Write as an algebraic expression and then simplify if possible The distance traveled by a train in three hours with a constant speed of r miles per hour.

[tex]|\Omega|=9[/tex]

b)

[tex]|A|=2\\\\P(A)=\dfrac{2}{9}\approx22\%[/tex]

c)

[tex]|A|=3\\\\P(A)=\dfrac{3}{9}=\dfrac{1}{3}\approx33\%[/tex]

a) The possibility space is completed with the potential outcomes of spinning both spinner A and spinner B.

b) The probability of getting a negative score is 2/9.

c) The probability of scoring more than 3 is also 2/9.

a) **Possibility Space:**

```

                            Spinner A

                             2         4         6

Spinner B    3       1          -1        -3

                       6       4          0         -2

                       9       7          3          1

```

In the possibility space, each cell represents the outcome of spinning both spinner A and spinner B. The score is obtained by subtracting the number on spinner A from the number on spinner B.

b) **Probability of Getting a Negative Score:**

To calculate the probability of getting a negative score, count the number of occurrences where the result is negative and divide it by the total number of possible outcomes. In this case, there are two instances (-1 and -2) where the score is negative. The total number of outcomes is 9.

Probability of negative score = Number of negative outcomes / Total number of outcomes

Probability of negative score = 2 / 9

c) **Probability of Scoring More Than 3:**

To find the probability of scoring more than 3, count the number of occurrences where the result is greater than 3 and divide it by the total number of possible outcomes. In this case, there are two instances (4 and 7) where the score is more than 3.

Probability of scoring more than 3 = Number of outcomes > 3 / Total number of outcomes

Probability of scoring more than 3 = 2 / 9

Answer:

The function f(x) intercepts the x-axis at (0,0), thus it touches the x-axis once.The graph of the function g(x) does not intercept the x-axis at all.

Step-by-step explanation:

In this question you first form the table for values of x with corresponding values of f(x) that you will use to graph the function f(x)=x².Then do the same for the function g(x)=x²+2.Take a point from the parent function f(x) and compare it with its image in the function g(x) to identify the transformation that occurred.Graph the two equations to visually see the x-intercepts in both equations.

In the parent function f(x)=x² form a table as shown below;

x                      f(x)=x²          coordinate to plot

-3                     -3²=9                (-3,9)

-2                      -2²=4                (-2,4)

-1                        -1²=1                 (-1,1)

0                         0²=0               (0,0)

1                           1²=1                 (1,1)

2                          2²=4               (2,4)

3                           3²=9               (3,9)

Use the coordinates to plot the graph of f(x)=x² on a graph tool and see the number of x-intercept values

In the function g(x)=x²+2 also form your table for values of g(x) with corresponding values of x

x                              g(x)=x²+2                                          coordinate to plot

-3                          -3²+2=9+2=11                                          (-3,11)

-2                          -2²+2=4+2=6                                          (-2,6)

-1                           -1²+2=1+2=3                                             (-1,3)

0                            0²+2=2                                                    (0,2)

1                             1²+2=1+2=3                                              (1,3)

2                            2²+2=4+2=6                                             (2,6)

3                            3²+2=9+2=11                                             (3,11)

Use the coordinates to plot the graph of g(x)=x²+2  on a graph tool to determine the number of x intercept values

You can determine the transformation that occurred too, how?

Take a point on the parent function f(x) and compare it with its image in the function g(x)

Let take point (-3,9) and compare it to (-3,11).You notice x coordinate did not change but the y coordinate shifted 2 units upwards along the y-axis.To determine this dilation you subtract the coordinates of object point from that of image point.

[tex]=(\frac{0-0}{11-9}) =(\frac{0}{2} )=(0,2)[/tex]

The dilation was (0,2)

Solution

From the graphs, the function f(x), intercepts the x-axis at (0,0), thus it touches the x-axis once.The graph of the function g(x) does not intercept the x-axis at all.

Answer:

68°

Step-by-step explanation:

To find the angles represented by the percentages , you should have in mind that the total sum of all angles in the pie-chart equals 360°

The percentages given are;

The total percentages for the items

[tex]=34+8+11+12+15+20=100[/tex]

To get the angles represented by each percentage

Angle x=item/100 ×360°

Where x is the angle of an item in the circle graph

Calculating angles for carrot and potatoes

[tex]C=\frac{11}{100} *360=39.6\\\\\\P=\frac{8}{100} *360=28.8\\\\\\P+C=39.6+28.8=68.4[/tex]

The combined angle will be 68.4°

Answer:

Possible values of dimensions are (24,16,2) or (24,8,4)

Step-by-step explanation:

We are given the volume of the Cuboid and length . We are required to find the possible values of width and height from this information.

Let us say that the width is x and height is y

Length = 24

Volume of a cuboid = length * width * height

Volume = 768

768=24*x*y

[tex]xy=\frac{768}{24}\\xy=32\\[/tex]

xy=32

Now the possible factors of 32

32=1*32 ( Which shall not be taken into consideration as length is already given as 24 and width or height can  not be more length)

32=2*16

32=4*8

Hence the possible values width are 8, 16 and that of height 4 and 2

Hence the possible values of dimensions are (24,16,2) or (24,8,4)

Answer:

Step-by-step explanation:

The answer is TS ≅ HG. C

Answer:

The correct option is TS ≅ HG. As, The side TS is ≅ to side HG.

Step-by-step explanation:

Given information;

The triangle GHJ is rotated about a point x.

Which results in formation of another triangle STR.

Now, according to the given information if any triangle is rotated 90 degree about a point the two side will be ≅ to each other.

Hence, The side TS is ≅ to side HG.

Hence, option (c) is correct.

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Answer:

The resulting vector b - a is <-5 , 7>

The resulting vector 2a - b is <8 , -9>

Step-by-step explanation:

* Use the graph to solve the problem

- The vector a is <3 , -2>

- The vector b is <-2 , 5>

* We can add and subtract the vectors

∵ a = <3 , -2>

∵ b = <-2 , 5>

- To find b - a subtract a from b

∴ b - a = <-2 , 5> - <3 , -2> = <(-2 - 3) , (5 - -2)> = <(-5) , (7)>

∴ The resulting vector b - a is <-5 , 7>

* 2a means multiply vector a by 2

∵ a = <3 , -2>

∴ 2a = <(2 × 3) , (2 × -2) = <6 , -4>

* Now lets find the resulting vector 2a - b

- Subtract b from 2a

∵ 2a = <6 , -4>

∵ b = <-2 , 5>

∴ 2a - b = <6 , -4> - <-2 , 5> = <(6 - -2) , (-4 - 5> = <(8) , (-9)> = <8 , -9>

∴ The resulting vector 2a - b is <8 , -9>

Answer:

[tex]\frac{124}{175}[/tex] vials

Step-by-step explanation:

You have [tex]4\frac{3}{7}[/tex] = [tex]\frac{31}{7}[/tex] grams of a substance.

You want to divide it into vials of [tex]6\frac{1}{4}[/tex] = [tex]\frac{25}{4}[/tex] grams each.

Number of vials you can fill is:  [tex]\frac{31}{7}[/tex] ÷ [tex]\frac{25}{4}[/tex] = [tex]\frac{31}{7}[/tex] × [tex]\frac{4}{25}[/tex] = [tex]\frac{124}{175}[/tex] vials

the equation of the trend line is y = -7x + 4.

To find the equation of the trend line using two points, we need to determine the slope (m) and the y-intercept (b) of the line. The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points.

For the points (-4, 32) and (7, -45), the slope would be:

m = (-45 - 32) / (7 - (-4))

m = (-77) / (11)

m = -7

Now, we use the slope and one point to find the y-intercept using the point-slope form of the equation of a line, y - y1 = m(x - x1), and then we convert it to the slope-intercept form, y = mx + b.

Using point (-4, 32), the equation becomes:

32 = -7(-4) + b

32 = 28 + b

b = 32 - 28

b = 4

So, the equation of the trend line is y = -7x + 4.

Answer: D is correct dotted and shaded below

Step-by-step explanation:

It’s a dotted line because the symbol is < or >

Everything below the line will be shaded because it’s y<, if it were y> then everything would be shaded above

Answer:

A shaded region below a dashed boundary line

Step-by-step explanation:

Conveniently it has been established, that in inequalities graph dashed lines indicate that all the points ∈ line expressed by y< -1/2x+5 part of the inequality are not included. So we represent by shaded regions below dashed lines.

If this inequality was then expressed by y<= -1/2x +5 then a solid line would then represent.

Check it out below

Answer:

[tex]\large\boxed{V=\dfrac{4}{3}\pi R^3=\dfrac{D^3}{6}\pi}\\\\\boxed{V=\dfrac{500\pi}{3}\ in^3\approx523.33\ in^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{A diameter}\ D=2R\Rightarrow R=\dfrac{D}{2}.\\\\\text{Therefore}\\\\V=\dfrac{4}{3}\pi\left(\dfrac{D}{2}\right)^3=\dfrac{4}{3}\pi\left(\dfrac{D^3}{8}\right)=\dfrac{D^3}{6}\pi[/tex]

[tex]\text{We have the dimater}\ D=10in.\ \text{Substitute:}\\\\V=\dfrac{10^3}{6}\pi=\dfrac{1000}{6}\pi=\dfrac{500\pi}{3}\ in^3[/tex]

For this case we have that by definition, the volume of a sphere is given by:

[tex]V = \frac {4} {3} \pi * r ^ 3[/tex]

Where:

r: It is the radius of the sphere

We are told as data that the diameter of the sphere is 10in, so the radius is 5in:

[tex]V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi\\V = 523.33in ^ 3[/tex]

Answer:

[tex]V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi[/tex]

Any of the three given expressions can be used to find the volume of the sphere.

Find the ratio of the known sides 10 and 12

12/10 = 1.2

The larger kite is 1.2 times the size of the smaller kite.

Multiply 7 by 1.2:

x - 7 * 1.2

x = 8.4

Answer:

[tex]y=-0.10x+60[/tex]

Step-by-step explanation:

Let

y -----> gallons of water remaining in the barrel

x-----> number of minutes elapsed

we know that

Water leaks out of the barrel at a rate of 1 gallon every 10 minutes

so

[tex]1/10=0.10\frac{gal}{min}[/tex]

The linear equation that represent this situation is  

[tex]y=-0.10x+60[/tex]

The graph in the attached figure

Answer:

Option A y-3=2(x-1)

Step-by-step explanation:

we know that

The equation of a line into point slope form is equal to

y-y1=m(x-x1)

In this problem we have

(x1,y1)=(1,3)

m=2

substitute

y-3=2(x-1)

For this case we must simplify the following expression:

[tex]\frac {\frac {4t ^ 2-16} {8}} {\frac {t-2} {6}} =[/tex]

Applying double C we have:

[tex]\frac {6 (4t ^ 2-16)} {8 (t-2)} =[/tex]

Simplifying:

[tex]\frac {3 (4t ^ 2-16)} {4 (t-2)} =[/tex]

We take common factor 4 from the parentheses of the numerator:

[tex]\frac {3 * 4 (t ^ 2-4)} {4 (t-2)} =[/tex]

We simplify:

[tex]\frac {3 (t ^ 2-4)} {(t-2)} =[/tex]

We factor the numerator:

[tex]t ^ 2-4 = (t + 2) (t-2)[/tex]

We rewrite the expression:

[tex]\frac {3 (t + 2) (t-2)} {(t-2)} =[/tex]

We simplify:

[tex]3 (t + 2) =\\3t + 6[/tex]

Answer:

[tex]3t + 6[/tex]

Answer:

Option C.

[tex]x=2\sqrt{2}[/tex]

[tex]y=2\sqrt{6}[/tex]

Step-by-step explanation:

step 1

Find the value of x

In the right triangle of the figure

[tex]sin(30\°)=\frac{x}{4\sqrt{2}}[/tex] -----> opposite side angle of 30 degrees divided by the hypotenuse

Remember that

[tex]sin(30\°)=\frac{1}{2}[/tex]

so

[tex]\frac{1}{2}=\frac{x}{4\sqrt{2}}[/tex]

[tex]x=\frac{4\sqrt{2}}{2}[/tex]

[tex]x=2\sqrt{2}[/tex]

step 2

Find the value of y

In the right triangle of the figure

[tex]cos(30\°)=\frac{y}{4\sqrt{2}}[/tex] -----> adjacent side angle of 30 degrees divided by the hypotenuse

Remember that

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

so

[tex]\frac{\sqrt{3}}{2}=\frac{y}{4\sqrt{2}}[/tex]

[tex]y=\frac{4\sqrt{6}}{2}[/tex]

[tex]y=2\sqrt{6}[/tex]

bearing in mind that the rate of change will just be the slope or namely the derivative of the expression.

[tex]\bf f(x)=3+e^x(x-5)^3\implies \cfrac{df}{dx}=0+\stackrel{\textit{product rule}}{e^x(x-5)^3+\stackrel{\textit{chain rule}}{e^x\cdot 3(x-5)^2\cdot 1}} \\\\\\ \cfrac{df}{dx}=e^x(x-5)^3+3e^x(x-5)^2\implies \cfrac{df}{dx}=\stackrel{\textit{common factor}}{e^x(x-5)^2[(x-5)+3]} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{df}{dx}=e^x(x-5)^2(x-2)~\hfill[/tex]

Answer:

12

Step-by-step explanation:

We are given the following equation and we are to solve for the variable r and find its value:

[tex] - 1 . 5 ( 4 - r ) = - 1 2 [/tex]

Expanding the brackets to get:

[tex]6-1.5r=-12[/tex]

[tex]-1.5r=-12-6[/tex]

[tex] - 1 . 5 r = - 1 8 [/tex]

[tex] r = \frac { - 1 8 } { - 1 . 5 } [/tex]

r = 12

Answer:

-4

Step-by-step explanation:

-1.5 (4 - r) = -12

(4 - r) = [tex]\frac{-12}{-1.5}[/tex]

-r =  [tex]\frac{12}{1.5}[/tex] - 4

r = 4 -  [tex]\frac{12}{1.5}[/tex] = -4

Answer:

Options b and D

Step-by-step explanation:

It's a question of Boolean's algebra

We will find the truth values of each statement p, q, r, and s first.

p : An isosceles triangle has two congruent sides.

Means truth value is True

q ; A right angle measures 90°

Truth value of this statement will be True

r : Four Points are always coplanar.

Truth value of this statement will be False.

s : A decagon has 12 sides

Truth value of the statement will be False.

Now we come to the options.

a. Four points are always coplanar and a right angle measures 90°.

Here "and" means conjunction and truth value of conjuncion of two statements will be true if only both the statements are true.

r        q         r ∧ q

T        T            T

But the truth value is given as false so not the correct option.

b. Four points are always coplanar and a right angle measures 90°.

As we have discussed in option a. truth value of the conjunction is True so this option will be the correct option.

c. Four points are always coplanar or a right angle measures 90°

OR means it's a disjunction and truth value of disjunction is false only when both the statements are False.

r         q        r ∨ q

T        T           T

But the truth value is given as False, so this option is not correct.

d. Four points are always coplanar or a right angle measure 90°

As discussed in option c. Truth value will be True. so this option will be the correct option.

Options b and d are the correct options.  

Answer:

Acute, Equilateral

Step-by-step explanation:

Acute because all angles (which are 60 degrees) are less than 90 degrees.

Equilateral because all sides are equal.

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Answer:

The correct options are

A.  Acute

E. Isosceles

F. Equilateral

Step-by-step explanation:

From the figure we can see a triangle.

To find the correct options

1). From figure we get  all the angles are equal.

Each angle is equal to 60°

60 < 90

Option A. Acute is TRUE

2). Also all the sides of the triangles are equal,

Therefore the given triangle is equilateral triangle.

Option F. Equilateral is TRUE

Every equilateral triangle is Isosceles triangle.

Therefore option D. is also true

Answer:

A=62cm

Step-by-step explanation:

Length : 5 cm

Width: 3 cm

Height: 2 cm

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Answer:

62 cm^2

Step-by-step explanation:

Each two lengths given forms a rectangle. There are two rectangles of each size. Find their areas and add them up.

2(5 cm * 3 cm) + 2(5 cm * 2 cm) + 2(3 cm * 2 cm) =

= 2(15 cm^2) + 2(10 cm^2 + 2(6 cm^2)

= 2(15 cm^2 + 10 cm^2 + 6 cm^2)

= 2(31 cm^2)

= 62 cm^2

Answer:

Step-by-step explanation:

It's the right isosceles triangle.

Right triangle with angles 45°, 45°, 90°. The sides are in ratio 1 : 1 : √2

(look at the picture).

Therefore

x = 7

y = 7√2

Answer:

[tex]\boxed{2n+2}[/tex]

Step-by-step explanation:

You remove parenthesis.

-n-3+3n+5

Group like terms

 ↓

-n+3n-3+5

Add numbers from left to right.

-n+3n=2n

2n-3+5

Adding and subtracting numbers from left to right.

-3+5=2

2n+2 is the correct answer.

Answer:

2n+2

Step-by-step explanation:

-n+(-3)+3n+5

Combine like terms

-n +3n -3+5

2n +2

Answer:

6x - 10 + 10 = 5x - 13

6x = 5x -13

x = -13

Answer:

The correct answer is option C.  -6x³ - 6x

Step-by-step explanation:

It is given an expression,

(4x³ + 3x² - 6x) - ( 10x³ + 3x²)

To find the simplified form

(4x³ + 3x² - 6x) - ( 10x³ + 3x²) = 4x³ + 3x² - 6x - 10x³ - 3x²

 = 4x³ - 10x³ + 3x² - 3x² - 6x

 = -6x³ + 0 - 6x

 = -6x³ - 6x

Therefore the correct answer is option C.  -6x³ - 6x

Answer:  −6x3 − 6x

Step-by-step explanation:

Answer:

Acute

Step-by-step explanation:

Note the definitions:

Obtuse: At least one of the angles are greater than 90°

Equilateral: All angles are congruent & equal to 60°

Acute: All angles are less than 90°

Right: At least one angle is equal to 90°

In this case, the triangle is a D) acute, for it fits the requirement for being an acute... all angles are less than 90°.

~

Hello There!

The triangle shown in the image would be an acute triangle

An acute triangle is a triangle where all three sides are less than 90°

In the image, none of the angles shown are greater than 90° so this

is an example of an acute triangle

For this case we have to:

Let[tex]u = x + 1[/tex]

So:

[tex]u ^ 2-4u + 2 = 0[/tex]

We have the solution will be given by:

[tex]u = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 1\\b = -4\\c = 2[/tex]

Substituting:

[tex]u = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (1) (2)}} {2 (1)}\\u = \frac {4 \pm \sqrt {16-8}} {2}\\u = \frac {4 \pm \sqrt {8}} {2}\\u = \frac {4 \pm \sqrt {2 ^ 2 * 2}} {2}\\u = \frac {4 \pm2 \sqrt {2}} {2}[/tex]

The solutions are:

[tex]u_ {1} = \frac {4 + 2 \sqrt {2}} {2} = 2 + \sqrt {2}\\u_ {2} = \frac {4-2 \sqrt {2}} {2} = 2- \sqrt {2}[/tex]

Returning the change:

[tex]2+ \sqrt {2} = x_ {1} +1\\x_ {1} = 1 + \sqrt {2}\\2- \sqrt {2} = x_ {2} +1\\x_ {2} = 1- \sqrt {2}[/tex]

Answer:

[tex]x_ {1} = 1 + \sqrt {2}\\x_ {2} = 1- \sqrt {2}[/tex]

Answer: 1st - x = 1 + √2 & 4th- x= 1 - √2

Step-by-step explanation:

Answer:

C. 21

Step-by-step explanation:

g(x) = x² - 4

Give: x = 5

Plug in 5 for x in the equation:

g(5) = 5² - 4

Simplify. Remember to follow PEMDAS. First, solve the exponent, then subtract:

g(5) = (5 * 5) - 4

g(5) = 25 - 4

g(5) = 21

C. 21 is your answer.

~

Answer:

Red

Step-by-step explanation:

P = 30/120 = 1/4

The spinner is divided into 8 equal sections.  1/4 of 8 is 2.  So we're looking for a color that appears on exactly 2 of the sections.

The color is red.

Answer:

It's an acute angled triangle.

Step-by-step explanation:

15^2 = 225

12^2 = 144

10^2 = 100

Adding:

10^2 + 12^2 = 244.

So as 15^2 <  12^2 + 10^2 this is an acute angled triangle.

The triangle with given sides of 10 inch , 12 inch and 15 inch is an acute angled triangle.

The length of three sides of a triangle are given

Length of first  side = 10 inch

Length of second side = 12 inch

Length of third side = 15 inch

here we can observe that the third side is the longest side for the given triangle

Let us check whether the given triangle satisfies the Pythagorean theorem

For a right angled Pythagorean theorem is given by equation (1)

[tex]\rm H^2 = P^2 + B^2 .........(1)\\where \\H = Hypotenuse\\P = Perpendicular\\B = Base\\[/tex]

From the given data we can conclude that

[tex]\rm 15 ^2 = 225 \\10^2 = 100\\12^2 = 144 \\15^2 \neq 10^2 +12^2 \\\\Since\; 225\neq 244[/tex]

The given triangle does not satisfies the Pythagorean theorem and hence it is not a right angled triangle

also [tex]225< 244[/tex]

So we can conclude that it is an acute angled triangle.

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Answer:

x^2-3x+6/x^2-2x

Step-by-step explanation:

Answer:

Step-by-step explanation: