The domain of the function g(x) = loga (x^2 - 9) is
(-[infinity], ___) and ( ___, [infinity])

The point estimate of the population mean is 9

The point estimate of the population standard deviation is 2.83

Part a

Point estimate of population mean:

Given the sample data is 5,8,10,7,10,14

Number of samples, n is 6

Population mean=\(\frac{\sum x }{n}\)

                           =(5+8+10+7+10+14)/6

                           =54/6

                           =9

Point estimate of mean=9

Part b

Point estimate of population standard deviation:

Mean=9

Data (x)     (x-mean)^2

5                16

8                1

10               1

7                 4

10               1

14               25

Total           48

Standard deviation=√(x-mean)^2/n

                               =√48/6

                               =√8

                               =2.83

Hence, the point estimate of population standard deviation is 2.83

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Therefore, Andrea has 25 dimes in 37 coins, all nickels and dimes and the value of the 37 coins is $3.10.

Let's represent the number of nickels by "n" and the number of dimes by "d".

From the problem, we know that:

n + d = 37 (equation 1) ---(the total number of coins)

0.05n + 0.1d = 3.10 (equation 2) ---(the total value of the coins in dollars)

To solve for d, we can rearrange equation 1 to get:

n = 37 - d

Substitute this expression for n into equation 2 and simplify:

0.05(37-d) + 0.1d = 3.10

1.85 - 0.05d + 0.1d = 3.10

0.05d = 1.25

d = 25

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Answer:

slope = - 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 5) and (x₂, y₂ ) = (4, 1)

m = \(\frac{1-5}{4-2}\) = \(\frac{-4}{2}\) = - 2

The distance between the point (2, 6, -4) and the line r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩ can be calculated using the formula d = ||PQ||/||v||, where PQ is the vector connecting the point P to any point Q on the line, and v is the direction vector.

To find the distance between the point P(2, 6, -4) and the line defined by the parametric equations r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩, we can use the formula for the distance between a point and a line in three-dimensional space.

The formula for the distance between a point and a line is given by:

d = ||PQ||/||v||

where PQ is the vector connecting the point P to any point Q on the line, v is the direction vector of the line, and || || represents the magnitude of a vector.

Let's first find the direction vector of the line. By examining the parametric equations, we can see that the direction vector of the line is v = ⟨1, 4, -2⟩.

Now, we need to find the vector PQ connecting the point P(2, 6, -4) to any point Q on the line. We can represent PQ as the difference between the coordinates of P and Q:

PQ = ⟨2 - 1, 6 - 3t, -4 - 1, 4t, -4 - 3, -2t⟩ = ⟨1, 6 - 3t, -5, 4t, -7, -2t⟩

Next, we calculate the magnitude of PQ:

||PQ|| = √(1^2 + (6 - 3t)^2 + (-5)^2 + (4t)^2 + (-7)^2 + (-2t)^2)

= √(1 + 36 - 36t + 9t^2 + 25 + 16t^2 + 49 + 4t^2)

= √(29t^2 - 36t + 111)

Finally, we calculate the magnitude of the direction vector v:

||v|| = √(1^2 + 4^2 + (-2)^2) = √(1 + 16 + 4) = √21

Now we can substitute these values into the formula for the distance:

d = ||PQ||/||v|| = (√(29t^2 - 36t + 111))/√21

To find the minimum distance between the point P and the line, we need to minimize the function d with respect to t. We can accomplish this by finding the critical points of the function and determining the value of t that gives the minimum distance.

Taking the derivative of d with respect to t and setting it equal to zero, we have:

d' = (29t - 18)/(√21(√(29t^2 - 36t + 111))) = 0

Solving for t, we get:

29t - 18 = 0

29t = 18

t = 18/29

By substituting this value of t into the formula for d, we can find the minimum distance between the point P and the line.

d = (√(29(18/29)^2 - 36(18/29) + 111))/√21

Simplifying this expression will give us the final value of the distance.

In summary, the distance between the point (2, 6, -4) and the line r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩ can be calculated using the formula d = ||PQ||/||v||, where PQ is the vector connecting the point P to any point Q on the line, and v is the direction vector

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Answer:

A. Point A > -2

Answer:

45/51 is:

Step-by-step explanation:

make it a whole:

1 6/51

GCF:

1 2/17 is ur answer. Please consider marking me as brainliest if you can! Have an amazing day lovely! <3

Answer:

I think it would be 9/17

For the second one

The value of θ for which | r | has maximum value if r = sinθ is θ = π/2.

Given r = sinθ and the range of θ is 0 < θ < π

If 0 < θ < π the range of sinθ is:

                                      0 ≤ sinθ ≤ 1

So, in  0 < θ < π, the maximum value of sinθ is 1 and this value occurs at θ = π/2.

Now, we are asked to determine the value θ for which | r | is maximum and it is also given that r = sinθ and we have already found out that the maximum of sinθ in 0 < θ < π is 1.

Therefore, the maximum value of | r | is 1 and this value occurs at θ = π/2.

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Answer:

3√2

Step-by-step explanation:

x² + y² - 4x - 4y - 10 = 0

We need to complete the square in x and y.

x² - 4x + y² - 4y = 10

x² - 4x + 4 + y² - 4y + 4 = 10 + 4 + 4

(x - 2)² + (y - 2)² = 18

(x - 2)² + (y - 2)² = (3√2)²

Compare to:

(x - h)² + (y - k)² = r²

We have:

r = 3√2

Answer:

\(3\sqrt{2}\) units

Step-by-step explanation:

Convert general form to standard form:

\(Ax^2+Bxy+Cy^2+Dx+Ey+F=0\)

\(1x^2+0xy+1y^2-4x-4y-10=0\) (Since \(A=C\), the conic section is a circle)

\(x^2+y^2-4x-4y-10=0\)

\(x^2-4x+y^2-4y-10=0\)

\(x^2-4x+y^2-4y=10\)

\(x^2-4x+4+y^2-4y+4=10+4+4\)

\((x-2)^2+(y-2)^2=18\)

Since we have our equation in standard form, we can see that the radius is \(\sqrt{18}=3\sqrt{2}\) units

To find the upper class limits for a given set of data with a specified number of classes, we need to determine the class width, lower class limits, and upper class limits.

The class width can be found by subtracting the minimum value from the maximum value and dividing it by the number of classes. In this case, the class width is (61 - 13) / 7 = 48 / 7 = 6.857.

To determine the lower class limits, we start with the minimum value and add the class width successively. The correct lower class limits are 13, 20.857, 27.714, 34.571, 41.429, 48.286, and 55.143.

The upper class limits can be obtained by subtracting a small value (0.001) from the lower class limit of the next class. The correct upper class limits are 20.856, 27.713, 34.57, 41.428, 48.285, 55.142, and 62.

Based on the given options, the correct choices for the lower class limits and upper class limits are:

Lower class limits: D. 12, 23, 36, 47, 59, 72

Upper class limits: OD. 24, 36, 48, 60, 72, 83

These choices correspond to the calculated values and follow the pattern of adding the class width to the lower class limits and subtracting a small value to obtain the upper class limits.

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Sewage treatment and industrial wastewater treatment processes have similarities and differences in terms of influent characteristics, treatment processes, effluent quality, and sludge generation.

Both processes involve removing pollutants from water, but the types and concentrations of pollutants can differ. The effluent quality and sludge characteristics also vary based on the treatment processes employed.

Influent Characteristics: Sewage influent typically consists of domestic wastewater, including organic matter, nutrients, and pathogens. Industrial wastewater influent varies depending on the industry, containing specific pollutants such as heavy metals, oils, chemicals, and high organic loads.

Treatment Processes: Both sewage treatment and industrial wastewater treatment involve primary, secondary, and tertiary treatment stages. Primary treatment includes physical processes like sedimentation and screening. Secondary treatment involves biological processes such as activated sludge or trickling filters.

Tertiary treatment, which may be employed for advanced treatment, includes processes and factor like filtration, disinfection, and nutrient removal. However, industrial wastewater treatment may require additional specialized treatment processes to target specific pollutants.

Effluent and Sludge: The effluent quality for sewage treatment aims to meet specific standards for parameters like biochemical oxygen demand (BOD), suspended solids (SS), and fecal coliforms.

Industrial wastewater treatment focuses on meeting discharge limits specific to the industry's pollutants. The sludge generated in sewage treatment is typically organic and can be used for beneficial purposes like composting. Industrial sludge may contain a wider range of pollutants and require additional treatment or disposal measures.

For the effluent with BOD5 of 18mg/L and SS of 45mg/L, suitable applications could include irrigation for non-food crops, industrial cooling water, or groundwater recharge. The treated water meets the standard set by the Environmental Quality Act and can be reused in these applications to conserve freshwater resources and reduce the demand for potable water.

Composting and incineration are two common methods for sludge stabilization. Composting involves the biological decomposition of organic matter in the sludge, resulting in a stable end product that can be used as fertilizer.

Advantages of composting include the production of a useful product, reduction in sludge volume, and potential cost savings. In contrast, incineration involves the combustion of sludge, reducing its volume and destroying pathogens.

Advantages of incineration include volume reduction, pathogen destruction, and energy recovery. Disadvantages of composting include longer processing time and potential odor issues, while incineration requires high-energy input and can release air pollutants if not properly controlled.

The choice between composting and incineration depends on factors such as regulations, available land, energy requirements, and end-use considerations.

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Answer:

130°

Step-by-step explanation:

22x -2 = 21x +4 ; because alternate interior angles are congruent

22x -21x = 4 +2; subtract 21x and add 2 to both sides

x= 6

the angle measure is

22*6 -2 = 130°

The three positive numbers whose sum is 270 and whose product is a maximum is 67.5, 135, 67.5.

Let x, y, and z be the three positive numbers.

Write an equation relating x, y, and z based on the given constraint: x + y + z = 270.

Use algebra to solve for one of the variables in terms of the others.

Solving for z in terms of x and y: z = 270 - x - y.

Substitute the expression for z into the equation for the product of the three numbers:

P = x * y * z = x * y * (270 - x - y).

Expand the expression for P and simplify as P = 270xy - x²y - xy².

Using calculus to find the critical points of P, which occur when the derivative of P with respect to x is zero:

dP/dx = 270y - 2xy - y²= 0.

Solving for x in terms of y: x = (270y - y²)/(2y).

Simplify the expression for x as x = 135 - (y/2).

Since x and y must be positive, we know that 0 < y < 270/2 = 135.

Therefore, we can choose y = 135.

Using the equation for x in terms of y, we can find x as x = 135/2 = 67.5.

Using the constraint x + y + z = 270, we can find z as z = 67.5.

 Check that x, y, and z are positive and that they add up to 270.

Therefore, the three positive numbers whose sum is 270 and whose product is a maximum are 67.5, 135, and 67.5.

The product of these three numbers is (67.5) * (135) * (67.5) = 614062.5.

So the maximum product is 614062.5.

Thus, the answer is: 67.5, 135, 67.5.

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Answer:

D.) 5 x 25 = 125

Step-by-step explanation:

The two numbers are 25 and 5. If you take 1/5 of 25, or simply divide by 5, you will get 5.

Answer:

A) X + Y = 30

B) X = .2Y OR X - .2Y = 0

We subtract B) from A)

1.2Y = 30

Y = 25  X = 5

X * Y = 125

Answer is d.) 125

Step-by-step explanation:

The number of watts which is the power of the turbine for each case is respectively; 600 W; 506.25 W; 300 W

We are given;

Density of air; ρ = 1.2 kg/m³

Area; A = r² with r being the blade length

Formula for power in turbine is;

P = ¹/₂ρAv³

1) v = 10 m/s and r = 1 m.

Thus;

P = ¹/₂ * 1.2 * 1² * 10³

P = 600 W

2) v = 15 m/s and r = 0.5 m.

Thus;

Power = ¹/₂ * 1.2 * 0.5² * 15³

P = 506.25 W

3) v = 20 m/s and r = 0.25 m.

Thus;

Power = ¹/₂ * 1.2 * 0.25² * 20³

P = 300 W

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Answer:

Divisible by none

Step-by-step explanation:

9,953 is odd

9+9+5+3 = 2 + 6 = 8 (not divisible)

53/4 is not a whole number

9,953 doesn't end with 5 or 0.

9 + 9 + 5 + 3 = 26 (not divisible by 9)

9,953 has no 0 at end.

You are welcome!

Kayden Kohl

8th Grade Student

The number 9,953 is divisible by neither of the digits 2, 3, 4, 5, 9, 10.

The importance of knowing divisibility rules is that we can determine whether a number is divisible by certain numbers generally from 1 to 20 or not without actually dividing.

Given, 9,953. Is this number divisible by 2, 3, 4, 5, 9, 10 or not.

A number is divisible by 2 if it's unit digit is divisible by 2.

A number is divisible by 3 if the sum of the digits is divisible by 3.

A number is divisible by 4 if the last two digits is divisible by 4.

A number is divisible by 5 if its unit digit is 5 or 0.

A number is divisible by 9 if the sum of the digits is divisible by 9.

A number is divisible by 10 if its unit digit is 0.

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Answer:

See below.

Step-by-step explanation:

Here is one pair of angle of each type. There are more correct answers.

corresponding angles: <K, <O

alternate interior angles: <N, <P

alternate exterior angles: <I, <S

same-side interior angles: <N, <Q

vertical angles: <P, <R

supplementary angles: <J, <M

a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

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Answer:

the farmer has 242 apples left

Step-by-step explanation:

A = awnser

M= Monday

T= Tuesday

M= 242

T= 109

W = amount sold or 109

(M+T)-W= total amount left

use order of operations and add whats in the (   )

( 242+109 ) = 351 or ( M+T )

then you would use the sum of ( M+T ) and subtract W or 109 wich would then equal 242 so the equation

( 242+109 ) - 109 would equal 242 or ( M+T ) - W = A

Answer:

28

Step-by-step explanation:

24/6=4 then take the 4 and multiply it by 7(other number in ratio) and you get 28

Answer:

True

Step-by-step explanation:

Answer:

True!

Step-by-step explanation:

“Rate of change” means the same as “slope.” If you are asked to find the rate of change, use the slope formula or make a slope triangle.

Answer:

B) 9

Step-by-step explanation:

110 + 75 + 11x - 9 + 8x + 13 = 360

19x + 189 = 360

19x (+ 189 - 189) = 360 - 189

19x = 171

19x/19 = 171/19

x = 9

Answer:

600

Step-by-step explanation:

Given parameters:

    Number that rode in columns = \(3\frac{2}{3}\) times the number that rode in rows.

       2200 rode in columns

Unknown:

Number of people that rode in rows = ?

Solution:

  Let the number of people that rode in columns  = C

   Let the number of people that rode in rows  = R

                 C = \(\frac{11}{3}\)R

Number of people that rode in rows  = 2200;

            2200 =  \(\frac{11}{3}\)R

             11R  = 2200 x 3

                R  = \(\frac{2200 x 3}{11}\)

                R = 200 x 3

               R  = 600

Number of people that rode in rows  = 600

Answer:

3/2

Step-by-step explanation:

Answer:

Exact Form: \(\frac{3}{2}\)

Decimal Form: 1.5

Mixed Number Form: \(1\frac{1}{2}\)

Step-by-step explanation:

In pic

(Credits: Symbolab)

(Hope this helps can I pls have brainlist (crown)☺️)

Answer:

250

Step-by-step explanation:

-17+n/5=33

add 17 to both sides

n/5=50

now multiply both sides by 5

n/5x5=n 50x5=250

n=250

Answer:

Step-by-step explanation:Idon't say you have to mark my ans as brainliest but my friend if it has helped you don't forget to thank me...

The volume of the cylindrical water tank with the given value of radius and height to the nearest whole number is 1459ft³.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

We substitute our values into the expression above.

V = π × r² × h

V = 3.14 × (6.5ft)² × 11ft

V = 3.14 × 42.25ft² × 11ft

V = 1459ft³

The volume of the cylindrical water tank with the given value of radius and height to the nearest whole number is 1459ft³.

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Answer:

The answer is 35cm squared :D

Step-by-step explanation:

Answer:

The answer is 35! I just did it, and it's 35!

Step-by-step explanation:

Answer:

$380

Step-by-step explanation:

add the money then add the other numbers

The probability that the amount dispensed per box will have to be increased is 0.

To answer this question, we need to know the target amount that should be distributed per carton.

Assuming that the target amount is also 1 pound, we can use the concept of the normal distribution to estimate the likelihood that we will have to increase the amount distributed per case.

hence the probability of having to increase the amount is 0.

z = (target volume - mean) / standard deviation

z = (1 - 1) / 0.2

z = 0

A Z-score of 0 indicates that the target volume is equal to the mean. A standard normal distribution table or calculator can be used to find the probability that the amount should be increased.

However, the target amount is equal to the mean value,

In summary, without knowing the target amount to be dispensed in each case, it is not possible to determine the potential for volume increases.

If the target amount is to be £1 and the mean and standard deviation is also £1 and 0.2 respectively, then the probability of having to increase the amount is 0.

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Answer:

Step-by-step explanation:

Converting to decimal (nearest hundredth if needed)

Hey there!

Convert to decimals,

1/4 = 0.25

1/5 = 0.20

1/2 = 0.50

1/9 = 0.11

2/11​ = 0.18

Greatest to least = 1/2 > 1/4 > 1/5 > 2/11 > 1/9.

Greatest = 1/2

Least = 1/9

Hope this helps ya!