\(216^{\frac{2}{3}}=?\) A.36 B.6 C.108 D.12

Answers

Answer 1

Answer:

36

Step-by-step explanation:

(216) ^ (2/3)

Rewriting 216 as 6^3

(6^3) ^ (2/3)

We know that a^ b^c = a^ (b*c)

6 ^ (3*2/3)

6^2

36

Answer 2
the answer is A which is 36

Related Questions

Explain how to solve 5x2-3x = 25 by completing the square. What are the solutions?

Answers

Answer:

x= 3 +√509/10

Or

x= 3 - √509/10

Step-by-step explanation:

Given:

5x2-3x = 25

Using completing the square method of solving quadratic equation

Step 1: Factor out the coefficient of the x^2 term.

5(x^2 - 3x/5) = 25

Step 2: Add a number that would complete the square inside the parenthesis and also add this to the other side of the equation.

Take (1/2) of (3/5)

1/2 × 3/5

= 3/10

Square 3/10

We have, 9/100

We have,

5(x^2 - 3x/5 + 9/100) = 25 + 9/100

Step 3: Simplify

x^2 - (3/5)x + 9/100 = 25 + 9/100

5(x^2 - 3x/5 + 9/100) = 5 + 9/20

Step 4:

factor the right side

(x - 3/10)^2 = 509/100

Take both roots

√ (x - 3/10)^2 = √509/100

x - 3/10 = ±√ [509/100]

x = [ 3 ±√509 ] / 10

x= 3+√509/10

Or

x= 3 - √509/10

You're going to multiply 5 times 2
= 10
then it will be 10-3x=25
move the 10 to the other side
which will be
-3x=25-10 note when moving it to the other side the signs change meaning it'll be negative
25-10=15
-3x =15
then ur going to divide -3 divided by -3 cancelled each other out and 15divided by-3 which gives u
-5
your answer will be
x= -5

GUYS PLEASE HELP WILL MARK BRAINLIEST

Answers

Answer:

14 yards²

Step-by-step explanation:

To find the area of this complex shape, we can break it down into two parts.

I've broken it down into the left shape (with side lengths of 2, 2, 4 and 4) and the right shape (with side lengths of 2, 2, 2 and 3).

Looking at the shape on the left, the width is 4 yards and the length is 2 yards. Multiplying these numbers will get the area for that shape.

[tex]2\cdot4=8[/tex] yards².

Now in the right shape, the length is 3 and the width is 2, so:

[tex]3\cdot2=6[/tex] yards².

Now we can add both of these to get the total area of the figure.

[tex]6+8=14[/tex] yards².

Hope this helped!

Answer:

14 yds^2

Step-by-step explanation:

We can split this into two rectangles

There is a vertical rectangle on the left, 4 yds by 2 yds

The area is 4*2 = 8 yd^2

There is a horizontal rectangle on the right  3 yds by 2 yds

The area is 3*2 = 6 yd ^2

Add the areas together

8+6 = 14

jodi has $8,525 in her savings account earning 1.8% annually. how much is in jodi’s account after 8 years? round answer to the nearest cent.

Answers

Answer: $32,207,620.36

Step-by-step explanation:

What you need to do is use the formula A = P(1+r)^n

A = Your answer

P = Is the amount Jodi started with.

R = Is the annual interest

N = Number of years

Then plug in your numbers. Always make sure you use PEMDAS. This means parenthesis, exponents, multiplication, division, addition, and subtraction. You always start with the things in the parenthesis and go on down the list. Once you finish the (1 + (1.8)) = 2.8 you will have. A = 8,535 (2.8)^8. You then multiply 2.8 with the exponent 8. Then multiply 8,535 and your answer for 2.8 times 8 and you get your answer.

Good luck on other questions kid

I’m pretty sure the answer is 9,752.6

PLEASE HELP!! URGENT

A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° Use the
information provided and the diagram below to determine the height of the tree. Round to the nearest
whole foot.
532 it
256 ft
479 ft
231 ft
13672 ft
< Previous
Next >

Answers

Answer:

The answer is option 1.

Step-by-step explanation:

You have to apply Tangent Rule, tanθ = opposite/adjacent. Then, you have to substitute the following values into the formula :

[tex]tan(θ) = \frac{oppo.}{adj.} [/tex]

[tex]let \: θ = 25.7 \: , \: oppo. = h \: , \: adj. = 532[/tex]

[tex] \tan(25.7) = \frac{h}{532} [/tex]

[tex]532 \tan(25.7) = h[/tex]

[tex]h = 256 \: feet \: (3s.f)[/tex]

The value of height of tree is,

⇒ h = 256 feet

We have to given that,

A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° .

Hence, By given figure we get;

By using trigonometry formula, we get;

⇒ tan 25.7° = Opposite / Adjacent

⇒ tan 25.7° = h / 532

⇒ 0.4812 = h / 532

⇒ h = 0.4812 × 532

⇒ h = 256 feet

Therefore, The value of height of tree is,

⇒ h = 256 feet

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A bag contains red, white, and blue marbles. If 1/4 of the marbles are red and 2/3
of the marbles are white, what fractional part of the marbles are blue?

Answers

Answer: 1/12

Step-by-step explanation: 1/4=3/12. 2/3=8/12. 3/12+8/12=11/12. The remaining 1/12 is blue.

1/12 find the greatest common denominator

The t distribution approaches the _______________ distribution as the sample size ___________.

Answers

Answer:

Normal; increases.

Step-by-step explanation:

In Statistics and probability, a student t-distribution also known as the t-distribution refers to the continuous probability distribution which can be used to estimate population parameters when the population variance or standard deviation is not known (unknown) and the sample population is relatively small. The student t-distribution is a statistical distribution which was published in 1908 by William Sealy Gosset.

The t-distribution approaches the normal distribution as the sample size increases because the parameters becomes negligibly smaller.

This ultimately implies that, when the degree of freedom of a t-distribution curve is increased in comparison with that of a normal distribution, the value of probability becomes significantly similar.

Normal; increases!!!

this is a calculus question.
The volume of a cube increases at a constant rate of 10 cm^3 per second. find the rate of change in its total surface area at the instant when its when its sides are 20 cm long.

Answers

Answer:

2 cm^2/sec

Step-by-step explanation:

side of cube ---- x cm

volume = x^3

d(volume)/dt = 3x^2 dx/dt

when c = 20, d(volume)/dt = 10 cm^3/sec

10 = 3(20^2) dx/dt

dx/dt = 10/1200 = 1/120 cm/sec

Surface area = SA = 6x^2

d(SA)/dt = 12x dx/dt

so when x = 20, as above

d(SA)/dt = 12(20)(1/120) cm^2/sec

= 2 cm^2/sec

In a certain country, the heights and depths of a road are measured in relation to sea level. Sea level has a value of 0. The lowest point of the country lies at −8 feet. The highest point of the country lies at +107 feet. Which of the following statements best describes the lowest and the highest points?

The lowest point is 8 feet above sea level, and the highest point is 107 feet below sea level.

The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.

The lowest point is 8 feet below sea level, and the highest point is 107 feet above the lowest point.

The lowest point is 8 feet above sea level, and the highest point is 107 feet below the lowest point.

Answers

A negative value would mean it is below sea level. A positive value would be above sea level.

-8 is 8 feet below sea level

+107 is 107 feet above sea level.

The answer Is:

The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.

Answer:

Step-by-step explanation:

The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.  

Evaluate 3a2 + 4b2 for a =
2 and b = 3.
O
168
48
O
36

Answers

Answer:

48

Step-by-step explanation:

a=2

b=3

3a^2+4b^2

3(2)^2+4(3)^2

3(2)(2)+4(3)(3)

3(4)+4(9)

12+36

48

Hope this helps ;) ❤❤❤

48 done hope this helps

colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?

Answers

Answer: 24

Step-by-step explanation:

Colleen painted 7 windows, some of which were her mother's.

Her dad painted 7+1 (8) windows, and that is twice as much as what her mother was supposed to do. Her mother was supposed to do 4 windows. That means Colleen's share was 3 windows.

If all the kids had to do an equal amount of windows, than each kid had to do 3 windows.

8+7+3+3+3=24

The total windows in the house are 21.

What is an algebraic expression?

It is an expression contains a relation between different parameters (variables). It contains variable and constant values, along with algebraic operations.

In our given problem, the algebraic relation between different members work output and total windows can be expressed as:

Windows painted by colleen and her mother = 7

Windows painted by father = (Windows painted by colleen and her mother + 1)

                                          = (7 + 1) = 8

∴ Windows painted by father = 8

Now, as given,

2 Windows painted by mother = Windows painted by father

∴ Windows painted by mother = [tex]\frac{8}{2}[/tex] = 4

and Windows painted by colleen = 7 - 4 = 3

Colleen and her 2 brothers paint equal windows;

∴  They painted 3 windows each.

The total windows in the house is equal to total painted windows by mother, father, colleen and her two brothers:

⇒ 4 + 8 + 3 x 3 = 12 + 9 = 21

Hence the total windows in the house are 21.

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The ground temperature at sea level is 60 degrees F. For every 100-foot increase in elevation, the temperature rises 1/10 of one degree. At an altitude of 2,000 feet, what will be the likely temperature? A. 58 degrees F B. 62 degrees F C. 72 degrees F D. 80 degrees F Show ALL work please!!

Answers

Answer: B. 62 degrees fahrenheit

====================================================

Explanation:

x = elevation in feet

y = temperature in fahrenheit

The temperature goes up 1/10 = 0.1 degrees for every 100-foot increase of elevation. So the slope is 0.1/100 = 0.001, which tells us how fast the temperature is increasing. In other words, the temperature goes up 0.001 degrees each time the elevation goes up by 1 foot.

The ground temperature is 60 degrees, which is our starting temperature. It's the value of y when x = 0. Therefore, 60 is the y intercept.

We have a slope of m = 0.001 and a y intercept of b = 60. The equation y = mx+b becomes y = 0.1x+60

Now plug in x = 2000 to find the temperature at this elevation

y = 0.001x+60

y = 0.001*2000+60

y = 2+60

y = 62

Answer:

B.62

Step-by-step explanation:

60 + (2000/100)            We find 20 is the answer to the division

60 + (20 * 1/10)           We find 2 is the answer to the multiplication

60 + (2)  

We can then + for elevation or - or depression or decrease.

= 62

= 62 degrees.

what is the value of x

Answers

Answer:

x = 78

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

Answer:

78 degrees

Step-by-step explanation:

According to vertical angles theorem (vertical angles, angles that are opposite to each other and formed by two intersecting straight lines, are congruent) 78 and x are congruent

How does 4D shape look like?

Answers

Answer:

here you go

i hope i helped you

Step-by-step explanation:

Answer:

It would look like these shapes on the picture

Step-by-step explanation:

It is a shape with another one of it inside it, you should see it on the pictturres.

Hope this helped you

Please mark as brainlist.

please help me with this questions. Will Mark brainliest.

Answers

Answer: 355

And 33 eggs

Step-by-step explanation:

8 × 40 = 320

7/8 × 40= 35 Add 35+320 = 355

2 × 12= 24 3/4 of 12 = 9

Add 9+24=33

You can also make an improper fraction. Multiply the denominator by the whole number then add the numerator.

2 3/4 becomes 4×2=8

8+3=11 Divide the other factor by the denominator: 12÷4=3

Then multiply by the "improper" numerator 3×11=33

8 7/8 becomes 71/8

40/8=5

5×71=355

Answer:

355

Step-by-step explanation:

So, you first multiply 8 with 8 = 64

Then 64 + 7 = 71

So, 71 is the numerator and 8 stays the denominator.

Now you have 71/8 *40.

You "cut" 40 into five and 8 into 1, Because 40 divided by 8 is 5, so 40 becomes 5 and 8 becomes 1.

Now we have 71 * 5 = 355

hope it helps!

PLEASE brainliest me!

Lance can paint the room in 5 hours, while Kim can paint the same room in 4 hours.
How many hours would it take for them to paint the room together?

Answers

Answer:

1.5 hours

Step-by-step explanation:

the painting of kim and lance would take up to one/1 hour or an half

(07.05 LC)

Which statement is true for the equation 4n − 3 = 4n − 2?

It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.

Answers

Answer:

The answer is (A); there is no solution.

Step-by-step explanation:

It doesn't require any calculations, really, just logic.  Look, 4n = 4n wil be equal because they are the same numbers multiplied by the same variable - no matter the variable's value.  However, if you subtract both values by different numbers, you won't get the same number:

Let's say n = 5

4n = 4n

= 4(5) = 4(5)

= 20 = 20

Now,

4n - 3 = 4n - 2

= 4(5) - 3 = 4(5) - 2

= 20 - 3 = 20 -2

= 17 ≠ 18

Hope this helps!  Tell me if I was wrong!

Answer:

It has no solution.

Step-by-step explanation:

If we try and solve it we end up with nonsense, so it has no solutions:

4n - 3 = 4n - 2

4n - 4n = - 2 + 3

0 = 1

-  which is, of course, absurd.

Also, just by looking at the equation we can see that  the term 4n  -3  cannot in any way be equal to 4n - 2.

Step 2 Using Proportional Relationships

Answers

Answer:

a ( 567 miles to unit)

b( looks like 2 units so i would say 1134 miles

Answ: the scale is

Step-bstep explanatio

AHH, I need help .....again. ik this one is easy my brain is just - also, what is a good excuse to tell my teacher because this assignment is past due by one day bc i thought it was due on the 6 but .... it wasn't . And idk what to say plz help !!! thx :D

Answers

Answer:

fraction: 87/100. decimal: 0.87

Step-by-step explanation:

Because there are 10 rows and 10 colums, you know the denominator is 100 because it is 10x10.

Then I counted the first 80 blue squares and knew it was 80 because it is 8 rows and 10 colums. Then I added 7 blue squares because that is above the 80, and 80+7 is 87. So, the fraction is 87/100.

100ths places in decimals is two places, so the 87 would be in the first two decimal places, so it would be 0.87.

Sorry if this is confusing, and I hope it helps :)

Answer:

Fraction = 87 over 100 or [tex]\frac{87}{100}[/tex]  The decimal = 0.87

Step-by-step explanation:

first what I did was I counted all of the total squares which was 100 then I counted all of the Shaded squares which was 87.then I put 87 over 100 as a fraction and try to figure out if that was its simplest form which it was. for the decimal all I had to do was take 87 and divide it by 100

solve for m. √m-7 = n+3 It is worth like 40 points

Answers

Answer:

sqrt of (m-7) = n+3

m = (n+3)^2 + 7 or m= n^2 + 6n + 16

sqrt of (m)-7 = n+3

m = (n+10)^2 or m =n^2 + 20n + 100

Step-by-step explanation:

(2) move the constants to the other side, and square

or  (1) square and move constants

then you can solve for m

Answer:

[tex]n^2+6n+16[/tex]

Step-by-step explanation:

I'm going to assume you meant [tex]\sqrt{m-7} = n+3[/tex], not  [tex]\sqrt{m} - 7 = n+3[/tex].

[tex](\sqrt{m-7}) ^2 = (n+3)^2\\\\(\sqrt{m-7}^2) = (n+3)^2\\\\(m-7)^{\frac{2}{2} } = (n+3)^2\\\\m - 7 = (n+3)^2\\\\m - 7 = n^2 + 2n\cdot3 + 3^2\\\\m - 7 = n^2 + 6n + 9\\\\m - 7 + 7 = n^2 + 6n + 9 + 7\\\\m = n^2 + 6n + 16[/tex]

Hope this helped!

Create diagrams to represent the possible cases for common tangents between two circles. Your diagram can be created using multimedia sources or drawn by hand. They should not be copied and pasted from a website. Explain why your diagrams satisfy the given criteria. One Common Tangent (10 points) Diagram: Justification:

Answers

Answer:

draw 2 lines and draw 2 circles in the lines with the edge touching the line

Step-by-step explanation:

In between two circles, there might be 0, 1, 2, 3, and 4 tangents are there.

What is the tangent of a circle?

"A tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior.

1. When one circle is in between another and one circle does not touch the other one, then tangent is not possible.

2. When one circle is in between another and one circle touches the other one at a point inside the circle, then only one tangent is possible.

3. When one circle intersects the other one, then two tangents are possible.

4. When one circle touches the other one at a point outside, then three tangents are possible.

5. When one circle neither intersects the other one nor inside the other one, then four tangents are possible.

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Find the area of the ACTUAL gym

Answers

Step-by-step explanation:

The three main types of exercise are cardiovascular exercise, strength training and stretching. All three types of exercise are important for physical fitness. Cardiovascular aerobic exercise is repetitive, rhythmic exercise that increases your heart rate and requires you to use more oxygen.

Answer:

6.67

Step-by-step explanation:

Using the function f(x)=-x^2+8x-13 find f(4)

Answers

Answer:

f(4) = 3

Step-by-step explanation:

f(x) = -[tex]x^{2}[/tex] + 8x - 13

To find f(4), substitute 4 for all instances of x:

f(4) = -(4[tex])^{2}[/tex] + 8(4) - 13

Simplify the exponent:

f(4) = -16 + 8(4) - 13

Multiply:

f(4) = -16 + 32 - 13

Combine terms:

f(4) = 3

Answer:

3

Step-by-step explanation:

You plug in 4.

f(4)= -(4)^2+8(4)-13

f(4)= -16+32-13

f(4)= 16-13

f(4)=3

11. In a box-and-whisker plot, the interquartile
range is a measure of the spread of the
middle half of the data. Find the interquartile
range for the data set: 10, 3, 7, 6, 9, 12, 13.
A 12
© 6
B 7
D 8

Answers

The answer to the question would be 6 because it’s in the middle
6. The range is the middle number in a sequence. That’s how you will find your awsner. You are welcome:)

What is the area of the polygon shown below? (in the image). A. 322 mm^2 B. 364 mm^2 C. 520 mm^2 D. 584 mm^2 Show all work please!

Answers

Answer:

A.

Step-by-step explanation:

Find the area of the triangle: 26-20=6. 14x6=84/2=42. Now that we calculated the triangle's area, we need to find out the rectangle's. 20x14=280. Add them up: 280+42=322 mm^2. Triangle: b x h/2. Rectangle: l x h.

The area of a 2D form is the amount of space within its perimeter. The area of the given figure is 322 mm². The correct option is A.

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The given figure can be broken into a rectangle and a right-angle triangle, in order to calculate the area of the given polygon.

The area of the rectangle with a length of 20mm and height of 14 mm is,

Area of the rectangle = 20mm × 14mm

                                    = 280 mm²

The area of the right-angled triangle with a base length of 6mm and height of 14 mm is,

Area of the triangle = (1/2) × 6mm × 14mm

                                 = 42 mm²

Now, the total area of the given figure can be written as,

The total area of the given figure

= Area of the rectangle + Area of the triangle

= 280 mm² + 42 mm²

= 322 mm²

Hence, the area of the given figure is 322 mm².

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What’s x ?? Help plzzz

Answers

Answer:

x = 69°

Step-by-step explanation:

1). JFGHI is a pentagon, every angle in a Pentagon is equal to 108°.

2). angle JIH + angle HIE = 180°; angle JIH = 108, so angle HIE = 72°.

3).  angle JDI is equal to 39° and angle IEH; so angle IEH = 39°

4). Now we know 2 out of the three angles in the triangle IHE, so we can find x!

5). x + angle HIE + angle IEH = 180°

    x + 72° + 39° = 180°

    x = 69°

Find X. Round your answer to the nearest tenth of a degree.

Answers

Answer:

48.6 degrees

Step-by-step explanation:

The sine function is appropriate here:

                 9

sin x = ------------- = 0.75

                12

The inverse sine function arcsin x provides with the angle measurement:

arcsin 0.75 = 0.848 radian, or 48.6 degrees

48.6 digress
I had this one

During a science experiment, the temperature of a certain substance was recorded at three different times. Use this information to complete the statements below. The time at which the temperature is below 0°C is ___ (3:00,4:00,5:00) The time with the highest temperature is ___(3:00,4:00,5:00) The temperature at 3:00 is ____(closer too, farther from) 0°C than is the temperature at 4:00. HELP ASAP

Answers

Answer:

Step-by-step explanation: The time at which the temperature is below 0°C is 3:00

The time with the highest temperature is 4:00 The temperature at 3:00 is closer too zero than the temp at 4:00

Somebody please help me on this math problem

Answers

Answer:

I believe that the answer is F.

Step-by-step explanation:

The y coordinate is about the test score (per question is assume).  

It if is per question then 5 points will be handed out for every four questions or 1.25 per question.

Answer:

F

Step-by-step explanation:

Find the slope:

two points were given (1, 5/4) and (0, 0) because if you get zero question right you will recieve zero points.

Slope: 5/4

y= (5/4)x

Lets check F

You get 4 questions rights then you will get 5 points.

Find the median of the data in the dot plot below.

Answers

Answer:

it's 40

Step-by-step explanation:

because, there's five numbers on each side of 40

Answer:

Step-by-step explanation:40

2) A furlong is 1/8 of a mile. What part of a mile is 4 furlongs?

Answers

Answer:

1/2 mile

Step-by-step explanation:

(1/8)*4 = 1/2 mile

Answer:

4/8 or 1/2

Step-by-step explanation:

becuase 4 times 1/8 is 4/8 which is 1/2

Other Questions
f(x) = x2 x-1What is the average rate of change of f over the interval -1 < x < 1? When the electron is moving in the plane of the page in the direction indicated by the arrow, the force on the electron is directed:_____a. into the page. b. toward the left c. toward the right d. toward the bottom of the page. e. toward the top of the page. f. out of the page. Ratio analysis:___________. a) Includes estimating the net present value of the investment opportunity. b) Is generally adequate to fully assess an investments expected return. c) Requires cash flow estimates for the investments entire expected holding period. d) Serves as an initial evaluation of the adequacy of an investments expected cash flows. 17. a(y + c) = b(y - c)How do I isolate y? The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does the sample data show a significant increase in the average birthrate at a 5% level of significance? A. Fail to reject the null hypothesis and conclude the mean is 6.6 lb. B. Reject the null hypothesis and conclude the mean is lower than 6.6 lb. C. Reject the null hypothesis and conclude the mean is greater than 6.6 lb. D. Cannot calculate because the population standard deviation is unknown Choose the answer that makes the sentence most effective. The employee thought, in his opinion, that the company was at fault. A.if you asked him B.according to him C.Eliminate this part. During the ENSO cycle, in the Nino 3.4 monitoring region of the Equatorial Pacific, the typical sea surface temperature departure from normal is 6 C or more.a. Trueb. False What are some of the moral issues surrounding immigration? Read this story and then answer the question that follows:Sarah saw them, again. Out of the corner of her eye she could see the kids ganging up on the new girt, Lara. She was late to her band practice and only had a few minutes to get there. I barelyknow her," she muttered to herself as she walked quickly to the car. "I'm sure she can take care of herself." Sarah knew this was an important rehearsal and could not miss it. "Hurry up,shouted her mom from the driver's seat. Sarah threw her guitar in the back seat and slammed the door. "Let's go," she said. As they rounded the comer and stopped at the stop sign--her heartracing-Sarah looked at her mom. "Mom, Lara needs our help. Let's go back."Which of the following is an example of the topic In this story? (5 points)FriendshipViolenceResponsibilityMusic Jacinta has been a victim of discrimination in her neighborhood. Which common outcome is most likely to be seen in Jacinta?A. low self-esteemB. rebellious behaviorC. the ability to adapt to changesD. a high tolerance level differences between properties of convalent and ionic bond. Factor 4(20) + 84. 4(20 + 21) 4(21 + 20) 20(4 + 84) 20(4 + 4) Will give Brainliest, Please show work. What is foreign aid ? Why do you like or dislike foreign aid? Present your critical analysis in eight points. A dolphin is swimming with her friend. The dolphin jumps to a height of 4.5 meters above the surface of the water as her friend swims 9.8 meters directly below her. Provide the name(s) for the tertiary alcohol(s) with the chemical formula C6H14O that have a 4-carbon chain. Although stereochemistry may be implied in the question, DO NOT consider stereochemistry in your name. Alcohol #1______ Alcohol #2: ______Alcohol #3______ Let $n$ be a positive integer. (a) Prove that \[n^3 = n + 3n(n - 1) + 6 \binom{n}{3}\]by counting the number of ordered triples $(a,b,c)$ of positive integers, where $1 \le a,$ $b,$ $c \le n,$ in two different ways. (b) Prove that \[\binom{n + 2}{3} = (1)(n) + (2)(n - 1) + (3)(n - 2) + \dots + (k)(n - k + 1) + \dots + (n)(1),\]by counting the number of subsets of $\{1, 2, 3, \dots, n + 2\}$ containing three different numbers in two different ways. A plumber (come) ____________ to our house yesterday. He (want) _____________ to repair our washing machine. While he (repair) _______________ the washing machine, I (watch) ___________________ the news. Suddenly, I (realize) ____________ that they (show) ____________________ our street on TV. The reporter said that a car had crashed into a stop sign just before reaching the crossroads. While I (listen) _________________ carefully to what had happened, someone (knock) ________________ at my door. I (open) ______________ the door and (see) ___________a police officer standing there. He (ask) ____________ for the plumber. As it (turn out) ________________, it (be) __________ our plumbers car that had rolled down the street. In haste, the plumber had forgotten to put the handbrake on. A premature infant develops jaundice. Laboratory test results are negative for hemolytic disease of the newborn, but the infants bilirubin level continues to rise. Abnormal urinalysis test results include a dark yellow color, positive Ictotest, and needle-shaped crystals seen on microscopic examination. What is the most probable cause of the infants jaundice? _____consists of 6 different dimensions-physical, emotional, intellectual, spiritual, social, and environmental. A. Health B. Wellness C. Risk Factors D. Diseases