Given two events E and F with Pr(E) = 0. 4, Pr(F) = 0. 5, and Pr(EnF) = 0. 3, a) Pr(E|F) = b) Pr(F|E) = c) Are E and F independent? (Enter YES or NO)

The solutions to the equation −11x − 7 = \(-3x^2\), rounded to the nearest tenth, are x ≈ -1.1 and x ≈ 6.1.

An equation is a mathematical statement that shows that two expressions are equal. It is usually written as an expression on the left-hand side (LHS) and an expression on the right-hand side (RHS) separated by an equal sign (=).

The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that can vary, while the constants are fixed values that do not change.

Equations are used to represent mathematical relationships or describe real-world situations. They can be used to solve problems, make predictions, and test hypotheses.

To solve an equation, one must find the value of the variable that makes the LHS equal to the RHS. This is done by performing mathematical operations on both sides of the equation to isolate the variable. The goal is to get the variable by itself on one side of the equation, with a specific value on the other side.

Equations can be simple or complex, linear or nonlinear, and can involve one or more variables. Examples of equations include:

2x + 5 = 13

y = \(3x^2\) - 2x + 7

4a + 2b - 3c = 10

Equations are used in many areas of mathematics and science, including physics, chemistry, and engineering, among others.

We are given the equation \(-11x - 7 = -3x^2\).

To solve for x, we can rearrange the equation into a quadratic form by bringing all terms to one side:

\(-3x^2 + 11x + 7\) = 0

We can solve this quadratic equation by using the quadratic formula:

x = (-b ± sqrt(\(b^2\) - 4ac)) / 2a

where a = -3, b = 11, and c = 7.

Substituting these values, we get:

x = (-11 ± sqrt(\(11^2\) - 4(-3)(7))) / 2(-3)

Simplifying inside the square root:

x = (-11 ± sqrt(121 + 84)) / (-6)

x = (-11 ± sqrt(205)) / (-6)

Using a calculator, we can approximate this to:

x ≈ -1.1 or x ≈ 6.1

Therefore, the solutions to the equation \(-11x - 7 = -3x^2\), rounded to the nearest tenth, are x ≈ -1.1 and x ≈ 6.1.

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Answer:

B

Step-by-step explanation:

Answer:

a: 2 cm; b: 34 cm; c: 46 cm^2

Step-by-step explanation:

the missing side length is 2

9 - (4 + 3) = 2

when you add them all together you get

5 + 4 + 2 + 2 + 3 + 3 + 6 + 9 = 34

the perimeter is 34

you can split the shape up in multiple ways

you can split it into three rectangles

(5 * 4) + (2 * 4) + (3 * 6)

20 + 8 + 18 = 46

Answer:

a) 2 cm

b) 34 cm

c) 44 cm²

Step-by-step explanation:

a) 9 cm - 4 cm - 3 cm = 2 cm

b) 9 cm + 5 cm + 4 cm + 2 cm + 2 cm + 3 cm + 3 cm + 6 cm = 34 cm

c) 5 cm × 4 cm + 2 cm × 3 cm + 3 cm × 6 cm = 44 cm²

Answer:

F.Scalene

Step-by-step explanation:

every angles and sides of scalene triangle is not equal

To make an equation for Mateo's money, let's assign variables to the number of loonies and toonies he has. So, the equation is 1x + 2y = 32

Let's say Mateo has x loonies and y toonies. Since each loonie is worth $1 and each toonie is worth $2, we can write the equation: 1x + 2y = 32

In this equation, 1x represents the value of the loonies (x loonies * $1/loonie) and 2y represents the value of the toonies (y toonies * $2/toonie). The sum of these values should equal $32. Now, Mateo can solve this equation to find the values of x and y that satisfy it.

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The area of the triangle from the vertices is 3 square units

From the question, we have the following parameters that can be used in our computation:

D(1, 1), E(3, -1), and F(4, 4)

Represent the vertices properly

So, we have

D = (1, 1)

E = (3, -1)

F = (4, 4)

The area of the triangle is calculated using

Area = 0.5 * |Dx(Ey - Fy) + Ex(Dy - Fy) + Fx(Dy - Ey)|

Substitute the known values in the above equation, so, we have the following representation

Area = 0.5 * |1 * (-1 - 4) + 3 * (1 - 4) + 4 * (1 + 1)|

Evaluate the sum of products

Area = 0.5 * |-6|

Remove the absolute bracket

Area = 0.5 * 6

Evaluate

Area = 3

Hence, the area of DEF with vertices is 3 square units

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The maximum value of f(x,y) is e^27, and the minimum value of f(x,y) is approximately 203.64.

The method of Lagrange multipliers can be used to find the maximum and minimum values of f(x, y) subject to the constraint x^3 + y^3 = 54.

Let g(x,y) = x^3 + y^3 - 54 be the constraint equation. We need to solve the system of equations:

grad(f) = λ grad(g)

g(x,y) = 0

where λ is the Lagrange multiplier.

Taking partial derivatives of f(x,y), we get:

fx = ye^xy = λ 3x^2

fy = xe^xy = λ 3y^2

Taking partial derivatives of g(x,y), we get:

gx = 3x^2 = 0

gy = 3y^2 = 0

Solving for x and y, we get:

x = y = (54/2)^(1/3) = 3∛18

The value of λ can be found by substituting the values of x and y into the equation grad(f) = λ grad(g):

ye^xy = λ 3x^2

xe^xy = λ 3y^2

Substituting x = y = 3∛18, we get:

λ = e^(18) / (9∛2)

To find the maximum and minimum values of f(x,y), we need to evaluate f(x,y) at the critical point (x,y) = (3∛18, 3∛18) and at the endpoints of the constraint region. The constraint x^3 + y^3 = 54 is satisfied on the boundary of the region, which is a compact set, so we can apply the extreme value theorem.

At the critical point, we have:

f(3∛18, 3∛18) = e^(54/2) = e^27

On the boundary of the region, we have:

f(x,y) = e^xy = e^(54-x^3) at y = (54-x^3)^(1/3)

Taking the derivative with respect to x, we get:

f'(x) = -3x^2 e^(54-x^3) + ye^(54-x^3) = 0

Substituting y = (54-x^3)^(1/3), we get:

-3x^2 e^(54-x^3) + (54-x^3)^(1/3) e^(54-x^3) = 0

Solving numerically, we get:

x = 2.8964, y = 3.8406 or x = 3.8406, y = 2.8964

At these points, we have:

f(2.8964, 3.8406) ≈ 203.64

f(3.8406, 2.8964) ≈ 203.64

Therefore, the maximum value of f(x,y) is e^27, and the minimum value of f(x,y) is approximately 203.64.

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Given:

Ricardo is 4 years less than twice as old as his sister.

The sum of their ages is 20.

To find:

Ricardo's age.

Explanation:

Let R be Ricardo's age.

Let S be his sister's age.

According to the question,

Substituting equation (1) in (2) we get,

Substituting S = 8 in equation (2) we get,

Therefore, Ricardo's age is 12.

Final answer:

Ricardo's age is 12.

Answer:

400 dollars

Step-by-step explanation:

Following are the different types of angles:

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The unit circle's sixteen unique angles, each indicated at the terminal point and measured in radians. These angles are frequently used as a parameter in trigonometric functions like the sine or cosine.

In the 1 figure,

∠1 and ∠2 are same - side interior angles

In the 2 figure,

∠1 and ∠2 are Alternate interior angles

In the 3 figure,

∠1 and ∠2 are corresponding angles

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1. The amount of manufacturing overhead cost that would have been applied to the Koopers job is $9,840.

2. Using departmental predetermined overhead rates, the total manufacturing cost of the Koopers job is $47,040.

3. The bid price would have been $70,560.

The plantwide predetermined overhead rate for the current year is $2.40 per direct labour dollar ($4,032,000 ÷ $1,680,000).

The amount of manufacturing overhead cost that would have been applied to the Koopers job is $10,200 ($30,000 × 0.34).  

The predetermined overhead rate for each department is:

Department A = $0.60 per direct labour dollar ($672,000 ÷ 1,120,000)

Department B = $0.96 per direct labour dollar ($1,344,000 ÷ $1,400,000)

Department C = $0.72 per direct labour dollar ($1,008,000 ÷ $1,400,000)

The amount of manufacturing overhead cost that would have been applied to the Koopers job is $9,840 ($48,000 × 0.205 + $84,000 × 0.172 + $54,000 × 0.144).

Using a plantwide predetermined overhead rate, the total manufacturing cost of the Koopers job is $48,500 ($18,000 + $20,000 + $10,200).

Thus, the bid price is $72,750 (150% × $48,500). Using departmental predetermined overhead rates, the total manufacturing cost of the Koopers job is $47,040 ($18,000 × 0.205 + $20,000 × 0.172 + $10,000 × 0.144 + $18,000 + $20,000 + $10,000).

Thus, the bid price would have been $70,560 (150% × $47,040).

Hence, the solution to the problem is as follows: The company's plantwide predetermined overhead rate for the current year is $2.40 per direct labour dollar. The amount of manufacturing overhead cost that would have been applied to the Koopers job is $10,200.

Suppose that instead of using a plantwide predetermined overhead rate, the company had used departmental predetermined overhead rates based on direct labour cost. The predetermined overhead rate for each department for the current year is:

Department A = $0.60 per direct labour dollar

Department B = $0.96 per direct labour dollar

Department C = $0.72 per direct labour dollar

The amount of manufacturing overhead cost that would have been applied to the Koopers job is $9,840.Using a plantwide predetermined overhead rate, the total manufacturing cost of the Koopers job is $48,500.

Thus, the bid price is $72,750.Using departmental predetermined overhead rates, the total manufacturing cost of the Koopers job is $47,040. Thus, the bid price would have been $70,560.

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Answer:

75%

Step-by-step explanation:

Answer:

A... 25%

Step-by-step explanation:

75/300 = 1/4

0.25 = 25%

The correct pair of constraints that needs to be added to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units is: P24 - P25 <= 80; P25-P24 <= 80. Therefore, the correct option is 5.

Here, the given information is Pij = the production of product i in period j. We need to find the pair of constraints that will specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Thus, let the production of product 2 in period 4 and in period 5 be represented as P24 and P25 respectively.

Therefore, we can write the following inequalities:

P24 - P25 <= 80

This is because the production of product 2 in period 5 can be at most 80 units less than that of period 4. This inequality represents the difference being less than or equal to 80 units.

P25-P24 <= 80

This is because the production of product 2 in period 5 can be at most 80 units more than that of period 4. This inequality represents the difference being less than or equal to 80 units.

Therefore, we need to add the pair of constraints P24 - P25 <= 80 and P25-P24 <= 80 to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Hence, option 5 is the correct answer.

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Answer:0.2

Step-by-step explanation:

The page number on the right hand side is 73.

What is a Quadratic Equation?

A quadratic equation in x is any equation of the type ax2 + bx + c = 0, where a, b, and c are coefficients and a = 0.

Solution:

Let, the number of the page on the left hand side be x

So, the number on the right hand side of the book will be (x + 1)

According to the Question,

(x)(x + 1) = 6162

\(x^{2} + x = 6162\)

x = 72 and - 79

Since, the page of book can not be negative

Therefore, the page on the left hand side is 72

This implies that the page on the right hand side is 73.

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The appropriate hypothesis which is used to test the dropout rate are \(H_{0}:p > =0.081\\\) and \(H_{1}: p < 0.081\).

Given Drop out rate through 24 year old who are not enrolled is 8.1%, sample size=1000 and we have to find the hypothesis to test the drop out rate of the school.

The variable which needs to be studied is X=Number of individuals with age between 16 and 24 years old that are high school dropouts.

The parameter of interest is the proportion to high school drop outs is p.

Sample proportion=\(p^{1}\)=0.065

The hypothesis can be formed as under:

\(H_{0}:p > =0.081\)  (null hypothesis)

\(H_{1}:p < 0.081\)      ( alternate hypothesis)

Null hypothesis is a hypothesis which is tested for its validity and alternate hypothesis is hypothesis which is opposite of null hypothesis means if null hypothesis is rejected then the alternate hypothesis will be true.

\(Z_{H_{0} }=(p^{1}-p)/\sqrt{p*(1-p)/n}\)

=\(0.065-0.081/\sqrt{(0.081*0.0919)/1000}\)

=-1.85

Hence the appropriate hypothesis  are \(H_{0}:p > =0.081\) and \(H_{1}:p < 0.081\).

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The correct option is Option A:  x > 38° this statement about x value is true.

Given in triangle ΔNPO the angle ∠ PNM is the exterior b to the interior angle ∠ PNO of the triangle.

Given the angle ∠NPO= 38°

∠PON= 39°

As we know the exterior angle is the sum of the two farthest interior angles of the triangle.

Then we can write the angle ∠PNM as

So, ∠PNM = ∠NPO + ∠PON

⇒ x = 38° + 39° = 77° {Given that ∠ PNM = 38° and ∠ PON = 39°}

{Since the exterior angle of an interior angle is equal to the sum of the other two interior angles of a triangle}

As x=77°

which satisfies the relation x=77° >38°.

Therefore,The correct option is Option A:  x > 38° this statement about x value is true.

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ANSWER

The light intensity is 7.0

STEP-BY-STEP EXPLANATION:

What to find? The value of the proportionality constant.

Given parameters

• Light intensity = 569 lumens

• Distance = 9

According to the question, Light intensity (I) is proportional to the inverse square of the distance.

This can be expressed mathematically as

Let the intensity of light be represented as I

Let the distance be represented as d

The next thing is to introduce a constant k

Recall that,

I = 569 lumens

d = 9

The next thing is to substitute the parameters into the above formula

Answer:

A

Step-by-step explanation:

A is correct because 3+4 = 7

B is incorrect because 9/3=3 ,not 3/9

There is no x in C

D is incorrect because 8×3=24

E is incorrect because 3-10= -7 (negative)

hope this helped :)

Answer: 20%

Explanation:

1. Turn it into a fraction (224/280)

2. Divide the numerator (224) by the denominator (280). (224÷280=0.8)

3. Subtract 1 by 0.8 (or 100% by 80%) that should give you the answer 0.2 (20%)

Checking work:

280x0.2=56

280-56=224

(a) (Q ∧ ¬P) → (P → ¬Q) is neither a tautology nor a contradiction. The truth table for (a) is shown below.

| P   | Q   | ¬P  | Q ∧ ¬P | P → ¬Q | Q ∧ ¬P → P → ¬Q |
| --- | --- | --- | ------ | ------ | ---------------- |
| T   | T   | F   | F      | F      | T                |
| T   | F   | F   | F      | T      | T                |
| F   | T   | T   | T      | T      | T                |
| F   | F   | T   | F      | T      | T                |

(b) ((P ∧ R) ∨ (Q ∧ ¬P)) ∧ ¬(Q ∧ R) is neither a tautology nor a contradiction. The truth table for (b) is shown below.

| P   | Q   | R   | ¬P  | Q ∧ ¬P | P ∧ R | (P ∧ R) ∨ (Q ∧ ¬P) | Q ∧ R | ¬(Q ∧ R) | ((P ∧ R) ∨ (Q ∧ ¬P)) ∧ ¬(Q ∧ R) |
| --- | --- | --- | --- | ------ | ----- | ----------------- | ----- | -------- | --------------------------------- |
| T   | T   | T   | F   | T      | T     | T                 | T     | F        | F                                 |
| T   | T   | F   | F   | F      | F     | F                 | F     | T        | F                                 |
| T   | F   | T   | F   | F      | T     | T                 | F     | T        | F                                 |
| T   | F   | F   | F   | F      | F     | F                 | F     | T        | F                                 |
| F   | T   | T   | T   | T      | F     | T                 | T     | F        | F                                 |
| F   | T   | F   | T   | T      | F     | T                 | F     | T        | F                                 |
| F   | F   | T   | T   | F      | F     | F                 | F     | T        | F                                 |
| F   | F   | F   | T   | F      | F     | F                 | F     | T        | F                                 |

In (a), we use a truth table to test if the given statement is a tautology, contradiction, or neither. By analyzing the truth table, we can see that the statement is neither a tautology nor a contradiction since there are both true and false values in the column that gives the output of the statement.In (b), we also use a truth table to test if the given statement is a tautology, contradiction, or neither. By analyzing the truth table, we can see that the statement is neither a tautology nor a contradiction since there are both true and false values in the column that gives the output of the statement.

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Answer:

-15

Step-by-step explanation:

df(x, y) / dy = lim (f(x, y+h) - f(x, y)) / h =

lim (e^x^2 - 15y - 15h - e^x^2 ‐ 15y) / h = lim -15h / h = -15

so, the first derivative of f(x,y) by y is simply a constant : -15

fy (x, y) = -15 for any and every values of x and y.

the fast track would be derivative calculation :

the derivative by y makes x a constant. and every constant is eliminated for derivation.

so, e^x^2 goes away (= 0 in the derivative).

that leaves -15y = -15×y¹. its derivative simply is

1×-15×y⁰ = -15

Answer:

Correct choices are:

Choice 1:   (-5, 5)
Choice 4:  (-10, -3)
Choice 5:  (0, -2)

Step-by-step explanation:

Note:

The inequalities you have posted and the screenshot are different. I a going with the screenshot

Plug in each of the x, y values in each answer choice into each of the two inequalities

If one pair of (x, y) values violates even one inequality, it does not satisfy

(x, y) values in both inequalities must be satisfied

System of inequalities
\(y > x - 6\quad\quad(1)\\ y < -2x \quad\quad(2)\)

You have chosen two of the correct answers:
First option (-5, 5)

4th option: (-10, -3)

Plug in each of the values and see that it is consistent

I will provide explanation for two of them since you have already got two right

Choice 2 : (0, 0)
Substituting x = 0, y = 0 gives
For (1): 0 > 0 - 6==>   0 > - 6  True
For (2); 0 < -2(0) ==>  0 < 0  False  
Choice 2 →  (0, 0) does not satisfy inequality (2)

Choice 5: (0, - 2)
Substituting x = 0, y = -2  gives
For (1): y > x - 6
==> -2 > 0 - 6 ==> -2 > -6  True

For (2):  y < -2x
==> -2 < -2(0) ==> -2 < 0 True
Choice 5, (0, -2) satisfies both inequalities

Not of the other choices result in a consistent system

Answer:

B. 5

Step-by-step explanation:

Step 1: Rewrite the equation a bit

\(\frac{7^\frac{3}{4}}{7^\frac{x}{8}}=\sqrt[8]{7}\\7^\frac{3}{4}^-^\frac{x}{8}=7^\frac{1}{8}\)

Step 2: Place a logarithm base 7 on both sides

\(7^\frac{3}{4}^-^\frac{x}{8}=7^\frac{1}{8}\\log_77^\frac{3}{4}^-^\frac{x}{8}=log_77^\frac{1}{8}\\(\frac{3}{4}-\frac{x}{8})log_77=\frac{1}{8}log_77\\(\frac{3}{4}-\frac{x}{8})1=\frac{1}{8}1\\\frac{3}{4}-\frac{x}{8}=\frac{1}{8}\)

Step 3: Solve for x

\(\frac{3}{4}-\frac{x}{8}=\frac{1}{8}\\\frac{6}{8}-\frac{x}{8}=\frac{1}{8}\\-\frac{x}{8}=-\frac{5}{8}\\\frac{x}{8}=\frac{5}{8}\\x=5\)

Neat exponent question :)

Answer:

25.4 degrees

Step-by-step explanation:

Use the inverse sine function to calculate

The answers are:

a) it has a absolute maximum/minimum, it does not decrease for x > 0.

b) it does not have a absolute maximum/minimum, it does decrease for x > 0.

c) it does not have a absolute maximum/minimum, it does decrease for x > 0.

One rule we can use to know if there are absolute minimums/maximums is to look at the degree.

If it is even, we can have absolute minimums/maximums, if it is odd, we can't.

So the first option has, and the second and third don't

Now the behavior for x > 0.

The first function is x^2, and it increasese when x increases.

The second function is -5x^3, due to the negative sign, it decreases for positive values of x.

The last function is a linear one; -2x + 2, again, for the negative sign, it decreaess for x > 0.

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Answer:

120

Step-by-step explanation:

Answer: 120

Step-by-step explanation: hope this helps

Applying the Squeezing Theorem,  the value of the limit is 0.

The given function is sin(2x), and we have to evaluate it using the Squeezing Theorem. Also, the given limit is lim X→√3x.

In order to apply the Squeezing Theorem, we have to find two functions, g(x) and h(x), such that: g(x) ≤ sin(2x) ≤ h(x)for all x in the domain of sin(2x)and, lim x→√3x g(x) = lim x→√3x h(x) = L

Now, let's evaluate the given function: sin(2x).

Since sin(2x) is a continuous function, the given limit can be solved by substituting x = √3x:lim X→√3x sin(2x) = sin(2 * √3x) = 2 * sin (√3x) * cos (√3x)

Now, we have to find two functions g(x) and h(x) such that:g(x) ≤ 2 * sin (√3x) * cos (√3x) ≤ h(x)for all x in the domain of 2 * sin (√3x) * cos (√3x)and, lim x→√3x g(x) = lim x→√3x h(x) = L

First, we will find g(x) and h(x) such that they are greater than or equal to sin(2x):

Since the absolute value of sin (x) is less than or equal to 1, we can write: g(x) = -2 ≤ sin(2x) ≤ 2 = h(x)

Now, we will find g(x) and h(x) such that they are less than or equal to 2 * sin (√3x) * cos (√3x):Since cos(x) is less than or equal to 1, we can write: g(x) = -2 ≤ 2 * sin (√3x) * cos (√3x) ≤ 2 * sin (√3x) = h(x)

Therefore, the required functions are: g(x) = -2, h(x) = 2 * sin (√3x), and L = 0.

Applying the Squeezing Theorem, we get: lim X→√3x sin(2x) = L= 0

Therefore, the value of the limit is 0.

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