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lisabon 2012 [21]
3 years ago
8

The price of a flight was increased by 3% to £650. What was the price before the increase?

Mathematics
1 answer:
liubo4ka [24]3 years ago
8 0

Answer:

£ 631

Step-by-step explanation:

Hi this is a simple mathematics issue.

First, let's imagine what is 3%. '3 percents' means 3/100. If your family have 100 apples and you have 3 apples, that means you have 3% of your family apples.

Now, get back to this problem. We need to find the price before increase. Let's say the price was £ X. Now we will find the X number.

It's said that the price was increased by 3%. That means they took 3% of X and added that amount to X to have the new price : £ 650. That means we have this equation :

650 = X + 3%×X

Let's make it easier to look :

650 = X + 3/100 ×X

650 = X×( 1+ 3/100)

= X × 103/100

So we can see 650 is equaled to X multipled by 103/100.

To find the correct answer, simply divide 650 by 103/100.

*A hint: When you divide a number by a fraction, you can simply put the number multiplied by the "flipped" fraction .

Hope you learn with Joy and High Grades !!!

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12x – 5y = -20<br> y = x +4
kari74 [83]

Answer:

x = \frac{-40}{7} , y = -1.71

Step-by-step explanation:

sub y = x+4 in the first equation to get:

12 x - 5 (x+4) = -20

Simplify:

12 x - 5 x + 20 = -20

Further simplify:

7 x = - 40

Divie both sides by 7 to get:

x = \frac{-40}{7}

--> x = -5.7

Sub x = \frac{-40}{7}  in the second equation to get:

y = \frac{-40}{7}  + 4  = -1.71

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Emily wants to make a rectangular model with a height of one cube
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Step-by-step explanation:


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All ways of connecting two cubes result in the same shape. So answer is larger than two.


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Hence, three cubes can only make a straight shape or an angled shape.


Four cubes can make a straight shape, a L shape, a Γ shape (but flipping it over through 3 dimensions makes L and Γ identical), a T shape, and a square shape. That is either four or five different objects depending on if they can be lifted from the table. Anyway, it is more than two.

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3 years ago
Calcium is essential to tree growth because it promotes the formation of wood and maintains cell walls. In 2010, the concentrati
sergij07 [2.7K]

Answer:

The p-value obtained from the hypothesis test is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & say that there isn't enough evidence from the sample to conclude that the the calcium concentrations have changed since 2010.

Step-by-step explanation:

To perform this test, we need to first obtain the sample mean and sample standard deviation.

The data is 0.065 0.087 0.070 0.262 0.126 0.183 0.120 0.234 0.313 0.108

Mean = (sum of variables)/(sample size)

= (0.065+0.087+0.070+0.262+0.126+0.183+0.120+0.234+0.313+0.108)/10

= 0.1568 milligram per liter

Standard deviation = σ = √[Σ(x - xbar)²/N]

Σ(x - xbar)² = 0.00842724+0.00487204+0.00753424+0.01106704+0.00094864+0.00068644+0.00135424+0.00595984+0.02439844+0.00238144

= 0.0676296

σ = √[Σ(x - xbar)²/N] = √(0.0676296/10) = 0.08224 milligrams per liter

To do an hypothesis test, we need to first define the null and alternative hypothesis

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis would be that there is no significant evidence to suggest that the the calcium concentrations have changed since 2010. That is, the calcium concentrations haven't changed since 2010.

The alternative hypothesis is that there is significant evidence to suggest that the the calcium concentrations have changed since 2010. That is, the calcium concentrations haven't changed since 2010.

Mathematically,

The null hypothesis is represented as

H₀: μ = 0.11 milligrams per liter

The alternative hypothesis is given as

Hₐ: μ ≠ 0.11 milligrams per liter

To do this test, we will use the t-distribution because no information on the population standard deviation is known

So, we compute the t-test statistic

t = (x - μ₀)/σₓ

x = sample mean = 0.1568 milligram per liter

μ₀ = the mean calcium concentrations from 2010 = 0.11 milligrams per liter

σₓ = standard error = (σ/√n)

where n = Sample size = 10

σ = Sample standard deviation = 0.08224 milligrams per liter

σₓ = (σ/√n) = (0.08224/√10) = 0.026

t = (0.1568 - 0.11) ÷ 0.026

t = 1.80

checking the tables for the p-value of this t-statistic

Degree of freedom = df = 10 - 1 = 10 - 1 = 9

Significance level = 0.05

The hypothesis test uses a two-tailed condition because we're testing in two directions. (Greater than and less than)

p-value (for t = 1.80, at 0.05 significance level, df = 9, with a two tailed condition) = 0.105391

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.105391

0.105391 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there isn't enough evidence to conclude that the the calcium concentrations have changed since 2010.

Hope this Helps!!!

8 0
3 years ago
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