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3 years ago

A musician plans to perform 6 selections. in how many ways can she arrange the musical selections?

Mathematics

2 answers:

Ymorist [56]3 years ago

7 0

Answer:720 ways

Step-by-step explanation:

We use permutation to solve this,

6! = 6×5×4×3×2×1=720

Olenka [21]3 years ago

5 0

Order counts, that's a permutation of 6 things,

$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$

Answer: 720

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What is the slope and y-intercept of this<br> equation? y = 5x

denis-greek [22]

Answer:

Slope- 5 y-int- (0,0)

Step-by-step explanation:

y=mx+b, where m=slope and b=y-int. m=5, and we don't see a b, so it must be 0.

8 0

3 years ago

Plz..... Solve this questions for me...

faust18 [17]

$6.\\\text{We know}\ 9=3^2.\ \text{Therefore}\\\\9^2=(3^2)^2\\\\\text{use}\ (a^n)^m=a^{nm}\\\\9^2=(3^2)^2=3^{2\cdot2}=3^4\\\\\boxed{3^4=9^2}\\=================$

$7.\\METHOD\ 1:\\\\\sqrt{7^4}=\sqrt{7^{2\cdot2}}\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(7^2)^2}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\boxed{7^2}\\\\METHOD\ 2:\\\\\text{use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\\\\\sqrt{7^4}=7^\frac{4}{2}=\boxed{7^2}\\=================$

$8.\\5^a\times5^b=5^{11}\\\\a)\\\text{use}\ a^n\times a^m=a^{n+m}\\\\5^a\times5^b=5^{a+b}\\\\5^{a+b}=5^{11}\Rightarrow a+b=11\\\\11\ \text{is odd. The sum of even and odd is odd. Therefore}\ a\ \text{and}\ b\ \text{can't be even.}\\--------------------\\\\b)\\5\ \text{solutions}\\\\11=5+6\\11=4+7\\11=3+8\\11=2+9\\11=1+10$

3 0

2 years ago

Based on a study of population projections for 2000 to 2050, the projected population of a group of people (in millions) can b

Olegator [25]

Answer:

(a) 0.107 million per year

(b) 0.114 million per year

Step-by-step explanation:

$A(t) = 11.19(1.009)^t$

(a) The average rate of change between 2000 and 2014 is determined by dividing the difference in the populations in the two years by the number of years. In the year 2000, $t=0$ and in 2014, $t=14$ . Mathematically,

$\text{Rate}=\dfrac{A(2014) - A(2000)}{2014-2000}=\dfrac{11.19(1.009)^14-11.19(1.009)^0} {14}$

$A(0)=\dfrac{12.69-11.19}{14}=\dfrac{1.5}{14}=0.107$

(b) The instantaneous rate of change is determined by finding the differential derivative at that year.

The result of differentiating functions of the firm $y=a^x$ (where $a$ is a constant) is $\dfrac{dy}{dx}=a^x\ln a$ . Let's use in this in finding the derivative of $A(t)$ .

$A\prime(t) = \dfrac{A}{t}=11.19\cdot1.009^t\ln1.009$

In the year 2014, $t=14$ .

$A\prime(14) =11.19\cdot1.009^14\ln1.009=0.114$

6 0

3 years ago

Peter is at a lumber yard. He gets 2 free boxes of nails for every 10 boards he buys. Write an expression for the number of boxe

Sati [7]

A. The number of 10-boards Peter bought is equal to n divided by 10. Then, each of the 10-boxes will get two boxes of nails. The number of boxes of nails that Peter will have after buying n boards will be,

N = (2)(n/10)

Simplifying,

<em> N = n/5</em>

b. If the number of boards are 90 then,

N2 = (90/10)(2)(100 nails/box)
N2 = 1800

Answer: 1800

7 0

3 years ago

Read 2 more answers

You have 10 liters of juice that is 40% juice and 60% water. You want the mixture to be 70% juice and 30% water. How many liters

damaskus [11]

Answer:

14 liters

Step-by-step explanation:

10 liters : 4 liters of juice and 6 liters of water

4/10 of juice and 6/10 of water

make it to 70% of juice and 30% of water

add 14 liters of juice

14/20=70% of juice

6/20=30% of water

4 0

3 years ago