George does not like the fact that his neighborhood makes it mandatory to pay a yearly fee to use the pool. He conducts a survey of all the neighborhood families to help support his case that the yearly fee should be voluntary. The survey asks questions about pool usage and financial statistics of the families. Is this a valid survey? Why or why not?

I don't know if this is right but I got 0.14

Answer:

The correct option is A.

Step-by-step explanation:

The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) .

The relation between coordinates of preimage and image is defined as

[tex](x,y)\rightarrow (x,-y)[/tex]

Sign of y-coordinate changes but x-coordinate remains the same. It is possible it the figure is reflection across the x-axis.

Therefore the correct option is A.

To find f(1/4) when f(x)=2x^2+9x-7, substitute x=1/4 into the function and simplify.

To find f(1/4) when f(x) = 2x² + 9x - 7, we substitute x = 1/4 into the function.

Plugging in the value of x, we have f(1/4) = 2(1/4)² + 9(1/4) - 7.

Simplifying the expression, we get f(1/4) = 2/16 + 9/4 - 7. Evaluating the fractions and subtracting, we find that f(1/4) = -45/16.

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Answer with explanation:

Mean of this data set

[tex]=\frac{\text{sum of all the observation}}{\text{Total number of observation}}\\\\=\frac{30+37+37+41+22+69+45+64+51+22+63+31+64+65+25+51+26+48+28+49}{20}\\\\=43.4[/tex]

Arranging the data set in ascending order

22, 22,25, 26, 28,30,31,37,37,41,45,48,49,51,51,63,64,64,65,69

Median =Middle observation ,if number of terms is odd

and if number of terms is even, divide number of terms by ,2 and then follow the procedure

[tex]=\frac{10^{th term}+11^{th term}}{2}\\\\=\frac{41+45}{2}\\\\=43[/tex]

To find the Outlier

[tex]Q_{1}=\frac{28+30}{2}=29,Q_{3}=\frac{51+63}{2}=57[/tex]

Interquartile range = 57 - 29=28

Data values are approximately equally distributed on both sides of median.

That is, 43-22=21, and ,69 -43=26

So,we can say that there will be no outliers.

Graph will be positively skewed.

Mean > Median

So,mean will be better measure of central tendency because, 43.4-22=21.4, and 69-43.4=25.6

Option A: There are no outliers.

And, Option C: The Mean is good measure of central tendency.

The Correct answer is 462

The radius of the circle with an area of 324π sq cm is  18 cm.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know, The area of a circle is πr².

So, We can equate the given area with the general formula,

324π = πr².

r² = 324.

r = 18 cm.

A clock can be thought of as a circle having 12 steps and we know that circle is 360°,

So, the measure of each integer step of a clock is 30°.

Also, If we want to find some portion(arc) of the circumference we use the formula, s = rФ.

learn more about circles here :

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Answer:  [tex]\frac{8}{17}[/tex] or 8:17

Step-by-step explanation:

For any angle x (other than right angle) in a right triangle ,the trigonometric ratio of sin x is given by :-

[tex]\sin x=\frac{\text{side opposite to x}}{\text{Hypotenuse}}[/tex]

Given: A right triangle with hypotenuse = 68 units

The side adjacent to S =  60

Let h be the side opposite to S, then using Pythagoras in the given right triangle, we get

[tex](68)^2=60^2+h^2\\\\\Rightarrow\ h^2=68^2-60^2\\\\\Rightarrow\ h^2=1024\\\\\Rightarrow\ h=\sqrt{1024}=32[/tex]

Thus, the side opposite to S = 32 units

Now,  the trigonometric ratio for sin S is given by :-

[tex]\sin S=\frac{\text{side opposite to S}}{\text{Hypotenuse}}\\\\\Rightarrow\sin S=\frac{32}{68}=\frac{8}{17}[/tex]

Hence, the  trigonometric ratio for sin S =[tex]\frac{8}{17}[/tex] or 8:17

Given :The scented burns [tex] \frac{1}{12} [/tex] inches in 20 minutes

The scented candle will burn [tex] \frac{1}{12} times 3 =\frac{1}{4} [/tex] inches in one hour.

The unscented candle burns [tex] \frac{1}{6} [/tex] inches in 30 minutes

In one hour it will burn [tex] \frac{1}{6} times 2=\frac{1}{3} [/tex] inches .

Burn rate of scented is [tex] \frac{1}{4} [/tex] inches per hour.

Burn rate of unscented is [tex] \frac{1}{3} [/tex] inches per hour.

Solution:

we are given that

water hose is leaking at a rate of 0.25 cups per hour.

We have been asked to find that

how many gallons did you hose leak in a full 24 hour day.

Since water hose is leaking at a rate of 0.25 cups per hour.

It mean the tank will leak by [tex] 0.25*4=1 \ Cup [/tex] in 4 Hours.

So in 24 Hours the tank will leak by [tex] \frac{24}{4}*1=6*1=6 \ Cups [/tex] .

As we know that 1 Gallon=16 Cups.

It mean in 24 Hours the tank leaked by [tex] \frac{1}{16}*6= 0.375 \ Gallon [/tex]

Final answer:

The probability that the unknown removed marble is white is 1/2, and the probability that it is black is also 1/2. This is calculated by considering the outcomes of the draws, their probabilities, and the fact that drawing a white marble after another without replacement affects the outcomes.

Explanation:

The question involves calculating conditional probabilities in a scenario where marbles are drawn from an urn without replacement. Initially, the urn contains two white marbles and one black marble. A marble is drawn and set aside (its color unknown), and then a second marble is drawn, which is observed to be white. We are asked to find the probability that the first marble drawn was white, and the probability it was black.

To solve this, we consider the two possible scenarios for the first draw: drawing a white marble or drawing a black marble, and then drawing a white marble in the second draw. The probability of drawing white then another white (WW) equals, the probability of drawing a white marble first (2/3) multiplied by the probability of drawing the second white marble given the first was white (1/2). This gives (2/3)*(1/2) = 1/3. Alternatively, the probability of drawing a black then a white marble (BW) equals the probability of drawing a black marble first (1/3) multiplied by the probability of drawing a white marble given the first was black (2/2) = 1/3, simplifying to (1/3)*(1) = 1/3

To find the probability that the unknown marble is white, we see that both scenarios WW and BW result in drawing a white marble second, so we only need to calculate the probability of the WW scenario over the total probability of drawing a white marble in the second draw. This gives us 1/3 / (1/3 + 1/3) = 1/2. Therefore, the probability that the unknown marble is white is 1/2, and by complement, the probability it is black is also 1/2

Trigonometric identities are equations that hold true for all permissible values of the involved variables. They are fundamental to many areas of mathematics and have applications in various fields such as physics and engineering.

Trigonometric identities are equations that are true for all values of the variables where both sides of the equation are defined. They are fundamental to the study of mathematics, particularly in geometry, calculus and physics.

Some of the basic trigonometric identities include:

Trigonometric identities are widely used in solving trigonometric equations and proving other identities, and in many fields such as engineering, physics and computer science.

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