The equation y = 2x2 – 4x – 3 models the cross-section of a sculpture that sits in the water, where x is horizontal distance, and y is height above sea level. At what two x-values is the sculpture at sea-level?

Answer:

Pricing a product too low may cause the producer of the product to be unable to produce it further along, as in reality they must not only hit even with the cost of the raw materials used but also make enough profit to live off of. In this way, trying to undercut competitors may cause a foodservice operator to lose money and go out of business. There is also a high possibility that consumers will see the low prices and assume the product is low quality. This makes it difficult to build a consumer base of loyal customers.

Answer:

The population of deer at any given time = 200(e^0.03t)  ÷ (1.5 + (e^0.03t))

Step-by-step explanation:

This is an example of logistic equation on population growth

carrying capacity, k = 200

Rate, r = 3% = 0.03

Initial Population, P1 =  80

P(t) =?

P(t) = (P1 (k)(e^rt)) ÷ (k- P1 + P1(e^rt))

P(t) = (80 (200)(e^0.03t)) ÷ (200 - 80 + 80(e^0.03t))

     = (16000(e^0.03t))  ÷ (120 + 80(e^0.03t))

      = 200(e^0.03t)  ÷ (1.5 + (e^0.03t))

The ratio of non-winners in group A is 3/5 and in group B is 527/579. And the ratio of non-winners in group A to non-winners in group B will be 78/527.

Let's review the information given to us to answer the question correctly:

People in group A = 130

People in group B = 579

People in group A that will be selected to win US$ 50 fuel cards = 2/5

People in group B that will be selected to win US$ 50 fuel cards = same amount that group A

Group A

If winners are 2/5, non-winners will be 1 -2/5

1 - 2/5 = 5/5 - 2/5 = 3/5

Now, let's calculate the number of winners:

2/5 * 130 = 52 winners ⇒ 78 non-winners

Group B

Number of winners = 52 (Same amount that group A)

Ratio of winners = 52/579

Ratio of non-winners = 1 - 52/579 = 579/579 - 52/579 = 527/579

The ratio of non-winners in group A is 3/5 and in group B is 527/579. And the ratio of non-winners in group A to non-winners in group B will be 78/527

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Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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The rates that credit card companies charge their customers for the use of their credit cards is in range of 1.5% to 3.5% of each transaction's total.

A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.

Given is the rates that credit card companies charge their customers for the use of their credit cards.

Credit card processing fees will typically cost a business 1.5% to 3.5% of each transaction's total.

Therefore, the rates that credit card companies charge their customers for the use of their credit cards is in range of 1.5% to 3.5% of each transaction's total.

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Answer:

Step-by-step explanation:

If you use pre-tax dollars, then it lowers your taxable income now and most likely when you retire, your income will be lower, so you'll pay a lower tax rate  then.

Answer: D

Answer:

The calculated value |t| = |-3.082| =3.082 > 2.0322 at 0.05 level of significance

The null hypothesis is rejected

An alternative hypothesis is accepted

There is evidence that the machine should be stopped and production wait for repairs

Step-by-step explanation:

Step(i):-

Given that the mean of the Population(μ) = 8 ounces

Given that the sample size 'n' = 35

The mean of the sample(x⁻) = 7.91

The variance of the sample  S² = 0.03 ounces

                                           S = √0.03 =  0.1732

Step(ii):-

Null Hypothesis: H₀: There is no evidence that the machine should be stopped and production wait for repairs

Alternative Hypothesis: H₁: There is evidence that the machine should be stopped and production wait for repairs

\(t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }\)

\(t = \frac{7.91 -8}{\frac{0.1732}{\sqrt{35} } }\)

t = - 3.082

|t| = |-3.082| =3.082

Degrees of freedom

ν = n-1 = 35-1=34

t₀.₀₅ =  2.0322

The calculated value |t| = |-3.082| =3.082 > 2.0322 at 0.05 level of significance

The null hypothesis is rejected

An alternative hypothesis is accepted

conclusion:-

There is evidence that the machine should be stopped and production wait for repairs

Volume of the cylinder =  6838.92 cubic inches

We have to given that;

Sam needs to fill a cylindrical container with punch.

And, The container has a radius of 11 inches and a height of 18 inches.

Since, To determine the amount of cat litter the cylinder can hold, we need to calculate the volume of the cylinder.

Volume of a cylinder = πr²h

Where,

r=radius

h= height

Then,

π=22/7 or 3.14 (constant value)

r=11 inches

h=18 inches

Volume of a cylinder is,

= 3.14 × (11)² × 18

= 6838.92 cubic inches

Hence, Volume of the cylinder =  6838.92 cubic inches

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Answer:

The y-intercept is -4

y= -2/3 + (-4)

The only automorphism of a well-ordered set is the identity.

To prove this statement, we need to show that any automorphism of a well-ordered set must be the identity function. An automorphism is a bijective function that preserves the order structure of the set.

Assume we have a well-ordered set (W, ≤), where W is the set and ≤ is the order relation.

Let f: W → W be an automorphism of the set.

We aim to prove that f is the identity function, i.e., f(x) = x for all x ∈ W.

Suppose, for contradiction, that there exists an element a ∈ W such that f(a) ≠ a.

Since f is a bijective function, there must exist some b ∈ W such that f(b) = a.

Since (W, ≤) is well-ordered, there is a least element c in the set {x ∈ W : f(x) ≠ x}.

Let d = f(c). Since f is an automorphism, f(c) ≠ c, and thus d ≠ c.

Since (W, ≤) is well-ordered, there is a least element e in the set {x ∈ W : f(x) = d}.

Consider the element f(e). Since f is a bijective function, there must exist some f^{-1}(f(e)) = e' ∈ W such that f(e') = f(e) = d.

By the definition of automorphism, f(f^{-1}(y)) = y for all y ∈ W. Applying this property to e', we have f(f^{-1}(f(e'))) = f(e') = d.

However, f^{-1}(f(e')) = e' ≠ c, and thus f(e') ≠ d. This contradicts the fact that e is the least element in the set {x ∈ W : f(x) = d}.

Therefore, our assumption that there exists an element a such that f(a) ≠ a is false.

Since we assumed f(a) ≠ a for arbitrary a ∈ W, it follows that f(x) = x for all x ∈ W.

Hence, the only automorphism of a well-ordered set is the identity function.

Therefore, we have proven that the only automorphism of a well-ordered set is the identity function.

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Answer:

4/5 times 40 = 32

1/6 times 48= 8

5/8 times 64= 40

Step-by-step explanation:

Hope this helps chu! Credit to the person below as well!

To solve the equation 7(x + 3) = 7(x + 5), we can start by simplifying both sides of the equation:

7x + 21 = 7x + 35

Subtracting 7x from both sides, we get:

21 = 35

This is a contradiction, as 21 is not equal to 35. Therefore, the equation has no solution.

However, the problem states that the equation has an infinite number of solutions. This can only happen if the missing number is a factor that appears on both sides of the equation, and therefore cancels out when we simplify the equation.

Looking at the equation, we can see that both sides have a factor of 7, which cancels out when we simplify the equation. Therefore, the missing number must be the factor that was torn off, which is 7 multiplied by the difference between the two numbers inside the parentheses:

7(5 - 3) = 14

Therefore, the missing number is 14, which corresponds to answer option B.

Answer:

I would say A.

Step-by-step explanation:

The chance of getting no fives in 20 spins with 8 equal sectors is 1 in 160. The data is also slightly skewed left. All the other graphs are not skewed and have 1 or more outcome for each box. This indicates an unfair data-generating process for plot A.

I won't go into much depth of this analysis, but it should be enough to make you understand what is going on.

Hope this helps!

Answer:

b yes c yes

Step-by-step explanation:

9.72 × 10^4 = 97200

1.04 x 10^5 = 104000

Answer:

I think answer is D but it could be wrong not sure

Step-by-step explanation:

remember, y = f(x)

so, the question is really for what x is y = 1 ?

and what is the y-value for x = -1 ?

a)

when we imagine a horizontal line through y = 1, at what points (x-value) does this line cross the function graph ?

as we can see, at x = -2 and x = 2.

pick one for your answer.

b)

now we imagine a vertical line through x = -1.

at what point (y-value) does this line cross the function graph ?

as we can see, at y = 4.

f(-1) = 4

The number in an expanded form is 700,000 + 182 + 0.009

The number is given as:

seven hundred thousand one hundred eighty-two and nine thousandths

Next, we split the numbers:

seven hundred thousand = 700,000

one hundred eighty-two = 182

and nine thousandths = 0.009

Next, we add the numbers

700,000 + 182 + 0.009

Hence, the number in an expanded form is 700,000 + 182 + 0.009

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Answer:

Step-by-step explanation:

18 * 10 - 8 * 4    (remember pemdas)

180 - 32 =

148 cm²

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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Answer:

Below

Step-by-step explanation:

(x-10)^2 = 90     sqrt both sides

x-10  =  ± sqrt (90)

x  =   10 ± sqrt (90)

Answer:

D the 4th one that starts with-13.

Answer:

Perimeter = 19.42 in and area = 26.13 in^2.

Step-by-step explanation:

The perimeter = 2 * 5 + length of the semicircle

= 10 * 3.14 * 3

= 19.42 in.

Total area = area of the semicircle + area of the triangle

= 1/2 * 3.14 * 3^2 + 3 * 4

= 26.13 in^2.

The APY for super apple sauce APY is 13.4%, markers inc APY is 37.9%. The total return for super apple sauce is 137%, markers inc is 400%.

Interest refers to the amount of money that is charged or earned in relation to a principal amount of money.

To calculate the APY (annual percentage yield) for each investment, we need to use the following formula:

APY = (1 + r/n)^n - 1

1) For Super Apple Sauce, the return is $135 for every $57 invested in 5 years. Annual interest rate of:

r = (135/57)^(1/5) - 1 ≈ 0.134

Since the interest is compounded yearly, n=1. Using the formula, we get:

APY = (1 + 0.134/1)^1 - 1 ≈ 0.134 or 13.4%

Therefore, the APY for Super Apple Sauce is approximately 13.4%.

2) For Markers Inc., the return is $5 for every $1 invested in 5 years. Annual interest rate of:

r = (5/1)^(1/5) - 1 ≈ 0.379

Since the interest is compounded yearly, n=1. Using the formula, we get:

APY = (1 + 0.379/1)^1 - 1 ≈ 0.379 or 37.9%

Therefore, the APY for Markers Inc. is approximately 37.9%.

The total return for each investment:

Total Return = (Ending Value - Beginning Value) / Beginning Value

3) For Super Apple Sauce, the beginning value is $57 and the ending value is $135, so the total return is:

Total Return = ($135 - $57) / $57 ≈ 1.37 or 137%

Therefore, the total return for Super Apple Sauce is approximately 137%.

4) For Markers Inc., the beginning value is $1 and the ending value is $5, so the total return is:

Total Return = ($5 - $1) / $1 = 4 or 400%

Therefore, the total return for Markers Inc. is 400%

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Answer:

2*3

Step-by-step explanation:

first name last sw do

Stefany Tolesteros and LOLOftes thanks me later

The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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