Find the equation of the linear function represented by the table below in slope-intercept form.

Answer:

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

Step-by-step explanation:

as shown in photo attached :")

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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well, 61.53 is really 10 + 10 + 10 + 10 + 10 + 10 + 1.53.

well, 1.53 doesn't really come nowhere near close to round up to 10, so it boils down to 0, so 61.53 will just be 10 + 10 + 10 + 10 + 10 + 10 + 0 or just 60 once rounded up, now, what's 15% of 60?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 60}}{\left( \cfrac{15}{100} \right)60}\implies 9[/tex]

well, we can get the 15% of 61.53 by just (15/100) * 61.53

however, the exercise is asking on rounding it up to "tens" first

61.53 has "10" six times plus 1.53, the rounding happens with the "surplus"

in this case the surplus is 1.53.

now, for rounding anything the tipover point is at the half, for $10 the half is $5, so if the amount is $5 or more, rounds up to $10, if less than that goes to 0.

1.53 is nowhere near 5, which is the halfpoint or tipover point, because of that, it rounds up to 0, so 61.53 rounded up to "tens" only will be "six tens" only, or 60.

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.

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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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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Answer:  14.7%

Step-by-step explanation:

% error = (estimated - actual) / (actual) x 100

% error = (17 - 19.5) / 17 x 100 = - 14.7%

The negative sign means that he underestimated the time needed

Answer:

55 L

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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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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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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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 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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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".

The product of the improper fraction 3 1/4 and 1/2 is 1 5/8.

What is mixed fraction?

 A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. a fraction when the denominator (bottom number) and the numerator (top number) are both more than or equal (the bottom number). When the numerator is equal to or more than the denominator, the fraction is said to be improper fraction. It always has a value of one or higher.

Here the given fraction 3 1/4 convert into 13/4.

Now the product of the fractions is

=> 13/4 × 1/2

=> 13/8

=> 1 5/8.

Therefore product of the given fraction is 1 5/8.

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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

If the solution is blue-green, this indicates that some copper is still present in the solution and that not all of it has precipitated. Expect it to be too low because you will have less mass.

With very few exceptions, all copper(I) (cuprous) compounds are diamagnetic and colorless. Cu2O, Cu2Cl2, and cuprous sulfide are a few of the significant commercial compounds of copper(I) (Cu2S).

The molar mass of the element copper is determined by looking at its average atomic mass, which is 63.55 AMU on the periodic table. Since it is also our molar mass, we will now put it in a different unit: grams over moles (63.55 gmol). That is copper's molar mass.

If the solution is blue-green, there is still copper in the solution and not all of it has precipitated. Because you will have less bulk, anticipate it to be too low.

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The size of the angle x = 54 degrees

The regular pentagon is given

Number of sides of the pentagon = 5

O is the center  of the pentagon

The sum of all the angle around a point is 360 degrees

From the figure we can see that the it equally divided by 5 parts

The measure of each angle = 360/5

= 72 degrees

Consider the corresponding triangle

Sum of all the interior angles of the triangle is 180  degrees and the two sides of the triangle is equal, therefore it is an isosceles triangle

Then,

x + x+ 72 = 180

2x + 72 = 180

2x = 180- 72

2x = 108
x = 108/2

x = 54 degrees

Hence, the size of the angle x = 54 degrees

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The graph of the function [tex]y+3=\frac{5}{2}(x - 5)[/tex] is attached below.

What is graph of the function?

In mathematics, the set of ordered pairings where f(x)=y exists is the graph of a function. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

Consider the given function, [tex]y+3=\frac{5}{2}(x - 5)[/tex]

It is in the form [tex]y-y_1=m(x-x_1)[/tex]

Where,  [tex](x_1, y_1)[/tex]is the point and m is the slope.

Graph passes through the point [tex](x_1, y_1)[/tex] and having slope m.

Here, [tex](x_1, y_1) = (5, -3), m = \frac{5}{2}[/tex]

Therefore, graph passes through the point (5, -3) and having slope 5/2.

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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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[tex](\stackrel{x_1}{-12}~,~\stackrel{y_1}{-56})\qquad (\stackrel{x_2}{-57}~,~\stackrel{y_2}{39}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{39}-\stackrel{y1}{(-56)}}}{\underset{run} {\underset{x_2}{-57}-\underset{x_1}{(-12)}}} \implies \cfrac{39 +56}{-57 +12} \implies \cfrac{ 95 }{ -45 } \implies {\Large \begin{array}{llll} - \cfrac{19 }{ 9 } \end{array}}[/tex]

Answer:

- 19/9

Step-by-step explanation:

The slope formula is y1 - y2 divided by x 1 - x2. What u do is u take the y coordinates from both points, and subtracted them. And you do he same for the x coordinates. Then you divide the y coordinates by the x coordinates. IN this case, this is how we would solve it.

-56 - 39 / -12 - (-57) = -95 / 45 = - 19/9

The probability that it will be detected in the next hour is 0.04.

For a system, a fault test each hour is a Bernoulli with success defined as detecting a fault.

The probability of success is 0.78

Let 'x' denote the number of tests conducted up to and including the test that detected a fault.

Then x* - Geometry (0.78).

The probability mass function of the random variable x is;

P(x) = { P( 1 - P )ˣ⁻¹   x = 1,2, . . .

         { 0                 otherwise

The Probability that a fault will be detected on the third hour, given that it has gone undetected during the first two hours is;

P(X = 3 / x = 2) = P(X = 3 and x > 2) / P(x > 2)

                        = P( x = 3 ) / 1-  P(x ≤ 2)

                        = P( x = 3 ) /  1-P(x = 1) - P(x = 2)

                        = P(3) /  1-P(1) - P(2)

                        = (0.78)(0.2)² / 1 - (0·78)(0.2) - (0.78)(0.2)

                        = (0.78)(0.04) / 1 - (0.78)(0.2) - (0.78)(0.2)

                        = 0.0312 / 1 - 0.156 - 0.156

                        = 0.0312 / 0.688

                        = 0.04

The probability that it will be detected in the next hour is 0.04

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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 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:

357 national parks

Step-by-step explanation:

420x85/100

420x17/20

21x17=

357

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.