Solve each inequality for x and graph the solutions.
3x – 6<15

Answer:

(7, 0), (-8, 0), (0, 0)

Step-by-step explanation:

y = f(x) = 0

the real solutions are the ones that cross the x-axis because when a point is on the x-axis, its y coordinate will be 0.

=> (7, 0), (-8, 0), (0, 0)

Answer:

the answer is y = 3x + 1

The inequality:

Basically tells us that the solutions will be the numbers strictly greater than 5, so:

Therefore, the solutions are:

8, 10, 6

Yes, the line r is parallel to the line s and the line p is parallel to the line q.

Here the given lines are p, q, r, s.

Line p and q are parallel to each other.

and the line p is parallel to the line q.

Therefore, Yes, the line r is parallel to the line s and the line p is parallel to the line q.

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The elements of the truth set for statement i) of Exercise 1 are given below using P({1,2}) as the universe for each of A and B. For all sets A and B, A ⊆ B.Elements of the truth set for statement As is the universe for A and B.

There are four possible subsets of {1,2}:(∅, ∅)(∅, {1,2})({1}, {1,2})({1,2}, {1,2})As there are four possible ordered pairs for A and B, so the truth set contains four elements. The four elements are: {(∅, ∅), (∅, {1,2}), ({1}, {1,2}), ({1,2}, {1,2})}.b) The truth set for statement iii) of Exercise 1 using Z as the universe for w is given below Statement iii) : For every integer w, there exists an integer x such that x > w. Elements of the truth set for statement iii): We can select any integer w from Z. For that integer w, we can always find an integer x greater than w. Therefore, the truth set is the set of all integers, i.e., Z itself. :For part a), the elements of the truth set for statement i) are {∅, ∅), (∅, {1,2}), ({1}, {1,2}), ({1,2}, {1,2})} using P({1,2}) as the universe for each of A and B.

For part b), the truth set for statement iii) of Exercise 1 using Z as the universe for w is the set of all integers, i.e., Z itself. :Part a):The statement i) of Exercise 1 is: For all sets A and B, A ⊆ B. The universe for both A and B is P({1,2}). To find the truth set for statement i), we need to find all possible ordered pairs of subsets of {1, 2}.There are four possible subsets of {1, 2}, which are:∅{1}{2}{1, 2}We can choose any subset of {1, 2} as a set A. Thus, we get the following possible ordered pairs for A and B:

A = ∅,

B = ∅,

(A, B) = (∅, ∅)

A = ∅,

B = {1, 2},

(A, B) = (∅, {1, 2})

A = {1},

B = {1, 2},

(A, B) = ({1}, {1, 2})

A = {1, 2},

B = {1, 2},

(A, B) = ({1, 2}, {1, 2}) The set of all these ordered pairs is the truth set for statement i) of Exercise 1. Therefore, the truth set is {(∅, ∅), (∅, {1,2}), ({1}, {1,2}), ({1,2}, {1,2})}.Part b):The statement iii) of Exercise 1 is: For every integer w, there exists an integer x such that x > w. The universe for the variable w is Z (set of all integers).The truth set for statement iii) of Exercise 1 is the set of all integers because we can choose any integer w from Z and find an integer x > w (such as x = w + 1). Therefore, the truth set for statement iii) is Z itself.

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Answer:

29.8258

rounded is 30

Work Shown:

area = length*width

length = area/width

length = 162/9

length = 18 meters

Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

The binomial expansion of (y - 3)⁴ is B) y⁴ - 12y³ + 54y² - 108y + 81.

The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.

An expression of two terms having a degree n can be represented as,

(a - b)ⁿ = \(^nC_na^n - ^nC_{n-1}a^{n-1}b+^{n}C_{n-2}a^{n-2}b^2+...(-1)^n\times^nC_0a^0b^n\).

Given, (y - 3)⁴ = \(^4C_4y^4.3^0 - ^4C_3y^3.3 + ^4C_2y^23^2-^4C_1y.3^3+^4C_0y^03^4\).

(y - 3)⁴ = y⁴ - 12y³ + 54y² - 108y + 81.

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when graphing inequalities, we use an open  point when the sign is greater or less than  when the sign is ,and a closed point when the sign is greater or less than or equal to

Graph following inequalities.

1) x≥3

2) x<-2

3) x< 7

4) x ≤ -4

explanation

To find the equation of a linear function from its graph:

Find the slope by finding the rise and run.

Find the y-intercept (the point where the line crosses the y-axis)

Substitute the value into the function f(x)= mx+b .

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At the upper triple point, solid graphite, liquid carbon, and gaseous carbon dioxide coexist in equilibrium.

In a phase diagram for carbon, the upper triple point represents a specific combination of temperature and pressure where all three phases of carbon—solid (graphite), liquid (carbon), and gas (carbon dioxide)—coexist in equilibrium.

At this point, there is a delicate balance between the three phases, and any deviation from the exact temperature and pressure values would cause one or more phases to dominate.

The upper triple point is a unique set of conditions where solid graphite, liquid carbon, and gaseous carbon dioxide can exist simultaneously.

It's important to note that the precise values of temperature and pressure at the upper triple point may vary depending on the specific phase diagram being referenced.

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Answer:

To find the inverse, locate points on the graph. In this case, the plotted points are (4, -5) (5,-4) and (6,-1). To figure out the inverse, we just swap those around. (-5, 4) (-4, 5) and (-1, 6).

Some more points that you can plot are: (2, -1) (3, -4) and swap those around for (-1, 2) and (-4, 3).

Step-by-step explanation:

The probability that she requires 8 or fewer cases to obtain her first win is \(\(P(C \ \leq \ 8) = \frac{{58975}}{{65536}}\)\).

To compute P(C ≤ 8), we can use the formula for the sum of a finite geometric series. Here, C represents the number of cases required to obtain the first win, and each case is won with a probability of 3/4.

The probability that she wins on the first case is 3/4.

The probability that she wins on the second case is (1 - 3/4) \(\times\) (3/4) = 3/16.

The probability that she wins on the third case is (1 - 3/4)² \(\times\) (3/4) = 9/64.

And so on.

We need to calculate the sum of these probabilities up to the eighth case:

P(C ≤ 8) = (3/4) + (3/16) + (9/64) + ... + (3/4)^7.

Using the formula for the sum of a finite geometric series, we have:

P(C ≤ 8) = \(\(\frac{{\left(1 - \left(\frac{3}{4}\right)^8\right)}}{{1 - \frac{3}{4}}}\)\).

Let us evaluate now:

P(C ≤ 8) = \(\(\frac{{1 - \left(\frac{3}{4}\right)^8}}{{1 - \frac{3}{4}}}\)\).

Now we will simply it:

P(C ≤ 8) = \(\(\frac{{1 - \frac{6561}{65536}}}{{\frac{1}{4}}}\)\).

Calculating it further:

P(C ≤ 8) = \(\(\frac{{58975}}{{65536}}\)\).

Therefore, the probability that she requires 8 or fewer cases to obtain her first win is \(\(P(C \ \leq \ 8) = \frac{{58975}}{{65536}}\)\).

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The value of x and y in the right triangle are as follows:

x = 6 units

y = 6√3 units

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the value of x and y in the right triangle. Using trigonometric ratios,

sin 60 = y / 12

√3 / 2 = y / 12

cross multiply

2y =12√3

y = 12√3 / 2

y = 6√3

Therefore, let's find x as follows:

cos 60 = adjacent / hypotenuse

1 / 2 = x / 12

cross multiply

12 = 2x

divide both sides by 2

x = 12 / 2

x = 6

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The indefinite integral of (-6-6tan²θ) with respect to θ is -6(tanθ - (tanθsec²θ)/2 - ln|secθ + tanθ| + C)

To begin, let's recall the basic formula for the integral of the square of the tangent function:

∫tan²θdθ = tanθ - θ + C

where C is the constant of integration.

We can use this formula to solve the given integral by first factoring out -6 from the integrand:

∫(-6-6tan²θ)dθ = -6∫(1+tan²θ)dθ

Next, we can substitute u = tanθ and du = sec²θdθ to get:

-6∫(1+tan²θ)dθ = -6∫(1+u²)(du/sec²θ)

Simplifying, we get:

-6∫(1+u²)(du/sec²θ) = -6∫(sec²θ + sec⁴θ)dθ

Now, we can use the power rule for integration:

∫sec²θdθ = tanθ + C1

and

∫sec⁴θdθ = (tanθsec²θ)/2 + (1/2)∫sec²θdθ + C2

where C1 and C2 are constants of integration.

Substituting these integrals back into our equation, we get:

-6∫(sec²θ + sec⁴θ)dθ = -6(tanθ + C1 - (tanθsec²θ)/2 + (1/2)∫sec²θdθ + C2)

Simplifying further, we get:

-6(tanθ - (tanθsec²θ)/2 - ln|secθ + tanθ| + C)

where ln is the natural logarithm and C is the constant of integration.

Therefore, the indefinite integral of (-6-6tan²θ) with respect to θ is:

∫(-6-6tan²θ)dθ = -6(tanθ - (tanθsec²θ)/2 - ln|secθ + tanθ| + C)

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Given the equation of the line:

The slope-intercept form is: y = m * x + b

Where (m) is the slope

So, we will solve the given equation for (y)

so, the answer will be the slope-intercept form:

We cannot provide a value for k as requested in the question. Hence, our answer is: No, we cannot determine whether the function f is a k-to-1 correspondence for some positive integer k without having the function f.

justify your answer," we need to first understand what a k-to-1 correspondence is.

A k-to-1 correspondence is a function in which each element in the range has exactly k preimages. In other words, if the function f maps elements from set A to set B, then for each element b in set B, there are exactly k elements in set A that map to b.

In this case, we need to determine if the function f is a k-to-1 correspondence for some positive integer k.Now, let's justify our answer. Since we do not have the function f, we cannot determine whether it is a k-to-1 correspondence or not. Therefore, we cannot provide a value for k as requested in the question. Hence, our answer is: No, we cannot determine whether the function f is a k-to-1 correspondence for some positive integer k without having the function f.

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Answer:

\(P(T_1\ n\ T_2) = \frac{2}{21}\)

Step-by-step explanation:

From the comments in your question; we have

Stars = 4

Triangles = 5

Circles = 3

Squares = 3

Required  

Determine the probability of both shapes being triangles

First, calculate the total

\(Total = 4 + 5 + 3 + 3\)

\(Total = 15\)

Next, calculate the probability of the first selected shape being a triangle;

P(T₁) = Number of triangles divided by total number of shapes

\(P(T_1) = \frac{5}{15}\)

\(P(T_1) = \frac{1}{3}\)

Next, calculate the probability of the second selected shape being a triangle;

P(T₂) = Number of triangles divided by total number of shapes

Because it's probability without replacement. the number of triangle left is 4 and the number of shapes left is 14;

So:

\(P(T_2) = \frac{4}{14}\)

\(P(T_2) = \frac{2}{7}\)

Hence:

\(P(T_1\ n\ T_2) = P(T_1) * P(T_2)\)

\(P(T_1\ n\ T_2) = \frac{1}{3} * \frac{2}{7}\)

\(P(T_1\ n\ T_2) = \frac{2}{21}\)

Hence, the required probability is \(\frac{2}{21}\)

Answer:

2/21

Step-by-step explanation:

There are 4 stars, 5 triangles, 3 circles, and 3 squares

For the first drawing there are 5 triangles and a total of 15 shapes.

p(first triangle) = 5/15 = 1/3

Since there is no replacement, for the second drawing, and one triangle has been taken, now there are 4 triangles left and 14 total shapes left.

p(second triangle) = 4/14 = 2/7

p(two triangles) = p(first triangle) * p(second triangle)

p(two triangles) = 1/3 * 2/7

p(two triangles) = 2/21

Answer:

I believe the answer is 1/2

Step-by-step explanation:

4*3=12+2=14,14/3

1*3=3+1=4

14/3+4/3=18/3 divided by 2=6/3 simplified to 1/2

I got the 6/3 by dividing 18 by 2 and 3 by 1

Answer:

4

Step-by-step explanation:

If you know what Pemdas is then you must do dividing first.

1 1/3 divided by 2 is 2/3. 4 and 2/3 minus 2/3 equals 4.

Hope this helps. :)

The individual in this study on having a cellphone out is a student.

An observational study can be defined as a type of scientific study in which a researcher observes and measures the effect of a diagnostic test, risk factors, and specific treatments on individuals without intervening, manipulating or changing those who are or aren't exposed to it (controlled conditions).

In this scenario, 250 byu students volunteered to participate in the observational study that is focused on determining the effect of having a cellphone out on productivity.

In conclusion, the individual in this observational study on having a cellphone out is a student.

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Answer:

They ate 3/4 of the pizza. 1/4 of it was left.

Step-by-step explanation:

Answer:

They ate 3/4 of the pizza.

Bilal had 1/4 of the pizza

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

In an arithmetic sequence the common difference d is

d = a₂ - a₁ = 10 - 8 = 2

To obtain the next term in the sequence add d to the previous term, that is

a₅ = 14 + 2 = 16

a₆ = 16 + 2 = 18

a₇ = 18 + 2 = 20

The next 3 terms in the sequence are 16, 18, 20

The n th term equation for an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 8 and d = 2, thus

\(a_{n}\) = 8 + 2(n - 1) = 8 + 2n - 2 = 2n + 6

Answer:

79ft²

Step-by-step explanation:

find the unknow side a

a = √(18² - 14²)

a = √(324 - 196)

a = √128

a = 11.31 ft

---------------------

find area

(11.31 * 14) : 2 =

79.17ft²

so your answer is 79ft²

Answer:

Step-by-step explanation:

7 students from the Junior class.

6 students from the Senior class.

4 new members are to be chosen.

Required: Find the number of ways 4 new members can be chosen if 2 or fewer must be from the senior class. So, Therefore, the correct answer is 560 ways.

The system of equation to represents the relation between cakes and pie is given by 6x + 15y = 99 , x + y = 9.

The number of cakes sold is equal to 4.

Let x be the number of cakes sold

And y be the number of pies sold.

A cake costs $6

A pie costs $15,

Total revenue from selling x cakes and y pies is given by,

6x + 15y = total revenue

In one day the store sold 9 baked goods for a total of $99,

x + y = 9

System of equations in two variables,

6x + 15y = total revenue

x + y = 9

To solve for x, we can use substitution.

Solving the second equation for y, we get,

y = 9 - x

Substituting  into first equation, we get,

⇒6x + 15(9 - x) = 99

Simplifying and solving for x, we get,

⇒6x + 135 - 15x = 99

⇒-9x = -36

⇒x = 4

The store sold 4 cakes.

Number of pies sold,

x + y = 9

Substituting x = 4,

⇒4 + y = 9

⇒y = 5

store sold 5 pies

Therefore, from the system of equations 6x + 15y = 99, x + y = 9 the store sold 4cakes and5 pies.

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Answer:

The total number of winners is 17.

Step-by-step explanation:

Let's assume that the number of winners is "x". Then the number of participants who did not win is "45 - x".

The amount of money awarded to the winners is 1000x rupees.

The amount of money awarded to the participants who did not win is 200(45 - x) rupees.

According to the question, the total amount of prize money distributed is 22600 rupees. So we can write:

\(\sf\implies 1000x + 200(45 - x) = 22600 \)

Simplifying this equation:

\(\sf\implies 1000x + 9000 - 200x = 22600 \)

\(\sf\implies 800x = 13600 \)

\(\sf\implies x = 17 \)

Therefore, the total number of winners is 17.

Hope it helps!

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

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Answer:Solve for x 2x-4=10 2x − 4 = 10 2 x - 4 = 10 Move all terms not containing x x to the right side of the equation. Tap for more steps... 2x = 14 2 x = 14 Divide each term in

Step-by-step explanation:

Answer: OD, 1/5

Step-by-step explanation:

Well what I did was take DE and seen how many time it could fit into BC. BC would take up a total of 5 DE's. So since we already have one which is DE then we would have 1/5.

HOPE THIS HELPS! ^_^