After the antibiotic Streptomycin is given to a patient, the population (in million) of Mycobacterium in the body is given by the function f(t) = -0.02(t)2 + 3, where t is in hours. Find the rate at which the population of the bacteria is changing after 4 hours.

Answer:

it may be not

take an example x=(1) y={123) and define a relation of R as the set of pairs (1,1) (1,2)(1,3) so this not a function

Answer:

  (a)  m^6·n^9

Step-by-step explanation:

You want to know an expression equivalent to (m^-2·n^-3)^-3.

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  [tex](m^{-2}n^{-3})^{-3}=m^{(-2)(-3)}n^{(-3)(-3)}=\boxed{m^6n^9}[/tex]

The  equations that can be used to solve for the length of the room are

(b) y²-5y=750  ,    (c) 750-y(y-5)=0  and   (e) (y+25)(y-30)=0

Given that:

The area of rectangular room is 750 square feet.

Let the length of the rectangular room be y feet.

Since the width of the rectangular 5 less than the length of the room.

Then the width of the given rectangular room is (y-5) feet.

We know the area of a rectangular plot is = Length×width.

Thus , the area of the rectangular room is = y(y-5) square feet

According to problem,

area of the rectangular room =  750 square feet

⇒ y(y-5) =750.........(1)

⇒ y²-5y=750 .......(2)

⇒ y²-5y-750=0

⇒ y²-30y+25y-750=0

⇒ y(y-30)+25(y-30)=0

⇒ (y-30)(y+25)=0 ......(3)

⇒ y-30=0 or, y+25=0

⇒ y= 30, -25

∵ the length of a rectangle can't be negative.

So, y=30.

We can rewrite the equation (1) in form of

(i)

y(y-5) =750

⇒750= y(y-5)

⇒750-y(y-5)=0.......(4)

(ii)

y(y-5) =750

⇒y(y-5) -750=0.......(5)

Hence , the  equations that can be used to solve for the length of the room are

(b) y²-5y=750  ,    (c) 750-y(y-5)=0  and   (e) (y+25)(y-30)=0

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The equation in the form of y=mx+b will be y= -3/4x+2

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that the inequality is y< -3/4x+2,

We have to write the inequality in the form of y=mx+b

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Thus, the equation in the form of y=mx+b will be y= -3/4x+2

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The equation of the number of dollar cins giuliana has,  is found to be

0.25(22 – d) + d = 10.75.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Giuliana has 22, quarters and dollar coins worth a total of $10.75.

Let the number of dollar coins be represented by d, while the number of quarter coins be represented by (22-d). Therefore, the sum of the total amount that is with Giuliana can be written as,

(1 x d) + (0.25 x (22-d)) = 10.75

d + 0.25(22-d) = 10.75

Hence, the equation can be used to find d, the number of dollar coins Giuliana has is 0.25d + 22 – d = 10.75.

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Hello!

Let's use 'x' to represent the cost of the burger, and 'y' to represent the cost of the hotdog.

2x + y = 482

× + 2y = 370

2x + 47 = 740

-3y = -258

y = 86 cents

2x + 86 = 482

2x = 396

x = 198

A burger costs $1.98 and a hot dog costs $.86

I hope this didn't confuse you, I'm not very good at explaining!

Answer: y=-[tex]\frac{5}{2}[/tex]x+2  or 5x+2y=4

Step-by-step explanation:

let’s make l1: 2x+5y=10,

then 5y=-2x+10

then y=-[tex]\frac{2}{5}[/tex]x+2

Answer:

No

Step-by-step explanation:

A function can have only  output for each input.  The input 3 has two outputs 3 and 5.  

The input 4 has two outputs 4 and 6.

Step-by-step explanation:

part (a) - you plug 25 into the given function they give you and that'll be your answer

part (b) - 200 is your original amount given by the function so what is half of 200? 100. So set 100 on the right side of your function and solve for t to find the year

Answer:

15 inches

Step-by-step explanation:

The shortcut for finding the side lengths on a 30°-60°-90° triangle is that the long leg is

the short leg × √3.

So for your question:

5√3 × √3

= 5 × √3 × √3

= 5 × 3

= 15

Just in case it comes up next, the other shortcut is that the hypotenuse is double the short leg. Hypotenuse =

2 × 5√3 = 10√3

Answer: 6,3

Step-by-step explanation:

Answer:

6,3

Step-by-step explanation:

The thing that 47.3 mean in the context of the problem is D. If no rain fell, 47.3 bushels of wheat would be produced.

It is important to note that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, Margot is studying the yield of bushels of wheat in comparison to the amount of rainfall, in inches, that occurs. She finds the linear regression equation to be y = 47.3 +0.78x.

It should be noted that when no rain fell, 47.3 bushels of wheat would be produced. This is the constant value.

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Answer:31

Step-by-step explanation: solve it

The equations have no solution.

6x – 2 – 3x = 3x – 2

10 + 6x = 15 + 9x – 3x

11 + 3x – 7 = 6x + 5 – 3x.

We have determine from the given option which option has no solution.

When an equation has a solution?

An equation with no solution will be an equation when simplified, which will be a false statement.

The equation, 6x – 2 – 3x = 3x – 2

add like terms,

3x-2=3x-2

So we get,This equation has no solution

10 + 6x = 15 + 9x – 3x

10+6x=15+6x

add like terms we cannot find the value of x.

Therefore the given equation has no solution.

11 + 3x – 7 = 6x + 5 – 3x.

add like terms,

4+3x=3x-5

we cannot find the value of x.

So this equation has no solution.

Therefore, The equations 6x – 2 – 3x = 3x – 2,10 + 6x = 15 + 9x – 3x and 11 + 3x – 7 = 6x + 5 – 3x have no solution.

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Answer:

is 2(x minus 1)(5x + 1)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

area of triangle  = 1/2*B*H

Assuming its one leg we write

24 = 1/2*6*h

h= 8

With this info we can use Pythagoras Theorum

[tex]a^{2} = b^{2} + c^{2}[/tex]

[tex]x^{2} = 8^{2} + 6^{2}[/tex]

[tex]x^{2} = 100[/tex]

[tex]\sqrt{100}[/tex]

[tex]x = 10[/tex]

in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time is a True statement.

In a simple linear regression equation, the independent variable is the one that is used to predict the dependent variable. In this case, time would be the independent variable and sales would be the dependent variable. Therefore, it is true that in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time.A linear regression equation is used to describe the relationship between two variables, where one is the independent variable and the other is the dependent variable. The independent variable is the one that is used to predict the dependent variable. In this case, time series data is being used to forecast the trend in sales, so time would be the independent variable and sales would be the dependent variable. Therefore, it is true that in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time.

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Last option: The height and weight distributions, respectively, show positive and negative skews.

Graphs are used to represent information in bar charts. To depict values, it makes use of bars that reach various heights. Vertical bars, horizontal bars, clustered bars (multiple bars that compare values within a category), and stacked bars are all possible options for bar charts.

There isn't a lot of data, but it shows that the weights have a negative skew and the heights have a positive skew, with the long tails pointing in opposite directions.

[tex]\frac{change}{strating point } X 100%[/tex]

2.5 millions of books were sold in 1991.

Millions of books sold in 1992 equaled 3.4.

Change = 0.9 (in millions).

[tex]\frac{0.9}{2.5} X 100 = 36[/tex]%

The height and weight distributions, respectively, show positive and negative skews.

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1) The length of AC is 14.

2) The length of AB is 8.

3) The length of BC is 17.

4) The length of AB is 29.1.

5) The length of BC 53.

6) The measure m∠C is 53.8°

What is sine rule of a triangle?

AB/sin C = BC/ sin A = AC / sin B

1)

Applying sum rule of interior angle

∠A + ∠B + ∠C = 180°

22° + 118° + ∠C = 180°

∠C = 40°

Applying sine law in △ABC:

AB/sinC=BC/sinA=AC/sin B

Putting AB = 24, ∠C = 40°, and ∠B = 22°:

AB/sinC=AC/sin B

24/sin 40° = AC/ sin 22°

AC = 13.98

AC ≈ 14

2)

Applying sine law in △ABC:

AB/sinC=BC/sinA=AC/sin B

Putting AC = 7, ∠B = 44°, and ∠C = 53°:

AC/sin B=AB/sin C

7/sin 44° = AB/ sin 53°

AB = 8.047

AC ≈ 8

3)

Applying sum rule of interior angle

∠A + ∠B + ∠C = 180°

39° + ∠B +  51°= 180°

∠B = 90°

Applying sine law in △ABC:

AB/sinC=BC/sinA=AC/sin B

Putting AC = 27, ∠B = 90°, and ∠A = 39°:

BC/sinA=AC/sin B

BC/sin 39° = 27/ sin 90°

BC = 16.99

BC ≈ 17

4)

Applying sum rule of interior angle

∠A + ∠B + ∠C = 180°

∠A + 101° +  63°= 180°

∠A = 16°

Applying sine law in △ABC:

AB/sinC=BC/sinA=AC/sin B

Putting CB = 9, ∠A = 16°, and ∠C = 63°:

AB/sinC=BC/sinA

AB/sin 63° = 9/ sin 16°

AB = 29.09

AB ≈ 29.1

5)

Applying sum rule of interior angle

∠A + ∠B + ∠C = 180°

93° + ∠B + 58°  = 180°

∠B = 29°

Applying sine law in △ABC:

AB/sinC=BC/sinA=AC/sin B

Putting AC = 16, ∠B = 29°, and ∠A = 93°:

AC/sinB=BC/sin A

16/sin 29° = BC/ sin 93°

BC = 32.95

BC ≈ 33

6)

Applying sine law in △ABC:

AB/sinC=BC/sinA=AC/sin B

Putting AB = 21, ∠A = 88°, and BC= 26:

AB/sinC=BC/sinA

21/sin C = 26/ sin 88°

sin C/21 = sin 88°/26

C = 53.82

C ≈ 53.8

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The quadratic equation that models the company's costs is y = 25(x - 16)² + 1000

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

Minimum cost of $1000 at 16 hours

Operating cost of $2600 at 8 hours

A quadratic equation is represented as

y = a(x - h)² + k

The minimum point is the vertex

So, we have

(h, k) = (16, 1000)

Substitute (h, k) = (16, 1000) in y = a(x - h)² + k

y = a(x - 16)² + 1000

The cost of $2600 at 8 hours means

(x, y)  = (8, 2600)

So, we have

2600 = a(8 - 16)² + 1000

Evaluate the difference

1600 = a(8 - 16)²

So, we have

64a = 1600

Divide by 64

a = 25

Substitute a = 25 in y = a(x - 16)² + 1000

y = 25(x - 16)² + 1000

Hence, the equation is y = 25(x - 16)² + 1000

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7 is a value of k that transforms f into g, where g(x) = f(x) + k. Using the concept of x and y-axis:

A two-dimensional number line, like two perpendicular axes, can be used as a coordinate system. This coordinate system is typical: The x-axis and y-axis are the names of the horizontal and vertical axes, respectively. The origin is the point at which all lines in a coordinate system intersect.

The coordinates that are shown on the x and y axes give rise to their respective names. The vertical y-axis is aligned with the horizontal x-axis. They are referred to as axes because they are perpendicular to one another.

From the graph it is observe that,

Graph of Function f(x) cut at y axis in the point 3

graph of function g(x)  cut y axis in the point 4

So, the difference between the cut of y axis is k

Thus, {g(x)-f(x)=k}

Hence, k = [4 - (-3)] = 7

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Use the picture equation

Answer:

Yes, they are parallel.

Step-by-step explanation:

61 + 119 = 180

One line is 180 degrees.

Answer: The answer is: a

Answer: The value 550 represents the initial balance in the account, which means the account started with $550.

Step-by-step explanation:

The 550 represents the start balance that was put into the account. The (1+0.05t0 is the interest being added every t years/months.

Inequalities are used to compare unequal expressions.

The actual comparison is: -3.5F < 5F or 5F > -3.5F

Given,

In the question:

Compare the weather on two different days using an inequality. Then see if their comparisons change by finding the absolute value of each.

Now, According to the question:

The temperatures are given as:

Temperature: -3.5F, 5F, 1.5F, -0.5F, -2F, 2.5F, -4F

From the above list, we have:

Day 1 : -3.5F

Day 2 :- 5F

By comparison,

-3.5F < 5F or 5F > -3.5F

Using absolute values, the inequalities are:

|-3.5F| < |5F| or |5F| > |-3.5F|

Hence, the actual comparison is:

-3.5F < 5F or 5F > -3.5F

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Answer:

Step-by-step explanation:

2 + 3/8 = 7/8

2 x 7/8 = 7/4

2 + 5/8 = 9/8

2 x 9/8 = 9/4

2 + 6/8 = 8/8

2 x 8/8 = 16/8

2 + 7/8 = 15/8

2 x 15/8 = 15/4

Answer:

Step-by-step explanation:

I am not 100% positive but I am 75% positive it is B.