athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the medals be distributed?

The linear inequality that is graphed in the xy plane is: C. 2x + 3y ≤ 4.

Values in the shaded part are the solution of a a linear inequality. Thus, a dotted or dashed line is used on the graph when the inequality sign is either "<" or ">". On the other hand, when a line that is not dotted or dashed is used when the inequality sign is either "≤" or "≥". These lines, dotted or not are the boundary lines.

Also, when the shaded area is above the boundary line, the sign "≥" or ">" is used. When the shaded part is beneath the boundary line, "≤" or "<" is used in the linear inequality.

The graph given has a boundary line that is not dashed or dotted, and also, the shaded part is beneath the boundary line. Therefore, the inequality sign to use is "≤".

Find the slope:

Slope (m) = rise/run = -4/3 / 2 = -4/6

m = -2/3

y-intercept (b) = 4/3.

Substitute m = -2/3 and b = 4/3 into y ≤ mx + b:

y ≤ -2/3x + 4/3

Rewrite

3y ≤ -2x + 4

2x + 3y ≤ 4

The answer is: C. 2x + 3y ≤ 4.

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Based on the mean of the sample and the proportion who read below grade level, the probability that a second sample would have a proportion greater than 0.54 is 0.9772.

The probability that the second sample would be selected with a proportion greater than 0.54 can be found as:

P (x > 0.54) = P ( z > (0.54 - 0.30) / 0.12))

Solving gives:

P (x > 0.54) = P (z > 2)

P (x > 0.54) = 0.9772

In conclusion, the probability that the second sample would be selected with a proportion greater than 0.54 is 0.9772.

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What is ordinary number?

1 : a number designating the place (such as first, second, or third) occupied by an item in an ordered sequence — see Table of Numbers. 2 : a number assigned to an ordered set that designates both the order of its elements and its cardinal number.

Answer: B. All real numbers

Step-by-step explanation:

See attached image.

DE ≅ CE given that side AD and side BC are equal and angle ∠BCD and angle ∠ADC are equal. This can be obtained by using triangle congruency theorems.

Triangle congruency theorems required in the question,

In the question it is given that,

⇒ Side DE and side CE are equal ⇒ AD ≅ BC

⇒ angle ∠BCD and angle ∠ADC are equal ⇒ ∠BCD ≅ ∠ADC

Therefore we can say that,

ΔADC ≅ ΔBCD according to the SAS triangle congruency theorem

ΔAED ≅ ΔBEC according to the AAS triangle congruency theorem

Thus DE ≅ CE since corresponding parts of congruent triangles are congruent (CPCTC).

Hence DE ≅ CE given that side AD and side BC are equal and angle ∠BCD and angle ∠ADC are equal.

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Answer:

10 ≤ f(x) < 52

Step-by-step explanation:

the range is the values of f(x) given by the domain - 2 ≤ x < 5

substitute the end points of the interval into f(x)

f(- 2) = 2(- 2)² + 2 = 2(4) + 2 = 8 + 2 = 10

f(5) = 2(5)² + 2 = 2(25) + 2 = 50 + 2 = 52

then range is 10 ≤ f(x) < 52

Answer:

A

Step-by-step explanation:

x - 4 / (x + 5)(x - 1)

let's expand:

x - 4 / x² + 4x - 5

4 - 4 / 16 + 16 - 5 = 0 so answer is 4

Answer:

(11,0)

Step-by-step explanation:

Answer:

A. [tex]\frac{17}{52}[/tex]

B. [tex]\frac{17}{52}[/tex]

C. [tex]\frac{2}{13}[/tex]

Step-by-step explanation:

A.

There are 52/4 diamonds in the deck and 4 '5's in the dech of cards

52/4 = 13 + 4 = 17

Therefore, you have a  [tex]\frac{17}{52}[/tex] chance of drawing one of those cards.

B.

There are 13 hearts in the deck and 4 jacks. Therefore, your odds are the same : [tex]\frac{17}{52}[/tex]

C.

There are 4 jacks in a deck of cards and 4 '8's in a deck of cards

Therefore your probability is [tex]\frac{8}{52}[/tex] which simplifies to [tex]=\frac{2}{13}[/tex]

As per brainly guidelines I can only answer 3 questions in one answer

A total of 204 textbooks were sold with 153 math textbooks and 51 psychology textbooks being sold, as the number of math textbooks was three times the number of psychology textbooks.

Given that,

The combined total of math and psychology textbooks sold in a week is 204.

The number of math textbooks sold is three times the number of psychology textbooks sold.

To solve this problem,

Assign variables to represent the number of math and psychology textbooks sold.

Let's say "M" represents the number of math textbooks and "P" represents the number of psychology textbooks.

We know that the combined total of math and psychology textbooks sold is 204,

So the equation be:

M + P = 204  .....(i)

We are also given that the number of math textbooks sold was three times the number of psychology textbooks sold.

In equation form, this can be expressed as:

M = 3P

Now, we can substitute the value of M in terms of P into the equation (i):

3P + P = 204

Combining like terms, we get:

4P = 204

Dividing both sides by 4, we find:

P = 51

So, the number of psychology textbooks sold is 51.

To find the number of math textbooks sold,

Substitute this value back into the equation:

M = 3P

M = 3(51)

M = 153

Therefore, the number of math textbooks sold is 153.

Hence,

153 math textbooks and 51 psychology textbooks were sold.

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Answer:

(4,8)

Step-by-step explanation:

hihihihihihihihohihih

4. Compute the derivative.

[tex]y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1[/tex]

Find when the gradient is 7.

[tex]4x - 1 = 7 \implies 4x = 8 \implies x = 2[/tex]

Evaluate [tex]y[/tex] at this point.

[tex]y = 2\cdot2^2-2-1 = 5[/tex]

The point we want is then (2, 5).

5. The curve crosses the [tex]x[/tex]-axis when [tex]y=0[/tex]. We have

[tex]y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4[/tex]

Compute the derivative.

[tex]y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}[/tex]

At the point we want, the gradient is

[tex]\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}[/tex]

6. The curve crosses the [tex]y[/tex]-axis when [tex]x=0[/tex]. Compute the derivative.

[tex]\dfrac{dy}{dx} = 3x^2 - 4x + 5[/tex]

When [tex]x=0[/tex], the gradient is

[tex]\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}[/tex]

7. Set [tex]y=5[/tex] and solve for [tex]x[/tex]. The curve and line meet when

[tex]5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92[/tex]

Compute the derivative (for the curve) and evaluate it at these [tex]x[/tex] values.

[tex]\dfrac{dy}{dx} = 4x + 7[/tex]

[tex]\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}[/tex]

[tex]\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}[/tex]

8. Compute the derivative.

[tex]y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b[/tex]

The gradient is 8 when [tex]x=2[/tex], so

[tex]2a\cdot2 + b = 8 \implies 4a + b = 8[/tex]

and the gradient is -10 when [tex]x=-1[/tex], so

[tex]2a\cdot(-1) + b = -10 \implies -2a + b = -10[/tex]

Solve for [tex]a[/tex] and [tex]b[/tex]. Eliminating [tex]b[/tex], we have

[tex](4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}[/tex]

so that

[tex]4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}[/tex].

From the standard normal table, the respective probabilities are; 0.908 and 0.841

Formula for calculating the standard score or z score is:

z = (x - μ)/σ

where:

z is the standard score

x is the raw score

μ is the population mean

σ is the population standard deviation

A) We are given;

x = 95

μ = 110

σ = 15

Thus;

z = (95 - 110)/15

z = 1.33

From the normal standard distribution table we can find the probability from the z-score as;

P(x > 95) = 1 - 0.091759.

P(x > 95) = 0.908

B) We are given;

x = 125

μ = 110

σ = 15

Thus;

z = (125 - 110)/15

z = 1

From the normal standard distribution table we can find the probability from the z-score as;

P(x > 95) = 1 - 0.158655.

P(x > 95) = 0.841

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The maximum area of a rectangular piece of metal with perimeter of 27.75 in² has length of 6.9375 in and width of 6.9375 in.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length and y represent the width. hence:

Perimeter = 2(x + y)

27.75 = 2(x + y)

y = 13.875 - x

Area (A) = xy

A = x(13.875 - x)

A = 13.875x - x²

Maximum area is at A' = 0, hence:

A' = 13.875 - 2x

13.875 - 2x = 0

x = 6.9375

y = 6.9375

The maximum area of a rectangular piece of metal with perimeter of 27.75 in² has length of 6.9375 in and width of 6.9375 in.

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The sequence of angles from smallest to largest is m∠T,m∠S,m∠R.

Given three angles be m∠T=4x-52°,m∠S=x+38°,m∠R=2x+47°.

We are required to arrange the angles in ascending order.

Ascending order means values that are written in a way that smallest values come first and larger values comes last.

First we have to find the angles at one value of x.

The values will differ as the values of x differ so we have to choose point or value of x.

Suppose x=20.

Then the angles are:

m∠T=4x-52°

=4*20-52

=80-52

=28°

m∠S=x+38°

=20+38

=58°

m∠R=2x+47°

=2*20+47

=40+47

=87°

Hence the sequence of angles from smallest to largest is m∠T,m∠S,m∠R.

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Answer:

-7

Step-by-step explanation:

8-15 = -7 but since it's an absolute value, it is 7 and then you add the negative sign in front since it is not in the absolute value.

Answer:

  (a)  π + (-π) = 0

Step-by-step explanation:

You want a counterexample for the statement that irrationals are closed under addition.

A set is closed under addition if adding members of the set always results in a member of the set.

This shows that adding members of the set can result in a rational number. This is the counterexample you're looking for.

Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.

An example of a sum that is an element of the set. This is not a counterexample.

Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.

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Answer:

below

Step-by-step explanation:

If a data set contains three points, and two of the residuals are -10 and 20, the third residual is 10 (option B).

A residual is the difference between the observed value and the estimated value of the quantity of interest.

The residual of a data points should normally sum up to zero (0). This means the following applies:

-10 + 20 + x = 0

x = 10

Therefore, if data set contains three points, and two of the residuals are -10 and 20, the third residual is 10.

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The lower-priced speaker docks and higher-priced speaker docks is 9 and 36 respectively.

Higher-priced speaker = 170 × x

= 170x

Lower-priced speaker = 80 × 4x

= 320x

Total sales = $4,410

170x + 320x = 4,410

490x = 4,410

divide both sides by 490

x = 4,410 / 490

x = 9

So,

Number of lower-priced speaker = 4x

= 4 × 9

= 36

Number of higher-priced speaker = x

= 9

Therefore, the lower-priced speaker docks and higher-priced speaker docks is 9 and 36 respectively.

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Answer:

A

Step-by-step explanation:

If digits can be repeated, that means there are 10 options for each place in the pin code. 10*10*10*10 = 10,000

If digits can not be repeated, there are 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and 7 options for the fourth digit. 10*9*8*7 = 5040

The given statement that's true about the function is g(-13) = 20 is true for g.

From the information given, the function, g, has a domain of -20 < x < -5 < g(x) <45 and that g(0)= -2 and g(-9)= 6.

Let's analyze the options that are given in the scenario. g(7) = -1. It should be noted that 7 isn't in our domain. Therefore, this isn't possible.

g(-13) = 29

x = 13 is in our domain and 20 is also is in our range. Therefore, this is true for g.

g(0) = 2.

This isn't true because it is given that g(0) = 2

In conclusion, the given statement that's true about the function is g(-13) = 20 is true for g.

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[tex]l = sec {}^{2} x - 1 \\ l = \frac{1}{cos {}^{2} x} - \frac{cos {}^{2} x}{cos {}^{2} x} \\ l = \frac{1 - cos {}^{2} x}{cos {}^{2}x } \\ l = \frac{sin {}^{2} x}{cos {}^{2} x} = ( \frac{sinx}{cosx} ) {}^{2} = tan {}^{2} x[/tex]

Using it's concept, the percentage of employees with 8 or more years at the company reported that email is their preferred method of communication is:

D. 44.79%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

In this problem, there are 96 employees with 8 or more years of experience, of which 43 prefer email, hence the percentage is:

P = 43/96 x 100% = 44.79%.

Hence option D is correct.

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Answer: its the 3rd one if im wrong im sorry

:3

need help I don't know the answer

Answer:

[tex]\frac{x^2}{9}+\frac{y^2}{4}=1[/tex]

Step-by-step explanation:

So an ellipse can be expressed in two different but very similar forms:

Horizontal Major Axis:

   [tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Vertical Major Axis:
   [tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]

In both equations the length of the major axis is "2a" and the length of the minor axis is "2b"

In the equation you provided, the major axis is horizontal, and the minor axis is vertical.

So looking at the horizontal length, you can see that it's 6, and since this ellipse has a horizontal major axis, that means 2a=6, which means a=3

Looking at the vertical length, you can see that it's 4, and since the ellipse has a vertical minor axis, that means 2b=4, which means b=2

The last thing to note is that the center of an ellipse is (h, k) in the equation, and since here the center is (0, 0) it's (x-0)^2 and (y-0)^2 in the denominator which is just x^2 and y^2

So let's plug in the values into the equation:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

(h, k) = (0, 0)

a = 3

b = 2

[tex]\frac{x^2}{3^2}+\frac{y^2}{2^2}=1\\\\\frac{x^2}{9}+\frac{y^2}{4}=1[/tex]

Here we go ~

The given figure is of a horizontal ellipse with :

so, a = 3

hence, b = 2

And as it's shown in the figure, the ellipse has its centre at origin, so we can write it's equation as :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{b {}^{2} } = 1[/tex]

[ now, plug in the values ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {3}^{2} } + \cfrac{ {y}^{2} }{2 {}^{2} } = 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {9}^{} } + \cfrac{ {y}^{2} }{4 {}^{} } = 1[/tex]

That's all, ask me if you have any questions ~