Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.
A) 6x + 4x - 6 + 24 + 9x
B) 25 - 4x = 15 - 3x +10 - x
C) 4x + 8 = 2x + 7 + 2x - 20

The cost of the tomatoes, in dollars per pound, using proportions, is of:

$0.86 per lb.

A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of a problem.

In this problem, the costs is obtained as follows:

Hence the cost in dollars per kg of the tomatoes is obtained as follows:

1.74 x 1.09 = $1.8966 per kg.

The relationship between kg and pounds is given as follows:

1 kg = 2.20 lb.

Hence the cost is written as follows:

$1.8966 per 2.20 lb.

The cost per pound of the tomatoes is of:

1.8966/2.20 = $0.86 per lb.

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Tommy will pat bounce the ball 225 times in 405 seconds which was found using the given data.

Given: In 45 seconds, Tommy bounces a basketball 25 times.

Number of times he will pat bounce the ball in 405 seconds will be given as follows:

= (405 × 25)/45

=225

Therefore, Tommy will pat bounce the ball 225 times in 405 seconds which was found using the given data.

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Answer:

45.47368421 (round as much as you need)

Step-by-step explanation:

We can model the equation using G(h) = -19h + 872, where -19 is the rate at which the bucket is emptying and 872 is the amount of gallons the bucket starts with.

Since gallons is the output, we would have 8 = -19h + 872 and we simply need to solve for h

[tex](8 = -19h+872)-872\\\frac{(-864=-19h)}{-19} \\h=45.47368421[/tex]

Answer:tell me the math soulation first

Step-by-step explanation:

The probability of drawing 2 Diamonds is 1/17.

The probability of drawing 1 diamond and 1 heart is 13/204.

How to find probability for a deck of cards?

According to the given question:

Since there are 52 cards, the probability of getting a diamond in the first draw is 13/52.

After the first card is drawn, there are just 12 diamonds left.

So, the probability of drawing the diamond now is 12/51.

The total probability is the product of two probabilities

So, P = 13/52 x 12/51 = 1/4 x 4/17

P = 1/17 ≈ 0.058

So the probability of drawing 2 Diamonds is 1/17.

Similarly, we know probability of getting a diamond in first is 13/52.

Also the probability of drawing a heart from 51 cards is 13/51.

The total probability P = 13/52 x 13/51

P = 1/4 x 13/51

P = 13/204 ≈ 0.063

So the probability of drawing 1 diamond and 1 heart is 13/204.

More likely outcome is the one whose probability is closer to unity. Since 13/204 > 1/17 that is 0.063 > 0.058 therefore drawing a heart and a diamond is a more likely outcome.

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There will be 319 boards be required

and the total cost be $223,720.

Given, a classroom ceiling measures 6.8m by 4.7m. It is covered by boards measuring 1m by 1m.

Now, we have to find the number of boards needed altogether

So, the area of the ceiling is

Area = 6.8×4.7

Area = 319.6 m²

Now, the area of the board is

Area = 1 m²

So, 319 boards will be required to cover the ceiling.

Now, if one board costs $700 then,

the total cost be

= 700×319.6

= $223,720

Hence, There will be 319 boards be required

and the total cost be $223,720.

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The statements that are true according to the equation  h (x) = –3 |x – 1| + 4. are

The graph of the described function is attached

The vertex is marked (1, 4) in the graph

The y intercept is marked (0, 1) in the graph

Also from the equation, the y intercept is solved by

h (x) = –3 |x – 1| + 4

plugging the value of x

h (x) = –3 |0 – 1| + 4

h (x) = –3 |– 1| + 4

removing the modulus sign

h (x) = –3 * 1 + 4

h (x) = –3 + 4

h (x) = 1

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Answer: 114

Step-by-step explanation:

firstly, convert meters to centimeters:

2.5m * 100cm in a meter = 250 cm

let the length of the first shelf equal x:

250 = x + (2x + 18) + (x - 12) + (x + 4)

combine like terms:

250 = 5x + ( 18 - 12 + 4) = 5x +10

subtract 10 from both sides:

240 = 5x, then solve for x

240/5 = x

x = 48 cm

the length of the second shelf was 2x + 18, so plug in 48 for x:

2(48) + 18 = 114

Answer:

114 [cm].

Step-by-step explanation:

1) if the length of the 1st shelf is 'x', then

2) the length of the 2d shelf is '2x+18', the 3d shelf is 'x-12' and the 4th shelf is 'x+4';

3) the sum of the all 4 shelves is 250 [cm], then it is possible to make up the equation:

x+(2x+18)+(x-12)+(x+4)=250;

4) the root of the equation above is x=48, then

5) the required length of the 2d shelf is 2*48+18=114 [cm].

The expression we get from the given functions f and g defined for all real numbers x.

(f+g)(x)=4x+1

(f-g)(x)=2x+11

(f.g)(3)=-30

Given that,

All real numbers x are defined by the functions f and g.

f(x)=3x+6

g(x)=x-5

We have to find the expression

(f+g)(x), (f-g)(x) and (f.g)(3)

Take the functions,

f(x)=3x+6

g(x)=x-5

Now, First

(f+g)(x)

f(x)+g(x)           (Substitute in the place of f and g functions)

Which is

3x+6+x-5

4x+1

(f+g)(x)=4x+1

Now, second

(f-g)(x)

f(x)-g(x)

Which is

3x+6-(x-5)

3x+6-x+5

2x+11

(f-g)(x)=2x+11

Now, third

(f.g)(3)

f(3)×g(3)

Which is

(3(3)+6)×((3)-5)

(9+6)×(3-5)

15×-2

-30

(f.g)(3)=-30

Therefore, The expression we get from the given functions f and g defined for all real numbers x.

(f+g)(x)=4x+1

(f-g)(x)=2x+11

(f.g)(3)=-30

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Answer:

√43

Step-by-step explanation:

Implement the Pythagorean formula to solve for sides of a right triangle: a^2 + b^2 = c^2, where "a" and "b" are the legs and "c" is the hypotenuse.

a = √6 and c = 49

√6^2 + b^2 = 49

6 + b^2 = 49

b^2 = 43

b = √43

Answer:

The square root of 43

Step-by-step explanation:

 I did this in class the other day

Answer:

sada

Step-by-step explanation:

Please Add A Picture

By  calculating profit function to break even, the company needs to produce 23 units.

The amount received when a good or service is sold for a price is referred to as revenue. The cost of a product or service is the amount spent on its sale. Profit is defined as the difference between revenue and costs. A profit function is a relationship that shows the difference between the cost and revenue functions. The graph of a profit function can show the best combination of revenue and costs to produce the most profit. This is known as optimization.

Profit is defined as revenue less costs. This means that there is a profit function, P(x).

P(x) = R(x) - C(x)

Breaking even is the point at which revenue begins to exceed costs. It is thus the point at which P(x) = 0. Because these are all linear functions, you know that the business will be profitable after that point.

P(x) = 0

R(x) - C(x) = 0

R(x) = 24x

C(x) = 17x + 161

From the above equation,

R(x)=C(x)

24x=17x+161

7x=161

x=161/7

x=23

For the company to break even, 23 units must be produced.

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The amount that each student will have to raise on average in order to meet the goal would be $40

First, find the remaining amount that the members of the Westview Journalism Club are trying to raise:
= Amount to raise - Amount already raised

= 2, 100 - 1, 180

= $920

The amount that each student in the club will have to raise on average can be found as:

= Amount remaining to be raised / Number of students in the Westview Journalism Club

= 920 / 23

= $40

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Answer:

They spent a total of 1 and 1/2 hours swimming.

Step-by-step explanation:

It is because 1 1/4 plus 1 1/4 equals 1 2/4 which mean 2/4=1/2 so in total they spent 1 1/2 hours swimming

The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = 0.051

Given,

Consider the interview of a person is a trial.

Lets consider it success if a person  owns a dog and consequently , a person without a dog will be a failure.'

Let the random variable X represent the number of persons to be interviewed to get 5 dog owner: in other words, to get 5 successors.

Probability of a success in each trial is p = 0.3. Therefore probability of a failure in each trial is q = 1 - p = 0.7 .

Because trials are independent. X has a negative binomial distribution with parameters k = 5, p = 0.3

P(X =x ) = b(x: k, p) = [tex][(x-1)(k-1)] p^kq^r^-^k[/tex]

where, x = k , k + 1 , k + 2......(1)

Now, Lets find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog

Using equation (1), we get:

P(X = 10) = b(10: 5, 0.3)

                = [(10-1) (5 - 1)][tex](0.3)^5(0.7)^1^0^-^5[/tex]

               = [(9)(4)] [tex](0.3)^5(0.7)^1^0^-^5[/tex]

               = 0.05146

Hence, The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = 0.051

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Answer:

depends on how you peel it

Step-by-step explanation:

if you peel it with one quick peel, you will have only one

if you do it with 2, you will have 2 peels an so on

The amount of peels will be greater in the bigger potato as compared to the smaller potato.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given data in the question,

There are two potatoes, a small one and a bigger one.

If you peel the bigger one, because of the bigger surface area, you will get more peels as compared to the smaller potato because the surface are is small, and you will get less number of peels.

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Answer:$27

Step-by-step explanation:

$33.75/15 = $2.25 per book

12 books x $2.25/book =  $27

Answer:

450 ducks

Step-by-step explanation:

75% can be rewritten as 75/100

75/100 of 600 can be rewritten as 75/100 * 600

Solve 75/100 = 0.75

0.75 * 600 = 450

The equation of the line is y = -4x -4.

We need to calculate the line which is parallel to y = -4x +3 and passes through the point (4, -20)

The given equation is y = -4x +3

Comparing this equation with the general equation of the line, y = mx +c, we get the slope of the equation is -4.

Now, When two lines are parallel to each other, their slopes are equal.

So, the slope of the required equation is -4.

Now, the equation of the line which passes through the points, [tex](x_{1} ,y_{1} )[/tex] and has slope m, is given by

[tex]y - y_{1} = m(x-x_{1} )[/tex]

Putting the values in the general equation, we get,

y - (-20) = -4(x - 4 )

y + 20 = -4x +16

y +4x = 16 -20 = -4

The equation of the line is y = -4x -4.

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Considering the discrete probability distribution, it is found that:

a) The mean is of: 6.3

b)

The mean of the distribution is given by the sum of each outcome multiplied by it's probability, hence it is obtained as follows:

E(X) = 0.1 x 2 + 0.3 x 5 + 0.4 x 7 + 0.2 x 9 = 6.3.

The variance of the distribution is given by the sum of the difference squared between each observation and the mean, multiplied by it's probability, hence it is obtained as follows:

Var(X) = 0.1 x (2 - 6.3)² + 0.3 x (5 - 6.3)² + 0.4 x (7 - 6.3)² + 0.2 x (9 - 6.3)² = 4.01.

The standard deviation is the square root of the variance of the distribution, hence it is obtained as follows:

S(X) = sqrt(4.01) = 2.

We have that:

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Answer:

1. 4√5

2. 3√5

3. √149

4. √58

Step-by-step explanation:

The Pythagorean theorem states "a^2 + b^2 = c^2",  where "a" and "b" are the legs, while "c" is the hypotenuse.

Knowing this, we can substitute each variable with given values on the triangles

1.  "4" and "8" are legs "a" and "b" and we need to find the hypotenuse "c"

4^2 + 8^2 = c^2

16 + 64 = c^2

80 = c^2

√80 = c

4√5 = c

2. "6" and "3" are legs "a" and "b" and we need to find the hypotenuse "c"

6^2 + 3^2= c^2

36 + 9 = c^2

45 = c^2

√45 = c

3√5 = c

3. "7" and "10" are legs "a" and "b" and we need to find the hypotenuse "c"

7^2 + 10^2 = c^2

49 + 100 = c^2

149 = c^2

√149 = c

4. "3" and "7" are legs "a" and "b" and we need to find hypotenuse "c"

3^2 + 7^2 = c^2

9 + 49 = c^2

58 = c^2

√58 = c

Making the subject as x, the expression is x = u/9

The given equation is

9x = u

It can be written as

u = 9x

We need to make x as the subject in the given expression

9x = u

u = 9x

here u is the subject

9x = u

x = u/9

Therefore, making the subject as x, the expression is x = u/9

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The value of the residual is 2.

We are given a fitted linear regression equation. The equation is given below.

ŷ = 6 - 2x

The x-value for the data points is 3, and the corresponding y-value is 2. We have to find the value of the residual.

We will substitute the given values in the equation of the regression line.

ŷ = 6 - 2x

ŷ = 6 - 2(3)

ŷ = 6 - 6

ŷ = 0

Thus, the predicted value of y in the given regression equation is 0. The actual value of y is 2. The residual is the difference between the actual and predicted values of y. Let the residual be denoted by the variable "r".

r = y - ŷ

r = 2 - 0

r = 2

Hence, the residual is 2.

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Answer:

B

Step-by-step explanation:

OR means that they don't overlap and based on the answer you have in you know how to solve the innequality.

The best firm for the Appliance manufacturer for the repair work is Firm 2 .

In the question ,

it is given that ,

An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis .

The acceptable range of the repair time is 50 minutes to 90 minutes.

the mean repair time for firm 1 = 74 minutes and standard deviation of 4 minutes .

the mean repair time for firm 2 = 72 minutes and standard deviation of 5.1 minutes .

the range is calculated using the formula

Range = Mean ± Standard Deviation

So , for firm 1 ,

the Range = 74 ± 4

= 74 [tex]+[/tex] 4       and      74 - 4

= 78     and   70

the range for firm 2 is

= 72 ± 5.1

= 72 [tex]+[/tex] 5.1      and      72 - 5.1

= 7.1        and       66.9  

The second company has a lower range and it should be preferred .

Therefore ,  The best firm for the Appliance manufacturer for the repair work is Firm 2 .

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