A farmer plants 7 1/5acres of green apples in his orchard. This makes up 3/8 of his entire orchard. How many acres make up the farmer's orchard?

A Farmer Plants 7 1/5acres Of Green Apples In His Orchard. This Makes Up 3/8 Of His Entire Orchard. How

Answers

Answer 1

The area, in acres, used to plant the green apples is

\(7\frac{1}{5}=7+\frac{1}{5}=\frac{5\cdot7+1}{5}=\frac{35+1}{5}=\frac{36}{5}\)

And this area corresponds to 3/8 of the entire orchard.

So, calling x the area of the entire orchard, we have the following proportion:

Area in acres Fraction of the orchard

36/5 3/8

x 1

Then, cross multiplying the above values, we obtain:

\(\begin{gathered} \frac{3}{8}x=\frac{36}{5} \\ \\ \frac{8}{3}\cdot\frac{3}{8}x=\frac{8}{3}\cdot\frac{36}{5} \\ \\ x=\frac{8}{5}\cdot\frac{36}{3} \\ \\ x=\frac{8}{5}\cdot12 \\ \\ x=\frac{96}{5} \\ \\ x=\frac{95}{5}+\frac{1}{5} \\ \\ x=19\frac{1}{5} \end{gathered}\)

Therefore, the area of the framer's orchard is 19 1/5 acres.


Related Questions

What is the y-intercept of the line describe by the equation below? Y=5x-22

Answers

Answer:

The y intercept is (0,-22)

Step-by-step explanation:

The y intercept is the value when x =0

Y=5x-22

y = 5*0 -22

y = -22

The y intercept is (0,-22)

Of the 32 students in Joe's class, 8 students ride their bikes to school, 5 walk to school, 4 get a ride to school in a car, and 15 take the bus to school. What is the experimental probability of choosing a student who walks to school?

Answers

The experimental probability of choosing a student who walks to school is given by 0.15625 or 15.625%.

Given data ,

The experimental probability of choosing a student who walks to school can be calculated by dividing the number of students who walk to school by the total number of students in Joe's class.

Number of students who walk to school = 5

Total number of students in the class = 32

Experimental probability = Number of students who walk to school / Total number of students

= 5 / 32

P = 0.15625

Hence , the experimental probability of choosing a student who walks is 0.15625 or 15.625%.

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paul is going to a college where tuition for one year is $14,200. He has a scholarship worth $1,500 and a grant worth $200. He earns $125 a week at this job how many weeks does paul need to work to pay 50% of the remaining tuition.

Answers

if paul is going to a college where tuition is 14,000 then that’s the answer but if he has a scholarship then you divide it then multiply it then there’s your answer

Answer:

50

Step-by-step explanation:

if you want an explanation just ask.

The 4th term of an AP is 6. If the sum of the 8th and 9th terms is -72, the com. mon difference is:​

Answers

Answer:

t(4) = 6 ---- a + 3d = 6

t(8) + t(9) = -72

a+7d + a+8d = -72

2a + 15d = -72

double the first equation

2a + 6d = 12

subtract them

9d = -84

d = -84/9 = -28/3

Step-by-step explanation:

mayas penny bank is 1/2 full. after she adds 120 pennies,it is 2/3 full. How,many pennis can mayas bank hold?

Answers

Answer:

720

Step-by-step explanation:

We are looking for the difference between 2/3 and 1/2, which we know to be 120. To subtract fractions of different denominators, we need to find the common denominator (this can be found by finding the LCM of both denominators)

120 = 2/3 - 1/2 = 4/6 - 3/6
1/6 = 120

We can multiply 120 by 6 to find the value of the full bank.

1/1 = 720

if the lengths of the legs of a right triangle are labelled x and y, and if its hypotenuse length is labelled z, then the pythagorean theorem states

Answers

The Pythagorean for the triangle with a length of two legs x and y and the hypotenuse length as z is z²=x²+y².

The perpendicular, base (adjacent), and hypotenuse (opposite) are the names of the triangle's three sides. Perpendicular forms a right angle with the triangle base. The hypotenuse is the greatest side opposing the right angle (90 degrees) of a triangle. According to the Pythagorean Theorem, the square of the length of the hypotenuse will always result from adding the squares of the lengths of two legs of a right-angle triangle.

Given the length of one leg is x and the length of another leg is y. The length of the hypotenuse is z. Then, by the Pythagorean Theorem, z²=x²+y².

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What is the circumstance of the circle

What is the circumstance of the circle
What is the circumstance of the circle

Answers

Answer:

8pi

Step-by-step explanation:

circumference of the circle=2 pi r(radius)

=2pi×d(diameter)/2

=2 × pi × 8/2

=8 pi cm

You are getting your carpet cleaned. You have three bedrooms (9x10’); 10x12 and 11x16), a living room (14’x16’) and dining room (14x14’ ) . Perfco Carpet Cleaning Co. charges $0.50/sq for carpet cleaning. What is your charge?

Answers

Answer:

Under 800 square feet of carpet to be cleaned: $0.53 per square foot

800 - 1,500 square feet: $0.49 per square foot

Over 1,500 square feet: $0.42 per square foot

Stairs (standard size): $4.16 each stair

There are 3 cats in the room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail.

Answers

Answer:

ok soooo whats the question like bruhhhhhh i here to anwser now tell me the question

Step-by-step explanation:

What is the distance between (-10,7) and (2,-9)

Answers

Answer:

20 (units)

Step-by-step explanation:

Sqrt of (x-x1)^2+(y-y1)^2

So define which coordinate is (x,y) and what (x1,y1)

I’m going to define (-10,-7) as (x,y) and (2,9) as (x1,y1)

So plug in your variables!

Sqrt(-10-2)^2+(-7-9)^2

Sqrt-12^2+-16^2

Sqrt144+256

Sqrt400

The distance would be 5,486 kilometers.

Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7

Answers

The steps Sergey could use to solve the quadratic equation by completing the square is 5(x2 + 4x) = –7

How to use the completing the square method?

We should know that in completing the square method both sides of the equation are made perfect squares.

The given equation is 5x²+20x-7=0

Solving this equation by completing the square method we have

5(x²+4x+4)=-7

This means that (x+2)=±√27/5

Simplifying further we have

5(x²+4x)=7

Then expanding to make ²HS a perfect square we have

5(x²+4x+4)=7+20

This means that 5(x²+4x)=-7

Therefore the step he could use is 5(x²+4x)=-7\

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true/false. given an int variable datum that has already been declared, write a statement that reads an integer value from standard input into this variable.

Answers

True.

Here's an example statement in Python that reads an integer variables from standard input and stores it in an existing integer variable called datum:

datum = int(input("Enter an integer value: "))

This statement first prompts the user to enter an integer value by printing the string "Enter an integer value: " to the console. The input() function then reads the user's input from the console as a string. Finally, the int() function converts the string to an integer and assigns the result to the datum variable.

Note that the specific syntax and function calls may vary depending on the programming language being used, but the general concept of reading an integer value from standard input into an existing variable is applicable to most programming languages.

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PLZ HELP !!!

Find the value of X.

PLZ HELP !!!Find the value of X.

Answers

9514 1404 393

Answer:

  60°

Step-by-step explanation:

The sum of angles in a quadrilateral is 360°. The interior angle adjacent to x will have measure 180°-x. So, the equation can be written ...

  100° +50° +90° +(180° -x°) = 360°

  420° -x° = 360° . . . . simplify

  x = 420 -360 . . . . . . divide by °, add x-360

  x = 60

A chemical company makes two brands of antifreeze. The first brand is 40% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 180 gallons of a mixture that contains 55% pure antifreeze, how many gallons of each brand of antifreeze must be used?

First brand =
Second Brand=

Answers

Answer:

Step-by-step explanation:

Let x be the portion of 60%

180 - x is the portion of 40%

0.60x + 0.40(180 - x) = 0.55(180)

0.60x + 72 - 0.40x = 99

0.20x = 27

x = 135

180 - 135 = 45

First brand = 45 gallons of 40%

Second Brand = 135 gallons of 60%

Pls answer correctly I’ll give you brainliest

Pls answer correctly Ill give you brainliest

Answers

Answer:

Step-by-step explanation:

y=mx+b

so inset the first point into the equation

-3 for x and 7 for y.

7=m(-3)+b

y=mx+b

1 for x and -1 for y

-1=m(1)+b

now put them together and solve for m and b.

-1=m+b

7=-3m+b

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

-1-b=m

7=-3m+b

inset m into the equation

7=-3(-1-b)+b

7=3+3b+b

4=4b

b=1

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

insert b back in for -1=m+b

-1=m+1

m=-2

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

Now insert it back into y=mx+b

y=(-2)x+1

so this line contains those points that were given

Hope this helps :)

Diane, Sam, and Boris served a total of 54 orders Monday at the school cafeteria. Diane served 6 fewer orders than Sam. Boris served 2 times as
many orders as Sam. How many orders did they each serve?
Number of orders Diane served:
Number of orders Sam served:
Number of orders Boris served:

Answers

Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

5 2/5 divided by 3/2

Answers

Answer:

5 2/5 ÷ 3/2 = 3.6

I hope this is right

what is the perimeter of a rectangular whose area is 92 square mm and length is 11.5 mm​

Answers

We are given

Area of rectangular is = 92 square mmLength of rectangular is = 11.5 mm

We are asked to find out the value of perimeter of the rectangular! Let's find it's breadth first!

We know that–

\(\qquad\)\( \purple{\bf\longrightarrow Area_{(Rectangular)} = Length \times Breadth} \)

\(\qquad\)\( \sf \longrightarrow 92 = 11.5 \times Breadth \)

\(\qquad\)\( \sf \longrightarrow Breadth = \cancel{\dfrac{92}{11.5}}\)

\(\qquad\)\( \purple{\bf \longrightarrow Breadth = 8 \: mm}\)

Now, Perimeter of rectangular –

\(\qquad\)\( \pink{\bf \longrightarrow Perimeter _{(Rectangular) } = 2( Length + Breadth) }\)

\(\qquad\)\( \sf \longrightarrow Perimeter _{(Rectangular) }= 2( 11.5 +8) \)

\(\qquad\)\( \sf \longrightarrow Perimeter _{(Rectangular) } = 2 \times 19.5\)

\(\qquad\)\(\pink{ \bf \longrightarrow Perimeter _{(Rectangular) } = 39\: mm}\)

Henceforth, Perimeter of rectangular is 39mm.

_______________________________________

Answer:

Perimeter = 39 mm

Step-by-step explanation:

In this question we are given with ,

Area of rectangle = 92 sq mm

Length of rectangle = 11.5 mm

And we're asked to find the perimeter of rectangle .

Solution : -

We know that ,

\( \pink{ \boxed{\sf{Area \: of \: rectangle = L × W}}}\)

Where ,

L = length of rectangle

W = width of rectangle

So from this formula we can find the width of rectangle and equating it with 92 ( because 92 is the given area ) . Substituting value of length :

\( \longmapsto \: 11.5 \times W = 92\)

Step 1 : Multiplying 11.5 and W :

\( \longmapsto \: 11.5W = 92\)

Step 2 : Dividing by 11.5 on both side :

\( \longmapsto \: \frac{ \cancel{11.5}W}{ \cancel{ 11.5}} = \frac{92}{11.5} \)

On further calculations we get :

\( \longmapsto \: W = \cancel{\frac{920}{115} }\)

Step 3 : By cancelling 920 by 115 we get :

\( \longmapsto \: \purple{\boxed{ \bold{W = 8 \: mm}}}\)

Therefore , width of rectangle is 8 mm .

Finding Perimeter :

We know that ,

\( \blue{ \boxed{ \sf{Perimeter \: of \: rectangle = 2 ( L +W )}}}\)

Where ,

L = Length of rectangle

W = Width of rectangle

Substituting values in formula :

\( \longrightarrow \: 2(11.5 + 8)\)

Step 1 : Solving parenthesis :

\( \longrightarrow \: 2(19.5)\)

Step 2 : Multiplying 2 with 19.5 :

\( \longrightarrow \: \green{\boxed{ \bold{39 \: mm}}}\)

Therefore, perimeter of rectangle is 39 mm.

#Keep Learning

the perimeter of rectangle math is 297 cm. the ratio of the length to width is 3:8. what is the width of the rectangle?

Answers

Answer:

Width = 108 cm

Step-by-step explanation:

Perimeter =  2 x (length + width)

297 = 2 x (length + width)

148.5 = Length + width

Ratio of Length to Width = 3 : 8

Sum of ratio = 11

\(Length = \frac{3}{11} \times 148.5 = 40.5 \ cm\\\\Width = \frac{8}{11} \times 148.5 = 108 \ cm\)

What is the answer help

What is the answer help

Answers

Answer: 162°

Step-by-step explanation:

To find the answer to this question, we need to find what 45% of 360 degrees (a circle) is.

First, a percent divided by 100 becomes a decimal.

       45% / 100 = 0.45

Next, "of" means multiplication in mathematics.

       0.45 * 360 = 162

The central angle will be 162°.

the bakers want to sell their house for 145,500.After 2 months,the bakers decided to mark down the price of their house 8% to sell more quickly. How much are the bakers selling their house for now?

Answers

Answer:

133,860

Step-by-step explanation:

The baker was going to sell his house for 145,500 but he found that no one came to buy, so he decreased the amount by "8%".

* No we have our key elements:

- Starting amount = 145,500

- Rate of change = 8%

* We will get the "8%" of the number 145,500

- Firstly, "8%" means 8/100

- So, 0.08 will be our new rate of change.

* 145,500 will be multiplied by 0.08 to find the final answer because when we talk about the percentage of a number, we are going to talk about a part of it.

- 145,500 × 0.08 = 133,860 ; the same as

145,500 × 8/100 = 133,860

HELP HELP HELP help help

HELP HELP HELP help help

Answers

Answer:

C

Step-by-step explanation:

Gina and Marty are selling tickets for the school dance. On Monday, they sold 15 tickets, on Tuesday 23, on Wednesday 20, and on Thursday 32. What was their average daily income if each ticket cost $2.00?

Answers

Answer:

$45

Step-by-step explanation:

15×2=30

23×2=46

20×2=40

32×2=64

30+46+40+64=180

180÷4=45

Average=45

Answer:

Their average daily income would be 45 dollars a day.

Step-by-step explanation:

To solve this, add the 15 tickets, 23, 20, and 32 tickets from Monday to Thursday. This should get you a total of 90 tickets. Since each ticket cost 2 dollars, multiply the 90 by 2. This should get you 180. TO find the average, you must divide the total(180) by the amount of days(4) that passed. This should get you 45.

Answer:

45$

The figure above shows a store's supply-demand graph for coffee makers. If the store sells $600 worth of coffee makers, which of the following is a valid possible price for them?

A. $15

B. $30

C. $40

D. $55

The figure above shows a store's supply-demand graph for coffee makers. If the store sells $600 worth

Answers

The possible price for the items if the store sells $600 is (c) $40

How to determine the possible price for the items?

From the question, we have the following parameters that can be used in our computation:

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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Bean Seed Growth Temp 25 20 15 10 Days S 7 9 If the trend continues, how many days will it take at 10 degrees?​

Bean Seed Growth Temp 25 20 15 10 Days S 7 9 If the trend continues, how many days will it take at 10

Answers

The needed number of days at 10 degrees is given as follows:

11 days.

How to define a linear function?

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

m is the slope.b is the intercept.

For this problem, we have that when x decreases by 5, y increases by 2, hence the slope m is given as follows:

m = -2/5

m = -0.4.

Hence the time needed for a temperature of 10 degrees is given as follows:

9 + 2 = 11 days.

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If the mean of x, x + 2, x + 4, x + 6, x + 8 is 11, find the value of x​

Answers

Answer:

x=7

Step-by-step explanation:

Answer:

Your answer is.....

x= 7

Mark it as brainlist answer . follow me for more answer.

Step-by-step explanation:

can someone help please

can someone help please

Answers

The slope of the line is 2.

Describe Slope?

Slope is a measure of the steepness of a line or a surface. In geometry and mathematics, slope refers to the rate at which a line rises or falls as it moves horizontally. It is calculated as the ratio of the vertical change between two points on a line (the rise) to the horizontal change between those same two points (the run).

The slope of a line can be expressed as a fraction or a decimal. A positive slope indicates that the line is increasing as it moves from left to right, while a negative slope indicates that the line is decreasing as it moves from left to right. A slope of zero indicates a horizontal line, and a slope that is undefined indicates a vertical line.

In real-world applications, slope is used in a variety of fields, such as physics, engineering, and architecture. For example, slope is used to calculate the angle of a roof or a ramp, the rate of change in the value of a stock or a commodity, or the rate of change of a moving object. Understanding slope is an important concept in mathematics and has many practical applications in the real world.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Here, the given two points are (0, 2) and (-1, 0). Substituting these values into the slope formula, we get:

m = (0 - 2) / (-1 - 0) = (-2) / (-1) = 2

Therefore, the slope of the line is 2.

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At which angle will the hexagon rotate onto itself?
60
90°
120°
180°

At which angle will the hexagon rotate onto itself?6090120180

Answers

Answer:

120 i think im pretty good a geometry

Find non-invertible matrices A,B such that A+B is invertible. Choose A,B so that (1) neither is a diagonal matrix and (2) A,B are not scalar multiples of each other.A = [_____ _____][_____ _____]B = [_____ _____][_____ _____]

Answers

Matrices A and B are non-invertible matrices that can be added together to form an invertible matrix. To find these matrices, we can use the following steps:

Step 1: Choose a matrix A that is not a diagonal matrix and is not invertible. One example of such a matrix is

\(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\)

Step 2: Choose a matrix B that is not a diagonal matrix, is not invertible, and is not a scalar multiple of matrix A. One example of such a matrix is
\(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\)


Step 3: Add the matrices A and B together to form the matrix A+B. This matrix will be invertible, as shown below:

\(A+B = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]+\left[\begin{array}{ccc}0&0\\1&1\end{array}\right]=\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\)

Step 4: Verify that the matrix A+B is invertible by finding its determinant. The determinant of a 2x2 matrix is given by:

det(A+B) = (1)(1) - (1)(1) = 0



Since the determinant of the matrix A+B is not equal to zero, the matrix is invertible.

Therefore, the matrices \(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\) and \(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\) are non-invertible matrices that can be added together to form an invertible matrix \(A+B =\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\).

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Let u = ⟨–2, –3⟩ and v = ⟨3, –1⟩. Which graph shows u – v?

Answers

A) The first graph

Correct on Edge

Let u = 2, 3 and v = 3, 1. Which graph shows u v?
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Is in-house production associated with the Fordist or Post-Fordist period? the automatic system of the duplex mind makes use of a series of mental shortcuts in order to obtain quick information about the likelihood of different outcomes. these shortcuts are known as . 20 cm3 of 1m ba(oh)2 solution and 80cm3 of 0.2m hcl solution are mixed together. the concentration of h+ in the final solution what was the significance of mount olympus to the ancient greeks? Q.3 Answer the following questions in detail.1. Give information about qualitative changes in population?2. Why is the human resource considered as the most important resource for anation? students who are interested in fitness-, health-, or therapy-related careers can increase their professional marketability by _____. please helpppppp !!! He represented Massachusetts and the interest of the North. The writer is considering changing the method of development used in sentences 4 and 5 (reproduced below) to provide a clearer line of reasoning for the audience.The discovery was remarkable not only because of the cheeses age and well-preserved state, but because of a new protein analysis performed on the cheese by chemist Enrico Greco at the University of Catania in Italy. This cutting-edge analysis allowed Dr. Greco to unlock the cheeses contents and reveal new insights into life in ancient Egypt.Should the writer use a different method of development in sentences 4 and 5 ? Rewrite the sentence with an indirect object pronoun. J'cris souvent mon cousin. Jan Hunt was a football coach at the University of Oklahoma. Hunt attended an invitational secondary school track meet that his son was participating in. Sometime in the afternoon, Hunt laid down on a row of bleachers to sunbathe while waiting for his sons next event. Nearby, Geoff a member of the board of directors of Eagle Resources Company (Eagle), told his spouse that he wanted to dispose of or liquidate Eagle, that several companies were bidding on Eagle, and that an announcement of a "possible" liquidation of Eagle might occur the following week. Geoff told this to his spouse in the context of his anticipated business schedule the following week in order to make necessary childcare arrangements.Unbeknownst to Geoff, Hunt overheard the conversation about Eagle. After the track meet, Hunt purchased Eagle stock based on the overheard information. The Securities and Exchange Commission (SEC) learned of the trades and filed an action against Hunt claiming that he committed insider trading.Geoff would be treated as an outsider in regard to Eagle and possessed a fiduciary duty to the company. 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Assume that Geoff and Hunt were close friends, and Geoff told Hunt about the pending liquidation of Eagle in exchange for 50% of the profits that Hunt made from the trade. In this case, Geoff is likely be found guilty of insider trading because Geoff did breach a duty not to disclose inside information. The disclosure was made for Geoff personal benefit. Hunt is likely to be found guilty of insider trading. A court would likely find that Hunt knew or should have known about the breach of duty by Geoff and also received personal gain.Are bolded words correct? A 19-year old marine was brought to the infirmary after passing out during basic training. He had repeatedly complained of severe weakness, dizziness, and sleepiness during the preceding 4 weeks of boot camp. In a previous episode 3 weeks earlier, he had drowsiness and generalized tiredness, and was brought to the infirmary, where after IV administration of saline, he was returned to duty with the diagnosis of dehydration. Upon questioning, he reported unquenchable thirst, and the repeated need to urinate. Although he ate all of his rations as well as whatever he could get from his fellow trainees, he had lost 19 pounds. (Baseline body weight was 150 pounds, height 5'8"). On the last day, he complained of vague abdominal pain, which was worse on the morning of admission. He had vomited once. During examination, he was oriented but tachypneic. He appeared pale, dehydrated with dry mucous membranes, and poor skin turgor. His respiratory rate was 36/minute with deep, laborious breathing; his heart rate was 138/minute regular, and his blood pressure was 90/60. His chest was clear, heart tones were normal. There was an ill-defined generalized abdominal tenderness, which was otherwise soft to palpation and showed no rebound. There was a generalized muscular hypotonia; his deep tendon reflexes were present but very weak. Laboratory, on admission, showed glucose of 560 mg/dl, sodium 154, potassium 6.5, pH 7.25, bicarbonate 10 mM/liter, chloride 90, BUN 38 mg/dl, creatinine 2.5 mg/dl. (Normal values: glucose, 70-114 mg/dl; Na = 136-146; K, 3.5-5.3; Cl, 98-108; CO2, 20-32 [all in mM/l]; BUN, 7-22mg/dl; creatinine, 0.7-1.5 mg/dl). A urine sample was 4+ for glucose and had "large" acetone. HbA1c was 14% (n=4-6.2%). Serum acetone was 4+ undiluted, and still positive at the 4th dilution. Beta-Hydroxybutyrate level was 20 millimols/liter (normal=0.0-0.3 mM/l).He was treated with insulin and saline I.V. By the 4th hour of treatment, potassium chloride was added to the IV at a rate of 15 mEq/hour. Sixteen hours later, he was active, alert, well hydrated and cheerful, indicating he felt extremely well. He requested that his IV be discontinued. His physician decided to switch his insulin to subcutaneous injections and to start a liquid diet. He was later put on a diabetes maintenance diet and treated with one injection of Human Lente insulin in the morning. Although his blood sugars the next morning were 100-140 mg/dl, he had frequent episodes of hypoglycemia during the day, and his HbA1c was 9%. Eventually, he was put on 3 injections of regular insulin/day, and a bedtime intermediate duration (Lente) insulin.Questions1.Why did the patient improve after being given IV saline in his first admission?2. Why was dyspnea his presenting symptom?3. He was hyperkalemic on admission, and yet, why was potassium later added to the IV infusion?4. What is the possible reason why a single injection of insulin in the morning failed to control his diabetes without causing hypoglycemia? The brightness of certain stars can fluctuate over time. Suppose that the brightness of one such star is given by the following function. B (t) = 11.3 -1.8 sin 0.25t In this equation, B (t) represents What is the first term of the series?a1 =Answer each question about the followinggeometric series10k-1S10 = 32k-1How many terms are in the series?COMPLETE3(2): -What is the last term of the series?a1 =1DONE2910COMPLETE Why were the colonist not concerned with separating church and state? Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.Does the table show a probability distribution? Select all that apply.Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Multiply using cancellation:2/50 x 5/18 =3/4 x 4/9 =7/8 x 2/5 = HELP PLEASE!!!!!! What should a group do before a discussion takes place? A characteristic of reconciled data that means the data reflect an enterprise-wide view is:_________ a. detailed. b. comprehensive. c. normalized. d. historical. Select all that apply.The early Muslims greatly advanced knowledge in _____.mathematicsmedicineastronomywarfarelinguistics