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olga_2 [115]
3 years ago
12

If y varies inversely as x and y is 2.5 when x is 6, what is y when x is 4? a. 3.75 b. 1.67 c. 0.1 d. 7.5 Please select the best

answer from the choices provided
Mathematics
2 answers:
REY [17]3 years ago
8 0
Because y varies inversely as x, therefore
y= \frac{k}{x}
where k =  constant.

When x = 6, y = 2.5. Ther efore
\frac{k}{6} = 2.5
Cross multiply.
k = 6 x 2.5 = 15

The equation is
y =  \frac{15}{x}

When x = 4, obtain
y =  \frac{15}{4}= 3.75

Answer: a. 3.75

Sphinxa [80]3 years ago
3 0
Inverse proportion is given in the form
y= \frac{k}{x}

We need to work out the constant, k, by substituting x = 6 and y = 2.5
2.5= \frac{k}{6}
k=2.5*6
k=15

The value of y when x = 4
y =  \frac{15}{x}
y= \frac{15}{4}
y=3.75
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Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.
amm1812

Answers:

  • (a) 73440
  • (b)  3060

=====================================================

Explanation for part (a)

Consider four slots labeled A,B,C,D.

We have

  • 18 choices for slot A
  • 17 choices for slot B
  • 16 choices for slot C
  • 15 choices for slot D

We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440

You can use the nPr permutation formula as an alternative method

_nP_r = \frac{n!}{(n-r)!}

in this case n = 18 and r = 4. The exclamation marks indicate factorial.

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

Explanation for part (b)

Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.

Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.

There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)

73440/24 = 3060

You could use the nCr combination formula to get the same result

_nC_r = \frac{n!}{r!(n-r)!}

where n = 18 and r = 4 are the same from last time.

The connection between nPr and nCr is this

_nC_r = \frac{_nP_r}{r!}

which can be rearranged into

_nP_r = r!*\left( _nC_r \right)

these formulas are handy to help us go back and forth between nCr or nPr.

8 0
2 years ago
John has 6 rubber bands. Sophia has 78 rubber bands.
vovikov84 [41]

Answer: 13 times

Step-by-step explanation:

78 / 6 = 13 times

6 0
2 years ago
A scoop of ice cream has 1.5 inch radius. How talk should the cream cone of the same radius be in order to contain all of the ic
MAVERICK [17]

Answer:

The cream cone should be <u>6 inches</u>.

Step-by-step explanation:

Given:

A scoop of ice cream has 1.5 inch radius.

Now, to find the height of the cream cone.

So, we need to get the volume of scoop by putting formula:

Radius (r) = 1.5 inch.

Using the value π = 3.14.

Volume=\frac{4}{3} \pi r^3

Volume=\frac{4}{3}\times 3.14\times 1.5^3\\\\Volume=\frac{4}{3}\times 3.14\times 3.375\\\\Volume=14.13\ inches^3.

<em>Thus, the volume of the ice cream scoop is 14.13 cubic inches.</em>

<em>So, to put all of the ice cream inside the cone.</em>

<em>We take the cream cone volume as the scoop volume.</em>

Let the height of cone be h.

<em>As, given radius is same.</em>

Now, to get the height of the cream cone we put formula of volume:

Volume=\pi r^2\frac{h}{3}

14.13=3.14 \times (1.5)^2\times \frac{h}{3}\\\\14.13=3.14\times 2.25\times \frac{h}{3}

<em>Multiplying both sides by 3 we get:</em>

<em />42.39=3.14\times 2.25\times h\\\\42.39=7.065\times h<em />

<em>Dividing both sides by 7.065 we get:</em>

6=h

h=6\ inches.

<u><em>Hence, the height of the cone = 6 inches.</em></u>

Therefore, the cream cone should be 6 inches.

7 0
2 years ago
You are considering leasing a store site that has 1,500 square feet. The landlord is asking for a rent of $50 per square foot, p
tigry1 [53]

Answer:

$75000/year

$6250/month

Step-by-step explanation:

1500 ft²*$50/(ft²*year) = $75000/year

1 year = 12 month

$75000/12 month= $6250/month

3 0
2 years ago
Consider two congruent triangular prisms. Each rectangular face of prism A has a width of x + 2 and each rectangular face of pri
Bumek [7]
35
this is the correct answer if you're on usatestprep
5 0
3 years ago
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