A wall is supported by a brace 10 feet long, as shown in the diagram. If one end of the brace is placed 6 feet from the base of the wall, how many feet up the wall does the brace reach?

The big chip cookie's 95% confidence interval for the amount of chocolate chips per cookie is [8.325,6.474].

Given that,

The quantity of chocolate chips in each big chip cookie at Lian's bakery is something she wants to promote. She chooses a sample of 46 cookies at random and discovers that the average amount of chocolate chips per cookie has a standard deviation of 2.7 and a mean of 7.4.

We have to find what is the big chip cookie's 95% confidence interval for the amount of chocolate chips per cookie.

We know that,

The formula is

=x±Z(S/√n)

=7.4±2.326(2.7/√46)

=8.325 and 6.474

Therefore, the big chip cookie's 95% confidence interval for the amount of chocolate chips per cookie is [8.325,6.474].

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The value for x in the given equation is -24.

Combine.  1/2 and x.

2x/6 + 24/3 = (x/6 + 14/2) -3

2x/6 + 48/6 = (x+42)/6 - 18/6

2x = 42 - 18 - 48

2x = -48

x = -24

A direct variation is a proportionality relationship in which two quantities follow a direct relationship.

An INEQUALITY is a statement which shows that two quantities are not equal or may not be equal. If two quantities are not equal, then one is greater than the other.

≥ (greater than or equal to) means at least that amount or more.

≤ (less than or equal to) means at most that amount or less.

To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Please click the image to view the graph

6x + 2y > 10

Replace the input variable in the formula with the value provided.

Calculate the result.

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Answer:

9 x (x - 2) and (2 x - 3) (2 x + 3)

Step-by-step explanation:

Factor the following:

9 x^2 - 18 x

Factor 9 x out of 9 x^2 - 18 x:

Answer: 9 x (x - 2)

Factor the following:

4 x^2 - 9

4 x^2 - 9 = (2 x)^2 - 3^2:

(2 x)^2 - 3^2

Factor the difference of two squares. (2 x)^2 - 3^2 = (2 x - 3) (2 x + 3):

Answer: (2 x - 3) (2 x + 3)

(a) SST = 1772,   SSR= 1420.79,  SSE=353.05

(b) Coefficient of determination is 0.8018.

(c) Sample correlation coefficient is 0.8954.

The average score can be obtained as

y = ∑y / n

  = 330 / 6

y = 55

The least-square regression line is given as:

y' = 23.221 + 0.318x

Using the above stated regression equation; the predicted values of overall score can be obtained for the given values of price.

y' = 23.321 + 0.318(170) = 77.281

(a) The formula for computing SST is given as:

SST = ∑ (yi - y)²

SST = 1772

Hence the value of SST is 1772.

The formula for computing SSR is given as:

SSR = ∑ (yi' - y)²

SSR = 1420.79

Hence the value of SSR is 1420.79.

The formula for computing SSE is given as:

SSE = ∑(yi - y')²

SSE = 353.05

(b) The coefficient of determination is given by the formula:

R² = [tex]\frac{SSR}{SST}[/tex]

   = [tex]\frac{1420.79}{1772}[/tex]

R²= 0.8954

Hence the value of the coefficient of determination is 0.8018.

(c) The correlation coefficient is computed as:

r = [tex]\sqrt{R^{2} }[/tex]

 = [tex]\sqrt{0.8018}[/tex]

r = 0.8954

Hence the value of the correlation coefficient is 0.8954.

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To find the equivalent expression, we can simplify the fraction by using the rule for exponents that says that when we divide two powers with the same base, we can subtract the exponents. Using this rule, we get:

(8^(-10)) / (8^4 * 8^0) = 8^(-10) / 8^4 = 8^(-10+4) = 8^(-6)

So the equivalent expression is: 1/8^6 = 8^(-6)

The correct answer is: 1 divided by 8 raised to the fourteenth power = 8^(-6)

To find the equivalent expression for the fraction 8^(-10)/8^4*8^0, we can use the property of exponents that states that any number raised to the power of 0 is equal to 1. Therefore, 8^0 is equal to 1.

Using the quotient rule of exponents, which states that when dividing two powers of the same base, we can subtract the exponents, we can simplify the expression to:

8^(-10)/8^4*8^0 = 8^(-10)/8^4 * 1 = 8^(-6).

Therefore, the equivalent expression to 8^(-10)/8^4*8^0 is 8^(-6). The correct answer is therefore 1 divided by 8 raised to the fourteenth power, or option A.

If the unknown value y varies inversely with the cube of x and when x = 4 ,then y = 1. then, if x = 1 the value of y equals to 1/64.

What do you mean by inversely proportional?

When two values are inversely proportionate, or when an increase in one causes a reduction in the other and vice versa, this relationship is referred to as inverse proportionality. Direct proportion is in opposition to it. Alternatively, if one variable is directly proportional to the reciprocal of the other, they are said to be inversely proportional.

As given in the question, the unknown value y varies inversely with the cube of x.

It means,

[tex]\frac{y}{x^3} = constant[/tex]

Putting the values as,

When x=4 , then y=1

constant = 1/64

Putting this value is constant in above equation,

1/64 = y/x³

1/64 = y/1

y = 1/64

Hence, the value of y = 1/64.

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Answer:

The first way is rectangular. You also converted it wrong for the first one. the inches aren's squared. you're converting regular inches into regular feet, instead it should be square inches into square feet.

And Ping is sewing a square tablecloth, not a rectangular one. you have to add the 9 inches on both sides, not just one. You can convert it either way you want, but you have to add the 9 inches to both.

Heteroscedastic residuals will have roughly the same variance for any value of X. Hence:

The correct option is C.

Hetero means that they are different/vary. Homoscedastic would mean that they do not change as the value of x changes.

When the variance of the residuals is uneven throughout a range of measured values, this is referred to as heteroskedasticity. The analysis results may be flawed if heteroskedasticity is present and the population employed in the regression has unequal variance.

One presumption regarding the residuals/errors in OLS regression is that they have the same, but unmeasured, variance. The term "constant variance" or "homoscedasticity" refers to this. Heteroscedasticity is the issue when this presumption is broken.

Hence we get the required answer.

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Answer:

Let's call the number of diners at the Italian restaurant x, and the number of diners at the Mexican restaurant y. We can set up the following system of equations to represent the problem:

Italian restaurant: $20 + 2x = $30 + $1y

Mexican restaurant: $30 + $1y = $20 + 2x

Subtracting $20 from both sides of the first equation and $30 from both sides of the second equation, we get:

Italian restaurant: 2x = $10 + $1y

Mexican restaurant: $1y = $10 + 2x

Multiplying both sides of the first equation by 1/2, we get:

x = $5 + $0.5y

Substituting this expression for x in the second equation, we get:

$1y = $10 + 2($5 + $0.5y)

Expanding the expression on the right side, we get:

$1y = $10 + $10 + $1y

Subtracting $1y from both sides, we get:

0 = $10

This equation is true, so the system of equations is consistent.

Since the total donations from each restaurant would be the same, we can set the total donations equal to each other and solve for the number of diners at each restaurant. The total donation from the Italian restaurant is $20 + 2x, and the total donation from the Mexican restaurant is $30 + $1y. Setting these expressions equal to each other, we get:

$20 + 2x = $30 + $1y

Subtracting $20 from both sides and $1 from both sides, we get:

2x - 2 = $10 + $1y - $1

Combining like terms on both sides, we get:

2x - 2 = $10 + $1y - $1

2x - 2 = $9 + $1y

2x - $9 - $1y = 2 - $9

2x - $1y = -$7

Dividing both sides by 2, we get:

x - $0.5y = -$3.5

Substituting this expression for x in the first equation, we get:

$20 + 2(-$3.5) = $30 + $1y

Simplifying the expression on the left side, we get:

$20 - $7 = $30 + $1y

Subtracting $20 from both sides, we get:

-$7 = $10 + $1y

Subtracting $10 from both sides, we get:

-$17 = $1y

Dividing both sides by -1, we get:

$17 = -$1y

Multiplying both sides by -1, we get:

-$17 = $1y

Dividing both sides by $1, we get:

-$17/$1 = $1y/$1

Simplifying the expression on the left side, we get:

-17 = y

Thus, the number of diners at the Mexican restaurant is -17, and the number of diners at the Italian restaurant is x = $5 + $0.5y = $5 + $0.5(-17) = $5 - $8.5 = -$3.5.

Since the number

The ΔABC and ΔDEF are congruent by SSS congruent criteria

According to the question,

We have to prove ΔABC and ΔDEF are congruent

Coordinates of ΔABC are given as :

A(-2 , -2) , B(4 , -2) and C(4,6)

By using Distance formula ,

AB = √(-2-(-2))²+ (4 - (-2))²

=> √(-2 + 2)² + (4 +2)²

=> √ 6²

=> 6

AC = √(6-(-2))²+ (4 - (-2))²

=> √(6 + 2)² + (4 +2)²

=> √ 56 + 36

=> √92

BC = √(6-(-2))²+ (4 - 4)²

=> √(6+ 2)²

=> √ 8²

=> 8

Coordinates for ΔDEF,

D(5 , 7) , E(5,1) and F(13 , 1)

By using Distance formula ,

DE = √(1 - 7)²+ (5 -5)²

=> √(-6)²

=> √36

=> 6

DF = √(1-7)²+ (13 - 5)²

=> √(-6)² + (8)²

=> √ 56 + 36

=> √92

EF= √(1 - 1)²+ (13 - 5)²

=> √ 8²

=> 8

Now, two triangles are congruent if they are equal sides or equal angles

Therefore , In ΔABC and ΔDEF

AB = DE

AC = DF

BC =EF

By the SSS criteria , ΔABC and ΔDEF are congruent

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Answer:

Only I

Step-by-step explanation:

I. √36 > 5

√36 = 6

6 > 5

Its true

II. 7 < √10

√10 = 3.16 approximately

Hence, 7 > √10

But 7 < √10 is wrong

III. √(17 - 8) > √(17 + 8)

√(17 - 8) = √9 = 3

√(17 + 8) = √25 = 5

√(17 - 8) < √(17 + 8)

But, √(17 - 8) > √(17 + 8) is wrong

Answer:

1.) √36 > 5

Step-by-step explanation:

1.) √36 > 5

= 6 > 5( it is true because 6 is greater than 5)

2.) 7 < √10

= 7 < 3.16 ( it is false because 7 is greater than 3.16)

3.)√17–√8 > √17 + √8

= 4.12 – 2.82 > 4.12 + 2.82

= 1.3 > 6.94( it is false because 6.94 is greater than 1.3)

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The coordinate of point X on the line segment PQ is 4.

What is a number line?

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Given that the coordinate of P is -5 and the coordinate of Q is 7. A point X lies on PQ.

Assume that the coordinate of X is a.

The distance between P and X is a - (-5) = a + 5.

The distance between Q and X is 7 - a.

Given that the ratio of PX and XQ is 3:1.

According to question,

(a + 5) : (7 - a) = 3:1

(a + 5) / (7 - a) = 3/1

Cross multiply :

5 + a = 21 - 3a

Add 3a on both sides:

a + 3a = 21 - 5

4a = 16

Divide both sides by 4:

a = 4.

The coordinate of X is 4.

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Answer: (4, 6)

Step-by-step explanation:

You change the numbers places (x to y and y to x) while switching the sign of the original y value.

Answer: 6

Step-by-step explanation: To solve we first start by adding like terms in our equation which is 30 + 54 = x(5+9) which becomes 84=x(14). Now we need to isolate the x variable by dividing both sides by 14.

x(14) ÷ 14 = x, 84 ÷ 14 = 6

This leaves us with the answer x = 6

The coordinates of point C are (-5.5, 3.2)

Coordinates:

A coordinate is a set of numbers that describes a point in a specific space. It is used to pinpoint a location, whether on a map, a graph, a plane, or in a three-dimensional space. In 2-D space, coordinates are usually written in the form (x, y), where x indicates the horizontal position and y is the vertical position of the point. In 3-D space, a third coordinate (z) is needed to specify the depth. Coordinates are also used to identify points on a graph. Finally, coordinates can be used to define a plane in three-dimensional space, where 3 coordinates are needed to define the plane’s position.

Given,

(x,y) = (x + 4.5, y -6.2)

So,

(x + 4.5, y -6.2) = (-1,-3)

Therefore;

x + 4.5 = -1

= -1 - 4.5

= -5.5

y - 6.2 =  -3

= - 3 + 6.2

= 3.2

hence, the coordinates of point C are (-5.5, 3.2)

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The concept of the line with the geometric shapes and the real life examples has been explained

The line is defined as the two dimensional figure that has length, the line do not has width. So we can says that line is the formed by using the set of points together in the straight line. There are different types of lines like straight line, curved line

Using the lines we can form different types of geometric shapes like triangle, rectangle etc. The triangle can be formed by using three straight lines and the rectangle can be formed by using four straight line

The real life example of the lines are, the pen and pencil represents the straight line

Therefore, the concept of straight line has been explained

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The value of x + y +z is 15.

A whole number is what?

a variety of numbers that contains both zero and the natural number.

Fractions and decimals are excluded.

Real numbers that are not divisible by two are referred to be odd numbers.

X, Y, and Z are all full numbers in the equation.

x, y, and z all have values larger than 2.

xyz² = 735

A value for x + y + z must be found.

Assuming x = 3, the preceding statement results in y = 5 and z = 7

These are odd numbers with a difference of 2 and are greater than 2.

They must satisfy the condition that xyz2 = 735.

= 3 * 5 * 7²

= 735

These are the variables' values and as a result,

The sum of x, y, and z equals.

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Answer:

For the boys' team, the tallest kid is 84 inches while the shortest is 75 inches making the range 9.

For the girls, the tallest is 75 inches tall while the shortest is 66, making the range 9.

Both the boys and the girls have a range of 9 but together, with the tallest boy and the shortest girl, the range is 18 inches.

Hope this helps! Have a nice day!

The equation of circle will be;

⇒ x² + y² = 25

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle with the center at the origin and which passes through the point (4,-3).

Now,

Since, The center of circle = (0, 0)

And, The point passes through the circle = (4, - 3)

We know that;

The equation of circle with center (0, 0) and radius 'r' is,

⇒ x² + y² = r²

Here, The circle with the center at the origin and which passes through the point (4,-3).

Hence, The radius is distance between the (0, 0) and (4, - 3).

So, We get;

⇒ r = √(4 - 0)² + (- 3 - 0)²

⇒ r = √ 16 + 9

⇒ r = √25

⇒ r = 5

Thus, The equation of circle with Centre (0, 0) and radius '5' is,

⇒ x² + y² = 5²

⇒ x² + y² = 25

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complete analysis (carrying out steps A-H in section 4.4 from the Stewart textbook)

results as The graph of f(2) = et te is a straight line with a y-intercept of 1.

A) f(2) = et te

Step A) Identify the domain and range of the function:

Domain: All real numbers

Range: All real numbers

Step B) Find any x-intercepts:

x-intercepts: None

Step C) Find any y-intercepts:

y-intercept: f(0) = e0te = 1

Step D) Find any vertical asymptotes:

Vertical asymptotes: None

Step E) Find any horizontal asymptotes:

Horizontal asymptote: None

Step F) Find any points of inflection:

Points of inflection: None

Step G) Find any symmetry:

Symmetry: None

Step H) Sketch the graph:

The graph of f(2) = et te is a straight line with a y-intercept of 1.

B) f(x) = tan-(+)

Step A) Identify the domain and range of the function:

Domain: All real numbers

Range: All real numbers except -π/2, π/

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"Parameter" is the descriptive measure of the population. The description, that if the data refuses the assumption of a parameter is the main goal of the tests of hypothesis.

There are many population parameters. Some examples of the population parameters include:

In general, it is not possible to measure the parameters of a population, as it requires to collect information from each and every member of the population. That is why, 'sample statistics' is conducted.

What is a sample statistics?

In sample statistics, samples are collected from each and every aspect of the population and then the samples are tested in order to derive a conclusion. For example: the mean diastolic blood pressure of more than one sample, the mean body weight of more than one population, etc.

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The python function is, [1, 4, 9, 16, 25] [1, 4].

What is square of a number?

It is easy to determine a number's square. To determine the given number's square, we must multiply it by itself. A number raised to the power of 2 is always used to represent the square term.

For instance, the square of 6 is equal to 6 times 6, or 6 x 6 = 6^2 = 36.

A "Square Number" is the product of multiplying an integer or number (not a fraction) by itself.

For instance, 3 x 3 = 3^2, or 3 multiplied by 3 equals 3 squared. In essence, a square number is the result of multiplying an integer or number by itself exponentially.

Hence, the python function is, [1, 4, 9, 16, 25] [1, 4].

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Answer:

I think it's 1428 : 2499

Step-by-step explanation:

1428 divided by 4 = 357

7 times 357 = 2499

Basically you have to balance both ratios to get the correct answer.

From the given sequences following are the arithmetic sequences :

1. 3, 7, 11, 15, 19

5. 1, 1/2, 0, -1/2

7. 1, 0, -1, -2, -3

10. 9.5, 7.5, 5.5, 3.5, ...

As given in the question,

Arithmetic sequences are :-

1) yes, because the difference between the terms is same.

7 - 3 = 11-7 = 15 -11 = 4

5)yes, because the difference between the terms is same.

1/2 -1 = 0 -1/2 = -1/2 -0 = -1/2

7)yes, because the difference between the terms is same.

0 - 1 = -1 -0 = -2 -(-1) = -1

10)yes, because the difference between the terms is same.

7.5 - 9.5 = 5.5 - 7.5 = 3.5 -5.5 = -2

Difference between consecutive terms of these sequences are not equal . so these are not arithmetic sequences :-

2,3,4,6,8, 9

Arithmetic sequence

In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 .. is arithmetic because the difference between consecutive terms is always two.

Therefore, the arithmetic sequences are :

1. 3, 7, 11, 15, 19

5. 1, 1/2, 0, -1/2

7. 1, 0, -1, -2, -3

10. 9.5, 7.5, 5.5, 3.5, ...

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Random error is the variation in a statistic from sample to sample due to chance. It is the difference between a sample statistic and the true population parameter that it is estimating.

Good sampling techniques help to reduce the amount of random error in a sample by reducing the variability of the sample results.

Random error is the variability of a statistic from sample to sample due to chance. It occurs when a statistic from a sample does not accurately reflect the true population parameter it is attempting to estimate. Random error can be minimized through the use of good sampling techniques, such as randomization and stratification, as these help to reduce the variability of results from sample to sample. Good sampling techniques also help to ensure that the sample is representative of the population, thus reducing the amount of random error.

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Answer:

8 x 7 is the same as 7 x 8.

An expression that is equal to 8 x 7 would also be an expression that has the same solution.  

7 x 8 = 56

4 x 14 = 56

2 x 28 = 56

1 x 56 = 56

The expression could also have division instead of multiplcation, for example, 7 x 8 = 56 could also be written as 56 ÷ 8 = 7, or 56 ÷ 7 = 8

I hope this helps :)

Linear, polynomial, and quadratic functions can be both increasing or decreasing functions. Exponential function is monotonically increasing function. The derivative of a function may be used to determine whether the function is increasing or decreasing. Exponential functions eventually exceed all other increasing functions.

Function, in mathematics, refers to an expression or rule that describes a relationship between two or more variables. A function is said to be an increasing function when the y-value increases as the x-value increases and vice versa. In order to determine whether the function is increasing or decreasing, the derivative of a function may be used on any intervals in its domain.  If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I. From the given function options, Exponential functions eventually exceed all other increasing functions as the one of variable is in the exponential leading an exponential increase and not a constant increase.

Note: The question is incomplete. The complete question probably is: From the following, Which functions are increasing? How to know if a function is increasing or decreasing?; Which section of the function is increasing?; Which type of increasing function eventually exceeds all other increasing functions? A) linear B) exponential C) polynomial D) quadratic.

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Answer:

  c = 5

Step-by-step explanation:

You want to solve 24c +60 = 36c.

This is sometimes referred to as a "2-step linear equation," because it can be solved in two steps.

The first step collects the variable terms on one side of the equal sign. This is done by subtracting the unwanted variable term from both sides of the equation.

  24c +60 -24c = 36c -24c . . . . . . subtract 24c

  60 = 12c . . . . . . . . . collect terms

The second step is to divide by the coefficient of the variable. This gives you the variable by itself:

  60/12 = (12c)/12

  5 = c . . . . . . . . . . . perform the division

The solution is c = 5.

__

Additional comment

As you can see, we like to write the answer as "variable = constant." We solved the equation to give "constant = variable." Of course, the properties of equality tell you these are interchangeable forms.

The point here is that some folks unnecessarily go to the trouble to manipulate the equation so the variable term ends up on the left. The solution is just as valid when the variable term ends up on the right side of the equal sign.

If you recognize that all of the numbers have a common divisor of 12, you can divide by that first:

  24c +60 = 36c

  2c +5 = 3c

Then subtract the variable term on the left to get the answer.

  2c +5 -2c = 3c -2c

  5 = c

Answer:

  2093pi/90 cm

Step-by-step explanation:

You want the exact length of the arc subtended by a 182° central angle in a circle of radius 23 cm.

The length of an arc of a circle is given by ...

  s = rθ

where θ is the central angle in radians.

The radian measure of an angle of 182° is ...

  182°(π/180°) = 91π/90 . . . . radians

Then the arc length is ...

  s = (23 cm)(91π/90) = 2093π/90 cm