Use the Intermediate Value Theorem to show that at least one zero lies in the given interval for the given polynomial. f (x) = x^3 - 6x + 1, between x = 2 and x = 3 Substitute x = 2 and x = 3 into the function and simplify. f (2) = f (3) = Interpret the results using the Intermediate Value Theorem. Because f is a polynomial function and since f (2) it and f (3) is, there is at least one real zero between x = 2 and x =

The population of the city grew most rapidly in the year 1988.

Given, the population of a city is modeled by a function

P(t) = 250/(1 + 480e^-0.8t)

we have to find that when the population is growing most rapidly.

On differentiating, we get

P'(t) = 250/(1 + 480e^-0.8t)²×(-384e^-0.8t)

Again differentiating we get

P''(t) = 96000(e^-1.6t)(-0.8e^-0.8 + 384)

Putting P''(t) = 0, we get

e^0.8t = 0

t = 8

So, the population of the city grew most rapidly in the year (1980 + 8) = 1988.

Hence, the population of the city grew most rapidly in the year 1988.

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Some of the real life examples of parallel lines cut by transversal are: chessboard, graph paper,railway tracks,net on the tennis court etc.

When two lines don't intersect, they are said to be parallel. Parallel lines are two lines that run parallel to each other and meet at infinity.

A transversal is formed when a line intersects two lines at distinct points.

Real life examples of parallel lines cut by transversal line are:

Thus, in real life situations parallel lines cut by transversal can be observed very frequently.

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Answer:

Step-by-step explanation:

54=t

Answer:

7/24 ft

Step-by-step explanation:

Triangle area is 1/2(b)(h) so we fill it in

1/2(7/8)(2/3)

1/2(14/24)

14/48

7/24

Hopes this helps please mark brainliest

The cost of the jersey that Charlotte wanted to buy  who is visiting to Brazil, in U.S. dollars based on the exchange rate is $16.39.

What is the exchange rate?

The exchange rate is the rate at which two nations currencies are exchanged in the foreign exchange market.

The exchange rate depends on the purchasing power of each currency.

Data and Calculations are as follows :

Cost of jersey = Br. 89

Exchange rate = $1 : Br. 5.43

Cost of jersey in US dollars = $ (Br. 89/Br. 5.43)

Thus, the cost of the jersey that Charlotte in U.S. dollars based on the exchange rate is B. $16.39.

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The result for simplifying;

[tex] {( \frac{2a²b×b⁴}{2a²b×9 {a}^{2} } )}^{ \frac{1}{2} } [/tex]

is;

[tex] \frac{ {b}^{2} }{3b} [/tex]

Simplification of an algebraic expressions is the process of writing an expression in the most efficient and compact way, that is in their simplest form, without changing the value of the original expression.

The greatest common factor the numerator and denominator is 2a²b and so we divide through with it to give;

[tex] {( \frac{b⁴}{9 {a}^{2} } )}^{ \frac{1}{2} } [/tex]

evaluate the square root, we have;

[tex] {( \frac{2a²b⁵}{18 {a}^{4}b } )}^{ \frac{1}{2} } = {( \frac{b²}{3a})} [/tex]

Therefore,

[tex] {( \frac{b²}{3a})} [/tex]

is the result after simplifying the algebraic expression

[tex] {( \frac{2a²b⁵}{18 {a}^{4}b } )}^{ \frac{1}{2} } [/tex]

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There are 7nickels, 13dimes and 15quarters of coins which the Cashier has using algebra.

We first represent the the value of nickels with an unknown value x, and then the values of dimes and quarters in are expressed in terms of x. then multiply each derived number of coins with their value in cents and equate them to their total of 540cents converted from $5.40.

A nickel = 5cents, a dime = 10cents, a quarter = 25cents and $5.40 = 540cents

Let the number of nickel coins be represented by x, hence there are (2x - 1) dimes and (36 - 3x) quarters.

Thus we have;

x nickel = 5x cents

(2x - 1) dimes = 10(2x - 1)cents

(36 - 3x) quarters = 25(36 - 3x)cents

5x + 10(2x - 1) + 25(36 - 3x) = 540

5x + 20x - 10 + 900 - 75x = 540 {collect like terms}

75x - 25x = 350

50x = 350

x = 350/50

x = 7

Therefore, there are 7nickels, [2(7) - 1] = 13dimes, and [36 - 3(7)] = 15quarters by substituting 7 for x from our derived value of coins

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A sinusoidal function of the form y = a sin(x - c) + d is changed by increasing d by 2. The new graph will have moved right.

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function. The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse.

Given,

A sinusoidal function of the form y = a sin(x - c) + d is changed by increasing d by 2.

The new graph will have moved right.

For periodic functions, phase shift refers to a horizontal shift to the left or the right. The sine wave is moved to the left if c = 2. if, the sine wave is then three degrees to the right. Despite going in the opposite way from what you may anticipate, this follows the general transformational principles for all functions.

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The variable that is used to predict the volume of timber in this tree using a simple linear regression model is Diameter .

In the question ,

a scatter plot is given ,

the scatter plot shows the relationship between height , diameter and the volume .

and diameter of tree is measured 4.5 feet above the ground .

it is given that suppose , we have height and diameter measurements for another black cherry tree ,

we have to find the variable that help in predicting the volume of the timber .

So , from the scatter plot given below ,

we can say that , the relationship between diameter and volume of these trees is strong  than height .

So , diameter is used to predict the volume of timber in this tree using a linear regression model.

Therefore , the variable that help in predicting the volume of the timber is Diameter .

The given question is incomplete , the complete question is

The scatterplots below show the relationship between height, diameter, and volume of timber in 31 felled black cherry trees. The diameter of the tree is measured 4.5 feet above the ground .

Suppose you have height and diameter measurements for another black cherry tree. Which of these variables would be preferable to use to predict the volume of timber in this tree using a simple linear regression model ? Explain your reasoning.

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Answer:

A and E

Step-by-step explanation:

The geometric series which has the common ratio 2 is 0.0625, 0.125, 0.25, 0.5, 1, … thus option (C) is correct.

A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.

For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.

As per the given,

Common ratio r = 2

Common ratio = next term / previous term

In the series 0.0625, 0.125, 0.25, 0.5, 1, … the common ratio is 2.

In the series [tex]a_{n}[/tex] = (1/2) × [tex]a_{n-1}[/tex]

a₁ = 2 so

a₂ = (1/2)a₁ 1

The ratio is 1/2, not 2.

Hence "The geometric series which has the common ratio 2 is 0.0625, 0.125, 0.25, 0.5, 1, …".

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The correct option; y = negative x + 5 is the a side perpendicular to side s's equation.

Using (4,1) as the line s's coordinate, and (1,4).

Obtain this line's equation;

Slope m = 4 - 1 / 1 - 4

Slope m = 3/-3

m = -1

Using, y - y0 = m(x - x0)

Add any point, like (4, 1), and m = -1 to the equation above;

y - 1 = -1(x - 4)

y - 1 = -x + 4

y + x = 4 + 1

y + x = 5

y = -x + 5

Thus, y = negative x + 5 is the a side perpendicular to side s's equation.

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A. The bacteria that had a smaller initial population is of:

Sample A: 100 bacteria.

B. The correct option regarding which sample was larger in the 5th week is of:

Sample A; 8,300.

An exponential function is defined as follows:

[tex]y = ab^x[/tex]

In which the meaning of each parameter is given by:

For Sample A, the values of these parameters are given as follows:

Hence the function is:

f(x) = 100(3)^x.

In the 5th week, the population was of:

f(5) = 100 x 3^5 = 24,300.

For Sample B, the function is:

g(x) = 500(2)^x.

Hence, from the parameters, we have that:

In the 5th week, the population was of:

g(5) = 500 x 2^5 = 16,000.

Hence the difference of the larger population in Sample A by the smaller population in Sample B is of:

24,300 - 16,000 = 8,300.

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The days that must elapse for a sample of neptunium-239 to decay to 0.0100% of its original quantity is calculated to be 31.33

The equation for radioactive decay in this case can be given as

N = N₀exp(-λt)

To determine the decay constant, λ, we have;

λ = -(lnN/N₀)/t    

here

t illustrates the half-life of Neptunium-239 which is equal to 2.35 days

N/N₀ = 1/2 where N represents the Quantity of Neptunium-239 after half-life and N₀ represents the initial quantity of Neptunium-239

Therefore, λ = -(ln(1/2)) ÷ 2.35

λ = 0.294/day.

Now for Neptunium-239 to decay to 0.0100 % of its initial value,

N/N₀ × 100 % = 0.0100%

N/N₀ = 0.0100 / 100

N/N₀ = 0.0001

From the equation for radioactive decay, we determine the time it takes for 239np to decay to this value as follows;

t = -(lnN/N₀)/λ = -(ln(0.0001))/0.294/day = 31.33 days

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Answer: Ky-4x=2

Step-by-step explanation:

Answer:

x=2

y=5

Step-by-step explanation:

fill in x

5y+(y-3)=27

6y-3=27

  +3.  +3

6y=30

/6.  /6

y=5

now fill in y to find x

x=5-3

x=2

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Answer:

x = 4 ; y = 12

Step-by-step explanation:

y = 3x

5x - 3x = 8

2x = 8

2/2 x = 8/2

x = 4

y = 3(4)

y = 12

Answer:

The equality sign should be present in the null hypothesis during hypothesis testing. In a two-tailed hypothesis test, the rejection region's area in each tail is equal to [tex]\alpha[/tex]. If you choose an alpha of 0.01 then beta will equal 0.99

solution of the linear system depends upon the slope of the line and it is different in different situations

How can you tell how many solutions a linear equation has?

If the slopes are the same but the y-intercepts are different, the system has no solution. If the slopes are different, the system has one solution. If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.

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The 99% confidence interval would be given (0.04;0.46).  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

pA represent the real population proportion A  

^pA = 0.67 represent the estimated proportion A

pB represent the real population proportion B  

^pB = 0.48 represent the estimated proportion B

z represent the critical value for the margin of error  

The population proportion have the following distribution  

p ~ N(p,√p(1-p)/n

The confidence interval for the difference of two proportions would be given by this formula  

(^pA - ^pB) ± zα/2 √^pA(1-^pA)/nA + ^pB(1-^pB)/nB

For the 99% confidence interval the value of  α = 1-0.99 = 0.01 and α/2 = 0.005 , with that value we can find the quantile required for the interval in the normal standard distribution.

zα/2 = 2.576

The standard error is given by:

= 0.084

And replacing into the confidence interval formula we got:  

(0.67-0.42) - 2.576(0.084) = 0.04

(0.67-0.42) + 2.576(0.084) = 0.46

And the 99% confidence interval would be given (0.04;0.46).  

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The person is making money more than the half of the population of the teachers.

Given, a person is making the median salary for a construction worker.

we have to find that more than how many teachers the person is making money

as, we know that the median is more than the half of the population.

So, the person is making money more than the half of the population of the teachers.

Hence, the person is making money more than the half of the population of the teachers.

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The transformations is rotate 180° and translate down.

Transformations:

Transformations can be non-rigid (when the preimage's size or shape is unaltered) or stiff (where the size is changed but the shape remains the same). These are the fundamental guidelines that this concept abides by. It is a straightforward approach to alter 2D forms. Planar transformations and spaces can be distinguished from one another using the dimensions of the operand sets. Their characteristics can also be used to classify them.The image of a shape will resemble the pre-image when its size is increased or decreased. The dimensions of the comparable figures are proportionately equal.

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The creation of anxiety to decrease maladaptive behavior occurs in  Aversion therapy; the induction of relaxation to increase an adaptive behavior occurs in Systematic desensitization.

Given,

In the question:

The question is based on fill in the blanks:

The creation of anxiety to decrease maladaptive behavior occurs in _____ therapy; the induction of relaxation to increase an adaptive behavior occurs in _____.

Let's Know:

Maladaptive Behaviour:

Maladaptive behaviors are things that you do that may shield you from changing in accordance with circumstances. Frequently found in those with social nervousness issue (SAD), maladaptive behaviors are utilized to attempt and lessen tension and dread at the time. You may accidentally build up these propensities to adapt in social and execution circumstances since it feels like they are helping you deal with your anxiety.  

Now, According to the question:

The creation of anxiety to decrease maladaptive behavior occurs in _____ therapy; the induction of relaxation to increase an adaptive behavior occurs in _____.

Hence, In the first fill up :

The answer is Aversion.

In the second fill up:

The answer is Systematic desensitization.

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Two shapes of the same size and shape are congruent. There are five conditions or rules for two triangles to be congruent. They are SSS, SAS, ASA, AAS, and RHS joint properties.

Triangle Congruence:

The congruence of two or more triangles depends on the measurements of their sides and angles. The three sides of a triangle determine its size, and its three angles determine its shape.

Two triangles are considered congruent if their pairs of corresponding sides and corresponding angles are equal.

SSS (side-side-side) :

According to this criterion, two triangles are congruent if his three sides of one triangle are equal to the corresponding sides of the other triangle.

ASA ( Angle-Side-Angle ) :

According to the ASA criterion, two triangles are congruent if any two angles and the inner side of one triangle between them are equal to the corresponding angles and inner sides of the other triangle.

SAS (Side Angle Side)

According to this criterion, two triangles are congruent if two sides and included angles of one triangle are equal to the corresponding sides and included angles of the other corresponding triangle.

AAS ( Angle - Angle Side) :

According to the AAS standard, two triangles are congruent if any two angles and the excluded side of one triangle are equal to the corresponding angles and the excluded side of the other triangle

RHS (Right Angle Two-sided)

According to this criterion, two triangles are congruent if the hypotenuse and side of one right triangle are equal to the hypotenuse and corresponding side of another right triangle.

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The matching vocabularies are;

1.  Factor

2. Algebraic

3. Denominator

4.  Improper fraction

5. Coefficient

Given,

1. A number that divides evenly into a given number

2. Expressions, equations, and operations involving variables

3. The bottom part of a fraction, represents the whole

4. A fraction with a numerator that is larger than or equal to the denominator

5. The number in an algebraic term improper fraction

We have to match the vocabulary to the proper definition;

Here,

1. A number that divides evenly into a given number  - Factor

2. Expressions, equations, and operations involving variables  -Algebraic

3. The bottom part of a fraction, represents the whole - Denominator

4. A fraction with a numerator that is larger than or equal to the denominator - Improper fraction

5. The number in an algebraic term  - Coefficient

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A scatter plot allows a researcher to visually inspect the plotted points and possibly to spot a systematic nonlinear relationship.

The scatter plot is defined as the graph that shows the set of points plotted on a horizontal and vertical axes. The scatter plot is used to shows the extend of correlation therefore it is important in the statistics. It also used to show how much one variable is affected by another variable. In scatterplot usually the dots are used to represents the numeric variables

Hence, a scatter plot allows a researcher to visually inspect the plotted points and possibly to spot a systematic nonlinear relationship.

The complete question is

a _____ allows a researcher to visually inspect the plotted points and possibly to spot a systematic nonlinear relationship.

a) Multiple line graph b) Scatter plot c) Stacked bar chart d) Line graph

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The x-intercept is ( 3,0)  and The y-intercept is  ( 0, -1)

Why does x-intercept matter?

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

-x + 3y = -3 is a linear equation in standard form:.

X-intercept: value of x when  y = 0

Substitute 0 for y and solve for x.

-x + 3 * 0 = -3

-x = -3

x = 3

The x-intercept is (3,0)

Y-intercept: value of y when x = 0

Substitute 0 for x and solve for y.

0 + 3y = -3

3y = -3

  y = -1

The y-intercept is ( 0,-1)

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The complete question is -

What is the X intercept of -x + 3y = -3?.

The regression line that forecasts home equity using the FICO credit score as the explanatory variable has the equation Y' = 1798X + 0.

Due to the fact that this linear regression model includes two parameters that need to be estimated from training data, it has two degrees of freedom. One additional column in the data (one additional input variable) would provide the model one extra degree of freedom.

An equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable, represents a linear regression line. A line's intercept (the value of y when x = 0) is equal to the slope of the line, which is b.

Hence we get the required answer.

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The steps of the analytical problem-solving model include: identifying the problem, exploring alternatives, building an implementation plan, implementing a solution, and evaluating the situation.

Analytical problem solving, as we've defined it above, refers to the approaches and methods you use rather than the particular issue you're trying to resolve.

Analytical issue solving is a crucial prerequisite for problem resolution; the problem itself does not determine whether you need it.

Analytical problem solving involves recognising a problem, investigating it, and then creating ideas (such as causes and solutions) around it.

Solving analytical problems calls for inquiry, examination, and analysis that encourages additional study of the subject (including causality, symptoms, and solution).

According to the steps involved in analytical problem solving model:

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The rectangular coordinates of each point is (5/2,5√3/2).

Given:

For questions 1 - 3, the polar coordinates of a point are given. find the rectangular coordinates of each point:

(5,π/3)

we know that,

x = r cosθ

y = r sinθ

r = 5, θ=π/3

x = 5 cos(π/3)

= 5*1/2

= 5/2

y = 5 sin(π/3)

= 5*√3/2

= 5√3/2

Therefore The rectangular coordinates of each point is (5/2,5√3/2).

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Full question:

For questions 1 - 3, the polar coordinates of a point are given. find the rectangular coordinates of each point

(5,π/3)