Consider two dice-throwing experiments. Find the probabilities
of the following events.
Let X = sum of the two dice:
P (X = 5)
P( 2 ≤ X ≤ 6)
P(X = 5 or X = 10

Step-by-step explanation:

Option A is the right answer.

Therefore , the solution of the given problem of fraction comes out to be  214 kilowatt hours of electricity for the month.

Any combination of equal portions or fractions can be combined to represent a whole. In standard English, the quantity of a certain size is defined as a fraction. 8, 3/4. Wholes also include fractions. The ratio of numerator to ratio is a mathematical symbol for integers. All of these number fractions are simple fractions. There is a fraction inside of the fraction but rather remainder in a difficult fraction. because the values, numerators, and numerators of real fractions vary

Here,

We must divide the total amount of electricity used by the number of businesses in order to calculate how many kilowatt hours each business is responsible for paying for:

=> 14, 14 businesses x 2,996 kilowatt hours = 214 kilowatt hours per company

As a result, each company is required to pay for roughly 214 kilowatt hours of energy per month.

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The amount of water filled in bucket  6 hours is found as 1 gallon.

Mathematical proportions are comparisons of two numbers that categorize or persons. They are frequently expressed as fractions or with a colon. There are two ways to write mathematical proportions. You can use colons to compare the numbers, or you can use equivalent fractions to represent the proportion.

Now,

Let the amount of water filled in 6 hours be 'x'.

Using proportion:

4/24 = x/6

x = 4*6 / 24

x = 1 gallon

Thus, the amount of water filled in bucket  6 hours is found as 1 gallon.

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The complete question is attached.

Therefore, f(x) = [[x − 2]] is discontinuous at x = k - 2 and x = k + 2. The discontinuities at these points are removable.

The function f(x) = [[x − 2]] is discontinuous at any value of x that is two units away from an integer. That means it is discontinuous at x = k - 2 and x = k + 2, where k is any arbitrary integer.

The discontinuities at x = k - 2 and x = k + 2 are both removable. That is because the discontinuities occur when the left- and right-hand limits of the function are not equal, and the limits can be made equal by redefining the value of the function at the point of discontinuity.

To solve the problem, set the left- and right-hand limits equal to each other and solve for x.

Left-hand limit: lim x→k-2  f(x) = lim x→k-2 [[x − 2]] = [[k - 2 - 2]] = [[k - 4]]
Right-hand limit: lim x→k+2  f(x) = lim x→k+2 [[x − 2]] = [[k + 2 - 2]] = [[k]]

Equating the two limits, we have [[k - 4]] = [[k]]. Solving for x, we get x = k - 2 and x = k + 2.

Therefore, f(x) = [[x − 2]] is discontinuous at x = k - 2 and x = k + 2. The discontinuities at these points are removable.
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The statement, a number divided by 6 equals 3, is written as an equation is x/6 = 3

Algebraic expressions are simply defined as expressions that are made up of terms, coefficients, variables, constants and factors.

These expressions are also identified with arithmetic operations, such as;

From the information given, we have that;

A number divided by 6 equals 3

Now, let's say the number be x

This is represented as an equation thus;

x/6 = 3

Hence, the equation is x/6 = 3

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So, the experimental probability that the next student Meg talks will pick football is 0.2 or 20%.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. It is used to quantify the uncertainty or risk associated with a particular event or situation.

Given by the question.

The experimental probability of an event is the ratio of the number of times the event occurs to the total number of trials or observations. In this case, the event is selecting football as the favorite sport, and the trials are the number of students Meg talks to.

Based on the information given in the problem, Meg surveyed a total of 10 students (2 who selected football and 8 who selected other sports). Therefore, the probability of the next student she talks to selecting football as their favorite sport is:

P (selecting football) = number of students who selected football / total number of students surveyed

P (selecting football) = 2 / 10

P (selecting football) = 0.2

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The value of d when t=3 is 45 miles. This means that Jake has covered a distance of 45 miles in 3 hours riding his bike at a rate of 15 miles per hour.

Distance is a measure of the length between two points. To calculate distance, we need to know the coordinates of the two points. We can use the Pythagorean theorem to calculate the distance.

The formula d=rt is used to calculate the distance traveled when a rate, r, and time, t, are given. In this case, Jake is riding his bike at a rate of 15 miles per hour for 3 hours. To calculate the distance, d, traveled, we can substitute the given values into the formula.

d = 15 * 3

d = 45

Therefore, the value of d when t=3 is 45 miles. This means that Jake has traveled 45 miles in 3 hours riding his bike at a rate of 15 miles per hour. This formula can also be used to calculate the time, t, when the rate, r, and distance, d, are known. To find the time, t, simply divide the distance, d, by the rate, r.

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The law of sines (LOS) or law of cosines (LOC) should be used to begin solving a triangle depending on the given information. The law of sines is used when we are given two sides and an opposite angle (SSA) or two angles and an opposite side (AAS). The law of cosines is used when we are given three sides (SSS) or two sides and the included angle (SAS).

a) ????,????,???????????? c: Use the law of cosines (LOC) since we are given two sides and the included angle (SAS).

b) ????,????,???????????? ????: Use the law of sines (LOS) since we are given two angles and an opposite side (AAS).

c) ????,????,???????????? c: Use the law of cosines (LOC) since we are given two sides and the included angle (SAS).

d) ????,????,???????????? ????: Use the law of sines (LOS) since we are given two angles and an opposite side (AAS).

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Dalton flies the plane at a speed of 251 mph when there is no wind.

To solve this proble,m we can use the formula for distance, which is distance = speed × time. We can also use the fact that the speed of the plane with the wind is the sum of the speed of the plane without the wind and the wind speed, and the speed of the plane against the wind is the difference between the speed of the plane without the wind and the wind speed.

Let x be the speed of the plane without the wind, and t be the time it takes for the return trip with the wind. Then we can write the following equations:

4661 = (x - 10) × (t + 20)  (1) for the trip against the wind
4661 = (x + 10) × t  (2) for the return trip with the wind

Multiplying equation (2) by (t + 20) and subtracting equation (1) from it, we get:

4661t + 93220 = 4661t + 20x^2 + 200x - 200x - 200
20x^2 = 93220
x^2 = 4661
x = 251

Therefore, Dalton flies the plane at a speed of 251 mph when there is no wind.

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Answer:

Step-by-step explanation:

20c is the answer

Answer:

ans is 14

Step-by-step explanation:

i do not think is this by i know is 14

The answer is 49

To evaluate the given expression, we will use the special product formula for the square of a binomial:

(a+b)^(2)=a^(2)+2ab+b^(2)

In this case, we have:

52^(2)=(5+2)^(2)=5^(2)+2(5)(2)+2^(2)=25+20+4=49

Therefore, the answer is:

52^(2)=49

So, using the special products of algebraic expressions, we can evaluate the given expression to be 49.

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Answer:

Since the diagonals of a rectangle bisect each other, we know that angle AEB is congruent to angle CED. Therefore, we can set the expressions for these angles equal to each other and solve for x:

13x = 3x - 5

Subtracting 3x from both sides gives:

10x = -5

Dividing both sides by 10 gives:

x = -0.5

Therefore, the value of x that satisfies the equation is x = -0.5. Note that this means that angle measures are negative, which doesn't make sense in this context. It's possible that there is an error in the problem statement or that some additional information is needed to determine a valid value of x.

Answer: bob

Step-by-step explanation:

92199+20923+29290+83292+2819+99279+38471+378141

= 744414

Answer:

A

Step-by-step explanation:

6x° and 54° form the angle of 90° , that is

6x + 54 = 90 ( subtract 54 from both sides )

6x = 36 ( divide both sides by 6 )

x = 6

then

6x = 6 × 6 = 36°

Therefore, the solution to the system of equations is x = 7 and y = -2.

Answer: x = 7, y =- 2.

a statement describing the relationship between the two phrases on either side of a sign. A single variable and an equal sign are typically present. Comparable is the equation 2x - 4 = 2. The variable x is present in the previous instance.

We are given the following system of equations:

-2x - 9y = 4    ---(1)

-5x - 10y = -15 ---(2)

We can use the method of substitution to solve this system of equations.

From equation (1), we can solve for x in terms of y:

-2x - 9y = 4

-2x = 4 + 9y

x = -2 - (9/2)y ---(3)

Now we can substitute this expression for x into equation (2) and solve for y:

-5x - 10y = -15

-5(-2 - (9/2)y) - 10y = -15

10 + (45/2)y - 10y = -15

12.5y = -25

y = -2

We have found the value of y to be 5. We can substitute this value back into equation (3) to find the value of x:

x = -2 - (9/2)y

x = -2 + (9/2)(2)

x = 7

Therefore, the solution to the system of equations is x = 7 and y = -2.

Answer: x = 7, y = -2.

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We have saved approximately 15% of the total cost.

What is the process to calculate the percentage saved in a sale?

When items are on sale, they are usually offered at a discounted price. The percentage saved is a measure of the amount that a buyer has saved on the original price of the item. The process to calculate the percentage saved in a sale involves determining the original price, the discounted price, and then using a formula to find the percentage saved.

The formula for the percentage saved is:

Percentage saved = (Amount saved / Original price) x 100%

Calculation of  the total amount saved and the percentage saved :

For the paperbacks, the original price is $9 each and we bought four of them, so the total original price is:

$9/book × 4 books = $36

With a 10% discount, the discounted price of each paperback is:

$9/book × 0.10 = $0.90 discount

$9/book - $0.90 discount = $8.10 discounted price

So, the total discounted price for the four paperbacks is:

$8.10/book × 4 books = $32.40

Therefore, we saved:

$36 - $32.40 = $3.60

For the hardbacks, the original price is $20 each and we bought two of them, so the total original price is:

$20/book × 2 books = $40

With a 20% discount, the discounted price of each hardback is:

$20/book × 0.20 = $4 discount

$20/book - $4 discount = $16 discounted price

So, the total discounted price for the two hardbacks is:

$16/book × 2 books = $32

Therefore, we saved:

$40 - $32 = $8

The total original price of all the books is:

$36 + $40 = $76

The total discounted price of all the books is:

$32.40 + $32 = $64.40

Therefore, we saved:

$76 - $64.40 = $11.60

Plugging in the values , we get:

percentage saved = ($11.60 / $76) × 100%

percentage saved ≈ 15%

Therefore, we have saved approximately 15% of the total cost.

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Yes, the given trinomial is a perfect square trinomial.

To determine whether a trinomial is a perfect square trinomial, we can use the formula:
(a-b)^(2) = a^(2) - 2ab + b^(2)

In this case, we can compare the given trinomial with the formula and see if it matches.

16a^(2)-40ab+25b^(2) = (4a)^(2) - 2(4a)(5b) + (5b)^(2)

This matches the formula, so we can conclude that the given trinomial is a perfect square trinomial.

Another way to determine whether a trinomial is a perfect square trinomial is to factor it and see if it can be written as a binomial squared.

In this case, we can factor the given trinomial as follows:

16a^(2)-40ab+25b^(2) = (4a-5b)(4a-5b) = (4a-5b)^(2)

Since the trinomial can be written as a binomial squared, we can conclude that it is a perfect square trinomial.

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The number of stamps given for the books in question are :

To find the number of stamps needed for 1 book, the formula is :

= Stamps needed for 19 books / Number of books

= 380 / 19

= 20 stamps

For 7 books :

= 7 books x 20 stamps per book

= 140 stamps

For 12 books :

= 12 books x 20 stamps per book

= 240 stamps

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Answer:

342.02

Step-by-step explanation:

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

To prove that C is a field, we need to show that it satisfies the following 11 axioms of a field:

C is closed under addition: For all a, b ∈ C, a + b ∈ C.

C is closed under multiplication: For all a, b ∈ C, ab ∈ C.

C is associative under addition: For all a, b, c ∈ C, (a + b) + c = a + (b + c).

C is associative under multiplication: For all a, b, c ∈ C, (ab)c = a(bc).

C has an additive identity: There exists 0 ∈ C such that for all a ∈ C, a + 0 = a.

C has a multiplicative identity: There exists 1 ∈ C such that for all a ∈ C, a1 = a.

C has additive inverses: For all a ∈ C, there exists b ∈ C such that a + b = 0.

C has multiplicative inverses: For all a ≠ 0 ∈ C, there exists b ∈ C such that ab = 1.

C is commutative under addition: For all a, b ∈ C, a + b = b + a.

C is commutative under multiplication: For all a, b ∈ C, ab = ba.

Multiplication distributes over addition: For all a, b, c ∈ C, a(b + c) = ab + ac.

Proofs of the 11 axioms:

To show that C is closed under addition, we can use the fact that the sum of two complex numbers is also a complex number. That is, for any a, b ∈ C, a + b = (a + bi) + (b + di)i, where i is the imaginary unit. This is clearly a complex number, so C is closed under addition.

To show that C is closed under multiplication, we can use the fact that the product of two complex numbers is also a complex number. That is, for any a, b ∈ C, ab = (a + bi)(b + di) = (ab - bd) + (ad + bc)i, which is also clearly a complex number, so C is closed under multiplication.

To show that C is associative under addition, we can use the associative property of addition for real numbers. That is, for any a, b, c ∈ C, (a + b) + c = a + (b + c).

To show that C is associative under multiplication, we can use the associative property of multiplication for real numbers. That is, for any a, b, c ∈ C, (ab)c = a(bc).

To show that C has an additive identity, we can use the fact that the real number 0 is also a complex number, and that for any a ∈ C, a + 0 = a.

To show that C has a multiplicative identity, we can use the fact that the real number 1 is also a complex number, and that for any a ∈ C, a1 = a.

To show that C has additive inverses, we can use the fact that for any a ∈ C, there exists a complex number -a such that a + (-a) = 0. This is because the real numbers have additive inverses, and the imaginary unit i has an additive inverse -i.

To show that C has multiplicative inverses, we can use the fact that for any a ≠ 0 ∈ C, there exists a complex number 1/a such that a(1/a) =

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Answer:

jimmy has 12 candy bars left

Step-by-step explanation:

28-7-9=12

Answer:

Jimmy has 12 candy bars.

Step-by-step explanation:

Subtract 28 from 7.
=21

21-9=12.
Jimmy has 12 candy bars left if he eats 7 and his mom takes 9.

put y = 5x in equation 1 :

2x + 3 (5x) = 34

2x + 15x = 34

17x = 34

x = 2

Now put x = 2 in any of the two equation to get

y :

y = 5x

y = 5 × 2

y = 10

The simplified result of is (6m^(2) + 13m - 15) / (m^(2) + 9m + 18).

Step 1: Flip the second fraction:

(mn)/(m^(2)+9m+18) ÷ (m)/(6m^(2)+13m-15) = (mn)/(m^(2)+9m+18) × (6m^(2)+13m-15)/(m)

Step 2: Change the division sign to multiplication:

(mn)/(m^(2)+9m+18) × (6m^(2)+13m-15)/(m)

Step 3: Multiply the numerators and denominators:

= (mn)(6m^(2)+13m-15) / (m^(2)+9m+18)(m)

Step 4: Simplify the result:

= (6m^(3)n + 13m^(2)n - 15mn) / (m^(3) + 9m^(2) + 18m)

= (mn)(6m^(2) + 13m - 15) / (m)(m^(2) + 9m + 18)

= (6m^(2) + 13m - 15) / (m^(2) + 9m + 18)

So the simplified result is (6m^(2) + 13m - 15) / (m^(2) + 9m + 18).

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A - B is 5.

To find A - B, subtract each corresponding element in B from the corresponding element in A.

For the element in row 3, column 2, it is 2 - (-3) = 5.

Therefore,

the element in row 3, column 2 of A - B is 5.

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The measures of the other three angles are: ∠2 = ∠3 = 67.5° and ∠4 = 0°.

An angle is a geometric figure formed by two rays that share the same endpoint called vertex. It is measured in degrees, radians or gradians and is usually denoted by the vertex letter in its center, with the endpoints labeled by two other letters or points.

Since the sum of the measures of the angles in a triangle is 180 degrees, we can use this information to find the measures of the other three angles.

If ∠1 has a measure of 45°, then we know that the sum of the measures of ∠2 and ∠3 is 135° (180° - 45°).

If the triangle is isosceles, then ∠2 and ∠3 have the same measure. Therefore, we can divide 135° by 2 to get:

∠2 = ∠3 = 67.5°

Finally, we can use the fact that the angles of a triangle add up to 180° to find the measure of ∠4:

∠4 = 180° - 45° - 67.5° - 67.5° = 0°

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The answer to 0.03 as a fraction is 1/300. But as a percentage, it is 3%.

Fractions and percentages are both ways of expressing parts of a whole. A fraction represents a part of a whole, which is divided into equal parts, while a percentage is a fraction expressed as a number out of 100.

The main difference between fractions and percentages is their format. Fractions are typically written as a ratio of two numbers, with the numerator representing the part and the denominator representing the whole. Percentages, on the other hand, are typically written as a number followed by the symbol "%", which represents the part out of 100.

Full question "What is 0.03 as a fraction?"

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Answer:

-5 - 2sqrt6

Step-by-step explanation:

To simplify (sqrt2+sqrt3)/(sqrt2-sqrt3), we can rationalize the denominator, which involves multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of sqrt2-sqrt3 is sqrt2+sqrt3, so we can multiply both the numerator and denominator by sqrt2+sqrt3:

(sqrt2+sqrt3)/(sqrt2-sqrt3) * (sqrt2+sqrt3)/(sqrt2+sqrt3) = ((sqrt2+sqrt3)(sqrt2+sqrt3))/((sqrt2-sqrt3)(sqrt2+sqrt3))

Expanding the numerator and simplifying, we get:

(sqrt2+sqrt3)^2 / (sqrt2^2 - sqrt3^2)

= (2 + 2sqrt2sqrt3 + 3) / (2 - 3)

= (5 + 2sqrt6) / (-1)

= -5 - 2sqrt6

Therefore, (sqrt2+sqrt3)/(sqrt2-sqrt3) simplifies to -5 - 2sqrt6.

The simplest form of the expression (√2 + √3) / (√2 - √3) is - (5 + 2√6).

We have,

To simplify the expression (√2 + √3) / (√2 - √3), we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.

The conjugate of (√2 - √3) is (√2 + √3).

Multiplying the numerator and denominator by (√2 + √3), we get:

[(√2 + √3) x (√2 + √3)] / [(√2 - √3) x (√2 + √3)]

Expanding both the numerator and denominator:

[(√2 + √3)(√2 + √3)] / [√2 x √2 - √2 x √3 + √3 x √2 - √3 x √3]

Simplifying:

[2 + 2√2√3 + 3] / [2 - 3]

Combining like terms:

[5 + 2√6] / [-1]

Since the denominator is -1, we can multiply both the numerator and denominator by -1 to simplify further:

[5 + 2√6] / 1

Finally, we have:

(5 + 2√6)

Therefore,

The simplest form of the expression (√2 + √3) / (√2 - √3) is - (5 + 2√6).

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The function is relative minima

If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative maximum of f. If f(b) < f(x) in an open interval containing b, x ≠ b, then the function value f(b) is a relative minimum of f.

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The cοrrect statement is the segment GC is transversal tο segments KG and QC.

A line that crοsses twο οr mοre lines in the same plane at different lοcatiοns is said tο be transversal. Accοrding tο the fundamental prοpοrtiοnality theοrem (alsο knοwn as Thales' theοrem), if three οr mοre parallel lines crοss acrοss twο transversals, they prοpοrtiοnally cut οff the transversals.

We have given the statements are:

A). KG QC.

B) KG and QC intersect at a right angle.

C) KQ || GC.

D) GC is transversal tο KG and QC.

Therefοre, here in the figure, segment GC intersects segments KG and QC in the same plane at different lοcatiοns.

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As per the concept of compound interest, the balance after 7 years will be $2,200.24.

In your case, you have a savings account balance that is compounded annually. The interest rate is 2% per year, which means that at the end of each year, the balance will increase by 2% of the previous year's balance. So, if your current balance is $1,932.00, the balance after one year will be:

Balance after one year = $1,932.00 + 2% of $1,932.00

= $1,932.00 + $38.64

= $1,970.64

After two years, the balance will be:

Balance after two years = $1,970.64 + 2% of $1,970.64

= $1,970.64 + $39.41

= $2,010.05

The formula for compound interest is:

A = P(1 + r/n)ⁿˣ

where:

A = the final amount

P = the principal amount (initial balance)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

ˣ = the number of years

In your case, the interest is compounded annually, so n = 1. The annual interest rate is 2%, which is equivalent to 0.02 as a decimal. The initial balance is $1,932.00, and you want to know the balance after 7 years, so t = 7. Using these values in the formula, we get:

A = $1,932.00(1 + 0.02/1)¹ˣ⁷

= $1,932.00(1.02)⁷

= $2,200.24

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