are constants. This form is called the vertex form because it represents the graph of the quadratic equation as a parabola, with the vertex of the parabola located at the point (h,k).
The vertex form of a quadratic equation is useful because it allows us to easily identify the vertex of the parabola and the direction in which the parabola opens. If a is positive, the parabola opens upwards and the vertex is the minimum point of the parabola. If a is negative, the parabola opens downwards and the vertex is the maximum point of the parabola.
Overall, the vertex form of a quadratic equation is a standard form that represents the graph of a quadratic equation as a parabola with a specific vertex location. It is useful for identifying the characteristics of the graph and for solving problems involving quadratic equations.
help with my thing and get 16 point
Bonsoir j'ai cette exercice a faire pour demain on peut m'aider ?
Maria and Franco are mixing port drink for a track meet. Maria ue 3/4cup of powdered mix for every 3 gallon of water. Franco ue 1 2/3 cup of powdered mix for every 5 gallon of water. Quetion 1 Part A What i the unit rate of cup of powered mix per gallon for each peron? Enter the correct anwer in the boxe. Maria: $$ cup of powdered mix per gallon Franco: $$ cup of powered mix per gallon
The unit rate of cup of powered mix per gallon for each person by
Maria: 3 cups
Franco: 1/3 cups
Rate of powdered mix = number of cups ÷ number of gallons of water
Keep the values in formula to find the unit rate of cup of powdered mix
Rate of powdered mix by Maria = (3/4)÷3
Rate of powdered mix by Maria = 3/(4×3)
Cancelling 3 as it is common
Rate of powdered mix by Maria = 3 cups per gallon
Firstly converting the amount of cups from mixed fraction to fraction
Amount of cups = 1 [tex] \frac{2}{3} [/tex]
Amount of cups = 5/3 cups
Rate of powdered mix by Franco = (5/3)÷5
Rate of powdered mix by Franco = 5/(5×3)
Cancelling 5 as it is common
Rate of powdered mix by Franco = 1/3 cups per gallon
Thus, Maria's powdered mix is 3 cups per gallon while Franco's powdered mix is 1/3 cups per gallon.
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The combined volume of all the tanks at an aquarium is 1.25x10^6
gallons. The aquarium plans to install a new dolphin tank with a volume of 250,000gallons. What will be the total volume of all of the tanks at the aquarium after the new dolphin tank is installed?
Answer: The total volume of all the tanks at the aquarium after the new dolphin tank is installed will be 1.25x10^6 gallons + 250,000 gallons = 1.5x10^6 gallons.
This is the equivalent of 1,500,000 gallons.
Step-by-step explanation:
for how many pairs of consecutive integers in {1000,1001,1002,...,2000} is no carrying required when the two integers are added?
156 pairs of consecutive integers in {1000,1001,1002,...,2000} is no carrying required when the two integers are added
You will need to consider four cases.
when _999 and _000 are the last three digits of consecutive numbers. Just possible cases are 1999, 2000
At the point when the last 2 digits of the continuous numbers are _ _ 9 9 and _ _ 0 0. 5 possible scenarios (corresponding to (0,1), (1,2), (2,3), (3,4), and (4,5) at the hundredth place) exist.
when the last digit of consecutive numbers is in the form ____ 9 and ____ 0. 5*5 = 25 possible scenarios.
when none fall into that category, possible case=. 5*5*5 = 125,
and the answer is 125+25+5+1 = 156.
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What are the values of x and y? Question options:
A) x = 18√3 y = 9√3
B) x = 9; y = 9√3
C) x = 9√2 ; y = 9
D) x = 9√3 ; y = 9
Answer:
Given:
A figure of a triangle.
To find:
The values of x and y.
Solution:
From the given triangle it is clear that the base angles of the triangle are equal, so the triangle is an isosceles triangle.
Altitude on the base of the isosceles triangle from from the opposite angle is a median. It means, it divides the base in two equal parts.
In the given triangle, the altitude divides the base in two equal parts and the measure of each part is 9 units.
Step-by-step explanation:
Answer:
B) x = 9; y = 9√3
Step-by-step explanation:
x = 9 = ( 9 )
y = 9√3 = ( 15.588 )
Hope this helps!
if the residuals from a fitted regression violate the assumption of homoscedasticity, we know that a. they are normally distributed. b. they are independent of one another. c. there are extreme outliers. d. their variance is not constant.
Option D is the correct answer. if the residuals from a fitted regression violate the assumption of homoscedasticity their variance is not constant.
Homoscedasticity: It is an assumption of equal or similar variances in different groups are being compared. It is a condition in which the variance of the residual, or error term, in a regression model, is constant.
This is one of the most important assumptions of parametric statistical tests because they are sensitive to any dissimilarities. It is valid when X and Y are independent.
To deal with this First, we have attempted to transform your target using square root, log, reciprocal square root, or reciprocal transformations.
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the multiple regression/correlation model is a model with: group of answer choices multiple dependent variables and multiple independent variables multiple dependent variables and a single independent variable. single dependent variable and multiple independent variables single dependent variable and single independent variable
The multiple regression model is a model with single dependent variables and multiple independent variables.
The term regression referred as a statistical method that helps us to analyze and understand the relationship between two or more variables of interest.
Here we have to find the missing term in the statement "the multiple regression/correlation model is a model with"
In order to find the solution, we must know the definition of multiple regression model.
Multiple Regression model in statistics is defined as the is a statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables.
Based on these definition, we have identified that it has single dependent variable and multiple independent variable.
Therefore, option (c) is correct.
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Pleaseeee helppppp meee
Answer:
A
Step-by-step explanation:
w = 12500p + 250
250 is a fixed number of words.
12500 is the slope
For each dollar the price increases, the number of words increases by 12,500.
Answer: A
The graph below represents the distance of a dog from a trainer after a command is given.
A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10, and the vertical axis shows Distance (yards) numbered 4 to 40. The line shows an increase, then decrease, then constant distance.
Which statement could describe the dog’s movement at 5 seconds once the command was given?
The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer to receive a treat.
The dog was running away from the trainer to chase a squirrel.
The dog was stopped but began running towards the trainer.
The statement dog was running towards the trainer to receive a treat.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that graph represents the distance of a dog from a trainer after a command is given.
A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10,
The vertical axis shows Distance (yards) numbered 4 to 40.
The line shows an increase, then decrease, then constant distance.
At the point on the graph where time is 5 seconds, the slope of the distance vs time curve is negative, indicating the dog is moving toward the trainer.
The motivation of the dog is unknown, so the above answer choice involves speculation that is not supported by the problem statement.
Hence, the statement dog was running towards the trainer to receive a treat.
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how much water should we add to 20kg of sea water to change its concentration from 2% to 3%
Answer: 10 kg
Step-by-step explanation:
3% = 0.03
First, take 20 times 0.03 = 0.6kg of salt
We know that the 2% solution of seawater
So, we take 100 times 0.6, then divide by 2 = 30kg
Then take 30 - 20 = 10kg
So, to make a solution from 3% to 2%, we have to add 10 kg of water with a 20 kg solution.
How much power is needed to get up the stairs, if I can do this with 30 Joules of work in 3 seconds?
Answer:
10 Joules/second
Step-by-step explanation:
To find the power needed to get up the stairs, we need to divide the amount of work done (30 Joules) by the time it took to do the work (3 seconds):
Power = Work / Time
Power = 30 Joules / 3 seconds
Power = 10 Joules/second
Therefore, it takes 10 Joules/second of power to get up the stairs.
a local department store estimates that 10 percent of its customers return the merchandise they purchase. let the random variable r represent the number of returns for a random sample of 40 customers. assume that random variable r follows a binomial distribution. what is described by the value of (408)
The value of (408) is (0.1)8(0.9)32 for a local department store estimates that 10 percent of its customers return the merchandise they purchase.
The value of (408)(0.1)8(0.9)32 represents the probability of getting 8 returns out of a sample of 40 customers, given that the store estimates that 10% of customers return merchandise.
This probability is calculated using the binomial probability formula, which is used to calculate the probability of a specific number of successes (in this case, returns) in a certain number of trials (in this case, customer purchases), given a certain probability of success (in this case, the estimated probability of customers returning merchandise).
The value of (408)(0.1)8(0.9)32 ( 40 8 ) ( 0.1 ) 8 ( 0.9 ) 32 describes the probability of getting 8 returns out of 40 customers when the probability of a customer returning the merchandise they purchase is 0.1.
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tomas is thinking of a number. if he triples it and subtracts 13, the result is 305. of what number is tomas thinking of
Answer:
106
Step-by-step explanation:
(305+13)/3=106
A 3-gallon container of laundry detergent cot $33. 60. What i the price per cup?
As per the unitary method, the price of the cup is $2.958
Unitary method in statistics is defined as in which the value of one article is first obtained to find out the value of any required articles
Here we have given that the 3-gallon container of laundry detergent cost $33. 60.
And we need to find the price per cup.
While we looking into the given question, we have identified the following details that cost of 3 gallon container of laundry detergent is $33.60.
So, the cost for 1 gallon container of laundry detergent cost,
=> 33.60/3
=> 11.20
Let us consider that the cup can hold 1 liter.
As we know that 1 gallon = 3.78541 liter.
Then the cost of 1 liter is calculated as,
=> 11.20/3.78541
=> 2.958
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If the term of a sequence increases in value what is true about the common difference
Answer:
Common Difference is positive
Step-by-step explanation:
If the common difference is negative, the value is decreasing every time the term increases.
If the common difference is positive, the value is increasing every time the term increases.
Because, in this case, when the term increases, the value increases, the common difference is positive.
find the area of this triangle
Answer: a is about 7.416, rounding to two significant digits, 7.4, to one significant digit, 7.
Step-by-step explanation:
We will use the Pythagorean Theorem.
a²+b²=c²
c² is the longest side, so 8cm.
lets make the bottom side b², so 3cm
We are trying to find h, so let's make that a².
Applying the Theorem:
a²+3²=8²
--- a² + 9 = 64
subtract 9 from both sides.
-- a² = 55
Take the square root of both sides
a is about 7.416, rounding to two significant digits, 7.4, to one significant digit, 7.
Answer:
22.249 cm^2 (THIS IS ROUNDED)
Step-by-step explanation:
to find the area we first need to find h using Pythagorean theorem
a^2+b^2=c^2
We need to isolate a^2 on one side
a^2+b^2=c^2
-b^2. -b^2
a^2=c^2-b^2
a^2=8^2-3^2
a^2=64-9
a^2=55
√. √
a=7.416
Now we multiply by 3 to find the area
7.416x3
About 22.249 cm^2
Hopes this helps
please help me solve this
Answer:
8+5x
Step-by-step explanation:
Perimeter = sum of the all sides of triangle
= 6+3x-4+2x + 6
= 8+5x
Answer:
5x + 8
Step-by-step explanation:
To find the perimeter, add up all the sides
6 + 3x-4 + 2x +6
Combine like terms
5x + 8
What is the average of 129 and 47?
Answer:
the average for 129 is 159 and the average for 47 is 49
Step-by-step explanation:
is (x+1) a factor of polynomial x^3+2x^2-19x-20
Answer:
Step-by-step explanation:
3
Explain how to find the volume and surface area
The volume and the surface area of the regular octogonal prism are given as follows:
Volume: [tex]56(1 + \sqrt{2})[/tex] cubic inches.Surface area: [tex]S = 128 + 8\sqrt{2}[/tex] square inches.How to obtain the volume of the prism?
The volume of the prism is given by the multiplication of the base area of the prism by the height of the prism.
The base is a regular octagon of side length 2 inches, hence it's area is given as follows:
[tex]A = 2a^2(1 + \sqrt{2})[/tex]
Hence, considering that a = 2, the base area is given as follows:
[tex]A = 8(1 + \sqrt{2})[/tex]
The height is of 7 inches, hence the volume, in cubic inches, is given as follows:
[tex]V = 7 \times 8(1 + \sqrt{2}) = 56(1 + \sqrt{2})[/tex]
How to calculate the surface area?The prism is composed by:
Eight rectangles of dimensions 2 inches and 7 inches.Two regular octagons of side length 2 inches.Hence the surface area of the prism, in square inches, is calculated as follows:
[tex]S = 2 \times 8(1 + \sqrt{2}) + 8 \times 2 \times 7[/tex]
[tex]S = 128 + 8\sqrt{2}[/tex]
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Find the measure of each angle indicated.
A. 127 degrees
B. 53 degrees
Help!!!
Answer:
B. 53 degrees
Step-by-step explanation:
Because the ?-angle is equal to the 53-degree angle. So, the answer is B. 53 degrees
PLEASE HELP
What is the approximate volume of the cone
Use 3.14 for TT.
57 cm3
339 cm3
509 cm3
1526 cm3
The volume of the Illustrated cone used as an example is 51.3cm³.
How to calculate the volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.
A cone is a recognizable three-dimensional geometric shape with a flat and curved surface that is pointed upward. The formula for the volume of a cone is V=1/3hπr²
Let's say the radius is 7cm. The volume will be:
= 1/3 × 3.14 × 7²
= 51.3cm³
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