a class has a ratio of boys to girls of 3:4 for each statement below

The power dissipated by the heater is 1260 watts (W).

What is a polynomial?

A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.

Given:

Current (I) = 10.5 A

Potential Difference (V) = 120 V

Unknown:

Power (P) = ?

The formula to calculate the power is:

P = VI

Substituting the given values:

P = 120 V × 10.5 A

P = 1260 W

It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:

P = 1260 W (rounded to three significant digits).

Therefore, the power dissipated by the heater is 1260 watts (W).

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Answer:

Step-by-step explanation:

It will take you 8 hours to ski a distance of 24 miles at a speed of 6 miles per 30 minutes. This is because you will have to travel the 24 miles at a rate of 6 miles every 30 minutes, so you will need to travel for 4 hours at this rate to cover the full distance. Thus, it will take you 8 hours to ski the full 24 miles at a rate of 6 miles per 30 minutes.

Answer:

120 minutes / 2 hours

Step-by-step explanation:

time = distance / velocity

[tex]time = \frac{24}{(6/30)} \\time = 120 minutes[/tex]

The Fourier series for f(x) is f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...].

The square wave function can be defined as:

f(x) = {1 -π ≤ x < 0

-1 0 ≤ x < π

To find the Fourier series for this function, we first need to determine the coefficients a_n and b_n.

a_n = (1/π) ∫_0^π f(x) cos(nx) dx

= (1/π) ∫_0^π (-1) cos(nx) dx + (1/π) ∫_(-π)^0 cos(nx) dx

= (2/π) ∫_0^π cos(nx) dx

= (2/π) [sin(nπ) - sin(0)]

= 0

b_n = (1/π) ∫_0^π f(x) sin(nx) dx

= (1/π) ∫_0^π (-1) sin(nx) dx + (1/π) ∫_(-π)^0 sin(nx) dx

= -(2/π) ∫_0^π sin(nx) dx

= -(2/π) [cos(nπ) - cos(0)]

= (2/π) [1 - (-1)^n]

Therefore, the Fourier series for f(x) is:

f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...]

To find the first three Fourier approximations, we truncate this series at the third term.

F_1(x) = -(4/π) sin(x)

F_2(x) = (4/π) sin(x) + (4/3π) sin(3x)

F_3(x) = (4/π) sin(x) + (4/3π) sin(3x) - (4/5π) sin(5x)

These are the first three Fourier approximations of the square wave function f(x). The more terms we include in the Fourier series, the closer the approximations will be to the original function.

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The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x))​ is 1

Given that

f(x) = 3 - 2x

Rewrite as

g(x) = -x² + x + 1

Express as vertex form

g(x) = -(x - 0.5)² + 1.25

Express as equation and swap x & y

x = -(y - 0.5)² + 1.25

Make y the subject

y = 0.5 + √(1.25 - x)

So, the inverse is

g⁻¹(x) = 0.5 + √(1.25 - x)

Here, we have

f(g(x)) = g(f(x))​

This means that

f(g(x)) = 3 - 2(-x² + x + 1)

g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1

Using a graphing tool, we have

f(g(x)) = g(f(x))​ when x = 1

Hence, the value of x is 1

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Complete question

f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers

Find the inverse of G and the value for x for which f(g(x)) = g(f(x))​.

Step-by-step explanation:

There are 8 fluid ounces in a cup....

   divide the number of ounces by 8 to find the number of cups

# ounces /  8 ounces/cup    =    cups

Answer: 25

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

New width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

The area of the tennis court is given by:

A = lw

where l is the length of the court and w is the width of the court.

Substituting the given values, we have:

[tex]$$260.7569 = l \cdot 10.97$$[/tex]

Solving for l, we get:

[tex]$l = \frac{260.7569}{10.97} \approx 23.76 \text{ m}$$[/tex]

To find the area of the court without the white bands, we need to subtract the areas of the two white bands from the total area. Since the white bands are on the top and bottom, we need to subtract twice the product of the width of the court and the width of the white band. The width of the white band is not given, but we know that the width of the court will be reduced by 25%, so the new width of the court will be:

w' = w - 0.25w = 0.75w

Substituting the given values, we have:

[tex]$$\begin{aligned}A' &= lw' - 2(0.75w)(l) \ &= l(0.75w) - 1.5wl \ &= 0.5625lw\end{aligned}$$[/tex]

where A' is the new area of the court without the white bands. Substituting the values of l and w that we found earlier, we have:

[tex]$$A' = 0.5625 \cdot 23.76 \cdot 10.97 \approx 146.17 \text{ m}^2$$[/tex]

Therefore, the new area of the court is reduced by 25%.

To find out if the width of the land is also reduced by 25%, we need to compare the original width w with the new width w'. We have:

[tex]$w' = 0.75w$$[/tex]

Dividing both sides by w, we get:

[tex]$\frac{w'}{w} = 0.75$$[/tex]

This means that the new width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

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Answer:

Solution: Given, the equation is x3 + 6x2 - 9x - 54. We have to find the real zeroes of the given equation. Therefore, the roots of the equation are +3, -3 and -6.

Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:[tex]\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\][/tex] Multiplying the equation by the least common multiple of the denominators, we get:[tex]\[16 + 8 = 2x\][/tex] Simplifying, we get:[tex]\[2x = 24\][/tex]Dividing both sides by 2, we get:[tex]\[x = 12\][/tex]Therefore, it takes Cindy 12 hours to rake the yard alone.

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Answer: 1.2 miles

Step-by-step explanation:

1 hour = 60 min

60 x 0.02 = 1.2         1 minute and 20 seconds has elapsed

60 miles/ every 60 minutes or 1 mile a minute

1 x 1.2 = 1.2

she has traveled 1.2 miles

Answer: The answer is 120 mph (miles per hour)

Step-by-step explanation:

The one thing you need to do is to figure out how many mph did Ella drive for 2 hours.

So, you need to do 60 x 2, and you will get the answer 120.

And there's your answer!

The resultant value of the given expression 4(x²+3)-2y is 157 respectively.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra.

Here, we refer to these letters as variables.

An expression is a group of words with operators between them.

The equation is the union of two expressions joined by the symbol "equal to" (=).

For instance, 3x-8. Ex: 3x-8 = 16.

So, the value would be:

4(x²+3)-2y

Insert values as follows:

=4((-6)²+3)-2(-1/2)

=4(36+3)+1=157

Therefore, the resultant value of the given expression 4(x²+3)-2y is 157 respectively.

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Complete question:

What is the value of this expression when x= -6 and y= -1/2? 4(x2+3)-2y

The given third-order linear equation is (t - 2t^2)y' - 4y'' = -2t with y(3) = -2, y'(3) = 2, y''(3) = -3.

We can write this equation as a system of first-order linear equations with initial values by introducing three new variables x_1, x_2, and x_3 such that:

x_1 = y

x_2 = y'

x_3 = y''

with initial values x_1(3) = -2, x_2(3) = 2, x_3(3) = -3.

The resulting system of equations is:

x_1' = x_2

x_2' = x_3

x_3' = (2t^2 - t)x_2 - 4x_3 + 2t

This system can be solved numerically for the unknown functions x_1, x_2, and x_3 with the initial conditions given.

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The two remaining angles are 58°, and the length of the third side of the triangle is 6.5 inch.

In order to determine the other two angles of each triangle as well as the length of the third side, we need to use the Cosine Rule. According to the Cosine Rule, for any triangle with sides of length a, b, and c, and angles of A, B, and C, the following equation holds:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

For the first triangle, we are given that the side of length 5 is adjacent to an angle of 61°. Therefore, a = 5, C = 61°. Using the information provided, we can also determine that b = 4.8. Substituting these values into the Cosine Rule equation, we get:

[tex]c^2 = (5)^2 + (4.8)^2 - 2(5)(4.8) cos(61°)[/tex]

We can solve this equation to get c = 6.5. Therefore, the length of the third side in the first triangle is 6.5. Additionally, we can use the Triangle Angle Sum theorem to determine the other two angles. According to this theorem, the sum of the three angles of a triangle is 180°. Therefore, for the first triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.

For the second triangle, we use the same process, but with the given side lengths reversed. That is, we set a = 4.8, b = 5, and C = 61°. Again, substituting these values into the Cosine Rule equation, we get:

[tex]c^2 = (4.8)^2 + (5)^2 - 2(4.8)(5) cos(61°)[/tex]

We can solve this equation to get c = 6.5. Therefore, the length of the third side in the second triangle is also 6.5. We can use the Triangle Angle Sum theorem again to determine the other two angles. Again, for the second triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.

In conclusion, for each triangle, the two remaining angles are 58°, and the length of the third side is 6.5 inch.

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Answer:

$63 more in tax

Step-by-step explanation:

Takis is 5.25 in tax  

PlayStation is 68.25

well, we know the tax is 10.5% so let's get them for both.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10.5\% of 49.99}}{\left( \cfrac{10.5}{100} \right)49.99} ~~ \approx ~~ 5.25[/tex]

[tex]\stackrel{\textit{10.5\% of 649.99}}{\left( \cfrac{10.5}{100} \right)649.99} ~~ \approx ~~ 68.25\hspace{9em}\underset{ \textit{taxes' difference} }{\stackrel{ 68.25~~ - ~~5.25 }{\approx\text{\LARGE 63}}}[/tex]

Answer:

f(x) = (5/6)x - (1/4)

f(-8) = (5/6)(-8) - (1/4)

f(-8) = (5/3)(-4) - (1/4)

f(-8) = (-20/3) - (1/4)

f(-8) = (-80-3)/12

f(-8) = -83/12

If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.

To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.

Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:

30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches

The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.

The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.

Now, we can calculate the volume of the box by multiplying its length, width, and height:

Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.

In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.

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The value of m∠B is 212 - 24x.

The totality of the angles in a quadrilateral is always amount to 360°. This is a primary property of all quadrilaterals, irrespective of their shape or size.

As a result, irrespective of the shape say if you are dealing with a square, rectangle, parallelogram, trapezoid, or any other type of quadrilateral, the totality of the angles will always be sum to 360°.

To determine the value of m∠B, one can employ the notion that the sum of the angles in a quadrilateral is 360°.

Thus,

m∠A + m∠B + m∠C + m∠D = 360

Substituting the given values, we get:

(16x)° + m∠B + (8x+20)° + 128° = 360

Simplifying and solving for m∠B, we get:

m∠B = 360 - (16x)° - (8x+20)° - 128°

m∠B = 212 - 24x

Therefore, the value of m∠B is 212 - 24x.

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Answer:

Step-by-step explanation:

To find the product

Its gonna be

12g^4h^5

from the given circle having tangents, the value of x is 130°.

A line that touches a curve at one point, y = f(x), is said to be the curve's tangent line. (x0, y0). The point at which it is drawn is substituted into the derivative f'(x) to find its slope (m), and y - y0 = m is used to find its equation. (x - x0).

In geometry, a tangent is a straight line that touches a curve or a surface at a single point, without intersecting it at that point. In the case of a curve, the tangent line at a point on the curve has the same slope as the curve at that point.

In trigonometry, the tangent is a mathematical function that relates the angles of a right triangle to the ratio of the length of the opposite side to the length of the adjacent side.

From the given figure,

We know that

50 + AB = 180

AB = 180 - 50

AB = 130

The value of x or arc AB is 130°.

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Answer:

Using the property of logarithms that says log_a(a^b) = b, we can simplify the expression:

7^(log_7(12)) = 12

Therefore, the value of the expression is 12.

The percentiles for the standard normal distribution

a. 0.93

b. -0.88

c. 0.67

d. -0.65

e. -1.28

To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.

The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.

Step 1: Write down the given percentiles as a decimal and round to two decimal places.

For example, for the 81st percentile, 0.81 will be used.

Step 2: Use the standard normal distribution table to find the corresponding z-score.

Step 3: Round off the obtained answer to two decimal places.

a) 81st percentile:

The area to the left of the z-score is 0.81.

The corresponding z-score is 0.93.

Hence, the 81st percentile for the standard normal distribution is 0.93.

b) 19th percentile:

The area to the left of the z-score is 0.19.

The corresponding z-score is -0.88.

Hence, the 19th percentile for the standard normal distribution is -0.88.

c) 76th percentile:

The area to the left of the z-score is 0.76.

The corresponding z-score is 0.67.

Hence, the 76th percentile for the standard normal distribution is 0.67.

d) 24th percentile:

The area to the left of the z-score is 0.24.

The corresponding z-score is -0.65.

Hence, the 24th percentile for the standard normal distribution is -0.65.

e) 10th percentile:

The area to the left of the z-score is 0.10.

The corresponding z-score is -1.28.

Hence, the 10th percentile for the standard normal distribution is -1.28.

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The equivalent fraction of the distance from City A to City B that Kelly traveled on the third day is D) 1−2/5−2/3(1−2/5).

The fraction represents a portion or part of a whole.

There are proper, improper, and complex fractions depending on the value of the numerator and the denominator.

The fractional distance traveled on day one = ²/₅

The remaining fractional distance = ³/₅ (1 - ²/₅)

The fractional distance Kelly traveled on day two = ²/₅ (²/₃ of ³/₅)

The fraction of the distance from City A to City B that Kelly traveled on the third day = ¹/₅ (1 - ²/₅ - ²/₅)

Thus, the equivalent fractional distance Kelly traveled on the third day is Option D.

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As the demand for tobacco is inelastic so the consumers are the group who are less responsive to a higher price as an outcome of it the consumers will have to bear the largest share of the tobacco tax.

This inelasticity of demand will lead to only a small decline in the quantity demanded after the tax have been leived , therefore the deadloss weight will be in really small degree. the percentage increase in price of any amount will overcome a smaller decline in the quantity which eventually would lead to a rise in the tax revenue collection.

Inelasticity of demand refers to the degree to which the quantity demanded of a particular good or service changes in response to a change in its price. When demand is inelastic, a change in price will result in a proportionally smaller change in quantity demanded. This is typically the case for goods or services that are considered necessities or have few substitutes available.

For example, if the price of insulin, a life-saving medication for diabetics, increases by 10%, it is unlikely that the quantity demanded will decrease by 10%. People with diabetes require insulin to manage their condition, and there are few substitutes available, so they are willing to pay a higher price to maintain their health.

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Complete Question: -

Suppose the supply of tobacco is elastic and the demand for tobacco is inelastic. If an excise tax is levied on the suppliers of tobacco, will the incidence fall mostly on consumers or mostly on producers? Will there be a large amount or small amount of deadweight loss? Will tax revenue from the tobacco tax fall or rise?

Answer:

the chance of a blizzard tommorrow is 5%. write the complement of this event

Step-by-step explanation:

The complement of an event is the event that it does not happen, so the complement of a blizzard occurring tomorrow with a 5% chance is that a blizzard does not occur tomorrow with a probability of:

100% - 5% = 95%

Therefore, the complement event is that there is a 95% chance that a blizzard does not occur tomorrow.

Answer:

x = 4

Step-by-step explanation:

Alternative interior angles means these angles are equal in magnitude and sign

[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]

The percentage of customers who do not purchase clubs or balls is 0.66 or 66%.

Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is 0.66.

Given that, The percentage of customers who purchase golf clubs = 10%The percentage of customers who purchase golf balls = 30%The percentage of customers who purchase both clubs and balls = 6%To find out the percentage of customers who do not purchase clubs or balls, we have to subtract the percentage of customers who purchase either clubs or balls or both from 100%.

Percentage of customers who purchase either clubs or balls or both = 10% + 30% - 6% = 34% Percentage of customers who do not purchase clubs or balls = 100% - 34% = 66%.

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Therefore, the measure of ∠D is approximately 60.96 degrees.

A measure is a function that assigns a number to each set in a given space, typically with the goal of describing the size or extent of the set. For example, the Lebesgue measure is a way of assigning a "volume" to sets in n-dimensional Euclidean space.

by the question.

To find the measure of ∠D in a right triangle with sides of 25 feet and 45 feet, we can use the inverse tangent function:

[tex]tan(∠D) = opposite/adjacent = CD/BC = 45/25[/tex]

Taking the inverse tangent of both sides, we get:

[tex]∠D = tan⁻¹(45/25) = 60.95 degrees[/tex]

Rounding this to the nearest hundredth, we get:

[tex]angleD = 60.95 degrees =60.96 degree.[/tex]

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The equations of straight lines are \hat{y} = 2h, \hat{y} = 23r + 4 and \hat{y}= 2s + 3t. Option(A),(B) and (F) are correct.

A line in the coordinate plane can be described with the help of a linear equation, that is, an equation that has a first-degree expression, like y = 2x – 3.

There are many ways to put the equation of a line in the form y = mx + b,

where m is the slope and

b is the y-intercept,

but they all require the use of algebraic properties of equations, such as addition, subtraction, multiplication, division, and substitution.

The equations of straight lines among the following are:  \hat{y} = 2h,  \hat{y} = 23r + 4 and \hat{y}= 2s + 3t

Hence, the correct options are:Option A: \hat{y} = 2h , Option B: \hat{y} = 23r + 4  and Option F: \hat{y}= 2s + 3t.

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Answer:

18 times bigger

Step-by-step explanation:

Answer:

A is correct

Step-by-step explanation:

Whatever value you put in for "y" will keep both of the equations equal