Shen and Kaitlin each opened a savings account today. Shen opened his account with a starting amount of $770, and he is going to take out $30 per month.
Kaitlin opened her account with a starting amount of $935, and she is going to take out $45 per month.
Let x be the number of months after today.
(a) For each account, write an expression for the amount of money in the account after x months.
Amount of money in Shen's account (in dollars) =
Amount of money in Kaitlin's account (in dollars) =
(b) Write an equation to show when the two accounts would have the
same amount of money.

Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

[tex]\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }[/tex]

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

[tex]\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}[/tex]

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

[tex]\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }[/tex]

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

[tex]\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}[/tex]

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

Permutations and combinations have many practical applications in various fields such as statistics, Probability theory, and computer science.

Permutations and combinations are two concepts in mathematics that deal with counting and arranging elements in a set.

Permutations refer to the number of ways in which a set of objects can be arranged or ordered. In other words, permutations involve counting the number of possible ways in which a group of objects can be arranged in a particular order. For example, if we have three objects A, B, and C, the possible permutations would be ABC, ACB, BAC, BCA, CAB, and CBA. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged.

Combinations, on the other hand, refer to the number of ways in which a subset of objects can be selected from a larger set, without regard to the order in which they are selected. In other words, combinations involve counting the number of possible subsets that can be formed from a larger set. For example, if we have three objects A, B, and C, the possible combinations would be AB, AC, and BC. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects being selected.

The key difference between permutations and combinations is that permutations involve ordering objects, while combinations do not. Another important distinction is that in permutations, each arrangement is considered distinct, whereas in combinations, different arrangements that contain the same objects are considered identical.

Permutations and combinations have many practical applications in various fields such as statistics, probability theory, and computer science. For example, they are commonly used in solving problems related to probability, combinations of locks, and permutations of passwords. Understanding these concepts is essential in order to effectively analyze and solve problems in these fields.

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hi

we have an aroithmetic serie of first term 1 and  pace  2

so sum of 12 first terms, namming  1 as  S1 and  12th term as  S12

S12 =  1 + 2*11 = 23

formula of summ :      number of term *  (  final term + first term) / 2

So sum of terms  from S1 +S12 =    12   ( S12 +S1 )  / 2  =  12 * ( 23+1) /2

12*  12=  144

-

Answer:

Step-by-step explanation:

Elasticity Demand

(Q1 - Q2)/(Q1 + Q2)

(P1 - P2)/(P1 + P2)

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The standard deviation is approximately 0.01307. See the explanation below.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.

Step 1: First, lets calculate the variance.

The formula for variance is:

[tex]\sigma^2 = \frac{\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]

To get the variance ( s2 ) we must first get the mean. Our mean is 0.99892.

We subtract each value by the mean and square the difference.

(0.978-0.99892)² = 0.0004376464

(0.982-0.99892)² = 0.0002862864

(0.983-0.99892)² = 0.0002534464

(0.984-0.99892)² = 0.0002226064

(0.987-0.99892)² = 0.0001420864

(0.988-0.99892)² = 0.0001192464

(0.989-0.99892)² = 9.84064e-05

(0.99-0.99892)² = 7.95664e-05

(0.992-0.99892)² = 4.78864e-05

(0.992-0.99892)² = 4.78864e-05

(0.993-0.99892)² = 3.50464e-05

(0.994-0.99892)² = 2.42064e-05

(0.996-0.99892)² = 8.5264e-06

(0.997-0.99892)² = 3.6864e-06

(1-0.99892)² = 1.1664e-06

(1.001-0.99892)² = 4.3264e-06

(1.006-0.99892)² = 5.01264e-05

(1.007-0.99892)² = 6.52864e-05

(1.011-0.99892)² = 0.0001459264

(1.015-0.99892)² = 0.0002585664

(1.015-0.99892)² = 0.0002585664

(1.015-0.99892)² = 0.0002585664

(1.018-0.99892)² = 0.0003640464

(1.02-0.99892)² = 0.0004443664

(1.02-0.99892)² = 0.0004443664.

Step 2: Add all these numbers above

0.0004376464+0.0002862864+0.0002534464+0.0002226064+0.0001420864+0.0001192464+9.84064e-05+7.95664e-05+4.78864e-05+4.78864e-05+3.50464e-05+2.42064e-05+8.5264e-06+3.6864e-06+1.1664e-06+4.3264e-06+5.01264e-05+6.52864e-05+0.0001459264+0.0002585664+0.0002585664+0.0002585664+0.0003640464+0.0004443664+0.0004443664

=0.00410184

Step 3: Now we divide the sum by how many numbers there are. In this case we have 25.

We'll call this number n.

So n=25

For a sample (use 0.00410184 divided by (n-1) ):

So s2 =0.00410184 divided by 24

s2 = 0.00017091

Step 4 - Solve for Standard deviation:

The standard deviation is the square root of the variance. Our variance is 0.00017091.

So we only apply a square root on the variance.

= √ 0.00017091

s = 0.0130732551

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Full Question:

A statistical process control monitoring system samples the inside diameter of ball bearing every hour. Measurements were taken every hour for 25 hours. The target thickness, T, is the average.

0.992 1.015 0.988 0.996 1.015 1.000 0.989 0.994 1.018 0.997 1.020 1.007 1.006 0.982 1.001 0.992 1.020 0.993 0.978 0.984 0.990 1.015 0.983 1.011 0.987

What is the population standard deviation, σ?

The population parameter value and the point estimate differ because a sample is not census of the entire population,  but it is being used to develop the point estimate.

According to the question,

The population parameter value and the point estimate differ because a sample is not census of the entire population,  but it is being used to develop the point estimate.

The sample proportion p, is a point estimate of the population proportion.

Hence, the correct answer is point estimate. Thus, the population parameter value and the point estimate differ because a sample is not census of the entire population,  but it is being used to develop the point estimate.

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The volume of the shape will be 50cm3.

It should be noted that the volume van be found by multiplying the area by the height. The volume will be:

= 10 × 5

= 50cm³

The standard deviation volume will be:

= 0.1 × 50

= 5cm

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Answer: 6.5

Step-by-step explanation:

Since all squares are rhombi, and diagonals of a rhombus intersect at right angles, this means that

[tex]13x+5.5=90\\\\13x=84.5\\\\x=6.5[/tex]

Answer:

a  =   1.5 in.

Step-by-step explanation:

Use the Pythagoras Theorem:

1.7^2 = a^2 + 0.8^2

a^2 = 1.7^2 - 0.8^2

      = 2.25

a  =   1.5 in.

Answer:

a = 1.5 in.

Explanation:

Using Pythagoras theorem:

a² + b² = c²

insert values

a² + 0.8² = 1.7²

a² = 1.7² - 0.8²

a² = 2.89 - 0.64

a² = 2.25

a = √2.25

a = 1.5

Answer: Option (4)

Step-by-step explanation:

From the diagram, we know that

[tex]\sin 60^{\circ}=\frac{BC}{15}\\\\\cos 60^{\circ}=\frac{AB}{15}[/tex]

This means we can eliminate options 1 and 2.

Now, if we multiply both sides by 15, we get

[tex]15\cos 60^{\circ}=7.5[/tex].

This gives us Option (4).

Answer:

Step-by-step explanation:

already

Answer:

No

Step-by-step explanation:

So to determine whether this is a function, we first need to know what a function is. A function is defined as for each input, there is only 1 output.

This output doesn't have to be unique and other inputs can output this output, but it only matters that each input outputs only one output.

So let's look at what you provided and specifically these two points:

(3, 5)

(3, -3)

This input 3, outputs 5 and -3, which is not a function since this input outputted 2 different outputs. One thing to note is had you provided the two points: (3, 5), (3, 5) instead then it would still be a function because the input outputted the same output of 5 both times.

Using the domain concept, the only value of x that is not on the domain of [tex]f(x) = \frac{1}{3x + 5}[/tex] is given as follows:

[tex]x = -\frac{5}{3}[/tex]

The domain of a function is the set that contains all possible input values for the function. For a rational function, for example, the zeros of the denominator are excluded from the domain. Another example is an even root, where the inside term has to be positive.

The rational function for this problem is given by the function f(x) presented below:

[tex]f(x) = \frac{1}{3x + 5}[/tex]

The denominator is 3x + 5, hence the restriction in the domain of f(x) is given as follows:

3x + 5 = 0

3x = -5

[tex]x = -\frac{5}{3}[/tex]

The solution to the equation above is the only value of x that is not part of the domain of f(x).

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Answer:

25k x 3

Step-by-step explanation:

Applying exponential properties, the simplified base for the function is given as follows:

[tex]f(x) = 2(3)^{2x}[/tex]

The function is represented by the following definition:

[tex]f(x) = 2\sqrt[3]{27^{2x}}[/tex]

As an exponent, the function is given by:

[tex]f(x) = 2(27)^{\frac{2x}{3}}[/tex]

27 can be simplified as follows:

27 = 3 x 3 x 3 = 3³

Hence:

[tex]f(x) = 2(3^3)^{\frac{2x}{3}}[/tex]

Then, the 3 at the exponent multiplies 2x and can be simplified with the 3 of the root, hence:

[tex]f(x) = 2(3)^{\frac{3 \times 2x}{3}} = 2(3)^{2x}[/tex]

Hence the simplified base for the function is given as follows:

[tex]f(x) = 2(3)^{2x}[/tex]

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Answer:

Step-by-step explanation:

hello :

A) X=In(125)

The independent variable that caused a change in the dependent variable is called cofounding variable.

Given the Factors that are unequal across groups and can prevent a researcher from concluding that it was the independent variable that caused a change in the dependent variable are called _____ variables.

These are variables in statistics other than the dependent and independent variables which can also be important to a researcher because it affects the dependent variable.

Confounding variables can also be called influences, external factors or third variables because they mostly affect the outcome of a research and prevent a researcher from achieving its objectives.

Hence, Factors that are unequal across groups and can prevent a researcher from concluding that it was the independent variable that caused a change in the dependent variable are called cofounding variables.

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Answer:

25%

Step-by-step explanation:

3/12 = 0.25 = 25%

Answer:

25%

Step-by-step explanation:

$3 pent out of the original $12.  We can ask what is the percentage of $12 that is equal to $3?  This can be written as:

X($12) = $3, where X is the percentage.

X = (3/12)

X = 0.25 or 25%

The information about the coordinate plane shows that the slope of XV is 1.

From the information, the slopes of the diagonals are negative reciprocals. Therefore, the slope of UW is -1 and the slope of XV is 1.

The diagonals of kite UVWX are perpendicular.

It should be noted that negative reciprocals in a kite create a perpendicular bisector. So the two lines share a midpoint so they are perpendicular.

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Answer:

Step-by-step explanation:

The slope of XV is

1

The slope of UW is

–1

The slopes of the diagonals are

negative reciprocals

The diagonals of kite UVWX are

perpendicular

.

The given limit indicates that there is a vertical asymptote at x = 2.

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator. When x tends to these values laterally, the limit of f(x) goes to infinity.

In this problem, the function is:

[tex]f(x) = \frac{x^2 - 4x - 12}{x - 2}[/tex]

The vertical asymptote is:

x - 2 = 0 -> x = 2.

Hence:

[tex]\lim_{x \rightarrow 2^+} f(x)[/tex] and [tex]\lim_{x \rightarrow 2^-} f(x)[/tex] are either positive infinity or negative infinity.

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The percent of the class who voted for Math also voted for Science is 38.8%

Therefore,

1 = p(m) + p(s) - p(m ∩ s)

Hence,

p(m)  = 45% = 0.45

p(s)  = ?

p(m ∩ s) = 35% = 0.35

Therefore,

1 = 0.45 + p(s) - 0.35

1 - 0.45 + 0.35 = p(s)

p(s) = 0.9

Therefore,

p(m | s) = 0.35 / 0.9 = 0.38888888888 = 38.8%

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If both faucets are used together, it time taken by them to fill the tub is 4.8 minutes.

Time and work share a fundamental idea in common with other arithmetic topics, namely the idea of proportionality.

When the amount of work is constant, efficiency is inversely proportional to the length of time required.

Important Time and Work Formula:

Calculation for the time taken by both faucet to fill the tub.

The unit should be tub per minute.

Then, do the reciprocal of the result to have minute per tub.

The hot water faucet can fill the tub in 12 minutes.

The cold water faucet can fill the tub in 8 minutes.

The filling rate for both faucets filling the tub at the same time is the sum of their rates.

Let 't' be the time taken by both faucets.

Then,

[tex]\frac{1}{12} +\frac{1}{8} =\frac{1}{t}[/tex]

[tex]\frac{8+12}{8*12} =\frac{1}{t}[/tex]

[tex]\frac{1}{t} =\frac{20}{96}[/tex]

[tex]\frac{t}{1} =\frac{96}{20}[/tex]

t = 4.8

Therefore, the time taken by both faucets to fill the tub is 4.8 minutes.

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Answer:

0.40x = 320

Step-by-step explanation:

If 40% of the total houseplants watered = 320

0.40 times x (total houseplants) = 320

Answer:

[tex]\frac{x}{0.40} = 320 Plants[/tex]

Step-by-step explanation:

[tex]\frac{x}{0.40} = 320 Plants[/tex]

[tex]X = (0.40)(320)Plants[/tex]

[tex]X = 128Plants[/tex]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the explanation ~

Zeros or roots of a function is the value of independent variable (usually x - coordinate or absicca) where the value of dependent variable (y - coordinate or ordinate) is 0.

That is :

The point where it cuts the x - axis, it has an x - coordinate = -6

Therefore, we can conclude that The zero of given function is -6

Answer:

x = -6.

Step-by-step explanation:

It is where the graph cuts the x-axis  (where the function is zero).

That is -6.

The total number of small drinks 's' bought by Maria is 7.

The total number of medium drinks 'm' drinks bought by Maria is 6.

A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).

Formation of the linear equation for the drinks bought by Maria:

The total number of drinks bought by the Maria is 13.

Lets say 'm' represents the number of medium drink.

's' represents the number of small drink.

Total drinks comprises of medium drinks and small drinks.

Thus,

s + m = 13, is the first linear equation.

Now medium drinks cost $3.

Total cost for purchasing medium drinks = (price of one medium drink)×(total number of medium drinks)

Total price for medium drinks = 3×m

Similarly,

Total cost for purchasing small drinks = (price of one small drink)×(total number of small drinks)

Total price for small drinks = 2×s

Total cost = total cost of medium drink + total cost of small drink

          32  = 3×m + 2×s, is second linear equation.

From equation first substitute the value of 'm' in second equation to fine the total number of drink.

32 = 3×(13 - s) + 2×s

32 = 39 - 3s + 22

s = 7

Put s = 7 in first equation and calculate 'm'.

m = 13 -7

m = 6

Therefore, The total number of small drinks 's' bought by Maria is 7.

The total number of medium drinks 'm' drinks bought by Maria is 6.

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Step-by-step explanation:

Let the number of stamps of John be x.

Then number of Minghua's stamps:

John's: x

Minghua's: (3/2)x

rhumbos

it is the most precise name because it gives more information about the quadrilateral

The linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

Cubic equations are polynomials of third grade, whose standard and factor forms are shown below:

Standard form

y = a · x³ + b · x² + c · x + d

Factor form

y = (x - r₁) · (x - r₂) · (x - r₃)

Where r₁, r₂, r₃ are the zeros of the cubic equation.

There are several approaches to find the roots of the polynomial, in this question we decided to use the graphical approach, which offers sufficiency and quickness for analysis. The roots of the polynomials are the points that pass through the x-axis.

In accordance with the image attached below, the polynomial has three real roots: r₁ = - 20, r₂ = - 5, r₃ = 15. Then, the linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

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The function that can be used to find the number of rides Jay went on is, f(x) = 4.5x + 10 = 46.5. Hence, the first option is the right choice.

Also, on solving the function we get that, Jay went on 8 rides.

We assume the number of rides Jay spent to be x.

The cost of each ride is given to be $4.50.

Thus, the total amount Jay spent on rides = $4.50x.

The entrance fee to the park is given to be $10.50.

Thus, the total expenditure of Jay can be shown as $(4.5x + 10.5).

But, in the question we are given that Jay spend $46.50 altogether.

Thus, the function to find the number of rides Jay went on can be shown as:

f(x) = 4.5x + 10 = 46.5.

Hence, the first option is the right choice.

To find the number of rides he went, we can solve this function as:

4.5x + 10 = 46.5,

or, 4.5x = 46.5 - 10.5 = 36,

or, x = 36/4.5 = 8.

Thus, Jay went on 8 rides.

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