Christian had brochures printed for a new business venture, Christian originally ordered 4 boxes of black-and-white
brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3
boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?
If she let x = the number of black and white brochures and y = the number of color brochures, which system of
equations would she use?

Answer:

See.. there are two solutions for this question…

First one:—

(1×1)=1

(2×2)=4

(3×3)=9

(4×4)=16

(5×5)=25

(6×6)=36

(7×7)=49

(8×8)=64

(9×9)=81

(10×10)=100…. So as you saw that the pattern above is the square of consecutive numbers from 1 to 7… and the rest are the square of 8..9 nd 10…

Bow second method…

The series above is…

1…4…9…16…25…36…49

Here…

4-1=3

9-4=5

16-9=7

25-16=9

36-25=11

49-36=13…

So u can see that the difference between each term is a prime number ….and they form a series itself…

Series of odd no…..u can call it in Aritthmetic progression too…

3..5..7..9..11..13.. and the next odd no. Are 15..17 nd 19….

So the next 3 no. In the pattern are…

49+15=64

64+17=81

81+19=100

Step-by-step explanation:

My age is 2 years from the given condition.

Given that, if you square my age and subtract 28 times my age, the result is 60.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let x be my age.

Now, square my age is x²

28 times my age =28x

The square of my age and subtract 28 times my age, the result is 60.

x²-28x=60

⇒ x²-28x-60=0

⇒ x²+30-2x-60=0

⇒ x(x+30)-2(x+30)=0

⇒ (x+30)(x-2)=0

⇒ x=2

Hence, my age is 2 years from the given condition.

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Given :

The Tourist Information Center is  located at (11,0) and the Bus Station is located at (-1,-10).

Also , Tourist Information Center is between a Bus Station and a Train Station.

To Find :

The point of location of train station .

Solution :

Let , point of location of train station is ( x,y ).

We know , mid-point of two points ( a, b) and ( c, d ) is given by :

\((\dfrac{a+c}{2},\dfrac{b+d}{2})\) .

Since , Tourist Information Center is between a Bus Station and a Train Station.

So , it is given by :

\(( 11 , 0 ) = (\dfrac{-1+x}{2},\dfrac{-10+y}{2})\)

Comparing both coordinate :

\(\dfrac{x-1}{2}=11\\\\x=22+1\\\\x=23\)

and

\(\dfrac{y-10}{2}=0\\\\y=10\)

Therefore , Train Station is located at point ( 23 , 10 ) .

Hence , this is the required solution .

The order approximately 1.1111 cubic yards of topsoil from the dirt store.

The volume of topsoil required in cubic feet.

The area of the garden is:

The area of the garden is found by multiplying the length and width of the garden. In this case, the garden is 15 feet by 12 feet, so the area is 15 ft x 12 ft = 180 sq ft.

Since we want a 2 inch thick layer of topsoil, we need to convert the thickness to feet:

2 inches = 2/12 feet = 0.1667 feet

The volume of topsoil required in cubic feet is therefore:

180 sq ft × 0.1667 ft = 30 cubic feet

To convert this to cubic yards, we divide by 27 (since there are 27 cubic feet in a cubic yard):

The dirt store sells topsoil by the cubic yard, so we need to convert our answer from cubic feet to cubic yards. Since there are 27 cubic feet in a cubic yard (3 feet x 3 feet x 3 feet)

30 cubic feet ÷ 27 = 1.1111 cubic yards

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Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.

The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.

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Answer:

Step-by-step explanation:

You want to know the value of x and the angle measures in a figure having angles marked (7x +4)° and (6x -6)° forming a linear pair.

The angles of a linear pair are supplementary:

  (7x +4)° +(6x -6)° = 180°

  13x -2 = 180

  x = (180 +2)/13

  x = 14

Then the exterior angle is ...

  (7x +4)° = (7·14 +4)° = 102°

and the interior angle is ...

  (6x -6)° = 6(14 -1)° = 78°

<95141404393>

The measure of x is 14 degree, exterior angle is 102° and interior angle is 78°.

We know, Linear pair refers to a pair of adjacent angles that share a common side and whose non-common sides form a straight line.

So, on a starlight line the sum of angle formed a semicircle is 180 degree or supplementary.

So, 7x+ 4 + 6x- 6= 180 (Linear Pair)

13x - 2 = 180

13x = 182

x= 182/13

x = 14

So, the exterior angle is

=  (7x +4)°

= (7(14) +4)°

= 102°

and the interior angle is

= (6x -6)°

= 6(14 -1)°

= 78°

Thus, the exterior angle is 102° and the interior angle is 78°.

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Answer:

2,880

Step-by-step explanation:

P + 60N = x

1500 + 60(23) = x

1500 + 1380 = x

2880 = x

Answer:

What exactly are we trying to find? There is two equation marks.

Step-by-step explanation:

The slope is -5/4 and the equation of the line in point-slope form is       y-5 = -5/4(x+4) + c.

The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.

For the given situation,

The points are  (x1,y1) is (−4,5) and (x2,y2) is (0,0)

The formula of slope is

\(m=\frac{y2-y1}{x2-x1}\)

⇒ \(m=\frac{0-5}{0-(-4)}\)

⇒ \(m=\frac{-5}{4}\)

The equation of the line in point-slope form is

\(y-y1=m(x-x1)\)

⇒ \(y-5=\frac{-5}{4} (x-(-4))\)

⇒ \(y-5=\frac{-5}{4} (x+4)\)

Hence we can conclude that the slope is -5/4 and the equation of the line in point-slope form is y-5 = -5/4 (x+4).

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The cross marked at the points (-2.5 , -5) and  (0 , -1.5) is shown below .

The x and y coordinate helps in identifying a point in the coordinate axis and it is written as a ordered pair (x,y) .

where x represents the position of point with reference to the x-axis

and y represents the position of point with reference to the y axis .

In the question ,

points are given , we have to plot them and mark a cross .

Part(a)

point is (-2.5 , -5)

So , the x coordinate is -2.5

means the point is 2.5 units left from the origin  ,

and y coordinate is -5 .

means the point is 2.5 units down from the origin  .

the cross mark on the point is shown below .

Part(b)

point is (0 , -1.5)

So , the x coordinate is -2.5

means the point is 0 units units from the origin ,

and y coordinate is -1.5 ,

means the point is 1.5 units down from the origin  .

the cross mark on the point is shown below .

Therefore , The cross marked at the points (-2.5 , -5) and  (0 , -1.5) is shown below .

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Domain of the given function is R - {-4}. and Range of the function will be a real number.

What is a function ?

A function is a relationship between inputs and outputs where each input has precisely one output and the output can be linked to its input.

A function is given which is f(x) = [x² - 3x - 28] / (x + 4). We have to find out the domain and ranges of the given function.

Domain will be :

f(x) = \(\frac{x^{2} - 3x - 28}{x+4}\)

f(x) = [x² - 7x + 4x - 28] / (x+4)

f(x) = [x(x-7) + 4(x-7)] / (x+4)

f(x) = [(x-7) (x+4)] / (x+4)

Here, the function f(x) is defined only if :

x+4 ≠ 0

x ≠ -4  

So , domain will be : R - {-4}.

Now , Range will be :

y = [(x-7) (x+4)] / (x+4)

y = x  - 7

or

x = y + 7

So , range will be a real number.

Therefore , Domain of the given function is R - {-4}. and Range of the function will be a real number.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The ratio of the horizontal change to the vertical change of a line would not be used to describe a slope. Thus the correct option is option C.

The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) of a line.

Slope=Vertical Change/Horizontal Change

This is also represented as the "ratio of rise to run of a line".

Slope=Rise/Run

In the given question, however, option C states that the "ratio of the horizontal change to the vertical change of a line".

Horizontal Change/ Vertical Change= 1/slope

This is an incorrect statement since the ratio of the horizontal change to the vertical change of a line is the reciprocal of the correct ratio.

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Answer:

Step-by-step explanation:

Quadrant 2 or Quadrant II

Answer:

The answer Is d

quadrant 2

Answer:

=> membership fee = $50

=> monthly fee = $55

=> First month = 105$

=> 50 + 55(x)

=> 50 + 55 (15)

=> 50 + 825

=> 875

Workout gym

=> membership fee = $200

=> monthly fee = $45

=> First month = 245$

=> 200 + 45(x)

=> 200 + 45(15)

=> 200 + 675

=> 875

Answer:

x= 45 degrees

Step-by-step explanation:

the top angle is a eight angle which is equal to 90 all triangles are 180 degrees both bottom angles are equal and 180 minus the 90 degree from the right angle is 90 degrees you divide that by 2 and you have your answer

Answer:

y=0.25x^2−2x

Step-by-step explanation:

You have to use the disruptive property.

1. The probability that exactly 12 students drive to school is 0.169.

2.The probability that more than 15 students drive to school is 0.027.

3. The probability that no more than 10 students drive to school is 0.004.

4. The mean and standard deviation of the sample are 13.6 and 2.4, respectively.

5. The percentage falling within 1 standard deviation of the mean is approximately 68%, which satisfies the empirical rule for normal distributions.

This problem involves the binomial distribution, since each student either drives to school (success) or does not (failure), and the probability of success is given as 0.68 for each student.

(1) The probability that exactly 12 students drive to school is given by the binomial probability mass function:

P(X = 12) \(= (20 choose 12) * (0.68)^12 * (1 - 0.68)^(20 - 12) = 0.169\)

(2) The probability that more than 15 students drive to school is given by the complement of the probability that at most 15 students drive to school:

P(X > 15) = 1 - P(X <= 15) = 1 - sum[(20 choose i) * \((0.68)^i * (1 - 0.68)^{20 - i)}\) for i = 0 to 15.

This is approximately 0.027.

(3) The probability that no more than 10 students drive to school is given by the cumulative distribution function:

P(X <= 10) = sum[(20 choose i) * \((0.68)^i * (1 - 0.68)^{20 - i}\) for i = 0 to 10. This is approximately 0.004.

(4) The mean of the binomial distribution is given by the formula np, where n is the sample size and p is the probability of success.

Thus, the mean is 200.68 = 13.6.

The standard deviation of the binomial distribution is given by the formula sqrt(np(1-p)), which is approximately 2.4.

(5) The percentage falling within one standard deviation of the mean is approximately 68% by the empirical rule, which is the same as the percentage of students who drive to school in the university.

However, the empirical rule applies to normal distributions, and the binomial distribution is not exactly normal.

Nonetheless, for large sample sizes, the binomial distribution can be approximated by a normal distribution using the central limit theorem, which would make the empirical rule applicable.

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Answer: 9

Step-by-step explanation:

9*9 = 81

Answer:

9

Step-by-step explanation:

9*9=81

The solution (10, 7) represents that the box contains 10 batteries that provide 1.5 volts each and 7 batteries that provide 9 volts each.

Option C is the correct answer.

We have,

The solution (10, 7) in the given equation represents the values for x and y that satisfy the equation 1.5x + 9y = 78.

In the context of the problem,

x represents the number of batteries that provide 1.5 volts each, and y represents the number of batteries that provide 9 volts each.

The equation 1.5x + 9y = 78 represents the total voltage provided by all the batteries in the box, which is 78 volts.

By substituting the values x = 10 and y = 7 into the equation, we can verify if it holds true:

1.5(10) + 9(7) = 15 + 63 = 78

Since the equation is satisfied by these values, (10, 7) is a solution to the equation.

Therefore,

The solution (10, 7) represents that the box contains 10 batteries that provide 1.5 volts each and 7 batteries that provide 9 volts each.

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The height of triangle ABE is 24 cm

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

The triangle

From the triangle, we have the following ratios

h : 20 = (36 - h) : 10

Express as fraction

h/20 = (36 - h)/10

So, we have

h/2 = (36 - h)

This gives

h = 72 - 2h

So, we have

3h = 72

Divide

h = 24

Hence, the height is 24 cm

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The slope of parallel lines is equal and the slope of a perpendicular line is equal to the negative of the inverse of the slope of the line.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

The properties of parallel line are that the slope of the parallel lines are equal,

The slope of the perpendicular line is negative of the inverse of the slope of the line.

Suppose two lines y = mx + c and y = tx + d are parallel, then the slopes,

m = t

Suppose two lines y = ax + b and y = cx + d  are perpendicular then the slope of the second line, c = -1 / a.

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The given expression r1 r2 f1 r3 f2 f3 r3 represents a Reflection.

Given, r1, r2, and r3 represent rotations from dn and f1, f2, and f3 represent reflections from dn.

we have to determine that whether r1 r2 f1 r3 f2 f3 r3 is a rotation or a reflection.

So, on solving the expression, we get

r1 r2 give 2 rotations.

then, f1 give 1 reflection

after that r3 give again one rotation

then, f2 f3 give 2 reflections

and at last r3 give one rotation.

as, a result we got a reflection.

So, the given expression r1 r2 f1 r3 f2 f3 r3 represents a Reflection.

Hence, the given expression r1 r2 f1 r3 f2 f3 r3 represents a Reflection.

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Answer:

452.38934 yd^3

Step-by-step explanation:

Answer:

a = 159

Step-by-step explanation:

180 - 21 = a

a = 159

Answer:

159°

Step-by-step explanation:

Both the angles add up to 180° since they lie along a straight line.

So do 180 - 21 to get the measure of angle a.

a = 159°

The first 10 terms of the sequence are as follows: a1 = x, a2 = 8x, a3 = 16x, a4 = 24x, a5 = 32x, a6 = 40x, a7 = 48x, a8 = 56x, a9 = 64x, and a10 = 72x.

We know that the general formula for the nth term of an arithmetic sequence is given as a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term and d is the common difference.

Substituting the values in the formula, we get

a_n = a_1 + (n-1)d

a_n = x + (n-1)8x

a_n = x(1 + 8(n - 1)

a_n = 8nx

Now, we need to find the first 10 terms of the sequence. Therefore,

n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Putting the values of n in the formula we get,

a1 = x (when n = 1)

a2 = 8x (when n = 2)

a3 = 16x (when n = 3)

a4 = 24x (when n = 4)

a5 = 32x (when n = 5)

a6 = 40x (when n = 6)

a7 = 48x (when n = 7)

a8 = 56x (when n = 8)

a9 = 64x (when n = 9)

a10 = 72x (when n = 10)

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Answer: 42 kmh

Step-by-step explanation:

Speed = distance / time

= 189 / 4.5

= 42 kmh

Answer:

Average Speed = 42 km/hr

Step-by-step explanation:

Given:

Distance = 189 km

Time = 4.5 hours

Required:

Average Speed = ?

Formula :

Average Speed = Total Distance Covered/ Total Time Taken

Solution:

Putting the givens

Average Speed = 189/4.5

Average Speed = 42 km/hr

Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

J. Hewlett invested $3500 at 8% and $3500 - $1500 = $2000 at 9%.

Let's assume J. Hewlett invested x dollars at 8% and (x - 1500) dollars at 9%.

The income from the investment at 8% is given by:

Income from 8% investment = x * 0.08

The income from the investment at 9% is given by:

Income from 9% investment = (x - 1500) * 0.09

According to the problem, the income from the smaller investment (9%) is $100 less than the income from the larger investment (8%). We can set up the following equation:

(x - 1500) * 0.09 = x * 0.08 - 100

Simplifying and solving for x:

0.09x - 135 = 0.08x - 100

0.09x - 0.08x = -100 + 135

0.01x = 35

x = 35 / 0.01

x = 3500

Therefore, J. Hewlett invested $3500 at 8% and $3500 - $1500 = $2000 at 9%.

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