The yearly income of a family is Rs. 500000. The ratio of the expenditure and saving of the family is 4 : 1. Find the amount of expenditure and saving.​

The range of the scores of the basketball games played by the Lady Bugs basketball team is equal to option D. 12.

Scores of the games played by  Lady Bugs basketball team is equal to

57, 50, 57, 53, 53, 62, 57

Arrange the scores of the team in ascending order we get,

50, 53, 53, 57, 57, 57, 62

Highest score of the team = 62

Lowest score of the team = 50

Range = highest score - lowest score

Substitute the value in the formula we get,

⇒ Range = 62 - 50

⇒ Range = 12

Therefore, the range of the score of the game played by basketball team is equal to option D. 12.

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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 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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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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Step-by-step explanation:

Option A is the right answer.

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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Answer: 7.59

Step-by-step explanation: I added all of the miles he traveled up together. ( don't overthink questions like this)

Answer:

Point D is the solution to the system of equations.

Step-by-step explanation:

When asked for a solution involving 2 equations, the goal is to find a point (x,y) that would be a solution to both equations.  Any point on a line that is defined by an equation is a solution to that equation.  For an equation of y = 2x + 2, possible solutions are (1,4), (2,6), (5,12) etc.  These points all lie on the line formed by that equation.  There are an infinite number of possible solutions.  If a second eqaution is added, there is now a constraint on the possible answers.  The goal is to find a point that satisfies both equations.

If a seond equation of y = 1x + 3 were matced with y=2x+2, both are straight lines, but with different slopes.  So they will intersect at some point.  One may either solve mathematically using substitution, or by graphing, as was done here.  

Matematically:

y = 2x + 2

y = 1x + 3

Rearrange either equation to isolate a variable, x or y.  These are already isolated (since I made them up) so go to the next step of substituting one expression of y into the other:

y = 1x + 3

2x + 2 = 1x + 3

x = 1

Now use this value of x to find y:

y = 2x + 2

y = 2*(1) + 2

y = 4

The point these two lines intersect is (1,4) and is the "solution" to this series of equations.

See the attached graph.

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: J. A = 12 (4⋅6).

Step-by-step explanation:

Answer: J. A = 12 (4⋅6).

This equation can be used to find the area of the triangle in the diagram because it uses the formula for the area of a triangle, which is A = 1/2 * b * h, where b is the base and h is the height. Since the triangle in the diagram has a base of 4 and a height of 6, the equation A = 12 (4⋅6) can be used to find the area.

Answer:

The diagram is not provided, so it's difficult to determine the exact dimensions of the triangle and parallelogram. However, we can make some general observations to determine which equation can be used to find the area of the triangle.

First, we know that the area of a triangle is given by the formula:

A = 1/2 * base * height

We also know that the area of a parallelogram is given by the formula:

A = base * height

In the diagram, the triangle can be formed into a parallelogram by taking one of its sides and using it as the base of the parallelogram. The height of the parallelogram is the same as the height of the triangle.

Based on these observations, we can conclude that the equation that can be used to find the area of the triangle is:

A = 1/2 * base * height

where the base is one of the sides of the triangle, and the height is the height of the parallelogram (which is the same as the height of the triangle).

None of the answer choices provided match this equation, so the correct answer is not given.

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.

Answer:

Step-by-step explanation:

Multiply each then divide by the first number you started off with.

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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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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The equation of the parabola in the form y = a(x - r)(x - s) is y = -2(x + 2)(x + 8).

To determine the equation of the parabola in the form y = a(x - r)(x - s), we need to find the values of a, r, and s. We are given the x-intercepts and the vertex, so we can use this information to find these values.

The x-intercepts are -2 and -8, so we know that r=-2 and s=-8. The vertex is (-5,-18), so we can plug these values into the equation and solve for a:

y = a(x - r)(x - s)
-18 = a(-5 + 2)(-5 + 8)
-18 = a(-3)(3)
-18 = 9a
a = -2

So the equation of the parabola is y = -2(x + 2)(x + 8).

In standard form, this equation is y = -2x² - 20x - 32.

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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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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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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:

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 line intersecting at the axes (2,0)and (0,2) will not pass through (2,2).

Given, a line intersects at the axis (2,0)and (0,2)

let the line intercept be expressed as

[tex]ax+by=1[/tex] where a and b are the x & y intercept.

since the intercept points are the axis (2,0)and (0,2)

a=2 and b=2

[tex]2x+2y=1[/tex]

when the point (2,2) is considered and put in equation

2(2)+2(2)=4≠1

Therefore, point (2,2) doesn't satisfy the equation and line doesn't pass through (2,2).

From the graph also, we can say that the line passing through (2,0) and (0,2) intersecting the axes do not pass through the point (2,2).

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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.

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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Answer:

342.02

Step-by-step explanation:

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

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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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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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 two possible values for the middle numbers in the geometric progression are +35 and -35.

We know that the three numbers form a geometric progression. Let the middle number be x:

5, x, 245

Since these numbers form a geometric progression, we know that:

x^2 = 5 * 245

So we have:

x = ± √(5 * 245)

x = ± 35

Therefore, the two possible values for the middle number are +35 and -35. To find the two possible values for the middle number in the geometric progression, we used the fact that the product of the first and third terms of a geometric progression is equal to the square of the second term.

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There are 1,000 ways to construct a 3-digit code if numbers can be repeated. This is because there are 10 possible numbers (0-9) for each digit, and since numbers can be repeated, each digit has 10 options. So the total number of ways to construct a 3-digit code is 10 × 10 × 10 = 1,000.

Here is a step-by-step explanation:
1. Start with the first digit. There are 10 possible numbers (0-9) that can be used for this digit.
2. Move on to the second digit. Again, there are 10 possible numbers (0-9) that can be used for this digit, since numbers can be repeated.
3. Finally, move on to the third digit. There are 10 possible numbers (0-9) that can be used for this digit, since numbers can be repeated.
4. Multiply the number of options for each digit together to get the total number of ways to construct a 3-digit code: 10 × 10 × 10 = 1,000.

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Answer:

580

Step-by-step explanation:

He painted 60/100 x 1450 = 870

Unpainted = 1450-870

Remaining = 580ft²

The expression that shows the number of laps Glenn swam during the week is 2 * 7 + 3(2) = 20.

A mathematical expression is a grouping of numbers, variables, and operations without the equal sign. It may be condensed or given a single value. On the other hand, an equation is a declaration that employs the equal sign to demonstrate the equality of two expressions. To get the value of the variable that makes an equation true, equations can be solved.

Given that, 2 laps every morning for 7 days:

2 * 7

3 laps with his friends one Tuesday and Thursday.

3(2)

Total laps = 2( 7) + 3(2) = 20

Hence, expression that shows the number of laps Glenn swam during the week is 2 * 7 + 3(2) = 20.

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