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2 years ago

5

There are 11 students participating in a spelling bee. in how many ways can the students who go first¸ second¸ and third in the

bee be chosen

1 answer:

Valentin [98]2 years ago

6 0

Three ways because it alternates. 1st, 2nd and 3rd.

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What is the y-intercept of the function y = negative one-half cosine (three-halves x)?

Jet001 [13]

A. Sorry if I’m wrong

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2 years ago

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A teacher gave a quiz to her class of 30 students. However, she misplaced one of the quizzes. The teacher calculated the mean of

Zina [86]

Answer:

B

Step-by-step explanation:

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2 years ago

Compare the functions shown below: f(x) = 4x + 5 g(x) tangent function with y intercept at 0, 2 h(x) = 3 sin(2x + π) − 2 Which f

KATRIN_1 [288]

The y-intercept of the graph of a function is the value of f(0) for any function f.
That is, it is the y-value in the pair (0, y)

The y-intercept of <span>f(x) = 4x + 5 is f(0)=4*0+5=5

The y-intercept of (0, 2) is 2.

The y-intercept of </span>h(x) = 3 sin(2x + π) − 2 is:

h(0) = 3 sin(2*0 + π) − 2=3 sin(π) − 2=3*0-2=-2

<span>Answer: The function f has the greatest y-intercept.

</span>

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2 years ago

Given that tangent theta = negative 1, what is the value of secant theta, for StartFraction 3 pi Over 2 EndFraction less-than th

Rashid [163]

Answer:

$sec(\theta)=\frac{2}{\sqrt{2} }=\sqrt{2}$

Step-by-step explanation:

Start by noticing that the angle $\theta$ is on the 4th quadrant (between $\frac{3\pi}{2}$ and $2\pi$ . Recall then that in this quadrant the functions tangent and cosine are positive, while the function sine is negative in value. This is important to remember given the fact that tangent of an angle is defined as the quotient of the sine function at that angle divided by the cosine of the same angle:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

Now, let's use the information that the tangent of the angle in question equals "-1", and understand what that angle could be:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\-1=\frac{sin(\theta)}{cos(\theta)}\\-cos(\theta)=sin(\theta)$

The particular special angle that satisfies this (the magnitude of sine and cosine the same) in the 4th quadrant, is the angle $\frac{7\pi}{4}$

which renders for the cosine function the value $\frac{\sqrt{2} }{2}$ .

Now, since we are asked to find the value of the secant of this angle, we need to remember the expression for the secant function in terms of other trig functions: $sec(\theta)=\frac{1}{cos(\theta)}$

Therefore the value of the secant of this angle would be the reciprocal of the cosine of the angle, that is: $sec(\theta)=\frac{2}{\sqrt{2} }=\sqrt{2}$

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2 years ago

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Isabella filled her pool with water at a constant rate.

Anon25 [30]

Answer:

The size of Isabella's pool is 220 liters.

Step-by-step explanation:

Let the size of Isabella's pool be $x$ liters, $R$ be the rate of fill, $t$ be the time of fill and $V$ be the volume of water filled in the pool.

As the rate of fill is constant,

Therefore, volume of water filled in the pool can be given as,

$V= Rt$

Volume of water left is given as $x-V=x-Rt$

From the table,

Volume of water left after $t=2$ minutes is 184 liters.

So, $x-R(2)=184\\x-2R=184$ -------- 1

Volume of water left after $t=12$ minutes is 4 liters.

So, $x-R(12)=4\\x-12R=4$ ------------2

Multiply equation 1 by 6 and equation 2 by -1, we get

$6x-12R=1104\\-x+12R=-4$

Now, we add the above equations, we get

$(6x-x)+(12R-12R)=1104-4\\5x=1100\\x=\frac{1100}{5}=220$

Therefore, the size of Isabella's pool is 220 liters.

6 0

2 years ago