A bicycle manufacturer builds both Racing bikes and Recreational bikes from it's local warehouse. It takes one person 5 hours to assemble a Racing bike and 2 hours to finish painting it. It takes one person 4 hours to assemble a Recreational bike and 3 hours to finish painting it. Assembly can take no more than 180 hours throughout the week, and painting can take no more than 135 hours hours per week. If x represents the number of Racing bikes and y represents the number of Recreational bikes, which of the following systems represents the weekly constraints on assembly and painting?

Answer:

Step-by-step explanation:

He made a mistake in step one turning the 7 into a -7

[tex]x^{2}[/tex] - 3x + 7 = 0

Solving:

[tex]1x^{2}[/tex] - 3x + 7 = 0  ← If the term doesn't have a coefficient, it is considered that the coefficient is 1.

[tex]1x^{2}[/tex] + (-3x) + 7 = 0 ← Identify the coefficients a, b, and c of the quadratic equation.

a = 1, b = -3, c = 7

x = - (-3) ±√[tex](-3)^{2}[/tex] - 4 x 1 x 7

                 2 x 1

x = 3 ± √[tex](3)^{2}[/tex] - 4 x 7

                2

x = 3 ± √9 - 4 x 7

                2

x = 3 ±√9 - 28

             2

x = 3 ± √-19

         2

The square root of a negative number does not exist in the set of real numbers.  

x = ∉ R

The original price of the T.V is 350 dollars

a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

le the original price of T.V be x.

so if the t.v was sold 40% off, I means that the sale price of T.V  = 60x/100

0.6x.

if the original price is 140 more than sale price, it means sale price is 140 less = x - 140

Equating both expressions we have

x - 140 = 0.6x

x - 0.6x = 140

0.4x = 140

x = 140/0.4

x = 350 dollars

In conclusion, the original price of tv is 350 dollars

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The simplified form of the given expression has a numerator of (x + 9)(2x + 1) and the denominator of (x + 7) and the expression does exist when (x = 9) and this can be determined by factorizing the given expression.

By identifying the biggest factors that the terms in the equation have in common, factoring is a technique used in mathematics to simplify algebraic expressions.

Given :

Expression - [tex]\frac{3x^2 - 27x}{2x^2+13x-7}[/tex] ÷ [tex]\frac{3x}{4x^2-1}[/tex]

First, factorize the expression, [tex]4x^2-1[/tex]

So, [tex]4x^2-1[/tex] = [tex](2x-1) (2x+1)[/tex]

Now, factorize the equation: [tex]2x^2+13x-7[/tex]

[tex]2x^2+13x-7[/tex] = [tex]2x^2+14x -x -7[/tex]

                     = [tex]2x(x+7) -1(x+7)[/tex]

                     = [tex](2x-1) (x+7)[/tex]

Now, factorize the equation: [tex]3x^2-27x[/tex]

So, [tex]3x^2-27x[/tex] = [tex]3x(x-9)[/tex]

Now, substitute the factorized terms in the given expression:

= [tex]\frac{3x(x-9)}{(2x-1) (x+7)}[/tex] ÷ [tex]\frac{3x}{(2x-1) (2x+1)}[/tex]

= [tex]\frac{(x+9) (2x+1)}{(x+7)}[/tex]

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The complete question is as follows:

Select the correct answer from each drop down menu. The simplest form of this quotient has a numerator of... and a denominator of.... The expression does exist when x=......

Not enough information to answer

Option C is the correct answer.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

A roller-coaster goes over a 12 m tall hill and then approaches a 30 m hill.

The minimum velocity the roller-coaster would need when going over the 12 m hill to make it to the top of the 30 m hill.

To find the minimum velocity we need to know the acceleration of the roller coaster that comes down the 12 m tall hill.

The value of the acceleration is not given.

So,

We can not find the minimum velocity.

Thus,

Not enough information to answer

Option C is the correct answer.

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Answer: About 20.82 liters.

Step-by-step explanation:

         To go from gallons to liters, we will multiply by 3.785. Since we are in half gallons, we will multiply 11 by 0.5 for 5.5 full gallons. Now, we will multiply;

        5.5 gallons * 3.785 = 20.8198 ≈ 20.82 liters

Answer:

5

Step-by-step explanation:

The answer to this Question based on Profits is No they cant make 5000$ profit

What is profit?

Profit is simply the extra money we earn on selling good etc things and there are tonnes of different ways of making money and profit

Solution:

Here Diego high school soccer team started a fundraiser selling treats at their games

Initial money spent = 1000$

They decided to make 0.3$ revenue on both candy and soda hence total 0.6$ revenue in one pack

one pack costs for 2$ where 0.6$ is revenue and actual cost is 1.4$

Total packs to sell = 1000/1.4

= 714 packs

hence total profit = 714 * 0.6 = 428$

hence maximum revenue they can make is 428$ and it is maximum

hence they cant make 5000$ profit

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The required quadratic equation is x² - 12x + 36 Or (x - 6)².

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know (a - b) = a² - 2ab + b².

Given, An expression 36 - 12x + __

now, here b² = 36 ⇒ b = 6,

∴ - 2ab = - 2(a)(6).

So, a = 1.

∴ The required quadratic equation is x² - 12x + 36 Or (x - 6)².

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Answer:

Step-by-step explanation:

(-3)(k) = -15

-3k = -15

k = -15/-3

k = 5

(2x+3)(x+5) = 0

2x + 3 = 0

2x = -3

x = -3/2

x+ 5 = 0

x = -5

Time required to spread the rumor so that half of the given heard the rumor is equal to 15 hours (approximately).

As given in the question,

Number of people among whom rumor is spread = 400

Number of people is represented by N(t)

Time is represented by 't' hours

Function representing relation between number of people who heard about the rumor and time

N(t) = 400/ ( 1+ 399 × e^(-0.4t) )

Condition : Half of the given number of people heard the rumor

N(t) = 400/2

      = 200

Substitute the value in the function we get,

200 = 400/ ( 1+ 399 × e^(-0.4t) )

⇒ ( 1+ 399 × e^(-0.4t) ) = 400 ÷ 200

⇒  1 +  399 × e^(-0.4t)  = 2

⇒  399 × e^(-0.4t)  = 2 - 1

⇒ e^(-0.4t)  = 1 ÷ 399

⇒ e^(-0.4t) = 0.002506

⇒ -0.4t = [tex]log _{e}[/tex] (0.002506)

⇒ t= 14.97 hours

⇒ t= 15 hours (round off)

Therefore, time required to spread the rumor among half of the given number of people is equal to 15hours(approximately).

The complete question is:

A rumor spreads among a group of 400 people. The number of people, N(t), who have heard the rumor by the time t in hours since the rumor started to spread can be approximated by a function of the form

N(t) = 400 / (1+399e^(-0.4t))

Approximately how long will it take until half the people have heard the rumor?

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Answer:

[tex]y=\frac{1}{2}x+2[/tex]

Step-by-step explanation:

Using the points [tex](0,2)[/tex] and [tex](2,3)[/tex], the gradient is [tex]\frac{3-2}{2-0}=\frac{1}{2}[/tex].

The [tex]y[/tex]-intercept is [tex](0,2)[/tex], so the equation is [tex]y=\frac{1}{2}x+2[/tex].

Answer: To solve the equation "-5/8x + 10" for x when x equals -8, we can first substitute -8 for x in the equation:

-5/8(-8) + 10

Next, we can simplify the expression by performing the calculations within the parentheses:

-5/8(-8) + 10 = 5/8(8) + 10 = 5(8)/8 + 10 = 40/8 + 10 = 5 + 10 = 15

Therefore, the value of "-5/8x + 10" when x equals -8 is 15.

The required system of equations is x+y = 21 and 7x +14y = 252.

Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.There are three methods typically used to solve systems of linear equations: graphing, the substitution method, and the elimination method. These methods can be applied to more complex systems of nonlinear equations as well.

Let the number of small boxes be x.

Let the number of large boxes be y.

The volume of each small box is 7 cubic feet.

The volume of each large box is 14 cubic feet.

The total number of boxes is 21.

Total volume of all boxes is 252 cubic feet.

So, x+y = 21.

This is the first equation.

Also, the total volume is equal to the sum of the volumes of all individual boxes.

So,  7x + 14y = 252

Thus, the required system of equations is x+y = 21 and 7x +14y = 252.

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The required system of equations is x + y = 21 and 7x + 14y = 252 using the concept of equations.

A system of equations in algebra is made up of two or more equations that are solved together to obtain the solution for a two or more variable problem.

Volume of each small box is 7 cubic feet and volume of each large box is 14 cubic feet. Take the number of small boxes to be x and number of large boxes to be y.

Given total number of boxes shipped is 21. Therefore using the concept of equation,

x + y = 21  --- (1)

Total volume of small box is given by:

Total volume of small box = (Volume of a small box) * (Number of small box)

Total volume of small box = 7x

Similarly the total volume of large box is,

Total volume of small box = 14y

Given the total volume of carried box is 252 cubic feet. Using the concept of equations,

7x + 14y = 252  ---(2)

The equations (1) and (2) gives the required system of equations.

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Answer:

ANS:- = -25/18

Step-by-step explanation:

= (5/6)/(-3/5)

=5*5/6*(-3)

=25/-18

= -25/18

Khadija has 8 nickels and 2 quarters

From the question, we have the following parameters that can be used in our computation:

Worth of coins = $0.90

Type of coins = Dimes and quarters

Represent the nickels with n and the quarters with q

So, we have the following representation

n + q = 10

0.05n + 0.25q = 0.9

Make n the subject

n = 10 - q

So, we have

0.05(10 - q) + 0.25q = 0.9

Evaluate the products

0.5 - 0.05q + 0.25q = 0.9

This gives

0.2q = 0.4

Divide both sides by 0.2

q = 2

Recall that

n = 10 - q

So, we have

n = 10 - 2

Evaluate

n = 8

Hence, the number of nickels is 8

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The correct order to solve the equation is given below .

In the question ,

it is given that ,

the equation is 3*([tex]2^{2 t - 5}[/tex]) - 4 = 10  ,

Step(1) , adding 4 to each side of the equation ,

3*([tex]2^{2 t - 5}[/tex]) = 14

Step(2) , dividing both sides of the equation by 3 ,

we get ,  ([tex]2^{2 t - 5}[/tex]) = 14/3  .

Step(3) , taking log on each side ,

log([tex]2^{2 t - 5}[/tex]) = log(14/3)

Step(4) , Using the Exponential Property and writing 14/3 in decimal form ,

we get ,

(2t - 5)*log(2) = log(4.67)

Step(5) , Dividing each side by log(2)  ,

we get ,  2t-5 = log(4.67)/log(2) .

Step(6) , Add 5 to each side of equation

we get , 2t = 2.23 + 5  ;

Step(7) , Simplifying we get  ,

we get , t = 3.625  .

Therefore , the the solution of the given equation is t = 3.625   .

The given question is incomplete , the complete question is

Arrange the steps in the correct order to solve the equation,

3*([tex]2^{2 t - 5}[/tex]) - 4 = 10  .

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The​ manager's likely​ error is $20 if a store is instructed by corporate headquarters to put a markup of ​11% on all items. An item costing ​$18 is displayed by the store.  

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

A markup of ​11% on all items. An item costing ​$18 is displayed by the store manager at a selling price of ​$2.

The manager’s likely error was forgetting to add the $2 back to the $18.

$2= 11% of $18 = 1.98(=2)

For a markup,

= $2 + $18

= $20

Thus, the​ manager's likely​ error is $20 if a store is instructed by corporate headquarters to put a markup of ​11% on all items. An item costing ​$18 is displayed by the store.

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Answer:

  7.6

Step-by-step explanation:

You want to know the number of 360 ft football fields tall the 2722 ft Burj Khalifa building is.

The ratio of height to football field length is ...

  (2722 ft)/(360 ft/field) ≈ 7.6 fields

The height of the building is about 7.6 football field lengths.

If a boy grows 5 inches, he will be one half a tall as his sister , his sister is 68 inches tall. So the height of the boy is 29 inches

In mathematics, the opposite of multiplication is the process called division. Finding the number of times one quantity is included within another is the procedure. The letters "/" or "" are typically used to denote this. For instance, 8 boys divided by 2 may be expressed as 8/2 or 82. The outcome in this situation would be 4, which is the quantity that 2 may be found in 8 times. The quotient, or outcome of the division, and the remainder, or quantity remaining after dividing, may both be found using division. Calculus, algebra, geometry, and other branches of mathematics all make use of the crucial mathematical notion of division.

How to solve?

If the boy grows 5 inches, he will be 68/2 =34 inches tall

The boy's current height is 34 - 5 = 29 inches

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Answer:

Step-by-step explanation:

12

x=12y

2:3

3:14

nope-60/2=30

495/9=55

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_3(y)=11.03\hspace{5em}\log_3(z)=7.74\hspace{5em}\log_3(t)=5.44 \\\\[-0.35em] ~\dotfill[/tex]

[tex]12\log_3\left( \cfrac{z^7}{y^5 t^2} \right)\qquad \textit{let's nevermind the 12 for now} \\\\\\ \log_3\left( \cfrac{z^7}{y^5 t^2} \right)\implies \log_3(z^7)-\log_3(y^5 t^2)\implies \log_3(z^7)-[\log_3(y^5)+\log_3(t^2)] \\\\\\ \log_3(z^7)-\log_3(y^5)-\log_3(t^2)\implies 7\log_3(z)-5\log_3(y)-2\log_3(t) \\\\\\ 7(7.74)-5(11.03)-2(5.44)\implies \stackrel{\textit{let's put back the 12}}{12 ~~ [7(7.74)-5(11.03)-2(5.44)]} \\\\\\ ~\hfill \text{\LARGE -142.2}~\hfill[/tex]

Answer:

y + 9 = 2(x + 5): slope is 2

y - 4 = -3(x - 3): slope is -3

(12/5, 29/5)

Step-by-step explanation:

y + 9 = 2(x + 5)

y + 9 - 9 = 2(x + 5) - 9   ==> subtract both sides by 9 to isolate y

y = 2(x + 5) - 9 ==> simplify

y = 2x + 2*5 - 9  ==> distribute x and 5 by multiplying them by 2

y = 2x + 10 - 9

y = 2x + 1  ==> slope is 2

y - 4 = -3(x - 3)

y - 4 + 4 = -3(x - 3) + 4  ==> add both sides by 4 to isolate y

y = -3(x - 3) + 4

y = -3x - 3(-3) + 4  ==> multiply x and -3 by -3 by distributive property

y = -3x - (-9) + 4

y = -3x + 9 + 4  ==> simplify

y = -3x + 13  ==> slope is -3

Since y = -3x + 13 and y = 2x + 1:

2x + 1 = -3x + 13  ==> solve for x

2x + 3x + 1 = -3x + 3x + 13

5x + 1 = 13

5x + 1 - 1 = 13 - 1

5x = 12

x = 12/5

y = 2x + 1

y = 2(12/5) + 1  ==> plug in 12/5 for x

y = 24/5 + 1  ==> solve for y

y = 24/5 + 5/5

y = (24+5)/5  ==> y = 29/5   ==> (x, y) = (12/5, 29/5)

Answer:

y = 4x + 2

Step-by-step explanation:

24 coins gained after 6 weeks

24 / 6 = 4 coins a week

y = 4x + 2

The class intervals appropriate to use in creating a histogram of the data are 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130. The correct option is B.

A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.

The width of the intervals must be equal. This means that the difference between the lower bound and the upper bound must be equal. Also, the upper bound of the preceding interval must be the same as the lower bound of the next interval.

This means that the intervals must be overlapping. Of all the options, it is 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130 that satisfy both conditions.

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Answer:first option

Step-by-step explanation:

The values of sin2x, cos2x and tan2x is  [tex]-\frac{3\sqrt{13}}{11}[/tex], 2/11 and  [tex]-\frac{3\sqrt{13}}{2}[/tex] respectively.

What is tan function?

The tan function, one of the primary six trigonometric functions, is typically expressed as tan x. It is the ratio of the angle's opposite and adjacent sides when a right-angled triangle is being considered.

Tangent is a verb that means "to touch" in Latin, from the root tangere. A circle is precisely the point at which a line tan to it intersects. In trigonometry, the tan function, a periodic function, is crucial. Utilizing the unit circle will make understanding the tangent function the simplest possible.

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Answer: It should not be able to

Step-by-step explanation:

It should always be in the middle, aka its name, "Median"

If Kareem has 3.5 cups of sugar then the amount of flour that Kareem need to make the muffins is 7 cups  .

In the question ,

it is given that ,

the ratio that Kareem uses to make the muffin is 3.5 cups of flour for every 1.75 cups of sugar .

let the number of cups of flour be "y" and

the number of cups of sugar be "x" .

So , y ∝ x ,

y = k*x , where k is the constant of proportionality .

From the given data ,

3.5 = k*1.75

k = 3.5/1.75

k = 2 .

we have to find the cups of flour that Kareem needs , if he has 3.5 cups of sugar .

the equation becomes ,

y = 2*3.5

y = 7

Therefore , Kareem needs 7 cups of flour .

The given question is incomplete , the complete question is

Kareem makes muffins using a ratio of 3. 5 cups of flour for every 1. 75  cups of sugar. If he has 3. 5 cups of sugar, how much flour does he need to make the muffins ?

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Answer: y= -2/3x + 0

Step-by-step explanation: y=mx+b

The Y-intercept is at (0,0), so b is 0

Slope is -2/3

So the equation is y=-2/3x + 0