Solve the equation. (Round your answer to four decimal places.) e2x − ex − 12 = 0 x =

Answer:

300km

Step-by-step explanation:

if 1 hr=80

then take 80 and multiply it by 3.75

hope this helps!

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Answer:

300km

Step-by-step explanation:

The precise middle value of a data set when it is ordered is called the median.Consequently, 7 is the needed median for the specified data set.

The precise middle value of a data set when it is ordered is called the median.Separating the lowest 50% of data from the top 50% of values is a measure of central tendency.If you have an odd or even number of data points, the processes for calculating the median will be different.

The exact middle value in an ordered data set is known as the median.It is a metric of central tendency that separates the bottom and top half of the data.

Sort the provided data set into the following order: 1, 4, 5, 7, 8, 9, 15, and 16.

Eight terms total, all even.

The data set's median is equal to the nth term, the eighth term, and the fourth term. = 7

Consequently, 7 is the needed median for the specified data set.

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a) The population of the valley in 1990 can be found by setting t=0 in the function:

P(t) = 35t^2 + 105t + 140 + 70

P(0) = 35 * 0^2 + 105 * 0 + 140 + 70

= 210

So, the population of the valley in 1990 is 210 thousands.

b) The population of the valley at the beginning of year 2000 can be found by setting t=10 in the function:

P(t) = 35t^2 + 105t + 140 + 70

P(10) = 35 * 10^2 + 105 * 10 + 140 + 70

= 3500 + 1050 + 210

= 4860

So, the population of the valley at the beginning of year 2000 is 4860 thousands.

c) The average rate of change in the population between 1990 and 2000 can be found by dividing the difference in population by the difference in time:

P(10) - P(0) = 4860 - 210 = 4650

Average rate of change = (P(10) - P(0)) / (10 - 0) = 4650 / 10 = 465

So, the average rate of change in the population between 1990 and 2000 is 465 thousands per year.

d) To find the expected population of the valley in the long term, we need to find the limit of P(t) as t approaches infinity.

Since the function P(t) contains a t^2 term, which grows much faster than the linear term as t increases, the limit of P(t) as t approaches infinity will be infinity.

So, the expected population of the valley in the long term is infinity.

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The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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The word that describes the slope of the line representing the data in the table is "negative."

To determine the slope of the line representing the data in the table, we need to examine the relationship between the number of cards sold and the remaining amount of money needed.

Looking at the given data, we observe that as the number of cards sold increases, the remaining amount of money needed decreases. This indicates an inverse relationship between the two variables.

The slope of a line represents the rate of change between two variables. In this case, the slope is negative because the line decreases as we move from left to right.

Therefore, the word that describes the slope of the line representing the data in the table is "negative."

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The graph of the given polynomial function is graph 2 given that the degree of the polynomial function is 3 and the roots of the equation when f(x) = 0 are −1, 0, and 4. This can be obtained by

Here in the question it is given that,

We have to find the graph of the polynomial function f(x).

As given in the question the polynomial f(x) has 3 roots.

Now, when f(x) = 0, we are told that the 3 roots are,

⇒ x = - 1

⇒ x = 0

⇒ x = 4

The roots of a polynomial on a graph are the points where the graph curve crosses the x - axis which are called the x-intercepts.

By observing all the given graphs, the only graph that crosses the x-axis at the points x = - 1, x = 0, and x = 4 is the second graph which is graph 2.

Hence the graph of the given polynomial function is graph 2 given that the degree of the polynomial function is 3 and the roots of the equation when f(x) = 0 are −1, 0, and 4.    

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Answer:

5/11

Step-by-step explanation:

-3/11 + 8/11= 5/11

The capacity of the bottle is 16 ounces

From the question, we have the following parameters that can be used in our computation:

A water bottle is 3/4 full.

When half of the water is drained, we have

Remainder = 1/2 * 3/4x

Evaluate

Remainder = 3/8x

Where x is the capacity of the bottle

We understand that 6 ounces of water remain in the bottle.

This means that

3/8x = 6

So, we have

x = 8 * 6/3

Evaluate

x = 16

Hence. the capacity of the bottle is 16 ounces

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Answer:

192in^3

Explanation

Volume of a triangular prism = Base area * Height of prism

Since the base is triangular shaped, then;

Base Area = 1/2 * base * height

BAse Area = 1/2 * 8 * 4

Base Area = 8 * 2

Base Area = 16m^2

Height of prism = 12m

Volume of the prism = 16 * 12

Volume of the prism = 192m^2

Hence the volume of the right triangular prism is 192in^3

The mean body mass of the Adelie species is  3706.164 g.

Original chunk of code:

penguins %>%

drop_na() %>%

group_by(species) %>%

The code chunk summarize(mean(body_mass_g)) lets you find the mean value for the variable body_mass_g. The correct code is

penguins %>% drop_na() %>% summarize (mean(body_mass_g)).

The summarize () function displays summary statistics. We can use the summarize() function in combination with other functions - such as mean(), max(), min() - to calculate specific statistics. In this case, you use mean() to calculate the mean value for body mass.

Hence, The mean body mass for the Adelie species is 3706.164 g.

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Answer:

the domain is the input or the x value, while the range consists of y values or the output of an input output table.

Step-by-step explanation:

6 inches more than 2 times the height, 54 square inches the base and height is

b=13.8 inches

h=3.9 inches

Let base and height be b and h respectively,

So ,

b=2h+6

Area = b*h= 54 square inches

So,

(2h+6)(h)=54

2h²+6h=54

h²+3h=27

h²+3h-27=0

h= \(\frac{-3 +\sqrt{3^{2}-4(-27)(1) } \\}{2}\)

h=\(\frac{-3 +\sqrt{9+108} \\}{2}\)

h=\(\frac{-3 +\sqrt{117} \\}{2}\)

h=\(\frac{-3 +10.8\\}{2}\)

h=3.9 inches

b=2h+6=13.8 inches

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The quantity of unit squares necessary to completely cover a shape is its area. As a result, it is stated and measured in square units.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

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Answer:

2.5

Step-by-step explanation:

40 ounces = 2 12 pounds

So, 40 ounces = 4016 = 2 12 or 2.5 pounds.

Hope this helps and sorry if it doesn't

Can I get brainliest

Answer:

2750=-510

Step-by-step explanation:

hope this helps ._.

Answer:

Y = 5/2x - 22

Step-by-step explanation:

The equation of the line with slope 5/2 through the point (8, -2) in slope intercept will be y = (5/2)x – 22.

The equation of line is given as

y = mx + c

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

The slope is 5/2, then the equation will be

y = (5/2) x + c

The equation of line passing through (8, -2).

-2 = (5/2)(8) + c

-2 = 20 + c

c = -22

Then the equation will be

y = (5/2)x – 22

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Answer:

Step-by-step explanation:

( i )

\(p(x) = 4x^2 -3x + 7\\\\p(1) = 4(1)^2 - 3(1) + 7 = 4 - 3 + 7 = 1 + 7 = 8\)

( ii)

\(q(y) = 2y ^3 -4y + \sqrt{11}\\\\q(1) = 2( 1)^3 - 4(1) + \sqrt{11} = 2 - 4 + \sqrt{11} = -2 + \sqrt{11}\)

(iii)

\(r(t) = 4t^4 + 3t^3 -t^2+6\\\\r(p) = 4(p)^4 + 3(p)^3 - (p)^2 + 6= 4p^4 + 3p^3 -p^2 + 6\)

(iv)

\(s(z) = z^3 -1\\s(1) = (1)^3 -1 = 1 - 1 = 0\)

(v)

\(p(x) = 3x^2+5x-7 \\\\p(1) = 3(1)^2 + 5(1) - 7 = 3 + 5 - 7 = 8 - 7 = 1\)

(vi)

\(q(z) =5z^3 -4z +\sqrt{2}\\\\q(2) = 5(2)^3 - 4(2) \sqrt2 = (5 \times 8) - ( 4 \times 2) + \sqrt 2 = 40 - 8 + \sqrt 2 = 32 + \sqrt2\)

Answer:

the first one

Step-by-step explanation:

Answer:Option A is correct. (light blue color in the triangle choices)

It will take 15 days for the hair to grow from 12mm to 16.5mm

By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.

Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):

16.5mm - 12mm = 4.5mm

Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:

4.5mm ÷ 0.3mm/day = 15 days

Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.

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Answer:

$800 at 3%, $1,200 at 5%

Step-by-step explanation:

\(.03x - .05(2000 - x) = 84\)

\(100 - .02x = 84\)

\(.02x = 16\)

\(x = 800\)

\(2000 - x = 1200\)

The equation of the line of best fit is: y = (-2/3)x + 26/3

To estimate the line of best fit using two points on the line, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

Given the two points (7, 4) and (10, 2), we can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the points:

m = (2 - 4) / (10 - 7)

m = -2 / 3

Now that we have the slope, we can substitute it into the equation and solve for the y-intercept (b). Let's use the coordinates of one of the points, such as (7, 4):

4 = (-2/3)(7) + b

4 = -14/3 + b

To find the value of b, we can rearrange the equation:

b = 4 + 14/3

b = 12/3 + 14/3

b = 26/3

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Given the point:

(x, y) ==> (9, 8)

Let's find the distance from the point to the vertical axis of the graph.

The vertical axis of a graph is the y-axis.

Hence, the distance from any pointy to the vertical axis is the unit of the x-coordinate of the point.

From the given point, we have:

x-coordinate = 9

y-coordinate = 8

The x-coordinate of the point is 9.

Therefore, the distance from the given point (9, 8) to the vertical axis (y-axis) is 9 units

ANSWER:

9 units

The intersection points are: (0, -3) and (10, 2)

The bounded area is -20.83 unit²

(a) The  intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:

(0, -3) and (10, 2)

(b) The integral terms of y which gives the area bound are:

a = -3, b = 2 (These are the y values of the intersection points)

Since we have x = y² + 3y and x = 2y + 6, we can say:

y² + 3y = 2y + 6

y² + 3y - 2y - 6 = 0

y² + y - 6 = 0

Thus, h(y) =

Using a = -3 and b = 2  with h(y) = y² + y - 6, we have the bounded area as:

\(Area = \int\limits^b_a {y} \, dy\)

\(Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy\)

Integrating the area:

Area = [y³/3 + y²/2 - 6y + C]²₋₃

Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]

Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]  

Area = [-22/3] - [27/2]

Area = -125/6

Area = -20.83 unit²

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Step-by-step explanation:

everything is directly proportional, so your are going to do cross muliplication

y= -24/7

We will see that the linear function h(x) is:

h(x) = -21x - 15

The slope is -21, and the y-intercept is -15.

Remember that a general linear function is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we start with the linear function:

f(x) = -7x + 9

First, we need to add 2 to the input of f (the input is x) to get function g(x), so we have:

g(x) =f(x + 2)

Replacing the actual function we will get:

g(x) = -7*(x + 2) + 9

Now we multiply the output of function g by 3 to get h(x), then:

h(x) = 3*g(x)

We will get:

h(x) = 3*[-7*(x + 2) + 9]

h(x) = -21*(x + 2) + 27

h(x) = -21x - 42 + 27

h(x) = -21x - 15

So we can see that the slope of function h(x) is -21, while the y-intercept is -15.

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Answer:

r€R

Step-by-step explanation:

3r-8>3(r-6)

3r-8>3r-18

-8>-18

= r € R

Answer:

Step-by-step explanation:

4/5x+4/5=x

x=4

Answer:

the answer is 4

Step-by-step explanation:

if you click on the image it will show you the problem full screen :)

9514 1404 393

Answer:

  1. area DEF = 2π cm²

  2. arc JK = 2π cm

Step-by-step explanation:

1. The area is given by ...

  A = 1/2r²θ . . . . . where r is the radius and θ is the central angle in radians

Your sector has an area of ...

  A = (1/2)(3 cm)²(80(π/180)) = (1/2)(9 cm²)(4/9π)

  A = 2π cm²

__

2. The length of an arc is ...

  s = rθ . . . . . . . where r is the radius and θ is the central angle in radians

  s = (5 cm)(72(π/180)) = (5 cm)(2/5π)

  s = 2π cm . . . arc length

_____

Additional comment

There are π radians in 180°, so an angle in degrees can be converted to an angle in radians by multiplying by π/180°. (The units of degrees cancel, leaving a pure number. "Radians" have no units.)

Answer:

see below and attachment

Step-by-step explanation:

a=30°

because, the marked angle of 30° is an alternate interior angle to angle a.  Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.

b=50°

because the marked angle of 50° is a vertical angle to angle b.  Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.

c=50°

because the marked angle of 50° is a corresponding angle (same side angle) to angle c.  These corresponding angles are congruent because the 2 horizontal lines are parallel.

d=100°

because the 3 interior angles of a triangle must add up to 180°.  We have 30°, 50°, so the last angle must be 100°.  We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°.  We have angle a as 30°, angle c as 50°, so angle d must be 100°.

Hope this helps!  See attachment for visual.