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Akimi4 [234]
3 years ago
11

The container that holds the water for the football team is 1/2 full. After pouring in 3 gallons of water, it is 7/10 full. How

many gallons can the container hold?
Mathematics
1 answer:
timurjin [86]3 years ago
4 0
Make the bottom number the same to find the increase

find the increase
from 1/2 to 7/10
1/2 times 5/5=5/10
from 5/10 to 7/10 is 2/10 or 1/5 increase
3 gallons was added
so 3 gallons=1/5 of the container
times 5/1 both sides
15 gallons=5/5 of the container

the container can hold 15 gallons of water
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There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4. There are 180 students at Winthrop Midd
zavuch27 [327]

Given:

Total number of students at Colfax Middle School = 270

Ratio of boys to girls is 5:4.

Total number of students at Winthrop Middle School = 180

Ratio of boys to girls is 4:5.

The two schools hold a dance and all students from both schools attend.

To find:

The fraction of the students at the dance are girls

Solution:

There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4.

5+4=9

Number of boys =270\times \dfrac{5}{9}=150

Number of girls =270\times \dfrac{4}{9}=120

There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5.

4+5=9

Number of boys =180\times \dfrac{4}{9}=80

Number of girls =180\times \dfrac{5}{9}=100

Now,

Total number of students in both schools = 270+180

                                                                = 450

Total number of girls in both schools = 120+100

                                                         = 220

The fraction of the students at the dance are girls is

\text{Required fraction}=\dfrac{\text{Total number of girls in both schools}}{\text{Total number of students in both schools}}

\text{Required fraction}=\dfrac{220}{450}

\text{Required fraction}=\dfrac{22}{45}

Therefore, the required fraction is \dfrac{22}{45}.                                

7 0
3 years ago
NEED ASAP!!!!!!!!!!!!. Multiply and express the result in scientific notation:
Snezhnost [94]
Your answer is 8.4 X 10^7.

Hope this helped!
4 0
3 years ago
M/5 + 4 x 6 is how many terms?
inysia [295]

Answer: It's 36

Step-by-step explanation: add 5+4(equals 9) then multiply 9 by 6(whih equals 36

Hope this helps

please mark branliest

it would make my day :D

5 0
1 year ago
Read 2 more answers
Given h (x) =2x+5, find h (-6)
yawa3891 [41]
H(-6) = 2(-6) + 5
h(-6) = -12 + 5
Solution: h(-6) = -7
8 0
2 years ago
Suppose that you are in charge of evaluating teacher performance at a large elementary school. One tool you have for this evalua
Strike441 [17]

Answer:

a) Standard error = 2

b) Range = (76.08, 83.92)

c) P=0.69

d) Smaller

e) Greater

Step-by-step explanation:

a) When we have a sample taken out of the population, the standard error of the mean is calculated as:

\sigma_m=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{25}}=\dfrac{10}{5}=2

where n is te sample size (n=25) and σ is the population standard deviation (σ=10).

Then, the standard error of the classroom average score is 2.

b) The calculations for this range are the same that for the confidence interval, with the difference that we know the population mean.

The population standard deviation is know and is σ=10.

The population mean is M=80.

The sample size is N=25.

The standard error of the mean is σM=2.

The z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

MOE=z\cdot \sigma_M=1.96 \cdot 2=3.92

Then, the lower and upper bounds of the confidence interval are:

LL=M-t \cdot s_M = 80-3.92=76.08\\\\UL=M+t \cdot s_M = 80+3.92=83.92

The range that we expect the average classroom test score to fall 95% of the time is (76.08, 83.92).

c) We can calculate this by calculating the z-score of X=79.

z=\dfrac{X-\mu}{\sigma}=\dfrac{79-80}{2}=\dfrac{-1}{2}=-0.5

Then, the probability of getting a average score of 79 or higher is:

P(X>79)=P(z>-0.5)=0.69146

The approximate probability that a classroom will have an average test score of 79 or higher is 0.69.

d) If the sample is smaller, the standard error is bigger (as the square root of the sample size is in the denominator), so the spread of the probability distribution is more. This results then in a smaller probability for any range.

e) If the population standard deviation is smaller, the standard error for the sample (the classroom) become smaller too. This means that the values are more concentrated around the mean (less spread). This results in a higher probability for every range that include the mean.

6 0
3 years ago
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