write 36 as a product of its prime factor writethe factor in order from smalest to largest

Answers

Answer 1

The factors of 36 are 2×2×3×3

Order from smallest to largest: 2×2×3×3


Related Questions

Two numbers are selected randomly from the set s={1,2,3,4,5,6} without replacement one by one the probability that minimum of the two numbers is less than 4 is

Answers

Less than 4=1,2,3
Therefore 3/6 = 1/2

12 The price of a house is originally listed at $120,000. The owners are having a hard time selling it and decide to reduce the price to $110,400 What is the percentage decrease of the price of the house?​

Answers

Answer:

I think its 4% but I might be wrong so sorry if I am.

Original price of the house = $ 245000
Due to problems in selling, the price was reduced to = $203350
Hence, the reduced amount is =
=
Percentage decrease =

= =17%
Hence, the decrease percentage of the house is 17%.

non-normality of the residuals from a regression can best be detected by looking at the residual plots against the fitted y values.truefalse

Answers

The statement that non-normality of the residuals from a regression can best be detected by looking at the residual plots against the fitted y values is a false statement.

We have a statement and we need to find out if it is true. A negative residual indicates that the model did not fit. This means that the error produced by the model is not the same between variables and observations (that is error is not random). The content is not regular, that is, the content is distributed regularly and we can conclude that the linear model is the appropriate model. If the subject sees a curvilinear pattern such as a U-shaped pattern, we can conclude that a linear pattern is not suitable and a non-linear pattern would be better. These charts are useful for identifying inconsistencies, inconsistencies in error variance, and inconsistencies. Two well-known tests for normality of residues are the Kolmogorov Smirnov test and the Shapiro-Wilk test. So, residual plot can't be used to check the non-normality of the residuals from a regression. Therefore, it is false statement.

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How many degrees is 2/9 of a semicircle?

Answers

A semicircle is just half of a circle. A circle is 360 degrees, so a semicircle would be 180 degrees. Therefore,

180 * (2/9) = 40 degrees.

Hope this helps!

A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn.

a. What is the probability of selecting a purple marble and then a white marble?

b. What is the probability of selecting two white marbles?

c. Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work.

Answers

Answer:

Step-by-step explanation:

a. The probability of selecting a purple marble on the first draw is 7/9. Since the marble is not replaced, there are 6 purple marbles and 1 white marble left in the bag. The probability of selecting a white marble on the second draw is 2/7. Therefore, the probability of selecting a purple marble and then a white marble is (7/9) * (2/7) = 2/9.

b. The probability of selecting a white marble on the first draw is 2/9. Since the marble is not replaced, there is only 1 white marble left in the bag. The probability of selecting a white marble on the second draw is 1/8. Therefore, the probability of selecting two white marbles is (2/9) * (1/8) = 1/36.

c. To compare the probability of selecting two white marbles in a row and two purple marbles in a row, we need to calculate the probabilities of each event separately. The probability of selecting two white marbles in a row is 1/36, as calculated in part (b).

The probability of selecting two purple marbles in a row is (7/9) * (6/8) = 21/36, since there are 7 purple marbles and 9 total marbles on the first draw, and then 6 purple marbles and 8 total marbles on the second draw (assuming the first marble was not replaced).

Therefore, there is a greater chance of selecting two purple marbles in a row than two white marbles in a row.

Hope this helped!

Please help me with this. It's worth 100 points. Questions are in the picture

Please help me with this. It's worth 100 points. Questions are in the picture

Answers

Answer:

it c

Step-by-step explanation:

it well retun but it L to q but P in the way so that answer wod be c

∂²p/∂r² + 1/r ∂p/∂r = ϕμC/k ∂p/∂t
derivation of equations
1-partial derivative diffusivity equation spherical flow
2- partial derivative diffusivity equation hemi- spherical flow

Answers

The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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Isaac and his wife received an award of $ 9,000 each for their work as researchers.
Isaac invests his money and earns 9% annual simple interest while his wife invests it at 9% compound interest per year. How much more money did Isaac's wife make than Isaac after 10 years?

F $5,500.00
G $3,455.50
H $4,206.30
J $4,998.50

Answers

Answer:

H

Step-by-step explanation:

I don't know if I did it wrong because I got 4,206.27 but I probably did

A glue company needs to make some glue that it can sell for $120 per barrel. It wants to use 150 barrels of glue worth $100 per barrel, along with some glue worth $150 per barrel and glue worth $190 per barrel. It must use the same number of barrels of $150 and S190 glue. How much of the $150 and $190 glue will be needed? How many barrels of $120 glue will be produced

Answers

4860 i think that is the answer

if x=0 & y=3x+3 what is y

Answers

Step-by-step explanation:

Put ' 0 ' where 'x' is and solve:

y = 3(0) + 3 = 3

Find the difference.

Find the difference.

Answers

Answer:

\(t^{4}\) + 8\(t^{2}\) + 8t - 12

Hope this helps!

Step-by-step explanation:

\(t^{4}\) - 1.5\(t^{2}\) + t - 12 + 9.5\(t^{2}\) + 7t : Combine like terms

\(t^{4}\) + ( 9.5 - 1.5 )\(t^{2}\) + ( 7t + t ) - 12

\(t^{4}\) + 8\(t^{2}\) + 8t - 12

Find the value of x. Round to the nearest tenth. 19 20°

Answers

The value of x is approximately 9.8.

In this question, we are given an equation, and we need to find the value of x in the equation.

The equation that is given to us is as follows: 19 cos 20° + x = 29

To find the value of x, we need to isolate it on one side of the equation.

First, we will subtract 19 cos 20° from both sides of the equation.

This gives us: x = 29 - 19 cos 20°Now we can use a calculator to evaluate the right-hand side of the equation.

Rounding to the nearest tenth, we get: x ≈ 9.8

Therefore, the value of x is approximately 9.8.

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20. Q(-1, 4), R(-1, -9), S(11, -2), T(11, 6)
Parallel
Perpendicular
Neither

Please help fast must be turned in in 3 hours!

20. Q(-1, 4), R(-1, -9), S(11, -2), T(11, 6)ParallelPerpendicularNeitherPlease help fast must be turned

Answers

Answer:

Parallel

Step-by-step explanation:

QR and ST both parallel to y axis.

The lines are parallel each other. Therefore, option A is the correct answer.

The given coordinate points are Q(-1, 4), R(-1, -9), S(11, -2), T(11, 6).

What is the graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

After plotting the given points on the graph, we can see that the lines are parallel to each other.

The lines are parallel each other. Therefore, option A is the correct answer.

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20. Q(-1, 4), R(-1, -9), S(11, -2), T(11, 6)ParallelPerpendicularNeitherPlease help fast must be turned

A simple difference is also called a.an interaction effect. b.a marginal means difference. c.a factorial design. d.a main effect.

Answers

A simple difference is also called a marginal means difference. Option B

In experimental design and statistical analysis, a simple difference refers to the comparison of means between two groups or conditions. It represents the difference in average scores or values between the groups being compared. It is often used to assess the impact of an independent variable on a dependent variable by examining the variation in means between different levels of the independent variable.

The term "marginal means difference" emphasizes that the comparison is based on the average or marginal means of the groups being compared. It helps to distinguish it from other types of differences, such as interaction effects or main effects, which involve more complex comparisons or analyses in factorial designs.

Overall, a simple difference or marginal means difference is a straightforward way to evaluate the effect of an independent variable on a dependent variable by comparing the average values between different groups or conditions.

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If the vertex of a parabola is (3,5), what is the symmetry

Answers

Answer:

axis of symmtery: x = 3 or h = 3

Step-by-step explanation:

The vertex (h, k) of a parabola is the point wherein the graph intersects the axis of symmetry—the imaginary straight line that bisects a parabola into two symmetrical parts, where x = h.

In the standard form of quadratic equation, y =  ax² + bx + c, the equation of the axis of symmetry is:  \(x = \frac{-b}{2a}\).In the vertex form of the quadratic equation, y = a(x - h)² + k, the equation of the axis of symmetry is:  \(h = \frac{-b}{2a}\).

Regardless of whether the quadratic equation is in standard or vertex form, the x-coordinate (h) of the vertex determines the axis of symmtetry, hence, x = h.

Therefore, given that the vertex of a parabola is at point (3, 5), then it means that the axis of symmetry occurs at x = 3 or h = 3.      

According to a study, 90 % of adult smokers started smoking before 21 years old. 14 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.

Round all of your final answers to four decimal places.

1. The probability that at least 5 of them started smoking before 21 years of age is
2. The probability that at most 11 of them started smoking before 21 years of age is
3. The probability that exactly 13 of them started smoking before 21 years of age is

Answers

The probability that at least 5 of them started smoking before 21 years of age is 0.9997.2. The probability that at most 11 of them started smoking before 21 years of age is 0.9982.3. The probability that exactly 13 of them started smoking before 21 years of age is 0.000006.

(1) The probability that at least 5 of them started smoking before 21 years of age isThe probability of at least 5 smokers out of 14 to start smoking before 21 is the probability of 5 or more smokers out of 14 smokers who started smoking before 21.  Using the complement rule to find this probability: 1-P(X≤4) =1-0.0003

=0.9997Therefore, the probability that at least 5 of them started smoking before 21 years of age is 0.9997.

(2) The probability that at most 11 of them started smoking before 21 years of age isThe probability of at most 11 smokers out of 14 to start smoking before 21 is the probability of 11 or fewer smokers out of 14 smokers who started smoking before 21. Using the cumulative distribution function of the binomial distribution, we have:P(X ≤ 11) = binomcdf(14,0.9,11)

=0.9982

Therefore, the probability that at most 11 of them started smoking before 21 years of age is 0.9982.(3) The probability that exactly 13 of them started smoking before 21 years of age isThe probability of exactly 13 smokers out of 14 to start smoking before 21 is:P(X = 13)

= binompdf(14,0.9,13)

=0.000006Therefore, the probability that exactly 13 of them started smoking before 21 years of age is 0.000006.

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What is the value of X? (giving brainliest and thanks to all!)

What is the value of X? (giving brainliest and thanks to all!)

Answers

Answer:

I believe it is A

Step-by-step explanation:

I dont quite remember the formula, but I belive that 30 would be correct because if im remembering correctly the formulas are "a + b = c" and "c - (a/b) = (a/b)

a/b = a or b, depending what they give you

Answer:

45°

Step-by-step explanation:

This is a isosceles triangle and also a right triangle, so it means it have an 90° ingernal angle and the other two internal angles have the same value. Remember that the sum of the internal angles of a triangle is always 180°, so:

180° -90° = 90°

90°/2 = 45°

In ΔSTU, s=97, u=32 and ∠V=10° find all possible values of ∠S to the nearest 10th of a degree.​

Answers

Answer:

a

Step-by-step explanation:

a

Answer:

31.8, 148.2

Step-by-step explanation:

dont do 31.08, i tried and it marked me wrong :(

A 1.0 l buffer solution is 0.15 m in hcn and 0.10 m in nacn. which action will destroy the buffer?

Answers

The buffer will probably be destroyed by the addition of HCN.

What is buffer solution?

A weak acid and the conjugate base of the weak acid, or a weak base and the conjugate acid of the weak base, are combined to form the buffer solution, a water-based solvent solution. They withstand being diluted or having modest amounts of acid or alkali added to them without changing their pH.

Given that a 1.0 l buffer solution is 0.15 m in HCN and 0.10 m in NaCN.

We need to find a action which one destroy the buffer solution.

buffer is a substance made of salt and a weak acid that is beneficial. From the aforementioned chemicals, HCN is a potent acid and NaCN is a salt between HF and NaCN. Therefore, the buffer will probably be destroyed by the addition of HCN.

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The number of hours slept at night is related to the number of minutes spent exercising that day. A collection of data on the number of minutes spent exercising, x, and the number of hours slept, y, is shown in the table.

x 30 37 40 45 52 55 61 65 71 76
y 6.25 6 6.5 7 6.5 7.25 7.5 8 8.65 8.5
Which linear equation best models the relationship between x and y?

The number of hours slept at night is related to the number of minutes spent exercising that day. A collection

Answers

Answer:

the answer is A

Step-by-step explanation:

took the test

a bar chart might be used for

Answers

When presenting chunks of information, bar charts should be used. As long as there aren't too many categories to contrast, vertical bar charts can be useful for comparing several discrete or categorical variables, such as age groups, courses, and schools. For time series data, they are also highly beneficial.

Why would one use a bar chart?

To show a frequency distribution for qualitative data, bar charts are frequently employed.

                   The axis used to measure the bars should always begin at zero, unless there is a valid reason for doing otherwise.

                  Otherwise, the axis can be stretched to magnify differences in the lengths of the bars. A title and the axis labels are required for bar charts.

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A rigid motion of the Euclidean plane E is a bijection from E to itself which preserves distances: if f: EE is a rigid motion, then
dist (f(P), f(Q)) = dist (P, Q) for all P, Q € E.
Show that the set of all rigid motions forms a group under function composition.

Answers

The set of all rigid motions forms a group under function composition. This means that it satisfies the four group axioms: closure, associativity, the existence of an identity element, and the existence of inverses.

Each rigid motion is a bijection from the Euclidean plane to itself, preserving distances. Function composition of rigid motions results in another rigid motion, demonstrating closure. The associativity of function composition follows from the associativity of composition in general. The identity element is the identity function, which does not alter the position of any point. Finally, the inverse of a rigid motion is another rigid motion that undoes the transformation. Therefore, the set of all rigid motions forms a group.

To prove that the set of all rigid motions forms a group, we need to demonstrate that it satisfies the four group axioms. Firstly, let f and g be two rigid motions. Since rigid motions preserve distances, the composition of f and g will also preserve distances, showing closure.

Secondly, function composition is associative, meaning that (f ∘ g) ∘ h = f ∘ (g ∘ h) for any three rigid motions f, g, and h. This follows from the associativity of composition in general.

Thirdly, the identity element of the group is the identity function, which leaves every point unchanged. Composing any rigid motion with the identity function will result in the same rigid motion, satisfying the identity axiom.

Finally, for every rigid motion f, there exists an inverse rigid motion denoted as f^(-1). This inverse function undoes the transformation performed by f, preserving distances. Composing f with its inverse or the inverse with f will yield the identity function.

Since the set of all rigid motions satisfies all four group axioms, it forms a group under function composition.

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x -57=207 please help ​

Answers

Answer:

264

Step-by-step explanation:

if you take away 57 from 264 you get 207

so x is 264

Line C has a slope of -8/3. Line D is parallel to line C. what is the slope of line C?

Answers

Since line C has a slope of -8/3 and line D is parallel to line C, the slope of line C is equal to -8/3.

What is the point-slope form?

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

m represents the slope.x and y represents the data points.

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂

This ultimately implies that, the slope of the two lines are equal and the same:

Slope of line C = Slope of line D

-8/3 = -8/3.

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please answer for brainliest

please answer for brainliest

Answers

Answer:

B

Step-by-step explanation:

abs value of -9 is still 9, so it should be "="

what is the probability that a month starting with a vowel is drown​

Answers

There are 12 months in a year.
3 out of the 12 start with a vowel: April, August, and October.
Probability can be calculated by taking
# of desired outcomes/total # of outcomes
So, the chance of randomly selecting a month that starts with a vowel is 3/12, or 1/4, which is 0.25 or 25%.

A man takes a renovation loan of $28 800 for 4 years at 3.75% per annum. (a) Find the simple interest payable. (b) Find the monthly repayment.​

Answers

To find the simple interest payable, we can use the formula:

Simple Interest = Principal × Rate × Time

where:

Principal = $28,800

Rate = 3.75% per annum (expressed as a decimal, so 3.75% = 0.0375)

Time = 4 years

(a) The simple interest payable is $4,320.

Simple Interest payable:

Simple Interest = $28,800 × 0.0375 × 4

Simple Interest = $4,320

Therefore, the simple interest payable is $4,320.

(b) The monthly repayment amount is approximately $690.

To find the monthly repayment, we need to calculate the total amount to be repaid and then divide it by the number of months in the loan term.

Total amount to be repaid = Principal + Simple Interest

Total amount to be repaid = $28,800 + $4,320

Total amount to be repaid = $33,120

The loan term is 4 years, which is equivalent to 4 × 12 = 48 months.

Monthly repayment = Total amount to be repaid / Number of months

Monthly repayment = $33,120 / 48

Monthly repayment ≈ $690

Therefore, the monthly repayment amount is approximately $690.

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Residents in a city are charged for water usage every three months. the water bill is computed from a common fee,
along with the amount of water the customers use. the last water bills for 40 residents from two different
neighborhoods are displayed in the histograms.

Answers

The interval that contains the median water bill is D: $200 - $225.

The data in tabular form is as follows: ata  :

Class interval ------- Frequency -------- Cummulative frequency

100 to 125, ----------- 1 --------------------1

125 to 150 -----------2--------------------3

150 to 175----------- 5 --------------------8

175 to 200----------- 10 ------------------18

200 to 225-----------13------------------ 31

225 to 250 ------------8 -----------------40

Median class = Cumulative frequency / 2

Cumulative frequency= 40

So

Median class = 40 / 2

Median class = 20

The class interval containing the 20th frequency is "200 - 225"

Therefore it is concluded that the interval which contains the median water bill is $200 - $225.

"

Complete question

A histogram titled Neighborhood Monthly water bill has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8.

Which interval contains the median water bill?

$150–$175

$175–$200

$200–$225

$225–$250

"

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find the. change in temperature or elevation from -2°c to 13°v​

Answers

Answer:

I'm pretty sure it's -15

Step-by-step explanation:




A solid shape is made from centimetre cubes.


Here are the plan, side elevation and


Centimetre cubes are added to


front elevation of the shape.


make this cuboid.


Plan Side elevation Front elevation


40


4 cm


3 cm


How many cubes are added?


Write your final answer as,... cubes are added.​

Answers

Answer:

30 cubes are added

Step-by-step explanation:

The image of the solid shape is attached.

From the Plan, Side elevation and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks is needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.

The number of blocks needed to make the cuboid = 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added = 48 cubes - 18 cubes = 30 cubes.

30 cubes are added

A solid shape is made from centimetre cubes.Here are the plan, side elevation andCentimetre cubes are

The number of cubes that are added is 30.

What is Cube?

A cube's form is occasionally referred to as "cubic." Another way to put it is that a block with uniform length, width, and height is regarded to be a cube. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an equilateral cuboid, and a square parallelepiped. One of the platonic solids, the cube is a convex polyhedron with all of its faces being square. The cube has either cubical symmetry or octahedral symmetry. The square prism is a specific instance of a cube.

From the Plan, Side elevation, and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks are needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.

The number of blocks needed to make the cuboid

= 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added

= 48 cubes - 18 cubes

= 30 cubes.

30 cubes are added.

Hence, The number of cubes that are added is 30.

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if brody fails to achieve control over urination beyond the "normal" age for attaining bladder control, he may have __________. Which of the following inferences about Huck is best supported by his interactions with Miss Watson in Paragraph 7?A. Huck has a crush on Miss Watson and will do what she says.B. Huck is more receptive to Miss Watsons religion lessons than he is Widow Douglass.C. Huck is only misbehaving for Miss Watson because he imitates Tom.D. Huck knows that to get along in the house, he will have to keep some of his own feelings to himself. How do structural differences between starch and cellulose lead to functional differences in plants? you implement a plug-in that formats five columns when saving a record. editing and saving records is significantly slower after implementing the plug-in. you need to troubleshoot the plug-in. which tool should you use? 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We have come to dedicate a portion of that field as a final resting-place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. But in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow this ground. The brave men, living and dead who struggled here have consecrated it far above our poor power to add or detract. The world will little note nor long remember what we say here, but it can never forget what they did here. It is for us the living rather to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us-that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion-that we here highly resolve that these dead shall not have died in vain, that this nation under God shall have a new birth of freedom, and that government of the people, by the people, for the people shall not perish from the earth."What is the best summary of the events described in the speech's first two sentences? (5 points)A massive battle was fought on the site of the speech, and many thousands of soldiers died.Many years ago people came together to form a nation, and now a war takes place there.The founders of the nation could not agree on how to best organize it, so war began.The speaker and listeners have decided to gather on this site to honor the memory of others. identify all of the data dependencies in the following code. which dependencies are data hazardsthat will be resolved via forwarding? which dependencies are data hazards that will cause a stall? s1: add $3, $4, $6 s2: sub $5, $3, $2 s3: lw $7, 100($5) s4: add $8, $7, $2 Which property is not used to simplify the following expression?(x+2)-5-7 = 5(x + 2) -7== (5x + 10) 7= 5x + (10 7=5x+3O commutative property of additionO commutative property of multiplicationassociative property of additionOO distributive property What is a theme? The life lesson the author teaches through the story The decision the character makes to succeed in life The person who works against the protagonist The problems that occur throughout a piece of fiction Identify whether the verb is finite or non finite. State the type of non finite word used. 1. She sings beautifully.2. They were running in the park.3. The dog loves chasing squirrels4. The students are studying for their exams.5. He wants to eat pizza for dinner.6. I have never seen such a beautiful sunset. 7. The athlete ran the marathon in record time.8. He decided to study engineering in college.9.The broken vase lay on the floor.10. Skiing down the mountain was an exhilarating experience.11. Writing poetry is his passion.12. We decided to take a vacation in Hawaii.13. The frightened dog ran away from the thunderstorm.14. The fried chicken smelled delicious.15. Learning a new language can be challenging but rewarding. Drag each expression to the correct location on the table.Match each expression to its simplified form. Consider the function f(x) = x1/3(x + 2)2/3 whose domain is ([infinity], [infinity]).(a)Find the intervals on which f is increasing. (Enter your answer as a comma-separated list of intervals.)_______Find the intervals on which f is decreasing. (Enter your answer as a comma-separated list of intervals.)______(b)Find the open intervals on which f is concave up. (Enter your answer as a comma-separated list of intervals.)_____Find the open intervals on which f is concave down. (Enter your answer as a comma-separated list of intervals.)____(c)Find the local extreme values of f. (Round your answers to three decimal places.)local minimum value _____local maximum value _____(d)Find the global extreme values of f on the closed, bounded interval [3, 2].(Round your answers to three decimal places.)global minimum value ______global maximum value ______ To convert a Celsius temperature, C, to a Kelvin temperature, K, add 273.15 to the Celsius temperature. What is -16C in degrees Kelvin? Imagine that you were to conduct an experiment by placing an aluminum wire into a solution of nickel chloride: 2 Al(s) + 3NiCl2(aq) What are the products of this reaction? A. AlCl3(aq) + Ni(s) B. 2 Al(s) + 3 Ni(s) + 3 Cl2(g)D. No reaction occurs, so there are no products. E. 2A1C13(aq) + 3 Ni(s)