Answer:
12
Step-by-step explanation:
1/ Expliquer brièvement la nécessité du dévloppement des énergies renouvelables.
2/ Le dispositif contient un alternateur qui rend possible la conversion réalisée. Nommer et expliquer brièvement le phénomène physique permettant cette conversion
Answer:
1. Ce qui fait des énergies renouvelables une raison de se développer, c'est parce qu'elles utilisent une source qui peut être éternelle. Les combustibles fossiles sont notre principale énergie, mais cela ne durera pas éternellement.
2) Le courant alternatif rend cela possible.
Si vous recherchez un phénomène naturel, il peut s'agir du solaire, de l'hydroélectricité, du vent, de la biomasse, etc. Selon le contexte.
Help me with my math!!!!!
Answer:
g=3.5
f=42
Step-by-step explanation:
The sampling distribution of the sample mean will always have the same _________ as the original distribution.
The sampling distribution of the sample mean will always have the same Mean as the original distribution.
Sampling distribution:
Sampling distribution means a probability distribution of a statistic that is obtained through repeated sampling of a specific population.
Given,
Here we have the statement "The sampling distribution of the sample mean will always have the same _________ as the original distribution."
Now, we have to find the missing word in the statement.
We know that, the mean of the sampling distribution of the sample mean will always be the same as the mean of the original non-normal distribution. Simply said that the sample mean is equal to the population mean.
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A researcher who selects a sample of people of varying ages and studies them at one point in time is, by definition, using the ___________ method
The researcher in question is using a cross-sectional research method.
This method involves selecting a sample of individuals from a population and studying them at one point in time, usually in a single session. The purpose of the research is to gather information about the relationships between variables and to describe the population characteristics.
One of the primary advantages of the cross-sectional method is its efficiency. Researchers can gather a large amount of data in a relatively short amount of time, which can be helpful for studying large populations or for answering research questions that are time-sensitive.
However, there are also limitations to the cross-sectional method. For example, because it only captures data from one point in time, it cannot be used to study how variables change over time. Additionally, cross-sectional research cannot establish causality, as the data only shows correlations between variables, not their causal relationships.
Overall, the cross-sectional method is useful for gathering information about a population's characteristics and relationships between variables, but it should be used in conjunction with other research methods to gain a more comprehensive understanding of a phenomenon.
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Cecilia Alvarez had always wanted to see Singapore. This was her chance. A round-trip airfare on Singapore Airlines (premium economy) from San Francisco where she lived was SNG1344.31. A three-night stay at the Mandarin Oriental, an excellent hotel overlooking the marina (and just so happens to have one of the best breakfasts in all of Singapore) was quoted to at SNG2998.28. If the current spot rate was SNG1.4140=USD1.00, what would just air travel and hotel cost Cecilia in U.S. dollars? Round to two decimal places.
Therefore, the total cost of air travel and hotel for Cecilia in U.S. dollars is =\(USD3073.04.\)
To calculate the cost of air travel and hotel in U.S. dollars for Cecilia's trip to Singapore, we need to convert the costs from Singapore dollars to U.S. dollars using the given spot rate of SNG1.4140 = USD1.00. The airfare cost of SNG1344.31 and hotel cost of SNG2998.28 can be converted to U.S. dollars to determine the total cost.
To convert the costs from Singapore dollars to U.S. dollars, we multiply the costs by the conversion rate of SNG1.4140 = USD1.00.
For the airfare, the cost in U.S. dollars is calculated as:
USD cost of airfare = SNG1344.31 * (1 USD / SNG1.4140)
For the hotel, the cost in U.S. dollars is calculated as:
USD cost of hotel = SNG2998.28 * (1 USD / SNG1.4140)
Using the conversion rate, we can compute the values:
USD cost of airfare = SNG1344.31 * (1 USD / SNG1.4140) = USD950.44 (rounded to two decimal places)
USD cost of hotel = SNG2998.28 * (1 USD / SNG1.4140) = USD2122.60 (rounded to two decimal places)
Therefore, the total cost of air travel and hotel for Cecilia in U.S. dollars is approximately USD950.44 + USD2122.60 = USD3073.04.
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6. Find the coordinates of the orthocenter of AABC with vertices A (2,6), B (8,6), and C(6,2). (1 point)
O (5,4)
O (1,2)
O (6,4)
O (6,8)
The coordinates of the orthocenter of ABC are (6,4).
The correct option is C) (6,4).
What is an orthocenter of a triangle?
In geometry, an orthocenter is a point in a triangle that is the intersection of the three lines containing the altitudes of the triangle. An altitude of a triangle is a line segment from a vertex of the triangle to the line containing the opposite side, and is perpendicular to that side. The orthocenter of a triangle is the point where all the altitudes of a triangle meet.
To find the orthocenter of a triangle, the first step is to find the equation of the altitudes from each vertex. Then, we can find the point of intersection of these three lines.
Given the triangle ABC with vertices A (2,6), B (8,6), and C(6,2),
The equation of altitude from vertex A is (x-2) = -2(y-6)
The equation of altitude from vertex B is (x-8) = -2(y-6)
The equation of altitude from vertex C is (x-6) = 2(y-2)
By solving the system of these three equations, we can find the coordinates of the orthocenter.
Hence, The coordinates of the orthocenter of ABC are (6,4).
The correct option is C) (6,4)
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A year membership to Fun Zone costs $45 plus $1 per visit. A one-month membership costs $5 plus $3 per visit. Which multi-step equation, with variable on both sides, represent this situation
Answer:
y = $45 + x
y = $5 + 3x
Step-by-step explanation:
The computation of the multi-step equations be shown below:
Let us assume the number of visits be x
So the first equation would be
y = $45 + x
And, the second equation would be
y = $5 + 3x
These are the multi-step equations with variable on the both sides
A group of 328 people consists of men ,women, and children. There are five times as many men than children and twice as many women then children. How many women are there
Step-by-step explanation:
Ultimately we know:
Men = * 5
Women = * 2
Children =
We can already make the estimation that the amount of children will be below 50. So by trial and error you will get to your answer by substituting with 41.
Children - 41
Women - 41 x 2 = 82
Men - 41 x 5 = 205
205 + 41 + 82 = 328
So your answer is 41
Write the general term for a geometric sequence whose first term is \( 1 / 8 \) and common ratio is 4 .
The general term for the geometric sequence with a first term of 1/8 and a common ratio of 4 is aₙ = 2²ⁿ ⁻ ⁵.
What is the general term of the geometric sequence?The general term of a geometric sequence can be expressed as:
aₙ = a₁ × r⁽ ⁿ ⁻¹ ⁾
Where:
aₙ represents the nth term of the sequence,
a₁ is the first term of the sequence, and
r is the common ratio of the sequence.
Given that:
First term a₁ = 1/8
Common ratio r = 4
Plug these into the above formula and solve simplify:
aₙ = a₁ × r⁽ ⁿ ⁻¹ ⁾
aₙ = 1/8 × 4⁽ ⁿ ⁻¹ ⁾
aₙ = 8⁻¹ × 4⁽ ⁿ ⁻¹ ⁾
aₙ = 2⁻³ × 2²⁽ ⁿ ⁻¹ ⁾
Simplify using same base theorem:
aₙ = 2⁻³ ⁺ ²⁽ ⁿ ⁻¹ ⁾
aₙ = 2⁻³ ⁺ ²ⁿ ⁻ ²
aₙ = 2²ⁿ ⁻ ² ⁻ ³
aₙ = 2²ⁿ ⁻ ⁵
Therefore, the general term is aₙ = 2²ⁿ ⁻ ⁵.
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in how many ways can a president, a vice-president, and a secretary be selected from an organization of 37 members?
A president, a vice-president and a secretary can be selected from an organization of 37 members is 46,620 ways.
The number of members in an organization
= 37
The number of positions for which members are to be selected from an organization of 37 members = 3
The number of ways in which r people/ members/ things can be selected from n people/ members/ things
= nPr = n!/(n-r)!
Therefore, the number of ways by which a president, a vice-president and a secretary can be selected from an organization of 37 members
= 37P3 = 37! /(37-3)! = 46,620 ways.
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find the area between a large loop and the enclosed small loop of the curve r = 2 + 4 cos(3θ).
Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.
To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.
Setting the equation of the curve equal to itself, we have:
2 + 4cos(3θ) = 2 + 4cos(3(θ + π))
Simplifying and solving for θ, we get:
cos(3θ) = -cos(3θ + 3π)
cos(3θ) + cos(3θ + 3π) = 0
Using the sum to product formula, we get:
2cos(3θ + 3π/2)cos(3π/2) = 0
cos(3θ + 3π/2) = 0
3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...
Solving for θ, we get:
θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6
We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.
To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.
Using the formula for the area enclosed by a polar curve, we have:
A = 1/2 ∫[a,b] (r(θ))^2 dθ
where a and b are the angles of intersection.
For the small loops, we have:
A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ
Using trigonometric identities, we can simplify this to:
A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ
Evaluating the integral, we get:
A1 = 10π/3
For the large loops, we have:
A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)
Using the same trigonometric identities, we can simplify this to:
A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)
Evaluating the integrals, we get:
A2 = 80π/3
Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:
A = A2 - A1 = (80π/3) - (10π/3) = 70π/3
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Can someone please help me, determine if they are equivalent yes or no I’ll mark brainliest please
Answer:
from the top-
yes
no
no
no
If I took any two distinct prime numbers, and the number "1", would these numbers always be pairwise relatively prime? True O False
The statement is true. If we take any two distinct prime numbers, and the number "1", these numbers will always be pairwise relatively prime.
Two numbers are said to be pairwise relatively prime if their greatest common divisor (GCD) is equal to 1. In this case, since we are considering distinct prime numbers, their GCD will always be 1 since prime numbers have no common factors other than 1 and themselves. Therefore, any two distinct prime numbers will be relatively prime.
Similarly, when we consider the number "1", it is relatively prime to any other number because its only divisor is 1. Hence, when "1" is paired with any prime number, the GCD will be 1.
In summary, whether we consider two distinct prime numbers or pair them with the number "1", the resulting numbers will always be pairwise relatively prime.
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1. Luzcel real estate owns 8000 square meters of lot area and decides to construct two different styles of houses, B and C. The lot area of house B is 250 sq. m. and house C lot area is 200 sq. m. The construction engineer has a maximum of 6400 man-hours of labor for the construction. Let your variables be the number of units of house B and the number of units of house C to be constructed. a) Write an inequality which states that there are 8000 sq. m. of land available. b) A unit of house B requires 160 man-hour and a unit of house C requires 256 man-hour. Write an inequality that the engineer has at most 6400 man-hour available for construction. c) If material cost 600 thousand pesos for a unit of house B and 800 thousand for a unit of house C, write an inequality stating that the engineer has at least 12 million pesos to spend for materials. d) Labor cost 1.1 million pesos for constructing a unit of house B and 1.3 million pesos for constructing a unit of house C. If a unit of house B sells for 3.5 million and a unit of house C selis for 4 million, how many units of house B and house C should be constructed to obtain the maximum profit? Show the graph.
Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.
Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:
160B + 256C ≤ 6400c
Inequality stating that the engineer has at least 12 million pesos to spend for materials:
600B + 800C ≤ 12000d
. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C
Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.
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a) What type of distribution does this represent?
b) This information could be considered a sample for the entire league. If
number of teams from the league were selected to create a larger sample, what type of sampling would it represent? Explain.
a.) The type of distribution that is represented by the histogram is a left skewed histogram.
b.) The type of sampling this will represent is a simple random sampling.
What is a left skewed histogram?A left skewed histogram can be defined as the type of distribution where by the tails is displayed towards the left of the histogram. This is represented in the histogram given in the diagram above.
A simple random sampling is defined as the type of sampling whereby every member of a population is given an equal chance to be selected. Since the information represented is the sample of an entire league, making another bigger league from it gives them all equal chance to be selected.
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which is right?????
Answer:
C
Step-by-step explanation:
When talking about multiplication two negatives do, in fact, make a positive but if there is only one negative in the equation, the product(answer) will be negative. Therefore, C 31(-10)=-310 is the only problem that is correct.
Answer:
C.\(31\left(-10\right)=-310\)
Step-by-step explanation:
\(31\left(-10\right)\)
\(\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a\)
\(=-31\cdot \:10\)
\(\mathrm{Multiply\:the\:numbers:}\:31\cdot \:10=310\)
\(=-310\)
PLEASE HELP I WOULD MAKE THIS 1,000,000,000 POINTS IF I COULD
'Performance Task: Circle Constructions'
I need to finish this class PLEEEEAAAAASSSSSSE QmQ
Answer:
\( \huge \color{purple}{answer}\)
To draw a circle whose radius is given, we require a ruler and compasses. Given that the radius is 5 cm, the steps to be followed are:
Step 1: Place the pointer of the compass at the initial point of the ruler (0 cm) and extend the other end of the pencil measuring 5 cm from the initial point (i.e. 5 cm)
Step 2: Mark a point O on a piece of paper. This point is supposed to be the center of the circle that you are about to construct.
Step 3: Place the pointer of the compass at point 0.
Step 4: Turn the compass slowly through 360 degrees to draw a circle.
\( \small\color{pink}{point \: to \: remember}\)Make sure that you hold the point of the compass stiffly on the paper. You are also required to move the compass through the 360 degrees in one go for accuracy and neatness.
A circle is a locus of all points in 2 dimensional space which are equidistant from some fixed point. The constructed circle with radius 5 units is constructed below.
How to construct a circle with specific radius?We need two tools. first is ruler, and second is compass.
Take some fixed point on a paper. Let it be called OTake the ruler and draw an 'r' unit sized line segment OA.Use the compass, place its pointy tip on the fixed point O and the pen or pencil of compass on the second endpoint A of the constructed line segment.Now make a full rotation of the compass so that a ring like figure is created.This is the needed circle.
One such circle (radius of 5 units) is constructed is attached below.
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60>5(6-2x) ok help me so I can get an answer
Inequalities are used to represent unequal expressions
The solution to the inequality is: \(x > -3\)
How to determine the inequality solutionThe inequality is given as:
60>5(6-2x)
Rewrite the inequality properly as:
\(60>5(6-2x)\)
Divide both sides of the inequality by 5
\(12>6-2x\)
Subtract 6 from both sides of the inequality
\(6>-2x\)
Divide both sides of the inequality by -2
\(-3
Rewrite the inequality as
\(x > -3\)
Hence, the solution to the inequality is: \(x > -3\)
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define a relation r on the set {1, 2, 3, 4} as follows: r = {(1, 4),(2, 3),(2, 4),(4, 1),(2, 1),(1, 2),(3, 2)} (a) is r symmetric? justify your answer. (b) is r transitive? justify your answer.
We have a relation r on the set {1, 2, 3, 4} as follows: r = {(1, 4),(2, 3),(2, 4),(4, 1),(2, 1),(1, 2),(3, 2)} so we have t is neither symmetric nor transitive.
A = {1,2,3,4}
T = {(1,4), (2,3), (2,4), (4,1), (2,1), (1,2), (3,2)}
T is a relation (R) from A→A
t is a set of ordered pair (a,b) where a,b∈ A
Symmetric relation
a relation R on set get A is called symmetric if (b,a) ∈ R whenever (a,b)∈A
Using quantifier, we see that the relation R on the set A is symmetric.
T is not symmetric because (2,4)∈T but (4,2)∉T, violating the property of symmetric relation.
Transitive relation,
A relation R on a set A is called transitive if whenever (a,b)∈R and (b.c)∈R , then (a,c) ∈R
Using the quantifier, we see that the relation R on a set A is transitive if we have .
T is not transitive because, (1,4)∈ T and (4,1)∈T but (1,1)∉T violating the property of transitive relation .
Hence, t is neither symmetric nor transitive.
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4) Penny dreadful
On page 60 of the March 31, 2008 issue of the New Yorker David Owen wrote that you'd earn less than the federal minimum wage if you took longer that 6.15 seconds to pick up a penny.
a) Use the information in the quotation to figure out the minimum wage when Owen wrote his article. Use arithmetic, not the web. That's part b).
b) Check Owen's arithmetic by comparing your answer to the actual federal minimum wage at that time. This information is available on the web.
c) How much time would you need to spend picking up a penny if you wanted to earn the minimum hourly wage today for your work.
d) What is the origin of the phrase "penny dreadful"?
a) At the time the article was published, the federal minimum wage was $5.85 per hour.
b) According to the US Department of Labor website, the federal minimum wage in 2008 was $6.55 per hour.
c) To earn the current federal minimum wage of $7.25 per hour, a person must pick up a penny in 4.97 seconds.
d) The phrase "penny dreadful" is a British expression referring to cheaply printed stories of sensational and sometimes gruesome content that were sold for a penny in the 19th century.
A) The minimum wage when Owen wrote his article can be calculated by using the equation:
Minimum wage = (Amount of money earned)/(Amount of time taken to earn it)
In this case, the amount of money earned is $0.01 (the value of a penny) and the amount of time taken to earn it is 6.15 seconds. Therefore:
Minimum wage = ($0.01)/(6.15 seconds) = $0.00162601626 per second
To convert this to an hourly wage, we can multiply by the number of seconds in an hour (3600):
Minimum wage = ($0.00162601626 per second) x (3600 seconds per hour) = $5.85365854 per hour
Minimum wage = $5.85
B) According to the U.S. Department of Labor, the federal minimum wage in 2008 was $6.55 per hour.
Therefore, Owen's arithmetic was slightly off, as his calculated minimum wage is lower than the actual minimum wage at that time.
C) To calculate how much time you would need to spend picking up a penny in order to earn the current minimum wage, we can use the same equation as before, but rearrange it to solve for the amount of time:
Amount of time = (Amount of money earned)/(Minimum wage)
The current federal minimum wage is $7.25 per hour, or $0.00201388889 per second. Therefore:
Amount of time = ($0.01)/($0.00201388889 per second) = 4.97 seconds
So you would need to spend 4.97 seconds picking up a penny in order to earn the current minimum wage.
D) The phrase "penny dreadful" refers to a type of cheap, sensationalist fiction that was popular in the 19th century. These stories were typically published in weekly installments and sold for a penny each, hence the name "penny dreadful."
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4. the highest point on the graph of the normal density curve is located at a) an inflection point b) its mean c) μ σ d) μ 3σ
The highest point on the graph of the normal density curve is located at its mean represented by μ.
The highest point on the graph of the normal density curve is located at its mean. The normal density curve or the normal distribution is a bell-shaped curve that is symmetric about its mean. The mean of a normal distribution is the measure of the central location of its data and it is represented by μ. It is also the balancing point of the distribution. In a normal distribution, the standard deviation (σ) is the measure of how spread out the data is from its mean.
It is the square root of the variance and it determines the shape of the normal distribution. The normal distribution is an important probability distribution used in statistics because of its properties. It is commonly used to represent real-life variables such as height, weight, IQ scores, and test scores.
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4•(2+5)^2 -5^2 how do I solve this?
Answer:
4•(2+5)^2 -5^2 = 171
Step-by-step explanation:
Do BIDMAS
(brackets, indices, division, multipy, add, sub)
so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps
Answer: Brackets => 4 x (7)^2 - 5^2
Indices/Orders => 4 x 49 - 25
Multiplication => 196 - 25
Subtraction => 171
The Rosens found a house selling for $113,500. The taxes on the house are $1200
per year, and insurance is $320 per year. They are requesting a conventional loan from the local bank. The bank
is currently requiring a 15% down payment and 3 points, and the interest rate is 10%. The Rosen’s gross
monthly income is $4750. The have more than 10 monthly payments remaining on a car, a boat, and furniture.
The total monthly payments for these items is $420. Their bank will approve a loan that has a total monthly
mortgage of principal, interest, property taxes, and homeowners insurance that is less than or equal to 28% of
their adjusted monthly income.
In order to calculate the maximum loan amount the Rosens can afford, we can use the 28% rule of thumb..Down Payment + Points = 15% Down Payment + 3 Points Down Payment + Points = 15% x 113,500 + 3 Points
In order to calculate the maximum loan amount the Rosens can afford, we can use the 28% rule of thumb. This rule states that the total monthly mortgage payment (principal, interest, taxes, and insurance) should not exceed 28% of the Rosens’ adjusted monthly income. The adjusted monthly income is calculated by subtracting the total monthly payments for their car, boat, and furniture from their gross monthly income To calculate the maximum loan amount, we can use the following formula :Maximum Loan Amount = (Adjusted Monthly Income x 28%) - (Monthly Property Tax + Monthly Home Insurance)For the Rosens, the adjusted monthly income is 4750 - 420 = 4330. The maximum loan amount is then calculated as follows: Maximum Loan Amount = (4330 x 0.28) - (1200/12 + 320/12)Maximum Loan Amount = 1208 - 200 Maximum Loan Amount = 1008.The maximum loan amount the Rosens can receive is then calculated by subtracting the down payment and points from the maximum loan amount .Down Payment + Points = 15% Down Payment + 3 Points Down Payment + Points = 15% x 113,500 + 3 Points.
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Felicity has two $10 and a $5 bill. She spends
$8.20 on a game and $4.80 on a poster.
How much money does she have left?
Answer:
$12
Step-by-step explanation:
8.20 plus 4.80 would equals 13
so 13 subtracted by 25 equals 12
the middle number; put the values in order from lowest to highest, then find the number that is exactly in the middle
I will give 20 points
Answer:
This is like quadratic equation you just say y=1x+-2 and then you get the answer
how many rows and columns must a matrix a have in order to define a mapping from r4 into r5 by the rule t .x/ d ax?
The matrix A must have the following form:
A = [ a11 a12 a13 a14 ]
[ a21 a22 a23 a24 ]
[ a31 a32 a33 a34 ]
[ a41 a42 a43 a44 ]
[ a51 a52 a53 a54 ]
In order for a matrix A to define a mapping from R4 into R5 by the rule T(x) = Ax, the matrix A must have 5 rows and 4 columns.
This is because the number of rows in the matrix determines the dimension of the output space, while the number of columns determines the dimension of the input space. In this case, the output space is R5 and the input space is R4, so the matrix must have 5 rows and 4 columns.
In general, if a matrix A is used to define a mapping from Rn into Rm by the rule T(x) = Ax, then the matrix A must have m rows and n columns.
So, the matrix A must have the following form:
A = [ a11 a12 a13 a14 ]
[ a21 a22 a23 a24 ]
[ a31 a32 a33 a34 ]
[ a41 a42 a43 a44 ]
[ a51 a52 a53 a54 ]
where each aij is a scalar.
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What are the formula in coordinate geometry for Class 9?
The formula in coordinate geometry for Class 9 include distance formula, midpoint formula, section formula, equation of a line, slope of a line, equation of a circle, equation of a parabola, equation of an ellipse, equation of a hyperbola, area of a triangle, and area of a circle.
The distance formula is used to determine the distance between two points in a coordinate plane. The midpoint formula is used to find the midpoint between two points. The section formula is used to calculate the area of a triangle formed by three points. The equation of a line is used to define the line in terms of its slope and intercept. The slope of a line is used to calculate the angle of the line in relation to the x-axis. The equation of a circle is used to determine the equation of a circle with a given center and radius. The equation of a parabola is used to determine the equation of a parabola with a given focus and directrix. The equation of an ellipse is used to determine the equation of an ellipse with a given center and major and minor axes. In coordinate geometry the equation of a hyperbola is used to determine the equation of a hyperbola with a given center and asymptotes. The area of a triangle is used to find the area of a triangle given the three vertices. The area of a circle is used to find the area of a circle given the radius.
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A=4ℼR2 solve for R
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Given problem;
A = 4 π R²
To solve for R, we have to make it the subject of the expression.
Since
A = 4 π R² , follow these steps to find R;
Multiply both sides by \(\frac{1}{4\pi }\)
A x \(\frac{1}{4\pi }\) = \(\frac{1}{4\pi }\) x 4 π R²
\(\frac{A}{4\pi }\) = R²
Then find the square root of both sides
√R² = \(\sqrt{\frac{A}{4\pi } }\)
R = \(\sqrt{\frac{A}{4\pi } }\)
The solution is \(\sqrt{\frac{A}{4\pi } }\)
Solve the equation |2x + 1| = 2(x + 1). Are there any extraneous solutions?
Answer:
\(x=-\frac{3}{4}\)
Step-by-step explanation: