Match the following definitions with the correct term.

The standard error with "mean of 7 for some characteristic of interest and a standard deviation of 9.6 and a sample is drawn from this population of size 64" is 1.2.

Standard deviation of the theoretical distribution of a large population of such estimates is equal to the standard error, which is a measure of an estimate's statistical accuracy. The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error. It reveals how much the sample mean would change if a study were to be repeated with fresh samples drawn from a single population.

Here,

Sample size=64

Standard deviation= 9.6

Error=Standard deviation/Sample size

=σ/√n

=9.6/√64

=9.6/8

=1.2

The sample is taken from this population of 64 people, with a mean of 7 for some relevant characteristics, a standard deviation of 9.6, and a standard error of 1.2.

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Answer: positive

Step-by-step explanation:

123 1/23 + (-123 1/23)

123 1/23 - 123 1/23 = 0

0 is a positive number and not negative so the answer is negative

A minimum of 3 weighings are required to identify the heavy marble out of 8 marbles.

As all the marbles weigh the same except one which is heavier, therefore firstly 8 marbles are divided into half. 4 marbles are placed in one pan while the other 4 are placed in another pan. In this two-pan balance, the pan which is lower than the other contains a heavier marble.

Now, the pan with heavier marble has 4 marbles which are again divided into half. 2 marbles are placed in each pan. Similarly, the pan with heavier marble goes down as compared to another pan with 2 marbles of the same weight. Now the final weighing is done by placing 1 marble in each pan out of 2 marbles taken from the pan which went down before as compared to another pan.

The pan with heavier marble will move down and thus with 3 weighings, a heavier marble is identified.

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The sum of the first 16 terms of the defined arithmetic sequence is given as follows:

-520/16.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, being called common difference d.

The nth term of an arithmetic sequence is given by the equation presented as follows, called general equation:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the arithmetic sequence.

The sum of the first n terms is given by the equation presented as follows:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

The sequence in this problem is defined as follows:

[tex]a_n = \frac{5}{8} - \frac{5}{16}n[/tex]

The first term is of:

[tex]a_1 = \frac{5}{8} - \frac{5}{16} = \frac{5}{16}[/tex]

Hence the 16th term of the sequence is of:

[tex]a_{16} = \frac{5}{8} - \frac{5}{16}(16) = \frac{5}{8} - 5 = -\frac{35}{8}[/tex]

Hence the sum of the first 16 terms of the arithmetic sequence is defined as follows:

[tex]S_{16} = 8\left(\frac{5}{16} - \frac{35}{8}\right) = 8 \times \left(-\frac{65}{16}\right) = -\frac{520}{16}[/tex]

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The equation to show the total no. of minutes Carlos spends routing calls is y = 2x

To find the required equation, use the following given data:

Time taken by Carols for routing each call = 2 minutes

Total number of calls = x

Total number of minutes Carol spends routing calls = y

The one-dimensional function takes up a single input value (x) and outputs a single evaluation of the given input (y).

So, by practical application of one-dimensional function,

Total number of minutes Carols spends routing calls (y) = Time taken by Carols for routing each call * Total number of calls (x)

∴ The equation will be y = 2*x

Thus, y = 2x shows the total number of minutes Carlos spends routing the calls.

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The quadratic regression model of the data is 0.007x² + 0.168x + 56.63 and the  the test score of a student who studies for 60 minutes is 94.114

Quadratic regression model:

Quadratic regression refers the process of determining the equation of a parabola that best fits a set of data.

The set of data is a given set of graph points that make up the shape of a parabola.

The general equation of the parabola is y = ax² + bx + c, where a can never equal zero.

Given,

Here we have the following data represents the amount of time Algebra II students at NVLA prepare for their math exams.

Now, we need to find the the quadratic regression model of the data and then, predict the test score of a student who studies for 60 minutes. Show your work.​

When we plot these value of the graphing calculator, then we get the following graph.

Through the graph we have identified that the value of

a = 0.007

b = 0.168

c = 56.63.

Therefore, the quadratic regression model of the data is 0.007x² + 0.168x + 56.63

And through the graph we have identified that  test score of a student who studies for 60 minutes is approximately 94.114.

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The area of the trapezoid is maximum when the fourth side be 20 inches.

Trapezoids are quadrilaterals with two parallel and two oblique sides. It is also known as a trapezium. A trapezoid is a four-sided closed shape or figure with a perimeter that covers some area.

By applying Pythagorean theorem,

[tex]c^2=a^2+b^2[/tex]

[tex]10^2=h^2+x^2[/tex]

[tex]100=h^2+x^2[/tex]

[tex]h^2=100-x^2[/tex]

[tex]h=\sqrt{100-x^2}[/tex]

Area of the trapezoid is,

[tex]A=\frac12 \times h\times (b_1+b_2)[/tex]

By substituting  the values of h, b1, and b2 in the above equation,

[tex]A=\frac12 \times \sqrt{100-x^2} \times (10+2\times x+10)[/tex]

[tex]A=\sqrt{100-x^2} \times (x+10)[/tex]

If we take the derivative of both sides of the equation in relation to x, we get

[tex]\frac{dA}{dx}=\frac{d}{dx}[\sqrt{100-x^2} \times (x+10)][/tex]

[tex]\frac{dA}{dx}=\sqrt{100-x^2} \ \frac{d}{dx} (x+10) + (x+10) \ \frac{d}{dx} \sqrt{100-x^2}[/tex]

[tex]\frac{dA}{dx}=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]

[tex]\frac {dA}{dx}=0[/tex]

[tex]0=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]

[tex]\sqrt{100-x^2} = \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]

100-x²=x²+10x

2x²+10x-100=0

x²+5x-50=0

(x-5)(x+10)=0

If, x+10=0

x=-10

The above value is not accepted because it is a negative value,

If, x-5=0

x= 5

The value is accepted because it is positive value

The length of the trapezium which should be fourth is,

b₂=2x+10

b₂= 2(5)+10

b₂=20

The area of the trapezoid is maximum when the fourth side be 20 inches

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Answer:

Step-by-step explanation:

Re-order terms so constants are on the left

Then divide both sides by the same factor its -2

then Simplify answer is 1

Answer:

[tex] {x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4x + 1[/tex]

Step-by-step explanation:

as shown in photo attached :")

Step-by-step explanation:

A

it is an exponential function.

for a linear function the charge rate would have to be constant between any pair of data points.

the change rate is

( f ( interval end ) - f ( interval begin ) ) /

( interval end - interval begin )

between (1, 2) and (2, 4) we have a charge rate of

(4 - 2) / (2 - 1) = 2

between e.g. (3, 8) and (4, 16) we have a charge rate of

(16 - 8) / (4 - 3) = 8

the change rate is therefore not constant, and it is not a linear function.

B

we see

x1 = 1, y1 = 2

x2 = x1 + 1, y2 = y1×2

x3 = x2 + 1, y3 = y2×2

we get the impression that

xn = xn-1 + 1 = x1 + (n - 1)

yn = yn-1 × 2 = y1 × 2^n

so, while going linearly along the x-axis, y increases by the powers of 2.

the function is then

f(x) = 2^x

C

the change rate between station 2 and 4 (NOT day 2 and 4) is

(16 - 4) / (4 - 2) = 12/2 = 6

The simple interest on the loan of $600 at rate of 8% over a time period of 16 months is $664 and the interest generated is $64

The formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.

Simple interest formula is given as:

S.I = P(1 + rt)

Substituting the values into the formula

S.I = 600(1 + 0.08 * 16)

S.I = 664

The interest generated is $64

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Translation: What is the interest generated by $600, placed at 8% per year for 1 year 4 months?

The equivalent expression that represents the amount Anna can better understand how her money is invested is 5000(1+0.0005)^12t.

The correct answer option is option c.

Based on the expression given, Anna's investment is compounded monthly.

The formula for calculating future value:

FV = P (1 + r)^(nm)

Where,

5000(1.0005)^12t

Given options:

a) 5000(1.0005^12)^t

False

b) 5025^12t

False

c) 5000(1+0.0005)^12t

= 5,000(1.0005)^12t

True

d) 5000(1.0005^t)^12

False

e) (5000+2.5)^12t

False

f) 5000(1+0.06/12)^12t

= 5000(1 + 0.005)^12t

= 5000(1.005)^12t

False

In conclusion, the expression equivalent to Anna's investment is 5000(1+0.0005)^12t

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The  equivalent monthly growth rate is 7.2 %

Since the number of computer security breaches is expected to increase at a yearly rate of 86%. Using the exponential growth model we need to determine the equivalent monthly rate

.

The exponential growth model is given by y = A(1 + r)ⁿ where

This is the rate at which the function increases.

Since the number of computer security breaches is expected to increase at a yearly rate of 86% we have that the growth rate, r = 86% per year.

To find the monthly growth rate, we covert this to per month by dividing by 12.  

So, the monthly growth rate r' = r/12

= 86%/12

= 7.16 %

≅ 7.2 %

So, the  monthly growth rate is 7.2 %

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Answer:

5.3%

Step-by-step explanation:

I took the test.

24 meters per second = 53.6865 miles per hour

53.6865 to 1 d.p = 53.7

Answer: 53.7

After a counterclockwise 90° rotation, the coordinates of A'B'C' are:

So, the coordinates after the counterclockwise rotation of 90°:

After counterclockwise 90° rotation, coordinates of A'B'C' are:

(Refer to the graph attached below)

Therefore, after a counterclockwise 90° rotation, the coordinates of A'B'C' are:

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24 groups of participants would be needed to partially counterbalance a within-subjects experiment with three treatment conditions.

Given that;

How many groups of participants would be needed to partially counterbalance a within-subjects experiment with three treatment conditions.

Every participant in an experiment is exposed to every treatment or condition in a within-subject design, sometimes referred to as a repeated measures design.

The term "between-subjects design" is comparable to this within-subjects design. People are solely assigned to one treatment in a between-subjects design. As a result, one therapy would be given to one group of volunteers, while a different treatment would be given to another group. After that, the variations between the two groups would be contrasted.

24 groups would be required for a perfectly counterbalanced design for even four treatment conditions. This would obviously be impracticable because a large enough sample size would be required to conduct such an experiment.

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There are 84 ways.

acc  to our question-

hence,There are 84 ways.

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There are zero or null real fourth roots of -1.

This means that the square root of the square root of a number is equal to the number's fourth root. Symbolically, the fourth root is also represented by multiplying the radical by 4, creating the number 4. The fourth root of 16, for instance, is 2, which means that 2 2 2 2 = 16. n, also known as the degree of the root, is a positive integer in this situation. The terms "square root" and "cube root" are used to describe roots of degree 2 and 3, respectively. The ordinal numbers fourth root, twentieth root, etc. are used to refer to roots of higher degree. It is a root extraction to calculate the nth root. A integer y such that y2 = x is referred to as the square root of an x in mathematics.

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Answer:  x = -2 through 1

Step-by-step explanation:

The domain are the x values that exist on the line. The line goes between -2 and 1. Therefore, that's the domain!

Answer:

Let the width be x feet. As length is 3 feet longer, it is x+3 feet. As perimeter is twice of te sum of length and width, it is 2×(x+3+x)=2×(2x+3)=4x+6 feet.

Step-by-step explanation:

The expected value of a player's winnings on each roll is: $30.

We can calculate the expected value of a player's value on each winning by first understanding that there are only two multiples of three on the six-sided die. These multiples are 3 and 6.

So, if 3 is obtained facing upward, the player wins 3 × 20 = $60

Also, if the player obtained 6 facing upward, the player wins 6 × 20 = $120

So, the total amount is $180.

However, the question expects us to calculate the expected value of a player's winnings on each roll. Thus, we will have $180 ÷ 6 = $30.

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Answer: 17 Dimes.

Step-by-step explanation:

Answer:

357 national parks

Step-by-step explanation:

420x85/100

420x17/20

21x17=

357

The value of 'm' in the absolute value equation is 3

A linear equation can be described as an equation having the highest power of the variable as 1.

It is also referred to as a one-degree equation.

Example;

x + 1 = 4

Absolute value of a number can be defined as the value of that number irrespective of its direction to zero on the number line.

The value must take a positive sign.

The symbol used to represent the absolute value of a number is '| '

We have the equation;

|m-2|-1=4

Let's take the absolute value

m + 2 - 1 = 4

Now, collect like terms, we get;

m = 4 - 1

Add or subtract like terms

m = 3

Hence, the value is 3

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The total amount of the money earned by Paige will be $1591.92.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Paige works at a department store and has a commission rate of 3 per cent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter.

The total amount of earnings will be,

TA = ( 50 x 30 ) + ( 0.02 x 4596)

TA = 1500 + 91.92

TA = $1591.92

Therefore, the total amount of the money earned by Paige will be $1591.92.

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Answer:

6

1/3

Step-by-step explanation:

Similar triangles

The corresponding side on triangle A is 18 units

18 * 1/3 = 6

The side length of the missing side on B is 6 units

Side B                5

------       =    -----------   = 1/3

Side A              15

The ratio is 1/3

Answers:

question one:  6

question two: 1/3

==========================================

Explanation:

The side 12 from triangle A corresponds to the side 4 from triangle B.

The scale factor is A/B = 4/12 = 1/3 which tells us that sides in triangle B are 1/3 as long compared to sides in triangle A. This takes care of the second question.

We'll use this scale factor to determine the missing side of triangle B.

The side 18 in triangle A corresponds to this missing side in triangle B.

Take 1/3 of 18 to get (1/3)*18 = 6 which is that missing side.

--------------

Another way to look at it: Take any side of triangle B, triple it, and you'll get a corresponding side of triangle A.

Example: The jump from 5 to 15 is "times 3".

As per the given equation of the parabola, the directrix of the parabola is equal to y = -2.5.

What is directrix?

A directrix in mathematics is a curve which is associated with the process generating a geometric object, such as:

Directrix - conic section

Directrix - generatrix

Directrix - rational normal scroll

The equation of a quadratic function, with vertex (h,k), is:

y = (a)(x - h)² + k

In which, a is the leading coefficient.

The directrix is: y = k + 4a.

In this problem, the equation of parabola is given as:

y = (1/8)(x-2)² - 3

The coefficients in the given equation are a = 1/8 = 0.125,

h = 2, k = -3,

Hence the directrix is given by:

y = -3 + 4 x 0.125

y = -3 + 0.5

y = -2.5.

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Answer:

(x+10,y+8)

Step-by-step explanation:

If you look at the point (0,2) and it image (10,10)  To go from 0 to 10 you must move 10 spaces to the right.  That would be x + 10.

If you look at the same two points.  You would have to move up 8 spaces to go from 2 to 10.  That would be y + 8.

The same thing is true with the second two points given.