00
Which could be the base shape of the cylinder?
Oline
O non-square rectangle
O circle
O square

The equation to model the situation is given below. And the months will the populations of the towns be​ equal will be 12.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A town's populace is 43,200. Around 125 individuals move out of the town every month. Every month, 175 individuals on the normal move into town. A close by the town has a populace of 45,900. It has nobody moving in and a normal of 175 individuals moving away consistently.

Let y be the total population and x be the number of months. Then the equations are given as,

y = (175 - 125)x + 43200

y = 50x + 43200           ...1

y = -175x + 45900        ...2

From equations 1 and 2, then we have

50x + 43200 = - 175x + 45900

50x + 175x = 45900 - 43200

225x = 2700

x = 2700 / 225

x = 12

The months will the populations of the towns be​ equal will be 12.

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Answer:

Step-by-step explanation:

the answer is "downward". If you say "why", it is because of the degree coefficient.

in the equation, the latest degree is 2 (which is quadratic equation) so from the degree its coefficient is -3. If it is negative, it should be downward like -3. But if it is positive it should be upward like 3, 1, 44.

Answer:

64

Step-by-step explanation:

119+89+145=353-289=127+74+88
^
64

The average rate of change in the number of cars the manufacturer sold between 2002 and 2006 is B. 225 cars per year.

The average rate of change shows the slope line over the stated interval.

We can find the average rate of change by dividing the change in y-values by the change in x-values.

Year        No. of cars sold

                in (hundreds)

2000                 45

2002                 51

2004                53

2006                60

2008                77

The total number of cars sold between 2002 and 2006 = 16,400

The number of cars sold in 2002 = 5,100

The number of cars sold in 2006 = 6,000

The increase in car sold between 2002 and 2006 = 900 (6,000 - 5,100)

OR:

Increase in the number of cars sold in 2004 = 200 (5,300 - 5,100)

Increase in the number of cars sold in 2006 = 700 (6,000 - 5,300)

Total change in y-values = 900 (6,000 - 5,100)

Total change in x-values = 4 (2006 - 200)2

Average rate of change = 225 (900/4)

Thus, we can conclude that for 4 years, car sales increased on, average, by 225 each year.

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Answer:

25

Step-by-step explanation:

Let the age of Thomas be x.

Huilan is 11 years older than Thomas,

Huilan = x + 11

The sum of their ages is 61.

x + x + 11 = 61

2x + 11 = 61

2x = 61 - 11

2x = 50

x = 50/2

x = 25

Hence,

Thomas's age is 25.

The probability that the second ball drawn is yellow is of:

0.2926 = 29.26%.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

In this problem, the possible outcomes to obtain a yellow ball on the second draw are:

Then the probability of an yellow ball on the second draw is given as follows:

p = (3/11) x (3/11) + (8/11) x (3/10) = 0.2926 = 29.26%.

The problem asks for the probability that the second ball drawn is yellow.

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The missing x and y values in the ordered pair of the equation are:

x = 1

y = -4

Given the ordered pair (x, y) of an equation, y = mx + b, we can find their values by plugging in the given value of either of the x or y coordinates to find the other coordinate value.

The ordered pairs of y = -2x + 4 are given as:

(4, y) and (x, 2)

To find the value of y, substitute x = 4 into the equation y = -2x + 4:

y = -2(4) + 4

y = -8 + 4

y = -4

The value of y is -4.

To find the value of x, substitute y = 2 into the equation y = -2x + 4:

2 = -2x + 4

2 - 4 = -2x

-2 = -2x

-2/-2 = x

1 = x

x = 1

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Abdiel's total if he uses a coupon for 12% off the subtotal and leaves a 25% tip before the discount is $27.46

The correct answer option is option B

Amount of total after discount = 12% × $24.30

= 0.12 ×24.30

= $2.916

Amount of abdiel's tip = 25% × $24.40

= 0.25 × 24.30

= $6.075

Abdiel's total after discount before tip = (Amount of abdiel's tip + Abdiel's subtotal) - Amount of total after discount

= (6.075 + 24.30) - $2.916

= $30.375 - $2.916

= $27.459

Approximately,

$27.46

Therefore, the total amount Abdiel paid after discount before tip is $27.46

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Answer: y = -x - 8

Step-by-step explanation:

    Slope-intercept form is given in y = mx + b where m is the slope and b is the y-intercept.

    We can see our b, the y-intercept, is -8 since the line intercepts the y-axis at (0, -8).

    For our slope, we can see that the line moves down one and right one for a slope of 1/1=1. Since it's moving downwards, the slope is -1.

    Now, we will write the full equation:

y = -x - 8

The correct statement of the expression (x + 6) / ( x² - 9x + 18 ) is f(x) is increasing for all x > 6

Information given in the question

f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity

This is written as (x + 6) / ( x² - 9x + 18 )

factorizing the denominator gives

(x + 6) / {( x - 6)( x - 3)}

In the denominator

At x = 6 and at x = 3 the equation will result to infinity which is a very high value. hence:

f(x) is decreasing for all x < 6: contains  x = 3 and result to a higher value

f(x) is decreasing for all x < 3: will result to negative numbers which will end up increasing

f(x) is increasing for all x < 3: contains values which will be decreasing like x = 4

Therefore the correct option is f(x) is increasing for all x > 6

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Number lines are significant because they depict numbers as they appear in daily life.

What is number line?

A number line is a representation of a graduated straight line in elementary mathematics that serves as a visual representation of the real numbers. It is assumed that every point on a number line corresponds to a real number, and that vice versa.

Research has revealed that number lines are crucial because they foster sound mental number sense and arithmetic procedures.

They assist in providing a mental approach for addition and subtraction. Number lines are crucial, we can all agree on that.

Number lines are significant because they depict numbers as they appear in daily life.

Primarily because they make it possible for negative integers to be represented in a meaningful fashion.

The ability to display all real numbers, even enigmatic irrational numbers such π, -π, √2, -√ 2, etc., was a secondary but no less significant result.

Hence, number lines are significant because they depict numbers as they appear in daily life.

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The sum of first 50 terms of the sequence a(n) = 3n + 2 is  3925

In this question, we have been given a sequence a(n) = 3n + 2

We need to find the sum of the first 50 terms of the sequence

a(1) = 3 + 2

      = 5

a(2) = 6 + 2

      = 8

a(3) = 9 + 2

      = 11

a(4) = 12 + 2

      = 14

...

Given sequence is arithmetic sequence with common difference d = 3 and the first term a = 5

Using the formula for the sum of first n terms of AP

Sum of n terms of A.P. = n/2[2a + (n - 1)d]

For n = 50

S(50) = (50/2) * [2(5) + (50 - 1)3]

S(50) = 25 * [10 + (49 * 3)]

S(50) = 25 * 157

S(50) = 3925

Therefore, the sum of first 50 terms of the sequence a(n) = 3n + 2 is  3925

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Answer:

kind423

Step-by-step explanation:

Answer: 2(1.9)+1.30x<10

Step-by-step explanation:

Orange= $1.30/lb

Pear= $1.90/lb

$1.30/lb = $y/2lb

y=1.30*2

y=$2.6 for 2lb of orange

So

She spent

2(1.30)+1.90x< $10

2.6+1.90x<10

1.90x<10-2.6

1.90x<7.4

x<7.4/1.90

x<3.89

According to 2(1.30)+1.90x< $10

2.6+1.90*3.89<10

9.991<10

The BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.

Given:

1 ≤ x ≤ 3

we know x is between 1 and 3 so the best estimate is 2 even though the answer could also be 3 but that will be skewed.

1 ≤ 2 ≤ 3 is the best estimate.

Therefore the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.

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The solution set for the inequality is (-3, 3)

Here we have the absolute value inequality

|2x| - 6  < 0

To solve this, we need to isolate the variable, which in this case is x.

Adding 6 in both sides we get:

|2x| -6 + 6 < 0 + 6

|2x| < 6

This can be decomposed in the inequality:

-6 < 2x < 6

Now to competely solve the inequality, we will divide both sides by 2, so we get:

-6/2 < 2x/2 < 6/2

-3 < x < 3

So the solution set is (-3, 3)

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Answer:

Step-by-step explanation:

We know that:

Then 6 gallons is:

Add 3 quarts to get total:

Answer:

27 quarts

Step-by-step explanation:

Now we have to,

→ find how many quarts does 6 gallons 3 quarts of paint measure.

Formula we use,

→ 1 gallon = 4 quarts

Now the required solution will be,

→ (6 × 4) + 3

→ 24 + 3

→ 27 quarts

Hence, the answer is 27 quarts.

Using differentiation, 36 feet is the maximum height, in feet, that the object will reach.

In the given question,

An object is launched directly in the air at a speed of 32 feet per second from a platform located 20 feet above the ground.

The position of the object can be modeled using the function [tex]f(t)=-16t^2+32t+20[/tex], where t is the time in seconds and f(t) is the height, in feet, of the object.

We have to find the maximum height, in feet, that the object will reach.

The given function is [tex]f(t)=-16t^2+32t+20[/tex].

To find the maximum height we differentiate the function with respect to t

[tex]\frac{df}{dt}=-32t+32[/tex]

As we know that at the maximum point the slope of the tangent is zero.

So df/dt = 0

So -32t+32=0

Subtract 32 on both side

-32t+32-32=0-32

-32t=-32

Divide by -32 on both side

-32/-32 t = -32/-32

t=1

Therefore at t=1 the function have maximum value. So we put t=1 in the given equation.

[tex]f(1)=-16(1)^2+32\times1+20[/tex]

f(1)=(-16)×1+32×1+20

Simplifying

f(1)=-16+32+20

f(1)=36 feet.

Hence, 36 feet is the maximum height, in feet, that the object will reach.

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Answer:

15 more appetizers

Step-by-step explanation:

A restaurant has 60 menu items. Of these menu items, main dishes outnumber appetizers by a ratio of 4:1. How many more appetizers would the restaurant have to add to the menu to bring the ratio to 2:1?

at a ratio of 4e:1a and having 60e: there are (60/4=15) 15 appetizers

at a ratio of 2e:1a and having 60e: there are (60/2=30) 30 appetizers

Because they already have 15 appetizers, they will need:

30 appetizers - 15 appetizers  = 15 more appetizers

As per the proportional relationship, the constant of the proportionality is 1/3

Proportional relationship

A relationship is said to be proportional if each pair of data values are related in the same way, by multiplying by a factor.

The standard form of proportional relationship is written as.

y = k x

where k refers the constant of proportionality.

Given,

The table shows the proportional relationship between h and j.

Now, we need to find the constant of proportionality from h to j and we have to express the answer as a fraction in reduced terms.

We know that the standard form of the proportionality is written as,

y = k x

So, here y takes the value of j and x takes the values of h.

Then we have to take the points as (18, 6) and apply t on the standard form to get the value of k,

=> 6 = k (18)

Here we need the value of k, so move the number to the other side then we get,

=> k = 6/18

When we reduce this, then we get,

=> k = 1/3

Therefore, the constant of proportionality is 1/3.

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Answer: x < 3

Explanation: Once you reach step 3, you divide -2 on both sides. -2x cancels out, and -6 divided by -2 is 3

Answer:

1/4

Step-by-step explanation:

rise/run                                          you can count it but it doesn't always work

If you want to know the mathematical way of doing it it's:

m(slope) = y2-y1/x2-x1                 Choose any two points I chose (-4,5) & (0,6)

m = 6-5/0-(-4)                               Then subtract 6 - 5 and 0-(-4)  

m = 1/4

1/2 - 5i/4 is the simplified form of the expression ( 5 + 2i ) / 4i.

Given the expression in the question;

( 5 + 2i ) / 4i

To simplify, multiply the numerator and denominator by the conjugate of 4i

( 5 + 2i ) / 4i

( 5 + 2i ) × i / 4i × i

( 5 + 2i )i / 4ii

Apply distributive property

( 5i + 2ii ) / 4ii

Not that i × i = i² = -1

( 5i + 2i² ) / 4i²

( 5i + 2( -1 ) ) / 4( -1 )

( 5i - 2 ) / -4

( -2 + 5i ) / -4

Split the fraction

-2/-4 + 5i/-4

1/2 - 5i/4

Therefore, the simplified form is 1/2 - 5i/4.

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The five number from the box plot is presented as follows:

A box and whisker plot shows five things of a distribution, listed as follows:

The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.

The data set's maximum value.

These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.

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The artist will take 5 hours to decorate 25 clay pots.

Given,

Number of pots to be decorated in 3 hours =40

Number of pots he decorated in 3 hours =[tex]\frac{3}{8}*40=3*5=15[/tex]

So, the artist took 3 hours to decorate 15 pots instead of 40 pots.

It means to decorate 1 pot he took time=[tex]\frac{Total time}{Number of pots decorated} =\frac{3}{15} =\frac{1}{15} hour[/tex]

So, to decorate 25 pots he need time,

[tex]time=\frac{1}{5}*25= 5 hours[/tex]

Thus, the artist need 5 hours to decorate 25 clay pots.

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The surface area of the cone is  282.6 [tex]in^2[/tex].

What is surface area of cone?

  The region that a cone's surface occupies in three dimensions is known as the surface area of a cone. The whole area a cone's surface covers is known as the cone's surface area. The overall surface area will include the cone's lateral and base surfaces. A three-dimensional solid construction with a circular base is referred to as a cone. A cone can be thought of as a collection of irregularly shaped circular discs that have been stacked on top of one another while maintaining a constant ratio between the radii of the adjacent discs. It is the total of the cone's lateral area and base area.

Here the given ,

=> Height h= 12in

=> Radius r = 5 in

Using surface area of cone formula,

=> Surface area SA = [tex]\pi[/tex]r(r+ [tex]\sqrt{r^2+h^2}[/tex]) square unit.

=> surface area SA = 3.14*5(5+[tex]\sqrt{12^2+5^2}[/tex])

=> surface area SA = 15.7(5+[tex]\sqrt{144+25}[/tex])=15.7(5+13)

=> surface area SA = 15.7*18=282.6 [tex]in^2[/tex]

Therefore surface area of the cone 282.6 [tex]in^2[/tex].

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Answer:

m∠D = 54°

Step-by-step explanation:

The sum of the measures of the interior angles of a triangle is 180°.

The sum of the measures of an interior angle and its corresponding exterior angle is 180°.

With this knowledge, we can construct the equation:

50° + (3x + 18)° + (180 - (8 + 8x))° = 180°

and solve for x.

50° + (3x + 18)° + (180 - 8 - 8x)° = 180°

(50 + 18 + 180 - 8)° + (3x - 8x)° = 180°

240° - 5x° = 180°

5x° = 240° - 180°

5x° = 60°

x° = 12°

Now, we can solve for m∠D by plugging in the x value that we solved for.

m∠D = (3x + 18)°

m∠D = 3(12)° + 18°

m∠D = 36° + 18°

m∠D = 54°

Margin did the successful candidate win is 5375 - 4300 = 1075.

Given:

In an election for a corporation seat, there were two candidates. A total of 9,791 votes were polled.

116 votes were declared invalid. The successful candidate got 5 votes for every 4 votes his opponent had.

Number of valid votes = 9791 - 116 = 9675.

Let the number of votes of successful candidate = 5x

Let the number of votes of opponent = 4x

5x + 4x = 9675

9x = 9675

divide by 9 on both sides

x = 9675/9

x = 1075

Hence the votes for successful candidate = 5*1075 = 5375.

votes for opponent = 4*1075 = 4300.

Margin by which the successful candidate wins = 5375 - 4300 = 1075.

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The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

Given that, [tex]\frac{d}{dx}(e^x) =e^x[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Differentiate using the Exponential Rule which states that [tex]\frac{d}{dx}(a^x)[/tex] is [tex]a^xln(a)[/tex] where [tex]a=e.e^x[/tex]

So, now [tex]\frac{d}{dx}(e^x) =e^x[/tex]

The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

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The stack of paper will have the height of 1048576 papers

The first cut will produce 2 papers, the second cut will produce 4 papers, the third cut will produce 8 papers and the fourth cut will produce 16 papers.

If you examine the stages of cut and the number of papers, the relationship between them is:

1st cut: number of papers = 2¹ = 2  

2nd cut: number of papers = 2² = 4

3rd cut: number of papers = 2³  = 8

4th cut: number of papers = 2⁴  = 16

nth cut: number of papers = 2ⁿ

So if the  process is repeated 20 times, the number of papers will be:

Number of paper = 2²⁰ = 1048576

Therefore, the stack of paper will be as high as 1048576 papers

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