Working together, two pumps can drain a certain pool in 3 hours. If it takes the older pump 12 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?

the greatest distance the dog can be from the origin is 15 feet.

A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.

Well first we have to find the distance from the origin to the point (4,3). Now to do this we use the distance formula. I didn't want to type this out so i found a picture.

Now the origin point is (0,0) So now we have two points we can plug in to find the difference between them. Now the X1 and X2 as well as y1 and y2 are interchangeable within their brackets.

So D= [tex]\sqrt{(4)^{2} } + (3^{2} )[/tex] Which means D= the square root of 25 which is 5. This means the distance from the origin to (4,3) is 5 feet. Now the dog can go 10 more feet in the opposite direction of the origin so 5 + 10 (pretty easy math) = 15. The dog can be (at its farthest) 15 feet from the origin.

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A) (i) (1, 5) is possible solution of equation.

(ii) (-2, 0) is not possible solution of equation.

B)  Solution of graph 1);

⇒ (- 2, - 2)

And, Solution of graph 2);

⇒ (4, 1)

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

A) Substitute the given coordinate in system of equation and check it is solution or not as;

1) System of equation are,

⇒ - 5m + 6n = 25

⇒ - 7m + 8n = 33

Coordinate = (1, 5) = (m, n)

Substitute in equations;

⇒ - 5m + 6n = 25

⇒ - 5 (1) + 6(5) = 25

⇒ - 5 + 30 = 25

⇒ 25 = 25

⇒ - 7m + 8n = 33

⇒ - 7(1) + 8(5) = 33

⇒ - 7 + 40 = 33

⇒ 33 = 33

Thus, (1, 5) is possible solution of equation.

2) System of equation are,

⇒ 8x - 3y = - 16

⇒ - 9x - 2y = 50

Coordinate = (- 2, 0) = (x, y)

Substitute in equations;

⇒ 8x - 3y = - 16

⇒ 8(-2) - 3(0) = - 16

⇒ - 16 = - 16

⇒ - 9x - 2y = 50

⇒ - 9(-2) - 2(0) = 50

⇒ 18 ≠ 50

Thus, (-2, 0) is not possible solution of equation.

B) The solution of graph of lines are intersection point of both lines.

Hence, Solution of graph 1);

⇒ (- 2, - 2)

And, Solution of graph 2);

⇒ (4, 1)

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The standard deviation of x is 3 cars. So the option A is correct.

Suppose that x is the number of cars per minute that pass through a certain intersection, and that x has the Poisson distribution.

If the mean of x is equal to 9 cars, then we have to determine the standard deviation of x.

An indicator of how much variance from the mean there is is the standard deviation, which can be expressed as spread, dispersion, or spread. A "typical" departure from the mean is represented by the standard deviation. As a result of returning to the data set's original units of measure, it is a well-liked measure of variability.

The Mean = 9 cars

Standard Deviation = Square Root of Mean

Standard Deviation = √9

Standard Deviation = 3 cars

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The measure of the angles numbered 1 and 2 in the figure of the kite are;

m∠1 = 90°

m∠2  = 72°

A kite is a quadrilateral that has consecutive congruent sides and perpendicular diagonals. A kite has a reflection symmetry across one of the diagonals.

The specified quadrilateral in the figure has a reflection symmetry about the horizontal diagonal,  the figure is therefore a kite

The diagonals of a kite are perpendicular, therefore, the measure of the angle ∠1, by the definition of perpendicular lines, is 90°

m∠1 = 90°

The base angles in the 90° clockwise rotated isosceles triangle are the same
The angle on the other side of the horizontal diagonal at the right vertex is also 18°

The measure of the angle ∠2 is therefore;

m∠2 = (180° - 2 × 18°)/2 = 72°

m∠2 = 72°

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The solution of the given expression (0.4k^3)^3 can be simplified as :0.064K^9.

The concept that will be used is simpilification. To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. Be aware of the workflow. You can't just multiply, add, subtract, and so on in a straight line when simplifying math formulas.

The given expression is (0.4k^3)^3

This can be simplify as :

(0.4)^3 *(k^3)^3

This can be further simplified by finding the cubing the terms involved which can be done as :

0.064K^9

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(a) The markup is $3.9.

(b) The selling price of the CD is $11.70.

The markup of the CD is calculated by applying the following formula.

The markup = 50% x $7.80

The markup = ( 50 / 100 ) x $7.80

The markup = 0.5 x $7.80

The markup = $3.9

The selling price of the CD is calculated as follows;

selling price = $7.80 + $3.9

selling price = $11.7

Thus, the selling price of the CD is a function of the cost price, and mark up price. So the final selling price of the CD is $11.7 while the mark up is $3.9

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The values of the function when x = -2 and when = 4 are,

⇒ g (-2) = 0

⇒ g (4) = - 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ g (x) = 6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x ≤ 4

           = - 4 ; 4 ≤ x ≤ 10

Now, The value of function are,

At x = - 2;

⇒ g (x) =  6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x ≤ 4

           = - 4 ; 4 ≤ x ≤ 10

⇒ g (- 2) = 0

At x = 4;

⇒ g (x) =  6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x < 4

           = - 4 ; 4 ≤ x ≤ 10

⇒ g (4) = - 4

Thus, The values of the function when x = -2 and when = 4 are,

⇒ g (-2) = 0

⇒ g (4) = - 4

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Answer: 35 is 70% of 50

Step-by-step explanation:

Steps to solve "35 is 70 percent of what number?"

We have, 70% × x = 35

or,

70

100

× x = 35

Multiplying both sides by 100 and dividing both sides by 70,

we have x = 35 ×

100

70

x = 50

If you are using a calculator, simply enter 35×100÷70, which will give you the answer.

Answer:

50

Step-by-step explanation:

35 + 15 = 50

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

15 is 30% of 50 There fore 50 is the correct answer

I took this exam, its the 5.08 Ratios and rates practice exam right?

Have an amazing Day and good luck (:

By critically observing the triangular prism shown in the image attached above, the base shape of this triangular prism is a:

C) triangle.

A triangular prism can be defined as a geometric shape (figure) with five (5) faces in total. Generally, a triangular prism comprises two (2) triangular bases and three (3) rectangular lateral faces.

Now, By critically observing the triangular prism, we can logically deduce that the base shape of this prism is a triangle.

Hence, A triangular prism has five faces in total.

There are two triangular bases and three rectangular lateral faces. Few examples of triangular prism are - a camping tent, Toblerone chocolate shape. The base of a prism is also a face.

In conclusion, the base shape of this triangular prism is a triangle.

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Answer:The coefficient in this expression is 3.

Step-by-step explanation:

What is a Coefficient?

By definition, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic.

What is a variable?

A variable is a symbol that represents a mathematical object. So for example, 9p + 2. In this equation, the variable would be the letter "p."

Using the graph we will see that line q can be written as:

y = (-1/2)*x + 3

Remember that the general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Using the graph we can identify the two points (0, 3) and (2, 2), then the slope is:

a = (2 - 3)/(2 - 0) = -1/2

And the y-intercept is y = 3, then the linear equation is:

y = (-1/2)*x + 3

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The required quarts of frozen yogurt made in 36 hours as per the given information is equal to 720 quarts.

Quarts of frozen yogurt made by factory is equal to 100 quarts

Time required to make 100 quarts of frozen yogurt is equal to 5 hours

Let 'x' quarts of frozen yogurt made in 36 hours

5 hours = 100 quarts of frozen yogurt

⇒ 1hour = ( 100 / 5 ) quarts of frozen yogurt

⇒ 36 hours =  ( 100 / 5 ) × ( 36 ) quarts of frozen yogurt

⇒ 36 hours =  ( 20 ) × ( 36 ) quarts of frozen yogurt

⇒ 36 hours =  ( 720 ) quarts of frozen yogurt

Therefore, the quarts of frozen yogurt made in 36 hours is equal to 720 quarts.

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The slope of these lines are:

Slope can be calcualted by comparing the change in y-axis with the change in x-axis. Then, let's discuss every lines we have:

1. We take 2 points: (3, 1) and (-2, -1)

m = y₂ - y₁

      x₂ - x₁

m = -1 - 1

      -2 - 3

m = - 2/ -5

m = 2/5

2. We take 2 points: (2, 2) and (-3, -3)

m = y₂ - y₁

      x₂ - x₁

m = -3 - 2

     -3 - 2

m = -5/-5

m = 1

3. We take 2 points: (1, 3) and (-1, -2)

m = y₂ - y₁

      x₂ - x₁

m = -2 - 3

      -1 - 1

m = -5 / -2

m = 5/2

4. We take 2 points:  (1, 0) and (-1, -2)

m = y₂ - y₁

      x₂ - x₁

m = (-2 - 0) / (-1 - 1)

m = -2/-2 = 1

We subtitute one point: (1, 0)

y = mx + c

0 = 1 (1) + c

c = -1 --> y = x - 1

5. We take 2 points:  (3, -1) and (-2, -2)

m = y₂ - y₁

      x₂ - x₁

m = -2 - (-1)

      -2 - 3

m = -1 / -5 = 1/5

We subtitute one point: (3, -1)

y = mx + c

-1 = 1/5 (3) + c

-5/5 = 3/5 + c

c = -8/5 --> y = 1/5 x - 8/5

6. We take 2 points: (2, -1) and (-1, 3)

m = y₂ - y₁

      x₂ - x₁

m = (3 - (-1)) / (-1 - 2)

m = 4/(-3)

m = - 4/3

We subtitute one point: (2, -1)

y = mx + c

-1 = - 4/3 (2) + c

-3/3 = -8/3 + c

c =5/3 --> y = -4/3 x + 5/3

7. m = Δy / Δx

m = 8/24

m = 1/3

8. m = Δy / Δx

m = 100/1000

m = 1/10

9. (1, 3) and (4, 7)

m = y₂ - y₁

      x₂ - x₁

m = (7 - 3) / (4 - 1)

m = 4/3

10. (3, 5) and (2, 6)

m = y₂ - y₁

      x₂ - x₁

m = (6 - 5) / (2 - 3)

m = 1 / (-1) = -1

11. (4, 0) and (5, 5)

m = y₂ - y₁

      x₂ - x₁

m = (5 - 0) / (5 - 4)

m = 5/1 = 5

Please refer to the graphs attached below for the graph number 4, 5, and 6.

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The length Thebe the HCF (highest common factor) of the given dimensions that are 168mm and 196 mm. Hence, the length of each square will be equal to 28mm.

The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers. As a result, it is also known as the greatest common factor (GCF). If M is the greatest common factor of N, then M is the greatest possible number that divides N.

The length of the each square will be given by the HCF of the dimensions that are 168mm and 196mm.

[tex]168=2*2*2*3*7\\196=2*2*7*7[/tex]

So, the length of the each square paper=[tex]2*2*7=28mm.[/tex]

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Check the picture below.

so the triangle with the 35° angle is an isosceles, namely a triangle with twin sides stemming from the center of the circle, well, twin sides make twin angles, and since the center of the circle makes a central angle, well, any arc will get its degrees from that.

To find the average, one adds up all the scores and then divides by the total number of scores.

Joan had to find the average of the scores of her friends. To find the average, one adds up all the scores and then divides by the total number of scores. In this case, Joan had to find the sum of 10 different scores of her friends and then divide by 10. This will give her the average of the scores of her friends, which is a single value representing the central tendency of the scores. The average is a commonly used statistical measure that provides an overall idea of the data. In this case, the average of the scores of Joan's friends will give her an idea of the overall performance of her friends in the test she is preparing for.

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At present, Tyrone is 48 years old and his daughter is 24 years old.

Let's start by using variables to represent the ages of Tyrone and his daughter.

Let T be Tyrone's current age and D be his daughter's current age.

We know that Tyrone is twice as old as his daughter, so we can write:

T = 2D

We also know that in 6 years, Tyrone's age will be three times what his daughter's age was six years ago. Six years ago, Tyrone's age was T - 6 and his daughter's age was D - 6. So we can write:

T + 6 = 3(D - 6)

Now we have two equations with two variables, so we can solve for T and D.

First, substitute T = 2D from the first equation into the second equation:

2D + 6 = 3(D - 6)

Simplifying this equation, we get:

2D + 6 = 3D - 18

Add 18 to both sides:

2D + 24 = 3D

Subtract 2D from both sides:

24 = D

So Tyrone's daughter is 24 years old now.

We can use the first equation to find Tyrone's age:

T = 2D = 2(24) = 48

Therefore, Tyrone is 48 years old now.

So at present, Tyrone is 48 years old and his daughter is 24 years old.

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Tyrone is twice as old as his daughter. in 6 years Tyrone's age will be three times what his daughters age was six years ago. how old will they be at present?

Sam can jump 4 steps at a time and Nina can jump 5 steps at a time. on 20th of the steps will both meet if both start jumping together. we can find it out with the help of HCM and LCM

GIVEN

Sam can jump four steps at a time and Nina can jump five steps at a time.

TO DETERMINE

On which of the steps will both meet if both start jumping together

EVALUATION

Here it is given that Sam can jump 4 steps at a time and Nina can jump 5 steps at a time.

Now we find the LCM of 4 and 5

Since 4 and 5 are prime to each other

So LCM of 4 and 5 = 4 × 5 = 20

Hence after 20 steps both meet if both start jumping together

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Answer: 90

Step-by-step explanation:

The number that you need to find because it is missing in the equation is 48.

Let's assume the number we're trying to find is "x."

According to the problem, one-third of the number is (1/3)x, and one-fourth of the number is (1/4)x.

We're told that the sum of one-third of the number and one-fourth of the number is 28, so we can write the equation as follows:

(1/3)x + (1/4)x = 28

To solve this equation, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can rewrite the equation as:

(4/12)x + (3/12)x = 28

Combining the fractions, we get:

(7/12)x = 28

To isolate x, we multiply both sides of the equation by the reciprocal of (7/12), which is (12/7):

x = 28(12/7)

Simplifying the right side of the equation, we have:

x = 48

Therefore, the number we're looking for is 48.

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The variable "Points scored in a football game" , is a numerical variable, specifically a discrete variable.

The Discrete Numerical Variables represent counts or whole numbers, such as the number of students in a class or the number of items sold in a store.

The Continuous Numerical Variables represent measurements, such as height, weight, or time, and can take on any value within a range.

In this case, the variable represents the number of points scored in a game, and it can only take on specific integer values (for example, 0, 1, 2, etc.) and cannot take on fractional or decimal values.

The given question is incomplete , the complete question is

State whether the Variable is Categorical or Numerical ?

If the variable is numerical, then specify whether the variable is discrete or continuous.

(a) Points scored in a football game .

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The given example of a high school student regarding video game playing is quantitative data collection.

Quantitative data can be measured or counted. The high school student in this example is compiling numerical information about how much time each member of their homeroom class spends playing video games.

The student can first add up the total number of hours each person spends playing video games each week in order to determine the average number of hours spent playing video games each week.

The student can then divide the total number of hours spent playing video games by the number of students in their homeroom class to determine the weekly average.

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The total interest charger after 20 years for the balloon mortgage would be = $170,500

Simple interest is defined as the extra amount of money that is being paid to an individual following an amount of money that was invested for a stated period of time.

The formula for simple interest= P×T×R/100

The principal amount for the mortgage = 275,000

The time for the mortgage = 20 years

The rate = 3.1%

Therefore interest generated;

= 275,000×3.1×20/100

= 17050000/100

= $170,500

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1. Yes 2. no 3. no 4. yes

1. -.5g + 2.5

2. .5g - 2.5

3. -.5g - 2.5

4. -.5g + 2.5

The normal probability plot can reveal information about the population from which the data were drawn. A straight line pattern indicates normality, whereas deviations from the straight line indicate non-normality.

A normal probability plot is a graphical method for determining whether a set of data values is normally distributed. The plot depicts sample data values on the y-axis and theoretical normal deviate values on the x-axis.

If the plotted points follow a roughly straight line, the population is likely to be normally distributed. If the points plotted deviate significantly from a straight line, the population is not normally distributed.

As a result, the shape of the normal probability plot can provide insight into the normality of the population from which the data were drawn. A straight line pattern indicates that the distribution is normal, whereas deviations from the straight line indicate non-normality.

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The conclusion is that there is sufficient evidence at the 0.01 level to support the mayor's claim that under 62% of the residents favor construction of the bridge.

The mayor rejects the null hypothesis at the 0.01 level, which means that the results from the hypothesis test show that the actual proportion of residents who favor construction is less than 62%. The alternative hypothesis would be that the true proportion is less than 62%. After gathering information from 110 voters, the results of the hypothesis test were used to make a decision on whether to reject or fail to reject the null hypothesis. If the hypothesis test showed that the null hypothesis could be rejected at the 0.01 level, it means that there was sufficient evidence to support the mayor's claim that less than 62% of the residents favor the bridge construction. However, it's important to note that hypothesis testing is not a perfect method and other factors such as sample size and sampling method should also be considered when interpreting the results.

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In ΔJKL using the angle bisector theorem the value for x is obatined as 48.6 units.

What is angle bisector theorem?

The opposite side of a triangle is divided into two pieces by the angle bisector in proportion to the other two sides. If the interior point of a triangle is equally spaced from its two sides, that point will be on the angle bisector of the angle created by the two line segments.

The measurement for line segment JK = 54 units.

The measurement for line segment LK = x units.

The measurement for line segment LM = 36 units.

The measurement for line segment JM = 40 units.

In ΔJKL line segment KM is an angle bisector.

So, according to the angle bisector theorem -

JM / LM = JK / LK

Substitute the values in the equation -

40 / 36 = 54 / x

Simplify to find the value of x -

x = (54 × 36) / 40

x = (27 × 9) / 5

x = 48.6 units

Therefore, the value of x is 48.6 units.

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Answer:

you take the perimeter and subtract 2*the length. Then you divide that answer by 2

Step-by-step explanation:

This is because a rectangle is made up of 2 pairs of heights. 2 equal sides represent the height and 2 equal sides represent the width.

When we subtract the lengths of the 2 sides that represent the height we get a number that we then have to divide by 2 to get the width of the triangle.

Hope this helps. It's a little difficult to explain but the answer is correct :)

The length and width each need to be 230 feet, and the area of the outdoor enclosure will be A=(230)(230)=52900 sq. ft.

The owner of the used tire store wants to construct a fence to enclose a rectangular outdoor storage area. The side of the store is 240 feet long and there are 460 feet of fencing available for the other three sides. The formula for the area of a rectangle is A=LxW, where A is the area, L is the length, and W is the width. To find the dimensions of the outdoor enclosure with the most area, the length and width must be equal so that all of the fencing is used. Therefore, the length and width each need to be 230 feet, and the area of the outdoor enclosure will be A=(230)(230)=52900 sq. ft.

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