All categories

2 years ago

Leena walked 2/3 of a mile What is 2/3 written as a sum of unit fractions with the denominator of nine

1 answer:

3 0

Bear in mind that multiplying anything, and anything whatsoever by 1, has a product of the anything itself.

so, let's multiply 2/3 by 1 then and check about,

$\bf \cfrac{same}{same}=1\qquad thus\cfrac{2}{3}\cdot 1\implies \cfrac{2}{3}\cdot \cfrac{3}{3}\implies \cfrac{6}{9}
\\\\\\
\textit{now, we can split that and write it as a sum}\implies \cfrac{1+5}{9}\implies \cfrac{1}{9}+\cfrac{5}{9}$

You might be interested in

What is the value of z in the equation 3z - 7 = 14?

aleksandr82 [10.1K]

Answer:

7

Step-by-step explanation:

You need to solve for z

Add 7 to both sides

3z = 21

Divide by 3

z = 7

5 0

2 years ago

Read 2 more answers

A player of a video game is confronted with a series of four opponents and an 80% probability of defeating each opponent. Assume

mixer [17]

Answer:

(a) 0.4096

(b) 0.64

Step-by-step explanation:

The probability that the player wins is,

$P(W)=0.80$

Then the probability that the player losses is,

$P(L)=1-P(W)=1-0.80=0.20$

The player is playing the video game with 4 different opponents.

It is provided that when the player is defeated by an opponent the game ends.

All the possible ways the player can win is: {L, WL, WWL, WWWL and WWWW)

(a)

The results from all the 4 opponents are independent, i.e. the result of a game played with one opponent is unaffected by the result of the game played with another opponent.

The probability that the player defeats all four opponents in a game is,

P (Player defeats all 4 opponents) = $P(W)\times P(W)\times P(W)\times P(W)=[P(W)]^{4} =(0.80)^{4}=0.4096$

Thus, the probability that the player defeats all four opponents in a game is 0.4096.

(b)

The probability that the player defeats at least two opponents in a game is,

P (Player defeats at least 2) = 1 - P (Player losses the 1st game) - P (Player losses the 2nd game) = $1-P(L)-P(WL)$

$=1-(0.20)-(0.80\times0.20)\\=1-0.20-0.16\\=0.64$

Thus, the probability that the player defeats at least two opponents in a game is 0.64.

(c)

Let X = number of times the player defeats all 4 opponents.

The probability that the player defeats all four opponents in a game is,

P(WWWW) = 0.4096.

Then the random variable $X\sim Bin(n=3, p=0.4096)$

The probability distribution of binomial is:

$P(X=x)={n\choose x}p^{x} (1-p)^{n-x}$

The probability that the player defeats all the 4 opponents at least once is,

P (X ≥ 1) = 1 - P (X < 1)

= 1 - P (X = 0)

$=1-[{3\choose 0}(0.4096)^{0} (1-0.4096)^{3-0}]\\=1-[1\times1\times (0.5904)^{3}\\=1-0.2058\\=0.7942$

Thus, the probability that the player defeats all the 4 opponents at least once is 0.7942.

3 0

2 years ago

Ursula Works At A Print Shop. She Uses A Printer That Can Print 12 Pages Per Minute. Yesterday She Started Printing Flyers For A

BigorU [14]

Answer:

10:30 am.

Step-by-step explanation:

We have been given that Ursula uses a printer that can print 12 pages per minute.

Ursula started printing flyer for an order yesterday. Today at 8 am she continued working on the order, and by 9 a.m. she had 420 flyers for the order completed. The order was to print 1500 pages.

Let us find the number of pages left to print.

$\text{Number of the pages left to print}=1500-420$

$\text{Number of the pages left to print}=1080$

To find the time it will take to print 1080 pages we will divide number of pages left to print by number of pages printed per minute.

$\text{Time it will take to print 1080 pages}=\frac{1080\text{pages}}{\frac{\text{12 pages}}{\text{minute}}}}$

$\text{Time it will take to print 1080 pages}=\frac{1080\text{pages}}{12}\times \frac{\text{minute}}{\text{page}}}$

$\text{Time it will take to print 1080 pages}=90\text{ minutes}$

90 minutes will be 1.5 hours , so 1.5 hours after 9 am will be 10:30 am. Therefore, the job was finished at 10:30 am.

8 0

2 years ago

The quality control manager at a light bulb factory needs to estimate the mean life of a batch (population) of light bulbs. We a

Nadusha1986 [10]

Answer:

a)95% confidence intervals for the population mean of light bulbs in this batch

(325.5 ,374.5)

The calculated value Z = 4 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The manufacturer has not right to take the average life of the light bulbs is 400 hours.

Step-by-step explanation:

Given sample size n = 64

Given mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

The tabulated value Z₀.₉₅ = 1.96

95% confidence intervals for the population mean of light bulbs in this batch

$(x^{-} - Z_{\frac{\alpha }{2} } \frac{S.D}{\sqrt{n} } , x^{-} + Z_{\frac{\alpha }{2} }\frac{S.D}{\sqrt{n} } )$

$(350 - 1.96\frac{100}{\sqrt{64} } , 350 + 1.96\frac{100}{\sqrt{64} } )$

$(350 -24.5, 350 +24.5)$

(325.5 ,374.5)

Explanation:-

Given mean of the Population μ = 400

Given sample size n = 64

Given mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

Null hypothesis : H₀:The manufacturer has right to take the average life of the light bulbs is 400 hours.

μ = 400

Alternative Hypothesis: H₁: μ ≠400

The test statistic

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{350 -400}{\frac{100}{\sqrt{64} } }$

|Z| = |-4|

The tabulated value Z₀.₉₅ = 1.96

The calculated value Z = 4 > 1.96 at 0.05 level of significance

Null hypothesis is rejected.

Conclusion:-

The manufacturer has not right to take the average life of the light bulbs is 400 hours.

5 0

2 years ago

One pound of grapes costs $1.55. Which equation correctly shows a pair of equivalent ratios that can be used to find the cost of

Fiesta28 [93]

1.55 / 1 = x / 3.5....$ 1.55 to 1 lb = $ x to 3.5 lbs

first one <==

it could have also been : 1 / 1.55 = 3.5 / x...but that is not an answer choice

6 0

2 years ago

Read 2 more answers