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3 years ago

Determine the quotient

Mathematics

1 answer:

nexus9112 [7]3 years ago

8 0

Answer:

option 2: $\large \frac{10}{12}$

Step-by-step explanation:

when dividing fractions, you can actually multiply them together by the reciprocal of the second one. (reciprocal is just flipping the fraction)

so, $\frac{2}{3}$ ÷ $\frac{4}{5}$

becomes $\frac{2}{3} * \frac{5}{4}$

to multiply fractions together, just multiply the top and bottom.

2 * 5 = 10

3 * 4 = 12

so the answer would be $\frac{10}{12}$

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onsider the equation 0.5 times e4z =13 solve the equation for z. express the solution as a logarithm in base e

olga_2 [115]

Answer:

$z=\frac{ln(26)}{4}$

Step-by-step explanation:

The given equation is:

$0.5\,e^{4z}=13$

so, we first isolate the exponential form that contains the unknown "z" in the exponent, by dividing both sides by 0.5:

$0.5\,e^{4z}=13\\e^{4z}=\frac{13}{0.5}\\e^{4z}=26$

Now we bring the exponent down by applying the natural log function on both sides, and then solve for "z":

$e^{4z}=26\\ln(e^{4z})=ln(26)\\4\,z=ln(26)\\z=\frac{ln(26)}{4}$

5 0

4 years ago

Suppose that you are provided with the following data for your country for a particular month: 200 million people are working, 2

lisov135 [29]

Answer:

$Unemployement\,\,rate=23%$

Step-by-step explanation:

To find the unemployment rate we have the next expression:

$Unemplyment\,\,rate=\frac{Unemployment\,\,people}{Total\,\, labor\,\, force}\cdot 100$

We have the next data:

200 million employed

20 million unemployed

40 million umemployed are not looking for a job

Then the total labor force will be the employed and the unemployed population then de have 260 million

$Unemployement\,\,rate=\frac{60million}{260million}\cdot 100$

$Unemployement\,\,rate=\frac{6}{26}\cdot 100$

$Unemployement\,\,rate=0.23\cdot 100$

$Unemployement\,\,rate=23%$

7 0

3 years ago

One hundred items are simultaneously put on a life test. Suppose the lifetimes

romanna [79]

Answer:

a) $\mathrm{E}[\mathrm{T}]=\sum_{\mathrm{H}}^{5} \frac{200}{101-i}$

b) $\mathrm{Var}[\mathrm{T}]=\sum_{k=1}^{5} \frac{(200)^{2}}{(101-i)^{2}}$

Step-by-step explanation:

Given:

The lifetimes of the individual items are independent exponential random variables.

Mean = 200 hours.

Assume, Ti be the time between ( $i-1$ )st and the $ith$ failures. Then, the $T_{i}$ are independent with $\mathrm{T}_{\mathrm{i}}$ being exponential with rate $\frac{(101-i)}{200} .$

Therefore,

a) $E[T]=\sum_{i=1}^{5} E\left[\tau_{i}\right]$

$=\sum_{i=1}^{5} \frac{200}{101-i}$

$\therefore \mathrm{E}[\mathrm{T}]=\sum_{\mathrm{H}}^{5} \frac{200}{101-i}$

$b)$

The variance is given by, $\mathrm{Var}[\mathrm{T}]=\sum_{i=1}^{5} \mathrm{Var}[T]$

$\therefore \mathrm{Var}[\mathrm{T}]=\sum_{k=1}^{5} \frac{(200)^{2}}{(101-i)^{2}}$

7 0

4 years ago

50 Points!!

____ [38]

Answer:

a) g(x) = f(x) + 3

So g(x) is a vertical translation of f(x), 3 units upwards

b) g(x) = 3x² - 1 + 3

g(x) = 3x² + 2

The graph has shifted 3 units upwards, so has the vertex.

The vertex of f is (0,-1)

Whereas the vertex of g is (0,2)

-1 + 3 = 2

8 0

3 years ago

Write an expression equivalent to h^6/h^3 in the form of h^m

Pavel [41]

Answer:

$h^3 = h^m$

Step-by-step explanation:

$\frac{h^6}{h^3} = h^m$

6 - 3 = 3

keep the base same, therefore

$h^3 = h^m$

Hope this helps!

3 0

3 years ago