Alyssa and Caleb ate 5/6 of the nachos together.
To calculate the fraction of nachos that Alyssa and Caleb ate together, add the fractions representing the portions that they each ate. However, because the fractions have different denominators, we must first find a common denominator.
2 and 3 share a common denominator of 6. With a denominator of 6, we can rewrite 1/2 and 1/3 as follows:
1/2 = 3/6
1/3 = 2/6
We can now add these fractions:
3/6 + 2/6 = 5/6
As a result, Alyssa and Caleb shared 5/6 of the nachos.
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to avoid a near midair collision (nmac) with a manned airplane, you estimate that your small ua climbed to an altitude greater than 400 feet agl. to whom must you submit a written report of the deviation?
you estimate that your UA climbed to an altitude greater than 400 feet above ground level (AGL), you must submit a written report of the deviation to the Federal Aviation Administration (FAA).
If you are operating a small unmanned aircraft (UA) and have had a near mid-air collision (NMAC) with a manned airplane, and you estimate that your UA climbed to an altitude greater than 400 feet above ground level (AGL), you must submit a written report of the deviation to the Federal Aviation Administration (FAA).
According to the FAA regulations, any UAS operator involved in an NMAC with a manned aircraft must submit a report to the FAA within ten days of the incident. This report must include the date, time, and location of the incident, as well as a detailed description of the events leading up to the NMAC.
You can submit the report online via the FAA's Aviation Safety Reporting System (ASRS) website. The ASRS is a voluntary reporting system that allows pilots and UAS operators to report incidents without fear of enforcement action, provided that the incident was not a result of reckless or intentional behavior.
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The table represents an exponential function. What is the multiplicative rate of change of the function?
The multiplicative rate οf change οf the given expοnential functiοn is 1/5.(1st οptiοn).
What is expοnential functiοn?An expοnential functiοn is a Mathematical functiοn which is οf the fοrm
f (x) = aˣ, where “x” is variable here and a real number and “a” is a cοnstant which is called the base οf the functiοn where a shοuld be greater than zerο.
The expοnential functiοn is given here in tabular fοrm.
Here frοm the table οf expοnential functiοn we get when x= 2 then
y= 2/5
again when x= 3 then y= 2/25
sο (2/5)×(1/5) = 2/25
again fοr x= 4 , y= 2/125
(2/25)×(1/5) = 2/125
sο every time the expοnential functiοn is multiplied by 1/5 and we get the next result.
Hence, The multiplicative rate οf change οf the given expοnential functiοn is 1/5.
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olympic gold medal has a gram of 586 grams. what is the mass of a 2018 olympic gold medal in hectograms
The mass of a 2018 Olympic gold medal in hectograms is 58.6 hg.
First, we need to know the mass of the Olympic gold medal in grams. According to the question, the mass of an Olympic gold medal is 586 grams.
To convert grams to hectograms, we need to divide the mass in grams by 100. This is because there are 100 grams in 1 hectogram.
To do the division, we can use a calculator. Dividing 586 by 100 gives us 5.86.
The answer we get is in hectograms, so we can write it as 5.86 hg. This means that the mass of a 2018 Olympic gold medal is 5.86 hectograms.
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HELP PLEASE ¨"half-life problem¨¨ A certain computer loses half of its value every four years. If the value of the computer after 6 years is $835, what was the initial value of the computer?
Thus, the computer was initially worth $3340 as the PC will be worth $835 after six years.
what is unitary method ?In mathematics, the unitary approach entails determining the value of a single unit in a certain circumstance and using that value to resolve other issues that are connected to it. It is a quick and efficient method for handling issues involving direct proportion, indirect proportion, and other circumstances of a same nature. In disciplines including mathematics, science, business, and engineering, the unitary technique is widely employed.
given
Let V be the computer's starting value.
The computer's value drops to V/2 after four years.
The computer's value is decreased to V/2 1/2 = V/4 after six years.
We are informed that the PC will be worth $835 after six years. When we set this equal to V/4, we obtain:
V/4 = 835
Adding 4 to both sides results in:
V = 4 × 835 = $3340
Thus, the computer was initially worth $3340 as the PC will be worth $835 after six years.
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Find m∠AZJ using the figure below
In Linear pair, 52° is the value ∠AZJ .
What is Linear pairs?
When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's total angles are always equal to 180 degrees.
A pair of adjacent angles is said to be a linear pair if the total of the two angles' (measured) angles is 180°. This means that a linear pair of angles always adds up to 180°. The linear pair of 30°, for instance, is 150°; the linear pair of 70°, 110°; etc.
∠JZF or ∠HZG
Linear pairs form supplementary angles.
∠AZJ = ∠AZH - ∠HZA
= 90° - 38°
∠AZJ = 52°
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Joe has 2 strips of card each strip Is 36cm long one strip is divided into 3 equal parts the other strip is divided into 4 equal parts joe uses 2 strips to make this shape what is the total length of joes shape
The total length of Joe's shape will be the sum of these lengths, which is 12 + 9 + 9 = 30cm.
To find the total length of Joe's shape, we first need to determine the length of each part of the strips.
For the first strip, which is divided into three equal parts, each part will be 36/3 = 12cm long. For the second strip, which is divided into four equal parts, each part will be 36/4 = 9cm long.
To make the shape, Joe will need to use two strips. Let's assume that Joe places the strip with three equal parts horizontally and the strip with four equal parts vertically. He will then need to cut each strip into the appropriate lengths to create the shape.
To create the shape, Joe will need to use one 12cm length from the first strip and two 9cm lengths from the second strip. He will then need to connect these lengths together to create the shape.
These lengths will add up to a total length for Joe's shape of 12 + 9 + 9 = 30 cm.
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Which of the contexts below represents exponential growth?
A town's population shrinks at a rate of 8.1% every year.
A taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile.
A town's population grows at a rate of 4% every year.
A radioactive compound decays at a rate of 5% per hour.
The exponential function [tex]P(t) = P0 \times 1.04^t[/tex] represents the exponential growth of Option C: A town's population grows at a rate of 4% every year.
What is an exponential function?
The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The context that represents exponential growth is "A town's population grows at a rate of 4% every year."
Exponential growth occurs when a quantity grows at an increasing rate over time, which is exactly what is happening with the population of the town.
As the population grows, the growth rate also increases, resulting in an exponential increase over time.
Let P(t) be the population of the town after t years, where t is a positive integer.
The exponential function that models the population growth is -
[tex]P(t) = P0 \times (1 + r)^t[/tex]
where P0 is the initial population, r is the growth rate as a decimal, and t is the time in years.
In this case, the growth rate is 4% per year, which can be written as a decimal as r = 0.04.
Therefore, the exponential function for the town's population growth is -
[tex]P(t) = P0 \times (1 + 0.04)^t[/tex]
Simplifying the expression, we get -
[tex]P(t) = P0 \times 1.04^t[/tex]
This function can be used to calculate the population of the town after a given number of years, assuming the growth rate remains constant.
In contrast, the other contexts represent either a steady decrease (town's population shrinking at a rate of 8.1% per year and the radioactive compound decaying at a rate of 5% per hour) or a linear increase (taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile).
Therefore, the exponential growth is displayed by town's population growing 4% every year.
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each letter of the alphabet is written on a piece of paper and put in a hat. if a piece of paper is chosen at random, what is the probability that it will be a vowel? the number of favorable outcomes is . the number of possible outcomes is . so p(vowel)
The probability of selecting a vowel from a hat with letters of the alphabet is 5/26 or approximately 0.1923. There are 5 vowels and 26 total letters.
There are 5 vowels in the English alphabet: A, E, I, O, and U. Therefore, the number of favorable outcomes (i.e., the number of vowels in the hat) is 5.
There are a total of 26 letters in the English alphabet. Therefore, the number of possible outcomes (i.e., the number of letters in the hat) is 26.
The probability of selecting a vowel is the ratio of the number of favorable outcomes to the number of possible outcomes:
P(vowel) = number of favorable outcomes / number of possible outcomes
P(vowel) = 5 / 26
Therefore, the probability of selecting a vowel is 5/26 or approximately 0.1923 (rounded to four decimal places).
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Answer:
5
26
5/26
19
Step-by-step explanation:
deduce that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the slim. in particular, the sum cannot be uniformly distributed on the numbers from 2 to 12. g
We know that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the sum. In particular, the sum cannot be uniformly distributed on the numbers from 2 to 12.
Explanation:
When we roll a fair die (i.e. an unbiased die), the probabilities of getting any one of the six possible numbers {1, 2, 3, 4, 5, 6} are equal to 1/6 each. But, when we use a biased die, the probabilities of getting any of the six possible numbers will no longer be equal. Some numbers will be more likely to occur, while others will be less likely to occur
For example:
if one of the dice has a weight in such a way that it always rolls a 6, then the probability of getting a sum of 2 will be zero, the probability of getting a sum of 7 will be 1/6, and the probability of getting a sum of 12 will be zero.However, if the dice are biased in some other way, we can still get non-zero probabilities for the sums of 2, 7, and 12. But, the probability of getting those three sums will not be the same. For instance, if one die is biased to always roll a 1, and the other die is biased to always roll a 6, then the probabilities of getting each of the sums 2, 7, and 12 are as follows:
P(2) = P(1, 1) = (1/6)² = 1/36
P(7) = P(1, 6) + P(6, 1) + P(2, 5) + P(5, 2) + P(3, 4) + P(4, 3) = 6(1/6)(1/6) = 1/6P(1
2) = P(6, 6) = (1/6)² = 1/36
So, the probability of getting a sum of 7 is six times as likely as getting a sum of 2 or 12. Therefore, the sum cannot be uniformly distributed on the numbers from 2 to 12.
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Please hurry and help
Answer: 90
Step-by-step explanation: I've done this before, this was the correct answer
Answer:90
Step-by-step explanation:
r=2 s=3 t=5
2x3 squared is 2x(3x3)=18
18x5=90
timothy was asked to write the following verbal expression as a mathematical one.seven less than ten times a numberwhich expression is correct?
The expressions 10x-7 and 7-10x represent the statement "seven less than ten times a number".
The verbal expression "seven less than ten times a number" can be written mathematically in different ways, depending on the intended meaning. One possible expression is:
10x - 7
In this expression, "10x" represents ten times a number, and "-7" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting 7 from the product of 10 and the number x.
Another possible expression is 7 - 10x
In this expression, "10x" represents ten times a number, and "7 - 10x" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting the product of 10 and the number x from 7.
If the focus is on finding the result of subtracting 7 from ten times a number, the first expression is more appropriate. If the focus is on finding the result of subtracting the product of 10 and a number from 7, the second expression is more appropriate.
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Small pizzas at Ponnie's Pizza are cut into 6 pieces. The circumference of a small pizza is 12π inches. A large pizza is cut into 8 pieces. The diameter of a large pizza is 16 inches.
Joannie eats 2 slices of a small pizza. Mark eats 5 slices of a large pizza.
How many times greater are the square inches of pizza that Mark ate than the square inches of pizza that Joannie ate?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
Mark ate 3.3 times the square inches of pizza than Joannie ate.
Step-by-step explanation:
Small pizzaThe formula for the circumference of a circle is C = 2πr (where r is the radius). If the circumference of a small pizza is 12π inches, then its radius is:
[tex]\implies \sf Radius_{small\;pizza}=\dfrac{circumference}{2\pi}=\dfrac{12\pi}{2\pi}=6\;inches[/tex]
The formula for the area of a circle is A = πr² (where r is the radius).
Therefore, the area of a small pizza is:
[tex]\implies \sf Area_{small\;pizza}=\pi \cdot 6^2=36\pi \; in^2[/tex]
If the small pizzas are cut into 6 congruent pieces, the area of one slice of small pizza is:
[tex]\begin{aligned}\implies \sf Area_{small\;slice}&=\sf \dfrac{Area_{small\;pizza}}{6}\\\\&=\dfrac{36 \pi}{6}\\\\&=6 \pi \; \sf in^2\end{aligned}[/tex]
Therefore, the area of one slice of small pizza is 6π square inches.
[tex]\hrulefill[/tex]
Large pizzaThe diameter of a circle is twice its radius.
If the diameter of a large pizza is 16 inches then its radius is:
[tex]\implies \sf Radius_{large\;pizza}=\dfrac{diameter}{2}=\dfrac{16}{2}=8\;inches[/tex]
The formula for the area of a circle is A = πr² (where r is the radius).
Therefore, the area of a large pizza is:
[tex]\implies \sf Area_{large\;pizza}=\pi \cdot 8^2=64 \pi \; in^2[/tex]
If the large pizzas are cut into 8 congruent pieces, the area of one slice of large pizza is:
[tex]\begin{aligned}\implies \sf Area_{large\;slice}&=\sf \dfrac{Area_{large\;pizza}}{8}\\\\&=\dfrac{64 \pi}{8}\\\\&=8 \pi \; \sf in^2\end{aligned}[/tex]
Therefore, the area of one slice of large pizza is 8π square inches.
[tex]\hrulefill[/tex]
If Joannie eats 2 slices of small pizza, the square inches of pizza she ate is:
[tex]\implies \sf Joannie=2 \times 6 \pi = 12 \pi\;in^2[/tex]
If Mark eats 5 slices of large pizza, the square inches of pizza he ate is:
[tex]\implies \sf Mark =5 \times 8 \pi = 40\pi\;in^2[/tex]
To calculate how many times greater are the square inches of pizza that Mark ate than the square inches of pizza that Joannie ate, divide the area Mark ate by the area Joannie ate:
[tex]\implies \sf \dfrac{40 \pi}{12 \pi} = \dfrac{10}{3}=3.3\;(nearest\;tenth)[/tex]
Therefore, Mark ate 3.3 times the square inches of pizza than Joannie ate.
HELP 20 POINTS
NO WRONG ANSWERS OF LINKS THEY WILL GET REPORTED
Answer:
The second one, (x+1)(3x+2)
The answer is (x+1)(3x+2)
hope it helps
if you deposit $4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, how much money will you have in the account in 20 years ? how much will you have if you make deposits for 40 years ?
If you deposit 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, you will have 347,401.59 in the account in 20 years. You will have 2,545,025.81 if you make deposits for 40 years.
Given that you deposited 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest. Now you have to find out how much money you will have in the account in 20 years and how much will you have if you make deposits for 40 years.
The formula to calculate the future value of an annuity due is:
[tex]FV = PMT \times [(1 + r)^{(n - 1)} / r] \times(1 + r)[/tex]
Where,
FV = Future Value
PMT = Payment (amount) each period
r = Interest Rate per period
n = Number of periods
To find the future value of an annuity due for 20 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(20 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{19} / 0.097] \times (1.097)\\FV = 4500 \times [(6.226)] \times (1.097)\\FV = 347,401.59[/tex]
To find the future value of an annuity due for 40 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(40 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{39} / 0.097] \times (1.097)\\FV = 4500 \times [(38.84)] \times (1.097)\\FV = 2,545,025.81[/tex]
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Which number is a perfect square
Responses
2
8
16
20
Answer:
16
Step-by-step explanation:
because it is a square number. The other numbers, if you square root them you won't get a whole number.
City pollution in Singapore (scientific notation)?
According to the World Air Quality Report 2020, the annual average PM2.5 concentration in Singapore was 14.8 μg/m³ (micrograms per cubic meter which can be expressed in scientific notation as 1.48 x 10^-5 g/m³.
What is important fact on city pollution in Singapore?The PM2.5 concentration refers to fine particulate matter that can pose health risks when inhaled, and sources of such pollution in urban areas can include traffic, industrial activities, and power generation.
Despite its relatively low PM2.5 concentration compared to many other cities in the world, Singapore continues to work on improving air quality and reducing pollution through measures such as promoting the use of public transportation, implementing emission standards for vehicles, and encouraging the adoption of clean energy technologies.
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I need help on this asap!
In linear equation, 0.75x + 2y ≤ 16 , 2x + 4y ≤ 40 are the solution represent .
What is the most effective way to explain linear equations?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x). In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.
if the small pair is x, the large pair is y.
45 minutes = 0.75 hour
120 minutes = 2 hour
so, 0.75x + 2y ≤ 16
2x + 4y ≤ 40
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aml exam four minimum pieces of identifying information for individuals are required in the identity verification process. which of the following is correct?
In the identity verification process, at least four pieces of identifying information are needed for individuals to be able to confirm their identities. The following are the correct minimum pieces of identifying information for individuals required in the identity verification process:
Full nameA valid photo ID, such as a driver's license, passport, or national ID number Date of birth Address According to the anti-money laundering laws and regulations, these four identifying pieces of information are necessary to confirm an individual's identity. The goal of identity verification is to ensure that a customer is who they claim to be and to avoid fraudulent activity. Identity verification has become an important part of any institution's compliance efforts as a result of increased regulatory scrutiny. It is critical that businesses and organizations are aware of their regulatory obligations when it comes to verifying customer identities, and that they implement effective identity verification methods to mitigate the risk of fraud and ensure regulatory compliance .
Therefore, when verifying the identity of a customer, the above information should be obtained in a secure and confidential manner, with the customer's consent. These documents must be checked for signs of forgery or tampering, and the customer must be given the opportunity to provide additional documentation if necessary.
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jason is making a concrete driveway. he mixes dry cement and water in the correct ratio. the table shows how much dry cement to mix with different amounts of water. jason says a graph of the relationship includes the point (63, 140). is jason correct?
Jason is correct when he says that a graph of the relationship includes the point (63, 140).
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.
The relationship is defined according to the equation presented as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one, which is also the constant ratio of the relationship.
From the table given at the end of the answer, when x = 54, y = 120, hence the constant is given as follows:
k = 120/54
k = 2.2222.
Hence the equation is:
y = 2.2222x.
When x = 63, the output of the function is given as follows:
y = 2.2222 x 63
y = 140.
Hence Jason is correct when he says that a graph of the relationship includes the point (63, 140), as when x = 63, the output of the function is of y = 140.
Missing InformationThe table is given by the image presented at the end of the answer.
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There are 19 animals in the field. Some are cows and some are ducks. There are 60 legs in all. How many of each animal are in the field?
Answer:
There are 11 cows and 8 ducks
Step-by-step explanation:
x will represent number of cows and (19-x) will represent ducks
[tex]4x+2(19-x)=60[/tex]
multiply 2 with (19-x)
[tex]4x+38-2x=60[/tex]
add your x's
[tex]2x+38=60[/tex]
subtract 38 on both sides
[tex]2x=22[/tex]
then divided 2 on both sides
[tex]x=11[/tex] cows
now to find ducks subtract
[tex]19-11[/tex]
your answer will be 8
So there are 11 cows and 8 ducks
to double check do this
[tex]11*4 + 8*16\\=44+16\\=60[/tex]
Jane contributes 12% of the total cost of her individual health care. This is a $95.50 deduction from each of her biweekly paychecks.
A) Find Jane's share.
b) Total value of the insurance.
b) Calculate the employer's share.
A) Jane's share is 12% of X, which is equal to 0.12X.
B) the total cost of the insurance is $20,691.67
C) the employer's share is $18,208.67.
The total expense is what?Total cost is the collective term for the cost of production as a whole, which encompasses both fixed and variable costs. The expense necessary to produce a good is referred to in economics as the total cost. There are two parts that make up the total cost: a set price The expense is what never changes.
According to the given information:Let X be the total cost of Jane's individual health care, then:
A) Jane's share is 12% of X, which is equal to 0.12X.
B) We know that Jane's deduction from each biweekly paycheck is $95.50, so she pays a total of:
$95.50 * 26 = $2,483
This amount is equal to 0.12X, so we can set up an equation:
0.12X = $2,483
Solving for X, we get:
X = $20,691.67
Therefore, the total value of the insurance is $20,691.67.
C) The employer's share is the difference between the total cost of the insurance and Jane's share:
Employer's share = Total cost - Jane's share
Employer's share = $20,691.67 - $2,483
Employer's share = $18,208.67
Therefore, the employer's share is $18,208.67.
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Jane's share of the total cost of her individual health care is $795.83, The total value of the insurance is $795.83 + 0.88x and the employer's share is 0.88x.
What is cost?
In mathematics, cost refers to the amount of resources (such as money, time, effort, or materials) that are required to produce or obtain something.
A) To find Jane's share of the total cost of her individual health care, we can use the information that she contributes 12% of the cost, and that this is a $95.50 deduction from each of her biweekly paychecks.
Let x be the total cost of Jane's individual health care. Then:
12% of x = $95.50
0.12x = $95.50
x = $95.50 / 0.12
x = $795.83
Therefore, Jane's share of the total cost of her individual health care is $795.83.
B) To find the total value of the insurance, we can add up both Jane's share and the employer's share.
If Jane is contributing 12% of the total cost, then the employer is contributing the remaining 88% of the cost. So the employer's share can be calculated as:
88% of x = 0.88x
The total value of the insurance is then:
Total value = Jane's share + Employer's share
Total value = $795.83 + 0.88x
C) To calculate the employer's share, we can use the same information as above. The employer is contributing 88% of the total cost, so:
88% of x = 0.88x
Therefore, the employer's share of the total cost of Jane's individual health care is $0.88x, or approximately $700.33 (if we use the value of x that we found in part A).
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Wendy throws a dart at this square-shaped target:
Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work
Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work.
a) The probability of hitting the black circle inside the target is closer to zero.
b) The probability of hitting the white portion inside the target is closer to one.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total area of the region is given as follows:
10² = 100 units squared.
The black circle has a radius of one unit(as the diameter is of 2 units), hence it's area is given as follows:
A = 3.14 x 1²
A = 3.14 units squared.
Then the probability of hitting the black circle is of:
3.14/100 = 0.0314 -> closer to zero.
The probability of hitting the white circle is given as follows:
1 - 0.0314 = 0.9686 -> closer to one.
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Angela is using a game piece with faces labeled A, B, C, and D. What is the sample space for rolling the game piece?
The sample space for rolling the game piece is S = {A, B, C, D}
Describe Sets?In mathematics, a set is a well-defined collection of distinct objects, which can be anything like numbers, letters, people, or even other sets. A set is usually denoted by curly braces {} enclosing its elements separated by commas. For example, the set of natural numbers less than or equal to 5 can be denoted as {1, 2, 3, 4, 5}.
Sets can also be described by various methods such as by listing its elements, by set-builder notation, or by using a Venn diagram to visualize relationships between sets. A set can have any number of elements, including none (empty set), and can also have infinite number of elements.
Sets can be combined through set operations such as union, intersection, and complement. The union of two sets A and B is a set that contains all the elements that belong to either A or B (or both). The intersection of two sets A and B is a set that contains all the elements that belong to both A and B. The complement of a set A is the set of all elements that are not in A.
The sample space for rolling the game piece can be represented by the set of possible outcomes, which are the labels on the faces of the game piece. Therefore, the sample space is:
S = {A, B, C, D}
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Given:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
[tex] \tt \: \: x = \cancel{ \frac{12}{3} }[/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \green{ \: x = 4 \: }}}[/tex][tex] \: [/tex]
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find the surface area of the prism
The surface area of the prism is 264m²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces. There are different types of prism but the specific one we will be talking about here is triangular based prism.
The surface area of a prism is obtained by adding the area of the faces. Therefore surface area = 2B +ph
area of the base = 1/2 bh
= 1/2 × 6 × 8
= 1/2 × 48
= 24m²
using Pythagoras theorem, the hypotenuse of the triangle = √ 6²+8²
= √ 36+64
= √100 = 10m
perimeter of the base = 6+8+ 10
= 24m
Therefore SA = 2×24 + 24 × 9
= 48 + 216
= 264m²
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the estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line. True or false
The given statement "The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line" is true because it provides the best fit line.
The simple linear regression equation estimates the relationship between two variables - a dependent variable (y) and an independent variable (x) - by fitting a straight line through the data points.
The line is chosen so that the sum of the squared deviations (also known as the sum of squared errors or SSE) between the observed values of y and the predicted values of y on the line is minimized.
In other words, the simple linear regression equation finds the line that is closest to all the data points in terms of the vertical distance between the points and the line.
This line is chosen to minimize the sum of squared deviations because it provides the best estimate of the relationship between x and y, and it allows for the prediction of y values for a given x value.
Thus, minimizing the sum of squared deviations is a crucial aspect of the simple linear regression equation because it ensures that the line of best fit provides the most accurate estimate of the relationship between the variables.
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Compounds angles identities
Answer:
Compound angle identities are trigonometric identities that relate the trigonometric functions of the sum or difference of two angles to the trigonometric functions of the individual angles.
The main compound angle identities are:
1. sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
2. cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B)
3. tan(A ± B) = (tan(A) ± tan(B)) / (1 ∓ tan(A)tan(B))
where A and B are any two angles.
These identities can be used to simplify trigonometric expressions, solve trigonometric equations, and prove other trigonometric identities.
For example, we can use the compound angle identity for sin(A + B) to find sin(π/4 + π/6):
sin(π/4 + π/6) = sin(π/4)cos(π/6) + cos(π/4)sin(π/6)
sin(π/4 + π/6) = (√2/2)(√3/2) + (√2/2)(1/2)
sin(π/4 + π/6) = (√6 + √2) / 4
Compound angle identities are an important part of trigonometry and are used in various fields such as physics, engineering, and mathematics.
Mrs. Garcia is ordering pizza for students in the Homework Club. A large two-topping pizza is 20% off the regular price of $15. Mrs. Garcia wants to know the sale price. Which equation can be used to find the sale price, s, of the pizza
s = 0.8(15) s = 0.1(15) S = 0.115 S=0.8 15
Regular Price 100% $15
Sale Price 80% $ ?
Discount 20%
The equation that can be used to find the sale price, s, of the pizza is S = 0.8(15).
What is sale price?It is the final amount paid for a product or service and is often lower than the original asking price.
This equation uses the percentage discount of 20%, which can be represented as 0.8, to find the sale price.
To calculate the sale price, the equation multiplies the regular price of $15 by the discount, 0.8.
0.8*15 =12
Therefore, the sale price of the pizza is $12.
The other equations are not correct because they do not take into account the percentage discount of 20%.
S = 0.1(15) does not consider the discount of 20%, as it is multiplying the regular price of $15 by 0.1, which is equivalent to 10%, not 20%.
Similarly, S = 0.115 is incorrect because it is multiplying the regular price of $15 by 1.15, which is equivalent to 115%, not 20%.
Lastly, S=0.8 15 is incorrect because it is not multiplying the regular price of $15 by the discount of 20%, which is 0.8.
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a jar contains 21 brown and 19 blue marbles. a marble is drawn at random. what is the theoretical probability of drawing a blue marble?
The theoretical probability of drawing a blue marble from a jar containing 21 brown and 19 blue marbles is 19/40, or 0.475.
To calculate this, divide the number of blue marbles by the total number of marbles in the jar. 19 divided by 40 equals 0.475, or 19/40. This means that there is a 47.5% chance of drawing a blue marble from the jar.
The probability of drawing a specific marble from the jar can be expressed using the formula P(A) = n(A)/n(T).
In this example, the probability P(A) is the chance of drawing a blue marble, n(A) is the number of blue marbles (19) and n(T) is the total number of marbles in the jar (40). Therefore, P(A) = 19/40 = 0.475.
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one thousand dollars is deposited in a savings account where the interest is compounded continuously. after 6 years, the balance will be $1370.55 . when will the balance be $1711.03 ? round to the nearest tenth of a year.
If the balance will be $1370.55 after 6 years, then The balance will be $1711.03 after approximately 14.3 years.
The formula for calculating the balance in a continuously compounded account is:
[tex]A = Pe^{rt}[/tex]
Where:
A = final balance
P = principal (initial deposit)
e = Euler's number (approximately 2.71828)
r = annual interest rate
t = time in years
We know that the initial deposit is $1000 and the balance after 6 years is $1370.55, so we can use these values to solve for the annual interest rate:
[tex]1370.55 = 1000*e^{6r}[/tex]
⇒ [tex]ln(\frac{1370.55}{1000}) = 6r[/tex]
⇒ [tex]r = \frac{ln(\frac{1370.55}{1000})}{6}[/tex]
⇒ [tex]r = 0.0345[/tex]
Now we can use the same formula to find out when the balance will be $1711.03:
[tex]1711.03 = 1000*e^{(0.0345*t)}[/tex]
⇒ [tex]ln(\frac{1711.03}{1000}) = 0.0345*t[/tex]
⇒ [tex]t = \frac{ln(\frac{1711.03}{1000})}{0.0345}[/tex]
⇒ t = 14.3 years.
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