Find the zeros of the function. f(x)=9x^2-12x-5

Solution:

we are given with two kind of data set , one is Population data and the other is sample data.

we have been asked to Compare the mean of the population with the mean of the given sample.

Given Population Data
is

[tex] 4
, 5
, 3
,1
,3
,2,2
,3
,5
,7
,3
,6
,3
,0
,1
,5
,0
,4
,3
,6 [/tex]

Its mean can be calculated as below

[tex] Mean=\frac{4+5+3+1+3+2+2+3+5+7+3+6+3+0+1+5+0+4+3+6}{20} \\\\\Mean=\frac{66}{20}=3.3\\ [/tex]

Now the Sample data is

5,4,6,2,1

[tex] Mean=\frac{5+4+6+2+1}{5}\\\\Mean=\frac{18}{5}= 3.6\\ [/tex]

Hence the value of difference of the Mean is [tex] =3.6-3.3=0.3 [/tex]

Answer:

The answer is B. 0.3

Step-by-step explanation:

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The inverse of the statement "If you live in Toronto, then you live in Canada" is:

"If you do not live in Toronto, then you do not live in Canada."

A conditional statement is a type of logical statement that consists of two parts: a hypothesis (or antecedent) and a conclusion (or consequent).

The hypothesis is a statement that serves as a condition, while the conclusion is a statement that follows from the condition.

A conditional statement is usually written in the form "If p, then q", where p is the hypothesis and q is the conclusion.

The symbol "→" is often used to represent the phrase "if...then".

We have,

To make the inverse of a conditional statement "if p, then q", you simply negate both the hypothesis and the conclusion, and then switch their positions.

The inverse of "if p, then q" is "if not p, then not q".

This can be symbolically represented as:

Original Statement: If p, then q

Inverse Statement: If not p, then not q

So,

The inverse of a conditional statement:

If p, then q is If not p, then not q".

Therefore,

The inverse of the statement "If you live in Toronto, then you live in Canada" is:

"If you do not live in Toronto, then you do not live in Canada."

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The value of x is 7 and the right option is A. 7.

Perimeter is the total distance around an object.

To find the value of x, we use the formula of the perimeter of a rectangle.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for x

Hence, the value of x is 7 and the right option is A. 7.

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Final answer:

The simplified expression of 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n is -2 + 5.5n - 0.5p after combining like terms.

Explanation:

To simplify the algebraic expression 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n, we need to combine like terms. The constants 1 and -3 can be combined, and the terms with 'n' and 'p' can each be combined respectively. Let's do this step by step:

The simplified expression is -2 + 5.5n - 0.5p.

The equation that could be used to find the slope of line AB is m = p/q.

Two triangles are said to be similar if they have congruent corresponding angles and their corresponding sides are in equal proportion.

Given that, is a graph showing two similar triangles, we need find the equation of the slope of the line AB.

So,

The slope = rise / run = Δy / Δx

Here, Δy / Δx = m/n

Since, the triangles are similar so, m/n = p/q

Therefore,

Δy / Δx = p/q

Hence, the equation that could be used to find the slope of line AB is m = p/q.

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Answer:

Your friend walks about 0.48 miles farther than you.

Step-by-step explanation:

Find the circumference of the park.

C = πd Use the circumference formula.

C ≈ 3.14(0.85) Substitute for the diameter and π.

C ≈ 2.669 Multiply.

The circumference of the park is about 2.669 centimeters.

Find how far your friend walks when he or she walks halfway around the pond to meet you on the other side of the bridge. Divide the circumference by two.

0.785 ÷ 2 = 1.33

Your friend walks 1.33 miles.

Find how much farther your friend walks. Subtract the miles you walk from the miles your friend walks. Round your answer to the nearest hundredth.

1.33 − 0.85 ≈ 0.48

The distance from the plane to the rock can be calculated using trigonometry. Here, the tangent of the given angle is used, with the formula: Distance = 1200m / tan(28°).

The subject matter in the question relates to trigonometry. We can use the tangent of the given angle to find the distance to the rock. We are given an altitude of 1200m (which is equivalent to the opposite side in a right angle triangle) and an angle of depression of 28°. We know from trigonometry that the tangent of an angle is equal to the opposite side divided by the adjacent side (tan(θ) = opposite / adjacent).

Since we want to know the distance from the plane to the rock, we're trying to find the length of the hypotenuse. This forms a right-angled triangle with the height of the plane as the opposite side, and the line of sight to the rock as the hypotenuse.

We can use the following formula which is derived from the principles of trigonometry:

Distance to the rock (hypotenuse) = Opposite side / tan(θ)

Plugging the given values into this formula gives:

Distance to the rock = 1200m / tan(28°) This calculation will give the answer.

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Answer:

The last option is the correct answer: [tex]r=\sqrt{\frac{A}{\pi}}[/tex]

Step-by-step explanation:

The area of a circle is given by :

[tex]A=\pi r^{2}[/tex] ; where r is the radius.

Now, lets find the radius.

[tex]\frac{A}{\pi } =r^{2}[/tex]

[tex]\sqrt{\frac{A}{\pi}} =r[/tex]

or [tex]r=\sqrt{\frac{A}{\pi}}[/tex]

Therefore, the last option is the correct answer.

Answer:

Option A.(-5, 2).

Step-by-step explanation:

Picture attached in the question we know the coordinates of the point C are (5, -2). Now we rotate C with a rotation of 180° about the origin.

As we can see a line connecting C and a new point C'. This line shows the rotation of the poit by 180°.

Therefore the new coordinates of C will be C'(-5, 2).

Option A is the correct option.

Final answer:

Each box must hold a total of 300 widgets.

Explanation:

To determine how many widgets must each box hold, we need to calculate the rate of production and then use it to find the total number of widgets produced in 2 hours (the total time it takes to fill the box).

First, we'll find out how many widgets are produced per minute. Since 25 widgets are deposited in 10 minutes, we divide the number of widgets by the time (in minutes) to get the rate:

Rate of production = 25 widgets / 10 minutes = 2.5 widgets per minute.

Now, we need to find out how many minutes are in 2 hours:

2 hours = 2 hours * 60 minutes/hour = 120 minutes.

Finally, we multiply the rate of production by the total production time (in minutes) to find out the total number of widgets per box:

Total widgets per box = 2.5 widgets/minute * 120 minutes = 300 widgets.

The value of f(40) is 1400 .The sequence can be considered a function because each position has a unique value.

Let's analyze the given formulas for Bill's savings:

The recursive formula is: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1

The explicit formula is: f(n) = 35n

A recursive formula defines each term based on the previous terms, which we see in f(n) = f(1) + f(n-1). An explicit formula provides a direct calculation, shown in f(n) = 35n.

The explicit formula f(n) = 35n allows us to directly calculate:

f(40) = 35 * 40 = 1400

This method is chosen because it provides a straightforward calculation without needing to compute all the preceding values.

This sequence can be considered a function because each input (position in the sequence) has a unique output (value in the sequence).

D- subtraction and multiplication, in that order.

Step-by-step explanation:

EDG 2022

The sign notations for four Quadrants is as follows:

Quadrant I : both x and y positive.

Quadrant II : x negative and y positive

Quadrant III: x and y both negative.

Quadrant IV: x positive and y negative.

Point F has coordinates (1,-5)

x is positive and y is negative.

So point F is in quadrant IV.

The total number of dollars my sisters have is $60.

Given that, if I give my sister 17 dollars, then we will have the same amount of money.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of dollars I have be x and number of dollars my sisters have be y.

Now, if I give my sister 17 dollars, then we will have the same amount of money

y-17 = x

x - y = -17 ---------(1)

If she gives me 23 dollars, then I'll have three times as much money as she will have.

3(x-23) = y

3x-69 = y

3x-y = 69 ---------(2)

Subtract equation (1) from (2)

3x-y-(x-y) = 69 - (-17)

⇒ 2x = 86

⇒ x = $43

Put x = 43 in equation (1), we get

43 - y = -17

43+17 = y

y = $60

Therefore, the total number of dollars my sisters have is $60.

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The equation of line is, y= -2x-9.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

slope= -2

points= (-5, 1)

Now, using slope intercept form

y= mx+ b

1 = (-2)((-5) + b

1= 10 + b

b= -9

Thus, the equation of line

y= mx + b

y= -2x- 9

Hence, the equation of line is, y= -2x-9.

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Answer:

Step-by-step explanation:

49 million misquitos

Answer:

(A) Use stratified random sampling

Step-by-step explanation:

Since, the population include all the citizens of that country so it is quite large data and working on this population is quite time taken and costly. Thus, Sample must be taken and it must be taken by appropriate sampling method.

 Here Stratified Sampling is used because by this sampling method peoples of every state, every cities, every village can be taken without much expense and in less time.

Further,

If the samples from the population are chosen randomly, where each and every unit has an equal chance of selection in a sample. This type of sampling is called Simple Random Sampling.

If the observers collect the sample as his\her convenience, then this type of sampling method is called Convenience Sampling.

In Cluster Sampling the population is distributed into a distinct group (clusters) and one or more groups (clusters) are chosen as a sample.

In Systematic Sampling the selection of sample is taken by some criteria . Like he\she is taken every 7th unit as a sample from the population.