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2 years ago

A teacher is buying pencils for her classroom. If a dozen pencils cost $0.97, how many pencils can she purchase with $5?

Mathematics

1 answer:

mixas84 [53]2 years ago

6 0

Answer:

The teacher can purchase 61 pencils with $5

Step-by-step explanation:

This is a simple proportion problem. It can be solved by pure logic reasoning without any formulas

It a dozen pencils cost $0.97, each pencil cost $0.97/12=0.08083

With $5 she will be able to purchase 5/0.08083=61.85 pencils

We must round to the nearest lower integer

The teacher can purchase 61 pencils with $5

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The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and the

Lera25 [3.4K]

Answer:

The correct option is A

Step-by-step explanation:

From the question we are told that

The population is $\mu = 6.6$

The level of significance is $\alpha = 5\% = 0.05$

The sample data is 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds

The Null hypothesis is $H_o : \mu = 6.6$

The Alternative hypothesis is $H_a : \mu > 6.6$

The critical value of the level of significance obtained from the normal distribution table is

$Z_{\alpha } = Z_{0.05 } = 1.645$

Generally the sample mean is mathematically evaluated as

$\=x = \frac{\sum x_i }{n}$

substituting values

$\=x = \frac{9.0 + 7.3 + 6.0+ 8.8+ 6.8+ 8.4+6.6 }{7}$

$\=x = 7.5571$

The standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum [ x - \= x ]}{n} }$

substituting values

$\sigma = \sqrt{\frac{ [ 9.0-7.5571]^2 + [7.3 -7.5571]^2 + [6.0-7.5571]^2 + [8.8- 7.5571]^2 + [6.8- 7.5571]^2 + [8.4 - 7.5571]^2+ [6.6- 7.5571]^2 }{7} }$ $\sigma = 1.1774$

Generally the test statistic is mathematically evaluated as

$t = \frac{\= x - \mu } { \frac{\sigma }{\sqrt{n} } }$

substituting values

$t = \frac{7.5571 - 6.6 } { \frac{1.1774 }{\sqrt{7} } }$

$t = 1.4274$

Looking at the value of t and $Z_{\alpha }$ we see that $t < Z_{\alpha }$ hence we fail to reject the null hypothesis

What this implies is that there is no sufficient evidence to state that the sample data show as significant increase in the average birth rate

The conclusion is that the mean is $\mu = 6.6 \ lb$

8 0

2 years ago

a triangle has sides of 4 and 6 units. The measurement of the longest side is missing.Ted says that one possibility for the unkn

tester [92]

This is called the pythagorean theorem: a^2 + b^2 = c^2.
Basically, the sum of one side squared + the side of another side squared = the length of the longest side (or hypotenuse).

We have to do the following math:
4 * 4 = 16
6 * 6 = 36
16 + 36 = 52.

We know that 52 = c^2
So we have to $\sqrt{c}$ to get 7.21

You do not agree with Ted.

7 0

2 years ago

Mustafa, Heloise, and Gia have written more than a combined total of 2222 22 articles for the school newspaper. Heloise has writ

Papessa [141]

Answer: $m>8$

Mustafa could have written more than 8 articles for the newspaper.

Step-by-step explanation:

Given: Heloise has written 1/4 as many articles as Mustafa has. Gia has written 3/2 as many articles as Mustafa has.

Let m be the number of articles Mustafa writes.

Then articles written by Heloise= $\frac{1}{4}m$

And articles written by Gia= $\frac{3}{2}m$

The total number of articles = $m+\frac{1}{4}m+\frac{3}{2}m=\frac{4m+m+6m}{4}=\frac{11m}{4}$

Mustafa, Heloise, and Gia have written more than a combined total of 22 articles for the school newspaper.

$\frac{11m}{4}>22\\\Rightarrow\ m>\frac{22\times4}{11}\\\Rightarrow\ m>8$

Hence, Mustafa could have written more than 8 articles for the newspaper.

3 0

2 years ago

Read 2 more answers

Perry, maria, and lorna are painting rooms in a college dormitory. working alone, perry can paint a standard room in 3 hours, ma

Leviafan [203]

Answer:Perry and Lorna take the maximum time and Maria and Lorna take the minimum time when they work together.

Explanation: Since, according to the question- Perry takes time when he works alone = 3 hours

Similarly, Maria takes = 2 hours, While Lorna takes= 2 hours 30 minutes or 2.5 hours.

since, there are three people thus their are three possibility to choose any two of them.

1- when Perry and Maria work together then time taken by them is $\frac{1}{1/2+1/3}$ = $\frac{1}{5/6}$ = 6/5= 1 hour 12 minutes.

2- when Maria and Lorna work together then time taken by them is $\frac{1}{1/2 + 1/2.5}$ = 10/9= 1 hours 1/9 minutes ≈ 1 hours 7 min

3- when Perry and Lorna work together then time taken= $\frac{1}{1/3+1/2.5}$ = 15/11= 1 hour 4/11 minutes≈ 1 hours 21 minutes

From the above explanation, it has been proved that when we talk about 2 members team then Perry and Lorna take the maximum time. While Maria and Lorna take the minimum time when they work together.

3 0

2 years ago

Read 2 more answers

A recent poll of over 2,000 adults was designed to answer the question "Are adults superstitious?" One survey item concerned the

RSB [31]

Answer:

i think you can divide 2,000 and 30 it might get you the answers if not try these adding multiplucation or subtraction.

8 0

2 years ago