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svetoff [14.1K]
3 years ago
12

The numerator of a fraction is 15 less than twice its denominator. If the numerator is increased by 5 and the denominator is inc

reased by 7, the new fraction will be equal to 2/3. What is the original fraction?
Mathematics
1 answer:
denis-greek [22]3 years ago
7 0

Answer:

  7/11

Step-by-step explanation:

Let d represent the original denominator. Then the original numerator is ...

  2d-15

The new numerator is ...

  (2d-15) +5

and the new denominator is ...

  d+7

The ratio of these is 2/3, so we have ...

  \dfrac{2d-15+5}{d+7}=\dfrac{2}{3}\\\\3(2d-10)=2(d+7) \quad\text{cross multiply}\\\\4d=44 \quad\text{add 30-2d}\\\\d=11\\\\2d-15=2(11)-15=7

The original fraction is 7/11.

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Based on historical data, your manager believes that 43% of the company's orders come from first-time customers. A random sample
tatyana61 [14]

Answer:

Following are the solution to the question:

Step-by-step explanation:

p = 0.43\\\\n = 243\\\\\sigma =\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.43 (1 -0.43)}{243}}=0.0013

z-score for \hat{p}=0.2 will be:

z score for will be:

z=\frac{\hat{p}-p}{\sigma}=\frac{0.39 - 0.43}{0.0013}=-30.76

P(0.2 using excel method to calculate the value.

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4 years ago
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Answer:

4

Step-by-step explanation:

f(x) (8x² - 3x + 1) / (2x² + 2x +3)

the first thing I did was to graph the function to see if there was a horizonal asymptote using Desmos graphing calculator and there was and it was 4

you want to take the limit as x approaches infinity

essentially  lim(x to ∞) of f(x) = 8x²/ 2x²      is the dominate terms

                    lim(x to ∞) of f(x) = 8 / 2

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6 0
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Ms. Lee wants to know what kinds of things her students do prepare for her tests. Ms. Lee placed the names of her students into
Darina [25.2K]

Answers:

  • a) The sample is the set of students Ms. Lee selects from the box.
  • b) The population is the set of all students in Ms. Lee's classroom.

=============================================

Explanation:

The first sentence tells us what the population is: it's the set of all her students. She's not concerned with any other students in any other classroom. So her "universe", so to speak, is solely focused on this classroom only. Once the population is set up, a sample of it would be a subset of the population.

If set A is a subset of set B, then everything in A is also in B, but not vice versa. For example, the set of humans is a subset of the set of mammals because all humans are mammals. However, a dog is a mammal but not a human. This shows that A is a subset of B, but not the other way around. In this example, A = humans and B = mammals.

Going back to the classroom problem, we have A = sample and B = population. If Ms. Lee has 30 students, and she randomly selects 5 of them, then those 30 students make up set B and the 5 selected make up set A. Selecting the names randomly should generate an unbiased sample. This sample should represent the population overall. If the population is small enough, the teacher could do a census and not need a sample. Though there may be scenarios that it's still effective to draw a sample.

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3 years ago
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