(−6x−2)+(6x
2
−5x−10)

the probability that the distance between two randomly chosen points in a circle is less than the radius 1/3

Put the first point (P) somewhere on the circle (center O) - all the points are the same so it doesn’t matter where.

The other point (Q) will be somewhere on the circumference - length  2πr

It’s not clear if you want to measure distance around the circle or along a straight line.

If you measure around the circle, then there is an acceptable distance  r

 on either side of P and the probability is  2r/2πr=1/π

If you measure in a straight line, then Q can be a maximum distance r

 from P and OPQ is an equilateral triangle. We therefore have  60∘

 on each side of P and the probability is 120∘/360∘=1/3

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The money available for saving is 3350.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Monthly earnings = 6500

Expenses:

Rent = 1650

Electricity = 300

Car payment = 1200

Total expenses.

= 1650 + 300 + 1200

= 3150

Now,

Remaining amount.

= Earnings - Total expenses

= 6500 - 3150

= 3350

Thus,

The money remaining is 3350.

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Answer:

Below

Step-by-step explanation:

149 radians  x   180 degrees / radian =26 820 degrees

                                  (did you leave out a decimal point perhaps?)

The correct answer is - Yes we have two independent random samples and large sample size

Conditions for performing a two-sample

t-test: Random, Normal and Independent.

Random: Satisfied, because the samples have been given to be random samples.

Normal: Can be assumed to be satisfied, because the sample size of each sample is at least 30.

Independent: Satisfied. The random samples have been given to be separate and thus are independent. Moreover, the sample sizes are less than 10% of the population size.

Thus all three conditions have been satisfied and thus answer (e) is correct.

A t-take a look at is a statistical test that compares the method of  samples. it's far used in speculation trying out, with a null speculation that the distinction in institution manner is 0 and an change speculation that the distinction in institution manner isn't like zero

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The system of equations has one solution, it is (-3,-5)

Here we have the system of equations:

y = -8x - 29

y = 7x + 16

Because y is isolated in both of the equations, we can write:

-8x - 29 = 7x + 16

-29 - 16 = 7x + 8x

-45 = 15x

-45/15 = x

-3 = x

And the value of y is what we get when we evaluate one of the equations in x = -3

y = 7x + 16 = 7*(-3) + 16

                 = -21 + 16 = -5

The solution is (-3, -5)

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Answer:

see below

Step-by-step explanation:

12/14 = 6/7 = 18/21

so w = 21

The given sequence is arithmetic progression.

The common difference is d= -20.

The difference between any two successive terms in an

arithmetic series will be the same all the way through the sequence.

Given -13, -33, -53, -73, ............ be a sequence.

If any two consecutive terms in the series above differ by "d" along the sequence, then the sequence is arithmetic.

d = -33 - (-13) = - 33 + 13 = - 20

d = -53 - (-33) = - 53 + 33 = - 20

d = -73-(-53) = - 73 + 53 = - 20

The difference 'd' is called common difference.

Since the common difference area same, i.e., d= - 20 the given sequence is arithmetic progression.

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True. An outlier in a data set can significantly affect the value of the mean but not the median.

This is because the median is the middle value in a data set and is not affected by extreme values, while the mean is calculated by adding all the data values and then dividing by the total number of values, which can be significantly affected by extreme values or outliers.

To illustrate this, let's consider the data set {1, 2, 3, 4, 1000}. The median value of this data set is 3, since that is the middle value. The mean of this data set is 205, since it is calculated by adding all the values (1+2+3+4+1000) and dividing by the total number of values (5). The outlier value of 1000 has a significant effect on the mean, changing it from an average of 3.2 (1+2+3+4/4) to an average of 205 (1+2+3+4+1000/5). The median, however, remains unchanged (3). Therefore, it can be concluded that an outlier in a data set can significantly affect the value of the mean but not the median.

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A general solution of matrix to the system Ax = 0 in parametric vector form is given by: X = X_2 * [1 0 1 0 0] + X_3 * [0 1 0 1 0]

How to find all solutions of Ax = 0 in parametric vector form?

The matrix [2 -1 -4 2 6 -3] can be row-reduced to the row-echelon form [2 -1 -4 0 6 -9], which has a pivot in the first, second and fourth columns. This implies that the columns with zero entries in the row-echelon form correspond to free variables in the solution.

Since there are two free variables in the row-echelon form, the solution to the homogeneous linear system Ax = 0 will be in the form of a parametric vector, where X_2 and X_3 are the free variables and X_1, X_4, and X_5 are expressed in terms of X_2 and X_3.

A general solution to the system Ax = 0 in parametric vector form is given by the matrix

X = X_2 * [1 0 1 0 0] + X_3 * [0 1 0 1 0]

where X_2 and X_3 are arbitrary constants. This represents a two-dimensional subspace in R^5, which consists of all linear combinations of the two linearly independent vectors [1 0 1 0 0] and [0 1 0 1 0].

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Answer:

x₁ × x₂ = 3

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the product of the roots = [tex]\frac{c}{a}[/tex]

3x² + 15x + 9 = 0 ← is in standard form

with a = 3 and c = 9 , then

x₁ × x₂ = [tex]\frac{9}{3}[/tex] = 3

To create a relative frequency distribution, we need to count the number of occurrences of each response and divide it by the total number of responses, which is 20 in this case. The relative frequency of classmates who say their favorite month is June can be calculated as follows:

Number of classmates who say their favorite month is June: 2

Relative frequency of classmates who say their favorite month is June: 2/20 = 1/10 = 0.1

So, the relative frequency of his classmates who say their favorite month is June is 0.1 or 10%.

Relative frequency is a measure of the proportion or percentage of observations in a dataset that belong to a specific category or interval. It is calculated as the count of observations in a specific category or interval divided by the total number of observations in the dataset.

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Answer:

(0,-1)

Step-by-step explanation:

you only need to look where the graph and the y line cross each other.. and that is in the point (0,-1)

The value of f in the pentagon is 72 degrees.

A pentagon is a polygon with 5 sides. A regular pentagon is a polygon with 5 sides equal to each other. Therefore, In the regular pentagon, all of the exterior angles marked f are the same size.

Let's find the value of f as follows:

Therefore, the sum of exterior angles of a pentagon is 360 degrees.

Hence,

5f = 360 degrees

divide both sides of the equation by 5

5f / 5 = 360 / 5

f = 72 degrees

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If the Pascal's triangle row entries are 1,n,...,n,1 and the average is 2048 , then the value of n is  15  .

Let the number of entries in the row is = n + 1  .

Since the average of the entries is 2048,

So , the sum of the entries is = 2048 × (n + 1).

We know that the sum of the entries in a row of Pascal's Triangle is equal to 2ⁿ, so we have the equation as :

⇒ 2048 × (n + 1) = 2ⁿ ;

On simplifying ,

we get ;

⇒ n = -0.99975 and n = 15 .

Since the "n" cannot be in negative .So , n = 15   .

Therefore , the value of n is the  pascal's triangle is 15 .

The given question is incomplete , the complete question is

The entries in a certain row of Pascal's Triangle are 1,n,...,n,1 the average of the entries in this row is 2048. find  n  .

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If the number is rounded to the nearest hundred, then the last two digits of the number are replaced with zeros. For example, if the original number is 456, the rounded number to the nearest hundred would be 500.

If the rounded number has zeros, then this means that the last two digits of the original number were already zeros. In other words, the original number was already a multiple of 100.

For example, if the original number was 200, rounding to the nearest hundred would give 200, which has one zero. Similarly, if the original number was 1,000, rounding to the nearest hundred would give 1,000, which has three zeros.

Therefore, the answer to the question depends on the original number being rounded. If the original number was already a multiple of 100, then the rounded number will have zeros. If the original number was not a multiple of 100, then the rounded number may or may not have zeros, depending on the specific digits in the number.

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Answer:

Step-by-step explanation:

first plug in -21 as X

-21-3=-24

-24/4=-6

Based on the linear regression model, the correlation coefficient would be; between 0 and 1

The correlation coefficient is defined as a statistical measure of the strength of a linear relationship between two variables.

Now, In positively correlated variables, the value increases or decreases in tandem. In negatively correlated variables, the value of one increases as the value of the other decreases.

Correlation coefficients are expressed as values between +1 and -1. A coefficient of +1 indicates a perfect positive correlation. A coefficient of -1 indicates a perfect negative correlation

In this case, the slope is positive which is 0.48 and as such we can say that it has positive correlation and as a result the correlation coefficient will be between 0 and 1.

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Answer:ab power of 5 c

Step-by-step explanation: bc it stayed

The probability that a different catalyst is used on each run is 1, meaning it is certain to happen.

To calculate the probability that a different catalyst is used on each run, we can use the formula for combinations, which is given by n! / (n-k)!k!, where n is the number of items to choose from, k is the number of items being selected, and ! means factorial, which is the product of all positive integers up to that number.

In this case, we have 5 experimental runs and 5 different catalysts, so n = 5 and k = 5. The probability that a different catalyst is used on each run is given by:

5! / (5-5)!5! = 5! / 0!5!

= 120/120

= 1

--The question is incomplete, answering to the question below--

"An experimenter is studying the effects of temperature, pres-sure, and type of catalyst on yield from a certain chemical reaction. Three different temperatures, four different pressures, and five different catalysts are under consideration.

Suppose that five different experimental runs are to be made on the first day of experimentation. If the five are randomly selected from among all the possibilities, so that any group of five has the same probability of selection, what is the probability that a different catalyst is used on each run?"

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Answer: There is no answer.

Step-by-step explanation:

The closest answer is 0 but there is no answer since -1 would equal 2.

The best numerical summary of data from 288 participants' answers about the number of steps per day they walked would be a combination of median, IQR, and range (B) and number and percent of the total for each response option (C). Hence, option E is the correct answer.

The median represents the middle value of the data set and is not affected by outliers. The IQR (interquartile range) represents the spread of the middle 50% of the data and is a good indicator of variability.

The range represents the difference between the maximum and minimum values in the data set and gives a good idea of the overall variability of the data.

The number and percent of the total for each response option will give an idea of the distribution of the sample and show the frequency of each response.

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The complete question is -

edge joy a question asks: how many steps per day do you walk? what would be the best numerical summary of data from 288 participants' answers about the number of steps per day they walked?

a. mean, standard deviation, and range.

b. median, IQR, and range.

c. Number and percent of the total for each response option.

d. A or B depending on the distribution of the sample.

e.  B and C.

Answer: -3(x-8)

Step-by-step explanation:

Answer:

h

Step-by-step explanation:

d

Answer:

B = $5.15

Step-by-step explanation:

One way to solve this is by adding the whole numbers first, which gives you $4, and then adding the rest of the number, which is the decimal points, which gives you $1.15, then you add those two together, which gives you your answer of $5.15.

Answer:

B $5.15

Step-by-step explanation:

Add.

$2.35 + $1.15 + $1.65 = $5.15

Hope this helped!

The measurement of each diagonal is;

i. DB = 23.32 inches

ii. RY = 25.05 inches

A diagonal is a line drawn from one edge of a shape to another, which divides it into two equal shapes produced. Thus a diagonal is not the same as the line of symmetry.

NB: A shape may have more than one diagonal.

In the given question, we can apply Pythagoras theorem to have;

i. From triangle DHB,

/Hyp/^2 = /Opp/^2 + /Adj/^2

 DB^2 = DH^2 + HB^2

           = 20^2 + 12^2

           = 400 + 144

DB^2 = 544

DB = (544)^1/2

     = 23.324

DB = 23.32 inches

ii. From triangle HKR,

/Hyp/^2 = /Opp/^2 + /Adj/^2

KR^2 = HR^2 + HK^2

         = 16^2 + (8.72)^2

         = 256 + 76.0384

KR^2 = 332.0384

KR = (332.0384)^1/2

     = 18.2219

KR = 18.22

but,

YR = YK + KR

     = 6.83 + 18.22

     = 25.05

YR = 25.05 inches

The measurement of the diagonals are: DB = 23.32 inches, and  RY = 25.05 inches.

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Answer:

the answer is 128 fluid ounce

Step-by-step explanation:

The answers to each part is mentioned above.

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

Given are the functions as -

y = k/x  &  y = a/x

{ 1 } -

Refer to the graph attached. For the value of {k} > 0, the graph is

reflected along the {y} - axis.

{ 2 } -

Same is the case as in the option { 1 }. The graph is reflected along the

{y} - axis.

Therefore, the answers to each part is mentioned above.

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The formula for the area of a triangle is; Area = 125 units²

Using the concept of similar triangles, we can use the following proportion to fid x of the triangle;

20/x = x/5

Cross multiply to get;

x² = 100

x = √100

x = 10

The formula to find the area of a triangle is;

Area = ¹/₂ * base * height

Area = ¹/₂ * 25 * 10

Area = 125 units²

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Answer:

A

Step-by-step explanation:

The possible values for the given series, the interval notation will be calculated as follows:

Sn is the sum of a geometric series, and a1/(1-r).

R = x a1 = 4 in this mathematical sequence.

If you want the sum to be higher than 8, enter:.

r cannot equal 1 (the equation would have 0 in the denominator) and it cannot be GREATER than one. 8 1/2 Interval notation: (1/2, 1). We must limit it to 1. as the series becomes divergent and lacks a sum if it does.

Interval arithmetic is a general numerical computing technique that automatically generates guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff. Intervals are at the center of this technique.

The definition of intervals also applies to arbitrary totally ordered sets, such as integers or rational numbers. In the special section that follows, the notation of integer intervals is discussed.

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Note that the full question is:

The value of the series 4+4x+4x^2+4x^3... is a real number greater than 8. Find all possible values of x, giving your answer in interval notation.

Find  1+ 1/2+1/6+1/12 , where we alternately multiply by 1/2 and 1/3 to get the next term.

In a certain infinite geometric series, the first term is 1, and each term is equal to the sum of the two terms after it. (For example, the first term is equal to the sum of the second term and third term). If s is the sum of the series and r is the common ratio, find s - r.