which expression is equivalent to​

Answer:

4%

Step-by-step explanation:

Actual length of wire = 5 cm

The measured length of wire = 5.2 cm

We need to find the percent error in the measurement of the length of wire. It can be calculated as follows :

\(\%=\dfrac{\text{measured length-actiual length}}{\text{actual length}}\times 100\\\\=\dfrac{5.2-5}{5}\times 100\\\\=4\%\)

So, the required percent error is 4%.

Answer:

60

Step-by-step explanation:

600*10%

The apparent weight of the rock when submerged in water is 70 N.

When an object is submerged in a fluid, it experiences an upward buoyant force due to the displacement of the fluid. This buoyant force reduces the apparent weight of the object.

To calculate the apparent weight of the rock when submerged in water, we need to determine the buoyant force acting on it. The buoyant force is equal to the weight of the fluid displaced by the rock.

The volume of the rock is given as 0.00312 m^3. This volume represents the volume of water displaced by the rock when submerged.

The weight of the fluid displaced is equal to the weight of the water with the same volume. The density of water is approximately 1000 kg/m^3, so the weight of the displaced water is:

Weight of displaced water = density × volume × acceleration due to gravity

                        = 1000 kg/m^3 × 0.00312 m^3 × 9.8 m/s^2

                        ≈ 30.816 N

Since the buoyant force is equal to the weight of the displaced water, the apparent weight of the rock when submerged in water is:

Apparent weight = Weight in air - Weight of displaced water

              = 100 N - 30.816 N

              = 69.184 N

Rounding to the nearest Newton, the apparent weight of the rock when submerged in water is 70 N.

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Answer:

They will be equal at the 4th visit both paying $200.

Step-by-step explanation:

Club A: 40+40x

Club B: 100+25x

Answer:

\( \sf \: x = 6\)

Step-by-step explanation:

Given equation,

\( \sf \rightarrow \: x + x + ( \frac{1}{6} )x = 13\)

Now the value of x will be,

\( \sf \rightarrow \: x + x + ( \frac{1}{6} )x = 13\)

\( \sf \rightarrow \: 2x + ( \frac{1}{6} )x = 13\)

\( \sf \rightarrow \: ( \frac{12}{6} )x + ( \frac{1}{6} )x = 13\)

\( \sf \rightarrow \: \frac{13}{ 6} x = 13\)

\( \sf \rightarrow \: 13x = 13 \times 6\)

\( \sf \rightarrow \: x = \frac{78}{13} \)

\( \sf \rightarrow \boxed{ \sf x = 6}\)

Hence, the value of x is 6.

The distance traveled during the time interval [0,5] is equal to 19/6.

The velocity at time t, v(t), can be found by integrating the acceleration function, a(t). Integrating 2t+1 with respect to t gives us v(t) = t^2 + t + C, where C is the constant of integration.

To find the value of C, we can use the initial velocity, v(0) = -12. Plugging in t = 0, we get -12 = 0^2 + 0 + C, which means C = -12.

Therefore, the velocity at time t is v(t) = t^2 + t - 12.

To find the distance traveled during the time interval [0,5], we need to integrate the absolute value of the velocity function from 0 to 5.

The distance traveled, d, is given by the integral of |v(t)| dt from 0 to 5. Evaluating this integral, we have:

d = ∫[0,5] |t^2 + t - 12| dt

To simplify this integral, we need to consider the different cases when the velocity function is positive or negative. The absolute value of v(t) is equal to v(t) when v(t) is greater than or equal to 0, and it is equal to -v(t) when v(t) is less than 0.

For the interval [0,5], the velocity function v(t) = t^2 + t - 12 is negative when t < -4 and positive when t > 3. Therefore, we need to split the integral into two parts:

d = ∫[-4,3] -(t^2 + t - 12) dt + ∫[3,5] (t^2 + t - 12) dt

Integrating each part separately, we have:

d = [-1/3 * t^3 - 1/2 * t^2 - 12t] from -4 to 3 + [1/3 * t^3 + 1/2 * t^2 - 12t] from 3 to 5

Evaluating these integrals, we get:

d = (-1/3 * 3^3 - 1/2 * 3^2 - 12 * 3) - (-1/3 * (-4)^3 - 1/2 * (-4)^2 - 12 * (-4)) + (1/3 * 5^3 + 1/2 * 5^2 - 12 * 5) - (1/3 * 3^3 + 1/2 * 3^2 - 12 * 3)

Simplifying further, we find:

d = -171/6 + 190/6

Combining like terms, the distance traveled during the time interval [0,5] is equal to 19/6.

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Rounding to the nearest tenth, the area of the hexagon is 244.3 square inches.

The area of a regular hexagon is calculated using the formula (3√3 / 2) × s^2, where s is the length of a hexagonal side. Given that we are talking about a regular hexagon, it is important to remember that all of the sides are the same length. The formula Area of the Hexagon = (3√3 / 2) × s^2, where's' is the length of the hexagonal side, can be used to determine the area of a regular hexagon when one of its sides is known.

All of the sides of the hexagon are the same length because it is a regular shape.

Therefore, each side has a length of 57 inches / 6 = 9.5 inches.

To find the area of the hexagon, we can use the formula:

Area = (3√3 / 2) × s^2

where s is  length of a side.

Substituting s = 9.5 inches, we get:

Area = (3√3 / 2) × (9.5 inches)^2

Area ≈ 244.3 square inches

Rounding to the nearest tenth, the area of the hexagon is 244.3 square inches.

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So the amount of gain that can be deferred under the installment sale method is $424,879.16.

Percent is a way of expressing a number as a fraction of 100. The word "percent" means "per hundred" in Latin. When a number is expressed as a percentage, it is usually accompanied by the "%" symbol. Percentages are commonly used in many areas of everyday life, such as finance, taxes, and statistics. They are often used to express changes or differences, such as percentage increases or decreases in prices or quantities, or the percentage of people who hold a certain opinion or belong to a certain group.

Here,

To calculate the gain that can be deferred under the installment sale method, we need to first calculate the total gain on the sale. The total gain is equal to the selling price minus the adjusted basis of the property, which is the cost minus the accumulated depreciation.

Selling price = $99,800 cash + $998,000 note = $1,097,800

Adjusted basis = $798,400 - $479,040 = $319,360

Total gain = $1,097,800 - $319,360 = $778,440

To calculate the gain that can be deferred, we need to determine the gross profit percentage. The gross profit percentage is equal to the total gain divided by the selling price:

Gross profit percentage = Total gain / Selling price = $778,440 / $1,097,800 ≈ 0.7097 or 70.97%

Now we can calculate the amount of gain that can be deferred using the formula:

Gain deferred = Gross profit percentage × Payments received

Since the note is due in two years, Skylar will receive half of the payments in 2022 and the other half in 2023. Therefore, the payments received in 2022 are:

$99,800 + ($998,000 / 2) = $598,800

Substituting into the formula, we get:

Gain deferred = 0.7097 × $598,800 = $424,879.16

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Answer:

1w

Step-by-step explanation:

I want points

The set of ordered pairs that does not represent a function is the first one.

{(3,1), (2,1), (1,2), (3,2)}

Remember that a function is a relation where each input is mapped into only one output.

So any set where you can see an input (the first value of the ordered pair)  appears twice and is mapped into different outputs, then the set does not represent a function.

The first set of ordered pairs:

{(3,1), (2,1), (1,2), (3,2)}

Notice that the input x = 3 is mapped into two different outputs y = 1, and y = 2.

Then it is not a function.

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Answer:

plz give the ques properly

The probability that three points chosen uniformly and independently on a circle fall on a semicircle is 1/2 or 50%.

The probability of three points chosen randomly and independently on a circle falling on a semicircle is 1/2, or 50%. This is because the probability of a point landing on either side of the semicircle is equal. The points are chosen on a circle, so each point has an equal probability of being on either side of the semicircle. Therefore, the probability of three points randomly chosen on a circle landing on a semicircle is 1/2 or 50%.

Let A, B, and C be the three points chosen on a circle.

The probability that A, B, and C fall on the semicircle is:

P(A on semicircle) x P(B on semicircle) x P(C on semicircle)

= (1/2) x (1/2) x (1/2)

= (1/2)^3

= 1/8

Therefore, the probability that three points chosen randomly and independently on a circle fall on a semicircle is 1/8 or 12.5%.

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The probability that three points chosen uniformly and independently on a circle fall on a semicircle is written as 1/8.

The term probability in math is defined as the chances of something materializing based upon the ratio of its number of outcomes to the number of outcomes of the whole sample space the event relies upon.

While we looking into the given question, here let us consider that A, B, and C be the three points chosen on a circle.

Then the probability that A, B, and C fall on the semicircle is calculated as,

=> P(A on semicircle) x P(B on semicircle) x P(C on semicircle)

Now, we have to apply the value of each probability, then we get

=> (1/2) x (1/2) x (1/2)

Therefore, the resulting value is

=> (1/2)³ = 1/8

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Answer:

57

Step-by-step explanation:

The scale factor is 8:24  or 1:3

The perimeter of the smaller triangle is 19 so the perimeter of the larger triangle is 3 times as large

19*3 = 57

Answer:

57 units

Step-by-step explanation:

ANG is 3 times the size of TRI. multiply TRI's perimeter by 3 to get ANG's perimeter

The volume of the rectangular prism is, \(\(105 in^3\)\).

What is the volume of rectangular prism?
The amount of three-dimensional space that an object takes up is its volume. Cubic units are used to measure volume. When calculating the volume of a rectangular prism, we multiply the prism's length, width, and height.

Rectangle prism volume = length x width x height.

The given rectangular prism has length 7, width 3 and height 5.

So, Volume = length x width x height = 7 x 3 x 5.

Volume = 105 cubic units.

Therefore, the volume of the given rectangular prism is 105 cubic units.

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Answer:

105 in

explanation:

did the same test.

Answer: 1.5km

Step-by-step explanation:

The pedestrian is walking 3 kilometers per hour, we want to know how many kilometers he would walk in o.5 hours, so 0.5 is the same as 1/2, and 1/2 of an hour is 30 minutes, so if you split an hour in half, you have to do the same with the kilometers, so 3 divided by 2, gives us 1.5, so the answer would be 1.5km

Speed is measured as the ratio of distance to the time in which the distance was covered.

The distance the pedestrian walks in 1 hour and 30 minutes is 4.5 km.

Speed is the rate of change of position of an object in any direction.

It is measured as the ratio of distance to the time in which the distance was covered.

We have,

The pedestrian Speed = 3 km/h

We need to find the distance if the pedestrian walks for 1 hour and 30 minutes.

Speed = Distance / Time

Distance = Speed x Time

[ 1 hour = 60 minutes

30 minutes = 0.5 hours

1 hour and 30 minutes = 1 hour + 0.50 hour = 1.5 hour ]

Distance = 3 km/hour x 1.50 hours

Distance = 4.5 km

Thus the distance the pedestrian walks in 1 hour and 3o minutes is 4.5 km.

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The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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The distance between the two ships is 3.07 miles (approx). The given polar coordinates are converted into rectangular coordinates with the help of sine and cosine functions.

Given data:

The location of two ships from mays landing lighthouse, given in polar coordinates, are 3 mi, 170 and 5 mi, 150.

.To find:Distance between the ships

Formula used:

Distance between the ships = \(sqrt(d1^2 + d2^2 - 2*d1*d2*cos(theta1 - theta2)).\)

where d1 = 3 mi, theta1 = 170°, d2 = 5 mi, theta2 = 150°.

Calculation:Squaring and adding the given distances,sqrt(3² + 5² - 2*3*5*cos(170° - 150°))

:Distance between the ships is 3.07 miles (approx).

:Thus, the distance between the two ships is 3.07 miles (approx). The given polar coordinates are converted into rectangular coordinates with the help of sine and cosine functions. The formula used for finding the distance between the two ships is \(sqrt(d1^2 + d2^2 - 2*d1*d2*cos(theta1 - theta2)).\)

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Answer:

(a) x<=2

(b) x>-2

(c) x>=10

(d) x<-20

The value of the numerical expression 2 - [(2 + 10 × -1) / 2 + 1] will be 5.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The numerical expression is given below.

⇒ 2 - [(2 + 10 × -1) / 2 + 1]

Simplify the expression, then we have

⇒ 2 - [(2 + 10 × -1) / 2 + 1]

⇒ 2 - [(2 - 10) / 2 + 1]

⇒ 2 - [(-8 / 2) + 1]

⇒ 2 - (-4 + 1)

⇒ 2 - (-3)

⇒ 2 + 3

⇒ 5

The value of the numerical expression 2 - [(2 + 10 × -1) / 2 + 1] will be 5.

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Answer: 1: x = 2y - 1 This equation shows that the value of x is always 2 times the value of y minus 1.

2: y = 3x + 3 This equation shows that the value of y is always 3 times the value of x plus 3.

3: y = (x/4) - 1 This equation shows that the value of y is always the value of x divided by 4 minus 1.

4: y = x-5 This equation shows that the value of y is always the value of x minus 5.

Answer: 714 and 715

Step-by-step explanation:

In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime factors of each integer are equal: 714 = 2 × 3 × 7 × 17, 715 = 5 × 11 × 13, 2 + 3 + 7 + 17 = 5 + 11 + 13 = 29.

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a. The area of the family room is 162 ft².

b. 24 tiles will be needed to cover the floor.

c. Mr. Dieter will have to buy 2 boxes to tile the family room.

The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are thought to be sufficiently described by the four basic operations, also referred to as "arithmetic operations." The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.

a. There are two different shapes of which one is rectangle and other is triangle.

So,

⇒ Area of rectangle = length x width

⇒ Area of rectangle = 16 x 8

⇒ Area of rectangle = 128 ft²

Also,

⇒ Area of first triangle = \(\frac{1}{2}\) x base x height

⇒ Area of first triangle = \(\frac{1}{2}\) x 4 x 3

⇒ Area of first triangle = 6 ft²

Similarly,

⇒ Area of first triangle = \(\frac{1}{2}\) x base x height

⇒ Area of first triangle = \(\frac{1}{2}\) x 8 x 7

⇒ Area of first triangle = 28 ft²

On adding the three areas, we get

⇒ Area of family room = 128 + 6 + 28

⇒ Area of family room = 162 ft²

b. We will convert the area into inches.

We know that 1 feet = 12 inches.

So, using the multiplication, we get

162 feet = 162 * 12 in²

162 feet = 1944 in²

Now,

⇒ Area of tile = 9 * 9

⇒ Area of tile = 81 in²

So,

⇒ Number of tiles = \(\frac{1944}{81}\)

⇒ Number of tiles = 24

c. Since, tiles are sold in boxes of 12 so, using the division operation, we get

⇒ Number of boxes needed = \(\frac{24}{12}\)

⇒ Number of boxes needed = 2

Hence, the required solution has been obtained.

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Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

The string and the perimeter are not equal, so it is not enough to string light to outline the window light.

Given that,

We are to determine if 6 yards is enough t to go around the perimeter of the window

The length is not given, so we have to determine the length from the area

Area of a rectangle = length x breadth

19.24 = 3.5 x length

length = 5.49 feet

Perimeter = 2 x ( length + breadth )

2 x (5.49 + 3.5) = 17.98 feet

We need to convert the string to foot

1 yard = 3 foot

6 x 3 = 18 foot

The string and the perimeter are not equal, so it is not enough to string light to outline the window light.

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