Devan ran 27 miles last week, which was three times as far as Hailey ran.

By solving the mean value theorem, the value of c in the interval (1,2) is 0.75.

Explanation:

The mean value theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists at least one point c in (a,b) where the equation f'(c) = (f(b) - f(a))/(b - a) is satisfied.

For the specified interval (1,2) and given equation 1.2/x - 1.6, we can rearrange the equation to solve for c:

1.2/c - 1.6 = 0

1.2/c = 1.6

c = 1.2/1.6

c = 0.75

Therefore, the value of c in the interval (1,2) is 0.75.

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Answer:

Step-by-step explanation:

ax²+6x+c=0

disc=6²-4×a×c=36-4ac≥0,(∵ it has two real solutions.)

36-4ac≥0

36≥4ac

4ac≤36

ac≤9

Answer: first you have to find the speec of the bicycle by using the formula speed = distance/time

120/5=24miles per h

speed of the motorcycle is 3 times as fast as the bicycle so 24x3 = 72miles per hour is the speed for the motorcycle.

Step-by-step explanation:

The probability is 0.2005.

What is a probability distribution?

A probability distribution is a function that describes the probabilities of different outcomes in a random event or experiment. It is used to represent the likelihood of different outcomes occurring in a given situation.

Mean = 650 * 200 = 130000

[tex]\sigma \bar x = \sqrt{n}\times\sigma\\\\=\sqrt{200}*420\\=5939.6970\\\\\\P(X < 125000)=P[Z < \frac{125000-130000}{5939.6970}]\\\\P(X < 125000)=P[Z < \frac{-5000}{5939.6970}]\\\\P(X < 125000)=P[Z < -0.84]\\\\P(X < 125000)=0.2005[/tex]

Hence, the probability is 0.2005.

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The value of the variable 'x' in the given isosceles right angle triangle is 2√2. By applying the Pythagoras theorem, we get the required value.

An isosceles right angle triangle has a right angle and equal lengths of two sides. (the other two angles are also the same in measure for an isosceles triangle).

Given triangle has two angles of 45° and one angle of 90°, then the triangle is "an isosceles right angle triangle.

It is also given that, hypotenuse h = 4 and the opposite side is given by x.

Since it is an isosceles right triangle, the two sides are also equal in measure.

I.e., opposite side length = adjacent side length = x

Then, applying the Pythagoras theorem, we get

h² = (opp)² + (adj)²

⇒ (4)² = x² + x²

⇒ 16 = 2x²

⇒ x² = 8

∴ x = 2√2

Thus, the value of the length x = 2√2.

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The true statement regarding the equation x² + y² - 3x + 6y = 7x + 2 is that it has a area of 36π sq. unit ,  correct option is (b) .

In the question ,

it is given that ,

the equation is x² + y² - 3x + 6y = 7x + 2 ,

On simplifying and rewriting the equation ,

we get ,

x² - 10x + 25 + y² + 6y + 9 = 36

further it can be written as ;

(x - 5)² [tex]+[/tex] (y [tex]+[/tex] 3)² [tex]=[/tex] 36

(x - 5)² + (y + 3)² = 6²

the equation represents a circle .

So , the from the above equation we can conclude that :

the center of the circle will be  = (5,-3) .

the radius is = 6 units .

the diameter will be = 12 units , and

the area of the circle will be = πr² = 36π square units .

So , the statement that matches with the information is that the area is 36π square units .  

Therefore , the True statement is (b) it has a area of 36π sq. units  .

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Each of the three choices has a 12.25 standard deviation average returns during a 4-year timeframe.

In order to find standard deviation on a mutual fund, add up the rates of return for the period you want to measure and divide by the total number of rate data points to find the average return and take each individual data point and subtract your average to find the difference between reality and the average finally we have to square each of this numbers and then add them up.

Here, we had provided the predicted return on the asset, the standard deviation,

s x 10% 5%

y 15    8

Here we need to calculate the standard deviation of returns over the 4-year period for each of the three alternatives.

As per the definition of the standard deviation, we have identified that the values,

Count, N: 2

Sum, Σx: 23

Mean, μ: 11.5

Variance, σ2:  12.25

Here, we must embrace the alternative hypothesis that seems to be rejected hypothesis. The rejection zone is indicated by the z score of -0.40.

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Mathematics is a discipline that has a long and rich history. It has evolved over time from simple counting and measuring to a broad and complex subject that is used in many fields. The development of mathematics has been driven by the need to solve practical problems, as well as the desire to understand the underlying patterns and structures of the world around us.

Early forms of mathematics, such as counting and measuring, were developed by ancient civilizations to solve practical problems such as trade, construction, and agriculture. These early forms of mathematics were based on empirical observations and were often tied to the physical world.

As mathematics developed, it began to include more abstract concepts such as numbers, geometry, and algebra. These abstract concepts allowed for the development of more complex mathematical techniques and the ability to solve a wider range of problems.

Today, mathematics is used in a wide range of fields including science, engineering, economics, and even art. It is an essential tool for understanding and solving problems in the world around us.

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The proportion of the output that is unacceptable is; 0.32

The empirical rule of statistics is also called the 68 - 95 - 99.7 rule, and it states that states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations of the mean, and 99.7% will occur within three standard deviations of the mean.

We are told that the target diameter is 50 mm.

Mean; μ = 50 mm

Standard deviation; σ = 0.07 mm

An acceptable diameter is one within the range 49.93 mm to 50.07 mm. Thus;

50 ± x(0.07) = (49.93, 50.07)

Thus;

50 - 0.07x = 49.93

0.07x = 50 - 49.93

x = 0.07/0.07

x = 1

Thus, the proportion that is acceptable is 68% or 0.68.

Proportion unacceptable = 1 - 0.68 = 0.32

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The value of the variable 'w' for the given equation 7 ( w + 7 )³ = 7(6³)  is equal to w = -1.

As given in the question,

Given equation is equal to :

7 ( w + 7 )³ = 7(6³)

Divide both the side of the equation by 7 we get,

⇒ 7 ( w + 7 )³ / 7 = 7(6³) /7

⇒( w + 7 )³ = (6³)  

Take cube root both the side of the equation we get,

⇒∛( w + 7 )³ = ∛(6³)  

⇒ w + 7 = 6

Now subtract 7 from both the side of the equation we get,

⇒w + 7 - 7 = 6 - 7

⇒ w = -1

Therefore, the value of the variable 'w' for the given equation is equal to w = -1.

The complete question is:

Solve this equation:

7 ( w + 7 )³ = 7(6³)

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Using the null hypothesis test we calculate that variance is less than 6.25 .

Data sample is 0.05.

20 people make up the sample.

And ,

The theories are:

H₀ : μ² = 6.25

H₁ : μ² < 6.25

The critical value = 10.117.

If the test statistic is less than this number, the null hypothesis will be rejected. When the p-value is less than or equal to your significance level, we reject the null hypothesis. The alternative theory, which contends that the effect is widespread, is supported by your sample data. The null must be removed when the p-value is low, as a mnemonic device.

This is the test statistic:

2.976 × 19 / 6.25 = 9.047.

Therefore, we disregard the null hypothesis. The difference is less than 6.25 since it is not 6.25.

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Answer:

we know that

XY+YZ=XZ

solve for YZ

YZ=XZ-XY

XZ=21

XY=8

so

YZ=21-8

YZ=13

therefore

the answer is

YZ=13

Step-by-step explanation:

False.It represents that a is parallel to b.

The equation of line in the point slope form is y = 2x + 8

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Let temperature be denoted as x

Let the time be denoted as y

Let the initial temperature be = 0°F

Let the final temperature be = 1°F

Let the initial time be = 8 : 00 AM

Let the final time be = 10 :00 AM

And , the first point be P = P ( 0 , 8 )

The second point be Q = Q ( 1 , 10 )

Now , the slope of the equation is given as

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 10 - 8 ) / ( 1 - 0 )

Slope m = 2

Now , the equation of line is given as y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = 2 ( x - 0 )

y - 8 = 2x

Adding 8 on both sides of the equation , we get

y = 2x + 8

Therefore , the value of A is y = 2x + 8

Hence , the equation is y = 2x + 8

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The equation to represent money spend and the quantity of salad and pizza is E = $5.00*x + $2.00*y

where x represent the quantity of bowl of salad and y represent the quantity of slice of pizza.

What is equation in mathematics?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.

According to the given question:

The equation to represent money spend and the quantity of salad and pizza is E = $5.00*x + $2.00*y

where x represent the quantity of bowl of salad and y represent the quantity of slice of pizza.

The table to represent the result of above equation is

Budget (in $)             Salad (bowl)         Pizza (slices)

 40.00                              0                            20

 40.00                              2                            15

 40.00                              4                            10

 40.00                              6                             5

 40.00                              8                             0

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Answer:

987

Step-by-step explanation:

Clue 4: There is no 2, 4, 5.

Clues 1 & 2: There is no 1.

7 must be on the right.

_ _ 7

Clue 5: 9 is in the first or second place

9 _ 7   or   _ 9 7

937 or 987 or 397  or 897

Try all 4 possibilities above through all 5 clues.

Only 987 works.

Answer: 987

Answer:

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

Solve each and combine:

The common interval is x > 3.

By using addition, it can be calculated that, Sum of [tex]9x^2 + 6[/tex] and [tex]2x^2 - x - 10[/tex] is [tex]11x^2 - x -4[/tex]

What is addition?

Addition is a basic math operation that combines two or more numbers to create a new total. It is the process of combining two or more values to get a single sum. Addition is one of the four basic operations in math, alongside subtraction, multiplication, and division. It is a fundamental part of arithmetic and is widely used in everyday life for tasks such as counting, budgeting, and measuring. Addition can be performed with any type of number, including whole numbers, fractions, decimals, and even negative numbers. Addition is an incredibly useful tool for solving a variety of math problems.

Sum of [tex]9x^2 + 6[/tex] and [tex]2x^2 - x - 10[/tex]

[tex]9x^2 + 6 + 2x^2 - x - 10\\= 11x^2 -x - 4[/tex]

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Answer:

Wyzant

ALGEBRA WORD PROBLEM

Kieryn T. asked • 01/10/18

The length of a rectangle is 5 cm more than twice the width. The perimeter of the rectangle is 34 cm. Find the dimensions of the rectangle.

I am having trouble with this problem. I asked my parents and they didnt know what to do. I am stuck and i have looked through my notes and nothing has helped.

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Mikaila D. answered • 01/10/18

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The dimensions of the rectangle are two unknowns: The length "l" and the width "w"

The perimeter of a rectangle is found as P = 2*l + 2*w

We also know that the length is 5cm more than twice the width. l = 2*w + 5

These two equations gives us a system of linear equations.

P = 2*l + 2*w

l = 2*w + 5

We can use substitution to replace the "l" in the first equation with 2*w + 5

P = 2*(2*w + 5) + 2*w

P = 4*w + 10 + 2*w

P = 6*w + 10

We know that P = 34cm

34 = 6*w + 10

Subtract 10 from both sides

24 = 6 * w

Divide both sides by 6

4 = w

Now that we know the width, we can find the length by substituting 4 for "w" in the second equation.

l = 2*4 + 5

l = 8 + 5

l = 13

The area of the forest would decrease to 1360 km²

Divide the value of an investment at the end of the period by its value at the beginning of that period. Raise the result to an exponent of one divided by the number of years. Subtract one from the subsequent result. Multiply by 100 to convert the answer into a percentage.

Given here, an area of 2100 km² and each year it decreases by 4.25%

in the first year, the area of the forest becomes  (2100 - 4.25/100 × 2100)                                            

                                                                               = 2010.75 km²

in the second year, the area becomes 2100 × (1-4.25/100)²

                                                                       = 1925.29 km²

similarly, in the tenth year, the area becomes 2100 ×  ( 1-  4.25/100)¹⁰

                                                                         =  1360 km²

Hence, the area of the forest reduces to  1360 km²

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The power series representation for the given function is   1+ 9x + (9x) ^ 2 + (9x) ^ 3 + .... (9x) ^ n (where 0 ≤ n ≤ ∞).

Let u = 9x.

Return to the series above and replace each u with a 9x directly:

Where 0 n , 1 + 9x + (9x) 2 + (9x) 3 +.... (9x) n

Here, the interval of convergence is easily found. It follows that

|9x| 1 -1/9 x 1/9 because we know that geometric series must have | u | = 1

Finally, we may leverage the fact that geometric series have a sum to get the sum: S = a / (1 - u).

Here, u = 9x and a = 1

Therefore, the total is simply S = 1 /(1 - 9x).

Any sum can be calculated provided x is between -1/9 and x and less than 1/9.

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The function f(x) in slope-intercept form is Y= −3X−10.

In the given question, linear function f, f(2)=0 and f(4)=-6.

We have to write function f(x) in slope-intercept form.

We have to find equation for f(x)

f(2)=0, and f(4)=−6,

Now we have to find slope

Slope(m)=−6−0/4−2

m = −6/2

m=−3

Now the general equation of line is

Y=MX+C

where M = slope of the line, C is the Y intercept value, X is independent variable and Y is dependent variable.

At point (2,4)

4 = (−3)×(2)+C

4 = −6+C

Add 6 on both side, we get

C = 10

Equation for f(x) is.

Y=(−3)X−(10)

Y= −3X−10

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The correct statement regarding bias in either distribution is given as follows:

R is biased, and W is unbiased.

We use the graphs showing the sampling distributions for the two different point estimates to identify bias.

Then the criteria to determine that there will be bias is given as follows:

From the graphs given at the end of the answer, we have that:

As the point estimate of estimator R is not at the center, it contains bias, and thus the fourth statement is correct.

The graphs are given by the image shown at the end of the answer.

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The Linear probability model always contains heteroskedasticity when the dependent variable is binary unless all of the slope parameters are zero. It's true.

Probability is the branch of mathematics concerning numerical descriptions of how probable an event is to do, or how likely it's that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

In statistics, a direct probability model is a special case of a double retrogression model. Then the dependent variable for each observation takes values that are moreover 0 or 1.

The introductory sapience is that the direct probability model can be used whenever the relationship between probability and log odds is roughly direct over the range of modeled chances.

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the height of a binary tree is the number of edges in the longest path from the root to a leaf.The best-case height of a binary tree with seven nodes is 3.

A binary tree is a type of tree structure consisting of nodes that are connected by edges. The number of edges in the longest path from a binary tree's root to a leaf determines the tree's height.In the best-case scenario, the binary tree is perfectly balanced and each node has exactly two children. With seven nodes, the best-case height is three because each node has two children and three edges connect the root node to the leaves. This means that the longest path from the root to a leaf is three edges, resulting in a height of three.

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The remaining length of the board is 8 11/16 feet.

Length of board = 20 3/4 feet

Length that was cut off = 12 1/16 feet

To obtain the length of the remaining part of the board ;

We subtract the length that was cut off from the total length of the board ;

(Total length - length that was cut off)

20 3/4 = 83/4

12 1/16 = 193/16

(83/4 - 193/16) =

L. C. M of 4 and 16 = 16

(332 - 193)/16 = 139/16

139/16 = 8 11/16 feet

The remaining length of the board is 8 11/16 feet.

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Using ratio and scale factor, the value of x is 31 mm

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

This is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.

The value of x that will make the figure similar can be calculated by multiplying the smaller figure by the scale factor.

To determine the scale factor, let's find the ratio between two similar sides

scale factor = 29 / 14.5

scale factor = 2

The value of x will be 2 * 15.5 = 31 mm

The value must be 31mm

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