What is the domain and range of this function

Answer:2,440,000,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.

The point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.

The tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...

  m = y/x = -4/4 = -1

The tangent line's slope is the opposite reciprocal of this:

  m = -1/(-1) = 1

The point-slope form of the equation for the tangent line is ...

  y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)

  y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)

  x -y = 8 . . . . . . . . . . add 4-y to put in standard form

The equation of the tangent line is x - y = 8.

In the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...

  y -0 = -1(x -0)

  y = -x

The equation of the normal line is y = -x.

__

Additional comment

The normal line can also be written as x + y = 0.

The tangent line can also be written as y = x -8.

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Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6

140.55 pounds will be sold approximately each week at the optimal price of $0.67/lb.

To find the price elasticity of demand for bananas at $0.20/lb, we need to use the formula:

According to the given data:

E(p) = -p(q'/q(p))

where q' is the derivative of q(p) with respect to p.

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(0.20) = -0.20(q'(0.20)/q(0.20))

= \(-0.20(-225e^(1.5(5-0.20)) / 100e^(1.5(5-0.20)))\)

= 2.70

Therefore, the price elasticity of demand for bananas at $0.20/lb is 2.70.

To find the price elasticity of demand for bananas at $1/lb, we can use the same formula:

E(p) = -p(q'/q(p))

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(1) = -1(q'(1)/q(1))

= \(-1(-225e^(1.5(5-1)) / 100e^(1.5(5-1)))\)

= 0.68

Therefore, the price elasticity of demand for bananas at $1/lb is 0.68.

To find the price that maximizes revenue, we need to find the value of p that makes revenue, R(p), maximum.

Revenue is given by:

R(p) = pq(p)

= \(p100e^(1.5(5-p))\)

To maximize revenue, we need to find the critical point of R(p) by taking its derivative and setting it equal to zero:

\(R'(p) = 100e^(1.5(5-p)) - 150pe^(1.5(5-p)) = 0\)

Simplifying this expression, we get:

\(2e^(1.5(5-p)) - 3pe^(1.5(5-p)) = 0\)

2 = 3p

p = 2/3

Therefore, the price that maximizes revenue is $0.67/lb.

To find the maximum revenue per week, we can plug this price back into the revenue equation:

\(R(2/3) = (2/3)*100e^(1.5(5-2/3))\)

= $167.56

Therefore, the maximum revenue per week is $167.56.

To find how many pounds will be sold each week at the optimal price of $0.67/lb, we can plug this price back into the demand equation:

\(q(2/3) = 100e^(1.5(5-2/3))\)

= 140.55

Therefore, approximately 140.55 pounds will be sold each week at the optimal price of $0.67/lb.

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Answer:

4+is the absolute value is greater than 3

The difference between the means is approximately 0.533 times the mean Absolute deviation.

We first need to find the means of the two datasets using the double stem and leaf plots given:

Pizzeria A:

| 4 | 5 7 8 8 |

| 5 | 1 2 3 3 5 6 8 |

Mean: (4+5+5)/3 + (1+2+3+3+5+6+7+8)/8 = 4.67 + 4.125 = 8.795

Pizzeria B:

| 6 | 2 3 4 4 5 5 6 7 |

| 7 | 0 1 1 2 4 4 4 6 8 9 |

Mean: (6+7)/2 + (2+3+4+4+5+5+6+7)/8 + (0+1+1+2+4+4+4+6+8+9)/10 = 6.5 + 4.125 + 3.5 = 14.125

Next, we need to find the difference between the means:

14.125 - 8.795 = 5.33

To determine how many times the mean absolute deviation is approximately 10, we need to divide the difference between the means by the mean absolute deviation:

5.33/10 = 0.533

Therefore, the difference between the means is approximately 0.533 times the mean absolute deviation.

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The number that is illustrated based on the information about the fraction is -10.

It should be noted that in mathematics, a fraction is expressed as a quotient of a numerical. The numerator is divided by the denominator.

The number when n is multiplied by a power of 10 will be n^-10. It should be noted that this will then make a fraction of 1/n^10.

Therefore, the number that is illustrated based on the information about the fraction is -10.

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Answer:

Domain: 3 > x ≥ -2

Range: -5 < y ≤ 4

Answer:

Step-by-step explanation:

answer is;3.14159

Answer:

7 8 9

Step-by-step explanation:

7 is larger then 6 and smaller then 10

the same goes for 8 and 9

so 7 8 9 are the three numbers that u can use as a

The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.

First, let's calculate the margin of error:

Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055

Next, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%

Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%

Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

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The solution of the linear equation  is determined as x = -4.

The solution of the linear equation is calculated by applying the following method as follows;

The given linear equation;

2/x+3 - 1/x = -4/x² +3x

We can start by simplifying the equation and getting rid of the fractions.

Multiplying every term by x will help us achieve that:

2 + 3x - 1 = -4/x + 3x²

Simplifying further:

2 + 3x - 1 = (-4 + 3x²) / x

Combining like terms:

3x + 1 = (-4 + 3x²) / x

(x)(3x + 1) = -4 + 3x²

3x² + x = -4 + 3x²

We can subtract 3x² from both sides:

x = -4

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The given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

A vector space can be defined as a space (set) which comprises vectors, whose elements can be added under the associative and commutative operation, and can be multiplied by scalars under the associative and distributive operation.

This ultimately implies that, a vector space must be comprised of at least one element, which is generally regarded as its zero vector and the smallest possible vector space.

For every element {u, v and w} in vector (V), and element {a and b} in vector (F), this 8th axiom must be satisfied in order to have a vector space:

(k + m)u = ku + mu

Note: The above axiom (k + m)u = ku + mu is generally referred to as the "distributivity of scalar multiplication with respect to field addition."

Given the following vector:

k(x, y, z) = {k²x, k²y, k²z}

If x₁ · x₂ ≥ 0, then, (kx₁) · (kx₁) = k²x₁y₁ ≥ 0 [Closed in scalar multiplication].

If x₁ · x₂ ≥ 0, x₂ · y₂ ≥ 0, then (x₁ + x₂) · (y₁ + y₂):

x₁y₁ + x₂y₂ + x₁y₂ + x₂y₁ < 0

x₁y₁ + x₂y₂ < -(x₁y₂ + x₂y₁) [Not closed in vector addition].

In conclusion, we can infer and logically deduce that the given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

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Complete Question:

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail.

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = {k²x, k²y, k²z}.

Answer:

The slope is

\( - \frac{4}{3} \)

Step-by-step explanation:

To find the slope given two points we use the formula

\(m = \frac{y2 - y1}{x2 - x1} \)

where

m is the slope

(x1 , y1) and (x2 , y2) are the points

From the question

The points are (3,14) and (6,10)

The slope of the line (3,14) and (6,10) is

\(m = \frac{10 - 14}{6 - 3} = \frac{ - 4}{ 3} \)

\(m = - \frac{4}{3} \)

Hope this helps you

Answer:

(A) 2/3 [√(4-4x)]^3

(B) 2/3 [√(4-x)]^3

Step-by-step explanation:

Integrating the functions,

(A) Any function in square root is equal to or same as the function raised to the power of 1/2

To integrate, add 1 to the power of the function. That's 1/2 + 1 = 3/2

Divide the function by this new power 3/2. This implies multiplying the function by the inverse of 3/2. The inverse of 3/2 is 2/3.

Also, when a function is raised to the power of a fraction instead of a whole number, you take the 'denominator' root of the function, and then raise the function to the power of the numerator.

Here, the denominator is 2, so you take the square root of the function, and raise the function to the power of 3

So the integral of Y = √[4-4x] is

2/3 [√(4-4x)]^3

(B) In like manner, the integral of

Y = √[4-x] is

2/3 [(√4-x)]^3

Answer:

46.8 cm^3

Step-by-step explanation:

Answer:

-9x= 11-2

-9x= 9

×= 9+9

×= 18

An equation of the plane through the point (8, 5, 6) and with normal vector 4i 9j 3k is 4x + 9y + 3z = 95.

A plane in geometry is a level surface that never ends. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true examples of geometric planes, despite the fact that it is difficult to envision a plane in real life.

A point is given that is (8, 5, 6) and is passing through 4i + 9j + 3k so ,

4(x - 8) + 9(y - 5) + 6(z - 6) = 0

4x + 9y + 3z = 95.

A plane is a flat, infinitely long, two-dimensional surface in mathematics. A plane may appear as a subspace of a multidimensional space, such as one of the room's infinitely expanding walls, or it may live independently on its own, such as in the context of Euclidean geometry.

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Answer:

y = 6l + 43

Step-by-step explanation:

y=mx + b

y = y coordinate

m = slope

x = x coordinate

b = y intercept

The y intercept is when x = 0, so the initial cost before buying the laces, which was the cost of the sneakers

b = 43

The slope is you purchase one pair of laces, it increases by 6 each time

m = 6

The y coordinate will represent the total cost spent

y

The x coordinate will represent the total number of laces purchase and we are told that the variable is l

x = l

combine:

y = 6l + 43

Answer:

637.5 I think it's right

Step-by-step explanation:

2,500x.04=100x3=300

2,500x.045=112.5x3=337.5

300+337.5=637.5 interest

2,500x2+637.5=5,637.5

Answer:

$5,612.16

Step-by-step explanation:

Part 1) Account I earns 4% annual simple interest.

we know that

The simple interest formula is equal to A = P (1+rt)

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have:

t = 3 years

P = $2,500

r = 4% = 4/100 = 0.04

substitute in the formula above

A = 2,500 (1 + 0.04 * 3)

A = 2,500 (1.12)

A = $2,800

Part 2) Account II earns 4% interest compounded annually.

we know that    

The compound interest formula is equal to: A = P (1 + r/n)nt

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t = 3 years

P = $2,500

r = 4% = 4/100 = 0.04

n = 1

substitute in the formula above  

A = 2,500 * (1 + 0.04/1)3

A = 2,500 * (1.04)3

A = $2,812.16

Part 3) What is the sum of the balances of Account I and Account II at the end of 3 years?

Sum the two final investment:

$2,800 + $2,812.16 = $5,612.16

According to the unitary method,

A) The time taken for Peter to finish the job alone is 4 hours, 48 minutes.

B) The time taken for Emily and Peter to finish the job together is 2 hours, 36 minutes.

Unitary method:

In math, unitary method refers the process of finding the value of a single unit, and based on this value.

Given,

Emily, Ashley and Peter can clean a warehouse in 2 hours. If Emily does the job alone, she can finish it in 6 hours. If Ashley does the job alone she can finish it in 8 hours.

Here we need to find the following:

A) The time take for Peter to finish the job alone

B) The time taken for Emily and Peter to finish the job together

Let us consider x be the time taken for Peter to finish the job alone.

So, based on the given question we can write it as,

=> 1/6 + 1/8 + 1/x = 1/2

=> (8 + 6)/48 + 1/x = 1/2

=> 14/48 + 1/x = 1/2

=> 7/24 + 1/x = 1/2

=> 1/x = 1/2 - 7/24

=> 1/x = 12 -7/24

=> 1/x = 5/24

=> x = 24/5

=> x = 4.8

So, the time taken for Peter to finish the job alone is 4 hours, 48 minutes.

Then the time taken for Emily and Peter to finish the job together is calculated as,

=> 5/24 + 1/6

=> 5 + 4/ 24

=> 9/24

=> 3/8

Therefore, the time taken for Emily and Peter to finish the job together 2 hours, 36 minutes.

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None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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Answer:7:45

Step-by-step explanation:

The expression (32 ÷ (10 - 8)) ÷ 2 - 3 evaluates to 5 and includes the necessary parentheses to achieve this result.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To make the value of the expression equal to 5, we can use parentheses to change the order of operations. One possible way to do this is:

32 ÷ (10 - (8 ÷ 2) - 3)

First, we evaluate the expression inside the parentheses:

8 ÷ 2 = 4

10 - 4 - 3 = 3

So now the expression becomes:

32 ÷ 3

=10.67

This is not equal to 5.

To make the value of the expression equal to 5, we need to modify the expression inside the parentheses. One way to do this is:

32 ÷ (10 - (8 ÷ (2 - 3)))

Here, we use the parentheses to change the order of operations so that we subtract 3 from 2 before dividing 8 by the result. This gives us:

8 ÷ (-1) = -8

So now the expression inside the parentheses becomes:

10 - (-8) = 18

So the entire expression becomes:

32 ÷ 18 = 1.78

This is still not equal to 5.

Another way to make the value of the expression equal to 5 is:

(32 ÷ (10 - 8)) ÷ 2 - 3

Here, we use the parentheses to ensure that we divide 32 by the result of (10 - 8) before dividing the whole expression by 2 and subtracting 3. This gives us:

32 ÷ 2 - 3 = 13

So the entire expression becomes:

13

And this is equal to 5.

Therefore, one possible expression that includes a set of parentheses so that the value of the expression is 5 is:

(32 ÷ (10 - 8)) ÷ 2 - 3

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There were 172 children and 165 adults admitted to the amusement park.

Given that the admission fee for children is $1.50, so the total amount collected from children is 1.5c.

Similarly, the admission fee for adults is $4, so the total amount collected from adults is 4a.

We are also given that the total number of people admitted to the park is 337, so we can write the following equation based on the number of people:

c + a = 337

The total admission fees collected is $918.

1.5c + 4a = 918

Now we have a system of two equations.

From the first equation, we can express 'c' in terms of 'a':

c = 337 - a

Substituting this value of 'c' into the second equation:

1.5(337 - a) + 4a = 918

505.5 - 1.5a + 4a = 918

2.5a = 918 - 505.5

2.5a = 412.5

a = 412.5 / 2.5

a = 165

Substituting the value of 'a' back into the first equation:

c + 165 = 337

c = 337 - 165

c = 172

Therefore, there were 172 children and 165 adults admitted to the amusement park.

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Answer:

m^2+5m+25/4

perfect square trinomial^^

Answer:

270 mins if I'm not mistaking

Answer:

\(y = 10000 * 0.959^t\)

Step-by-step explanation:

Given

\(a = 10000\)

\(r = 4.1\%\)

Required

Express as an exponential function \(y =ab^t\)

First, we calculate the value of b;

Since the population decrease, then

\(b = 1 - r\) --- This represents decrement of decay factor

Substitute \(r = 4.1\%\)

\(b = 1- 4.1\%\)

\(b = 0.959\)

So:

\(y =ab^t\) becomes

\(y = 10000 * 0.959^t\)

The line an illustrates a linear function. Line a's slope is thus 1. Y = x + 2 is the equation for the line 'a'.

The steepness or slant of a line may be determined by looking at its slope. The slope is defined as the ratio of any two points on the line's vertical change (rise) to its horizontal change (run). The letter "m" is typically used to indicate slope.

The slope of a line connecting the coordinates (x1, y1) and (x2, y2) may be determined mathematically using the following formula:

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

Now, Evaluating slope of line 'a';

\(m=\frac{4-2 }{2-0 } = \frac{2}{2} =1\)

Hence, the slope of line 'a' is 1.

Final Plotted Graph is mentioned in image 3 attached.

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Complete Question : Draw a vertical y-axis on the left-hand side of your graph and label it. Then draw a horizontal x-axis at the bottom of your graph. Then label the coordinates of each corner of the sign on your graph(Refer to image attached). Draw line a on your graph. What is the slope of line a?