Write each expression in exponential form

[tex]\sqrt[4]{6^5}[/tex]

Answer:

  80 in²

Step-by-step explanation:

When side length and apothem of a regular polygon are given, the applicable area formula is ...

  A = 1/2Pa

where P is the perimeter of the polygon, and 'a' is its apothem.

__

The perimeter of a regular 8-sided polygon will be 8 times the side length, so the area is ...

  A = 1/2(8×4 in)(5 in) = 80 in²

Answer:

Step-by-step explanation:

let wind velocity=x

speed of plane=y

(x+y)*4=808

x+y=808/4=202   ...(1)

(y-x)*4=488

y-x=122 ...(2)

add (1) and (2)

2y=202+122=324

y=324/2=162

from (1)

x+162=202

x=202-162=40

wind velocity=40 m/hr

speed of plane=162 m/hr

Answer:

2,800

A = 2000(1 + (0.1 × 4)) = 2800

A = $2,800.00

It will take 4 year for the account to reach $5,500.

The formula we use to calculate the amount is

A = P(1+r)¹

Where, P= amount of money invested

r = interest rate percentage in decimal form

t = time in years

A = total money in the account at time

Tina wants to save money for school.

Tina invests $400 in an account that pays an interest rate of 8%.

A = P(1+r)¹

5500 = 400(( 1 + 0.08)^t

5500/ 400 = ( 1 + 0.08)^t

55/ 4 = (1.08)^t

13.75 = (1.08)^t

t = 4

It will take 4 year for the account to reach $5,500.

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The original height  of the water in a pool is 5 ft , Option B is the correct answer.

An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.

It is given in the question that

A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.

the height of the water is 4.75 feet.

The equation

4.75 = x + (negative 0.25)

can be used to find x, the original height of the water in a pool.

4.75 = x - 0.25

x = 5

Therefore the original height  of the water in a pool is 5 ft , Option B is the correct answer.

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Answer:

B

Step-by-step explanation:

Answer:

A. 56.5 cm

Step-by-step explanation:

circumference of the circle is Pi times diameter

diameter is radius times 2

diameter is 9 times 2

diameter is 18

circumference of the circle is Pi times 18

circumference of the circle is 3.14 times 18

circumference of the circle is 56.52

Answer:

irrational

Step-by-step explanation:

what are rational numbers ?

every number that can be expressed as a/b, with a and b being integer numbers, and b different to 0.

the square root of any number that is not a squared rational number is then an irrational number.

I am not sure, if the expression here is

sqrt(13) + 4

or

sqrt(13 + 4), which would then be sqrt(17).

but in both cases we are creating the square root of a not- squared rational number.

neither 13 nor 17 are the result of a multiplication of a rational number with itself.

in fact, 13 and 17 are prime numbers with no other factors than either 1 or themselves.

so, both, sqrt(13) and sqrt(17) are irrational numbers.

adding or subtracting rational numbers to irrational numbers result again in irrational numbers.

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find out if [tex]\pmb{\sqrt{13} +4}[/tex] is rational or irrational.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So, can we write [tex]\pmb{\sqrt{13} +4}[/tex] as a fraction? We can write 4 as a fraction, but we cannot write [tex]\pmb{\sqrt{13}}[/tex] as a fraction, because this number has infinitely many digits after the decimal point, and they never repeat; there's no pattern at all!

And even if we add 4, which is a rational number, to [tex]\pmb{\sqrt{13}}[/tex], we'll still get an irrational number.

Thus, [tex]\pmb{\sqrt{13}+4}[/tex] is irrational.

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students out :)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's find the volume of the given figure ~

[tex]\qquad \sf  \dashrightarrow \:Volume_{(cuboid)}= length \cdot width \cdot height [/tex]

[tex]\qquad \sf  \dashrightarrow \:Volume_{(cuboid)}= 4 \cdot x \cdot x [/tex]

[tex]\qquad \sf  \dashrightarrow \:Volume_{(cuboid)}= 4 {x}^{2} [/tex]

So, the correct choice is ~ C

Volume

Option C

An exponential decay function, and use it to approximate the population in 2027 is P(t) = 4001e^-(0.0037)(28) = P(t) = 4001e^-0.1036

The standard exponential function is expressed as:

P(t) = P0e^-rt

Substitute

P(t) = 4001e^-(0.0037)t

If t = 28 (by 2027)

An exponential decay function, and use it to approximate the population in 2027 is P(t) = 4001e^-(0.0037)(28) = P(t) = 4001e^-0.1036

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Answer:

Step-by-step explanation:

First, label it out:

Then, we add up 12 twice (Since the length is on 2 sides):

Now, we write down a 6 in the ?:

Width = 6.

We are not done!

Now, we have to solve for area.

Answer:

Missing number is 288, and the rule is +96

Step-by-step explanation:

First subtract 96 from 192, which is 96

then add that to 192 and the missing value is 288

you should also add 96 to 288 just to make sure it gets you to the last number which is 384.

Answer: Option 2

Step-by-step explanation:

[tex]|h-2|=4\\\\h-2=\pm 4\\\\h=-2, 6[/tex]

Based on the cost of the contract and the probability to win it, the total expected value of the contract proposal is -$2500.

The general formula to calculate the expected value is:

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8 - (-4)]^2 + [7 - (-3)]^2}\implies d=\sqrt{(-8+4)^2 + (7+3)^2} \\\\\\ d=\sqrt{(-4)^2 + 10^2}\implies d=\sqrt{116}\implies d\approx 10.77[/tex]

A point that is exterior to an angle is found on the acute side of the angle which is true.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

We know that the sum of the exterior angle and interior angle is equal to 180 degrees.

"If one of the exterior angles is an acute angle, then the corresponding interior angle is an obtuse angle."

A point that is exterior to an angle is found on the acute side of the angle which is true.

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Answer:

  41.3%

Step-by-step explanation:

The probability of interest is found by dividing the number of students passing either course by the total number of students.

The number passing only one of the courses is the number passing that course, less the number passing both courses. This is shown in the attached 2-way table.

__

The number passing either course will be the sum of the number passing one course (including the number passing both courses), and the number passing only the other course. It can also be found as the sum of the numbers passing either course, less the number passing both courses (since the latter would be counted twice).

Here those passing either (or both) Math or English will be ...

  90 +(85 -78) = 85 +(90 -78) = (90 +85) -78 = 97

So, the probability is ...

  p(passing either M or E) = 97/235 = 0.41277 ≈ 41.3%

Answer:

x-4*2

Step-by-step explanation:

Since we dont know the number, we can make it a variable. So, x is the unknown number.

4 less will mean subtraction. So. x-4.

Next we have to multiply with 2.

So, the expression is x-4*2.

Answer:

Hi,

Step-by-step explanation:

We can't solve that but reduce it to the same denominator.

[tex]\dfrac{x+5}{x}+\dfrac{x+8}{x-1}\\\\=\dfrac{(x+5)(x-1)+x(x+8)}{x(x-1)}\\\\=\dfrac{x^2+5x-x-5+x^2+8x}{x(x-1)}\\\\=\dfrac{2x^2+12x-5}{x(x-1)}\\[/tex]

The choice in the solution set of the equation 4x = 30 is x = 7.5

The equation is given as:

4x = 30

Divide both sides of the equation by 4

4x/4 = 30/4

Evaluate the quotients

x = 7.5

Hence, the choice in the solution set of the equation 4x = 30 is x = 7.5

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Step-by-step explanation:

hope you can understand

Calculating the z-score provides additional information regarding how each subject did overall as the z-score takes dispersion into account.

Z-score indicates how much a given value differs from the standard deviation.  For example, the mean of a test could be a 73 and if a student scored an 85, that's great.

However, if the data is not spread out, that 85 could be the highest in the class by 10 points. That's much more information than just 15 points above the mean. This way you can tell when someone not only did well but did exceptionally well in comparison to his or her peers.

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Answer:

(0, 3) (3, 0)

Step-by-step explanation:

part 1

6y = 42

part 2

x - 15 = 62

product means multiplication and difference means subtraction.

hope this helps

Trigonometric Formula's:

[tex]\boxed{\sf \ \sf \sin^2 \theta + \cos^2 \theta = 1}[/tex]

[tex]\boxed{ \sf tan\theta = \frac{sin\theta}{cos\theta} }[/tex]

Given to verify the following:

[tex]\bf (cos^2a) (2 + tan^2 a) = 2 - sin^2 a[/tex]

[tex]\texttt{\underline{rewrite the equation}:}[/tex]

[tex]\rightarrow \sf (cos^2a) (2 + \dfrac{sin^2 a}{cos^2 a} )[/tex]

[tex]\texttt{\underline{apply distributive method}:}[/tex]

[tex]\rightarrow \sf 2 (cos^2a) + (\dfrac{sin^2 a}{cos^2 a} ) (cos^2a)[/tex]

[tex]\texttt{\underline{simplify the following}:}[/tex]

[tex]\rightarrow \sf 2cos^2 a + sin^2 a[/tex]

[tex]\texttt{\underline{rewrite the equation}:}[/tex]

[tex]\rightarrow \sf 2(1 - sin^2a ) + sin^2 a[/tex]

[tex]\texttt{\underline{distribute inside the parenthesis}:}[/tex]

[tex]\rightarrow \sf 2 - 2sin^2a + sin^2 a[/tex]

[tex]\texttt{\underline{simplify the following}} :[/tex]

[tex]\rightarrow \sf 2 - sin^2a[/tex]

Hence, verified the trigonometric identity.

Answer:

See below ~

Step-by-step explanation:

Identities used :

⇒ cos²a = 1 - sin²a

⇒ tan²a = sin²a / cos²a

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

Solving :

⇒ (cos²a) (2 + tan² a)

⇒ 2cos²a + (cos²a)(tan²a)

⇒ 2(1 - sin²a) + sin²a

⇒ 2 - 2sin²a + sin²a

⇒ 2 - sin²a [∴ Proved √]

Answer:

3/7

Step-by-step explanation:

He took 6 out of 14 so that is 6/14 then simplify it to 3/7

The discrete data is (b) while the continuous data are (a) and (d)

These are data that can be represented using positive whole numbers.

Using the above definition as a guide, the discrete data is (b) The number of books in your apartment

These are data that can be represented using decimal numbers.

Using the above definition as a guide, the continuous data are (a) The weight of cows  and (d) The ounces of water that you drink each day

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Answer:

115.5

Step-by-step explanation:

the car is traveling at precisely 52.5 miles an hour

Answer:

B

Step-by-step explanation:

You can not know the original price unless you know the taxes percentage.

Answer:

Hi,

Step-by-step explanation:

a)

[tex]if\ \dfrac{x}{2}-3\ > \ 0\ then\ |\dfrac{x}{2}-3|=\dfrac{x}{2}-3\\\\\dfrac{x}{2}-3 > 4\\\\\dfrac{x}{2} > 7\\\\x > 14\\[/tex]

b)

[tex]if\ \dfrac{x}{2}-3\ < \0 \ then\ |\dfrac{x}{2}-3|=-(\dfrac{x}{2}-3)=-\dfrac{x}{2}+3\\\\-\dfrac{x}{2}+3\ > \ 4\\\\-\dfrac{x}{2}\ > \ 4-3\\\\-\dfrac{x}{2}\ > \ 1\\\\\dfrac{x}{2}\ < \ -1\\\\x\ < \ -2\\[/tex]

[tex]S=\{x\in\mathbb{R}\ :\ |\dfrac{x}{2}-3|\ > \ 4\}=(-\infty,-2[\ \cup\ ]14,\infty)\\[/tex]