In a bag there are 3 red marbles, 2 yellow marbles, and 1 blue marble. What is the likelihood of a yellow marble being selected on the first draw?
likely
unlikely
even chance
certain
Therefore, it is not even chance, but it is also not very unlikely. It is moderately likely that a yellow marble will be selected on the first draw.
What is Probability?Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It is a measure of the likelihood or chance of an event happening. Probability is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.
In other words, probability is a way of quantifying uncertainty. It is used in various fields, such as statistics, physics, finance, engineering, and more, to help make predictions and decisions based on uncertain information. Probability theory provides a set of rules and tools for analyzing and manipulating random variables and events, and for calculating the probability of complex events.
The likelihood of a yellow marble being selected on the first draw can be calculated by dividing the number of yellow marbles by the total number of marbles in the bag:
likelihood of selecting a yellow marble = number of yellow marbles / total number of marbles
So, in this case, the likelihood of selecting a yellow marble on the first draw is:
likelihood of selecting a yellow marble = 2 / (3 + 2 + 1) = 2/6 = 1/3
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Fill in the blanks to make the statement true.
Pi the ratio of the (choose your answer...) of a circle to its ( choose your answer....)
Pi is the ratio of the circumference of a circle to its diameter.
the area of Rectangle is 112 in sq. if the height is 8 in, what is the base length
Answer:
14cm
Step-by-step explanation:
112÷8=14
base length=14cm
Answer:
To find the base length of a rectangle, given its area and height, you can use the formula for calculating the area of a rectangle, which is:
Area = Length x Width
In this case, you are given that the area is 112 square inches and the height is 8 inches. Let's denote the base length as "x" inches.
So, the equation for the area of the rectangle becomes:
112 = x * 8
To solve for "x", you can divide both sides of the equation by 8:
112 / 8 = x
x = 14
Therefore, the base length of the rectangle is 14 inches.
Please help with this math question!
The exponential function of the population is P(x) = 15000 * 1.046^x
Calculating the exponential function of the populationFrom the question, we have the following parameters that can be used in our computation:
Initial, a = 15000
Rate, r = 4.6%
The equation of the function is represented as
P(x) = a * (1 + r)^x
Substitute the known values in the above equation, so, we have the following representation
P(x) = 15000 * (1 + 4.6%)^x
Evaluate
P(x) = 15000 * 1.046^x
Hence, the function is P(x) = 15000 * 1.046^x
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An average newspaper contains at least 9 pages and at most 46 pages. How many newspapers must be collected to be certain that at least two newspapers have the same number of pages?
We need to collect 46 newspapers to be certain that at least two newspapers have the same number of pages.
What is the minimum number of newspapers needed to guarantee that two newspapers have the same number of pages?According to the Pigeonhole Principle, if we have n+1 pigeons and n holes, then there must be at least one hole with two or more pigeons. Similarly, if we have n+1 newspapers with n possible page counts, then there must be at least one page count that appears in two or more newspapers.
In this case, we have a range of 38 possible page counts (46 - 9 + 1), so we need at least 39 newspapers to guarantee that each possible page count appears in at least one newspaper.
However, to guarantee that at least two newspapers have the same number of pages, we need one more newspaper than the number of possible page counts, so we need a total of 46 newspapers. Therefore, if we collect 46 newspapers, we can be certain that at least two of them have the same number of pages.
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Please I’ll give brainliest
A Ferris wheel reaches a maximum height of 60 m above the ground and takes twelve minutes to complete one revolution. Riders have to climb a m staircase to board the ride at its lowest point.
(a) [4 marks] Write a sine function for the height of Emma, who is at the very top of the ride when t = 0.
(b) [2 marks] Write a cosine function for Eva, who is just boarding the ride.
(c) (2 marks] Write a sine function for Matthew, who is on his way up, and is at the same height as the central axle of the wheel.
If Riders have to climb a m staircase to board the ride at its lowest point.
a. sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
b. a cosine function for Eva, who is just boarding the ride is: h(t) = m + 60 cos(π/6 t).
c. a sine function for Matthew is: h(t) = 30 sin(π/6 t).
What is the sine function for the height of Emma?(a) Let's assume that the Ferris wheel completes one full revolution in 12 minutes. The height of the Ferris wheel can be modeled by a sine function as it moves up and down periodically. When the Ferris wheel completes one revolution, it returns to its original position, so the period of the sine function is 12 minutes.
The maximum height of the Ferris wheel is 60 m, so the amplitude of the sine function is 60 m. When t = 0, Emma is at the very top of the ride, which means she is at the maximum height of the Ferris wheel. Therefore, the sine function for Emma's height, h(t), can be written as:
h(t) = 60 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 60 sin(π/6 t)
(b) Eva is just boarding the ride, which means she is at the lowest point of the ride when t = 0. The cosine function is ideal for modeling this situation, as it starts at its maximum value and reaches its minimum value after one-fourth of the period. Therefore, the cosine function for Eva's height, h(t), can be written as:
h(t) = m + 60 cos(2π/12 t)
Simplifying this equation, we get:
h(t) = m + 60 cos(π/6 t)
where m is the height of the staircase that Eva has to climb to board the ride.
(c) Matthew is at the same height as the central axle of the Ferris wheel, which means he is halfway between the maximum and minimum height of the ride. Therefore, the sine function for Matthew's height, h(t), can be written as:
h(t) = 30 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 30 sin(π/6 t)
Therefore sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
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20!!!!! POINTS!!!!!!! The bar graph shows the strengths of tornadoes that occurred in Alabama in 2011. What percent of the tornadoes were EF1s?
The percentage of tornadoes that were EF1s is 40%.
What is the percentage?
A figure or ratio stated as a fraction of 100 is called a percentage. The acronyms pct., pct., and occasionally pc are also used to indicate it, however, the percent sign is most frequently used. A % is a number without dimensions and without a standard measurement.
Here, we have
Given: the strengths of tornadoes that occurred in Alabama in 2011.
We have to find the percentage of tornadoes that were EF1s.
EF1s = 58
Total = 145
percentage of tornadoes = 58/145 = x/100
5800/145 = x
x = 40%
Hence, the percentage of tornadoes that were EF1s is 40%.
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What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice of sport?
1. We can see that brainstorming, we discover that sports the graph represents is 100-yard dash. This is because athletes start from a stationary position and accelerate to their maximum speed, which is usually reached halfway through the race, and then slow down to a stop at the finish line.
2. The vocabulary and properties of graphs and functions do you see represented in the graph are:
SpeedTimeVertical axisHorizontal axis.What is graph?A graph is a mathematical representation of a set of data or a relationship between two or more variables. It typically consists of a set of points, or vertices, connected by lines or curves, known as edges or arcs. Graphs are used to visualize and analyze data, and to model and solve real-world problems in a variety of fields, including mathematics, science, engineering, economics, and social sciences.
We see here that the vocabulary and properties of the graph shows the choice of sports as it tells us how the speed decreases as time increases.
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The complete question is:
Portfolio Option 1: Sports Graph
This portfolio problem will have you write. You will turn in a “mathematical paper” of about 1 page of writing. You can use this handout to write rough draft ideas first.
Brainstorm: Which of the above sports do you think the graph could represent? Why?
Brainstorm: What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice for the sport?
Use your brainstorms above to write a 1 page paper that talks about this graph, what sport you believe it could represent, and what properties of functions and graphs support your answer. You can add diagrams as well.
Please help me, I am confused on how to do this problem.
Find the exact value, cos(-pi/12). Use the half angle strategy.
Using the half angle formula, cos(-π/12) = ±√[2 + √3]/4]
What is the half angle formula?The half angle formula for cosine is cosФ/2 = ±√[(1 + cosФ)/2]
Since we want to find the value of cos(-pi/12) using the half angle formula, we have that cosФ/2 = cos(-π/12)
⇒ Ф/2 = -π/12
⇒ Ф = -π/12 × 2
⇒ Ф = -π/6
So, substituting this into the equation, we have
cosФ/2 = ±√[(1 + cosФ)/2]
cos(-π/6)/2 = ±√[(1 + cos(-π/6))/2]
= ±√[(1 + cos(π/6))/2]
Now, we know that cos(π/6) = √3/2
So, substituting this into the equation, we have that
cos(-π/6)/2 = ±√[(1 + cos(π/6))/2]
cos(-π/12 = ±√[(1 + cos(π/6))/2]
= ±√[(1 + √3/2)/2]
= ±√[[2 + √3]/2)/2]
= ±√[[2 + √3]/2 × 2]
= ±√[2 + √3]/4]
So, cos(-π/12) = ±√[2 + √3]/4]
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Calculating Income Tax Expense
Given the following.
Taxable Income $500k
Future taxable amounts $45k
Future deductible amounts $55k
Beginning Balances DTA $20k
Beginning Balances DTL $50k
Tax rate 40%.
1. What is the income tax payable?
2. What is the DTA year end balance?
3. What is the DTL year end balance?
4. What is the income tax expense?
5. What is the originating/reversing amount for the future taxable amount and for the deductible amount of the current year?
The income tax payable can be calculated as follows:
Taxable income = $500,000
Tax rate = 40%
Income tax payable = $500,000 x 40% = $200,000
What is the DTA year end balance?The DTA (Deferred Tax Asset) year-end balance can be calculated as follows:
Beginning balance DTA = $20,000
Future deductible amounts = $55,000
DTA year-end balance = $20,000 + $55,000 = $75,000
The DTL (Deferred Tax Liability) year-end balance can be calculated as follows:
Beginning balance DTL = $50,000
Future taxable amounts = $45,000
DTL year-end balance = $50,000 - $45,000 = $5,000
The income tax expense can be calculated as follows:
Income tax payable = $200,000
Add: Increase in DTL = $5,000
Less: Increase in DTA = $55,000 - $20,000 = $35,000
Income tax expense = $200,000 + $5,000 - $35,000 = $170,000
The originating/reversing amount for the future taxable amount and for the deductible amount of the current year can be calculated as follows:
Future taxable amount:
Origination amount = $45,000 x 40% = $18,000
Reversing amount = $18,000
Future deductible amount:
Origination amount = $55,000 x 40% = $22,000
Reversing amount = $22,000 - $20,000 = $2,000 (since the beginning balance of DTA was $20,000)
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The length of the altitude of an equilateral triangle is 4 square root of 3 . Find the length of a side of the triangle.
[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=4\sqrt{3} \end{cases}\implies 4\sqrt{3}=\cfrac{s\sqrt{3}}{2} \\\\\\ 8\sqrt{3}=s\sqrt{3}\implies \cfrac{8\sqrt{3}}{\sqrt{3}}=s\implies 8=s[/tex]
What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?
(x is -2,-1,0,1,2 and g(x) is 1,3,5,7,9?
f(x) = 2x^2 + x + 4
We see that f(-1) = g(1) = 5. Therefore, the solution to the system of equations is x = -1.
Describe System of equation?A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values for the variables that satisfy all of the equations in the system.
One way to solve a system of equations is by substitution. We can solve one of the equations for one of the variables in terms of the other variable, and then substitute that expression into the other equation to get an equation in one variable. We can then solve that equation for the variable, and use that value to find the value of the other variable.
Another way to solve a system of equations is by elimination. We can add or subtract the equations in the system to eliminate one of the variables, and then solve for the other variable. We can then use that value to find the value of the eliminated variable.
To find a solution to the system of equations that includes the quadratic function f(x) and the linear function g(x), we need to find the value of f(x) for each value of x and compare it to the corresponding value of g(x). If f(x) and g(x) are equal for any value of x, then that value is a solution to the system.
Substituting each value of x into the quadratic function f(x), we get:
f(-2) = 2(-2)² + (-2) + 4 = 10
f(-1) = 2(-1)² + (-1) + 4 = 5
f(0) = 2(0)² + 0 + 4 = 4
f(1) = 2(1)² + 1 + 4 = 7
f(2) = 2(2)² + 2 + 4 = 14
Comparing these values to the corresponding values of g(x), we see that f(-1) = g(1) = 5. Therefore, the solution to the system of equations is x = -1.
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what’s the surface area of this figure ?
Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.
Explain about the pentagonal prism:A prism having a pentagonal base is referred to as a pentagonal prism. It has two hexagonal bases, five parallelogram faces, and seven faces. Seven faces, fifteen edges, and ten vertices make up a pentagonal prism.
The two bases of each of the seven faces—two pentagons—and the remaining five faces—parallelograms—connect the bases of the pentagons.
Given data:
base area B = 84.3 sq. ftLength of rectangular side L = 7 ftwidth of rectangular side w = 4 ftsurface area of pentagonal prism = 2* base area + 5*rectangle area
surface area of pentagonal prism = 2* B + 5*L*w
surface area of pentagonal prism = 2* 84.3 + 5*7*4
surface area of pentagonal prism = 168.6 + 140
surface area of pentagonal prism = 308.6 sq. ft
Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.
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Can someone tell me what 2.72 as a fraction?
Answer:
68/25
Step-by-step explanation:
You are offered the following terms on a loan of $2250: 9.25 % interest per year paid back over 36 months. If monthly payments are $79.84, how much interest will you have paid once this loan is paid in full?
a) $624.24
b) $655.24
c) $2874.24
d) $1242.50
e) None of the above
Answer: $624.24.
Step-by-step explanation:
To find the total amount of interest paid on the loan, we first need to find the total amount of money repaid over the course of 36 months.
The total amount repaid is the monthly payment multiplied by the number of months:
Total amount repaid = Monthly payment x Number of months
Total amount repaid = $79.84 x 36 = $2,874.24
To find the total amount of interest paid, we need to subtract the original amount borrowed from the total amount repaid:
Total interest paid = Total amount repaid - Original amount borrowed
Total interest paid = $2,874.24 - $2,250 = $624.24
Therefore, the total amount of interest paid on the loan is $624.24.
Which two equations would be most appropriately solved by using the zero product property? Select each correct answer. Responses 3x2−6x=0 3 x squared minus 6 x equals 0 4x² = 13 4, x, ² = 13 0.25x2+0.8x−8=0 0.25 x squared plus 0.8 x minus 8 equals zero −(x−1)(x+9)=0
The two equations that can be most appropriately solved by using the zero product property are:
3x² - 6x = 0 and -(x - 1)(x + 9) = 0.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The zero product property can be used to solve equations that can be factored into the product of two or more expressions, where one or more of those expressions is equal to zero.
Therefore, the two equations that can be solved using the zero product property are:
3x² - 6x = 0
This equation can be factored as:
3x(x - 2) = 0
Using the zero product property, we get:
3x = 0 or x - 2 = 0
Solving for x, we get:
x = 0 or x = 2
-(x - 1)(x + 9) = 0
This equation can be factored using the difference of squares:
-(x - 1)(x + 9) = -(x² - 1² - 9x + 1x) = -(x² - 8x - 9) = 0
Using the zero product property, we get:
x - 1 = 0 or x + 9 = 0
Solving for x, we get:
x = 1 or x = -9
Therefore, the two equations that can be most appropriately solved by using the zero product property are:
3x² - 6x = 0 and -(x - 1)(x + 9) = 0.
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Aeronautical researchers have developed three different processes to pack a parachute. They want to compare the different processes in terms of time to deploy and reliability. There are 1,200 objects that they can drop with a parachute from a plane. Using a table of random digits, the researchers will randomly place the 1,200 items into three equally sized treatment groups suitable for comparison. Which design is the most appropriate for this experiment
- Randomly number each item with 1, 2, or 3. Assign the items labeled 1 to the process 1 group, assign the items labeled 2 to the process 2 group, and assign the items labeled 3 to the process 3 group.
- Number each item from 1 to 1,200.
Reading from left to right from a table of random digits, identify 800 unique numbers from 1 to 1,200. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
- Number each item from 0000 to 1199.
Reading from left to right on a random number table, identify 800 unique four-digit numbers from 0000 to 1199. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
- Select an item, and identify the first digit reading from left to right on a random number table. If the first digit is a 1, 2, or 3, assign the item to the process 1 group.
If the first digit is a 4, 5, or 6, assign the item to the process 2 group. If the first digit is a 7, 8, or 9, assign the item to the process 3 group. If the first digit is a 0, skip that digit and move to the next one to assign the item to a group. Repeat this process for each item.
Answer: The most appropriate design for this experiment is the third option:
- Number each item from 0000 to 1199.
- Reading from left to right on a random number table, identify 800 unique four-digit numbers from 0000 to 1199. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
This design ensures that the groups are equally sized and selected randomly without any biases. The use of a random number table to assign the groups helps to avoid any systematic patterns or preferences that might arise from numbering or labeling the items directly.
Step-by-step explanation:
helpppppppp plsssssssss
I think it might be:
Between 1754 and 1885 European imperialism was global. Nations like Britain, France, and Spain grew their Empires in the Americas, on the continent of Africa, and in parts of Asia. Their colonies created power and wealth for European businesses and governments. Eventually, many European countries held a meeting to decide how to divide up the world to avoid wars and conflict between themselves. This meeting was called the Conference.
Help me on this problem!
!!ILL GIVE BRAINLIST!!
Set up a proportion and use your proportion to solve for x.
Answer:
do how to do this is 16 x 16=256 and 8 x 8 =64 so 256+64=320
Please help please and thank u :)
Need help will give brainliest and 5 stars! (Check Picture)
Give the equation of a rational function which has all of the properties above.
Answer:
[tex]f(x) = \frac{(x - 1)(x - 2)(x - 6)}{(x - 1)(x - 3)(x - 5)} [/tex]
Clare lives in Iowa and pays 6% in sales tax. She just bought $135 in groceries, but $40 worth of those groceries were not taxable. What is the total amount that Clare paid for the groceries, including sales tax?
Answer:
$140.70
Step-by-step explanation:
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Round your answer to the nearest tenth of a degree
Answer:
57.8°
Step-by-step explanation:
SohCahToa
use sin^1 to get angle
sin^1(11/13)=57.7957725
to the nearest tenth=57.8°
Graph the circle x2+y²+16x-16y+124 = 0.
The graph of circle x² + y² + 16x - 16y + 124 = 0 has centre (-8, 8) and radius 2.
What is radius?
A circle's or sphere's radius is any line segment that connects the object's centre to its edge according to classical geometry; in more contemporary usage, the term also refers to the length of such line segments. The Latin origin of the word "radius" gives it the meanings of "ray" and "the spoke of a chariot wheel."
To graph the circle x² + y² + 16x - 16y + 124 = 0
We rewrite equation in standard form:
x² + 16x + y² - 16y + 124 = 0
(x² + 16x + 64) + (y² - 16y + 64) = -124 + 64 + 64
(x + 8)² + (y - 8)² = 4
The circle's centre (-8, 8) and radius (2) are now visible.
We may graph it by first plotting the centre point and then circling it with a radius of 2.
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A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 3points with99 % confidence assuming s=14 based on earlier studies? Suppose the doctor would be content with 95 %confidence. How does the decrease in confidence affect the sample size required?
We need a sample size of at least 154 subjects to estimate the mean HDL cholesterol within 3 points with 95% confidence.
Dcreasing the confidence level from 99% to 95% reduces the required sample size. This is because a higher confidence level requires a larger z-value, which increases the sample size needed to achieve the desired margin of error.
What is Standard deviation?The standard deviation is a measure of the amount of variation or dispersion of a set of data values. It is calculated as the square root of the variance, which is the average squared difference between each value and the mean.
What is mean?The mean is a measure of central tendency that represents the average value of a set of data. It is calculated by summing up all the values in the set and dividing by the number of values.
According to the given information:
To estimate the required sample size, we can use the formula:
n = (z-value)² × s² / E²
where:
z-value = the z-score corresponding to the desired level of confidence
s = the population standard deviation (given as 14)
E = the desired margin of error (3 points)
For a 99% confidence level, the z-value is 2.576 (obtained from a standard normal distribution table). Plugging in the given values, we get:
n = (2.576)² × 14² / 3²
n = 267.89
We need a sample size of at least 268 subjects to estimate the mean HDL cholesterol within 3 points with 99% confidence.
For 95% confidence, the z-value is 1.96. Using the same formula, we get:
n = (1.96)² × 14² / 3²
n = 153.44
We need a sample size of at least 154 subjects to estimate the mean HDL cholesterol within 3 points with 95% confidence.
As we can see, decreasing the confidence level from 99% to 95% reduces the required sample size. This is because a higher confidence level requires a larger z-value, which increases the sample size needed to achieve the desired margin of error.
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what even is 2 + 2?
Answer:
Definitely 4 always 4!!!
A 4-sided die, labeled 1–4 is rolled twice. Which outcome is not part of the sample space?
Answer: Let the experienced one help you out! Read the explanation down below! Brainliest?
Step-by-step explanation:
The sample space for rolling a 4-sided die twice consists of all possible pairs of outcomes, where each outcome is a number from 1 to 4. To find which outcome is not part of the sample space, we can list all the possible outcomes and then look for a number pair that does not appear.
Possible outcomes:
(1,1), (1,2), (1,3), (1,4)
(2,1), (2,2), (2,3), (2,4)
(3,1), (3,2), (3,3), (3,4)
(4,1), (4,2), (4,3), (4,4)
There are 16 possible outcomes, so one of the numbers from 1 to 16 is not part of the sample space. The missing outcome is (3,4) or (4,3), depending on the order in which the dice are rolled.
if 4-sided die, labeled 1–4 is rolled twice then 5,3 is not part of the sample space because the outcomes 5 and 3 are not part of the sample space.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
A sample space is a collection or a set of possible outcomes of a random experiment.
The sample space of rolling a 4-sided die twice can be represented by all possible ordered pairs of the outcomes, which can be listed as follows:
{(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}
Therefore, if 4-sided die, labeled 1–4 is rolled twice then 5,3 is not part of the sample space because the outcomes 5 and 3 are not part of the sample space.
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Which of these expressions could Alex and Taylor use to calculate the square footage of the tile Dining area? Find only the tile floor, and not the cabinets shown in black. Select all that apply.
A 34 foot by 13 foot grid. The kitchen is flush left. It has an 18 foot by 2 foot horizontal rectangle in the top left of the grid. Under the far left and right sides of the rectangle are two 6 foot by 2 foot vertical rectangles. There are two other horizontal rectangles on the bottom left of the grid that are 2 foot by 6 foot. There is a 4 foot gap between them. The dining room is on the right with a 12 foot by 2 foot rectangle in the top right of the grid.
Select answers
(16 x 13) - (12 x 2)
(4 x 13) + (12 x 2) + (12 x 11)
(17 x 11) + (4 x 2)
(4 x 13) + (12 x 11)
Expressions for the square footage of the tile Dining area, Considering only the tile floor, and not the cabinets shown in black will be (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11)
How to calculate the area of rectangle?The area of a rectangle is a measure of the amount of space it occupies in two-dimensional (2D) space. It is calculated by multiplying the length of the rectangle by its width. Mathmatically,
[tex]Area=length*width[/tex]
Now, Solving given problem,
The total area of the grid will be:Length of grid = 16 ft, Width of grid = 13 ft
Total area of grid = Length x Width = 16 ft x 13 ft = 208 sq ft
The area of the rectangle in the top right :Length of rectangle = 12 ft, Width of rectangle = 2 ft
Area of rectangle = Length x Width = 12 ft x 2 ft = 24 sq ft
To remove the top right rectangle from the tile dining area, subtract its area from the total area of the grid:
(Total area of grid) - (Area of rectangle in top right) = (208 sq ft -24 sq ft )= 184 sq ft
So, the expression for this calculation will be: (16 x 13) - (12 x 2) = 184 sq ft
The area of the vertical rectangles on the far left and right sides is calculated as follows:Width of vertical rectangles = 4 ft, Length of grid = 13 ft
Area of vertical rectangles = Width of vertical rectangles x Length of grid = 4 ft x 13 ft = 52 sq ft
The area of the rectangle in the top right:Length of rectangle = 12 ft, Width of rectangle = 11 ft
Area of rectangle = Length x Width = 12 ft x 11 ft = 132 sq ft
Add the areas of the vertical rectangles and the rectangle in the top right to get the total area of the tile dining area:
Area of vertical rectangles + Area of rectangle in top right = 52 sq ft + 132 sq ft = 184 sq ft
So, the expression for this calculation is: (4 x 13) + (12 x 11) = 184 sq ft
Hence, both of these expressions- (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11) gives the square footage of the tile dining area based on the given information.
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4
You draw five cards from a standard deck of 52 cards. P(heart) =
What type of probability is illustrated and why?
5
O A. theoretical; the result is based on the number of possible outcomes
O B. theoretical; the result is found by repeating an experiment
OC. experimental; the result is based on the number of possible outcomes
O D. experimental; the result is found by repeating an experiment
vered
Answer: The type of probability illustrated here is theoretical probability, and option A correctly identifies it as such.
Theoretical probability is based on mathematical reasoning and analysis of possible outcomes. In this case, we know that there are 52 cards in a deck, and 13 of them are hearts. So, the probability of drawing a heart on the first card is 13/52. After the first card is drawn, there are 51 cards remaining in the deck, including 12 hearts. So, the probability of drawing a heart on the second card is 12/51. Continuing this process, we find the probability of drawing five hearts in a row to be:
P(heart) = (13/52) x (12/51) x (11/50) x (10/49) x (9/48) = 0.0104 or about 1.04%
This probability is based purely on mathematical reasoning and analysis of possible outcomes, and does not involve any actual experimentation. Therefore, it is an example of theoretical probability.
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