How to show the numbers 1/2 and 1/3 on the number line

The distance that the spring compresses is:

\(v\sqrt{m/k}\)

So, by  kinetic and elastic potential energy

Kinetic and Elastic Potential Energy

The kinetic energy of an object of mass m traveling at a speed v is:

\(K = 1/2 mv^{2}\)

The elastic potential energy of a spring of constant k that compresses a distance x is:

\(E = 1/2kx^{2}\)

The block of mass m is moving at a speed v when compresses a spring of constant k. The kinetic energy will eventually transform into elastic energy, but before that, both energies will be equal. It happens when:

\(1/2mv^{2} = 1/2kx^{2}\)

Simplifying:

\(mv^{2} = kx^{2}\)

Dividing by k:

\(x^{2} = mv^{2} / k\)

Taking square root:

\(x = \sqrt{mv^{2} /k\\\\\)

= v\(\sqrt{m/k}\)

The distance that the spring compresses is

\(v\sqrt{m/k}\)

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The Task objective chosen is: A Measuring Task

The Objective is: To investigate the fairness of a local athlete's track for runners starting on different lines.

To carry about the investigation, follow the steps given below.

Lastly, make a crossword puzzle that includes mathematical vocabulary in a clever manner.

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```Class IX```

*Mathematics Project work*

*Do any one*

1. *A Measuring Task*

To investigate your local athletes track to see whether it is worked fairly for runners who start on different lines.

2. *Design a crossword puzzle with mathematical terms*

To review mathematics vocabulary, to give the opportunity for creative expression in designing puzzles, to act as a means of motivating the study of a given unit and to given recreation .​

Answer: 3/8

Step-by-step explanation:

There is no effect between flipping a coin and chosing a number.

This situation is known as a independent event.

P(AnB) = P(A)*P(B)

The situation A = Heads or tails of money = 1/2

The situation B = 6/8

It can be calculated as below:

Probability = Desired / All Event

Desired || Numbers between 3 and 10 are : 4,5,6,7,8,9 = 6 pieces

All Event || Numbers between 1 and 10 are : 2,3,4,5,6,7,8,9 =8 pieces

Consequently product the fractions.

1/2 * 6/8 = 6/16 = 3/8

We can use the two-point form to find the equation of the line passing through the two given points:

y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)

where (x1, y1) = (1, 7) and (x2, y2) = (3, 3).

Substituting the values, we get:

y - 7 = ((3 - 7)/(3 - 1))(x - 1)

Simplifying the equation, we get:

y - 7 = (-2/2)(x - 1)

y - 7 = -x + 1

Adding 7 to both sides, we get:

y = -x + 8

Therefore, the equation of the line passing through the points (1, 7) and (3, 3) is y = -x + 8.

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To find the length of the segment between the given points, we can use the distance formula. The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
\[d = \sqrt{{(x_2 - x_1)^2 + (y_2 - y_1)^2}}\]

Let's apply this formula to the given points: $(2a, a-4)$ and $(4, -1)$.

The distance between these two points is $2\sqrt{10}$ units. So we have:
\[2\sqrt{10} = \sqrt{{(4 - 2a)^2 + (-1 - (a-4))^2}}\]

Simplifying the equation, we get:
\[4\sqrt{10} = \sqrt{{(4 - 2a)^2 + (-5 - a)^2}}\]

Squaring both sides of the equation, we have:
\[160 = (4 - 2a)^2 + (-5 - a)^2\]

Expanding the equation, we get:
\[160 = 16 - 16a + 4a^2 + 25 + 10a + a^2\]

Combining like terms, we have:
\[0 = 5a^2 - 6a + 1\]

Now, we can solve this quadratic equation for the possible values of $a$.

Factoring the equation, we have:
\[0 = (5a - 1)(a - 1)\]

Setting each factor equal to zero and solving for $a$, we get:

\[5a - 1 = 0 \quad \Rightarrow \quad a = \frac{1}{5}\]
\[a - 1 = 0 \quad \Rightarrow \quad a = 1\]

Therefore, the possible values for $a$ are $\frac{1}{5}$ and $1$. The product of these values is:
\[\left(\frac{1}{5}\right) \cdot 1 = \frac{1}{5}\]

So, the product of all possible values for $a$ is $\frac{1}{5}$.

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Answer:

Step-by-step explanation:

1) tan = opposite / adjacent

tan * adjacent = opposite

adjacent = opposite/tan

adjiacent = 60/1,600335 = 37.5

2) the two leg are congruent so the two angles are congruent

the sum of the inner angles of a triangle is 180 degrees

so

a = 45 degrees

b = 45 degrees

3) cos = adjacent/hypotenuse

adjacent = cos * hypotenuse

adjacent = 0,920505 * 45

adjacent = 41.4

The area of the trapezoid is 12 sqrt(39) square centimeters.

To find the area of a trapezoid, you need to use the formula:

Area = (a + b) * h / 2

where a and b are the lengths of the parallel sides, and h is the height or perpendicular distance between them.

In this case, we have three sides of the trapezoid given as 8 cm, 5 cm, and 16 cm. However, we do not know which sides are parallel, so we cannot directly calculate the area.

To find the parallel sides, we can use the fact that opposite sides of a trapezoid are equal in length. Since 5 cm is not equal to either 8 cm or 16 cm, we know that the 5 cm side is not parallel to either of the other two sides. Therefore, the parallel sides must be the 8 cm and 16 cm sides.

Next, we need to find the height or perpendicular distance between the parallel sides. To do this, we can draw a line segment from the 5 cm side to the line connecting the parallel sides. This line segment is perpendicular to both the 5 cm side and the line connecting the parallel sides. The length of this line segment is the height of the trapezoid.

To find the length of this line segment, we can use the Pythagorean theorem. The 5 cm side and the height form the two legs of a right triangle, and the length of the hypotenuse is the difference between the lengths of the parallel sides, which is 16 cm - 8 cm = 8 cm. Therefore, we have:

height^2 + 5^2 = 8^2

height^2 = 39

height = sqrt(39) cm

Now that we know the lengths of the parallel sides and the height, we can plug these values into the formula for the area:

Area = (8 cm + 16 cm) * sqrt(39) cm / 2

Area = 24 cm * sqrt(39) cm / 2

Area = 12 cm * sqrt(39) cm

Therefore, the area of the trapezoid is 12 sqrt(39) square centimeters.

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Complete Question

Find the area of the following trapezoids where three sides are 8 cm, 5 cm , 16 cm

Answer:

3 green apples and 7 red apples.

Step-by-step explanation:

1. Start with the ratio of green apples to red apples, which is 3 to 7.

2. Multiply 3 (the number of green apples) by any number to get a number that is divisible by 7 (the number of red apples).

3. In this case, multiplying 3 by 2 gives 6, which is divisible by 7.

4. Since 6 is divisible by 7, that means that the solution is 3 green apples and 7 red apples.

Answer:

It would take him 12 hours to drive 696 miles

Step-by-step explanation:

hope this helps!!

The length of the similar right triangles is x = 5 units

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔXYZ

The triangles are similar and corresponding sides of similar triangles are in the same ratio.

Now , the corresponding sides are

AB / XY = BC / YZ

where the length of the corresponding sides are:

x / 2.5 = 6 / 3

Multiply by 2.5 on both sides , we get

x = 2.5 x 2

x = 5 units

Hence , the similar triangles is solved and x = 5 units

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This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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Approximately 6.25% of the average difference in wages can be attributed to differences in work experience.

Regression estimates the return to experience for men, denoted as 'b,' to be 0.25. To understand the portion of the average difference in wages attributable to differences in work experience, we need to consider the data for both men and women. Let's assume that the average difference in wages between men and women is denoted as 'D.'

The average difference in wages between men and women can be decomposed into two components: one due to differences in work experience and another due to factors other than work experience (such as discrimination, education, industry, etc.). Let's denote the portion attributable to differences in work experience as 'P.'

We can express the average difference in wages as follows:

D = P + Q

where P represents the portion attributable to differences in work experience, and Q represents the portion due to other factors.

Given that the regression estimates the return to experience for men (b) as 0.25, we can calculate P by multiplying the average difference in work experience between men and women (W) by 'b':

P = b * W

The portion attributable to differences in work experience can be expressed as a percentage of the average difference in wages (D):

P% = (P / D) * 100

Substituting the value of P from the equation above, we get:

P% = (b * W / D) * 100

In this case, since the value of b is given as 0.25, we can calculate the percentage as:

P% = (0.25 * W / D) * 100

Therefore, the estimated portion of the average difference in wages attributable to differences in work experience is 6.25% when b = 0.25.

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When he made $1000 for the week, his 15% commission is;

It is known that he too $450 home for the week, then;

His new flat rate salary is $450 - $150 = $300

Answer:

4

Step-by-step explanation:

8.0,8.1,8.2,8.3...........

8÷2=4

It's actually 4.1 or by rounding off its 4.

We can prove this because 8÷2=4, so, 8.1÷2=4.1

Or 4.

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Answer:

42

Step-by-step explanation:

5 * 4 + (6 / [ 2 + 1 ] ) *11

5 * 4 +2 * 11

20 +2 * 11

20+ 22

42

Answer:

Step-by-step explanation:

5 x 4 + 6/3 x 11

20 + 2 x 11

20 + 22

42

Answer:

$20.97

Step-by-step explanation:

3 people, meaning to multiply each one by 3.

Total price of Hot Dogs= 9.00

Total price of Fries=7.47

Total price of Drinks=7.50

7.50 - 3= $4.50

9.00+7.47+4.50= $20.97

Answer:

6

Step-by-step explanation:

60 = 12+8 divided 2 times height

60 = 20/2 x H

60 = 10 x H

60/10 = h

6 = H

Answer:

C. Ferris wheel

Step-by-step explanation:

Circumference = pi x diameter

Take each of the entries from the diameter column and multiply by 3.14. They are all correct except for the Ferris wheel.

70.5 x 3.14 = 221.37

The required answer is the double declining-balance method is $9,840.

To calculate the depreciation expense for 2020 using the double declining-balance method, we first need to determine the asset's straight-line depreciation rate. This is calculated by subtracting the residual value from the cost of the asset and dividing by the asset's useful life:

Depreciation base = $30,000 - $3,000 = $27,000
Annual depreciation expense (straight-line) = Depreciation base / Useful life = $27,000 / 5 = $5,400

Next, we need to determine the double declining-balance rate, which is twice the straight-line rate. Therefore:
Double declining-balance rate = 2 x (1 / Useful life) = 2 x (1 / 5) = 0.40 or 40%
Now we can calculate the depreciation expense for 2020:
Depreciation expense (2020) = Book value (beginning of year) x Double declining-balance rate

The book value at the beginning of 2020 would be the cost of the asset minus accumulated depreciation for the first year:
Book value (beginning of 2020) = $30,000 - ($5,400 x 1) = $24,600
As a result, depreciation increases during the initial year of possession and decreases thereafter.

Therefore:

Depreciation expense (2020) = $24,600 x 0.40 = $9,840

So the amount of depreciation expense for 2020, the second year of the asset's life,

using the double declining-balance method is $9,840.

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Martha travels 8 miles per hour, which is the same as saying that she covers 8 miles in one hour.

We can express Martha's weekend bicycling information as a rate by dividing the distance traveled by the time taken. In this case, her rate would be:

\(\frac{12 miles}{1.5 hours} = $8 miles per hour\)

This tells us that Martha travels 8 miles for every hour that she spends bicycling.

We can express Martha's weekend bicycling information as a unit rate by dividing the distance traveled by the time taken and expressing the result in terms of one unit of time (usually one hour). In this case, her unit rate would be:

\($\frac{12 miles}{1.5 hour}. \frac{1 hour}{1} = \frac{8 miles}{1 hour}\)

This tells us that Martha travels 8 miles per hour, which is the same as saying that she covers 8 miles in one hour.

Expressing information as a rate or a unit rate allows us to compare different situations more easily. In this case, we could compare Martha's weekend bicycling rate with her weekday bicycling rate, or with the rates of other bicyclists, to see how they differ.

Therefore, Martha travels 8 miles per hour, which is the same as saying that she covers 8 miles in one hour.

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If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.

The quadratic formula includes the discriminant, which comes after the square root. The discriminant of a quadratic equation is important because it indicates the quantity and kind of solutions.  

The formula for the Discriminant of a Quadratic Equation ax²+bx +c = 0 is given by

Here we have

x² + 16x + c = 0 equation has only one real solution

Compare given equation with ax²+ bx + c = 0

=> a = 1, and b = 16  

As we know when an equation has only one real solution

then its Discriminant will be equal to zero

=> b² - 4ac = 0

By the above values,

=> 16² - 4(1)c = 0  

=> 256 - 4c = 0

=> 4c = 256

=> c = 256/4

=> c = 64

Therefore,

If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.

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∂z/∂s = -sin()cos()t9 + cos()sin()9st2 and ∂z/∂t = sin()cos()s - cos()sin()81t.

To find ∂z/∂s and ∂z/∂t, we use the chain rule of partial differentiation. Let's begin by finding ∂z/∂s:

∂z/∂s = (∂z/∂)(∂/∂s)[(st9) cos(s9t)]

We know that ∂z/∂ is cos()cos() - sin()sin(), and

(∂/∂s)[(st9) cos(s9t)] = t9 cos(s9t) + (st9) (-sin(s9t))(9t)

Substituting these values, we get:

∂z/∂s = [cos()cos() - sin()sin()] [t9 cos(s9t) - 9st2 sin(s9t)]

Simplifying the expression, we get:

∂z/∂s = -sin()cos()t9 + cos()sin()9st2

Similarly, we can find ∂z/∂t as follows:

∂z/∂t = (∂z/∂)(∂/∂t)[(st9) cos(s9t)]

Using the same values as before, we get:

∂z/∂t = [cos()cos() - sin()sin()] [(s) (-sin(s9t)) + (st9) (-9cos(s9t))(9)]

Simplifying the expression, we get:

∂z/∂t = sin()cos()s - cos()sin()81t

Therefore, ∂z/∂s = -sin()cos()t9 + cos()sin()9st2 and ∂z/∂t = sin()cos()s - cos()sin()81t.

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Answer: 13,36,-2,-2,pi

Step-by-step explanation:

You do exactly what it says for the rule to -6 to get your answer.

Budgeting for a household and a business both require setting financial goals, prioritizing expenses, and tracking income and expenses

Given that;

To find budgeting for a household be similar to budgeting for a business.

Since, Budgeting for a household and a business both require setting financial goals, prioritizing expenses, and tracking income and expenses.

Here,  In both cases, it's important to consider fixed and variable expenses, such as rent or mortgage payments, bills, food costs, and employee salaries.

And, Additionally, creating a contingency plan for unexpected expenses is essential for both households and businesses.

Hence, The main difference is that businesses may have more complex financial structures with investors or loans to consider, while households typically have simpler financial structures.

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To find the total distance of the hike, we can set up a proportion:

\(\[\frac{{\text{{Distance to first stop}}}}{{\text{{Total distance of the hike}}}} = \frac{{60}}{{100}}\]\)

Let's represent the total distance of the hike as "x" miles. The distance to the first stop is given as 12 miles:

\(\[\frac{{12}}{{x}} = \frac{{60}}{{100}}\]\)

To solve for "x," we can cross-multiply and solve for "x":

\(\[12 \times 100 = 60 \times x\]\)

\(\[1200 = 60x\]\)

Dividing both sides of the equation by 60, we get:

\(\[x = \frac{{1200}}{{60}} = 20\]\)

Therefore, the whole hike is 20 miles.

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Answer:

What do you need help with? :P

Step-by-step explanation:

Hav a gud day :3

The scores that separate the middle 60 percent from the extremes are none of the other alternatives are correct. Option D is correct.

To find the scores that separate the middle 60% from the extremes, we need to find the z-scores that correspond to the 20th and 80th percentiles, which will give us the values that separate the middle 60%.

Using a standard normal distribution table or calculator, we can find that the z-score that corresponds to the 20th percentile is -0.84, and the z-score that corresponds to the 80th percentile is 0.84.

We can then use the formula z = (x - mu) / sigma to convert these z-scores back to raw scores:

For the 20th percentile: -0.84 = (x - 32) / 3

x - 32 = -2.52

x = 29.48

For the 80th percentile: 0.84 = (x - 32) / 3

x - 32 = 2.52

x = 34.52

Therefore, the scores that separate the middle 60% from the extremes are approximately 29.48 and 34.52.

Hence, D. none of the other alternatives are correct is the correct option.

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