7) If A and B are independent events with P(A)= 0.2, P(B)=0.3, then calculate P(AUB) A) 0.44 B) 0.90 C) 0.76 D) 0.50

Over the interval [-3, 1], the local minimum is 0,  Over the interval [-1, 0], the local maximum is 4.39,  Over the interval [0, 3], the local minimum is -32.

By plot the function on a graphing tool and visually identify the local minimum and maximum values over the specified intervals .A function that is continuous for an interval [a,b], a is not equal to b, then there is a local maximum and minimum if:

Local maximum: f(d) > f(x), ∀ x ≠ d, a ≤ d ≤ b

Local minimum: f(c)< f(x), ∀ x ≠ to c, a≤c≤b

we can proceed to solve each question:

Over the interval [-3, 1], the local minimum is 0,

since f(-2) < f(x), ∀ x ≠ -2,-3 ≤ x ≤ -1 .

Over the interval [-1, 0], the local maximum is 4.39,

since f(-0.8) > f(x), ∀ x ≠ -0.8, -1 ≤ x ≤ -1.

Over the interval [0, 3], the local minimum is -32,

since f(-2) < f(x), ∀ x ≠ -2.0 ≤ x ≤3.

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Answer:

0

4.39

-32

Step-by-step explanation:

on edge

Answer:

10

Step-by-step explanation:

18-7=11 then you subtract 1 because 9*2=18 so the answer is 1o

In order to view more detail in the condensed data columns, we can expand the columns by clicking on the arrow icon located on the right side of the column header.

By clicking on the arrow icon located on the right side of the column header, this can expand column and show more detailed information of the fever report.

Effectively, the feature allows to easily access all the relevant data without having to switch between different views or reports which makes it more efficient and user-friendly. Also, we can also customize the columns and choose which data to display based on your preferences and needs.

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Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x=80/7

Decimal Form: x=11.428

or 11.44

Mixed Number Form: x=11 3/7

The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

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The definition of slope-intercept form y=mx+b is given below.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

In geometry, there are two types of lines: straight and curved. Vertical and horizontal straight lines are further divided into categories. Parallel, intersecting, and perpendicular lines are further types of lines.

In the given question:-

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope may be determined using a variety of approaches.

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The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.

Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.

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Greetings.

The answer is (5,4)

Explanation:

Solving by elimination can be done by adding or subtracting of first and two equation.

Find any terms that make themselves = 0.

And that is the y-term.

Our 2y and -2y. If we add each others, we'd get 0 for y-term.

Therefore, we eliminate the y-term first.

\(\left \{ {{-x+2y=3} \atop {3x-2y=7}} \right. \\2x=10\)

If you are wondering how I get 2x = 10 then here's the explanation.

So we simply add/subtract both equations.

We do -x + 3x = 2x

Then +2y - 2y = 0

And 3 + 7 = 10

That's how we get 2x = 10.

Basically Add/Subtract in Vertical way.

\(2x=10\\x=5\)

We may get the x-value but we need to know the y-value too.

Therefore, substitute x = 5 into any given equations. I suggest you to substitute the x-value in any equations with less coefficient value.

I'd rather substitute x = 5 in -x+2y = 3.

\(-x+2y=3\)

Substitute x = 5 in -x + 2y = 3

\(-5+2y=3\\2y=3+5\\2y=8\\y=\frac{8}{2}\\y=4\)

Therefore, when x = 5, y = 4. Since you want the answer in ordered pairs then It's (5,4).

Given:

Consider the given terms of the sequence are:

20, 10, 5, ...

To find:

The type of sequence (arithmetic or geometric) and the common difference / ratio in simplest form.

Solution:

We have,

20, 10, 5, ...

Difference between consecutive terms are:

\(10-20=-10\)

\(5-10=-5\)

Since \(-10\neq -5\), therefore the given sequence has no common difference, it means the given sequence is not arithmetic.

Ratio between consecutive terms are:

\(\dfrac{10}{20}=\dfrac{1}{2}\)

\(\dfrac{5}{10}=\dfrac{1}{2}\)

The given sequence has a common ratio \(\dfrac{1}{2}\), it means the given sequence is a geometric sequence.

Therefore, the given sequence is a geometric sequence with common ratio \(\dfrac{1}{2}\) it is also written as 0.5.

Answer:

∠C = 58°

Step-by-step explanation:

∠C = 180 - 70 - 52 = 58°

Answer:

$512

Step-by-step explanation:

Interest = 16% of 800

             = 16/100 x 800

             = $128

Interest for 4 years = 128 x 4

                                = $512

The matrix representing the relation r^4 is m^4, where m is the matrix representing relation r.

To find the matrix representing the relation r^4, we need to perform matrix multiplication of the matrix m four times. Let's denote the matrix representing the relation r as m. To calculate r^4, we multiply m by itself four times, i.e., m^4.

Each multiplication represents the composition of the relation with itself. We perform matrix multiplication of m with itself, then multiply the resulting matrix by m again, and repeat this process for a total of four times. The final result is the matrix m^4, which represents the relation r^4.

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54 outcomes are  in A

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.

Here (x) = 3x-1 and h (x) =x²-3x+8

Now lim x→3 x   g (x) = lim x→3 3x -1

=3x³-1

=9-1

=8

and lim x→3 h (x) = lim x→3 x²-3x+8

=9-9+8

= 8

value of f (x) when x approaches 3

since lim x →3  g (x) =8 and lim x→3 h (x) = 8

Then lim x→3 f (x) =8

hence lim x→3 f (x) = 8 

hence 54 outcomes  are in A

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The simplified expression is:

(x - 1) / (2(x - 4)

To simplify the expression, we can start by simplifying each individual fraction and then dividing them.

Let's break it down step by step:

Expression: ((x + 2)/(x² - 16)) ÷ ((2x + 4)/(x² + 3x - 4))

Step 1: Simplify each fraction individually.

The first fraction can be simplified by factoring the denominator:

(x + 2)/(x² - 16) = (x + 2)/((x - 4)(x + 4))

The second fraction can be simplified by factoring the denominator:

(2x + 4)/(x² + 3x - 4) = (2(x + 2))/((x + 4)(x - 1))

Now the expression becomes:

((x + 2)/((x - 4)(x + 4))) ÷ ((2(x + 2))/((x + 4)(x - 1)))

Step 2: Invert the second fraction and multiply.

Inverting the second fraction is equivalent to multiplying by its reciprocal:

((x + 2)/((x - 4)(x + 4))) × (((x + 4)(x - 1))/(2(x + 2)))

Step 3: Simplify the expression.

Now we can simplify the expression by canceling out common factors:

(x + 2) × ((x + 4)(x - 1)) / (((x - 4)(x + 4)) × (2(x + 2)))

Next, we can cancel out common factors between the numerators and denominators:

(x + 2) × (x + 4)(x - 1) / (2(x - 4)(x + 4)(x + 2))

Finally, we can cancel out the common factor of (x + 2) between the numerator and denominator:

(x + 4)(x - 1) / (2(x - 4)(x + 4))

Therefore, the simplified expression is:

(x - 1) / (2(x - 4)

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Given

Formula

Substitute the given into the formula

The final balance is ₦2,180.94

Answer:

This may be incomplete, i will try to answer this in a general way.

We have 4 bottles, A, B, C and D.

If A is the volume of Bottle A, B is the volume of bottle B, C is the volume of bottle C, and D is the volume of bottle D, we have that:

A = B + 3L.

D = A + 5L

C = A - 3L.

Let's solve this system the most we can (we can not fully solve the system because we have more variables than equations)

First, taking the third equation and adding 3L in both sides, we have:

C + 3L = A.

This is equivalent to the first equation, so we have that C = B.

now, we have two equations:

A = B  + 3L

D = A + 5L

We can replace the first equation into the second equation and get:

D = A + 5L = (B + 3L) + 5L = B + 8L

So bottle D can hold 8L more juice than bottle B (and because bottle B and bottle C have the same volume, bottle D can hold 8L more juice than bottle C)

Now, we can order the bottles depending on the volume:

Bottle D is the one with larger volume.

Bottle A comes next.

Bottles C and B are the smaller ones, and they are together because they have the same volume.

Answer:

The answer is 54.23489

Step-by-step explanation:

Hope this helps

The triangles that do not follow the similarity statement and therefore are not similar triangle are ACT and CAR

Similar triangles are triangles that have the same shape, but may have different sizes. Their corresponding angles are congruent, and the corresponding sides are proportional. In other words, if you were to enlarge or shrink one triangle uniformly, it would overlap exactly with the other triangle.

In this problem, we can find two triangles that are similar and that implies that they must be equal to one another.

In this case, we have

1. ART ≈ CAT

2. CAR ≈ CTA

Only ACT ≠ CAR

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In order for the system of equations to be a consistent system, the value of k must be equal to -4.

To determine the value of k that makes the system of equations consistent, we can use the method of elimination or substitution. Let's use the method of elimination.

First, we can multiply the first equation by 5, the second equation by -1, and the third equation by 2 to make the coefficients of x in the three equations cancel each other out when added together.

The modified system of equations becomes:

5x - 10y + 20z = 20

5x - 9y + 22z = 16

-4x + 6y - 20z = 2k

Now, let's subtract the first equation from the second equation:

(5x - 9y + 22z) - (5x - 10y + 20z) = 16 - 20

y + 2z = -4

Next, let's add this equation to the third equation:

(-4x + 6y - 20z) + (y + 2z) = 2k - 4

-4x + 7y - 18z = 2k - 4

For the system of equations to be consistent, there must be no contradictions or inconsistencies. This means that the equations must be linearly dependent, and the last equation must be a multiple of the second equation.

Comparing the last equation (-4x + 7y - 18z = 2k - 4) with the second equation (y + 2z = -4), we can see that the two equations will be dependent and consistent if 2k - 4 is equal to 0.

2k - 4 = 0

2k = 4

k = 2

Therefore, in order for the system of equations to be a consistent system, the value of k must be equal to -4.

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It is not possible to achieve the desired transformation of shifting downward 7 units and having a y-intercept of 1 with the given function f(x) = x^2.

The given function is f(x) = x^2.

To perform the transformation of shifting downward 7 units, we subtract 7 from the function:

g(x) = f(x) - 7

g(x) = x^2 - 7

The transformed function is g(x) = x^2 - 7.

To determine the equation of the resulting function after shifting downward 7 units and having a y-intercept of 1, we need to find the value of the constant term.

Since the y-intercept is 1, we can substitute x = 0 into the function and solve for the constant term:

g(0) = (0)^2 - 7

1 = -7

The equation -7 = 1 is not true, which means there is no constant term that would make the function have a y-intercept of 1 after the transformation.

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A function f is given, and the indicated transformation f(x)=x^(2); shift downward 7 units y=1

Answer:

if your talking about the earth i dont know because no one have ever compared some random planet and earths weight

Step-by-step explanation:

That’s because the planets weigh different amounts, and therefore the force of gravity is different from planet to planet. For example, if you weigh 100 pounds on Earth, you would weigh only 38 pounds on Mercury. That’s because Mercury weighs less than Earth, and therefore its gravity would pull less on your body.

Answer:

y =-0.5x-3

Step-by-step explanation:

hope that helps please mark as brainliest if correct

thank you

Answer:

first option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (6, 0) ← 2 points on the line

m = \(\frac{0-3}{6-0}\) = \(\frac{-3}{6}\) = - \(\frac{1}{2}\) = - 0.5

The line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = - 0.5x + 3 ← equation of line

If ū and ū have the same length, then the projection of u onto ū and the projection of ū onto ū will always have the same length. This is because the projection of a vector onto another vector is simply the vector that is parallel to the first vector and has the same length as the first vector.

If the two vectors have the same length, then the projection of one vector onto the other will also have the same length. If ū and ū do not have the same length, then it is possible for the projection of u onto ū and the projection of ū onto ū to have the same length.

This is because the projection of a vector onto another vector is not necessarily the same length as the first vector. If the two vectors are not parallel, then the projection of one vector onto the other will be shorter than the first vector. However, if the two vectors are perpendicular, then the projection of one vector onto the other will be the same length as the first vector.

The projection of a vector onto another vector is a vector that is parallel to the first vector and has the same length as the first vector. The projection of u onto ū can be calculated using the following formula:

proj_ū(u) = (u ⋅ ū) / ||ū||^2 * ū

where u ⋅ ū is the dot product of u and ū, and ||ū|| is the magnitude of ū. The projection of ū onto u can be calculated using the following formula:

proj_u(ū) = (ū ⋅ u) / ||u||^2 * u

where ū ⋅ u is the dot product of ū and u, and ||u|| is the magnitude of u. If ū and ū have the same length, then ||ū|| = ||u||. This means that the two formulas for the projection are the same, and the projection of u onto ū will have the same length as the projection of ū onto u.

If ū and ū do not have the same length, then ||ū|| ≠ ||u||. This means that the two formulas for the projection are not the same, and the projection of u onto ū may or may not have the same length as the projection of ū onto u. If the two vectors are not parallel, then the projection of one vector onto the other will be shorter than the first vector. However, if the two vectors are perpendicular, then the projection of one vector onto the other will be the same length as the first vector.

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Answer:

Explanation:

Here, we want to find the margin of error of the pool

From the question, we have the following:

n = 600

p = 43% = 43/100 = 0.43

q = 1-p = 1-0.43 = 0.57

At 95% confidence level, z = 1.96

We can calculate the margin of error by using the formula below:

Substituting the values, we have it that:

Answer:

1/4 and 3/8  = 2/8 and 3/8

1/4 and 1/2 = 1/4 and 2/4

2/16 ad 3/8 = 2/16 and 6/16

1/4 and 2/16 = 4/16 and 2/16

1/2 and 3/8 = 4/8 and 3/8

Step-by-step explanation:

Answer:

The first box goes with the third bottom box. The second box goes with the 5th bottom box. The third box goes with the first bottom box. The fourth box goes with the fourth bottom box. Lastly the 5th box goes with the second bottom box.

Hope this helps

2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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Answer:

y=(x+2)(x+7)

Step-by-step explanation: