There are 16 cups in a gallon. The equation c=16g gives the number of cups in terms of the number of gallons. Write another equation for this situation, giving the number of gallons in terms of the number of cups:

g=

The asymptotes of the hyperbola with equation\((x - 2)^2/81 (y + 2)^2/4 = 1\)are \(y = +(x - 2) + 2.\)

The given hyperbola has a horizontal transverse axis and its center is at (2, -2). The standard form of a hyperbola with a horizontal transverse axis is\((x - h)^2/a^2 - (y - k)^2/b^2 = 1\) , where (h, k) is the center of the hyperbola, a is the distance from the center to each vertex along the transverse axis, and b is the distance from the center to each vertex along the conjugate axis.

Comparing the given equation to the standard form, we can see that

\(a^2\)= 81, so a = 9, and \(b^2\) = 4, so b = 2. Therefore, the distance between the center and each vertex along the transverse axis is 9, and the distance between the center and each vertex along the conjugate axis is 2.

The asymptotes of a hyperbola with a horizontal transverse axis have equations y = +/- (b/a)(x - h) + k. Substituting the values of a, b, h, and k, we get:

y = +(2/9)(x - 2) - 2 and y = -(2/9)(x - 2) - 2

Therefore, the equations of the asymptotes for the given hyperbola are

y = +(x - 2)/9 - 2 and y = -(x - 2)/9 - 2.

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⇒ x² - 6x = -8

\(\sf add \ 9 \ on \ both \ sides\)

⇒ x² - 6x + 9 = -8 + 9

\(\sf simplify \ and \ complete \ square\)

⇒ x² - 3x - 3x + 9 = 1

\(\sf factor \ common \ term\)

⇒ x(x - 3) - 3(x - 3) = 1

\(\sf collect \ into \ groups\)

⇒ (x - 3)² = 1

\(\sf square \ root \ both \ sides\)

⇒ x - 3 = ±√1

\(\sf simplify\)

⇒ x - 3 = ±1

\(\sf change \ side\)

⇒ x = 1 + 3, -1 + 3

\(\sf simplify\)

⇒ x = 4, 2

\(\rightarrow \sf 4x^2 + 12x + 11 = 0\)

\(\rightarrow \sf 4\left(x^2+3x+\dfrac{11}{4}\right) = 0\)

\(\rightarrow \sf 4\left(x^2+3x+\dfrac{11}{4}+\left(\dfrac{3}{2}\right)^2-\left(\dfrac{3}{2}\right)^2\right) = 0\)

\(\rightarrow \sf 4\left(x+\dfrac{3}{2}\right)^2+2 = 0\)

\(\rightarrow \sf \left(x+\dfrac{3}{2}\right)^2 = -\dfrac{2}{4}\)

\(\rightarrow \sf \left(x+\dfrac{3}{2}\right)^2 = -\dfrac{1}{2}\)

\(\rightarrow \sf x+\dfrac{3}{2} = \pm \sqrt{-\dfrac{1}{2} }\)

\(\rightarrow \sf x+\dfrac{3}{2} = \pm i\sqrt{\dfrac{1}{2} }\)

\(\rightarrow \sf x= \pm i\sqrt{\dfrac{1}{2} }-\dfrac{3}{2}\)

Work Shown:

L = 54 = length

W = 36 = width

P = 2(L+W) ... perimeter of the rectangle

P = 2(54+36)

P = 2(90)

P = 180

She needs 180 inches of ribbon.

To convert to feet, divide by 12. So 180 inches = 180/12 = 15 feet.

Answer:

1. B

2. A

3. A

4. C

Step-by-step explanation:

ask specific questions for explanations of the answers

Answer:

x=5/3

Step-by-step explanation:

10-7=3x+2x

3=5x

x=5/3

Answer:

3/5

Step-by-step explanation:

rerange terms

10−2x=3x+7

−2+10=3+7

subtrace 10 on each side

−2+10−10=3+7−10

then simplify

Answer:

yes; the next number is 3(n+1)

Step-by-step explanation:

Answer:

Yes, 3(n+1)

Step-by-step explanation:

Please listen to your teachers lessons lol.

Answer:

65

Step-by-step explanation:

180-100 (40+60) =80

80+35= 115

180-115=65

The price of a 12-month short call option is £1.30.

The calculation of the price of a 12-month short call option using a two-step binomial tree procedure. The given information includes the spot price (So) of £15, the strike price (K) of £16, the annual risk-free rate (r) of 5%, and the volatility (o) of 30%.

To calculate the price of the option, we use a binomial tree approach, which involves constructing a tree with two possible price movements at each step, an upward movement and a downward movement. By calculating the expected value at each node of the tree and discounting it back to the current time, we can determine the option price.

In this case, we start by calculating the up and down factors. The up factor (u) is calculated as e^(o*√(T)), where T represents the time in years. The down factor (d) is calculated as 1/u. In this scenario, T is 1 year, so we have u = e^(0.30*√1) and d = 1/u.

Next, we calculate the risk-neutral probability of an upward movement (p) using the formula p = (e^(r*T) - d) / (u - d). Once we have the up and down factors and the risk-neutral probability, we can proceed with building the binomial tree.

Starting from the final nodes of the tree, we calculate the option payoffs at expiration. For a call option, the payoff is the maximum of (S - K, 0), where S represents the spot price. We then move backward through the tree, calculating the expected value at each node by discounting the future payoffs using the risk-free rate.

Finally, we reach the root of the tree, which represents the current option price. In this case, the price of the 12-month short call option is determined to be £1.30.

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Answer:

The semi-circles form an entire circle with a diameter of 74.

The radius is 37

The area of the rectangle is 95 x 74 = 7030

The area of the circle is 3.142 x 37*37 = 4298.66

The total area is 11328.66

Answer:

14

Step-by-step explanation:

5+x-y (x-y=9) so -----> 5+9=14

Answer:

5+9 = 14

Step-by-step explanation:

x-y = 9, so 5+x-y would be equal to 5+9

5+9 is 14

hope this helps!

Step-by-step explanation:

At the circle's center, the arc's radius and angle are 9 cm and 4/3 radians, respectively.

Any section of a circle's circumference is considered an arc. Remember that the circumference of a circle is its perimeter or distance.

Given the length of the arc is 12cm and the area of the arc is 108 cm Square.

Since the length of the arc = θ × r

Area of the arc (A) =  (θ/360°) × πr2

Substituting values in the formulas

12  = θ × r

108 = θ × r²

comparing both equations

r = 9 cm

θ = 4/3 radian

Therefore, the radius and the angle subtended at the center of the circle by the arc are 9 cm and 4/3 radian respectively.

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Answer: give me the context please

Step-by-step explanation:

The simplest radical form of √5/12 is 1/2√5/3

Radical form:

Radical means the opposite of an exponent that is represented with a symbol '√' also known as root.

Given,

Here we have the number √5/12.

Now, we have to convert this into simplest radical form.

To convert this into radical form, first we have to expand the given terms,

Then we get,

=> √5 x √1/12

We know that, 4 x 3 is 12, So, we have to replace 12 with the expression 4 x 3, then we get,

=> √5 x √1/4 x 3

We know that the value of √4 is 2,

Then the expression is rewritten as,

=> 1/2√5/3

Therefore, the simplest radical form is 1/2√5/3.

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Answer:

Step-by-step explanation:

As,

4 + (-7)

= 4 - 7

= -3

It is also shown on the number line.

Answer:y=28

Step-by-step explanation:

all triangles add up to 180 and this triangle is an isosceles triangle so 34 should be equal to x-5 meaning that two of the angles are 34 degrees and you just need to subtract 34(2) from 180 which is  180-68 to give you 112. Then since this is the value of 4 times y, just divide 112 by four to isolate the variable and you get 28.

Yes, this statement is true, if m and n are positive rational numbers

Answer:

C is the answer

they're dependent because they're the y-values. the y-values in this graph are dependent on the x-values. how many points you earn in total, is dependent on how many balloons are popped.

Step-by-step explanation:

I hope this helps :))

Answer:

A sector of a circle is simply a part of a circle that is enclosed by two radii and a part of the circle's circumference (arc). If the arc makes an angle θ at the center of the circle, then the area of the sector is equal to A=θ360πr2 A = θ 360 π r 2 .

Step-by-step explanation:

Hello!

45% of x = 7.2

45x/100 = 7.2

45x = 7.2 * 100

45x = 720

x = 720/45

x = 16

the number = 16

Step-by-step explanation:

Given points,

( -2 , 3) and (4,3)

we know,

slope = y_2 - y_1 / x_2 - x_1

so according to it we got,

→ (3 - 3)/4 - (-2)

→ 0/6

hope this answer helps you dear! take care.

Hello!

To find the slope when we have 2 points, we use the following formula:

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

m=\(\frac{3-3}{4-(-2)} \\\frac{0}{6} \\0\)

Here's something for you to remember:

Hope it helps!

~Just a determined gal

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\(MysteriousNature\)

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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Answer:

sssssssssssuuuuuuuuuurrrrrrreeeeeee

Step-by-step explanation:

Answer:

66. 67%

Step-by-step explanation:

2/3=100%*2/3= 66.67%

Answer: 8/10 + 1/1000

Step-by-step explanation: in decimal form we have 0.800 + 0.001

to convert this into a fraction you'd do 8/10 + 1/1000

(8 is in the tenths place therefore 8/10 and 1 is in the thousandths place therefore 1/1000)

A result is called "statistically significant" when the p-value is less than the significant level, typically 0.05.

This means that there is less than a 5% chance that the results are due to chance alone, and suggests that there is a real effect present in the data.

The Null Hypothesis is the assumption that there is no significant difference between the measured phenomenon and a certain value or set of values. A statistically significant result means that the observed data are inconsistent with the assumption of no difference, or no effect.

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Answer:

Step-by-step explanation:

This problem bothers on probability

Given that two dice are expected to give an outcome of sum greater than 8

But in the problem statement the first die is already settled since it is showing 6 already.

Now for the second die, the possible outcomes that will add up with the first die to produce a figure greater than 8 are (3,4,5,6)  

The probability of obtaining either of these numbers is 4/6= 2/3

Having the first die settled, this means that the probability of obtaining a sum of 8 is 2/3

The theorem that explains why ∠4 ≅ ∠8 is the Alternate Interior Angles Theorem. The same side interior angles pair are ∠3 and ∠5, and ∠4 and ∠8.

Alternate Interior Angles theorem states that if two parallel lines are intersected by a transversal, then the alternate interior angles formed are congruent.

The same-side interior angles are the angles that are on the same side of the transversal and inside the two parallel lines. In the given diagram, the same-side interior angle pairs are ∠3 and ∠5, and ∠4 and ∠8.

All the angle pairs formed by the intersection of the two parallel lines and the transversal are

Corresponding angles are ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8

Alternate interior angles are ∠3 and ∠5, ∠4 and ∠8

Alternate exterior angles are ∠1 and ∠7, ∠2 and ∠6

Vertical angles are ∠3 and ∠4, ∠5 and ∠6, ∠1 and ∠2, ∠7 and ∠8

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The closest option to this value is d) 10.75, but none of the options is an exact match.

To find the interquartile range (IQR) of the data, we need to first find the first quartile (Q1) and the third quartile (Q3).

To do this, we can arrange the data in order from smallest to largest:

98, 100, 104, 105, 106, 110, 112, 115, 116, 118, 120, 122, 126, 130, 136, 140

The median of the data is the average of the two middle values, which are 112 and 115. So, the median is (112 + 115) / 2 = 113.5.

To find Q1, we need to find the median of the data values below the median. These are:

98, 100, 104, 105, 106, 110, 112, 115

The median of these values is (106 + 110) / 2 = 108.

To find Q3, we need to find the median of the data values above the median. These are:

116, 118, 120, 122, 126, 130, 136, 140

The median of these values is (122 + 126) / 2 = 124.

Now we can calculate the interquartile range (IQR) as the difference between Q3 and Q1:

IQR = Q3 - Q1 = 124 - 108 = 16.

Therefore, the interquartile range of the data is 16, or in decimals 16.00.

The closest option to this value is d) 10.75, but none of the options is an exact match.

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