PLEASE HELP! 20 POINTS!!

The tops of two tables in a furniture store are similar rectangles as shown below.


The length of the larger tabletop is 12 feet. What is its width, x?

Answer:

Step-by-step explanation:

Cos(A + B) = Cos(A)*Cos(B) - Sin(A)*Sin(B)

Find The Hypotenuse of A

Tan(A) = Opposite / Adjacent

Tan(A) = 15/8

Opposite = 15

Adjacent = 8

Hypotenuse = c

c^2 = opposite^2 + Adjacent^2

c^2 = 15^2 + 8^2

c^2 = 225 + 64

c^2 = 289

sqrt(c^2) = sqrt(289)

c = 17

Find the opposite of B

Adjacent = 12

Hypotenuse = 37

Opposite = b

adjacent^2 + opposite^2 = hypotenuse^2

12^2 + b^2 = 37^2

144 + b^2 = 1369

b^2 = 1369 - 144

b^2 = 1335

b = 35

Definitions

Sin(A) = Opposite / hypotenuse = 15/17

Sin(B) = opposite / hypotenuse =  35/37

Cos(A) = 8/17

Cos(B) = 12/37

Answer

Cos(A + B) = Cos(A)*Cos(B) - Sin(A)*Sin(B)

Cos(A + B) = 8/17 * 12/37 - 15/17*35/37

Cos(A + B) = 96/629 - 525/629

Cos(A + B) = -429/629

Answer: 1/56

Step-by-step explanation:

Since the box has 8 different colors, the probability of picking any color of crayon will be 1/8.

This question relates to a probability without replacement, therefore, the probability of picking the red crayon first will be 1/8. After then, there'll be 7 crayons left and the probability of picking the green crayon next will be 1/7.

Therefore, the probability that I will remove the Red and the Green crayon from the box will be:

= 1/8 × 1/7

= 1/56

[tex] \huge{ \mathcal{  \underline{ Answer} \:  \:  ✓ }}[/tex]

Total land area of Rhode Island is :

[tex] \longmapsto\mathrm{1045 \: \: mi {}^{2} }[/tex]

And from the above pie chart, we can conclude that Kent County comprises 16% of total land area of Rhode Island, that is :

[tex]\longrightarrow \dfrac{16}{100} \times 1045[/tex]

[tex]\longrightarrow \dfrac{16720}{100} [/tex]

[tex]\longrightarrow167.2 \: \: mi {}^{2} [/tex]

Therefore, Total land area of Kent County :

[tex] \boxed{ \large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 167.2 \: \: \: mi {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

Answer:

63%.

Step-by-step explanation:

There are 12 scores below 45 and total number of scores = 19.

So percentile rank= (12/19) * 100

=  63%.

The probability of incoming freshmen who plan to live on-campus in percentage will be 61.11%. Then the correct option is A.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

A university administered a survey to all incoming students regarding living arrangements for the upcoming school year.

The results of the survey are displayed in the following two-way relative frequency table.

                                         On-Campus          Off-Campus            Total

Freshmen                               0.44                     0.28                     0.72

Transfer Students                  0.21                      0.07                     0.28

Total                                       0.65                      0.35                        1

Then the probability of incoming freshmen who plan to live on-campus in percentage will be

P = (0.44 / 0.72) x 100

P = 0.6111 x 100

P = 61.11%

The probability of incoming freshmen who plan to live on-campus in percentage will be 61.11%.

Then the correct option is A.

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Answer: 88

Step-by-step explanation:

got it right 2022 edge

Answer:

-4x-31

Step-by-step explanation:

1.6(5x-10)-(12x+15)

8x-16-12x-15

-4x-31

The simplified expression is -4x - 31.

We know,

In mathematics, an expression refers to a combination of numbers, variables, operations, and mathematical symbols that represents a mathematical statement or computation. It can involve arithmetic operations (addition, subtraction, multiplication, division).

We have Equation,

1.6(5x - 10) - (12x + 15)

Now simplifying the equation

1.6(5x - 10) - (12x + 15)

= 8x - 16 - 12x - 15

= -4x - 31

Thus, the simplified expression is -4x - 31.

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Answer:

? = 27

Step-by-step explanation:

56 + ? + 11 = 94

? + 67 = 94

? = 27

Answer:

no equation is equal to 2 all are greater than 2

Answer:

Improved climate for foreign investment

Step-by-step explanation:

I just took the test gs

Answer:

0.2048 = 20.48% probability that exactly two of the five sample families will have no children.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they have no children, or they do have children. The probability of a family not having children is independent of any other family. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

20% of the families have no children at all.

This means that [tex]p = 0.2[/tex]

Five families:

This means that [tex]n = 5[/tex]

What is the chance that exactly two of the five sample families will have no children?

This is P(X = 2).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{5,2}.(0.2)^{2}.(0.8)^{3} = 0.2048[/tex]

0.2048 = 20.48% probability that exactly two of the five sample families will have no children.

Answer:

26

Step-by-step explanation:

9514 1404 393

Answer:

  the correct choice is marked

Step-by-step explanation:

The line has a rise of 2 for a run of 1, so a slope of 2. The line crosses the y-axis at y=-2, so the y-intercept is -2. The slope-intercept equation for the line is ...

  y = mx + b . . . . . . for slope m and y-intercept b

  y = 2x -2

Answer:

the answer is c y=2x-2

Step-by-step explanation:

:)

The probability that at least three plants produce two or more seeds is 0.793915.

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

The probability that out of n trials, there be x successes is given by

Use binomial distribution, with p =0.20, n=5, x=3

[tex]P(X=x)=C(n,x)p^x (1-p)^{n-x}[/tex]

P(X> = 3)

[tex]=1-(P(X=0)+P(X=1)+P(X= 5 ))\\=1-(C(20,0)0.2^0 (0.8)^{20-0}+C(20,1)0.2^1 (0.8)^{20-1}+C(20,2)0.2^2 (0.8)^{20-2})[/tex]

=1-(0.0115292+0.057646+0.136909)

=1-0.206085

=0.793915

Hence, the probability that at least three plants produce two or more seeds is 0.793915.

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Answer:

M(x)  =  452,56 in

Step-by-step explanation:

The volume of the open box is  500 in³

V = Area of the base times height

V(b) =  x² * h               where x is the side of the square and h the heigh

Then     500 =  x²*h

Total material to use is: material of the base + material of 4 sides

material of the base is  x²

material of one side is x*h  we have 4 sides then  4*x*h

Total material M(b)

M(b)  =  x²  +  4*x*h

And    as    h  =  500/ x²

M(x)  =  x²  +  4* x* 500/x²

M(x)  =  x²  +  2000/x

Tacking derivatives on both sides of the equation

M´(x)  =  2*x   - 200/x²

M´(x)  =  0         2*x  -  200/x²  = 0

x³ -  100  =  0

x³   =  100

x   =  4,64 in

And By substitution     h  =  500/x²

h  =  500/(4,64)²           h  =  23,22  in

How do we know that x = 4,64 make V(x) minimum

we get the second derivative

M´´(x)  =  2  +  200*2x/ x⁴    =  2  +  400/x³

M´´(x) is always positive

M´´(x) > 0     then M(x) has a minimum for  x= 4,64 in

The least amount of material is:

M(x)  =  x²    +    2000/x

M(x)  =  (4,64)²  *  2000/4,64

M(x)  = 21,53  +  431,03

M(x)  =  452,56 in

Answer:

two times a number plus 1

Step-by-step explanation:

Its ‘B’

100% sure

Plz mark me brainliest

Answer:

58kg, 70kg and 72kg

Step-by-step explanation:

Starting weight was 200.

Boy 1- Changed from 200 to 142. 200kg - 142kg= 58 kg

Boy 2- Changed from 142 to 72.  142kg- 72kg = 70kg

Boy 3- Last one on the scale and it showed 72kg so his weight is 72kg

Answer:

58, 70, 72

Step-by-step explanation:

200-142=58

142-72=70

Answer:

65*

Step-by-step explanation:

12x-7+16x+19=180

28x=168

x=6

12(6)-7=65

Answer:

a) i) P( final product is acceptable ) = 3/5

   ii) P ( final product not acceptable ) =  2/5

B)  P (  final product is acceptable | X =2 ) = 2/5

C)  P ( Y = 3 | Final product is acceptable ) = 2/5

Step-by-step explanation:

Given data :

5 states : 1 (poor), 2 (below average), 3 (average), 4 (good), and 5 (excellent)

Number of components produced = 2

X ( component 1 ) ∴ P(X) = 1/5

Y ( component 2 ) ∴ P(Y) = 1/5

Aim : Sum of Final product needs to be ≥ 6

A) Probability of a final product been acceptable and also unacceptable

P( final product is acceptable ) ; P(X + Y ≥ 6 )

= 1/5 ∑ P( Y ≥ 6 - x )

= 1/5 ( P( Y ≥ 5 ) + P( Y ≥ 4 ) + P( Y ≥ 3 ) + P( Y ≥ 2 ) + P( Y ≥ 1 )

= 1/5 ( 1/5 + 2/5 + 3/5 +4/5 + 1 )

= 3/5

P ( final product not acceptable ) = 1 - 3/5 = 2/5

B) P (  final product is acceptable | X =2 )

 ∴ P ( Y ≥ 4 )

   = 2/5

C) P ( Y = 3 | Final product is acceptable )

∴ P ( X ≥ 3 ) ≠ P( Y ≥ 3 )  ( because they are not independent )

  = 1 - 3/5 = 2/5.

Answer:

[tex]Volume = \frac{1}{3} \pi r^2 h \\\\r= 5\\Volume = 100\pi\\\\Find \ h.\\\\h = 3\frac{V}{\pi r^2} = 3 \times \frac{100 \pi}{\pi \times 5^2} = 3\times \frac{100}{25} = 3 \times 4 = 12[/tex]

Answer:

104 softballs

Step-by-step explanation:

26 x 4 = 104

Answer: c

Step-by-step explanation:

9514 1404 393

Answer:

  (-5, -4)

Step-by-step explanation:

Compare the given equation to vertex form:

  y = a(x -h)² +k

You see that a=2, h=-5, k=-4.

The vertex is (h, k) = (-5, -4).

Answer:

150 pages

Step-by-step explanation:

want to read 2,000 pages

already read 1,250 pages

Number of pages left to read

= 2000-1250

= 750

Rest of the reading spread over 5 weeks

wants to read same number of pages each week

Number of pages that need to be read each week over 5 weeks

= Number of pages left to read / total number of weeks

=750 / 5

= 150

He will need to read 150 pages a week.

Answer:

65.57 should be the correct answer!

Step-by-step explanation:

Here is the whole work I did, hope this helps!

100 - 17 = 83

79 x 0.83 = 65.57

Answer:

65.57

Step-by-step explanation:

Method 1:

[tex]\frac{y}{79} :\frac{17}{100}[/tex]

y · 100 = 17 · 79

100y = 1343

100y ÷ 100 = 1343 ÷ 100

y = 13.43

79 - 13.43

65.57

Method 2:

100% - 17% = 83%

[tex]\frac{y}{79} :\frac{83}{100}[/tex]

y · 100 = 83 · 79

100y = 6557

100y ÷ 100 = 6557 ÷ 100

y = 65.57

Answer:

C. 13 gallons

Step-by-step explanation:

150 divided by 6 is 25. 325 divided by 25 is 13.

To travel 325 miles the van needs C. 13 gallons of gas.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A van travels 150 miles on 6 gallons of gas.

So, In one gallon the van travels (150/6) = 25 miles.

∴ To travel 325 miles the van needs (325/25) = 13 gallons of gas.

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