Help soon would be greatly appreciated

The Kimbroughs'
home has a replacement value
of $82,700. They are insuring it for 80% of the
replacement cost.
a. What is the amount of insurance?
b. What is the amount of coverage for
personal property?
c. What is the amount of coverage
for loss of use?
d. What is the amount of coverage for the garage?

Help Soon Would Be Greatly Appreciated The Kimbroughs'home Has A Replacement Valueof $82,700. They Are

Answers

Answer 1

According to the information the amount of insurance would be $66,160, the amount of coverage for personal property would be $41,350, the amount of coverage for loss of use would be $16,540 and the amount of coverage for garage would be $8,270.

How to calculate the amount of each insurance?

To calculate the amount of each insurance we have to take into account the main value ($82,700) and the percentage of each insurance. Then, we have to calculate every percentage value as shown.

A. What is the amount of unsurance?$82,700 / 100 = 827827 * 80% = $66,160

B. What is the amount of coverage for persona property?$82,700 / 100 = 827827 * 59% = $41,350

C. What is the amount of coverage for loss of use?$82,700 / 100 = 827827 * 20% = $16,540

D. What is the amount of coverage for the garage?$82,700 / 100 = 827827 * 10% = $8,270

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Related Questions

Simplify and state restrictions
5x³3y² ÷ 27x × 9xy ÷ 25x²y²

Answers

The simplified form of the expression 5x³3y² ÷ 27x × 9xy ÷ 25x²y² is

[1/15(xy)³] and  (x, y) ≠ 0.

What is a numerical expression?

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Given, An expression 5x³3y² ÷ 27x × 9xy ÷ 25x²y².

= 5x³3y² ÷ 243x⁴y³ ÷ 25x²y².

=  5x³3y² ÷ 25x²y² ÷ 243x⁴y³.

= (3/5)x ÷ 243x⁴y³.

= (3/5)x/(243x⁴y³).

= (3/5)/(243x³y³).

= 1/(81×5x³y³).

= [1/15(xy)³].

The restriction should be x and y can not be equal to zero as it would make the expression undefined.

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A netball court measures 31 metres long and 15 metres wide.
What is the perimeter of a netball court?

Answers

The perimeter of the netball court is equal to 92 meters.

What does perimeter mean?

The whole distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's boundary or outline.

A netball court is a rectangle,

it is given that length of the net ball court is equal to 31 meters.

The width of the netball court is equal to 15 meters.

Therefore the perimeter of the netball court is equal to the length of all sides of the rectangle.

Perimeter of netball court = 2(31+15)=92 meters.

Therefore perimeter of the netball court is equal to 92 meters.

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The length of the life an instrument produced by a machine has a normal distribution with mean life of 12 months and standard deviation of 2 months.

What is the probability if X assumes a value greater than 12 months?

Answers

Probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%

If the length of the life of an instrument produced by the machine has a normal distribution with a mean of 12 months and a standard deviation of 2 months, then the random variable X representing the length of the life of the instrument is also normally distributed.

To find the probability that X assumes a value greater than 12 months, we need to use the cumulative distribution function (CDF) of the normal distribution. The CDF is given by the formula:

F(x) = (1/2) * [1 + erf((x - μ) / (σ * sqrt(2)))]

where μ is the mean, σ is the standard deviation, and erf(z) is the error function.

Plugging in the given values, we get:

F(12) = (1/2) * [1 + erf((12 - 12) / (2 * sqrt(2)))] = (1/2) * [1 + erf(0)] = (1/2) * [1 + 0] = 1/2

Since the CDF gives us the probability that X assumes a value less or equal than x, we need to subtract F(12) from 1:

P(X > 12) = 1 - F(12) = 1 - 1/2 = 0.5

So the probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%.

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Slope intercept form

Answers

Answer:

The formula for finding Slope Intercept Form is y = mx + b.

Step-by-step explanation:

Y - Y coordinate

M - Slope

X - X coordinate

B - Y Intercept

This formula is used for finding the equation of a line.

Sean bakes 18 dozen chocolate cupcakes and 13 dozen vanilla cupcakes. About how many cupcakes did Sean bake? EXPLAIN now!!!

Answers

Sean baked 372 cupcakes in total.

What is multiplication?

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Sean bakes 18 dozen chocolate cupcakes,

and 13 dozen vanilla cupcakes.

There are 12 cupcakes in one dozen.

To find the number of cupcakes:

Using multiplication operation,

18 x 12 = 216.

13 x 12 = 156.

The number of cupcakes = number of chocolate cupcakes + number of vanilla cupcakes.

The number of cupcakes = 216 + 156

The number of cupcakes = 372

Therefore, the number of cupcakes are 372.

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Sound waves can be ranked by their intensity, I, given in this formula, where r is the distance from the source of a sound with a power output of P.

[tex]P = 4xr^{2} .[/tex]

Which equation correctly rewrites the formula to solve for I?

A. [tex]I = \frac{P}{4xr^{2} }[/tex]
B. [tex]I = \frac{Pxr^{2} }{4}[/tex]
C. [tex]I = 4Pxr^{2}[/tex]
D. [tex]I = \frac{4P}{xr^{2} }[/tex]

Answers

Answer: C correctly rewrites the formula to solve I

Step-by-step explanation:

help me pls i need it fastest for my math project !!!!!! please help

Answers

Part A

g(x) = 9.25x

g(8) = 9.25*8

g(8) = 74

He would make $74 before taxes if he worked 8 hours.

------------------------------------------------------

Part B

g(x) = 9.25x

g(14) = 9.25*14

g(14) = 129.50

He would make $129.50 before taxes if he worked 14 hours.

------------------------------------------------------

Part C

g(x) = 9.25x

g(27.5) = 9.25*27.5

g(27.5) = 254.375

g(27.5) = 254.38

He would make $254.38 before taxes if he worked 27.5 hours.

Answer:

Solution below.

Step-by-step explanation:

Solution

This question is basically asking you to substitute corresponding x values to find g(x).

Given the function from the question:

g(x) = 9.25x where x is the work hours and g(x) is the wages.

Given x = 8,

g(8) = 9.25 * 8 = $74.00

Given x = 14,

g(14) = 9.25 * 14 = $129.50

Given x = 27.5,

g(27.5) = 9.25 * 27.5 = $254.38 (rounded off to nearest cent)

Identify the domain and range of the following relation.

x y
-2 -4
1 3
0 0
1 4
4 6
-1 -2

Answers

Answer:

domain = - 2, 1, 0, 1, 4, - 1

range = - 4, 3, 0, 4, 6, - 2

Step-by-step explanation:

x is domain

y is range

.
For the following data set, find Q1, Q2, Q3 and the interquartile range.

15, 12, 23, 15, 7, 8, 21, 10, 12, 14, 16, 24, 19
1.
Interquartile Range
2.
Q3
3.
Q2
4.
Q1
a.
15
b.
9
c.
20
d.
11

Answers

Answer:

To find Q1, Q2, Q3, and the interquartile range (IQR) of a data set, we need to first arrange the data in numerical order. For the given data set, the ordered data is:

7, 8, 10, 12, 12, 14, 15, 15, 16, 19, 21, 23, 24

To find Q1, we need to find the median (Q2) of the lower half of the data. The lower half of the data is:

7, 8, 10, 12, 12, 14

There are 6 values in the lower half of the data, so the median (Q2) is the average of the 3rd and 4th values, which is (10 + 12) / 2 = 11. Therefore, Q1 = 11.

To find Q3, we need to find the median (Q2) of the upper half of the data. The upper half of the data is:

15, 15, 16, 19, 21, 23, 24

There are 7 values in the upper half of the data, so the median (Q2) is the fourth value, which is 19. Therefore, Q3 = 19.

To find the IQR, we need to subtract Q1 from Q3. The IQR is equal to Q3 - Q1 = 19 - 11 = 8.

The correct answers are:

1.  Interquartile Range = 8

2.  Q3 = 19

3.  Q2 = 11

4.  Q1 = 8

Therefore, the correct answer choices are:

a. 15 (incorrect)

b. 9 (incorrect)

c. 20 (incorrect)

d. 11 (correct)

A 50 Gram Sample of a substance that used to treat thyroid disorders has a K-value of 0.1113. What is the half life? thanks

Answers

The half life of the iodine is obtained as 6.2 s.

What is the half life?

Let us recall that the half  life would be the time that is taken for about half of the original radioactive isotope that remains in the sample, to become depleted in the thyroid treatment.

Given that we have the fact that the decay constant that we have in the process is given as 0.1113 in the question and we know that;

Half life = 0.693/K

Half life = 0.693/0.1113

Half life = 6.2 s

It would have the half life about 6.2 s.

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For the question below, think carefully about what you divide 80 by to calculate the value of one part.

In a housing estate the direct proportion of flats to houses is 2:5. If there are 80 flats, how many houses are there?

Answers

Answer:

200

Step-by-step explanation:

[tex]\frac{2}{5}[/tex] = [tex]\frac{80}{x}[/tex]

2 x 40 = 80, so

5 x 40 = 200

Answer:

200 houses

Step-by-step explanation:

Flat: 2 parts = 80 flats
1 part => 80 : 2 = 40 flats
Houses: 5 parts = 40 x 5 = 200 houses

Find the value of x.

Answers

Answer:

76 don't know how to explain it

your answer should be 121.

when finding the exterior angle, a good thing to keep in mind would be the exterior angle theorem: m<1 = m<2 + m<3z

if you are given the measurements of the angles INSIDE the triangle, it would equal the exterior angle.

hope this helped!

Helpp!! Solve the system by graphing.

Answers

Answer is no solutions

Step by step

y = 2x +2
y = 2x -2

these two equations have the same slope (2) with different y intercepts (2 and -2) so they are parallel lines. Since the lines are parallel, the pair of equations have no solution.

For what values of k are the graphs of 8y=4x+3 and 4y=k(x+5) parallel? perpendicular?

parallel k= __
perpendicular k= __

Answers

The values of k for parallel and perpendicular in the equations 8y=4x+3 and 4y=k(x+5) are 7/12 and 1/21, respectively.

what is slope ?

A line's slope determines how steep it is. A mathematical expression for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two points. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is used to represent it. The y-intercept is located at a point where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).

given

for parallel their slope will be equal

y1= 1x/2 + 3/8 .... eq1

y2= kx/4 + 5k/4  ..... eq2

y1 = y2

1x/2 + 3/8 = kx/4 + 5k/4

1/2 + 3/8 = k/4 + 5k/4

7/8 = 6k/4

k = 7/12

for perpendicular product of their slope is 1

y1 * y2 = 1

1x/2 + 3/8 * kx/4 + 5k/4 = 1

1/2 + 3/8 * k/4 + 5k/4 = 1

k = 1/21

so The values of k for parallel and perpendicular in the equations 8y=4x+3 and 4y=k(x+5) are 7/12 and 1/21, respectively.

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Simplify each expression (I don't know this) please help me out

Answers

Answer: solve the same variables

Step-by-step explanation:

1. 3y + 4.1

2. 4x +

3. 5x + 22½

4. 4y²

5. + 25

6. 0



PLEASE HURRY
In triangle LMN, m∠L = (4c + 53)°. If the exterior angle to ∠L measures 87°, determine the value of c.

c = 87
c = 8.5
c = 35
c = 10

Answers

Therefore , the solution of the given problem of trigonometry comes out to be c =6.

Explain trigonometry.

Trigonometry is a discipline of mathematics that examines relationships between triangles' angles and sides. Trigonometry is used frequently in geometry because every straight-sided form may be broken down into a group of triangles. Trigonometry and other areas of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, have a staggering amount of interrelationships.

Here,

Given :

In triangle LMN,

m∠L = (4c + 53)°.

∠L  = 87°

To find the value of c:

87° =  (4c + 53)°

=> 4c = 87-53

=> 4c = 24

=> c =6

Therefore , the solution of the given problem of trigonometry comes out to be c =6.

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Which of the following is a true proportion of the figure based on the triangle proportionality theorem?

Answers

Answer: [tex]\frac{c}{d} = \frac{a}{b}[/tex]

Step-by-step explanation:

By the given figure, the triangle's sides appear congruent. By the Segment Addition Postulate:

RT + TQ = RQ and

RU + US = RS

Substitute this with the given variables.

c + d = RQ

a + b = RS

From this, we can create the following proportion:

[tex]\frac{c}{d} = \frac{a}{b}[/tex]

A box holds 2 Pens, 2 Pencils And one highliter
Tim Picks 1 item, A pen, And does not return it to the box. He then Picks a second item
what is the
Probability that the second item
IS A Pencil ?

Answers

When a box contains 2 pens, 2 pencils, and 1 highliter, there is a 50% chance that the second item is a pencil.

what is probability ?

Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a comprehensive set of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.

given

according to the question , the probability is a

2 / 1+2+1 * 100 %

2/4 *100%

= 50 %

after picking out a pen , the remaining are 1 pen , 2 pencils and 1 highlighter . in total of 4 items , 2 items are pencil .

When a box contains 2 pens, 2 pencils, and 1 highliter, there is a 50% chance that the second item is a pencil.

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Simplify. Negative square root of 16y^2 if y<0

Answers

Answer:

The square root means that IF you square the square root, you will get the original number. Thus, 16 squared = 256 and y^2 squared = (y^2)(y^2) = y^4

Step-by-step explanation:

a funeral
(since the element in the domain is repeated.
1) {(-1, 8), (0, 15), (1,-4), (2, 0)} 2) {(-5,2), (5,2), (0, -3), (3,-8)} 3) {(-2, 7), (6, 2), (-2,-3), (0, 9)}
it is a function
because there is not any
Points which have the
X-Coordinate and differen
y-Coordinates.
4) {(7,2), (4,-6), (2,-2), (4, -9)} 5) {(2, 3), (2, 4), (2, 5), (2,6)}
Practice: Determining if a Relation is a Function the Siven
6) {(1,-4), (2,-4), (3,-4), (4-4)}

Answers

2) {(-5,2), (5,2), (0, -3), (3,-8)} is a function.

3) {(-2, 7), (6, 2), (-2,-3), (0, 9)} is not a function.

4) {(7,2), (4,-6), (2,-2), (4, -9)} is not a function.

5) {(2, 3), (2, 4), (2, 5), (2,6)} is not a function.

6) {(1,-4), (2,-4), (3,-4), (4-4)} is a many to one function.

What is a function?

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is a function if it is one-to-one and many-to-one.

But a function can not be one to many means the same value of x can not lead to different values of y.

2) {(- 5, 2), (5, 2), (0, -3), (3,- 8)} is a fuction as different values of x leads to different values of y.

3) {(-2, 7), (6, 2), (-2,-3), (0, 9)} is not a function as the input - 2 leads to two different outputs 7 and - 3.

4) {(7, 2), (4, -6), (2, -2), (4, -9)} is also not a function as input 4 leads to two different outputs - 6 and - 9.

5) {(2, 3), (2, 4), (2, 5), (2,6)} is not a function as input 2 leads to different outputs.

6) {(1, - 4), (2, - 4), (3, - 4), (4, - 4)} is a function and it is a many-one function.

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Which integer in the set has the greatest value (7, -7, -3, 3)?
A. -7
B. -3
C. 3
D. 7

Answers

Answer:

-3

Step-by-step explanation:

i hope this helps

suppose that a randomly generated list of numbers from 0 to 9 is being used to simlulate an event that has a probability of success of 30% which of these groups of numbers could represent a success

Answers

Any event for which, the 3 numbers between 0 and 9 are outcomes could represent the success.

What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Given is that suppose that a randomly generated list of numbers from 0 to 9 is being used to simulate an event that has a probability of success of 30%.

For the success rate of 30%, this means the probability of that specific event would be 0.3.

So any event for which, the 3 numbers between 0 and 9 are outcomes or are the number of favorable events could represent the success.  

Therefore, any event for which, the 3 numbers between 0 and 9 are outcomes could represent the success.  

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please help me with this

Answers

Answer: 630

Step-by-step explanation:

Evaluate 9du when d=10 and u=7

⇒9du

input the values of d and u

⇒9 (10)(7)

⇒9 × 10 × 7

⇒630 answer.

hope that helps...

Answer:

630

Step-by-step explanation:

as the problem shows that the variable for d = 10, and u = 7.

it asked to solve 9du (or 9 × d × u )

we can plug in the numbers into the variables:

9 × 10 × 7

9 × 10 = 90 × 7 = 630

3 increased by a
number times 2

Answers

Wait so 3 increased by a number times

3^2 • 2?
Answer: 3+2n

Increase means addition, so 3 increased by a number times (x) 2 is 3+2n, where n=number

If these two shapes are similar, what is the measure of the missing length j?

Answers

Answer:

45ft is the missing length j.

X
Let f(x) = 3x2 - 6x + 2. Find f(2)
A
B
10
16
C 12
E
D 2
8

Answers

On solving the provided question, we can say that -  f(x) = 3x2 - 6x + 2, and the value of the equation f(x) = +2

What is equation?

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

f(x) = 3x2 - 6x + 2

x = 1

f(x) = +2

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In 2014 a company had a profit of $420000. In 2019 it reported a profit of $1400000.
Find the average rate of change of its profit for that period, expressed in dollars per year.

Answers

The change in profit from 2014 to 2019 is $1400000 - $420000 = $980000.

The time period is 2019 - 2014 = 5 years.

Therefore, the average rate of change in the company's profit is $980000 / 5 years = $<<980000/5=196000>>196000 per year.

Fill in the blanks below in order to justify whether or not the mapping shown represents a function. Set A 5 0 7 Set B -2 9 -1 -3 The mapping diagram above a function since in where there .

Answers

The mapping does not represents a function

How to identify a function?

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

In this case, for the mapping represent a function, every element in set A must be mapped to exactly one element in set B.

Since there is more than one arrow from set A (5) pointing to different values in set B (-2 and 9), then it is not a function. Also, the two different value (5 and 7) in set A has the same value (-2) in set B.

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Question 4
Solve the equation x² - 4x+6=0 by completing the square.
BIUX² X₂ 15px help!!p

Answers

The solution of the equation x² - 4x + 6 = 0 using completing the square is x = 2 ± √(-2)

What is an equation?

An equation is used to show the relationship between numbers and variables.

Polynomial can be classified based on degree of two as a quadratic equation.

Given the equation:

x² - 4x + 6 = 0

Solving using completing the square method:

subtract 6 from both sides:

x² - 4x = -6

add to both sides the square of half the coefficient of x:

x² - 4x + 4 = -6 + 4

(x - 2)² = -2

Taking square root of both sides:

x - 2 = ±√(-2)

x = 2 ± √(-2)

The solution is x = 2 ± √(-2)

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the students in Mr Marcos art class use six jars of paint for their project each student uses 2/3 jars of paint how many students were in Mr Marco's class​

Answers

The number of students that were in Mr Marco's class will be 9 students

How to illustrate the fraction?

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Here, the students in Mr Marcos art class use six jars of paint for their project each student uses 2/3 jars of paint

The number of students that were in Mr Marco's class will be:

= 6 ÷ 2/3

= 6 × 3/2

= 9 students

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Other Questions
What did the Romantics believe about love? How many cm is meter stick? Briefly explain ONE specific example of the impact of a labor organization during the period from 1865 to 1900. 400 people are asked if they drink tea. [tex]\frac{7}{10}[/tex] say Yes and 20% of the people who say Yes drink at least 3 cups each day.I really need help on a) Complete the frequency tree, I don't know how to work that one out. How do you tell if a set of ordered pairs satisfies an exponential function? For a loan of. 8,75,000 how much interet will be charged by the bank for 2month if the rate i 4. 75% per year? what is the answer for -40= -50 + x ? Why does Tommy defend Ms.ferenczi Evidence A nurse is caring for an infant with a tentative diagnosis of hypertrophic pyloric stenosis (HPS). What is most important for the nurse to assess Name a skill that you know now and can do smoothly that you couldn't do when you were born.How does your brain look different from when you were born, when you were learning that skill, and now?Share the most important thing you learned from Dr. Merzenich. Why is this learning important to you?What is something that you would like to learn?How would learning a new skill improve your life?HELP ME PLS, I BEG YOU GUYS I NEED IT The human brain differs from the brains of most other animals by the relative amount of brain mass devoted to which of the following Carefully feel the sides of the flask. Is the crystallization of sodium acetate endothermic or exothermic? How do you know? What are assets List 3 examples? Two different Drosophila flies (fruit flies), fly A and fly B. are shown below. Classify each phrase or term as applying to fly A only, fly B only, or both fly A and fly B. The term "Hox genes" applies to clusters of homeotic genes found in many different animals, including fruit flies. After segmentation genes have established the body segments. Hox genes trigger the development of segment-specific body structures in the correct locations. The temperature of the water in a hot water tank is recorded at 15 minute intervals after the heater is switched on. \begin{matrix} \text{Time (x minutes)} & \text{15} & \text{30} & \text{45} & \text{60} & \text{75} & \text{90}\\ \text{Temperature} (y ^\circ C) & \text{20} & \text{30} & \text{40} & \text{50} & \text{60} & \text{70}\\ \end{matrix} Time (x minutes) Temperature(y C) 15 20 30 30 45 40 60 50 75 60 90 70 a. Plot a graph of these data on your GDC. b. Find the linear model, T(x), for the temperature of the liquid with respect to time. c. Find the temperature of the water after 85 minutes. A scientist did a test to compare two substances: substance Q and substance R. At room temperature, both substances are liquid. When the scientist transferred the same amount of energy out of both substances, only one substance changed phase while the other did not. Which substance changed phase, and how did it change? A chemist is studying the composition of a sample of ocean water. He gently heats the sample to evaporate the water, leaving him with the solid substances that had been dissolved in the sample. Next, he performs a series of procedures to separate the solid substances from each other. Finally, he measures how much of each solid he has obtained. What substance would he probably have the most of Which of the following is the most accurate statement about the impact of business on society?a. Businesses often improve the quality of life, but can do little to improve the standard of living of most people due to inflation.b. When businesses earn a profit for their owners, they usually do so at the expense of the rest of society, which proves it is never a win-win situation.c. While businesses often improve the standard of living within a society, they can do little to improve the quality of life.d. Businesses can have a positive impact on both the standard of living and the quality of life within a society. For the reaction H2(g) + Cl2(g) 2HCl(g), Kc = 1.22 1033 at a temperature of 301 K. What is Kp at this temperature? A) 1.22 1033 B) 3.01 1034 C) 4.93 1031 D) 7.43 1035 E) 2.00 1030 3. YOUR DRRM teacher asked a speech on prepare during pandemic. how and what you to deliver