A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant "k" for the bacteria? (Round k to two decimal places.)

The amount in the account at the end of 1 year is $5400.

The amount in the account at the end of 2 year is $5832.

What do you mean by interest rate?

The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.

According to data in the given question,

We have:

Deandre places $5000 in an account that pays 8% interest compounded each year.

And no withdrawals are made from the account.

Now, we need to determine the amount of 8% interest on the $5000,

[tex]=\frac{5000}{100}*8\\ =400[/tex]

Then, the amount in the account at the end of 1 year =$5000+$400

=$5400.

Now, we need to determine the amount of 8% interest on the $5400,

[tex]=\frac{5400}{100}*8\\ =432[/tex]

So, the amount in the account at the end of 2 year =$5400+$432

=$5832.

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Answer:

Volume of a pyramid with a sqaure base is 14.5 ft³.

The perimeter of a form represents the gap around it, the vicinity of a form is the surface or flat area that the shape covers (in 2D) even as the quantity of a form is the distance it occupies in actual lifestyles (in 3D).

The perimeter of the base is 8.7ft

The length of the side of the base is:

8.7÷4=2.175 ft

The area of the base

S=(2.175)² =4.730625 ft²

The volume of the rectangular pyramid =

V= 1/3 × area of its base ×area of heights

V = 1/3 × 4.730625 ×9.2

V≅ 14.3 ft³

Hence, the volume of a square base is 14.3 ft³.

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The sale price is $13.5 and discount is $1.5.

A price that is lower than the usual price.

Given that, a store sells a shirt at $15, and there is a discount of 10%.

Price reduced after discount = 10% of 15 = $1.5

Selling price = 15 - 1.5 = $13.5

Hence, The sale price is $13.5 and discount is $1.5.

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Answer:

Step-by-step explanation:

2/3 = 1/2x

2/3 / 1/3 = x

x = 4/3

Answer: The answer is 4/3

Step-by-step explanation: I have my ways ;>

The table that represents a function is the table in the top left corner.

A function is a relation between two variables x and a y, that maps the elements of the domain (possible values of x) into the elements of the range (possible values of y).

Such that each element in the domain is mapped into only one element of the range.

For example, if you look at the second option you can see the ordered pairs (4, 0) and (4, 1).

The element x = 4 is being mapped into two different values of y, then this is not a function.

The only table where no element of the domain is repeated is the first table, so that is the correct option.

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The value in fraction form is 2/5

From the question, we have

1/2 x 4/5

=2/5

The value in fraction form is 2/5

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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There will be 35 chocolate bar cut out from the 13-meter chocolate bar.

Division is breaking a number up into an equal number of parts.

Given that, Willy Wonka makes a 13-metre chocolate and the chocolate bar is then cut into 4/11 of a metre.

Number of bars made = 13/4/11 = 35.75 ≈ 35

Hence, There will be 35 chocolate bar cut out from the 13-meter chocolate bar.

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The straight line has the equation, y = 5x - 4.

A straight line is made up of an infinite number of points that are joined on both sides of the point.

Any straight line's slope 'm' is given by:

m = y2 - y1 / x2 - x1

In slope-intercept form, a linear equation has the formula y = mx + b. The variables in the equation are X and Y. The values m and b represent the slope (m) of the line and the value of y when x = 0.

The obtained points from the graph are (0,-4) and (1,1)

The slope is ,

m = 1-(-4) / 1-0

   = 5/1

   = 5

Because it intersects the y-axis at the point where the intercept C = -4,

The line's equation will be:

⇒ y = mx + c

⇒ y = 5x + (-4)

⇒ y = 5x - 4

As a result, the equation for the straight line shown below is y = 5x - 4.

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Applying the exterior angles and triangle sum theorems, the statements that are true are:

C. m∠5 + m∠6 = 180°

D. ∠2 + m∠3 = m∠6

E. m∠2 + m∠3 + m∠5 = 180°

All three interior angles of a triangle is equal to a sum of 180 degrees, based on the triangle sum theorem, while the exterior angle theorem states that the exterior angle of a triangle is equal to the two remote interior angles of the triangle.

Given the image showing the triangles and its exterior angles, the following can be deduced:

m∠2 + m∠3 + m∠5 = 180° [based on the triangle sum theorem]

m∠2 + m∠3 = m∠6 [based on the exterior angles theorem]

m∠5 + m∠6 = 180° [based on the triangle sum theorem]

Therefore, the true statements are:

C. m∠5 + m∠6 = 180°

D. ∠2 + m∠3 = m∠6

E. m∠2 + m∠3 + m∠5 = 180°

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Answer:

Take away the equal sign , track the graph ( solid or dotted ) , determine the inequality sign by seeing the direction in graph are the few steps to be known while writing an inequality

Step-by-step explanation:

Linear inequalities are two mathematical expressions that are compared using the inequality symbol. The expression could be either just one or both numerical and algebraic.

Few steps which we need to know while writing an inequality

1. Identify the line's equation. Once we take away the equal sign, this gives us the fundamental shape of our inequality.

2. Keep track of whether the line is solid or dotted. Remember that in an inequality, solid lines denote ≤ or ≥ and dotted lines denote < or >.

3. Determine which direction your inequality sign will face by using the shading on the graph.

Take away the equal sign , track the graph ( solid or dotted ) , determine the inequality sign by seeing the direction in graph are the few steps to be known while writing an inequality

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Answer: Lenny = 12.5%

Leo = 15%

Candice = 10%

Josie = 20%

Step-by-step explanation:

Lenny = (18-16)/16 = 0.125

Leo = (11.5-10)/10 = 0.15

Candice = (13.2-12)/ 12 =0.1

Josie = (24-20)/20 = 0.2

For percentage, multiply each number by 100

Answer:

Graph the order pair (0,2)

Step-by-step explanation:

(0,2) is the y-intercept.  This is where the graph crosses the y axis.  From that point, you would then go down 4 and right 3.  That is what the slope tells you.  You would be at the point( (-4, 5).  Now that you have two points, you would draw a straight line through them.

Answer: 12 inches

Step-by-step explanation:

Answer: 15 cm

Step-by-step explanation:

Answer: 36 cm= 8, 112 cm=1.25, 183.75 cm= 12.25

The Punnett square is a square diagram that is used to predict the genotypes of a particular cross or breeding experiment.

The genotypes of a certain cross or breeding experiment are predicted using the Punnett square, a square diagram. It bears Reginald C. Punnett's name, who developed the method in 1905. Biologists use the graphic to estimate the likelihood that a child will have a specific genotype.

The likelihood that a cross would produce children with a specific genotype is represented by a Punnett square. It does not depict live children. For instance, the Punnett square in Figure 3 demonstrates that there is a 25% chance that the cross Aa x Aa will produce homozygous recessive offspring.

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The pressure is 38.5 Newton per square meter (N/m²)

Temperature can be defined as the quantity that is used to measure the degree of hotness or coldness of a body in °Kelvin or ° Celsius.

When the pressure of a glass varies directly with the temperature, this means that once there is an increase in temperature there should be an increase in pressure of the medium too.

To calculate the new pressure the gas formula is used;

Where,

P1 = 18.9N/m²

T1 = 90k

V1 = 20m³

T2 = 110k

V2 = 12m³

P2 = X

P1V1/T1 = P2V2/T2

Make P2 the subject of formula;

P2 = P1V1T2/T1V2

P2 = 18.9×20×110/90×12

P2 = 41580/1080

P2 = 38.5 N/m²

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Side-Angle-Side Theorem can be used to prove the congruency

What is theorem ?

A statement that has been proven or that can be proven is referred to in mathematics as a theorem. A logical argument is used to demonstrate a theorem using the deductive system's inference rules, demonstrating how the theorem follows logically from the axioms and other theorems that have already been proven.

The Side-Angle-Side Theorem (SAS) states that two triangles are congruent if two sides and the angle between those two sides of one triangle are equal to two sides and the angle between those two sides of another triangle.

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The points of concurrency of perpendicular bisectors of triangle is circumcenter.

A point of concurrency shared by three or more lines is referred to as a single point of concurrency. Constructed lines in triangle interiors are excellent places to look for points of convergence.

When you construct a triangle's medians, perpendicular bisectors, angle bisectors, or altitudes, you create a point of concurrency for each of them.

Because the triangle can have four distinct types of line segments, it can have four distinct points of convergence. Each point of concurrency represents the intersection of a particular type of line segment: centroid, circumcenter, incenter, and orthocenter.

Thus, the points of concurrency of perpendicular bisectors of triangle is circumcenter.

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Answer:

BM = 20m

YZ = 13m

m∠B = 39

m∠M = 34

m∠Y = 107

Step-by-step explanation:

CM = 16m

BM = 20m

YZ = 13m

m∠B = 39

m∠M = 34

m∠Y = 107

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The balance in the account after 15 years is $6, 269.73.

The balance on the account after 15 years is referred to as the future value of the account. To find this future value, the future value formula can be used which is:
Future value = Amount invested x ( 1 + Periodic rate ) ^ number of periods

Amount invested = $4, 000

Periodic Rate = 3% APR / 12 months in year = 1/4 %

Number of periods = 15 years x 12 months = 180 months

The balance in the account after 15 years is:

= 4, 000 x ( 1 + 1/4 %) ¹⁸⁰

= 4, 000 x 1.0025 ¹⁸⁰

= $6, 269.73

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The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.

Given, a destroyed angle

A destroyed angle is called a figure in Geometry also known as Rectangle.

A rectangle is a quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.

So, A destroyed angle is the quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.

Therefore, the destroyed angle is a rectangle.

Hence, The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.

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The slope of the line is - 3

The equation of the line is given by,

3x + 1y = 3

y = -3x + 3  ---(1)

The  slope- intercept form of a line is given by ,

y = mx + c    ---(2)

where ,m is the slope

c  is the y intercept

Comparing (1) and (2)

The slope of the line is , m = -3

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Answer:

If p=3 and q-5,find

p+q+2

3+(-5) +2

= 0

Step-by-step explanation:

The center of the circle is (-9, -6).

What is the center of the circle?

A circle's center is the point from which all of the distances to the other points on the circle are equal. The radius of the circle is the measurement at issue.

Here, we have

The equation of a circle is written as:

(x - h)² + (y - k)² = a²

Where (h, k) is the center and a is the radius of the circle.

Where (h, k) is the center and a is the radius of the circle.

(x + 9)² + (y + 6)² = 10² (Given)

From the equation, the center of the circle is (-9, -6)

The radius of the circle is 10.

In general form, the equation can be written as

x² + 18x + 81 + y² + 12y + 36 = 100

x² + y² + 18x + 12y + 17 = 0

Hence, the center of the circle is (-9, -6).

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An isosceles triangle therefore has both two equal sides and two equal angles.

What is traiangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

What is isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the previous illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg).

An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal. Therefore, an equilateral triangle is a specific example of an isosceles triangle that has equal sides and angles on all three of its faces. The isosceles right triangle is yet another unique instance of an isosceles triangle.

The Pythagorean theorem can be used to determine the height of the isosceles triangle shown in figure:

[tex]h = \sqrt{b^2-\frac{1}{4}a^2 }[/tex]

Consequently, the region is given by:

A=1/2ah

A = [tex]\frac{1}{2}a\sqrt{b^2-\frac{1}{4}a^2 }[/tex]

[tex]A = \frac{1}{2}a^2\sqrt{\frac{b^2}{a^2}-\frac{1}{4} }[/tex]

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Answer:

y=3x+6

Step-by-step explanation:

the equation of a line in

slope-intercept form

is.

xy=mx+b

The range and the domain of the function f(x) =  1 - x^2 is less than or equal to 1 and all values of x are a real number (R).

Domain: x ∈ R

Range: f ( x ) ≤ 1, ∈ R

f ( x ) = 1 − x^2 is defined for all Real values of x, and therefore the domain is all real values ( R ).

x^2 has a minimum value of 0 (for x ∈ R ) and therefore − x^2 has a maximum value of 0 and − x^2 + 1 = 1 − x^2 has a maximum value of 1.

Therefore f (x) has a maximum value of 1 and the range of f ( x ) is ≤ 1.

So, the range of f(x)≤ 1, and the domain is all real values ( R ).

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Answer:

Step-by-step explanation:

i just need the points bro

A system of linear equation can have three possible types of solutions

(i) infinite solutions

(ii) No solution

(iii) One distinct Solution

Though a linear equation can have any one of the above three number of solutions but Linear equations mostly have One distinct solution.

A system of quadratic equations with coefficients being real or complex have two solutions. The two solutions can further be:

(i) Real and distinct

(ii) Real and same

(iii) Imaginary  and Distinct

For a quadratic equation the roots can be found out by 2 ways;

Either by factorizing the middle term such that the product of the factors is equal to the product of the a and c.

Where,

f(x) = ax²+bx+c

OR

By using the formula given below:

Solution = ±[tex]\frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex]

where one root is [tex]\frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex] while the other is[tex]-(\frac{-b + \sqrt{b^2 - 4ac} }{2a})[/tex]

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I will choose retirement plan 1, which will give me a future value of $600,000 when I retire at 55 years, and not Plan 2's $358,426.60.

The future value of Retirement Plan 1 is the product of the multiplication of the annual payment for each year of service and the number of service years before retirement.

The future value of Retirement Plan 2 is worked out using an online finance calculator by compounding the present value (deposit) into the future.  It can also be computed using the FV factor of 18% for 30 years.

However, the choice of retirement plan depends on three factors: service years, periodic deposits, and compounding rate.

If the worker retires above 60 years, Retirement Plan 2 will be more favorable.  Similarly, if Retirement Plan 2 compounds more than yearly, it will offer a better choice than Retirement Plan 1.

Lastly, if Retirement Plan 2 makes a yearly deposit of $2,500 into the savings account, it will offer a far better option than Retirement Plan 1.

The number of years worked at 55 years = 30 (55 - 25)

Retirement plan 1's future value = $600,000 ($20,000 x 3)

Retirement plan 2's future value =  $358,426.60

N (# of periods) = 30 years

I/Y (Interest per year) = 18%

PV (Present Value) = $2,500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $358,426.60

Total Interest = $355,926.6

Thus, given the plan requirements and based on their future values,  Retirement Plan 1 should be chosen.

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Which retirement plan do you choose, assuming you retire at 55 years?