True or False: the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.

Answer:

Step-by-step explanation:

The length of a curve can refer to the arc length of a function, or the distance along a curved path between two points.

Arc Length of a Function:

For a continuous and differentiable function y = f(x) defined over an interval [a, b], the arc length of the curve between x = a and x = b can be found using the following definite integral:

L = ∫_a^b √(1 + (dy/dx)^2) dx

Where L is the arc length, dy/dx is the derivative of the function with respect to x, and the integral is taken from x = a to x = b.

Length of a Curved Path:

For a curved path defined by a continuous and differentiable function y = f(x), the length of the path between two points (x1, y1) and (x2, y2) can be found using the same definite integral formula as the arc length of a function:

L = ∫_(x1)^(x2) √(1 + (dy/dx)^2) dx

Where L is the length of the path and the integral is taken from x = x1 to x = x2.

Note that finding the exact length of a curve can sometimes be difficult and may require numerical methods such as numerical integration or approximation techniques like Simpson's rule.

The axis of symmetry, vertex, domain, and range of each of the quadratic function are as follows;

Axis of symmetry = 3.

Vertex = (3, 3).

Domain = {-∞, ∞}.

Range = {-∞, 3}.

Axis of symmetry = 4.

Vertex = (4, -2).

Domain = {-∞, ∞}.

Range = {-2, ∞}.

Mathematically, the axis of symmetry (vertex) of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry (vertex), Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

Note: The domain of a quadratic function (parabola) is always all real numbers on the x-axis of a cartesian coordinate.

For the given quadratic function y = -2x² + 12x - 15, we have:

Axis of symmetry (vertex), Xmax = -b/2a

Axis of symmetry (vertex), Xmax = -12/2(-2)

Axis of symmetry (vertex), Xmax = -12/-4 = 3.

Vertex (h, k) = (3, 3).

Domain = {-∞, ∞} or x ∈ R.

Range = {-∞, 3}.

x      y

1      2

1      4

3     3

For the given quadratic function y = 2x² - 16x + 30, we have:

Axis of symmetry (vertex), Xmax = -b/2a

Axis of symmetry (vertex), Xmax = -(-16)/2(2)

Axis of symmetry (vertex), Xmax = 16/4 = 4.

Vertex (h, k) = (4, -2).

Domain = {-∞, ∞} or x ∈ R.

Range = {-2, ∞}.

x      y

3     0

5     0

4     -2

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The measure of angle B is given as follows:

<B = 295º.

Angles A and B in the context of this problem are reflex angles, meaning that the sum of their measures is of 360º.

The measures are given as follows:

Hence the measure of angle B is obtained as follows:

65 + <B = 360

<B = 360 - 65

<B = 295º.

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Step-by-step explanation:

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Answer:

[tex]\sin A=\frac{a}{b}[/tex]

[tex]\cos A=\frac{c}{b}[/tex]

[tex]\tan A=\frac{a}{c}[/tex]

[tex]\csc A=\frac{b}{a}[/tex]

[tex]\sec A=\frac{b}{c}[/tex]

[tex]\cot A=\frac{c}{a}[/tex]

Step-by-step explanation:

Here are the definitions of the trig functions listed in the picture

[tex]\sin x=\frac{O}{H}[/tex]

[tex]\cos x=\frac{A}{H}[/tex]

[tex]\tan x=\frac{O}{A}[/tex]

[tex]\csc x=\frac{H}{O}[/tex]

[tex]\sec x=\frac{H}{A}[/tex]

[tex]\cot x=\frac{A}{O}[/tex]

Note:

[tex]A[/tex] = side adjacent to angle

[tex]O[/tex] = side opposite to angle

[tex]H[/tex] = hypotenuse

All 6 questions are about angle A.

The side adjacent to angle A is side c.

The side opposite to angle A is side a.

The hypotenuse is side b.

Therefore we can write

[tex]A=c\\O=a\\H=b[/tex]

Knowing that we can fill out the table.

[tex]\sin A=\frac{a}{b}[/tex]

[tex]\cos A=\frac{c}{b}[/tex]

[tex]\tan A=\frac{a}{c}[/tex]

[tex]\csc A=\frac{b}{a}[/tex]

[tex]\sec A=\frac{b}{c}[/tex]

[tex]\cot A=\frac{c}{a}[/tex]

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Answer:

The polygon has 8 sides, so the sum of its interior angles is 1080 degrees. Each interior angle is equal to 135 degrees

the interior angle of a regular polygon is equal to the total number of its sides minus two, multiplied by 180 degrees divided by the number of sides. For example, in a regular polygon with 8 sides, one interior angle would equal 1080 degrees (8 - 2) x 180/8 = 1080.

The value of x where both curve and line intersect with each others are -0.44 and 1.69

Using the linear-quadratic system, both curve and line are intersecting in 2 points where:

f(x) = g(x)

8x2 - 13x + 8 = 14 - 3x

8x2 - 10x - 6 = 0

We will use the ABC theorem, where:

x = -b ± √(b2 - 4ac)

               2a

x = - (-10) ± √((10)2 - 4(8)(-6))

                  2(8)

x = 10 ± √(100 + 192)

             16

x = 10 ± 2√73

           16

x1 = 10 - 2√73  = -0.44

           16

x2 = 10 + 2√73 = 1.69

             16

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The temperature of an apple pie during the time it spends in the oven shows the continuous relationship.

In mathematics, a continuous function is a function that does not have discontinuities that means any unexpected changes in value. A function is continuous if we can ensure arbitrarily small changes by restricting enough minor changes in its input.

A function f(x) is said to be a continuous function in calculus at a point x = a if the curve of the function does NOT break at the point x = a.

A continuous function, on the other hand, is a function that can take on any number within a certain interval. For example, if at one point, a continuous function is 1 and 2 at another point, then this continuous function will definitely be 1.5 at yet another point.

Therefore, option C and E are the correct answers.

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Jada can get 4 albums or she can get 80 individual songs for $20. The equation will be written as 0.25s + 5a = 20.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that It costs $0.25 to download an individual song and $5 to download an album. Jada has $20 to spend downloading music.

The equation will be written as,

0.25s + 5a = $20

The number of individual songs will be,

0.25s = 20

s = 20 / 0.25

s = 80

The number of albums,

5a = 20

a = 20 / 5

a = 4

The complete question is given below.

It costs $0.25 to download an individual song and $5 to download an album. Jada has $20 to spend downloading music.

a. Make a table showing three ways Jada can spend $20 downloading individual songs and albums. (s the being number of individual songs and a being the number of albums.)

b. Write an equation relating the number of individual songs (s) and the number of albums(a) in standard form.

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The required solution is given as,

f(x) = 22 + x   = Linear

f(x) = x²+1       = Non-linear

f(x) = x³ +2x+1 = Non-linear

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Linear functions are functions that can be represented by a straight line on a graph. These functions have a constant rate of change and can be written in form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.

Non-linear functions are functions that do not have a constant rate of change and cannot be represented by a straight line on a graph.

Thus, the required solution is given as,

f(x) = 22 + x   = Linear

f(x) = x²+1       = Non-linear

f(x) = x³ +2x+1 = Non-linear

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The tangent of the smaller acute angle in a right triangle is tanФ = 5/12 taking side 5 as opposite side and 12 as adjacent side.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent or (base and perpendicular)

The Formula of tangent is opposite side/ adjacent side

Given, a right triangle with side lengths 5, 12, and 13.

We can see that largest side i.e., 13 is a hypotenuse of triangle and other two sides are base and perpendicular length.

Tangent taking side 5 as opposite side and 12 as adjacent side

tanФ = 5/12.

Tangent taking side 12 as opposite side and 5 as adjacent side

tanФ = 12/5

so, the  tangent of the smaller acute angle in a right triangle is 5/12.

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Answer: $6

Step-by-step explanation:

Divide $390 by 65 to find $6 per ticket.

Answer:

$6

Step-by-step explanation:

$390/65=6

The equation of the context is, 3.5x + 2y = 42 and

The y-intercept is when x = 0, indicating that no funnel cakes were purchased, and the x-intercept is when y = 0, indicating that no deep-fried Oreos were purchased.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

From, The given information the equation can be modeled as,

3.5x + 2y = 42.

The x-intercept is when y = 0 which states no deep fried oreos bought and the y-intercept is when x = 0, states no funnel cakes bought.

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Answer:

The answer is B.

The owner's claim is incorrect. Since the highest bar is those that make between $50,000 and $100,000, the average salary would be about $75,000 since that is the mode.

Answer:

x ≈ 73.4°

Step-by-step explanation:

using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{23}{24}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{23}{24}[/tex] ) ≈ 73.4° ( to the nearest tenth )

If (63, x, 105) generate a Pythagorean Triple, the value of x is 84.

Before starting to solve this problem we must know that the Pythagorean theorem is a theorem that realizes the sides of a right triangle and has many applications for it.

A Pythagorean Triple is a set of three integers that satisfy the Pythagorean Theorem, [tex]a^2 + b^2 = c^2[/tex]. In this case, 63 and 105 are two sides of a right triangle, and x is the third side. We can plug in the values and solve for x:
63² + x² = 105²
3969 + x² = 11025
x² = 7056
x = √7056
x = 84

Therefore, the value of x is 84, and the Pythagorean Triple is (63, 84, 105).

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The doubling time formula is used to calculate the time required for a quantity to double in size at a constant growth rate. The formula is: doubling time = ln(2) / r

Where ln(2) is the natural logarithm of 2, and r is the annual growth rate expressed as a decimal. The doubling time represents the number of time units it takes for the quantity to double, such as years, months, or days, depending on the time unit used for the growth rate. This formula is commonly used in many fields, such as finance, biology, and demography, to estimate the future growth of a quantity based on its current growth rate.

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In the image line segment SE is the tangent. The secant line making an angle with tangent line SE is NS. So the angle is ∠GSE. So option B is the correct answer.

Tangent is a line which intersect with only a single point on the curve. The point where the line meets is the point of tangency. Tangent line is always perpendicular to the radius drawn to the point of tangency. Here the tangent line is SE, point of tangency is S.

Secant lines are the lines which passes through two points of a curve. A chord drawn to the circle is a secant line. Here there are two secant lines NS and NA. Here only NS makes an angle with the tangent line.

So the angle made by a tangent and secant line is ∠GSE.

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The image for the question is attached below.

The approximate percent increase in consumption from 1986 to 1997 is 30%.

Percent refers to a ratio or proportion expressed as a fraction of 100. When we talk about the percent increase or decrease of a quantity, we are interested in finding out by how much it has grown or declined relative to its original value.

In this case, we are asked to determine the approximate percent increase in consumption from 1986 to 1997.

To answer this question, we would need to have data on the consumption levels in both years and calculate the difference between the two.

Then, we would divide the difference by the consumption level in 1986 and multiply by 100 to express the result as a percentage.

From the options given, it appears that the closest answer is C, with a 30% increase in consumption.

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The number of cup servings in a bag of trail mix is 5[tex]\frac{1}{5}[/tex] cups.

Math operations include division as one of its types. This technique involves splitting the phrases or numbers into the same amount of components.

Given:

There are 1[tex]\frac{1}{4}[/tex] cup servings in a bag of trail mix.

And a bag of trail mix contains 6 ½ cups of mix.

The number of cup servings in a bag of trail mix is,

= 6 ½ ÷ 1[tex]\frac{1}{4}[/tex]

= 13/2 ÷ 5/4

= 26/5

= 5[tex]\frac{1}{5}[/tex]

Therefore, the required number of cups is 5[tex]\frac{1}{5}[/tex].

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Carol pays a 10% deposit, it means the amount of deposit she pays is £234,900.

To work out the amount of deposit paid by Carol, we need to find 10% of the house price. We can do this by multiplying the house price by 10/100 or 0.10.

Here are the steps to find the amount of deposit paid by Carol:

1. Start with the house price: £2349000
2. Multiply by 0.10 to find 10% of the house price: £2,349,000 x 0.10 = £234,900
3. The amount of deposit paid by Carol is £234,900.

So, the answer is £234,900.

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We are are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.242895 in first simulation and between 0.1948 and 0.2732 in second simulation.

A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.

A 95% confidence interval gives us a range of values that we are 95% confident contains the true proportion of wins that the new game strategy will produce in the long run. To construct the confidence interval for each simulation, we can use the following formula:

CI = p ± 1.96 * sqrt(p * (1 - p) / n)

where p is the sample proportion of wins, n is the number of trials, and 1.96 is the z-score corresponding to a 95% confidence level.

For the first simulation, p = 212 / 1000 = 0.212 and n = 1000, so the confidence interval is:

CI = 0.212 ± 1.96 * sqrt(0.212 * (1 - 0.212) / 1000)

CI = (0.1812, 0.2428)

This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.2428.

For the second simulation, p = 235 / 1000 = 0.235 and n = 1000, so the confidence interval is:

CI = 0.235 ± 1.96 * sqrt(0.235 * (1 - 0.235) / 1000)

CI = (0.1948, 0.2732)

This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1948 and 0.2732.

In general, larger sample sizes lead to narrower confidence intervals. In this case, both confidence intervals overlap, indicating that the two simulations are consistent with each other. This gives us additional confidence in the estimated proportion of wins using the new strategy.

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Answer:

the confidence interval for the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.

Step-by-step explanation:

got it right on the test :)

The required equation model for the given situation is 1/6 (c + 24) = 15. Option C is correct.

The concept of the equation model is a fundamental part of mathematics, and it is used in a wide range of applications. Here are some ways in which the equation model is used,
1. Solving equations    2. Modeling real-world situations 3.Understanding relationships between variables.

here,
According to the question let the Pokémon cards Mark intially had be c,
So as per the given condition, Mark has c + 24 card and he gives 1/6 of his card to his little brother, which is 15 cards
The equation model of the situation is given as,
1/6(c + 24) = 15

Thus, the required equation model for the given situation is 1/6 (c + 24) = 15. Option C is correct.

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on solving the provided question we can say that for parallel combination, the equation will be  1/R = 1/R1 + 1/R2.

A mathematical equation is a formula that links two assertions and signifies equivalence with the equals sign (=). In algebra, a mathematical statement that proves the equality of two mathematical expressions is referred to as an equation. The equal sign, for instance, separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14. There is a mathematical formula that explains the link between the two phrases that appear on either side of a letter. Frequently, the symbol and the single variable are the same. like in 2x - 4 = 2, for example.

we have,

Total Resistance (R) = 1.403 kilo-ohm.

R1 = 2.0 Kilo-ohm.

1.403 kilo-ohm = 1403 ohm.

for parallel combination, the equation will be

1/R = 1/R1 + 1/R2

[tex]1/1403 = 1/2000 + 1/ R2\\.1/1043 - 1/2000 = R2\\2000 - 1403 / 1403 x 2000 = 1/R2\\597/ 1403 x 2000 = 1/R2\\R2 = 1403 x 2000 / 597 = 2806000 / 597 = 4700.16\\R2 = 4700.16 ohm[/tex]

103 ohm = 1 kilo-ohm =>  4700 ohm = 4.7 kilo-ohm

so, R2 = 4.7 kilo-ohm.

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The value of m∠J in the triangle is 65°

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We have triangle HIJ and m∠H = (4x + 1)°, m∠I = (2x-6)° and m∠J = (6x-7)°.

Since the sum of angle in a triangle is 180°. We can say:

m∠H +  m∠I +  m∠J = 180°

(4x + 1)° + (2x-6)° + (6x-7)° = 180°

4x + 1 + 2x-6 + 6x-7 = 180

12x - 12 = 180

12x = 180 + 12

12x = 192

x = 192/12

x = 16

To find m∠J = (6x-7)°, put x = 12 into  m∠J = (6x-7)°. That:

m∠J = 6(12) - 7

m∠J = 72 - 7

m∠J = 65°

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The expression 1/2 × 5/4 has the value greater than 1/2. Therefore, option D is the correct answer.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Here,

A) 1/2 × 4/5

= 2/5

= 0.4

B) 1/2 × 4/4

= 1/2

= 0.5

C) 1/2 × 5/5

= 1/2

= 0.5

D) 1/2 × 5/4

= 5/8

= 0.625

Therefore, option D is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Which expression has the value greater than 1/2

A) 1/2 × 4/5

B) 1/2 × 4/4

C) 1/2 × 5/5

D) 1/2 × 5/4

The coordinates of equation y is (0, 3), (1, 4) and (3,5).

The graph is attached below.

The graph's x-axis (horizontal line) should contain the independent variable, and the y-axis should contain the dependent variable (vertical line). At the origin, where the coordinates are, the x and y axes intersect (0,0).

Given:

y= x+ 3.

Now, put x= 0

y= 0+3

y=3

and, x= 1

y= 1+3

y= 4

and, x= 2

y= 2+ 3

y= 5

Thus, the coordinates of equation y is (0, 3), (1, 4) and (3,5).

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The Questions attached here is seems to incomplete, the options for the graph is attached below.

Answer:

Many test takers have found the Reading and English section to be moderately difficult. However, many TEAS takers vouch that the Science and Math section are more complex and challenging. The timed nature of the exam can be difficult for some.

Step-by-step explanation:

Answer: For Jon, buying 3 shirts for $20 can be written as a rate as follows:

The number of shirts Jon buys per dollar spent = 3 shirts / $20 = 3/20 shirts/dollar

For Brenda, recording 76 songs on 4 albums can be written as a rate as follows:

The number of songs Brenda records per album = 76 songs / 4 albums = 19 songs/album

So, the rate of songs Brenda records per album can be written as 19 songs/album.

Step-by-step explanation: