the event containing the outcomes belonging to a or b or both is the __________ of a and b.

Answer:

3rd option

Step-by-step explanation:

(5y - 16) and (3y + 20) are a linear pair and sum to 180° , that is

5y - 16 + 3y + 20 = 180

8y + 4 = 180 ( subtract 4 from both sides )

8y = 176 ( divide both sides by 8 )

y = 22

then

5y - 16 = 5(22) - 16 = 110 - 16 = 94°

3y + 20 = 3(22) + 20 = 66 + 20 = 86°

The distance between the two given points on a number line is: 33/4 units.

The absolute difference between two points that are on a number line is the distance that exist between the two points.

For example, if a and b are two points on a number line, the distance between them can be calculated as: |a - b| units.

Given the coordinate of the two points, -5/2 and -23/4:

Distance between the two points = |-5/2 - 23/4|

Distance between the two points = |(-10 - 23)/4|

Distance between the two points = |-33/4|

Distance between the two points = 33/4 units.

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Answers:

9^{3} = 9 x 9 x 9

so 9^{3} = 3 x 3 x 3 x 3 x 3 x 3

so 9^{3} = 3^{y} where y = 3^{6}

Answer:

-80

Step-by-step explanation:

PEMDAS is Parentheses, exponent, multiplication, division, addition, subtraction.

the '-' is not a subtract sign, it is saying it is negative. Therefore, 4 * -20 = -80

Answer:the answer is -80

Step-by-step explanation:

The factored expression of the expression given as -6x² + 18x is -6x(x - 3)

The expression is given as

-6x² + 18x

Group the expression in 2's

So, we have

-6x² + 18x= (-6x² + 18x)

Factor each group

So, we have

-6x² + 18x= x(-6x + 18)

Rewrite as

-6x² + 18x= -6x(x - 3)

Hence, the factored expression is -6x² + 18x= -6x(x - 3)

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Step-by-step explanation:

look at the picture

*for the equation you can choose any of the two points

The given numbers 7 min and 28 min. The greatest common difference is 7 for the given numbers.

Given that,

We have to find the fraction of the given numbers

7 min and 28 min

We just have to find the greatest common difference.

The largest positive integer number that divides all the numbers in the set evenly and leaves no residual is referred to as the greatest common difference (also called highest common divisor, largest common factor, or highest common factor) of a group of numbers. It has the largest multiple of all the numbers in the set.

The GCD is most often computed for two numbers when reducing fractions to their smallest terms. Two numbers are considered coprime or substantially prime if their greatest common difference is 1.

Therefore, the greatest common difference is 7 for the given numbers.

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The height of the building B is 140 feet which is 7 times taller than building A.

Scale factor defines how many times more or less two things are relative to each other.

When we need to find out how many times more we multiply and when we want to find how many times less we divide. We can also call scale factor as a method or way of comparing things in terms of size or time or any other variable.

Given, Building A is 20 feet tall. Building B is 7 times as tall.

∴ The height of building B is (20×7) = 140 feet.

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The center  ( x - 6)² + (y + 4)² = 1 of circle does not lies in second quadrant.

it lies in fourth quadrant.

A circle equation with centers (h, k) and radius r is ,

                       ( x - h)² + (y - k)² = r²

Regarding the given question,

The circle equations have been given to us.

Each circle's center is located.

We know that any point in the second quadrant has coordinates of the form (-x, y)

The x-coordinate must be a negative number, and the Y-coordinate must be a positive number.

( x - 6)² + (y + 4)² = 1

( x - 6)² + (y + 4)² = 1²

By comparing the above circle equation with ( x - h)² + (y - k)² = r²,  

we get the center = (6, -4) and the radius = 1.

The circle's center is located in the fourth quadrant. The x-axis in this quadrant is positive, while the y-axis is negative.

So here  ( x - 6)² + (y + 4)² = 1 does not lies in second quadrant .

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The value that is closest to the probability that Chris's guess ends up being exactly 4 less than the result is 1/3 .

Probability theory, which is widely used in domains such as statistics, mathematics, science, money, gambling, cognitive computing, pattern recognition, machine learning, game theory, and philosophy, has formalized these concepts mathematically.

Dice is fair.

Sample space ={1,2,3,4,5,6} = 6

Two dice are rolled

Sample space =  6² = 36

Probability theory is also used to understand the intrinsic mechanics and generalizations of complex systems. Like other theories, the theory of probability is a formal representation of its concepts—that is, terms that can be investigated independently of their meaning.

therefore the required probability is given by=

P(X)=12/36 = 1/ 3

To manage these formal notions, the laws of mathematics and logic are utilized, and any conclusions are evaluated or till around into the problem area and favorable outcome .

Hence the value that is closest to the probability that Chris's guess ends up being exactly 4 less than the result is 1/3 .

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Given the equation:

Let's rewrite the equation for H.

To rewrite for H, first multiply both sides by H:

Now divide both sides by cos32:

ANSWER:

Proved our result using weak induction.

Given:

If n lines are drawn on a plane, no two lines are parallel, and all lines intersect at different points, how many sections do they separate the plane into, assume that no more than two lines intersect at any one point.

Suppose it is true for n .Now add a new line , the number of  vertices increases by n one with each of the old line and the number of line segments increases by 2n+1 ( Each of the n old lines is broken into one more piece and the new line has n+1 segments , hence by euler's theorem on planar graphs the number of regions (F) increases by n+1 since V - E + F is constant and V - E is reduced by n+1.

so we now have

[tex]n^{2}[/tex]+n+2/2 + n + 1 = [tex](n+1)^{2}[/tex]+ n+1+2/2  vertices are desired

Therefore proved our result using weak induction.

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The value of inverse function when x = 0 is 1, when x = 1 is infinity or not defined, and when x = 3 is -1/2.

What is function?

A function in mathematics is an expression, rule, or law that determines the relationship between two variables, one of which is independent, and the other of which is dependent (the dependent variable). The traditional notion of function was first proposed by German mathematician Peter Dirichlet in 1837.

The function for the line shown in the graph can be written as:

y = -x + 1

Here, y = f(x)

[tex]\frac{1}{f(x)} = \frac{1}{-x+1}[/tex]

[tex]f^{-1}(x) = \frac{1}{-x+1}[/tex]

We can put the given values in place of x in this function:

[tex]f^{-1}(0) = 1[/tex]

[tex]f^{-1}(1) = infinity[/tex] or ( not defined)

[tex]f^{-1}(3) = -\frac{1}{2}[/tex]

This is the required answers.

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Answer:

12.656

Step-by-step explanation:

1) BODMAS = 23.98-(1.49*7.6)

2) 1.49*7.6 = 11.324

3) 23.98-11.324 = 12.656

Hope this helps, have a great day! :)

Answer:

12.656

Step-by-step explanation:

You have to subtract the first two numbers(23.98-1.49).The answer you will get you will then multiply it buy the last number(7.6)

The value of p for given inequality would be:

p is greater than or equal to negative twenty one halves

In this question, we have been given a statement for an inequality.

two thirds times p plus 10 is greater than or equal to 3

i.e., (2/3)p + 10 ≥ 3

We need to find the value of p

(2/3)p + 10 ≥ 3

(2/3)p + 10 -10 ≥ 3 - 10

(2/3)p ≥ -7

(2/3)p * (3/2) ≥ -7 (3/2)

p ≥ -21/2

This means, p is greater than or equal to negative twenty one halves

Therefore, the value of p for given inequality would be:

p is greater than or equal to negative twenty one halves

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The image of the point (-3, 1) after dilation is (−6,2).

Dilation is a process of increasing size of an object while maintaining its own shape. Depending on the scale factor, the object's size is either increased or decreased. The scale factor is the proportion of the new image's size to that of the previous image's size.

Given point is (-3, 1).

The dilation of the point is calculated as

Dilation = multiply each coordinate by scale factor.

(x,y) to (2x,2y)

Dilations  = multiply by a scale factor

(-3, 1) to (2*-3,2*1)=(−6,2)

Therefore, the image of the point (-3, 1) after dilation will be (−6,2).

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The value of x is 1.5

The parallel lines are the coplanar straight lines  that are at equal distance from each other and never meet.

When two parallel lines are cut by a transversal, the formed alternate exterior angles will be congruent

Here two parallel lines L1 and L2 cut by a transversal L3, the marked angles in the given picture is called alternate exterior angles. The alternate angles are congruent.

Therefore

x+1 = 3x-2

Move 3x to left hand side and 1 to right hand side of the equation

x-3x = -2-1

-2x = -3

x = -3/-2

x = 1.5

Hence, the value of x is 1.5

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      We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression. We take out brackets by expanding them, often known as multiplying out. It is the factorization procedure in reverse.

(t -t2)(t +5)(t-4) (t-4)

Replacing it with: f(t) = (t -t2)(t +5) (t-4)

Instead, resolve:  d/dt ((t -t2)(t +5)(t-4) )

Solution:

(t -t2)(t +5)(t-4) (t-4)

Expand:

(t -t2) (t +5) (t-4) ; t³ - t²- 22t + 40

Steps:

(t -t2)(t +5)(t-4) (t-4)

Parentheses distributed as: t ²t+ t² (-4)+3tt+3t(-4)-10t-10t-10(-4)

Reduce t ²t+ t² (-4)+3tt+3t(-4)-10t-10t-10(-4);

t³-t²-22t+40.

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The percentage of variation that is in the differences in the number of volunteers is 86.1

We have to take the square of the correlation coefficient in other to get the solution to this problem.

The formula for variation is given a r squared

r = r²

The value of r is given as r = 0.928

Then we have the square of r = r²

= 0.928²

= 0.861

The percentage would be gotten by 0.861 x 100

= 86.1%

Hence the percentage of variation that is in the bags of trash that has been collected is 86.1

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Answer:

x=1

Step-by-step explanation:

Answer:

eèeeeeeeeeeeeeeeeeeweeeeeee

Based on the probability distribution of a random variable "q" which goes as,

Value of "q"                  Probability

       0                                 0.22

       1                                  0.21

       2                                0.257

The standard deviation of "q" will be

As per the question statement, we are provided with a probability distribution of a random variable "q" which goes as,

Value of "q"                  Probability (P)

       0                                  0.22

       1                                   0.21

       2                                 0.57

We are required to determine the standard deviation of "q"

From the question mentioned table,

Expected value (qₙ) of random variable = [(q₁ * P₁) + (q₂ + P₂) + (q₃ + P₃)]

= [(0 * 0.22) + (1 * 0.21) + (2 * 0.57)] = 1.35

Therefore, Variance (V) of the random variable = ∑[P * (q - qₙ)²]

= [{0.22 * (0 - 1.35)²} + {0.21 * (1 - 1.35)²} + {0.57 * (2 - 1.35)²}]

= [{0.22 * (-1.35)²} + {0.21 * (-0.35)²} + {0.57 * (0.65)²}]

= [(0.22 * 1.8225) + (0.21 * 0.1225) + (0.57 * 0.4225)]

= (0.419175 + 0.025725 + 0.240825)

= 0.686265

Finally, Standard Variance of the variable "q" = √V

                                                                           = √(0.686265)

                                                                           = 0.8284

                                                                           ≈ 0.83

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Answer:

x² + y² = 13 ---1

y = x + 1 ---2

First make one of the unknowns the subject so you can substitute it into the other equation. Since 2 already has y as the subject, we can substitute 2 into 1 to find x.

Substitute 2 into 1:

x² + (x +1)² = 13

x² + (x² + 2x + 1) = 13

2x² + 2x - 12 = 0

2 is a common factor so we factorize it out.

2(x² + x - 6) = 0

x² + x - 6 = 0

Factorize the equation further.

(x - 2)(x + 3) = 0

x - 2 = 0     or      x + 3 = 0

x = 2          or       x = - 3

Substitute values of x into 2 to find y.

y = 2 + 1     or      y = - 3 + 1

  = 3                      = - 2

Hence, x = 2 and y = 3 or x = - 3 and y = - 2.

The domain and the range are 0 ≤ t ≤ 6 and 2 ≤ d(t) ≤ 5, respectively

The domain of the function is the set of input values the function can take

The function is given as

d(t) = 1/2t + 2

Where t represents the number of days

And d represents the inches of rainfall

From the question, we have

Total number of days = 6

This means that the domain is 0 to 6.

This is represented as 0 ≤ t ≤ 6

For the range, we have

Set t = 0 in d(t) = 1/2t + 2

d(0) = 1/2(0) + 2 = 2

Set t = 6 in d(t) = 1/2t + 2

d(6) = 1/2(6) + 2 = 5

This means that the range is 2 to 5.

This is represented as 2 ≤ d(t) ≤ 5

Hence, the domain is 0 ≤ t ≤ 6 and the range is 2 ≤ d(t) ≤ 5

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Answer:

761058.745

Step-by-step explanation:

2.9 x 5 is 14.5

I believe your using x for multiplying and it's not a variable?

If you're problem is altogether it's 761,058.745

Answer: 14.5x2

Step-by-step explanation:

Answer:

y=6x-12

Step-by-step explanation:

rise over run is 6/1 which is just 6

y intercept is -12

Answer:

=2.79×10^23

Step-by-step explanation:

Multiply the 2 numbers is all you need to do, but that can be difficult as the 2 numbers are in scientific form / standard form :

So convert one of the numbers into a number in non-standard form but with the same power as the other (Got that ? Let me show you below) :

Each person has 3.72×10^13 cells

Population is 7.5×10^9

Let's make the top number / number of cells to the power of 9 instead of 13 :

3.72×10^13 = 37.2×10^12 = 372×10^11 = 3720×10^10 = 37200×10^9

Now we have :
37200×7.5×(1×10^9)²

The reason it's squared as both population and cells are now to power of 9 .

=2.79×10^23

Hope this helped and have a good day

Answer:

Model as computed by a quadratic equation calculator is
y (in thousands) = 0.0264x² -0.016x + 1.6
where y = number of users in thousands and x = number of weeks since introduction

Prediction for number of users after 32 weeks is 28,122

Step-by-step explanation:

Plotting the data appears to show the relationship between number of people using scooters and the number of weeks after which the scooters were introduced is quadratic in nature

Letting x = number of weeks and y the number of users (in thousands), using a quadratic regression calculator, the regression equation was

y (in thousands) = 0.0264x² -0.016x + 1.6

The correlation coefficient is high , r = 0.998937848

To predict number of users after 32 weeks, use x = 32 in the regression equation:

y (in thousands) = [tex]y \text{ (in thousands) } = 0.0264(32)^2\:-0.016(32)\:+\:1.6 = 28.1216\\\\[/tex]

Since this figure is in 1000's the actual number of users predicted would be:

28.1216 x 1000 ≈ 28,121.6 ≈ 28,122

I hope that my premise and calculations are correct, I simply used an online calculator to model and predict

PS. The decimal occurs because the numbers are in thousands

So for 1 week it is 1.5 which is actually 1.5 x 1000 = 1500 users

For week 20, it is 12.3 = 12.3 x 1000 = 12, 300 and so on