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11 days ago

The marked price of an article is Rs.2080. After allowing d% discount and levying

Mathematics

1 answer:

AnnZ [9K]11 days ago

7 0

Answer:

13%

Detailed breakdown:

Information provided:

MP = 2080
Discount = d%
VAT = (d-2)%
Cost = 1997.84

Applying the discount:

2080 - d% = 2080*(1 - 0.01d)

Including VAT:

2080*(1 - 0.01d) + (d - 2)%
2080*(1 - 0.01d) * (1 + (d -2)/100)
2080*(1 - 0.01d) * (0.98 + 0.01d) = 1997.84
(1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080
0.98 + 0.01d - 0.0098d - 0.0001d² = 0.9605
- 0.0001d² + 0.0002d + 0.98- 0.9605 = 0
0.0001d²- 0.0002d - 0.0195 = 0
d² - 2d + 195 = 0

Solving this quadratic equation yields:

d = 15

Therefore

VAT rate = 15 - 2 = 13%

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If SA=1/2lp+B, find p<br><br> What is the formula for finding p?

Svet_ta [9486]

<span>To isolate p, start by subtracting B from both sides: SA-B=1/2lp. Next, multiply both sides by 2 to eliminate the 1/2: 2SA=lp. Finally, divide both sides by l to derive p: (2SA)/l=p.</span>

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1 month ago

A new weight-watching company, Weight Reducers International, advertises that those who join will lose an average of 10 pounds a

Inessa [8989]

Answer:

The value calculated is Z = 2.53, which exceeds 1.96 at a significance level of 0.05

This leads to the rejection of the null hypothesis H₀

Thus, we accept the alternative hypothesis

This implies that individuals participating in Weight Reducers will lose more than 10 pounds

Step-by-step explanation:

Step(i):-

The size of the random sample 'n' = 50

The new weight-loss program, Weight Reducers International, claims that members will shed an average of 10 pounds within the initial two weeks, with a standard deviation of 2.8 pounds.

Population mean 'μ' = 10 pounds

Population standard deviation 'σ' = 2.8 pounds

Sample mean 'x⁻' = 9

Significance level ∝ = 0.05

Step(ii):-

Null hypothesis: H₀: μ < 10

Alternative hypothesis: H₁: μ > 10

Test statistic calculation

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

$z= \frac{9 - 10}{\frac{2.8}{\sqrt{50} } } = \frac{-1}{0.395} = 2.53$

The determined Z value is 2.53

In this case, the critical value Z is 1.96 at the 0.05 significance level

Step(iii):-

Calculated Z value of 2.53 is greater than 1.96 at a significance level of 0.05

Consequently, we reject the null hypothesis H₀

We accept the alternative hypothesis

Conclusion:-

We determine that individuals who sign up for Weight Reducers will experience a weight loss exceeding 10 pounds

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25 days ago

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the

Inessa [8989]

Answer:

a) $P(X>20)=P(\frac{X-\mu}{\sigma}>\frac{20-\mu}{\sigma})=P(Z>\frac{20-15}{3.5})=P(z>1.43)$

The probability can be determined using the complement rule, with the standard normal distribution, an excel sheet, or a calculator.

$P(z>1.43)=1-P(z$

b) $P(X$

This probability can also be calculated using the normal standard distribution, an excel sheet, or a calculator.

$P(z$

c) $P($

For this one, the probability can likewise be derived from the standard normal distribution, excel, or a calculator, with specific adjustments:

$P(-1.43$

Step-by-step explanation:

Previous concepts

Normal distribution refers to a symmetric probability distribution centered around the mean, indicating that occurrences near the mean are more common than those far from it.

The Z-score is a statistic that represents a value's relationship to the average of a set of values, expressed in terms of how many standard deviations it is away from the mean.

Part a

Let X denote the random variable representing the lengths within a population, and for our case, the distribution for X is as follows:

$X \sim N(15,3.5)$

Where $\mu=15$ and $\sigma=3.5$

We seek the probability:

$P(X>20)$

The most effective way to solve this is by leveraging the normal distribution and the corresponding Z-score:

$z=\frac{x-\mu}{\sigma}$

By applying this formula, we can find the probability:

$P(X>20)=P(\frac{X-\mu}{\sigma}>\frac{20-\mu}{\sigma})=P(Z>\frac{20-15}{3.5})=P(z>1.43)$

Again, this probability can be obtained either using the complement rule, the standard normal distribution, or a calculator.

$P(z>1.43)=1-P(z$

Part b

$P(X$

This probability can also be computed using either the normal standard distribution, an excel sheet, or a calculator.

$P(z$

Part c

$P($

In this case, the probability can similarly be acquired with the help of the standard normal distribution, an excel sheet, or a calculator, with particular adjustments:

$P(-1.43$

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21 day ago

Adrianne jogs for 15 minutes at 6 miles per hour. How many miles does she jog?

Svet_ta [9486]

Response: 3.2

Detailed explanation:

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25 days ago

Read 2 more answers

We can calculate EE, the amount of euros that has the same value as DD U.S. dollars, using the equation E=\dfrac{17}{20}DE=

Leona [9260]

Response:

The equation provided is e=\frac{17}{20}d, where e represents euros and d denotes the equivalent value in U.S. Dollars.

We aim to determine the number of euros for 1 U.S. Dollar.

Substituting d=1 in the above equation

results in

e=\frac{17}{20}(1)

Simplifying gives us

e=\frac{17}{20}

By dividing 17 by 20, we get 0.85.

Thus, 0.85 euros are equivalent to 1 U.S. Dollar.