Question 6
Isosceles trapezoids ABCD and PQRS are similar. The perimeter of ABCD is 72.8 inches and
the perimeter of PQRS is 91 inches. If the legs of ABCD measure 12.4 inches, what are the measures of the legs of PQRS?
O 19.375 inches
O 30.6 inches
O 15.5 inches
O9.92 inches

Answer:

the answer is 128 fluid ounce

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

you can use the website desmos and literally type the exact equations in and it will show the graph.

Answer: I think the answer is A

Step-by-step explanation: It goes from 128 to 150.

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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Answer:

h

Step-by-step explanation:

d

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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The number is 60.

A multiple is defined as the the number resulting form the process of multiplication of two numbers.

For example, 6 is a multiple of 2 and 3 since 2 × 3 = 6.

Let x be the number.

x < 70

Multiples of 12 less than 70 = 12, 24, 36, 48, 60

Multiples of 15 less than 70 = 15, 30, 45, 60

Multiple common to 12 and 15 = 60

Hence the number here is 60.

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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

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.

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:

(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 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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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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The answer is A) 10,000,000 seven-digit numbers; B) The number is  20,000 ; C)  5,314,410 identification numbers are possible if no two adjacent digits are the same.

Seven-digit identification number:

A.) The number of possible identifying numbers

Possible digits are 0 up to 9.

Total number of digits: 10

Any of the 10 digits may be used for each;

Hence,

10×10×10×10×10×10×10 equals 10,000,000 potential outcomes.

B.) For it to start begin with either 023 and 003.

- the first digit must be 0 (1 possible value)

- 2nd digit must be 2 or 0 (2 possible values)

- 3rd digit must be 3 (1 possible value)

- 4th and 5th can be filled with any digit (10 × 10 possible values)

Which gives

1×2×1×10×10×10×10 = 20,000

3.) no two adjacent digits are the same that is no two digits that follows each other are the same.

In this case only one digit have 10 possible values.

The other four digits have 9 possible values each.

Which gives:

10×9×9×9×9×9×9 = 10× [tex]9^{6}[/tex] = 5,314,410

The full question:

A certain identification number is a sequence of seven digits. (a) How many identification numbers are possible? (b) How many of them begin with either 023 or 003? (c) How many identification numbers are possible if no two adjacent digits are the same? (For example, 123-4-567 is permitted, but not 123-3-456.).

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The greatest positive integer n such that [tex]$2^n$[/tex]divides k is 18.

The product k can be expressed as [tex]$(b - a)_{1 \le a < b \le 20}$[/tex] . Since [tex]$2$[/tex] is the only even number between [tex]$1$[/tex] and [tex]$20$[/tex], the product can be written as [tex]$(2 - 1)_{1 \le a < b \le 20}$[/tex]. Since the product of [tex]$(b - a)$[/tex]  is the same for all pairs of integers a and b that satisfy [tex]$1 \le a < b \le 20$, $k$ is equal to $(2 - 1)^{19}$.[/tex]

To determine the greatest positive integer n such that [tex]$2^n$[/tex]divides k, we need to calculate the largest exponent m  such that [tex]$2^m$[/tex] is a factor of [tex]$(2-1)^{19}$[/tex]. To do this, we can factor [tex]$(2-1)^{19}$[/tex] using the equation [tex]$(2-1)^{19} = 2^{19} - 1$[/tex]. This equation can be written as [tex]$2^{19} = (2-1)^{19} + 1$[/tex], which can be rewritten as [tex]$2^n(2^{19-n}+1) = (2-1)^{19}$[/tex]  for any positive integer n. Since the factor [tex]$(2-1)^{19}$[/tex] is odd, the greatest positive integer n such that [tex]$2^n$[/tex] divides k is 18, since [tex]$2^{19}$[/tex] is the greatest power of 2 that divides [tex]$(2-1)^{19}$.[/tex]

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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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A linear function is a mathematical function that defines a straight line when plotted on a coordinate plane.

It is defined by an equation of the form:

[tex]$y = mx + b$[/tex]

where [tex]$y$[/tex] is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope of the line is the rate at which the dependent variable changes with respect to the independent variable. In other words, it represents how much the dependent variable will change for each unit change in the independent variable.

In the case of the cost of renting a car for a day, the dependent variable is the cost (C) and the independent variable is the number of miles driven (x). The equation for the cost is:

[tex]$C = 42 + 0.65x$[/tex]

The slope of the line is 0.65, which means that for each additional mile driven, the cost of renting the car will increase by $0.65. The units of the slope are dollars per mile, since it represents the additional cost per mile driven.

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The 95% confidence interval for the amount of time spent on personal issues is (4.805, 4.95).

Mean time that employees spend on personal issues each week(M) = 4.9 hours

Standard deviation = 0.35 hours

The following formula is used to get the confidence interval for the sample mean and standard deviation given:

μ = M ± t(sM)

where; M = sample mean

t = T-statistic based on confidence interval

Degree of freedom = n - 1

From the question, n = 55

Degree of freedom = 55 - 1

Degree of freedom = 54

(Standard errors)sM = √(s^2/n)

Now putting the value

sM = √(0.352/55)

sM = 0.05

t = 2.005 This is determined using the Excel formula =T.INV.2T at a confidence level of 0.95 and a degree of freedom of 55-1=54. (0.05,54)

Now the confidence interval

μ = M ± t(sM)

μ = 4.9 ± 2.005 × 0.05

μ = 4.9 ± 0.095

μ = (4.9 - 0.095, 4.9 + 0.095)

μ = (4.805, 4.95)

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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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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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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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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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The value of the fractions will be:

1. 4/10 + 2/10 = 6/10

2. 9 /12 + 3/12 = 1

3. 6/10 + 4/10 = 1

4. 2/8 + 3/8 = 5/8

5. 2/7 + 6/7 = 1 1/7

6. 11/9 + 8/9 = 2 1/9

7. 5/13 + 10/13 = 1 2/13

8. 3/5 + 7/10 = 1 3/10

9. 7/8 + 13/16 = 1 11/16

10. 9/30 + 3/5 = 9/10

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

It should be noted that in order to add the numbers it's essential to have a common denominator. For example, 7/8 + 13/16 will be:

= 7/8 + 13/16

= 14/16 + 13/16

= 27/16

= 1 11/16

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The constant term for the expression 5g³ + 2 is 2.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the expression,

5g³ + 2,

a linear equation consists of three terms,

variables, coefficient of variables, and constant.

A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Compared with the given expression,

g is the variable and 5 is the coefficient,

2 is the constant term.

Hence 2 is constant.

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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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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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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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Answer: -3(x-8)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

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.