in a region where we have had big earthquakes (magnitude 7 and above) roughly every 200 years, what is the probability that we will not have a big earthquake in this region in the next two years?

Answer: 31

Step-by-step explanation:

the prime factorization of 961 is 31×31  the value of the square root of 961 is 31.

Hope this helps! Have a good day! :)

The 10th term of an arithmetic sequence is found as the 49.

As per the stated values in question.

Fifth term a5 = 24

8th term a8 = 39.

Let the first term be 'a' and the common difference be 'd'.

Then,

a5 = a + 4d

24 = a + 4d .....eq 1

a8 = a + 7d

39 = a + 7d .....eq 2

Solving eq 1 and 2.

3d = 15

d = 5

a = 4

Now,

a10 = a + 9d

a10 = 4 + (9 x 5)

a10 = 4 + 45

a10 = 49

Thus, the 10th term of an arithmetic sequence is found as the 49.

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The function g(x) is a horizontal dilation of scale factor k = 5/2 of function f(x).

We know that f(x) is a linear function:

f(x) = 2x + 4

Here we know that:

g(x) = 2*(0.4x) + 4

Notice that function g(x) can be written as:

g(x) = f(0.4*x)

So we have a horizontal dilation, remember a horizontal dilation of scale factor k can be written as:

g(x) =f(x/k)

Notice that 0.4 = 2/5

Then we have a horizontal dilation of scale factor 5/2.

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The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

Therefore, let's examine the provided graph first in order to locate the solution.We can see that 1 batch of cookies need 2 cups of flour

This provides us with a ratio of 2:1.

Constant proportionality is the ratio of two proportional quantities having a constant value.

Since the batch of cookies grows by 1 for every 2 cups added, we have a constant proportionality of 2 cups.

3y=2x

Divide each term in 3y=2x

by 3

and simplify.

Tap for more steps...

y=2x3

Since the equation can be written in the form y=kx

, y varies directly with x and k. The constant of variation, k, is 23

23

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The length of AC which is the hypothenuse is equal 15.5mm

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle.

In this question, triangle ABC forms a right-angle triangle at angle B and this makes it possible to use Pythagoras theorem.

Using the formula;

AC² = AB²  + BC²

AC²  = 7²  + 13.8²

AC = 15.5mm

The length of the hypothenuse is 15..5mm

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Eli will take 12 hours alone to complete the task.

Acc to our question-

Hence,Eli will take 4 hrs.

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Answer:

yeah i think so

Answer:

$11.96

Step-by-step explanation:

Now we have to,

→ find the 23% of $52.

Let's solve the problem,

→ 23% of $52

→ (52/100) × 23

→ 0.52 × 23

→ $11.96

The similar expression is,

→ 0.23 × 52

→ $11.96

Hence, answer is $11.96.

Balck car can overtake the red car in 2 hrs  

The Relationship between Speed, Distance & Time can be understood by the following formulas

Speed = Distance/Time  

Time = Distance / Speed

Distance = Speed X Time  

Constant speed is also called the uniform rate which involves something traveling at a fixed and steady pace or something moving at some average speed.

Here we have

Two cars are traveling in the same direction along the same route.  

The speed of the Red car = 40 miles per hr

The speed of the Black car = 50 miles per hr  

From above data

The difference between speeds of cars = 50 - 40 = 10 miles per hr

Which means the Black car is chasing the Red car at 10 miles per hr

Given that distance between two cars = 20 miles  

The time taken by the Black car to cover 20 miles

=> Distance/ speed = 20/10 = 2hrs

Balck car can overtake the red car in 2 hrs  

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The values of x and y in the similar triangles are 3 and 2 respectively.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, using similar triangle ratio, let's find the value of x and y.

x / 6 = 1.5 / 3

cross multiply

3x = 1.5 × 6

3x = 9

divide both sides by 3

x = 9 / 3

x = 3

Let's find y.

y / 4 = 1.5 / 3

cross multiply

3y = 6

divide both sides by 3

y = 6 / 3

y = 2

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The graph has no vertex

The transformations from the parent function are

To determine the vertex of a graph, we look for the location of the maximum or the minimum point of the graph

Because the graph is a cubic function, the graph has no maximum or minimum (by definition)

This means that there is absence of a vertex in the graph

In (a), we have

We can see that the graph is a cubic function

This function is represented as

y = ∛x

In this graph, we can see that the graph is 4 units to the left  i.e. y = ∛(x - 4)

And 2 units below the origin i.e. y = ∛(x - 4) + 2

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Answer:

9.4

Step-by-step explanation:

The equation the function after the transformation is (c) g(x) = -√x  - 3

The equation of the function is given as

f(x) = √x ---- i.e the square root parent function

The sequence of transformations is given as follows:-

When the above transformations are combined, we have:

Translate up by 3 units: g(x) = f(x) + 3

Reflection across the x-axis: g(x) = -(f(x) + 3)

So, we have

g(x) = -(√x + 3)

Expand

g(x) = -√x  - 3

Hence, the function g(x) is (c) g(x) = -√x  - 3

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Answer:

-30  I don't see -30 as an answer option.  Please check the problem.

Step-by-step explanation:

c²a + 2a÷b

c²a + 2a/b   Enter values for a, b and c for a = -3, b= 2 and c = 3.

(3)²(-3) + 2(-3)/(2)

(9)*(-3) + (-6)/(2)

-27 + (-3)

-27 - 3 = - 30

Answer: 5/8

Step-by-step explanation:

5/8 is already a fraction

The dimension of the rectangle of the largest area in an equilateral triangle is √3/4L.

Here we have to find the dimension of the rectangle of the largest area.

Let the distance from the tip of the base of the triangle to the point that the top of the rectangle meets the triangle be x.

The width of the rectangle is √3/2 x.

By this, we can find the area of the rectangle

Area = √3/2x ( L -x) = √3/2 xL - √3/2x²

To find the maximum area we have:

dA/ dx = 0

dA / dx = √3/2L - √3x = 0

From we have to find the value of x,

√3 x = √3/2L

x = L/2

The dimension of rectangle is √3/2x = √3/2(L/2)

                                                             = √3/4 L

Therefore the dimension of the rectangle is √3/4 L.

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The change  y=210(1.092)^x represent exponential growth

The percentage rate of increase is 9.2 percent increase

Exponential functions are functions that consist of three part say c(b)^d

the part that says whether the function is growth or decay is b

b is called the base function and it is used as follows to determine growth or decay function

Comparing with the given function 1.092 > 1 hence a growth function

The percentage is solved as follows

1.092 * 100 = 109.2%

109.2% is also referred to as 9.2 percent increase since it is an increment of 9.2%. this is shown below

100% + 9.2% = 109.2%

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The table of solutions for this quadratic equation (y = -2x²) include the following:

x                    y_

-2                  -8

-1                   -2

0                   -0

1                    -2

2                   -8

Also, a graph of the solution of this quadratic equation is shown in the image attached below.

In Mathematics, the valid and true solutions to the given quadratic equation (y = -2x²) are referred to as ordered pairs and they can be determined by substituting the x-values contained in the table into the quadratic equation as follows;

When x = -2, the y-value for this quadratic equation is given by:

y = -2x²

y = -2(-2)²

y = -2 × 4

y = -8

When x = -1, the y-value for this quadratic equation is given by:

y = -2x²

y = -2(-1)²

y = -2 × 1

y = -2

When x = 0, the y-value for this quadratic equation is given by:

y = -2x²

y = -2(0)²

y = -2 × 0

y = 0

When x = 1, the y-value for this quadratic equation is given by:

y = -2x²

y = -2(1)²

y = -2 × 1

y = -2

When x = 2, the y-value for this quadratic equation is given by:

y = -2x²

y = -2(2)²

y = -2 × 4

y = -8

In conclusion, you would notice that a graph of this quadratic equation is parabolic (u-shaped) in nature with a slope of -2.

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The slope-Intercept form of the given line is y=x-1.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The given line passes through (0,-1) and (1,0). Therefore, the slope of the given line can be written as,

Slope of the line, m = [0 - (-1)]/(1 - 0)

                                 = 1 / 1

                                 = 1

Now, the equation of the line passing through (0,-1) can be written as,

y = mx + c

(-1) = 1(0) + C

-1 = 0 + C

C = -1

Substitute all the value in the equation of the line,

y = m(x) + c

y = 1(x) + -1

y = x - 1

Hence, the equation of the given line is y=x-1.

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The equation of the line from the given graph can be written as  y = x + 1.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

From the given graph the points on the straight line can be determined as (1, 0) and (2, 1).

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is given as slope = (y₂ - y₁) / (x₂ - x₁).

Then, the slope of the line is (2 - 1) / (1 - 0) = 1

Now, the equation of the line can be written as,

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

⇒ y - 1 = x

⇒ y = x + 1

Hence, the equation of the line in slope-intercept form is given as y = x + 1.

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Step-by-step explanation:

OR

The neighbour us an amount of $160 for the work that we did for him.

As per the agreement the never will pay 20 dollars were every hour that we work.

We worked for a total of 8 hours on Saturday.

So, according to the unitary method,

Total amount of money owned by the neighbour = number of hours for which we work x the amount received for working per hour.

Total amount of money owned by the neighbour = 8 × 20

Total amount of money owned by the neighbour = 160 dollars.

The total amount of money owned by the neighbour to us is 160 dollars.

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To perform Rotation in coordinate plane the following information may help you.

What is Geometric Rotation ?

In geometry, rotation is a type of rigid motion or transformation that involves the movement of a shape about a point while preserving the shape, size, and distance between the points on the shape.The center of rotation is the location around which the shape is rotated.

To perform Rotation in coordinate plane

Last two questions sum up and I'm explaining like that,

      When a point is reflected in the x-axis then signs of it's ordinate (y-axis) change.

Mₓ (x, y) = (x, - y)

When a point is reflected in the y-axis then signs of it's abscissa (x-axis) change.

My (x, y) = (-x, y)

When a point is reflected in the origin , the signs of it's Abscissa and ordinate change.

M₀ (x, y) = (-x, -y)     (in origin the sign become opposite if there is '+' then it changes to '-' and vice versa)

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Answer:

(y+12)/5=x

Step-by-step explanation:

y=5x-12

get x by itself

y+12=5x

divide both sides by 5

(y+12)/5=x

Answer:

for example 2(3+1)

to solve with the distributive property you multiply the number outside the parentheses(2) with each inside number(3 and 1) individually.

2(3)+2(1)

now solve

6+2=8

now to check it by solving the regular way

2(3+1), 3+1=4 so

2(4)

8

we can see that the answers are the same.

to use the distributive property with x in it

for example, -3(x-6)

multiply the outside number(-3) with each inside number(x and -6)

-3(x)+(-3)(-6)

simplify

-3x-(-18)

-3x+18

hope this helps!

1000/x - 1000/(x + 1) = 4.5 is an equation in terms of x that simplifies to this quadratic equation 9x² + 9x - 2000 = 0 as shown below.

In Mathematics, the standard form of a quadratic equation is given by this mathematical expression:

ax² + bx + c = 0.

Since Winston changed 1000 rand into euros in both 2014 and 2015, this can be represented by this mathematical expression:

1000/x - 1000/(x + 1) = 4.5

Taking the lowest common multiple (lcm), we have:

1000/x(x + 1) = 4.5

1000/(x² + x) = 4.5

Cross-multiplying, we have the following:

1000 = 4.5(x² + x)

1000 = 4.5x² + 4.5x

Multiplying both sides of the equation by 2, we have:

2 × (1000 = 4.5x² + 4.5x)

2000 = 9x² + 9x

Rearranging the terms and equating to zero, we have:

9x² + 9x - 2000 = 0.

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Answer:

I believe the unit price would be $2.97

Step-by-step explanation:

Hope this helps! :))
Please let me know if its incorrect.

The total amount that was shared  $245000 .

In the question ,

the ratio of amount shared by JoJo and Frifi is given

the ratio is given as 3:4  .

the amount that JoJo get = 3x

the amount that Frifi get = 4x

given that Frifi got $140000 .

So , 4x = 140000

Dividing both sides by 4 ,

we get ,

x = 140000/4

x = 35000

total amount shared = 3x + 4x = 7x

Substituting the values of x = 35000 , we get

total amount shared = 7*35000

= 245000

Therefore , The total amount that was shared  $245000 .

The given question is incomplete , the complete question is

JoJo and Frifi shared an amount in the ratio 3:4 respectively , if Frifi had $140000 , then find the total amount that was shared ?

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As replacing a draw is an independent event, the dependent events are

B. drawing a black card and then a red card from a well-shuffled 52-cards deck.

D. Getting two heads when a coin is tossed twice.

If the outcome of one event has an impact on the outcome of another, then two events are dependent. For instance, if you draw two colored balls at random from a bag and don't replace the first ball before drawing the second, the result of the second draw will be influenced by the result of the first.

From the given options we conclude that the dependent events are

Drawing a black card and then a red card from a well-shuffled 52-cards deck.

Getting two heads when a coin is tossed twice.

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Answer:

1) ∠5 and ∠6 are supplementary angles not vertical angles this statement is false.

2) ∠2 and ∠7 are alternally interior angles yeah that statement is true.

3) ∠2 and ∠4 are supplementary angles no they are not complementary, because sum of those two angles i.e. ∠2+∠4 =180.

so this statement is false

Step-by-step explanation:

Step-by-step explanation:

here ∠2+∠5=180°; ∠1+∠6=180; ∠4+∠7=180°; and for ∠3+∠7=180°;

here ∠6+∠8=180°; ∠1+∠3=180°; ∠2+∠4=180°; ∠5+∠7=180; here the

∠1=∠4; ∠2=∠3; ∠5=∠8; ∠6=∠7 (opposite angles are equal)

Answer:

c) x+4

Step-by-step explanation:

1. The original expression can be re-written as (I just rewrote each fraction so that there are no mixed numbers):

[tex]\frac{x}{2}+\frac{9}{2}+\frac{x}{2}-\frac{1}{2}[/tex]

2. Next, you want to group all the terms with the variable x, and all the terms without a variable. All the fractions should be rearranged:

[tex]\frac{x}{2}+\frac{x}{2}+\frac{9}{2}-\frac{1}{2}[/tex]

3. You can now simplify and add the variable terms and the non-variable terms.

[tex]\frac{x+x}{2}+\frac{9-1}{2}[/tex]

Simplify further:

[tex]\frac{2x}{2}+\frac{8}{2}[/tex]

[tex]x+4[/tex]

So your answer is choice c