How do I solve my problem?

The magnitude of the normal( vertical) element is = 48.5 pounds

The magnitude of the element of the force parallel to the ramp = 12.09 pounds

The term" magnitude" refers to an object's topmost size and direction. Scalar and vector amounts both use magnitude as a common factor. We're apprehensive that scalar amounts are those that have just magnitude by description. Those amounts with both magnitude and direction are considered vector amounts.

A force is an effect that changes, or accelerates, the haste of a mass- moving object( similar as one that's travelling from a state of rest). It's a vector quantity since it can be a drive or a pull and always has magnitude and direction. It's denoted by the letter F and is measured in newtons( N), the SI unit of force.

According to question,

Magnitude of normal element = X/ 50 = Cos14

= 48.5 pounds

Magnitude of parallel element = Y/ 50 = Sin10

= 12.09 pounds

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a) The angular velocity = 0.4π rad/s b) The linear velocity of the hamster = 4π cm/s.

Linear velocity is the rate of change of an object's position with respect to time. It measures how fast an object is moving in a straight line, and is often expressed in units of distance per time, such as meters per second or kilometers per hour.

a) The angular velocity of the wheel can be calculated as follows:

Angular velocity = (2π * number of revolutions) / time

Here, the wheel completes one revolution in 5 seconds, so the number of revolutions is 1 and the time is 5 seconds. Therefore,

Angular velocity = (2π * 1) / 5

Angular velocity = 0.4π rad/s (or approximately 1.26 rad/s)

b) The linear velocity of the hamster can be calculated as follows:

Linear velocity = radius * angular velocity

Here, the radius of the wheel is 10 cm, and the angular velocity we found in part (a) is 0.4π rad/s. Therefore,

Linear velocity = 10 cm * 0.4π rad/s

Linear velocity = 4π cm/s (or approximately 12.57 cm/s)

So the hamster is running at a linear velocity of approximately 12.57 cm/s.

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Therefore, the reference angle of 7π/4 is 3π/4, and tan 0 = 1.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, especially right triangles. It involves the study of trigonometric functions such as sine, cosine, tangent, and their inverses, as well as their applications in various fields such as physics, engineering, and navigation. Trigonometry is an important tool for solving problems involving angles, distances, and heights, among others.

Here,

The reference angle for an angle θ is the positive acute angle formed by the terminal side of θ and the x-axis.

To find the reference angle for 7π/4, we can subtract π from it since the angle is in the fourth quadrant.

Reference angle = 7π/4 - π

= 3π/4

To find tan 0, we need to use the tangent function:

tan θ = opposite/adjacent

Since we don't know the sides of the triangle, we need to use the reference angle to find the ratio.

The reference angle of 3π/4 is in the second quadrant, where x is negative and y is positive. We can draw a triangle with sides of length 1, 1, and √2, where the hypotenuse is the line with angle 3π/4.

Then, tan(3π/4) = opposite/adjacent

= 1/-1

= -1

So, tan 0 = tan (7π/4)

= tan (3π/4 + π)

= -tan(3π/4)

= -(-1)

= 1.

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Is the graph increasing, decreasing, or constant: C. Constant.

In Mathematics and Geometry, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

By critically observing the graph shown above, we can reasonably infer and logically deduce that the graph is constant because it assumes only one y-value, which is represented by this equation y = 3.

In conclusion, the above is constant, rather than increasing or decreasing.

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The only equations n + 6 = 12 and 4 • n = 24 have n = 6 as a solution.

An equation is a collection of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division that are balanced by the equal sign. The equation's right-hand side (RHS) is on the right, and its left-hand side (LHS) is on the left.

To check if a given equation has n = 6 as a solution, we simply substitute n = 6 into the equation and see if it is true.

2 + n = 6 : 2 + 6 = 8, not true for n = 6.

n + 6 = 12 : 6 + 6 = 12, true for n = 6.

4 • n = 24 : 4 • 6 = 24, true for n = 6.

n • 3 = 2 : 6 • 3 = 18, not true for n = 6.

Therefore, only the equations n + 6 = 12 and 4 • n = 24 have n = 6 as a solution.

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we can place 10 marbles with a radius of 1 1/2 inches in a box that is 5” by 5” by 6”.

How to solve the question?

To calculate the maximum number of marbles that can be placed in the given box, we need to first determine the volume of the box and the volume of a single marble.

The volume of the box is calculated by multiplying its three dimensions, which gives us:

5 x 5 x 6 = 150 cubic inches

The volume of a marble can be calculated using the formula for the volume of a sphere:

(4/3) x π x r³

where r is the radius of the marble. Since the radius of the marble is given as 1 1/2 inches, we convert it to a decimal form by adding 1 to 1/2, which gives us a radius of 1.5 inches. Substituting this value into the formula, we get:

(4/3) x π x 1.5³ ≈ 14.14 cubic inches

Now, we divide the volume of the box by the volume of a single marble to find the maximum number of marbles that can be placed in the box:

150 ÷ 14.14 ≈ 10.61

Since we cannot have a fraction of a marble, we round down to the nearest whole number, which gives us a maximum of 10 marbles that can be placed in the box.

Therefore, we can place 10 marbles with a radius of 1 1/2 inches in a box that is 5” by 5” by 6”.

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The shaded area covers around 0.8664 square feet of space.

The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.

Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.

Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:

0.9332 - 0.0668 = 0.8664

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The surface soil of the entire garden within the fencing that needs to be turned prior to planting is approximately 176.625 square feet.

Radius is a mathematical term that refers to the distance from the center of a circle, sphere, or other curved object to any point on its circumference or surface. It is typically denoted by the letter "r".

Let's call the radius of the circular garden "r". We know that the circumference of the garden (the length of the fence) is 47.1 feet, so we can set up the equation:

2πr = 47.1

Simplifying this equation by dividing both sides by 2π, we get:

r = 47.1/(2π)

Using 3.14 as a substitute for π, we can calculate:

r ≈ 7.5 feet

Now that we know the radius of the garden, we can calculate the area of the garden by using the formula for the area of a circle:

A = πr²

A = 3.14 * 7.5²

A ≈ 176.625 square feet

Therefore, the surface soil of the entire garden within the fencing that needs to be turned prior to planting is approximately 176.625 square feet.

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Answer:

18gall

Step-by-step explanation:

Answer:

40 cm²

Step-by-step explanation:

you have to multiply the top of the triangle by the base(40) which is 80 then you divide by two since it's a triangle then you get 40 again since your finding the area you have to put the 2 above the cm

The law of demand applies during online sales of shoes; that is when consumers rush to buy products at 50% discount.​

In Mathematics and Economics, the law of demand can be defined as an economic theory which states that there exist a negative relationship between the price of a product (good) and the quantity of the product (good) that is being demanded by consumers.

This ultimately implies that, holding all the other factors constant, there would be a significant decrease (fall or decline) in the demand for a product (good) and service when the price of a product (good) and service in the market increases (rises), and vice-versa in accordance with the law of demand.

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Complete Question:

The law of ___________applies during online sales of shoes; that is when consumers rush to buy products at 50% discount​

Answer:

y = 0.028t + 230,000 Step-by-step explanation: We know t = number of years since the start of the study y = be the city's population Each year the population

Step-by-step explanation:

Answer:

x and y are the variables.

Step-by-step explanation:

The flow chart is complete and the answers are given below.

Those figures that have same shape and size are called Congruent Figures.

The flow diagram will be completed as follows

∠2 ≅ ∠4 (  vertical angle theorem )

∠1   ≅  ∠2  ( Given )

∠1  ≅ ∠ 3  ( Vertical Angle Theorem)

∠3   ≅  ∠4  ( Transitive Property of congruence)

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After solving the given expression 2 - 0.4 ÷ 0.2 the resultant answer is an integer which is 0.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers.

The inverse additives of the equivalent positive numbers are the negative numbers.

The boldface Z is a common mathematical symbol for the set of integers.

Numbers that are negative: -1, -2, -3, -4, -5, and so on indefinitely.

Non-negative integers include 0 and all whole numbers that are positive, such as 6, 7, 8, 9, 10, and so forth.

Positive integers include 1, 2, 3, 4, 5, and on indefinitely.

So, we have the expression:

= 2 - 0.4 ÷ 0.2

Now, evaluate using the BODMAS rule as follows:

= 2 - 0.4 ÷ 0.2

= 2 - 2

= 0

Therefore, after solving the given expression 2 - 0.4 ÷ 0.2 the resultant answer is an integer which is 0.

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Answer:

-5

Step-by-step explanation:

subtract 25 by 25 and do it to the other side than the last thing to do is just divided 15 by -3 and we get -5.

PLS GIVE BRAINLIST
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Answer:

-3x=40-25

resta los términos

-3x=15

multiplica ambos lados

3x( -1/3)=15 (-1/3)

3x(-1/3)=-5

x=-5

Answer:

x = 0, x = -2

Step-by-step explanation:

We are given that the two fractions are equal. Similarly to proportions, we can multiply the "means" and "extremes," and then set them equal to each other. For example,

[tex]\frac{a}{b} = \frac{c}{d} =\\ad=cd[/tex]

Let's do this with the given algebraic fractions.

[tex]\frac{2x}{2x+4} = \frac{3x}{x+2} =\\ 2x(x+2) = 3x(2x+4) =\\2x^2+4x=6x^2+12x\\[/tex]

Now that we've simplified the products, let's operate on the like terms.

[tex]2x^2+4x=6x^2+12x=\\4x^2+8x = 0[/tex]

Take these two terms and factor out their greatest common factor.

[tex]4x^2+8x= 0 =\\4x(x+2) = 0[/tex]

When two things are being multiplied, and the product is zero, it must mean that at least one of the factors equals zero (since zero times any number equals zero). Let's set each factor equal to zero.

[tex]4x = 0 =\\x = 0[/tex]

So, one of our answers is x = 0.

[tex]x+2=0 =\\x = -2[/tex]

Our other answer is x = -2.

So, the answer is x = 0 and x = -2.

Answer:

-3x² +7x - 18

Step-by-step explanation:

Subtraction of expression:

   Multiply each term of 5x² - x + 7 by (-1)

2x² + 6x - 11 - (5x² - x + 7) = 2x² + 6x - 11 - 5x² + x - 7

Combine like terms. Like terms have same variable with same exponent.

2x² and (-5x²) are like terms. 2x² - 5x² = -3x²

6x and x are like terms. 6x + x = 7x

-11 and (-7) are constants. -11 - 7= -18

                                         = 2x² - 5x² + 6x + x - 11 - 7

                                         = -3x² + 7x - 18

The value of cos(7π/6) = -√3/2

Explain values

Values are principles or beliefs that guide our behavior and decision-making. They are deeply ingrained in our personalities and are shaped by our upbringing, culture, and experiences. Values can be ethical, moral, social, or personal and influence how we prioritize our goals and interact with others. Understanding our own values can help us make better choices, build stronger relationships, and lead a more fulfilling life.

According to the given information

The cosine of π/6 is √3/2, so the cosine of 7π/6 is:

cos(7π/6) = -cos(π/6) = -√3/2

Therefore, cos(7π/6) = -√3/2.

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Answer:

-√3/2

Steps:

Rewrite the angle as a sum or difference with its reference angle:cos ([tex]\pi[/tex] + [tex]\frac{\pi }{6}[/tex])

Simplify the expression using the general reduction formula: -([tex]\frac{\pi }{6}[/tex])

Evaluate the expression: -√3/2

Answer:

1. √6/2

2. (√35-3√7)/2

3.  6√5+√10

4.  3^√22

Step-by-step explanation:

1. Simplify 6/( square root of 2). 6√2 6 2. Step 1. Multiply 6√2 6 2 by √2√2 2 2 . 6√2⋅√2√2 6 2 ⋅ 2 2. Step 2. Combine and simplify the denominator.

2. To simplify √7/√5+3, we need to rationalize the denominator by multiplying both the numerator and denominator by √5-3. This gives us (√7)(√5-3)/(√5+3)(√5-3), which simplifies to (√35-3√7)/2.

3. We can simplify √5(6+√2) by distributing the √5, which gives us 6√5+√10.

4. 3^√6•3^√16 can be simplified by using the rule that a^b • a^c = a^(b+c). This gives us 3^√22.

Step-by-step explanation:

From 1860 to 2018 is  158 years

 Use compounding formula

$ 28.95    =   $ 1   ( 1 +i) ^158       where i is decimal inflation rate %

[tex]\sqrt[158]{28.95}[/tex]  = 1 + i

i = .0215       = 2.15 %

The formula for calculating the balance of an account with continuous compounding is given by A = Pe^(rt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), t is the time in years, and e is the mathematical constant approximately equal to 2.71828.

In this case, the initial principal balance P is $3600, the annual interest rate r is 8% or 0.08 as a decimal, and the time t is 3 years. Plugging these values into the formula gives us:

A = 3600 * e^(0.08 * 3)

Evaluating this expression gives us a final amount of approximately $4293.25 in the account after three years.

Answer:

Ten times greater

Step-by-step explanation:

700 x 10 = 7000

Answer:

it will be ten times greater

Step-by-step explanation:

Answer:

3/6, 4/8, 5/10, 6/12, 7/14, 8/16, 9/18, 10/20, etc...

Step-by-step explanation:

The left digit it always half of the one on the right, increasing by one every time.

1/2 ===> 2/4 ===> 3/6 ===> 4/8...

An equation of the trend line in the scatter plot is equal to y = -4x/9 + 9.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 9)/(9 - 0)

Slope (m) = -4/9

At data point (0, 9) and a slope of -4/9, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 9 = -4/9(x - 0)  

y - 9 = -4x/9

y = -4x/9 + 9

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Answer: There are a total of 6 x 6 = 36 possible outcomes when rolling a pair of dice. We can count the number of outcomes where the sum of the dice is odd or a multiple of 3.

For the sum to be odd, we can have:

A 1 on one die and an even number on the other, or

A 3 on one die and an even number on the other, or

A 5 on one die and an even number on the other, or

A 2 on one die and an odd number on the other, or

A 4 on one die and an odd number on the other, or

A 6 on one die and an odd number on the other.

There are a total of 18 outcomes that satisfy this condition.

For the sum to be a multiple of 3, we can have:

A 1 on one die and a 2 on the other, or

A 1 on one die and a 5 on the other, or

A 2 on one die and a 1 on the other, or

A 2 on one die and a 4 on the other, or

A 3 on one die and a 3 on the other, or

A 4 on one die and a 2 on the other, or

A 4 on one die and a 5 on the other, or

A 5 on one die and a 1 on the other, or

A 5 on one die and a 4 on the other, or

A 6 on one die and a 3 on the other.

There are a total of 10 outcomes that satisfy this condition.

However, we have counted twice the outcomes that satisfy both conditions (i.e., the outcomes where the sum is both odd and a multiple of 3). There are 5 such outcomes: (1,2), (1,5), (5,1), (5,4), and (4,5).

Therefore, the total number of outcomes where the sum of the pair of dice is odd or a multiple of 3 is 18 + 10 - 5 = 23.

The probability of getting one of these outcomes is therefore 23/36.

Step-by-step explanation:

Answer: 46 ft by 92 ft

Step-by-step explanation:

The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.

Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.

From the label, we see that the serving size contains 3.5g of saturated fat.

To calculate the %DV for saturated fat, we use the equation:

%DV = (amount of nutrient per serving / DV) x 100%

Plugging in the values for saturated fat, we get:

%DV = (3.5g / 19g) x 100%

%DV = 0.1842 x 100%

%DV ≈ 18%

Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

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