What would be the equation of the midline of this graph?

Answer:

E. y = 1/4x

Step-by-step explanation:

Using y = 1/4x. Do rise over run. The graph rises 1 on the y-axis for every 4 on the x-axis

We will see that the linear equations are:

Parallel line: x = -9

Perpendicular line: y = 3

Here we have the vertical line:

x = -2

A parallel line to this one will also be vertical, of the form:

x = a

And a perpendicular line to this one will be horizontal, of the form:

y = b

We want the parallel line to pass through (-9, 3)

So our line x = a needs to pass through that point, then:

x = -9

Is the parallel line.

And if the perpendicular line y = b needs to pass through that point, then:

y = 3

Is the perpendicular line.

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Answer:

Step-by-step explanation:

1) 21 x 21 = 441cm²

2) 16/4=4 4 x 4 = 16cm²

3) 100-40 = 60/2 = 30cm

4)18 x 8 = 144cm/2=72 72x 4=288cm

5) π x 9²=81πcm²

Answer:

Step-by-step explanation:

1) to calculate the area of ​​a square you must do: side x side so 21 x 21 = 441

2) The perimeter is calculated by: side x 4

So to find the length of a side, you divide 16 by 4.

Next, you have to calculate the area of ​​this square with a side of 16 cm.

You just have to do 16 x 16

3) The formula to calculate the perimeter of a rectangle is: Length x Width

So you divide 100 by 20 and you get the length of your rectangle

Answer:

1) x=1/2-y/2-3z

2)x= 16/3- 2y/3- 5z/3

3)x= 11/7- 3y/7+ 4z/7

Step-by-step explanation:

isolate the variable, to do that divide each side by the factors that don't contain the variable

The integral for the area of the surface obtained by rotating the curve about the x-axis and the y-axis, are:

S = ∫[3,5] 2πxe−x√(1+(e−x−xe−x)²)dx and S = ∫[3e−3,5e−5] 2π(ln(y)/y)√(1+(1/y−ln(y)/y)²)dy respectively.

To set up the integral for the area of the surface obtained by rotating the curve about the x-axis and the y-axis, we need to use the formulas for surface area of revolution.

For rotation about the x-axis, the formula is:
S = ∫2πy√(1+(dy/dx)²)dx

For rotation about the y-axis, the formula is:
S = ∫2πx√(1+(dy/dx)²)dy

Plugging in the given curve y = xe−x and the bounds 3 ≤ x ≤ 5, we get:

For rotation about the x-axis:
S = ∫[3,5] 2πxe−x√(1+(e−x−xe−x)²)dx

For rotation about the y-axis:
S = ∫[3e−3,5e−5] 2π(ln(y)/y)√(1+(1/y−ln(y)/y)²)dy

These are the integrals that need to be evaluated to find the area of the surface obtained by rotating the curve about the x-axis and the y-axis.

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A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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To find a polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i, we know that the complex conjugate of 2-i, which is 2+i, must also be a zero. This is because complex zeros of polynomials always come in conjugate pairs.

So, we can start by using the factored form of a polynomial:

f(x) = a(x - r1)(x - r2)(x - r3)...

where a is a constant and r1, r2, r3, etc. are the zeros of the polynomial. In this case, we have:

f(x) = a(x - 5)(x - (2-i))(x - (2+i))

Multiplying out the factors, we get:

f(x) = a(x - 5)((x - 2) - i)((x - 2) + i)
f(x) = a(x - 5)((x - 2)^2 - i^2)
f(x) = a(x - 5)((x - 2)^2 + 1)

To make sure that f(x) only has real coefficients, we need to get rid of the complex i term. We can do this by multiplying out the squared term and using the fact that i^2 = -1:

f(x) = a(x - 5)((x^2 - 4x + 4) + 1)
f(x) = a(x - 5)(x^2 - 4x + 5)

Now, we just need to find the value of a that makes the degree of f(x) as small as possible. We know that the degree of a polynomial is determined by the highest power of x that appears, so we need to expand the expression and simplify to find the degree:

f(x) = a(x^3 - 9x^2 + 24x - 25)
Degree of f(x) = 3

Since we want the least degree possible, we want the coefficient of the x^3 term to be 1. So, we can choose a = 1:

f(x) = (x - 5)(x^2 - 4x + 5)
Degree of f(x) = 3

Therefore, the polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i is:

f(x) = (x - 5)(x^2 - 4x + 5)
To find a polynomial function f(x) of least degree with real coefficients and zeros of 5 and 2-i, we need to remember that if a polynomial has real coefficients and has a complex zero (in this case, 2-i), its conjugate (2+i) is also a zero.

Step 1: Identify the zeros
Zeros are: 5, 2-i, and 2+i (including the conjugate)

Step 2: Create factors from zeros
Factors are: (x-5), (x-(2-i)), and (x-(2+i))

Step 3: Simplify the factors
Simplified factors are: (x-5), (x-2+i), and (x-2-i)

Step 4: Multiply the factors together
f(x) = (x-5) * (x-2+i) * (x-2-i)

Step 5: Expand the polynomial
f(x) = (x-5) * [(x-2)^2 - (i)^2] (by using (a+b)(a-b) = a^2 - b^2 formula)
f(x) = (x-5) * [(x-2)^2 - (-1)] (since i^2 = -1)
f(x) = (x-5) * [(x-2)^2 + 1]

Now we have a polynomial function f(x) of least degree with real coefficients and zeros of 5, 2-i, and 2+i:
f(x) = (x-5) * [(x-2)^2 + 1]

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Answer:

The answer is 18.

Step-by-step explanation:

The ratio of the original height of candle x to the original height of candle y is 13:8. This means that candle x is 13/8 times taller than candle y.

The ratio of the original height of candle x to the original height of candle y can be found by considering their burning rates and the time it takes for them to reach the same length. Based on the given information, candle x burns at a rate of 1/13 of its height per hour, while candle y burns at a rate of 1/24 of its height per hour. After burning for 9 hours, both candles have the same length.

Let's assume the original height of candle x is Hx and the original height of candle y is Hy. Candle x burns at a rate of 1/13 of its height per hour, so after burning for 9 hours, its remaining height would be (1 - 9/13)Hx = (4/13)Hx. Similarly, candle y burns at a rate of 1/24 of its height per hour, so after burning for 9 hours, its remaining height would be (1 - 9/24)Hy = (15/24)Hy.

Given that both candles have the same length after burning for 9 hours, we can equate their remaining heights:

(4/13)Hx = (15/24)Hy

To find the ratio of the original heights, we divide both sides of the equation by Hy:

(4/13)Hx / Hy = (15/24)

Simplifying the equation, we get:

Hx / Hy = (15/24) * (13/4) = 13/8

Therefore, the ratio of the original height of candle x to the original height of candle y is 13:8. This means that candle x is 13/8 times taller than candle y.

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The key features of the absolute value function y = |x - 2| - 4 include the following:

In Mathematics and Geometry, an absolute value function is a type of function that comprises an algebraic expression, which is placed within absolute value symbols, and it typically measures the distance of a point on the x-axis to the x-origin (0) of a graph.

When y = 0, the x-intercept can be determined as follows;

f(x) = |x - 2| - 4

0 = |x - 2| - 4

4 = -x + 2

x = 2 - 4

x = -2

When x = 0, the y-intercept can be determined as follows;

f(0) = |0 - 2| - 4

f(0) = 2 - 4

f(0) = -2

Based on the graph shown in the image attached above, we can logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-4, ∞] or {y | y ≥ -4}.

In conclusion, the the graph of parent absolute value function y = |x| was translated by 2 units to the right and 4 units down in order to produce the graph of the transformed absolute value function y = |x - 2| - 4.

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The probability of a carryout order being ready within 20 minutes is approximately 0.5507

We know that the time required for a carryout order to be ready for customer pickup follows an exponential distribution with a mean of 25 minutes. The probability density function for an exponential distribution is given by

f(x) = λe^(-λx)

where λ is the rate parameter

We can find the rate parameter λ using the mean

mean = 1/λ

λ = 1/mean = 1/25 = 0.04

So the probability of a carryout order being ready within 20 minutes is

P(X ≤ 20) = ∫₀²⁰ λe^(-λx) dx

P(X ≤ 20) = [-e^(-λx)]₀²⁰

P(X ≤ 20) = [-e^(-0.04x)]₀²⁰

P(X ≤ 20) = [-e^(-0.8)] - [-1]

P(X ≤ 20) = 0.5507

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The given question is incomplete, the complete question is:

Collina’s Italian Café in Houston, Texas, advertises that carryout orders take about 25 minutes (Collina’s website, February 27, 2008). Assume that the time required for a carryout order to be ready for customer pickup has an exponential distribution with a mean of 25 minutes. What is the probability than a carryout order will be ready within 20 minutes?

The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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The value of investment at maturity is $15094.

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

a=9000

r= 0.09

t=6

y=a(1+r)ᵗ

=> y=9000(1+0.09)⁶

=> y= 9000(1.09)⁶

=> y= 15093.900

Rounded to whole number : $15094

The value of investment at maturity is $15094

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Answer:

30 terms

Step-by-step explanation:

The n th term of an AP is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here d = 5 and a₃ = 13, thus

a₁ + 2d = 13

a₁ + 2(5) = 13

a₁ + 10 = 13 ( subtract 10 from both sides )

a₁ = 3

Thus

\(a_{n}\) = 3 + 5(n - 1) = 148 ( subtract 3 from both sides )

5(n - 1) = 145 ( divide both sides by 5 )

n - 1 = 29 ( add 1 to both sides )

n = 30

The progression has 30 terms

Answer:

110 for every 2 minutes because 290 - 180 gives you 110 every 2 minutes

The sample proportion of the random sample of 50 students is 64% or 0.64.

Given:

the college administrator was only able to survey a random sample of 50 students.

she finds that 32 of these students report having a full- or part-time job.

we are asked to determine the sample proportion = ?

Based on the given conditions, we formulate:

32÷50

simplify:

16/25

= 64% or 0.64

hence we get the required sample proportion.

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If you want to round a number within an arithmetic expression, you should use the ROUND function.

The ROUND function allows you to specify the number of decimal places to which you want to round a given number. It is commonly used in programming languages and spreadsheet software.

The syntax for the ROUND function typically involves specifying the number or expression you want to round and the number of decimal places to round to. For example, if you want to round a number, let's say 3.14159, to two decimal places, you would use the ROUND function like this: ROUND(3.14159, 2), which would result in 3.14.

Using the ROUND function ensures that the rounded number is calculated within the arithmetic expression, providing the desired level of precision in the calculation.

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the greatest common factor (GCF) of 12, 24, and 48 is 12.

Answer:

GCF of 24 and 48 is 24

Step-by-step explanation:

Answer:

Average speed = 3.17 km/h and Average velocity = 1.5 km/h

Step-by-step explanation:

It is given that,

Eric walks 7 km East in 2 hours and then 2.5 km West in 1 hour.

Average speed = distance/time

Distance = 7km + 2.5 km = 9.5 km

Time = 2 h + 1 h = 3 h

Average speed,

\(s=\dfrac{9.5\ km}{3\ h}\\\\s=3.17\ km/h\)

Average velocity = displacement/time

Displacement = 7 km +(-2.5 km) = 4.5 km

Average velocity,

\(v=\dfrac{4.5\ km}{3\ h}\\\\v=1.5\ km/h\)

So, 3.17 km/h is the average speed and 1.5 km/h is the average velocity for the whole journey that Eric takes.

The probability that Laurent's number is greater than Chloe's number is 3/4.

Suppose Laurent's number is in the interval \($[ 0, 2017 ]$\).

Then, by symmetry, the probability of Laurent's number being greater is \($\dfrac{1}{2}$\).

Next, suppose Laurent's number is in the interval [ 2017, 4034 ].

Then Laurent's number will be greater with a probability of 1.

Since each case is equally likely, the probability of Laurent's number being greater is \($\dfrac{1 + \frac{1}{2}}{2} = \dfrac{3}{4}$\)

Hence the probability that Laurent's number is greater than Chloe's number is 3/4.

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The length of the pendulum using equation is 43.56 feet.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation that represent the time of pendulum for one swing is

=> T = \(\frac{2\sqrt L}{3.3}\)

Now T = 4 sec then ,

=> 4 = \(\frac{2\sqrt L}{3.3}\)

=> 4*3.3 = 2\(\sqrt L\)

=> \(\sqrt L = 2\times3.3 = 6.6\)

=> L = 43.56 feet.
Hence the length of the pendulum using equation is 43.56 feet.

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Thus, equation that Tracy needs to use to obtain the number of tablespoons of flour to use in making 10 pancakes.

The unitary method is a method for determining the value of one unit from the values of several units or the other way around.

The unitary approach is a strategy for problem-solving that involves first determining the value of one unit, then multiplying that value to determine the required value.

Given data:

4 pancakes --->  6 teaspoon of flour.

For 1 pancake, divide above expression with 4 on both side.

1  pancakes --->  6/4 teaspoon of flour.

Now, for 10 pancake, multiply  above expression with 10 on both side.

10  pancakes --->  10* 6/4 teaspoon of flour.

Thus, equation that Tracy needs to use to obtain the number of tablespoons of flour to use in making 10 pancakes.

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The angle between vectors u and v is approximately 43.7 degrees to the nearest tenth of a degree.

To find the angle between two vectors, we can use the dot product formula and the magnitude of the vectors. The dot product of two vectors u and v is given by:

u · v = |u| |v| cos(theta)

where |u| and |v| are the magnitudes of vectors u and v, respectively, and theta is the angle between the vectors.

Given vectors u = <6, 4> and v = <7, 5>, we can calculate their magnitudes as follows:

|u| = sqrt(6^2 + 4^2) = sqrt(36 + 16) = sqrt(52) ≈ 7.21

|v| = sqrt(7^2 + 5^2) = sqrt(49 + 25) = sqrt(74) ≈ 8.60

Next, we calculate the dot product of u and v:

u · v = (6)(7) + (4)(5) = 42 + 20 = 62

Now, we can substitute the values into the dot product formula:

62 = (7.21)(8.60) cos(theta)

Solving for cos(theta), we have:

cos(theta) = 62 / (7.21)(8.60) ≈ 1.061

To find theta, we take the inverse cosine (arccos) of 1.061:

theta ≈ arccos(1.061) ≈ 43.7 degrees

Therefore, the angle between vectors u and v is approximately 43.7 degrees to the nearest tenth of a degree.

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The height of the cylinder is \(3 inch\)

Based on the attached figure,

Volume of the cylinder = 282.7 square inches

Radius of the cylinder =5 inches.

The height of the cylinder = ?

The volume of the cylinder  can be found with the formula as :

\(V=pi r^{2} h\)

\(h=\frac{V}{pi r^{2} } \\\\h = \frac{282.7}{3.142 * 5^{2} } \\\\=3 inch\)

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The correct answers are:

a. less a discount to yield 6.20%

d. plus a premium to yield 6.36%

Based on the provided information, the T bills maturing on August 2nd (8-2) are being offered at a bid yield of 6.36% and an ask yield of 6.20%.

To determine whether the T bills are being offered at a discount or a premium, we compare the bid yield and ask yield to the stated yields.

a. To yield 6.20% (ask yield), the T bills are being offered at a discount. Therefore, option a. "less a discount to yield 6.20%" is correct.

b. To yield 6.20%, the T bills are not being offered at a premium. Therefore, option b. "plus a premium to yield 6.20%" is incorrect.

c. To yield 6.36% (bid yield), the T bills are not being offered at a discount. Therefore, option c. "less a discount to yield 6.36%" is incorrect.

d. To yield 6.36%, the T bills are being offered at a premium. Therefore, option d. "plus a premium to yield 6.36%" is correct.

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Answer:

Children: 51

Adults: 259

Step-by-step explanation:

Children = c Adults = a

$1.25 c + $2.00 a = $581.75

$1.25 c + $2.00 (310 - c) = $581.75

Multiply: $2.00 * 310 to get $620

Multiply: $2.00 * - c to get - $2.00 c

$1.25 c + $620 - $2.00 c = $581.75

Subtract both sides by $620

-$0.75 c = -$38.25

Divide both sides by -0.75

We now know there are 51 children.

Overall, there are 310 people so we subtract:

310 - 51 = 259

This means:

To check our answer:

51 * 1.25 = 63.75

259 * 2.00 = 518

518 + 63.75 = $581.75

Answer:

D. y= 0.3x2

Step-by-step explanation:

In quadratic functions, the value of a affects the wideness of the graph. The smaller the absolute value of a, the wider the graph. In these choices, 1/3 and 0.3 are the smallest. To understand which is smaller convert both to decimals; 1/3 is 0.3333 repeating. Therefore, 0.3 is slightly smaller and wider.

Answer:

4. (a) y=12x²-18x. le + y = 0

(b) y=2ײ-6×-8

○=12x²-18x. 0=2ײ-6×-8

6x(2×-3) =0. 2(ײ -3x -4)=0

6x=0 2x-3=0. 2(x-4) (×+1)=0

x=0. 2x=3. x-4=0 x+1=0

x=3/2. x=4 x=-1

5. y=2 (0)²-7(0)+9

y=9

The z-values for the given situations are approximate:

a. The area to the left of z is 0.1827. z = -0.90

b. The area between −z and z is 0.9830. z = 2.17

c. The area between −z and z is 0.2148. z = 0.85

d. The area to the left of z is 0.9997. z = 3.49

e. The area to the right of z is 0.6847. z= -0.48

a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.

b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.

c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.

d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.

e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.

In summary, the z-values for the given situations are approximate:

a. -0.90

b. 2.17

c. 0.85

d. 3.49

e. -0.48

These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.

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