Solve the following inequality, 6 < 3r-45 < 36 Which graph shows the correct solution?

The population of the small city in the year 2020 using the given growth rate is; 51600 people

We are given that;

Population of the small city in the year 2010 = 36000

Population in the year 2015 = 43800

Now, we are told that the growth rate occurs at the same rate per year. Thus;

Population change from 2010 to 2015 = 43800 - 36000 = 7800

Thus, the population increases by 7800/5 = 1560 people each year.

General form of exponential function is; y = bˣ

where b is rate of growth while x is number of years

But here we will use sequence to get;

y(10) = 1560 * 10 = 15600

Thus;

Population in 2020 = 36000 + 15600 = 51600 people

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Answer:

so? what is your question here?

Step-by-step explanation:

Input data

Point = (1, 2)

m = 2/3

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

The equation of the line that passes through the point (1,2) with a slope of 2/3

The given information is:

Andrea is 108 miles away from Destiny.

Destiny travels 9 mph faster than Andrea.

They meet after 4 hours.

Let's convert that information into equations:

Let's call x the distance that Destiny travels to find Andrea and y the distance Andrea travels to find Destiny, then:

If they meet after 4 hours, the equation for the distance Destiny traveled is:

But the problem also says that Destiny travels 9 mph faster than Andrea, then let's call z the mph that Andrea is traveling, thus:

And the equation for the distance Andrea traveled is:

Then you have a system of 3 equations and 3 variables.

Let's solve it to find how fast each was traveling.

From equation 3 you know that y=4z. You can replace the y-value into equation 1, you will obtain:

Next, you can solve for x in terms of z, from equation 4:

Replace the x-value into equation 2 and solve for z:

Then if z=18 mph, this is how fast Andrea is traveling.

And Destiny travels 9 mph faster than Andrea, then Destiny travels at (z+9)=18+9=27 mph

The cost of the sheet metal per square foot is $30.

The first step is to determine the square feet that the contractor used. This can be determined by subtracting the square feet of sheet she bought from the sheet metal she has used so far.

Sheet metal used = 8.2 - 2.1 = 6.1 square feet.

This means that 6.1 square feet costs $183.

The second step is to determine the cost of one square feet of sheet metal. This can be determined by dividing $183 by 6.1

$183 / 6.1 = $30

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Answer:the real answer is (-2,1), (-1,4), (1,2)

Step-by-step explanation:

pls mark brainliest

80.64% probability that a component is at least 10 centimeters long.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean  and standard deviation , the z-score of a measure X is given by:

Z = x - μ / σ

Z-scores are used to measure how far a measure is from the mean. We find the p-value associated with this Z-score by looking at the z-score table after finding the Z-score. The p-value represents the probability that the measure is smaller than X, which is the percentile of X. The probability of the measure being greater than X is calculated by subtracting 1 from the pvalue.

μ = 14

Variance is 9.

The standard deviation is the square root of the variance.

So,

σ = √9 = 3

This is the pvalue of Z when X = 10

z = 10 - 14/3

z = -1.3

z = -1.3 has a p value of0.1936

1-0.1936 = 0.8064

80.64% probability that a component is at least 10 centimeters long.

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Answer:

0.7475

Step-by-step explanation:

The mean is μ=14, and the standard deviation is σ=9‾√=3.Open Excel.  Click on an empty cell.  Type =NORMDIST(12,14,3,1) and press ENTER.The probability, rounded to four decimal places, is P(X<12)≈0.2525.The desired probability is P(X≥12), so subtract from 1 to get P(X≥12)=1−0.2525=0.7475

Answer:

Shorter leg = 2.5 ft

Longer leg = 6.5 ft

Step-by-step explanation:

          Let the shorter leg = x ft

                       Longer leg =  (x + 4) ft

                     Hypotenuse = 7 ft

                   [tex]\sf x^2 + (x +4)^2 = 7^2[/tex]

     x² + x² + 2*x*4 + 4²   = 49

        x² + x²+ 8x + 16      = 49

         2x² + 8x + 16 - 49 = 0

           2x² + 8x - 33       = 0  

This is a quadratic equation. We can use the below mentioned formula to find the value of x.

a = 2 ; b = 8 ; c = -33

b² - 4ac = 8² - 4 * 2 * (-33)

             = 64 + 264

             =328

[tex]\sf x = \dfrac{-b \± \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\sf x = \dfrac{-8 \±\sqrt{328}}{2*2}\\\\\\x= \dfrac{-8 \±18.11}{4}\\\\\\x =\dfrac{-8+18.11}{4} ; \ x=\dfrac{-8-18.11}{4} > > \text{this is rejected because sides of } \\\\ \text{a triangle cannot be measured in negative value}[/tex]

[tex]\sf x = \dfrac{-8+18.11}{4}[/tex]

[tex]\sf x = \dfrac{10.11}{4}\\\\x =2.5275[/tex]

x+ 4 = 2.5275 + 4 = 6.5275

Shorter leg = 2.5 ft

Longer leg = 6.5 ft

Answer: the length of the shoter leg is 2,5 feet

               the length of the longer leg is 6.5 feet

Step-by-step explanation:

Let the length of the shoter leg is x feet

Than the length of the longer leg is (x+4) feet

We use Pythagoras' theorem:

[tex]\displaystyle\\x^2+(x+4)^2=7^2\\\\x^2+x^2+2(x)(4)+4^2=7(7)\\\\2x^2+8x+4(4)=49\\\\2x^2+8x+16-49=49-49\\\\2x^2+8x-33=0\\\\D=b^2-4ac\\\\Hence,\\\\D=8^2-4(2)(-33)\\\\D=8(8)+8(33)\\\\D=64+264\\\\D=328\\\\\sqrt{D}=\sqrt{328} \\\\x=\frac{-bб\sqrt{D} }{2(a)} \\\\x=\frac{-8б\sqrt{328} }{2(2)} \\\\x=-6.5277\notin (x > 0)\\\\x=2.5277\ feet\\\\x+4=2.5277+4\\\\x+4=6.5277\ feet[/tex]

Given:

The total = 846.

The number of hot dogs sold at Tuesday night = 150.

Required:

We need to find the approximate probability of a person buying a hot dog and going to a Tuesday night game.

Explanation:

The total possible outcomes = 846.

Let A be the given event.

The favourable outcomes = The number of hot dogs sold at Tuesday night = 150.

The approximate probability of a person buying a hot dog and going to a Tuesday night game.

Final answer:

Answer: -42g-29

Step-by-step explanation:

-6(8g+4)    -5+6g

-48g-24 -5+6g

-48g+6g=-42g

-24-5=-29

Considering the linear equation in slope-intercept form:

The y-intercept of the line is the constant of the equation, in this case, the y-intercept is -1.

The slope of the line corresponds to the coefficient of the x-term, i.e. the value that multiplies x. For this line, the slope is equal to 11.2

Explanation

Step 1

to find the answer just replace the values for x and y

for x=3 and y =4

I hope this helps you

Answer

The equation of the line is

y = (-x/7)

We can cross multiply and write it in the form of

7y = -x

OR

x + 7y = 0

Explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

The relationship between the slopes of two lines that are perpendicular to each other is

m₁m₂ = -1

m₁ = Slope of line 1

m₂ = Slope of line 2

For the given equation, if we compare its equation with y = mx + b,

y = 7x - 3

y = mx + b

m = 7, b = -3

We can now find the slope of the line we want.

m₁m₂ = -1

m₁ = 7

m₂ = ?

m₁m₂ = -1

(7)m₂ = -1

7m₂ = -1

Divide both sides by 7

(7m₂/7) = (-1/7)

m₂ = (-1/7)

Then we can find the equation of the line we want.

For that line,

m = slope = (-1/7)

b = y-intercept (where the line crosses the y-axis) = 0

This is obtained from the point given that the line passes through the origin, (0, 0)

So, we can write y = mx + b

y = (-1/7)x + 0

y = (-x/7)

We can cross multiply and write it in the form of

7y = -x

OR

x + 7y = 0

Hope this Helps!!!

Let's begin by listing out the information given to us:

Expanded notation is a form of writing in which the value of each digit; it arranges the digit in their values of tens, hundreds, tens etc.

Hence, option B is the correct answer

Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]

Answer:

The answer is B.

Step-by-step explanation:

The circle is filled in so we know the answer cannot be A. All the numbers after 4 are greater than or equal to 4. The arrowing is pointing toward the numbers after 4.

The expression that could represent how much flour Lena uses for baking cookies and bread is 2c + 2 1/2b + 1/2.

What is an algebraic expression?

An algebraic expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

For example 2x + 4, 58m + 2n, 100p + 3q + r.

According to the given question:

(Question with options is attached below)

Let c be the number of cookie batches and b be the number of bread loaves Lena makes.

Lena makes 2 cups of flour for a batch of cookies

∴ Flour used to make cookie batches = 2c

She uses 2 1/2 cups for loaf of bread

∴ Flour used for bread loaves = 2 1/2 b

Ans 1/2 cup flour is used for dusting workbench

Hence expression for the amount of flour used is sum of flour used for making batches of cookies, bread loaves and for dusting.

The expression is 2c + 2 1/2b + 1/2

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The average force that the table applies to the cat is 40N, by using newton's law.

What is the meaning of acceleration?

Acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting.

Given that the mass of the cat is 4 kg. The gravity is 10 meters per second-squared.

Force is the product mass and acceleration.

Mass = 4 kg

Acceleration = 10 ms⁻².

The force that  the table applies to the cat  is (4 kg × 10 ms⁻²) = 40 N.

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The smallest value of x is 2 for which these three numbers 2, 60, and 240 have an LCM of 240.

LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.

Given, Are three numbers x, 60, and 240 of which x is unknown.

The lowest common multiple of these three numbers will be when x is the smallest.

Let x be 2 therefore the numbers are now, 2, 60, and 240.

And LCM of 2, 60, and 240 is 240 as it is the smallest number that is divisible by all these three numbers.

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A system of equations is simply a collection of equations that can be dependent, independent, consistent, or inconsistent.

2x + y = 8x - 2y = -6 is x,y = 2,4

Given equation,

2x + y = 8x - 2y = -6

x,y = 2,4

[1]    2x + y = 8

[2]    x - 2y = -6

Solve [2] for the variable  x

[2]    x = 2y - 6

Plug this in for variable  x  in [1]

[1]    2•(2y-6) + y = 8

[1]    5y = 20

Solve [1] for the variable  y

[1]    5y = 20

[1]    y = 4

By now we know this much

x = 2y-6

y = 4

Use the  y  value to solve for  x

x = 2(4) -6 = 2

Hence, {x,y} = {2,4}

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Statement Reason

WXYZ is a parallelogram Given

WX || ZY and WZ || XY Definition of a parallelogram

∠ZYW ≅ ∠XWY Alternate interior angles

WX ≅ YZ Definition of a parallelogram

WY ≅ WY Reflexive property of congruence

ΔWXY ≅ ΔZYW SAS

∠X ≅ ∠Z CPCTC

ANSWER

Options: II and IV

EXPLANATION

Mean: Is the sum of data values divided by the total number of data values

Deviation: Is the difference between an individual data item and the set's mean.

Absolute value: Is the distance (a positive quantity) between any two points on a number line.

Variability: This relates to how dispersed (or clustered) the values in a data set are. High variability indicates that the data is dispersed. Low variability indicates that the data is grouped together (close together).

MAD: Is the average distance between each data value and the mean is the Mean Absolute Deviation (MAD) of a set of data. The higher the MAD, the more data variability there is (the data is more spread out).

Hence, II and IV are most likely to have the greatest number of values in common because they both have higher MAD (8) meaning that they have more data variability (their data is more spread out) compared to I and III which have MADs equal 4 and 2 respectively.

The depth of the diver after 4 minutes when a scuba diver descends below the surface of a lake at a rate of 12 feet per minute is 48 feet.

The concept that is used in the solution is the concept of rate in mathematics. A rate can be described as a special ratio having two terms that are in different units.

The rate that is been given is 12 feet per minute which implies that 12 feet will operate at the time of 1 minute. Then we were now given the depth of the diver after 4 minutes, using the given rate, then ;

12feet = 1mins

X feet = 4mins

where X is the depth of the diver after 4 minutes then we can cross multiply,

X= (4mins *12feet) / 1mins

= 48feets.

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a) Given the triangle ABC, you have to do a counterclockwise 90º rotation of the figure.

To make said rotation you have to invert the coordinates of each point of the figure and invert the sign of the x-coordinate of the image point.

In general:

Preimage point; Image point

P(x,y) → P'(-y,x)

The y-coordinate turns into the x-coordinate and the x-coordinate turns into the y-coordinate.

The x-coordinate of the image point must have the opposite sing as the original one.

So for triangle ABC:

A to A'

(3,-2) → (-(-2),3)= (2,3)

B to B'

(3,-6) → (-(-6),3)= (6,3)

C to C'

(9,-2) → (-(-2),9)= (2,9)

The coordinates for the 90º counterclockwise rotation are A'(2,3), B'(6,3) and C(2,9)

b) Triange A'B'C' was translated a certain number of units, its new position is given as triangle A''B''C'':

A''(-3,-4)

B''(1,-4)

C''(-3,2)

To determine what kind of translation was done, first step is to draw triangle A''B''C'' and compare it to triangle A'B'C':

As you can see in the graphic, triangle A'B'C' was translated horizontally to the left a k number of units and vertically downwards a m number of units.

Horizontal translation

These translations are made over the x-axis, the translation factor k is added (movement to the rigth) or subtracted (movement to the left) from the x-coordinate of each point:

In this case the translation was made to the left, so:

Preimage point; Image point

P(x,y) → P'(x-k,y)

Vertical translation

These translations are made over the y-axis, this means that the translation factor m will be added (↑up) or subtracted (↓down) from the y-coordinates of each point.

For the example, the movement was downwards so we can express it as:

Preimage point; Image point

P(x,y) → P'(x,y-m)

You can unite both movements in the same expression as:

Preimage point; Image point

P(x,y) → P'(x-k,y-m)

Going a little further you can determine the amount of units the figure was translated by comparing a set of points from the preimage and image:

Given A'(2,3) and A''(-3,-4)

For the horizontal movement compare the x-coordinates. We know that to determine the x-coordinate of A'', k units were subtacted from the x-coordinate of A', so:

2-k=-3

-k=-3-2

-k=-5

k=5

For the vertical movement, compare the y-coordinates of both point. We know that m units were subtracted from the y-coordinate of A' to determine the y-coordinate of A'', so:

3-m=-4

-m=-4-3

-m=-7

m=7

This means that the translation rule for A'B'C' → A''B''C'' is (x-5,y-7)

Answer the answer is 12 units:

Step-by-step explanation:

Answer: smallest area- 56.25cm2      largest area- 70.56cm2

Given:

1. Arrange the expression, with the variables are written first

2. Distribute the "minus" operation

3. Expand by multiplying the first two expressions

*multiply the first terms

*multiply the outer terms

*multiply the inner terms

*multiply the last terms

This will give us:

*combine like terms

*Remove the parenthesis

4. Combine like terms

The final answer would be:

Given that:

and we are given that:

we can say that:

adjacent = 7, hypothenus = 8

And we can apply the Pythagorean theorem which is:

Thus, we have that: