A gold, a silver, and a bronze medal are awarded in an Olympic event. In how many possible ways can the medals be awarded for a 200-meter sprint in which there are 12 runners

Answer:

Step-by-step explanation:

[tex]y^2 = 100 + 196 = 296\\\\y = \sqrt{296} \\\\y = 17.20[/tex]

Answer:

the option C

Step-by-step explanation:

have a great day

Answer:

[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]

Step-by-step explanation:

The cotangent function can be rewritten by trigonometric relations, that is:

[tex]\cot 330^{\circ} = \frac{1}{\tan 330^{\circ}} = \frac{\cos 330^{\circ}}{\sin 330^{\circ}}[/tex] (1)

By taking approach the periodicity properties of the cosine and sine function (both functions have a period of 360°), we use the following equivalencies:

[tex]\sin 330^{\circ} = \sin (-30^{\circ}) = -\sin 30^{\circ}[/tex] (2)

[tex]\cos 330^{\circ} = \cos (-30^{\circ}) = \cos 30^{\circ}[/tex] (3)

By (2) and (3) in (1), we have following expression:

[tex]\cot 330^{\circ} = -\frac{\cos 30^{\circ}}{\sin 30^{\circ}}[/tex]

If we know that [tex]\sin 30^{\circ} = \frac{1}{2}[/tex] and [tex]\cos 30^{\circ} = \frac{\sqrt{3}}{2}[/tex], then the result of the trigonometric expression is:

[tex]\cot 330^{\circ} = -\frac{\frac{\sqrt{3}}{2} }{\frac{1}{2} }[/tex]

[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]

The exact value of cot 330° with a rational denominator is √3.

To find the exact value of cot 330°, we can first determine the reference angle. The reference angle for 330° is 30°, as it is the angle between the terminal side of 330° and the x-axis.

Cotangent (cot) is the reciprocal of the tangent function, so we need to find the tangent of the reference angle, which is tan 30°. The tangent of 30° is √3/3.

Since cot is the reciprocal of tan, the cotangent of 330° is the reciprocal of √3/3, which is 3/√3.

To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is √3.

(3/√3) x (√3/√3) = 3√3/3

Simplifying further, we can cancel out the common factor of 3:

(3√3/3) = √3

Therefore, the exact value of cot 330° with a rational denominator is √3.

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Answer:

In order of increasing angle measure, the fourth roots of -3 + 3√3·i are presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left({-\dfrac{\pi}{12} } \right) + i \cdot sin\left(-\dfrac{\pi}{12} } \right) \right][/tex]

[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{5 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{5 \cdot\pi}{12} } \right) \right][/tex]

[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{11 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{11 \cdot\pi}{12} } \right) \right][/tex]

[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{17 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{17 \cdot\pi}{12} } \right) \right][/tex]

Step-by-step explanation:

The root of a complex number a + b·i is given as follows;

r = √(a² + b²)

θ = arctan(b/a)

The roots are;

[tex]\sqrt[n]{r}[/tex]·[cos((θ + 2·k·π)/n) + i·sin((θ + 2·k·π)/n)]

Where;

k = 0, 1, 2,..., n -2, n - 1

For z = -3 + 3√3·i, we have;

r = √((-3)² + (3·√3)²) = 6

θ = arctan((3·√3)/(-3)) = -π/3 (-60°)

Therefore, we have;

[tex]\sqrt[4]{-3 + 3 \cdot \sqrt{3} \cdot i \right)} = \sqrt[4]{6} \cdot \left[cos\left(\dfrac{-60 + 2\cdot k \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-60 + 2\cdot k \cdot \pi}{4} \right) \right][/tex]

When k = 0, the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 0 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 0 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({-\dfrac{\pi}{12} } \right) + i \cdot sin\left(-\dfrac{\pi}{12} } \right) \right][/tex]

When k = 1 the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 1 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 1 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{5 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{5 \cdot\pi}{12} } \right) \right][/tex]

When k = 2, the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 2 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 2 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{11 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{11 \cdot\pi}{12} } \right) \right][/tex]

When k = 3, the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 3 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 3 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{17 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{17 \cdot\pi}{12} } \right) \right][/tex]

Answer:

Step-by-step explanation:

Just took the test.

1) 4sqrt6 cis(pie/6)

2) 4sqrt6 cis (2pie/3)

3) 4sqrt6 cis(7pie/6)

4) 4sqrt6 cis (5pie/3)

Answer:

It's B

Step-by-step explanation:

I took the test

Answer:

B= (√30 - 2√5)

Step-by-step explanation:

Answer:

Rates :

$95 per hour and $105 per hour

Step-by-step explanation:

Let their rate = x and y respectively :

10x + 15y = 2475 - - - - (1)

x + y = 200 - - - - (2)

x = 200 - y - - (3)

Put (3) into (1)

10(200 - y) + 15y = 2475

2000 - 10y + 15y = 2475

5y = 2475 - 2000

5y = 475

y = 95

x = 200 - y

x = 200 - 95

x = 105

Answer:

do (3x2+4x+7)+y=0

y=-3x^2-4x-7

Answer:

10

Step-by-step explanation:

5x2

Answer:

I think it's c but I'm not 100%

Step-by-step explanation:

sorry if I'm wrong

Answer:

(a) 1, 2, 3, 6, 8

Step-by-step explanation:

Given

[tex]Median = 3[/tex]

[tex]Mean = 4[/tex]

Required

The sequence of hours worked each day

See attachment for options

From the question, we understand that:

[tex]Median = 3[/tex]

This means that, the middle number is 3 (when sorted)

So, we can conclude that (b) and (c) cannot be true because their middle numbers are 6 and 5 respectively

Next, is to determine the mean of (a) and (d)

The mean of a data is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

(a)

[tex]\bar x = \frac{1+ 2+ 3+ 6+ 8}{5}[/tex]

[tex]\bar x = \frac{20}{5}[/tex]

[tex]\bar x = 4[/tex]

(d)

[tex]\bar x = \frac{1+ 2+ 3+ 4+ 5}{5}[/tex]

[tex]\bar x = \frac{15}{5}[/tex]

[tex]\bar x = 3[/tex]

Option (a) is true, because it has:

[tex]Median = 3[/tex]

[tex]Mean = 4[/tex]

Answer:

301.44 ft

Step-by-step explanation:

Answer:

38.46

Step-by-step explanation:

Percentage Calculator: 20 is what percent of 52? = 38.46.

Answer: 88 gallons

Step-by-step explanation:

Every 2 vanillas = 11 chocolates

so 16 vanillas = 88 chocolates

i did this by multiplying both numbers by 8

sorry if this is wrong

Answer:

345

Step-by-step explanation:

Answer:

0.166

Step-by-step explanation:

Step-by-step explanation:

(I) A number which can be expressed in the form m/n, where m and n are integers and n is not equal to zero, is called a Rational Number .

(ii) If the integers m and n have no common divisor other than 1 and n is positive, then the rational number m/n is said to be in the Simplest form .

(iii) Two rational numbers are said to be equal, if they have the same Simplest form .

(iv) If m is a common divisor of x and y, then x/y = (x ÷ k)/( y ÷ k) .

(v) The standard form of -1 is -1/1

(vi) If m/n is a rational number, then n cannot be 0

(vii) Two rational numbers with different numerators are equal, if their numerators are in the same ratio as their denominators.

Answer:

h(g(4)) = -27

Step-by-step explanation:

first find g(4):

[tex]g(x)=x^2-1\\\\g(4)=4^2-1\\\\= 16 - 1\\\\= 15[/tex]

then plug that into h(x):

[tex]h(x)=-2x+3\\\\h(15)= -2(15) + 3\\\\= -30 + 3\\\\=-27[/tex]

Answer:

8,

4 and 8

3,4,8,9

6

Step-by-step explanation:

Answer:

D is your correct answer.

Answer:

V = 27π or approx 85 cubic inches

Step-by-step explanation:

V(cyl) = πr²h

V = π·3²·3

V = 27π

In this number line, we marked -7/6 to the left of -1, and 4/3 to the right of 1.

To plot the numbers -1 1/6 and 4/3 on a number line, we need to find their relative positions and mark them accordingly.

Let's start with -1 1/6:

-1 1/6 can be written as a mixed number or an improper fraction. To simplify the plotting process, let's convert it to an improper fraction.

-1 1/6 = -(6/6 + 1/6) = -7/6

On the number line, we start from zero and move to the left because it is a negative number. Since -7/6 is less than -1, we will place it closer to zero but to the left of -1.

Next, let's plot 4/3:

4/3 is already in the form of an improper fraction. To plot it, we start from zero and move to the right since it is a positive number. 4/3 is greater than 1, so we will place it to the right of 1.

On this number line, we marked -7/6 to the left of -1, and 4/3 to the right of 1.

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Answer:

i think the answer may be acute and isosceles

Answer:

125

Step-by-step explanation:

1,000/8 because all the outcomes are evenly likely

Answer: $285

Step-by-step explanation:

First and foremost, we should note that from January 1 to April 1 is 3 months. Since Mario had a savings account balance of $2742 on January 1 and by April 1, his balance had increased to $3597. The increase in balance will be:

= $3597 - $2742

= $855

Then the average savings rate will be:

= Total amount saved / Number of months

= $855/3

= $285

He had an average savings of $285 per month.

Answer:

p^2 - q^2

Step-by-step explanation:

This is an example of "the product and difference of two squares."

The relevant formula is (a - b)(a + b) = a^2 - b^2 (no middle term).

Here,the desired product is (p - q)(p + q) = p^2 - q^2.

Answer:

(p - q)(p+q). :p²-q²....

Answer:

0.461538

Step-by-step explanation:

brainlest pls im try to rank up to ace

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{13x = 6}[/tex]

[tex]\huge\textsf{DIVIDE 13 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{13x}{13}=\dfrac{6}{13}}[/tex]

[tex]\rm{CANCEL \ out: \dfrac{13}{13} \ because \ that \ gives \ you \ 1}[/tex]

[tex]\rm{KEEP: \dfrac{6}{13} \ because \ that \ gives \ you \ the \ value \ of \ x}[/tex]

[tex]\boxed{\boxed{\mathsf {Answer: x = \bf \dfrac{6}{13}}}}\huge\checkmark[/tex]

[tex]\boxed{\textsf{or you could say \boxed{\mathsf{x = \underline{\bf 0.461538}}} they both equal to the same thing}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

25

Step-by-step explanation:

Consider that,

x^2+4x+4 = (x+2)(x+2)

x^2+7x+10 = (x+2)(x+5)

Dividing those expressions leads to

(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)

The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.