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3 years ago

7

There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 7 8 . There are 72 m

arbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.

1 answer:

Arturiano [62]3 years ago

8 0

Answer:

63 red marbles.

Step-by-step explanation:

Because the probability of drawing a red marble is 7/8, the number of red marbles = 7/8 * 72

= 7 * 9

= 63.

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What is the following quotient?

seropon [69]

Answer: Choice B) $\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\$

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

Work Shown:

$\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\$

This shows why choice B is the answer.

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

Explanation:

In the second step, I multiplied top and bottom by $(\sqrt{11}+\sqrt{3})$
This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.

So in general, if the denominator is $\sqrt{a}-\sqrt{b}$ and you want to rationalize the denominator, then you should multiply top and bottom by $\sqrt{a}+\sqrt{b}$ . The same applies in reverse as well.

This leads to the denominator becoming $(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}) = (\sqrt{a})^2-(\sqrt{b})^2 = a-b$

Keep in mind that $a \ge 0$ and $b \ge 0$

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2 years ago

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Nonamiya [84]

Answer:

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Step-by-step explanation:

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3 years ago

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Rosters Chicken advertises "lite" chicken with 30% fewer calories than standard chicken. When the process for "lite" chicken

PilotLPTM [1.2K]

Answer:

UCL (x bar) = 424

LCL (x bar) = 376

Step-by-step explanation:

Given:

Average calories contained, μ = 400

Standard deviation, σ = 30 calories

Sample size, n = 25

a) UCL (x bar) = $\mu+\frac{4\sigma}{\sqrt{n}}$

On substituting the respective values, we get

UCL (x bar) = $400+\frac{4\times30}{\sqrt{25}}$

or

UCL (x bar) = 424

Similarly,

LCL (x bar) = $\mu-\frac{4\sigma}{\sqrt{n}}$

On substituting the respective values, we get

LCL (x bar) = $400-\frac{4\times30}{\sqrt{25}}$

or

LCL (x bar) = 376

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3 years ago

Item 3 Amelie's bird cage is shaped like a rectangular prism. The cage has a height of 26 inches and a volume of 7,280 cubic inc

lisov135 [29]

Answer:

Step-by-step explanation:

The Volume of a rectangular prism is expressed as;

V = Base area * height of prism

Given

Volume of prism V = 7,280 cubic inches.

height of prism = 26in

Required

Base Area

Substitute the given parameter into the formula;

7280 = 26B

B = 7280/26

B = 280in²

Hence the area of the newspaper on the bottom of the cage is 280in²

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2 years ago

The time required for a skilled worker to produce x shirts is given by the function T(x) = 4x + 2, where T is measured in hours.

solong [7]

Answer:

A. $1,110

B. 50 units.

Step-by-step explanation:

A. Substitute $x=18$ into the function $T(x)=4x+2$ for calculate the time in hours required for the worker to produce 18 units:

$T(18)=4(18)+2=74$

Now you need to substitute $T=74$ into the function $S(T)=15T$ to calculate the amount in dollars she will be paid for 74 hours:

$S(74)=15(74)=1,110$

She will be paid $1,110.

B. To calculate the number of units that the worker needs to produce to be paid $3,030 , you need to substitute $S(T)=3,030$ into the function $S(T)=15T$ and solve for T (to find the number of hours she requires to work to be paid $3,030)

$3,030=15T\\\\T=\frac{3,030}{15}\\\\T=202$

Now, substitute $T(x)=202$ into $T(x)=4x+2$ and solve for x, to calculate the number of units she produces in 202 hours:

$202=4x+2\\\\202-2=4x\\\\x=\frac{200}{4}\\\\x=50$

She would need to produce 50 units to be paid $3,030

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3 years ago