The formula A=23.1 e^{0.0152t} models the population of a US state, A, in millions, t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was ? million.

The percentage of her students that ride the school bus every morning would be = 84%

A percentage expression is an representation of a data set to a fraction of 100.

The total number of students = 25 students

The number of students that ride the school bus = 21

To calculate the percentage of the students that ride the bus the following is done;

= 21/25 × 100

= 2100/25

= 84%

Therefore, the percentage of her students that ride the school bus every morning is 84%

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Answer:

24 inches

Step-by-step explanation:

To find the longest possible length of the shorter pieces that Terri can saw, you need to find the greatest common factor (GCF) of the three original lengths: 30 inches, 48 inches, and 72 inches.

The GCF of 30, 48, and 72 can be found by finding the prime factorization of each number and taking the lowest exponent for each prime factor.

30 = 2 * 3 * 5

48 = 2^4 * 3

72 = 2^3 * 3^2

The GCF is 2^3 * 3 * 5, or 24 inches. Therefore, the longest possible length of the shorter pieces that Terri can saw is 24 inches.

Hello,

I hope you and your family are doing well!

To find the GCF is to use the Euclidean algorithm, which involves repeatedly dividing the larger of the two numbers by the smaller one until the remainder is 0. This can be a quicker method for finding the GCF of larger numbers.

For example:

72 / 30 = 2 with a remainder of 12

30 / 12 = 2 with a remainder of 6

12 / 6 = 2 with a remainder of 0

The last non-zero remainder is 6, so the GCF is 6.

Regardless of the method used, the GCF of 30, 48, and 72 is 6, so the longest possible length of the shorter pieces that Terri can saw is 6 inches.

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Answer:

:))

Step-by-step explanation:

The maximum value is 22 as the last small line (end of the "whisker") is marked at 22. Hope this helps!! Pls mark as brainliest and lots of points, help ya girl out!!!

Answer:

see explanation

Step-by-step explanation:

from the table we can obtain that

f(x ) = 6x³ + 8x - 12 ( 6  0  8  - 12 , being the coefficients of the polynomial )

f(x) is divided by (x + 7) , since evaluated at - 7

the quotient is

6x² - 42x + 302 ( 6  - 42  302, are the coefficients of the quotient )

with remainder - 2126

The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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The absolute value function that is represented in the graph is f(x) = |x + 1.5| So the correct option is D.

The general absolute value function is:f(x) = |x|This absolute value function has a vertex at the point (0, 0). We know that the graphed function has a vertex at the point (-1.5, 0).

So basically we had a horizontal translation of -1.5 units or 1.5 units to the left. That is written as: g(x) = f(x + 1.5)

Replacing the absolute value function we get:g(x) = |x + 1.5|

Then the correct option is D.

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The coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).

What are the coordinates of the vertices of the triangle?

The coordinates of the vertices of a triangle are (x1,y1), (x2,y2), and (x3,y3). The line joining the first two is divided in the ratio l:k and the line joining this point of division to the opposite angular point is then divided in the ratio m:k+l.

To find the coordinates of the other vertices of the triangle, you can use the fact that the midpoint of a line segment is located at the average of the coordinates of the endpoints of the segment.

If the midpoint of one side of the triangle is located at (a, 0), then the coordinates of the two endpoints of this side must be (a, 0) and (2a, 0). The coordinates of one of the vertices is (2a, 0), and since this vertex is not the one located at the origin, the coordinates of the other vertex must be the origin, or (0, 0).

If the midpoint of another side of the triangle is located at (2a, b), then the coordinates of the two endpoints of this side must be (2a, b) and (2a, 0). One of the endpoints is (2a, 0), which we already know is a vertex of the triangle. The other endpoint, (2a, b), is also a vertex of the triangle.

Finally, if the midpoint of the third side of the triangle is located at (a, b), then the coordinates of the two endpoints of this side must be (a, b) and (0, 0). One of the endpoints is (0, 0), which we already know is a vertex of the triangle. The other endpoint, (a, b), is also a vertex of the triangle.

Hence, the coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).

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The number of the digits after the decimal point is 7. The correct option is C.

A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.

Given that the numbers are 0.3568 and 0.042. The multiplication of the two numbers will be done as,

P = 0.3568 x 0.042

P = 0.0149856

The number of the digits after the decimal is 7.

Therefore, the number of the digits after the decimal point is 7. The correct option is C.

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Answer:

No real solutions.

Step-by-step explanation:

No real solutions.

Length of the rectangle is 25 and width of the rectangle is 14.

What do you mean by algebraic expression?

A combination of terms through addition, subtraction, multiplication, division, and other operations is known as an algebraic expression (or variable expression). An algebraic expression is composed of various parts.

Any algebraic expression's variables, constants, terms, and coefficients.

A variable is a symbol that doesn't have a set value. Any value may be used.

It is given that the length of a rectangle is 3 less than twice the width and the perimeter of the rectangle is 78 inches.

Let the width of the rectangle be x

Length of the rectangle become  2x - 3

Perimeter of rectangle = 2(length + width)

78 = 2(2x - 3 + x)

78 = 2(3x - 3)

78 = 6x - 6

78 + 6 = 6x

84 = 6x

x = 84/6

x = 14

length of the rectanle is 2x - 3 = 2(14) - 3 = 28 - 3 = 25

Width of the rectangle is x = 14

Therefore, length of the rectangle is 25 and width of the rectangle is 14.

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does it want the answer in a specific form?

slope intercept form; y = mx + b

slope = 2

b = -1

plug the values in

y = 2x -1 or y = 2/1x -1

Answer:

55

Step-by-step explanation:

Because you would minus 180-125 to get angle 1 and they said that angle 2 is parallel so they would be the same anwser so the answer is 55.

There are 3 tens in 7x30 or 30x7.

What is an equation?

A mathematical statement is referred to as an equation when two expressions are connected by the equal sign. A mathematical equation serves as the connection between two expressions on each side of the sign. Usually, there is only one variable and an equal sign.

Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.

An equation is created by joining two expressions with an equal sign. The solution to an equation is a number that may be used as the variable to generate a true number statement.

Here, we have

7x30 = 7 x 10 x 10 x 10

The value of 7x30 = 210

Hence, there are 3 tens in 7x30 or 30x7.

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Answer:

The last option is the correct answer.

Step-by-step explanation:

Eddie and Brad together shovel the snow in 1 hour 26 minutes.

Two or more expressions with an Equal sign is called as Equation.

Given that it takes Eddie 2 hours to shovel the snow from a driveway and sidewalk.

Brad can shovel the snow from the same driveway and sidewalk in 5 hours.

We now find how long would it take them working together to shovel the snow.

Eddie does 1/2 in 1 hour or x/2 in x hours

Brad does 1/5 in 1 hour or x/5 in x hours

the sum is 1 full job

(x/2)+(x/5)=1

multiply both sides by 10

7x=10

x=(10/7) hours or 600/7 minutes =86 minutes

As we know 1 hour has 60 minutes.

We can write 86 minutes as 1 hour and 26 minutes.

Hence, 1 hour 26 minutes is the time taken by Eddie and Brad to shovel the snow.

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The circumference of the circle will be 56.52 m.

And, The area of a circle will be 254.34 m².

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The radius of circle = 9 m

Now,

Since, The area of circle = πr²

Hence, The area of circle = 3.14 × 9²

                                        = 3.14 × 81

                                        = 254.34 m²

And, The circumference of the circle = 2πr

                                                         = 2 × 3.14 × 9

                                                         = 56.52 m

Thus, The circumference of the circle will be 56.52 m.

And, The area of a circle will be 254.34 m².

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The lakefront company should make the investment as in 5 years they'll have a profit of 10000.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, the lakefront company is considering investing in a new dock that will cost 560,000.

So, a Capital cost of 10% is (560000/10) = 56000

The company's borrowing rate is 8%.

∴ SI = (560000×8×5)/100.

SI = 5600×8×5.

SI = 224000.

So, The total cost is (560000 + 56000 + 224000) = 840000.

After 5 years they can sell it for 300000.

And has a cash flow of 110000, so in 5 years it is 550000.

So, total earnings is (300000 + 550000) = 850000.

Total profit is (850000 - 840000) = 10000 so it is profitable.

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Assuming that the tips are approximately normally distributed, an interval to estimate the true average tip (as a percent of the bill) with 90% confidence is (10.47, 11.73).

Assuming that the tips are approximately normally distributed, we would determine both the lower limit and upper limit for the confidence interval where 90% of the sample means occur as follows;

Lower limit = μ - σ/√x

Lower limit = 11.1 - 2.8/√20

Lower limit = 11.1 - 0.63

Lower limit = 10.47

For the upper limit, we have:

Upper limit = μ - σ/√x

Upper limit = 11.1 + 2.8/√20

Upper limit = 11.1 + 0.63

Upper limit = 11.73

For 90% of the sample means to occur, the confidence interval is as follows;

Confidence interval = (10.47, 11.73)

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The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by N - 1

Population variance is a measure of dispersion that determines how far each data point is from the population mean.

On the population, the population variance is calculated. When the number of observations grows, a few data points are chosen to represent the entire population.

The variance calculated on these specific data points is referred to as the sample variance. The population variance can be estimated using the sample variance.

When the population variance is unknown , we estimate the population variance by using sample variance

The formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it by N-1

Formula of sample variance  = [tex]s^2 = \frac{\sum f_i(x_i - \bar{x})}{N-1}[/tex]

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Answer:

[tex]\triangle CRQ \cong \triangle CSU[/tex] by SAS

Step-by-step explanation:

[tex]\angle QCR \cong \angle SCU[/tex] because of vertical angles.

Therefore , the inverse function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .

In mathematics, a function from a set X to a set Y assigns each item in X exactly one element in the other set. The sets X and Y represent the function's domain and codomain, respectively.

Here,

Given :

function :8-9x/5-4x

To find the inverse ,

Inverse of 8-9x. 8-5x 5 4x -4x+9

Steps Function Inverse definition A function g is the inverse of function F if for y=√(x), x=g(v)

y= 8-9x 5-4x

Replace x with y

x = 8-9y/ 5-4y

Solve for y,

x = 8-97/ 5-4y

=>8-5x /-4x+9

Therefore , the inverse  function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .

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The correct option is All real values of a.

What is the real number?

The positive and negative integers, as well as the fractions created from them (also known as rational numbers), as well as the irrational numbers, are all real numbers.

We have,

3x² + 2xy = 4    ...................(1)

x + y = a             ...................(2)

By converting the second equation equals to y:

y = a - x             .....................(3)

By substituting the (3)rd equation into (1), we get

3x² + 2xy = 4

3x² + 2x(a - x) = 4

3x² + 2ax - 2x² = 4

x² + 2ax = 4

x² + 2ax - 4 = 0

Discriminant  = 4a² + 16 >=  0

2 distinct solutions & is ok for all a.

hence, the correct option is All real values of a.

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y = -2/5 x -11/5 is the equation of line with slope -2/5 that passes through the point (2, -3).

The slope of the line is the rise to run ratio, or the rise divided by the run. It expresses the slope of a line in the coordinate plane.

The standard form of an equation is y = mx+c.

Here given,

A line with a slope of -2/5 that passes through the point (2, -3).

Simplify y = mx+c with m=2/5 and (x, y)=(2, -3). That is to say,

-3 = -2/5 (2)+c

⇒ -3 = -4/5 +c

⇒ c = -3 + 4/5

⇒ c = (-15 + 4) / 5

=> c = -11/5

When m = -2/5  and c = -11 /5 are substituted in y = mx+c, we get

y = -2/5 x -11/5

As a result, an equation for a line with a slope of -2/5 that passes through the point (2,-3) is y = -2/5 x -11/5.

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Answer:

  C.  2x+ 5y = −11

Step-by-step explanation:

You want the equation of the line with slope -2/5 through point (2, -3).

The equation of a line with slope m through point (h, k) can be written as ...

  y -k = m(x -h)

Then the equation of the line with slope -2/5 through point (2, -3) will be ...

  y +3 = -2/5(x -2)

We can put this in standard form by ...

  5(y +3) = -2(x -2) . . . . . multiply by 5

  5y +15 = -2x +4 . . . . . . eliminate parentheses

  2x +5y = -11 . . . . . . . . . add 2x-15 to both sides

The desired equation is 2x +5y = -11.

Answer:

5 weeks

Step-by-step explanation:

20 inches  /  ( 4 inches/week ) = 5 weeks

Answer:

(a) Equation of parallel line is y = x + 4

(b) Equation of perpendicular line is y = - x + 8

Step-by-step explanation:

Given line is

x - y = 4

Rewrite this as

x - 4 = y

or

y = x - 4

This is the equation of a line in slope intercept form which is generally

y = mx + b

where m is the slope and b the y-intercept

Here m = 1, b = -4

(a) A parallel line will have the same slope but a different y-intercept
So for starters we can write the equation of the parallel line as
y = x + b

Since this passes through (2,6) sub 2 for x and 6 for y to get

6 = 2 + b

==> b = 4

Equation of the line is
y = x + 4

(b) A perpendicular line will have as slope -1/m where m is the slope of the original line

Here m = 1, so -1/m = -1/1 = -1

Equation will be of the form
y = -x + b

Since this also passes through (2,6)
6 = -2 + b

==> b = 6 + 2 = 8

Equation of perpendicular line is
y = -x + 8

Answer: 2. 37.8%

3. 30% decrease

Step-by-step explanation:

Increase = New Number - Original Number

Then:  divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

36.99-22.99=14

100(14/36.99)

37.8%

First: work out the difference (decrease) between the two numbers you are comparing.

Decrease = Original Number - New Number

Then: divide the decrease by the original number and multiply the answer by 100.

% Decrease = Decrease ÷ Original Number × 100

2.50-1.75=0.75

100(0.75/2.5)

30%

The required length of the longest side will be 28/5 cm in the triangle.

The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.

We have been given that the three sides of a triangle are in the ratio of 3:5:7

Let's assume the sides are 3x, 5x, 7x

Since the perimeter of the triangle is 12 cm.

So, 3x+5x+7x = 12

Apply the addition operation,

15x = 12

x = 12/15

Reduce the above fraction to the simplest form

x = 4/5

So, longest side = 7x = 28/5 cm

Thus, the required length of the longest side will be 28/5 cm in the triangle.

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Answer:

  2184

Step-by-step explanation:

You want to know the possible number of ways 3 flavors can be chosen from 14 when order matters.

The number of permutations of 14 flavors taken 3 at a time is ...

  14 × 13 × 12 = 2184

There are 14 ways to choose the bottom flavor, then 13 ways to choose a different middle flavor, and finally 12 ways to choose a different top flavor. Each flavor can go with any combination of the others, so the total number is the product of 14·13·12, or 2184.

The formula for the number of n things taken k at a time is ...

  P(n, k) + n!/(n-k)!

For n=14, k=3, this is the product shown above.