One hose can fill a small swimming pool in 75 minutes. A larger hose can fill the pool in 50 minutes. How long will it take the two hoses to fill the pool working together?

Answer: 20 000 000

(the first value is two because the one after the second one (9) is greater than 5 therefore you should add 1 to the the number in front)

Using the formula x=-b/2a, find the quadratic's vertex, and then substitute the result for y in the original equation.

Three points produce a quadratic function of the formula f(x) = ax^2 + bx + c. A quadratic function can be determined by finding a, b, and c algebraically given three locations on the graph. Because two points do not define a particular parabola, it is not possible.

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The linear equation for this scenario is y = 2x + 10 and $20 was charged for 5 ATM transactions

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the total cost for x monthly transactions.

$10 is charged monthly plus $2 per transaction, hence:

m = 2, b = 10

y = 2x + 10

For 5 ATM transactions:

y = 2(5) + 10 = $20

The linear equation for this scenario is y = 2x + 10

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The measure of an angle is  5π/12 radians

Let us assume that the complement of the angle measures x degrees.

We have been given the measure of the angle is five times its complement.

So we get the measure of the angle = 5 × x

We know that two angles are complementary when their measures add to 90 degrees (π/2 radians).

So from the definition of complementary angles we get an equation,

x + 5x = π/2

We solve above equation to find the value of x.

x + 5x = π/2

6x = π/2

x = π/12 radians

This means, the measure of complement of angle is π/12 radians.

So, the measure required angle would be,

5 × π/12 = 5π/12 radians

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The comple question is:

An angle is equal to 5 times its complement determine its measure?.

The equation that represents the situation in terms of x is 4x = 50 -13.5,

and there will be 9 whole pieces of wire of 4 feet.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given the total length of wire = 50 feet

length used = 13.5 feet

length of wire left = 50 - 13.5

A. wire is cut into 4 feet pieces

let there are x pieces,

expression for the pieces is

4x = 50 -13.5

B. 4x = 50 - 13.5

4x = 36.5

x = 36.5/4

x = 9.125

the whole number is 9

so there will be 9 pieces in a whole.

Hence the expression is 4x = 50 -  13.5,

and there will be 9 pieces of wire.

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Equation of the form are considered quadratic equations: ax² + bx + c = 0, where a, b and c are constants. The most straightforward method of solving a quadratic equation by factoring is to express the equation in its factored form, and then solve for the values of x that make it true.

To solve, start by setting the equation equal to zero. This will simplify the equation and make it easier to factor.

The equation has to be factored after that. To do this, you will need to identify the factors of c that add up to b. For example, if c = 15 and b = 6, the factors are 3 and 5, since 3 + 5 = 6.

Once you have identified the factors, you can rewrite the equation in its factored form. For example, if c = 15 and b = 6, the equation can be rewritten as (x+3)(x+5) = 0.

Finally, you can solve the equation by setting each factor equal to zero. For instance, if the equation is (x+3)(x+5) = 0, then x+3 = 0 and x+5 = 0. Solving each equation separately, you get x = -3 and x = -5. Therefore, the solutions to the equation are x = -3 and x = -5.

In conclusion, to solve a quadratic equation by factoring you will need to set the equation equal to zero, identify the factors of the constant c that add up to the coefficient b, and then rewrite the equation in its factored form. Finally, you can solve for the values of x that make the equation true by setting each factor equal to zero.

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Answer:

Step-by-step explanation:

We know that 1 hour = 60 minutes.

Set equal proportions for both Laisha and Jefford to find the distance x and y they bike in 60 minutes:

Laisha will bike farther by:

In the last basketball game, the ratio of baskets made to the total shots taken was 4:7 and if the team shot a total of 56 baskets in the game then the total basket they made is 40.

The ratio is 4:7, this means that for every 7 shots taken, 4 of them were made. If the team shot a total of 56 shots in the last game, then they made

(4/7) ×56 = 40 baskets.

This calculation can be broken down into simpler terms. For every 7 shots, 4 shots were made. Therefore, for 56 shots, 40 shots were made. Therefore, the team made 40 baskets in the last game.

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The descriptors that are applicable for factor by grouping is 4 terms and 3 terms.

What is group factorization?

Factorization by grouping requires that we first group the terms according to their common factors. Method of factorization by term grouping:

(i) A factor can be extracted from each group of the supplied expression's groupings.

(ii) Factorize each group.

(iii) Next, eliminate the factor shared by the newly created group.

To factorize 4 terms use the method -

The first step is to group the first and last two terms together.

Then create a GCF by factoring each individual binomial.

Factor out the common binomial in step three.

To factorize 3 terms use the method -

Factoring out the GCF of the full phrase is the first step (from all 3 terms). There might not always be a GCF to account for (that is, the GCF is 1).

Next, select two terms to think about jointly (we may need to split a term into two parts). Subtract the two terms' GCFs.

Consider the remaining terms along with the factored pair and determine if there is any additional factoring that can be done (if anything).

A binomial cannot be factored by factor by grouping method as it contain only two terms which doesn't require further factoring using grouping method.

Both terms are not always perfect squares, there can be times when the factors are written as roots.

Therefore, descriptors are 4 terms and 3 terms.

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A bar graph would be the best graphical representation to display the data. The correct answer would be an option (D).

A random sample of 130 purchases from a particular pharmacy was taken. The type of item purchased was recorded, and a table of the data was created.

Item Purchased      Health & Medicine     Beauty     Household     Grocery

Number of Purchases       55                       23               22               30

A bar graph would clearly and effectively show the number of purchases for each category of item (Health & Medicine, Beauty, Household, and Grocery) and allow for easy comparison between the categories.

Thus, a bar graph would be the best graphical representation to display the data.

Hence, the correct answer would be option (D).

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force = M × A

115 = M × 0.657

make M which is the mass the subject by dividing by 0.657 on both sides

115/0.657 = 0.657M/0.657

M = 115/0.657

M = 175.0380518

M = 175kg

Answer: (Only for homework, no tests, please!)

Step-by-step explanation:

Hello! An easy way to help you solve this is to use graph paper.  Make a coordinate grid using a ruler to help you form the trapezoid and plot the points at the proper coordinates.  It should look something like this but with a line going through BC and AD.  Draw the midpoint of line segments AD and BC by measuring their lengths with a ruler and divide the length in half to plot the points.  Connect the midpoints with a ruler to form the midsegment.  Hope this helps you with your homework!

The percent error for Anita's measurement is 8%

To calculate the percent error, you need to find the difference between the measured value and the actual value, then divide that by the actual value and multiply by 100. The formula for percent error is:

% error = (|measured value - actual value| / actual value) x 100

In this case, the measured value is 0.46 cubic centimeter and the actual value is 0.50 cubic centimeter.

% error = (|0.46 - 0.50| / 0.50) x 100

% error = (0.04 / 0.50) x 100

% error = 0.08 x 100

% error = 8%.

Hence, Anita's measurement using the water displacement method has a percent error equivalent to 8%.

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The side length UX which have the segment UW tangent to the circle is equal to 3.4.

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

Considering the triangle ∆UVX; we will observe that the side XV consists of the circle diameter which is perpendicular to the side UV tangent to the circle, this implies the ∆UVX is a right triangle and we can solve for the side length UX using the Pythagoras rule as follows;

UX² = 3² + 1.6²

UX² = 9 + 2.56

UX² = 11.56

UX = √11.56 {take square root of both sides}

UX = 3.4.

In conclusion, we have the length of side UX = 3.4 which have the segment UW tangent to the circle.

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The graph of the piece-wise function f(x) is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

The extreme points of the function in this problem are given as follows:

Hence the graph of the function in this problem is composed as follows:

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The table for given phrase shows non-linearity.

The complete explanation is given below.

The graph of a linear function is a straight line. The following is the form of a linear function.

a + bx = y = f(x).

One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.

Given:

There were 50 mosquitos near a pond.

The population doubles every month.

For 4 next four months, the population of mosquitos,

Number of months (x) → Population (y)

1  →  50

2 →  100

3 →  200

4 →  400

If the table shows linear relationship,

then its first difference is constantly equal.

That means,

100 - 50 = 50

200 - 100 = 100

400 - 200 = 200

First difference is not equal.

Therefore, the table shows non-linearity.

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It depends on the values of a,b,d and e in the equations , different values may lead to different answers.

What is linear equation ?

A linear equation is an equation in which the highest power of the variable is 1. Linear equations can be written in the form of y = mx + b, where m is the slope of the equation, x is the variable, and b is the y-intercept, the point where the line crosses the y-axis. These equations are called linear because they describe a straight line when graphed.

It depends on the specific equations and the values of a, b, d and e in the system of equations. Multiplying both sides of an equation by a non-zero constant does not change the solution set of the equation.

However, if Jim wants to use the method of elimination, which is multiplying one equation by a constant and adding or subtracting it from the other equation, then it is important to ensure that the coefficients of one variable in the two equations are opposite in sign after the multiplication. This will enable him to eliminate one variable and find the value of the other variable.

It depends on the values of a,b,d and e in the equations , different values may lead to different answers.

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Answer:

5

Step-by-step explanation:

Figure B's cone has a volume of 678.24 cu ft.

The Volume of Cone in figure B is 678.24 cu ft.

Given:

Figure A~ Figure B

Figure A: where V = 25.12 cu ft and r = 2 feet

Figure B: r= 6 ft

Now, the formula for volume of cone

= 1/3 πr²h

As, Figure A and B are similar

So, [tex]r(B) / r(A) =h(A) / h(B)\\[/tex]

                       [tex]= 6/2[/tex]

                       =3

Now, r(B) = 3 r(A)

and, h(B) = 3 h(A)

So, the volume of figure B is

V = 1/3 π(3 r(A))² (3h (A))

[tex]V = 1/3 \times 27\times 3\times \pi r^2(A) h(A)[/tex]

V = 27 πr(A)²h(A

V = 27 V(A)

V = 27 * 25.12

V = 678.24 cu ft

Thus, the volume is 678.24 cu ft.

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Jackson's company $1.2 more than Micaela's.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Micaela charges a $3.50 pickup fee and $1.30 per mile.

And, The table represents what Jackson's company charges.

Now, Micaela charges a $3.50 pickup fee and $1.30 per mile.

Hence, The equation that represents Mathew's charges is given as,

⇒ y = 1.30x + 3.50  .. (i)

And, From table,

The equation that represents Jackson's charges is given as:

Take two points (x, y) = (10, 30.50) and (30, 88.50)

Hence, The equation is,

⇒ y - 88.50 = (88.50 - 30.50)/(30 - 10)  (x - 10)

⇒ y - 88.50 = 50/20 (x - 10)

⇒ y - 88.50 = 2.5 (x - 10)

⇒ y - 88.50 = 2.5x - 25

⇒ y = 2.5x + 88.50 - 25

⇒ y = 2.5x + 63.50  .. (ii)

We know that;

A linear equation is represented as:

⇒ y = mx + b

Where: m represents the slope/rate.

Hence, Jackson's company $1.2 more than Micaela's.

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The percentage error is 8.3%. ((60 - 55) / 60) x 100 = 8.3%.

(60 - 55) / 60 = 0.083

0.083 x 100 = 8.3

Brianna estimated that he would spend $60 hopping for school supplies before the start of the school year. However, she actually spent $55. To calculate the percent error for her estimate, we first subtract the actual amount spent ($55) from the estimated amount ($60). This gives us 0.083, which is then multiplied by 100 to get 8.3%. This means that Brianna's estimate was 8.3% off from the actual amount spent. This result can help her understand how close her estimate was to the actual amount spent and can help her improve her estimating skills in the future.

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The expression can be simplified by combining any like terms, which in this case are 5g and 5g. When added together, they become 10g.

The expression 5g5g–10g can be simplified by performing the following steps:

1. Multiply 5g and 5g, to get 25g2.

Subtract 10g from 25g, to get 15g.

3. Simplify to 10g.

Simplifying the expression 5g5g–10g involves combining like terms. Like terms are terms that have the same variable, in this case the letter g. To simplify, first we need to multiply the two 5g terms together, giving us 25g. Then, we subtract 10g from 25g, to get 15g. Finally, we can simplify further by combining any remaining like terms, which in this case there are none. Therefore, when all is said and done, the expression can be simplified to 10g. This is because 10g is the only like term in the expression.

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Julian's average speed for the whole journey was 8 miles per hour.

To find Julian's average speed for the whole journey, we can use the formula:

average speed = total distance / total time

We know that Julian walked from his house to the library for 2 hours at a speed of 4 miles per hour and then returned home by bicycle at a speed of 12 miles per hour.

To find the total distance, we can add the distance he walked to the distance he rode his bicycle:

total distance = distance walked + distance rode by bicycle

To find the distance he walked, we can use the formula:

distance = speed x time

distance walked = 4 miles/hour x 2 hours = 8 miles

distance rode by bicycle = 12 miles/hour x 2 hours = 24 miles

total distance = 8 miles + 24 miles = 32 miles

We know that Julian walked for 2 hours and rode for 2 hours, so we can add those times to find the total time:

total time = time walked + time rode by bicycle = 2 hours + 2 hours = 4 hours

Now we can use the formula to find Julian's average speed for the whole journey:

average speed = total distance / total time = 32 miles / 4 hours = 8 miles/hour

Therefore, Julian's average speed for the whole journey was 8 miles per hour.

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The equation of the line that passes through (-3, 5) and is perpendicular to the line y = -3x - 1 is y = (1/3)x + (20/3).

What is the equation of the line?

The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y-intercept.

To write an equation of the line that passes through (-3, 5) and is perpendicular to the line y = -3x - 1, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope of the line that passes through (-3, 5). Since the line is perpendicular to y = -3x - 1, we know that the slope of the line is the negative reciprocal of -3, which is 1/3. So the slope of the line is 1/3.

Next, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Plugging in the point (-3, 5) and the slope 1/3, we get:

y - 5 = (1/3)(x + 3)

Simplifying we get:

y = (1/3)x + (20/3)

Hence, the equation of the line that passes through (-3, 5) and is perpendicular to the line y = -3x - 1 is y = (1/3)x + (20/3).

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The 12th term of the geometric  sequence is -341796875.

The common ratio (r) is:

[tex]\frac{a_{1} }{a_{2} } =-\frac{35}{7} =-5[/tex]

[tex]\frac{a_{3} }{a_{2} } =\frac{175}{-35} =-5[/tex]

(r)=-5

The sum is :

[tex]S_{n}[/tex]=a·{[tex]\frac{1-r^{n} }{1-r^{} }[/tex]}

[tex]S_{3}[/tex]= 147

So. The general form is:

[tex]a_{n}[/tex]=7·-[tex]5^{n-1}[/tex]

Now, The nth term is:

[tex]a_{1}[/tex]=7

[tex]a_{2}[/tex] = [tex]a_{1}[/tex]·[tex]r^{n-1}[/tex] = 7· [tex]-5^{2-1}[/tex] = 7 · [tex]-5^{1}[/tex] = 7 · -5 = -35

[tex]a_{3}[/tex] = [tex]a_{1}[/tex]·[tex]r^{n-1}[/tex] = 7· [tex]-5^{3-1}[/tex] = 7 · [tex]-5^{2}[/tex] = 7 · 25 = 175

[tex]a_{4}[/tex] = [tex]a_{1}[/tex]·[tex]r^{n-1}[/tex] = 7· [tex]-5^{4-1}[/tex] = 7 · [tex]-5^{3}[/tex] = 7 · -125 = -875

[tex]a_{5}[/tex] = 4375

[tex]a_{6}[/tex] = -21875

.......  so, [tex]a_{12}[/tex] = - 341796875

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A. Kevin will have $5040 if he use Bet Bank.

B. Kevin will have $14,707.7 if he use Primo Bank.

C. Kevin would use Primo Bank due to high amount generation.

The formula to be used for simple interest is -

SI = PRT/100, where SI is simple interest, P is principal, R is rate of interest and T is time.

The formula for compound interest is -

A = [tex] {P(1 + r)}^{n} [/tex], where n is times interest is calculated.

To answer first part -

SI = 8000 × 9 × 7/100

Performing multiplication

SI = 504,000/100

SI = $5040

Amount generated = 8000 + 5040

Performing addition

Amount generated = $1340

To answer second part -

A = 8000(1+ 7/100)⁹

Convert rate to decimal

A = 8000 (1+0.07)⁹

Performing addition

A = 8000 × 1.07⁹

Taking power

A = 8000 × 1.84

Performing multiplication

A = $14,707.7

The money generated in Primo Bank is more. Hence, Kevin must choose this bank.

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The 4 systems of equations are Quadratic Equation, Linear Equation,

Exponential Equation and Rational Equation.

Linear Equations: Each term involved in the linear equation is either a constant, a single variable, or a product of a constant. The general form of this equation with two variables is shown by

Y = mx + c,   m ≠ 0

Where m is the slope

C is the intercept of the y-axis

Quadratic Equations: The quadratic equation is a second-order equation in which any one of the variables contains a power of 2. The general form is

px² + qx + r = 0, p ≠ 0

Exponential Equations: This math equation contains the variables in place of exponents. By using the properties, an exponential equation can be solved.

[tex]a^{x}=a^{y}[/tex] ⇒x = y

Rational Equations: A rational math equation involves rational expressions.

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The slope of the equation y=-2x+10 is -2.

The slope of a line is a measure of its steepness and direction. In the equation y = -2x + 10, the slope is -2.

To understand this, let's first look at the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

In this case, the equation is already in the slope-intercept form and we can see that the slope is -2. The negative sign indicates that the line is sloping downward. The bigger the absolute value of the slope, steeper the line is.

In other words, the slope of a line tells us how much y changes for each unit of change in x. In this case, the slope is -2, which means that for each unit increase in x, y decreases by 2 units.

It's also worth noting that, if the slope is positive, the line will rise from left to right, if the slope is negative, the line will fall from left to right.

Therefore, The slope of the equation y=-2x+10 is -2.

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The area of the major sector is 2807. 1 cm²

The perimeter of a sector given by the formula:

P = θ/360 × 2πr

where r is the radius and θ is the angle subtended at the centre

Since the perimeter of a major sector is 168cm and the angle subtended by the minor arc is 72 degrees. We can say:

angle subtended by the major arc  = 360 -72 = 288 degrees

P = θ/360 × 2πr

168 = 288/360 × 2πr

210 = 2πr

r = 210/2π

r = 33.42 cm

Thus, the radius of the major arc is 33.42 cm

The area of a sector given by the formula:

A = θ/360 × πr²

A = (288/360) × π × 33.42²

A = 2807. 1 cm²

Thus, the area of the major sector is 2807. 1 cm²

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