The doubling period of a bacterial population is 20 minutes. At time t=120 minutes, the bacterial population was 90000.

What was the initial population at time t=0?

Find the size of the bacterial population after 3 hours.

The quotient for both the parts are 9.375 and 175.01.

What is quotient?

In arithmetic, a quotient may be a amount created by the division of 2 numbers. The quotient has widespread use throughout arithmetic, and is usually brought up because the number a part of a division, or as a fraction or a quantitative relation.

Main body:

A) 3.75/ 0.4

 first removing the decimals,

= 375/ 40

=  9.375

B) 8750.50/50

same process of removing decimals,

= 8755050/ 5000

= 175.01

Hence the value of quotient for both the parts are 9.375 and 175.01.

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The correct option regarding the residuals are given as follows:

2 negative residuals and 6 positive residuals.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Then the residuals of this data-set in the table are given as follows:

As for each point, the actual value is given and then the predicted value.

Then the numbers of each positive and negative residuals are given as follows:

Hence the first option is the correct option.

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The value of the variables x, y , z are 28.75° , 135.5°, and 44.5° respectively .

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.

When two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

Corresponding angles are equal to each other. This means that (6x/5 +10)°=z= (2x-13)°

therefore( 6x/5 +10)° =(2x-13)°

collect like terms

10+13= 6x/5-2x

23= (10x-6x)/5

multiply both sides by 5

115=4x

x= 115/4= 28.75°

z= (2x-13)°

z= 2×28.75-13

z= 57.5-13

z= 44.5

z+y= 180( sum of angles on a straight line)

y= 180-44.5

y= 135.5

therefore the values x, y , z are 28.75° , 135.5°, and 44.5° respectively .

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The sales Sam need to make $733.50 per week before taxes is $3475.

Given, Sam is paid $14 per hour plus 6% of sales.

If he worked 37.5 hours in one week, what would his sales need to make

$733.50 per week before taxes = ?

Let the sales be represented by x

Amount made from no of hours worked :

= $14 × 37.5 hours

=$525

Sales made = 6% of x

=0.06x

Total = 0.06x+$525

=$733.50

0.06x=733.50-$525

=$208.5

x=$3,475

Hence we get the required answer.

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A graph which represents the solutions of p + 1 < -1 or p - 5 > 7 is shown in the image attached below.

In Mathematics, an interval notation simply refers to a set of real numbers which consist of all the real numbers that represents a continuous function and lies between two set of numbers.

This ultimately implies that, an interval notation should be used for writing all of the subsets of a real number line (graph) as shown below:

For the first interval, we have:

p + 1 < -1

p < -1 - 1

p < -2

Therefore, in interval notation, we have:

p = {∞, -2}

For the second  interval, we have:

p - 5 > 7

p < 7 + 5

p < 12

Therefore, in interval notation, we have:

p = {12, ∞}

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Answer:

y=11x

Step-by-step explanation:

we use formula y2-y1/x2-x1 with 2 of the order pairs

22-11/2-1

11/1

11 is the slope

We find y intercept by finding when x is equal to zero and we subtract 11 until we find the 0 x unit since it goes down 11 every time

When x is zero y is zero so we write it like this

Y=11x

Hopes this helps please mark brainliest

Answer:

1

Step-by-step explanation:

anything to the power of 0 is equal to 1

Hopes this helps please mark brainliest

The dimensions of the shape will be 175 meters and 87.5 meters

The largest area that can be enclosed is 15312.5m².

Based on the information given, the equation to illustrate this will be:

2x + y = 350

y = 350 - 2x

Note that area = length × width

= x × y

We'll substitute the value into the equation. This will be:

A = x × (350 - 2x)

A(x) = 350x - 2x²

Differentiating the area, x will be 87.5

Width = 87.5m

Since y = 350 - 2x

= 350 - 2(87.5)

= 350 - 175

= 175

Length = 175m

Area = Length * Width

= 175 × 87.5

= 15312.5m²

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The solution in set builder notation is given by = {y:3>y≥-1}

Given the inequalities are,

y-1<2 ............(i)

y+2 ≥ 1 ..............(ii)

Solving the first inequality we get,

y-1 < 2

y-1+1 < 2+1, adding 1 to both sides

y < 3

Solving second inequality we get,

y+2 ≥ 1

y+2-2 ≥ 1-2

y ≥ -1

So the range is 3>y≥-1

So the solution in set builder notation is = {y:3>y≥-1}

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The linear equation is y = x+25.

What is linear equation?

An equation for a straight line is called a linear equation. The general representation of the straight-line equation is y=mx+b, where m is the slope of the line and b is the y-intercept. Linear equations are those equations that are of the first order.

Let the linear equation shown in data be written as

y = mx+b

Here, the value of m

53-45 = 8

for y,

68-60 = 8

m = 8/8 = 1

Hence,

60 = 1(45)+c

c = 25

hence, y = x +25

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Answer:

Below

Step-by-step explanation:

Since it is given this is a linear equation, we can find the slope, m, between any two points as   (y1-y2)/(x1-x2)

using the first two points  (45,60) and (53,68)  

      m = ( 60 - 68) / (45-53) = 1

 so for the slope intercept form of a line  (  y = mx + b ) we have

      y = (1) x + b     plug in any of the points to calculate 'b'  

          70 = (55) + b    shows b = 15

so you line equation becomes   y = x + 15

Answer:

D = 30/7; R =32/7

Step-by-step explanation:

First, we need to find the scale of the number line.  We can see that there are 7 ticks between 4 and 5.  Thus, we can use (5-4)/7 to find the scale which is 1/7.  

Since D is two ticks away from 4, we can use the equation:

[tex]4+2(\frac{1}{7})=D\\ 4+\frac{2}{7}=D\\ 4\frac{2}{7}=D\\ 4*7=28+2=\frac{30}{7}=D[/tex]

Since R is two ticks away from D or 30/7, we can use a similar equation:

[tex]\frac{30}{7}+2(\frac{1}{7})=R\\ \frac{30}{7}+\frac{2}{7}=R\\ \frac{32}{7}=R\\ 4\frac{4}{7}=R[/tex]

Your problem doesn't tell us whether we need to we use improper or mixed fractions, but I've included both for you.

The measures of  the angles formed by the common transversal to the parallel lines are;

1. Angle 1 = 87°

Angle 2 = 100°

2. Angle 1 = 78°

Angle 2 = 78°

Parallel lines are lines that have the same slope but pass throuh different points.

The diagram consists of parallel lines that have a common transversal, therefore;

1. The 87° angle and the Angle 1 are alternate interior angles, therefore;

87° ≅ Angle 1

87° = Angle 1

The 87° angle and the Angle 2 are same side interior angles

Therefore;

87° + Angle 2 = 180°

Angle 2 = 180° - 80° = 100°

Angle 2 = 100°

2. The 78° angle and the Angle 1 are corresponding angles, therefore;

78° ≅ Angle 1

Angle 1 = 78° (by the definition of congruency)

Angle 1 and Angle 2 are vertical angles

Therefore, Angle 1 is congruent to Angle 2 by vertical angle theorem

Angle 1 = Angle 2 by definition of congruency

Angle 1 = 78° = Angle 2

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Answer:

The answer is B false

Step-by-step explanation:

Answer:

A decimal or consecutive tenths decimals. Also 0.1 away from each other.

Step-by-step explanation:

They have decimal endings: .1 and .2

And are 0.1 away.

The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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The slope is, 1/4.

And the y - intercept is (0, -1).

What is slope and y-intercept?

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.

A y-intercept, also known as a vertical intercept, is a point in analytical geometry where the graph of a function or relation meets the y-axis of the coordinate system, employing the convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Thus,

x = 0 is satisfied at these sites.

Let the x - intercept is 4.

The x - intercept is the point on x - axis, when y = 0.

So, the x - intercept is (4, 0).

The y - intercept is -1.

y-intercept is the point on the y - axis, when x is zero.

So, the y - intercept is (0, -1).

Here we have two points (4, 0) and (0, -1).

By using these points we can find the slope.

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \frac{-1-0}{0-4}= \frac{-1}{-4} = \frac{1}{4}[/tex]

Hence, the slope is 1/4 and the y - intercept is (0, -1).

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The linear function tangent to the graph of f(x) = (x + 3)/(x - 8) at the point (0, -38) is:

y = -11x/64 - 38.

The slope-intercept representation of a linear function is given by the rule shown as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The line is tangent to the curve at point (0,-38), meaning that the line passes through point (0,-38), hence the intercept is given as follows:

b = -38.

Since the line is tangent to f(x), the slope of the line is the derivative of f(x) at x = 0.

The function f(x) is defined as follows:

f(x) = (x + 3)/(x - 8)

Applying the quotient rule, the derivative is given as follows:

f'(x) = [x - 8 - x - 3]/(x - 8)²

f'(x) = -11/(x - 8)²

At x = 0, the numeric value of the derivative is found replacing the lone instance of x by zero, hence:

f'(0) = -11/(0 - 8)² = -11/64.

Thus the equation of the tangent line to f(x) at point (0, -38) is given as follows:

y = -11x/64 - 38.

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Monthly Mortgage Payment is $495.88

Mortgage is a long-term amortized loan where loan is provided to buy certain capital asset and pay back total sum due in small periodic annuities. In Mortgage title of asset lies with lender and passes to borrower after complete mortgage payment.

Hence,

Mortgage Amount is $77,000

Monthly Payment for each $1,000 is $6.44

Monthly Mortgage Payment is $495.88

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Answer:

(3z)^3

Step-by-step explanation:

27 = 3 * 3 * 3 = 3^3

3^3 z^3   = (3z)^3

The function that represents the 6% popularity growth per month is P(x) = 500 + 0.06x

Function:

Function also known as an expression, rule, or law that defines a relationship between one variable called independent variable and another variable called dependent variable.

Given,

Before gaining popularity in the music industry, a young artist had 500 social media followers. As her popularity grew, her social media following increased at a rate of 6% per month.

Here we need to find the function that represents the given situation.

Let us consider the number of months to be modeled as x.

Then P(x) is the function that represents the situation.

And from the given question we know that, the initial population was 500.

And the population growth per month is 6%.

When we convert this percentage value into decimal then we get the growth rate as, 0.06.

Through this details, the function is written as,

P(x) = 500 + 0.06x

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Step-by-step explanation:

3x = 6y - 30

6y = (6y - 30)+ 30

6y - 6y = -30 + 30

0 = 0

y = {any rational number}

Answer:

y = 5/6x

Step-by-step explanation:

Solve for the slope of the function by using two points from the graph.

(12,10) and (6,5)

Use the slope formula

(10-5)/(12-6) = 5/6

The y-intercept is 0 because the line crosses at (0,0) at the y-axis.

y = 5/6x + 0

The probability that you select two rock concert tickets is 0.25.

What is the probability?

Probability is the branch of mathematics concerned with numerical descriptions of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, where 0 represents the event's impossibility and 1 represents certainty.

We have,

[tex]Probability =\frac{number \ of favorable outcomes}{total number \ of outcomes}[/tex]

Number of favorable outcomes  = 6

Total number of outcomes = 24

Probability rock concert tickets = 6/24

= 1/4

Probability rock concert tickets =  0.25

Hence, the probability that you select two rock concert tickets is 0.25

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Answer:

I believe this should be it,

Step-by-step explanation:

344.8572

Answer of the following questions:

As given in the question,

For a coordinate plane,

Line passes through the points (-6, 8) and (2,6).

Slope of the line = ( y₂ - y₁)/ (x₂ - x₁)

                          = ( 6 - 8) / (2- (-6))

                          = -2 /8

                          = -1/4

Slopes of the parallel line are always equal.

Equation of the line parallel to the given line and passes through (-2, -4)

is given by:

y -(-4) = (-1/4)(x -(-2))

⇒y + 4 = -x/4-1/2

⇒ y = -x/4 -9/2

y-intercept of the line which is parallel to the given line and passes through (-2, -4) is given by:

x = 0

y = -9/2 is the y-intercept.

Therefore,  answer of the questions for the given condition :

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Answer:

Step-by-step explanation:

89,83,91,92,93,x

n=6

average=91

total=91*6=546

89+83+91+92+93+x=546

448+x=546

x=546-448=98

Answer:

Step-by-step explanation:

1)

Let Andre's grade needs to be a x on his next test

Hence,

[tex]\displaystyle\\\frac{89+83+91+92+93+x}{6} =91\\\\\frac{448+x}{6} =91[/tex]

Multiply both parts of the equation by 6:

[tex]448+x=91(6)\\\\448+x=546\\\\448+x-448=546-448\\\\x=98[/tex]

2)

[tex]\displaystyle\\\frac{1000+1181+1191+1200+1268+1328+2584+x}{8} =1344\\\\\frac{9752+x}{8}=1344[/tex]

Multiply both parts of the equation by 8:

9752+x=1344(8)

9752+x=10752

9752+x-9752=10752-9752

x=$1000

3)

302, 293, 218, 330, 199, 253, 288

Arrange this series:

199, 218, 253, 288, 293, 302, 330

[tex]\displaystyle\\a)\ the \ median = \$288\\\\b) \ the\ mean =\frac{199+218+253+288+293+302+330}{7} \\\\=\frac{1883}{7} \\\\=\$269\\c)\\\\\frac{1883+x}{8} =269+5\\\\\frac{1883+x}{8} =274[/tex]

Multiply both parts of the equation by 8:

1883+x=274(8)

1883+x=2192

1883+x-1883=2192-1883

x=$309