A stadium has 45,000 seats. Seats sell for ​$30 in Section​ A, ​$24 in Section​ B, and ​$18 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in ​$1,168,200 from each​ sold-out event. How many seats does each section​ hold?

Answer:

Step-by-step explanation:

[tex]1-\frac{4}{2\cdot \:7+4}\\\\\frac{4}{2\cdot \:7+4} = \frac{2}{9} \\\\=1-\frac{2}{9}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:1=\frac{1\cdot\:9}{9}\\\\=\frac{1\cdot \:9}{9}-\frac{2}{9}\\\\Since\:the\:denominators\:are\:equal,\\\:combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{1\cdot \:9-2}{9}\\\\1\cdot \:9-2 =7\\\\=\frac{7}{9}[/tex]

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Option C is correct, the set of vectors is linearly dependent because one of the vectors is the zero vector.

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

To determine if the set of vectors is linearly independent, we need to check if any of the vectors can be expressed as a linear combination of the others.

Let's consider the first vector [8 -6 4].

If we try to express this vector as a linear combination of the other vectors, we get:

[8 -6 4] = a[12 -9 6] + b[0 0 0]

where a and b are constants.

We can immediately see that this equation has infinite solutions, because the third component of the second vector is zero, which means we can choose any value for b and still satisfy the equation.

Therefore, the set of vectors is linearly dependent.

Hence, Option C is correct, the set of vectors is linearly dependent because one of the vectors is the zero vector.

To learn more on Matrices click:

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Determine by inspection whether the vectors are linearly independent. Justify your answer.

[8  -6  4][12  -9  6]

A. The set of vectors is linearly independent because nothing times the first vector is equal to the second vector. ​(Type an integer or a simplified​ fraction.)

B. The set of vectors is linearly dependent because nothing times the first vector is equal to the third vector. ​(Type an integer or a simplified​ fraction.)

C. The set of vectors is linearly dependent because one of the vectors is the zero vector.

D. The set of vectors is linearly independent because none of the vectors are multiples of the other vectors.

Answer:

3w-4 = 68

Hope this helped!

Answer:

1 x 1 = 1

Step-by-step explanation:

Anything that is multiplied by 1, is going to stay the same

Example would be 1 x 5

that would equal 5

Hope this helped<3

Answer:

it is one, no matter what

Step-by-step explanation: if u take on and make it bigger (multiply it) one time, u still only get one!!

Brainliest please!! Have a great day!!

Answer:

15p^2. Hope this helps

Step-by-step explanation:

Answer:

(2x + 3) • (x + 2) • (x - 1)

Step-by-step explanation:

Percent - 24%

Decimal - 0.24

Fraction - 24/100=6/25

Answer: m = -3/2

Step-by-step explanation: In algebra, we use the word slope

to describe how steep a line is and slope can be found using

the ratio rise/run between any two points that are on that line.

Let's start from the point (0, 0).

From this point, we go down 3 units and to the right 2 units.

So our rise is -3 and our run is 2.

So our slope or rise/run is -3/2.

The variable that's used to represent slope is m.

So we say that m = -3/2

Answer:

-3/2

Step-by-step explanation: Rise 3 from the first (lower) dot then run 2 to the higher dot. Its negative because it is going down from left to right.

Answer:

36

Step-by-step explanation:

half of 8 is 4 so half of 24 is 12 and 12 plus 24 is 36

Answer:

$36

Step-by-step explanation:

First divide the $24 to find how much each tennis ball costs.

24 / 8 = 3

Then multiply 3 (the cost per tennis ball) by 12 (the amount of tennis balls)

3 x 12 = 36

36 is your answer

Answer:

(1,4) and (0,-1)

Answer:

The answer is

[tex] \huge \boxed{y = 3x - 10}[/tex]

Step-by-step explanation:

To find an equation of a line given the slope and a point we use the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

m is the slope

( x1 , y1) is the point

From the question the point is (2, 4) and the slope is 3

The equation of the line is

[tex]y - 4 = 3(x - 2) \\ y + 4 = 3x - 6 \\ y = 3x - 6 - 4[/tex]

We have the final answer as

[tex]y = 3x - 10[/tex]

Hope this helps you

Answer:

interest rate= 4.5%

Step-by-step explanation:

steve paid back=7945

loan------------------7000

total interest for 3 years=945

for one year-----------------=315

rate of interest= (315 X 100)/7000= 4.5%

Answer:

y=1/8x + 15

Step-by-step explanation:

y=1/8x+15 because 1/8 hours and add 15

Answer: 9/16

Explanation: When dividing by a fraction, we can change

the division sign to multiplication and flip the second fraction.

So 3/8 ÷ 2/3 means the same thing as 3/8 · 3/2.

So when dividing by a fraction, we can just multiply

by the reciprocal of that fraction or that fraction flipped.

Now multiplying across the numerators and denominators, we have 9/16.

Since 9/16 is in lowest-terms, it's or final answer.

Answer:

Vertex

Step-by-step explanation:

I think

Answer:

my name is keff 4

Step-by-step explanation:

Step-by-step explanation:

6 goes in ones or the green

3 goes in tenths or the yellow

2 goes in hundreths or the purple

4 goes in thousands or the orange

Answer: 6 goes in the ones then the 3 goes tenths 2 in hundredths and 4 in the thousands

eight hundredths six tens three ones decimal one tenths four hundredths one thousand

Step-by-step explanation:

Answer:

35/5 and 60/30

Step-by-step explaning

i got it right on enginuity

Answer:

35/5 and 60/30

Answer:

I solved it and my answer is 43

Step-by-step explanation:

25×{8- (7)} +18

25 (1) +18

25×1=25

25+18=

43

I have attached the graph

Answer:

People drank 75 cups, First find the amount of juice that Mrs. Jackson bought .Then subtract the 3 cups of juice that were left over

5 x 16=80

80-3= 77

Answer:

5,12

Step-by-step explanation:

because 7-2 is 5 and it would take 12 to get to 7

Answer: YES

Step-by-step explanation:

Answer:

the corrects answer is -3

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

because a is the missing number. Well, 21 minus or -  8 is equal to 13.

[tex](x - 13)(x + 3) \\ = x {}^{2} + 3x - 13x - 39 \\ = x {}^{2} - 10x - 39 [/tex]

Answer:

135/512

Step-by-step explanation:

In a deck of card, there are 13clubs.

A deck of card contains 52cards

Total clubs = 13cards

Probability of selecting a club and replacing is expressed as P(C) = total number of clubs/total card

P(C) = 13/52 = 1/4

q = 1-p

q = 1-1/4

q =3/4

Let X be probability function used is a binomial distribution formula expressed as:

Since 5cards is drawn at random, n = 5

P(X = x) = nCx q^(n-x)p^x

P(X = x) = 5Cx 3/4^(5-x)•(1/4)^x

The probability of the sequence is expressed as:

P(X = x) = 5Cx 3/4^(5-x)•(1/4)^x

x is the number of clubs present

b) To find the probability of getting exactly 2 clubs in a sequence of 5 cards drawn at random with replacement from a 52 card deck, we will substitute x = 2 into the probability function in (a) a shown;

P(X = 2) = 5C2•3/4^(5-2)•(1/4)^2

P(X = 2) = 5C2•3/4^(3)•(1/4)^2

P(X = 2) = 5C2•27/64•(1/16)

P(X = 2) = 5C2•27/1024

P(X = 2) = 5!/(5-2)!2!•27/1024

P(X = 2) = 5!/3!2!•9/1024

P(X = 2) = 5×4×3!/3!2•27/1024

P(X = 2) = 5×4/2•27/1024

P(X = 2) = 10•27/1024

P(X = 2) = 135/512

Hence the probability of getting exactly 2 clubs in a sequence of 5 cards drawn at random with replacement from a 52 card deck is 135/512

Answer:

The decision rule is  

Reject the null hypothesis

The conclusion

There is sufficient evidence to conclude that mean daily consumption of regular-coffee drinkers greater than that of decaffeinated-coffee.

The p-value  is  [tex]p-value  = 0.03682 [/tex]

Step-by-step explanation:

From the question we are told that

   The first sample size is  [tex]n_ 1 = 50[/tex]

   The first sample mean is [tex]\=x_1  =  3.84[/tex]

The first sample standard deviation is  [tex]s_1  = 1.26[/tex]

    The second sample size is  [tex]n_2  =  40[/tex]      

   The second  sample mean is   [tex]\=x_2  =  3.35 [/tex]

    The second sample standard deviation is [tex]s_2  =  1.36[/tex]

    The level of significance is  [tex]\alpha =  0.05[/tex]

The  null hypothesis is  [tex]H_o  :  \mu_1  = \mu_2[/tex]

The alternative hypothesis is  [tex]H_a  :  \mu_1  >  \mu_2[/tex]

Generally the test hypothesis is mathematically represented as

 [tex]t =  \frac{( \= x_1 - \= x_2 ) - 0}{ \sqrt{ \frac{s^2_1 }{n_1}  + \frac{s^2_2}{n_2} } }[/tex]

=>  [tex]t =  \frac{( 3.84 - 3.35  ) - 0}{ \sqrt{ \frac{1.26^2 }{50}  + \frac{1.36^2}{40} } }[/tex]

=>   [tex]   t =  1.789  [/tex]      

Generally the p-value is mathematically represented as

      [tex]p-value  =  P(t > 1.789)[/tex]

From the z table  

    [tex]\Phi (1.789) =  0.03682[/tex]

So

   [tex]p-value  =  P(t > 1.789) =  0.03682 [/tex]

From the value obtained we see that [tex]p-value < \alpha[/tex] hence

The decision rule is  

Reject the null hypothesis

The conclusion

There is sufficient evidence to conclude that mean daily consumption of regular-coffee drinkers greater than that of decaffeinated-coffee