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larisa86 [58]
3 years ago
7

Screen-printing a batch of shirts requires 3 minutes per shirt in addition to 12 minutes of initial set-up time. If it takes 45

minutes to screen-print a batch of shirts,how many shirts are in the batch?
Mathematics
1 answer:
Furkat [3]3 years ago
4 0

Answer:

  11 shirts

Step-by-step explanation:

Since 12 of the 45 minute are devoted to setup, the actual printing time is 33 minutes. At 3 minutes per shirt, that's enough time for ...

  (33 min)/(3 min/shirt) = 11 shirts

A batch consists of 11 shirts.

_____

<em>Alternate solution</em>

Another way to consider this is to realize that the setup time is the time required to print 4 shirts. 45 minutes would be enough time to print 45/3 = 15 shirts, but the time for 4 shirts is spent setting up. That leaves the batch size at 15 -4 = 11 shirts.

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. In a study of air-bag effectiveness it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashes
jok3333 [9.3K]

Answer:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

0.00885... < 0.01

The test statistic of 46 is significant

There is sufficient evidence to reject H₀ and accept H₁

Air bags are more effective as protection than safety belts

Step-by-step explanation:

821 crashes

46 hospitalisations where car has air bags

7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts

α = 0.01 or 1% ← level of significance

One-tailed test

We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;

The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;

So we are testing if hospitalisations in cars with air bags is less than 0.078;

So, firstly:

Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags

X~B(821, 0.078)

Null hypothesis (H₀): p = 0.078

Alternative hypothesis (H₁): p < 0.078

According to the information, we reject H₀ if:

P(X ≤ 46 | X~B(821, 0.078)) < 0.01

To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;

If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:

P(X = r) = nCr * p^{r}  * (1 - p)^{n - r}

You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

Now, we need to consider if the condition for rejecting H₀ is met and recognise that:

0.00885... < 0.01

There is sufficient evidence to reject H₀ and accept H₁.

To explain what this means:

The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;

In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.

5 0
2 years ago
PLEASE HELP ASAP! Question 12. Thank you
a_sh-v [17]

Answer:

Step-by-step explanation:

In the first column, put days at the top and pounds at the bottom.

So Day 1 = 75 pounds, Day 2=150 pounds, Day 3 = 225 pounds, etc..

8 0
3 years ago
Use scientific notation to determine the answer :
vampirchik [111]
A= 1.5 × 10^10




Hope that helps
3 0
3 years ago
I rent a gym for $200.00 for 30 students. A year later I rent the gym for $330 for 70 students.
Anna [14]

let X be number of students

and y be total cost

when 30 students (30,X)where at the gym it's costs 200 (y,200)

=that is (X,y)=(30,200)

when 70 students where at the gym

=(X,y)= (70,330)

now we find the slope

M=y2-y1/x2-x1

= 330-200/70-30

= 100/40

= 2.5=3

now

Y=Mx+b

Y=2x+b

we need to find the value of b

so,we substrate for X and Y

X=30,200

200=2(30)+b

re-arrange

B+60=200

B=200-60

=140

y=2x+140

For the other questions, I can look at the equation I got. The y-intercept (b value) is $200. That means that we are adding $200 on to the price all the time. That's the price for the empty bus. The 2x means to multiply the number of people by two and add this to the $120. So each person is $2.

hope it's helpful

and please I really need brainliest, thanks

7 0
2 years ago
Given two points (3, 7) and (6, 8) with a line drawn through the points, calculate the slope of the line
vredina [299]

Answer:

1/3

Step-by-step explanation:

Given two points on the line, we can find the slope using

m = (y2-y1)/(x2-x1)

    = (8-7)/(6-3)

    = 1/3

3 0
3 years ago
Read 2 more answers
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