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2 years ago

Tim must choose 4 graphic novels out of a collection of 13 to take on vacation.

Mathematics

2 answers:

Vsevolod [243]2 years ago

7 0

$C(13,4)=\dfrac{13!}{4!9!}=\dfrac{10\cdot11\cdot12\cdot13}{2\cdot3\cdot4}=715$

Kay [80]2 years ago

7 0

there are 715 ways to choose (C, 715)

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A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4

Natasha2012 [34]

Reflection on the -x axis

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2 years ago

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Molly shared a spool of ribbon with 12 people. Each person received 3 feet of ribbon. Which equation can she use to find r, the

koban [17]

Answer:

d. r/12 = 3

Step-by-step explanation:

r = 3(12)

r/12 = 3

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2 years ago

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25. To produce the graph of the function y=0.5cos(0.5x), what transformations should be applied to the graph of the parent funct

soldi70 [24.7K]

Answer:

C. A horizontal stretch to produce a period of $2\pi$ and a vertical compression.

Step-by-step explanation:

We are given the parent function as $y= \cot x$

It is given that, transformations are applied to the parent function in order to obtain the function $y=0.5\cot (0.5x)$ i.e. $y=\frac{1}{2}\cot (\frac{x}{2})$

That is, we see that,

The parent function $y= \cot x$ is stretched horizontally by the factor of $\frac{1}{2}$ which gives the function $y=\cot (\frac{x}{2})$ .

Further, the function is compressed vertically by the factor of $\frac{1}{2}$ which gives the function $y=\frac{1}{2}\cot (\frac{x}{2})$ .

Now, we know,

If a function f(x) has period P, then the function cf(bx) will have period $\frac{P}{|b|}$ .

Since, the period of $y= \cot x$ is $\pi$ , so the period of $y=\frac{1}{2}\cot (\frac{x}{2})$ is $\frac{\pi}{1/2}$ = $2\pi$

Hence, we get option C is correct.

3 0

2 years ago

A 96-ft high transmission tower casts a 72-ft long shadow. An anchor wire runs from the top of the tower to the tip of the shado

galben [10]

See attached picture and check solution below.
We are given with the following values:
A = length of transmission line = 96ft
B = length of shadow = 72 feet
C = distance of ladder to base of transmission line = 66 feet

Solve for angle created between the wire and tip of the shadow:
tan x = opposite/ adjacent
tan x = 96 feet / 72 feet
x = 53.13°

Solving for the height of the ladder:
tan x = Ladder length / (72-66)
tan 53.13° * (72-66) = ladder length
ladder length = 8 feet

The answer is letter "B" which is 8 feet.

5 0

2 years ago

Ella purchased a game that was on sale for 12% off. The sales tax in her county is 6%. Let y represent the original price of the

klio [65]

Answer:

The expression that can be used to determine the final cost of the game is

1.06(0.88 y) ⇒ (C)

Step-by-step explanation:

If the price of an item is discounted, that mean its new price will be less its initial price

The taxes on item, makes its new price greater than the initial price because tax is add

Let us solve the problem

∵ Ella purchased a game that was on sale for 12% off

→ That means the new price will (100% - 12%) of the initial price

∵ y represented the initial price of the game

→ Multiply y by (100% - 12%) to get the new price

∴ The new price = y (100% - 12%)

∴ The new price = y (88%)

→ Change 88% to normal number by divide it by 100

∴ The new price = y ( $\frac{88}{100}$ )

∴ The new price = 0.88 y

∵ The sales tax in her county is 6%

→ That means the final cost will be (100% + 6%) of 0.88 y

∴ The final cost = (100% + 6%) × (0.88 y)

∴ The final cost = 106% × (0.88 y)

→ Change 106% to normal number by divide it by 100

∴ The final cost = $\frac{106}{100}$ × (0.88 y)

∴ The final cost = 1.06(0.88 y)

The expression that can be used to determine the final cost of the game is 1.06(0.88 y)

4 0

2 years ago