What is the result when the number 14 is increased by 50%?

The radius of the cylindrical bucket is 11 inches.

Now, According to the question:

We have the given data is :

A cylindrical bucket that is 30 inches tall

A cylindrical 11,400 cubic inches of water.

We have to find the radius of bucket's.

Height (h) = 30 inches tall

Volume of cylinder is 11,400

We know that the:

Volume of cylinder is = [tex]\pi r^2h[/tex]

Plug all the values in the formula.

[tex]\pi =3.14[/tex]

11,400 = 3.14[tex](r)^2[/tex]× 30

11,400 = 94.2[tex](r)^2[/tex]

[tex](r)^2[/tex] = 11400/94.2

r = [tex]\sqrt{121.00}[/tex]

r = 11

Hence, The radius of the cylindrical bucket is 11 inches.

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The probability of a house valued less than $ 500, 000 is =  0.34 + .37 = 0.71

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Basic Probability Properties are :

The probability of a house valued less than $ 500, 000 is

(P < $500,000) = P(X<$250,000) + P($250,000 <x <$500,000)

                          =  0.34 + .37 = 0.71

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In a coordinate plane, a vertical line is an upward and downward straight line perpendicular to the y-axis. Like the x-axis, the horizontal line travels straight, left, and right.

A line that runs horizontally is one that does so from left to right. You are viewing the dawn across a horizontal line when you stare at it beyond the horizon. An illustration of a horizontal line is the x-axis.

A line that runs up and down is called a vertical line. The legs of a table are vertical lines, like in the example to the right. An illustration of a perpendicular line is the y-axis.

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Answer:

0-a/c-0 = -a/c

Step-by-step explanation:

A go-fuel kart's and maintenance costs are calculated as follows: c=10x+1200, where x is the number of rides. $40 is the cost per ride. it takes x = 40 to break even.

The cost function given here is

c(x) = 10x + 1200

Where x = number of rides

c(x) is the total cost including the fixed cost.

Also it is given that each ride costs $40

So Revenue function for x number of rides shall be

R(X) = 40x

For break even

the cost must be equal to the revenue

Hence

R(x) = C(x)

40x = 10x + 1200

Subtracting 10x from both sides we get

30x = 1200

Dividing by 30 on both sides

We get

x = 40

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The cost of admission to the fair  (A)  $18 (B)  2.50x +18  (C)   Coefficient of x-term represents the cost for each ride ticket and constant term represents the cost of admission to the fair.

Note that the county fair charges $2.50 per ticket for the rides and Henry bought 15 tickets for the rides.

So, the total cost of the 15 tickets will be:  (2.5* 15)r = $37.50

He spent total $55.50 on ride tickets and fair admission.

So, the cost of admission to the fair will be:  

(B) If x represents the number of ride tickets and  represents the total cost, then the cost for  number of ride tickets is 2.50x +18

So, the linear equation that can be used to determine the cost for anyone who pays for ride tickets and fair admission will be:  

(C) In the above linear equation, coefficient of x-term is 2.50, which represents the cost for each ride ticket.

And the constant term is 18, which represents the cost of admission to the fair.

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complete question

The county fair charges $2.50 per ticket for the rides. Henry bought 15 tickets for the rides and spent a total of $55.50 at the fair. Henry spent his money only on ride tickets and far admission. The price of the fair admission is the same for everyone. Use x to represent the number of tide tickets and y to represent the total cost.

(A) Find the cost of admission to the fair. Explain how you found the cost of admission.

(B) Write a linear equation that can be used to determine the cost for anyone who pays for ride tickets and fair admission.

(C) Explain what the coefficient on x and the constant of your linear equation represent.

The ratio of the central angle measure to the circumference of a circle is called the "arc measure" and it is given by the formula:

arc measure = central angle measure / circumference

For a given central angle measure in degrees, the formula will be:

arc measure = (central angle measure in degrees) / 360

It's worth noting that this ratio is equal to the fraction of the circumference that the arc of the central angle measures.

For example, if the central angle measure is 90 degrees, the arc measure will be 90/360 = 1/4, meaning that the arc that is formed by the central angle measure is 1/4 of the circle's circumference.

It's also important to note that this ratio is also equal to the fraction of the total area of the circle that the sector formed by the central angle measures.

It's also worth noting that this ratio is always less than 1, since the central angle can't be greater than 360 degrees.

Therefore, The ratio of the central angle measure to the circumference of a circle is called the "arc measure" and it is given by the formula: arc measure = central angle measure / circumference

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Answer: a = 1, b = -11, and c = -42.

Step-by-step explanation:

The solutions to the equation x² - 11x - 42 = 0 are x = -6 and x = 7.

You can find the solutions by factoring the equation, or by using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.

In this case, a = 1, b = -11, and c = -42.

Orthocenter: Solve system of 3 eqs. using 3 altitudes' equation & vertices' coordinates.

What is coordinate ?

Coordinate is a value or set of values that identify the position of a point in a certain space. Represented by ordered pair or triple of numbers (x,y) or (x,y,z) respectively.

The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. To find the orthocenter of a triangle with coordinates, you can use the following steps:

1) Find the equation of the three altitudes of the triangle. To do this, you will need the coordinates of the three vertices of the triangle, as well as the slope of the line perpendicular to the side opposite each vertex.

2) Once you have the equations of the three altitudes, you can use them to find the coordinates of the orthocenter. To do this, you will need to solve a system of three equations with three variables (the x and y coordinates of the orthocenter, and the y-intercept of the altitude).

3) Once you have the coordinates of the orthocenter, you can use them to check your work by verifying that the point is indeed on each of the three altitudes.

Orthocenter: Solve system of 3 eqs. using 3 altitudes' equation & vertices' coordinates.

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Answer:

x³ - x² - 6x + 60

Step-by-step explanation:

you can write the polinom in this form: (x+2) × (x-3) × (x-10)

(x+2 = 0 => x = -2) same for other two zeros

(x² -3x +2x -6) × (x - 10) =

(x³ - 10x - 3x² + 30x + 2x² - 20x - 6x + 60) =

x³ - x² - 6x + 60

Answer: (-8.5, 0), (0, 34), and (2, 42)

Answer:

Step-by-step explanation:

That equals 4/6 which is 2/3. Hope that was helpful!!!

Given the above image, the estimated scale factor used in the dilation are given as follows:

Dilation A -  3/4

Dilation B - 1/4

Dilation C - 1/2

The scale factor is a metric for figures with similar appearances but differing scales or measurements. Assume two circles appear identical but have different radii. The scale factor specifies how much larger or smaller a figure is than the original figure.

When the new and original dimensions are specified, the scaling factor may be determined. The fundamental formula for determining a figure's scale factor is: Scale factor = Dimension of the new shape ÷ Dimension of the old shape.

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If the seed sprouted and grew [tex]\frac{2}{3}[/tex] foot in 3 months , then the growth rate of the plant is   [tex]\frac{2}{9}[/tex] foot per month .

the time in which the seed sprouted and grew  [tex]\frac{2}{3}[/tex]  feet = 3 months ,

to find the growth rate of the plant , we have to divide the length of plant grown by the time required for the growth .

that means , Growth Rate = [tex]\frac{\frac{2}{3} }{3}[/tex] ;

simplifying , we can write the fraction as : [tex]\frac{2}{9}[/tex] ;

So , the growth rate of the plant is [tex]\frac{2}{9}[/tex] foot per month , that means that there will be a [tex]\frac{2}{9}[/tex] foot increase in the length of the plant .

The given question is incomplete , the complete question is

A seed sprouted and grew 2/3 of a foot in 3 months. What was its rate of growth ?

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The slopes for the given pairs are:

If a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by:

a = (y₂ - y₁)/(x₂ - x₁)

Using the first pair of points (9, 10) and (7, 2) the slope is:

s = (2 - 10)/(9 - 7)

s = -8/2 = -4

For the second pair:

(5, -6) and (2, 3)

Here the slope is:

s = (3 + 6)/(2 - 5)

s = 9/3 = -3

The last pair of points is (4,7) and (6, 2) the slope is:

s = (2 - 7)/(6 - 4)

s = -5/2

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Answer: n=6, m=12

Step-by-step explanation:

Since the triangle is a 30-60-90 triangle, the ratio of its sides is [tex]2 : \sqrt{3} : 1[/tex].

Since one side is 6[tex]\sqrt{3}[/tex], n is 6 and m is 12, according to the ratio.

We can solve this using sin/cos/tan, too.

Answer:

D

Step-by-step explanation:

given 2 sides of a triangle then the third side SU is in the interval

difference of 2 known sides < SU < sum of 2 known sides , that is

52 - 39 < SU < 52 + 39

13 < SU < 91

To multiply two numbers, use the multiplication operator (*) between them. The product is the answer you get when you multiply the two numbers. For example, if you wanted to multiply 3 and 5, you would write 3 * 5 and the product would be 15.

1. Choose the two numbers to be multiplied.

2. Place the multiplication operator (*) between the two numbers.

3. Calculate the product of the two numbers.

4. The product is the answer you get when you multiply the two numbers.

To multiply two numbers, use the multiplication operator (*) between them. The product is the answer you get when you multiply the two numbers. For example, if you wanted to multiply 3 and 5, you would write 3 * 5 and the product would be 15.

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The scale factor showing the view of the original building as a dilation of the toy is 0.00111.

The scale factor is a smaller or bigger representation of an object or shape.

The scale factor shows the ratio of the bigger or smaller scale to the original scale.

The scale factor shows the dilation of the toy when the new scale is reduced.  It can also show the larger transformation of the toy when the original scale is increased by the scale factor.

The area of the scale model of the front side of the toy building = 1 ft²

The area of the front side of the original building = 900 ft²

The scale factor = 0.00111 (1 ft²/900 ft²)

Thus, we can conclude that the toy train's scale model is dilated by a scale factor of 0.00111.

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The probability that you select a greater proportion of orange peanut M&M's than of orange M&M's milk chocolate candies is 0.7881

We have to use the available data to solve this problem

We have The probability 1 = P1 = 20%

= 0.20

We have the probability 2 = p2 = 23%

= 0.23

The difference between p1 - p2

0.20 - 0.23

= - 0.03

n1 = 240

n2 = 240

[tex]\sqrt{\frac{p1 (1-p1)}{n1} +\frac{p2(1-p2)}{n2} } \\\\\sqrt{\frac{0.20 (1-0.20)}{240} +\frac{0.23(1-0.23)}{240} }[/tex]

= 0.0375

Then Z value = -0.03 / 0.0375

= -0.80

We have to find the p value

The p value = 1 - p(z ≤ -0.80)

= 1 - 2119

= 0.7881

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The equation of the line that has an undefined slope and passes through the point (4, 7) is y = 4.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know if a line has an undefined slope it is parallel to the y-axis and passes through the point (4, 7).

As it is parallel to the y-axis x-coordinate point remains the same.

So, The equation of the line must be, y = 4.

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The rate of change of a horizontal line is zero, this is because it does not rise vertically (i.e. y1 − y2 = 0).

A rate of change of a horizontal line is the same as its slope, which is the change in y over the change in x, or rise over run.

For the horizontal line that is shown in the graph below, the rate of change for this line is 0, and this can be confirmed by utilizing the slope calculation method.

This makes sense because the change in y of the line is zero, which means it it does not rise vertically (i.e. y1 − y2 = 0).

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Nico, Raj and Sandra are correct.

And the explanation is given.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

An equation,

2/5(5 +x) = 8.

Nico, Aditi, Erick, Raj, and Sandra are solving the equation.

Approach 1:

Multiply by 5/2.

(5/2)(2/5)(5 +x) = 8(5/2)

5 + x = 20

x = 15.

Approach 2:

Multiply by 1/2 both sides

(1/2)(2/5)(5 +x) = 8(1/2)

5 + x = 4(5)

x = 15.

Approach 3:

Simplifying,

2 + 2/5x = 8

2x/5 = 6

x = 30/2

x = 15.

Therefore, Nico, Raj and Sandra are correct.

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The ratio comparing the 6 bowls to all the dishes will be 6 over 26. The correct option is B.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that Jaidon counted dishes in the kitchen cabinet. The table shows what was found. Plates 8 Bowls 6 Cups 12.

The ratio will be calculated as,

Ratio = 6 / ( 6 + 12 + 8 )

Ratio = 6 / 26

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On solving the provided question, we can say that from graph we have a equation ,[tex]y = 4x^2[/tex]  because it's a parabola

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here,

On solving the provided graph

we have a equation , [tex]y = 4x^2[/tex]

because it's a parabola

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Expressing 1.9 as a quotient of integers is 19/10.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. It is not a fraction, a decimal, or a percentage. A number such as 7, -11, or 0 is an integer. Integers are used in everyday life and are also used in computer programming.

This is equivalent to 1 9/10 which is a fraction. To write it as a quotient of integers, 19 is the numerator and 10 is the denominator. This means that if you take 19 parts of a whole and divide it into 10 equal parts, each part will be equal to 1.9.

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Answer:

y = 5/2 x - 13

Step-by-step explanation:

A line perpendicular to y=-2/5x-1 has a slope equal to the negative reciprocal of -2/5. The slope of the line passing through (2,-8) can be calculated as follows:

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

The equation of the line in point-slope form is:

y - (-8) = (5/2)(x - 2)

Expanding the equation gives:

y + 8 = 5/2 x - 5

Solving for y:

y = 5/2 x - 5 - 8

y = 5/2 x - 13

The equation of the line is:

y = 5/2 x - 13

The statement explaining why Chris will incorrectly determine the cost of taking the taxi cab to the airport is D. Chris should have multiplied 2.4 by d as shown by the equation c=(2.4d).

An equation is a mathematical statement proving two or more mathematical expressions to be equivalent or equal.

Equations use the symbol (=) to depict the equality of the expressions.

The equation to show the total cost of hiring a tax cab should multiply the distance (miles) by the unit rate.

The tax cab charge (rate) per mile = $2.40

The cost function or equation is C = distance x $2.40

= 2.40d

Thus, the correct cost equation is Option D.

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Number of miles in 8,400 feet are 1.6 miles.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, there are 5,280 feet in 1 mile.

Let the number of miles in 8,400 feet be x.

So, 5280/1 = 8400/x

5280x=8400

x= 8400/5280

x= 1.6 miles

Therefore, number of miles in 8,400 feet are 1.6 miles.

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