In 1965, the population of a certain town was 2010. In 1995, the population was 3620. If the population during this time period grew according to an exponential model, what will the population be in 2050?

By just expanding the products, we can see that the expression can be written as:

(x - 1)*(x + 2)*(x + 3) = x³ + 4x² + x - 6

Here we want to expand the expression:

(x - 1)*(x + 2)*(x + 3)

We can start to expand the first two parts, writing:

(x - 1)*(x + 2)*(x + 3) = [(x - 1)*(x + 2)]*(x + 3)

[x² + (-1)*x + x*2 + (-1)*2]*(x + 3)

[x² - x + 2x - 2]*(x + 3)

[x² + x - 2]*(x + 3)

Now we can finish the expansion:

[x² + x - 2]*(x + 3) = (x²)*x + (x²)*3 + x*x + x*3 + (-2)*x + (-2)*3

= x³ + 3x² + x² + 3x - 2x - 6

= x³ + 4x² + x - 6

That is the polynomial written in standard form.

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The range of the set of data is 11 and the standard deviation of the set of data is 4.06

What is Standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

Given, set of data.

11, 10, 5, 13, 16

First of all we will arrange them

5, 10, 11, 13, 16

To find the range we have to;

Range = Biggest number - smallest number

           = 16 - 5

Range = 11

Thus, the range of the given set of data is 11

Now, for standard deviation,

By first squaring the discrepancies between the observations and the mean, and then taking the square root of the sum of the squares of the differences divided by the number of observations minus 1, the standard deviation is computed.

Mean = Sum of Observations/Total Observations

Mean = (5 + 10 + 11 + 13 + 16)/5

         = 55/5

         = 11.

Square of the mean = 11² = 121

Now subtracting the mean from each observation and squaring it gives:

(5 - 11)² = (-6)² = 36

(10 - 11)² = (-1)² = 1

(11 - 11)² = (0)² = 0

(13 - 11)² = (2)² = 4

(16 - 11)² = (5)² = 25

Sum of squares = 36 + 1 + 0 + 4 + 25
                          = 66
variance = 66 / n-1

              = 66 / (5 - 1)

              = 66 / 4

              = 16.5

Standard deviation = √variance

                                = √16.5

                                = 4.06

Thus, the Standard deviation of the set is 4.06

Hence, The range and standard deviation of the set of data is 11 and 4.06 respectively

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The profit that the upcoming business would be making after 10 years is  $122 million.

The profit of the business in 10 years can be modelled with an exponential equation. This is because the rate of growth of profit each year would be 10% of the last year's profit.

The equation that is used to determine the profit in 10 years is:

FV = P (1 + r)^n

Where:

FV = 100 x (1 + 0.02)^10

FV = $100 million x (1.02^10) = $122 million

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The y-intercept (0, 120), and the point (55, 17), on the graph of the exponential function of the population of mammals with the population decreasing at 3.5% per year indicates;

A. The y-intercept represents the number of mammals when they were originally counted was 120

B. The line y = 0 is an asymptote of the graph

D. The y-intercept is 120

F. The asymptote indicates that as years pass, the number of mammals will approach 0

An asymptote is a line on a graph that the curve of a graph approaches as the values of the graph increases to infinity.

The points on the graph of the exponential function are;

(0, 120) and (55, 17)

The rate at which the population is decreasing = -3.5%

The output of the graph, y = The number of mammals x years after counting

The key features of the exponential function are;

The y-intercept of the graph is the point x = 0, which corresponds to year 0, or the time when the mammals were originally counted and the y-value at the y-intercept represents the number of mammals when they were counted originally, therefore option A is correct

The coordinates of the y-intercept is (0, 120)

The y-intercept is therefore the point y = 120

Therefore, option D is correct

The general form of the growth exponential function is presented as follows;

f(x) = a·bˣ + k

r = b - 1

b = 1 + r

Therefore;

b = 1 - 0.035 = 0.965

a = The first term = 120

Plugging in the known values from the graph, we get;

f(0) = 120 = a + k

120 = 120 + k

k = 120 - 120 = 0

k = 0 = The asymptote

Therefore, an asymptote is the line y = 0 option B is therefore correct

The  number of mammals approach the asymptote, y = 0 as the number of mammals approach infinity

Therefore as the years pass the number of mammals will approach 0, option F is correct

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Answer:

Step-by-step explanation:

157m is the answer.

Answer:

Step-by-step explanation:

It has to be $3.00 because It says Mrs. West bought 3 dozen of cookies and she has $6.00 and the cookies had to be 1$ each so the answer should be $3.00 ( sorry if I'm wrong)

Check the picture below.

Answer:

Step-by-step explanation:

Angles 4 and 5 are congruent and are on the inner side of lines r and s, and opposite side from line l.

If two angles are on the inner sides of two lines and opposite sides of the line intersecting the two lines are equal, then these angles are alternate interior angles.

The two lines are parallel and the intersecting line is the transversal.

Lines r and s are parallel and line l is transversal.

The linear equation that could be used to find the price of a tire patch is of:

The slope-intercept representation of a linear equation is shown by the rule presented as follows:

y = mx + b.

In the context of this problem, the meaning of the variables are given as follows:

The values of these intercept is given as follows:

b = 22.2.

Hence the function is:

y = -mx + 22.2.

He bought four tires, hence x = 4, and had y = 1.9, hence the cost of a tire is found as follows:

-4m + 22.2 = 1.9.

Hence the options are:

The problem is given by the image shown at the end of the answer.

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Answer:

1287.72 [tex]ft^{2}[/tex]

Step-by-step explanation:

Area of the rectangle is length times width

a = (35)(28) = 980

Area of a circle is [tex]\pi r^{2}[/tex], but this is half of a circle so we will divide the answer by 2

a = [tex]\frac{3.14(14^{2}) }{2}[/tex] = [tex]\frac{3.14 x 196}{2}[/tex] =[tex]\frac{615.44}{2}[/tex] = 307.72

Add the half circle and the rectangle

980 + 307.72 = 1287.72

Answer:

$0.45

Step-by-step explanation:

6 ÷ 20 = 0.3

Which means each candy bar costs $0.3.

9 ÷ 6 = 1.5

0.3 × 1.5 = 0.45

20 × 0.45 = 9

So he must charge $0.45 for each candy bar.

Answer: There is a difference of 1.88

Step-by-step explanation: Pls brainiest.

Answer:

1.88

Step-by-step explanation:

hopethishelpsya:)

Answer:

6

Step-by-step explanation:

3/4 ÷ 1/8

= 3/4 . 8

= 24/4

= 6

The simplification form of the expression (4/3)(3/7) is 4/7 after canceling 3 from the numerator and denominator.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The expression is:

= (4/3)(3/7)

= (4x3)/(3x7)

Cancel 3 from the numerator and denominator

= 4/7

Thus, the simplification form of the expression (4/3)(3/7) is 4/7 after canceling 3 from the numerator and denominator.

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The pieces of long bunting is 22.

From the question, we have

The room is 4m long and 3m wide.

perimeter of room = 2×(4+3)

=14 m = 1400 cm

she has lots of 70 cm lenghts of bunting.

1400 cm/70 cm = 20

she needs to use 50mm =5 cm of each piece of string for the knot.

20×5 = 100

100/70 ≈2

pieces of 70 cm long bunting = 20+2 =22

Divide:

Split is to divide into two or more equal sections, places, groupings, or divisions in its most basic form. To divide something simply means to provide it to a group in equal quantities or to cut it up into equal pieces. Let's imagine a diagonal divides a square into two triangles with equal areas. An integer may or may not be the result of a division operation. Sometimes the result will be expressed as decimal numbers.

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The probability that they two people are chosen and travel by different transport is 47/144

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Probability is given as sample space / total outcome

Probability to travel by car p(C)= 5/12

Probability to travel by bus P(B)= 4/12=1/3

Probability to travel by train P(T)= 3/12= 1/4

for two people chosen at random

P(C ×B)= 5/12×1/3= 5/36

P(B×T)= 1/3×1/4= 1/12

P(C×T)= 1/4×5/12= 5/48

Therefore the probability that the two chosen travel by different car is

P(C ×B)+P(B×T)+P(C×T)= 5/36+1/12+5/48

= 141/432

divide through by 3

= 47/144

Hence the get the required answer.

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The value of the expression which shows the amount he paid for lunch is 7 dollars.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and divisions.

Given that Frankie orders two hamburgers and a soda for lunch. A hamburger is $3 and a soda is $1.00.

Now here is the expression-

1+(2x3)= 2 x 3 = $6

Cost of lunch = ($3 / hamburger) (2) + ($1 / soda) (1)

Cost of lunch = $6 + $1

Cost of Frankie's  lunch = $7

Therefore, the value of the expression which shows the amount he paid for lunch is 7 dollars.

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Answer: ?????

Step-by-step explanation:

The true statements are:

The center of the circle lies on the x-axis

The radius of the circle is 3 units.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The standard equation of a circle is expressed as:

x²+y²+2gx+2fy+C=0

Centre is (-g, -f)

radius = √g²+f²-C

Given a circle whose equation is

x²+y²-2x-8=0

Get the centre of the circle

2gx = -2x

2g = -2

g = -1

Similarly, 2fy = 0

f = 0

Centre = (-(-1), 0) = (1, 0)

This shows that the center of the circle lies on the x-axis

r = radius = √g²+f²-C

radius = √1²+0²-(-8)

radius =√9 = 3 units

The radius of the circle is 3 units.

For the circle x² + y² = 9, the radius is expressed as:

r² = 9

r = 3 units

Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Hence we get the required answers.

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Any of the following information can be used to show that ΔFGH is congruent to ΔJKL by SAS.

The criteria for proving that two triangles are congruent to each other by the SAS congruence postulate are:

In the image given that shows triangle FGH and triangle JKL, we are given the following:

∠F ≅ ∠J and ∠H ≅ ∠L [two pairs of congruent angles]

No two congruent sides are marked in the triangles. Therefore, the additional information that may be needed to prove the triangles are congruent by SAS can be:

a. FH ≅ JL and FG ≅ JK

b. FH ≅ JL and HG ≅ LK

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Answer:

Step-by-step explanation:

Hi  Debbie,  the tricky part about these types of problem is recognizing that you know the total angle.   180°   for the ABCD question and the angles are equal to each other for the TUWXY   question , this tip lets   you find X for each.

just add the two angle and set equal to 180 in each problem.  I'll do the problems below, but , now that you know how, maybe you could try them and check your answer against mine.

The ABCD question

4x+7  +  2x -1 = 180

6x +6 = 180

6x = 174

x = 29

4(29)+7 = 123°

2(29)-1 = 57°

The TUWXY question

6x+13 = 10x-7

20 = 4x

5=x

then

6(5)+13 = 43°

and the next one should be the same

10(5) -7 =43°

check.   so there are your answers. :)  get it?

Considering the Central Limit Theorem, it is found that:

a)

b) The shape of the distribution is approximately normal.

The Central Limit Theorem defines the distribution of the sampling distribution of sample means with size n of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex].

For the sampling distribution of sample means, the mean and the standard deviation are given as follows:

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, the sample size is greater than 30, hence the shape of the distribution is guaranteed to be approximately normal.

The standard deviation is given as follows:

[tex]s = \frac{\sigma}{\sqrt{49}} = \frac{\sigma}{7}[/tex]

As for the mean, it is the same as the mean of the sample means, you have to calculate all the sample means and then divide by 20.

The problem is incomplete, hence the answer was given in general terms.

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Answer:

34

Step-by-step explanation:

When estimating the product of an integer and a decimal, first round the decimal to its nearest whole number.

Therefore,

So an estimate of the product is:

[tex]\implies 17 \times 1.68 \approx 17 \times 2[/tex]

Partition 17 into tens and units:

[tex]\implies17 \times 2= (10+7) \times 2[/tex]

Apply the distributive property of multiplication over addition:

[tex]\begin{aligned}\implies (10+7) \times 2&=(10 \times 2)+(7 \times 2)\\&=20+14\\&=34\end{aligned}[/tex]

Therefore:

[tex]\boxed{17 \times 1.68 \approx 34}[/tex]

Answer:

≈ 34

Step-by-step explanation:

The estimate value of 1.68,

→ 17 ≈ 17

→ 1.68 ≈ 2

Then the estimated product is,

→ 17 × 1.68

→ 17 × 2 = 34

Therefore, the product is 34.

Using an exponential decay equation, we will see that after 11 hours the element will decay to 299 grams.

We know that we have an element with a half-life T, and it has a decay equation that can be written as:

f(t) = A*e^(-t*ln(2)/T)

Where A is the initial amount of the element, and f(t) is the amount of the element t hours after.

In this case the given values are:

A = 500g

T = 15h

Then the exponential decay is:

f(t) = 500g*e^(-t*ln(2)/15h)

And we want to find the value of t such that f(t) = 299g, then we can solve:

299g =  500g*e^(-t*ln(2)/15h)

299/500 = e^(-t*ln(2)/15h)

If we apply the natural logarithm in both sides we get:

ln(299/500) = -t*ln(2)/15h

-ln(299/500)*15h/ln(2) = t

11 h = t

It will take 11 hours to go from 500 grams to 299 grams.

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39,916,800 ternary strings are there with exactly 3 zeros, 5 ones and 3 twos.

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.

Given that, A ternary string is an ordered string of characters which consists of digits (0,1, or 2). For example, the ternary string 2122010 consists of exactly 2 zeros, 2 ones and 3 twos

This is just the number of permutations of the set {0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2}. There are 11 elements in the set, so there are 11! = 39,916,880 possible ternary strings with exactly 3 zeros, 5 ones and 3 twos

Hence, 39,916,800 ternary strings are there with exactly 3 zeros, 5 ones and 3 twos.

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The transformation that is applied to the ΔABC to get the ΔA'B'C' is vertical translation by 6 units downwards.

The triangle has the vertices  A(-2, 3), B(2, 1), and C(1, 0)

They are transformed such that:

A(-2, 3)→A'(-2,-3)

B(2, 1)→B'(2,-5)

A(-1, 0)→A'(-2,-6)

Now if we carefully observe we can see that the y-coordinate of A' is 6 less than that of A.

Similarly for B and C the coordinates are 6 units less than that of the object, but the x-coordinate remains the same.

This proves that the graph follows a vertical transformation and since the new ordinates are 6 units smaller, so the graph is translated 6 units downwards.

A function, f, that maps to itself is known as a transformation, or f: X→X'. The pre-image X will change into the picture X' following the transformation. This transformation can use any operation, or a combination of operations, including translation, rotation, reflection, and dilation.

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Answer:   She practices 5 hours a day

Step-by-step explanation:  6 days a week x 4 weeks = 24 days

120 hours of practice / 24 days = 5 hours of practice a day

Answer:

5hrs

Step-by-step explanation:

120 ÷ 4 = 30. 30 ÷ 6 = 5. She practices for 5hrs a week.

The fourth coordinate of rectangular piece of material is (2.8 , -2.7)

According to the question,

Charles drew a plan for a rectangular piece of material that he will use for a blanket. Three of the vertices are (-1.4, -2.7), (-1.4,3.7), and (2.8,3.7).

As we know , the opposite sides of rectangle are equal

If we locate these coordinates in our graph and join them

Length of rectangle will be = 2.8+1.4 = 4.2cm

Breadth of rectangle will be = 3.7 + 2.7 = 6.4cm

So, the fourth coordinate should lie 6.4cm far from  (2.8,3.7)

Subtracting 6.4 from y-axis,

Fourth coordinate = 3.7 - 6.4

= -2.7

Therefore , The fourth side of rectangle = (2.8 , -2.7)

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Answer:

Step-by-step explanation:

Simply check for x-coordinate of - 8, we see only the first option has it, all the others have x = 0 or x = 8 which is impossible to have on the line x = - 8.

It is parallel to the y-axis and x = - 8 for any value of y.

Correct choice is A or 1.

Similar to above, we exclude all the options with a different value of y other than 8.

There are two possible options left:

Consider line x = 0, this is overlapping with the y-axis.

x ≥ 0 gives us the y-axis (because of equal sign) and all the points to the right from it.

This is matching the description of option E or 5.

Answer:

(a)  The line parallel to the y-axis that intersects the x-axis at (-8, 0).

(b)  The line parallel to the x-axis that intersects the y-axis at (0, 8).

(c)  The set of all points to the right of and on the y-axis.

Step-by-step explanation:

Part (a)

Given condition:  x = -8

The equation of a vertical line is x = a.  

This line is parallel to the y-axis (since it is vertical) and intersects the x-axis at (a, 0).

Therefore, the description that satisfies the given condition is:

Part (b)

Given condition: y = 8

The equation of a horizontal line is y = a.  

This line is parallel to the x-axis (since it is horizontal) and intersects the y-axis at (0, a).

Therefore, the description that satisfies the given condition is:

Part (c)

Given condition:  x ≥ 0

The "≥" symbol means greater than or equal to.

x is greater than zero for all points to the right of the y-axis.

x is equal to zero for all points on the y-axis.

Therefore, the description that satisfies the given condition is: