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2 years ago

1) The product of two rational numbers is 15/56. If one of the numbers is −5/48 ,find the other .

Mathematics

1 answer:

Zinaida [17]2 years ago

3 0

Answer:

$unknown \: = x \\ then \: x \times \frac{ - 5}{48} = \frac{15}{56} \\ x = \frac{15}{56} \times \frac{ - 48}{5} \\ x = \frac{ - 720}{280} = \frac{18}{7} \\ thank \: you$

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The SAT mathematics scores in the state of Florida are approximately normally distributed with a mean of 500 and a standard devi

ivann1987 [24]

Since the range of the scores given was between 300 and 700 (which is 2 standard deviations below and above the mean), the probability that a randomly selected student's math score - as based on the empirical rule of statistics - is 95%. In decimal form, it is .95.

6 0

2 years ago

Read 2 more answers

A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

dusya [7]

The sum of arithmetic series is given by:
Sn=n/2(a1+an)
where:
n=number of terms
a1=first term
an=nth term
but
n=18, an=275, Sn=4185
plugging the values in the formula we get:
4185=18/2(a1+275)
simplifying this we get:
4185=9(a1+275)
dividing through by 9 we get:
465=a1+275
thus
a1=465-275
a1=190

Answer: first number is 190

3 0

2 years ago

A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wave

erma4kov [3.2K]

Answer:

A Pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm and 96 cm but does not resonate at any wavelengths longer than these. This pipe is:

A. closed at both ends

B. open at one end and closed at one end

C. open at both ends.

D. we cannot tell because we do not know the frequency of the sound.

The right choice is:

B. open at one end and closed at one end .

Step-by-step explanation:

Given:

Length of the pipe, $L$ = 120 cm

Its wavelength $\lambda_1$ = 480 cm

$\lambda_2$ = 160 cm and $\lambda_3$ = 96 cm

We have to find whether the pipe is open,closed or open-closed or none.

Note:

The fundamental wavelength of a pipe which is open at both ends is 2L.
The fundamental wavelength of a pipe which is closed at one end and open at another end is 4L.

So,

The fundamental wavelength:

⇒ $4L=4(120)=480\ cm$

It seems that the pipe is open at one end and closed at one end.

Now lets check with the subsequent wavelengths.

For one side open and one side closed pipe:

An odd-integer number of quarter wavelength have to fit into the tube of length L.

⇒ $\lambda_2=\frac{4L}{3}$ ⇒ $\lambda_3=\frac{4L}{5}$

⇒ $\lambda_2=\frac{4(120)}{3}$ ⇒ $\lambda_3=\frac{4(120)}{5}$

⇒ $\lambda_2=\frac{480}{3}$ ⇒ $\lambda_3=\frac{480}{5}$

⇒ $\lambda_2=160\ cm$ ⇒ $\lambda_3=96\ cm$

So the pipe is open at one end and closed at one end .

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2 years ago

Solve the following multiplication and division problems. a. 8 T. 1,398 lb. 14 oz. × 6 b. 349 lb. 6 oz. ÷ 130 c. 6 T. 294 lb. ÷

tester [92]

Answer: a) 278382 oz

b) 43 oz

c) 64.1 oz

Step-by-step explanation:

a) 8 T. 1,398 lb. 14 oz. × 6

First we need to change it in 'oz'.

As we know that

$1\ ton=32000\ oz\\\\1\ lb=16\ oz$

so, it becomes,

$8\times 32000+1398\times 16+14\ oz\\\\=278382\ oz$

8 T. 1,398 lb. 14 oz. × 6 becomes

$278382\times 6\\\\=1670292\ oz$

b) 349 lb. 6 oz. ÷ 130

It becomes,

$349\times 16+6\ oz\\\\=5590\ oz\\\\\text{ at last it becomes}\\\\=\frac{5590}{130}\\\\=43\ oz$

c) 6 T. 294 lb. ÷ 3,071

First it becomes,

$6\times 32000+294\times 16\ oz\\\\=196704\ oz$

At last it becomes,

$\frac{196704}{3071}\\\\=64.1\ oz$

Hence, a) 278382 oz

b) 43 oz

c) 64.1 oz

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2 years ago

Read 2 more answers

the time taken by a student to the university has been shown to be normally distributed with mean of 16 minutes and standard dev

Naya [18.7K]

Answer:

a) 2.84% probability that he is late for his first lecture.

b) 5.112 days

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 16, \sigma = 2.1$

a. Find the probability that he is late for his first lecture.

This is the probability that he takes more than 20 minutes to walk, which is 1 subtracted by the pvalue of Z when X = 20. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{20 - 16}{2.1}$

$Z = 1.905$

$Z = 1.905$ has a pvalue of 0.9716

1 - 0.9716 = 0.0284

2.84% probability that he is late for his first lecture.

b. Find the number of days per year he is likely to be late for his first lecture.

Each day, 2.84% probability that he is late for his first lecture.

Out of 180

0.0284*180 = 5.112 days

4 0

2 years ago