A survey asked 1,200 students which movie genre was their favorite. The results of the survey are shown in the circle graph.
Favorite Movie Genre
Science Fiction
10%
Comedy
20%
Drama
15%
Action
45%
Romance
10%
How many total students chose romance and science fiction movies?

Therefore , the solution of the given problem of proportionality comes out to be connection is not proportional as a result.

When a relationship consistently has the same number, it is considered to be proportional. For instance, the average amount of apples created by each tree determines how many trees there are in an area and how many apples are harvested. Mathematicians refer to a linear relationship between two numbers or factors as being proportional. The other amount doubles if the original amount does.

Here,

When there is a constant multiple between two variables in a relationship, that relationship is called a proportional relationship.

The expense of the 10 apples, which cost $4 plus a $0.20 surcharge, is not directly related to the quantity because the surcharge is a set price regardless of the quantity of apples.

The quantity being measured is growing by a fixed proportion (in this instance, 100%) every time period, so the bacteria doubling every day is an exponential relationship rather than a proportional one.

Last but not least, because the price per book varies, the $9 cost of 4 volumes is also not proportional. We would anticipate spending $18 if we were to purchase 8 books, which is not twice as much as 4 books. The connection is not proportional as a result.

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The value of the constant of variation for the direct variation is k = -1/2.

Variation depicts the relationship between two variables and how it changes. Often, a ratio is used to illustrate this connection. When we remark that a variation is continuous, we are referring to how consistently the ratio changes. Hence, whenever you read the phrase "constant of variation," just keep in mind that it refers to the stability of the relationship between the variables.

The direct variation is given by the following relations:

y = kx

Now, using the table substitute the value of y = f(x) and x:

y = kx

-2 = k(4)

k = -2/4

k = -1/2

Hence, the value of the constant of variation for the direct variation is k = -1/2.

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Answer:

5,6 and 7.

Step-by-step explanation:

I am not sure what the three step method is, but here is how I solved it.

Consecutive integers means integers in a row.  For example, 5,6 7 are consecutive integers or -4,-3,-2 are consecutive integers.

Integers are all the whole numbers (0,1,2,3...) and their opposites (..., -3, -2, -1)  1/2 or -.23 are not integers.

Let x = the first number

Let x + 1 = the second number

Let x + 2 = the third number

x + (x + 1) + (x + 2) = 18  I do not need the parentheses, but I want you to see that  the first number, plus the second number, plus the third number equals 18.

x + x + 1 + x + 2  = 18  Combine like terms

3x + 3 = 18  Subtract 3 from both sides of the equation

3x + 3 - 3 = 18 - 3

3x = 15  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] = [tex]\frac{15}{3}[/tex]

x = 5

The first number is 5.  The second number is 6 and the last number is 7.

Check:

5 + 6 + 7 = 18

18 =18 Checks.

Helping in the name of Jesus.

Answer:

X: 45° Y:16°

Step-by-step explanation:

by help of teacher

Answer:

[tex]\large\boxed{\textsf{Option B. Right Scalene Triangle.}}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked which triangle has no equal sides and a right angle.}[/tex]

[tex]\textsf{Let's review the types of triangles, according to the options.}[/tex]

[tex]\large\underline{\textsf{What is an Isosceles Triangle?}}[/tex]

[tex]\textsf{An Isoceles Triangle is a triangle that has \underline{2 congruent sides}.}[/tex]

[tex]\textsf{Option A is incorrect.}[/tex]

[tex]\large\underline{\textsf{What is a Right Scalene Triangle?}}[/tex]

[tex]\textsf{An Isoceles Triangle is a triangle that has \underline{no congruent sides} and has \underline{1 right angle}.}[/tex]

[tex]\boxed{\textsf{Option B is correct.}}[/tex]

[tex]\large\underline{\textsf{What is a Right Isosceles Triangle?}}[/tex]

[tex]\textsf{A Right Isoceles Triangle is a triangle that has \underline{2 congruent sides}. and 1 right angle}[/tex]

[tex]\textsf{Option C is incorrect.}[/tex]

[tex]\large\underline{\textsf{What is a Right Triangle?}}[/tex]

[tex]\textsf{A Right Triangle is a triangle that has \underline{1 right angle}.}[/tex]

[tex]\textsf{We're not sure how many equal sides this triangle has as it can be none, or 2.}[/tex]

[tex]\textsf{Option D is incorrect.}[/tex]

The period of the function f(x) = cos(2.22x+0.19) is 2.8323 and the period of the function f(x) = sin(1.05x)  is 5.9834

The period of a trigonometric function, we use the formula:
Period = 2π/|B|
where B is the coefficient of x in the function.

For the first function, f(x) = cos(2.22x+0.19), the coefficient of x is 2.22. Therefore, the period is:
Period = 2π/|2.22| ≈ 2.8323

For the second function, f(x) = sin(1.05x), the coefficient of x is 1.05. Therefore, the period is:
Period = 2π/|1.05| ≈ 5.9834

So, the period of the first function is 2.83 and the period of the second function is 5.98. Both answers are rounded to four decimal places.

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The change is negative, Rachel needs to provide an additional $1.25 to pay for the sweater.

What is the basic arithmetic operations?

The four basic arithmetic operations are Addition, subtraction, multiplication, and division.

To calculate Rachel's change, we first need to determine the sale price of the sweater after the discount and then subtract it from the $10 bill.

Let's say the original price of the sweater was $30, and it was discounted by 50% to $15. Rachel's coupon gives her an additional 25% off the sale price, so she can get the sweater for 75% of the sale price.

To calculate the final price Rachel will pay, we can multiply the sale price by 0.75:

Final price = $15 * 0.75 = $11.25

Rachel pays with a $10 bill, so her change will be:

Change = $10 - $11.25 = -$1.25

Hence, the change is negative, Rachel needs to provide an additional $1.25 to pay for the sweater.

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Answer:

Hi

Step-by-step explanation:

im pretty sure this the answer

hope this helps

good luck;)

Answer:

y≤7

Step-by-step explanation:

-8y+25≤-31

take away 25 from both sides

-8y≤-56

then divided by -8 on both sides

y≤7

The quotient of the polynomial long division problem (3x2 + 20x + 30) : (x + 5) is 3x + 25 and the remainder is 0.

To solve this, use polynomial long division. First, divide the leading coefficient of the dividend (3) by the leading coefficient of the divisor (1). The quotient is 3 and this is placed above the dividend.

Then, multiply the quotient (3) by the divisor (x + 5) and subtract the product from the dividend (3x2 + 20x + 30). The difference is 3x + 25.

Finally, multiply the quotient (3x + 25) by the divisor (x + 5) and subtract the product from the difference (3x + 25). Since the difference is 0, the remainder is 0.

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The value of the account at the end of the specified time period is option B.$6749.81. It can be calculated using the formula for compound interest, which is:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the given values, we get:

A = 6000(1 + 0.04/4)^(4*3)

A = 6000(1.01)^12

A = 6749.18

Therefore, the correct answer is B. $6749.18 using the compound interest formula.

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This inequality will be true when b is between -6 and 6. So any value of b in this range will result in no real solutions for the equation. For example, we could choose b=4, and the equation would have no real solutions.

To find a value for b that results in no real solutions for the equation x^(2)+bx+9=0, we need to use the discriminant. The discriminant is the part of the quadratic formula under the square root sign: b^(2)-4ac. If the discriminant is less than 0, the equation will have no real solutions.

In this case, a=1, b=b, and c=9. Plugging these values into the discriminant gives us:

b^(2)-4(1)(9)=b^(2)-36

We want this to be less than 0, so:

b^(2)-36<0

We can solve this inequality by factoring:

(b+6)(b-6)<0

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A rectangular prism actually has three pairs of bases. Each pair of bases is a set of two opposite and parallel faces on the rectangular prism.

The first pair of bases is the two opposite and parallel rectangles on the top and bottom of the prism. The second pair of bases is the two opposite and parallel rectangles on the front and back of the prism. The third pair of bases is the two opposite and parallel rectangles on the left and right sides of the prism.

Each pair of bases is congruent, meaning they have the same shape and size. This is because a rectangular prism is a type of polyhedron with six rectangular faces, and each pair of opposite faces is parallel and congruent to each other.
In conclusion, a rectangular prism has three pairs of bases, each consisting of two opposite and parallel rectangular faces.
I hope this helps! Let me know if you have any further questions.

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Answer:

Step-by-step explanation:

1) ballet club

2) ballet club

The equation of the sinusoidal graph will be y = 3 sin[(2/π)x] - 3.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The graph is represented by the sinusoidal equation.

From the graph, the amplitude of the graph is 3 units and the graph is shifted 3 units down.

And the value of constant k is given as,

k = 4/2π

k = 2/π

Thus, the equation of the sinusoidal graph will be y = 3 sin[(2/π)x] - 3.

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The temperature on mountaintop was -10° and the temperature on the ground was 10°. The solution has been obtained by using the linear equation.

What is a linear equation?

One is the degree of the linear equation. It is obvious that there are no variables in linear equations with exponents greater than 1. The graph's equation results in a straight line.

We are given that the temperature on the mountaintop was 20° lower than temperature on the ground.

Let the temperature on the ground be 'x'.

So, temperature on the mountaintop = x - 20

Also, the temperature on a mountaintop and the temperature on the ground had opposite values.

So,

x = - (x - 20)

On solving this, we get

⇒x = -x + 20

⇒2x = 20

⇒x = 10°

So, x - 20 = 10 - 20 = -10°

Hence, the temperature on mountaintop was -10° and the temperature on the ground was 10°.

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Answer:   3. 200ft  4. 21ft

5. 37.5m  6. h=4.2ft

Step-by-step explanation:

Answer: Your welcome!

Step-by-step explanation:

a) The expression to model this situation is (50/5) + (25/3) + (30/2). This expression represents the amount of money Mr. Lindsey has in the fund at each week, starting at $50 for the first 5 weeks, then adding $25 for the remaining 3 weeks, and then adding $30 for the last 2 weeks.

b) If 4% interest is paid over the period, the winner of the fund will get a total of $70.14. This is calculated by multiplying the expression from part a) by 1.04 (1.04 = 1 + 4%) to get the total amount of money in the fund at the end of the period. In this case, (50/5) + (25/3) + (30/2) * 1.04 = 70.14.

The solution of the system of equations is x=7 and y=-9.

To find the solution of the system of equations, we need to solve for x and y. We can do this using the elimination method.

Multiply the first equation by 3 and the second equation by 5 to eliminate the x variable.
3(5x-y=44) -> 15x-3y=132
5(-3x-y=-12) -> -15x-5y=-60

Add the two equations together to eliminate the x variable.
15x-3y=132
-15x-5y=-60
-----------
-8y=72

Step 3: Solve for y.
-8y=72
y=-9

Substitute the value of y back into one of the original equations to solve for x.
5x-(-9)=44
5x+9=44
5x=35
x=7

Check the solution by substituting the values of x and y back into the original equations.
5(7)-(-9)=44
35+9=44
44=44

-3(7)-(-9)=-12
-21+9=-12
-12=-12

The solution is correct.

Submit the answer.
The solution of the system of equations is x=7 and y=-9.

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The value of the model expression when simplified is (d)

From the question, we have the following representation that can be used in our computation:

Using the above as a guide, we have the following:

The given expression is

3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square

This gives

-3x + 2x - 2 + 1

Evaluate the like terms

-x - 1

This means

1 Black triangle and 1 Black square

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Step-by-step explanation:

for % questions always find 100% and/or 1%. everything else can be calculated based on these.

100% = $115

1% = 100%/100 = 115/100 = $1.15

how many % are $21 ?

as many as times 1.15 (1%) fits into 21 :

21/1.15 = 18.26086957...% ≈ 18.26%

1) a) X approaches negative infinity, f(x) approaches positive infinity.

b) The degree of f(x) is 3.

c) The maximum number of turning points for f(x) is 2.

d) The leading coefficient of f(x) is -1.

e) The end behavior of f(x) is "as x approaches infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches positive infinity.

2) a) a) The end behavior of g(x) is determined by the leading term x⁴. As x approaches infinity, g(x) approaches positive infinity. As x approaches negative infinity, g(x) approaches positive infinity.

b) The degree of g(x) is 4.

c) The maximum number of turning points for g(x) is 3.

d)The leading coefficient of g(x) is 1.

e)The end behavior of g(x) is "as x approaches infinity, g(x) approaches positive infinity; as x approaches negative infinity, g(x) approaches positive infinity.

Given f(x)=-x³ + 6x³ - 9x
a) The end behavior of f(x) is determined by the leading term -x³. As x approaches infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches positive infinity.
b) The degree of f(x) is 3, as the highest exponent in the polynomial is 3.
c) The maximum number of turning points for f(x) is 2, as it is one less than the degree of the polynomial.
d) The leading coefficient of f(x) is -1, as it is the coefficient of the leading term -x³.


Given g(x)=x(x+2)(x-2)²
b) The degree of g(x) is 4, as the highest exponent in the polynomial is 4.
c) The maximum number of turning points for g(x) is 3, as it is one less than the degree of the polynomial.
d) The leading coefficient of g(x) is 1, as it is the coefficient of the leading term x⁴.

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The new message is more likely to be classified as spam.

Based on the given data, we can use the class conditional independence to calculate the probability that a message containing the terms Donation and Unsubscribe, but not Ransom or Shows, will be classified as spam or ham. By applying Bayes' Theorem, we can calculate that the probability of the message being classified as spam is P(spam/Donation, Unsubscribe) = (P(Donation/spam)P(Unsubscribe/spam)) / P(Donation, Unsubscribe) = (4/20 x 10/20) / (5/100 x 8/100) = 0.8. Therefore, the new message is more likely to be classified as spam.

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Yes

Yes, \( W \) is a subset of \( R^{2} \) since it consists of vectors of the form
\[ \mathbf{x}=\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right] \]. Therefore, for Exercises \( 1-8 \), the answer is yes.

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Statement C is true: Either quarterback could have completed more passes

What are basic attributes of a good conclusion?

Rephrase the thesis statement first, then explain what you mean and back it with information from the prompt to show what you mean. Describe how the evidence supports your claims in further detail.

We cannot determine which quarterback completed more passes based solely on their completion percentages.

For example, if Drew Brees attempted 100 passes and completed 73.5% of them, he would have completed 73.5 passes. If Patrick Mahomes attempted 200 passes and completed 68.8% of them, he would have completed 137.6 passes, which is more than Drew Brees.

On the other hand, if Drew Brees attempted 200 passes and completed 73.5% of them, he would have completed 147 passes, which is more than Patrick Mahomes' 137.6 completed passes in the above example.

Therefore, statement C is true: either quarterback could have completed more passes, depending on the number of passes attempted.

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The domain of the function f(x) = 4[(x-2)^(1/2)]-8 is the set of all real numbers x such that x ≥ 2.

This is because the expression (x-2)^(1/2) is only defined for x ≥ 2. The range of the function is the set of all real numbers y such that y ≥ -8. This is because the expression 4[(x-2)^(1/2)]-8 is always greater than or equal to -8 for all values of x in the domain.

So, the domain and range of the function f(x) = 4[(x-2)^(1/2)]-8 are:
Domain: [2, ∞)
Range: [-8, ∞)

In conclusion, the domain and range of the function f(x) = 4[(x-2)^(1/2)]-8 are [2, ∞), [-8, ∞).

The domain of the function f(x) = 4[(x-2)1/2]-8 is the set of all real numbers x such that x ≥ 2. This is because the expression (x-2)1/2 is only defined for x ≥ 2. The range of the function is the set of all real numbers y such that y ≥ -8. This is because the expression 4[(x-2)1/2]-8 is always greater than or equal to -8 for all values of x in the domain.

So, the domain and range of the function f(x) = 4[(x-2)1/2]-8 are:

Domain: [2, ∞)

Range: [-8, ∞)

In conclusion, the domain and range of the function f(x) = 4[(x-2)1/2]-8 are [2, ∞), [-8, ∞).

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The area of the shaded region is 90 cm².

The space filled by the surface of an object or any flat shape can be thought of as the area in terms of geometry. The quantity of unit squares that cover an object's surface when it is closed is known as the area of the object. Inches, millimeters, square feet, and other square measurements are used to determine the area.

The area of shaded region = area of given square - area of all given triangles

Now, Area of given square = side × side

                                             = 12 × 12

                                             = 144 cm²

Similarly, Area of all triangles

             = 4 × (area of small triangle) + 4 × (area of big triangle)

             = 4 × ( 1/2 × 3× 3) + 4 × ( 1/2 × 3 × 6)

             = 18 + 36

             = 54 cm²

∴ The area of shaded region = 144 - 54

                                                = 90 cm²

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Answer: g(g(1)) = 4 and g(g(g(1))) = 5 1/2

Step-by-step explanation:

We will first find g(1). To do so, we plug 1 in for x.

g(1) = (1) + 3/2 = 5/2 = 2 1/2

To find g(g(1)) we will plug in 5/2 for x.

g(g(1)) = (5/2) + 3/2 = 8/2 = 4

To find g(g(g(1))) we will plug in 4 for x.

g(g(g(1))) = (4) + 3/2 = 11/2 = 5 1/2

Hope this helps!

The equation of the tangent line of y = sqrt(3x) passing through (3, 3) is y = (1/2)x + 3/2.

To use Descartes' method of slopes, we need to find the derivative of the function first.

Taking the derivative of y = sqrt(3x) gives:

y' = (1/2) * (3x)^(-1/2) * 3 = (3/2√(3x))

Now we can find the slope of the tangent line at (3, 3) by plugging in x = 3 into the derivative:

y' = (3/2√(3*3)) = 3/6 = 1/2

So the slope of the tangent line is 1/2.

Next, we use the point-slope form of a linear equation to find the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (3, 3).

Plugging in the values, we get:

y - 3 = (1/2)(x - 3)

Simplifying, we get:

y = (1/2)x + 3/2

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Given:

What is the interest earned when $46,230 is invested for 9 years at 7.8% p.a?

To find:

The interest

Solution:

The 6-day SMA for the given closing prices is as follows:

Day 1: 2.63

Day 2: 2.63

Day 3: 2.61

Day 4: 2.59

Day 5: 2.54

To calculate the 6-day Simple Moving Average (SMA) for the given closing prices, we need to take the sum of the last six closing prices and divide it by 6. Then we move one day forward and repeat the process until we have calculated the SMA for each day.

Here are the calculations:

Day 1: SMA = (2.65 + 2.63 + 2.70 + 2.63 + 2.50 + 2.65) / 6 = 2.63

Day 2: SMA = (2.63 + 2.70 + 2.63 + 2.50 + 2.65 + 2.66) / 6 = 2.63

Day 3: SMA = (2.70 + 2.63 + 2.50 + 2.65 + 2.66 + 2.56) / 6 = 2.61

Day 4: SMA = (2.63 + 2.50 + 2.65 + 2.66 + 2.56 + 2.52) / 6 = 2.59

Day 5: SMA = (2.50 + 2.65 + 2.66 + 2.56 + 2.52 + 2.37) / 6 = 2.54

Therefore, the 6-day SMA for the given closing prices is as follows:

Day 1: 2.63

Day 2: 2.63

Day 3: 2.61

Day 4: 2.59

Day 5: 2.54

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