How to derive Universal Law of Gravitation ?​

(a) No, a triangle cannot have two obtuse angles. (b) No, a triangle cannot have two right angles.
(c) If no angle of a triangle measures more than 60°, then the triangle is an acute triangle.


(a) In a triangle, the sum of all three angles must be 180°. Since two obtuse angles would sum to more than 180°, it is not possible for a triangle to have two obtuse angles.
(b) In a triangle, the sum of all three angles must be 180°. Since two right angles would sum to 180°, it is not possible for a triangle to have two right angles.
(c) In an acute triangle, all three angles are less than 90°. If no angle of a triangle measures more than 60°, then all three angles are less than 90°, making it an acute triangle.

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Answer:

y = 17 - 4x or y = 17 + (-4x)

Step-by-step explanation:

Plug the slope (m) into the equation y=mx+b so it becomes y = -4x + b

Then see how much your line changed from the point to the y-axis. In this case, it changed by negative 12. So you have to go up 12 points to reach the y-intercept. (5+12=17)

Then, plug that number into the equation.

y = 17 - 4x

The combination formula can be used to calculate the number of ways that a group of people can be divided into teams of a certain size. In this case, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.

To find out how many ways 18 people can be divided into 2 teams of 9 people, we need to use the combination formula. The formula for combination is nCr = n!/r!(n-r)!, where n is the total number of people and r is the number of people in each team.
In this case, n=18 and r=9. Plugging in the values into the formula, we get:
18C9 = 18!/9!(18-9)! = (18x17x16x15x14x13x12x11x10)/(9x8x7x6x5x4x3x2x1)
Simplifying the expression, we get:
18C9 = 48,620
Therefore, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.
It is important to note that the order of the teams does not matter. For example, team A consisting of 9 people and team B consisting of the remaining 9 people is the same as team B consisting of 9 people and team A consisting of the remaining 9 people.
In conclusion, the combination formula can be used to calculate the number of ways that a group of people can be divided into teams of a certain size. In this case, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.

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Answer:

u said following but u didnt show the following answers

Step-by-step explanation:

The approximate volume of sand in the container is about 0.2 gallons. To find the volume of the sand, we need to find the volume of the cylinder container. We can use the formula for the volume of a cylinder: V=πr²h.

First, we need to find the radius by dividing the diameter by 2: r = 12/2 = 6. So, the volume of the cylinder is: V = 3.14 x 6² x 10 = 1,128 cubic inches. To convert cubic inches to gallons, we divide by 231 (the number of cubic inches in a gallon): 1,128/231 ≈ 4.9 gallons. Rounding this to the nearest gallon gives us 5 gallons.

However, the child completely filled the container with sand, which means that some sand may have spilled over the top. So, it's safe to assume that the actual volume of sand in the container is slightly less than 5 gallons. We can estimate the volume to be about 0.2 gallons.

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The value of x in the given equation will be 2/5

From the data,

We have to determine the value of x.

The given equation is: 18x-16=-12x-4

For determining the value of x, we will first shift the like terms on one side of the equation.

So, for solving the value of x we will shift the terms containing x and the constant on both sides of the equation.

So, shifting -12x from the right-hand side of the equation to the left-hand side of the equation,

We will get it as:

18x+12x = -4+16

30x=12

Now for solving the value of x we will shift x from the left side of the equation to the right side of the equation.

So, the value of x will be = 12/30 = 2/5

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The correct question may be:

What is the value of x

18x-16=-12x-4

Enter your answer in the box.

The expression for f(x) is:

f(x) = eˣ + x² + 9x

Given that f'''(x) = eˣ, f''(0) = 3, f'(0) = 10, we need to find f(x)

To find the function f(x), we will integrate the given derivative equations successively.

Given: f'''(x) = eˣ

Integrating f'''(x), we get:

f''(x) = ∫ eˣ dx = eˣ + C₁

Given: f''(0) = 3

Substituting x = 0 and f''(x) = 3:

f''(0) = e⁰ + C₁ = 1 + C₁ = 3

Solving for C₁, we find C₁ = 2.

Substituting the value of C₁ into the expression for f''(x):

f''(x) = eˣ + 2

Integrating f''(x), we get:

f'(x) = ∫ (eˣ + 2) dx = ∫ eˣ dx + ∫ 2 dx = eˣ + 2x + C₂

Given: f'(0) = 10

Substituting x = 0 and f'(x) = 10:

f'(0) = e⁰ + 2(0) + C₂ = 1 + C₂ = 10

Solving for C₂, we find C₂ = 9.

Substituting the value of C₂ into the expression for f'(x):

f'(x) = eˣ + 2x + 9

Integrating f'(x), we get:

f(x) = ∫ (eˣ + 2x + 9) dx = ∫ eˣ dx + ∫ 2x dx + ∫ 9 dx = eˣ + x² + 9x + C₃

The final expression for f(x) is:

f(x) = eˣ + x² + 9x + C₃, where C₃ is the constant of integration.

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Complete question =

Given that f'''(x) = eˣ, f''(0) = 3, f'(0) = 10, we need to find f(x)

The percent error in Jessica's calculation is 4.17%.

To calculate the percent error in Jessica's calculation, we can use the formula:

Percent Error = (|Measured Value - Actual Value| / Actual Value) * 100

Given that Jessica's measured value was 125 seconds and the actual value was 120 seconds, we can substitute these values into the formula:

Percent Error = (|125 - 120| / 120) * 100

Simplifying further:

Percent Error = (5 / 120) * 100

Percent Error = 0.0417 * 100

Percent Error = 4.17%

This means that Jessica's recorded time of 125 seconds differs from the actual time of 120 seconds by approximately 4.17% in relative terms. The positive sign indicates that Jessica's recorded time was greater than the actual time.

Percent error is a way to quantify the discrepancy between a measured value and the true value. It provides a measure of the accuracy of a measurement or calculation, allowing us to understand the degree of error or deviation involved.

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For a straight line graph, the point at which the line crosses the y axis is called the y intercept. From the information given, the line crosses the y axis at - 5. This means that the y intercept is - 5

We would write the equation in the slope intercept form whicg is expressed as

y = mx + c

Where m represents the slpoe

We would substitute x = 2, y = 3 and c = - 5 in the equation above to determine the slope, m. It becomes

3 = m * 2 - 5

3 = 2m - 5

3 + 5 = 2m

2m = 8

m = 8/2

m = 4

The equation would be

y = 4x - 5y interceptF

The equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.

The area of the rectangle is the product of its length and its breadth.

As it is given that the length of the rectangular frame is (2x+10), while the width of the rectangular frame is (2x+6). Also, it is mentioned that the area of the rectangular frame is 140 in².

Now we know the area is the product of length and breadth, therefore,

\(\rm \text{Area of rectangle} = length \times breadth\)

\(140 = (2x+10)(2x+6)\\\\140 = 4x^2 + 12x + 20x + 60\\\\0=-140+4x^2 + 12x + 20x + 60\\\\4x^2 + 32 x -80=0\)

Hence, the equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.

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Answer:

A.)  4x2 + 32x − 80 = 0

Step-by-step explanation:

Just took the test

Answer:

3.408 × 10-6 i think

Step-by-step explanation:

Answer:

Z= 31.6666666666666666

Step-by-step explanation:

x/5 - 4 = 2 1/3

x/5 = 6 1/3

x=6 1/3 times 5

x=31.66 repeated

Answer:

84.5 cubic meters

Step-by-step explanation:

Hello, I can help you with this.the solution is shown in the problem

let's remember el volume of a pyramid

\(Volume= \frac{1}{3}*B*h\)

where B is the area of the base of the pyramid, and h is its height.

Step one

all you have to do is put the values into the equation

Let

B=42.25 square meters

h=6 meters

\(Volume= \frac{1}{3}*B*h\\Volume= \frac{1}{3}*42.25\ m^{2} *6\ m\\Volume=\frac{1*42.25*6\ m^{3}}{3} \\Volume=84.5\ m^{3}\)

I really hope this helps you, have a great day.

Answer:

84.5 cubic meters

Step-by-step explanation:

Hello, I can help you with this.the solution is shown in the problem

let's remember el volume of a pyramid

where B is the area of the base of the pyramid, and h is its height.

Step one

all you have to do is put the values into the equation

Let

B=42.25 square meters

h=6 meters

Answer:

The total number of winners is 17.

Step-by-step explanation:

Let's assume that the number of winners is "x". Then the number of participants who did not win is "45 - x".

The amount of money awarded to the winners is 1000x rupees.

The amount of money awarded to the participants who did not win is 200(45 - x) rupees.

According to the question, the total amount of prize money distributed is 22600 rupees. So we can write:

\(\sf\implies 1000x + 200(45 - x) = 22600 \)

Simplifying this equation:

\(\sf\implies 1000x + 9000 - 200x = 22600 \)

\(\sf\implies 800x = 13600 \)

\(\sf\implies x = 17 \)

Therefore, the total number of winners is 17.

Hope it helps!

The required probability is P(A and C) is 0.2 which is represented in the tree diagram.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The given tree diagram represents an experiment consisting of two trials.

The tree diagram represents an experiment consisting of two trials. In this case, the probability of event A and event C occurring is represented by the intersection of branches A and C in the tree diagram.

This probability can be calculated by multiplying the probability of each individual event together.

As per the given question, we have

P(A) = 0.5

P(C|A) = 0.4

So, P(A and C) = 0.5 × 0.4 = 0.2

Thus, the required probability is P(A and C) is 0.2

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In match play, when the players agree to consider the hole tied after it has begun, the ruling is known as "halving the hole."

In match play, if the players agree to consider the hole tied after it has begun, the hole is deemed halved, and the players move on to the next hole without any penalty strokes. This is called "conceding the hole" and is a common practice in match play.

This means that both players receive half a point for the hole, and the match proceeds to the next hole.

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Answer: 300

Step-by-step explanation: 25 times 12 = 300. 20 times 12 = 240. 5 times 12 = 60. 60 + 240 = 300

Answer:

300

Step-by-step explanation:

25 times 12 = 300. 20 times 12 = 240. 5 times 12 = 60. 60 + 240 = 300

Answer:

88% of the coins are quarters.

To find out, you can convert the fraction 44/50 to a percentage by multiplying it by 100.

(44/50) * 100 = 88%.

The perimeter of the figure is equivalent to 8x + 8

The given diagram is a composite figure. The perimeter of the figure is the sum of all the sides.

Taking the sum of all the sides

Sum = 3x - 2 + (x + 6) + (x + 5) + x + (x + 2) + (x - 3)

Sum = (3x + x + x + x + x + x) - 2 + 6 + 5 + 2 - 3

Sum = 8x + 4 + 7 - 3

Sum = 8x + 8

Hence the sum of the perimeter of the figure is 8x + 8

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Answer:

C. 7.50 hrs

Step-by-step explanation:

Since it takes 90 mins to clean 11 windows, the rate that it takes the washer per window is \(\frac{90}{11}\) minutes. At this rate, if he were to clean 55 windows it would take him \(\frac{90}{11}(55) = 450\) minutes. This translates into 7.50 hrs.

The petrol cost for Anne's journey of 120km is $16.236

Her car has a fuel consumption of 8.2 litres per 100 km .

Therefore,

100 km = 8.2 litres

120 km = ?

cross multiply

volume(litres) = 8.2 × 120 / 100 = 984 / 100 = 9.84 litres

Therefore,

1 litres = 1.65 dollars

9.84 litres = ?

cross multiply

cost of fuel used = 1.65 × 9.84 / 1

cost of fuel used = $16.236

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Answer:

In 24 years there will be 140 foxes

Step-by-step explanation:

The line drawing tool is used to draw the equations Y=1+1.50X and Y= 18-1.25X and the intersection point is labeled.

To draw the lines and indicate the point of intersection, you can follow these steps:

1. Draw a coordinate system on a piece of paper or using a drawing software.

2. For line A, plot two points on the coordinate system using the equation Y = 1 + 1.50X. Choose any two X values and calculate the corresponding Y values using the equation.

3. Connect the two points with a straight line and label it as line A.

4. For line B, plot two points on the coordinate system using the equation Y = 18 - 1.25X. Choose any two X values and calculate the corresponding Y values using the equation.

5. Connect the two points with a straight line and label it as line B.

6. Find the point of intersection between line A and line B. This is the point where both equations are equal. You can calculate this point by solving the system of equations Y = 1 + 1.50X and Y = 18 - 1.25X simultaneously.

7. Once you find the X and Y values of the point of intersection, mark it on the coordinate system and label it as 'Equilibrium'.

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Answer:

6+3i

Step-by-step explanation:

4+2=6

-3i+6i=3i

6+3i

Answer:

6+3i

Step-by-step explanation:

just got it right besties

Answer:

the first answer is correct

Step-by-step explanation:

before we started we had not caught any fish

Answer:

I think a is correct bc the rest aren't true

hope this helped

Answer:

must sell atleast 26 T shirts

Step-by-step explanation:

First, let's create an expression.

x = # of t-shirts.

$10.99x - ($280 + $3.99x)

Now, let's set our expression equal to 0.

$10.99x - ($280 + $3.99x) = 0

Distribute the negative sign.

$10.99x - $280 - $3.99x = 0

Combine like terms.

$7x - $280 = 0

Add $280 to both sides.

$7x = $280

Divide both sides by $7

x = 40

The students would have to sell 40 t-shirts to break even.

Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

The fundamental presumptions of the binomial distribution are that each trial has only one possible outcome, that each trial has the same success probability, and that each trial is independent of the others or mutually exclusive.

The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.

Hence, Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).

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Answer:

height of person ≈ 6 ft

Step-by-step explanation:

using the tangent ratio in the right triangle.

let the height of the person be h , then

tan16° = \(\frac{h}{21}\) ( multiply both sides by 21 )

21 × tan16° = h , then

h ≈ 6 ft ( to the nearest whole number )

Answer:

2:5 is less than 7:15

Step-by-step explanation:

7:15 = 7/15 = .47 = .5

the other given ratios are,

9:15 = 3:5 = 3/5 = .6

2:5 = 2/5 = .4

3:5 =3/5 = .6

24:45 = 8:15 = 8/15 = .5

thus, the ratio which is less than 7:15 is 2:5