From a sample of 500 items, 30 were found to be defective. the point estimate of the population proportion defective will be

(7^2)x = 1

7^2 = 49

49x = 1

x = 1/49

(7^0)x=1

7^0 = 1 (anything raised to 0 = 1)

1x = 1

x = 1

Answer:  The required probability that the child took a green marble is 40%.

Step-by-step explanation:  Given that there are 9 red and 6 green marbles in a bag and a child reaches in the bag and randomly takes one marble.

We are to find the probability that the child took a green marble.

Let S denote the sample space of choosing a marble from the bag and A be the event of choosing a green marble.

Then,

n(S) = 9 + 6 = 15   and   n(A) = 6.

Therefore, the probability of event A will be

[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{6}{15}=\dfrac{2}{5}\times 100\%=40\%.[/tex]

Thus, the required probability that the child took a green marble is 40%.

The point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].

To find the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1), we first need to calculate the slope (m) using the formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Given points:

[tex]\((-5, 6)\) and \((0, 1)\)[/tex]

Calculate the slope m:

[tex]\[ m = \frac{1 - 6}{0 - (-5)} = \frac{-5}{5} = -1 \][/tex]

Now that we have the slope m = -1, we can use the point-slope form of the equation of a line, which is:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Choose one of the points, let's use [tex]\((-5, 6)\) as \((x_1, y_1)\)[/tex]:

[tex]\[ y - 6 = -1(x + 5) \][/tex]

Now, simplify and compare with the given options:

[tex]\[ y - 6 = -1(x + 5) \][/tex]

So, the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].

The number .50 in the context of this question represents the proportion (or probability) of people in the sample who have brown eyes. It's calculated by dividing the count of individuals with brown eyes by the total number of individuals in the sample.

In this context, the number .50 represents the proportion or probability of people with brown eyes in the sample. This number is obtained by dividing the number of people with brown eyes (25) by the total number of people in the sample (50).

Hence, .50 means there is a 50% chance that a randomly selected person from the sample will have brown eyes. This is often used in the field of statistics where proportions are utilized to represent probabilities of outcomes.

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Individuals shall draw a table consisting of 21 boys in each column and 21 girls in each row as shown on the image below.

The table will have 21x21 = 441 boxes. Mark each box with a letter showing the problem solved by both that boy and girl. Since at least one problem was solved by a girl and a boy, therefore each box will have a letter. Each entrant solved at most six questions, so there can be at most six letters in any row or column. This means six different letters can be there in a row only if at least 11 of the boxes contain letters appearing three or more times in the row. Individuals go through each row and color all the boxes, say blue. Therefore, 11 boxes in each row must be colored blue.

The number of the boxes that must be colored blue = 21 x 11 = 231. Individuals can apply the same process to the columns and color at least 231 boxes, say green. But the total boxes are 441 only. Therefore, by Pigeonhole principle, there will be some boxes which will be both blue and green. The problem of doubly colored boxes represents a problem solved by at least three boys and three girls.

The Pigeonhole Principle is used to show that there must be a question solved by at least three girls and three boys in a math competition with 21 girls and 21 boys.

To show that there is a question solved by at least three girls and three boys, we will use the Pigeonhole Principle.

The angle between a side of a polygon and the extension of its adjacent side is the exterior angle at that vertex, forming a linear pair with the adjacent interior angle.

Angle between a side of a polygon and the extension of its adjacent side: When considering a polygon, the angle between a side and the extension of its adjacent side is equal to the exterior angle of the polygon at that vertex. This angle forms a linear pair with the adjacent interior angle of the polygon.

The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line 2x + 5y = 10 is:

2x + 5y = 10

5y = -2x + 10

y = -2/5x + 10

Hence the slope of the line 2x + 5y = 10 is -2/5

Since both lines are parallel, hence the slope of the other line is the same (-2/5). Hence the equation of the line is:

[tex]y-y_1=m(x-x_1)\\\\y-(-4)=-\frac{2}{5} (x-5)\\\\y+4=-\frac{2}{5} x+2\\\\y=-\frac{2}{5} x-2[/tex]

The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2

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7 and 8 have to equal 180 degrees

180- 92 = 88

 so angle 8 is 88 degrees

Answer:

The correct option is B) 88°.

Step-by-step explanation:

Consider the provided information.

Consider the figure 1,

m∠7=92°, then by using the property of liner pair angles, we have

m∠7 + m∠8 = 180° (Liner pair angles)

⇒m∠8 + 92° = 180°

⇒m∠8 = 180 - 92

⇒m∠8 = 88°

Therefore, the measure of m∠8 is 88°.

Hence, the correct option is B) 88°.