Aside from beautiful places, Tagaytay is also known for its
pasalubong items. Rowena's offers different tarts: (Buko, Ube, Pineapple, Yema
and Mango). A box of tart contains 9 pieces and you are allowed to have a
maximum of three different flavors per box, how many different combinations
are there?
a. There is only one flavor Solution:
How many fiavors are there?
b. There are two flavors Solution:
How many different flavors can you pair with Buko?
How many different flavors can you pair with Ube?
How many combinations of two flavors are there?
c. There are three flavors Solution:
How many different flavors can you pair with Ube?
How many different flavors can you pair with Pineapple and Ube?
How many different flavors can you pair with Ube and Mango?
How many combinations of three different flavors are there?​

From the given information provided, the percent of apartments in the building that are small is 85%.

If the ratio of small apartments to regular apartments is 17 to 3, this means that for every 17 small apartments, there are 3 regular apartments.

We can think of the total number of apartments in the building as a multiple of the ratio 17:3. Let's call this multiple "x". Then, the total number of small apartments would be 17x, and the total number of regular apartments would be 3x.

The percentage of apartments in the building that are small can be calculated as follows:

percentage of small apartments = (total number of small apartments / total number of apartments) x 100%

= (17x / (17x + 3x)) x 100%

= (17x / 20x) x 100%

= 85%

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#1

\(\sf \longmapsto3x-4y=11\)

\(\sf \longmapsto3x−4y+4y=11+4y\)

\(\sf \longmapsto3x=4y+11\)

\(\sf \longmapsto \frac{3x}{3} = \frac{4y + 11}{3} \)

\(\sf \longmapsto{x} = \frac{4}{3} y + \frac{11}{3} \)

#2

\(\sf \longmapsto3x+2y=2\)

\(\sf \longmapsto3x+2y+−2y=2+−2y\)

\(\sf \longmapsto3x=−2y+2\)

\(\sf \longmapsto \frac{3x}{3} = \frac{ - 2y + 2}{3} \)

\(\sf \longmapsto \: x = \frac{ - 2}{3} y + \frac{2}{3} \)

Answer:

Yes it would

Step-by-step explanation:

Lanie's room is in the shape of a parallelogram.

Lanie has a rectangular rug that is 6 feet wide and 10 feet long.

Area of a rectangle = Length × Width

Area of the rectangular rug = 10 feet × 6 feet

= 60 square feet

We are told that:

The floor of her room is shown below and has an area of 108 square feet.

Hence, the rug would fit on the floor of her room because it's area is within the area of the floor of her room.

Both Sugeno and Yager Complements satisfy the involution property, \(N(N(a)) = a\).

To show that the Sugeno and Yager Complements satisfy the involution requirement, let's consider each complement function separately.

1. Sugeno Complement:

The Sugeno Complement is defined as \(N(a) = 1 - a\).

Now, let's calculate \(N(N(a))\):

\[N(N(a)) = N(1 - a) = 1 - (1 - a) = a\]

Thus, we have \(N(N(a)) = a\), satisfying the involution requirement.

2. Yager Complement:

The Yager Complement is defined as \(N(a) = \sqrt{1 - a^2}\).

Now, let's calculate \(N(N(a))\):

\[N(N(a)) = N(\sqrt{1 - a^2}) = \sqrt{1 - (\sqrt{1 - a^2})^2} = \sqrt{1 - (1 - a^2)} = \sqrt{a^2} = a\]

Therefore, we have \(N(N(a)) = a\), satisfying the involution requirement.

Hence, both Sugeno and Yager Complements satisfy the involution property, \(N(N(a)) = a\).

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The Sugeno and Yager Complements in the field of fuzzy set theory satisfy the involution requirement N(N(a))=a. The Sugeno Complement is calculated using N(a)=1-a, and the Yager Complement is calculated using N(a)=1-a^n, where n denotes the complementation grade. Both simplify back to a when N(N(a)) is computed.

The Sugeno and Yager Complements are operations in the field of fuzzy set theory. They satisfy the involution requirement mathematically as follows:

For the Sugeno Complement, if N(a) denotes the Sugeno complement of a, it is calculated using N(a)=1-a. Therefore, N(N(a)) becomes N(1-a), which simplifies back to a, hence satisfying N(N(a))=a.

Similarly, for the Yager Complement, N(a) is calculated using N(a)=1-an, where n denotes the complementation grade. Hence, when we compute N(N(a)), it becomes N(1-an). Bearing in mind that n can take the value 1, this simplifies back to a, also satisfying the requirement N(N(a))=a.

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(a) The position vector of the baseball at the time t is  <( 90cos(55).t), (90sin(55).t - 16t²)>

(b)  The velocity vector of the baseball at time t is <(90cos(55)), 90sin(55)>

(c) Hit is not a home run.

(d) At the time 4.455475 seconds, a baseball hit the fence.

What is the angle of elevation?

The angle of elevation is generated by the intersection of the horizontal line and the line of sight. If the line of sight is directed upward from the horizontal line, the resulting angle is an angle of elevation.

Here, we have

Given: A baseball leaves the bat at an angle of 55° from the horizontal traveling at 90 feet per second. A 20- foot fence boundary fence is 230 feet from the batter in a direct line where the ball is hit.

(a) At time t seconds horizontal distance traveled by the ball = μcos(θ).t

Horizontal distance x(t) = 90cos(55).t

Vertical distance =  μ.t = 1/2gt²

μ = 90sin(55).t, g = 32

Vertical distance y(t) = 90sin(55).t - 16t²

The position vector of the baseball at time t in the second :

S(t) = <( 90cos(55).t), (90sin(55).t - 16t²)>

(b) Horizontal component of velocity = 90cos(55)

The vertical component of velocity = 90sin(55)

Velocity vector = V(t) = <(90cos(55)), 90sin(55)>

(c) The horizontal distance of the fence = 230 feet

Height of fence = 20 feet

Horizontal distance= 230 = 90cos(55)t

t = 90cos(55)/230

t = 4.455475

Now, the vertical distance at time 4.455475 seconds

y(t) = 90sin(55)(4.455475) - 16(4.455475)²

= 10.854

baseball hit at the height of  10.854.

Hence, baseball didn't clear the fence, and it is not a home run.

(d) At the time 4.455475 seconds, a baseball hit the fence.

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Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

<95141404393>

Answer:

y = -6x -8

Step-by-step explanation:

4 = -6(-2) -8

4 = 12-8

4 = 4

The explaination above shows how to verify your answer.

Hope this helps u!

Answer

a

\(\Phi (2.5) = 0.9938\)

b

\(P(5800 <  X < 5900 ) =  0.13591 \)  

c

\(x = 5835.5 \)

Question

From the question we are told that

   The mean is  \(\mu  =  6000 \  kg/cm^2   \)

    The standard deviation is  \(\sigma  =  100 \  kg/ cm^2 \)

Generally the probability that a samples strength is less than 6250 kilograms per square centimeter is mathematically represented as

        \(P(X < 6250  ) =  P(\frac{ X - \mu}{\sigma } <  \frac{6250 - 6000 }{100}  )\)

Generally \(\frac{X - \mu }{\sigma }  =  Z(The  \ standardized \  value  \ of  \  X )\)

         \(P(X < 6250  ) =  P(Z< 2.5 )\)

From the z-table  

      \(\Phi (2.5) = 0.9938\)

Generally the probability that a samples strength is between 5800 and 5900 kilograms per square centimeter is mathematically represented as

    \(P(5800 <  X < 5900 ) =  P(\frac{5800 - 6000}{100} < \frac{X -\mu}{\sigma} <  \frac{5900 - 6000}{100}   )\)

=> \(P(5800 <  X < 5900 ) =  P(-2< Z< -1   )\)

=> \(P(5800 <  X < 5900 ) =  P(Z <  -1)  - P( Z< -2 )\)  

From the z-table  

    \(P(Z <  -2)  = 0.02275\)

and

    \(P(Z <  -1)  = 0.15866\)

So

    \(P(5800 <  X < 5900 ) =  0.15866 - 0.02275\)    

=>    \(P(5800 <  X < 5900 ) =  0.13591 \)  

Generally the strength that is exceeded by 95% is mathematically evaluated  as

        \(P(X >  x) = 1-  P(\frac{X - \mu }{\sigma} \le  \frac{x- 6000}{100}) = 0.95 \)

=> \(P(X >  x) =  P(Z \e \frac{x- 6000}{100}) = 0.05 \)

From the normal distribution table  the critical value  of  0.05 is  

    \(z = - 1.645\)

So

      \(\frac{x- 6000}{100} = - 1.645\)

=>   \(x = (-1.645 * 100) + 6000\)

=>   \(x = 5835.5 \)

Answer: 34

Step-by-step explanation:

Vertical angles are congruent.

Answer: The correct is 114

Step-by-step explanation: Hope this helps

Answer:

8 ÷ 15 = 0.5333333333333333 or 0.53

Step-by-step explanation:

Answer:

0.5333  as a decimal

5333/10000

53.33%

Step-by-step explanation:

Answer: you can use a calculator, -0.75

Step-by-step explanation:

-2+-8+9

The + and - make a - so you can simplify to

-2-8+9

-1x3

-3/4

Answer:

(x + 8)² = 36

Step-by-step explanation:

When you are trying to complete the square and the equation already has a constant, you add or subtract that value to the other side of the equation so you can cancel it out.

x² + 16x + 28 = 0

x² + 16x + 28 - 28 = 0 -28

x² + 16x = -28

Now, you find (\(\frac{b}{2}\))² (divide b by 2 and raise the quotient to the second power). Half of 16 is 8, and 8² is 64. Add 64 to both sides.

x² + 16x + 64 = -28 + 64

x² + 16x + 64 = 36

Now, you just factor the equation on the left. To factor it, you will always use the number you got to make the constant, which in this case is 8.

(x + 8)² = 36

Based on the given information, we know that the function f is both continuous and differentiable for -2< x < 1. This means that there are no sudden jumps or breaks in the graph of f, and that the slope of the tangent line to the graph of f exists at every point in the interval.

Because f is continuous on this interval, we can use the intermediate value theorem to conclude that f takes on every value between f(-2) and f(1). Additionally, because f is differentiable on this interval, we know that the derivative of f, denoted as f'(x), exists at every point in the interval.

Knowing that f is differentiable allows us to make certain conclusions about the behavior of f. For example, if f'(x) > 0 for all x in the interval, then we know that f is increasing on the interval. Similarly, if f'(x) < 0 for all x in the interval, then we know that f is decreasing on the interval.

In summary, because f is both continuous and differentiable on the interval -2< x < 1, we can make certain conclusions about the behavior of f, such as its increasing or decreasing behavior, and we know that f takes on every value between f(-2) and f(1).

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Answer:

\(8x^{3}+30x^{2}+17x+6\)

Step-by-step explanation:

Answer:

the area is -155/8

Step-by-step explanation:

can't tell you what the volume is because  there is no height to solve volume

We have that, if all the diagonal entries are positive, then all the eigenvalues have a positive real part, where the proof is based on the transpose and the hermetic matrix

Since \($A$\) is an \($n \times n$\) matrix, and all diagonal entries of \($A$\) are positive. Let the eigenvalue of \($A$\) be \($\lambda$\) and the eigenvector of \($A$\) be \($x$\). So

\($$Ax = \lambda x$$ $$\Rightarrow x^{*}Ax = \lambda x^{*}x$$\)

Here, \($x^{*}$\) It is the transpose of \($x$\). We know that\($A$\) is a Hermitian matrix, so\($A = A^{*}$\). Therefore

\($x^{*}Ax = x^{*}A^{*}x = (Ax)^{*} x = (\lambda x)^{*}x = \lambda^{*}x^{* }x$\)

Now we have

\($$x^{*}Ax = \lambda^{*}x^{* }x \geq 0$$\)

Therefore, we can conclude that

\($\lambda^{*} \geq 0$\) \($\text{Re}(\lambda) \geq 0$\)

Thus, we have proved that if all the diagonals are positive, then all the eigenvalues have a positive real part.

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Answer:

Step-by-step plotttt

Answer:

23.54

Step-by-step explanation:

The unit price in dollars per orange is $ 4. 2

A unit price is the price for a given commodity or service that includes all extra costs attached to the item.

It is described as the product's average price.

It is determined by dividing the product's total sales revenue by the total units sold for the product.

It is known as the price per unit of the product.

From the information given, we have that;

$3.84 for a bag of 16 oranges

The unit price;

= 16/3. 84

Divide the values

= $4. 166

=$ 4. 2

Hence, the value is $ 4. 2

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Answer:

3^3 m^2 is area. If it is a square, the sides are 3 each.

Step-by-step explanation:

The time that the object hits the ground is given as follows:

B. t=5.

The equation giving the height of the object after t seconds is given as follows:

h(t) = -16t² + 80t.

The object hits the ground when:

h(t) = 0.

Hence the time is obtained as follows:

-16t² + 80t = 0

16t² - 80t = 0

16t(t - 5) = 0.

Hence the non-zero time is given as follows:

t - 5 = 0

t = 5 seconds.

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The expression for ∫f(3x+2)dx is `\(F(x) = \sum_(n=0)^\infty [(-1)^{(n+1)}2^{(n-1)}3^{(2n-3)}/(n+1)](x+1)^(2n+1) + C\)` where `C` is the constant of integration.

Given that `\(f(x) = \sum_(n=1)^\infty2^{(n-1)}(-1)^{n}(x+1)^{(2n-3)}\)` where `x∈R`

To find ∫f(3x+2)dx.

We need to substitute `3x+2` for `x` in `f(x)` which gives,

`\(f(3x+2) = \sum_(n=1)^\infty2^{(n-1)}(-1)^n((3x+2)+1)^{(2n-3)}`\\=`\sum_(n=1)^\infty2^{(n-1)}(-1)^n(3x+3)^{(2n-3)}\)`

Simplifying the above equation by pulling out the constants and writing it in a form of `(x-a)` so that we can get the power series:

\(\sum_{(n=1)}^\infty[(-1)^{(n+1)}2^{(n-1)}3^{(2n-3)}](x+1)^{{2n-3}}]\)

which is in a form of ∑_(n=0)^∞ a_n(x-a)^n where `a_n = [(-1)^(n+1)2^(n-1)3^(2n-3)]` and `a = -1`

Therefore the expression for ∫f(3x+2)dx is `\(F(x) = \sum_{(n=0)}^\infty (a_n/(n+1))(x-a)^(n+1) + C\)` where `C` is the constant of integration.

To get the value of `a_n/(n+1)` from `a_n` we can divide `a_n` by `n+1`.

Therefore, `\(a_n/(n+1) = [(-1)^{(n+1)}2^{(n-1)}3^{(2n-3)}]/(n+1)\)`

Hence the expression for ∫f(3x+2)dx is `\(F(x) = \sum_(n=0)^\infty [(-1)^{(n+1)}2^{(n-1)}3^{(2n-3)}/(n+1)](x+1)^(2n+1) + C\)`where `C` is the constant of integration.

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Given function is:

$$f(x)=\sum_{n=1}\(x^{2}\){\infty} 2^{n-1}(-1)^n(x+1)^{2n-3}, x \in R$$

To find $\int f(3x+2)dx$, we need to substitute $u = 3x+2$ to make the limits of integration same as in original function. Hence, we get:$$\int f(3x+2)dx=\frac{1}{3}\int f(u)du$$$$=\frac{1}{3}\int \sum_{n=1}^{\infty} 2^{n-1}(-1)^n(u+1)^{2n-3}du$$
$$=\sum_{n=1}^{\infty} \frac{(-1)^n}{3} 2^{n-1}\int(u+1)^{2n-3}du$$$$=\sum_{n=1}^{\infty} \frac{(-1)^n}{3} 2^{n-1} \frac{(u+1)^{2n-2}}{2n-2}+C$$$$=\sum_{n=1}^{\infty} \frac{(-1)^n}{3} 2^{n-1} \frac{(3x+3)^{2n-2}}{2n-2}+C$$$$=\sum_{n=1}^{\infty} (-1)^{n-1} 2^{n-1} \frac{(x+1)^{2n-2}}{n-1}+C$$

We know that the expression is a power series.

The center of the power series is $a=-1$ and $C$ is a constant of integration.

Hence, the expression of $\int f(3x+2)dx$ is:$$\int f(3x+2)dx=\sum_{n=1}^{\infty} (-1)^{n-1} 2^{n-1} \frac{(x+1)^{2n-2}}{n-1}+C$$

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Answer:

8

Step-by-step explanation:

so basically if the tenth is 5 and or up you round up

if  it is lower then 5 you round down.

The equation that represents the table is y = 4x.

A term with x as the highest power appears in a linear equation, which is a polynomial equation of the first degree. Y = mx + b, where m is the slope (the rate of change of y with respect to x) and b is the y-intercept (the value of y when x = 0), is the typical form of a linear equation. Straight lines can be used to express linear equations on a coordinate plane, with the slope denoting the line's steepness and the y-intercept designating the line's point of intersection with the y-axis. Linear equations are important to the study of algebra and calculus and have numerous applications in math, science, engineering, economics, and other disciplines.

The slope of the line is given by the formula:

m = change in y / change in x

Using the coordinates from the table we have:

m = 24 - 12 / 6 - 3

m = 12 / 3 = 4

The equation of the line is given as y = mx + b.

Substituting the value of slope we have:

y = 4x + b

The equation that has the slope 4 is y = 4x.

Hence, the equation that represents the table is y = 4x.

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The required formula to calculate exterior angle and an interior angle are  360°/n and (n-2) * 180°/n.

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides). To create a closed figure, a minimum of three line segments must be connected end to end.

The measure of an exterior angle of a regular polygon with n sides is given by 360°/n. The measure of an interior angle of a regular polygon with n sides is given by (n-2) * 180°/n.

So if you provide the number of sides of the polygon, I can give you the measures of the exterior and interior angles rounded to the nearest tenth if necessary.

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A two-dimensional form that occupies an area is called a shape.

Shapes can be various types such as rectangles, circles, triangles, and many others, and they are defined by their properties such as sides, angles, and vertices. They are defined by their boundaries or edges and exist within a plane. These forms have dimensions of length and width, but not depth. Shapes play a fundamental role in geometry and are studied extensively in mathematics and art. They can be simple or complex, symmetrical or asymmetrical, and are used to represent objects, patterns, or designs. Whether in the natural world or man-made creations, shapes are integral to our understanding and appreciation of visual compositions.

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The examples of exponential growth include bacteria population growth and compound interest and a real life example of exponential decay is radioactive decay.

Exponential growth is the pattern of data that shows sharper increases over time. Savings accounts with a compounding interest rate can show exponential growth.

There are many real-life examples of exponential decay. An example, is thatsuppose that the population of a city was 100,000 in 1980. Then every year after that, the population has decreased by 3% as a result of heavy pollution. This is an example of exponential decay.

One of the best examples of exponential growth is the observed in bacteria. It takes bacteria roughly an hour to be able to reproduce through prokaryotic fission. In this case, if we placed 100 bacteria in an environment and recorded the population size each hour, we would observe an exponential growth.

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Answer:

i don't think 3 works for x because the only solution for x was 8

Step-by-step explanation: