The population of insects in an experiment has
been increasing by 9% each week. If there were 16
insects at the beginning of the experiment, predict
how many insects there will be after 8 weeks.
First, complete the equation:
Future Amount = 16 (1 + 0.09)
8
Now solve. Round to the nearest whole number

the interest the bond paid off is $7507.8125.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

a bond that paid 7.75% simple interest earned $3,875 interest.

S = (3875*7.75*25)/100 = $7507.8125

Hence the interest the bond paid off is $7507.8125.

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The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

/-37/, /-24/, /-6/, /2/, /18/, /23/

Answer:

C

Step-by-step explanation:

3^5 = 3*3*3*3*3

You are multiplying 5 3s

Answer:

multiply 3 factors of 5

Step-by-step explanation:

it means you're multiplying 3 five times

An equation can be written to determine the number of students that went on this trip is: C. \(\frac{1259}{s} + 12=\frac{1259}{s+9}\)

In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;

Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;

\(\frac{1259}{s} + 12=\frac{1259}{s+9}\)

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Complete Question:

A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.

However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.

Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip

What equation can be written to determine the number of students that went on this trip?

The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.

A line segment in mathematics has two different points on it that define its boundaries.

A line segment is sometimes referred to as a section of a path that joins two places.

Six-year-old students at an elementary school were given a 20-yard head start in a race. The graph shows how far the average student ran in 30 seconds.

A line graph with Distance, in yards, on the x-axis and Age of the Runner on the y-axis. The x-axis has a scale from 0 to 80 in increments of 10. The y-axis has a scale of 0 to 8 in increments of 2. A straight line connecting 20, 6, and 60, 6 is drawn.

The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.

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Answer:

the correct option is D

Step-by-step explanation:

Answer:

20 lbs of sugar per gallon as time goes to infinity

Step-by-step explanation:

Because of the statement ... as time goes to infinity...I am inclined to approach this problem using derivatives and limits

Let the amount of sugar in the tank at any time t(in minutes) be

\(S(t) \;lbs/gal\)

We have \(S(0) = 0\)  since the initial quantum of water has zero sugar

The inflow rate of sugar is given as 3  gal/min and each gallon contains 0.2 lbs of sugar
\therefore The rate of sugar increase in the tank n lbs/gal
= 0.2 lbs /gal \times 3 gal/min

=  0.6 lbs/min

Outflow rate = 3 gal/min
At any time t, the tank contains 100 gal
The amount of sugar at time t = \dfrac{S(t)}{100} lbs/gal

Therefore the outflow rate of sugar = 3 gal/min \times \dfrac{S(t)}{100} lbs/gal

= 0.03S(t) lb/min

The net rate is given by inflow rate - outflow rate

= 0.6 - 0.03S(t)

In calculus terms the net rate =  \(\dfrac{dS(t)}{dt}\)

Therefore
\(\dfrac{dS(t)}{dt} = 0.6 - 0.03S(t)\)

\(\dfrac{dS(t)}{dt} - 0.03S(t) = 0.6\\\\\)    (1)

A trick to solving differential equations of this type is to use the method of integrating factors

In general,  if we have a differential equation of the type
\(\dfrac{dy}{dx} + Py = Q\\\\\)
where P and Q are functions only of x

then the integrating factor is \(e^{\int\ {P} \, dx }\)

which you use to multiply both sides of the differential equation first

In equation (1) above,

y = S(t) which well simply write as S for convenience

Writing S' for \(\dfrac{dS(t)}{dt}\) for convenience we get equation (1) as

\(S' + 0.03S =0.6\)   (2)

From the above we see that P in the generalized differential equation corresponds to 0.03

Therefore the integrating factor is
\(\mbox {\large e^{\int 0.03dt} = e^{0.03t}}\)

Multiply equation (2) throughout by this integrating factor to get

\(\mbox{\large e^{0.03t} S' + 0.03S e^{0.03t} = 0.6 e^{0.03t} }\)

The left side is nothing but the first derivative of \(\mbox{\large (e^{0.03t}S) }\\\\\)
\(= \mbox{\large (e^{0.03t}S)'\\\\}}\)

Integrating both sides we get

\(\mbox{\large e^{0.03t}S = 0.06 \int e^{0.03t}dt}\\\\\)    (3)

\(\textrm{By using the fact that $\int e^{ax} dx = \dfrac{e^{ax}}{a} + C$}:\\\\\mbox{\large \int e^{0.03t}dt} = \dfrac{e^{0.03}}{ 0.03}} + C\\\\\)  

Therefore equation (3) becomes
\(e^{0.03t}S = 0.06 \cdot \dfrac{e^{0.03}}{0.03}} + C\\\\e^{0.03t}S = 0.06 \cdot 33.333 \cdot e^{0.03} + C\\\\e^{0.03t}S = 20 \cdot e^{0.03} + C\\\)

Dividing by \(e^{0.03} \textrm{ (same as multiplying by $e^{-0.03}$) both sides}\):

\(S = 20 + Ce^{-0.03t}\\\\\textrm{Plugging back S(t):}\\\\S(t) = 20 + Ce^{-0.03t}\\\)

We are asked to find the level of sugar content as t ⇒ ∞

At t = 0, S(t) = 0; there is no sugar content

S(0) = 0 = 20 + Ce⁰

0 = 20 + C
C = -20

\(S(t) = 20 -20e^{-0.03t}\\\\\)

As t ==>  ∞
we get

\(\lim _{x\to \infty }S\left(t\right)=\:\lim _{x\to \infty }\left(20\:-\:20e^{-0.03t}\right)=\:\:20\:-\:0\:=\:20\)

Therefore as time goes to infinity the eventual sugar content
= 20 lbs/gallon

Answer:

Tens:11,410

Ten thousand :10,000

Hundred : 11,400

From the graph, if we look for the corresponding y-value for Time = 16 hours:

The approximate number of bacteria after 16 hours is 50

Answer:

8 hours/day is the answer.

Answer:

P [ 40000 ≤ X ≤ 45000 ] =  0,02773    or  2,8 %

Step-by-step explanation:

P [ 40000 ≤ X ≤ 45000 ]  = ?

To find the probablity    P [ X ≤ 40000 ] =  ?

z(s)  = ( X - x ) / σ

z(s)= ( 40000 - 6000 )/ 8300

z(s) =  -20000/8300

z(s) ≈  - 2,41

Then

from z-table we find P [ X ≤ 40000] =  0,00820

Now again:

For  P [ X ≤ 45000 ]

z₂  = ( X - x ) / σ

z₂ =  ( 45000 - 6000 ) / 8300

z₂ = - 15000 / 8300

z₂ = - 1,8072

z₂ ≈ 1,81

From z - table

For  P [ X ≤ 45000 ] =   0,03593

Then:

P [ 40000 ≤ X ≤ 45000 ] = 0,03593 - 0,00820

P [ 40000 ≤ X ≤ 45000 ] =  0,02773    or  2,8 %

Using L'hopital we can see that the limit is equal to 1/22

Here we want to take the limit of x tending to zero for x/sin(22x)

Notice that when x = 0, both numerator and denominator are zero, so we need to take the limit of the first derivatives, for:

y = x

y' = 1

And for:

y = sin(22x)

y' = 22*cos(22x)

Now taking the limit we will get:

\(\lim_{x \to 0} \frac{1}{22cos(22x)} = \frac{1}{22cos(0)} = 1/22\)

That is the value of the limit.

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The set of input values (x-coordinates): (-7, -3, 0, 5) and the set of output values (y-coordinates): (1, 2, -2, -5) make up the domain and range of this set of ordered pairs.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input.

After we enter an x value, the function outputs this sequence of values.

So, we have the ordered pair:

{(-1, 2), (0, 5), (2, 7)}

Now, get the domain and range as follows:

The set of input values (x-coordinates): (-7, -3, 0, 5) ⇒ Domain

The set of output values (y-coordinates): (1, 2, -2, -5) ⇒ Range

Therefore, the set of input values (x-coordinates): (-7, -3, 0, 5) and the set of output values (y-coordinates): (1, 2, -2, -5) make up the domain and range of this set of ordered pairs.

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The value of m that satisfies the equation -3 + m = 9 is m = 12.

To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.

-3 + m = 9

To move -3 to the other side, we can add 3 to both sides of the equation:

-3 + 3 + m = 9 + 3

Simplifying, we have:

m = 12

Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.

None of the provided answer options (A, B, C, D) match the correct solution.

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The two numbers that add together to make -4 but subtract to make +8 are 2 and -6.

Two numbers that add together to make -4 but subtract to make +8, we can set up a system of equations.

Let's call the two numbers x and y.

We can set up the following equations:

Equation 1: x + y = -4

Equation 2: x - y = 8

To solve this system of equations, we can use the method of elimination. Adding Equation 1 and Equation 2 eliminates the variable y:

(x + y) + (x - y) = -4 + 8

2x = 4

x = 2

Now, we can substitute the value of x into either Equation 1 or Equation 2 to solve for y.

Let's use Equation 1:

2 + y = -4

y = -6

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The value of the expression a(b + c) when a = 2, b = 3, and c = 4 is 14.

Given the expression in the question:

a( b + c )

Also, a = 2, b = 3, and c = 4

To evaluate the expression a( b + c ) when a = 2, b = 3, and c = 4, we substitute these values into the expression:

Hence:

a( b + c )

Plug in a = 2, b = 3, and c = 4

2( 3 + 4 )

First, we simplify the parentheses by adding 3 and 4:

2( 7 )

Next, we multiply 2 and 7:

14

Therefore, the value of a(b + c) is 14 .

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Answer: 6/4 In simplest form is 3/2

Step-by-step explanation:

Answer:

The ratio of jumping jacks to minutes is 120:2 or 60:1. He can do 60 Jumping jacks in 1 minute

Step-by-step explanation:

Answer:

ratio: 2 to 120

He can 60 jumping jacks in one minute

Step-by-step explanation:

By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The 3 correct answers of the figures that could be the base for the pyramid that has a height of 5 inches and a volume of 60 cubic inches are:

The formula to find the base of a pyramid given its height and volume,

Volume of pyramid = (1/3) * Base area * Height

Substituting in the given values, we have:

60 = (1/3) * Base area * 5

Base area = 36 square inches

In conclusion, any figure with a base area of 36 square inches could be the base for this pyramid.

The following figures have a base area of 36 square inches:

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Answer:

18

40

41

do the operations in parentheses first according to pemdas.

The possible price for the items if the store sells $600 is (c) $40

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

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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Answer:

See below ~

Step-by-step explanation:

Given

Solving

Take Equation 1 and rewrite it so that it is equal to x.

Take Equation 2 and rewrite it so that it is equal to z.

Now, substitute these values in Equation 3.

Substitute the value of y in Equation 1.

Substitute the value of y in Equation 2.

Add the values of x, y, and z together.

Answer:

yellow, black, cyan, magenta

Step-by-step explanation:

If y = √(2x + 1), then differentiating both sides implicitly with respect to t gives

dy/dt = 1/2 • 1/√(2x + 1) • 2 • dx/dt = 1/√(2x + 1) • dx/dt

(a) If dx/dt = 9 and x = 4, then

dy/dt = 1/√(2•4 + 1) • 9

dy/dt = 1/√(8 + 1) • 9

dy/dt = 1/√9 • 9

dy/dt = 9/3

dy/dt = 3

(b) If dy/dt = 3 and x = 40, then

3 = 1/√(2•40 + 1) • dx/dt

3 = 1/√(80 + 1) • dx/dt

3 = 1/√81 • dx/dt

3 = 1/9 • dx/dt

dx/dt = 27

Answer:

Its perimeter is 23 units

Step-by-step explanation:

The perimeter of any figure is the sum of the lengths of its outline sides

The rule of the distance between two points is:

In the given figure ABCD:

Its perimeter = AB + BC + CD + DE + EA

→ Find the length of each side using the rule above

A = (-4, -2), B = (-1, 2), C = (2, 2), D = (5, -1), E = (2, -4)

→ Substitute them in the rule above to find the lengths of its sides

\(AB=\sqrt{(-1--4)^{2}+(2--2)^{2}}=\sqrt{(-1+4)^{2}+(2+2)^{2}}\\\\=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}\)

∴ AB = 5

\(BC=\sqrt{(2--1)^{2}+(2-2)^{2}}=\sqrt{(2+1)^{2}+(0)^{2}}\\\\=\sqrt{(3)^{2}+0}=\sqrt{9+0}=\sqrt{9}\)

∴ BC = 3

\(CD=\sqrt{(5-2)^{2}+(-1-2)^{2}}=\sqrt{(3)^{2}+(-3)^{2}}\\\\=\sqrt{9+9}=\sqrt{18}\)

∴ CD = \(\sqrt{18}\)

\(DE=\sqrt{(2-5)^{2}+(-4--1)^{2}}=\sqrt{(-3)^{2}+(-4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(-3)^{2}}=\sqrt{9+9}=\sqrt{18}\)

∴ DE = \(\sqrt{18}\)

\(EA=\sqrt{(-4-2)^{2}+(-2--4)^{2}}=\sqrt{(-6)^{2}+(-2+4)^{2}}\\\\=\sqrt{(-6)^{2}+(2)^{2}}=\sqrt{36+4}=\sqrt{40}\)

∴ EA = \(\sqrt{40}\)

→ Add them to find the perimeter of the figure ABCDE

∴ Its perimeter = 5 + 3 + \(\sqrt{18}\) + \(\sqrt{18}\) +\(\sqrt{40}\) ≅ 22.8098

→ Round it to the whole number

∴ Its perimeter = 23 units