(b) Use the defining formula to compute the sample standard deviation s_ Recall the defining formula used to compute the sample standard deviation $ where x is a F = member of the data set, x is the mean, and n is number of data values Before using the formula, we must determine x and n There are five values in the data set 1, 2, 4, 7, 8, so n Calculate the mean X by taking the average of the data values, which is dividing the sum of the data values by the number of data values: 1 + 2 + 4 + 7 + 8 22 Step 3 In order to use the defining formula for sample standard deviation, it is helpful to first calculate (x each data value in the data set 1, 2, 4, 7, 8. for Use the values in the data set and the previously determined mean, x = 4.4,to complete the following table_ 4.4 4.4 4.4 4.4 4.4 X-* ~3.4 0.4 3.6 11.56 5.76 6.76 (iX?

Using the slope-intercept form of the equation of a line, the correct statement are:

The slope of the line is 5/3

The y-intercept of the line is 0

From the question, we are to determine the statements about the given line that are correct

The given equation is

y/x = 5/3

To determine the statements that are correct, we will write the equation of the line the slope-intercept form of a line

The slope-intercept form of a line is given by

y = mx + b

Where m is the slope

and b is the y-intercept

Writing the equation in the slope-intercept form

y/x = 5/3

y = 5/3(x)

By comparing with the slope-intercept form of a line,

m = 5/3

c = 0

Thus,

The slope is 5/3

and the y-intercept is 0

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If the dimensions of the cardboard sheet is 16 inches by 10 inches , then the maximum volume of the box is  144 in³ .

In the question ,

it is given that the length of the sheet is = 16 inch

and width of the sheet is = 10 inch

let width of box be ⇒ "w" ,

let length of box be ⇒ "l"

let the length of the corner cut out be = "x"

let volume of box be ⇒ "V" ;

we need to find the point of dV/dx that is maximum ,

given width = 16 ; and length = 10 ,

we have : width = x + w + x ⇒ w = 2(8 - x)

length = x + l + x = 10 ⇒ l = 2(5 - x)

the Volume of rectangular box is written as ; V = w*l*x ;

substituting the values of w , l and x ,

we get ;

V = 2(8 - x)2(5 - x)x

V = 4x³ - 52x² + 160x

differentiating with respect to "x" , and for critical point equating it to 0 ,

we have ;

12x² - 104x + 160 = 0

solving the above quadratic, we get ;

x = 2 & x = 20/3 .

On substituting the values , in d²V/dx² = 24x - 104 < 0 for x = 2 ,

that is maximum ;

Substituting x = 2 , in the V = 4x³ - 52x² + 160x ,

we get ;

Volume of the box as 144 in³ .

Therefore , the maximum volume of the box is = 144 in³ .

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Answer:

d

Step-by-step explanation:

d

Answer:

Add and subtract the second term to the expression and factor by grouping.

     (2 x -1) ( x^2 + 4)

Hope this helps!

The histogram that depicts the higher standard deviation is the one that has a wider spread of data, meaning the distribution has more dispersion.

This can be seen by the points in the histogram being more spread out and having a larger range of values. The bars may be higher than the average bar in b, but that does not necessarily mean it has a higher standard deviation. Similarly, a more bell-shaped distribution does not necessarily indicate a higher standard deviation.The histogram that depicts the higher standard deviation is the one that has a wider spread of data, meaning the distribution has more dispersion. This is because a higher standard deviation indicates that the data points are more spread out, and the range of values is larger. This can be seen by looking at the histogram and observing that the points are more spread out and have a larger range of values. The bars in the graph may be higher than the average bar in b, but this does not necessarily mean that it has a higher standard deviation. Similarly, a more bell-shaped distribution does not necessarily indicate a higher standard deviation.

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The measure of the smallest angle in the triangle is 10.8°

An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length.

The corresponding angles of the two equal lengths in an isosceles triangle are equal. This means that if we represent the two angles by x and the the third angle by y , then 2x+y = 180.

using cosine rule c² = a²+b²+2abcosC

a = 8, b = 8 and c = 3

3² = 8²+8²+2×8×8cos C

9 = 64+64+128cos C

128cosC = 9- 128

cos C = -119/128

cos C = -0.93

C = cos^-1 0.93

C = 158.4°

therefore 158.4 + A+ B = 180

A= B

2A = 180-158.4

2A = 21.6

A = 21.6/2

A = 10.8°

therefore A = B = 10.8°. This means the value of the smallest angle is 10.8°

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Option A is correct.

For testing, if x is a significant predictor of y in simple linear regression, we need to determine if the slope is significantly different from zero.

What is linear regression?

A statistical technique known as linear regression is used to represent the connection between a scalar answer and one or more explanatory factors. When there is just one explanatory variable, simple linear regression is employed; when there are numerous explanatory variables, multiple linear regression is utilized.

Based on the value of another variable, linear regression analysis makes predictions about the value of the first variable. The dependent variable is the one you're trying to forecast. The independent variable is the one you are utilizing to make a prediction about the value of the other variable.

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On solving the provided question, we got to know that - they are perpendicular, they are perpendicular and they are intersecting lines

A straight line that intersects another straight line at a 90° angle is said to be perpendicular. A little square is placed in the middle of two vertical lines to represent a 90° angle, often known as a right angle, as illustrated. The two straight lines in this instance are perpendicular to one another since they connect at a right angle.

1) For this case, we have to define perpendicular lines:

[tex]m1 * m2 = -1[/tex]

[tex]m1 = 1/5\\m2 = -5\\so, m1*m2 = -1\\[/tex]

they are perpendicular

2) they are perpendicular

3)  they are intersecting lines

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Rev is seeking independent contractors with extensive experience in audio transcription and translation. After the projects are finished, they frequently grade the work of the employees. One needs to be quick on the keyboard, attentive, comprehend appropriate punctuation, have a solid command of language and spelling, be able to pick up the format of the transcription, and be a critical thinker in order to work with them on a consistent basis. These are the characteristics Rev is seeking for in a freelancer.

Rev.com generally serves as a liaison between businesses and freelancers. One of the jobs that may be done from home carefully screens all of its applicants. The business ensures that they only employ the best individuals for their workforce. It strives to provide independent contractors with a setting where they may develop and display their talents. They can socialize with other independent contractors as a result.

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Answer:

x=-9

y=-2

z=4

Step-by-step explanation:

5x+2y-2z=-57

3x-10y-z=-11

y=-2

5x+2(-2)-2z=-57

3x-10(-2)-z=-11

y = -2

5x-4-2z=-57

3x+20-z=-11

y = -2

5x-2z=-53

3x-z=-31

y = -2

5x-2z=-53

3x+31=z

y = -2

5x-2(3x+31)=-53

3x+31=z

y = -2

5x-6x-64=-53

3x+31=z

y = -2

-x=9

3x+31=z

y = -2

x=-9

3(-9)+31=z

y = -2

x=-9

-27+31=z

y = -2

x=-9

z=4

y = -2

A function that represents this situation of selling 3 duct tape wallet per day out of of 160 duct tapes wallets produced is

Information from the problem

You have made 160 duct tape wallets to sell

If you sell 3 each day

From the information we can deduce that

assuming amount left is y and the number of days x the  we have

y = 160 - 3x

Therefore we can say that the expression to represent the situation of selling 3 duct tape wallet per day is  y = 160 - 3x

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Oscar's statement that he can use the expression a = 2 to always know his sister's age is false

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

Oscar = 12

His sister = 6

Equation: a = 2x

Where x = his sister's age

The above equation means that

He is always twice as old as his sister

This statement is false, because the equation is only true when he is twelve

When he is 13, his sister will be 7

And a =2x, will be false

Hence. Oscar's statement  is false

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Equation to determine the diver’s initial depth is [tex]x + 10 \frac{3}{4} = 56\frac{1}{2}[/tex].

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable.

The equation in one variable means the equation containing only one variable. Let’s have a look at the below equations.

Let the distance of diver at a certain depth be x.

After some time he ascends [tex]10\frac{3}{4}[/tex] feet.

The final position of diver is : [tex]56\frac{1}{2}[/tex] feet.

Using given information we get the required equation: [tex]x + 10 \frac{3}{4} = 56\frac{1}{2}[/tex].

where x = distance of diver at a certain depth.

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3) The value of x is 40°.

4) The value of x is 54.67°.

5) The value of x is 11.15.

6) The value of x is 30.33.

What is sine of an angle?

Sine and cosine are trigonometric functions of an angle in mathematics. In the context of a right triangle, the sine and cosine of an acute angle are defined as the ratio of the length of the side directly opposite the angle to the length of the longest side of the triangle (the hypotenuse), and the neighboring leg's length to the hypotenuse, respectively. The sine and cosine functions are abbreviated sin and cos for an angle theta.

3)

The height of the triangle is 9.

The hypotenuse of the angle is 14.

The angle between base and hypotenuse is x°.

sin θ = height/hypotenuse

Putting θ = x°, height = 9  and hypotenuse = 14:

sin x = 9/14

x = 40°.

4)

The height of the triangle is 31.

The hypotenuse of the angle is 38.

The angle between base and hypotenuse is x°.

sin θ = height/hypotenuse

Putting θ = x°, height = 31  and hypotenuse = 38:

sin x = 31/38

x = 54.67°.

5)

The height of the triangle is x.

The hypotenuse of the angle is 17.

The angle between base and hypotenuse is 41°.

sin θ = height/hypotenuse

Putting θ = 41°, height = x  and hypotenuse = 17:

sin 41 = x/17

x = 17 × sin 41

x = 11.15.

6)

The height of the triangle is 29.

The hypotenuse of the angle is x.

The angle between base and hypotenuse is 73°.

sin θ = height/hypotenuse

Putting θ = 73°, height = x  and hypotenuse = 17:

sin 73 = 29/x

x = 29 / sin 73

x = 32.33

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The absolute value of the complex number - 3 + 2i is √13 plotted on the z plane(a + ib).

As the name suggests it is a combination of real numbers and imaginary numbers.

A complex number (a + ib) where a is the real part and b is the imaginary part.

'i' here is called iota and i = √-1, i² = - 1, i³ = - i and i⁴ = 1.

We know the absolute value or magnitude of a complex number

z = a + ib is | z | = [tex]\sqrt{a^2+b^2[/tex].

∴ The absolute value of z = -3 + 2i is,

| z | = [tex]\sqrt{(-3)^2 + (2)^2[/tex].

| z | = [tex]\sqrt{13}[/tex].

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The new length is 35+10=45 and the new width is 18+10=28.

To Find the Area of a rectangle is length times the width.

Given that enclosure at the zoo is 35 feet long by 18 feet wide. It means the length is 35 feet and the width is 18 feet.

Area of Rectangle=Length × Width

=35×18

=630

The zoo wants to double the area of the enclosure by adding the same distance x to the length and width.

(35+x)×(18+x)=1260

630+35x+18x+x2=1260

x2+53x+630-1260=0

x2+53x-630

Now we will apply the quadratic formula we get

x=10.

The new length is 35+10=45

The new width is 18+10=28.

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Answer:

6. X, Y and Z are different numbers. X is a factor of Y. Z is a multiple of Y. Which of the following is DEFINITELY true?

7. The following graph shows Vinit's journey as he cycled from his home to a park, 4 kilometers away in 800 seconds. Which of these can be said based on this graph?

8. How many TENS must be added to 7 000 to make it 70 000.

Step-by-step explanation:

A range of values estimated to have a high probably of containing the population value is called Confidence interval.

A confidence interval is a range of values that is likely to contain the true value of a population parameter, such as a mean or proportion. The degree of confidence associated with a confidence interval is the probability that the population parameter falls within the range of the confidence interval.

Population parameter : In statistics, a population parameter is a numerical measure of a population, such as its mean, variance, or proportion of a certain characteristic. It is usually estimated from a sample of the population and is usually not known precisely.

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One would expect the foreword of a book to be found:

C. At the beginning of the book

The foreword in a book refers to the introductory part of the book that is written by an expert on the subject discussed by the book. The foreword of a book is located at the beginning part of the book and it provides reasons that readers should consider reading the book.

The foreword is not meant to dissuade the readers but to encourage them on the importance and content of the book. It is logical then to expect this feature of books to be located at the beginning of the book.

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The scale factor of the dilation is 2 which can be shown in the details given below.

In geometry, a line segment is bounded with the aid of using awesome factors on a line. Or we are able to say a line phase is a part of the road that connects  factors. A line has no endpoints and extends infinitely in each the course however a line phase has constant or particular endpoints.

QS : QS'

= 4 : 8

= QU : QU'

= 5 : 10

= 1 : 2

Then the scale factor is of the dilation is 2 (magnification).

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Complete question

Line segment SU is dilated to create S'U' using point Q as the center of dilation.

The scale factor of the dilation is:

Answer:

x=- 5

Step-by-step explanation:

A vertical  line has an undefined slope (the rise is divided by zero, since there is no change in x.  x is always -5.

The required equation of the vertical line will be x = -5 which passes through the points (-5,-2).

The equation of a vertical line is of the form x = k, where k is the x-coordinate of the point through which the line passes.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

We know that a vertical line's equation is x = k, where k is the x-coordinate of the point at which the line crosses.

As per the given question, the line passes through the point (-5, -2), so the equation of the line is x = -5.

A vertical line has an undefined slope (since there is no change in x, the rise is divided by zero). x is always a negative five number.

Therefore, the required equation of the vertical line will be x = -5.

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The required missing value for the values representing the direct variation is -3.2.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,

let the missing number be x.
From the table given,
-22/-4.4 = -16 / x
x = -16 / 5
x = -3.2

Thus, the required missing value for the values representing the direct variation is -3.2.

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Answer:

I just know one of them but I think it's "step one:distributive property"

Step-by-step explanation:

im sorry I wasn't able to get the third one

An equation which suggests how the range of skeins of yarn remaining, y, relies upon at the range of hats Anna knits, x is y =6- 1.2x.

An expression is a mathematical equation that is used to reveal the connection present among or extra variables and numerical quantities.

Let y constitute the range of skeins of yarn remaining. Let x constitute the range of hats Anna knits.

Mathematically, an equation which fashions the connection among x and y is given by: Mathematically, an equation which fashions the connection among x and y is given by

Remaining yarn = Total quantity of yarns -

Number of yarns used in keeping with hats

Substituting the given parameters into the formula, we have;

y = 6 - 1.2x

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The two levels of correlation coefficients are as follows:

A correlation coefficient less than -0.7.

A correlation coefficient greater than +0.7.

A correlation coefficient is a statistical degree of the diploma to which modifications to the fee of 1 variable expect alternate to the fee of another. In definitely correlated variables, the fee will increase or decreases in tandem.

The two levels of correlation coefficients are as follows:

A correlation coefficient less than -0.7.

A correlation coefficient greater than +0.7.

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The graph of inequality 7 ≤  y  - 3x < 11 is attached below.

Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal.

Given:

The inequality =  7≤ y -3x < 11

Therefore, the graph of inequality 7 ≤  y  - 3x < 11 is attached below.

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Let a be the area of smaller pentagon. Then area of the smaller pentagon is a=8 [tex]in^{2}[/tex] .

A pentagon is a 2D polygon with five sides and five angles. The word "pentagon" is created by combining the Greek words "penta" (which means "five") and "gon," which means "angles."

The President and the Secretary of Defense have exercised global command and control over the nation's armed forces from the Pentagon. Since its construction, the Pentagon has served as a national and international emblem. It is, above all, a metaphor for American strength and influence, with all the positive and negative connotations that entails.

Similar figures' surfaces have an area that is proportional to the square of their sides.

The ratio of the sides is on the left, and the ratio of their areas is on the right, therefore we may write this as a proportion.

Keep in mind that the ratio of the sides is squared because we are working with areas.

[tex]\frac{side_{1} ^{2} }{side_{2} ^{2} } =\frac{area_{1} }{area_{2} }[/tex]

Let area a smaller pentagon is a

[tex]\frac{7^{2} }{2^{2} }=\frac{98}{a}[/tex]

a=[tex]\frac{98*4}{49}[/tex]

a= 8 [tex]in^{2}[/tex]

So the area of the smaller pentagon is 8 [tex]in^{2}[/tex]

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Answer: 30% of 105 (= 31.5)

Step-by-step explanation:

30% of 105 is 31.5 and

32% of 98 is 31.36

The question asks for the multiplicative rate of change which has a formula:[ f(x2) / f(x1) ] / (x2 - x1). The answer is 2.

If we want to find the multiplication. Tive rate of change of a function, that just means we need to divide one item by the one that comes before it to find out how much it multiplies Given one change in acts.

A ratio is a divisional comparison of two numbers by dividing the second output by the first one and using the first two outputs, -1/8 and -1/4, we can determine the ratio:

-1/4 ÷ -1/8

When dividing fractions, we multiply by the reciprocal:

-1/4 × -8/1

To multiply fractions, multiply straight across:

(-×-8)/(4×1) = 8/4 = 2.

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