the answer to the question is A. 5 hours. This information is essential for accurately modeling the tide using a trigonometric function and predicting the water level at any time in the future or past within the 5-hour cycle
How to solve the question?
The given data represents the variation of water level at Sunny Beach over a period of 5 hours. As Joe arrived at 12:00 p.m., we can assume that the highest tide occurred at that time, and the water level started to decrease until it reached its lowest point after 3 hours. Then, the water level started to increase again until it reached its highest point after 5 hours, completing one full cycle of the tide.
To model this variation of water level over time, we can use a trigonometric function, specifically a sine or cosine function. These functions have a repeating pattern over a fixed period, which makes them suitable for modeling cyclic phenomena such as tides.
The period of a sine or cosine function represents the length of one complete cycle. In this case, the period of the function that models the tide is 5 hours because the tide completes one cycle over a 5-hour period, as observed from the given data.
Therefore, the answer to the question is A. 5 hours. This information is essential for accurately modeling the tide using a trigonometric function and predicting the water level at any time in the future or past within the 5-hour cycle
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) Rewrite as an exponential equation.
log8 1/64 =2
(b) Rewrite as a logarithmic equation.
3 0=1
a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]
b) the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
What is exponential equation?
An exponential equation is one in which the exponent contains a variable.
(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation
log8 1/64 = 2
means that 8 raised to the power of 2 is equal to 1/64:
[tex]8^2 = 1/64[/tex]
Thus, we can write the exponential equation as:
[tex]1/64 = 8^{(-2)}[/tex]
Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]
(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation
[tex]3^0 = 1[/tex]
means that the logarithm of 1 to the base 3 is equal to 0:
log3 1 = 0
Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
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find the reduced racial form of each expression:
1: 3^√4/9m^2 ?
2:√63-√700–√112 ?
3: (a^2b^8/a^1/3)^3/4 ?
4: ^4√1024x^9y^12 ?
5:4^3√81 - 2^3√72 - ^3√24 ?
6: ^5√2pq^6 • 2 √2p^3q ?
HELP PLEASE ILL DO ANYTHING. (show explanation pls)
The reduced radical forms of the expressions provided are as follows:
1. 3^(4/9m)
2. -11√7
3. a^(1/2) * b^6
4. 2x^(9/4) * y^3
5. 16 - ^3√24
6. 4p^(9/10)q^(7/10)
What is a reduced radical form?A reduced radical form is a way of simplifying expressions that contain radicals such as square roots and cube roots, as much as possible. In a reduced radical form, the radical is simplified to its lowest possible terms.
To obtain the reduced radical forms of the expresions, we can proceed with the workings:
1. 3^(√4/9m^2) = 3^(2/3 * 1/3√4m^2) (since √4 = 2)
= (3^(2/3))^(1/3√4m^2)
= (3^(2/3))^(2/3m)
= 3^(4/9m)
2. √63 = √(9 * 7) = 3√7
√700 = √(100 * 7) = 10√7
√112 = √(16 * 7) = 4√7
√63 - √700 - √112 = 3√7 - 10√7 - 4√7
= -11√7
3. (a^2b^8/a^1/3)^3/4 = (a^2/1/3√a)^3/4 * b^8^3/4
= (a^(2/3))^3/4 * b^6
= a^(1/2) * b^6
4. ^4√1024x^9y^12 = (^4√1024) * (^4√x^9) * (^4√y^12)
= 2 * x^(9/4) * y^(12/4)
= 2x^(9/4) * y^3
5. 4^3√81 = 4^3 * 3 = 64
2^3√72 = 2^3 * 2√9 = 16√9 = 48
^3√24 can't be simplified any further
4^3√81 - 2^3√72 - ^3√24
= 64 - 48 - ^3√24 or 16 - ^3√24.
6. ^5√2pq^6 • 2 √2p^3q
= 2p^(3/5)q^(6/5) * 2p^(3/2)q^(1/2)
= 4p^(9/10)q^(7/10)
So, the results are the simplified or reduced forms of the expressions.
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Find the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum.
Answer: The formula for compound interest is:
A = P(1 + R/100)^t
where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.
Here, P = Rs. 3,500, R = 8%, and t = 2 years.
So, the amount after 2 years will be:
A = 3,500(1 + 8/100)^2
= 3,500(1.08)^2
= 3,892.32
Therefore, the compound interest for 2 years will be:
CI = A - P
= 3,892.32 - 3,500
= 392.32
Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.
Step-by-step explanation:
Divide and give your answer as a decimal. Round your answer to the nearest thousandth (3 digits behind the decimal).
2/9
Answer:
0.222
Step-by-step explanation:
2 divided by 9 is:
0.222 (rounded to the nearest thousandth)
Help please i dont know
The histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2.The bin from 16 to 25 should be increased by one.The bin from 26 to 35 should be increased by one.The bin from 46 to 55 should be increased by one.What is shown by an histogram?A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.
Then the height of the histogram gives the number of observations into each data interval.
Hence the histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2. -> two measures of 12.The bin from 16 to 25 should be increased by one. -> measure of 16.The bin from 26 to 35 should be increased by one. -> measure of 26.The bin from 46 to 55 should be increased by one. -> measure of 48.More can be learned about histograms at https://brainly.com/question/25983327
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carpet is sold in square yards how much carpet would a person need to buy for a rectangle that has dimensions of 10 yards by 18 feet
A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
How to determine the amount of carpet needed for a rectangular room?
To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.
The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),
18 feet ÷ 3 feet/yard = 6 yards
So the dimensions of the room in yards are 10 yards by 6 yards.
To find the total area of the room, we need to multiply the length and width,
10 yards × 6 yards = 60 square yards
Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
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Determine the equation of the circle with center (-7, -4) containing the point
(-1,-8).
Answer:
(-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52
Step-by-step explanation:
i literally just learned this today so here we go:
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
We are given the center of the circle as (-7, -4), so we can substitute these values for h and k:
(x - (-7))^2 + (y - (-4))^2 = r^2
(x + 7)^2 + (y + 4)^2 = r^2
We also know that the circle contains the point (-1, -8).
We can substitute these values for x and y, and solve for r:
(-1 + 7)^2 + (-8 + 4)^2 = r^2
36 + 16 = r^2
r^2 = 52
Substituting this value of r^2 into the equation for the circle, we get:
(x + 7)^2 + (y + 4)^2 = 52
Therefore, the equation of the circle with center (-7, -4) containing the point (-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52
HELP ASAP PLEASE!!!!!!!!!!!!!
The currencies of both Polish Zolty and Australian dollars appreciated from January to March
What is appreciation?Appreciation refers to an increase in the value of a currency in relation to another currency.
This can happen due to various reasons such as a country's strong economic performance, higher interest rates, or an increase in demand for its exports.
Appreciation can have both positive and negative effects on the economy. It can make imports cheaper but exports more expensive, which can impact trade balance. It can also affect inflation, employment, and economic growth.
From the image shown, we can see that the value of the currencies of the countries appreciated to;
Polish Zolty; from $4. 5 to $4. 08
Australian dollar; from $1. 85 to $1. 67
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Spring Basketball Tournament Expenses and Income Guidelines:
1. A permit for the event is required and costs $75.60. It takes 8 hours to run a tournament for 8 teams.
2. Each player will be charged a $32 entry fee.
3. There will be exactly 8 players on each team.
4. The rent for a gym in a high school is $62.50 an hour.
5. A caretaker must be present for a Saturday permit and earns $56 an hour.
** List below all income and expenses created from this tournament **
The total expenses of the tournament are $1,023.60 and the total income is $2,048. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
With the help of the four fundamental operations, often known as "arithmetic operations," any real number may be explained. Operations like quotient, product, sum, and difference come last in mathematics, while operations like division, multiplication, addition, and subtraction come first.
From the information given in the question, we have
⇒ Expenses include:
Permit for the event costing $75.60
Rent of the Gym for 8 hours = $62.50 x 8 = $500
Cost of caretaker for 8 hours on a Saturday = $56 x 8 = $448
Now, using the addition operation, we get
Total expenses = $75.60 + $500 + $448
Total expenses = $1,023.60
Similarly, using multiplication operation, we have
⇒ Income including
Entry fee per player = $32 x 8 = $256 per team
Income from 8 teams = $256 x 8 = $2,048
So,
Total income = $2,048
Hence, the total expenses of the tournament are $1,023.60 and the total income is $2,048.
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Find tn for the geometric sequence where t3 = 24 and t9 = 1536. Why are there 2 answers? (4 marks)
2. Lee has a catering company. His staff is making pies for an event. He needs to make sure all the 123
pies have the correct filling: strawberry, rhubarb or cherry. The pies can have 1, 2 or 3 of the different
fillings and all pies have at least one of these three. He writes down the following information as he looks
them all over.
68 pies have cherries
73 pies have strawberries
30 pies have rhubarb and cherries
●
23 pies have rhubarb and strawberries
12 pies have only strawberry and cherry
828
14 pies have all three fillings
A101
Lee finishes writing his notes and all 123 pies are accounted for and ready to go to the event. How many
pies have only rhubarb in them?
DERE
810
d
If Lee has a catering company. His staff is making pies for an event. there are 41 pies that have only rhubarb filling.
How many pies have only rhubarb in them?To find the number of pies that have only rhubarb filling, we need to subtract the pies that have rhubarb filling and another filling(s) from the total number of pies that have rhubarb filling.
We can use the given information to create a Venn diagram to visualize the relationships between the different fillings:
_______________
/ (3) \
/______ 14 ______\
/ / \ \
/ (1) / (5) \ (2) \
/_____/_______ \______\
/ \ \
/ (4) \______\
(1) represents the number of pies that have only cherry filling,
(2) represents the number of pies that have only strawberry filling,
(3) represents the number of pies that have only rhubarb filling,
(4) represents the number of pies that have cherry and strawberry filling, but not rhubarb filling,
(5) represents the number of pies that have rhubarb and strawberry filling, but not cherry filling.
We can use the given information to fill in the values in the Venn diagram:
68 pies have cherry filling (1) + (4) + (6) + (7) + (8) + (9) + (10) + (14) = 68
73 pies have strawberry filling (2) + (4) + (5) + (7) + (8) + (9) + (10) + (14) = 73
30 pies have rhubarb and cherry filling (6) + (7) + (10) + (14) = 30
23 pies have rhubarb and strawberry filling (5) + (7) + (9) + (10) + (14) = 23
12 pies have only strawberry and cherry filling (7) = 12
14 pies have all three fillings (14) = 14
To find the number of pies that have only rhubarb filling, we can start by adding up the pies that have rhubarb filling and no other fillings: (3) + (6) + (9) + (10).
(3) is already the number of pies that have only rhubarb filling. For the other three regions, we need to use the values in the Venn diagram to calculate the number of pies with the given combinations of fillings:
(6) is the number of pies that have both rhubarb and cherry fillings, but not strawberry filling. Therefore, the number of pies that have rhubarb and no other fillings is 30 - 6 = 24.(9) is the number of pies that have both rhubarb and strawberry fillings, but not cherry filling. Therefore, the number of pies that have rhubarb and no other fillings is 23 - 9 = 14.(10) is the number of pies that have all three fillings, so they do not have only rhubarb filling.Adding up the number of pies that have only rhubarb filling from each region, we get:
Number of pies that have only rhubarb filling = (3) + (24) + (14) + (0) = 41.
Therefore, there are 41 pies that have only rhubarb filling.
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An ice cream stand uses the expression 1 + 0.75x to determine the cost (in dollars) of an ice cream cone that has x scoops of ice cream. How much does an ice cream cone with 3 scoops cost?
Answer:
$3.25
Step-by-step explanation:
An ice cream cone that has x scoops of ice cream costs 1 + 0.75x.
So an ice cream cone that has 3 scoops of ice cream costs
1 + 0.75×3 = 3.25 (dollars)
using truth table show that (p^q) =~pv~q please help meeee
The truth table for the given expression can be given using p= T q = T, p^q = T, ~p = F, ~q = F, ~q v ~p = T, and (p ^ q) =~p v ~q = T, thus proving the required.
What is propositional logic?The field of symbolic logic known as propositional logic, also referred to as sentential logic or statement logic, is concerned with propositions or statements, which are declarative phrases that can be true or untrue. To represent propositions and their relationships, propositional logic employs symbols and operators.
Many disciplines, including mathematics, computer science, philosophy, and others, employ propositional logic as a tool for debating the truth or falsity of propositions and analysing arguments.
The truth table for the given expression can be given as:
p | q | p ^ q | ~p | ~q | ~q v ~p | (p ^ q) =~p v ~q
-------------------------------------------------------------
T | T | T | F | F | T | T
T | F | F | F | T | T | T
F | T | F | T | F | T | T
F | F | F | T | T | T | T
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The owner of a stereo store wants to advertise that she has many different sound systems in stock. The store carries 5 different CD players, 8 different receivers, and 10 different speakers. A sound system consists of one of each item. How many different sound systems can the store owner advertise?
The owner can advertise 400 different sound systems. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
All real numbers can be explained using the four fundamental operations, generally known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.
We are given that the owner of a stereo store carries 5 different CD players, 8 different receivers, and 10 different speakers and each sound system consists of one of each item.
So, the different sound systems that the owner can advertise is obtained by using the multiplication operation, which gives:
⇒ Different sound systems = 5 * 8 * 10
⇒ Different sound systems = 400
Hence, the owner can advertise 400 different sound systems.
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I need help pls, I don't understand
Answer:
Step-by-step explanation:
40 de grese
Answer:
52°
Step-by-step explanation:
The angle between two secants drawn from the point outside the circle is half the difference of the intercepted arcs.
[tex]\sf \boxed{\bf \angle \ Y =\dfrac{far \ arc - near \ arc}{2}}[/tex]
[tex]\sf \angle Y = \dfrac{m\overset{\frown}{GK} - m\overset{\frown}{CE}}{2}\\\\50 = \dfrac{152-m\overset{\frown}{CE}}{2}[/tex]
[tex]50*2 = 152 - m\overset{\frown}{CE}\\\\100 = 152 - m\overset{\frown}{CE}[/tex]
[tex]100 + m\overset{\frown}{CE} = 152\\\\[/tex]
[tex]\sf m\overset{\frown}{CE}= 152 - 100\\\\m\overset{\frown}{CE} = 52^\circ[/tex]
Help corrections due in 3 hours! giving 25 points and brainlist
The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.
How to find the value of GH ?Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.
cos(35°) = adjacent side (FH) / hypotenuse (GH)
We know that FH = 18.4 in. So, we can write the equation as:
cos(35°) = 18.4 / GH
GH = 18.4 / cos(35°)
GH = 18.4 / 0.81915
= 22.46 inches
So, the length of GH, the hypotenuse, is approximately 22.46 inches.
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50pts!!!!
Many investors use interest-only loans to buy shares or property. For such loans the principal stays constant and only the interest is paid back each month.
She buys an investment property for $300 000 and borrows the full amount at 7% p.a. simple interest. She rents out the property at $1500 per month and pays $3000 per year in rates and other costs to keep the property.
Find the amount of interest she needs to pay back every month.
Find her yearly income from rent.
By considering the other costs in keeping the property, calculate her overall loss in a year.
she hopes that the property’s value will increase enough to cover any loss she is making. By what percentage of the original price will the property need to increase in value per year?
Step-by-step explanation:
to find the interest she needs to pay back every month, we need to use this formula:
I = PRT/12
in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:
I = (300,000)(7)(1)/12 = $17,500 in interest every month
to find her yearly income from rent, we have to multiply the monthly rent by 12
1500 × 12 = $18,000
to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000
she said that she hopes the property's value will increase to cover the loss she made.
to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as
Percentage increase = (difference in increase/Original price) × 100
so
percentage increase = (15000/300000) × 100 = 5%
so the property needs to increase in value by at least 5% per year to cover the loss.
The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.
Explanation:First, let's calculate the monthly interest she needs to pay. 7% of $300,000 is $21,000 for a year. To find the monthly interest, we divide this by 12, resulting in $1750.Her yearly income from rent is $1500 multiplied by 12, giving us $18,000.To calculate her overall loss, we add the yearly interest and the costs to keep the property, then subtract the yearly rent income. So, $21,000 + $3000 - $18,000 = $6000 loss per year.Lastly, to find out by what percentage the property value needs to increase, we divide the loss by the original price and multiply by 100, giving us 2% increase per year.Learn more about Interest and Profit Calculation here:https://brainly.com/question/32651816
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
15,9, 27/5
Find the 10th Term
Therefore , the solution of the given problem of sequence comes out to be the sequence's roughly 10th term is 0.049 (rounded to the closest thousandth).
What is sequence?A sequence is a grouping of range numbers, or "terms." There are phrases like 2, 5, but choose 8. Certain narrative arcs can be made to go on forever by choosing to capitalise on a certain pattern that they exhibit. Use the designs 2, 5, 8, and then 3 to lengthen it. In a list of words for words, there exist formulas that show where to look. In mathematics, a sequence is a group of items that are ordered in some way.
Here,
The first three terms in the given sequence are 15, 9, and 27/5.
We must determine the pattern or rule that underlies the sequence in order to determine the tenth word.
=> 9 = 15 * (27/5) / 15
=> 27/5 = 9 * (27/5) / 9
Thus, each term is obtained by multiplying the constant value by (27/5) / 15, which may be written as 9/25.
In order to get the next phrase in the series, we can keep multiplying the preceding term by 9/25 using this constant value:
=> 9 * (9/25)⁷
When we compute this expression, we obtain:
=> (Rounded to the closest thousandth) 9 * (9/25)⁷
As a result, the sequence's roughly 10th term is 0.049 (rounded to the closest thousandth).
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28) The number of hours per week that high school students spend on computers is normally distributed, with a mean
of 5 hours and a standard deviation of 2 hours. 70 students are chosen at random. Let y represent the mean number
of hours spent on the computer for this group. Find the probability that y is between 5.1 and 5.7.
The probability that y is between 5.1 and 5.7 is approximately 0.4292.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.
According to question:Since the sample size is large (n = 70), we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean as normal with mean μ = 5 and standard deviation σ/sqrt(n) = 2/sqrt(70) ≈ 0.24.
Now we want to find the probability that y, the sample mean, is between 5.1 and 5.7. We can use the standard normal distribution to do this by standardizing y:
z = (y - μ) / (σ / sqrt(n)) = (y - 5) / 0.24
The probability that y is between 5.1 and 5.7 is equivalent to the probability that z is between:
z1 = (5.1 - 5) / 0.24 ≈ 0.42
and
z2 = (5.7 - 5) / 0.24 ≈ 2.92
Using a standard normal distribution table or calculator, we can find that the probability of z being between z1 and z2 is approximately 0.4292.
Therefore, the probability that y is between 5.1 and 5.7 is approximately 0.4292.
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¿Qué velocidad requiere una partícula de 6kg para alcanzar una energía cinética de 20 joule?
O a. 2.58 m/S
O b. 0.39 m/s
O c. 6.67 m/s
O d. Ningunas
La velocidad requerida para que una partícula de 6 kg alcance una energía cinética de 20 joule es de aproximadamente 2.58 m/s. La respuesta es A.
Velocidad
La fórmula para calcular la energía cinética es:
E_cinética = 1/2 * m * v^2
Donde m es la masa de la partícula y v es su velocidad.
Dado que la energía cinética y la masa de la partícula son conocidas, podemos despejar la velocidad de la siguiente manera:
20 J = 1/2 * 6 kg * v^2
20 J = 3 kg * v^2
v^2 = 20 J / 3 kg
v = √(20 J / 3 kg)
v ≈ 2.58 m/s
Por lo tanto, la velocidad requerida para que una partícula de 6 kg alcance una energía cinética de 20 joule es de aproximadamente 2.58 m/s. La respuesta es a).
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Chloe claims that Point A=−6 and Point B=1 . Which of the following statements provide support for Chloe's claim? Select ALL that apply. A A<0 because A is to the left of zero B A>0 because A is to the left of zero C A 0 because B is to the left of zero F B>0 because B is to the right of zero
The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.
Describe Comparison Algebra?Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.
Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.
In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.
The statements that provide support for Chloe's claim are:
A. A<0 because A is to the left of zero.
F. B>0 because B is to the right of zero.
Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.
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I need to know the answers to number 7, 8, 9, 10
From given box plot that represents average minute time per night spent on homework
Min = 0
Q1 = 20
Q2 = 48
Q3 = 60
Max = 190
7. percent of the sophomores spend more than 60 minutes on homework per night= 25% because 60 represent the Q3 that is 75th percentile , so above that 25 % are remains.
8. range of times that the middle 50% of the sophomores spend on homework per night= 20 to 60 minutes Middle 50% that is from Q1 to Q3
60 - 20 = 40
9. No of sophomores do not do homeworkHere given box plot is for average Time sophomores spend on homework per night. So it not gives the information about number of students. So we can not identify No of sophomores do not do homework from box plot .
10. percent of the sophomores spend less than 20 minutes per night on homework = 25% because 20 represents the Q1 that is 25th percentile so below that value 25% of data are fall.
7)25%
8)40
9) can not decide
10)25%
7. Sophomores that spend more than 60 minutes are 25%. 8. The range of times that the middle 50% of the sophomores spend on homework per night = 40.
What is box plot?A box plot, also called a box-and-whisker plot, is a statistical graph that shows how a dataset is distributed. As it enables a visual comparison of their median, range, and distribution, it is very helpful when comparing several datasets.
Two whiskers extend from a rectangular box that makes up a box plot. The whiskers reflect the minimum and maximum values that are not outliers, while the box represents the interquartile range (IQR), which is the middle 50% of the data. Each solitary point outside the whiskers represents an outlier.
From the given box plot that the five number summary can be calculates as follows:
Min = 0
Q1 = 20
Q2 = 48
Q3 = 60
Max = 190
7. Now, the percent of the sophomores that spend more than 60 minutes on homework per night= 25%.
As 60 represent the Q3 that is 75th percentile. Above this the remaining value is 25%.
Thus, sophomores that spend more than 60 minutes are 25%.
8. The range of times that the middle 50% of the sophomores spend on homework per night= 20 to 60 minutes
Middle 50% that is from Q1 to Q3
60 - 20 = 40
9. Time sophomores spend on homework per night is not given. So we can not identify number of sophomores do not do homework from box plot .
10. The percent of the sophomores spend less than 20 minutes per night on homework = 25%
As 20 represents the Q1 that is 25th percentile so below that value 25% of data are fall.
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Equipment accusers on January 8 at cost of $212,000 has an estimated useful life of 15 years, has an estimated residual value of $14,000, and is depreciated by the straight line method
Answer: To calculate the annual depreciation expense of the equipment using the straight-line method, we need to first determine the depreciable cost of the asset, which is the cost of the asset minus its estimated residual value.
Depreciable Cost = Cost of asset - Estimated Residual Value
Depreciable Cost = $212,000 - $14,000
Depreciable Cost = $198,000
Next, we can use the following formula to calculate the annual depreciation expense:
Annual Depreciation Expense = Depreciable Cost / Useful Life
Annual Depreciation Expense = $198,000 / 15 years
Annual Depreciation Expense = $13,200 per year
Therefore, the annual depreciation expense of the equipment using the straight-line method is $13,200 per year.
Step-by-step explanation:
find the factors to this polynomials i need help SHOW YOUR WORK.
Answer:
hope this will help you...
In order to develop a more appealing cheeseburger, a franchise uses taste tests with 11 5 different buns, 3 different cheeses, 4 types of lettuce, and types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers?
It would take approximately 1,980 minutes (33 hours) for the tester to eat all possible cheeseburgers.
Consider the given density curve.
What is the value of the median?
O-10
O-7
O-6
O-2
Note that the median of the distribution or the density curve is -6. (Option C)
What is the explanation for the above response?If the curve is a straight line and the area under the curve appears to be a rectangle, then we can assume that the density curve is a uniform distribution. In this case, the median of the distribution is simply the midpoint of the interval, which would be
(-10 + (-2))/2
= -6.
A density curve is a mathematical model used to describe the overall pattern of a dataset. It is a smooth curve that approximates the distribution of the data and shows the relative frequencies of observations at different values.
The area under the curve represents the total proportion of observations in the dataset, and the curve is normalized such that the total area under the curve equals one. Density curves are used in statistics to analyze and interpret data, and can be used to make predictions about future observations.
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Which expression can be used to determine the reference angle for an angle, x, measuring 150°?
A 180-X
B X-180
C360-X
D X-360
Answer:
The expression that can be used to determine the reference angle for an angle, x, measuring 150° is A) 180 - X.
The reference angle is the acute angle between the terminal side of an angle and the x-axis in standard position. To find the reference angle for an angle greater than 90 degrees, we subtract the angle from 180 degrees.
In this case, the angle is x = 150 degrees. So, the reference angle would be:
180 - x = 180 - 150 = 30 degrees.
Therefore, the reference angle for an angle measuring 150 degrees is 30 degrees.
Complete the flow chart proof
The flow chart is complete and the answers are given below.
What is meaning of Congruent Figures?Those figures that have same shape and size are called Congruent Figures.
The flow diagram will be completed as follows
∠2 ≅ ∠4 ( vertical angle theorem )
∠1 ≅ ∠2 ( Given )
∠1 ≅ ∠ 3 ( Vertical Angle Theorem)
∠3 ≅ ∠4 ( Transitive Property of congruence)
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Given this equation what is the value of y at the indicated point?
Value of indicated point is 2.
Define straight lineIn mathematics, a straight line is a geometric object that extends infinitely in both directions and is perfectly straight, meaning that it does not curve or bend. A straight line is defined by any two points on the line, which can be connected by a line segment that lies entirely on the line.
The equation of a straight line can be written in various forms, such as slope-intercept form, point-slope form, or standard form, but they all describe the same line. The equation of a straight line is y = mx + b in slope-intercept form.
Given equation;
3x-y=1
Given coordinate (1,y)
Putting the value of coordinate in equation, we get
3-y=1
3-1=y
y=2
Hence, value of indicated point is 2.
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write a polynomial function of least degree with rational coefficients, so that P(x)=0 has the given roots.
x=-2,x=8
P(x)=
A polynomial function of least degree with rational coefficients, so that P(x)=0 has the given roots is P(x) = x^2 - 6x - 16.
What is roots?If the roots of P(x) are -2 and 8, then the factors of P(x) are (x+2) and (x-8), since if we plug in -2 or 8 for x, one of these factors will be equal to zero, making the whole expression equal to zero.
To find the polynomial with these roots, we can multiply these factors together:
P(x) = (x+2)(x-8)
Multiplying this out, we get:
P(x) = x^2 - 6x - 16
Therefore, the polynomial function of least degree with rational coefficients that has roots of -2 and 8 is:
P(x) = x^2 - 6x - 16
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The polynomial function of least degree with rational coefficients and roots at x=-2 and x=8 is P(x) = x² - 6x - 16.
What is polynomial?A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using only the operations of addition, subtraction, and multiplication, and in which the variables appear only with positive integer exponents. The degree of a polynomial is the highest power of the variable in the expression.
Define roots?Roots refer to the values that satisfy an equation, making it equal to zero.
Using the zero product property, we know that a polynomial with roots at -2 and 8 can be written as:
P(x) = (x + 2)(x - 8)
Expanding this expression, we get:
P(x) = x² - 6x - 16
Therefore, the polynomial function of least degree with rational coefficients and roots at x=-2 and x=8 is P(x) = x² - 6x - 16.
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