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3 years ago

How many of each type of box is it carrying?

Mathematics

2 answers:

CaHeK987 [17]3 years ago

8 0

Answer:

Number of large boxes: 55

Number of small boxes:65

Step-by-step explanation:

Let be "l" the number of large boxes and "s" the number of small boxes.

Set up a system of equations:

$\left \{ {{l+s=120} \atop {60l+30s=5250}} \right.$

Use the methof of elimination. Mulitply the first equation by -60 and add both equations. Then solve for "s":

$\left \{ {{-60l-60s=-7200} \atop {60l+30s=5250}} \right.\\.........................\\-30s=-1950\\s=65$

Substitute s=65 into any of the original equations and solve for "l":

$l+65=120\\l=55$

garri49 [273]3 years ago

6 0

Answer:

Number of large boxes = 55

Number of small boxes = 65

Step-by-step explanation:

We know that large boxes weight 60 pounds each while small boxes weight 30 pounds each and they are 120 boxes in total which weigh 5250 pounds in total.

Assuming $l$ to the number of large boxes and $s$ to be the number of small boxes, we can write the following equations:

$l+s=120$ --- (1)

$60l+30s=5250$ --- (2)

From equation (1):

$l=120-s$

Substituting this value of $l$ in (2):

$60(120-s)+30s=5250$

$7200-60s+30s=5250$

$60s-30s=7200-5250$

$30s=1950$

s = 65

Now finding the value of $s$ :

$l=120-65$

l = 55

Therefore, number of large boxes = 55 and number of small boxes = 65.

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If we sample from a small finite population without replacement, the binomial distribution should not be used because the event

seropon [69]

Answer:

5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

$\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}$

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

As we see, the situation is exactly the same, but changing the numbers. So the answer would be

$\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}$

Now compute each combination separately:

$\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700$

and now replace the values:

$\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}$

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

6 0

3 years ago

traveling at 65 mph, how many minutes, rounded to the nearest whole number, does it take to drive 125 miles from San Diego to ma

kkurt [141]

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3 years ago

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sashaice [31]

Answer:

The solution is in the attached file

Step-by-step explanation:

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5 0

3 years ago

There are eight boxes. Each box holds one sweater. There are 3 blue, 2 brown, 1 green, and 2 red sweaters. What is the probabili

Reil [10]

3 + 2 + 1 + 2 = 8, which is the amount of sweaters.
The probability of a brown sweater is 2 / 8 = 0.25
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Multiply the two probabilities together to get the probability of choosing brown then green:
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To convert a decimal to fraction, you multiply the numerator and denominator, or in this case $\frac{0.03125}{1}$ by 1000 which gets $\frac{31.25}{1000}$

Which can be simplified to:
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Hope this helps.

8 0

3 years ago

Read 2 more answers

How do you do this question?

Lisa [10]

Answer:

Correct integral, third graph

Step-by-step explanation:

Assuming that your answer was 'tan³(θ)/3 + C,' you have the right integral. We would have to solve for the integral using u-substitution. Let's start.

Given : ∫ tan²(θ)sec²(θ)dθ

Applying u-substitution : u = tan(θ),

=> ∫ u²du

Apply the power rule ' ∫ xᵃdx = x^(a+1)/a+1 ' : u^(2+1)/ 2+1

Substitute back u = tan(θ) : tan^2+1(θ)/2+1

Simplify : 1/3tan³(θ)

Hence the integral ' ∫ tan²(θ)sec²(θ)dθ ' = ' 1/3tan³(θ). ' Your solution was rewritten in a different format, but it was the same answer. Now let's move on to the graphing portion. The attachment represents F(θ). f(θ) is an upward facing parabola, so your graph will be the third one.

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3 years ago