a rectangle has a perimeter of 38. find the length and the width of the rectangle if the length is 5 less than twice the width. hint: the equation for the perimeter of a rectangle is:

The surface area of the cuboid is 94 m² while The surface area of the triangular pyramid is 259.695 in²

An equation is an expression showing the relationship between numbers and variables.

Surface area is the sum of each area of the solid surface.

7) For the cuboid:

Surface area = 2(3 m * 4 m) + 2(3 m * 5 m) * 2(4 m * 5 m) = 94 m²

The surface area of the cuboid is 94 m²

8) For the triangular pyramid:

Surface area = 3(1/2 * 17.4 in * 8.7 in) + (1/2 * 8.7 in * 7.5 in) = 259.695 in²

The surface area of the triangular pyramid is 259.695 in²

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Step-by-step explanation:

I think the actual equation you meant to write was 5x⁴ + 7x³ - 2x² - 3x + c.

You're going to equate the whole equation to 0 and replace x for -1( because x + 1 is a factor)

= 5(-1)⁴ + 7(-1)³ - 2(-1)² - 3(-1) + c = 0

= 5 - 7 - 2 + 3 + c = 0

= - 1 + c = 0

Therefore c = 1

The solutions to this equation are x=5 and x=2.

What is the factor of the equation?

A factor in an expression is something that is multiplied by something else. It can be a number, variable, term or any other longer expression. For example, the factors of 2xy are 2, x and y.

We have,

(√x-1) - 5 = x - 8

To solve this equation, you can start by isolating the variable (x) on one side of the equation.

You can begin by adding 5 to both sides of the equation, which will give you (√x-1) = x-3.

Then, you can square both sides of the equation, which will give you x-1 = x^2-6x+9.

To solve for x, you can add 1 to both sides, which will give you x^2-6x+10=0.
You can then factor this equation to get (x-5)(x-2)=0.

Hence, The solutions to this equation are x=5 and x=2.

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[tex]y=\frac{3}{2}x-4[/tex]

Linear functions can be written in different forms such as standard and slope-intercept form.

Rewriting the Equation

To rewrite standard form (Ax + By = C) into slope-intercept, simply solve for y. To solve for y, we need to isolate it. We can do this using the properties of equality. Firstly, move x to the opposite side.

Subtract 3x from both sides.

Then, divide both sides by -2.

This is the slope-intercept form.

Interpreting the Values

Slope-intercept form is written as y = mx + b, m is the slope and b is the y-intercept. This means that the slope of the line we were given is 3/2. Additionally, the y-intercept is -4.

Answer:

y = 3/2 x - 4

Step-by-step explanation:

The given equation is:

Recall that the slope-intercept form is of the form:

Therefore the equation can be rewritten as follows:

The 25th term in the sequence is 620.

To find the 25th term in the sequence, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a1 + (n-1)d

where a1 is the first term, d is the common difference, and n is the term number.

Substituting the known values:

aₙ  = 20 + (25-1) × 25

aₙ  = 20 + (24 ×25)

aₙ = 20 + 600

aₙ = 620

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The domain of the function is, All real numbers.

And, The range of the function, {- 24}

The set of all inputs of the function is called Domain of set.

We have to given that;

The function is,

⇒ f (x) = - 24

Now, We know that;

The domain is where the function is defined.

Hence, The domain of function f (x) = - 24 is,

⇒ Domain = (- ∞, ∞)

And, The range is the set of values that correspond with the domain.

Hence, The range of the function, {- 24}.

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The regression equation to predict the head circumference of a child who is 24.25 inches tall y=17.20 inches

The regression line with the least squares

y = 0.1827*x + 12.4932

Children that are 25.25 inches tall should have a mean head circumference that we can anticipate.

Let x = 25.75

y is thus equal to 0.1827*25.75 plus 12.4932.

b) The mean head circumference of kids who are 25.25 inches tall falls within the 95% confidence interval of

The Mean of the head circumference is 17.327, the standard deviation is 0.219, there are 11 participants, and there are 10 participants in step c.

y = 0.1827*x + 12.4932

The head circumference of a youngster who is 25.25 inches tall must be predicted.

Let x = 25.75

y is thus equal to 0.1827*25.75 plus 12.4932.

y=17.20 inches.

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Jake said you can compare two fractions and determine which fraction is larger when two fractions have the same denominator by only comparing the numerators.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

Two fractions have the same denominator.

Then,

you can determine which fraction is larger when two fractions have the same denominator by only comparing their numerators.

That means,

1/n and 2/n are the two fractions.

Then,2 > 1.

So, 2/n > 1/n.

Therefore, you can determine which fraction is larger when two fractions have the same denominator.

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Answer:

  17

Step-by-step explanation:

You want the determinant of the coefficient matrix for the equations ...

The matrix of coefficients is formed by listing the coefficients of the equation variables on rows of the matrix, in the same order for each row.

Here it is:

  [tex]\left[\begin{array}{cc}3&4\\-2&3\end{array}\right][/tex]

The determinant of a 2×2 matrix is the difference between the product of terms on the down diagonal and that on the up diagonal.

  det = (3)(3) -(-2)(4) = 9 + 8 = 17

The determinant of the coefficient matrix is 17.

__

Additional comment

Many scientific and graphing calculators can find this for you. A spreadsheet can be useful for this purpose, too.

The determinant is only defined for a square matrix. For sizes larger than 2×2, the arithmetic is a little different.

The rate of change of the angle of elevation is the rate at which the angle between the rope and the horizon changes over time.

The angle of elevation is the angle formed by the rope attached to the boat and the horizon. It is measured from the horizon line and can be used to measure the height of the boat relative to the horizon. The rate of change of the angle of elevation is the rate at which the angle between the rope and the horizon changes over time. This rate of change can be calculated by measuring the change in the angle over a specific time period and dividing it by the time period. This rate of change can be used to determine the speed at which the boat is moving up or down relative to the horizon. It can also be used to measure the rate of acceleration or deceleration of the boat.

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The complete question is

What is the rate of change of the angle of elevation, which is the angle formed by the rope attached to the boat and the horizon, given the speed of the boat and the distance from the boat to the horizon?

first off, next time make sure your screenshot is sharp enough and clear enough.

so if we notice the two points on the midline that you took, the horizontal distance will be from -4.5 to 3.6 which gives us a distance over the x-axis of 8.1 units, now half of that will be to the "orange" area, half of 8.1 is 4.05.  Now, the ending of the "orange" part is not really clear, but that'd be the period, because that is the part that's repeating.

How long is it?

well, our 4.05 half ends after the "2", so without a better calibration of the picture, hmmm 2.20 or thereabouts, let's make an assumption the "orange" section ends at 16, so that'd be 4.05 + (16 - 2) ≈ 18.05.

The amount of money gives to my friend today so that the repayment of $500 in 2 weeks is equivalent to a simple interest loan with a rate of 153% per year is,  $477.10

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

Given that,

Loan agreed on simple interest rate =  153% per year

He knows that he can pay me back $500 in 2 weeks or 2/52 years

Suppose, money given to him = P

So, simple interest of amount P in 2 weeks

I   = P × 125 ×(2/52) /100

   = 0.048P

Total repayment = P + 0.048P

He can pay back only $500

Total repayment = $500

P + 0.048P         = $500

1.048P = 500

P       =    477.10

Hence, the loan amount is  $477.10

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Such a plot is evidence of a linear relationship between the explanatory and response variables, which is a condition for these inference procedure

These are the four presumptions: Relatively linear residuals Continuity of residuals The residuals are distributed normally. residual variance is same.

Linearity: We plot the residuals and y values in a scatter plot. Y values are shown on the horizontal x axis and standardized residuals, or ZRESID in SPSS, are derived from the vertical y axis. The linearity assumption is satisfied if the scatter plot displays a linear pattern (rather than a curved pattern).

We generally have two types of data: cross sectional and longitudinal. Cross -sectional datasets are those where we collect data on entities only once. For example we collect IQ and GPA information from the students at any one given time.

Independence is a concern when working with longitudinal datasets. With a longitudinal dataset, observations are gathered from the same subject across time. For example, in stock price information, we gather price information on the same stock, the subject, throughout time.

The two forms of data that we typically use are longitudinal and cross sectional. Datasets that are cross-sectional are those for which entities' information is only collected once. For instance, we constantly get IQ and GPA data from the kids.

We gather GPA data from the same student over time in a longitudinal data set.

We do not need to worry about the Independence assumption in cross-sectional datasets. It is "assumed" that it will be.

Normality: First, we create a histogram of the residuals, and then we check to see if they are normal. The assumption is met if the residuals do not exhibit skewness.

A scatterplot of the residuals vs the explanatory variable values shows a haphazard distribution of dots around the line.

Correct. This inference technique requires a linear relationship between the explanatory and response variables, which is demonstrated by a plot like this.

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.

Answer: 0.002. 0.127 - 0.125 is 0.002

Answer:

f = 2÷7. I hope this helped your experience

It is neither row echelon form nor reduced row echelon form matrix

How do you know if a matrix is in echelon form or reduced echelon form matrix ?

A matrix is in reduced row-echelon form if it satisfies the following:

In each row, the left-most nonzero entry is 1 and the column that contains this 1 has all other entries equal to 0. ...

The leading 1 in the second row or beyond is to the right of the leading 1 in the row just above.

if you look at the two row echlon form you can see that it has leading entries(starting form left) that all one and there are no-zero elements above diagonal which can be any numbers (2,3,4, 6, x,y,x).

However reduced row echelon of has always leading elements 1 and are on diognal, this form is always like this therefore we can infer that reduced row echlon form is always uniqe as oppose to row echelon form.

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The sample for this situation is People who responded to the survey.

What is the sample?

A sample is a group of elements chosen from the population. The features that describe the population are called the parameters and the properties of the sample data are known as statistics. Population and sample both are important parts of statistics.

A sample is a subset of the population that is selected for a study.

In this case, the population is the group of people who might be interested in visiting the theme park in Florida.

The park wants to attract more visitors, so they post a survey on a travel website asking viewers which attractions they would like to see at the park.

The sample is the group of people who responded to the survey, as it represents the subset of the population that the park is trying to gather information from.

Hence, The sample for this situation is People who responded to the survey.

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Answer:

h = 40 cm

Step-by-step explanation:

1. Let's calculate the total volume of 1920 cubes, size 5 x 5 x 5 cm:

V one =  5 cm x 5 cm x 5 cm = 125 cm³
V all = 1920 x 125 = 240,000 cm³

2. Divide this volume by the area of the paper to get the height, given that 1 m = 100 cm:

S paper = 100 cm x 60 cm = 6,000 cm²

h = V all / S paper = 240,000 / 6,000 = 40 cm

A solid whose cross-section is defined by a(x), the volume of the solid given by      [tex]\int\limits^a_b {A(x)} \, dx[/tex]

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The values would be

log √7= 0.291

log 23/6= 0.585

What is a logarithm?

A logarithm is a mathematical function that calculates the power to which a given number (called the base) must be raised to produce a given value. The most common base used in logarithms is base 10, but logarithms can be defined with any base. If the base of a logarithm is not specified, it is assumed to be base 10. The logarithm of a number is represented by the symbol log.

log √7 = (1/3)log7

Log 23/6 = log(23) - log(6)

The logarithm of a number is the exponent to which the base must be raised to produce that number. If the base of the logarithm is not specified, it is assumed to be base 10.

The square root of 7 is around 2.646, and log2.646 is around 0.874, so

log √7 = (1/3)log7 = (1/3)*0.874 ≈ 0.291

The logarithm of 23 is around 1.363 and the logarithm of 6 is around 0.778, so

Log 23/6 = log(23) - log(6) = 1.363 - 0.778 = 0.585

Hence, the values would be

log √7= 0.291

log 23/6= 0.585

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Answer:

[tex]f(a)=8a+5\\\\f(x+h)=8x+8h+5\\\\\frac{f(x+h)-f(x)}{h}=8[/tex]

Step-by-step explanation:

When we're asked to write what f(x+h) or f(a) is equal to, all we really have to do is substitution. The original function is provided as [tex]f(x)=8x+5[/tex], and all that "x" represents is input, now we can manipulate what that input is by simply substituting in new input. So if we want to write f(x+h), we substitute in "x+h" for "x".

For this problem, we just do what was stated about and replace all of the x's, with a's, meaning: [tex]8x+5\to 8a+5[/tex].

We essentially do the same thing here, although we will have to simplify more, but the first step is as follows: [tex]8x+5\to 8(x+h)+5[/tex], now from here we want to expand out the [tex]8(x+h)[/tex] by using the distributive property, so it becomes: [tex]8x+8h[/tex] and plugging this into our equation we get: [tex]8x+8h+5[/tex]

For this last question, I think it's also important to note that this is the formula to calculate the slope between point "x" and the point "h units away" or "x+h".

We already know what f(x+h) is and what f(x) is, so let's plug those into the equation:

[tex]\frac{(8x+8h+5)-(8x+5)}{h}[/tex]

Now let's distribute the negative sign to get:

[tex]\frac{8x+8h+5-8x-5}{h}[/tex]

Now let's group like terms:

[tex]\frac{(8x-8x)+(5-5)+8h}{h}[/tex]

Now let's simplify the grouped terms

[tex]\frac{8h}{h}[/tex]

Now let's divide by h to get:

[tex]8[/tex]

And this is our answer!

Answer:

Step-by-step explanation: Hello!

To find angle EOD, you are already given two angle measurements.  The measure of angle AOB is 55 degrees and the measure of angle BOC is 30 degrees.  The important thing that you have to remember to solve this problem is that vertical angles are congruent. (I won't be explaining the definition of vertical angles, but you can find a lot of images and explanations online). This means the two angles formed by two lines intersecting each other in any way is always congruent.  Angles AOB and EOD are congruent by the definition of vertical angles.  This means that the measure of angle EOD is 55 degrees.  

Now, you have to find the measurement of angle DOC.  By the definition of straight lines, you know that the angles formed by a straight line all add up to 180 degrees.  This means that:

EOD + DOC + COB = 180 degrees.  You are already given two of these measurements.  (Angle EOD which you just figured out and Angle COB which was already given).  Fill these numbers in the equation.

55 + DOC + 30 = 180.  Combine like terms (55 + 30)

85 + DOC = 180.  Then subtract 85 from both sides using the subtraction property of equality.

(85 - 85) + DOC = (180 - 85)

DOC = 95.

The measure of angle DOC = 95.

You can check this by substituting the new measurement for angle DOC back into the equation.

Does 55 + 30 + 95 = 180?

85 + 95 = 180

180 = 180.

The measure of angle DOC is 95 degrees and the measure of angle EOD is 55 degrees.

The sample size of the data set is the total number of plants in the experiment. The mean is the average of the data set, the standard deviation is the measure of how much the values in the data set vary from the mean, and the standard error is a measure of the accuracy of the mean.

The sample size of the data set is the total number of plants in the experiment and can be determined by counting the total number of plants in the experiment. The mean is the average of the data set and can be calculated by taking the sum of all the values divided by the sample size. The standard deviation is the measure of how much the values in the data set vary from the mean and can be calculated by taking the square root of the sum of all the squared differences divided by the sample size minus one. The standard error is a measure of the accuracy of the mean and can be calculated by taking the standard deviation divided by the square root of the sample size.

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The greatest integer function is a function that gives the greatest integer less than or equal to a given number.  The standard graph is in the picture.

The graph you have is that function, shifted down by 2 units.

The answer is c.

The determinant of a matrix is a scalar value that can be used to determine if a set of vectors is linearly independent.

It is calculated by taking the product of the elements in each row or column and subtracting the product of the elements in the other row or column. For example, if we have a matrix with two columns and two rows, A and B, the determinant can be calculated using the following formula: det(A) = (A11*A22) - (A12*A21). If the determinant is equal to zero, then the set of vectors is linearly dependent, as this implies that all of the elements in the matrix are multiples of each other. On the other hand, if the determinant is non-zero, then the set of vectors is linearly independent. This can be seen because all of the elements in the matrix are not multiples of each other and thus the set of vectors cannot be expressed as a linear combination of each other.

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Answer:

aₙ = 9 + 2n

Step-by-step explanation:

Formula for the nth term of an arithmetic sequence, aₙ with a common difference of d and first term of a₁ is

aₙ = a₁ + d(n-1)

The common difference is the difference between two consecutive terms and is a constant

Here d = 13- 11 = 15-13 = 2

First term is 11

nth term:

aₙ = 11 + 2(n-1)

aₙ = 11 + 2n -2

aₙ = 9 + 2n

So if you wanted the 10 term say it would be

a₁₀ = 9 + 2x 10 = 9 + 20 = 29

The function h(x) = 5 square root x e^-x is increasing on the interval (0, ∞) and decreasing on the interval (-∞, 0).

1. Calculate h'(x) = 5 (1/2 x^-1/2 e^-x - x^1/2 e^-x)

2. Set h'(x) = 0 to find the critical points.

3. Since h'(x) < 0 for x < 0 and h'(x) > 0 for x > 0, h(x) is decreasing for x < 0 and increasing for x > 0.

4. Therefore, h(x) is increasing on the interval (0, ∞) and decreasing on the interval (-∞, 0).

The derivative of h(x) = 5 square root xe^-x is h'(x) = 5 (1/2 x^-1/2 e^-x - x^1/2 e^-x). Setting h'(x) = 0 gives the critical points of the function. Since h'(x) is negative for x < 0 and positive for x > 0, this tells us that the function is decreasing for x < 0 and increasing for x > 0. So, h(x) is increasing on the interval (0, ∞) and decreasing on the interval (-∞, 0). We can also conclude from the graph of the function that it is concave down for x < 0 and concave up for x > 0.

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The pdf of the random variable Z = X + Y is given by the convolution of the pdfs of X and Y. The convolution is denoted by h(z) = (f * g)(z) = ∫f(x)g(z-x)dx. It represents the probability of the sum of two random variables taking on a certain value.

In other words, it is the probability of X taking on a certain value x and Y taking on a certain value z-x simultaneously. The convolution is only defined if X and Y are independent random variables, and the integral converges. It is also important to note that the convolution of two pdfs does not necessarily result in a pdf, it can also result in a cdf, if integral from minus infinity to z is taken instead of from minus infinity to infinity.

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The values of m and n are m = 123,000 and n = (123,000 - m1) / 2 + 1.

The given number is 123,000 which is the mth number in the nth row.

The rows contain two more numbers than the previous row.

Let us assume that the first row has m1 numbers.

Therefore, the second row has m1 + 2 numbers, the third row has m1 + 4 numbers, and so on.

We can represent the above information in a general formula as;

m1 + 2 (n - 1) = m

where m1 is the number of elements in the first row and n is the row number in which 123,000 is present.

By solving the above equation, we get

m1 = m - 2 (n - 1)

Now, we can calculate the value of n as;

n = (m - m1) / 2 + 1

Substituting the values of m and m1, we get

n = (123,000 - m1) / 2 + 1

Therefore, the values of m and n are m = 123,000 and n = (123,000 - m1) / 2 + 1.

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