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3⁵.2⁴.2¹.3⁶.(3²)⁴ and down (2³)².3⁶<br>

BARSIC [14]

Answer:

$\dfrac{3^{13}}{2}$

Step-by-step explanation:

Given expression:

$\dfrac{3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot (3^2)^4}{(2^3)^2 \cdot 3^6}$

$\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\implies \dfrac{3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot 3^8}{2^6 \cdot 3^6}$

$\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:$

$\implies \dfrac{3^{(5+6+8)} \cdot 2^{(4+1)}}{2^6 \cdot 3^6}$

$\implies \dfrac{3^{19} \cdot 2^{5}}{2^6 \cdot 3^6}$

$\implies \dfrac{3^{19} \cdot 2^{5}}{3^6 \cdot 2^6}$

$\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies 3^{(19-6)} \cdot 2^{(5-6)}$

$\implies 3^{13} \cdot 2^{-1}$

$\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:$

$\implies \dfrac{3^{13}}{2^1}$

$\textsf{Apply exponent rule} \quad a^1=a:$

$\implies \dfrac{3^{13}}{2}$

4 0

2 years ago

Classify each pair of angels listed below as adjacent or vertical.

Stolb23 [73]

Answer:

ntersecting lines DA and CE.

To find:

Each pair of adjacent angles and vertical angles.

Solution:

Adjacent angles are in the same straight line.

Pair of adjacent angles:

(1) ∠EBD and ∠DBC

(2) ∠DBC and ∠CBA

(3) ∠CBA and ∠ABE

(4) ∠ABE and ∠EBD

Vertical angles are opposite angles in the same vertex.

Pair of vertical angles:

(1) ∠EBD and ∠CBA

(2) ∠DBC and ∠EBA

5 0

3 years ago

Standard deviation of a normal data distribution is a _______.

Keith_Richards [23]

Answer:

Measure of Data Dispersion

Step-by-step explanation:

Standard deviation is used to show the variation and dispersion in a group of data. It shows how separated the data's are to each other and how each data can be related to the other.

A normal data distribution are those group of data, that are distributed in a wide range. The standard deviation helps to to measure how they are been spread out.

Standard deviation does not measure the shape, quality, and center of data. This are measured with graphs, range, mean and median.

5 0

2 years ago

Read 2 more answers

Last week the price of apples at a grocery store was $1.20 per pound. Today, the store has

lions [1.4K]

Answer:

$0.54

Step-by-step explanation:

Start by multiplying 4.5 times 1.20. That’s the normal price of the apples when they’re not on sale. $5.40. Move the decimal place back by one and you get 0.54. That’s the total price of the apples.

5 0

3 years ago

a ball is thrown into the air with an upward velocity of 36 ft/s. it’s height h in feet after t seconds is given by the function

lukranit [14]

Complete the square:

$h(t)=-16t^2+36t+9=-16\left(t^2-\dfrac94t\right)+9=-16\left(\left(t-\dfrac98\right)^2-\dfrac{81}{64}\right)+9$

$h(t)=-16\left(t-\dfrac98\right)^2+\dfrac{117}4$

That is, the graph of $h(t)$ is a parabola with vertex at $(t,h(t))=\left(\dfrac98,\dfrac{117}4\right)$ , meaning the ball reaches its maximum height of $\dfrac{117}4=29.25\,\mathrm{ft}$ after $t=\dfrac98=1.125\,\mathrm s$ of being thrown.

5 0

3 years ago