45% of the Walton High School student body are male. 90% of Walton females love math, while only 60% of the males love math. What percentage of the student body loves math?

Answer:

(fg)(x) = x^4 - x^3 + 15x^2 - 6x + 54

Step-by-step explanation:

We want to multiply and simplify as much as possible:

f(x) * g(x)

(x^2 + 6)(x^2 - x + 9)

(x^2 * x^2) + (x^2 * - x) + (x^2 * 9) + (6 * x^2) + (6 * - x) + (6 * 9)

Note that when you're multiplying exponents, we add them:

x^4 + - x^3 + 9x^2 + 6x^2 - 6x + 54

Now we add 9x^2 and 6x^2 as they are like terms:

x^4 - x^3 + 15x^2 - 6x + 54

Thus, (fg)(x) simplified is x^4 - x^3 + 15x^2 - 6x + 54.

Optional:  Check the validity of the answer:

We can check that our answer is correct by plugging in a number for x in both the unsimplified and simplified expression and seeing if we get the same answer.  Let's try 5:

Plugging in 5 for x in (x^2 + 6)(x^2 - x + 9):

(5^2 + 6)(5^2 - 5 + 9)

(25 + 6)(25 - 5 + 9)

(31)(20 + 9)

(31)(29)

899

Plugging in 5 for x in x^4 - x^3 + 15x^2 - 6x + 54:

5^4 - (5)^3 + 15(5)^2 - 6(5) + 54

625 - 125 + 15(25) - 30 + 54

625 - 125 + 375 - 30 + 54

500 + 375 - 30 + 54

875 - 30 + 54

845 + 54

899

Thus, our answer is correct.

The exact volume of a cone with the same dimensions is 9428.57 cubic inches

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

The cylinder

The volume of the cone with the same dimensions is calculated as

Volume = 1/3 * Volume of cylinder

So, we have

Volume = 1/3 * 22/7 * (30/2) * (30/2) * 40

Evaluate

Volume = 9428.57

Hence, the exact volume of a cone with the same dimensions is 9428.57 cubic inches

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The perimeter of the rectangle is 140 inches.

Let's denote the width of the rectangle as w. According to the given information, the length of the rectangle is six times its width, so we can express the length as 6w.

The area of a rectangle is given by the formula A = length × width. Substituting the values we have:

A = (6w) × w

600 = 6w^2

To solve for w, we divide both sides of the equation by 6:

w^2 = 100

Taking the square root of both sides:

w = ±10

Since width cannot be negative in this context, we discard the negative value and consider the positive value, w = 10.

Now that we have the width, we can find the length of the rectangle:

Length = 6w = 6 × 10 = 60

The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values:

P = 2(60 + 10)

P = 2(70)

P = 140

Therefore, the perimeter of the rectangle is 140 inches.

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Answer:

Step-by-step explanation:

Of course! I'd be happy to help you.

Let's simplify the expression f(x) + 8x - 8x^3 - x^4 + 6 step by step:

The given expression is: f(x) + 8x - 8x^3 - x^4 + 6

Since we don't have any specific information about f(x), we'll assume that f(x) is a constant or a function that doesn't depend on x. In that case, f(x) can be treated as a constant term.

Combining like terms, we have:

f(x) - x^4 - 8x^3 + 8x + 6

There is no further simplification we can do without additional information about the function f(x) or any specific values of x. Therefore, the simplified expression is:

f(x) - x^4 - 8x^3 + 8x + 6

Answer:

(- 4, - 4 )

Step-by-step explanation:

x - 5y = 16 → (1)

4x - 2y = - 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x + 20y = - 64 → (3)

add (2) and (3) term by term to eliminate x

(4x - 4x) + (- 2y + 20y) = - 8 - 64

0 + 18y = - 72

18y = - 72 ( divide both sides by 18 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (1)

x - 5(- 4) = 16

x + 20 = 16 ( subtract 20 from both sides )

x = - 4

solution is (- 4, - 4 )

The equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.

To form a system of equations that has an infinite number of solutions when graphed with the given equation, we need to find an equation that represents the same line or is a multiple of the given equation.

The given equation is: y + 4x - 1 = 0

To find an equation with an infinite number of solutions, we can multiply the given equation by a non-zero constant.

Let's multiply the given equation by 2:

2(y + 4x - 1) = 2(0)

2y + 8x - 2 = 0

The equation 2y + 8x - 2 = 0, when graphed with the given equation y + 4x - 1 = 0, will form a system that has an infinite number of solutions. The two equations represent the same line, just with different coefficients.

Therefore, the equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.

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Answer: O (4, -4)

Step-by-step explanation:

To solve the system of equations using elimination, we can multiply the second equation by -3 to eliminate the y term:

Original equations:

5x + 3y = 8 (Equation 1)

4x + y = 12 (Equation 2)

Multiply Equation 2 by -3:

-3(4x + y) = -3(12)

-12x - 3y = -36 (Equation 3)

Now we can add Equation 1 and Equation 3 to eliminate the y term:

(5x + 3y) + (-12x - 3y) = 8 + (-36)

Simplifying:

5x - 12x + 3y - 3y = 8 - 36

-7x = -28

Divide both sides by -7:

x = -28 / -7

x = 4

Now substitute the value of x back into either of the original equations, let's use Equation 2:

4(4) + y = 12

16 + y = 12

y = 12 - 16

y = -4

Therefore, the solution to the system of equations is x = 4 and y = -4.

Answer:

Step-by-step explanation:

To solve the equation (2/3)t - (1/5)t = 2 for t, we need to combine like terms and isolate the variable t. Here are the steps:

(2/3)t - (1/5)t = 2

To combine the fractions, we need to find a common denominator for 3 and 5, which is 15.

[(2/3)(5/5)]t - [(1/5)(3/3)]t = 2

(10/15)t - (3/15)t = 2

[(10 - 3)/15]t = 2

(7/15)t = 2

To isolate t, we can multiply both sides of the equation by the reciprocal of (7/15), which is (15/7).

[(7/15)t][(15/7)] = 2[(15/7)]

t = (2 * 15) / 7

t = 30/7

Therefore, the solution for t in the equation (2/3)t - (1/5)t = 2 is t = 30/7 or t ≈ 4.286.

Answer:

(a) To find the average cost in 2011, substitute 11 for x in the function.

g(11) = -1,736.7 + 1,661.6 ln 11 = $2,247.64

The average cost in 2011 was $2,247.64.

(b) Using the graphing calculator, graph the function in the viewing window

[6, 15] by [1,000, 3,000].

The correct graph is B.

(c) A. The average cost increases at a slower rate as time goes on.

In a trial of 10 versus 500, the experimental probability is expected to be closer to the theoretical probability when there are more trials (500 in this case).

The experimental probability and theoretical probability can be compared in a trial of 10 versus 500 by understanding the concepts behind each type of probability.

Theoretical probability is based on mathematical calculations and is determined by analyzing the possible outcomes of an event. It relies on the assumption that the event is equally likely to occur, and it can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Theoretical probability is often considered the expected or ideal probability.

On the other hand, experimental probability is determined through actual observations or experiments. It involves conducting the event multiple times and recording the outcomes to determine the relative frequency of a specific outcome. The experimental probability is an estimation based on the observed data.

In the given trial of 10 versus 500, we can expect the experimental probability to be closer to the theoretical probability when the number of trials (or repetitions) is larger. In this case, with 500 trials, the experimental probability is likely to be a more accurate representation of the true probability.

When the number of trials is small, such as only 10, the experimental probability may deviate significantly from the theoretical probability. With a smaller sample size, the observed outcomes may not accurately reflect the expected probabilities calculated theoretically.

In summary, in a trial of 10 versus 500, the experimental probability is expected to be closer to the theoretical probability when there are more trials (500 in this case). As the number of trials increases, the observed frequencies are likely to converge towards the expected probabilities calculated theoretically.

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The point A divides the line segment AB into the ratio 3:1, while the point B divides it into the ratio 1:3.

1. To find the ratio in which each point divides AB, we need to calculate the distances from each endpoint to the dividing point.

2. Let's calculate the distance from point A to the dividing point. The x-coordinate of point A is -7, and the y-coordinate is -14. Similarly, the x-coordinate of point B is 5, and the y-coordinate is 10.

3. We'll use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

  distance = sqrt((x2 - [tex]x1)^2 + (y2 - y1)^2)[/tex]

4. Applying the distance formula, we find the distance from point A to the dividing point:

[tex]distance_A[/tex] = sqrt((5 -[tex](-7))^2 + (10 - (-14))^2)[/tex]

             = sqrt((5 + [tex]7)^2 + (10 + 14)^2)[/tex]

             = sqrt([tex]12^2[/tex] + [tex]24^2[/tex])

             = sqrt(144 + 576)

             = sqrt(720)

             = 12√5

5. Similarly, let's calculate the distance from point B to the dividing point:

[tex]distance_B[/tex] = sqrt((-7 - [tex]5)^2 + (-14 - 10)^2)[/tex]

             = sqrt((-[tex]12)^2 + (-24)^2)[/tex]

             = sqrt(144 + 576)

             = sqrt(720)

             = 12√5

6. The dividing ratio can be determined by comparing the distances from each endpoint to the dividing point. Since distance_A:distance_B = 3:1, we conclude that point A divides the line segment AB into the ratio 3:1, and point B divides it into the ratio 1:3.

Thus, the endpoints A and B divide the line segment AB into the ratios 3:1 and 1:3, respectively.

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Answer:

the ratio for point C is 1 : 2.

the ratio for point D is 3 : 1.

the ratio for point E is 2 : 1.

Step-by-step explanation:

I just got it right on the test

Answer:   D

Step-by-step explanation:

Similar means that if you multiplied all of the sides by the same number it would proportionally be that much larger.

D)    4x2=8

       12x2=24

       15x2=30      All sides were multiplied by 2 so D is similar

Answer:

D)

Step-by-step explanation:

Figure D is similar in all mesurements .

...

1. The difference of two supplementary angles is 70° which is the larger angle?

A/ 135°

B/145

C/55

Answer:

  4

Step-by-step explanation:

You want the sum of digits of the largest number that divides 1305, 4665, and 6905 with the same remainder.

We can look at 4665/1305 ≈ 3.57 and 6905/1305 ≈ 5.29 for a clue as to the divisor of interest. These quotients tell us that one possibility is the value that would give quotients of 4 and 6 after the remainder is subtracted from each of the numbers.

For 1305 and 4665, if r is the remainder, we require ...

  4(1305 -r) = 4665 -r

  5220 -4665 = 4r -r

  555/3 = r = 185

If 185 is the remainder in this scenario, then 1305 -185 = 1120 is the divisor. Checking the remainder with 6905, we find ...

  6905/1120 = 6 r 185

The sum of digits of this divisor is 1 + 1 + 2 + 0 = 4.

The sum of the digits in N is 4.

Answer:

Step-by-step explanation:

a. sin(0) = 0

The sine of 0 degrees is 0.

b. tan(N) = 6√5

We don't have enough information to determine the value of tan(N) without knowing the specific value of N.

c. cos(0) = 1

The cosine of 0 degrees is 1.

d. cos(N) = 6√5/6

Again, we can't determine the specific value of cos(N) without knowing the value of N.

The vertex and the x-intercepts of the quadratic equation are:

The vertex is (-1, -4)

The x-intercepts are -3 and 1.

To express the quadratic equation [tex]y = x^2 + 2x - 3[/tex]in vertex and intercept form, we need to complete the square to find the vertex and rewrite the equation in terms of the x-intercepts.

First, let's complete the square to find the vertex. We can do this by taking half the coefficient of x, squaring it, and adding/subtracting it to both sides of the equation:

[tex]y = x^2 + 2x - 3\\y = (x^2 + 2x + 1) - 1 - 3\\y = (x + 1)^2 - 4[/tex]

Now we have the equation in the form [tex]y = a(x - h)^2 + k[/tex], where the vertex is at the point (-h, k). The vertex is (-1, -4).

Next, let's find the x-intercepts by setting y = 0:

[tex]0 = x^2 + 2x - 3\\0 = (x + 3)(x - 1)[/tex]

The x-intercepts are -3 and 1.

In vertex and intercept form, the equation is:

[tex]y = (x + 1)^2 - 4[/tex]

The vertex is (-1, -4)

The x-intercepts are -3 and 1.

This form allows us to easily identify the vertex and the x-intercepts of the quadratic equation.

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Answer: 2 1/2 pounds of more clay

Step-by-step explanation:

To calculate how much more clay Ms. Garcia needs, we need to add up the clay requirements for each grade level and then subtract the amount she already has.

For the sixth graders:

Number of students: 25

Clay required per student: 3/4 pound

Total clay required for sixth graders: 25 * (3/4) = 75/4 = 18 3/4 pounds

For the seventh graders:

Clay required for sculptures: 20 pounds

Total clay required for both grade levels: 18 3/4 + 20 = 38 3/4 pounds

Clay leftover from last year: 5 2/5 pounds

To find out how much more clay Ms. Garcia needs, we subtract the clay she already has from the total required:

38 3/4 - 5 2/5 = 38 3/4 - 27/5 = 38 3/4 - 27/5 = (155 - 108 + 3)/20 = 50/20 = 5/2 = 2 1/2 pounds

Therefore, Ms. Garcia needs an additional 2 1/2 pounds of clay.

0.612 can be rewritten as the simplified fraction 153/250.

Question: Rewrite as a simplified fraction. 0.612
To rewrite 0.612 as a simplified fraction, we need to convert the decimal into a fraction.
Step 1: Count the number of decimal places.
In this case, 0.612 has three decimal places.
Step 2: Write the decimal as a fraction with the decimal part as the numerator and the denominator as the place value of the rightmost digit.
Since there are three decimal places, the denominator will be 1000 (10 raised to the power of 3).
0.612 = 612/1000
Step 3: Simplify the fraction.
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. In this case, both the numerator and denominator are divisible by 4.
612/1000 = (612 ÷ 4) / (1000 ÷ 4) = 153/250

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Answer:

Comparing the centers of the data sets:

- The median for Data Set A is greater than the median for Data Set B.

- The mean for Data Set A is greater than the mean for Data Set B.

Comparing the variability of the data sets:

- The range of Data Set A is 22, while the range of Data Set B is 27. Therefore, the range of Data Set B is greater.

- The standard deviation of Data Set A is greater than the standard deviation of Data Set B, indicating higher variability in Data Set A.

The calculated length of the arc JK is 7π

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

Central angle = 140 degrees

Radius, IJ = 9 inches

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

JK = Central angle/360 * 2 * π * Radius

Substitute the known values in the above equation, so, we have the following representation

JK = 140/360 * 2 * π * 9

Evaluate

JK = 7π

Hence, the length of the arc is 7π

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For accelerated motion, changes in distance compare with equal changes in velocity as follows:

B. Distance increases faster than time.

A reason why a person will not compute a slope for the accelerated motion graph is that it graphed as a straight line.

Accelerated motion is a form of motion in which the motion is not equal and the object moving does not complete the same distances in the same intervals of time.

The graph formed in the case of an accelerated motion is not a straight line. So, a reason why a person would not compute a slope for the accelerated motion is that it graphed as a straight line.

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Answer:

Step Reason

∠NYR and ∠RYA form a linear pair

∠AXY and ∠AXZ form a linear pair Given

∠RYA≅∠AXY Given

∠NYR and ∠RYA are supplementary Definition of Linear Pair

If two angles form a linear pair, then they are supplementary angles Definition of Linear Pair

∠NYR and ∠AXY are supplementary Transitive Property of Equality

m∠NYR+m∠RYA=180

m∠AXY+m∠AXZ=180 Definition of Supplementary Angles

m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality

m∠NYR+m∠RYA=m∠NYR+m∠AXZ Substitution Property of Equality

m∠RYA=m∠AXZ Subtraction Property of Equality

∠NYR and ∠AXY are supplementary Definition of Supplementary Angles

m∠NYR+m∠AXY=180

m∠NYR+m∠RYA=m∠NYR+m∠AXY Substitution Property of Equality

m∠RYA=m∠AXY Subtraction Property of Equality

∠NYR≅∠AXY Definition of Congruent Angles.

Answer: C

Step-by-step explanation:

The function exists at all points on the interval with no discontinuities (such as jump discontinuities).

The transformation that moves the shape is (a) translation

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

The figure

Where, we have:

This means that the only transformation is translation

So, the transformation is (a) translation

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Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:

C

Step-by-step explanation:

x ≥ 25

Because this inequality has an equal sign, it will be a close circle. x ≥ -25 meaning the x go to the right of -25.

So, the answer is C

Answer: The statement that correctly describes the data is:

The typical value is 17. Most values are close to 17, except 4, which is an extreme value.

This is because the value 17 appears most frequently in the data set, making it the mode or the typical value. The value 4 is an extreme value as it is the minimum value in the data set. The maximum value of 18 is not the typical value because it is not as representative of the overall distribution of ages in the data set as the mode, which is 17.

Step-by-step explanation:

Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).

The given functions are f(x) = 3x² and g(x) = -2².

To understand the difference between their graphs, let's examine the characteristics of each function individually:

Function f(x) = 3x²:

The coefficient of x² is positive (3), indicating an upward-opening parabola.

The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.

The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.

Function g(x) = -2²:

The coefficient of x² is negative (-2), indicating a downward-opening parabola.

The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.

The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.

Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.

Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.

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