A rectangle is 42 square feet. what percent of the area of the rectangle is a square with side lengths of 6 feet?

Answer:

6 to the tenth power over 7 to the sixth power

Step-by-step explanation:

Given phrase,

6 to the fifth power over 7 cubed all raised to the second power,

[tex]\implies (\frac{6^5}{7^3})^2[/tex]

By using [tex](a^m)^n=a^{mn}[/tex]

[tex]=\frac{6^{5\times 2}}{7^{3\times 2}}[/tex]

[tex]=\frac{6^{10}}{7^6}[/tex]

= 6 to the tenth power over 7 to the sixth power

Simplify the expressions

(6⁵/7³)² = 2143588816/117649

(6⁷/7¹⁰) = 279936/282475249

(6¹⁰/7⁶) = 60466176/117649

(6³/7) = 216/7

(12⁵/14³) = 90855/1001

To simplify the given expressions, we can calculate the numerical values and perform the necessary operations. Let's evaluate each expression:

(6⁵/7³)²:

First, calculate the numerator and denominator:

Numerator: 6⁵ = 6 × 6 × 6 × 6 × 6 = 7776

Denominator: 7³ = 7 × 7 × 7 = 343

Now, substitute the values into the expression and square the result:

(7776/343)² = (7776/343) × (7776/343) = 2143588816/117649

The simplified form is 2143588816/117649.

(6⁷/7¹⁰):

Calculate the numerator and denominator:

Numerator: 6⁷ = 6 × 6 × 6 × 6 × 6 × 6 × 6 = 279936

Denominator: 7¹⁰ = 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 = 282475249

Substitute the values into the expression:

279936/282475249

This expression cannot be simplified further.

(6¹⁰/7⁶):

Calculate the numerator and denominator:

Numerator: 6¹⁰ = 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 = 60466176

Denominator: 7⁶ = 7 × 7 × 7 × 7 × 7 × 7 = 117649

Substitute the values into the expression:

60466176/117649

This expression cannot be simplified further.

(6³/7):

Calculate the numerator and denominator:

Numerator: 6³ = 6 × 6 × 6 = 216

Denominator: 7

Substitute the values into the expression:

216/7

This expression cannot be simplified further.

(12⁵/14³):

Calculate the numerator and denominator:

Numerator: 12⁵ = 12 × 12 × 12 × 12 × 12 = 248832

Denominator: 14³ = 14 × 14 × 14 = 2744

Substitute the values into the expression:

248832/2744 = 90855/1001

The simplified form is 90855/1001.

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Simplify 6 to the fifth power over 7 cubed all raised to the second power. 6 to the seventh power over 7 to the tenth power 6 to the tenth power over 7 to the sixth power 6 cubed over 7 12 to the fifth power over 14 cubed

(6⁵/7³)²

(6⁷/7¹⁰)

(6¹⁰/7⁶)

(6³/7)

(12⁵/14³)

area = H/2*(b1+b2)

8.1 = 1.5/2*(6.7 +b2)

8.1=0.75*(6.7+b2)

10.8=6.7+b2

b2=10.8-6.7

b2=4.1m

The rate of change in words per minute will be [tex]35[/tex] words per minute.

Rate of change is a rate that tells how one quantity changes in relation to another quantity.

i.e. Rate of change [tex]=\frac{Change\ in\ words}{Change\ in\ time}[/tex]

We have,

At [tex]4:04[/tex] pm typed [tex]275[/tex] words,

By [tex]4:18[/tex] pm you have [tex]765[/tex] words.

So,

Change in type [tex]= 4:18\ PM -4:04\ PM=14[/tex]

So,

Rate of change [tex]=\frac{Change\ in\ words}{Change\ in\ time}[/tex]

                            [tex]=\frac{765-275}{14}[/tex]

                            [tex]=\frac{490}{14}[/tex]

Rate of change [tex]=35[/tex] words per minute

So, the rate of change is  [tex]35[/tex] words per minute which is given in option [tex](D)[/tex].

Hence, we can say that the rate of change in words per minute will be [tex]35[/tex] words per minute.

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To find the perpendicular line's equation, first find the negative reciprocal of the original line's slope. Next, use the point-slope form with the given point. Lastly, rearrange the equation into standard form, resulting in x + 4y = 22.

To find the equation of a line that is perpendicular to another line and passes through a given point, you need to perform a series of steps. The first line's equation is given as 4x - y = 2. Firstly, solve for y to put it in slope-intercept form, y = mx + b. Here, the equation becomes y = 4x - 2, so the slope (m) is 4. The slope of the perpendicular line will be the negative reciprocal of this, which is -1/4.

The next step is to use the point-slope form of the line, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes. For the point (2,5), the equation of the line is y - 5 = -1/4(x - 2). Multiplying both sides by 4 to clear the fraction gives 4y - 20 = -x + 2.

Finally, rearrange the equation to get it into standard form, Ax + By = C, giving us x + 4y = 22. This is the standard form of the equation we were seeking.

Answer:

AB overbar congruent to CD overbar

Explanation:

The question is asking whether Line segment AB is CONGRUENT to line segment CD.

The meaning of congruent is having the same shape and size.

Congruent ≅

Element ∈

Equal =

Similar ~

In conclusion, you could say:

AB ≅ CD

I cannot type the lines over the top AB and CD but they are there.

(I know this question is probably old, and i am also tying this so I remember as well, but the other answer didn't have a bit bigger explanation so if anyone comes across this i hope this helped. :)

If two or more objects are the same copy in length and shape then that will be said to be congruent thus AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent thus options (B) and (C) is correct.

If two figures are exactly the same in sense of their length side all things then they will be congruent.

In other meaning, if you can copy a figure then that copy and the original figure will be congruent.

All line segments are in the same shape and have degrees as one in the equation therefore only one criterion which is length is needed to prove congruency.

So, congruent lines are lines whose lengths are the same.

The sign of congruency is ≅ so AB ≅ CD.

Hence " AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent to AB ≅ CD".

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Answer:

Option B is correct.

The approximate area of regular octagon is, 101 square ft.

Step-by-step explanation:

Given: A regular octagon has a radius of 6 ft and a side length of 4.6 ft.

To find the area of a regular octagon(A) of side length a is given by :

[tex]A=2\cdot(1+\sqrt{2})a^2[/tex]

Given the length of side, a= 4.6 ft

Substitute the value of a=4.6 ft in the given formula of area:

[tex]A=2\cdot(1+\sqrt{2})\cdot(4.6)^2[/tex] or

[tex]A=(2+2\sqrt{2})\cdot (21.16)[/tex] or

[tex]A=(2+2.828)\cdot(21.16)[/tex]

Simplify:

[tex]A=4.828\cdot 21.16 =102.16048[/tex] square ft.

therefore, the approximate area of regular octagon is, 101 square ft

p=(5.25-5.00)/5.00

p=0.25/5.00

p=0.05

p = 5% increase

Answer:37

Step-by-step explanation:

12•12=144

35•35=1225

1225+144=1369

Square root 1369=37

Answer:

A. 0.135%

Step-by-step explanation:

We have been given that adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall.  

We need to find the area of normal curve above the raw score 79.

First of all let us find the z-score corresponding to our given raw score.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

[tex]z=\text{z-score}[/tex],

[tex]x=\text{Raw-score}[/tex],

[tex]\mu=\text{Mean}[/tex],

[tex]\sigma=\text{Standard deviation}[/tex].

Upon substituting our given values in z-score formula we will get,

[tex]z=\frac{79-70}{3}[/tex]

[tex]z=\frac{9}{3}[/tex]

[tex]z=3[/tex]

Now we will find the P(z>3) using formula:

[tex]P(z>a)=1-P(z<a)[/tex]

[tex]P(z>3)=1-P(z<3)[/tex]

Using normal distribution table we will get,

[tex]P(z>3)=1-0.99865 [/tex]

[tex]P(z>3)=0.00135[/tex]

Let us convert our answer into percentage by multiplying 0.00135 by 100.

[tex]0.00135\times 100=0.135%[/tex]

Therefore, approximately 0.135% of the adult male population is taller than the average basketball player and option A is the correct choice.

Answer:

Step-by-step explanation:

To solve this problem, we need to use the Intersecting Chords Theorem which states "when two chords intersect each other inside a circle, the products of their segments are equal".

Applying this theorem, we have

[tex]AE \times EB = CE \times ED[/tex]

Where [tex]AB=AE+EB[/tex] and [tex]CD=CE+ED[/tex], also [tex]AB \cong CD[/tex], which means

[tex]AE+EB=CE+ED[/tex]

However, if both chords are equal, then their arcs are also equal, that's the easiest way to deduct it, that is

[tex]arc(AB) \cong arc(CD)[/tex]

Because an arc is defined by its chord basically, and in this case they are congruent.

Answer:

Step-by-step explanation:

the answer is a

Look at the picture.

Answer: A. (3.5, -4)

The volume of parallelepiped with 8 vertices is 75 units.

A parallelepiped's volume is determined by multiplying its surface area by its height.

The area of the parallelogram base is the cross product's magnitude, ∥a×b∥ , according to its geometric specification, and the vector a×b direction is perpendicular to the base.

Given:

let the 8 vertices are (0,0,0), (3,0,0), (0,5,1), (3,5,1), (2,0,5), (5,0,5), (2,5,6), and (5,5,6).

so, Volume = det [tex]|\left[\begin{array}{ccc}0&3&2\\5&0&0\\1&0&5\end{array}\right] |[/tex]

                    = |0( 0- 0) - 3(25- 0) + 2(0 - 0)|

                    = |0 - 75 + 0|

                    = |- 75|

                    = 75 units

Hence, the volume of parallelepiped with 8 vertices is 75 units.

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To find the interest Candis would make from a 15,400% interest rate on a $220 investment for one year, we calculate using the simple interest formula, resulting in $33,880.

The question asks us to determine how much interest Candis would make from a payday loan with an effective interest rate of 15,400% if she invested $220 for a year. To calculate the interest earned, we can use the formula for simple interest which is I = Prt, where I is interest, P is principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.

Converting 15,400% to a decimal, we get 154. Then, apply the formula:

I = $220 × 154 × 1

This gives us:

I = $33,880

Therefore, Candis would make $33,880 in interest after one year, which corresponds to option D.

there is a 1/2 probability of getting heads on any one flip

 since the first one landed on heads you have a 1/2 probability f getting a 2nd one

Probability = 1/2

To solve this problem, we make use of the z statistic. A population of 5% means that we are looking for the population at >95%, P = 0.95. Using the standard distribution tables for z, a value of P = 0.95 indicates a value of z of z = 1.645

Now given the z and standard deviation s and the mean u, we can calculate for the value of IQ of the top 5% (x):

x = z s + u

x = 1.645 (15) + 100

x = 24.675 + 100

x = 124.675

Therefore the minimum iq score for the top 5% of the population is around 124.675

The minimum IQ score for the top 5% of the population, with a normal distribution mean of 100 and a standard deviation of 15, is approximately 124.7. This is found by using the z-score that corresponds to the 95th percentile, which is 1.645, and applying it to the formula for a score in a normal distribution.

To determine the minimum IQ score for the top 5% of the population, given that human IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution. Typically, the top 5% of values on a normal distribution lie above a certain z-score threshold. This z-score corresponds to the point on the distribution where the cumulative area to the left is 95% (100% - 5%), since we are looking for the score above which the top 5% of scores fall.

To find this z-score, we look up the value in a standard normal distribution table or use a statistical software or calculator. The z-score that corresponds to the 95th percentile is typically around 1.645. To find the actual IQ score, we can then apply the following formula:

IQ Score = Mean + (Z-score * Standard Deviation)

Plugging the values in:

IQ Score = 100 + (1.645 * 15)

IQ Score = 100 + 24.675

IQ Score = 124.675

Therefore, the minimum IQ score for the top 5% of the population is approximately 124.7 (since IQ scores are usually reported to the nearest whole number).