Using diagonals from a common vertex, how many triangles could be formed from the polygon pictured below?

Answer:

4 + 4i

Step-by-step explanation:

Add the real part and add the imaginary part.

9 + 7i + (-5  - 3i) = 9 + 7i - 5 - 3i

                          = 9 - 5 + 7i - 3i

                          = 4  + 4i

Answer:

44

Step-by-step explanation:

Okay so we are given (9 + 71) + (-5 - 31).

We need to figure out the value of this expression.

First, let's solve the expression (9 + 71).

1.  (9 + 71) = 80.

Now we have 80 + (-5 - 31).

Next, let's solve the expression (-5 - 31).

2.  (-5 - 31) = -36.

We're left with 80 + (-36).

Finally, let's add the two numbers together.

80 + (-36) = 44

So (9 + 71) + (-5 - 31) = 44

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Based on the speed that light travels and the distance around the Earth along the Equator, the number of times the space ship would travel in 1 second is 0.133 times

The number of times that the space ship would travel around Earth around the Equator, going at the speed of light is:

= Distance around the Earth along the Equator / Speed of light

Solving for the number of times around the Earth for the space ship gives:

= 2.48×10⁴  / 1.86×10⁵

= 24,800 / 186,000

= 0.133 times

In conclusion, going at the speed of light, the space ship would go around the Earth, along the equator, 0.133 times.

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Answer:

y = -6/5 x -9

Step-by-step explanation:

if you plug -5 as x in the equation you get m = -6/5. then you just put it bact to get the answer

This indicates that Talia earned a total of $131250.

Talia's annual earnings are equal to her regular pay ($65000) plus any commissions she receives. Now, in order to determine the commission, you must determine the 2.65% of her total sales ($2.5 million).

1. Given that this indicates a total of 100%, divide the total sales of 2,500,000 by 100.

2,500,000 ÷ 100 = 25000

2. Increase this amount by the specified proportion (2.65)

25000 x 2.65 = 66250

Add the commission to the annual pay now.

65000 + 66250 = 131250

This indicates that Talia earned a total of $131250.

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Answer:

2x⋅(7x2−3x+6y 2 )

Step-by-step explanation:

Answer:

16%

Step-by-step explanation:

Blue = 6

Green = 7

Purple = 5

Red = 4

Orange = 3

25 Students in total

Probability of Red = 4/25

Or 16/100

16%

Answer:

Probability of Red = 4/25

Step-by-step explanation:

Hope it helps!!!

The equation be 2(x-2)-5=√x+3-1 then the graphical solution of the equations exists approximately x = 3 and x = 6.

The solution of an equation creates that equation true.

The equation of can be simplified, therefore:

2(x-2)-5=√x+3-1

simplifying the above equation, we get

2x -9 =√x+2

4 x²-37x + 79 = 0

The graphical solution of the equations exists at approximately x = 3 and

x = 6

In ending, the solution of an equation makes the equation true.

Therefore, the graphical solution of the equations exists approximately x = 3 and x = 6

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The surface area is increasing at the rate of (60 x + 150) cm² per second.

Let the side of the cube be x cm.

s = x cm

Surface area of the cube will be:

S = 6 x² cm²

Now, we are given that, the side of the cube is expanding 5 cm per second.

So, the side of the cube after 1 second will be:

s' = x + 5 cm

Surface area will be:

S' = 6 (x + 5)² cm²

S' = (6x² + 150 + 60 x) cm²

Change in the surface area is:

ΔS = (6x² + 150 + 60 x) cm² - 6 x² cm²

ΔS = (60 x + 150) cm²

Therefore, the surface area is increasing at the rate of (60 x + 150) cm² per second.

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15% of the students scored higher than Henry on the accounting exam.

Percentiles are a measure of the relative standing of a value within a set of values. The nth percentile is a value such that n% of the values are less than or equal to that value.

So, if Henry's score is in the 85th percentile, it means that 85% of the scores in the class are less than or equal to his score.

Therefore, 100% - 85% = 15% of the scores in the class are higher than Henry's score. So, 15% of the students scored higher than Henry on the accounting exam.

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Answer:

sqrt 51

Step-by-step explanation:

You should use the pythagorean theorem, which states a^2+b^2=c^2. So the missing side length for the smaller triangle is sqrt{2^2+3^2}=sqrt{4+9}=sqrt{13}. And the side length x is sqrt{8^2-sqrt{13}^2}=sqrt{64-13}=sqrt{51}

Answer:

4.5×10−3 (note that as we have moved decimal three point to right we are multiplying by 10−3 .

The number 0.0045 can be expressed in scientific notation as 4.5 × 10⁽⁻³⁾.

In scientific notation, a number is written in the form of "a × 10ⁿ," where "a" is a number between 1 and 10 (in this case, 4.5) and "n" represents the exponent that determines the scale (in this case, -3).

The negative exponent indicates that the decimal point is shifted three places to the left, making the number smaller. So, 0.0045 written in scientific notation emphasizes the significance of the decimal point and the smallness of the value, making it easier to handle and compare with other numbers of varying magnitudes.

Therefore, The number 0.0045 can be expressed in scientific notation as 4.5 × 10⁽⁻³⁾.

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Answer:

y=7.5x+6.2

Step-by-step explanation:

Hopefully this is the answer

Answer:

y=7.5x+6.2

Step-by-step explanation:

Hopefully this is the answer

The probability that x is less than 6 is 5/8.

If x is a discrete uniform random variable ranging from one to eight, then each value from one to eight is equally likely to occur, and the probability of any particular value is 1/8.

To find p(x < 6), we need to add up the probabilities of all the values of x that are less than 6:

p(x < 6) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5)

Since x is a discrete uniform random variable, the probability of each of these values is 1/8, so we can substitute that into the equation:

p(x < 6) = (1/8) + (1/8) + (1/8) + (1/8) + (1/8)

Simplifying, we get:

p(x < 6) = 5/8

Therefore, the probability that x is less than 6 is 5/8.

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Answer:  \(525 \frac{2}{5}\)

Step-by-step explanation:

The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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The value of shaded area comes out to be 2.27m².

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons. The shaded region can be located at the center of a polygon or the sides of the polygon.

A shape that has four straight sides of the same length and four angles of 90 degrees.

Area of Square =side× side

=2×2= 4m²

Area of triangle = 1/2×base×height

base=2m but inorder to find height we will use pythagoras theorem

2²= 1²+(height)²

height= 1.73m

Therefore Area of triangle= 1/2×2×1.73

=1.73m²

Area of shaded figure=(4-1.73)m²

=2.27m²

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Answer:

63 days

Explanation:

Given the total number of days in a yesr = 180 days

Percent of the time he walks to school = 35 %

Number of days he walks to school = 35% of 180

Number of days he walks to school = 0.35 * 180

Number of days he walks to school = 63 days

Hence the number of days he walked to schools is 63 days

To compare the 3-month and 12-month moving average forecasts using the mean absolute deviation (MAD) criterion, we need to calculate the MAD for each model and then compare them. The MAD is a measure of the average magnitude of the forecast errors, and a lower MAD indicates a better forecast.

To calculate the MAD for the 3-month moving average model, we need to first calculate the forecasted values for each month by taking the average of the unemployment rates for the previous 3 months. For example, the forecasted value for April 2018 would be the average of the unemployment rates for January, February, and March 2018. We then calculate the absolute deviation between the forecasted value and the actual value for each month, and take the average of those deviations to get the MAD for the 3-month moving average model.

We can repeat this process for the 12-month moving average model, but instead of taking the average of the previous 3 months, we take the average of the previous 12 months.

Once we have calculated the MAD for both models, we can compare them to determine which model yields better results. Generally, a lower MAD indicates a better forecast. However, it is important to note that the MAD criterion only considers the magnitude of the forecast errors and does not take into account the direction of the errors (i.e., overestimation versus underestimation).

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Full Question ;

The accompanying dataset provides data on monthly unemployment rates for a certain region over four years. Compare 3- and 12-month moving average forecasts using the MAD criterion. Which of the two models yields better results? Explain. Click the icon to view the unemployment rate data. Find the MAD for the 3-month moving average forecast. MAD = (Type an integer or decimal rounded to three decimal places as needed.) A1 fx Year D E F G H I 1 2 3 1 с Rate(%) 7.8 8.3 8.5 8.9 9.4 9.6 9.4 9.5 9.7 9.9 9.8 10.1 9.9 9.7 9.8 9.91 9.7 9.4 9.6 9.4 9.3 9.5 9.9 9.5 9.2 9.1 8.9 A B Year Month 2013 Jan 2013 Feb 2013 Mar 2013 Apr 2013 May 2013 Jun 2013 Jul 2013 Aug 2013 Sep 2013 Oct 2013 Nov 2013 Dec 2014 Jan 2014 Feb 2014 Mar 2014 Apr 2014 May 2014 Jun 2014 Jul 2014 Aug 2014 Sep 2014 Oct 2014 Nov 2014 Dec 2015 Jan 2015 Feb 2015 Mar 2015 Apr 2015 May 2015 Jun 2015 Jul 2015 Aug 2015 Sep 2015 Oct 5 7 3 ) 1 2 3 1 5 7 9.1 ) 9. 1 2 3 1 5 7 ) 9.1 8.9 8.9 8.9 8.9 8.7 8.4 8.3 8.3 8.4 8.1 8.1 8.4 8.2 8.3 7.7 7.9 7.9 7.8 1 2 2015 Dec 2016 Jan 2016 Feb 2016 Mar 2016 Apr 2016 May 2016 Jun 2016 Jul 2016 Aug 2016 Sep 2016 Oct 2016 Nov 2016 Dec 3 1 5 3 2 2

The 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.

Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.

Let the 3 numbers be x ,x+2 , x+4

The sum of numbers is 45

⟹x+x+2+x+4=45

3x+6=45

3x=39

x=13

Hence , the 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .

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Answer:

A. 4 hours

Step-by-step explanation:

100 divided by 25

Answer:The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Add 10 10 to both sides of the equation. Using the slope-intercept form, the y-intercept is 10 .

Step-by-step explanation:

Answer:

x=1.5

Step-by-step explanation:

4x=6

divide both sides by 4

x =1.5

The property that should be used to continue simplifying the above equation is A-^1A = 1. So, correct option is C.

We can start with the equation AB = AC and multiply both sides by A^-1 on the left:

A^-1(AB) = A^-1(AC)

Using the associative property of matrix multiplication, we can simplify the left-hand side:

(A^-1A)B = (A^-1A)C

Using the fact that A^-1A = I (the identity matrix), we get:

IB = IC

Simplifying further using the fact that I times any matrix is that matrix itself, we obtain:

B = C

Therefore, the equivalent equation to AB = AC using A^-1 that simplifies to B = C is A^-1(AB) = A^-1(AC), and the property used to continue simplifying the equation is A^-1A = I.

The correct option is (C) A^-1A = 1, which is equivalent to A^-1A = I, since the identity matrix is denoted as 1 in some contexts.

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Given statement 'another name for result variables is independent variables.' is False

In this question, we have been given a statement 'another name for result variables is independent variables.'

We need to state whether the given statement is true or false.

We know that an independent variables are also called as an explanatory variables as they explain an event or outcome

the predictor variables as they can be used to predict the value of a dependent variable

the input variable

On the other hand the dependent variables are also called response variable, output variable or result variable.

This means, the another name for result variables is dependent variables.

Therefore, given statement is False.

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Answer:

D. Knowing that 5² + 12² = 13², draw the 5 cm side and the 12 cm side with a right angle between them. The 13 cm side will fit to form a right triangle.

Step-by-step explanation:

Given;

side lengths = 5 cm, 9 cm, 12 cm and 13 cm.

The sides that corresponds to Pythagoras triple are, 5 cm, 9 cm and 13 cm

5² + 12² = 13²

25 + 144 = 13²

169 = 13²

The correct procedure in given in option is D.

D. Knowing that 5² + 12² = 13², draw the 5 cm side and the 12 cm side with a right angle between them. The 13 cm side will fit to form a right triangle.

The required solution of the given simultaneous equation is x = 5 and y = -9.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
Given a system of equations,
6x + 5y = -15 - - - - -(1)
-4x - y = -11 - - - - (2)

Multiply equation 1 by 1 and multiply equaiton 2 by 5 then add both the equation,
6x + 5y -20x -5y = -15 -55
-14x = -70
x = 5

Now,
-4(5) - y = -11
-20 - y = -11
-y = -11 +20
y = -9

Thus, the required solution of the given simultaneous equation is x = 5 and y = -9.

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The solution of the lines y = - x + 5 and y = 2x - 1 will be (2, 3).

Given that:

y = - x + 5

y = 2x - 1

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If the slopes are different then the system has one solution.

The lines are drawn on the graph. And the solution of the lines will be (2, 3).

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a. The probability of selecting a red ball from Urn A and then the probability of selecting a red ball from Urn B after one red ball has been transferred. b. The probability of selecting a red ball from Urn B, taking into account the transfer of one ball from Urn A. c. The probability that the first ball was red can be calculated using conditional probability.

a. To calculate the probability that both balls chosen are red, we multiply the probability of selecting a red ball from Urn A (2 out of 5) by the probability of selecting a red ball from Urn B (6 out of 7, since one red ball was added). So the probability is (2/5) * (6/7) = 12/35.

b. To calculate the probability that the second ball chosen is red, we consider that there are now a total of 6 red balls and 7 balls in Urn B. Therefore, the probability is 6/7.

c. To find the probability that the first ball was red given that the second ball is red, we use conditional probability. The probability that both balls are red (12/35) divided by the probability that the second ball is red (6/7) gives us (12/35) / (6/7) = 4/5. Therefore, the probability that the first ball was red given that the second ball is red is 4/5.

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Josie has a total of 5 quarters.

Josie has 16 coins. Each of her coins is either a quarter or a dime.

Let

x = number of quarters

y = number of dime

she has 6 more dimes than quarters.

Therefore,

y = 6 + x

x + y = 16

-x + y = 6

2y = 22

y = 11

11 = 6 + x

x = 11 - 6

x = 5

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