A​ town's population is 42,975. About 125 people move out of the town each month. Each​ month, 150 people on average move into town. A nearby town has a population of 45,225. It has no one moving in and an average of 200 people moving away every month. In about how many months will the populations of the towns be​ equal? Write an equation to model the situation. Then solve the equation and answer the question.

Answer:

Step 2

1 2/3 was converted as 5/2 instead of 5/3

Step-by-step explanation:

Each batch = 1 2/3

Total = 10 5/6

Number of batches

10 5/6 : 1 2/3 =

65/6 : 5/3 =

65/6 * 3/5 =

65/10 =

6.5

Solution by Janice:

10 5/6 : 1 2/3 =

65/6 : 5/2 =

65/6 * 2/5 =

130/30 =

4 1/3

Error made at step 2:

StartFraction 65 over 6 EndFraction divided by five halves = StartFraction 65 over 6 EndFraction times StartFraction 2 over 5

1 2/3 was converted as 5/2 instead of 5/3

Answer:

The Ans. {2, 3, 4, 5}

Step-by-step explanation:

5x – 2 ≥ 8 when we will replace the given values{1, 2, 3, 4, 5} insted of X we get true solution set by {2, 3, 4, 5}

Sonny get 240=240 because  the cross products of the proportion are equal.

Proportion : Two ratios are said to be in proportion when the two ratios are equal.

For Example , If Smith walks 5 km in 1 hour then he will walk 25 km in 5 hours. denoted by

[tex]\frac{5}{1} =\frac{25}{5} \\ \\ 5=5[/tex].

According to the given question the equation can be written as

[tex]\frac{16}{x} =\frac{48}{15}[/tex]

Sonny substituted 5 for x in the proportion , the equation can be written as

[tex]\frac{16}{5} =\frac{48}{15} \\ \\ Doing .the .cross.product\\ \\ 16*15=48*5\\ \\ 240=240[/tex]

Therefore , Sonny get 240=240 because  the cross products of the proportion are equal.

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The the rectangular solid with maximum volume for given surface area is, in fact, a cube with side 4.5.

Which formula represents the volume of a rectangular prism?

Let x = the side of the square base and y = height

Let V = volume = x2y

The surface area = 2x2 + 4xy = 121.5

Solve the surface area equation for y = (121.5 - 2x2)/4x and substitute this into the volume equation

V = x2(121.5 - 2x2)/4x = x(121.5 - 2x2)/4

the derivative of V with respect to x = (x/4)(-2x) + (1/4)(121.5 - 2x2) = 0 at the maximum

(1/4)(-4x2 + 121.5 - 2x2) = 0'

6x2 = 121.5

x2 = 20.25

x = 4.5

y = (121.5 - 40.5)/(4 * 4.5) =81/18 = 4.5

The the rectangular solid with maximum volume for given surface area is, in fact, a cube with side 4.5.

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The true statements regarding this situation are as follows:

The diagram is missing, but it is given on the graph at the end of the answer. (not drawn to scale)

The alternate interior angles are between the two parallel lines, one in each side, and they are congruent.

Hence:

Angles 3 and 6 are congruent because they are alternate interior angles.

Straight angles are angles of 180º on a line, hence:

Angles 1 and 3 add to 180º as they are straight angles.

Since angles 3 and 6 are congruent(alternate interior), angles 1 and 6 will also be supplementary, as they add to 180º.

A similar problem, in which a transversal cuts two parallel lines, is given at the end of the answer.

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Answer:

Step-by-step explanation:

It means she made a rectangle. 2cm wide, 5cm high.

The equation of the parabola that models the given situation is y=-1/6 (x-3)^2 +1.5.

Define parabola and its types.

A parabola is a roughly U-shaped mirror-symmetrical plane curve. It corresponds to a number of seemingly unrelated mathematical descriptions that all define the same curves.

To represent a parabola algebraically in the coordinate plane, the standard equation of a parabola is used. The general equation of the parabola is given by [tex]$\mathrm{y}=a(x-h)^2+\mathrm{k}$[/tex]or [tex]$\mathrm{x}=a(y-k)^2+\mathrm{h}$[/tex], where [tex]$(\mathrm{h}, \mathrm{k})$[/tex] denotes the vertex. A regular parabola's standard equation is y^2= 4ax

Now, the equation of parabola for the given situation is calculated as:

y=a(x-3)^2 +1.5

Now, put the value of x=0 and y=0.

0=a(0-3)^2+1.5

0=9 a+1.5

-9 a=1.5

a=-1.5 / 9

a=-1 / 6

Now, put the value of a in equation[tex]$\mathrm{y}=a(x-3)^2+1.5$[/tex] to obtain:

y=-1/6 (x-3)^2 +1.5

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The equation of the line in point-slope form is: y - 5 = -x + 2.

The equation of the line can be modelled as y - b = m(x - a), in point-slope form..

Given the following:

(2, 5) and (-1, 8), find the slope

Slope of the line (m) = change in y / change in x = (8 - 5)/(-1 - 2)

Slope of the line (m) = 3/-3

Slope of the line (m) = -1

Substitute (a, b) = (2, 5) and m = -1 into y - b = m(x - a):

y - 5 = -1(x - 2)

y - 5 = -x + 2

Therefore, the equation of the line in point-slope form is: y - 5 = -x + 2.

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The point at 1/5 of the coordinate points is (-11/5, -7/5)

The coordinates are given as:

(-3, -2) to (1, 1)?

The location 1/5 can be represented as

m : n = 1 : 4

The location of the point is then calculated as:

P = 1/5 * (mx2 + nx1, my2 + ny1)

This gives

P = 1/5 * (1 * 1 + 4 * -3, 1 * 1 + 4 * -2)

Evaluate

P = 1/5 * (-11, -7)

This gives

P = (-11/5, -7/5)

Hence, the point at 1/5 of the coordinate points is (-11/5, -7/5)

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Answer:

s/2πh

Step-by-step explanation:

dividing both sides by 2 will result in s/2 = πrh

dividing both sides by π will result in s/2π = rh

dividing both sides by h results in s/2πh = r

comment if you need further explanation

(no brainliest needed)

Answer: Kaelan spends more money. Kaelan spends 0.25 cents more.

Step-by-step explanation:please give brainliest if right.

The simplification of the number 2√15 is 7.74.

Squaring a number would be the inverse operation of square rooting it.

The given expression is;

= 2√15

For finding the value of √15; use long division method.

√15 = 3.87

Put the value;

=  2 × 3.87

=  7.74.

Thus, the value of the expression is found as 7.74.

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Answer:

1 1/3 or 4/3

Step-by-step explanation:

order of operations

[tex]\bold{H \: e \: y \: o \: !}[/tex]

__________________

[tex]\mathtt{\sqrt{\frac{9x^3}{4y^2}}}[/tex]

__________________

Apply radical rule: [tex]\mathtt{=\sqrt{\frac{a}{b}}} \: = \: \mathtt{\sqrt{\frac{a}{b}}},[/tex] assuming [tex]\mathtt{a \geq 0, \: b \: \leq 0}[/tex]

[tex]\mathtt{=\sqrt{\frac{9x^3}{4y^2}}}[/tex]

__________________

Simplify: [tex]\mathtt{\sqrt{9x^3}} \: : \: \mathtt{3x\sqrt{x}}}[/tex]

[tex]\mathtt{=\sqrt{\frac{3x\sqrt{x}}{4y^2}}}[/tex]

__________________

Simplify: [tex]\mathtt{\sqrt{4y^2}} \: : \: \mathtt{2y}[/tex]

[tex]\mathtt{\frac{3x\sqrt{x}}{2y}}[/tex]

Hope It Helps!

A n s w e r e d : -  ᴀᴅʀɪᴀɴɴᴏɪʀ

Answer:

y = 8x - 3

Step-by-step explanation:

The point where the line crosses the y-axis is the y-intercept and the intercept we're looking for. We know the slope 8 and the intercept -3, so we can just provide the answer

[tex]\large\textsf{{Hi! In this problem we need to find the equation of a line}}\\\textsf{in slope-intercept form: \textbf{y=mx+b}, where \textbf{m} is the slope}\\\textsf{and \textbf{b} is the y-intercept}}.\\\\\\\\\textsf{The question provides us both the slope \& the y-intercept}\\\textsf{This means we can find the equation by}\\\textsf{plugging the numbers into the formula:}\\\\\textbf{y=mx+b}\\\\\textbf{y=8x+(-3)}\\\\\textbf{y=8x-3}\twoheadleftarrow\boldsymbol{Answer!}\ddot\smile[/tex]

As given the sum of squares of three consecutive integers,  four digits which never occur in the ones place are 1,3,6,8.

As given,

Let x -1 , x , x +1 are three consecutive integers.

Sum of the squares of three consecutive integers

= (x -1)² +x² + (x+1)²

= x² -2x +1 +x² +x² +2x +1

=3x² +2

Now substitute x = 0,1,2,3,4,5,6,7,8,9

Sum = 2, 5,14,29, 50, 77, 110, 149, 194, 245

Four digit never occur at ones place = 1,3,6,8

Therefore, as given the sum of squares of three consecutive integers,  four digits which never occur in the ones place are 1,3,6,8.

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0.45  is the probability someone who studies very hard for the bar passe.

What is probability?

Odds of passing = 1.22  = p ( passing)/ P(not passing)

P(Pass)/P( fail)  = 1.22

p (pass) = 1.22 p (fail)

P(pass) + P(fail) = 1

1.22 p (fail) + p(fail) = 1

2.22 p(fail) = 1

P (fail) = 0.4505   ≅ 0.45

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Answer:

2(-2-8)

Step-by-step explanation:

The difference between -2 and 8 is -2-8. The product of 2 and the difference is (-2-8)*2 which is 2(-2-8).

La partie « Exercez-vous »

➺ Exercez-vous

Je m'appelle Catherine… elle est italienne… Il est

anglais. – Et vous, vous êtes française ? – Oui, je suis

française.

➺ Exercez-vous

« vous » entre adultes qui ne se connaissent pas (dessin du haut) – « tu » entre étudiants (dessin du

milieu) quand un adulte s'adresse à un enfant (dessin

du bas).

The cans of paint that are needed is 25 cans.

It should be noted that the sides of the cube will be:

= 3✓2197

= 13

Each side is 13m

Therefore, the total surface area will be:

= 6s²

s = sides

= 6(13)²

= 1014m²

Therefore, the cans needed will be:

= 1014/40

= 25

Therefore, 25 cans are needed.

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Answer:

See below

Step-by-step explanation:

Plug in each number for x to test each equation

X=1

Y=-3x + 22 = - 3(1) + 22 = 19

X=3

Y= -3(3) + 22 = - 9 + 22 = 13

And so on, if they match the y row, then it's the correct answer

Cross sectional data are collected from several entities at the same point in time.

In statistics and econometrics, cross-sectional data, often known as a cross section of a research population, is a type of data gathered by watching numerous participants all at once. It's also possible that the analysis disregards variations in time.

You evaluate a data set at a certain point in time when you conduct a cross-sectional data analysis. Cross-sectional data is frequently sourced from surveys and public records. The datasets document observations of various variables at a specific time.

In conclusion, the correct option is A.

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The probability that a gorilla will live longer than 26 years is between 15.8 and 24.2 years.

Likelihood is the part of science concerning mathematical portrayals of how likely an occasion is to happen, or how likely it is that a recommendation is valid.

P (A) is the probability of an event “A”

n (A) is the number of favorable outcomes

n (S) is the total number of events in the sample space

The likelihood of an occasion is a number somewhere in the range of 0 and 1, where, generally talking, 0 shows difficulty of the occasion and 1 demonstrates conviction. The higher the likelihood of an occasion, the almost certain it is that the occasion will happen. A straightforward model is the throwing of a fair coin. Since the coin is fair, the two results are both similarly likely; the likelihood of "heads" approaches the likelihood of "tails"; and since no different results are conceivable, the likelihood of by the same token "heads" or "tails" is 1/2.

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if the terminal point indicated by t is in the provided quadrant, the first equation in terms of the second quadrant iv; cos(t), sin(t). [tex]\sin t=\sqrt{1-\frac{1}{\sec ^2 t}}[/tex]

Trig identities come in handy when we need to express one trig function in terms of another. The most famous trig identity is derived straight from the Pythagorean Theorem:

sin² t +  cos² t = 1

For an angle t in Quadrant IV, we know sin t is positive.

From the trig identity sin² t +  cos² t = 1

we can also write as:

sin t + cos t:

Now,

sin² t + cos² t = 1

sin² t   = 1 -  cos² t

sin t = ±√( 1 -  cos² t)

As noted above,

sin t is positive for t in the Quadrant IV, and so we have

sin t = √( 1 -  cos² t)

We know that

[tex]\cos t=\frac{1}{\sec t}[/tex]

So, the equation will be

[tex]\sin t=\sqrt{1-\frac{1}{\sec ^2 t}}[/tex]

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The scale of the drawing is 36 inches.

So, it is given that the house's driveway is 3 inches wide in the drawing and the actual driveway is 15 feet wide.

Therefore, the scale of the drawing is 36 inches.

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The correct question is given below:
Albert measured a house and its lot and made a scale drawing. The house's driveway is 3 inches wide in the drawing. The actual driveway is 15 feet wide. What is the scale of the drawing? 1 inch: feet

Answer:

x [tex]\geq[/tex] -40.6

Step-by-step explanation:

9/5x + 23 [tex]\geq[/tex] -50 (subtract 23 over to other side)

9/5x [tex]\geq[/tex] -73 (multiply by 5)

9x [tex]\geq[/tex] -365 (divide by 9)

x [tex]\geq[/tex] -40.6

Answer:

A.  {-4, 2, 3, 8}

Step-by-step explanation:

The range of a function is the set of all possible output values (y-values).

From inspection of the graph, the coordinates of the points are:

Therefore, the set of y-values is {-4, 2, 3, 8}.  This is the range of the graphed function.

Answer:

(-3/2 ; -3/2)

Step-by-step explanation:

Midpoint (x;y)

x = (x1+x2)÷2 = (-5+2)÷2 = -3/2

y = (y1+y2)÷2 = (-7+4)÷2 = -3/2

Therefore midpoint = (-3/2 ; -3/2)

Answer:

7 (x + 1)

Hope this helps :)

Step-by-step explanation:

The equation above shows the statement, "Seven times the sum of a number and 1."