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Answer:

\(x^2 = 2y\) --- equation

\((x,y) = (0,\frac{1}{2})\) --- focus

\(y = -\frac{1}{2}\) --- directrix

\(Width = 2\) ---- focal width

Step-by-step explanation:

Given

\(depth = 2\)

\(diameter = 4\)

Required

The equation of parabola

The depth represents the y-axis. So:

\(y = 2\)

The diameter represents how the parabola is evenly distributed across the x-axis.

We have:

\(diameter = 4\)

-2 to 2 is 4 units.

So:

\(x = [-2,2]\)

So, the coordinates of the parabola is:

\((-2,2)\ and\ (2,2)\)

The equation of the parabola is calculated using:

\(x^2 = 4py\)

Substitute (-2,2) for (x,y)

\((-2)^2 = 4p*2\)

\(4 = 8p\)

Divide by 8

\(p = \frac{4}{8}\)

\(p = \frac{1}{2}\)

So, the equation is:

\(x^2 = 4py\)

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

\(x^2 = 2y\)

The defining features

(a) Focus

The focus is located at:

\((x,y) = (0,p)\)

\((x,y) = (0,\frac{1}{2})\)

(b) Directrix (y)

\(y = -p\)

\(y = -\frac{1}{2}\)

(c) Focal width

\(Width = 4p\)

\(Width = 4*\frac{1}{2}\)

\(Width = 2\)

Answer: h(k(x))=-3x+31

Step-by-step explanation:

To find h(k(x)), you want to plug k(x) into h(x).

h(k(x))=3(9-x)+4          [distribute]

h(k(x))=27-3x+4          [combine like terms]

h(k(x))=-3x+31

Now, we know that h(k(x))=-3x+31.

Answer:

h(k(x)) = -3x + 31

Step-by-step explanation:

To find h(kx)), plug in k(x) in as x in the function h(x)

h(x) = 3x + 4

Plug in k(x) as x:

h(k(x)) = 3(9 - x) + 4

h(k(x)) = 27 - 3x + 4

h(k(x)) = -3x + 31

The two numbers that multiply to 81 and add to 18 are 9 and 9. This is determined either by factoring the number 81 or by solving the algebraic equations derived from the given conditions.

To find two numbers that multiply to 81 and add to 18, we can use factoring or algebraic methods. Let's explore both approaches:

Factoring:

Start by factoring 81 into its prime factors: 3 * 3 * 3 * 3.

Since the two numbers must multiply to 81, we can consider pairs of factors and check if their sum is 18:

Pair 1: 1 * 81 = 81 (sum = 1 + 81 = 82)

Pair 2: 3 * 27 = 81 (sum = 3 + 27 = 30)

Pair 3: 9 * 9 = 81 (sum = 9 + 9 = 18)

Therefore, the pair of numbers that multiply to 81 and add to 18 is 9 and 9.

Algebraic method:

Let's assume the two numbers are x and y.

According to the given conditions, we can write the following equations:

xy = 81 ...(1)

x + y = 18 ...(2)

To solve this system of equations, we can rearrange equation (2) to express one variable in terms of the other:

y = 18 - x ...(3)

Substitute equation (3) into equation (1):

x(18 - x) = 81

Simplifying the equation:

18x - x^2 = 81

Rearrange the equation and set it equal to zero:

x^2 - 18x + 81 = 0

Now, we can factor this quadratic equation:

(x - 9)(x - 9) = 0

The equation yields a repeated factor (x - 9) since both values are the same.

Thus, the solution is x = 9.

Substituting x = 9 into equation (3):

y = 18 - 9

y = 9

Therefore, the pair of numbers that multiply to 81 and add to 18 is 9 and 9.

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15.3/0.012=??????????????

Answer: 1275

Answer:

8 faces

Step-by-step explanation:

In geometry, the hexagonal prism is a prism with a hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices.

Hope this helps!

Answer: did you make that up ??

Step-by-step explanation:

Answer:

A. Alternate interior

B. Transitive property

C. Converse alternate interior angles theorem.

Correlation does not imply causation. It only says the two factors are related somehow - not that change in one affects the others directly. For example, the sales of ice-cream and sales of air conditioners may both go up during the summer season. Hence, they are correlated but one is not the cause of the other.

The value of c is 17.50 and the value of d is 2.40

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

Given

Equation for 4 days

C + 4d=27.10

Equation for 7 days

C + 7d=34.30

Solving simultaneously equation

C + 4d=27.10

- C + 7d=34.30

by simplifying,

0- 3d = - 7.20

d= -7.30/-3

=2.40

Replace the d 2.40 in either side

C+4d = 27.10

C=27.10 - 4d

=27.10 - 4(2.40)

=17.50

Therefore the value of c is 17.50 and the value of d is 2.40

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Answer:

74-69x

Step-by-step explanation:

8(10-6x)+3(-7x-2)

80-48x-21x-6

80-6-48x-21x

74-48x-21x

74-69x

The missing angles are sides are;

We can see that we would have to first apply the cosine rule here;

\(a^2 = b^2 + c^2 - 2abCos A\\a^2 = (17)^2 + (19.6)^2 - 2(17 * 19.6)Cos 30\\a^2 = 673.16 - 666.4Cos 30\)

a = 9.8

We can now apply the sine rule to obtain the angle B

\(a/Sin A = b/Sin B\\SinB = bSin A/a\\B = Sin-1 ( bSin A/a)\\B = Sin-1(17 * Sin 30/9.8)\)

B = 60

Then;

C = 180 - (30 + 60)

C = 90 degrees

Thus the triangle in the problem have been solved.

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The minimum amount of plastic wrap needed to completely wrap 6 containers is option C: 286.4 square inches.

Area of a circle is the area that is occupied by the given circle in a kind of two-dimensional plane. The total surface area of a cylindrical container  is solved by the equation:

A = πr²

where r is the radius of the end. The diameter of each container is given as 3.5 inches, so the radius is half of that, or 1.75 inches. Using π = 3.14, we get:

A = 3.14 x (1.75in)²

=3.14 x 3.06

= 9.61 in² (rounded to two decimal places)

The area of the rectangular side is:

A = h x  circumference

where:  h  = height of the container and circumference is the distance around the circular end. The circumference is equal to the diameter times π, so we have:

circumference = 3.5in x  π

= 3.5 x 3.14

= 10.99in

Using the given height of 4 inches, we get:

A = 4in x  10.99in

A = 43.96 (rounded to two decimal places)

Therefore, the total surface area of each container is:

A = 2 x   9.61 in²  + 43.96in²

A = 63.2in²

To wrap 6 containers, we need to multiply the surface area of each container by 6:

total surface area = 6 x 63.2in²

                      =379.2

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see correct text below

A deli wraps its cylindrical containers of hot food items with plastic wrap. The containers have a diameter of 3.5 inches and a height of 4 inches. What is the minimum amount of plastic wrap needed to completely wrap 6 containers? Round your answer to the nearest tenth and approximate using π = 3.14.

A. 44.0 in2

B. 63.2 in2

C. 379.2 in2

D. 505.5 in2

The indefinite integral is (1/2) ln |1 + x²| + C.

We have,

We can use the substitution method to evaluate the integral.

Let u = 1 + x^2, then du/dx = 2x or dx = du/(2x).

Substituting u and dx in the integral.

∫(1 / (1 + x²)) dx = (1/2) ∫(1 / (u)) du

= (1/2) ln|u| + C

Substituting back u in terms of x.

∫(1 / (1 + x²))dx = (1/2) ln |1 + x²| + C

where C is the constant of integration.

Thus,

The indefinite integral is (1/2) ln |1 + x²| + C.

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The value of x = 16, y = 172 and z = 2.

x - 4z = 12x - y - 6z = 42x + 3y - 2z = 8

let x - 4z = 8 be equation (1), 12x - y - 6z = 8 be equation (2) and 42x + 3y - 2z = 8 be equation (3)

x - 4z = 8

x = 8 + 4z

12x - y - 6z = 8

12(8 + 4z) -y - 6z =8

96 + 48z - y - 6z = 8

42z - y = -88

y = 42z + 88

42x + 3y - 2z = 8

42(8+4z) + 3(42z + 88) - 2z = 8

336 + 168z + 126z + 264 - 2z = 8

168z + 126z + 2z = 336+264 - 8

296z= 592

z = 2

substituting the value of z

x = 8 + 4z

= 8 + 4(2)

8+8 = 16

y = 42z + 88

42(2) + 88

84 + 88= 172

The value of x = 16, y = 172 and z = 2.

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Given that $OF = 9$ and $OF' = 12,$ where $F$ and $F'$ are the foci of the ellipse, we can determine the lengths of the major and minor axes.

In an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant. This property is expressed by the equation:

$$PF + PF' = 2a,$$

where $P$ is any point on the ellipse and $a$ is the semi-major axis. In our case, $P = O,$ and since $OF = 9$ and $OF' = 12,$ we have:

$$9 + 12 = 2a,$$

$$21 = 2a.$$

Therefore, the semi-major axis $a$ is equal to $\frac{21}{2} = 10.5.$

The distance between the center of the ellipse and each focus is given by $c,$ where $c$ is related to $a$ and the semi-minor axis $b$ by the equation:

$$c = \sqrt{a^2 - b^2}.$$

We can solve for $b$ using the distance to one focus:

$$c = \sqrt{a^2 - b^2},$$

$$c^2 = a^2 - b^2,$$

$$b^2 = a^2 - c^2,$$

$$b = \sqrt{a^2 - c^2}.$$

Substituting the known values:

$$b = \sqrt{10.5^2 - 9^2},$$

$$b = \sqrt{110.25 - 81},$$

$$b = \sqrt{29.25},$$

$$b \approx 5.408.$$

Therefore, the semi-minor axis $b$ is approximately $5.408.$

Finally, we can determine the lengths of the major and minor axes:

The major axis $\overline{AB}$ is twice the semi-major axis, so $\overline{AB} = 2a = 2(10.5) = 21.$

The minor axis $\overline{CD}$ is twice the semi-minor axis, so $\overline{CD} = 2b = 2(5.408) \approx 10.816.$

Therefore, the major axis $\overline{AB}$ is $21$ units long, and the minor axis $\overline{CD}$ is approximately $10.816$ units long.

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Answer:

81

Step-by-step explanation: 9 * 9 = -81 * -1 = 81

Answer:

Step-by-step explanation:

P(A)=1−P(not A)

We can use this here. Event A is that the clock is defective, so Event (not A) means the clock works.

0.02=1−P(not A)

P(not A)=0.98

Therefore, for all the clocks to pass, the probability is P(not A)11.

Now again, we can use complementary counting.

(probability of all clocks failing) = 1 - (probability of all clocks passing)

Probability of all clocks failing = 1−P(not A)11

The value of p is 18, it can be find out by using concepts of line and slope of a line.

What is the slope of a line?

Slope of line measures its steepness. Mathematically, its calculated as "rise over run".

Slope of a line : (y2 - y1)/(x2-x1)

In the given que,

given graph equation is of line ,

to find slope of graph : we need to differentiate the equation

\(\frac{d}{dx}\)(3y + 2x = 7) = 3\(\frac{dy}{dx}\) + 2 = 0

So, \(\frac{dy}{dx}\) = -2/3

We, if any line are perpendicular then

slope of one * slope of two = -1

So, slope of 1 = (-9-6)/(8-p)

                       = -15/(8-p)

     slope of 2 = -2/3

     Now product of both = -15/(8-p) * (-2/3 )

By simplifying all these equation,

we get p = 18.

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The weighted average cost of capital (WACC) for company C is 6.63%.

The weighted average cost of capital (WACC) is a financial metric that represents the average rate of return a company must earn on its investments to satisfy its shareholders and creditors. It takes into account the proportion of debt and equity in a company's capital structure and the respective costs associated with each.

To calculate WACC, we need to consider the cost of debt and the cost of equity. The cost of debt is the interest rate a company pays on its debt, adjusted for taxes. In this case, the pre-tax cost of debt is 2% and the tax rate is 24%. Therefore, the after-tax cost of debt is calculated as (1 - Tax Rate) multiplied by the pre-tax cost of debt, resulting in 1.52%.

The cost of equity represents the return required by equity investors to compensate for the risk associated with owning the company's stock. Here, the cost of equity for company C is 6%.

The debt represents 10% of the total capital, while the equity represents the remaining 90%. To calculate the weighted average cost of capital (WACC), we multiply the cost of debt by the proportion of debt in the capital structure and add it to the cost of equity multiplied by the proportion of equity.

WACC = (Proportion of Debt * Cost of Debt) + (Proportion of Equity * Cost of Equity)

In this case, the calculation is as follows:

WACC = (0.10 * 1.52%) + (0.90 * 6%) = 0.152% + 5.4% = 6.552%

Therefore, the weighted average cost of capital (WACC) for company C is approximately 6.63%.

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Answer:

196 tickets

Step-by-step explanation:

The total expenses to put on a 3-day production of a play is $980. Each ticket to go and watch the play is going to be sold for $5. The producer sells x number of tickets, x number of tickets would cost 5x. Therefore to find the number of tickets the producer must sell so as to make a profit the money generated from selling the tickets must be more than the cost of production. Therefore we use the formula:

5x ≥ 980

Dividing through by 5:

x ≥ 980

x ≥ 980/5

x ≥ 196

Therefore the producer must sell at least 196 tickets so as to make a profit

Answer:

g = 6

Step-by-step explanation:

Note that where the above is given, the reasons can be used to fill in the numbered blank spaces is "corresponding angles theorem (Option B)

Segment KL and segment JK is parallel to segment ML.

To prove: Opposite angles of parallelogram are equal.

Construction  - Extend segment JM beyond point M and draw point P, Extend segment JK beyond point J and draw point Q.

Proof  -

It is given that A parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML.

Extend segment JM beyond point M and draw point P--------By construction

and Extend segment JK beyond point J and draw point Q----By construction

thus, ∠MLK≅∠PML and ∠JML≅∠QJM (Alternate interior angles theorem) (1)

Then, ∠PML≅∠KJM and ∠QJM≅∠LKJ (corresponding angles theorem)  (2)

Using equation (1) and (2) and using the transitive property of equality, we have

∠MLK≅∠KJM and ∠JML≅∠LKJ

therefore, opposite angles of the given parallelogram JKLM are congruent.

QED

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The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:

Parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML. Extend segment JM beyond point M and draw point P, by Construction. An arrow is drawn from this statement to angle MLK is congruent to angle PML, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle PML is congruent to angle KJM, numbered blank 1. An arrow is drawn from this statement to angle MLK is congruent to angle KJM, Transitive Property of Equality. Extend segment JK beyond point J and draw point Q. An arrow is drawn from this statement to angle JML is congruent to angle QJM, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle QJM is congruent to angle LKJ, numbered blank 2. An arrow is drawn from this statement to angle JML is congruent to angle LKJ, Transitive Property of Equality. Two arrows are drawn from this previous statement and the statement angle MLK is congruent to angle KJM, Transitive Property of Equality to opposite angles of parallelogram JKLM are congruent.

Which reasons can be used to fill in the numbered blank spaces?

1Alternate Interior Angles Theorem

2Alternate Interior Angles Theorem

1Corresponding Angles Theorem

2Corresponding Angles Theorem

1Same-Side Interior Angles Theorem

2Alternate Interior Angles Theorem

1Same-Side Interior Angles Theorem

2Corresponding Angles Theorem

The probability that the date sara chose is a prime number is 0.2.

Given that, sara chose a date from the calendar.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favourable outcomes = 6

Now, probability = 6/30

= 1/5

= 0.2

Therefore, the probability that the date sara chose is a prime number is 0.2.

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The volume of the cylinder with radius 7cm and height 19 cm will be equal to 2923/34 cm³.

Cylinder is a 3 dimensional figure which can be formed by rolling a piece of paper. It consists of a diameter and a height. Cylinder can be open from both sides, top and bottom or it can be closed from both the sides, top and bottom. The volume of the cylinder can be calculated by using the formula expressed below

Volume of cylinder = π×r²×h

where r is the radius, h is height and value of π = 3.14

Volume of cylinder = 3.14×(7cm)²×19cm

Volume of cylinder = 2923/34 cm³

So, the required volume is 2923/34 cm³.

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part a.

Carter needs 116 yards of fencing to enclose the flat area of his backyard.

part b.

Carter needs 720 square yards of sod to cover the flat area of his backyard.

estimating the coordinates of the vertices of the figure and using  the distance formula to calculate the length of each side:

AB: √((16-(-16))^2 + (4-4)^2) = 32 yards n

BC: √((16-4)^2 + (4-12)^2) = 14 yards

CD: √((4-8)^2 + (12-16)^2) = 5 yards

DE: √((8-(-12))^2 + (16-(-8))^2) = 37 yards

EA: √((16-(-16))^2 + (4-(-8))^2) = 28 yards

The total perimeter is: 32 + 14 + 5 + 37 + 28 = 116 yards

b.

Rectangle ABED: 32 yards × 16 yards = 512 square yards

Triangle BCD: (1/2) × 4 yards × 8 yards = 16 square yards

Triangle DEA: (1/2) × 24 yards × 12 yards = 144 square yards

Triangle EFA: (1/2) × 8 yards × 12 yards = 48 square yards

The total area is: 512 + 16 + 144 + 48 = 720 square yards

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Answer:

325 hours

Step-by-step explanation:

Answer: Option D is correct.

y = -4x + 4

Answer:

y = -4x + 4

Step-by-step explanation:

D. is your answer ^^