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2 years ago

4 tons of mulch cost $28,320.00. What is the price per pound? (Will Mark)

Mathematics

1 answer:

Advocard [28]2 years ago

4 0

Answer:

$3.54 per pound

Step-by-step explanation:

Step 1: Find the unit cost per ton

28,320 / 4

$7,080 per ton

Step 2: Find the unit cost per pound

1 ton = 2000 pounds

7080 / 2000

$3.54 per pound

Answer: $3.54 per pound

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A triangle has side lengths of 9 in, 13 in, and 20 in. What is the measurement of this triangle’s largest angle?

zvonat [6]

1. Given any triangle ABC with sides BC=a, AC=b and AB=c, the following are true :

i) the larger the angle, the larger the side in front of it, and the other way around as well. (Sine Law) Let a=20 in, then the largest angle is angle A.

ii) Given the measures of the sides of a triangle. Then the cosines of any of the angles can be found by the following formula:

$a^{2}=b ^{2}+c ^{2}-2bc(cosA)$

2.

$20^{2}=9 ^{2}+13 ^{2}-2*9*13(cosA)

400=81+169-234(cosA) 150=-234(cosA)

cosA=150/-234= -0.641$

3. m(A) = Arccos(-0.641)≈130°,

4. Remark: We calculate Arccos with a scientific calculator or computer software unless it is one of the well known values, ex Arccos(0.5)=60°, Arccos(-0.5)=120° etc

4 0

3 years ago

Read 2 more answers

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number o

Ksenya-84 [330]

Answer:

Step-by-step explanation:

Step1:

We have Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α =8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter μ = 8t

Step2:

Let “X” the number of small aircraft that arrive during time t and it follows poisson distribution parameter “”

The probability mass function of poisson distribution is given by

P(X) = , x = 0,1,2,3,...,n.

Where, μ(mean of the poisson distribution)

a).

Given that time period t = 1hr.

Then,μ = 8t

= 8(1)

= 8

Now,

The probability that exactly 6 small aircraft arrive during a 1-hour period is given by

P(exactly 6 small aircraft arrive during a 1-hour period) = P(X = 6)

Consider,

P(X = 6) =

= 0.1219.

Therefore,The probability that exactly 6 small aircraft arrive during a 1-hour period is 0.1219.

1).P(At least 6) = P(X 6)

Consider,

P(X 6) = 1 - P(X5)

= 1 - {+++++}

= 1 - (){+++++}

= 1 - (0.000335){+++++}

= 1 - (0.000335){1+8+32+85.34+170.67+273.07}

= 1 - (0.000335){570.08}

= 1 - 0.1909

= 0.8090.

Therefore, the probability that at least 6 small aircraft arrive during a 1-hour period is 0.8090.

2).P(At least 10) = P(X 10)

Consider,

P(X 10) = 1 - P(X9)

= 1 - {+++++

5 0

3 years ago

The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?

omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

$T_5 = 160$

$T_7 = 40$

Required

$T_6$

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

$\frac{T_7}{T_5} = \frac{40}{160}$

Divide the numerator and the denominator of the fraction by 40

$\frac{T_7}{T_5} = \frac{1}{4}$ ----- equation 1

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Where n is the nth term

So,

$T_7 = a r^{6}$

$T_5 = a r^{4}$

Substitute the above expression in equation 1

$\frac{T_7}{T_5} = \frac{1}{4}$ becomes

$\frac{ar^6}{ar^4} = \frac{1}{4}$

$r^2 = \frac{1}{4}$

Square root both sides

$r = \sqrt{\frac{1}{4}}$

r = ± $\frac{1}{2}$

Next, is to solve for the first term;

Using $T_5 = a r^{4}$

By substituting 160 for T5 and ± $\frac{1}{2}$ for r;

We get

$160 = a \frac{1}{2}^{4}$

$160 = a \frac{1}{16}$

Multiply through by 16

$16 * 160 = a \frac{1}{16} * 16$

$16 * 160 = a$

$2560 = a$

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Here, n = 6;

$T_6 = a r^{6-1}$

$T_6 = a r^5$

$T_6 = 2560 r^5$

r = ± $\frac{1}{2}$

So,

$T_6 = 2560( \frac{1}{2}^5)$ or $T_6 = 2560( \frac{-1}{2}^5)$

$T_6 = 2560( \frac{1}{32})$ or $T_6 = 2560( \frac{-1}{32})$

$T_6 = 80$ or $T_6 = -80$

$T_6 =$ ±80

Hence, the 6th term is positive/negative 80

8 0

2 years ago

ammie pays $30 for a bag that she buys at a discount of 50%. What is the price of the bag without the discount? A. $30 B. $45 C.

Liula [17]

This would be C. 60$

This is because if she got the bag for 50% off, 30 divided by 2 is 15$, 45 divided by 2 is 22.5, 60 divided by 2 is 30$ so option C. Would be your answer.

7 0

3 years ago

Consider the graph of the cosine function shown below.

emmainna [20.7K]

Answer:

a. The amplitude should be 2.

The period should be 2\pi.

b. maximum value occurs in (0,1) at x = 0

minimum value occurs in (pi,-1) at x = pi

Step-by-step explanation:

8 0

2 years ago