If f(x) = 3x4 + 2x3 - x + 15,
what would be the list of
possible rational roots?

Answer:

(a) D y = 6x + 7

(b) A 6

Step-by-step explanation:

6x -6 = -7   Subtract 6x from both sides

6x - 6x - y = -6x - 7

-y = -6x - 7    Divide all the way through by -1

y = 6x + 7

The slope is the number before the variable x. (6)

Answer: 1/2

Step-by-step explanation:

Slope = Δy/Δx = -3/-6 = 1/2

If the bumper is at -1.6 units and It is programmed to move -2.3units. The bumper should be placed at -3.9 units

The location of the bumper is calculated by the concept of addition that takes place when the two values has negative signs values.

The negative numbers are located by the left of zero on the number line. The two points are both negative and have the value of -1.6 units and -2.3 units

Summing the two units together will result to

= -1.6 units + (-2.3 units)

= -1.6 - 2.3

= -3.9 units

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Any triangle's three interior angles add up to 180 degrees, according to the Triangle Sum Theorem.

Any triangle's three interior angles add up to 180 degrees, according to the Triangle Sum Theorem. m∠1+m∠2+m∠3=180∘.

Here,

According to the triangle sum theorem, a triangle's total angles equal 180°. Therefore, using the Substitution property

=> (3x)° + 90° + (x+10)° = 180°,

=>  m(A,B,C) = 180.

To find x, combine similar terms to get

=> 4x + 100 = 180. Then, using the subtraction condition of equality, convert => 13 1/2 to 80.

=> Finally, divide 80 by  5 ( 13 1/2) to find x.

The substitution property may be used to get the measure of the angle A, yielding mA = 5 ( 13 1/2) °.

When the expression is finally simplified, m < A = 66 2/3.

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a. The probability that the sample proportion will be within ±0.03 of the population proportion is 0.6456.
b. The probability that the sample proportion will be within ±0.03 of the population proportion is 1.985.

What is population proportion?
The probability that a specific event will occur in the population is known as the population proportion. It is a parameter, and the sample proportion statistic is used to estimate it. The percentage of occurrences that occur in the sample is known as the sample proportion.

a. The probability that the sample proportion will be within ±0.03 of the population proportion is P(-0.03 < p‌ - P < 0.003).
We Know that z-score of sample proportion is given by:
z = (p‌ - P)/SE(p‌), where SE(p‌) represents standard error.
⇒SE(p‌) = √(0.3 * 0.7)/200
⇒SE(p‌) = √0.00105
⇒SE(p‌) = 0.0324

Now, using the z score, the probability P(-0.03 < p‌ - P < 0.003) is computed as follows:
P(-0.03 < p‌ - P < 0.003) = P(-0.03/SE(p‌) < p‌ - P/SE(p‌) < 0.003/SE(p‌))
= P(-0.03/0.0324 < Z < 0.003/0.0324)
= P(−0.925926 < Z < 0.925926)
= 2P(0 < Z < 0.925926)


P(0 < Z < 0.925926) = 0.3228   (Using standard table)
So,
2P(0 < Z < 0.925926) = 2*0.3228 = 0.6456
Hence, the probability that the sample proportion will be within ±0.03 the population proportion is 0.6456.


b. The probability that the sample proportion will be within ±0.03 of the population proportion is P(-0.08 < p‌ - P < 0.008).
Also, SE(p‌) = 0.0324
Now, using z score,
P(-0.08 < p‌ - P < 0.008) = P(-0.08/SE(p‌) < p‌ - P/SE(p‌) < 0.008/SE(p‌))
= P(-0.08/0.0324 < Z < 0.008/0.0324)
= P(−2.469135 < Z < 2.469135)
= 2P(0 < Z < 2.469135)

P(0 < Z < 2.469135) = 0.9925   (Using standard table)
So,
2P(0 < Z < 2.469135) = 2*0.9925 = 1.985

Hence, the probability that the sample proportion will be within ±0.03 of the population proportion is 1.985.

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The value of information is directly related to how it assists decision makers in achieving the goals of the company. -Differentiate data from information and define the features used to assess data quality.

The value of information in decision analysis is the improvement in the consequences of our actions that we would expect if we could minimise or remove uncertainty before making a choice.

The value of information is determined by the influence of a choice on achieving the organization's goals and enhancing its profit-ability.

Management information systems give information on the organization's relative position and the underlying factors at work. It offers the necessary information for decision making and assists businesses in carrying out their control, planning, and operational activities successfully.

The interaction between information systems and decision making is a major problem in the subject of information systems (IS).

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Answer: 3/8

Step-by-step explanation:

5/8 of them want to, so you subtract 5/8 from 1

1-(5/8)

(8/8)-(5/8)

((8-5)/8)

3/8

There are 192 pennies in a stack that is 1 ft high.

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

Stack is 1 feet high.

Now, We know that;

⇒ 1 inch = 16 pennies

And, 1 feet = 12 inches

So, We get;

⇒ 1 ft = 12 inches

         = 12 × 16 pennies

         = 192 pennies

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For the Given Parallelogram: AC¯≅BD¯;AC¯⊥BD¯

The parallelogram is not a square because the statement "AC¯≅BD¯;AC¯⊥BD¯" means that opposite sides of the parallelogram are congruent and perpendicular but it's not enough to say that the parallelogram is a square, In a square, all four sides are congruent, and the diagonal bisect each other at right angles.

For the first Theorem, AC¯≅BD¯, congruent figures' corresponding sides are congruent(CPCTC) while the AC¯⊥BD¯ Theorem have opposite angles of a parallelogram that is useful (Parallelogram Opposite angles Theorem).

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The common difference of the sequence is -1/2

From the question, we have the following parameters that can be used in our computation:

3/8, -1/8, -5/8, -9/8

The common difference is the difference between successive terms

So, we have

Difference = -1/8 - 3/8

Evaluate the difference

Difference = -1/2

Hence, the common difference is -1/2

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Answer:5441 is the population increase per year and 123,000 is when we start added the population increase. to get this equation i found the population increase between 2007 and 1990 which is 215,500-123,000 which is 92,500. to find the population increase per year you divide that by 17 which is the difference between 2007 and 1990 and you would get 5441.176. but since you can have part of a person i rounded it to 5441.

Step-by-step explanation:

Answer:

The linear equation representing the population growth since 1990 is p = 92t + 123000.

Where p is the population, 92 is the growth rate (215500-123000)/(2007-1990), and t is the years after 1990.

Step-by-step explanation:

The lines are perpendicular

What is slope-intercept?

The slope-intercept form of a linear equation is a way of writing the equation of a line in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y- intercept )

3x + 5y = 10 ( subtract 3x from both sides )

5y = - 3x + 10 ( divide through by 5 )

y = -  x + 2 ← in slope- intercept form

with slope m = -

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

5x - 3y = - 6 ( subtract 5x from both sides )

- 3y = - 5x - 6 ( divide through by - 3 )

y =  x + 2 ← in slope-intercept form

with slope m =

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

• Parallel lines have equal slopes

clearly, the lines are not parallel

• the product of the slopes of perpendicular lines equals - 1

-  ×  = - 1

thus the 2 lines are perpendicular to each other

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Answer:

see explanation

Step-by-step explanation:

to find the y- intercept, the point where the line crosses the y- axis.

Any point on the y- axis has an x- coordinate of zero.

let x = 0 in the equation and solve for y

- 4(0) + 7 = 2y - 3

0 + 7 = 2y - 3

7 = 2y - 3 ( add 3 to both sides )

10 = 2y ( divide both sides by 2 )

5 = y

then y- intercept = (0, 5 )

to find the x- intercept, the point where the line crosses the x- axis.

Any point on the x- axis has a y- coordinate of zero.

let y = 0 in the equation and solve for x

- 4x + 7 = 2(0) - 3

- 4x + 7 = 0 - 3

- 4x + 7 = - 3 ( subtract 7 from both sides )

- 4x = - 10 ( divide both sides by - 4 )

x = [tex]\frac{-10}{-4}[/tex] = [tex]\frac{10}{4}[/tex] = [tex]\frac{5}{2}[/tex]

then x- intercept = ( [tex]\frac{5}{2}[/tex], 0 ) or (2.5, 0 )

Answer:

[tex] \displaystyle{ {f}^{ - 1} (x) = {(x - 4)}^{3} + 1}[/tex]

Step-by-step explanation:

Let y = f(x)

[tex] \displaystyle{y = \sqrt[3]{x - 1} + 4}[/tex]

Finding an inverse, swap x and y

[tex] \displaystyle{x = \sqrt[3]{y- 1} + 4}[/tex]

Then solve for y, first subtract 4 both sides

[tex] \displaystyle{ x - 4= \sqrt[3]{y- 1} + 4 - 4} \\ \\ \displaystyle{ x - 4= \sqrt[3]{y- 1} }[/tex]

Cube both sides

[tex] \displaystyle{ {(x - 4)}^{3} = \left(\sqrt[3]{y- 1} \right)^{3} } \\ \\ \displaystyle{ {(x - 4)}^{3} = y - 1}[/tex]

Add both sides by 1

[tex] \displaystyle{ {(x - 4)}^{3} + 1 = y - 1 + 1} \\ \\ \displaystyle{ {(x - 4)}^{3} + 1 = y}[/tex]

The final y is the inverse. Hence:

[tex] \displaystyle{ {f}^{ - 1} (x) = {(x - 4)}^{3} + 1}[/tex]

a. To subtract like terms, subtract the coefficients, not the variables b. Like terms are terms that contain the same variable e. Negative (negative x) is equivalent to Negative x, so Negative 5 x minus x = negative 6 x.

The expression can be made simpler by using these facts.

We may take the coefficients of the similar terms, which are x and -x, out using fact a. In this instance, the expression is simplified to read as Negative 5 x minus x = Negative 6 x.

According to fact b, terms that have the same variable raised to the same power are referred to as being like terms. As we can see, there are two like terms—Negative y and -2y—in this situation that can be joined. The similar terms' coefficients, which are -1 and -2, can be added. The total is y-3.

Negative (negative x) is equal to negative x, according to Fact e. We can see that Negative 5 x is Negative (negative x) in this situation and can be reduced to Negative 6 x.

Therefore, Negative 6 x -3 y + 3 z would be the abbreviated expression.

Due to the fact that fact C's computation does not use the same simplified formulation as the other facts, it is important to note that fact C is incorrect.

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The proportion for y is the value 6.9 to the nearest tenth value.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s. If both these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

Given the proportional relation,

11 / y = 8 / 5

Doing the cross multiplication,

11 × 5 = 8y

55 = 8y

8y = 55

y = 6.875

To the nearest tenth, the value is 6.9.

Hence the y value to the nearest tenth is 6.9

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The angles of the triangle KHP are P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°, respectively.

Here we have the case of a triangle where the lengths of three sides are known and measures of angles must be determined. The missing angles can be found by means of law of cosine, whose equations related to the triangle are introduced below;

p² = h² + k² - 2 · h · k · cos P

h² = p² + k² - 2 · p · k · cos H

k² = h² + p² - 2 · h · p · cos K

Given;

h, k, p - Sides

H, K, P - Angles

If we know that h = 16.1, p = 24.9 and k = 12.8, then the measures of the angles are;

cos P = (p² - h² - k²) / (- 2 · h · k)

cos P = (24.9² - 16.1² - 12.8²) / (- 2 · 16.1 · 12.8)

cos P = - 0.478

P ≈ 118.555°

cos H = (h² - p² - k²) / (- 2 · p · k)

cos H = (16.1² - 24.9² - 12.8²) / (- 2 · 24.9 · 12.8)

cos H = 0.823

H ≈ 34.614°

cos K = (k² - h² - p²) / (- 2 · h · p)

cos K = (12.8² - 16.1² - 24.9²) / (- 2 · 16.1 · 24.9)

cos K = 0.892

K ≈ 26.844°

Triangle KHP has the following missing angles: P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°;

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No, because the data values are the time spend in training, and are not points in time. (Option - A is correct )

Weather records, economic indicators and patient health evolution metrics — all are time series data. Time series data could also be server metrics, application performance monitoring, network data, sensor data, events, clicks and many other types of analytics data.

variance is NOT a time series component, it refers to the spread of a data set.

The three main types of time series models are moving average, exponential smoothing, and ARIMA. The crucial thing is to choose the right forecasting method as per the characteristics of the time series data.

y(t) = x(t)β + ε(t), where y(t) = {yt;t = 0,±1,±2,...} is a sequence, indexed by the time subscript t, which is a combination of an observable signal sequence x(t) = {xt} and an unobservable white-noise sequence ε(t) = {εt} of independently and identically distributed random variables.

Therefore,

No, because the data values are the time spend in training, and are not points in time. (Option - A is correct )

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The answer is $10.4

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.

Given here: Makayla invested $130. She earned a simple interest of 4% per year on the initial investment.

Then SI = 130×4×2 /100

              =$10.4

Hence, Simple Interest recieved is $10.4

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Answer:

-18

Step-by-step explanation:

-3-15=-18

Answer:

18

Step-by-step explanation:

One trip around the gym would be 138 ft.

If we cut the diagonal, we use the Pythagorean theorem to find the distance of the hypotenuse, which is 51 ft.

One trip with the shortcut is 119 ft. (24 + 45 + 51 = 119).

Subtract 119 ft. from 138 feet and you have 18 ft. shorter route than walking the entire perimeter.

Answer:

Out of all possible choices you've shown, I'd say the best answer would be A

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 816 = 600( 1 + 9r)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 816 = 600 + 5400r[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5400r = 816 - 600[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5400r = 216[/tex]

[tex]\qquad \sf  \dashrightarrow \: r = \dfrac{216}{5400} [/tex]

[tex]\qquad \sf  \dashrightarrow \: r= \dfrac{4}{100} [/tex]

[tex]\qquad \sf  \dashrightarrow \: r = 0.04[/tex]

The equation, 816 = 600(1 + 9r), represents the amount of money earned on a simple interest savings account. On solving the linear equation for r, we get r = 0.04 (a).

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Given in the question,

[tex]816 = 600(1 + 9r)\\\\\frac{816}{600} = 1+9r\\ \\\frac{816}{600} -1 = 9r\\\\\frac{216}{600} = 9r\\\\r = \frac{216}{600* 9 } = 0.04[/tex]

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IQ scores are normally distributed with mean mu equals 100 and standard deviation sigma equals 15. the standard deviation of the sampling distribution is 3.

Generally, The standard deviation of the sampling distribution, also known as the standard error, can be calculated using the formula:

standard error = (standard deviation of population) / (sqrt(sample size)).

In this case, the standard deviation of the population is 15, and the sample size is 25. So the standard error would be:

15 / sqrt(25) = 15 / 5 = 3

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Answer:

a). t = 5 years.

b). n = 25000 words.

Step-by-step explanation:

From the question it have been given a formula

which is n = 2450t + 500

a) The year

n = 12750 words

n = 2450t + 500

= 12750 = 2450t + 500

= 12750 - 500 = 2450t

= 12250 = 2450t

= 12250/2450 = 2450t/2450.

5 years = t

Or

t = 5 years.

b). The words

t = 10 years

= n = 2450t + 500

= n = 2450(10) + 500

= n = 24500 + 500

n = 25000 words.

We decide on 320 as the best-predicted value. EV(node 4) = 320. The answer is option (a).

What is Probability?

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Probability of S1 = 0.6

Probability of F = 0.40

Value of node y =?

As per the given value if probability of S1 = 0.6

Then the probability of S2 = 0.4

Using payoff values in table equation from except value.

[tex]EV(d_{i})=[/tex] ∑ [tex]V_{ij} S_{J}[/tex]

where [tex]V_{ij}[/tex] = value of payoff

We compute the expected value for each of decisions

EV(Node 8) = 0.6*100+0.4*300

                  = 180

EV(Node 9) = 0.6*400+0.4*200

             = 320

For Node 4, We select the best value from node 8 and node9

The best decision attractive is the line complex branch that  EV(node 8) = 180, For node 9,

Therefore, We select the best-predicted value i.e 320.

EV(node 4) = 320

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Analyzing the coordinates being provided, the scale factor is found to be 0.5, hence the image of point A(12,4) under the same dilation and the center of dilation as origin is A'(6,2).

A dilation is a transformation in Euclidean space that enlarges or reduces all the points in a figure by a scale factor. In the example given, the dilation maps (6, 10) to (3, 5) with a scale factor of 0.5, and the center of dilation is the origin (0,0). The image of a point A(x,y) under this dilation would be A'(x*0.5, y*0.5). It means the point is scaled down by 0.5 in both x and y coordinate.

The dilation described above can be used in real-world applications such as image processing, where it can be used to reduce the size of an image without losing important details, or to enlarge an image without introducing distortion. It can also be used in architectural design to create smaller or larger versions of floor plans and blueprints. Additionally, it can be used in cartography to change the scale of maps without altering the shape of the features on the map.

Analyzing the given dilation map , mapped from (6,10) to (3,5) ,the center of the dilation being origin. We can see that the scaling factor is 0.5.

So , using the same dilation for point A(12,4), The image of A will be,

A'(12*0.5,4*0.5) = A'(6,2)

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Answer:

Option A or 1 or   |-11.2 -4.7|

Step-by-step explanation:

Calculate the distance :

distance =

| 4.7 - (- 11.2) | =

| 4.7 + 11.2 | =

| 15.9 | =

15.9.

Should help

Answer:

  |-11.2 -4.7|

Step-by-step explanation:

You want the expression that represents the distance between 4.7 and -11.2 on a number line.

The distance on a number line is the positive difference between the coordinates of the points. Here, that would be either of ...

  |4.7 -(-11.2)|

or

  |-11.2 -4.7| . . . . . . matches an answer choice

__

Additional comment

Note that when we subtract the left coordinate from the right coordinate, the difference is already positive, so no absolute value function is needed.

Answer: k*6 and then you find the reciprocal of k*6 which is 1 over k*6

Step-by-step explanation: