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igomit [66]
3 years ago
6

5/8 of the 64 musicians in a music contest are guitarists. Some of the guitarists play jazz solos, and the rest play classical s

olos. The ratio of the number of guitarists playing jazz solos to the total number of guitarists in the contest is 1:4. How many guitarists play classical solos in the contest?
Mathematics
2 answers:
lyudmila [28]3 years ago
8 0

There are 64 musicians and 5/8 of them are guitarists:

5/8 * 64 = 40 ( the total numbet of guitarists )

x - the guitarists playing jazz slolo

x : 40 = 1 : 4

4 x = 40

x = 40 : 4

x = 10

Therefore there are 10 guitarists playing jazz solo.

40 - 10 = 30

Answer:

There are 30 guitarists who play classical solo.

motikmotik3 years ago
5 0

The first thing we must do for this case is find the number of total guitarists.

We have then:

(\frac{5}{8}) * (64) = 40

We now look for the relationship between the number of guitarists playing jazz alone to the total number of guitarists.

We have then:

\frac{x}{40} = \frac{1}{4}

Where,

x: number of guitarists playing jazz alone

From here, we clear the value of x.

x = (\frac{1}{4}) * (40)\\x = 10

Then, the number of guitarists who play classical solo is:

40 - 10 = 30

Answer:

30 guitarists play classical solos in the contest

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2 years ago
The common ratio of a geometric series is 3 and the sum of the first 8 terms is 3280.
Pavlova-9 [17]

Answer:

The first term of the geometric series is 1

Step-by-step explanation:

In this question, we are tasked with calculating the first term of a geometric series, given the common ratio, and the sum of the first 8 terms.

Mathematically, the sum of terms in a geometric series can be calculated as;

S = a(r^n-1)/( r-1)

where a is the first term that we are looking for

r is the common ratio which is 3 according to the question

n is the number of terms which is 8

S is the sum of the number of terms which is 3280 according to the question

Plugging these values, we have

3280 = a(3^8 -1)/(3-1)

3280 = a( 6561-1)/2

3280 = a(6560)/2

3280 = 3280a

a = 3280/3280

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6 0
2 years ago
A sales person is given a choice of two salary plans. Plan 1 is a weekly salary of 700 plus 4% commission of sales. Plan 2 is a
bezimeni [28]

Let 's' represent the amount of sales.

Plan 1:

\text{ \$700 + (4\% of s)}\begin{gathered} \text{ \$700+(}\frac{\text{4}}{100}\times s) \\ \text{ \$700+(0.04}\times s)=\text{ \$700}+0.04s \end{gathered}

Plan 2:

12\text{ \% of s}\begin{gathered} \frac{12}{100}\times s \\ 0.12\times s=0.12s \end{gathered}

Equating the two plans together and solving for the amount of sales,

\begin{gathered} \text{Plan 2=Plan 1} \\ 0.12s=\text{ \$700+0.04s} \\  \end{gathered}

Collecting like terms,

\begin{gathered} 0.12s-0.04s=\text{ \$700} \\ 0.08s=\text{\$700} \end{gathered}

Divide both sides by 0.08,

\begin{gathered} \frac{0.08s}{0.08}=\frac{\text{ \$700}}{0.08} \\ s=\text{ \$8750} \end{gathered}

Hence, the amount of sales is $8,750.

6 0
1 year ago
Quadratic equation whose vertex is (2,3) and y intercept is 11
never [62]

Answer:

y = 2(x - 2)² + 3      vertex form

y = 2x² - 8x + 11     standard form

Step-by-step explanation:

Vertex form

y = a(x - h)² + k

(h, k) = (2, 3)

y = a(x - 2)² + 3

To find "a" plug in the y-intercept (0, 11)

11 = a(-2)² + 3

11 = 4a + 3

Subtract 3 from both sides

8 = 4a

a = 2

y = 2(x - 2)² + 3

Expand

y = 2(x² - 4x + 4) + 3

y = 2x² - 8x + 11

5 0
3 years ago
What number should be added to the expression x^2+4x to change it into a perfect square trinomial?
sleet_krkn [62]
4

x^2+4x+4=(x+2)^2
8 0
3 years ago
Read 2 more answers
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