Given the following probabilities for choosing 2 marbles from a bag of 10 marbles, determine if the events are dependent or independent.
P(blue) = 3/10 , P(green) = 1/5 , and P(blue and green) = 3/100

the value of integration    [tex]\int\limits^{64}_0 {sinx} \, dx =5[/tex]   by the midpoint rule of approximate.

we want to approximate the integral

[tex]\int\limits^{64}_0 {sinx} \, dx \\using n=4[/tex]

the midpoint rule is given by.

[tex]\int^b_af(x)dx=\triangle x(f(\frac{x_{0} +x_1)}{2})+f(\frac{x_1+x_2}{2} )+....+f(\frac{x_{n-1}+x_n}{2}))[/tex]

where Δx=(b-a)/n

we know that a=0,b=64 and n=4

Δx=64/4=16

we need to divide the interval [0,64] into four subinterval of length Δx=16: 0,16,32,48,64.

now, we just evaluate the function at these endpoints.

[tex]f(\frac{x_1+x_0}{2} ) =f(\frac{0+64}{2} )\\f(8)=sin8=0.9894\\\\f(\frac{x_1+x_2}{2}) =f(\frac{16+32}{2} )\\\\f(24)=sin24=-0.9056\\\\similarly\\\\f(40)=sin(40)=0.7451\\\\f(56)=sin56=-0.5216[/tex]

finally, just sum up above values and multiply by Δx=16.

[tex]\int\limits^{64}_0 {sinx} \, dx=4.9168= 5[/tex]

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The domain of the function is not the set of all real numbers, that is why it is not from R to R

Here we want to see why the function f is not a function from R to R, where R is the set of the real numbers.

The function here is:

f(x) = 1/x

Notice that x is on the denominator, so we can't evaluate that function on x = 0.

So there is a real number that we can't use on that function, then the domain is not R, is R minus the element {0}

That is why f(x) is not a function from R to R, because the domain is not the set of the real numbers.

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This triangle is classified as an acute triangle since all three angles measure less than 90° (83⁰, 44⁰). It is also classified as an isosceles triangle since two of the sides (2 cm and 2.5 cm) are equal in length.

An acute triangle is a triangle in which all three angles measure less than 90 degrees. It is the opposite of an obtuse triangle, which has one angle measuring more than 90 degrees.

An acute triangle can also be referred to as a “sharp” triangle. The sum of all three angles in an acute triangle will always equal 180 degrees. An acute triangle can be either isosceles or scalene.

An isosceles triangle is a triangle with two sides of equal length and two equal angles opposite the two sides. The two angles are often referred to as the base angles, while the third angle is called the vertex angle. The two sides of an isosceles triangle are also often referred to as the legs, while the longest side is referred to as the base.

Isosceles triangles are studied in geometry, and the properties of such triangles can be used to solve many mathematical problems.

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The event A is that at least one of the books selected is an even-numbered copy. The event B is that exactly one of the copies selected is a first printing.

A tree diagram to display the 12 outcomes in the sample space would look like this:

1st Selection | 2nd Selection

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

1 | 2

1 | 3

1 | 4

2 | 1

2 | 3

2 | 4

3 | 1

3 | 2

3 | 4

4 | 1

4 | 2

4 | 3

The event A is that at least one of the books selected is an even-numbered copy. This would include outcomes 1-2, 1-4, 2-1, 2-3, 2-4, 4-1, 4-2, and 4-3.

The event B is that exactly one of the copies selected is a first printing. This would include outcomes 1-3, 1-4, 3-1, 3-2, 3-4, 4-1, 4-2, and 4-3.  

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The answer is O Congruent supplementary angles each have a measure of 90 or –12 + 11 < –1; true.

This can be proven by using the following formula:

p: 60 seconds = 1 minute

q: Congruent supplementary angles each have a measure of 90.

r: –12 + 11 < –1

For p, we can use the formula to calculate the number of minutes:

60 seconds * 1 minute = 60 minutes.

Therefore, 60 seconds = 1 minute.

For q, we can use the formula to calculate the measure of each angle:

2x = 90

Therefore, each angle has a measure of 45°.

For r, we can use the formula to calculate the result of the operation:

–12 + 11 = –1

Therefore, –12 + 11 < –1 is true.

In conclusion, the compound statement “Congruent supplementary angles each have a measure of 90 or –12 + 11 < –1” is true.

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The area of the rectangle will be 4.5 square units and the length and width are x=3 and y=1.5.

The equation for the line is y = -.5x + 3 (slope/intercept form).

Draw a random rectangle with the y-axis, x-axis, and the point (x,y) on the line y = -.5x + 3 as its corners.

This point's height from the x-axis (the length of the rec) will be equal to -.5x + 3 and its length from the y-axis will be x (the width of the rec).

Knowing that A = L*W equals the area of a rectangle

A(x) = (-.5x + 3) * x = -.5x^2 + 3x

In search of A'(x) = -x + 3. And we desire that A'(x) be 0.

As a result, y = -.5(3) + 3 = 1.5 and -x + 3 = 0 imply that x = 3.

So the maximum area of this rectangle is L*W = 1.5 * 3 = 4.5 square units. (We know this is a max and not a min since A’’(x) = -1 which makes the graph concave down)

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The square prism's volume is 135 meter

Either the total number of smaller prisms that make up the composite shape, or its volume. the distinction between a larger prism and a smaller prism that was taken out of it.

A composite shape is a shape that was produced from two or more fundamental shapes. Composite shapes are also referred to as compound and complex shapes frequently.

Any shape that is constructed from two or more geometric shapes is referred to as a composite or compound shape. The triangle and square in the following shape are joined together. The square and the rectangle that make up the blue shape. There are two triangles making up the green shape.

Detailed explanation:

The parameters listed are;

L = 15 meters is the cylinder's length.

D = 7 meters is the cylinder's diameter.

B = 3 meters is the square prism's base length.

Consequently, we have;

The square prism's volume is

= B² x  L

= 3² x 15

= 9 x 15

= 135 meter

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Based on the information provided, it can be concluded the student is not following the rule of allocating 50% to needs, 30% to wants, and 20% to savings.

Needs: 300 +10 + 50 +150 + 100 + 100=  $710

Now, let's calculate the percentage this represents:

710 x 100 / 1450 = 48%

Wants: 9.99 + 9.95 +9.99 + 19.99 + 25 + 500 + 65= $639.92

Now, let's calculate the percentage this represents:

639 x 100/ 1450 = 44%

Savings: 48 + 44 = 92 which means he can save 8%

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Answer:4

Step-by-step explanation:

A function is a relation in which each member in the domain is paired with exactly one element in the range.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

A phrase: A blank is a relation in which each member in the domain is paired with exactly one element in the range?

We have to find the blank word.

From the function definition,

A relation between a collection of inputs and outputs is known as a function.

A function is a connection between inputs in which each input is connected to precisely one output.

Each function has a range, co-domain, and domain.

Therefore, blank word is a function.

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The complete question:

A blank is a relation in which each member in the domain is paired with exactly one element in the range?

Answer:

25 Starburst

15 Twizzlers

========================================================

Explanation:

The ratio of Jolly Ranchers to Starburst to Twizzlers is 7:5:3

It means that you could have 7 Jolly Ranchers, 5 Starburst, and 3 Twizzlers.

In reality you actually have 35 Jolly Ranchers. So we'll multiply that "7" by 5. Do the same thing to all parts of the ratio to keep things balanced.

The ratio 7:5:3 scales up to its equivalent form 35:25:15

The cars receive the broadcast signal for length of about 36 miles.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

A condition on a variable (or variables) is a pair of expressions in the variable (or variables) that have the same value. The solution or root of the equation is the quantity at which the variable's value satisfies the equation. If you swap the LHS and RHS, an equation still makes sense.

Equations can be categorized as either identities or conditional equations. For each value of the variables, an identity holds true. Only specific values of the variables make a conditional equation true. An equals symbol ("="), separating two expressions, is used to represent an equation.

Simultaneous equations are obtained:

[tex]$$x^2+y^2=1620 \\y=-\frac{1}{3} x+30\end{array}\right.$$[/tex]

[tex]$x^2+\left(-\frac{1}{3} x+30\right)^2=1620$[/tex]

simplifying the above equation, we get

[tex]$x^2-18 x-648=0$[/tex]

(x - 36)(x + 18) = 0

x = -18 and x = 36

Therefore, the cars receive the broadcast signal for length of about 36 miles

The complete question is:

The range (in miles) of a broadcast signal from a radio tower is bounded by a circle given by the equation [tex]$x^2+y^2=1620$[/tex]. A straight highway can be modeled by the equation [tex]$y=-\frac{1}{3} x+30$[/tex]. For what length of the highway are cars able to receive the broadcast signal? Round your answer to the nearest tenth.

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The measure of all the angles are estimated.

For the stated question:

For ∠1

∠1 = 68 + 36 (sum of opposite interior angle equals exterior angle).

∠1 = 104

For ∠4.

∠4 = 180 - 70 - 65 (linear pair)

∠4 = 45

For ∠3.

∠3 = 65 (vertically opposite angle)

For ∠2.

∠2 = 180 - 65 - 36  (sum of angles of triangle are 180)

∠2 = 79

Thus, the measure of all the angles are estimated.

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Answer:  [tex]F^{-1} (n)=n-1[/tex]

Step-by-step explanation:

[tex]F(n)=n+1[/tex]

[tex]F(n)-1=n[/tex] Subtract 1 from both sides

Done!

We can rewrite as: [tex]F^{-1} (n)=n-1[/tex]

The two statements about risk and return that are true or potentially true are:

What is risk and return?

The risk connected to a particular investment and its returns are known as risk and return in financial management. High-risk investments typically produce higher financial returns, and low-risk investments typically produce lower returns. In other words, a given investment's risk and return are directly correlated.

As the risk of an investment increases, so does the potential for a higher return because there is a direct correlation between risk and return.

Also, holding stocks of companies of different sizes and from different sectors reduces investment risk in a portfolio because on diversifying the portfolio, risk also gets divided thus, giving a satisfactory return to the investor.

Hence, the above two statements are true.

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Answer: As the risk of an investment increases, so does the potential for a higher return. and Holding stocks of companies of different sizes and from different sectors reduces investment risk in a portfolio.

Step-by-step explanation: Increased price fluctuation, upward or downward, increases risk and the possibility of a high return or a huge loss. When the risk, or price fluctuation, is low, so is the return potential. Diversification helps decrease the risk of a group of investments because the value of individual investments will increase or decrease at different time periods and help to lessen value fluctuation in the overall portfolio.

The informal negation for each of the following statements:

1) No dog is ferocious.

2) Noboby is sad.

4) No suspicions were unsubstantiated.

5) No estimate is incorrect.

It is sometimes necessary in mathematics to determine the inverse of a given mathematical statement. This is commonly known as "negating" a statement. Keep in mind that if a statement is true, then its negation is false (and if a statement is false, then its negation is true). A conditional statement's negation is logically equivalent to a conjunction of the antecedent and the negation of the consequent. The logical negation symbol or is one of the statement connectives or operators that can be used to combine two or more statements to form new compound statements. It simply flips the truth value of any statement it appears in front of.

Here,

Each of the following statements has an informal negation:

1) No dog is ferocious.

2) Noboby is sad.

4) No suspicions were unsubstantiated.

5) No estimate is incorrect.

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Answer:

D subtract 2 from both sides

Step-by-step explanation:

x + 2 - 2 = 5- 2

==>    x = 3

The solution of the equation is x = 3.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

An equation,

x + 2 = 5.

To solve the equation:

Subtract 2 from both sides,

x +2 -2 = 5 -2

x = 3

Therefore, the solution is x = 3.

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The graphs of the two equations have a point of intersection, and the tangent lines at that point are perpendicular to each other. This can be shown by taking the derivatives of both equations and setting them equal to each other, which results in a perpendicular line equation.

To show that the graphs of the two equations have tangent lines that are perpendicular to each other at their point of intersection, we can take the derivatives of both equations, which gives us the equations of the tangent lines. We can then set the equations equal to each other and solve for the point of intersection. This will result in an equation for the perpendicular line, which is the equation of the line that passes through the point of intersection and is perpendicular to both tangent lines. We can then verify that the two tangent lines are perpendicular to each other at the point of intersection by calculating the slopes of both lines and showing that they are negative reciprocals of each other.

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A single basin of dry rice and beans 20 cups One bag of 40 basins 100 kilogrammes of rice is included in a sack.

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The determinant of the coefficient matrix 3x+4y=0 and -2x+3y=17 is 17.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.

Given:

A system of equations,

3x+4y=0

-2x+3y=17.

To find the determinant,

we will find the matrix from Cramer's rule,

A =

[tex]\left[\begin{array}{cc}3&4\\-2&3\end{array}\right][/tex]

So, determinant of matrix A

ΔA = 3 x 3 -(4 x -2)

ΔA = 9 + 8

ΔA  = 17.

Therefore, the determinant is 17.

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The  opportunity cost for four years of college is $46,000

We should know that opportunity costs represent the potential benefits that an individual, investor, or business misses out on when choosing one alternative over another.

The cost of education per year is = $12,000 + $2500 + $10000 = $24,500

The return if we decide not to go to college= $25000 - $12000 = $13000

We lose this return if we decide to go to college and we have to pay for room and board anyway.

The opportunity cost for four years of college is $24500-$13000)*4

This amounts to $11500*4 = $46,000

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Correct question:

Suppose that at your university, you will pay $12000 each year for tuition, $2500 each year for textbooks, and $10000 per year for room and board. Before you left for college, your boss at your high-school job offered you a job paying $25000 per year.

Assume that if you decided not to go to college, your parents would not let you live at home.

What is your opportunity cost for four years of college? $

The correct sample space for the gumballs in Julia's bag is {lemon-lime, watermelon, watermelon, grape, grape, grape} which makes option D correct.

The sample space for the gumballs in Julia's bag would be all the possible outcomes of selecting one gumball from the bag without replacement.

Since there are 1 lemon-lime, 2 watermelon, and 3 grape gumballs in the bag, the sample space would be expressed as:

sample space = {lemon-lime, watermelon, watermelon, grape, grape, grape}.

Therefore,we have 6 total outcomes in the sample space for the gumballs in Julia's bag.

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Answer:

6 in 6,275 is 100 times greater than  6 in 62.75

What is place value?

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.

as,  6 in 6,275 have a place value 6000.

and in 62.75, 6 have place value 60.

So, the difference is

6000/60

=100

Hence, 6 in 6,275 is 100  times greater than  6 in 62.75

Step-by-step explanation:

The value of the 6 in 62.75 is 60, while it is 6000 in the number 6275. This is due to the concept of place value in the decimal number system.

In terms of place value, the value of the 6 in 62.75 is 60, because it is in the tens place. However, the value of the 6 in 6,275 is 6,000 because it is in the thousands place. This is based on the concept of place value in the decimal number system where each digit has a value depending on where it is located within the number. The further to the left a digit is, the larger its value.

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The general solution to x squared dy over dx equals 3 plus 2y is given by 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant.

To calculate this, we begin by taking the derivative of both sides of the equation with respect to x. We then rearrange the equation to yield 2y + x^2 dy/dx = 3. We divide both sides by x^2 so that dy/dx is isolated on one side of the equation, yielding dy/dx = (3 - 2y) / x^2. We can then integrate both sides of the equation, with respect to x, to yield 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant. This equation is the general solution to x squared dy over dx equals 3 plus 2y.

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Answer is in attached photo.

Step-by-step explanation:

Solution is in the attached photo, do note that this question tests on the concept of Inequality.

[tex]5a > 5.45[/tex]

Divide both sides by 5:

[tex]\dfrac{5a}{5} > \dfrac{5.45}{5}[/tex]

Answer:

[tex]a > 1.09[/tex]

Answer: 20,000,000 + 6,000,000 + 400,000 + 30,000

Step-by-step explanation:

Answer:

6.94??????‽??????????????

Step-by-step explanation:

5÷4/5?????????

5×5?????????‽?/4

2.777777778/4

=69.4????????????????????

Note that if the family is to spend less than $60 dollars without further expenses, then they will have to spend nothing more than 6 hours. The inequality expression is given as: 36+4h < 60

First, the inequality expression is given as:

36+4h < 60

Where h is the number of hours they could spend.

We arrive at the above because we were given the following:

Cost of Movie = $36

Cost of parking Per Hour= $4

The maximum amount to be spent = $60

Thus, to find the number of hours the can spend without overshooting $60, we must find h. To do this, we must make h the subject of the formula by first removing 36 from both sides:

36+4h-36 < 60-36

4h < 24

h < 24/4

h < 6

What the above result show is that the number of hours that must be spent must be less than 6.

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The value of X is 4/5 if point P is on the unit circle and if the coordinate of P is -3/5 and P is in iV quadrant.

We know that unit circle is the circle of radius 1 unit. We are given the y-coordinate of P, that is y = -3/5. Now if we draw a perpendicular line at x-axis, and we know the length of line joining the P and the origin is 1 unit (h = 1). We can construct a right triangle. Then by pythagorean theorem.

x² + y² = h²

x² = √(h² - y²)

x² = √(1² - (-3/5)²)

x² = √(1 - (9/25))

x² = √(16/25)

x = 4/5

Since X is in the IV quadrant, where x is positive and y is negative.

So x = +4/5

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1. y = a(x + 5)^2 + 6

2. y = a(x - 1)^2 + 4

3. y = a(x + 2)^2 - 6

4. y = a(x - 4)^2 - 10

5. y = a(x + 2)^2 - 4

6. y = a(x - 3)^2 + 12

These are the equations of the quadratic in vertex form, where (h, k) are the vertex coordinates, and a is the coefficient of x^2. In each case, the x-intercepts provided are plugged into the equation to check if it equals zero, which is how we can confirm that it is a correct equation for the parabola.

I hope this helps :)