in a biology lab, a population of 50 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.
HELP ME

The equation after the transformation is y = -5x - 1

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

Equation: 5x - y = 15

Make y the subject

So, we have

y = 5x + 15

The rule of reflection across the y-axis is

(x, y) = (-x, y)

So, we have the following equation

y = -5x + 15

The rule of translation by (3 -1) is

(x, y) = (x + 3, y - 1)

So, we have the following equation

y = -5(x + 3) + 15 - 1

Expand

y = -5x - 15 + 15 - 1

So, we have

y = -5x - 1

Hence, the equation is y = -5x - 1

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The equation g(x) = |-x-3| + 2 would reflect the function over the y-axis.

The required value of f(3) is 10.

Reflection across the y-axis is defined as reflecting a point across they = x,  the x-coordinate, and y-coordinate places, the line y = -x is the coordinates (-x, y).

So reflected across the y-axis: f(x) → f(-x),

⇒ (x,y) → (-x , y)

As per the given question,

f(x) = |x-3| + 2

f(-x) = |-x-3| + 2 = g(x)

Thus, the equation g(x) = |-x-3| + 2 would reflect the function over the y-axis.

The function f(x) is given in the question,

f(x) = 4x - 2,

To determine the value of f(3)

Substitute the value of x = 3 in the given function,

f(3) = 4(3) - 2

f(3) = 12 - 2

f(3) = 10

Thus, the required value of f(3) is 10.

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Answer: [tex]\frac{5}{6}z+\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{5}{6}z+5-\frac{1}{2}-4\\\\\frac{5}{6}z+1-\frac{1}{2}\\\\\frac{5}{6}z+\frac{1}{2}[/tex]

Approximately, water does it hold two hours later is = 248.72 liters

Given that,

The holding tank contains 1000 liters of water

Water does it hold two hours later,

Then,

1) Integrate the function, from t =0 to t = 120 minutes to obtain the number of liters pumped out in the entire interval, and

2) Substract the result from the initial content of the tank (1000 liters).

So

We can write,

Let us assume,

Integral of (6 - 6 [tex]e^{-0.13t}[/tex] ) dt  ]from t =0 to t = 120 min

= 6t + 6 [tex]e^{-0.13t}[/tex] / 0.13

= 6t + 46.1538 6 [tex]e^{-0.13t}[/tex] ] from t =0 to t = 120 min

= 6*120 + 46.1538 e^(-0.13*120) - 0 - 46.1538

= 720 + 46.1538 (1.678) - 46.1538  

= 720 + 77.44 - 46.1538 liters

= 751.28 liters

2) If the holding tank contains 1000 liters of water,

1000 liters - 751.28 liters = 248.72 liters

Therefore,

Approximately, water does it hold two hours later is = 248.72 liters

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The ordered pair that describes the location of M' is (-5, -1)

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

Point M = (5, -1)

This point can be represented as

(x, y) = (5, -1)

Also, from the question, we have the transformation to be:

Point M is reflected over the y axis

Mathematically, this can be expressed as

(x, y) = (-x, y)

So, we have

Point M' = (-5, -1)

Hence, the image is (-5, -1)

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Answer:

If you divide 32.4 by 6, then you get 5.4 as an answer

A right circular cylinder with the largest volume that can fit within a sphere with a 10 cm radius will have a maximum radius of 8.165 cm and a maximum height of 11.55 cm. Additionally, the largest volume is 2417.82 cm³.

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.

Here,

radius=10 cm

r²+h²/4=10²

r²=10²-h²/4

volume=πr²h

=π(10²-h²/4).h

V=π(10²h-h³/4)

dV/dh=π(10²-3h²/4)

dV/dh=0

10²=3h²/4

10²*2²/3=h²

20/√3=h

h=11.55 cm

r²=10²-h²/4

=10²-(10²*2²/3)/4

r²=(100-400/12)

r²=100-33.33

r²=66.67

r=√66.67

r=8.165 cm

volume=πr²h

=3.14*8.165*8.165*11.55

volume=2417.82 cm³

The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm will be 8.165 cm radius and 11.55 cm height. Also the maximum volume is 2417.82 cm³.

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For the given inequality 14 - 3f > 2 the option that comes out be correct is

f < 4 i.e option 2.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.The majority of the time, size comparisons between two numbers on the number line are made.

Here, "Less than" and "Greater than" have new meanings.

Less-than sign is the symbol for such phrase.

14 - 3f > 2

adding 3f on both sides:

14 - 3f + 3f > 2 + 3f

14 > 2 + 3f

subtracting 2 on both sides:

14 - 2 > 2 + 3f - 2

12 > 3f

dividing 3 on both sides:

(12)/3 > (3f)/3

4 > f

which means f < 4

Therefore, option 2 is correct.

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No, the sample size is not practical.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We need to find grade-point averages.

The sample mean is within 0.009 of the population mean.

98% confidence level is desired

The formula for sample size is n = (z alpha/2× S/E)²

where n = sample size

z alpha/2 = critical value for 98% confidence = 2.58

S = 1.25 and

E = 0.009

n = (2.58 × 1.25 / 0.009)² = 128401.5 ~ 128402

Sample size does not seem practical.

Hence,  the sample size is not practical.

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Step-by-step explanation:

please see the attachment

Answer:

-3 and 3

Step-by-step explanation:

Absolute value makes a negative number positive and allows a positive number to stay the same. |-3| becomes 3, and |3| stays as 3, so the correct answers are -3 and 3.

Answer: Foot

Step-by-step explanation:

The point of intersection is called the foot of the perpendicular. I remember learning this in my Math class!

The graph of the given function, g(x) = -5^x + 5, is shown below

From the question, we are to graph the given function.

From the given information,

The given function is

g(x) = -5^x + 5

To graph the function, we will determine some of the points on the line

When x = -2

g(2) = -5^(-2) + 5

g(2) = -1/25 + 5

g(2) = 4 24/25 = 4.96

When x = -1

g(1) = -5^(-1) + 5

g(1) = -1/5 + 5

g(1) = 4 4/5 = 4.8

When x = 0

g(0) = -5^(0) + 5

g(0) = -1 + 5

g(0) = 4

When x = 1

g(1) = -5^(1) + 5

g(1) = -5 + 5

g(1) = 0

When x = 2

g(2) = -5^(2) + 5

g(2) = -25 + 5

g(2) = -20

Using the above points, the graph of the function is shown below.

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The gross profit of the Blog Inc would be $22,370.

Gross profit is the profit of a company or an entity after subtracting all the costs that are related to manufacturing and selling its products or services. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that  Sales: $50,000

Returns: $4,680

Cost of goods sold: $22,950

Therefore,

Net Sales: 50,000 - 4,680

= 45,320

We can calculate the Gross Profit;

Gross Profit = (Net Sales – Cost of Goods Sold)

                      = ($45,320- $22,950)

                       = $22,370

Hence, the gross profit would be $22,370.

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Answer:[tex]5^{18}[/tex]

Step-by-step explanation:

5^18

Answer:

  No

Step-by-step explanation:

You want to know if there is enough information to claim ∆PQT ≅ ∆SRT by the HL theorem.

The HL theorem tells you right triangles are congruent if they have one leg (L) and the hypotenuse (H) congruent.

Here, the triangles are not indicated as being right triangles, so the HL theorem cannot be applied.

__

Additional comment

There is not enough information here to permit the triangles to be declared congruent.

For congruence by any theorem, we'd need to know that angle T is the largest angle in each triangle, a condition not supported by the evidence.

Though rarely (if ever) seen in congruence discussions, a claim of SSA congruence can only be supported if the angle (A) is opposite the longest side. When the angle is 90°, this is called the HL congruence theorem. When the angle is known to be obtuse, it will always be opposite the longest side.

When the given angle is opposite the shortest of the two given sides, there are two possible triangles that can be constructed. Hence congruence cannot be guaranteed between two triangles with the same SSA dimensions.

Answer: 1.00585 or 1.585. Both are correct

Step-by-step explanation:

Answer:

its 5

Step-by-step explanation:

Answer:

450x-9000

Step-by-step explanation:

You will be 9,000 dollars in debt, and it costs 300 dollars to make but sells for 750.

750-300 = 450 (profit per desk)

Answer:

8

Step-by-step explanation:

x^3/3-y

3^3/3-1

27/3-1

9-1

8

Hopes this helps please mark brainliest

Answer:

see explanation

Step-by-step explanation:

if (x - h) is a factor of f(x) then f(h) = 0

(a)

if (x - 2) is a factor of f(x) then f(2) = 0

f(2) = 2³ - 7(2) + 6

     = 8 - 14 + 6

     =  - 6 + 6

    = 0

since f(2) = 0 then (x - 2) is a factor of f(x)

(b)

using synthetic division to factor f(x)

insert a zero in the x² position on the table

 2 | 1   0   - 7   6

      ↓  2     4   - 6

     -----------------------

       1  2    - 3    0

quotient is

x² + 2x - 3 = (x + 3)(x - 1)

Then

f(x) = (x - 2)(x + 3)(x - 1)

segment EH and segment E'H' both pass through the center of dilation.

A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.

The center, which may be found within, outside, or on a figure, is the only invariant (not changing) point under a dilation (k 1).

In the figure attached, triangle EFG is shown.

H is located at (0, 1)

The center of dilation is located at (0, 2)

Then, H' is located at (0, 0), so that the distance between the center of dilation and H' is twice the distance between the center of dilation and H.

E is located at (0, 5)

Then, E' is located at (0, 8), so that the distance between the center of dilation and E' is twice the distance between the center of dilation and E.

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Answer:

x = 11

Step-by-step explanation:

8(x-3) - 4x = 20

8x - 24 - 4x = 20

4x = 44

x = 11

Answer:

x=11

Step-by-step explanation:

8(x-3)-4x=20

8(x)+8(-3)-4x=20

8x-24-4x=20

4x-24=20

   +24. +24

4x=44

/x.  /x

x=11

Hopes this helps

The formula for 7 to the power of 4 is 74 = 7 7 7 7 = 2401.

The formula for 7 to the power of 4 is 74 = 7 7 7 7 = 2401.

To do this, you must multiply both the ordinates and the powers of ten portions of the two numbers (the mantissas).

In mathematics and algebra, multiplying seven occurrences of a given number by themselves yields the number's seventh power.

Consequently, n7 = n n n n n n.

Let's write 7 to the power of 4.0.2 to the power of 4 is 0.0016 one step at a time.

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Answer:

ez 2/1

Step-by-step explanation:

The required linear equation that defines the dependent variable, p, in terms of the independent variable, t is p = 3t + 4.

A linear equation is a mathematical condition of the structure y=mx+b. including just a steady and a first-request (straight) term, where m is the slant and b is the y-catch. Sometimes, the above is known as a "straight condition of two factors," where y and x are the factors.

Let linear equation be p = at + b

Where a and b are constant.

On putting the values from the table,

4 = 0×a + b

b = 4

and,

7 = 1×a + b ⇒ a + b = 7

a + 4 = 7

a = 3

Then,

p = 3t + 4

Thus, required equation is  p = 3t + 4.

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y>-2x+4 is the inequality of the given graph.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given line passes through (2,0) and (0,4)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=4/-2=-2

4=-2(0)+b

b=4

Hence equation of line y=-2x+4

The shaded region is the above the line and line is dotted. so we have to use greater than symbol.

Hence, y>-2x+4 is the inequality of the given graph.

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Answer:

Step-by-step explanation:

Answer:

what's 2+2?

a. fish

b.3

c.4

d.6,472

Im just giving away points to anyone who needs some.

c.4

Answer: 4

Step-by-step explanation:

2+2=4