The piece of music that I am learning is 60 measures long. There are 13 beats in every measure, and every eighth note lasts for
1 answer:
fraction of the whole piece you play middle C.
- A fraction is a portion of a whole or, more broadly, any number of equal parts.
- In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
- A common, vulgar, or simple fraction consists of a numerator above a line and a non-zero denominator below (or after) that line.
- Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.
To find for what fraction of the whole piece do you play middle C:
Since 7 out of every 13 beats in the finale are played at middle C, the finale is played at middle C.
The finale is 17 measures out of a 60-measure piece or of the whole piece.
of
is
x
Therefore, for a fraction of the whole piece you play middle C.
Know more about fractions here:
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<em><u>Statement:</u></em>
The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.
<em><u>To find out:</u></em>
The length of the larger side of the right angled triangle.
<em><u>Solution:</u></em>
Let us consider x as the smaller side and y as the larger side.
Then, in the right angled triangle,
x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]
Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).
And if the larger side is increased by 3 cm, then the larger side will be (y + 3).
Then, in the new right angled triangle,
(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]
or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²
or, x² + 4x + 4 + y² + 6y + 9 = (√117)²
or, x² + y² + 4x + 6y + 13 = (√117)²
Now, put the value of x² + y² from equation (I),
or, (2√13)² + 4x + 6y + 13 = (√117)²
or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)
or, 52 + 4x + 6y + 13 = 117
or, 4x + 6y = 117 - 52 - 13
or, 4x + 6y = 52
or, 4x = 52 - 6y
or, x = ...(II)
Now, put the value of x of equation (II) in (I),
x² + y² = (2√13)²
or, + y² = 52
or, = 52
or, 52y²-624y + 2704 = 52 × 16
or, 52y² - 624y + 2704 - 832 = 0
or, 52y² - 624y + 1872 = 0
or, 52(y² - 12y + 36) = 0
or, y²-12y +36 = 0 ÷ 52
or, y²-12y +36 = 0
or, (y)² - 2 × 6 × y + (6)² = 0
or, (y - 6)² = 0
or, y - 6=0
or, y = 6
We have taken y as the length of the larger side of the right angled triangle.
So, the length of the larger side is 6 cm.
<em><u>Answer:</u></em>
6 cm
Hope you could understand.
If you have any query, feel free to ask.
Answer:
There is not enough evidence to support the claim that the liquid diet yields a higher mean weight loss than the powder diet (P-value = 0.15).
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that the liquid diet yields a higher mean weight loss than the powder diet.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample 1 (powder diet group), of size n1=49 has a mean of 42 and a standard deviation of 12.
The sample 2 (liquid diet group), of size n2=36 has a mean of 45 and a standard deviation of 14.
The difference between sample means is Md=-3.
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this test are:
This test is a left-tailed test, with 83 degrees of freedom and t=-1.04, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.15) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the liquid diet yields a higher mean weight loss than the powder diet.