A: 49
B: 33
C: 57
D: 16

Answer:

0.294 = 29.4% probability that none of the chosen entrees contain spinach.

Step-by-step explanation:

The choices of entrees are chosen without replacement, which means that the hypergeomtric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

13 different entrees for an important banquet

This means that [tex]N = 13[/tex]

3 of which contain spinach.

This means that [tex]k = 3[/tex]

The guests will have a choice of 4 entrees.

This means that [tex]n = 4[/tex]

What is the probability that none of the chosen entrees contain spinach?

This is P(X = 0). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,13,4,3) = \frac{C_{3,0}*C_{10,4}}{C_{13,4}} = 0.294[/tex]

0.294 = 29.4% probability that none of the chosen entrees contain spinach.

Answer:

C

Step-by-step explanation:

I saw em in other ones

Answer:

Small jar

Step-by-step explanation:

Small jar

[tex]1.37 \div 360 = 0.0038[/tex]

Large jar

[tex]2.16 \div 540 = 0.004[/tex]

Answer:

p = 21, and q = 30

Step-by-step explanation:

If x is directly proportional to y, then we know:

y = 35x / 60

We can factor 5 out of that, giving us:

y = 7x / 12

We can also find the inverse of that relationship:

y = 7x / 12

12y = 7x

x = 12y / 7

So in the second row, where x = 36:

y = 7 × 36 / 12

y = 7 × 3

y = 21

And in the third row where y = 17.5:

x = 12 × 17.5 / 7

x = 210 / 7

x = 30

So p = 21, and q = 30

Answer:

Step-by-step explanation:The length is 3+l therefore the Expression is (3+l)>w

Answer:

r = 5.4

Step-by-step explanation:

Formula:

P = πr + 2r

27.756 = πr + 2r

27.756 = 3.14r + 2r

27.756 = 5.14r

r = 5.4

Answer:

Can I see a picture?

Step-by-step explanation:

9514 1404 393

Answer:

  D.  8 (m +12)

Step-by-step explanation:

One cannot factor the coefficient from the first term and apply that to both terms. The result is NOT equivalent.

  8m +12 ≠ 8(m +12) = 8m +96

Answer:

X = 56

Step-by-step explanation:

Answer:

I think D

Step-by-step explanation:

not completely sure

Because the fractions that contain the variable z are different in each side of the equal sign and there are no radicals in the equation, the answer would be:

It has one solution

Answer:

Circumference = π*diameter

If you get the circumference of a circle and then divide it into the diameters of said circle, you get exactly 3.1415962 ect. (most math formulas use 3.14 for pi so its more simpler)

hope that helped! if you have any questions, just ask them in the comments.

btw the answer is 50.24 inches.

From the above explanation, the option B statement is not correct.

From the given options we need to identify which statement is not correct.

An obtuse angle is any angle greater than 90° and less than 180°.

From option A:

100° angle is an obtuse angle, because which is greater than 90° and less than 180°.

From option B:

175° angle is a reflex angle because it is greater than 180° and less than 360°.

From option C:

Less than 90° lies in I quadrant, more than 90° and less than 180° lies in II quadrant and more than 180° and less than 270° lies in III quadrant.

From option D:

An 85° angle is an acute angle because it is greater than 0° and less than 90°.

From the above explanation, the option B statement is not correct.

To learn more about an obtuse angle visit:

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Answer:

6(5x-y)

Step-by-step explanation:

i hope this helps :)

Answer:

0.32 = 32% probability that an employee selected at random will need either corrective shoes or major dental work.

Step-by-step explanation:

We solve this question treating these events as Venn probabilities.

I am going to say that:

Event A: Needing corrective shoes.

Event B: Needing major dental work.

14% of the employees needed corrective shoes

This means that [tex]P(A) = 0.14[/tex]

21% needed major dental work

This means that [tex]P(B) = 0.21[/tex]

3% needed both corrective shoes and major dental work.

This means that [tex]P(A \cap B) = 0.03[/tex]

What is the probability that an employee selected at random will need either corrective shoes or major dental work?

This is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

So, from the values given by the exercise:

[tex]P(A \cup B) = 0.14 + 0.21 - 0.03 = 0.32[/tex]

0.32 = 32% probability that an employee selected at random will need either corrective shoes or major dental work.

Answer:

28

Step-by-step explanation:

It is 8 combination 4- using a TI 84, type in 8, then hit math- over to probability then nCr- then 6

Answer:

Total cost of patio = $560

Step-by-step explanation:

Given:

Length of patio = 14 m

Width of patio = 8 m

Height of patio = 1 m

Cost of 1 m³ concrete = $5

Find:

Total cost of patio

Computation:

Volume of patio = l x b x h

Volume of patio = 14 x 8 x 1

Volume of patio = 112 m³

Total cost of patio = Volume of patio x $5

Total cost of patio = 112 x $5

Total cost of patio = $560

The sum of the angles for a 4 sides figure must add up to 360.

Angle 1 and angle 2 are between similar sides so the 2 angles are identical.

Subtract the known angles from 360:

360 - 72 - 18 = 270

Divide that by 2:

270*2 = 135

Angle 2 = 135 degrees.

Answer:

A and B

Step-by-step explanation:

Answer:

305,080.0809 is the answer

Answer: 4096

Step-by-step explanation: 2^12

There are 4096 different color combinations are possible.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

Given that The shirt printing company offers 12 colors to choose from for the logo design.

Here, we need to get the possible number of color combinations possible.

Since any number of colors can be chosen, there are no restriction.

That means the number of possible color combinations are;

[tex]2^{12} = 4096[/tex]

There are 4096 different color combinations are possible.

Learn more about combinations and permutations here:

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Answer:

13.5

Step-by-step explanation:

The space inside a paper bag, the amount of water in a pond and the amount of soup a bowl will hold. Therefore, options A, B and D are the correct answers.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Volume is the amount of space taken up by an object, while capacity is the measure of an object's ability to hold a substance, like a solid, a liquid or a gas. Volume is measured in cubic units, while capacity can be measured in almost every other unit, including liters, gallons, pounds, etc.

Therefore, options A, B and D are the correct answers.

To learn more about the examples of volume visit:

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Answer:

x = -5 , x = 1

Step-by-step explanation:

f(x) = ⅔(x + 5)(x - 1)

0 = ⅔(x + 5)(x - 1) → x + 5 = 0 OR x - 1 = 0

x = -5 , 1

Answer:

the correct answer is 6 since 36\6 is 6

Answer:

23

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Answer:

B

Step-by-step explanation:

Look at the graph, it passes to (0,3), so you need to replace that coordinate into A,B,C,D. Then you can see, there is only B and C satisfies.

[tex]Y=3(\frac{1}{3} )^{0}=3.1=3.[/tex]

and

[tex]Y=(\frac{1}{2} )^{0}+2=1+2=3[/tex]

Next step, you can see when x approach to infinite then Y approach to 0.

Hence, we will take limit of B and C, if limit B or C equals to 0 then we will choose.

[tex]\lim_{x \to \infty} {3(\frac{1}{3})^x=3. \lim_{x \to \infty} {(\frac{1}{3})^x=3.0=0[/tex]

and

[tex]\lim_{x \to \infty} {[(\frac{1}{2})^x+2]}= \lim_{x \to \infty} {(\frac{1}{2})^x}+ \lim_{x \to \infty} {2}=0+2=2[/tex]

We can see that only B is satisfied.