In an instant lottery, your chances of winning are 0.1. if you play the lottery five times and outcomes are independent, the probability that you lose all five times is

Since the length of this rectangle is twice its breadth, the length is equal to 40 cm.

Mathematically, the area of a rectangle can be calculated by using this formula:

Area = Length × Width

Based on the information provided, we have:

Substituting the parameters into the formula, we have:

LB + 75 = (L - 5)(B + 5)

2B² + 75 = (2B - 5)(2B + 5)

2B² + 75 = 2B(B + 5) - 5(B + 5)

2B² + 75 = 2B² + 10B - 5B - 25

5B = 75 + 25

5B = 100

B = 100/20

B = 20 cm.

For the length, we have:

L = 2B

L = 2 × 20

L = 40 cm.

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Considering the given scatter-plot, the line of best-fit is given by:

y = 0.77857t + 3.7.

To find the equation, we need to insert the points (t,y) in the calculator.

In this problem, considering the scatter-plot, we have that:

Hence, using the calculator, the equation is:

y = 0.77857t + 3.7.

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B will be at the place of E after all three rotations. So the correct option is B.

Moving in a circular plane with respect to the fixed point is called as the rotation of the object.

If rotation maps to The three rotations for B will be

The given B after one rotation will shift in place of C

After the second rotation will shift in place of D

After the third rotation will shift in place of E

B will be at the place of E after all three rotations. So the correct option is B.

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Answer:

See below

Step-by-step explanation:

cos  2pi/3   =    -1/2

sin   2pi/3   =     sqrt (3)/2

cos   1 pi/6  =     sqrt(3)/2

sin   11 pi/6  =    - 1/2

so when you put in these values in  you will have :

(2*8) * (-1/2 + sqrt (3)/2 i )( sqrt(3)/2) + i (-1/2) )

= 16 ( - sqrt (3)4  + 1/4 i + 3/4 i - sqrt(3)/4  i^2 )        rememember i^2 =  - 1

= 16 ( 1/4  i  + 3/4  i )

= 16 i

Answer:

answer is B

Step-by-step explanation:

We know,

Opposite of a big arm has a big angle....the same way you can find the next two....

as 18>16>14

Answer:

5x-y≥ 1  

Step-by-step explanation:

Find the slope of the line to be :

y = 5x -1     <=====  the shaded area is less than or equal (because it is a SOLID line...not dashed)  to this :

y ≤ 5x-1      re-arrange to

5x-y ≥ 1

Answer:

x = 2

Step-by-step explanation:

In order to have the two sides of the equation be equal, the exponents must equal.

-3x + 7 = 7x - 13

Add 3x to both sides.

7 = 10x - 13

Add 13 to both sides.

20 = 10x

Divide by 10.

2 = x

Check:

3^(-3•2+7)=3^(7•2-13)

3^1 = 3^1

3 = 3

Answer:

y=(-5x)+(-7)

Step-by-step explanation:

The equation for slope is y=mx+b

so you would say -5x as the mx in the equation and -7 as the u intercept.

Hii!

_________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

y=-5x-7

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

For this question we will use the slope intercept form equation, because we are provided with the slope and the y-intercept.

The slope intercept form equation is [tex]\large\textsf{y=mx+c}[/tex]. In this formula m denotes the slope and c denotes the y-intercept.

Since we have both m and b, we can stick them into the formula. Upon doing this we obtain

[tex]\twoheadrightarrow\sf y=-5x+(-7)[/tex]

[tex]\bullet[/tex] Simplify

[tex]\twoheadrightarrow\sf y=-5x-7[/tex]

[tex]\bullet[/tex] Great job! We found the equation

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

The coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a trapezoid GHJK that was rotated 180° about the origin.

The rule for 180-degree rotation about the origin:

(x, y) → (-x , -y)

From the graph:

Coordinate of H' is (-3, -2)

(-3, -2) → (3, 2)

Thus, the coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.

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Lets solve the question,

Given dimensions are:

Length = 26 feet

Width = 14 feet

concrete walkway with width = c

After installing the concrete walkway dimensions of the walkway will be,

Length = 26 + 2c

Width = 14 + 2c

She wants to build a wooden deck around the pool with a concrete walkway of width = w

Thus the dimensions of the wooden deck around the pool will be,

Length = [tex]26 + 2c + 2w[/tex]

Width = [tex]14 + 2c + 2w[/tex]

Now the perimeter of the wooden deck will be,

Perimeter = 2(length + width)

 [tex]= 2[(26 +2c + 2w) + 2(14 + 2c + 2w)] = 2(40 + 4c + 4w) = (80 + 8c + 8w)[/tex]

Therefore, perimeter of the wooden deck would be: 80 + 8c + 8w

Perimeter = (80 + 8c + 8w)

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The variation equation is xy = a^3

An inverse variation is represented as:

xy = k

Where k is the constant of variation

When y = a and x =a^2, we have:

k = a * a^2

Evaluate

k = a^3

Substitute k = a^3 in xy = k

xy = a^3

Hence, the equation is xy = a^3

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Answer:

the graph of y=x^2-4x is parabola as shown in the image

Step-by-step explanation:

The graph of [tex]y = x^{2} -4x[/tex] by drawing the line y=x-4

so this gives us that the line  y=x-4 satisfies the equation  [tex]y = x^{2} -4x[/tex]

To get points put y = x - 4 in the equation  [tex]y = x^{2} -4x[/tex]

so we get x -4 = x( x- 4)

x =1 and x - 4 = 0

from here we get x = 1,4

now put these values in y = x -4

From here we get y = -3,0

so the points are (1 , -3) and ( 4 , 0)

Plot these on graph and we get the straight line .

For equation  [tex]y = x^{2} -4x[/tex]

As we know it is of type of parabola with shifted centre.

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A percentage is a way to describe a part of a whole. The amount that Kelly will pay for the dress is $33.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given Kelly wants to buy a dress that costs $40.00. She has a coupon for 25% off, and there is a 10% sales tax. Therefore, the amount she will pay is,

25% of $40.00 is,

0.25 × $40 = $10

After using the coupon, the sale price is,

$40 - $10 = $30

The 10% tax on the sale price is,

0.10 × $30 = $3

The final price is $

$30 + $3 = $33

Hence, the amount that Kelly will pay for the dress is $33.

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The graph is shown below:

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given:

h(t) = -16t² + 72

For t=-1,

h(-1) = -16 * (-1)² +72

h(-1) = -16 +72= 56

Ordered pair is ( -1, 56)

For t=1,

h(1) = -16 * (1)² +72

h(1) = -16 +72= 56

Ordered pair is ( 1, 56 )

For t=2,

h(2) = -16 * (2)² +72

h(2) = -64 +72=  8

Ordered pair is ( 2, 8 )

For t=3,

h(2) = -16 * (3)² +72

h(2) = -144 +72=  -72

Ordered pair is ( 3, -72)

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Clayman is 10 years old and Ato is 15 years old

Let the age of Clayman be x

Let the age of Ato be y

If the sum of ages of Clayman and Ato is 25 years. then;

x + y = 25

x = 25 - y ...... 1

In five years time;

Age of Clayman = x + 5

Age of Ato = y + 5

If in five years' time, the age of Ato will twice the age of Clayman now, then;

y+5 = 2x ............. 2

Substitute equation 1 into 2

y +5 = 2(25-y)

y + 5 = 2(30 - y)

y + 5 = 50 - 2y

3y = 45

y = 15

Since x + y = 25

x = 25 - 15

x = 10

Therefore Clayman is 10 years old and Ato is 15 years old

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Answer:

a)<BAC = EDC,<DEC =ABC,ACB=DFE
b)7

Step-by-step explanation:

According to the definition, two triangles are similar if their corresponding angles are congruent and corresponding sides are proportional. Hence, we can find the dimensions of one triangle with the help of another triangle. If ABC and DEF are two similar triangles, then by the help of below-given formulas, we can find the relevant angles and side lengths.

∠A = ∠D, ∠B = ∠E and ∠C = ∠F

AB/DE = BC/EF= AC/DF

Answer:

x = 20°

Step-by-step explanation:

(4x-10)+x=90

4x-10+x=90

4x+x-10=90

5x-10=90

5x=100

x=20

Answer:

20

Step-by-step explanation:

Straight line angles:

     Angles on a straight line add up to 180°.

 90 + 4x - 10 + x = 180

 90 - 10 + 4x + x = 180

Combine like terms.

         80 + 5x     = 180

Subtract 80 from both sides,

                 5x    = 180 - 80

                    5x = 100

Divide both sides by 5

                      x = 100 ÷ 5

                      [tex]\sf \boxed{x = 20^\circ}[/tex]

Table 3,4,5,6,7 has a greater value of the unit rate than the unit rate of the graph.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

The unit rate of the graph is;

[tex]r_g = \frac{26-0}{14-0} \\\\ r_g = \frac{13}{7} \\\\ r_g = 1.857[/tex]

The unit rate for the given tables;

[tex]\rm r_1 = \frac{26-13}{14-7}\\\\ r_1 = \frac{13}{7} \\\\ r_1 = 1.857[/tex]

[tex]\rm r_2 = \frac{26-13}{14-7} \\\\ r_2 = \frac{9}{5} \\\\ r_2 = 1.8 < 1.818[/tex]

[tex]r_3 = \frac{34-17}{18-9} \\\\r_3 = \frac{17}{9} \\\\ r_3 = 1.889 > 1.818[/tex]

[tex]\rm r_4 = \frac{42-21}{22-11} \\\\ r_4 = \frac{21}{11} \\\\ r_4 = 1.909 > 1.818[/tex]

[tex]\rm r_5 = \frac{38-19}{20-10} \\\\ r_5 = \frac{19}{10}\\\\ r_ 5 = 1.9 > 1.818[/tex]

[tex]\rm r_6 = \frac{50-25}{26-13} \\\\ r_6 = \frac{25}{13} \\\\ r_6 = 1.923 > 1.818[/tex]

[tex]r_ 7 = \frac{46-23}{24-12} \\\\ r_7 = \frac{23}{12} \\\\r_7 = 1.917 > 1.818[/tex]

Hence, table 3,4,5,6,7 has a greater value of the unit rate than the unit rate of the graph.

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The value of x = 3/5 or 0.6 will satisfy the equation given.

An equation is a mathematical statement which is formed when two expressions are equated by an equal sign.

It is given that

[tex]\rm \dfrac{1}{3x-1} = \dfrac{2}{x+1}\\[/tex]

It has to be solved and the value of x has to be determined

(x+1) = 2 (3x-1)

x +1 = 6x -2

5x = 3

x = 3/5

Therefore the value of x = 3/5 or 0.6 will satisfy the equation given.

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Answer:1 is exponential. 2 is linear. 3 is neither. 4 is linear. 5 is linear. 6 is exponential. 7a is  exponential. I think 7b could be 10x + y = 10 but I'm not too sure. 7c is (8,4).

Step-by-step explanation:1. the coordinates are moving in an exponential way or something im not sure the correct wording but that is what exponential graphs look like. 2 is a straight line so it is linear. 3 is neither because the graph isn't exponential or linear. 4 is linear because the coordinates are subtracting at the same number. 5 is linear for the same reason at 4. 6 is exponential because the coordinates are multiplied by 2 each time. 7a is exponential because the coordinates are divided by 2 each time. 7b I'm not sure on. 7c is 8/4 because August is the 8th month and the month before (7) is 8 so 8 divided by 2 equals 4. So the 8th month would have to be 4. I hope that helps!

From the given options the options B and C are correct for the given equation.

we have given the equation,

70=10+12r

We have to determine the correct option

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

Therefore from the given options the options B and C are correct for the given equation.

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Part (c)

[tex]\text{LHS}=\csc^{2} x-2\csc x\cot x+\cot^{2} x\\\\=(\csc x-\cot x)^{2}\\\\=\left(\frac{1}{\sin x}-\frac{\cos x}{\sin x} \right)^{2}\\\\=\left(\frac{1-\cos x}{\sin x})^{2}\\\\=\tan^{2} \left(\frac{x}{2} \right)\\\\=\text{RHS}[/tex]

Part (d)

[tex]\text{LHS}=[\cos x \cos y][\tan x+\tan y]\\\\=[\cos x\cos y]\left[\frac{\sin x}{\cos x}+\frac{\sin y}{\cos y} \right]\\\\=\sin x \cos y+\sin y \cos x\\\\=\sin(x+y)\\\\=\text{RHS}[/tex]

The product of 4 and 5g + 2.34 is 20g + 9.36

The expressions are given as:

4 and 5g + 2.34

As a product expression, we have:

4 * (5g + 2.34)

Evaluate the product

20g + 9.36

Hence, the product of 4 and 5g + 2.34 is 20g + 9.36

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Answer: A stretch by a factor of 2 for the exponential growth function f(x)= a(9/4)^x occurs when a =✔ 2

A stretch by a factor of 11/3  for the exponential decay function f(x)= a(3/5)^x occurs when a =✔ 11/3

A shrink by a factor of 1/3 for the exponential growth function f(x)= a(7)^x occurs when a =✔ 1/3

A shrink by a factor of 2/5  for the exponential decay function f(x)= a(2/9)^x occurs when a =✔ 2/5

Step-by-step explanation:

The exponential growth equation is stretched and compressed by a scale factor k = 2 , 11/3 , 1/3 and 2/5

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the exponential growth equation be represented as A

Now , the value of A is

For the exponential growth function f(x)= a(9/4)ˣ, a stretch by a factor of 2 occurs when a = 2

For the exponential decay function f(x)= a(3/5)ˣ, a stretch by a factor of 11/3 occurs when a = 11/3

For the exponential growth function f(x)= a(7)ˣ, a shrink by a factor of 1/3 occurs when a = 1/3

For the exponential decay function f(x)= a(2/9)ˣ, a shrink by a factor of 2/5 occurs when a = 2/5

Hence , the exponential equation is solved

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The 45 mi/h is equal to the 2640 ft/min.

To convert 30 miles per hour to feet per minute, we use dimensional analysis in the process.

We have given that, rate using dimensional analysis.

1 hour = 60 minutes.

1 mile is equal to 5280 feet and 1 hour is equal to 60 minutes.

Hence the formula of conversion is 30 miles / hour *(5280 ft/ mile) * (1 hour / 60 min).

The answer is 2640 ft/min.

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Answer:

Is the second expression written correctly?  It reduces to y>-2, since no x is in the equation.

Step-by-step explanation:

We can graph the two equations.  See attached image.  If y>2 is the correct expression, all points to the right.

If the equation was meant to read y=-3x+1, then graph the revised expression.

Answer:

Step-by-step explanation:

Answer:

Each point (or pair) in a proportional relationship must share the same difference is the false statement.

Answer:

cost of old motor bike =$5675

he spent on repair =$453

cost that he sold =$7265

profit he made=$7265-$5675+$453

=$7265-$6128

=$1137

Step-by-step explanation: