All categories

2 years ago

Determine whether the proportion is true or false. 15/20=14/18

Mathematics

2 answers:

Colt1911 [192]2 years ago

7 0

Answer:

Step-by-step explanation:

note :

a/b = c/d means : ad = bc

comparing : 15×18 and 14×20

15×18=270 and 14×20 = 280

conclusion : 15/20=14/18 is false

11111nata11111 [884]2 years ago

3 0

15/20 can be simplified down to 3/4

14/18 can be simplified down to 7/6

Comparing the two simplified forms, they do NOT equal each other, so the proportion would be false

You might be interested in

Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in

Hitman42 [59]

Answer:

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Step-by-step explanation:

We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of Americans who decide to not go to college = 48%

n = sample of American adults = 331

p = population proportion of Americans who decide to not go to

college because they cannot afford it

Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level

of significance are -1.645 & 1.645}

P(-1.645 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.645) = 0.90

P( $-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < $\hat p-p$ < $1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

P( $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

90% confidence interval for p = [ $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }$ , $0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }$ ]

= [0.4348, 0.5252]

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.

So, the margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

$0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }$

$\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}$

$\sqrt{n}$ = 54.79

n = $54.79^{2}$

n = 3001.88 ≈ 3002

Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

5 0

2 years ago

Pierce currently has $10,000. What was the value of his money five years ago if he has earned 5 percent interest each year?

tia_tia [17]

The first answer is correct, if you go back by 5% each year you will see that.

4 0

2 years ago

Read 2 more answers

A paint shop stocks 1800 liters of paint 24% of the paint is white. The shops sells 18% of the white paint and 7% of the rest of

Anuta_ua [19.1K]

Answer:The amount of paint that was sold altogether is 173.36 litres

Step-by-step explanation:

The total amount of paint that the paint shop stocks is 1800 litres.

24% of the paint is white. It means that the amount of white paint would be

24/100 × 1800 = 0.24 × 1800 = 432 litres.

The amount of the remaining paint other than white would be

1800 - 432 = 1368 litres

The shops sells 18% of the white paint. This means that the amount of white paint sold by the shop will be

18/100 × 432 = 0.18 × 432 = 77.6 litres.

The shops sells 7% of the rest of the paint.

This means that the amount of the rest paint sold by the shop will be

7/100 × 1368 = 0.07 × 1368 = 95.76 litres.

The amount of paint that was sold altogether would be

77.6 + 95.76 = 173.36 litres

5 0

2 years ago

3 A buoy is 30 feet from the shore. You swim 3/5 the way to the buoy. How much farther do you have to swim to reach the buoy?

disa [49]

Answer:

12 feet

Step-by-step explanation:

30 divided by 5= 6

6 times 3= how far youve already swam(18 feet)

6 times 2= how far you have left(12 feet)

8 0

2 years ago

On a very hot summer day, 5 percent of the production employees at Midland States Steel are absent from work. The production emp

Katyanochek1 [597]

Answer:

a) 60%

Step-by-step explanation:

This problem can be solved through binomial probability

Let's say probability of success is the probability of absent

p = 5% = 0.05

Probability of failure

q = 1-p = 0.95

The number of trial in this case is the number of employees randomly selected

n = 10

Since we are looking for 0 absent employee, we are looking for the probability that the success is nil (i.e 0)

x = 0

Binomial therorem

B(n,x,p) = B(10,0,0.05)

= C(10,0) * p^x * q^(n-x)

= 1 * (0.05^0) * (0.95^10)

= 1 * 1 * 0.95^10

= 0.59873693923

= 0.6 or 60%

6 0

2 years ago

​Determine whether the proportion is true or false. 15/20=14/18

Determine whether the proportion is true or false. 15/20=14/18