2 is what percent of 8?

Answer:

corresponding, supplementary, alternate interior, same side interior, vertical, alternate exterior, corresponding, alternate exterior, vertical, and alternate interior

In the figure 10, the pair of angles are alternate interior angles.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

From the given figure,

1) corresponding angles

2) Adjacent angles (Supplementary)

3) Alternate interior angles

4) Allied angles (Same side interior)

5) Vertically opposite angles

6) Alternate exterior angles

7) corresponding angles

8) Alternate exterior angles

9) Vertically opposite angles

10) Alternate interior angles

Therefore, in the figure 10, the pair of angles are alternate interior angles.

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Answer:

I need the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sample is the part of the population that somebody wants to study. therefore, the sample is the 100 male students interviewed

The boat must move 785.82 m closer to the cliff  for the angle of depression to become 19°.

We need to find how much closer to the cliff the boat must move for the angle of depression to change from 7° to 19°.

Calculate the distance from the boat to the base of the cliff at 7° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(7°) = 150m/distance
distance = 150m/tan(7°)

distance=1221.49

Calculate the distance from the boat to the base of the cliff at 19° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(19°) = 150m/distance
distance = 150m/tan(19°)

distance=435.6665

Calculate the difference between the two distances to find out how much closer the boat must move.
difference = distance at 7° angle of depression - distance at 19° angle of depression

Plugging in the values from Steps 1 and 2, we get:
difference = (150m/tan(7°)) - (150m/tan(19°))

difference=1221.49-435.6665

difference=785.8235

After calculating, we find that the boat must move approximately 785.82 meters closer to the cliff for the angle of depression to change from 7° to 19°.

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Answer:

  101 1/3 minutes

Step-by-step explanation:

You want to find the time for leaking 16 ounces of juice, given that leaking 3 ounces takes 19 minutes.

Writing the proportion as time (minutes)/volume (ounces), we have ...

  t/16 = 19/3

To solve this "using a giant one" we can use 1 = 3/3 on the left, and 1 = 16/16 on the right.

  \(\dfrac{t}{16}\times\dfrac{3}{3}=\dfrac{19}{3}\times\dfrac{16}{16}\\\\\\\dfrac{3t}{48}=\dfrac{304}{48}\\\\\\3t=304\qquad\text{equate numerators}\\\\\\t=\dfrac{304}{3}=101\dfrac{1}{3}\qquad\text{divide by 3}\)

It will take 101 1/3 minutes for the juice to leak out.

__

Additional comment

The method of "using a giant one" does not work well here, because the numbers in one proportion are not a simple multiple of the numbers in the other.

For this proportion, a better strategy is to multiply both sides by the denominator of the variable: 16. After the multiplications and division, that is effectively what we accomplished using more steps.

We could have used a "giant one" that was (16/3)/(16/3), and we would have gotten the same result: t = (19)(16/3).

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Answer: 4/9 or 0.4 with a reapeating 4.

Step-by-step explanation:

x^3 - a^3

The above expression represent differnt of 2 cubes

This can be re- written as

(x - a)^3

(x - a) ( x ^2 + ax + a^2)

expand the bracket

x * x^2 + ax*x + x *a^2 - a * x^2 - a * ax - a * a^2

= x^3 + ax^2 + a^2x - ax^2 - a^2x - a^3

collecting the like terms

= x^3 + ax^2 - ax^2 + a^2x -a^2x - a^3

ax^2 - ax^2 = 0

a^2x - a^2x = 0

Therefore

= x^3 + 0 + 0 - a^3

= x^3 - a^3

Answer:

Step-by-step explanation:

It is difficult to determine the rule for the table without further context or information. However, based on the pattern in the table, it appears that the rule for generating the second number in each row is to add 2 to the first number in that row. The rule for generating the third number in each row is to add 6 to the second number in that row. The fourth number is the sum of the first and the third number in that row.

If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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Answer:

$1.75 each

Step-by-step explanation:

5 people total

5 sodas at $5.50 =                      $27.50

5 hot dogs at $12.75  =               $63.75

                 Total =                        $91.25

Each paid $20  =                        $100.00

Change =                                        $8.75

Each receives:                             $1.75/each

Answer:

B because when at B angels are the same qnd A and c are also same

The probability of not getting result is found as 24.7%.

The number of times an event happened during the experiment as a percentage of all the times the experiment was run is known as the experimental probability of that event occurring.

So,

P(Result) = 0.753.

P(no result) = 1 - 0.753

P(no result) = 0.247

Thus, the probability of not getting that result is found as 24.7%.

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The correct question is-

If the probability of getting a result in an experiment is 75. 3%, what i the probability of not getting that result?

Answer:

d

Step-by-step explanation:

only a scalence triangle has all sides with different length

Step-by-step explanation:

if <1 is congruent with < 3 in. you know congruent means if the two triangles have the same shape and size so <1 and < 3 are the same size means < 3 is 110°

if < 2 is 70° and < 3 is 110° that are supplementary the total is 180°

Answer:

Step-by-step explanation:

a)

The best estimate for height of the lamp post will be 6m.

Given options for height of lamp post include heights in cm's but for a lamp post heights can not be this low because if height is very low such as 6cm and 60cm the light will not incident on proper place.

So for the lamp post height will be in the range of (5-15)m which is the ideal range for the height of lamp post. Thus option 4 is also neglected.

Hence 6m will be appropriate height for a lamp post.

b)

The best estimate for mass of a pear will be 10g.

Given estimates for a mass of pear can not be of the range kilograms.

As pear possess very less matter in it , the ideal weight of a pear will be in the range of grams.

Hence 10g will be appropriate for the estimation.


c)

Filled kettle will have 2 litres of water in it.

Given quantity of water in the kettle will be of the range in litres as a kettle that contains water will have (1-5)litres of capacity.

Hence for filled kettle the amount of water will be 2litres.

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Step-by-step explanation:

very simple : the terms with the same base (either a specific number or a variable with the same exponent, or a function ...) can be combined.

4a - 3b + 6a

which terms here have the same base ?

ah, 4a and 6a refer to the same variable (and with the same exponent : 1, as a = a¹).

therefore, I can combine them :

4a + 6a = a×(4+6) = a×10 or simply 10a

so the result is

10a - 3b

Answer:

y=(x+kh)1/h

Step-by-step explanation:

(y-k)h=c

hy-kh=c

hy=x+kh

y=(x+kh)1/h

To find the rate at which the diameter of the circle is changing, we'll first need to determine the relationship between the area of the circular ripple and its radius.

The area of a circle is given by the formula A = πr². In this problem, the area is increasing at a constant rate of 5 m²/second (dA/dt = 5).

Now, we'll use implicit differentiation with respect to time (t) to find the rate of change of the radius:

dA/dt = d(πr²)/dt

5 = 2πr(dr/dt)

Since we're interested in the rate of change of the diameter (D) when the radius (r) is 4 m, and D = 2r, we'll differentiate D with respect to time:

dD/dt = 2(dr/dt)

Now, we can solve for (dr/dt) when r = 4:

5 = 2π(4)(dr/dt)

5/(8π) = dr/dt

Finally, we find dD/dt:

dD/dt = 2(5/(8π))

dD/dt = 5/(4π)

So, when the radius of the circular ripple in the pond is 4 m, the diameter is changing at a rate of 5/(4π) meters per second.

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The probability that the student is a  girl and that her preferred fruit is an apple is 0.153.

We may use the following formula to determine the likelihood that a student chosen at random is a girl who selected apples as her preferred fruit:

P(girl and apple) = P(girl) * P(apple | girl)

where P(girl) is the likelihood that the student is a girl, P(girl | apple) is the likelihood that the student chose apples given that she is a girl, and P(girl and apple) is the likelihood that the student chose apples given that she is a girl.

The total number of students in the sample must first be determined:

total = 300

The sample's proportion of girls is then determined.

girls = 87

And the probability that a student chosen at random will be a girl

P(girl) = girls / total = 87 / 300 = 0.29

Next, The number of girls who selected apples as their preferred fruit is as follows:

girl and apple = 46

the probability that a lady student would have selected apples:

P(apple | girl) = girl and apple / girls = 46 / 87 = 0.529

Finally, the probability that a student chosen at random is a girl who selected apples as her preferred fruit is:

P(girl and apple) = P(girl) * P(apple | girl) = 0.29 * 0.529 = 0.153

So, The probability that the student is a  girl and that her preferred fruit is an apple is 0.153.

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The expression is |9 – x| is equivalent to the expression |x| − |9| if x>9, and |9|+|x| if x≤0 options (A) and (E) are correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The expression is:

|9 - x|

If x ≥ 9

Based on the mod function we can use the property of the mod functions.

|9 - x| = (9 - x)

If x < 9

|9 - x| = -(9 - x)

Thus, the expression is |9 – x| is equivalent to the expression |x| − |9| if x>9, and |9|+|x| if x≤0 options (A) and (E) are correct.

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Answer:

Step-by-step explanation:

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

a²+b²=c²

30²+72²=c²

900+5184=c²

\(\sqrt{6084} =c^{2}\)

c=\(\sqrt{6084} =78\)

Hope this helped!!

Answer:

78

Step-by-step explanation:

Answer:

x+2

hope this helps ;)

and cute pfp

Answer:

Step-by-step explanation:

x-1, because 3 fits the criteria, x>=1

Step 1

Given

Required: To find where the graph of both functions intersect. In other words the find the value of x and hence f(x) and g(x).

Step 2

Solve both equations simultaneously.

Subtract equation 2 from 1

Hence,

Step 3

Check

Hence the graph intersects at the point where x = 1.6 and y =6.2. Remember y = f(x) and g(x)

Since the angle at the center of the circle is twice the angle at the circumference that subtends it, we can find the measure of each arc by finding the central angle that subtends each arc and then doubling that angle.

The central angle that subtends arc AB is 60 degrees, so arc AB measures 2 × 60 = 120 degrees.

The central angle that subtends arc AC is 90 degrees, so arc AC measures 2 × 90 = 180 degrees.

The central angle that subtends arc BC is 210 degrees, so arc BC measures 2 × 210 = 420 degrees.

Therefore, arc AB measures 120 degrees, arc AC measures 180 degrees, and arc BC measures 420 degrees.

Answer:

x = 39.6

Step-by-step explanation:

\(cos49 = \frac{26}{x} \\ \\ x = 39.6\)

Answer:

Step-by-step explanation:

Given:

Square both sides:

Now, square the 2a - 2/a:

Find the square root:

The horizontal distance from the point where the ball is hit to the point where the ball lands on the ground is 1.8 meters.

To find the horizontal distance from the point where the ball is hit to the point where the ball lands on the ground, we need to find the value of d when the height h is 0 (since the ball is on the ground again).

The function provided is h(d) = -1.8 + d. Let's set h(d) to 0 and solve for d:

0 = -1.8 + d

Now, let's isolate d by adding 1.8 to both sides:

d = 1.8

So, the horizontal distance from the point where the ball is hit to the point where the ball lands on the ground is 1.8 meters.

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One way to tell if (x + 5) is a factor of the polynomial P(x) = x³ + 7x² - 5x - 75 is to use the factor theorem, which states that if (x - c) is a factor of a polynomial P(x), then P(c) = 0.

To apply the factor theorem, we substitute -5 for x in the polynomial P(x) and evaluate:

P(-5) = (-5)³ + 7(-5)² - 5(-5) - 75

= -125 + 175 + 25 - 75

= 0

Since P(-5) = 0, we can conclude that (x + 5) is a factor of P(x). This is because the factor theorem tells us that if P(c) = 0, then (x - c) is a factor of P(x), and we can use the equivalent expression (x + 5) = (x - (-5)) to conclude that (x + 5) is a factor.

Alternatively, we can perform polynomial long division by dividing P(x) by (x + 5) and checking if the remainder is zero. If the remainder is zero, then (x + 5) is a factor of P(x).

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Comparing the surface areas of the three containers, we find that the cylinder requires the least amount of material to make, with a surface area of approximately 39.99 cm².

To determine which container requires the least amount of material to make, we need to compare the surface areas of the three containers: the cylinder, the regular pentagon-based prism, and the square-based prism.

1. Cylinder:

The formula for the lateral surface area of a cylinder is given by:

A_cylinder = 2πrh,

where r is the radius of the base and h is the height of the cylinder.

Given that the volume of the cylinder is 20 cm³ and the height is 5 cm, we can calculate the radius:

V_cylinder = πr²h,

20 = πr²(5),

r² = 4/π,

r ≈ 1.27 cm.

Substituting the values into the lateral surface area formula, we get:

A_cylinder = 2π(1.27)(5) ≈ 39.99 cm².

2. Regular Pentagon-Based Prism:

To find the surface area of a regular pentagon-based prism, we need to know the apothem (a line segment from the center of the polygon to the midpoint of one of its sides) and the height of the prism.

Since the container holds 20 cm³ of water and has a height of 5 cm, each layer of water has a volume of 20/5 = 4 cm³. As the prism is regular, we can find the side length of the pentagon by calculating the square root of the prism's volume:

side length = √(4/tan(π/5)) ≈ 2.12 cm.

The apothem of a regular pentagon can be calculated using the formula:

apothem = side length / (2tan(π/5)) ≈ 1.85 cm.

The lateral surface area of the pentagon-based prism is given by:

A_pentagon = 5 × (1/2 × perimeter × apothem) = 5 × (5 × 2.12 × 1.85) ≈ 49.17 cm².

3. Square-Based Prism:

Since the container holds 20 cm³ of water and has a height of 5 cm, each layer of water has a volume of 20/5 = 4 cm³. Thus, the base area of the square is 4 cm².

The lateral surface area of a square-based prism is given by:

A_square = 4 × side × height,

where side is the length of one side of the base and height is the height of the prism.

Given that the base area is 4 cm² and the height is 5 cm, we can calculate the side length of the square base:

4 = side²,

side ≈ 2 cm.

Substituting the values into the lateral surface area formula, we get:

A_square = 4 × 2 × 5 = 40 cm².

Comparing the surface areas of the three containers, we find that the cylinder requires the least amount of material to make, with a surface area of approximately 39.99 cm².

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Answer:

45%

Step-by-step explanation:

Here, we want to know the probability of a randomly selected yard having 6 or more than 6 trees

To get this, we simply add up the probability of 6 yards and above

That is the probability of 6, 8 , 10 and 12 yards

This is obtainable from the histogram

We then proceed to add up from the graph

What we have is;

0.05 + 0.25 + 0.10 + 0.05

= 0.10 + 0.10 + 0.25 = 0.45

This is same as 45/100 which is otherwise 45%

The probability that a randomly selected yard will have 6 or more trees is 45%.

Probability of having 0-2 tree = 0.35

Probability of having 2-4 tree = 0.20

Probability of having 4-6 tree = 0.05

Probability of having 6-8 tree = 0.20

Probability of having 8-10 tree = 0.10

Probability of having 10-12 tree = 0.05

Probability is to quantify the possibilities or chances.

So, probability of having 6 or more trees

= (2*0.05 + 2*0.25 + 2*0.10 + 2*0.05)/(0.35*2+0.20*2+2*0.05 + 2*0.25 + 2*0.10 + 2*0.05)

=0.9/2

=0.45

=45%

So,  probability of having 6 or more trees =45%

Therefore, the probability that a randomly selected yard will have 6 or more trees is 45%.

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