a company charges $80 per day plus $0.30 per mile for truck rentals. If Greg rents a truck for 3 days and drives 200 miles, how much will the company charge?

To find the function n(t) that models the population of bacteria after t hours, we can use the exponential growth formula:

n(t) = n0 * e^(kt)

Where:

n(t) is the population after t hours,

n0 is the initial population size,

e is the base of the natural logarithm (approximately 2.71828),

k is the growth rate constant.

We can determine the value of k using the given information. After 1 hour, the bacteria count is 9500, which is the population at time t = 1. Plugging these values into the equation:

\(9500 = 1100 * e^(k*1)\)

To find k, we can divide both sides by 1100:

9500/1100 = e^k

Now, we can solve for k by taking the natural logarithm (ln) of both sides:

ln(9500/1100) = ln(e^k)

ln(9500/1100) = k

Now we have the value of k. We can plug it back into the exponential growth formula to obtain the function n(t):

\(n(t) = 1100 * e^(ln(9500/1100) * t)\)

To find the population after 1.5 hours, we can substitute t = 1.5 into the equation:

\(n(1.5) = 1100 * e^(ln(9500/1100) * 1.5)\)

To find the number of hours when the number of bacteria will reach 20,000, we can set n(t) equal to 20,000 and solve for t:

\(20,000 = 1100 * e^(ln(9500/1100) * t)\)

Finally, to sketch the graph of the population function, plot the values of t on the x-axis and the corresponding values of n(t) on the y-axis using the equation n(t) = 1100 * e^(ln(9500/1100) * t). The resulting graph will show the exponential growth of the bacteria population over time.

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Answer:

It is B because

Step-by-step explanation:

3 x 9 x 4 = 108

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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Probability = # of desired options / # of total options

Our desired option is blue and there are 9 blue marbles in the bag.

There are 32 total marbles (options) in the bag.

P(blue) = 9 / 32 = 0.28125 = 28.125%

Hope this helps!

\(\text {Hello! Let's Solve this Equation!}\)

\(\text {\underline {The First Step is to Simplify the Equation}}\)

\(\text {b=1 so b/2 becomes 1/2}\)

\(\text {Your New Problem Is: 1/2b-5=13}\)

\(\text {\underline {The Second Step is to Add 5}}\)

\(\text {1/2b-5+5=13+5}\)

\(\text {Your New Problem Is: 1/2b=18}\)

\(\text {\underline {The Final Step is to Multiply 2}}\)

\(\text {2*1/2b}=2*18}\)

\(\text {Your Answer Would Be:}\)

\(\fbox {b=36}\)

\(\text {Best of Luck!}\)

\(x^3=216\\x=\sqrt[3]{216}=6\)

This is a simple example. You (should) know that \(6^3=216\).

But you can solve it like this:

\(\begin{array}{r|l}216&2\\108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}\)

Therefore

\(\sqrt[3]{216}=\sqrt[3]{2^3\cdot3^3}=\sqrt[3]{2^3}\cdot\sqrt[3]{3^3}=2\cdot3=6\)

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the value of x in the equation \(\pmb{x^3=216}\).

\(\triangle~\fbox{\bf{KEY:}}\)

Is x by itself? No, it's cubed, or multiplied times itself three times.

So we need to use the opposite operation.

The opposite of cubing is taking the cube root, so we take the cube root of both sides:

\(\star~\large\pmb{\sqrt[3]{x^3}=\sqrt[3]{216}}\)

On the left, the cube root sign and the cube cancel, because they're opposite, and we're left with x.

On the right, we take the cube root of 216, which gives us:

\(\star~\large\pmb{x=6}\)

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Answer:

I don't know if you want to be a good

Answer:

  C. RP = 4.5

Step-by-step explanation:

You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given  three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.

Similarity can be shown if all three sides are proportional, or if two angles are congruent.

The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.

  C. RP = 4.5

__

Additional comment

The side ratios in the two triangles are ...

  AB : BC : CA = 10 : 9 : 6

  QP : PR : RQ = 5 : PR : 3

For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer:

The answer is 3k^2m^6/4

Answer:

Step-by-step explanation:

4(4) = -7(-3) - 5

16 = 21 - 5

16 = 16

answer is D

Answer: (-3.4)

Step-by-step explanation: took test 6.02

Foundations wrap up Systems of Equations

Answer:

Hi

please mark brainliest ❣️

Thanks

Step-by-step explanation:

10 + x / 3 = 12

Cross multiply

10 + x = 12× 3

10 + x = 36

Collect like terms

x= 36 - 10

x = 26

Answer:

742

Step-by-step explanation:

Answer:

742

Step-by-step explanation:

just put 7x106 in a calculator

Answer:

81

Step-by-step explanation:

divide 405 by 5 to get the number of rotations per minute.

Answer:

81 spins per minute

Step-by-step explanation:

Divide 405 by 5 to get 81 <(your unit rate)

Answer:

\(\textsf{1.} \quad f(x)=(x^2-14x+85)(x^2+8x+17)\)

\(\textsf{2.} \quad f(x)=(x-4)(x^2+12x+40)\)

\(\textsf{3.} \quad f(x)=x^2-2x+65\)

Step-by-step explanation:

Given information:

For any complex number  \(z=a+bi\), the complex conjugate of the number is defined as  \(z^*=a-bi\).  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if f(x) is a polynomial with real coefficients, and (7 + 6i) is a root of f(x)=0, then its complex conjugate (7 - 6i) is also a root of f(x)=0.

Similarly, if (-4 + i) is a root of f(x)=0, then its complex conjugate (-4 - i) is also a root of f(x)=0.

Therefore, the polynomial in factored form is:

\(f(x)=1(x-(7 + 6i))(x-(7 - 6i))(x-(-4 + i))(x-(-4 - i))\)

\(f(x)=(x-7-6i)(x-7+6i)(x+4-i)(x+4+i)\)

Expand the polynomial:

\(f(x)=(x-7-6i)(x-7+6i)(x+4-i)(x+4+i)\)

\(f(x)=(x^2-14x+49-36i^2)(x^2+8x+16-i^2)\)

\(f(x)=(x^2-14x+49-36(-1))(x^2+8x+16-(-1))\)

\(f(x)=(x^2-14x+85)(x^2+8x+17)\)

Given information:

For any complex number  \(z=a+bi\), the complex conjugate of the number is defined as  \(z^*=a-bi\).  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if f(x) is a polynomial with real coefficients, and (-6 - 2i) is a root of f(x)=0, then its complex conjugate (-6 + 2i) is also a root of f(x)=0.

Therefore, the polynomial in factored form is:

\(f(x)=1(x-4)(x-(-6-2i))(x-(-6+2i))\)

\(f(x)=(x-4)(x+6+2i)(x+6-2i)\)

Expand the polynomial:

\(f(x)=(x-4)(x^2+6x-2ix+6x+36-12i+2ix+12i-4i^2)\)

\(f(x)=(x-4)(x^2+12x+36-4i^2)\)

\(f(x)=(x-4)(x^2+12x+36-4(-1))\)

\(f(x)=(x-4)(x^2+12x+40)\)

Given information:

For any complex number  \(z=a+bi\), the complex conjugate of the number is defined as  \(z^*=a-bi\).  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if f(x) is a polynomial with real coefficients, and (1 + 8i) is a root of f(x)=0, then its complex conjugate (1 - 8i) is also a root of f(x)=0.

Therefore, the polynomial in factored form is:

\(f(x)=1(x-(1+8i))(x-(1-8i))\)

\(f(x)=(x-1-8i)(x-1+8i)\)

Expand the polynomial:

\(f(x)=x^2-x+8ix-x+1-8i-8ix+8i-64i^2\)

\(f(x)=x^2-2x+1-64(-1)\)

\(f(x)=x^2-2x+65\)

Answer:

x = 7.5 units

Step-by-step explanation:

10   *   .75    = 7.5

Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

Answer:

6 1/4

Step-by-step explanation:

15 x 5/12 = 15 x 5/12 = 75/12

75/12= 6 3/12 = 6 1/4

The product of 15 and 5/12 is 25/4.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Two numbers 15 and 5/12.

The product of 15 and 5/12:

Multiplying both numbers,

15 x 5/12,

= (15 x 5)/12

= 75/12

Simplifying further,

= 25/4

Here, 25/4 can not be simplified further.

Because the GCF of 25 and 4 is 1.

Therefore, the value is 25/4.

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the solution to the equation 3/5(4x + 1) = 3(2 - 4) + 9 is x = 2.4.

3/5(4x + 1) = 3(2 - 4) + 9

12/5x + 3/5 = -6 + 9

Simplify the right-hand side: 12/5x + 3/5 = 3

To find the x term, subtract 3/5 from both sides:

12/5x = 3 - 3/5

Simplify the right-hand side:

12/5x = 2 2/5

Divide both sides by 12/5, multiplied by the reciprocal:

x = (2 2/5) / (12/5)

Simplify the right-hand side:

x = (12/5) * (12/5) = 2.4

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Here,

5 and 13 are expressions for 2x.

The symbol "=" joins these two expressions.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

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√(a² + b²)²  - 4a²b²cos²θ is the product of the lengths of the two diagonals is given by the expression.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division.

                                An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.

we have AB as a, AD as b and the angle between them is theta.

So using the cosine rule, we have

  BD = √a² + b² - 2abcosθ

So now consider the triangle ABC

Here AB is a, BC is b and the angle is 180-theta

So using cosine rule, we get AC as

   AC = √a² + b² - 2abcosθ( 180 - θ )

    AC = √a² + b² - 2ab(-cosθ )

    AC = √a² + b² - 2abcosθ

Now we have the two diagonals AC and BD. So multiplying, we get

 AC × BD = √a² + b² + 2abcosθ × √a² + b² - 2abcosθ

Simplifying, we get

AC × BD = √(a² + b² + 2abcosθ) × (√a² + b² - 2abcosθ)

AC × BD = √(a² + b²)² - (2abcosθ)²

AC × BD = √(a² + b²)²  - 4a²b²cos²θ

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Answer:

P = 15h

I hope it helps.

The value of the segment UR is 9 in the parallelogram.

One of the earliest areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The diagonal two parts after the intersection points are equal to each other. A diagonal is a sloped or slanted line that joins two polygonal vertices, and those vertices must not be adjacent edges.

The length of the diagonal can be written as:-

TU = ( 1 / 2 ) x UR

TU = ( 1 / 2 ) x 18

TU = 9

Therefore, the value of the segment UR is 9.

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The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.

When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.

Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.

We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.

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Answer:

x² ≤ 16

x²-16 ≤ 0

x²-4²≤0

(x-4)(x+4) ≤ 0

-4 ≤ x ≤ 4

B. is the right answer.

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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