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3 years ago

I’ll mark the first person to answer

Mathematics

1 answer:

almond37 [142]3 years ago

4 0

Answer:

$3.00 per person $8.00 per vehicle

Step-by-step explanation:

2x3=6 6+8=14

4x3=12 12+8=20

8x3=24 24+8=32

Hope this helps

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The symphonic choir and the jazz choir are recording songs for an album. The album can be no more than 72 minutes long. The jazz

zimovet [89]

Answer:

The symphonic choir can record a maximum of 14 songs.

Step-by-step explanation:

We know that the album cannot be more than 72 minutes long, and the jazz choir records a total of $7 (3min) = 21$ song minutes.

If we call $c$ the number of songs the symphonic choir records , and each song is 3.5 minute long, then the song minutes for the symphonic choir are $3.5c$ ; therefore, we have the inequality

$3.5c+21\leq 72$ (this says the song minutes for jazz choir plus song minutes for symphonic choice cannot exceed 72 minutes )

We solve this inequality by subtracting 21 from both sides and then dividing by 3.5:

$3.5c\leq 51$

$c\leq \frac{51}{3.5}$

$c\leq 14.47$

The maximum integer value $c$ can take is 14; therefore, the maximum number of songs the symphonic choir can record is 14 songs.

3 0

3 years ago

By how many degrees did the direction of the boat change

gulaghasi [49]

Answer:

The boat turned 39° degrees when it made its first turn.

Step-by-step explanation:

The question is as following:

A boat traveled north for 28 miles, then tuned x° south west and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.

By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.

===================================================

See the attached figure which represent explanation of the problem.

The boat start from point A to point B then stopped at point C

AB = 28 miles, BC = 25 miles and AC = 18 miles.

It is required to find the angle x

By applying the cosine Rule:

AC² = AB² + BC² - 2 * AB * BC * cos x

18² = 28² + 25² - 2 * 28 * 25 * cos x

2 * 28 * 25 * cos x = 28² + 25² - 18²

1400 cos x = 1085

Cos x = 1085/1400 = 0.775

x = Cos⁻¹ 0.775 = 39.2° = 39° to the nearest degree.

So, the boat turned 39° degrees when it made its first turn.

8 0

3 years ago

How to differentiate y=x^n using the first principle. In this question, I cannot use the rule of differentiation. I have to do t

Zarrin [17]

By first principles, the derivative is

$\displaystyle\lim_{h\to0}\frac{(x+h)^n-x^n}h$

Use the binomial theorem to expand the numerator:

$(x+h)^n=\displaystyle\sum_{i=0}^n\binom nix^{n-i}h^i=\binom n0x^n+\binom n1x^{n-1}h+\cdots+\binom nnh^n$

$(x+h)^n=x^n+nx^{n-1}h+\dfrac{n(n-1)}2x^{n-2}h^2+\cdots+nxh^{n-1}+h^n$

where

$\dbinom nk=\dfrac{n!}{k!(n-k)!}$

The first term is eliminated, and the limit is

$\displaystyle\lim_{h\to0}\frac{nx^{n-1}h+\dfrac{n(n-1)}2x^{n-2}h^2+\cdots+nxh^{n-1}+h^n}h$

A power of $h$ in every term of the numerator cancels with $h$ in the denominator:

$\displaystyle\lim_{h\to0}\left(nx^{n-1}+\dfrac{n(n-1)}2x^{n-2}h+\cdots+nxh^{n-2}+h^{n-1}\right)$

Finally, each term containing $h$ approaches 0 as $h\to0$ , and the derivative is

$y=x^n\implies y'=nx^{n-1}$

4 0

4 years ago

The population mean annual salary for environmental compliance specialists is about $63 comma 500. A random sample of 31 specia

Nat2105 [25]

Answer:

0.0035289

Step-by-step explanation:

From the question;

mean annual salary = $63,500

n = sample size = 31

Standard deviation = $6,200

Firstly, we calculate the z-score of $60,500

Mathematically;

z-score = x-mean/SD/√n = (60500-63500)/6200/√(31) = -2.6941

So we want to find the probability that P(z < -2.6941)

We can get this from the standard normal table

P( z < -2.6941) = 0.0035289

3 0

3 years ago

Michael is 3 times as old as Brandon. 18 years ago, Michael was 9 times as old as Brandon.

Zigmanuir [339]

I hope this helps you

Brandon x

Michael 3x

18 years ago

Brandon x-18

Michael 3x-18

9 (x-18)=3x-18

9x-9.18=3x-18

9x-3x=9.18-18

6x=8.18

x=8.3

x= 24

5 0

3 years ago