6.
Which of the quadratic functions has the narrowest graph?


A. y = –x2

B. y = 4x2

C. \(y=\frac{1}{4} x^2\)

D. \(y=\frac{1}{9} x^2\)

Answer(x - 2, y + 6)

Step-by-step explanation: just remember where x and y are.

Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

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Solve for 12 - h(7)

First find h(7)

h(7) = 7^2+3(7)-2

h(7) = 49 + 21 - 2

h(7) = 68

12 - 68 = - 56

12 - h(7) = -56.

I'm not sure if the question wants h(-56) as well, but just plug that in.

H(-56)=2966

hope this helps :)

1. RA Using all fifth-grade classes in the campus demonstration school, a researcher divides the students in each class into two groups by drawing their names from a hat.

2. RS All students with learning handicaps in a school district are identified and the names of 50 are pulled from a hat. The first 25 are given an experimental treatment, and the remainder are taught as usual.

3. B All third-grade students in an elementary school district who are being taught to read by the literature method are identified, as are all students who are being taught with basal readers. The names of all students in each group are placed in a hat and then 50 students from each group are selected.

4. O Students in three classes with computer assistance are compared with three classes not using computers because no randomization is involved.

1. The first scenario describes a random assignment; hence RA is involved. This is because students are assigned to one group or the other by drawing their names from a hat.

2. The second scenario describes a random selection since students are identified and the names of 50 are pulled from a hat. Therefore RS is involved in this scenario.

3. The third scenario describes both random selection and random assignment. It describes how all third-grade students in an elementary school district who are being taught to read by the literature method are identified and those who are being taught with basal readers. Their names are placed in a hat and then 50 students from each group are selected.

Therefore, B is involved in this scenario.

4. In the fourth scenario, no randomization is involved. Students in three classes with computer assistance are compared with three classes not using computers. Therefore O is involved in this scenario.

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Answer:

$12.90

Step-by-step explanation:

To solve, multiply the cost before tax with tax, and then add the number gotten to the original amount.

12 x 7.5% = 12 x 0.075 = 0.9

12 + 0.9 = 12.9

$12.90 is your answer.

~

Answer:

After tax, the price should be $12.90

Step-by-step explanation:

multiply 12 by 1.075

Answer:

B

Step-by-step explanation:

Answer:

Sullivan is hanging on by 2 fingers.

Step-by-step explanation:

Since Sullivan has 8 fingers, a quarter of them (1/4) would be 8*1/4=2.

6 cans are needed to paint an area of 2200 units square.

The cans of paints and areas are illustrations of equivalent ratios.

The quantity of paint required for a certain area of house can be found out using the area of the house.

As the area is given in this problem, it is easier to calculate the amount of paint.

The given parameter is,

Cans: area = 1: 400

Putting it in the form of fraction,

Cans/area = 1/400

Cross multiplying, we have,

Cans = 1/400 × 2200 = 5.5 ≈ 6

Thus, 6 cans are needed to paint a 2200 square feet.

The question is incomplete. The complete question is 'How many cans of paint are needed to cover an area of 2200 square units if one can of paint covers in area 400 square units.'

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The correct answer is 1.22 mm per second. The height of the melted ice cream in the cone is rising at a rate of 1.22 mm per second when the cone is 10% full.

This is because the volume of the melted ice cream is increasing at a rate of 1.08 cm per second, and the volume of the cone is 125π cm3. The height of the melted ice cream is therefore rising at a rate of 1.08 cm/s / 125π cm3 = 1.22 mm/s.

The volume of the melted ice cream is increasing at a rate of 1.08 cm per second because the ice cream is melting at a rate of 1.08 cm per second. The volume of the cone is 125π cm3 because the cone has a radius of 5 cm and a height of 20 cm.

The height of the melted ice cream is therefore rising at a rate of 1.08 cm/s / 125π cm3 = 1.22 mm/s.

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Buffalo Mild Wings offers the lowest price per wing.

Lowest Price:

Demands for the lowest possible price are more commonly seen in markets with limited liquidity or low trading volume, or from traders in companies with very small market caps. This is because investors trading illiquid securities are less likely to fill buy and sell orders. Markets for less traded securities are more limited and other parties can charge prices that may not be ideal for investors. For example, investors who want to trade currency options in foreign currencies (i.e. currencies other than dollars, euros, pounds or yen) often use the lowest possible price.

According to the Question:

Given:

Buffalo Bills has 8 wings for $7.

Buffalo Mild Wings has 12 wings for $10.

Wingers has 20 wings for $17.

To Find:

Which restaurant offers the lowest price per wing?

Solution:

Find the price per wing in Buffalo Bills:

8 wings = $7

1 wing = 7 ÷ 8

1 wing = $0.875

Find the price per wing in Buffalo Mild Wings:

12 wings = $10

1 wing = 10 ÷ 12

1 wing = $0.833

Find the price per wing in Wingers:

20 wings = $17

1 wing = 17 ÷ 20

1 wing = $0.85

Now,

Comparing  $0.875 , $0.833 and $0.85:

$0.833 < $0.85 < $0.875

⇒ $0.833 is the cheapest

⇒ Buffalo Mild Wings is the cheapest

Answer: Buffalo Mild Wings offers the lowest price per wing

Complete Question:

Leah loves chicken wings and is comparing the deals at three different restaurants. Buffalo Bills has 8 wings for $7. Buffalo Mild Wings has 12 wings for $10. Wingers has 20 wings for $17. Which restaurant offers the lowest price per wing?

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90% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years in between 0.162 and 0.188.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

Given that, a survey of 2325 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 415 have donated blood in the past two years.

We know that, standard error = √(p(1-p)/n))

Where p = original sample proportion and n = sample size

Here, standard error = √(0.175(1-0.175)/2325)) = 0.00789

By using z table

To find the lower and upper bounds of the interval, we simply multiply the z value by the standard error. We then add it to the base proportion for the upper bound, and subtract it for the lower bound, as shown below:

Upper bound = 0.175 + (1.65)(0.00789) = 0.188

Lower bound = 0.175 - (1.65)(0.00789) = 0.162

Therefore, 90% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years in between 0.162 and 0.188.

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Answer:

y=18

Step-by-step explanation:

y=(2)⋅+9

Multiply 2 and 9 to get 18.

y=18

Mr Yang needs to be aware of his legal position before opening his new company, given his history as a director and auditor. He should seek professional advice to ensure that he complies with all the legal requirements and regulations and avoids any potential legal consequences.

It is important for Mr Yang to understand his legal position before opening a new company, given his history as a director of previously wound-up companies and as an auditor of his wife's company. Mr Yang should take into account the Companies Act 2016, which outlines the legal responsibilities and obligations of company directors, as well as the potential consequences of breaching these obligations.
Under the Companies Act 2016, a director has a fiduciary duty to act in the best interests of the company and its shareholders. They are required to exercise due care, skill, and diligence in carrying out their duties, and to avoid conflicts of interest. If a director breaches these obligations, they can be held personally liable for any losses suffered by the company.Given that Mr Yang's previous companies were wound up, it is possible that he may have breached his legal obligations as a director. If this is the case, he could face legal action or be disqualified from acting as a director in the future. Furthermore, as an auditor of his wife's company, Mr Yang should ensure that he is fulfilling his legal responsibilities and carrying out his duties impartially and professionally.In terms of setting up a new company, Mr Yang should ensure that he complies with all the legal requirements and regulations governing the incorporation of a limited by shares company. This includes registering the company with the Companies Commission of Malaysia (SSM), obtaining the necessary licenses and permits, and adhering to the requirements of the Companies Act 2016.

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The whole race is 12 3/4 kilometers.

The correct equations that represent this question are:

(8 1/2) ÷ 2/3 = ?

2/3 × ? = 8 1/2

(8 1/2) × 3/2 = ?

In this question we have been given Diego has run 2/3 of a race""s distance. He has run 8 1/2 kilometers.

We need to find the  length of the whole race.

Let the whole race be x.

Since Diego has run 2/3 of a race's distance which is 8 1/2 kilometers. The length of the whole race will be given by an equation:

2/3 × x = 8 1/2

x = (8 1/2) ÷ 2/3

x = (8 1/2) × 3/2

x = 17/2 × 3/2

x = 51/4

x = 12 3/4 kilometers.

Therefore, the length of the whole race= 12 3/4 kilometers.

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The choices for given question are given below.

a. the cross-correlation sequence is: ry[n] = {1.15, -6.54, -3.85, 34.62, 12.77}

b. the Lp-norm of q[n] when p = 2 is 2.03 (approx).

c. the poles of H(z) are located at z = 0.57, 0.9, and 0.625

a) Evaluation of the cross-correlation sequence, rₙ, between the two sequences, xₙ and yₙ, are shown below:

Let's solve for rₙ using the given formulas for the sequences xₙ and yₙ.rₙ = Σ x[k] y[k+n] ...(1)Here, xₙ = {5eⁿ, -e, en, -e⁻¹, 2e⁻¹} and yₙ = {6eⁿ, -en, 0, -2en, 2en} for -2 ≤ n ≤ 2.r₀ = Σ x[k] y[k+0] = 5e⁰ * 6e⁰ + (-e) * (-e) + e⁰ * 0 + (-e⁻¹) * (-2e⁻¹) + 2e⁻¹ * 2e⁻¹ = 34.62r₁ = Σ x[k] y[k+1] = 5e⁰ * 6e¹ + (-e) * (-e⁰) + e¹ * 0 + (-e⁻¹) * (-2e⁻²) + 2e⁻¹ * 0 = 12.77r₂ = Σ x[k] y[k+2] = 5e⁰ * 6e² + (-e) * (-e¹) + e² * 0 + (-e⁻¹) * 0 + 2e⁻¹ * (-2e⁻³) = -3.85r₋₁ = Σ x[k] y[k-1] = 5e⁰ * (-e¹) + (-e) * 0 + e⁻¹ * (-en) + (-e⁻¹) * 0 + 2e⁻¹ * 2e⁻² = -6.54r₋₂ = Σ x[k] y[k-2] = 5e⁰ * (-2e⁻²) + (-e) * (-2e⁻³) + e⁻² * 0 + (-e⁻¹) * (-en) + 2e⁻¹ * 0 = 1.15

Therefore, the cross-correlation sequence is: ry[n] = {1.15, -6.54, -3.85, 34.62, 12.77}

(b) The given qₙ is as follows:q[n] = x[n] + jy[n]

To determine the conjugate symmetric part of qₙ, let's first find the conjugate of qₙ and subtract it from qₙ.q*(n) = x*(n) + jy*(n)q[n] - q*(n) = x[n] - x*(n) + j(y[n] - y*(n))

However, the sequences xₙ and yₙ are all real. Therefore, q*(n) = x(n) - jy(n).So, q[n] - q*(n) = 2jy[n].

The conjugate symmetric part of q[n] is the real part of (q[n] - q*(n))/2j = y[n].Hence, the conjugate symmetric part of q[n] is y[n].

Now, let's calculate the Lp-norm of q[n] when p = 2.Lp-norm of q[n] when p = 2 is defined as follows: ||q[n]||₂ = (Σ |q[n]|²)¹/²= (Σ q[n]q*(n))¹/²= (Σ |x[n] + jy[n]|²)¹/²Here, q[n] = x[n] + jy[n].||q[n]||₂ = (Σ (x[n] + jy[n])(x[n] - jy[n]))¹/²= (Σ (x[n]² + y[n]²))¹/²= (25 + 1 + e² + e⁻² + 4e⁻²)¹/²= 2.03 (approx)

Therefore, the Lp-norm of q[n] when p = 2 is 2.03 (approx).

(c) The input to the system is x[n].

Therefore, let's write the input-output equation for an IIR LTI system:y[n] = 1.57y[n-1] - 0.81y[n-2] + x[n] - 1.18x[n-1] + 0.68x[n-2]Now, let's find the transfer function, H(z) of the system using the Z-transform.

The Z-transform of the input-output equation of the system is:Y(z) = H(z) X(z) ...(1)where X(z) and Y(z) are the Z-transforms of x[n] and y[n], respectively.

Substituting the given input-output equation, we get:Y(z) = (1 - 1.18z⁻¹ + 0.68z⁻²) H(z) X(z)Y(z) - (1.57z⁻¹ - 0.81z⁻²) H(z) Y(z) = X(z)H(z) = X(z) / (Y(z) - (1.57z⁻¹ - 0.81z⁻²) Y(z)) / (1 - 1.18z⁻¹ + 0.68z⁻²)H(z) = X(z) / (1 - 1.57z⁻¹ + 0.81z⁻²) / (1 - 1.18z⁻¹ + 0.68z⁻²)

Now, let's factorize the denominators of the transfer function H(z).H(z) = X(z) / (1 - 0.57z⁻¹) / (1 - 0.9z⁻¹) / (1 - 0.625z⁻¹)

Therefore, the poles of H(z) are located at z = 0.57, 0.9, and 0.625.

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The ratio of the corresponding sides of two similar triangles is equal. Since traingles BCD and EFG are similar, we can write

Two sides of triangle are equal triangle ABC acute scalene triangle. Option B right choice.

The type of triangle ABC can use the Pythagorean to check if it is a right triangle and the distance formula to check if it is an isosceles or scalene triangle.

Using the distance formula can find the lengths of the three sides of triangle ABC:

AB = √((6-0)² + (0-0)²) = 6

BC = √((3-6)² + (7-0)²) = √(58)

AC = √((3-0)² + (7-0)²) = √(58)

BC=AC ≠AB , and the triangle is a acute scalene triangle.

The triangle is a right triangle can use the Pythagorean:

If the triangle is a right triangle, then one of the sides must be the hypotenuse and the other two sides must be the legs.

Let's assume that AC is the hypotenuse and AB and BC are the legs. Then, we have:

(AC)² = (AB)² + (BC)²

Substituting the values we found earlier, we have:

(√58)² = 6² + (BC)²

58 = 36 + (BC)²

(BC)² = 22

22 is not a perfect square so (BC)² cannot be equal to the difference between two perfect squares.

Triangle ABC is not a right triangle.

Option B right choice.

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Answer:

x:b116.67

Step-by-step explanation:

120/100

140×100/120

Answer:

Below

Step-by-step explanation:

Because it is $7 per day and x = the length of rental days, our equation will look something like this :

     y = 7x + 3

Hope this helps!

Answer:

9. 64

10. 21

11. A (I believe)

Step-by-step explanation:

The first two were simple math problems, however 11. was a bit more complicated and I used logic to find the numbers that best fit into the problem. I am not sure that it is the right answer and if I were you I would wait for someone else to answer this question.

If X and Y are any random variables with E(X) = 5, E(Y) = 6, E(XY) = 21, V(X) = 9 and V(Y) = 10, then the relationship between x and y is a strong negative relationship.

A simple random sample can be defined as a subset of items that are selected from a statistical population or larger data set, and each member of the subset has an equal or the same probability of being selected.

This ultimately implies that, each member of the subset are selected randomly and by chance, and as such a simple random sample is an unbiased representation of a statistical population.

By calculating the covariance using the following expression, we have:

Cov(X, Y) = E(XY) - E(X)E(Y).

E(X) = 5, E(Y) = 6 and E(XY) = 21.

In conclusion, we can infer and logically deduce that the relationship between x and y is a strong negative relationship.

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Complete Question:

If X and Y are any random variables with E(X) = 5, E(Y) = 6, E(XY) = 21, V(X) = 9 and V(Y) = 10, then the relationship between X and Y is a:

-strong positive relationship

-strong negative relationship

-weak positive relationship

-weak negative relationship

Answer:

1. (-2, 3) 7

2. (5, 8) 5

3. (-6, 1/2) 2/3

Step-by-step explanation:

The equation of a circle is (x-h)^2+(y-k)^2=r^2 where the center is at point (h, k) and the r is the radius. Find the values that would fit the numbers in parenthesis to find the center of the circle, and take the squareroot of the number on the right side of the equation to find the radius.

lmk if im wrong, hope this helps!

Total weight of the Durains sold by Rowena is  5.8 kg

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.

The units of mass, the kilogram and the gram, must first be translated into grams before being added. Thereafter, the basic addition procedure must be followed. As with regular numbers, we can add two or more mass units expressed in kilograms and grams. Always write grams as three-digit figures, such as 3g = 003g.

In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.

The weight of the Durains are 1.3 kg, 1.5kg, 1.4 kg and 1.6kg

Total weight of the Durains sold by Rowena is

(1.3 + 1.5 + 1.4 + 1.6) = 5.8 kg

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We have converted the given exponential equations to logarithmic form as follows:
- \(e^x\) = 3 is equivalent to ln(3) = x, with a = 3 and b = x.
- \(e^3\) = x is equivalent to ln(x) = 3, with c = x and d = 3.

To express these equations in logarithmic form.
1. The equation \(e^x\) = 3 can be rewritten in logarithmic form using the natural logarithm, which is denoted as ln. In this case, we can say that ln(a) = b, where a is the base of the logarithm and b is the exponent. Since \(e^x\) = 3, we have a = 3 and b = x. Therefore, the logarithmic form of the equation is ln(3) = x.
2. The equation \(e^3\) = x can also be rewritten in logarithmic form using the natural logarithm. We can say that ln(c) = d, where c is the base of the logarithm and d is the exponent. Since \(e^3\) = x, we have c = x and d = 3. Therefore, the logarithmic form of the equation is ln(x) = 3.

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The given equation is dR/R = k dt, where dR represents the change in R and dt represents the change in time t. To solve this differential equation, we can separate the variables and integrate both sides.

Starting with the equation dR/R = k dt, we can rewrite it as dR = kR dt. Then, dividing both sides by R gives dR/R = k dt.

Next, we integrate both sides. On the left side, we have ∫dR/R, which evaluates to ln|R|. On the right side, we have ∫k dt, which evaluates to kt.

Therefore, the equation becomes ln|R| = kt + C, where C is the constant of integration.

To find the general solution, we can exponentiate both sides to eliminate the natural logarithm: |R| = e^(kt + C). Since e^C is a positive constant, we can rewrite this as |R| = Ce^kt. Finally, we can consider two cases: when R is positive, we have R = Ce^kt, and when R is negative, we have R = -Ce^kt. So, the general solution is R = Ce^kt or R = -Ce^kt, where C is an arbitrary constant.

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Answer:

Step-by-step explanation:

y= 1x-1

Slope= 1

Y intercept= -1

Answer:

Step-by-step explanation:

Slope m = (5 - 1) / (6 - 2) = 1

y - 1 = 1(x - 2)

y = x - 1 Slope intercept form of linear equation

y-intercept is ( - 1)

x - y = 1 Standard form of linear equation

Answer:

x = -16

Step-by-step explanation:

Answer: X = -16

Step-by-step explanation:

1. -2(2x + 5) - 3 = -3(x - 1)

2. -4x-10-3=-3x+3

3. -13=x+3

4. x=-16

check: -2(-16*2+5)-3=-3(-16-1)

51=51

Answer:

the equation you would use: y = 30x + 50

(x= months)

(y= cost)

then you would plug in the cost, 260, for y to get

260 = 30x + 50 --> 7 months

Step-by-step explanation:

I got the equation from the slope intercept form y = mx +b.

The 30 is the m, or slope, because you end up paying the same amount every month. The b value would be the 50 that he initially pays because that never changes.

Since you're given the y-value of 260, you just plug it in to your new equation of y = 30x + 50 to solve for x.

when solving the equation with the plugged in numbers, (260 = 30x + 50) first subtract 50 from both sides to get 210 = 30x,

then divide by 30 on both sides (to keep the equations equal to each other and find x) --> you should get 7

Therefore, Paul has been at the gym seven months if he has paid $260.

C) graph of a quadratic function with a minimum at 2.5, negative 2.25 and x intercepts at 1 and 4

Standard Form of a Quadratic Function: ax² + bx + c = 0, where a ≠ 0

Given function: x² - 5x + 4

⇒ a = 1, b = -5, c = 4

The minimum of a function is the lowest point of its parabola. We can use the following formula to find the vertex or the minimum of the function: \(x=\dfrac{-b}{2a}\) . This will give us the x-value of the vertex, and we will need to solve for the y-value.

The vertex or minimum.

Step 1: Find the x-value of the vertex.

\(\\\implies x=\dfrac{-(-5)}{2(1)}\\\\\implies x=\dfrac{5}{2}=2.5\)

Step 2: Find the y-value of the vertex by substituting 2.5 as the value of x in the given function.

\(\\\implies x^2 - 5x + 4\\\\\implies 2.5^2-5(2.5)+4\\\\\implies 6.25-12.5+4\\\\\implies -2.25\)

Vertex: (2.5, -2.25)

The x-intercepts (roots).

We can use the Quadratic Formula to find the roots of this function.

Quadratic Formula: \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\) when \(ax^2+bx+c=0\)

Equation: x² - 5x + 4 = 0

⇒ a = 1, b = -5, c = 4

Step 1: Substitute the values of a, b, and c into the formula. 

\(\\\implies x=\dfrac{\bold{-(-5)}\pm\sqrt{\bold{(-5)^2}\bold{-4(1)(4)}}}{\bold{2(1)}}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{25-16}}}{2}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{9}}}{2}\\\\\implies x=\dfrac{5\pm3}{2}\)

Step 2: Separate into two possible cases.

\(x_1=\dfrac{5-3}{2}\implies \dfrac{2}{2}\implies \boxed{1}\\\\x_2=\dfrac{5+3}{2}\implies \dfrac{8}{2}\implies \boxed{4}\)

The x-intercepts of the given function are 1 and 4.

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Answer:

Susie reaches the store first being ahead by 0.06 hours.

Step-by-step explanation:

20 miles going 45 miles/hour.

20 miles / (45 miles / hour) = 20 miles hours / 45 miles =

= 20 hours / 45 = 4/9 hours = 0.44 hours

25 miles going 50 miles/hour.

25 miles / (50 miles / hour) = 25 miles hours / 50 miles =

= 25 hours / 50 = 1/2 hours = 0.5 hours

So Susie needs less time (= arrives first).

the difference is 0.5 - 0.44 = 0.50-0.44 = 0.06 hours

as additional practice :

0.06 hours is 60 × 0.06 minutes.

60 × 0.06 = 60 × 6 / 100 = 360 / 100 = 3.6 minutes.