Find the area of the region bounded by the line y=3x−6 and line y=−2x+8. a) the x-axis.

Answer:

i) number of transactions for the month of January = 4

 number of transactions for the month of February = 4

 number of transactions for the month of March = 4

 number of transactions for the month of April = 4

ii) Mean of four months  = -495.7 /4 = -123.93

Step-by-step explanation:

i) number of transactions for the month of January = 4

 number of transactions for the month of February = 4

 number of transactions for the month of March = 4

 number of transactions for the month of April = 4

ii)     January              February              March            April

         -38.50                 250.00               -14.00           -86.80

         126.30                -135.20                 99.00          -570.00

         429.40                  35.50                -82.70           100.00

        -265.00                 -62.30                 -1.50           -280.10

Total  252.20                  88.20                 0.80            -836.9

Total of four months  = 252.2 + 88.20 + 0.80 - 836.9  =  -495.7

Mean of four months  = -495.7 /4 = -123.93

Answer:

1) number of transactions for the month of January = 252.20

number of transactions for the month of February = 88.00

number of transactions for the month of March = 1.70

number of transactions for the month of April = -836.90

2. mean total of the four months -123.93

Step-by-step explanation:

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 ×12=72 rounded to the nearest tenth 5 or more add one more 4 or less let it rest

72 it would be 70 because 2 is not more than 5

_

Answer:

infinite solutions

Step-by-step explanation:

Answer: A, B, E

Step-by-step explanation:

Answer:

A, B, E.

Step-by-step explanation:

The closure property of multiplication states that the product of two rational expressions is a rational expression.

The commutative property only holds true for the multiplication of rational expressions.

The properties of rational expression multiplication and division are parallel to the properties of rational number multiplication and division.

Answer:

3.6

Step-by-step explanation:

3y+2/5=-1/5

3y=-1/5-2/5

3y=-0.6

0.6/3=y

-3.6=y

y=-3.6

Answer:

4%

Step-by-step explanation:

To solve this problem we can use a modified version of the simple interest formula which is shown below:

[tex]r=\frac{I}{Pt}[/tex]

I = interest amount

P = principal amount

t = time (years)

Lets plug in the values:

[tex]r=\frac{480}{(6,000)(2)}[/tex]

[tex]r=0.04[/tex]

The last step is to convert 0.04 into a percent:

0.04(100) = 4

The interest rate is 4%.

If the committee decides to double the radius, the approximate area of the new playground is; A_new = 6000 sq.ft

We are given the area of a circular playground as;

A = 1500 ft²

Formula for area of Circle is;

A = πr²

Thus;

πr² = 1500

r = √(1500/π)

Now, they want to double the radius. Thus approximate area of the new playground is;

A_new = π * [2√(1500/π)]²

A_new = π * [4(1500/π)]

A_new = 6000 sq.ft

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Answer:

c

Step-by-step explanation:

time 4 learning and it was right people :)

Answer:

6

Step-by-step explanation:

27/4= 6 3/4

That doesn't work because we need whole numbers.

24/4=6

That is the solution. For $24 we buy 6 tubes for $4 each and we have $3 left over.

Answer:

6

Step-by-step explanation:

each tube of paint(one) = $ 4

(x) tube of paint = $ 27

Therefore,

x= (27/4)

 = 6.75 tubes ; which is equivalent to 6 whole tube of paint

Answer:

Are the following linear or nonlinear? Circle the correct response.

Step-by-step explanation:

The numder are hard to explain but

You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference.

Answer:Your answer i

Step-by-step explanation:You can tell if a table is linear by looking at how X and Y change.

Answer:

404 tickets to adults have been sold .

325 tickets to students have been sold .

Step-by-step explanation:

A system of linear equations is a set of two or more first degree equations, in which two or more variables are related.

In this case, a system of two linear equations with two unknowns is solved.

To assemble the system of equations you must first define the variables, which in this case will be:

On the one hand, you know that 729 tickets were sold, that is to say that tickets sold for students and adults must add 729. Expressed in an equation this is: x+y=729 equation (A)

On the other hand, you know that during a game, $ 2995 was raised for the sale of those 729 tickets. And you also know that tickets for a high school football game cost $ 3 for students and $ 5 for adults.

Then the proceeds from the sale of tickets for students is 3*x and for adults it is 5*y. And your sum must be $ 2995. Expressed in an equation this is:

3*x + 5*y=2995 Equation (B)

So the system of equations is:

[tex]\left \{ {{x+y=729} \atop {3*x+5*y=2995}} \right.[/tex]

There are several methods of solving a system of equations. In that case, the substitution method will be used, which consists of isolating an unknown element in one of the equations, which will be a function of the other unknown. In the other equation that has not been used, the same unknown is replaced by the expression previously obtained. In this case, the value of variable x in equation (A) will be isolated:

x+y=729 ⇒ x=729-y Equation (C)

Replacing this expression in equation (B) you get:

3*(729-y)+5*y=2995

Solving this equation:

3*729-3*y+5*y=2995

2187+2*y=2995

2*y=2995-2187

2*y=808

y=808÷2

y=404

Remembering that "y" is tickets for admission to a high school football game for adults. this indicates that 404 tickets to adults have been sold .

Replacing this value in equation (C), which is the previously isolated equation, you get:

x=729-y

x=729-404

x=325

Remembering that "x" is tickets for admission to a high school football game for students. this indicates that 325 tickets to students have been sold .

By setting up a system of linear equations, it's found that 325 student and 404 adult tickets were sold.

The subject of this question is a linear system, specifically related to the ticket sales at a high school football game. Let's denote 's' as the number of student tickets sold, and 'a' as the number of adult tickets sold. We'll use the following two equations to reflect the given information:

To solve the system of equations, one method is substitution or elimination. Using the elimination method, you could multiply the first equation by 3, getting 3s + 3a = 2187. Then, subtracting this from the second equation gives 2a = 808. Dividing by 2, we find that a = 404. Plugging this value into the first equation gives s = 729 - 404 = 325. Therefore, 325 student tickets and 404 adult tickets were sold.

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Answer: v = 2

Step-by-step explanation:

30-48v+12 = -54

-48v = -54-30-12

[tex]\frac{-48v}{-48}[/tex] = [tex]\frac{-96}{-48}[/tex]

v = 2

Answer:

2

Step-by-step explanation:

6(5−8v)+12=−54

Divide through by 6, we have

5 — 8v + 2 = — 9

Collect like terms

— 8v = —9 — 2 — 5

—8v = — 16

Divide both side by the coefficient of v i.e —8

v = — 16/ —8

v = 2

Answer:

35

Step-by-step explanation:

7 x 7 = 35

Answer:

3/25 is the fraction   .12 is the decimal

Step-by-step explanation:

Answer 4.6

Step-by-step explanation:

1. How much interest will Sara owe?

She will owe 5,966 dollars

2. How much will the payments be with a seven year agreement?

Sara will pay 21,666 dollars

The simple interest formula is as follows:

[tex]A=P(1+rt) \\ \\ \\ Where: \\ \\ A: \ is \ the \ Final \ Investment \Value \\ \\ P: \ is \ the \ Principal \ amount \ of \ money \ to \ be \ invested \\ \\ r: \ is \ the \ rate \ of \ interest \\ \\ t: \ is \ \ Number \ of \ Time \ Periods[/tex]

First, converting r percent to r a decimal

[tex]r = (5 \frac{3}{7})\%=(5+\frac{3}{7}))\%=\frac{38}{7}\% \\ \\ r=\frac{38/7}{100}=\frac{19}{350} \ per \ year[/tex]

Solving our equation:

[tex]A=15700 (1+\frac{19}{350}\times 7) \\ \\ A=15700(\frac{69}{50}) \\ \\ \boxed{A=\$21,666}[/tex]

So Sara will owe in interest the following amount of money:

[tex]I:Interest \\ \\ \\ I=21,666-15,700 \\ \\ \boxed{I=\$5,966}[/tex]

Finally, answering the questions:

1. How much interest will Sara owe?

She will owe 5,966 dollars

2. How much will the payments be with a seven year agreement?

Sara will pay 21,666 dollars

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you add them then divide ur answer by 2

Answer:

Height = 16.4 inches

Step-by-step explanation:

V = Length*Width*Height, so solving for the Height by dividing the Volume with the product of the Length and Width gives:

Height = Volume/Length*Width = 7193.45/(30.25*14.5) = 16.4 inches

Answer:

The required equation to the given slope m=-5 and a point (-1,3) is 5x+y+2=0

Step-by-step explanation:

Given that the slope  m=-5 and a point (-1,3)

Now we have to find an equation with the given slope and point :

Let [tex](x_1,y_1)[/tex] be the given point (-1,3)

The slope point formula is [tex]y-y_1=m(x-x_1)[/tex]

y-3=-5(x-(-1))

y-3=-5(x+1)

y-3=-5(x)-5(1) ( by using the distributive property a(x+y)=ax+ay here a=-5,x=x and y=1 )

y-3=-5x-5

y-3-(-5x-5)=-5x-5-(-5x-5) ( by using the distributive property a(x+y)=ax+ay  here a=-1,x=-5x and y=-5)

y-3+5x+5=-5x-5+5x+5

y+2+5x=0

5x+y+2=0 which is the required equation

Answer:

Therefore the correct option is a.) The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.

Step-by-step explanation:

i) Let p = 0.47

ii) therefore q = 1 - 0.47 = 0.53

iii) sample size, n =25

iii) standard deviation = [tex]\sqrt{\frac{p \times q}{n} } = \sqrt{\frac{0.47 \times 0.53}{25} } = 0.0998[/tex]

Therefore the correct option is

a.) The standard deviation is 0.0998. The 10% condition is met because it

    is very likely there are more than 250 catfish in the river.

The standard deviation of the sampling distribution of the sample proportion is 0.0998. To determine whether the 10% condition is met, the total population of catfish should be at least 10 times the sample size.

The question asks about determining the standard deviation of the sampling distribution of the proportion of catfish in a river and if the 10% condition is met for the sampling distribution to be approximately normal. First, to calculate the standard deviation of the sampling distribution of the sample proportion (p-hat), we use the formula √[(p(1-p))/n], where p is the population proportion and n is the sample size. In this case, p = 0.47, so 1 - p = 0.53, and n = 25. The standard deviation is then √[(0.47*0.53)/25], which is approximately 0.0998.

Next, the 10% condition checks whether we can consider the population large enough that the sample size doesn't affect the population proportion notably when taking without replacement. This condition states that the sample size, n, should be no more than 10% of the population. If there are indeed more than 250 fish in the river (10 times the sample size), we can be confident that the 10% condition is met. If not, the condition is not met.

Therefore, the correct response would state the standard deviation and appropriately evaluate whether the 10% condition is met based on the estimated number of catfish in the river.

Answer: A. 2,604

Step-by-step explanation:

According to the given information the number of sets in rows following arithmetic progression (in short form AP).

Where , 23rd term is 65.

Common difference = 65-63=2

nth term in AP: [tex]a_n=a+(n-1)d[/tex]

For n= 23 , we have [tex]a_{23}=65[/tex] , d= 2

[tex]23=a+(23-1)2\\\\ 23= a+(22)2\\\\ 23=a+44\\\\ a=44-23=21[/tex]

Formula for the sum of first n terms in AP= [tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

Since, There are 42 rows in the auditorium.

Then,

[tex]S_{42}=\dfrac{42}{2}[2(21)+(42-1)2]\\\\=21(42+82)\\\\=21(124)=2604[/tex]

Hence, the the auditorium contains 2,604 seats.

Thus , the correct answer is A. 2,604

We want to find the total number of seats in the auditorium, knowing that the number of seats is given by an arithmetic sequence.

The correct option is A: there are 2,604 seats in total.

We know that in the row before you (the number 22) there are 63 seats, in your row (number 23) there are 65 seats, and in the next row there are 67 seats, then we can write the 3 terms of a sequence:

[tex]a_{22}= 63\\a_{23} = 65\\a_{24} = 67[/tex]

Is simple to see that this is an arithmetic sequence, such that the difference between consecutive terms is 2, then the number of seats in the n-th row is given by:

[tex]a_n = a_{n-1} + 2[/tex]

or:

[tex]a_n = a_1 + (n - 1)*2[/tex]

Using this second equation, we can find the value of the first term of the sequence:

[tex]a_{23} = 65 = a_1 + 2*(23 - 1)\\\\65 - 44 = a_1 = 21\\[/tex]

Now, if we define d as the difference between consecutive terms in an arithmetic sequence, the sum of the first N terms is given by:

[tex]S(N) = N*(2*a_1 + (N - 1)*d)/2[/tex]

Here we have a total of 42 rows, so we use N = 42.

d =2

a₁ = 21

Then the total number of seats is:

[tex]S(N) = 42*(2*21 + (42 - 1)*2)/2 = 2,604[/tex]

This means that the correct option is A: there are 2,604 seats in total.

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Answer:

(4x3-6x) + (8x-12)= 2x

(4x3+8x) + (-6x2-12)= 2(2x-3) (x^2+2)

Step-by-step explanation:

All you have to do is simplify.

Answer:

A,B,E

Step-by-step explanation:

Did on edgen

[tex]A = 100\pi cm^{2}[/tex]

Step-by-step explanation:

Given that an engineer is planning to install a new water pipe.

The diameter of the circular pipe is

d = 20 cm

Let us find the radius (r)

radius = diameter / 2

r = 20 / 2 = 10 cm

The area of circle (A) is given as:

[tex]A = \pi r^{2}[/tex]

[tex]A = \pi 10^{2}[/tex]

[tex]A = 100\pi cm^{2}[/tex]

Vertex is calculated by -b/2a

So we have -(-5)/2(2)=5/4

The root is determined through the quadratic formula:

x=(-b+sqrt(b^2-4ac))/2a

x=(-(-5)+sqrt(-5^2-4(2)(-604)))/2(2)

x=(5+sqrt(25-4832))/4

x=(5+sqrt(-4807))/4

So the root is some imaginary number

Hope this helped!

Answer:

1 + 2 a^n

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

divide 1/2 and add 1

Answer:

1 = 2 - 3. is this what you mean?

Answer:

5x + 7 < 17

5x < 10

x < 2

answer is a

Step-by-step explanation: Notice that the fractions that we're comparing in this problem have different denominators.

When fractions have different denominators, they're called unlike fractions. To compare unlike fractions, we must first get a common denominator.

The common denominator of 4 and 3 will be the least common multiple of 4 and 3 or 12. To get a 12 in the denominator of 1/4, we multiply the numerator and the denominator by 3 which gives us 3/12. To get a 12 in the denominator of 1/3, we multiply the numerator and the denominator by 4 which gives us 4/12.

Now we have the fractions 3/12 and 4/12.

The fraction with the greater denominator is larger so 4/12 is bigger which means that 1/3 is bigger.

1/4 is not greater than 1/3. In fact it is less than 1/3.

We have two fractions, 1/4 and 1/3.

We know that,

For a fraction, when the value of the denominator increases, the value of the fraction decreases.

So here the denominator of 4 is greater than 3.

So 1/4 is less than 1/3.

In other words, 1/4 can be defined as a part when 1 is divided in to 4 parts.

1/3 is one part when 1 is divided in to 3 parts.

So clearly, 1/4 < 1/3.

Hence 1/4 is less than 1/3.

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