a cash register is worth 620$, 100 cash registers are worth 62000.

The cost per cash register increases by a rate of 7% continuously compounded. How much would one NEW cash register cost in 10 years’ time?

The value per cash register decreases at a rate of 7% each year. How much will one OLD cash register be worth in 10 years’ time?

The correct option is the third one, the recursive formula is:

aₙ = -4*aₙ₋₁

a₁ = 7

We know that the explicit formula for the sequence is:

aₙ = 7*(-4)ⁿ⁻¹

So we can see that we have a geometric sequence, where to get the next term, we need to multiply the previous one by -4, then the recursive formula is:

aₙ = -4*aₙ₋₁

We also need to define the first term, which is:

a₁ = 7*(-4)⁰ = 7

Then the correct option is the third one.

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Answer:

5 fours are being multiplied together

To determine the number of ways to assign 7 volunteers to 7 booths for the charity bazaar, we can consider the concept of permutations. Since each volunteer must be assigned to a different booth, we are essentially permuting the volunteers among the booths.

The number of ways to arrange 7 volunteers into 7 distinct booths can be calculated using the factorial function. The factorial of a number n, denoted as n!, represents the product of all positive integers from 1 to n.

In this case, we have 7 volunteers and 7 booths, so we need to calculate 7!.

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040

Therefore, the correct answer is C. There are 5,040 ways to assign 7 volunteers to 7 booths for the charity bazaar. Each arrangement represents a unique assignment of volunteers to booths, ensuring that each volunteer is assigned to a different booth.

It is worth noting that the factorial function grows rapidly as the number increases. In this case, with 7 volunteers and 7 booths, the number of possible arrangements is quite large.

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Angle BCF = 38 degrees

Angle BED = 79 degrees

Angle BDE = 63 degrees

Angle B = 79 degrees

Angle C = 79 degrees

Angle ACF = 38 degrees

Angle F = 104 degrees.

We have,

As ED//BC,

We can say that angle EDB = angle BCF = 38 degrees.

Also, in rhombus ABCF, angles BCF and CAF are equal,

So CAF = 38 degrees.

In triangle BED,

We have angle BED = 79 degrees and angle EDB = 38 degrees.

Angle BDE = 180 - (79 + 38) = 63 degrees.

In triangle BDE,

We also has angle B = angle EBD = 180 - (63 + 38) = 79 degrees.

In trapezium BCDE,

Angles B and C are equal, so angle C = 79 degrees.

Finally, in rhombus ABCF, angles CAF and ACF are equal,

So ACF = 38 degrees.

Therefore,

Angles A and C of triangle ACF equal 38 degrees each, and angle F is:

= 180 - (38 + 38)

= 104 degrees.

Thus,

angle BCF = 38 degrees

angle BED = 79 degrees

angle BDE = 63 degrees

angle B = 79 degrees

angle C = 79 degrees

angle ACF = 38 degrees

angle F = 104 degrees.

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The complete question.

In the figure, ABCF is a rhombus and BCDE is a trapezium. ED//BC, BCF=38 degrees, and BED= 79 degrees.

Find the following:

Angle BCF

Angle BED

Angle BDE

Angle B

Angle C

Angle ACF

Angle F

find the factors of 175

which are 1, 5, 7, 25, 35, 175

including the profit of $4

if the cupcakes are $5 then 35 need to be sold to break even

if the cupcakes are $7 then 25

if $25 then 7

if $35 then 5

if $175 then 1

The chocolate for 140 bon-bons would cost approximately $6.13.

1. Calculate the volume of each chocolate bon-bon using the formula for the volume of a sphere: V = (4/3)πr³, where r is the radius.

  V = (4/3)π(0.7 cm)³

  V ≈ 1.437 cm³

2. Determine the mass of each chocolate bon-bon using the density formula: density = mass/volume.

  density = 1.27 g/cm³

  mass = density * volume

  mass ≈ 1.27 g/cm³ * 1.437 cm³

  mass ≈ 1.826 g

3. Calculate the total mass of chocolate needed for 140 bon-bons.

  total mass = mass per bon-bon * number of bon-bons

  total mass ≈ 1.826 g * 140

  total mass ≈ 255.64 g

4. Determine the cost of the chocolate by multiplying the total mass by the cost per gram.

  cost = total mass * cost per gram

  cost ≈ 255.64 g * $0.04/g

  cost ≈ $10.2256

5. Round the cost to the nearest cent.

  cost ≈ $10.23

Therefore, the chocolate for 140 bon-bons would cost approximately $6.13.

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Answer:

ANSWER: A) 15/40 and 28/40

Step-by-step explanation: Ive done this before lol

A nurse should empty a Hemovac wound suction device when it is half full to ensure proper functioning and prevent discomfort or injury to the patient due to the device becoming too heavy.

The rationale for a nurse to empty a Hemovac wound suction device when it is half full is to ensure the device is functioning correctly and to prevent it from becoming too heavy and potentially causing discomfort or injury to the patient.

When a Hemovac wound suction device is half full, it may start to lose suction, which can result in less efficient drainage of fluid from the wound site. By emptying the device, the nurse can ensure that the device is functioning correctly and that the suction pressure is maintained.

Additionally, allowing the device to become too full can make it heavy and uncomfortable for the patient, potentially causing discomfort or injury to the wound site. Therefore, emptying the device when it is half full can help prevent these complications and ensure that the patient remains comfortable throughout the healing process.

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The subtraction of the numbers, involving scientific notation, is given as follows:

18 - 9.2 x 10^(-4) = 17.99908.

A number in scientific notation is given according to the rule presented as follows:

\(a \times 10^b\)

The base is \(a \in [1, 10)\), meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.

In this problem, we are given the following subtraction:

18 - 9.2 x 10^(-4).

When two numbers are subtracted, they must have the same base, hence we are going to convert 9.2 x 10^(-4) to base 0.

This means that 4 has to be added to the exponent, meaning that the base has to be divided by 10000 to compensate, then:

9.2 x 10^(-4) = 0.00092.

Then the result of the subtraction is given as follows:

18 - 9.2 x 10^(-4) = 18 - 0.00092 = 17.99908.

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Answer:

Cytoplasm

Step-by-step explanation:

Answer:

Cytoplasm

Step-by-step explanation:

Answer:

ii, the mpg for the trucks.

Step-by-step explanation:

A larger standard deviation means more variablilty

Step-by-step explanation:

as this is total 90°angle

68°+x = 90 °

x = 90°-68°

x = 22 °

also

68° + 22 ° = 90 °

Answer:

90 - 68 = 22

the whole angle is 90

if we substract 68 from 90 , we will get the answer.

Answer:

the slope of these points is 8/3

Expression B: 3x + 10y

Expression A: 7x - 4y

The difference in calculation of expression A vs expression B is due to the signs in between the parenthesis in both expression respectively. The sign of the 2nd parenthesis in expression B will change because of the the negative sign before it. While that of the 2nd expression in A will remain the same because of the positive sign.

Expression B: (5x + 3y) - (2x - 7y)

To solve this, we need to expand the parenthesis:

5x + 3y -(2x) -(-7y)

Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.

5x + 3y -2x + 7y

collect like terms:

5x-2x + 3y + 7y

= 3x + 10y

Expression A: (5x + 3y) + (2x - 7y)

To solve this, we need to expand the parenthesis:

5x + 3y +(2x) + (-7y)

Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.

5x + 3y + 2x - 7y

collect like terms:

5x +2x +3y -7y

= 7x - 4y

Answer:

36ft²

Step-by-step explanation:

A=a²=6²=36ft²

sorry if im wrong

Two steps that will complete the list correctly are:

4. The original measurement should be multiplied by the conversion factors.

5. Verify that it makes sense.

A conversion factor can be used to switch from one set of units to another by multiplying or dividing a number. When a conversion is necessary, the appropriate conversion factor to an equivalent value must be applied.

Let's use an example of converting from inches to centimeters to address this query.

10 inches should be converted to cm.

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Answer:

A

Step-by-step explanation:

The slope intercept form of a line is y=mx+b, where m is the slope and b is the y intercept. The y coordinate of the intercept of this line is therefore -1, meaning that it is located at the point (0,-1). Hope this helps!

The mistake that Shawn made in his definition of a reflection is that D. Shawn didn't make a mistake.

It should be noted that reflection simply means ten transformation of the shape of an object.

In this case, for any point R on the line of reflection L, the image R’ is at the same point as R. Furthermore, for any point P not on the line of reflection L, the image P’ is on the other side of L such that P and P’ are the same distance from L.

Therefore, Shawn is right as no mistake was made.

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Answer:

PP' must be perpendicular to the line of reflection. Whatever the distance is between P and L, there are infinitely many points on the other side of L that are the same distance from L.

Step-by-step explanation:

After answering the provided question, we can conclude that As a result, expression the correct answer is 26.9 yards, which is the closest option to 24.5 yards.

An expression in mathematics is a collection of representations, digits, and conglomerates that resemble a statistical correlation or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

We can use the formula for the distance from the centre of an ellipse to a point on the ellipse to find the distance along the minor axis:

\(c = √(a^2 - b^2)\)

where c represents the distance from the centre to a focus, a represents the length of the major axis, and b represents the length of the minor axis.

In this case, a = 50 yards (the major axis length) and c = 10 yards (the distance from the centre to a focus). When we solve for b, we get:

\(b = √(a^2 - c^2)\\= √(50^2 - 10^2)\\= √(2400)\\= 49 yd\\49 / 2 = 24.5 yd\\(x^2/a^2) + (y^2/b^2) = 1\\\)

where an is the major axis length and b is the minor axis length. We know the length of the major axis is 50, so a = 25. We also know that one focal point is at (0, 10). We can use the distance formula to find the other focus:

\(c = √(a^2 - b^2)\\= √(25^2 - 49^2)\\= 20.4 yd\)

The other focus is therefore at (0, -10).

\((x^2/25^2) + (y^2/49^2) = 1\\(y^2/49^2) = 1\\y^2 = 49^2\\y =49\)

As a result, the correct answer is 26.9 yards, which is the closest option to 24.5 yards.

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The general solution to (x+3)y′′−(9−x)y′+y=0, which converges at least on the interval (-3, 3), can be expressed as:

y = c0 \((1 - (1/6) x^2 + x^3 + x^4 + ⋯) + c1 (1/x + (9/6) x^2 + x^3 + x^4 + ⋯)\)

To solve the given differential equation (x+3)y′′−(9−x)y′+y=0, we follow the provided steps:

(1) By analyzing the singular points of the differential equation, we know that a series solution of the form y=∑[infinity]k=0ck xk for the differential equation will converge at least on the interval (-3, 3).

(2) Substituting y=∑[infinity]k=0ck xk into (x+3)y′′−(9−x)y′+y=0, we obtain the following expression:

1 c0 - 9 c1 + 6 c2 + ∑[infinity]n=1 [(n+1)\(c_n + (n^2 - 8n - 9) c_(n+1) + 3(n+2)(n+1) c_(n+2)] x^n\) = 0

Note that the subscripts on the c's should be increasing and in terms of n.

(3) We can solve for some of the terms in the series and find the recurrence relation:

(a) From the constant term in the series above, we have c2 = (9 c1 - c0) / 6.

(b) From the series above, we find that the recurrence relation is given by:

\(c_(n+2) = (9 - n) c_(n+1) - c_n / [3(n+2)],\) for n ≥ 1.

(4) The general solution to (x+3)y′′−(9−x)y′+y=0, which converges at least on the interval (-3, 3), can be expressed as:

y = c0 \((1 - (1/6) x^2 + x^3 + x^4 + ⋯) + c1 (1/x + (9/6) x^2 + x^3 + x^4 + ⋯)\)

Please note that the series representation above is an approximation and not an exact solution. The coefficients c0 and c1 can be determined using initial conditions or additional constraints on the problem.

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The scale factor of the dilation that maps triangle ABC onto triangle DBE is approximately 0.75. Option B.

To find the scale factor of the dilation that maps triangle ABC onto triangle DBE, we need to compare the corresponding side lengths of the two triangles.

Let's consider the length of side AC in triangle ABC, which is given as 16.12. Correspondingly, the length of side DE in triangle DBE is given as 12.09.

To find the scale factor, we divide the length of side DE by the length of side AC:

Scale factor = Length of DE / Length of AC

= 12.09 / 16.12

≈ 0.75 Option B is correct.

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Answers:

=========================================================

Explanation:

s = Sam's age right now

2s = the mother's age right now, since she is twice as old as Sam currently.

In 12 years time, Sam will be s+12 years old.

12 years ago from this current year, the mother was 2s-12 years old.

Since we're told these future and past ages line up, this means s+12 and 2s-12 are the same value

Set the expressions equal to one another and solve for s.

s+12 = 2s-12

s-2s = -12-12

-s = -24

s = 24

Sam is currently 24 years old.

His mother is currently 2s = 2*24 = 48 years old.

12 years ago, his mother was 2s-12 = 48-12 = 36 years old.

12 years from now, Sam will be s+12 = 24+12 = 36 years old.

Since we get 36 each time, this confirms we have the correct answers.

(i) State whether the term is a variable name or a variable value.

(ii) State the level of measurement.

A. age

(i) Variable name.

(ii) Ratio.

Explanation: "Age" is the name of the variable and it is a numerical value representing the number of years a person has lived. It is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).

B. conservative

(i) Variable name.

(ii) Nominal.

Explanation: "Conservative" is the name of b and it refers to a political ideology. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., conservative, liberal, socialist) and have no meaningful mathematical operations.

C. strongly oppose

(i) Variable value.

(ii) Ordinal.

Explanation: "Strongly oppose" is a value of the variable, and it refers to a person's opinion or attitude towards a certain issue. It is measured on an ordinal scale, meaning it has a rank or order (e.g., strongly oppose, somewhat oppose, neutral, somewhat support, strongly support). However, the difference between two values is not necessarily equal (e.g., the difference between strongly oppose and neutral might be different from the difference between neutral and strongly support).

D. region

(i) Variable name.

(ii) Nominal.

Explanation: "Region" is the name of the variable and it refers to a geographical area, such as the Midwest or the South. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Midwest, South, West, Northeast) and have no meaningful mathematical operations.

E. 57 years

(i) Variable value.

(ii) Ratio.

Explanation: "57 years" is a value of the variable "Age" and it represents the number of years a person has lived. As mentioned above, "Age" is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).

F. strictly enforced

(i) Variable value.

(ii) Ordinal.

Explanation: "Strictly enforced" is a value of a variable, and it refers to the level of enforcement of a rule or law. It is measured on an ordinal scale, meaning it has a rank or order (e.g., not enforced, loosely enforced, strictly enforced). However, the difference between two values is not necessarily equal (e.g., the difference between not enforced and loosely enforced might be different from the difference between loosely enforced and strictly enforced).

G. Catholic

(i) Variable name.

(ii) Nominal.

Explanation: "Catholic" is the name of the variable and it refers to a religious affiliation. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Catholic, Protestant, Jewish, Muslim) and have no meaningful mathematical operations.

H. Gender

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The distance between the man and the starting point will be 13.08 km.

Trigonometry is the branch of mathematics which set up a relationship between the sides and angles of right-angle triangles.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

Given that a man walks due west for 4km. He then changes direction and walks on a bearing of 197°.

The distance will be calculated as,

tanΘ = P/B

tan(73) = y / 4

y = 4tan73

y = 13.08 km

Therefore, the distance between the man and the starting point will be 13.08 km.

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the general equation of a graph is given by

y = mx + c

where m= slope

c=intercept

the equation given is

9x-5y=4

make y subject of formula

9x-4=5y

5y=9x-4

divide through by 5

y=9/5x-4/5

comparing with the general equation

mx=9/5x

m=slope=9/5

The statement one interesting feature of the natural numbers is that while each individual natural number is finite, the set of natural numbers is infinite is true.

The natural numbers, denoted by the set N = {1, 2, 3, 4, 5, ...}, represent a countable and infinite set. This means that for every natural number we can think of, there is always a larger natural number.

No matter how high we go, there is always another natural number that can be generated by adding 1 to the previous highest number.

To understand why the set of natural numbers is infinite, we can use a simple proof by contradiction. Suppose we assume that the set of natural numbers is finite, and there exists a highest natural number, say n.

However, by adding 1 to n, we can generate a new number, n + 1, which contradicts the assumption that n is the highest natural number. Therefore, the set of natural numbers cannot be finite.

This infinite nature of the set of natural numbers has profound implications in various mathematical and theoretical contexts. It forms the basis for concepts such as infinity, recursion, and mathematical induction.

The infinite set of natural numbers provides a foundation for the study of numbers, patterns, and mathematical structures, serving as a cornerstone of mathematics and its applications in various fields.

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The likelihood function for a sequence of coin tosses x1, . . . , xn with P[H] = p is given by:

L(p) = P(x1, . . . , xn | p) = P(x1 | p) * P(x2 | p) * . . . * P(xn | p)

Using the notation that 1 denotes H and 0 denotes T, we can write the likelihood function as:

L(p) = p^k * (1-p)^(n-k)

where k is the number of heads in the sequence and n-k is the number of tails.

To find the maximum likelihood estimate for p, we need to take the derivative of L(p) with respect to p and set it equal to zero:

dL(p)/dp = k*p^(k-1)*(1-p)^(n-k) - (n-k)*p^k*(1-p)^(n-k-1) = 0

Solving for p, we get:

p = k/n
Therefore, the maximum likelihood estimate for p is the number of heads in the sequence divided by the total number of tosses.

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a. The graph has one solution (10,300) when Elizabeth and Jayden meet after 10 minutes and at 300 stairs.

b. The graph has no solution as there is no intersection point and Robert and Meido do not meet at any point.

What is the intersection point?

Two lines are said to intersect when they have exactly one point in common. There is a point at which the intersecting lines meet. The point of intersection is the same location that appears on all intersecting lines.

a. Since both the lines intersect at single point The given system has one solution, which is at (10,300). The solution means that Elizabeth and Jayden meet after 10 minutes and at 300 stairs.

b. Since both the lines do not intersect at any point . The given system has no solution, as both the lines are parallel. The solution means Robert and Meido do not meet at any point.

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Answer:

The sum of the first 7 terms in the geometric sequence is -6558

Step-by-step explanation:

s7 refers to the sum of the first 7 terms of the geometric sequence

To calculate the sum of terms, we use the sum of terms formula

We have this generally given as;

Sn = a(1-r^n)/(1-r)

a refers to the first term, given as a1 which is -4374

r is the common ratio which is 1/3

n is the number of terms, which is 7

substituting these values;

s7 = -4374(1-(1/3)^7)/(1-1/3)

s7 = -4374(1-(1/3)^7)/2/3

s7 = (3 * -4374)/2 * (1- (1/3)^7

s7 = -6561 * (1-1/2187)

s7 = -6561 * (2187-1)/2187

= -6561 * 2186/2187

= -6558