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3 years ago

Consider the following numbers: 7000, 700, 70, 0.7, 0.07, 0.007

Mathematics

1 answer:

masya89 [10]3 years ago

6 0

Answer:

7000= 7 x 10^{3}, 700= 7 x 10^{2}, 70= 7 x 10^{1}, 0.7= 7 x 10^{-1}, 0.07= 7 x 10^{-2}, 0.007= 7 x 10^{-3}

Step-by-step explanation:

YES

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Lauren and her family went to Maggiano's for dinner and spent $92.00. Lauren's family wanted to leave a 15% tip. How much will L

Andrews [41]

Answer:

105.8

Step-by-step explanation:

6 0

3 years ago

Calculate the rate of change from the graph below

qaws [65]

Answer:

The rate of change is 0.75 gallons per minute

Step-by-step explanation:

The rate of change of the linear relation is represented by the slope of the line which represents this relation

The rule of the slope of a line is

m = Δy/Δx, where

Δy is the vertical change
Δx is the horizontal change

From the given graph

∵ The line passes through points (0, 0) and (4, 3)

∴ Δx = 4 - 0 = 4

∴ Δy = 3 - 0 = 3

→ Use the rule of the slope above to find the slope of the line

∴ m = $\frac{3}{4}$ = 0.75

∵ The x-axis represents the time in minutes

∵ The y-axis represents the amount in gallons

∵ m represents the rate of change

∴ The rate of change = 0.75 gallons per minute

7 0

3 years ago

Prove that H c G is a normal subgroup if and only if every left coset is a right coset, i.e., aH = Ha for all a e G

Kaylis [27]

$\Rightarrow$

Suppose first that $H\subset G$ is a normal subgroup. Then by definition we must have for all $a\in H$ , $xax^{-1} \in H$ for every $x\in G$ . Let $a\in G$ and choose $(ab)\in aH$ ( $b\in H$ ). By hypothesis we have $aba^{-1} =abbb^{-1}a^{-1}=(ab)b(ab)^{-1} \in H$ , i.e. $aba^{-1}=c$ for some $c\in H$ , thus $ab=ca \in Ha$ . So we have $aH\subset Ha$ . You can prove $Ha\subset aH$ in the same way.

$\Leftarrow$

Suppose $aH=Ha$ for all $a\in G$ . Let $h\in H$ , we have to prove $aha^{-1} \in H$ for every $a\in G$ . So, let $a\in G$ . We have that $ha^{-1} =a^{-1}h'$ for some $h'\in H$ (by the hypothesis). hence we have $aha^{-1}=h' \in H$ . Because $a$ was chosen arbitrarily we have the desired .