What is the geometric interpretation of dividing the b-value by 2 while completing the square?

For every 15 minutes of a show, there are two minutes to commercial. At this rate, if leila has seen 45 minutes of a show, how m

Ainat [17]

Answer:

51 minutes.

Step-by-step explanation:

We have been given that for every 15 minutes of a show, there are two minutes to commercial. At this rate, Leila has seen 45 minutes of a show. We are asked to find the time for which Leila has been watching TV.

We will use proportions to solve our given problem.

$\frac{\text{Minutes of TV show + Advertisement}}{\text{Minutes of TV show}}=\frac{15+2}{15}$

$\frac{\text{Minutes of TV show + Advertisement}}{\text{Minutes of TV show}}=\frac{17}{15}$

Upon substituting our given values, we will get:

$\frac{\text{Minutes of TV show + Advertisement}}{45}=\frac{17}{15}$

$\frac{\text{Minutes of TV show + Advertisement}}{45}\times 45=\frac{17}{15}\times 45$

$\text{Minutes of TV show + Advertisement}=\frac{17}{1}\times 3$

$\text{Minutes of TV show + Advertisement}=51$

Therefore, Leila has been watching TV together for 51 minutes.

8 0

3 years ago

Mark and don are planning to sell each of their marble collections at a garage sale. if don has 4 more than 5 times the number o

natita [175]

Mark and Don have to sell 11 and 59 marbles respectively.

Explanation

Lets assume, the number of marbles Mark has is $x$

As, Don has 4 more than 5 times the number of marbles mark has, so the number of marbles Don has $= 5x+ 4$

Question says that the total number of marbles is 70. So, the equation will be...

$x+(5x+4)= 70\\ \\ 6x+4= 70 \\ \\ 6x = 70-4\\ \\ 6x=66 \\ \\ x= \frac{66}{6}= 11$

So, the number of marbles Mark has = 11

and the number of marbles Don has = $(5*11)+4 = 55+4= 59$

6 0

3 years ago

Daniel [21]

The median for data A is greater.
the mean for data A is greater.

4 0

3 years ago

Find the surface area of the following shape?

Brilliant_brown [7]

It might be 8 because it said rhigt there 4 and if you use kind of a square it equals 8

7 0

4 years ago

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 225 vinyl? glov

romanna [79]

Answer:

a)

H₀: ρ₁ ≤ ρ₂

H₁: ρ₁ > ρ₂

b)

Z= $\frac{('p_{1} - 'p_{2}) - (p_{1} - p_{2})}{\sqrt{'p(1-'p)[\frac{1}{n_1} + \frac{1}{n_2} ]} }$ ≈ N(0;1)

c)

p-value < .00001

d)

Reject the null hypothesis.

The population proportion vinyl gloves that leak viruses is greater than the population proportion of latex gloves that leak viruses.

Step-by-step explanation:

Hello!

The objective is to test if the population proportion of vinyl gloves that leak viruses (population 1) is greater then the population proportion of latex gloves that leak viruses (population 2).

Sample 1 (Vinyl)

n₁= 225

Sample proportion 'ρ₁= 0.60

Sample 2 (Latex)

n₂= 225

Sample proportion 'ρ₂= 0.09

Pooled proportion: 'ρ= (x₁+x₂)/(n₁+n₂)= ( 'ρ₁ + 'ρ₂)/2= (0.60 + 0.09)/2= 0.345 ≅0.35

The hypothesis is:

H₀: ρ₁ ≤ ρ₂

H₁: ρ₁ > ρ₂

α: 0.05

The statistic to use is a pooled Z

Z= $\frac{('p_{1} - 'p_{2}) - (p_{1} - p_{2})}{\sqrt{'p(1-'p)[\frac{1}{n_1} + \frac{1}{n_2} ]} }$ ≈ N(0;1)

The critical region is one-tailed to the right (positive), the critical value is:

$Z_{1-\alpha } = Z_{0.95} = 1.64$

If Z ≥ 1.64, you will reject the null hypothesis.

If Z < 1.64, you will not reject the null hypothesis.

Z= $\frac{(0.6 - 0.09) - (0}{\sqrt{0.35(1-0.35)[\frac{1}{225} + \frac{1}{225} ]} }$ = 11.34

Since the calculated Z- value is greater than the critical value, the decision is to reject the null hypothesis. The population proportion vinyl gloves that leak viruses is greater than the population proportion of latex gloves that leak viruses.

P-value approach:

p-value < .00001

If you compare with the level of signification, you reach the same decision.

I hope it helps!

8 0

4 years ago