What are the types of triangles based on their sides and angles? How do you classify a triangle as equilateral, isosceles, scalene, acute, right, or obtuse? Give an example of each.
Answers
Based on their sides, the 3 triangles are classified as equilateral triangles, isosceles triangles, and scalene triangles.
A triangle is scalene if all of its three sides and angles are differentScalene-Triangle-1
In the figure, all three symbols that are given on each side are different, which denotes that all three sides are unequal.
If two of its sides are equal, a triangle is called an isosceles.One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.
A triangle with all three equal sides is called equilateral.The sum of all three angles of an equilateral triangle is equal to 180 degrees. 60° + 60° + 60° = 180°
Acute angles measure less than 90 degrees.the examples of acute angles are 25°, 36°, 47°, 64°, 55°, 72°, 80° and so on
Right angles measure 90 degrees.Examples of right angles are all around us. We can see right angles in the corners of a room, book, cube, windows, and at several other places.
Obtuse angles measure more than 90 degreesExamples of obtuse angles include 166°, 121°, 110°, 117°, and 91°.
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Related Questions
Mr. Stewart made ome pie. She old 3/5 of them and gave 1/4 of the remainder to the food bank. If he had 150 pie left how many pie did he ell
Answers
By applying the fraction concept, it can be calculated that Mrs. Stewart sold 300 cakes.
How does the concept of fractions apply in real life?
In real life, the concept of a fraction is often used when we want to talk about a part of a whole, a part of something, a part of a group of people, etc.
In this case, it is stated that Mrs. Stewart made several pies, some of which were sold and given to food banks, and some were left over.
If we know that 1/4 of the unsold pies were given to the food bank, then the unsold pies that were not given to the food bank = 1 - 1/4 = 3/4 part.
Additionally, we also know that the number of unsold pies that were not given to the food bank (leftover pies) was 150.
If x is the number of unsold cakes, then the two statements above can be written in mathematical notation:
3/4 x = 150
x = 150 : 3/4
= 150 x 4/3
= 200 pies
If pies made are y, then pies not sold = pies made - pies sold
x = y - 3/5y
= 2/5y
if we put the value of x into this equation it becomes:
200 = 2/5y
y = 200 : 2/5
= 200 x 5/2
= 500 pies
Then the pies were sold = 3/5y
= 3/5 x 500
= 300 pies
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the distribution of time spent brushing teeth for the 1,200 students in a school is multimodal with a mean of 43 seconds and a standard deviation of 8.99 seconds. if a random sample of 9 students is selected, is it appropriate to calculate the probability of the sample mean being less than 30 seconds using an approximately normal model?
Answers
No, it is not appropriate to estimate the probability using an approximately normal model because the population is not normal and the sample size is small.
The details given are,
Sample size = 9
mean = 43 sec
Standard deviation = 8.99
Therefore we conclude that is it not appropriate to calculate the likelihood of the sample mean being less than 30 seconds using an approximately normal model.
Mean is also know as the average of a given data . We calculate the mean by the formula : ∑xifi / ∑fi.
Normal Distribution is the probability density function ( pdf) for a continuous random variable in a system .
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The lit how the amount of each ingredient charlotte ued to make macaroni and cheee. 16 ounce 2 egg 2. 5 cup of milk 3 1/2 cup of chedder cheee
Answers
The combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.
According to the question,
We have the following information:
A sandwich hop serve 4 ounce of meat and 3 ounce of cheese on each sandwich. After making sandwiches for an hour the hop owner has used 91 combined ounce of meat and cheese.
Combined ounces for 1 sandwich:
Ounces of meat + ounces of cheese
4+3
7 ounces
It is given that in an hour 91 ounces of combined cheese and meat are used.
Now, we have:
Number of sandwiches made in 1 hour = 91/7
Number of sandwiches = 13
Ounces of meat used in 13 sandwiches can be found using multiplication as follows:
13*4
Ounces of meat used in 13 sandwiches = 52 ounces
Ounces of cheese used in 13 sandwiches can found using multiplication as follows:
13*3
Ounces of cheese used in 13 sandwiches = 39 ounces
Hence, the combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.
complete question is
A andwich hop erve 4 ounce of meat and 3 ounce of cheee on each andwich. After making andwiche for an hour, the hop owner ha ued 91 combined ounce of meat and cheee. How many combined ounce of meat and cheee are ued on each (1) andwich?
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Here is a number sequence.
31 26 21 16 11 ...
Write down the rule for continuing the sequence.
I don't need explanation, I only need the ANSWER
Answers
Answer: 11 16 21 26 31
Step-by-step explanation: the shows the sequence.
What part of ton is a gram?
Answers
Answer:
1/1000000 One gram is one millionth of a ton
Step-by-step explanation:
1 ton is 1000 kg = 1 million grams
1 gram = 1/1000000 ton
Hope this helps
Match each equation on the left of the equivalent equation on the right some answer options on the right will not be used
(left) log_2(0.25) = -2 , 5^2 =25 , log_2(32) = 5 , 25^-1 = 0.04 (right) 2^5 = 32 , 0.25^2 = -2, log_25 (0.04) =-1 , log_0.04(-1)=25, 2^-2 = 0.25, log_5(25) =2
Answers
The equations log₂ (0.25) = -2, 5² = 25, log₂ 32 = 5 and 25⁻¹ = 0.04 are equivalent to the equations 2⁻² = 0.25, log₅ 25 = 2, 2⁵ = 32, log₂₅ 0.04 = -1 respectively.
What are Logarithms?Logarithms are another way, which is the opposite of writing exponents. A number raised to some power will give some other values in case of exponentiation process. This power is called the logarithmic value.
We can write it as,
logₐ x = n ⇔ aⁿ = x
We have the equations on the left equivalent to the equations on the right using the definition of logarithms as,
log₂ (0.25) = -2 ⇔ 2⁻² = 0.25
5² = 25 ⇔ log₅ 25 = 2
log₂ 32 = 5 ⇔ 2⁵ = 32
25⁻¹ = 0.04 ⇔ log₂₅ 0.04 = -1
Hence the equations on the lefts log₂ (0.25) = -2, 5² = 25, log₂ 32 = 5 and 25⁻¹ = 0.04 are equivalent to the equations on the rights 2⁻² = 0.25, log₅ 25 = 2, 2⁵ = 32, log₂₅ 0.04 = -1 respectively.
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PLEASE HELP- ALGEBRA 2
PICTURE WILL BE PROVIDED
Graph each system of inequalities. Name the coordinates of the vertices of
the feasible region. Find the maximum and minimum values of the given
function for this region.
Answers
Answer:
Step-by-step explanation:
We need to graph all the given constraints(inequalities). The intersection of the of all the graphed system of inequalities gives the vertices of the feasible region.
The first inequality is .
This is very simple to graph. It is the region bounded by the horizontal lines,
and .
The next constraint or inequality is
To graph this inequality, we need to graph the corresponding linear equation .
We plot the intercepts and .
We then draw a solid line through the points.
Next, we test the origin to determine which half plane to shade.
This statement is true so we shade the lower half plane.
We now graph the inequality,
To graph this inequality, we need to graph the corresponding linear equation .
We plot the intercepts and .
We then draw a solid line through the points.
Next, we test the origin to determine which half plane to shade.
This statement is true so we shade the lower half plane.
The feasible region is shown in the above diagram.
The vertices of the feasible region are;
We substitute the vertices into the objective function to obtain;
Therefore the maximum value is and it occurs at .
The minimum value is and it occurs a
ANSWER TO QUESTIONS 14 We need to graph all the - 1
The first barn contained 3 times more hay than the second one. After 20 tons of hay
were removed from the first barn and 20 tons were added to the second barn, the
amount of hay in the second barn was -
of the amount remaining in the first barn.
How many tons of hay were there in each barn?
Answers
Answer:
find the size of unknown angle in the following figure
Step-by-step explanation:
angle PQR=115°angle POR=xref. angle POR =2pQRthe solve by putting the given valu
In triangle lmn, m∠l = (6c 35)°. if the exterior angle to ∠l measures 79°, determine the value of c.
Answers
The measure of angle c is 136/6 degrees
How to determine the measure of angle c?From the question, we have the following parameters that can be used in our computation:
∠l = (6c 35)°
Exterior of l = 79
As a general rule, the sum of an angle and its exterior is 180 degrees
This means that
6c - 35 + 79 = 180
Evaluate the like terms
So, we have
6c = 136
Divide both sides by 6
c = 136/6
Hence, the measure is 136/6 degrees
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what would be the coefficient of determination if the total sum of squares (sst) is 23.29 and the sum of squares due to regression (ssr) is 10.03?
Answers
The coefficient of determination if the total sum of squares is 23.29 and the sum of squares due to regression is 10.03 is 0.43
How to calculate regression?
The standard formula for simple linear regression is Y = mX + b, where Y is the response (dependent) variable, X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept.
Here we need to find the coefficient determination if the total sum of squares (sst) is 23.29 and the sum of squares due to regression (ssr) is 10.03.
Here we know that the value of the following are given,
Sum of square = 23.29
Sum of regression = 10.03
Then the coefficient determination is calculated as,
The coefficient of determination r2 = SSR/SST.
When we apply the value, then we get,
=> 10.03/23.29
=> 0.43
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work: solve the system of equations.
2) Xochitl is going to a carnival that has games and rides. Each game costs $2.50 and each ride
costs $5. Xochitl spent $30 altogether on 9 games and rides Graphically solve a system of
equations in order to determine the number of games Xochitl played and the number of
rides Xochitl went on, y.
Answers
6 games are played by Xochitl and 3 rides went on by Xochitl
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that the Xochitl is going to a carnival that has games and rides
The cost of each game is $2.50 and cost of each ride is $5.
Xochitl spent $30 altogether on 9 games
Let x represents the number of games and y represents the number of rides.
By the given information we form two equations.
x+y=9...(1)
2.5x+5y=30...(2)
From equation (1)
x=9-y
Now plug in x value in (2)
2.5(9-y)+5y=30
22.5-2.5y=30
Subtract 22.5 on both sides
-2.5y=30-22.5
-2.5y=7.5
Divide both sides by 2.5
y=3
x+y=9
x+3=9
x=6
Hence, the number of games Xochitl played is 6 and the number of rides Xochitl went on is 3.
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The bank
agrees to give you a loan of
$45,000 with 2% simple interest over 5 years.
How much will your monthly payments be?
Answers
The monthly payment will be $84.375 to the bank.
What is simple interest?
The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.S.I = Pnr / 100
where P = prinicipal
n= number of years
r = rate of interest
= 45000 * 2 * 8 / 100
= 810000 /100
= $8100
where, the divide by number of months
Balance= 8100 / 96
= $84.375
Hence, the monthly payment will be $84.375 to the bank.
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Eggs are generally sold in batches of 12 (or dozens). The image shows the 3 different ways that 12 eggs can be packaged into arrays. Note that the array 3 by 4 is taken to be equivalent to the array 4 by 3 and therefore is not included.
If it was decided that eggs should be sold in batches of 24, then these 24 eggs could be packaged into a total of ___
different arrays.
Answers
Eggs are generally sold in batches of 12 (or dozens). The image shows the 3 different ways that 12 eggs can be packaged into arrays. Note that the array 3 by 4 is taken to be equivalent to the array 4 by 3 and therefore is not included. If it was decided that eggs should be sold in batches of 24, then these 24 eggs could be packaged into a total of 4
different arrays.
How to find the different ways of packaging egg in order of 24The arrangement is checked by writing out the factors of 24
24 = 1, 2, 3, 4, 6, 8, 12, 24
grouping them in pairs
1 * 24
2 * 12
3 * 8
4 * 6
this gave a total of 4 arrays
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a detailed model that shows the overall structure for how data moves through a system is a(n) model.
Answers
A complete model that shows the system's whole data flow is a physical data model.
What is a physical data model?A thorough model that depicts the general flow of data through a system is a physical data model.
A physical data model is a thorough representation of the overall organizational data structure that is not dependent on a database management system or any other implementation factors.
A physical data model is a database-specific model that depicts relational data objects and their associations (such as tables, columns, primary keys, and foreign keys).
DDL statements can be produced from a physical data model and then delivered to a database server.
Examples of physical models include bridges, cell models, human organs, crash test dummies, landform models, building models, and chemical compound models.
Therefore, a complete model that shows the system's whole data flow is a physical data model.
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0. 5*
Zach and Naomi are studying geometric transformations. Zach is able to
move the triangle A to A' using the following sequence of basic
transformations:
1. Reflection across the x-axis
2. Reflection across the y-axis
3. Translation two units to the right
864
y
A
2
ON 4
-8-6-4-20 24 68
-2-
Jö
6
-8-
A
X
Naomi claims that the same three transformations, done in any order will
always produce the same result. Zach disagrees. Who is correct?
Answers
Answer:
Zach is correct
Step-by-step explanation:
You want to know if reflection across the two axes and translation right will achieve the same effect if the transformations are done in any order.
TransformationsTranslation right adds a value to the x-coordinate.
Reflection over the y-axis changes the sign of the x-coordinate.
If the order of these two transformations is changed, the result will change.
Example
Consider point (0,0) and the translation right 1 unit.
Reflection, then translation: (0, 0) ⇒ (0, 0) ⇒ (1, 0)
Translation, then reflection: (0, 0) ⇒ (1, 0) ⇒ (-1, 0)
Zach is correct that the transformations ...
Reflection over the x-axisReflection over the y-axisTranslation 2 units rightcannot be done in any order.
Answer:
Zach
Step-by-step explanation:
34. Write the equation of each line below.
Answers
The equation of the blue line is: y = 3x - 1.
The equation of the red line is: y = 3x + 2.
How to Find the Equation of a Line?To find the equation of a given line on a coordinate plane, find the slope along the line, m (rise / run), and also determine the value of the y-intercept (b), which is the point on the y-axis where the line intercepts it.
The equation of the red line:
Slope of the line (m) = rise / run = 3 units / 1 units
Slope (m) = 3
The red line intersects the y-axis at 2, this means the y-intercept of the line would be b = 2.
To write the equation of the red line, substitute m = 3 and b = 2 into y = mx + b:
y = 3x + 2
The equation of the blue line:
Slope of the line (m) = rise / run = 3 units / 1 units
Slope (m) = 3
The blue line intersects the y-axis at -1, this means the y-intercept of the line would be b = -1.
To write the equation of the blue line, substitute m = 3 and b = -1 into y = mx + b:
y = 3x - 1.
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PLEASE HELP MEE I DONT UNDERSTAND
Answers
So Valeria has 26 signatures as her starting point, and 6 signatures a day (x) as her rate. In slope-intercept (y = mx + b) form, this would be written y = 6x + 26, with y being the total number of signatures on x day.
Christina has 53 signatures as her starting point, and 3 signatures a day (x) as her rate. In slope-intercept (y = mx + b) form, this would be written y = 3x + 53, with y being the total number of signatures on x day.
To figure out how many days would it take to have the same amount of signatures, meaning the same y values, we have to set the equations equal to each other (bc each have the same y value as the other so they basically equal each other). That would mean:
6x + 26 = 3x + 53
To simplify this, get the numbers to one side and the xs to another by subtracting 3x and 26 from both sides. This would make it:
3x = 27, in which we can divide both sides by 3 to get x = 9. So the number of days after which they would have the same amount of signatures would be 9.
Now since we know the shared x value, we just plug it into one of the equations to get the resulting y value. I’ll pick Christina’s.
y = 6(9) + 26, which is 54 + 26, which is 80. So the number of signatures they both will have when they reach the same number is 80.
Hope this helps.
Michael buy a baket of mangoe on ale for \$ 4$4 before tax.
The ale tax i 12%.
What i the total price Michael pay for the baket of mangoe?
Answers
Total price paid by Michael for the basket of mangoes is $4.48.
For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -
Total price = 4 + 12%×4
Calculating the percentage of sales tax on Right Hand Side of the equation
Total price = 4 + 12×4/100
Solving the percentage part on Right Hand Side of the equation
Total price = 4 + 0.48
Performing addition on Right Hand Side of the equation
Total price = $4.48
Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.
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Learn more
At a restaurant, the bill comes to $70. If you decide to leave a 11% tip, how much is the tip? Give dollars and cents (like 1.23)
Answers
The tip is $7.70
10 Points! please help! There are 21 pieces of sports equipment at the gym. The ratio of volleyballs to handballs is 2 : 1 . How many volleyballs and handballs are at the gym?
Answers
Answer:
14 volleyballs and 7 handballs
Step-by-step explanation:
sum the parts of the ratio , 2 + 1 = 3 parts , then
21 ÷ 3 = 7 ← value of 1 part of the ratio , so
volleyballs = 2 × 7 = 14
handballs = 1 × 7 = 7
Answer:
Hey
volleyball = 14
Handball = 7
Step-by-step explanation:
21 pieces = 2:1n
step 1
Add the ratios together
21 = 3n
Step 2
divide both sides by 3
n = 21/3 = 7
where n = number of balls
volley ball = n × 2 = 7 × 2 = 14
handballs = n × 1 = 7 × 1 = 7
total = 21
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What i 464 divided by 60 with a remainder?
(trying to figure out how many hour i 464 minute)
Answers
When we divide the 464 by 60 we get the following remainder in our answer that is 44.
What do math remainders mean?The Remainder is the name for the value that is left behind after division. If an amount (reward) cannot be divided completely with another number, we are left with only a meaning (divisor). The remaining is the name for this amount. For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.
Briefing :7.733333333333333
=7 44/60 ⇔ 7 R 44
464 divided by 60
=7 with a remainder of 44
Here, we provide you the outcome of the dividing with remainder, often known as the Euclidean division, along with a brief explanation of the following terms:
464 divide by 60 yields a quotient and residual of 7 R 44.
464 is the dividend & 60 is the divisor; the division (numeric division) of 464/60 is 7; the remainder ("left over") is 44.
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Is y=4/x-3 linear or non-liner
Answers
Trust me it is
Using the net below, find the surface area
of the triangular prism.
20 cm
9 cm
8cm
6 cm
9 cm
20 cm
Surface Area = [?] cm²
Answers
Answer:
Get math teacher
Step-by-step explanation:
go talk to them.
During a flood, the water level in a river firt roe fater and fater, then roe more and more lowly until it reached it highet point, then went back down to it pre- flood level. Conider water depth a a function of time. (a) I the time of highet water level a critical point or an inflection point of thi function? (b) I the time when the water firt began to rie more lowly a critical point or an inflection point?
Answers
The time of highest water level is an inflection point of this functionand the time when the water first began to rise more slowly is a critical point of this function.
A critical point is a point on a graph at which the gradient of the graph (or the rate of change of the graph) is equal to zero. This means that the rate of change of the function at the critical point is neither increasing nor decreasing. An inflection point is a point on a graph at which the concavity of the graph changes. When the graph is concave up, the rate of change is increasing, and when the graph is concave down, the rate of change is decreasing.In the case of the rising and falling of a river during a flood, the time of highest water level is an inflection point because it marks the point at which the water level changes from rising to falling. The rate of change of the water level is increasing as it rises, and decreasing as it falls. At the time of highest water level, the rate of change is at a maximum and is equal to zero, making it an inflection point. The time when the water first began to rise more slowly is a critical point because it marks the highest point of the water level. The gradient of the graph at this point is equal to zero, making it a critical point.
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explain how regression toward the mean can describe two friends who have a fight then later go to the movies together.
Answers
Given the circumstances of the question, it is feasible that the two friends would feel that they overreacted during the argument, and as a result, they decide to see a movie together to make up for it.
Regression toward the mean is a statistical condition that involves events that the outcomes produce based solely on chance rather than on real facts. Therefore, it is impossible to forecast with precision what will happen in a regression towards the mean.
Example
Two military units are brought back, one with 20% casualties and the other with 50%. He compliments the first while criticizing the second. The two units return with the opposite outcomes the following time. He "learns" from this experience that praise reduces performance and berating strengthens it.
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State if the two triangles are congruent based on the given information. If they are, state
how you know (SSS, SAS, ASA, or HL). (2pts each)
Answers
By SAS congruence, the triangles LMO and LNO are concurrent.
What is congruent triangles?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.If two sides and the included angle of one triangle are congruent with two sides and the included angle of another, the two triangles are congruent.Here given,
LM ≅ ON
∠ M ≅ ∠ N
From the figure it is clear that, the side LO is shared by both triangles.
So, in the concurrency SAS, two sides of a triangle are equal, and an angle is equal.
As a result, the triangles LMO and LNO are congruent by SAS congruence if LM ≅ ON, ∠ M ≅ ∠ N .
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For the first 30 km, the bicyclist rode with a speed of v km/hour. For the remaining 17 km he rode with a speed which was 2 km/hour greater than his original speed. How much time did the bicyclist spend on the entire trip? Let t be the time (in hours), and find t in terms of v if v=15 and if v=18.
Answers
Answer:
t= 2.52 hours
Step-by-step explanation:
it is given that for first 30 km, the speed of bicyclist is v km/hour
time taken to cover first 30 km is given by
( )
for next 17 km the speed of bicyclist is 2 km/hour greater than his original speed
so the speed to cover next 17 km = v+2
time taken to cover next 17 km is given by
now total time t spent by the bicyclist to cover entire trip is given by
now if v=18 , we have
now to add fractions we make the denominator same
Hence we will find the LCM of 18 and 20
LCM of 18 and 20 = 180
now we need to make both the denominator equal to 180
hours (approx)
Hope it helps :) Make me as brainlest!
term to term rules: un+1=un^3+2
u0=-3
a)u1
b)u2
Answers
The first and the second terms of the recursive sequence are given as follows:
a) u(1) = -25.
b) u(2) = -15623.
How to solve the recursive sequence?The definition of the recursive sequence is presented as follows:
u(n + 1) = u(n)³ + 2.
The initial term is needed to solve the sequence, hence it is given as follows:
u(0) = -3.
Thus the term with index 1 is given as follows:
u(1) = u(0)³ + 2.
u(1) = -3³ + 2
u(1) = -27 + 2
u(1) = -25.
Considering the term with index 1, the term with index 2 is obtained as follows:
u(2) = u(1)³ + 2
u(2) = (-25)³ + 2
u(2) = -15623.
And then the same rule is obtained if needed to obtain the 3th, 4th terms, and so on, considering the previous term and the definition.
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Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
What conclusion can they reach based on the above output when they set the significance level to be 0.10?
a.The data does not provided statistical evidence that the average acrefeet from seeded clouds is more than 300.
b.The data does provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
c.The data does not provided statistical evidence that the sample average acrefeet from seeded clouds is more than 300.
d.Two of the above are correct.
e.We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme out
Answers
The conditions are not met by the extreme outliers, hence we are unable to draw inferences based on the statistical output presented above. So, option e is correct.
What is meant by null hypothesis?
The null hypothesis, often known as H₀, is the assertion that there is no difference between two sets of data or variables under analysis, or that there is no relationship between them. Because there is no underlying causative relationship, the null hypothesis holds that any experimentally detected difference is merely the result of chance; therefore, the name "null."
We can create a z-test hypothesis by assuming that the amount of rain produced by thunderheads follows a distribution that is nearly normal:
300 acre feet is the null hypothesis for the average quantity of rain that thunderheads produce on their own without fertilizing the clouds.
Alternative Hypothesis: The amount of rain that thunderheads often produce by seeding the clouds is greater than 300 acre feet.
This test has a right tail.
So, The conditions are not met by the extreme outliers, hence we are unable to draw inferences based on the statistical output presented above.
So, option e is correct.
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{(a^2-16)÷(a^2-25)}÷{(a^2-2a-8)÷(a^2+10a+25)}
Answers
The answer is -[tex]\frac{(a + 4) ( a +5) }{(a +2)( a - 5)}[/tex]
Simplify is making something simple. In mathematics, simplification means reducing the expression/ fraction/problem in a simpler form by using different operations.
In the process of simplification, some basic rules are needed to be used. The principle of BODMAS (B= Bracket, O = Of, D = Division, M = Multiplication, A = Addition, S = Subtraction)must be followed for solving the questions.
The equation is :
[tex]\frac{a^{2} - 16 }{ a^{2} - 25 }[/tex] ÷ [tex]\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}[/tex]
=[tex]\frac{a^{2} - 4^{2} }{a^{2} - 5^{2} }[/tex] ÷ [tex]\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}[/tex]
= [tex]\frac{ (a +4 ) ( a - 4 )}{ (a + 5) ( a - 5 )}[/tex] ÷ [tex]\frac{a^{2} - 4a + 2a - 8}{a^{2} + 5a + 5a + 25}[/tex] ( by applying middle term factor method)
(using [tex]a^{2} - b^{2}[/tex] formula )
= [tex]\frac{ (a+4) ( a-4 )}{(a +5 ) (a - 5)}[/tex] ÷ [tex]\frac{a(a -4) + 2 (a - 4)}{a (a + 5) + a (a + 5)}[/tex] ( by applying middle term factor method)
=[tex]\frac{( a + 4) ( a - 4)}{( a + 5) ( a - 5)}[/tex] ÷ [tex]\frac{(a + 2) ( a -4)}{( a +5) (a+5)}[/tex]
= [tex]\frac{( a +4)(a-4)}{(a + 5)(a - 5)\\}[/tex] * [tex]\frac{(a + 5) ( a + 5)}{(a + 2) ( a - 4)}[/tex]
=[tex]\frac{( a + 4) ( a + 5)}{(a + 2) ( a - 5)}[/tex]
so, the answer is - [tex]\frac{( a + 4 ) ( a +5) }{( a + 2) ( a - 5)}[/tex]
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