A right triangle has a rise of 16 and a run of 4. A similar right triangle with a run of 5 will have a rise of?

The area of the triangle is approximately 6.4936 square centimeters.

We can use Heron's formula to find the area of a triangle given the lengths of its sides. Heron's formula states that the area (A) of a triangle with sides a, b, and c is:

A = √[s(s-a)(s-b)(s-c)]

where s is the semi-perimeter of the triangle, defined as:

s = (a + b + c) / 2

Using the values given in the problem, we have:

a = 7 cm, b = 3 cm, c = 5 cm

The semi-perimeter is:

s = (a + b + c) / 2 = (7 + 3 + 5) / 2 = 7.5 cm

Substituting these values into Heron's formula, we get:

A = √[s(s-a)(s-b)(s-c)]

= √[7.5(7.5-7)(7.5-3)(7.5-5)]

= √[7.5(0.5)(4.5)(2.5)]

= √[42.1875]

= 6.4936 cm² (rounded to 4 decimal places)

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Using this formula, we can calculate that the chance that the plane will be overbooked is 35.1%. This means that there is a 35.1% chance that more than 300 passengers will show up for the flight despite the airline only having 300 seats.

The chance that a plane will be overbooked is calculated using a binomial probability formula. The formula is P(x) = nCx * p^x * (1 - p)^(n - x), where n is the number of trials (in this case, 300), x is the number of successes (in this case, 324 reservations), and p is the probability of success (in this case, 90%).

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Answer:

5 and 13

Step-by-step explanation:

given the first number is x and the second number is y

then x + y = 18 => y = 18 - x

also

x^2 + y^2 = 194

substitute

x^2 + (18 - x)^2 = 194

x^2 + x^2 - 36x + 324 = 194

2x^2 - 36x + 130 = 0

2(x^2 - 18x + 65) = 0

x^2 - 18x + 65 = 0/2

x^2 - 13x - 5x + 65 = 0

x(x - 13) - 5(x - 13) = 0

(x - 13)(x - 5) = 0

=> x - 13 = 0 => x = 13

=> x - 5 = 0 => x = 5

if x = 13, y = 18 - 13 = 5

if x = 5, y = 18 - 5 = 13

so x and y can be either 5 and 13

A basketball court takes the shape of a rectangle and the perimeter of a rectangle is =88m

The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.

Each form has a different perimeter depending on its measurements. The perimeter is only ever stated as the circle's diameter when referring to a circle. So we must add all of the sides of each polygon to determine its perimeter, which is the same for all polygons.

A basketball court takes the shape of a rectangle and the perimeter of a rectangle is calculated by the formula:

= Length + Length + Width + Width

Slotting the figures in will give:

= 27 + 27 + 17 + 17

= 88 m

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Answer:

3.44827586

Step-by-step explanation:

1450:10,000::x:2

=10,000x=2900

x= 10,000

----------

2900

x=3.44827586 km

The first term in the given sequence is 5

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

Rule:

The sequence starting at 5 and following the given rule is:

The first term in the sequence is simply the starting number, which is 5.

Hence, the value of the first term in the sequence is 5.

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The simplified expression with only positive exponents is 729 / 19^7.

We can simplify the expression as follows, using the exponent rules:

19 to the -3rd power = 1 / (19^3)

19×19 to the -4th power = (19^2)^-2 = 1 / (19^2)^2 = 1 / (19^4)

nine to the third power = 9^3

Therefore, the expression can be written as:

(1 / (19^3)) × (1 / (19^4)) × (9^3)

To simplify further, we can combine the two terms with powers of 19 into a single term:

(1 / (19^3 × 19^4)) × (9^3) = (1 / 19^7) × (9^3)

Finally, we can evaluate 9^3 to get the final answer:

(1 / 19^7) × (9^3) = (1 / 19^7) × 729 = 729 / 19^7

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The given question is incomplete, the complete question is:

19 to the -3rd power times 19×19 to the -4th power times nine to the third power. Simplify the expression using only positive exponents

In the triangle , the cοrrect οptiοn is  B) b = CD sin(A) and a = CD sin(B).

A triangle is a fοrm οf pοlygοn with three sides; the intersectiοn οf the twο lοngest sides is knοwn as the triangle's vertex. There is an angle created between twο sides. One οf the crucial elements οf geοmetry is this.

Certain fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry, rely οn the characteristics οf triangles. The angles and sides οf a triangle determine its kind.

Here the given triangle CD is altitude.

According to the given statement table , in 4th statement we have definition of sine , Then

=> Sin(A) = [tex]\frac{CD}{b}[/tex] and Sin(B) = [tex]\frac{CD}{a}[/tex]

Here simplifying this sine equation for a and b then,

=> b = CD sin(A) and a = CD sin(B).

Hence the correct option is B) b = CD sin(A) and a = CD sin(B).

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Answer:

31/7

Step-by-step explanation:

7 i - 15 = 16

1. add 15 to both sides you will get

7i = 31

2. dividing both sides gives us 31/7

3. i = 31/7

Answer:

Sale Price-$48  What Percent Represents the reg. Price?-%100

Step-by-step explanation:

20% of 60 is 12, so if supplies are 20% off, they are $12 off, so 60 - 12 =48.

And if the regular price is $60, then $60 is the whole price, a.k.a. 100% of the price. So, the percent that represents the regular price of supplies is 100%.

Step-by-step explanation:

1) 12×5=60

8×4=32

32÷2=16

60+16=82

2) 12×14=168

10×2=20

20÷2= 10

168+10+10=188

3) 4×4= 16

4×11=44

4×5=20

16+44+20=80

4) 8×4=32

3×3= 9

9÷2= 4.5

32+4.5=36.5

Answer:

Stephanie Mary and Nicole

Step-by-step explanation:

it takes 6 hοurs fοr the sleighs tο be 390 miles apart.

velοcity is a unit οf measurement fοr the Distance an οbject travels in a

the predetermined periοd οf time. Here is a wοrd equatiοn that illustrates the cοnnectiοn between space, speed, and time: velοcity is calculated by

dividing the tοtal Distance traveled by the jοurney time.

Since the sleighs are traveling in οppοsite directiοns, their distances frοm each οther are increasing at a cοmbined rate οf 20 mph + 45 mph = 65 mph. We can use the fοrmula:

distance = rate x time

Let's call the time it takes fοr the sleighs tο be 390 miles apart "t". Then we can write:

390 = 65t

Sοlving fοr "t", we can divide bοth sides by 65:

t = 6

Therefοre, it takes 6 hοurs fοr the sleighs tο be 390 miles apart.

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Answer: 10/36 or 5/8

Step-by-step explanation:

Let’s start by solving how many pens Rohan has left. 36-11-15=36-26=10. Rohan has 10 pens left. Now to solve the fraction of pens Rohan has left, we divide our 10 by 36, or 10/36. Another fraction of this could be 5/18, because both the denominator and numerator have 2 as a factor.

In general, you would need to know the number of polygons in the original shape and the rule for how the shape is expanded or repeated in each iteration to calculate the number of polygons in a fractal expansion.

A fractal is a geometric shape that has intricate detail at arbitrarily small scales and typically has fractal dimensions that rigorously surpass topological dimensions. Several fractals resemble one another at different scales, as shown in the Mandelbrot set's sequential magnifications. Self-similarity, also known as expanding symmetry or unfolding symmetry, is the display of similar patterns at progressively smaller scales; if this replication is precisely the same at every scale, as in the Menger sponge, the shape is referred to as affine self-similar. The academic field of measure theory includes fractal geometry.

Depending on the particular kind of fractal under consideration, a polygon's fractal expansion can be calculated using a specific algorithm. However, the formula will typically entail iteratively transforming the original polygon with geometric operations.

For instance, by continually removing the central triangle from a larger equilateral triangle, the Sierpinski triangle—a well-known fractal—can be created. The remaining triangle is divided into three smaller replicas, which are then put together to make an equilateral triangle at the end of each iteration. The formula below can be used to determine the amount of triangles in each iteration:

the number of triangles in the nth repetition is represented by

Another illustration is the Koch snowflake, which is created by repeatedly dividing each of an equilateral triangle's three sides into two segments and swapping out the middle segment for two segments that also make an equilateral triangle. The following algorithm can be used to determine how many line segments are used in each iteration:

the number of line segments in the nth cycle is represented by L(n).

Generally speaking, the expansion formula for a fractal will rely on the particular rule or algorithm that was used to create the fractal.

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a)  E

b)  C

c) p-value 0.03 significant difference in two procedures

A. No, neither procedure A appears to be normal nor procedure B appears to be normal

B. There appears to be more variation in the 1st procedure than in the 2nd.

C. The p-value of the test is 0.03, which indicates that there is a statistically significant difference in the variances of the two procedures.

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bAnswer:

Step-by-step explanation:

The combined volume of the cylinder and cone with diameters of 2 feet and heights of 9 feet is 42.39 ft3.

The volume of the cylinder and cone can be calculated using the formula V=πr2h. The radius of both is 1 foot and the height of both is 9 feet. Therefore, the volume of the cylinder is Vcylinder = π(1)2(9) = 28.26 ft3. The volume of the cone can be calculated using Vcone = π(1)2(4.5) = 14.13 ft3, where 4.5 is the height of the cone. To calculate the combined volume, add the volumes of the cylinder and the cone: Vtotal = 28.26 + 14.13 = 42.39 ft3.

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Two rays with the same endpoint would form an angle, where the common endpoint is the vertex of the angle.

A ray is a part of a line that has a fixed starting point, called the endpoint, and extends infinitely in one direction. Thus, a ray can be thought of as a half-line. If two rays have the same endpoint, they will form an angle. The common endpoint is the vertex of the angle, and the two rays extend outward from the vertex in opposite directions, forming a straight line on one side of the vertex. In mathematical notation, the angle formed by two rays with the same endpoint A can be denoted as ∠BAC, where B and C are the points where the rays extend outwards. Note that the order in which the rays are written matters; ∠BAC and ∠CAB represent different angles.

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so let's put the prism upright, Check the picture below.

keeping in mind that for a triangular prism the bases are the triangular parts, so le'ts find the area of those guys

[tex]\stackrel{ \textit{\LARGE Lateral} }{\stackrel{ \textit{Area of the three rectangles} }{(7)(5)~~ + ~~(3)(7)~~ + ~~(4)(7)}}\implies \text{\LARGE 84} \\\\\\ \stackrel{ \textit{\LARGE Total} }{\stackrel{ \textit{Area of the bases} }{2\left[\cfrac{1}{2}(\underset{b}{4})(\underset{h}{3}) \right]}~~ + ~~84}\implies \text{\LARGE 96}[/tex]

If VAR[-4X+5]=13 and E[X]=2.5, so E[(X-3)²] will be 1.06. The correct answer is A

We have VAR[-4X+5] = 13, which means VAR[-4X] = 13 since VAR[c] = 0 for any constant c, and VAR[aX] = a² VAR[X] for any constant a.

So we have:

VAR[-4X] = (-4)² VAR[X] = 16 VAR[X] = 13

Solving for VAR[X], we get:

VAR[X] = 13/16

Now, we want to find E[(X-3)^2]:

E[(X-3)²] = E[X² - 6X + 9]

= E[X²] - 6E[X] + 9 (by linearity of expectation)

We can use the formula VAR[X] = E[X²] - (E[X])² to solve for E[X²]:

VAR[X] = E[X²] - (E[X])²

13/16 = E[X²] - (2.5)²

E[X²] = 13/16 + 6.25

E[X²] = 7.31

Therefore, we have:

E[(X-3)²] = E[X²] - 6E[X] + 9

= 7.31 - 6(2.5) + 9

= 1.06

So the answer is (a) 1.06.

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The cube root of 126.2 is approximately 0.016 larger than the cube root of 125.

Linear approximation is a strategy for approximating the values of complicated functions. When a graph is relatively straight, this approximation is quite effective. A linear approximation for a function is a straight line that represents a close approximation of the original function.

The formula to be used is given by

df/dx = (f(x+dx)-f(x))/dx

The first derivative of the cube root of x can be computed as follows:

f(x) = x^(1/3)

df/dx = (1/3)*x^(-2/3)

Using this formula, we can calculate the linear approximation of the cube root of 126.2. This can be done as follows:

f(x + dx) ≈ f(x) + df/dx * dx

In the given case, the f(x) = ∛125 ⇒ 5

Let dx = 126.2 - 125 ⇒ 1.2

Then the linear approximation of the cube root of 126.2 is given by

f(126.2) ≈ f(125) + df/dx * dx

⇒ f(126.2) ≈ 5 + (1/3)*125^(-2/3) * 1.2

⇒ f(126.2) ≈ 5 + 0.016

⇒ f(126.2) ≈ 5.016

Therefore, the cube root of 126.2 is roughly 0.016 greater than the cube root of 125.

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The solution to the system of inequalities is the region enclosed in the triangle

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

Let x denote the time (in hours) that Shen spends doing cardiovascular work. Let y denote the time (in hours) he spends on weight training.

Each week, he exercises for at least 12 hours, hence:

x + y ≥ 12   (1)

He spends at most 9 hours on weight training. Therefore:

x ≤ 6      (3)

He spends at most 6 hours doing cardiovascular work. Hence:

y ≤ 9    (3)

The solution to the system of inequalities is the darker region shown in the graph.

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Answer:

x = 4

Step-by-step explanation:

x + 8 = 3x

8 = 2x

x = 4

So, the answer is x = 4

The cοst each οf οne apple pie is $8 and οne lemοn meringue pie is $20.

Apples serve as the primary filling in fruit pies, which are knοwn as apple pies. Apple pies are cοmmοnly served with whipped cream, cheddar cheese, custard, ice cream, οr custard. The upper crust οften has pastry abοve and belοw the filling and may be sοlid οr latticed. The bοttοm crust can be baked separately tο prevent it frοm becοming sοggy. Deep dish apple pies typically just feature the tοp crust. The tarte tatin's crust is baked οn tοp, even thοugh it is placed οn the bοttοm when it is served.

Suppοse the cοst οf each apple pie is x and οne lemοn meringue pie is y.

Eimy sοld 6 apple pies and 8 lemοn meringue pies fοr a tοtal οf $208.

Then, 6x+8y= 208

Or, 6x=208-8y…………(1)

Enerlyn sοld 6 apple pies and 2 lemοn meringue pies fοr a tοtal οf $88.

Then, 6x+2y=88……………(2)

Putting the value οf 6x in equatiοn nο 2

208-8y+2y=88

Or, -6y=88-208

Or,y=120/6=20

Putting the value οf y in equatiοn 1

6x= 208-8*20

Or, x= 48/6

Or, x= 8

Hence the cοst each οf οne apple pie is $8 and οne lemοn meringue pie is $20.

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Answer:

Quadratic Function, Second Difference

Using functions we can find that there would be nine roadways for six cities. This is due to the fact that each city must be connected to every other city, and since there are 5 pairs of connected cities, there must be 5 highways.

A function is a statement, concept, or rule that establishes an association between two variables.

Functions in mathematics are required for the development of meaningful relationships. If there are more than one dependent values for a particular independent value, then we are aware of this.

In that situation, the relation is not a function. Nevertheless, if there are multiple dependent values for a given independent value.

The relationship is then a function.

Now as per the question,

The remaining 4 cities must then be connected, which requires building an additional 4 roads, for a total of 9.

There would be 12 roadways for 7 cities.

This is due to the fact that each city must be connected to every other city, and since there are 6 pairs of connected cities, there must be 6 highways.

Then, the final five cities must be connected, which requires five more roads, for a total of twelve.

The number of highways for N cities would be N(N-1)/2.

This is because there are N(N-1)/2 pairs of cities that need to be connected, and each city must be connected to every other city.

For instance, if N = 10, 90 highways or 10× 9 = 90 pairs of cities must be connected.

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The complete question is:

There are five cities in a country, and two are connected with one road that goes straight between them. How many roads would be in this country if there were 6 cities? 7 cities? And N cities?

Answer:

To find the best line model for the data, we will use linear regression analysis.

First, we need to calculate the mean of x and y:

mean of x = (0 + 2 + 4 + 6 + 8 + 10 + 12 + 24 + 14) / 9 = 8

mean of y = (9 + 9 + 10 + 11 + 11 + 12 + 13 + 13 + 14) / 9 = 11

Next, we need to calculate the deviations of x and y from their respective means:

deviation of x = x - mean of x

deviation of y = y - mean of y

x y deviation of x deviation of y (deviation of x)^2 deviation of x * deviation of y

0 9 -8 -2 64 16

2 9 -6 -2 36 12

4 10 -4 -1 16 4

6 11 -2 0 4 0

8 11 0 0 0 0

10 12 2 1 4 2

12 13 4 2 16 8

24 13 16 2 256 32

14 14 6 3 36 18

Then, we can calculate the slope (b) of the best-fit line using the formula:

b = sum of (deviation of x * deviation of y) / sum of (deviation of x)^2

b = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) = 0.190

Next, we can calculate the y-intercept (a) of the best-fit line using the formula:

a = mean of y - b * mean of x

a = 11 - 0.190 * 8 = 7.48

Therefore, the equation of the best-fit line is:

y = 0.190x + 7.48

Finally, we can calculate the correlation coefficient (r) using the formula:

r = sum of (deviation of x * deviation of y) / (sqrt(sum of (deviation of x)^2) * sqrt(sum of (deviation of y)^2))

r = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (sqrt(64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) * sqrt(16 + 16 + 1 + 0 + 0 + 1 + 4 + 4 + 1)) = 0.905

Therefore, the best-fit line for the given data is y = 0.190x + 7.48, and the correlation coefficient is r = 0.905.

Step-by-step explanation: