Identify the values of the variables. Give your answers in simplest radical form. PLEASE HELP!!

The number of hours from the initial given time that will take for the bacteria to grow to 2500 number is 4.64 hours approx.

Suppose that a function is defined as;

[tex]y = f(x)[/tex]

Then, suppose that we want to know the instantaneous rate of the growth of the function with respect to the change in x, then its instantaneous rate is given as:

[tex]\dfrac{dy}{dx} = \dfrac{d(f(x))}{dx}[/tex]

Assuming that the bacterial growth can be approximated by a continous and differentiable function y = f(x), where x represents the number of hours spent from the initial time, we're given that:

Supposing the proportionality constant be k, then we get:

[tex]\dfrac{dy}{dx} = ky[/tex]

Solving this differential equation, we get:

[tex]\dfrac{dy}{y} = kdx\\\\\text{Integrating both the sides without limits}\\\\\int \dfrac{dy}{y} = \int x dx\\\\\ln(y) + \ln(c) = kx\\\\\ln(yc) =kx\\ yc = e^{kx}\\y = \dfrac{e^{kx}}{c}[/tex]

where ln(c) represents the integration constant. (we took ln(c) because, firstly, ln's range is whole real number (which gives us the access to use it as integration constant), and secondly that it can merge with ln(y) to simplify the work)

Since we're given that:

At x = t (for some value of t in hours), we're given that y = 500,

and for x = t+2, y = 1000,

so we get two equations as:

[tex]\\500 = \dfrac{e^{kt}}{c}\\\\1000 = \dfrac{e^{k(t+2)}}{c}\\[/tex]

Thus, we get:

[tex]\dfrac{e^{kt}}{500} = \dfrac{e^{k(t+2)}}{1000} \\\\kt = \ln(0.5) + k(t+2)\\\\k = \dfrac{-\ln(0.5)}{2}} \approx 0.3465[/tex]

Thus, we get:

[tex]\\500 = \dfrac{e^{kt}}{c} \\\\c = \dfrac{e^{0.3465t}}{500}[/tex]

Thus, we get:

[tex]y = \dfrac{e^{0.3465x}}{\dfrac{e^{0.3465t}}{500}} = 500e^{0.3465(x-t)[/tex]

Let from the initial given time t, it takes h hours more for bacterias to be 2500, then we get:

[tex]2500 = 500 \times e^{0.3465 (t+h - t)}\\0.3465(h) = \ln(5)\\\\h = \dfrac{\ln(5)}{0.3465} = 4.644 \: \rm hours \: approx.[/tex]

Thus, the number of hours from the initial given time that will take for the bacteria to grow to 2500 number is 4.64 hours approx.

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Answer:3/5

Step-by-step explanation:

First we change 500% to fractions

Changing percentage to fraction is dividing the number by 100

500% = 500/100

Putting this we get 3/(500/100)

Then when a number is being divided by a fraction, to get the answer, we multiply the number by the inverse of the fraction

3/(500/100) = 3 x 100/500 = 300/500 = 3/5

If contaminant is found in a solution at a level of 3/500%. Then 3/5  is fraction of the solution

A fraction represents a part of a whole.

Given,

A contaminant is found in a solution at a level of 3/500%

Let us convert five hundred percentage to a fraction.

500% is converted to fraction by dividing 500/100

So let us divide three by 500/100

3/ (500/100)

When a fraction is divided with another fraction, then the denominator is multiplied inversely with numerator

3×100/500

=300/500

3/5

Hence if contaminant is found in a solution at a level of 3/500%. Then 3/5  is fraction of the solution

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None of these questions have anything to do directly with the polynomial remainder theorem. The theorem says that the remainder upon dividing a polynomial [tex]p(x)[/tex] by [tex]x-c[/tex] is given by the value of [tex]f(c)[/tex].

For these questions, all you really have to do is evaluate the given polynomials at the given points, and IMO is much less work.

Question 2: [tex]f(5)=4(5)^2-5(5)+2=77[/tex]

Question 3: [tex]f(4)=3(4)^4-8)4)^2-2(4)+12=644[/tex]

Question 4: Here you have check the value of [tex]h(x)[/tex] and 2 and -2, then interpret them as points in the coordinate plane, [tex](x,h(x))[/tex].

[tex]h(-2)=2(-2)^5-4(-2)^4-2(-2)^2+15=-121[/tex]

[tex]h(2)=2(2)^5-4(2)^4-2(2)^2+15=7[/tex]

Question 5: Same as in question 4, but you have to check [tex]h(x)[/tex] at -4, -3, -2, -1.

[tex]h(-4)=72[/tex]

[tex]h(-3)=46[/tex]

[tex]h(-2)=26[/tex]

[tex]h(-1)=12[/tex]

- - -

If you insist on using the polynomial remainder theorem, it's a question of polynomial division. For instance, in question 2 you'd compute

[tex]\dfrac{4x^2-5x+2}{x-5}=4x+15+\dfrac{77}{x-5}\implies4x^2-5x+2=(4x+15)(x-5)+77[/tex]

so the remainder is 77, as we found by simply computing [tex]f(5)[/tex].

Answer:

x<=11

Step-by-step explanation:

2(x-3 ) <= 16

Distribute the 2

2x -6 <= 16

Add 6 to each side

2x -6+6<= 16+6

2x <= 22

Divide by 2

2x/2 <= 22/2

x<=11

Answer:

-5/3

Step-by-step explanation:

Parallel lines are lines which have the exact same slope but different y-intercepts. We can find the slope by converting to slope-intercept form, y=mx+b from standard form.

We convert by using inverse operations to isolate y.

5x+3y=7

5x-5x+3y=7-5x

0x+3y=-5x+7

3y=-5x+7

[tex]\frac{3y}{3} =\frac{-5x+7}{3} \\y=\frac{-5}{3}x+\frac{7}{3}[/tex].

The slope is -5/3. SInce parallel lines have the same slope, the slope for a parallel line will be -5/3.

Look at the picture.

(x, y) → (x + 2, y)

Translate the graph of f(x) 2 units right.

-------------------------------------------------------------

(x, y) → (x, y + n) - translate the graph n units up

(x, y) → (x, y - n) - translate the graph n units down

(x, y) → (x - n, y) - translate the graph n units left

(x, y) → (x + n, y) - translate the graph n units right

Answer:

$1237.50

Step-by-step explanation:

r = 4.5% = 0.045

I = prt

I = 5500*0.045*5

= $1237.50

Answer:

26, 37

Step-by-step explanation:

1,3,5,7,9,11

17 + 9 = 26

26 + 11 = 37

Answer:

option: A is correct

Step-by-step explanation:

kaisa's claim is incorrect. clearly the sum of the three angles is 180 degrees therefore we could easily create a triangle with the help of this information but we can't say that this traingle will be unique so we need to know some more information regarding its side.hence multiple triangles could be drawn with these angle measures.

hence option A is correct.

Answer:

A

Step-by-step explanation:

Answer:

your answer is 8/40 but is reduced to 1/5

Step-by-step explanation:

Answer:

A. 33

B. k=32

C. 1

D. [tex]\pm 1,\ \pm 2,\ \pm 4[/tex]

E. [tex]B=-2,\ D=5[/tex]

Step-by-step explanation:

In all parts for the quadratic equation [tex]ax^2+bx+c=0[/tex] use Vieta's formulas

[tex]x_1+x_2=-\dfrac{b}{a},\\ \\x_1\cdot x_2=\dfrac{c}{a},[/tex]

where [tex]x_1,\ x_2[/tex] are the roots of the quadratic equation.

A. For the equation [tex]x^2-5x-4=0,[/tex]

[tex]x_1+x_2=5,\\ \\x_1\cdot x_2=-4.[/tex]

Then

[tex](x_1+x_2)^2=x_1^2+2x_1\cdot x_2+x_2^2,\\ \\5^2=x_1^2+x_2^2+2\cdot (-4),\\ \\x_1^2+x_2^2=25+8=33.[/tex]

B. One of the roots of [tex]x^2+12x+k=0[/tex] is twice the other root, then [tex]x_2=2x_1.[/tex] By the Vieta's formulas,

[tex]x_1+x_2=3x_1=-12,\\ \\x_1\cdot x_2=2x_1^2=k.[/tex]

Then [tex]x_1=-4[/tex] and [tex]k=2x_1^2=2\cdot (-4)^2=2\cdot 16=32.[/tex]

C. The sum of the roots of the quadratic  [tex]4x^2-4x-4[/tex] is [tex]-\dfrac{b}{c}=-\dfrac{-4}{4}=1.[/tex]

D. Note that

[tex](Ax+B)(Cx+D)=ACx^2+x(AD+BC)+BD,[/tex]

then [tex]AC=a=4.[/tex] If [tex]A,\ B,\ C,\ D[/tex] are integers, then you should check [tex]A=\pm 1,\ \pm 2,\ \pm 4.[/tex]

E. Consider [tex]3x^2 - x - 10 = (x + B)(3x + D).[/tex] Note that

[tex]x_1+x_2=\dfrac{1}{3},\\ \\x_1\cdot x_2=-\dfrac{10}{3}.[/tex]

Then

[tex]x_1=2,\ x_2=-\dfrac{5}{3}.[/tex]

Then [tex]3x^2 - x - 10 = (x -2)(3x+5),[/tex] hence [tex]B=-2,\ D=5.[/tex]

A. The sum of the squares of the roots is 33, B. k = 32, C. The sum of the roots is 1, D. The possible values he should check are ±1, ±2, ±4, E. The ordered pair (B, D) is (2, -5).

Let's solve each part of the problem step-by-step:

A. First, find the roots of the quadratic equation using Vieta's formulas:

Now, the sum of the squares of the roots is given by: (α² + β²) = (α + β)² - 2αβ. Substituting the known values:
Hence, α² + β² = 25 - (-8) = 25 + 8 = 33.

B. Let the roots be α and 2α. Using Vieta's formulas again:

C. The sum of the roots is given by -b/a:

D. The quadratic can be written as 4x² + bx + c. The coefficient of x² on the right-hand side must be AC. Since a = 4:

E. The quadratic can be factored as (x + B)(3x + D). Let's determine B and D:

Thus, the ordered pair (B, D) is (2, -5).

Answer: [tex]\bold{Y = 450e^{(.054t)}}[/tex]

Step-by-step explanation:

The general formula for decay is:

[tex]A = Pe^{rt}[/tex]  ; where:

Given:

Equation:

[tex]Y = 450e^{(.054t)}[/tex]

Answer:

[tex]\frac{3\sqrt{13} }{2}[/tex]

Step-by-step explanation:

First we have to identify the parallel sides of the trapezium.

We know that the slopes are equal for parallel lines.

Slope of (x₁,y₁) and (x₂,y₂) is given by

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Slope of AB:

[tex]m_{AB} = \frac{3-5}{3-0}=-\frac{2}{3}[/tex]

Slope of BC:

[tex]m_{BC} = \frac{-2-3}{5-3}=-\frac{5}{2}[/tex]

Slope of CD:

[tex]m_{CD} = \frac{2+2}{-1-5}=-\frac{4}{6}=-\frac{2}{3}[/tex]

Slope of DA:

[tex]m_{DA} = \frac{2-5}{-1-0}=3[/tex]

We see that the slopes of AB and CD are equal, so, AB and CD are the parallel sides.

The length of the midsegment = (1/2)*(length of base1 + length of base2 )

Length of the bases can be calculated using distance formula,

[tex]d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

AB = [tex]\sqrt{(3-0)^{2}+(3-5)^{2}}= \sqrt{9+4} =\sqrt{13}[/tex]

CD = [tex]\sqrt{(-1-5)^{2}+(2+2)^{2}}= \sqrt{36+16} =\sqrt{52}=2 \sqrt{13}[/tex]

Length of the midsegment = (1/2) (√13 + 2√13) =3√13/2

Answer:

Yes she did

Step-by-step explanation:

There is .75 yards and she cut .1125 of it, it make it 15% as .75 x .15 = .1125

Answer:

y=-6

Step-by-step explanation:

y=-4(2)+2

y=-8+2

y=-6

(2,-6)

Answer:

y = - 6

Step-by-step explanation: You have to substitute 2 for x in order for you to get your solution.

y = - 4x + 2

y = - 4(2) + 2

y = - 8 + 2

y = - 6

Hope this helps you!!! :)

Answer:

Step-by-step explanation:

Answer:

The problem can not be solved since  information is missing.

The coldest surface temperature of the moon needs to be given in the text.

THIS IS THE ACTUAL ANSWER

NO JOKE

Answer:

C

Step-by-step explanation:

using the cosine ratio to find p

cos 45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{p}[/tex]

cross- multiplying gives

p × cos45° = 6 → [ cos 45° = [tex]\frac{1}{\sqrt{2} }[/tex]]

p × [tex]\frac{1}{\sqrt{2} }[/tex] = 6

multiply both sides by [tex]\sqrt{2}[/tex]

⇒ p = 6[tex]\sqrt{2}[/tex] ( third option on list )

To determine the value of p in simplest radical form, solve the equation by simplifying the denominator and taking the square root of both sides. The value of p is 2.

To identify the value of p, we need to solve the equation and simplify it to the simplest radical form. Let's start by simplifying the denominator and expressing it as a perfect square.

Next, we can take the square root of both sides of the equation to eliminate the square. This will help us isolate p. Once we do that, we can solve for p by getting rid of the square root on the left side of the equation. After simplifying, we find that p = 2.

So, the value of p is 2.

This can be represented by the inequality:

3x + 0.75 ≥ 4.5

Inequality shows the non-equal comparison between two numbers or mathematical expressions.

Let x represent the price of milk per gallon.

Since the price of milk tripled, and then rose another $0.75 per gallon, hence:

Price of milk = 3x + 0.75

The price is now is AT LEAST $4.50 per gallon, hence this can be represented by the inequality:

3x + 0.75 ≥ 4.5

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Answer:

The number of black ink pen are 15 pens.

Step-by-step explanation:

As given

Jared bought a package of pens containing 20 pens.

[tex]if\ \frac{3}{4}\ of\ the\ pens\ have\ black\ ink.[/tex]

Thus

[tex]Number\ of\ black\ ink\ pens = \frac{3}{4}\times Total\ number\ of\ pens[/tex]

Putting the value

[tex]Number\ of\ black\ ink\ pens = \frac{3}{4}\times 20[/tex]

Number of black ink pens = 3 × 5

                                          = 15 pens

Therefore the number of black ink pen are 15 pens.

Jared has 15 pens with black ink, which is calculated by multiplying 3/4 by the total number of pens he has (20 pens).

To determine the number of pens with black ink that Jared has, you need to multiply the total number of pens by the fraction representing the pens with black ink. Jared has a package containing 20 pens, and 3/4 of these have black ink. Here's how you calculate it:

Find the fraction of pens with black ink: 3/4 of the pens.

Multiply this fraction by the total number of pens: 3/4 × 20 pens.

Calculate the product to find the number of pens with black ink: 3/4 × 20 = 15 pens.

Therefore, Jared has 15 pens that contain black ink.

Answer:

[tex]\sqrt{3} * /sqrt{16} = 4\sqrt{3}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

square root of 3 times the square root of 16 looks like this

[tex]\sqrt{3} .\sqrt{16}[/tex]

we try to break the numbers inside the radical to there prime factors

so

[tex]\sqrt{3} .\sqrt{2.2.2.2}[/tex]

the prime factors which are in pair , comes out of the radical so

[tex]\sqrt{3} .2.2[/tex]

which simplifies to

[tex]4\sqrt{3}[/tex]

Answer:

Step-by-step explanation:

(a) The given numbers can be put directly into the form ...

... f(t) = (initial value) · (ratio)^(t/(time to achieve that ratio))

Here, we have an intial value of $100, and a ratio of $184.50/$100 = 1.845. The time to achieve that multiplication is 10 years (1967 to 1977). So, the equation can be written ...

... f(t) = 100·1.845^(t/10)

(b) You want to find f(38).

... f(38) = 100·1.845^(38/10) = 100·1.845^3.8 ≈ 1025.15 . . . dollars

Final answer:

Using the provided CPI data, an exponential function is found to model the change in cost of goods over time. The estimated cost of the same goods in 2005, using this model, is approximately $1019.03, illustrating changes in purchasing power and the cost of living.

Explanation:

The question involves finding an exponential function to model the Consumer Price Index (CPI) data and estimate the cost of goods in a future year based on past data. The data provided includes the cost of the same goods being $100 in 1967 (t=0) and $184.50 in 1977. An exponential function of the form y = abt can be used, where y represents the cost of goods, t represents the year, and a and b are constants to be found.

Given that the goods cost $100 in 1967, our initial condition gives us a as $100. We then use the information from 1977 (t=10) to solve for b. Plugging in the values, we get $184.50 = 100*b10, which solves to b approximately equal to 1.0653. Therefore, the exponential function modeling the CPI data is y = 100(1.0653)t.

To estimate the cost of goods in 2005, we substitute t with 38 (2005 - 1967), resulting in an estimated cost of goods y ≈ 100(1.0653)³⁸ ≈ $1019.03. This estimation illustrates how the Consumer Price Index can indicate changes in purchasing power and the cost of living over time.

Answer:

A point of sale transaction occurs when an ATM withdrawal is made- TRUE.

Step-by-step explanation:

A point of sale transaction occurs when an ATM withdrawal is made - This is TRUE.

A point of sale is the point when a transaction is finalized. This transaction is based on any form of payment like - cash, debit cards, credit cards etc.

Answer:3 percent because

Answer:

Percent = 62.5%

Step-by-step explanation:

Answer:

[tex]\log_4{(16384)}=7[/tex]

Step-by-step explanation:

The base of the exponent is the base of the logarithm. The exponent is the logarithm. The value the exponential expression is equal to is the argument of the logarithm.

Answer:

f(x) = 3x-8

Step-by-step explanation:

y −4 = 3 (x − 4)

We want to write the equation in y = mx+ b form

Distribute the 3

y-4 = 3x -3*4

y-4 = 3x -12

Add 4 to each side

y -4+4 = 3x-12+4

y = 3x-8

Since the want it in function form,  f(x)

f(x) = 3x-8

Answer:

We are given that a fair coin is tossed 3 times.

We know that if a fair coin is tossed 3 times, then there are 8 possible outcomes.

(a) what is the sample space for this chance process?

The sample space associated with tossing a fair coin three times are:

Ω = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Where:

H denotes the head and T denotes the tail.

(b) what is the assignment of probabilities to outcomes in this sample space?

We are given that a fair coin is tossed 3 times, which means that all the possible outcomes in the above mentioned sample space has equal chance being selected. Therefore, the assignment of probabilities to outcomes in this sample space is same for all outcomes and is given below:

[tex]p= \frac{1}{8}[/tex]

Answer:

I would say A. 7.8 x 10^-5

Step-by-step explanation:

7.8 x 10^-5 can also be written as 7.8 times 10 to the negative fifth power or the exponent of negative five. But, if you solve it you would get 0.000078 as the real number.