the number of cells in a specimen of bacteria doubles every hour. what type of function best represents the growth of the bacteria?

The four step to graphing the linear inequalities are: Always begin by separating the variable y from the inequality's left side, Replace the inequality symbol with the equality symbol, In XY plane, graph the boundary line from step 2, The final step is to shade a portion or one side of the border line.

In the given question we have to explain the 4 steps in graphing linear inequalities.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the inequality symbol with the equality symbol.

Step 3: In XY plane, graph the boundary line from step 2.

Step 4: The final step is to shade a portion or one side of the border line.

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Answer:

The missing value is -9

Step-by-step explanation:

Given

\(-7 = _ -(-2)\)

Required

Determine the missing value

Represent _ with a variable

\(-7 = x -(-2)\)

Open the bracket

\(-7 = x -1*-2\)

\(-7 = x + 2\)

Subtract 2 from both sides

\(-7 - 2 = x + 2 - 2\)

\(-9 = x\)

Reorder

\(x = -9\)

Hence, the missing value is -9

Answer:

The answer is 4=−2+6

Step-by-step explanation:

I checked on khan

Answer:

√61

Step-by-step explanation:

→ Find the distance between y coordinates

2 --4 = 6

→ Find distance between x coordinates

2--3 = 5

→ Find distance

√6² + 5² = √36 + 25 = √61

Answer:

25

Step-by-step explanation:

d= √l²+w²= √24²+7²= √576+49= √625= 25

Answer:

25

Step-by-step explanation:

In Pythagoras' theorem a^(2) + b^(2) = C^(2)

If we input put values, 7^(2)+24^(2)= 625

The square root of 625 is 25  

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

Let, length of the rectangle = (k) m

∴ Width becomes = (k - 11) m

We know, perimeter of a rectangle = 2(l + b)

∴ 2(l + b) = 54

⇒ (k) + (k - 11) = 27

⇒ 2k = 27 + 11 = 38

⇒ k = 19

∴ Dimensions = (k)(k - 11) = 19 m × 8 {answer}.

The first ordered pair is (850, 162.65), indicating that at a price of $162.65 per ounce, the daily demand of Virbog is 850 ounces. The second ordered pair is (1450, 132.05), indicating that at a price of $132.05 per ounce, the daily demand of Virbog is 1450 ounces.

These ordered pairs represent the relationship between the quantity demanded and the price per ounce of Virbog. It shows how the demand for Virbog changes with respect to its price.

The first ordered pair indicates that as the price per ounce increases to $162.65, the quantity demanded decreases to 850 ounces. The second ordered pair indicates that as the price per ounce decreases to $132.05, the quantity demanded increases to 1450 ounces. This information can be used to analyze the demand curve for Virbog and study its price elasticity.


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Answer:

d. vertical line

Step-by-step explanation:

A line with an undefined slope is a vertical line

Slope is the change in y over the change in x

When the slope is undefined, it means that the x does not change, which is a vertical line

Answer:

Line D

Step-by-step explanation:

Slope is defined as rise/run. Since a vertical line has zero run and infinite rise the equation is infinity/0 and anything divided by zero is undefined.

Given:

The cost y (in dollars) of renting a segway for x hours is

\(y=30x+25\)

To find:

The initial fee and the cost per hour.

Solution:

We have,

\(y=30x+25\)       ...(i)

The slope intercept form of a linear equation is

\(y=mx+b\)      ...(ii)

where, m is slope is b is y-intercept or initial value.

From (i) and (ii), we get

\(m=30,b=25\)

The value of m is 30, so the slope is 30. It means cost per hour is $30.

The value of b is 25, so y-intercept is 25. It means the initial fee is $25.

Answer:

Step-by-step explanation:

Let x be the hours Mary rented the bike.  Her total cost would be the sum of the $16 up-front service charge plus x (hours) times $6/hour, to account for the rental time.  We can write that as:

$16 +( $6/hr.)x = $66

16 + 6x = 66

6x = 50

x = (50/6) hours

x = (25/3) hours

x = 8 1/3 hours

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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The answer of the given question is positive linear relationship.

If the value of the sample covariance between the two random variables x and y equals 14.67, then we can conclude that x and y have a positive linear relationship.

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If the value of the sample covariance between the two random variables x and y equals 14.67, we can conclude that x and y have a positive linear relationship or association

Covariance measures the direction and strength of the relationship between two variables. A positive covariance indicates that as the values of x increase, the values of y tend to increase as well, and vice versa. In other words, there is a tendency for the variables to move in the same direction.

However, the value of covariance alone does not provide information about the strength or the exact nature of the relationship. To determine the strength and statistical significance of the relationship, additional analysis, such as calculating the correlation coefficient or performing hypothesis tests, may be necessary.

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Answer:

the length of the diagonal is 10cm

Step-by-step explanation:

C²=8²+6²

C²= 64+36

C²=100

√C²=√100

C=10cm

Plot the vertex at (0,-3), then go down 2 units and right units to plot a point at (5,-5). Then you can draw your line through the 2 points.

Given:

A transformation was performed on PQRS to form P'QʻR'S'.

To find:

The transformation.

Solution:

The given graph shows two similar polygons. It means, dilation was performed.

From the given graph it is clear that,

\(PS=2\) units

\(P'S'=1\) units

Now,

\(\text{Scale factor}=\dfrac{P'S'}{PS}\)

\(\text{Scale factor}=\dfrac{1}{2}\)

A dilation factor of \(\dfrac{1}{2}\) was performed on PQRS to form P'QʻR'S'.

Therefore, the correct option is (3).

The factor of x³ 2x² 5x 6 is (x-2)(x+3)(x-1). This means that x³ 2x² 5x 6 can be factored into three linear factors, each of which is a linear expression with one term. The three factors are (x-2), (x+3), and (x-1).

Divide the x³ term by the x term to get x².

Divide the 2x² term by the x term to get 2x.

Subtract the 5x term from the 2x term to get -3x.

Subtract the 6 term from the -3x term to get -3x-6.

Factor the x² term to get (x+2)(x-2).

Factor the -3x-6 term to get (x+3)(x-1).

Combine the two factors to get (x-2)(x+3)(x-1).

The factor of x³ 2x² 5x 6 is (x-2)(x+3)(x-1). This means that x³ 2x² 5x 6 can be factored into three linear expressions, each with one term. To factor this equation, we first divide the x³ term by the x term to get x², then divide the 2x² term by the x term to get 2x. Next we subtract the 5x term from the 2x term to get -3x, and subtract the 6 term from the -3x term to get -3x-6. We then factor the x² term to get (x+2)(x-2), and the -3x-6 term to get (x+3)(x-1). Finally, we combine the two factors to get (x-2)(x+3)(x-1).

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Answer:

16,6

Step-by-step explanation:

OK so I used the Sine Rule

(10÷Sin37) = (X÷Sin90) [Then cross multiply]

10Sin90 = XSin37

(10Sin90 ÷Sin37) = X = 16,62

Answer:

4188.79

Step-by-step explanation:

Formula for volume of a sphere: let V be volume and r be diameter:

V=(4/3)pi(r)^3

Pi can be written as 3.141593

The domain and range is Domain: All real numbers; Range: All real numbers, and option A is the correct answer.

The range of values that can be plugged into a function is known as its domain.

With a function like f, this set represents the x values (x).

The collection of values that a function can take on is known as its range. This collection of values after we enter an x value, that the method returns. Those are the values for y.

The domain of the function represents all the input values, that is all the c x-coordinates on the graph.

Here, the domain is:

Domain: R (all real numbers as the graph is continuously expanding)

The range of the function represents all the output values, that is all the y-coordinates on the graph.

Here, the range is:

Range: R(all real numbers)

Hence, the domain and range is Domain: All real numbers; Range: All real numbers, and option A is the correct answer.

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Given: A 180 degree rotation of a vertical angle will always map to the other vertical angle

To Determine: The prove that the vertical angles are congruent

Draw and label to vertical lines with an angle

The 180 degree rotation of the vertical angle BOC would give:

Note that the other vertical would be AOD

The students should respond that

Hence, the 180 degree rotation of a vertical angle will always map to the other vertical angle which are congruent to each other because:

The vertical angles are vertically opposite to each other

Answer:

4×(-3)=12,3×(-1)=-3;+3,c=-2

Answer: The person above me is correct. Here is a picture if you still dont get it..

Step-by-step explanation:

Using the hypergeometric distribution, it is found that the distribution is:

P(X = 0) = 0.0152

P(X = 1) = 0.1818

P(X = 2) = 0.4545

P(X = 3) = 0.3030

P(X = 4) = 0.0455

Hence:

A) There is a 0.0455 = 4.55% probability that all selected rats are female.

B) There is a 0.1818 = 18.18% probability that only one of the selected rats is female.

C) There is a 0.803 = 80.3% probability that at least two of the selected rats is female.

D) The mean of the probability distribution is of 2.18.

E) The standard deviation of the probability distribution is of 0.833.

The rats are chosen without replacement, hence the hypergeometric distribution is used to solve this question.

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The distribution is the probability of each outcome, hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,11,4,6) = \frac{C_{6,0}C_{5,4}}{C_{11,4}} = 0.0152\)

\(P(X = 1) = h(1,11,4,6) = \frac{C_{6,1}C_{5,3}}{C_{11,4}} = 0.1818\)

\(P(X = 2) = h(2,11,4,6) = \frac{C_{6,2}C_{5,2}}{C_{11,4}} = 0.4545\)

\(P(X = 3) = h(3,11,4,6) = \frac{C_{6,3}C_{5,1}}{C_{11,4}} = 0.3030\)

\(P(X = 4) = h(4,11,4,6) = \frac{C_{6,4}C_{5,0}}{C_{11,4}} = 0.0455\)

Item a:

P(X = 4) = 0.0455, hence:

There is a 0.0455 = 4.55% probability that all selected rats are female.

Item b:

P(X = 1) = 0.1818, hence:

There is a 0.1818 = 18.18% probability that only one of the selected rats is female.

Item c:

\(P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.4545 + 0.3030 + 0.0455 = 0.803\)

There is a 0.803 = 80.3% probability that at least two of the selected rats is female.

Item d:

The mean of the hypergeometric distribution is:

\(\mu = \frac{nk}{N}\)

Hence:

\(\mu = \frac{4(6)}{11} = 2.18\)

The mean of the probability distribution is of 2.18.

Item e:

The standard deviation of the hypergeometric distribution is:

\(\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}\)

Hence:

\(\sigma = \sqrt{\frac{4(6)(11-6)(11-4)}{11^2(11-1)}} = 0.833\)

The standard deviation of the probability distribution is of 0.833.

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Answer:

18.49 ounces

Step-by-step explanation:

The derivate of f(y) is -9y^6 - 33y^4 + 84y^2.

To differentiate the given function f(y), we will use the product rule and the chain rule of differentiation. Let's break down the function into two parts:

f(y) = (1 y^2 - 9 y^4) * (y + 3y^3)

Using the product rule, we can differentiate each part separately:

f'(y) = (1 y^2 - 9 y^4)' * (y + 3y^3) + (1 y^2 - 9 y^4) * (y + 3y^3)'

The derivative of the first part is:

(1 y^2 - 9 y^4)' = 2y - 36y^3

Now we need to differentiate the second part using the chain rule. Let's call the inner function u:

u = y + 3y^3

Using the power rule, the derivative of u with respect to y is:

u' = 1 + 9y^2

Now we can substitute these values back into our original equation:

f'(y) = (2y - 36y^3) * (y + 3y^3) + (1 y^2 - 9 y^4) * (1 + 9y^2)

Simplifying further:

f'(y) = 2y^2 + 6y^4 - 36y^4 - 108y^6 + y^2 + 9y^4 - 9y^6 + 81y^2

Combining like terms:

f'(y) = -9y^6 - 33y^4 + 84y^2

Therefore, the derivative of f(y) is -9y^6 - 33y^4 + 84y^2.

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Answer:

  a) 56.25 mph

  b) $1.59/lb

Step-by-step explanation:

The units of the "unit rate" tell you the math operation you need to perform.

Miles per hour (mi/h) is found by dividing miles by hours.

  (450 mi)/(8 h) = (450/8) mi/h = 56.25 mi/h

Dollars per pound ($/pound) is found by dividing dollars by pounds.

  ($7.95)/(5 pounds) = (7.95/5) $/pound = 1.59 $/pound

__

Additional comment

In the context of unit rates, "per" means "divided by."

What makes a rate a "unit rate" is the "1 unit" in the denominator. For miles per hour, the denominator is 1 hour. For dollars per pound, the denominator is 1 pound.

It would take a total of, 3,461,934 drops of rain to fill a 50-gallon rain barrel.

To determine how many drops of rain it would take to fill a 50-gallon rain barrel, we need to first convert the volume of the rain barrel to milliliters. One gallon is equal to approximately 3785 milliliters, so a 50-gallon rain barrel is,

3785 * 50 = 189,250 milliliters.

If it takes 202020 drops of rain to make 111 milliliters, then it would take approximately 189,250 / 111 = 1,697 sets of 202020 drops to fill a 50-gallon rain barrel.

Thus, it would take a total of 1,697 x 202020 = 3,461,934 drops of rain to fill a 50-gallon rain barrel.

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Step-by-step explanation

ten plus x multiplied by seven is equal to fourteen divided by X

Step-by-step explanation:

25 min. to get to the library

1-hour story = 60 min.

25 min. to go back home

25 + 25 + 60 = 110 min.

110. min = 1.83333 hrs.

9:15 am + 1.83333 = 10.98333 am

98 - 60 = 38

60 = 1 hr. -----> 60 + 60 = 120 minutes -----> 2 hrs.

11: 38 am

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