I need help mate.
You have $75 and need to buy 9 books at the bookstore and each book costs d dollars.

​Write an algebraic expression to represent the amount of money left over.

Measures of the variation of distribution are variance, standard deviation, range, interquartile range, and coefficient of variation.

Measures of the variation of distribution are used to quantify the spread or dispersion of the data points in the distribution.

The variance is a measure of the variation of distribution that represents how spread out the data points in a distribution are from the mean.

A higher variance indicates that the data points are more spread out, while a lower variance indicates that they are more tightly clustered around the mean.

The variance is useful when the data is normally distributed and there are no extreme outliers in the dataset.

Standard deviation is a measure that shows how the spread or dispersion of a set of data points from the mean.

The standard deviation can tell us how tightly or loosely the data points are clustered around the mean. A smaller standard deviation indicates that the data points are tightly clustered, while a larger standard deviation indicates that the data points are more spread out.

The standard deviation is useful when the data is normally distributed and there are no extreme outliers in the dataset.

Some of the measures of the variation of distribution are Range, Interquartile range, Coefficient of variation, etc.  

Therefore,

Measures of the variation of distribution are variance, standard deviation, range, interquartile range, and coefficient of variation.

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Punnett square is a diagrammatic representation of genotypes of a distinct cross in organisms.

Punnett square is a diagrammatic representation of genotypes of a distinct cross in organisms.

It is used to know the result of the genotype of the offspring having either having single or multiple traits.

The correct answers are:

1.Option C. 0%

In the Punnett square the cross is between the purebred dominant and purebred recessive parent.

This will result in all the offspring having a heterogeneous genotype trait carrying purple color. Hence 0% will carry white color.

2. Option D. 25%

It can be explained as:

Due to the presence of heterogenous parent species. It will result in 25% of offspring carrying white color.

Therefore, in question 1, 0% of plants will be white while in another question 25% of the offspring will carry the white color trait.

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Given:

There are given the equation:

Explanation:

According to the question:

We need to find the solution to the given quadratic.

Then,

To find the solution, we will use the quadratic equation formula.

Then,

From the equation:

Where,

Then,

Put all the value into the formula:

Then,

Then,

Therefore, the solution of the given quadratic equation:

Final answer:

Hence, the correct options are B and E.

The 7th term of the arithmetic sequence -3x+5, 2x+3, 7x+1, ... is: 27x-7.

To find the 7th term of the arithmetic sequence, we need to first determine the common difference between the terms. We can do this by subtracting the first term from the second term:

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

This means that the common difference between the terms is 5x - 2. Now, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1)d

Where an is the nth term, a₁ is the first term, n is the term number, and d is the common difference. Plugging in the values we have:

a₇ = (-3x+5) + (7 - 1)(5x - 2)

Simplifying the equation:

a₇ = -3x + 5 + 30x - 12

a₇ = 27x - 7

Therefore, the 7th term of the arithmetic sequence is 27x - 7.

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The expression \(\(3^{3} - \frac{27}{9} \cdot 2 + 11\)\) can be simplified by following the order of operations (PEMDAS/BODMAS). The result of the expression \(\(3^{3} - \frac{27}{9} \cdot 2 + 11\)\) is 32.

The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right), or BODMAS (Brackets, Orders, Division and Multiplication from left to right, Addition and Subtraction from left to right), is a set of rules that determines the sequence in which mathematical operations should be performed in an expression. By following these rules, we can ensure that calculations are carried out correctly.

Let's break it down step by step:

⇒ Calculate the exponent 3^{3}:

3^{3} = 3 x 3 x 3 = 27

⇒ Evaluate the division \(\(\frac{27}{9}\)\):

\(\(\frac{27}{9} = 3\)\)

⇒ Perform the multiplication 3 x 2:

3 x 2 = 6

⇒ Sum up the results:

27 - 6 + 11 = 32

Therefore, the final result of the expression \(\(3^{3} - \frac{27}{9} \cdot 2 + 11\)\) is 32.

Complete question -  Simplify \(\(3^{3} - \frac{27}{9} \cdot 2 + 11\)\) using order of operations.

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By using the z-score, it can be concluded that the percentage of employees earn approximately between $59000 and $67000 is 23.29%.

z-score is the standard value or the amount of deviation of a value from the mean.

z = (x - μ) / σ   where:

x = the observed value

μ = the mean

σ = the standard deviation

We know that x (salaries of employees) is normally distributed with:

μ = $55000

σ = $6200

We want to find the percentage of employees earning approximately between $59000 and $67000.

First, we find the z score of each salary limit:

z = (x - μ) / σ

  = (59000 - 55000) / 6200

  = 4000 / 6200

  = 0.65

z = (x - μ) / σ

  = (67000- 55000) / 6200

  = 12000 / 6200

  = 1.94

P(59000<x<67000) = P(0.65 < z < 1.94)

                                 = 0.25941 - 0.026465

                                 = 0.232945

                                 ≈ 23.29%

Thus the percentage of employees earn approximately between $59000 and $67000 is 23.29%.

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Fewer births and increased survival rates are changing the shape of the population from a pyramid to a(n): Rectangle

It is given that fewer births and increased survival rates are changing the shape of the population from a pyramid.

Survival rates is the percentage of people in a study or treatment group who are still alive for a certain period of time after they were diagnosed with or started treatment for a disease, such as cancer.

A population pyramid is a way to visualize two variables: age and sex. They are used by demographers, who study populations. A population pyramid is a graph that shows the distribution of ages across a population divided down the center between male and female members of the population.

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Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

Based on the computed 95% confidence interval, we can conclude that we are 95% confident that the true population mean falls within the range of 12.65 to 25.65.

A confidence interval is a range of values that provides an estimate of the true population parameter. In this case, we are interested in estimating the population mean (μ). The 95% confidence interval, as mentioned, is given as 12.65 ≤ μ ≤ 25.65.

Interpreting this confidence interval, we can say that if we were to repeat the sampling process many times and construct 95% confidence intervals from each sample, approximately 95% of those intervals would contain the true population mean.

The confidence level chosen, 95%, represents the probability that the interval captures the true population mean. It is a measure of the confidence or certainty we have in the estimation. However, it does not guarantee that a specific interval from a particular sample contains the true population mean.

Therefore, based on the computed 95% confidence interval, we can conclude that we are 95% confident that the true population mean falls within the range of 12.65 to 25.65.

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The required expression in terms of a0​ and a1​ that includes all terms up to order 3 is: y(x) = a⁰ + a¹x + a²x²+ a³x³ = 1 + 0x - x2/4 + 0x³.

The given differential equation is y′′+(x+2)y′+y=0.

To find the first four non-zero terms in a power series expansion about x=0 for a general solution to the differential equation,

let y= ∑n=0∞

an xn be a power series solution of the differential equation.

Substitute the power series in the differential equation. Then we have to solve for a⁰​ and a¹​.

Given that, y = ∑n=0∞

a nxn Here y' = ∑n=1∞ n a nxn-1

and y'' = ∑n=2∞n

an(n-1)xn-2

Substitute the above expressions in the differential equation, and equate the coefficients of like powers of x to zero. This yields the recursion formula for the sequence {an}. y'' + (x + 2)y' + y = 0 ∑n=2∞n

an (n-1)xn-2 + ∑n=1∞n

an xn-1 + ∑n=0∞anxn = 0

Expanding and combining all three summations we have, ∑n=0∞[n(n-1)an-2 + (n+2)an + an-1]xn = 0.

So, we get the recursion relation an = -[an-1/(n(n+1))] - [(n+2)an-2/(n(n+1))]

This recursion relation yields the following values of {an} a⁰ = 1,

a¹ = 0

a² = -1/4,

a³ = 0,

a⁴ = 7/96.

Hence the first four non-zero terms of the series solution of the differential equation are as follows: y = a⁰​+a¹​x+a²​x²​+a³​x³​+⋯  = 1 + 0x - x2/4 + 0x3 + 7x4/96.

Thus, the required expression in terms of a0​ and a1​ that includes all terms up to order 3 is: y(x) = a⁰ + a¹x + a²x²+ a³x³

= 1 + 0x - x2/4 + 0x3.

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All the coefficients \((\(a_1\), \(a_2\), and \(a_3\))\) are zero, so the power series expansion of the general solution is zero.

To find the power series expansion for the given differential equation, we assume a power series solution of the form:

\(\[y(x) = \sum_{n=0}^{\infty} a_n x^n\]\)

where \(\(a_n\)\) represents the coefficient of the nth term in the power series and \(\(x^n\)\) represents the term raised to the power of n.

Next, we find the first and second derivatives of \(\(y(x)\)\) with respect to x:

\($\[y'(x) = \sum_{n=0}^{\infty} a_n n x^{n-1}\]\[y''(x) = \sum_{n=0}^{\infty} a_n n (n-1) x^{n-2}\]\)

Substituting these derivatives into the given differential equation, we obtain:

\(\[\sum_{n=0}^{\infty} a_n n (n-1) x^{n-2} + (x+2) \sum_{n=0}^{\infty} a_n n x^{n-1} + \sum_{n=0}^{\infty} a_n x^n = 0\]\)

Now, let's separate the terms in the equation by their corresponding powers of x.

For n = 0, the term becomes:

\(\(a_0 \cdot 0 \cdot (-1) \cdot x^{-2}\)\)

For n = 1, the terms become:

\(\(a_1 \cdot 1 \cdot 0 \cdot x^{-1} + a_1 \cdot 1 \cdot x^0\)\)

For \(\(n \geq 2\)\), the terms become:

\(\(a_n \cdot n \cdot (n-1) \cdot x^{n-2} + a_1 \cdot n \cdot x^{n-1} + a_n \cdot x^n\)\)

Since we want to find the terms up to order 3, let's simplify the equation by collecting the terms up to \(\(x^3\)\):

\(\(a_0 \cdot 0 \cdot (-1) \cdot x^{-2} + a_1 \cdot 1 \cdot 0 \cdot x^{-1} + a_1 \cdot 1 \cdot x^0 + \sum_{n=2}^{\infty} [a_n \cdot n \cdot (n-1) \cdot x^{n-2} + a_1 \cdot n \cdot x^{n-1} + a_n \cdot x^n]\)\)

Expanding the summation from \(\(n = 2\) to \(n = 3\)\), we get:

\(\([a_2 \cdot 2 \cdot (2-1) \cdot x^{2-2} + a_1 \cdot 2 \cdot x^{2-1} + a_2 \cdot x^2] + [a_3 \cdot 3 \cdot (3-1) \cdot x^{3-2} + a_1 \cdot 3 \cdot x^{3-1} + a_3 \cdot x^3]\)\)

Simplifying the above expression, we have:

\(\(a_2 + 2a_1 \cdot x + a_2 \cdot x^2 + 3a_3 \cdot x + 3a_1 \cdot x^2 + a_3 \cdot x^3\)\)

Now, let's set this expression equal to zero:

\(\(a_2 + 2a_1 \cdot x + a_2 \cdot x^2 + 3a_3 \cdot x + 3a_1 \cdot x^2 + a_3 \cdot x^3 = 0\)\)

Collecting the terms up to \(\(x^3\)\), we have:

\(\(a_2 + 2a_1 \cdot x + (a_2 + 3a_1) \cdot x^2 + a_3 \cdot x^3 = 0\)\)

To find the values of \(\(a_2\), \(a_1\), and \(a_3\)\), we set the coefficients of each power of x to zero:

\(\(a_2 = 0\)\\\(a_3 = 0\)\)

Therefore, the first four nonzero terms in the power series expansion of the general solution to the given differential equation are:

\($\[y(x) = a_1 \cdot x + a_2 \cdot x^2 + a_3 \cdot x^3\]\[= 0 \cdot x + 0 \cdot x^2 + 0 \cdot x^3\]\[= 0\]\)

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The criterion that is least likely to be used in choosing bins (classes) in a frequency distribution is personal preference or subjective judgment.

When constructing a frequency distribution, it is important to consider objective criteria based on the nature of the data and statistical principles. Common criteria used for choosing bins include the range of the data, the desired number of bins, the shape of the data distribution, and the purpose of the analysis. These criteria help ensure that the bins effectively capture the variation in the data and provide meaningful insights. Personal preference or subjective judgment, on the other hand, may introduce bias and lack objectivity in determining the bin boundaries. It is essential to rely on objective criteria and statistical guidelines to make informed decisions when choosing bins for a frequency distribution.

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The expression ********** can be represented as 3333333333 in base four, 4444444444 in base five, and 7777777777 in base eight, according to the respective numerical systems.

a) In base four, each digit can have values from 0 to 3. The symbol "*" represents the value 3. Therefore, when we have ten "*", we can express it as 3333333333 in base four.

b) In base five, each digit can have values from 0 to 4. The symbol "*" represents the value 4. Hence, when we have ten "*", we can represent it as 4444444444 in base five.

c) In base eight, each digit can have values from 0 to 7. The symbol "*" represents the value 7. Thus, when we have ten "*", we can denote it as 7777777777 in base eight.

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Using the t-distribution, as we have the standard deviation for the sample, it is found that it can be concluded that the holes are being punched an average of 1. 84 cm.

At the null hypotheses, it is tested if the mean is of 1.84 cm, that is:

\(H_0: \mu = 1.84\)

At the alternative hypothesis, it is tested if the mean is different of 1.84 cm, that is:

\(H_1: \mu \neq 1.84\)

The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

Considering the hypothesis and the given sample, it is found that the parameters are as follows:

\(\overline{x} = 1.85, \mu = 1.84, s = 0.0235, n = 12\).

Hence, the test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{1.85 - 1.84}{\frac{0.0235}{\sqrt{12}}}\)

\(t = 1.47\)

Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.1 and 12 - 1 = 11 df, the critical value is of \(|t^{\ast}| = 1.7959\)

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and it can be concluded that the holes are being punched an average of 1. 84 cm.

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Part A

f(100) is largest

Part B

h(-100) is largest

Part C

f(1/100) is largest

The function

f(x) = 4x-5

g(x) = 4(x-5)

h(x) = (x/4) - 5

Part A

f(100) = 4(100)-5

= 395

g(100) = 4(100-5)

= 4(95)

= 380

h(100) = (100/4) - 5

= 20

f(100) is largest

Part B

f(-100) = 4(-100)-5

= -405

g(-100) = 4(-100-5)

= 4(-105)

= -420

h(-100) = (-100/4) - 5

= -30

h(-100) is largest

Part C

f(1/100) = 4(1/100)-5

= -4.96

g(1/100) = 4((1/100)-5)

= 4(-4.99)

= -19.96

h(1/100) = ((1/100)/4) - 5

= -4.99

f(1/100) is largest

Hence,

Part A

f(100) is largest

Part B

h(-100) is largest

Part C

f(1/100) is largest

The complete question is

Here are the equations that define three functions.

f(x) = 4x - 5

g(x) = 4(x - 5)

h(x) =x/4 -5

a. Which function value is the largest: f(100), g(100), or h(100)?

b. Which function value is the largest: f(-100), g(-100), or h(-100)?

c. Which function value is the largest: f(1/100), g(1/100), or h(1/100)

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Answer:

x = 5

Step-by-step explanation:

\(8x+38=-3(-6-4x)\\\\8x+38=18+12x\\\\8x+38-38=18-38+12x\\\\8x=12x-20\\\\8x-12x=12x-12x-20\\\\-4x=-20\\\\\frac{-4x=-20}{-4}\\\\\boxed{x=5}\)

Hope this helps!

Answer:

1450

Step-by-step explanation:

\(U_{1}=9500\\d=3500.\\n=14\\\\U_{n}=U_{1}+(n-1)d\\U_{n}=95000+(14-1)*3500\\\\U_{n}=140500\\\)

Answer:

20

Step-by-step explanation:

180-110=70

triangle=180

180=70+70+2x

2x=40

x=40/2

x=20

Answer:

3rd option

Step-by-step explanation:

(x + 7)(x - 9) = 25 ← expand left side using FOIL

x² - 2x - 63 = 25 ( add 63 to both sides )

x² - 2x = 88

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 1)x + 1 = 88 + 1

(x - 1)² = 89 ( take square root of both sides )

x - 1 = ± \(\sqrt{89}\) ( add 1 to both sides )

x = 1 ± \(\sqrt{89}\)

Answer:

True is the correct answer

Answer:

I believe the answer is true

Answer:

Hey there!

Your answer is close- but not quite! You chose y=10x, however, if you look closely, the cost is 10 at 2 sandwiches. Thus, the slope should be 5, and correct answer would be y=5x.

Let me know if this helps :)

Answer:

the answer should be C

We may build up a proportion and solve for the scale model radius of Neptune using the ratio between the radii of the two planets and the known scale model radius of the Earth. The scale model of Neptune that is produced has a radius of around 9.7 cm.

We may take advantage of the fact that the ratio between the two planets' radii and the ratio between their respective scale model radii is the same. Let's name the Neptune scale model radius "r" Then, we may set up the ratio shown below:

Neptune's radius is equal to the product of Earth's radius and its scale model.

With the provided values, we may simplify and obtain:

24620 km / 6370 km equals 2.5 cm / r

We obtain the following when solving for "r":

r = (24620 km * 2.5 cm) / (6370 km)

r ≈ 9.7 cm

Therefore, a scale model of Neptune would have to be drawn with a radius of approximately 9.7 cm.

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\(\huge\boxed{6.37500}\)

Explanation...

Let's divide the numerator by the denominator.

\(\boxed{3\;Divided\;by\;8=0.375}\)

Now, lets add the whole number (6) to 0.375.

\(\boxed{6+0.375=6.37500}\)

That's your final answer. (Above)

The number of solution for the equation  x₁ + x₂ + x₃ = 14 where x₁ , x₂ , x₃  are integers for different condition are

a. 91 solution for each variable greater than or equal to zero

b. 66 solution when each variable greater than or equal to one.

Total number of solution for the equation x₁ + x₂ + x₃ = 14.

a. Each variable x₁ , x₂, x₃ is an integer greater than or equal to zero.

When x₁ = 0 and x₂ , x₃ have different values

0 + 0 + 14 = 14

0 + 1 + 13 = 14

0 + 2 + 12 = 14

0 + 3 + 11 =14

0 + 4 + 10 =14 .......so on

0 + 13 + 1 = 14

Total outcome = 14

Two place needs to be fill one place is fixed by certain number.

Total number of possible solution is equal to

= ¹⁴C₂

= ( 14! ) / ( 14 - 2 )! 2!

= ( 14 × 13 ) / ( 2 × 1 )

= 7 × 13

= 91

b. Each integer is an integer greater than or equal to one

When x₁ = 1 and x₂ , x₃ have different values

1 + 1+ 12 = 14

1 + 2 + 11 = 14

1+ 3 + 10 =14

1 +4 + 9 =14 .......so on

1+ 12 + 1 = 14

Total outcome = 12

Total number of possible solution when each variable is greater than or equal to 1

= ¹²C₂

= ( 12! ) / (12 - 2)! 2!

= ( 12 × 11 ) / 2

= 66

Therefore , total number of solution for the equation having integer variable x₁ + x₂ + x₃ = 14 is

a. Each variable greater than or equal to zero has 91 solution.

b. Each  variable greater than or equal to one has 66 solution.

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The simplification form of the provided expression 6543549 ² × 4³ ÷8 is 3.4254×10¹⁴

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a mathematical expression:

= 6543549² × 4³ ÷ 8

Using BODMAS

= 6543549² × 8

= 3.4254×10¹⁴

Thus, the simplification form of the provided expression 6543549 ² × 4³ ÷8 is 3.4254×10¹⁴

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Answer:

Step-by-step explanation:

3444

The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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Answer:

A

Step-by-step explanation:

A because 16(x + y) = (16x + 16y)

Answer:

16(x+y)

Step-by-step explanation:

16 times x + 16 times y= 16x+16y

2(2x+6y)=4x+12y

(2x+6y)+(2x+6y)=4x+12y

4(x+3y)=4x+12y

Hence, 16(x+y) is not equivalent to 4x+12y.

Answer:

9.9 gallons

Step-by-step explanation:

250 mi/9 gas = 27.7777 miles per gallon of gas

275 mi/ (27.77 mi/gal) = 9.9 gallons

Answer:

your very welcome!

Step-by-step explanation:

2

passes through (4,7) slope is 2