Write 50,170,000,000 in scientific notation

Answer:

8% decrease

Step-by-step explanation:

50 x 2 = 100

46 x 2 = 92

100 - 92 = 8

y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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Answer:

y = -4x -3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Slope intercept form is y=mx+b

-8x-2y=6 add 8x to both sides

-2y=8x+6 divide both sides by -2

y=-4x-3

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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yes it is an arithmetic sequence.

To identify if it is a sequence ther must be a repetitive pattern.

in this case there is always a pattern of adding 3 to the term that was before. .

To find the common difference simply substract one term from the one before

Answer:

116.67 m

Step-by-step explanation:

Two triangles are said to be similar if their corresponding angles are equal and the ratio of their sides are in the same proportion.

From the image attached:

∠A = ∠C = 90° (right angled triangle).

∠ABE = ∠CBD (vertically opposite angles are equal to each other)

The angle-angle similarity postulate states that If two angles of one triangle are equal to two angles of another triangle, then both triangles must be similar. Hence:

Since, ∠A = ∠C and ∠ABE = ∠CBD, we can say that ΔABE and ΔCBD are similar triangles. Since they are similar, the ratio of their corresponding sides is equal. Therefore:

BC / AB = CD / AE

BC = 140 m, AB = 30 m, AE = 25 m

substituting:

140 / 30 = CD / 25

CD = (140 / 30) * 25

CD = 116.67 m

The width of the canal = CD = 116.67 m

Notice that the difference in the absolute values of consecutive coefficients is constant:

|-7| - 1 = 6

13 - |-7| = 6

|-19| - 13 = 6

and so on. This means the coefficients in the given series

\(\displaystyle \sum_{i=1}^\infty c_i a^{i-1} = \sum_{i=1}^\infty |c_i| (-a)^{i-1} = 1 - 7a + 13a^2 - 19a^3 + \cdots\)

occur in arithmetic progression; in particular, we have first value \(c_1 = 1\) and for \(n>1\), \(|c_i|=|c_{i-1}|+6\). Solving this recurrence, we end up with

\(|c_i| = |c_1| + 6(i-1) \implies |c_i| = 6i - 5\)

So, the sum to \(n\) terms of this series is

\(\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 \underbrace{\sum_{i=1}^n i (-a)^{i-1}}_{S'} - 5 \underbrace{\sum_{i=1}^n (-a)^{i-1}}_S\)

The second sum \(S\) is a standard geometric series, which is easy to compute:

\(S = 1 - a + a^2 - a^3 + \cdots + (-a)^{n-1}\)

Multiply both sides by \(-a\) :

\(-aS = -a + a^2 - a^3 + a^4 - \cdots + (-a)^n\)

Subtract this from \(S\) to eliminate the intermediate terms to end up with

\(S - (-aS) = 1 - (-a)^n \implies (1-(-a)) S = 1 - (-a)^n \implies S = \dfrac{1 - (-a)^n}{1 + a}\)

The first sum \(S'\) can be handled with simple algebraic manipulation.

\(S' = \displaystyle \sum_{i=1}^n i (-a)^{i-1}\)

\(\displaystyle S' = \sum_{i=0}^{n-1} (i+1) (-a)^i\)

\(\displaystyle S' = \sum_{i=0}^{n-1} i (-a)^i + \sum_{i=0}^{n-1} (-a)^i\)

\(\displaystyle S' = \sum_{i=1}^{n-1} i (-a)^i + \sum_{i=1}^n (-a)^{i-1}\)

\(\displaystyle S' = \sum_{i=1}^n i (-a)^i - n (-a)^n + S\)

\(\displaystyle S' = -a \sum_{i=1}^n i (-a)^{i-1} - n (-a)^n + S\)

\(\displaystyle S' = -a S' - n (-a)^n + \dfrac{1 - (-a)^n}{1 + a}\)

\(\displaystyle (1 + a) S' = \dfrac{1 - (-a)^n - n (1 + a) (-a)^n}{1 + a}\)

\(\displaystyle S' = \dfrac{1 - (n+1)(-a)^n + n (-a)^{n+1}}{(1+a)^2}\)

Putting everything together, we have

\(\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 S' - 5 S\)

\(\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 \dfrac{1 - (n+1)(-a)^n + n (-a)^{n+1}}{(1+a)^2} - 5 \dfrac{1 - (-a)^n}{1 + a}\)

\(\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} =\boxed{\dfrac{1 - 5a - (6n+1) (-a)^n + (6n-5) (-a)^{n+1}}{(1+a)^2}}\)

a) P(psychology student)  = 1/3. b) P(psychology or anthropology student)  = 5/6. c) P(not sociology student)= 5/6

(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:

P(psychology student) = 4/(6+2+4) = 4/12 = 1/3

(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:

P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6

(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:

P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6

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Answer:

v = 2.25 ft/s

Step-by-step explanation:

Given that,

A person is walking at a rate of 9 feet every 4 seconds.

We need to find their speed. We know that, the speed of total distance divided by time taken. So,

\(v=\dfrac{d}{t}\\\\v=\dfrac{9\ ft}{4\ s}\\\\v=2.25\ ft/s\)

So, the speed is 2.25 ft/s.

Answer:

Step-by-step explanation:

total interest paid is given as $4,643.46.

total payments = $429.95 x 36 months = $15,478.20

total lease payments = total payments - total interest

total lease payments = $15,478.20 - $4,643.46 = $10,834.74

Remaining balance = Total cost of the lease - Total lease payments

$23,495 - $10,834.74 = $12,660.26

Step-by-step explanation:

look for the LCM of 3 and 10 and since it does not have a LCM you will multiply the two variables. After multiplying, you will then divide your answer by the denominator and multiply it with the denominator

CHECK THE ABOVE PHOTO FOR THE REST

Answer:

Step-by-step explanation:

Easiest way would be to substitute points into the given equations and plot your answers.

E.g. if you substitute points into your first equation you get:

If x = 0, y = -4(0) +2 = 2

If x = 1, y = -4(1) +2 = -2

If x = -1, y = -4(-1) +2 = 6

Etc.

Second equation:

If x = 0, y= -(0) -1 = -1

If x = 1, y = -1 -1 = -2

If x = -1, y = -(-1) -1 = 0

Pretty much just plug in values for x into the equations to find y.

Once you have your points, draw a line :)

Where the two lines intercept would be the solution.

A triangle with 50 cm, 15 cm, 50 cm, and 22ยฐ length of its sides. The type of triangle is Isosceles triangle.

A triangle is a type of polygon with three sides, and the two sides that join the ends are called the vertices of the triangle. An angle is formed between the two sides. Classification of triangles by sides. A triangle with all sides equal is called an equilateral triangle. Any triangle with two equal sides is called an isosceles triangle. If no sides are equal, it is called an odd triangle. We have specified a triangle with side lengths 50 cm, 15 cm, and 50 cm. Here we see that the two sides of the triangle are equal. Therefore, the given triangle is an isosceles triangle.

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Answer:

33480783

Step-by-step explanation:

Geometric term is given by: Tn = ar^(n - 1)

and r = -3

T15 = 7 * (-3)^(15-1)

T15= 7 * 4782969

T15 = 33480783

Answer:

1 in 12 chance of landing on 3

1 in 12 chance of landing on 4

1 in 6 chance of landing on either 3 or 4

Step-by-step explanation:

12 equal sections means probability is 1 in 12 of landing on any one numbered section.

2 in 12 or 1 in 6 chance of landing on either of two numbered sections in one attempt.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

uhh

The answer is 3 cm. A space of 3 cm is left between the edge of the photograph and the frame.

Let x= width of the frame

width of the frame with picture=15+2x

length of frame with picture=24+2x

Area of frame with picture=(24+2x)(15+2x)=(360+78x+4x^2)

Area of picture alone=24*15=360

Area of the frame with picture-Area of picture alone=270

That is:  360+78x+4x^2 - 360 = 270

4x^2+78x-270=0

2x^2+39-135=0

On solving, the solutions are:

x = - 45 / 2 and x = 3

x can't be negative so x = 3 cm

Therefore space of the width of 3 cm is left between the edges of the photograph and the frame.

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Answer:

it's b

Step-by-step explanation:

Answer:

Top to bottom, splits it in half

Step-by-step explanation:

Answer:

130

Step-by-step explanation:

X is the alternate corresponding angle to 50.   50+y=180

y=130

x and y = the  same thing so 130 is the value of x

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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The length of the rectangle is 96 m, the width of the rectangle is 77 cm , the length of the rectangle is 1/8 mile, the length and width of the rectangle is 7 m and 42 m respectively, VW is  11 units.

According to the question,

1) Perimeter of rectangle = 344 M

Width = 76 M

Perimeter of rectangle = 2(length + width)

2(length+76) = 344

length+76 = 172

length = 172-76

Length of the rectangle = 96 M

2) Area of a rectangular window = 7315 \(cm^{2}\)

Length of the window is 95 cm.

Area of rectangle = length*width

95*width = 7315

width = 7315/95

Width of the rectangle = 77 cm

3) The perimeter of a rectangular garden is 5/8 mile.

The width of the garden is 3/16 mile.

Perimeter of rectangle = 2(length+width)

2(length+3/16) = 5/8

length+3/16 = 5/(2*8)

length = 5/16-3/16

Length of the rectangle = 2/16 or 1/8 mile

4) The area of a rectangular window is 8256 \(m^{2}\).

The length of the window is 86 m.

Area of rectangle = length*width

86*width = 8256

width = 8256/86

Width of the rectangle = 96 m

5)  The length of a rectangle is six times its width. The perimeter of the rectangle is 98 m.

Let's take width of the rectangle to be x m.

Length of rectangle = 6x m

2(length+width) = 98

2(6x+x) = 98

2*7x = 98

14x = 98

x = 98/14

x = 7 m

Width = 7 m

Length = 7*6 m or 42 m

6) The perimeter of the pentagon is 58 units.

3z+10+z+3+2z-1+10 = 58

6z+10+3-1+10 = 58

6z+22 = 58

6z = 58-22

6z = 36

z = 36/6

z = 6 units

VW = 2z-1

VW = 2*6-1

VW = 12-1

VW = 11 units

Hence, the answer to 1 is 96 m , 2 is 77 cm, 3 is 1/8 mile , 4 is 96 m , 5 is 7 m and 42 m and 6 is 11 units.

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The equation that is correct is 11.11 = 11² = 121. The correct answer is the fourth option: 11 dot 11 equals 11 Superscript 2 equals 121 (11.11 = 11² = 121)

From the question,

We are to determine which of the options is correct.

To determine which of the options is correct, we will evaluate the options one after the other.

8 dot 8 equals 8 Superscript 2 equals 16

That is,

8.8 = 8² = 16

Evaluating properly

8.8 = 8² = 8 × 8 = 64

Then, 8.8 = 8² ≠ 16

∴ This is NOT correct

9 dot 9 equals 2 left-parenthesis 9 right-parenthesis equals 18

That is,

9.9 = 2(9) = 18

Evaluating properly

9.9 = 9 × 9 = 9² = 81

Then, 9.9 ≠ 2(9) = 18

∴ This is NOT correct

10 dot 10 equals 2 left-parenthesis 10 right-parenthesis equals 100

That is,

10.10 = 2(10) = 100

Evaluating properly

10.10 = 10 × 10 = 10² = 100

Then, 10.10 ≠ 2(10) ≠ 100

∴This is NOT correct

11 dot 11 equals 11 Superscript 2 equals 121

That is,

11.11 = 11² = 121

Evaluating properly

11.11 = 11² = 11 × 11 = 121

Then, 11.11 = 11² = 121

This is correct.

Hence, the equation that is correct is 11.11 = 11² = 121. The correct answer is the fourth option: 11 dot 11 equals 11 Superscript 2 equals 121 (11.11 = 11² = 121)

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Step-by-step explanation:

hope I'm able to explain

#1

Fraction is

\(\\ \tt\hookrightarrow \dfrac{42}{98}=\dfrac{21}{49}=\dfrac{3}{7}\)

#2

Report left:-

\(\\ \tt\hookrightarrow 1-3/7\)

\(\\ \tt\hookrightarrow 7-3/7\)

\(\\ \tt\hookrightarrow 4/7\)