5. (8 points) A chemical substance has a decay rate of 8.8% per day. The rate of change of an
dN
amount N of the chemical after t days is given by =-0.088 N
dt
(i) Let No represent the amount of the substance present at to. Find the exponential function
that models the decay.
(ii) Suppose that 400g of the substance is present at to. How much will remain after 3 days?
(iii) What is the rate of change of the amount of the substance after 3 days?
(iv) After how many days will half of the original 400 g of the substance remain?

Answer:

Step-by-step explanation:

Yes, the length and width dimensions of the two rectangular boxes are similar.

Two objects are considered similar if they have the same shape, but not necessarily the same size. The ratio of the corresponding sides of two similar objects is called the scale factor.

For the first rectangular box, the ratio of length to width is 10/8, which can be simplified to 5/4.

For the second rectangular box, the ratio of length to width is 15/12, which can be simplified to 5/4 as well.

Since the ratio of the corresponding sides of the two boxes is the same, namely 5/4, we can conclude that the length and width dimensions of the two rectangular boxes are similar.

The maximum height of the ball is given as follows:

92 feet.

The quadratic function modelling the height of the ball is given as follows:

h(t) = -16t² + v(0)t + h(0).

In which:

The parameters for this problem are given as follows:

v(0) = 75, h(0) = 4.

Hence the equation is:

h(t) = -16t² + 75t + 4.

The coefficients are given as follows:

a = -16, b = 75, c = 4.

As the quadratic equation is concave down, the maximum height is at the vertex.

The t-coordinate of the vertex is given as follows:

t = -b/2a

b = -75/-32

b = 2.34375s.

Hence the maximum height is of:

h(2.34375) = -16(2.34375)² + 75(2.34375) + 4.

h(2.34375) = 92 feet.

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According to the Cartesian plane graph, it can be inferred that the circle was rotated and translated (option B).

To identify the movements that were made to circle 1 to become 2 we must carefully observe the graph. Once we have analyzed this graph we can infer the movements that were made to the circle. In this case, the rotation was performed because it can be seen that it was rotated having the coordinate (-1.5, 0.5) as a reference or point of rotation.

However, it was also translated because it was shifted a bit down and to the left. So the correct answer would be option B.

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Answer: rotation and translation

Step-by-step explanation: I took the quiz

Answer:

Its answer number 4

Step-by-step explanation:

According to the information we can infer that sentence is completed with the words mathematical procedure.

To complete the sentence we must identify the central idea and establish the right words to complete it. In this case, it is referring to a mathematical procedure then we could infer that these are the words that complete the sentence. Then the complete sentence would be like this:

Note: This question is incomplete. Here is the complete information:

Complementary information:

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Answer:

[tex]y = 4d + 8\\[/tex]

Step-by-step explanation:

Since d is the number of large drinks, and there is always a constant of 1 large popcorn, we go to (0, 8). This concludes that since we start off with the cost of 8 dollars with no large drink but a large popcorn, the popcorn will stay a constant cost of $8. (the equation for this scenario is as shown):

y = md + 8

y (total cost)

m (coefficient - in this sense the cost of the drinks.)

d (amount of drinks)

8 (the constant of 8 represents the cost of one large popcorn consistently)

Now, lets find the cost of the dink.

Go to (1, 12).

$12 dollars is the total cost, with one drink and one large popcorn bought.

We have already discussed that we will have a constant of 8 because no matter the amount of drinks we will get, we would have bought 1 large popcorn at $8.

Therefore, we must subtract 8 dollars from 12.

12 - 8 = 4

From the total cost of everything we bought (2 things) and subtracting it with the cost one of the things we bought, we get the cost of the other thing.

each drink will cost $4.

Therefore, with all the variables and their listed meanings, this will be our given equation:

y = 4d + 8

a. A ⋁ G: Elvis is alive or Elvis gained weight.

b. ~(A ⋀ G): Elvis is not both alive and gained weight.

c. G → ~A: If Elvis gained weight, then Elvis is not alive.

d. A ↔ ~G: Elvis is alive if and only if Elvis did not gain weight.

Answer:

1/9 and 1/2 one is greater then

Step-by-step explanation:

so if u look at it you will know that 1/2 is less then and 1/9 is greater then.

In the polynomial function given, the value of the limit as it approached infinity is 5/3

To evaluate this limit, we need to determine the behavior of the function as x approaches infinity. To do this, we can use the fact that for any polynomial p(x) and q(x) of the same degree, the limit of p(x)/q(x) as x approaches infinity is equal to the ratio of the leading coefficients.

In this case, both the numerator and denominator are polynomials of degree 2, so we can apply this property. The leading coefficient of the numerator is 6 and the leading coefficient of the denominator is 7. Therefore, the limit as x approaches infinity of the given expression is:

lim [ (6x² - 5) / (7x² + x - 3)]

x → ∞ = 5/3

Therefore, the limit of the given expression as x approaches infinity is equal to 5/3.

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The function g(x) is translation of f(x) 9 units up. The solution has been obtained by using transformation.

An operation known as a transformation involves moving a polygon or other two-dimensional object on a plane or coordinate system.

We are given that the function g(x) is a translation of the function

f(x) = x².

In the graph, we can see that the vertex of the parabola is at (0, 9).

This means that the function g(x) is 9 units up from the function f(x).

So, g(x) = x² + 9

Hence, the function g(x) is translation of f(x) 9 units up.

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Answer: 32 presents can be wrapped with 8 yards of ribbon

Step-by-step explanation:

Convert yards to inches

1 yard = 36 inches

8 yards = 288 inches

Divide 288 inches by 9 inches

288/9 = 32

Answer: You can wrap 32 presents with 8 yards.

Step-by-step explanation:

So, first, you need to know how many inches are in a yard. There are 36 inches in 1 yard.

Then, do 36 inches times 8 yards to figure out how many yards are in 8 yards. So in 8 yards, there are 288 inches.

Finally, do 288 divided by 9 to figure out how many present you can wrap with 8 yards (288 inches).

You can wrap 32 presents with 8 yards.

I hope this helped!

Answer:

The percent of Dan's average did he score during this game is 11.11%

What percent of Dan's average did he score during this game?

Dan's score in the high school basketball team during last game= 18 points

Dan's score in the high school basketball team during this season = 20 points

Percent of Dan's score during this game = (20 - 18) / 18 × 100

= 2/18 × 100

= 11.11%

In conclusion, Dan scored an average percentage of 11.11% during this game.

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Answer:

x - 5

Step-by-step explanation:

Okay to write this problem as an expression it would be x -5. x represents James and -5 represents less than.

Answer:

x-5

Step-by-step explanation:

we don't know how much James has but we know it is $5 less so what ever the original amount is we are putting as x for now and we will subtract 5 because it is $5 less making our x-5.

Answer:

Step-by-step explanation:

We can use the distributive property and basic algebraic operations to multiply the given expression:

(2x+3)(x^2 - 6x - 2)

= 2x(x^2 - 6x - 2) + 3(x^2 - 6x - 2) // Distribute 2x and 3

= 2x^3 - 12x^2 - 4x + 3x^2 - 18x - 6 // Multiply each term

= 2x^3 - 9x^2 - 22x - 6 // Combine like terms

Therefore, (2x+3)(x^2 - 6x - 2) simplifies to 2x^3 - 9x^2 - 22x - 6.

The length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.

Using the formula obtained from Pythagoras' theorem, distance can be computed.

The distance formula in coordinate geometry is:

(P, Q) = √ (x2 – x1)² + (y2 – y1)².

Given points: (5, 4) and (−3, −1)

d = √ (-3 - 5)² + (4 + 1)²

d = √ 64 + 25

d = √ 89

d = 9.43

Thus, the length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.

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The Panther I traveled approximately 2413 miles before reaching a speed of 130 mph.

A trapezoid is a quadrilateral having two parallel bases and one set of other sides called legs.

To estimate the distance traveled by the Panther I, we need to approximate the area under the velocity curve between 0 and 25.7 seconds. We can divide the area into trapezoids using the data given in the table.

The first trapezoid has a height of 30 mph and a base of 1.8 seconds. The second trapezoid has a height of 40 mph and a base of 1.3 seconds (the difference between 3.1 and 1.8).

Continuing in this way, we get the following table:

Speed       Height

Range    (mph) Base (s)  Area (mph * s)

0-30  30           1.8               54

30-40 40           1.3               52

40-50 50           1.1            55

50-60 60           1.3              78

60-70 70           1.9            133

70-80 80           1.8             144

80-90 90            2.3            207

90-100 100           3.1            310

100-120 120          6.3            756

120-130 130           4.8            624

To find the total area, we add up the areas of all the trapezoids:

54 + 52 + 55 + 78 + 133 + 144 + 207 + 310 + 756 + 624 = 2413

Therefore, the Panther I traveled approximately 2413 miles before reaching a speed of 130 mph.

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The number of men needed to complete the same job in 16 days working 6 hours a day is given as follows:

28 men.

The number of men is obtained applying the proportions in the context of the problem.

The rule of three is given as follows:

n/48 = 8/6 x 7/16.

(the time is inverse proportional to the number of men, hence the fractions are inverted).

Thus:

n/48 = 56/96

Applying cross multiplication, the number of men is obtained as follows:

96n = 48 x 56

n = 48 x 56/96

n = 28 men.

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Answer:

67.97%

Step-by-step explanation:

Answer:

67.97%

Step-by-step explanation:

We can state this by responding to the provided question Hence, the triangle longer limb is around 351.42 in length.

A triangle is a polygon because it includes four or so additional parts. It features a simple rectangular shape. A rectangle having edges A, B, and C is referred to as a triangle. When the sides are actually not collinear, Euclidean geometry yields a single plane and cube. If a triangle contains three parts and three angles, it is a polygon. The intersections of a triangle's three sides are referred to as its corners. The sum of a triangle's sides is 180 degrees.

In a triangle with three legs measuring 30, 60, and 90, the shorter leg is half as long as the hypotenuse while the larger leg is sqrt3 times as long.

Let's name the larger leg's length "x" for simplicity. Thus, we are aware of:

The shorter leg measures 203 in length.

The hypotenuse measures 406 times the length of the shorter leg.

Using the proportion of the hypotenuse and leg lengths in a 30-60-90 triangle, we may find:

x = sqrt3 times ($) 203 = 351.42$

Hence, the longer limb is around 351.42 in length.

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The time spent on country driving is 25/44 hour

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

Total time = 3/4

City driving = 2/11

Given that 2/11 hour was spent on city driving, we can find the time spent on country driving as follows:

Time spent on country driving = Total driving time - Time spent on city driving

Time spent on country driving = 3/4 hour - 2/11 hour

So, we have

Time spent on country driving = 25/44

Hence, the time spent is 25/44

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9. The discriminant is 33. And the roots are real and distinct.

10. The discriminant is 4. And the roots are real and distinct.

11. The discriminant is -23. And the roots are imaginary roots.

12. The discriminant is -4. And the roots are imaginary roots.

What is the discriminant?

The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,

D = b² - 4ac

9. 2x² + 3x - 3 = 0, the discriminant is given as,

D = 3² - 4 × 2 × (-3)

D = 33

Roots are real and distinct.

10. 4x² - 6x + 2 = y, the discriminant is given as,

D = (-6)² - 4 × 4 × (2)

D = 4

Roots are real and distinct.

11. 0 = x² - 3x + 8, the discriminant is given as,

D = (-3)² - 4 × 1 × (8)

D = - 23

Roots are imaginary.

12. y = 5x² + 4x + 1​, the discriminant is given as,

D = (4)² - 4 × 5 × (1)

D = -4

Roots are imaginary.

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Answer:

Step-by-step explanation:

[tex]\tt y+4+3\left(y+2\right)[/tex]

Expand by distributing terms:-

[tex]\tt y+4+3y+6[/tex]

Combine like terms:-

[tex]\boxed{\tt y+3y}+\boxed{\tt 4+6}[/tex]

[tex]\tt y+3y=\underline{\bf 4y}[/tex]

[tex]\tt 4+6=\underline{\bf 10}[/tex]

⇒ [tex]\underline{\bf 4y+10}[/tex]

Therefore, A. 4y + 10 is our answer!

_______________________

Hope this helps! :)

Answer:

4y+10

Step-by-step explanation:

у + 4 + 3(y + 2) =

y + 4 + 3y + 6

y + 10 + 3y

4y +10

The measure of side AC of the right triangle is 7.2 units.

The figure in the image is the of a right triangle.

To solve for the measure of side AC, we use trigonometric ratio.

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Tangent = Opposite / Adjacent

tan( A ) = BC / AC

Plug in the values and solve for side AC.

tan( 51° ) = 8.9 / AC

AC = 8.9 / tan( 51° )

AC = 8.9 / 1.234897

AC = 7.2

Therefore, side AC has a value of 7.2 units.

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As an example, the 78-mph speed limit in the United States is equivalent to the 130 km/h restriction in Germany.

How quick is that speed?

A connection with a speed of 100 Mbps or higher is considered fast internet. Broadband internet speed is defined by the federal communications regulator (FCC) as 25 Mbps for downloading and 3 Mbps for upload.

We can increase each number by 0.6 to convert overall speed limitations from kilometers per hour into miles per hour. Here is the revised table:

Country Speed Limit (km/h)  Speed Limit (mph)

Germany         130                    78

France             110                     66

Italy                 150                     90

Japan              100                      60

Australia          110                       66

United Kingdom 113              67.8

Hence, Because one kilometer is equivalent to 0.6 miles, it is evident that speed limits in the form of miles per hour were lower than those in kilometers per hour.

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Answer:

9 54 divided by 9 = 6  72 - 18 = 54

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

The x-intercepts and y-intercepts of the graph include the following:

x-intercept: B. -1.

y-intercept: D. none.

The equations for all vertical and horizontal asymptotes are as follows;

Vertical asymptote: x = 1.

Horizontal asymptote: y = 4.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).

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