Lisa and Bart spin this spinner 60 times the result are below/ black=17 blue=15 orange=21 purple=7 a. What is the experimental probability of a spin of orange? B which color had an experimental probability that matched its theoretical probability

Answer:  The x-intercept and y-intercept of the given line are (3.6, 0) and (0, -1.2) respectively.  

Step-by-step explanation:  We are given to find the x-intercepts and y-intercepts of the line described by the following equation :

[tex]3x-9y=10.8~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the x-intercept of a line is the point where the y co-ordinate is 0. Similarly, y-intercept is the point where the x co-ordinate is 0.

Substituting y = 0 in equation (i), we get

[tex]3x-9\times0=10.8\\\\\Rightarrow 3x-0=10.8\\\\\Rightarrow 3x=10.8\\\\\Rightarrow x=\dfrac{10.8}{3}\\\\\Rightarrow x=3.6.[/tex]

So, x-intercept is (3.6, 0).

And substituting x = 0 in equation (i), we get

[tex]3\times 0-9y=10.8\\\\\Rightarrow 0-9y=10.8\\\\\Rightarrow 9y=-10.8\\\\\Rightarrow y=-\dfrac{10.8}{9}\\\\\Rightarrow y=-1.2.[/tex]

So, y-intercept is (0, -1.2).

Thus, the x-intercept and y-intercept of the given line are (3.6, 0) and (0, -1.2) respectively.  

Answer:

[tex]r=\frac{25-bh}{h}[/tex]

Step-by-step explanation:

Given : Consider the following equation, [tex]bh+hr=25[/tex]

To find : Solving for r ?

Solution :

The equation is [tex]bh+hr=25[/tex] solve for r,

Subtract 'bh' both side,

[tex]bh+hr-bh=25-bh[/tex]

[tex]hr=25-bh[/tex]

Divide both side by 'h',

[tex]\frac{hr}{h}=\frac{25-bh}{h}[/tex]

[tex]r=\frac{25-bh}{h}[/tex]

Therefore, [tex]r=\frac{25-bh}{h}[/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. An equivalent expression for 1.5(3x+4)+0.25(6x+8) is 7x+8.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified as,

1.5(3x + 4) + 0.25(6x + 8)

= 4.5x + 6 + 2.5x + 2

= 7x + 8

Hence, an equivalent expression for 1.5(3x+4)+0.25(6x+8) is 7x+8.

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Option (b) 4(3-x)+6x=3x+12+2x is the equation that has the solution x = all real numbers because it simplifies to an identity, which is true for any value of x.

Among the given equations, the one that has the solution x = all real numbers is essentially an identity, meaning that for any value of x you plug into the equation, the equation will hold true. To determine which equation is an identity, each equation must be simplified.

Let's take option (b) as an example:

4(3−x)+6x=3x+12+2x

4∙3 - 4∙x + 6∙x = 3∙x + 12 + 2∙x

12 - 4∙x + 6∙x = 3∙x + 12 + 2∙x

12 + 2∙x = 5∙x + 12

12 - 12 + 2∙x - 2∙x = 5∙x - 2∙x + 12 - 12

0 = 3∙x - 3∙x

After simplifying, we end up with 0 = 0, which is an identity and is true for all values of x, hence this is the equation where x is all real numbers.

Answer:

Step-by-step explanation:dhdjdbfbd

The total number of sides in a polygon with n vertices is = n sides.

We have a Polygon with n vertices.

We have to determine the number of sides of this polygon.

In geometry, a polygon can be defined as a  plane, two-dimensional closed shape bounded with straight sides.

According to the question, we have -

A polygon with n vertices.

The total number of sides in a polygon with n vertices is = n sides.

The sides of the polygon are connected end to end in a cyclic order. The side with endpoints as nth and (n - 1)th vertices is connected to the side with endpoints as (n - 1)th and (n - 2)th vertices and so on.

Hence, the total number of sides in a polygon with n vertices is = n sides.

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The function that best represents the graph of the function which is given is:

               [tex]f(x)=(x-3)^2+1[/tex]

From the graph that is provided to us we observe that the graph passes through the point (3,1).

Hence, we will check which of the following function satisfies this point.

a)

[tex]f(x)=(x-3)^3-1[/tex]

when x=3 we see that:

[tex]f(x)=(3-3)^3-1\\\\i.e.\\\\f(x)=-1\neq 1[/tex]

Hence, option: a is incorrect.

c)

[tex]f(x)=(x+3)^3-1[/tex]

when x=3 we have:

[tex]f(3)=(3+3)^3-1\\\\i.e.\\\\f(3)=9^3-1\\\\i.e.\\\\f(3)=729-1\\\\f(3)=728\neq 1[/tex]

Hence, option: c is incorrect.

d)

[tex]f(x)=(x+3)^3+1[/tex]

when x=3 we have:

[tex]f(3)=(3+3)^3+1\\\\i.e.\\\\f(3)=9^3+1\\\\i.e.\\\\f(3)=729+1\\\\f(3)=730\neq 1[/tex]

Hence, option: d is incorrect.

Now we are left with option: b)

i.e.

b)

[tex]f(x)=(x-3)^2+1[/tex]

Also, when x=3 we have:

[tex]f(3)=(3-3)^2+1\\\\f(3)=0+1\\\\f(3)=1[/tex]

Hence, it passes through the point (3,1)

Also, when we will plot this function we observe that it matches the given graph.

The average rate of change of the function over the interval is 2

Finding the average rate of change

From the question, we have the following parameters that can be used in our computation:

The graph

The interval is given as

From x = -3 to x = 3

The function is a quadratic function

This means that it does not have a constant average rate of change

From the graph

y = -8, when x = -3

y = 4, when x = 3

This means that

f(-3) = -8

f(3) = 4

The average rate is calculated using

Rate = (Change in y values)/(Change in corresponding x values)

So, we have

Rate = (4 + 8)/(3 + 3)

Evaluate

Rate = 2

Hence, the average rate of change is 2

Answer:

abc(a + b + c)

That's your answer!!!

estimate  by rounded to the nearest dollars

2 +1 +5 +2 +3 +9 +1 =  $23

-2

23-2 = 21

 yes the amount is reasonable

Answer: 3+1+5+2+3+9+1-1-1=22

The total on the register is reasonable because if you estimate $21.77 to the nearest dollar you would get $22.00.

Step-by-step explanation:

The time it takes the rock to reach the canyon floor is after 3.99seconds

The intercept is the point where the axis is equal to zero. Give the quadratic equation that represents the height h (in feet) of an object t seconds after it is dropped expressed as:

h = -16t² + 255

The rock reaches the ground when h(t) = 0. Substitute

h = -16t² + 255

h = -16t² + 255 = 0
16t² = 255
t² = 255/16
t² = 15.9375

t = 3.99seconds

Hence the time it takes the rock to reach the canyon floor is after 3.99seconds

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Answer: You could use straight angles as a counterexample for the argument all angles are either right obtuse or acute .

Answer:

c.7 and d.5

Step-by-step explanation:

Given the following equation :

[tex]x^{2}-6x+40=6x+5[/tex]

This equation is equivalent to the following equation :

[tex]x^{2}-6x+40=6x+5[/tex]

[tex]x^{2}-6x+40-6x-5=0[/tex]

[tex]x^{2}-12x+35=0[/tex]

Given an equation [tex]ax^{2}+bx+c=0[/tex] we can find the solutions using the quadratic equation (x1 and x2 are the solutions) :

[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]

Using this equations :

[tex]x^{2}-12x+35=0[/tex]

[tex]a=1\\b=-12\\c=35[/tex] ⇒

[tex]x1=\frac{-(-12)+\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=7[/tex]

[tex]x2=\frac{-(-12)-\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=5[/tex]

Given the two solutions x1 and x2 we can write the equation :

[tex]ax^{2}+bx+c=0[/tex] ⇒ [tex]a.(x-x1).(x-x2)=0[/tex] ⇒

[tex]x^{2}-12x+35=0[/tex] is equivalent to

[tex](x-7).(x-5)=0[/tex]

The solutions for this equation are 7 and 5.

Therefore, c.7 and d.5 are the solutions for this exercise.

Answer:

False

Step-by-step explanation:

If f(x) is a function , then for each value of x  there should be  a single y values

For input 0 there is a output 0

for input 10, the output is 2

for input 15, output is 3

For input 5, we have two output 1 and 3

for single input 5, the function cannot have two outputs 1  and 3

So this f(x) is not a function

The principle being demonstrated is known as the Symmetric Property, which holds that if an equation or statement is valid, then its switched or flipped version will also be true.

The question refers to a fundamental property in mathematics called the Symmetric Property. The Symmetric Property states that if an equation or statement is true, then its mirror or flipped version will also hold true. In this case, if LM = JK, then under Symmetric Property, it must be true that JK = LM.

For instance: If 5 = 2 + 3, then 2 + 3 = 5.

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Answer:

The measure of length of equal side is 36 cm each.

B is correct.

Step-by-step explanation:

Isosceles triangle ABC has a perimeter of 96 centimeters.

The base of the triangle is BC and measures 24 cm

We need to find the length of equal side of triangle.

AB=AC

The perimeter of triangle is 96 cm

AB + AC + BC = 96

AB + AB + 24 = 96                          ( ∵ AB=AC)

              2AB = 96-24

              2AB = 72

                AB = 36

Hence, The measure of length of equal side is 36 cm each.

Answer-

Area of the kite is 14.0 sq.units

Solution-

[tex]\text{Area}_{WXYZ}=\text{Area}_{WXY}+\text{Area}_{WZY}[/tex]

From the graph, in the triangle WXY

Base = WY=4 units,

Height = 3 units

[tex]\text{Area}_{WXY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 3=6\ sq.unit[/tex]

From the graph, in the triangle WZY

Base = WY=4 units,

Height = 4 units

[tex]\text{Area}_{WZY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 4=8\ sq.unit[/tex]

[tex]\therefore \text{Area}_{WXYZ}=6+8=14\ sq.units[/tex]

The correlation coefficient r=0.23 will remain unchanged at 0.23 even after adding a constant to all x-variable values, doubling the y-variable values, and swapping the x and y variables, because the correlation coefficient is unaffected by such transformations.

The correlation between two variables is denoted by the symbol, r, and it measures the strength and direction of a linear relationship between two quantitative variables. When we add a constant to all values of the x-variable or multiply all values of the y-variable by a constant, the correlation coefficient does not change. However, interchanging the x and y variables also does not change the value of r since correlation is symmetrical. Therefore, if r=0.23 initially, after adding 0.14 to all values of x, doubling the y-variable values, and interchanging the two variables, the new correlation will still be 0.23.

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Cost for 5 weeks i.e. 15 classes = $108

Cost of per class is given by

[tex]\frac{108}{15}=7.2[/tex]

Cost for 8 weeks i.e. 24 classes = $125

Cost of per class is given by

[tex]\frac{125}{24}=5.21[/tex]

Amount of saving of per class by taking the 8 week class is given by

[tex]7.2-5.21=\$1.99[/tex]

Hence, Option 'C' is correct.

We can calculate for the slope of the line using the formula:

m = (y2 – y1) / (x2 – x1)

From the given values:

m = (4,000 – 10,000) ft / (15 – 0) min

m = -400 ft/min

This means that the altitude is decreasing by 400 ft per minute.

> The slope is –400 . This means that the helicopter descends 400 ft each minute.