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Lapatulllka [165]
2 years ago
15

Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling. Abha collected 178

more cans than Shane did. Write an inequality to determine the number of cans, S, that Shane could have collected.
Mathematics
1 answer:
Katarina [22]2 years ago
4 0

Answer:

2x+178\geq 2000

Step-by-step explanation:

Let, the number of cans collected by Shane = x.

So, the number of cans collected by Abha = x + 178.

Since, at least 2000 cans are required to be collected.

Thus, we have the inequality,

Number of cans by Shane + Number of cans by Abha ≥ 2000.

i.e. x+(x+178)\geq 2000

i.e. 2x+178\geq 2000

Thus, the required inequality is 2x+178\geq 2000.

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The GPA of accounting students in a university is known to be normally distributed. A random sample of 20 accounting students re
Vladimir79 [104]

Answer:

The 95% of confidence intervals

(2.84 ,2.99)

Step-by-step explanation:

A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16

given small sample size n =20

sample mean x⁻ =2.92

sample standard deviation 'S' =0.16

level of significance ∝ =  0.95

The 95% of confidence intervals

x^{-}  ± t_{\alpha } \frac{S}{\sqrt{n} }

the degrees of freedom γ=n-1 =20-1=19

t-table 2.093

(x^{-}  - t_{\alpha } \frac{S}{\sqrt{n} },x^{-}  + t_{\alpha } \frac{S}{\sqrt{n} })

(2.92 - 2.093(\frac{0.16}{\sqrt{20} } ,2.92+2.093(\frac{0.16}{\sqrt{20} } )

(2.92-0.0748,2.92+0.0748)

(2.84 ,2.99)

Therefore the 95% of confidence intervals

(2.84 ,2.99)

4 0
2 years ago
Coupons driving visits. A store randomly samples 603 shoppers over the course of a year and nds that 142 of them made their visi
s2008m [1.1K]

Answer:

The 95% confidence interval for the proportion of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 603, \pi = \frac{142}{603} = 0.2355

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 - 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2016

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 + 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2694

The 95% confidence interval for the proportion of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694)

7 0
1 year ago
A worker drives a 0.500 kg spike into a rail tie with a 2.50 kg sledgeham-
Marianna [84]

Total internal energy increases by 1760 J

Step-by-step explanation:

The kinetic energy of an object is the energy possessed by the object due to its motion.

It is calculated as

KE=\frac{1}{2}mv^2

where

m is the mass of the object

v is its speed

For the hammer in this problem:

m = 2.50 kg

v = 65.0 m/s

So its kinetic energy is

KE=\frac{1}{2}(2.50)(65)^2=5281 J

Then the problem says that 1/3 of the hammer's kinetic energy is converted into internal energy: therefore, the total internal energy increases by

\frac{1}{3}KE=\frac{1}{3}(5281)=1760 J

Learn more about kinetic energy:

brainly.com/question/6536722

#LearnwithBrainly

8 0
2 years ago
=
SOVA2 [1]

Answer:

Tn=13n-18

Step-by-step explanation:

Tn=-5(n-1)13

Simplify

this is using the a+(n-1)d

8 0
1 year ago
Read 2 more answers
Tan20+tan40+tan60.......+tan180=?
Leno4ka [110]
The answer is 0. 
assuming by the dots that it includes tan80 +tan100 +tan120 +tan140 +tan160 in the equation. 
5 0
2 years ago
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