Ann had twice as many candies as Susan. Then Ann ate 3 of her candies. This can be modeled using the following equation. A=2S-3. Solve the equation for the number of candies Susan has,S. S=a+__ ———— ———

Answer:

  -1/2

Step-by-step explanation:

You want the limit as x→0 of the ratio (6x -sin(6x))/(6x -tan(6x)).

The given expression evaluates at x=0 to (0 -0)/(0 -0) = 0/0, an indeterminate form. Hence, L'Hôpital's rule applies.

The ratio of derivatives of the numerator and denominator is ...

  (6 -6cos(6x))/(6 -6sec²(6x))

which still evaluates to 0/0 at x=0.

Applying L'Hôpital's rule a second time gives ...

  \(\dfrac{36\sin(6x)}{-72\sec^2(6x)\tan(6x)}=\dfrac{-\cos^3(6x)}{2}\)

At x=0, this evaluates to -1/2.

The limit as x→0 is -1/2.

__

Additional comment

We like to check these limits using a graphing calculator. The graph is in the second attachment.

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Answer:

15

Step-by-step explanation:

Answer:

꧁. ꧂

Step-by-step explanation:

꧁. ꧂꧁. ꧂

Answer:

3,6,9,12,15,18

Step-by-step explanation:

how i came up with this ordered pair is taking the multiples of three

this relation is a function because it is asking to list six ordered pairs showing the output of the thickness of the paper that he folds and the way that i came up with the ordered pairs in Part A is because you have to take the multiples of three or you could just take 6 and multiple it by 3 and you would get the same answer

The length of the path described by the parametric equations

 is 3/2units.

We can find the length of the path described by the parametric equations x=cos³t and y=sin³t by using the arc length formula.

The arc length formula for a parametric curve given by:

x=f(t) and y=g(t) is given by:

L = ∫[a,b] √[f'(t)² + g'(t)²] dt

where f'(t) and g'(t) are the derivatives of f(t) and g(t), respectively.

In this case, we have:

x = cos³t, so x' = -3cos²t sin t

y = sin³t, so y' = 3sin²t cos t

Therefore,

f'(t)² + g'(t)² = (-3cos²t sin t)² + (3sin²t cos t)²

= 9(cos⁴t sin²t + sin⁴t cos²t)

= 9(cos²t sin²t)(cos²t + sin²t)

= 9(cos²t sin²t)

Thus, we have:

L = ∫[0,2π] √[f'(t)² + g'(t)²] dt

= ∫[0,2π] √[9(cos²t sin²t)] dt

= 3∫[0,2π] sin t cos t dt

Using the identity sin 2t = 2sin t cos t, we can rewrite the integral as:

L = 3/2 ∫[0,2π] sin 2t dt

Integrating, we get:

L = 3/2 [-1/2 cos 2t] from 0 to 2π

= 3/4 (cos 0 - cos 4π)

= 3/2

Therefore, the length of the path described by the parametric equations x=cos³t and y=sin³t is 3/2 units.

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Option D is the correct answer.

We need to identify the absolute value functions from the given options.

The graph looks like a "V", with its vertex at (0, 0). Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex. We can translate, stretch, shrink, and reflect the graph.

The general form of an absolute value equation is f(x)=a|x-h|+k.

The variable a tells us how far the graph stretches vertically, and whether the graph opens up or down. The variables h and k tell us how far the graph shifts horizontally and vertically.

Therefore, option D is the correct answer.

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Answer:No more than 10 Days

Step-by-step explanation:$500.00 - $120=$380/$38=10

The volume of the tetrahedron is 1/18 cubic units.

To find the volume of the given solid, we can use a triple integral over the region of the volume of the tetrahedron is 1/18 cubic units.that corresponds to the solid.

The tetrahedron is enclosed by the coordinate planes (x=0, y=0, z=0) and the plane 3x + y + z = 2.

To set up the triple integral, we need to find the bounds of integration for x, y, and z.

From the equation of the plane, we can solve for z in terms of x and y:

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

Since z=0 is one of the coordinate planes bounding the tetrahedron, we can set (2 - 3x - y)/3 = 0 and solve for y in terms of x:

y = 2 - 3x

Similarly, since y=0 is another bounding plane, we can set (2 - 3x - y)/3 = 0 and solve for x in terms of y:

x = (2 - y)/3

Finally, since x=0 is the third bounding plane, we don't need to solve for anything.

Therefore, the bounds of integration are:

0 ≤ x ≤ 2/3

0 ≤ y ≤ 2 - 3x

0 ≤ z ≤ (2 - 3x - y)/3

The volume of the tetrahedron is then given by the triple integral:

V = ∭\(_ R dV = \int _0 ^{2/3} \int _ 0 ^ 2-3x \int _0 ^{(2-3x-y)/3} dz dy dx\)

Evaluating this integral yields:

V = 1/18

Therefore, the volume of the tetrahedron is 1/18 cubic units.

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Answer:

Triangles a, b, and d

Step-by-step explanation:

The three triangles have a side length measurement, an angle measure, then another side length measurement

in that order (the order matters)

Triangle a,b and d are the answers.

"SAS" is when you know the two sides and the angle between them. Use the cosine theorem to calculate the unknown edge, then use the sine and cosine theorem to find the smaller of the other two angles, and then use the three angles that are 180 ° to find the last angle. .. The side of the

angle refers to the two rays or line segments that form the angle. In the figure below, the rays BA and BC are the sides of the angle ABC. An angle is formed by rotating a ray around its endpoint.

Edge-side assumptions-> If the two sides and edges of a triangle are congruent with the two sides and the edges of another triangle, the two triangles are congruent by the side-angle assumptions.

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Answer:

a ratio compares two numbers by division

Step-by-step explanation:

i just know

Answer:

Ratio

Step-by-step explanation:

Ratio – A comparison of two quantities by division.

We have proven that \(a^k\) = [1 1 1 ... 1 0] for any positive integer k.

The art of demonstrating a claim, theorem, or formula that is regarded as true for each and every natural number n is known as proof. There are numerous generalized assertions in mathematics that take the form of n.

To prove a statement using mathematical induction, we need to show that it holds for a base case and then demonstrate that if it holds for a specific value, it also holds for the next value. Let's proceed with the proof:

Base Case:

For n = 1, we have:

\(a^1\) = [1]

Since the only element in \(a^1\) is 1, which is equal to fo, the statement holds for the base case.

Inductive Step:

Assume that the statement holds for some positive integer k, i.e., assume that \(a^k\) = [1 1 1 ... 1 0] with k elements, where the last element is 0.

We want to prove that the statement also holds for k + 1, i.e., we need to show that \(a^{(k+1)\) = [1 1 1 ... 1 0] with (k+1) elements, where the last element is 0.

Using the assumption, we have:

\(a^{(k+1)\) = \(a^k\) * a

Multiplying \(a^k\) by a, we get:

\(a^{(k+1)\) = [1 1 1 ... 1 0] * [1 1 1 0]

To obtain the product, we perform element-wise multiplication:

\(a^{(k+1)\) = [1*1 1*1 1*1 ... 1*1 0*0]

        = [1 1 1 ... 1 0]

Since the last element of \(a^k\) is 0, multiplying it by any value will still result in 0. Therefore, the last element of \(a^{(k+1)\) is 0.

Thus, the statement holds for k + 1.

By the principle of mathematical induction, the statement is proven to hold for all positive integers.

Therefore, we have proven that \(a^k\) = [1 1 1 ... 1 0] for any positive integer k.

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Answer:

Step-by-step explanation:

2. Perpendicular lines form right angles.

3. A right angle has a measure of 90 degrees.

4. Angle addition postulate

5. Angles that add to form a right angle have a measure of 90 degrees.

7. Congruent angles have equal measure.

8. Substitution

9. Angles with measures that add to 90 deg are complementary.

Answer:

He make a mistake in step 2

Given:

The equation is

\(7(x+1)+11x=-2x-5\)

To find:

The reason for each statement.

Solution:

We have,

\(7(x+1)+11x=-2x-5\)

Using distributive property, we get

\(7x+7+11x=-2x-5\)

On combine like terms, we get

\(18x+7=-2x-5\)

Using addition property of equality, add 2x on both sides.

\(20x+7=-5\)

Using subtraction property of equality, subtract 7 from both sides.

\(20x=-12\)

Using division property of equality, divide both sides by 20.

\(x=-\dfrac{12}{20}\)

\(x=-\dfrac{3}{5}\)

Therefore, the required reasons are:

2. Distributive property

3. Combining like terms

4. Addition property of equality

5. Subtraction property of equality

Answer:

4*0.40+5*0.75=5.35

Step-by-step explanation:

Answer:

like so i could get points pls, answer is in screenhot lol

Step-by-step explanation:

Answer:

1. 495

2. 367

3. 1835

4. 1887

5. 2627

6. 1890

7. 1929

Step-by-step explanation:

1.

Smallest number in the N column: 33

Largest number in the B column: 15

33 * 15 = 495

2.

Sum of numbers in the I column:

27 + 23 + 19 + 30 + 29 = 128

495 - 128 = 367

3.

Highest number in the O column: 72

Lowest number in the O column: 67

72 - 67 = 5

367 * 5 = 1835

4.

Average of the numbers in the G column:

(50 + 51 + 54 + 52 + 53)/5 = 52

1835 + 52 = 1887

5.

Reversed digits in answer: 1887 -> 7881

First number in B column: 11

Second number in B column: 8

11 - 8 = 3

7881/3 = 2627

6.

Sums of the numbers in I, G, and O columns:

27 + 23 + 19 + 30 + 29 + 50 + 51 + 54 + 52 + 53 + 72 + 70 + 67 + 71 + 69

= 737

2627 - 737 = 1890

7.

First number in column G: 50

First number in column B: 11

1890 + 50 = 1940

1940 - 11 = 1929

Answer:

85

Step-by-step explanation:

Answer

\(C=2.5\pi\)

Step-by-step explanation:

Radius is always half of the diameter so, \(\frac{2.5}{2} \\\) is equal to \(1.25\).

The Formula for Circumference is \(C=2\pi r\)

Since we found out the radius, we need to basically substitute (or insert) it into the radius spot so the next step will be: \(C=2\pi (1.25)\)

Then we multiply (2)(1.25) to get an answer of 2.5 (which we already know)

So our answer is going to be \(C=2.5\pi\)

Hope this helped and answers your question! Have a great rest of your day/night!

Step-by-step explanation:

must be _1/27 in my opinion it's that

Answer:

The correct option is (D) \(y=\frac{4}{7}\ x+\frac{1}{7}\).

Step-by-step explanation:

The two-point form for the equation of straight line is:

\((y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})\)

The two points provided are:

A = (5, 3)

B = (12, 7)

Compute the equation of the trend line as follows:

\((y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})\\\\(y-3)=\frac{7-3}{12-5}\ (x-5)\\\\(y-3)=\frac{4}{7}\ (x-5)\\\\y-3=\frac{4}{7}\ x-\frac{20}{7} \\\\y=\frac{4}{7}\ x-\frac{20}{7}+3\\\\y=\frac{4}{7}\ x+\frac{-20+21}{7}\\\\y=\frac{4}{7}\ x+\frac{1}{7}\)

Thus, the equation of the trend line is \(y=\frac{4}{7}\ x+\frac{1}{7}\).

The correct option is (D).

Answer:

D

Step-by-step explanation:

Answer:

hgktjeghuegkekhghkegkhetgkhekhjhkjeg

Step-by-step explanation:

If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides. If DE = BC, then ADDB=AEEC.

If a line parallel to one side of a triangle contacts the other two sides, the two sides are proportionately divided.

The formula for a proportional equation is y = kx. The letters y and x denote the variables in the equation. The letter k represents the proportionality constant, which is fixed.

Because matching angles produce the AA similarity shortcut, when a line is drawn parallel to one side of a triangle, two similar triangles are generated. Because the triangles are comparable, the parallel line segments are proportionate segments.

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Answer:

ok the answer is 10

Step-by-step explanation:

Just put 10 lol

The probability of selecting a human character randomly in the game is \(\frac{1}{3}\)

The probability that a human character will be chosen when the player selects a character randomly can be calculated by dividing the number of human characters by the total number of available characters.

There are 8 animal characters and 4 human characters, making a total of 12 characters to choose from. Therefore, the probability of selecting a human character randomly is:

P(Human) = Number of human characters / Total number of characters

P(Human) = 4 / 12

Simplifying this fraction, we find:

P(Human) = 1 / 3

Therefore, the probability of selecting a human character randomly is 1/3 or approximately 0.333.

In the given scenario, there are a total of 8 animal characters and 4 human characters, making a total of 12 characters to choose from. When a player selects a character randomly, each character has an equal chance of being chosen. Since there are 4 human characters, the probability of selecting one of them is determined by dividing the number of human characters (4) by the total number of characters (12).

When we simplify the fraction 4/12, we find that it is equal to 1/3.

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Answer:

Number of absent student in decimal = 0.005

Step-by-step explanation:

Given:

Number of student = 1,000

Number of absent student = 5 / 1,000

Find:

Write number of absent student in decimal

Computation:

Number of absent student = 5 / 1,000

Number of absent student in decimal = 5 / 1,000

Number of absent student in decimal = 0.005

Step-by-step explanation:

If triangle ABC is a right angle, it will allign with Pythagoras theorem where a² = b² +c²

A will be the longest side (hypotenuse)

10² = 6² + 8²

100 = 36 + 64

100 = 100

A is square root of 100 on both sides

It is a right angle triangle

The person has walked a total of 28 miles. To calculate total distance walked by the person, we add up the distances in each direction

5 miles East + 6 miles Southeast + 6 miles South + 7 miles Southwest + 4 miles East

When we add these distances together, we get:

5 + 6 + 6 + 7 + 4 = 28

Therefore, the person has walked a total of 28 miles.

In more detail, let's break down the distances walked in each direction:

- 5 miles East: This means the person walked 5 miles in the East direction.

- 6 miles Southeast: This means the person walked 6 miles in the direction that is both South and East.

- 6 miles South: This means the person walked 6 miles in the South direction.

- 7 miles Southwest: This means the person walked 7 miles in the direction that is both South and West.

- 4 miles East: This means the person walked 4 miles in the East direction.

By adding up these distances, we find that the person has walked a total of 28 miles.

#A person starts walking from home and walks: 5 miles East 6 miles Southeast 6 miles South 7 miles Southwest 4 miles East This person has walked a total of ---miles

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The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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Answer: 1236

its the answer from deltamath

The area of the triangle is 31.54 square units

From the question, we have the following parameters that can be used in our computation:

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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