Question 7 of 8
Indicate below whether the equation in the box is true or false.
6 = 1200
10
OA. True
OB. False

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.

We get the fixed cost as $ 150, cost of 25 items as $ 750, range as [0, 1500] and the domain as [0,150].

We are given the cost function:

C(x) = 10x + 500.

Fixed cost is when x = 0

C(0) = Fixed cost = 10 ( 0 ) + 500

Fixed cost = $ 500

Cost of making 25 products is x = 25

C(25) = 10 (25) + 500

C(25) = 250 + 500 = $ 750

Maximum cost allowed = $ 1500

Function becomes:

10x + 500 ≤ 1500

x + 50 ≤ 150

x ≤ 150 - 50

x ≤ 100

Range = [0, 1500]

Domain = [0, 150]

Therefore, we get the fixed cost as $ 150, cost of 25 items as $ 750, range as [0, 1500] and the domain as [0,150].

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Answer:

B

Step-by-step explanation:

Because 3/20 is 15%, 20%, 25%, 33%

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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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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 coordinate of X is at 8 units of P and at 4 units to the left of Q

So the coordinate of X is: -5 + 8 = 3

We know that point X is between points P and Q, in such a way that the ratio between the lengths of the segments PX and XQ is 2:1

First, we can length of the segment PQ is equal to the difference between their coordinates, so we get:

L = 7 - (-5) = 12

Then the length of segment PQ is 12 units, if we divide that in 3 we will get:

12/3 = 4 units.

So the segment PQ can be divided into 3 segments of 4 units each.

If the ratio PX to XQ is 2:1

Then the segment PQ must be divided into 3 parts, such that PX takes two of these parts and XQ is the remaining one.

Then the coordinate of X is at 8 units of P and at 4 units to the left of Q

So the coordinate of X is: -5 + 8 = 3

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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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Answer:

44.912, 44.120, 44.102,

Step-by-step explanation:

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

After solving the Linear equation, the value of the n becomes 18.4.

According to the statement

We have to find that the value of the n.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

The equation is 18 = (36.4-n)

Then we have to solve it

(36.4-n) = 18

36.4 -18 = n

After rearrange it then

n = 36.4 -18

Now subtract the equation, then

n = 18.4.

So, After solving the Linear equation, the value of the n becomes 18.4.

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Boris can expect to break even ( neither gain or lose money) is the answer.

The probability of a number is calculated by dividing Favorable outcome by Total outcome.

The probability of a number between 1 to 10 = Favorable outcome/Total outcome

Favorable outcome =1 (any one number )

Total outcome = 10

Here p(x) is equal to 1 divided by 10

P(X)= 1/10= 0.1

The table gives us the Amount when we multiple X to P(X),

Expected value = (XiP(Xi))

When we substitute the value we get,

=(10.1)+(-50.1)+(30.1)+(-50.1)+(50.1)+(-50.1)+(70.1)+(-50.1)+(90.1)+(-50.1)

=0

So we will get zero after substituting the value.

Hence, option C Bories can Expect to break even (Neither gain or lose money) is the correct answer.

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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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The measure of the other angle is  114.7.

Given that the angles are  supplementary,

Let the other angle be 'x'.

x + 65.3 = 180 degree

x = 114.7

hence, The other angle is 114.7 degrees.

The term "supplementary angles" refers to a pair of angles that always add up to 180°. These two perspectives are known as supplements. The term "supplementary" is derived from the Latin words "supply" and "plere," where "supply" means "supply" and "plere" means "fill." As a result, "supplementary" means "something that is supplied to complete a thing."

If two angles add up to 180 degrees, they are said to be supplementary angles. When supplementary angles are combined, they form a straight angle (180 degrees). In other words, if Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" in this case.

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Answer:

59.3° (nearest tenth)

Step-by-step explanation:

Cosine Rule (for finding angles)

[tex]\boxed{\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}}[/tex]

where:

From inspection of the given triangle:

Substitute the values into the formula and solve for G:

[tex]\implies \sf \cos(G)=\dfrac{6^2+15^2-13^2}{2(6)(15)}[/tex]

[tex]\implies \sf \cos(G)=\dfrac{36+225-169}{180}[/tex]

[tex]\implies \sf \cos(G)=\dfrac{92}{180}[/tex]

[tex]\implies \sf G=\cos^{-1} \left(\dfrac{92}{180}\right)[/tex]

[tex]\implies \sf G=59.26213133...^{\circ}[/tex]

Therefore, the measure of angle G is 59.3° (nearest tenth).

From the division of quadrants in the xy-plane, it is found that letter K represents the second quadrant.

There are four quadrants of points (x,y), and their signals are given as follows:

In this problem, we want Quadrant 2, in which:

Hence:

Letter K represents the second quadrant.

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Answer:

50.24 in²

Step-by-step explanation:

[tex]A = \frac{1}{4} \times (22/7) \times 8^2 = 0.25 \times 3.14 \times 64\\= 50.24[/tex]

➲ Hope this helps.

➲ Wish you the best of luck. :)

diameter of circle= 8 inch.

so, radius of circle= d/2 = 4 inch

now

area of circle=πr²

22/7 × (4)²

50.24 inc.

Answer:

Step-by-step explanation:

1.

scale factor=12.5/10=1.25

x/16=1.25

x=1.25×16=20

2.

correct.

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

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

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

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]\frac{4\sqrt{3} }{3} +\frac{1}{2}[/tex]

Step-by-step explanation:

You can either do this manually or use your calculator. Using your calculator, make sure that your calculator is in degree mode, then enter tan(30) + (1/tan(30)) + sin(60).  [1/tan(30) is equal to cot(30) because tangent and cotangent are inverse functions].

Manually, use the unit circle. Tangent is sine over cosine. Sine of 30 degrees is 1/2. Cosine of 30 degrees is [tex]\sqrt{3} /2[/tex]. 1/2 divided by [tex]\sqrt{3}/2[/tex] is [tex]\sqrt{3}/3[/tex]. Cotangent is 1/tangent so take 1/[tex]\sqrt{3}/3[/tex] which is [tex]\sqrt{3}[/tex]. Then we already said that sine of 30 degrees is 1/2, so add them all together.

[tex]\sqrt{3}/3+\sqrt{3}+\frac{1}{2}[/tex] which is equal to [tex]\frac{4\sqrt{3} }{3} +\frac{1}{2}[/tex] or approximately 2.8094.

Answer:

14 units,

Step-by-step explanation:

Just count down the graph

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Answer:

the answer would be 14 units

Step-by-step explanation:

you can count down between the distance with the first point and the second point

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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Answer:

Step-by-step explanation:

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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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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