Alan deposited $300 into a savings account. At the end of the first year the amount of money in the account has increased to $336. At the end of the second year he had $420. A) Find a percent increase in the amount of money in the savings account at the end of the first year. b) find the percent increase in the amount of money in his savings account from the end of the first year to the end of the second year

Answer:

you will multiply the new price plus the original price

Answer:

It's around 459. So 460 if need to round

Step-by-step explanation:

So, 40 randomly chosen people do not represent  the whole school, but using the ratio 27:40 you are given in the equation, you can divide the number of students (680) by the surveyed students (40) to get 17. What this means is there is 17 groups of 40 in the school, so to distribute the amount of people who are in a after-school activity, you must multiply 17 x 27 to get the assumption of about 459 kids. Hopefully you understand =)

Answer:

B. 7/16

Step-by-step explanation:

The answer to this question is the option whose value is closest to 1/2.

We know that the fraction 1/2 is 0.5, now we have to get that fraction out of all these fractions that is closest to the value 0.5

10/12 = 0.833

7/16 = 0.43

2/9 = 0.222

1/8 = 0.125

The value closest to 0.5 is obviously 0.43 from the above. Therefore we can conclude that the fraction 7/16 is closets to 1/2 given these other fractions.

Thank you!

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Answer:

$399.98

Step-by-step explanation:

Given

Mark down percent = 60%

Mark down price = $239.99

Required

Original price of the rack

Let x be the original price of the product. The equation to get x is as expressed below;

60% of x = 239.99

0.6x = 239.99

x = 239.99/0.6

x = 399.98

Hence the rack will ring up for $399.98 at the register

Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

The value of f(15) is approximately 346.42.

An exponential function is a mathematical function of the form f(x) = abˣ, where a and b are constant and b is greater than zero and not equal to 1. An example is f(x) = 2ˣ

We can use the properties of exponential functions to find the value of f(15). Since f(x) is an exponential function, we can write it in the form:

f(x) = a × bˣ

f(4.5) = 16 = a × b⁴.5

f(9.5) = 60 = a × b⁹.5

Dividing second equation by first equation gives:

f(9.5)/f(4.5) = (a × b⁹.5)/(a × b⁴.5) = b⁵

Substituting the given values, we get:

60/16 = b⁵

b = (60/16)¹/⁵

b ≈ 1.46

Substituting b into the first equation gives:

16 = a × 1.46⁴.5

a ≈ 0.30

Therefore, the exponential function is:

f(x) = 0.30 × 1.46ˣ

To find f(15), we can substitute x = 15 into the function:

f(15) = 0.30 × 1.46¹⁵

f(15) ≈ 346.42

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Answer: 310

Step-by-step explanation:

1.Find your constant difference of the sequence by subtracting from left to right which is 9

2. find your fomula by using Tn=bn+C (b is your constant difference you can find C by C=T1 -b ) which will then give us 9n-5

3. T(35)=9n-5=9(35)-5=310

The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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The velocity vector (-2, -2) points in the direction of the line joining the point (7, -4) to the point (5, -3).

To determine the direction in which the particle is moving as it passes through the point (3, -2), we need to find the velocity vector of the particle at that point.

The velocity vector is given by the derivative of the position vector with respect to time:

v(t) = (x'(t), y'(t))

where x'(t) and y'(t) are the derivatives of x(t) and y(t) with respect to t, respectively.

Taking the derivatives of x(t) and y(t), we get:

x'(t) = -2

y'(t) = 2t

So the velocity vector at time t is:

v(t) = (-2, 2t)

To find the velocity vector at the point (3, -2), we substitute t = -1 into the expressions for x(t) and y(t), since the particle passes through the point (3, -2) at time t = -1:

x(-1) = 5 - 2(-1) = 7

y(-1) = (-1)2 - 3 = -4

So the particle is at position (7, -4) when it passes through the point (3, -2).

Substituting t = -1 into the expressions for x'(t) and y'(t), we get:

x'(-1) = -2

y'(-1) = 2(-1) = -2

So the velocity vector at the point (7, -4) is:

v(-1) = (-2, -2)

The velocity vector (-2, -2) points in the direction of the line joining the point (7, -4) to the point (5, -3), which is to the left and slightly down from the point (7, -4). Therefore, the particle is moving in a direction that is slightly to the left and slightly down as it passes through the point (3, -2).

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answer

the number of buses is 3

the number of cars is 6

Step-by-step explanation:

total number of the students=165

total number of the vehicles=9

let x represent the number of cars

let y represent the number of buses

x+y=9...........equation 1

(the number of the cars plus the number of the buses= to the number of vehicles )

5x + 45y=165.......equation 2

(the number of student the car can hold plus the number of student the bus can hold= to the total number of the student in a class)

x+y=9.......eqn 1

5x +45y=165....eqn 2

make x the subject of the formula in eqn 1

x+y=9

x= 9-y

substitute for x= 9-y in eqn 2

5(9-y)+45y=165

45-5y+45y=165

-5y+45y=165-45

40y=120

divide both sides by 40

40y÷40=120÷40

y=3

since y represent number of buses,the numbet of bus is 3

Also,substitute for y=3 in eqn 1

eqn 1 is x+y=9

x+3=9

x=9-3

x=6

therefore,the number of cars is 6.

Answer:

49 $1 coins

Step-by-step explanation:

x is the number of $2 coins

2x + 1(3x - 5) = 85

5x - 5 = 85

5x = 90

x = 18

So there are 49 $1 coins

\( \boxed{ \sf{Area \: = 57 \: {cm}^{2} }}\)

\( \boxed{ \sf{Perimeter = 34 \: cm}}\)

See workings in the attached picture !

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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Answer:

A. 7950 sq. ft

Step-by-step explanation:

Volume of trailer = volume of a cuboid

Volume =  l × w × h

Volume = 53 × 15 × 10 = 7950

Answer:

y = 2*x + 5

Step-by-step explanation:

En este problema tenemos los datos de una tabla, y supongo que queremos encontrar la funcion que esta siendo representada por esta tabla.

La tabla es:

x:  -2   -1   0   1   2   3

y:   1    3   5   7   9   11

Esto parece ser una relación linear, las cuales se escriben como:

y = a*x + b

Donde a es la pendiente y b es la ordenada.

Si sabemos que la linea pasa por los puntos (x₁, y₁) y (x₂, y₂), entonces la pendiente será:

a = (y₂ - y₁)/(x₂ - x₁)

Entonces lo primero que debemos chequear es si utilizando distintos puntos de esa tabla obtenemos la misma pendiente, lo que significaría que los datos de la tabla se corresponden con una relación linear.

SI usamos los primeros dos puntos de la tabla, que son (-2, 1) y (-1, 3) la pendiente es:

a = (3 - 1)/(-1 - (-2)) = 2/1 = 2

Ahora si utilizamos por ejemplo el segundo y tercero, que son (-1, 3) y (0, 5) entonces la pendiente es:

a = (5 - 3)/(0 - (-1)) = 2/1 = 2

Ya vimos que para dos pares de puntos distintos la pendiente es igual a 2, entonces podemos concluir que la ecuación va a ser algo como:

y = 2*x + b

Para encontrar el valor de b, podemos usar cualquiera de los puntos de la tabla.

Si usamos el segundo punto, (-1, 3)

esto significa que cuando x = -1, tenemos y = 3

Si reemplazamos esos dos valores en la ecuación de arriba, obtenemos:

3 = 2*-1 + b

3 = -2 + b

3 + 2 = b

5 = b

Entonces la ecuación es:

y = 2*x + 5

The correct response is d) All the above. The arithmetic mean is equal to the median, the median is equal to the mode, and the mode is equal to the arithmetic mean.

If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.

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The standard deviation needed to achieve a process capability index of 2.0 is 0.003 feet.

To calculate the required standard deviation to achieve a process capability index of 2.0, we need to use the following formula:

Process Capability Index (Cpk) = (Upper Specification Limit - Lower Specification Limit) / (6 * Standard Deviation)

In this case, the upper specification limit is 1.788 feet, the lower specification limit is 1.752 feet, and the process capability index (Cpk) is 2.0.

Let's plug in the values into the formula and solve for the standard deviation:

2.0 = (1.788 - 1.752) / (6 * Standard Deviation)

Rearranging the equation:

Standard Deviation = (1.788 - 1.752) / (6 * 2.0)

Standard Deviation = 0.036 / 12

Standard Deviation = 0.003

Therefore, the standard deviation needed to achieve a process capability index of 2.0 is 0.003 feet.

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Answer:

lil ***** where ya mom at

Step-by-step explanation

lol

Answer: 90 sqare meters

Step-by-step explanation: you have to take 972 and divide it by 10.8 then you get your answer

The university administration should not trust the results from this study as it did not take a random sample.

The appropriate question to ask in order to assess the evidence provided by the sample data is, "How likely is it to observe a difference of 0.09 or more extreme if there is no difference in the mean GPA for male and female scholarship athletes?"

This is because the sample data shows a difference of 0.09, so we want to find out how likely it is to observe a difference of this size or greater, given that there is no actual difference between the GPA of male and female scholarship athletes.
Based on the investigation that the professor conducted which revealed that the study was given to all of the athletes on the basketball teams exclusively, the university administration should not trust the results from this study.

This is because the study was not taken from a random sample of scholarship athletes, meaning that the sample did not accurately reflect the population. If the sample does not accurately reflect the population, then the results may be biased and should not be trusted.

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answer:

the answers are undefined and zero ( and in that order )

step-by-step explanation:

for question 12,

x = 10

since that equation is just a vertical line, the slope is undefined!

but for question 13

y = -5

the equation is just a horizontal line rather then a vertical line, the slope is zero ( since it is not moving )

i hope this helps you and if you need anymore help then please feel free to ask me! :)

The dairy county school district appropriately uses a test that has a reliability of 0.89 to decide to conduct further assessment procedures.

Given,

Reliability of dairy county school

Here,

Reliability : It is an extent to which test scores are consistent, with respect to one or more sources of inconsistency—the selection of specific questions, the selection of raters, the day and time of testing.

Thus option D is correct .

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Complete question :

The Dairy County School District appropriately uses a test that has a reliability of 0.89 to

A) ​place children in special education if they earn a score below an established criterion.

B) ​move children to another school building to receive services for gifted children if they score above a certain point.

C) ​decide whether students should be placed in the Rainbow reading group or the Rainstorm reading group.

D) ​decide to conduct further assessment procedures.

The blanks in this two-column proof should be completed (filled) as follows:

Statements                              Reasons_______________

ΔADB ≅ ΔCDB                             HL.

AD ≅ CD                                    CPCTC.

In Mathematics, the Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two (2) triangles that are formed would be similar to each other, as well as the original triangle.

In Mathematics, CPCTC is an acronym for corresponding parts of congruent triangles are congruent and it states that the corresponding angles and side lengths of two (2) or more triangles are congruent if they are both congruent i.e AD ≅ CD.

Additionally, HL is an acronym for hypotenuse leg and it states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent i.e ΔADB ≅ ΔCDB.

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Answer:

ΔADB ≅ ΔCDB                             HL.

AD ≅ CD                                    CPCTC.

Step-by-step explanation:

or what the  guy said on top :D

Answer:

Physical means the actual wires.  Physical is concerned with how the wires are connected. Logical is concerned with how they transmit.

a. Logical

Step-by-step explanation:

...

The arrangement of network cabling between devices is a physical topology. which is the correct answer would be option (C).

The physical configuration of a network, such as the physical arrangement of wires, media (computers), or cables, is referred to as its topology. A link can connect two or more devices, and when the number of connections reaches two, they constitute a physical topology.

A physical network diagram depicts the connecting of devices via cables or wireless links. A logical network diagram, on the other hand, depicts data and signal transfer throughout a network.

Therefore, the arrangement of network cabling between devices is a physical topology.

Hence, the correct answer would be an option (C).

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Answer:

7 \(\frac{1}{2}\)

Step-by-step explanation:

45/6 = 7 Reminder 3

3/6 = 1/2

Therefore, the answer as a mixed number in simplest form is 7 \(\frac{1}{2}\)

Answer:

45/6

= 15/2

7½

This is the answer

The formula used is \($N(t) = N_0 e^{rt}$\). If a new social network has 1000 users currently and at growth rate of 10% per month, it can be predicted that there will be approximately 2452 users in seven and a half months assuming similar exponential growth.

In the formula used in the spreadsheet model for measuring exponential growth i.e. \($N(t) = N_0 e^{rt}$\)

N(t) is the number of cases at time t

N₀ is the initial number of cases

e is the mathematical constant approximately equal to 2.71828

r is the growth rate (expressed as a decimal)

To adapt this formula to predict the number of users of a new social network, we can replace the variables with the appropriate values. For example, if the new social network has 1000 users currently and is growing at a rate of 10% per month, we can write:

N(t) = 1000 x \(e^{rt}$\)

To find the predicted number of users in seven and a half months, we can substitute t = 7.5 into the equation and solve for N(7.5):

N(7.5) = 1000 x \(e^{rt}$\)

N(7.5) ≈ 2452.22

Therefore, we would expect to have approximately 2452 users on the new social network in seven and a half months if it continues to experience similar exponential growth.

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The complete question is :

What is the formula used in the spreadsheet model discussed in this module for measuring exponential growth of an epidemic, and how can it be adapted to predict the number of users of a new social network at a future date assuming similar exponential growth? In particular, if the new social network has 1000 users currently and is growing at a rate of 10% per month, how many users would we expect to have in seven and a half months?

Answer:

2 x 2+ 8 x 0= 4

Step-by-step explanation:

Answer:

c.16

hope this helps some one, have a nice day :)

Step-by-step explanation:

i just took the quiz and got it correct

Answer:

\(E(119.5)= 730m\)

Step-by-step explanation:

Given

\(E(t)= 1200(120-t)+520(120-t)^2\)

Required

Determine E(119.5)

\(E(t)= 1200(120-t)+520(120-t)^2\)

Simply substitute 119.5 for t

\(E(119.5)= 1200(120-119.5)+520(120-119.5)^2\)

Evaluate the expressions in bracket

\(E(119.5)= 1200(0.5)+520(0.5)^2\)

Solve 0.5²

\(E(119.5)= 1200 * 0.5+520*0.25\)

\(E(119.5)= 600+130\)

\(E(119.5)= 730\)

Hence;

\(E(119.5)= 730m\)