A paper airplane contest is being held. The following results are found: 80% of the participants used a triangle shape. The triangle shaped planes only won their trials 16% of the time. The other shaped planes won their trials 36% of the time. Create a tree diagram for this situation: What is the probability that a triangle plane won overall?Out of 100 planes, which shape has the most winners?A winning plane is selected at random, what is the chance it is triangle shaped?

The given triangle is a right angle triangle. The pythagorean theorem is expressed as

hypotenuse^2 = one leg^2 + other leg^2

From the diagram,

hypotenuse = AB = c

one leg = BC = 9

other leg = AC = 12

By applying the pythagorean theorem, we have

The missing length is 15 cm

To find the factors of a number, we can look for factors to divide it by subsequently.

It is easier to start with lower factors.

Let's start by "2".

Since "54" is even, it is divisable by "2":

So "2" is one of the factors.

Now, we have got 27. It is not even anymore, but it is divisable by "3":

So "3" is another factor.

Now we have got "9" and it is also divisable by "3":

So there is another "3" factor.

And since we have got now another "3", we know it is divisable by "3":

Now we have got to "1", so we found all the prime factors:

Now,, we need to combine them to find all possible combinations.

We will start from low to high.

"1" is always a factor.

There is "2" there, so it is also a factor.

Then we have "3" as another factor.

There is no need to combine "1" with another factor, so we will start b combining 2 and 3:

So, "6" is another factor.

We can combine 3 with 3:

"9" is another factor.

Now we start combining three of them:

So, "18" and "27" are factors.

And now we combine 4 of them, but this is get us back to "54" which is the last factor.

So, the factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54.

Answer:

Step-by-step explanation:

1 × 54 = 54, (1, 54) is a pair factor of 54.

2 × 27 = 54, (2, 27) is a pair factor of 54

3 × 18 = 54, (3, 18) is a pair factor of 54

6 × 9 = 54, (6, 9) is a pair factor of 54

Therefore, the positive pair factors are (1, 54), (2, 27),(3, 18) and (6, 9).

The table show piszzas (P) on the left column and the slices of Pepperonin (S) on the right column.

To determine the equation models first check the ratio S/P to determine whether they are proportinal or not.

Now as the ratios are constant it mean the variation is linear and the relationship is proportional.

Thus the model equation can be determine as,

Thus, the above equation gives the required model equation.

Answer: .1$ so 10cents

Step-by-step explanation:

hello

the question here is a word problem and we can either use alphabhets to represent the variables.

let lattes be represented by x and milk be represented by y

since the total ounce of liquid is equals to 30, we equate the whole sentence to 30.

The behavior of any polynomial function is determined by the exponent and the signal of the first term of the function.

In the case of f(x), the leading term is negative, and its expoent is odd. Therefore, when x is negative, the leading term will be positive and, when x is positive, the leading term is negative.

Therefore, we have:

Solution

For this case we can use the definition of average given by:

The final score needs to be 90 so we can do this:

And solving for x5 we got:

5*90 = 88+91+95+89+ x5

x5= 450 - 88- 91- 95 -89 = 87

Final answer:

c.87

Recall that the constant of variation of a straight line is the slope of the line.

To compute the slope we will use the following formula for the slope of a line:

Now, notice that points (-1,3) and (1,-3) are on the line, then substituting these points in the above formula we get:

Answer: -3.

The function representing the volume of the rectangular prism is given to be:

Since we are expected to find the volume using the graph, we can prepare a table of values for the function using values of h as integers from 1 - 5, such that:

The completed table is shown below:

Hence, we can plot these points on a graph using a graphing calculator for ease of work. This is shown below:

The maximum volume of the prism is represented by the highest point on the graph. The graph's highest point is at:

The corresponding value for the volume as can be seen on the graph is:

This is the maximum volume of the prism.

To the nearest cubic foot, the maximum volume of the rectangular prism is 24 cubic feet.

Since this situation can be represented by a right triangle, we can use the pythagorean theorem. Doing so, we have:

Speed formula:

d is the distance

t is the time

As you need to find a time having the distance and speed, solve the equation above for t:

Use the given data to find the time:

Answer:

29 units

Step-by-step explanation:

BC is a side of ACB, which is a 45 45 90 triangle. BC = AB/sqrt2

If In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Then BC is 29 units

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units.

We need to find BC

In triangle ACD,

tan 45° = CD/AD

CD = tan 45° x AD

= 1 x 20= 20 units

In triangle CDB,

tanФ = CD/BD

Ф = tan⁻¹(CD/BD)

= tan⁻¹(20/21)

= 43.6°

so, sin 43.6° = CD/BC

BC = CD/sin 43.6°

= 20/0.689

= 29 units

Hence the length of BC will be 29 units.

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the expression is

We must divide each value by the value of the denominator to obtain the unit ratio

so

the unit ratio is 2 inches per day

Let W be the time of the wong family and N the time of the Nguyen family. We are told that the output rate of the Wong family is 35 L/h and the output for the Nguyen family is 20 L/h, if the total water output is 2100 L, then we can write this mathematically as:

Where "35W" is the total water output of the wong family and "20N" is the total water output of the Nguyen family. The two outputs combined must be 2100. We are also told that the total time is 75 hours, therefore we have:

We get a system of two equations and two variables. We can solve for "W" in equation (2), by subtracting "N" from both sides:

Now we can replace this value in equation (1):

Now we apply the distributive property:

Now we add like terms;

Now we subtract 2625 from both sides:

Now we divide both sides by 15:

Now we replace this value in equation (2) where we already solved for W:

Therefore, the time for the Wong family is 40 hours and the Nguyen family is 35 hours.

Question 4

The x values for which g(x) = 3

From the graph, we have this value to be:

Question 5

f(x) = 6, What is x?

From the graph, we can determine the value of x corresponding to f(x)= 6:

Question 6:

f(x)= 0, What is x?

From the graph, we can determine the value of x corresponding to f(x) = 0

Question 7

The domain of the function:

The domain is the set of allowable inputs.

Question 8

The range is the set outputs

When two angles are adjacent on a straight line, then the sum of the two angles equals 180 (that is sum of angles on a straight line). Therefore;

The measure of r is 15

We will have the following:

We will recall that the surface area of a sphere is given by:

So, the surface area of the given sphere will be:

So, the surface area of the sphere will be 28 yd^2.

*The reason we can use "mental math" is that we are using an approximation of pi, which makes it so it cancels with the 3.14 in the denominator after a point; leaving a simple multiplication at the very end.

We have the following equation.

Where m is the number of feet in a mile.

Let us subtract 20,000 from both sides of the equation then simplify

The negative sign cancels out and the equation becomes

Finally, we can apply the Division Property of Equality which states that when we divide both sides of the equation with same number then the equation remains valid.

Let us divide both sides of the equation by 1.8939 then simplify

Therefore, there are 5280 feet in a mile (rounded to nearest whole number)

If I sent 4/9 of the leftover pizza home with your friends the pizza do I have left in the box is 16/45.

What is pizza?

Pizza is an Italian food consisting of a typically flat, spherical foundation composed of leavened wheat dough that is topped with cheese, tomatoes, and frequently a number of additional toppings. Following that, the pizza is baked at a high temperature, typically in a wood-fired oven. A small pizza is also known as a pizzetta. A pizza maker is referred to as a pizzaiolo.

To get the quantity of the leftover pizza, we need to subtract the pizza sent by me to home from the total pizza I had in my lunch box.

So,

Pizza I have left = Pizza in lunch box - Pizza I have sent

Pizza I have left = 4/5 - 4/9  

Pizza I have left = (4(9) - 4(5))/45

Therefore, Pizza I have left is 16/45.

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Answer:

19g

Explanation:

Given the starting amount as 155grams, the below amount will be left after the 1st half life;

After the 2nd half-life, the below amount will remain;

After the 3rd half-life, the below amount will remain;

We have a one-dimensional horizontal line segment. Three points are indicated on the line as follows:

In the above sketch we have first denoted a reference point at the extreme left hand as ( Ref = 0 ). This is classified as the origin. The point ( A ) is located on the same line and is at a distance of ( 21 units ) from Reference ( Ref ). The point ( B ) is located on the same line and is at a distance of ( 66 units ) from Reference ( Ref ).

The point is located on the line segment ( AB ) in such a way that it given as ratio of length of line segment ( AB ). The ratio of point ( P ) from point ( A ) and from ( P ) to ( B ) is given as:

The length of line segment ( AB ) can be calculated as follows:

We can form a relation for the line segment ( AB ) in terms of segments related to point ( P ) as follows:

We were given a ratio of line segments as ( Eq1 ) and we developed an equation relating the entire line segment ( AB ) in terms two smaller line segments as ( Eq2 ).

We have two equation that we can solve simultaneously:

Step 1: Use Eq1 and express AP in terms of PB.

Step 2: Substitute ( AP ) in terms of ( PB ) into Eq2

We already determined the length of the line segment ( AB ). Substitute the value in the above expression and solve for ( PB ).

Step 3: Solve for PB

Step 4: Solve for AP

Step 5: Locate the point ( P )

All the points on the line segment are located with respect to the Reference of origin ( Ref = 0 ). We will also express the position of point ( P ).

Taking a look at point ( P ) in the diagram given initially we can augment two line segments ( OA and AP ) as follows:

The point ( P ) is located at.

Answer:

Your answer can't be simplified but it's also slightly incorrect. No worries!

You can simplify (64v^4 - 225w^10) by applying the difference of squares --> a^2 - b^2 = (a + b)(a - b)

Here, (64v^4) is a^2, and (225w^10) is b^2.

[tex]\sqrt{64v^4 }[/tex] = a = 8v^2

[tex]\sqrt{225w^{10} }[/tex] = b = 15w^5

Substitute the values:

(8v^2 + 15w^5)(8v^2 - 15w^5)

Therefore, the factorization of [tex]64x^{4} -225w^{10}[/tex] is:

[tex](8v^{2} + 15w^5)(8v^2-15w^5)[/tex]

The factorization is already the simplest. It can't be simplified further.

Given:

To solve,

Step 1:

Express each value to a common decimal place.

We can express each value to two decimal places.

Thus, we have

Step 2:

Sum up the values.

Hence, 16.02 + 8.5 + 14 gives 38.52.

We have the following equation of a hyperbola:

Let's divide all the equations by 4, just to simplify it

Just to make it easier, let's put the term if "x" isolated

Now we can complete squares on both sides, just remember that

Now let's complete it!

We already completed one side, now let's complete the side with y^2, see that we will add 4 again, then

And now we can write it using the standard equation!

And now we can graph it like all other hyperbolas, the vertices will be:

And the foci

Then the foci are

Now we can plot the hyperbola!

The length of the building's shadow = 550.66 ft

The height of the Empie State Building = 1250 feet

The friend's height = 75 inches

The length of the friend's shadow = 33 inches

Answer:

Completing the table we have;

Explanation:

Given the table in the attached image, we want to complete the table;

For period 1;

simple interest;

Compound interest;

For period 2;

simple interest;

compound interest;

Total interest

simple interest;

Compound Interest;

Therefore, completing the table we have;

If two polygons are similar with the lengths of corresponding sides, we need to find the ratio between both figures:

Then:

So, the ratio is 5:3

The perimeter of LMNPQ is the same to say :

P of ABCDE = 25.2cm

Use the ratio

P of LMNPQ = 25.2 (5/3) cm

Then P = 42 cm

The total minutes in the game is 48. The total playing game for Jason is 32. The ratio is

Simplifying it, we have

So, the playing ratio is 2 to 3 for Jason.

Okay, here we have this:

Considering that in a parallelogram the opposite sides are congruent, we obtain the following:

AB=CD

AB=9 units

AC=BD

AC=4 units