(a) Which expression is equivalent to (​

Answer:

147/572

Step-by-step explanation:

The number of combinations of  n  things chosen  r  at a time is

[tex]\binom{n}{r}=\frac{n!}{r!(n-r)!}[/tex]  (Some writers use the symbol [tex]_nC_r[/tex])

Choose 4 women from the 7:

[tex]\binom{7}{4}=\frac{7!}{4!(7-4)!}=35[/tex]  ways

Choose 3 men from 9:

[tex]\binom{9}{3}=\frac{9!}{3!(9-3)!}=84[/tex]  ways

There are 35 x 84 = 2940 ways to choose both, out of

[tex]\binom{16}{7}=\frac{16!}{7!(16-7)!}=11440[/tex] ways to choose any 7 people from the group of 16.

Probability:

[tex]\frac{2940}{11440}=\frac{147}{572}[/tex]

P.S. As an example of how to calculate combinations, here's the calculation (by hand, a calculator is easier!) of [tex]\binom{9}{3}[/tex].

[tex]\binom{9}{3}=\frac{9!}{3!(9-3)!}=\frac{9!}{3!6!}[/tex]

When you write out the factorials, you can do a bunch of cancellation between the numerator and denominator.

[tex]\frac{9\cdot8\cdot7\cdot\cancel{6\cdot5\cdot4\cdot3\cdot2\cdot1}}{(3\cdot2\cdot1)(\cancel{6\cdot5\cdot4\cdot3\cdot2\cdot1)}}=\frac{9\cdot8\cdot7}{3\cdot2\cdot1}=84[/tex]

Answer:

(a) 552ft

(b) $220.8

Step-by-step explanation:

(a) TSA of cuboid = 2 (lb + bh + hl)

                        = 2 (12*8+8*9+9*12) = 2 ( 276) = 552 square feet.

(b) Cost of covering the box = $0.40 * 552 feet

                                          = $220.8

complete question

the probability of taking a freshman seminar, if a student is a science major, is:

a) a total probability.

b) a conditional probability.

c) a complete probability.

d) a joint probability.

Answer:

B. Conditional probability

Step-by-step explanation:

In this given question, what we ant to do is to find the probability thst a student who is a science major is taking a freshman seminar. This clearly a case of conditional probability.

In a conditional probability, we are trying to find out the probability of an event occurring given that another event has already occurred. since the student is a science major, the probability of the student taking a freshman seminar is to be determined.

Answer:

231 employees

Step-by-step explanation:

The ratio of men to women working for the company is 6 to 5, which means that for every 5 women working at the company, there are 6 men working at the company.

Since there are 105 women working at the company,

there are 6/5 * 105 = 126 men working at the company.

In total, there are 126 men + 105 women = 231 employees working for the company.

Answer:3,9

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

72/2 = 36

Square root of 36 is 6; 6 x 2 = 12

square root of 4 is 2 and 2^2 equals 4.

12 +4 =16

Mark me brainliest please

Answer:

16

Step-by-step explanation:

72/2=36

square root 36=6

6*2=12

root4 squared is 4

12+4=16

Hope that helps :)

Attributes of a parallelogram leads to, Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram.

The complete question is,

Which of the following attributes of a parallelogram leads to the conclusion that every square can be categorized as a parallelogram? Choose each option that applies.

four equal sides

two pairs of diametrically opposed equal angles

diagonals are cut in half.

two sets of parallel, opposed sides.

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Answer:

x = -1

Step-by-step explanation:

0.5(5-7x)=8-(4x+6)       note.......0.5   = 1/2

(1/2) ( 5 - 7x)  = 8 - 4x - 6

(1/2) (5 - 7x)  = 2 - 4x    multipy through by 2

5 - 7x   = 4 - 8x         add 8x  to both sides.......subtract 5 from both sides

x = -1

Answer:

the answer is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Based on the data gathered on that certain day, I would say NO, the store does not need to change its staffing. The data shows that the percentages calculated by the store are extremely close to the actual percentage of people that arrived at those given hours throughout the day. The problem with this solution is that it does not take into account special circumstances, such as specific days, events, holidays, new popular items, etc. All of these can drastically affect the number of people that enter the store at a given time.

1. The retail store should not change its staffing arrangement.

2. Changing the staffing arrangement may not favor the retail store.

Data and Calculations:

                                             8:00 am &   12:00 pm &   4:00 pm &   8:00 pm &

                                              12:00 pm       4:00 pm      8:00 pm      midnight

Expected % of customers        32%             21%              35%                12%

Actual number of customers  214               198              276                  134

Total Number of customers = 822 (214 + 198 + 276 + 134)

Actual % of customers            26%             24%             34%                 16%

Difference between expected percentage of

 customers and actual           6%                3%                1%                  -4%

Variation                                 0.36%           0.09%         0.01%            0.16%

Sum of variation = 0.62%

Standard Deviation = 0.787

Thus, based on the standard deviation, the store should not change its staffing.

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Answer:

[tex]x^{3}-5x^{2}+2x+8[/tex]

Answer:

B

Step-by-step explanation:

solution to the system is where they intercept

Answer:

Yes, Pythagorean theorem

Step-by-step explanation:

Yes, as by doing the Pythagorean theorem, a^2+b^2=c^2 you can confirm that it is.

8^2+15^2=17^2

64+225=17^2

289=17^2

(square root both sides)

17=17

Answer:

You would first divide the amount of months by the total amount of money that she has earned in 5 months.

(You put down 25, 00, 000 so Ima just write it as 2,500,000)

25,000,000/5 = 5,000,000

She earns 5,000,000 a month, and would earn 60,000,000 per year.

Anual salary is how much money you would earn per year, so the answer is 60,000,000. (sixty million).

Step-by-step explanation:

Hope it helps! =D

Answer:

hypotenuse

Step-by-step explanation:

Answer:

I believe it is D hypotenuse

Step-by-step explanation:

In geometry, a hypotenuse is the longest side of a right-angled triangle.

Answer:

she can fill 3 boxes completely and one book will be left over

Step-by-step explanation:

if a box can be filled with 4 book then we do 4 multiply 3 and then 12 books will can fill 3 box and there is 13 books so 1 book will be left over

Answer:

r=3

Step-by-step explanation:

use slope formula : y2-y1 / x2-x1

-5-3 / r-5

the numerator is -8 which means the denominator has to be -2 in order to have the slope be 4

so r-5 = -2

3-5 = -2

Step-by-step explanation:

first we need to identify the lines themselves.

the line from bottom left to top right is simply

y = x

the line is solid, so the points on the line are included.

the dotted line (the points on the line itself are not included) goes through

(0, 2) and (3, 0)

the y-intercept is therefore 2 (the y value when x = 0).

and for the slope

x changes by +3 (from 0 to 3).

y changes by -2 (from 2 to 0).

the slope is -2/+3 = -2/3

and the line is

y = (-2/3)x + 2

we see that the desired gray area is above both lines (">"), and we need to consider, whether the points in the lines are included or not.

so, the system of inequalities is

y >= x

y > (-2/3)x + 2

Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).

An equation is a mathematical representation of two identical variables, one on each side of a "equals" sign. Common difficulties can be solved using equations. We commonly seek pre algebra help to resolve problems in real life. Pre-algebra is the fundamental building block of mathematics.

Here,

[tex](x + 2)^{2}[/tex] / [tex]a^{2}[/tex] +  [tex](y-5)^{2}[/tex] /[tex]b^{2}[/tex] -=1 is (h, k).

the ellipse's nucleus

The major axis is the larger of the two axes, which are 2a and 26.

(H, a, k) and (H, k, b) are the vertices. Vertices are those along the major axis in this case, and covertices are those along the minor axis.

[tex](x + 2)^{2}[/tex]/16 + [tex](y-5)^{2}[/tex] /20 =1

can be written as

[tex](x + 2)^{2}[/tex]/ [tex]4^{2}[/tex]   +       [tex](y-5)^{2}[/tex] /(2√/5)2

hence centre is (-2, 5), maor axis is 2 x 2√√5 = 4√√5 and minor axis

is 2 x 4 = 8

Vertices are ( 2,5 25), or ( 2,5 25) and ( 2,5 + 25), while covertices are ( 2 4, 5) and ( 6,5), respectively.

As a result of the presence of a vertical major axis, eccentricity e and focii are

(h, k ± be). e is given by the relation a2 = b2(1 − e2) i.e.

=> e = [tex]\sqrt{1 - \frac{a^{2} }{b^{2}} }[/tex]

 a2= 16 and b2= 62

=> e = 1/√5

Focii (-2,5 ± (2√5 x 1/√5)

or (-2,5±2) i.e. (-2, 7) and (-2, 3).

Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).

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Answer:

The golf ball is 2 times a likely to be orange as it is to be pink

Step-by-step explanation:

A. green = 18, pink+white+orange = 23

    18 not > 23

B. pink [tex]\neq[/tex] white [tex]\neq[/tex] orange [tex]\neq[/tex] green

C. pink x 2 = orange?

    4 x 2 = 8

D. white x 7 = green?

    white = 11

     green = 18

   11 x 7 = 77 [tex]\neq[/tex] 18

Answer:

This is the right answer.

Answer:

The average rate of change is 44.

Step by step:

FIRST STEP:

[tex]\frac{(294-118)}{(6-2)}[/tex]

SECOND STEP:

[tex]\frac{176}{4}[/tex] = 44

Dana's estimated length was 66.67% far off the actual length and her estimated width was 25% far off the actual width.

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

Percent Error Formula

The formula for percent error is:

PE = (|Estimated value-Actual value|/ Actual value) × 100

Given,

Actual length of the book = 24 cm

Actual width of the book = 16 cm

Dana's estimated length of the book = 40 cm

Dana's estimated width of the book = 20 cm

Error in measurement of length of the book =

(Measured Length - Actual Length/Actual length) × 100

= (40 - 24/24) ×100 = 66.67%

Error in measurement of width of the book =

(Measured width - Actual width/Actual width) × 100

= (20 - 16 / 16) × 100 = 25%

Hence, Dana's estimated length and breadth was 66.67% and 25% far off the actual length and width of the book respectively.

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Answer:

23.16

Step-by-step explanation:

Answer:

F = ( 9/5) X c + 32

Step-by-step explanation:

Answer:

the answer is (b.)41.7cm²

the workings;;

9.2cm×4cm+5cm=41.8 or 41.7cm²

Answer:

33.3% that the marble is not yellow

The total length needed in inches will be 490.5 inches.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long  The total length needed in inches will be:

= (3 ft 4 7/8 inch × 12)

Note that 1 feet = 12 inches

= (12 × 3) + (4 7/8) × 12

= (36 + 4.875) × 12

= 490.5 inches

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Answer:

To find the resultant force of an object, we need to add up all the forces acting on it. The resultant force is the overall force that the object experiences, taking into account all the individual forces.

In this case, we are given four objects, A, B, C, and D, and the forces acting on them. To find the object with the largest resultant force, we need to calculate the resultant force for each object by adding up all the forces acting on it.

For object A, the forces acting on it are: 10 N, 10 N, and 10 N, for a total of 10 N + 10 N + 10 N = 30 N.

For object B, the forces acting on it are: 5 N, 5 N, 5 N, and 5 N, for a total of 5 N + 5 N + 5 N + 5 N = 20 N.

For object C, the forces acting on it are: 30 N and -5 N, for a total of 30 N + (-5 N) = 25 N.

For object D, the forces acting on it are: 10 N and -5 N, for a total of 10 N + (-5 N) = 5 N.

Therefore, the object with the largest resultant force is object C, with a resultant force of 25 N.

Step-by-step explanation:

please refer to sketch for detail