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VMariaS [17]
2 years ago
10

Enter the simplified form of the complex fraction in the box.

Mathematics
1 answer:
Ket [755]2 years ago
3 0

The problem is:

\frac{\frac{3}{x}+\frac{1}{4}}{1+\frac{3}{x}}

We now do L.C.M. of numerator and add, also do L.C.M. of denominator and add together:

\frac{\frac{12+x}{4x}}{\frac{x+3}{x}}

Dividing by a fraction is same as multiplying by its reciprocal, so we have:

\frac{12+x}{4x} * \frac{x}{x+3} \\

x cancels out, so can multiply and write:

\frac{12+x}{4} * \frac{1}{x+3} \\=\frac{12+x}{4x+12}

This is the simplified form.


ANSWER: \frac{12+x}{4x+12}

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Please help 20 points!!!!!
skad [1K]

Three students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. Then as per the given sample data,

(a) The sample means of the backpacks are: 6.375,6.375,6.625

(b) Range of sample means: 0.25

(c)The true statement is: The closer the range of the sample means is to 0, the less confident they can be in their estimate.

For the first sample, mean= 6.375

For the second sample, mean= 6.375

For the third sample, mean= 6.625

Range of sample means=Maximum Mean- Minimum Mean

                                        = 6.625 - 6.375

                                        = 0.25

The students will estimate the average backpack weight of their classmates using sample means, the true statement is:

The closer the range of the sample means is to 0, the more confident they can be in their estimate.

Learn more about range here:

brainly.com/question/24326172

#SPJ1

6 0
1 year ago
Reabilwe is conducting an experiment in which the temperature is measured carefully. The temperature was 106°C at the end of the
frosja888 [35]

The formula to calculate the temperature (T) after m minutes is -

T = 106 - 6m

We have Reabilwe who is conducting an experiment in which the temperature is measured carefully. The temperature was 106°C at the end of the first minute, and then it falls by 6°C every minute after that.

We have to tp determine a formula to calculate the temperature (T) after m minutes.

<h3 /><h3>Starting from x, if the bacteria count rises by 5 every second, then determine the formula to calculate the bacteria count after 30 seconds.</h3>

Initial count = x

Count increasing per second = 5

Assume that the bacteria count after t seconds is y. Then -

y = x + 5t

for t = 30 ↔ y = 150 + x

According to question, we have -

Initial Temperature = 106 degrees Celsius

Temperature increase per minute = 6 degrees Celsius

Assume that the Temperature fall after m minutes is T. Then -

T = 106 - 6m

Hence, formula to calculate the temperature (T) after m minutes is -

T = 106 - 6m

To solve more questions on Equation Modelling, visit the link below -

brainly.com/question/20876878

#SPJ1

5 0
1 year ago
It takes Ben 2 days to write reports, and it takes Kate 3 days to write reports. Bens rate, in reports per day, is how much grea
sergejj [24]

Answer:

Ben's rate is \dfrac{1}{6} greater than Kate's rate.

Step-by-step explanation:

1. If it takes Ben 2 days to write reports, then his rate is \dfrac{1}{2} of reports per day.

2. If it takes Kate 3 days to write reports, then her rate is \dfrac{1}{3} of reports per day.

3. Ben's rate is

\dfrac{1}{2}-\dfrac{1}{3}=\dfrac{3-2}{6}=\dfrac{1}{6}

greater than Kate's rate.

4 0
3 years ago
Drake buys a ring that costs $8,000, which depreciates at a rate of 9.5% per year.
Alex73 [517]

Answer:

$1129.93

Step-by-step explanation:

100 - 9.5 = 90.5

8000 - 90.5 = 7909.5

7909.5 ÷ 7 = 1129.93

i hope this helps

4 0
2 years ago
If a seed is planted, it has a 80% chance of growing into a healthy plant.
AlladinOne [14]

Answer:

0.336

Step-by-step explanation:

Use binomial probability:

P = nCr p^r q^(n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

Here, n = 8, r = 7, p = 0.8, and q = 0.2.

P = ₈C₇ (0.8)⁷ (0.2)⁸⁻⁷

P = 0.336

3 0
3 years ago
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