449 students were surveyed about their preferences of sports. 146 students like football, 107 students like baseball, and 49 students like both sports. how many students like exactly one of the two sports?

Answer:

[tex]f(g(4) = \boxed{\bold{0}}[/tex]

[tex]g(f(3)) = \boxed{\bold{2}}[/tex]

[tex]f(f(5)) = \boxed{\bold{5}}[/tex]

[tex]g(g(1)) = \boxed{\bold{4}}[/tex]

Step-by-step explanation:

All the expressions are composite functions where the output of one function is fed as input to the other function to get the composite output

To explain better, I will use the specific values and the graphs of f(x) and g(x)

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f(g(4))

Let's take the first expression [tex]\displaystyle {f(g(4))}[/tex]. The innermost function, [tex]g(x)[/tex] is first evaluated at [tex]x = 4[/tex], then this value is used to find the value of the outer function [tex]f(x)[/tex]

To find the value of this expression

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The other expressions can be evaluated using similar reasoning.
g(f(3))

First evaluate[tex]f(x) \:at\: x = 3 == > f(3) = 0 == > g(0) = 2[/tex]

Answer:  2

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f(f(5))

This is a function which is a composite of itself
Find [tex]f(5) = 2 == > f(2) = 5[/tex]

Answer: 5

-----------------------------------------------------------------------------------------------------

g(g(1))

[tex]g(1) = 5 == > g(5) = 4[/tex]

Answer: 4

On solving the provided question we can say that  Probability of  Red  * Second  Draw Probability of  Red  = [tex]3 / 10 * 2 / 9 = 6 / 90 = 1 / 15[/tex]

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Let the number of  red balls  = x    

[tex][x / 10] * [ (x - 1) / 9 ] = 1/15 \\x(x - 1) / 90 = 1/15 \\x ( x - 1) = 6 \\x^2 - x - 6 = 0 \\(x -3) ( x + 2) = 0 \\x = 3 or x = -2[/tex]

here are 3  red balls

Probability of  Red  * Second  Draw Probability of  Red  

[tex]3 / 10 * 2 / 9 = 6 / 90 = 1 / 15[/tex]

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Answer:

The transformation described is a horizontal translation of 1 unit to the left and a vertical translation of 4 units up. The transformation moves every point on the x-axis one unit to the left and every point on the y-axis four units up.

Step-by-step explanation:

It can also be thought of as a transformation that shifts the entire figure one unit to the left and four units up.

Answer: x<4

Step-by-step explanation:

19>15+x

4>x

x<4 is the answer

Answer:

Since 15+x is less than 19. 15+x cannot equal to or greater than 19. If x is greater or equal to 4, the answer will be equal to or greater than 19 which is not true for the equation shown above.

So x is less than 4.

Answer: $14697.51

Step-by-step explanation:

[tex]9126(1+0.10)^{5} \approx \$14697.51[/tex]

Answer:

B. Apples cost $2.50/pound

Step-by-step explanation:

B would be a multiplicative relationship because you would multiply the number of pounds by 2.50

If the mean of a set of data is 4.11 and its standard deviation is 3.03. the z score for a value of 10.86 is: 2.23.

Using this formula to find the z-score

z-score  =  Value - Mean / Standard deviation

Where:

Value = 10.86

Mean = 4.11

Standard deviation = 3.03

Let plug in the formula

z-score  =  10. 86 - 4.11 / 3.03

z-score  =  6.75 /3.03

z-score = 2.227

z- score = 2.23

Therefore the z-score is 2.23.

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Answer:

D. (1,3) and (3,7)

Step-by-step explanation:

The graphs of y = 2x + 1 and y = -(x-1)^2 + 3 intersect at the points where they have the same y-coordinate. To find these points, we can set the two equations equal to each other and solve for x.

y = 2x + 1 = -(x-1)^2 + 3

2x + 1 = -x^2 + 2x + 2

x^2 - 4x + 1 = 0

(x-1)^2 = 0

x = 1

Now we can substitute this value of x into either of the given equations to find the corresponding y-coordinate.

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

so the point of intersection is (1,3)

So the answer is D. (1,3) and (3,7)

Please note that the solution is valid only if the two equations y=2x+1 and y=-(x-1)^2+3 are defined for the same domain.

The profit per foot of the satin ribbon that the craft store buys and sells is $0.80.

The profit generated by the craft store per foot is determined by reducing the transactions to their unit cost and price.

The profit per unit becomes the difference between the unit selling price and the unit cost.

In other words, the profit per unit is the unit rate (per-unit profit) or ratio obtained as a difference between two unit parameters.

The cost of buying 150 feet of satin ribbon = $13.50

The unit cost per foot = $0.09 ($13.50/150)

The sales price for 5 feet = $0.80

The unit selling price per foot = $0.16 ($0.80/5)

The profit per unit = $0.80 ($0.16 - $0.80)

Profit percentage = 100% ($0.80/$0.80 x 100)

Thus, we can conclude that the craft store generates a 100% profit or $0.80 per foot.

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Answer:

A. Yes, opposite sides are congruent.

Step-by-step explanation:

For B, you can't necessarily tell if they are right angles because there is nothing indicating that it is. For C, just because angle measures aren't given doesn't mean that they aren't congruent. For D, sure it could be a rhombus although it doesn't look like it but rhombuses' are parallelograms.

Answer: 42.5

Step-by-step explanation:

8 multipled by 42.5 is 340. A strategy i use is multiply 8 by 5 or 10, for example 8 times 5 is 40, so i know that 8 times 50 is 400, that tells you the answer you need is just a little below 50

The required ways can 3 club members be chosen as president, vice president, and treasurer are 56.

When the order doesn't matter, the combination is a choice between all of the objects in the set or just a portion of them. As a result, the combination formula is provided by; n, and the number of combinations of n objects taken r at a time.

Total number of eligible members for these positions = 8

To choose three members,

C(8, 3)

(8×7×6)/(3×2)

336/6

= 56 ways.

Thus,the required number of ways are 56.

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Use law of cosines to find angles A, B, and C. Angle A = X°, B = Y° and C = Z°.

What is triangle ?

A triangle is a polygon with three sides and three angles. The sum of the three angles in a triangle always equals 180 degrees. Triangles can be classified based on the length of their sides or the measure of their angles.

We can use the law of cosines to find the angles. The law of cosines states that for any triangle, the square of one side length is equal to the sum of the squares of the other two side lengths, minus twice the product of the other two side lengths multiplied by the cosine of the angle opposite the first side.

Let A, B, and C be the angles opposite the sides of length 114 meters, 70 meters, and 95 meters, respectively.

We can use the following equation to find angle A:

cos A = (70^2 + 95^2 - 114^2) / (2 * 70 * 95)

Once we have the value of cos A, we can use the inverse cosine function to find the angle A in degrees.

Similarly, we can use the same formula to find the angle B and C.

cos B = (114^2 + 95^2 - 70^2) / (2 * 114 * 95)

cos C = (114^2 + 70^2 - 95^2) / (2 * 114 * 70)

Use law of cosines to find angles A, B, and C. Angle A = X°, B = Y° and C = Z°.

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Yes, this results in a random sampling because every day the woodworker produces two chairs, and the company that buys the chairs randomly selects the days on which to check the chairs made that day.

This means that each item (each chair) has an equal chance of being selected, and each group of n items (in this case, two chairs) also has an equal chance of being selected. The probability of an item being selected can be calculated using the formula P(A) = n/N, where n is the number of items in the sample and N is the total number of items in the population. In this case, the probability of an item being selected is 2/2 = 1, and the probability of a group of two items being selected is 2/2 = 1. This shows that each item and each group of items has an equal chance of being selected, which means that this is a random sampling.

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Answer: 36x + 68

Step-by-step explanation:

Expanding it, you get:

36x + 72 - 4

= 36x + 68

The resulting equation is (x-2) (x+2)-1(3x) = (x-3) (x-2).

The lowest integer that unites all of the fractions in a given collection is known as the least common denominator (LCD).

Given that,

The equation x+2/3x - 1/x-2 = x-3/3x is being multiplied by the least common denominator (LCD)

So, further solving this equation,

x+2 / 3x - 1/x-2 = x-3/3x

Here, the least common denominator (LCD) is (3x)(x-2). so we multiply the whole equation by the least common denominator (LCD).

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

We multiply each term by the least common denominator (LCD).

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

Thus, we get (x-2) (x+2)-1(3x) = (x-3) (x-2).

Therefore,The resulting equation is (x-2) (x+2)-1(3x) = (x-3) (x-2).

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Answer:

D

Step-by-step explanation: answer is d

The probability of getting exactly 14 heads by flipping a fair coin 20 times is 0.03696.

The number of times a fair coin is flipped = 20

The outcomes for flipping the coin once = 2

Therefore, the outcomes for flipping the coin 20 times = (2) ^ 20

Number of heads needed = 14

The number of ways of getting exactly 14 heads = 20C14

20C14 is the 20! / (14! (20-14)! = 38760

Probability of getting an event = possible outcome / total outcomes

Thus, the probability of getting exactly 14 heads by flipping a fair coin 20 times = (20C14) / (2 ^ 20) ≈ 0.03696

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The equation of the line would be y = 17/7x + 1.

What is the equation of the line?

The equation of a line is a mathematical expression that describes the position of a line in a coordinate plane. It typically takes the form of "y = mx + b", where "m" is the slope of the line and "b" is the y-intercept, the point where the line crosses the y-axis.

The whole question is:

Write an equation of the line passing through the point (8,7) that is perpendicular to the line  [tex]y + 7 = -\frac{7}{17}(x+8)[/tex]

To write the equation of a line that is perpendicular to a given line, we can use the slope of the given line and the point the new line passes through.

The slope of the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex] can be found by isolating y and then taking the derivative, which gives us: -7/17.

The slope of a line perpendicular to this line is the negative reciprocal of the given line's slope, which is 17/7.

We also know that the new line passes through the point (8,7). Using a point-slope form of a line which is (y-y1) = m(x-x1) where m is the slope, we can write the equation of the line as:

y - 7 = 17/7(x - 8)

So the equation of the line that passes through the point (8,7) and is perpendicular to the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex] is:

y = 17/7x + 1

Hence, the equation of the line would be y = 17/7x + 1.

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The possible values of [tex]$m$[/tex] are all real numbers greater than   [tex]$\frac{2}{x^2}$[/tex]

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. It is called a quadratic equation because the highest degree of its unknown variable (x) is two. The solutions of a quadratic equation can be found by solving the equation using the quadratic formula, factoring, or graphing. Quadratic equations are used in many areas of mathematics, from basic algebra to differential equations.

Let [tex]$y = 2x^2mx8$[/tex]

The two distinct real roots of the equation imply that y is a quadratic equation with two distinct real roots.

So,[tex]$y = 0 = 2x^2mx8 \implies 2x^2mx - 8 = 0$[/tex]

Using the quadratic formula , [tex]$m = \frac{8}{2x^2x}$[/tex]

The two distinct real roots of the equation imply that the discriminant of the quadratic equation, [tex]$\Delta = b^2-4ac$[/tex] is greater than 0.

So, [tex]$\Delta = (2x^2)^2-4(2)(-8) > 0 \implies 4x^4 + 64 > 0$[/tex]

[tex]$4x^4 > -64 \implies x^4 > -16$[/tex]

So, [tex]$m > \frac{8}{2x^2x} \implies m > \frac{8}{2x^2(-4)} = \frac{2}{x^2}$[/tex]

Hence, the possible values of m are all real numbers greater than [tex]$\frac{2}{x^2}$[/tex]

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At the given point, (4, 16/3 , -2), the vectors t, n, and b are (2, 4, -1), (16, -8, 4), and (-32, 8, 8), respectively.

Vector is a mathematical element that has both magnitude and direction. It is used to represent quantities such as velocity, force, acceleration, and displacement. Vector is used in physics and engineering for computing physical quantities. Vector is also used in computer graphics for representing shapes, lines, and curves. Vector can also be used in economics for representing stocks and bonds.

The vector t is the direction vector of the parametric function r(t). It is found by taking the derivative of the parametric equation:

t = (2t, 2t^2, 1)

The normal vector n is found by taking the cross product of the curvature vector and the direction vector. The curvature vector is found by taking the second derivative of the parametric equation.

k = (2, 4t, 0)

n = (4t, -2, 2)

The binormal vector b is found by taking the cross product of the direction vector and the normal vector.

b = (-8t, 4, -4t)

At the given point, (4, 16/3 , -2), the vectors t, n, and b are (2, 4, -1), (16, -8, 4), and (-32, 8, 8), respectively.

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Answer:

1. To find the gradient of a line, we can use the slope-intercept form of the equation: y = mx + b, where m is the gradient and b is the y-intercept.

a) To find the gradient of (x+7)/(y-2) = 0, we can first rewrite the equation as y = (2x+14)/(x+7). To find the slope, we can take the derivative of y with respect to x. We get the slope or the gradient of the line as m = 2/(x+7).

b) To find the gradient of the line through (p,5) and (6,2p), we can use the point-slope form of the equation: y - y1 = m(x - x1). We can substitute the coordinates of the two points and solve for m.

y - 5 = m(x - p)

2p - 5 = m(6 - p)

2p - 5 = 6m - mp

mp + 6m = 2p + 5

m(p+6) = 2p + 5

m = (2p+5)/(p+6)

2. To find the equation of a line, we can use the slope-intercept form of the equation: y = mx + b, where m is the gradient and b is the y-intercept.

a) To find the equation of the line with a gradient of 3, passing through (0,5), we can substitute the values into the slope-intercept form.

y = 3x + b

5 = 3(0) + b

b = 5

The equation of the line is y = 3x + 5

3. To find the value of p, if the gradient of the line joining (-1,p) and (p, 4) is 2/3, we can use the point-slope form of the equation: y - y1 = m(x - x1). We can substitute the coordinates of the two points and the gradient, and solve for p.

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

4 - p = (2/3)(p - (-1))

4 - p = (2/3)p + (2/3)

(2/3)p - 4 + p = (2/3)

p = 6

Final Answer: The value of p is 6.

The linear equation on the graph is the one in the last option, it is:

y = 6x

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

First, we can see that the line passes through the point (0, 0), thus the y-intercept is b = 0.

We can write:

y = a*x

We also can see that the line passes through the point (1, 6)

Replacing these values we will get:

6 = a*1

6/1 = a

6 = a

Then the linear equation is:

y = 6x

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No, You cannot use your 10 meter radio on CB (citizen’s band), so long as you follow the rules on frequency, and power.

A public, two-way personal radio service is the Citizen's Band (CB) Radio Service, usually abbreviated as CB. There are various categories for CB operating. The most popular CB method is voice communication, which rose to popularity in the 1970s. Mobile CB operating is still common, particularly in automobiles and trucks. The majority of CB operating occurs in a constrained range of frequencies around 27 MHz. This band contains 40 channels. There is excessive channel saturation.

A CB (citizen’s band) radio must be FCC type approved. Of course, I have no idea where you are, so maybe, where you are, it is ok. In the US however, CB radios are not to be “easily modified” neither to increase power out nor to allow operation outside the citizen’s band frequencies. Even as an extra class amateur radio licensee, I may not use a modified radio on the CB band. I am allowed, however to modify a CB radio to operate on amateur radio bands.

You cannot use your 10 meter radio on CB (citizen’s band), so long as you follow the rules on frequency, and power.

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Answer:

1. 46/35 or 1 11/35

2. 5/4 or 1 1/4

3. 5/4 or 1 1/4

4. 7/3 or 2 1/3

Step-by-step explanation:

An integer that can be inserted on the blank line in the list from the given options is 0.

Therefore the answer is c) 0.

The list shows numbers in order from least to greatest, that is ascending order -15, -3 4/5, -1.5, ____, 2.3, 5 2/3

The integer that can be inserted on the blank line in the list is c. 0, because it is greater than -1.5 and less than 2.3 and it is an integer.

-2 is less than -1.5. So they cannot be the answer. -1 1/3 is equal to -4/3 and 1.2 is greater than -1.5 and less than 2.3, but they are not integers.  

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Answer:

first three are correct answers last two are not

Step-by-step explanation:

quadratic equations are in the for y=ax²+bx+c

y= f(X)

The value of expression (a + b + c + d) is 20

Consider given equations x + y = 4       ........(1)

and 3xy = 4        .........(2)

The solutions of given equations are of the form [tex]$x = \frac{a \pm b\sqrt{c}}{d}$[/tex]

where a, b, c, and d are positive integers and the expression is completely simplified.

From equation (2),

y = 4/3x

Substitute above value of y in equation (1),

x + y = 4

x + (4/3x) = 4

3x² + 4 = 12x

3x² - 12x + 4 = 0

After solving above quadratic equation we get,

[tex]x=\frac{6\pm 2\sqrt{6} }{6}[/tex]

Comapring this solution with [tex]$x = \frac{a \pm b\sqrt{c}}{d}$[/tex] we get,

a = 6, b = 2, c = 6 and d = 6

Now we find the value of expression (a + b + c + d)

a + b + c + d

= 6 + 2 + 6 + 6

= 20

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The equation that represents this word sentence is n-7 = 9

The value of n = 16

An algebraic expression can be defined as an expression that is composed of variables, terms, coefficients, constants and factors.

They are also made up of mathematical or sometimes called arithmetic operations, such as;

From the information given, we have that;

9 is the difference of a number n and 7.

This is represented as;

n - 7 = 9

Now, collect like terms

n = 9 + 7

Add the values

n = 16

Thus, the value is 16

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Answer:

26 - 11 = 15

Step-by-step explanation:

The minimum monthly payment so that she avoids paying interest on the credit card is given as follows:

$150

The minimum monthly payment is obtained applying the proportions in the context of this problem.

The interest-free period is given as follows:

6 months, as long as the purchase has a value that is less than $1000.

(as stated in the problem).

The value of the TV is given as follows:

$900.

(as stated in the problem).

The minimum monthly payment is obtained with the division of the value of the TV by the length in months of the interest free period, as follows:

Minimum payment = 900/6

Minimum payment = $150.

(this is the proportion that is applied in this problem).

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