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Radda [10]
3 years ago
14

Find two numbers such that their product, sum and difference are in the ratio 5:4:1'

Mathematics
1 answer:
wel3 years ago
7 0

Answer:

3 1/3 and 2

Step-by-step explanation:

Let the numbers be x and y  and let z be the constant of proportion. Then

xy = 5z  ...............(1)

x + y = 4z ...........(2)

x - y = z ..............(3)     Adding (2) and (3)

2x = 5z

x = 5z/2   ................(4)

Substituting for x in equation 1:

5z/2 *  y = 5z

y = (5z * 2) / 5z = 2.

Substituting for  y in equations (2) and (3):

x + 2 = 4z

x - 2 = z            Subtracting:

4 = 3z

z = 4/3.

Substituting for z in equation (4)

x =  5(4/3) /2

x = 20/6 = 10/3 = 3 1/3.

So the 2 numbers are  3 1/3 and 2.

Checking the results:

xy = 2 * 10/3 = 20/3 = 5 * 4/3 = 5z

x + y = 10/3 + 2 = 16/3 = 4 * 4/3 = 4z.

x - y = 10/3 - 2 = 4/3 = z.

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The size of a television screen is given as 95 cm, correct to the nearest 5 cm.
erica [24]

Answer:

The upper bound is 97.5 cm

Step-by-step explanation:

The upper bound is given as the value that is larger than or equal to all values in a data set, for example, in the data set, {3, 6, 16, 23, 25}, an upper bound  is 25, however, where the accuracy of the data is given, the upper bound can be found by the following relation

Where the number is given to the nearest 100, add and subtract  half of hundred to obtain the upper bound and lower bound respectively

For the question, given that the size of the television is given as 95 cm, correct to the nearest 5 cm, we add add half of 5 cm to get the upper bound as follows;

Upper bound = 95 cm + 5/2 cm = 97.5 cm

The upper bound = 97.5 cm.

8 0
3 years ago
One of your employees has suggested that your company develop a new product. You decide to take a random sample of your customer
iren [92.7K]

Answer:

269

Step-by-step explanation:

The margin of Error is E = 0.05

The level of significance is, α = 1 - confidence level = 1 - 0.9 = 0.1

Assume that the proportion is, p =0.5

From the standard normal table, observe that the critical value of Z for two tail test and 10% level of significance is 1.64

The calculation of sample size is as follows: n = (Z/E)²p(1-p)

n = (1.64/0.05)²0.5 (1 - 0.5)

n = (1.64/0.05)² 0.25

n = 1075.84 × 0.25

n = 268.96 ≈ 269

The required sample size with the given margin of error approximately is 269. This value indicates the size of the customers who are using this company’s products.

6 0
3 years ago
The train station clock runs too fast and gains 7 minutes every 4 days. How many minutes and seconds will it have gained at the
Olegator [25]
16 minutes and 15 seconds.

4x2=8 8 days = 14 minutes
7/4=1.75= 2 minutes 15 seconds= total of 16min 15sec
3 0
3 years ago
Read 2 more answers
A reporter for a large sports television network wants to determine if "homefield advantage" is dependent upon the sport. He col
Ne4ueva [31]

Answer:

with 0.10 level of significance the P-VALUE that would be used in the hypothesis claim is 0.05%

Step-by-step explanation:

In hypothesis testing in statistics, we can say that the p-value is a probability of obtaining test results when we assume that the null hypothesis is correct.

The p-value is the probability that the null hypothesis is true.

A p-value less than or equals to 0.05  is statistically significant. It shows strong evidence against the null hypothesis, meaning  there is less than a 5% probability the null is correct and clearly we can say that the results are random.

8 0
3 years ago
How to add and subtract polynomials
Lorico [155]
You combine like terms

Example: 5x^3+3x+1-4x^3-2x-1

The answer would be x^3+x
6 0
3 years ago
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