Multiply or Divide. Write your answer in scientific notation. (3.2×10^8)(1.3×10^9) =

Please help with these 3 pretty easy problems and explain how you got it!!! 100 POINTS AND BRAINLIEST!!!! Serious answers please

natita [175]

Answer:

Step-by-step explanation:

1)

(x-3)/18=12/9, cross multiply

9(x-3)=18(12)

9x-27=216, add 27 to each side

9x=243, divide each side by 9

x=27

2)

(x-16)/(x+6)=3/5, cross multiply

5(x-16)=3(x+6)

5x-80=3x+18, subtract 3x from each side

2x-80=18, add 80 to each side

2x=98, divide each side by 2

x=49

3)

Since the triangles are similar we can say that

25/(4x-1)=10/(x+5), cross multiply

25(x+5)=10(4x-1)

25x+125=40x-10, subtract 40x from each side

-15x+125=-10, subtract 125 from each side

-15x=-135, divide each side by -15

x=9

7 0

3 years ago

Read 2 more answers

Find the volume of the pyramid with a square base, where the area of the base is 16.3ft and the height of the pyramid is 13.7ft

Deffense [45]

Answer:

oooooogg

Step-by-step explanation:

4 0

3 years ago

Please find the median, mode, range, and the Mean Absolute Deviation for the following

Ronch [10]

Answer:

The median is the first number the mode is middle number and rage is last number

7 0

3 years ago

4, Find a number x such that x = 1 mod 4, x 2 mod 7, and x 5 mod 9.

olchik [2.2K]

4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.

Start with

$x=7\cdot9+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 4, the last two terms vanish and we're left with

$x\equiv63\equiv64-1\equiv-1\equiv3\pmod4$

We have $3^2\equiv9\equiv1\pmod4$ , so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.

$x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 7, the first and last terms vanish and we're left with

$x\equiv72\equiv2\pmod7$

which is what we want, so no adjustments needed here.

$x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 9, the first two terms vanish and we're left with

$x\equiv140\equiv5\pmod9$

so we don't need to make any adjustments here, and we end up with $x=401$ .

By the Chinese remainder theorem, we find that any $x$ such that

$x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}$

is a solution to this system, i.e. $x=149+252n$ for any integer $n$ , the smallest and positive of which is 149.

3 0

3 years ago

A group of researchers wants to know whether men are more likely than women to contract a novel coronavirus. They surveyed two r

olasank [31]

Answer:

Test statistic Z= 0.13008 < 1.96 at 0.10 level of significance

null hypothesis is accepted

There is no difference proportion of positive tests among men is different from the proportion of positive tests among women

Step-by-step explanation:

Step(I):-

Given surveyed two random samples of 390 men and 360 women who were tested

first sample proportion

$p_{1} = \frac{360}{390} = 0.9230$

second sample proportion

$p_{2} = \frac{47}{52} = 0.9038$

Step(ii):-

Null hypothesis : H₀ : There is no difference proportion of positive tests among men is different from the proportion of positive tests among women

Alternative Hypothesis:-

There is difference between proportion of positive tests among men is different from the proportion of positive tests among women

$Z = \frac{p_{1}- p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } } }$

where

$P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1}+n_{2} }$

P = 0.920

$Z= \frac{0.9230-0.9038}{\sqrt{0.920 X0.08(\frac{1}{390}+\frac{1}{52} } )}$

Test statistic Z = 0.13008

Level of significance = 0.10

The critical value Z₀.₁₀ = 1.645

Test statistic Z=0.13008 < 1.645 at 0.1 level of significance

Null hypothesis is accepted

There is no difference proportion of positive tests among men is different from the proportion of positive tests among women

7 0

3 years ago

Multiply or Divide. Write your answer in scientific notation.(3.2×10^8)(1.3×10^9) =​

Multiply or Divide. Write your answer in scientific notation.(3.2×10^8)(1.3×10^9) =