4. What is the probability of pulling either a fork or a spoon out of the bag?

The perimeter and area of the complete rectangle is 52 units and 168 square units.

As per the question statement, We are given a big rectangle in which the area of two small rectangle is given as 40 square units and 30 square units.

We are supposed to find the perimeter and area of the complete rectangle.

Let us first consider the small rectangle with area [tex]A_{1}[/tex] 40 sq units as [tex]R_{1}[/tex] with length [tex]L_{1}[/tex] = 5 units.

Let width of [tex]R_{1}[/tex] be [tex]W_{1}[/tex]

Therefore [tex]L_{1} W_{1} = A_{1}[/tex]

therefore, [tex]5*W_{1} = 40\\W_{1}=8 units[/tex]

Let us now consider the small rectangle with area [tex]A_{2}[/tex] 30 sq units as [tex]R_{2}[/tex]

with length [tex]L_{2}[/tex] = 6 units.

Let width of [tex]R_{2}[/tex] be [tex]W_{2}[/tex]

Therefore [tex]L_{2} W_{2} = A_{2}[/tex]

[tex]6*W_{2} =30\\W_{2}=5 units[/tex]

Now the length of breadth of the big rectangle be L and W respectively.

Therefore L = [tex]5+7=12 units[/tex]

and W = [tex]6+8=14 units[/tex]

Therefore perimeter of main rectangle = [tex]2(L+W)=2(14+12)=52 units[/tex]

And area of main rectangle = [tex]L*W=14*12=168 square units[/tex]

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Answer: [tex]x-0.1x=27[/tex]

Step-by-step explanation:

Let x be the number that gets decreased by 10% of itself.

x decreased by 10% of x is 27.

x is 100%, so 100%-10%=90%

So, 90% of x equals 27.

90% = 0.9

0.9x = 27

x = 30

Answer:

x=-1

y=2

z=1

Step-by-step explanation:

After substitution we add common terms and make y and z the subject

y= 3-z

z= - 3+ 2y

We substitue the y

z = - 3+2(3-z)

z= 1

and now we subtitute the z to find y

y= 3-z

3-1 = 2

y=2

Now we substitue y and z to find x

x= - 2 - 3/2 + 5/2

x= - 1

Solution:

The word correlation is used in everyday life to denote some form of association. We might say that we have noticed a correlation between foggy days and attacks of wheeziness. However, in statistical terms, we use correlation to denote the association between two quantitative variables. We also assume that the association is linear, that one variable increases or decreases a fixed amount for a unit increase or decrease in the other. The other technique that is often used in these circumstances is regression, which involves estimating the best straight line to summarise the association.

Correlation coefficient

The degree of association is measured by a correlation coefficient, denoted by r. It is sometimes called Pearson’s correlation coefficient after its originator and is a measure of linear association. If a curved line is needed to express the relationship, other and more complicated measures of the correlation must be used.

The correlation coefficient is measured on a scale that varies from + 1 through 0 to – 1. Complete correlation between two variables is expressed by either + 1 or -1. When one variable increases as the other increases the correlation is positive; when one decreases as the other increases it is negative. The complete absence of correlation is represented by 0.

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Answer:

80

Step-by-step explanation:

Because 400 times 20% is 80 so 80 would be the missing value.

Answer: 2000

Step-by-step explanation:

20% of x = 400

20% = 0.2

[tex]0.2x=400[/tex]

x=2000

The appropriate value in the box will be 4. This will be illustrated as 4(5x + 6)

It should be noted that an expression is used to show the relationship between the variables involved.

In this case, the appropriate value in the box will be 4. This will be illustrated as:

= 4(5x + 6)

= 20x + 24

In conclusion, the value is 4.

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Given points           Reflected points             Dilated points              

D ( 6, 3 )                ⇒ D' ( -6, 3 )                  ⇒ D'' ( 2, -1 )

E ( 9, 3 )                ⇒ E' ( -9, 3 )                   ⇒ E'' ( 3, -1 )

F ( 9, 12 )              ⇒ F' ( -9, 12 )                  ⇒ F'' ( 3, -4 )

G ( 6, 12 )               ⇒ G' ( -6, 12 )                ⇒ G' ( 2, -4 )

Given data

The dimensions of the rectangle DEFG is

D ( 6, 3 )

E ( 9, 3 )

F ( 9, 12 )

G ( 6, 12 )

Reflecting across y axis

Reflecting across y axis is done for example A ( x, y ) to AA

AA will be ( -x, y ).

Using this procedure we get points D'E'F'G' as follows

D ( 6, 3 ) ⇒ D' ( -6, 3 )

E ( 9, 3 ) ⇒ E' ( -9, 3 )

F ( 9, 12 )  ⇒ F' ( -9, 12 )

G ( 6, 12 ) ⇒ G' ( -6, 12 )

To dilate by factor n with the center of dilation at the origin. for example B ( x, y ) to BB

BB will be ( -nx, -ny )

using the procedure we get the points D''E''F''G" as follows

D ( 6, 3 ) ⇒ D' ( -6, 3 ) ⇒ D'' ( 2, -1 )

E ( 9, 3 ) ⇒ E' ( -9, 3 )   ⇒ E'' ( 3, -1 )

F ( 9, 12 )  ⇒ F' ( -9, 12 )  ⇒ F'' ( 3, -4 )

G ( 6, 12 ) ⇒ G' ( -6, 12 ) ⇒ G' ( 2, -4 )

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complete question

The complete question is attached

Answer:

37

Step-by-step explanation:

WX = a

XY = a-9

WY = WX + XY = 65

So we substitute values:

WY = a + a -9 OR 2a - 9

65 = 2a -9

Then we collect like terms:

2a = 65 + 9

2a = 74 (divide both sides by 2 to get a)

a = 37

Answer: 50 points

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.

scale factor=12.5/10=1.25

x/16=1.25

x=1.25×16=20

2.

correct.

Building a regression line from the scatter plot, it is found that the predicted prize money in year 10 of the contest is of: $11,790.

To find the equation, we need to insert the entire set of points (x,y) given by the scatter plot in the calculator.

From the scatter plot, the points are approximated as follows:

(1, 9.5), (2,9), (3,7), (4,10), (5,11), (6, 10), (7, 10.5).

With the help of a calculator, the line of best fit to predict the amount of prize money in year x of the contest is given by:

P(x) = 0.32143x + 8.28571

To find the predicted amount in year 10, we have to find the numeric value when x = 10, hence:

P(10) = 0.32143(10) + 8.28571 = $11,500.

The closest option is $11,790, which is different from $11,500 because the coordinates of the points are approximated from the scatter plot and not exact.

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The numbers ordered from the greatest to the least is

4

15/5

0.5

-1/5

-1.2

-49

From the given question, we are to order the given numbers from the greatest to least.

The given numbers are

-49

-1/5

0.5

4

-1.2

15/5

First, we will convert the fractions to decimal or whole number

-1/5 = -0.2

15/5 = 3

Now, we will order the numbers from the greatest to the least

4 > 3 > 0.5 > -0.2 > -1.2 > -49

That is,

4 > 15/5 > 0.5 > -1/5 > -1.2 > -49

Hence, the numbers ordered from the greatest to the least is

4

15/5

0.5

-1/5

-1.2

-49

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All work and answers are provided in the attached screenshot! :)

Have a great day! :)

6b+3d-1=C Sorry if I'm wrong, I forgot of Algebra 1

The length of the school bus is 45 feet.

Given, School bus has a scale of 1/2 inch to 5 feet.

Length of the school bus is 4 1/2 inches on the scale drawing.

Actual length of the bus = ?

Given scale = 1/2 inch = 5 feet

⇒ 1 inch = 1/2 inch ₊ 1/2 inch

⇒ 1 inch = 5 feet ₊ 5 feet

⇒ 1 inch = 10 feet

Length of school bus = 4 1/2 inches = 4.5 inches.

Actual length:

length of school bus = length in inches × length in feet

4.5 inches = (4.5 × 10) feet

4.5 inches = 45 feet.

Hence we get the actual length of the school bus as 45 feet.

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The expression (4 + 15.6a) − (7 + 3.7a) in simplest form is − 3 + 11.9a

The expression is given as

(4 + 15.6a) − (7 + 3.7a)

Remove the bracket

So, we have

(4 + 15.6a) − (7 + 3.7a) = 4 + 15.6a − 7 - 3.7a

Collect the like terms

So, we have

(4 + 15.6a) − (7 + 3.7a) = 4  − 7 + 15.6a - 3.7a

Evaluate the like terms

So, we have

(4 + 15.6a) − (7 + 3.7a) = − 3 + 11.9a

Hence, the expression (4 + 15.6a) − (7 + 3.7a) in simplest form is − 3 + 11.9a

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Answer: 999994

Step-by-step explanation:

12+12=24

-3-3-3-3-3-3-3-3-3-3= -30

24-30= -6

-6 + 1000000=999994

Answer:

Step-by-step explanation:

2x + 11 + 70 + 75 = 180

2x = 180 - 11 - 70 - 75

2x = 24

x = 12

----------

check

75 + 70 + 11 + 2 * 12 =              ( remember pemdas)

75 + 70 + 11 + 24 =

180°

the answer is good

The correct option is D. The graph of f(x) is shifted 10 units down.

In mathematics, a graph is described as a pictorial depiction or diagram that organizes data or values.

The graph's points frequently represent the relationship among two or more things.

For the given question;

The function is given as; f(x) = 1/x

Where x is the domain which is shown on x axis.

and f(x) is the range which is shown on y axis.

Thus, for the relation of g(x) = 1/x -10.

Whatever the value of the input for x, the output is shown on y axis.

Now, as the value expression is decreased by 10, thus the output value for y will reduced by 10.

Therefore, the graph of f(x) will shift downward by 10 units.

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The graph of the equation y = m x + b where m = 2 and b = - 3 has been obtained.

We are given the function:

y = m x + b

We are also given that:

m > 0 and b < 0

Now lets assume m = 2 and b = -3

So, we get the equation as:

y = 2 x - 3

Now, we have to graph the equation.

We get some values of x and y as:

x        0        1        2

y      - 3      - 1        1

Therefore, the graph of the equation y = m x + b where m = 2 and b = - 3 has been obtained.

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The height of the tree in Jasmine's scale drawing is 6.25 inches.

A scale drawing is a smaller version of a larger image or drawing. The scale drawing is usually reduced at a constant dimension

Scale of the drawing = original dimensions / dimensions of the scale drawing

The first step is to determine the original height of the tree:

Height of the tree from Luis' scale drawing = (7.5 x 10) / 3 = 25 ft

Height of the tree in Jasmine's scale drawing = (5 x 25) / 20 = 6.25 inches

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Answer:

Step-by-step explanation:

8 = 11 - v

8 - 11 = 11 - v - 11   Subtract 11 from both sides of the equation.

-3 = -v

3 = v Multiply both sides by -1

v = 3

Check:

8 = 11 - 3

8 = 8

Answer:

3498

Step-by-step explanation:

Answer:

69,000,000

Step-by-step explanation:

UHhhHh 6.9 * 10^7 written in standard form is 69,000,000.

Answer:

6.9 × 10 × 10 × 10 × 10 × 10 × 10 × 10

_____________________________________________________
What is standard form?

We can think of the standard form as the most common way of representing a mathematical element, through numerical form.

Six point nine times 10 to the power of 7 is not in standard form, because the number is described using words.

Exponents are not included under standard form.

________________________________________________________
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Answer:

s(6)=62

Step-by-step explanation:

s(t)=t^2+4t+2

s(6)=6^2+4(6)+2

s(6)=36+4(6)+2

s(6)=36+24+2

s(6)=60+2

s(6)=62

Hope this helps.

Therefore the equation of the line in function-form is f(x)=-2x-1

An equation of a line on the cartesian plane is given by y=mx+c. Here m denotes the slope of the line and c denotes the y-intercept.

Slope of a line is defined as the inclination of the line along the positive   x- axis . Slope is calculated by the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}.[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points on the line.

y-intercept is defined as the point where the line passes through the y-axis.

From the graph we can see that the line passes through (0,-1)and (-1,1)

therefore slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\or, m=\frac{1-(-1)}{-1-0}\\or, m=-2[/tex]

Now we know that the equation of a line passing through a point [tex](x_1,y_1)[/tex] and with slope m is given by

[tex]y-y_1=m(x-x_1)\\[/tex]

Substituting the values in the equation we get

y-(-1)=-2(x-0)

or, y=-1-2x

Therefore the equation of the line in function-form is f(x)=-2x-1 .Hence the second option is correct.

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The y component of Z = N+L

Z=3(i)+5(j)-3(k)

Given:

N = 3(i) +3(j) + 10 (k)

L = 2(j) - 13 (k)

Z=3(i)+5(j)-3(k)

Vectors are represented by an alphabet with an arrow over it (or) by an alphabet written in bold. Vector addition can be used to combine two vectors, a and b, and the resultant vector is written as a + b. Before we can learn about the properties of vector addition, we must first understand the conditions that must be met when adding vectors. The following are the terms:

Vectors can only be added if they are of the same type. For example, acceleration should only be added with acceleration and not mass.

Vectors and scalars cannot be added together.

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Answer:

Step-by-step explanation: