You roll a number cube three consecutive times. What is the probability that you roll an even number the first two times and a 3 the last time?

Answer:

Geometric Sequence.

[tex]a_{n}=(2)^{n-1}[/tex]

Step-by-step explanation:

The x-coordinates represent the number of terms of the sequence while the y-coordinates represent the term of the sequence. So the series shown on the graph is:

1, 2, 4, 8

We can see that the ratio of two consecutive terms of the above sequence is constant. i.e.

2/1 = 2

4/2 = 2

8/4 = 2

Such a sequence in which the ratio of two consecutive terms is a constant is known as Geometric Sequence and this constant ratio is known as common ratio.

The general term of a geometric sequence is represented as:

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

Using the values for the given sequence we get:

[tex]a_{n}=1(2)^{n-1}[/tex]

[tex]a_{n}=(2)^{n-1}[/tex]

Where n represents the number of term.

Answer:

R(p) = -6p^2 + 60p....

Step-by-step explanation:

Revenue, R = quantity sold * price

Price = p

Quantity sold = q = -6p + 60

R(p) = q*p

where q=-6p + 60

= (-6p + 60) * p = -6p^2 + 60p

Answer: R(p) = -6p^2 + 60p....

Final answer:

To find the length of the pole, we can use the Pythagorean theorem.

Explanation:

To find the length of the pole, we can use the Pythagorean theorem. Since the base of the pole is 7 feet away from the wall and the top of the pole reaches 21 feet up the wall, we can envision a right triangle with the pole as the hypotenuse. Using the Pythagorean theorem, we can calculate:

c^2 = a^2 + b^2

Where c is the length of the pole, a is the base length (7 feet), and b is the height reached by the pole (21 feet).

Plugging in the values, we get:

c^2 = 7^2 + 21^2

Solving for c, we find that the length of the pole is √(7^2 + 21^2) feet.

Answer:

Given an exponential function of the form

y = a*(b)^x

The values of b that will result in the desired percentage values are:

Case 1

b = 23% decrease

1 - 0.23 = 0.77

y = a*(0.77)^x

Case 2

b = 8% increase

1 + 0.08 = 1.08

y = a*(1.08)^x

Case 3

b = 15% decrease

1 - 0.15= 0.85

y = a*(0.85)^x

Case 4

b = 120% increase

1 + 1.2 = 2.2

y = a*(2.2)^x

See attached picture for examples

The value of b in an exponential function is calculated as : For a 23% decrease = 0.77, For an 8% increase = 1.08, For a 15% decrease = 0.85, For a 120% increase = 2.20.

The student is trying to determine the corresponding exponential function base value (b) for a given percent rate of change.

In an exponential function y = abx, a positive b models exponential growth, while a value of b less than 1 models exponential decay.

We can convert the percent increase or decrease to a decimal and then add or subtract it from 1 to find the corresponding value of b.

For a 23% decrease, b = 1 - 0.23 = 0.77.

For an 8% increase, b = 1 + 0.08 = 1.08.

For a 15% decrease, b = 1 - 0.15 = 0.85.

For a 120% increase, b = 1 + 1.20 = 2.20.

Answer:

(0,7)

Step-by-step explanation:

This equation you are given is in slope-intercept form, the form y=mx+b.

It is called slope-intercept from because it gives us the slope and the y-intercept.

The slope is m.

The y-intercept is b.

If we compare y=8x+7 to y=mx+b, we should make the conclusion that m=8 and b=7.

This tells the slope is 8 while the y-intercept is 7.

The y-intercept is 7 is sometimes required to be represented by a point.  Since it is the y-intercept, the x is 0 so the point that represents the y-intercept is (0,7).

Answer:

0,7

Step-by-step explanation:

Answer:

look at explanation:

Step-by-step explanation:

1st picture: angle bisector

2nd picture: angle bisector

3rd picture: perpendicular bisector

4th picture: angle bisector

5th picture: perpendicular bisector

6th picture: perpendicular bisector

Answer:

(2,4)

Step-by-step explanation:

We have the system:

y=x+2

y=3x-2.

This is already setup for substitution.

I'm going to replace my first y with what the second y equals.

That is, I'm going to write 3x-2=x+2.

Time to solve the following for x:

3x-2=x+2

Subtract x on both sides:

2x-2= 2

Add 2 on both sides:

2x. = 4

Divide both sides by 2:

x. = 2

Now that we know x=2 and we have an equation that relates x to y: either y=x+2 or y=3x-2, doesn't matter which we use, we can find y.

So we y=x+2 with x=2 which means y=2+2=4.

So the solution, the intersection, is (2,4).

Answer:

(2, 4 )

Step-by-step explanation:

Given the 2 equations

y = x + 2 → (1)

y = 3x - 2 → (2)

Substitute y = 3x - 2 into (1)

3x - 2 = x + 2 ( subtract x from both sides )

2x - 2 = 2 ( add 2 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Substitute x = 2 into (1) for the corresponding value of y

y = x + 2 = 2 + 2 = 4

As a check

Substitute x = 2 into the 2 equations and check validity

(1) → y = 2 + 2 = 4 ← Correct

(2) → y = (3 × 2) - 2 = 6 - 2 = 4 ← Correct

Solution is (2, 4 )

For this case we have that by definition[tex]\pi[/tex] equals 180 degrees.

We must convert 135 degrees to radians, then:

[tex]135 * \frac {\pi} {180} =\\135 * \frac {3.14} {180} =\\\frac {423.9} {180} = 2.355[/tex]

Rounding off we have:

2.4 radians.

Answer:

2.4 radians

Answer:

a.$247

Step-by-step explanation:

39×5=195

195+52=247

Answer:

The answer is $247 (Option A)

Step-by-step explanation:

Pamela will have the car for 5 days.

The cost per renting is variable, and it increases as the days do.

5*$39= $195

And the LDW (Loss Damage Waiver) is an only once cost of $52

You can get the total rental cost by adding both of them:

$195+$52= $247 (Option A)

Answer:

- 24x + 9

Step-by-step explanation:

Differentiate each term using the power rule

[tex]\frac{d}{dx}[/tex] ( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

f(x) = - 12x² + 9x, then

f'(x) = (2 × - 12)x + (9 × 1) [tex]x^{0}[/tex]= - 24x + 9

Step-by-step explanation:

Write a proportion.  3 laps is to 2 km as 5 laps is to x km.

3 / 2 = 5 / x

Cross multiply:

3x = 10

Divide:

x = 10/3

x = 3⅓

Madison will have run 3⅓ kilometers.

y= mx+b ( equation for slope)

y= 4/5x-3

The slope (m)is 4/5

The y- intercept(b) is -3

Answer: slope is 4/5

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case:

m = 4/5

b = -3

This means that 4/5 is the slope of this line.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

A

Step-by-step explanation:

Given

x³ - 4x² - 3 divided by x + 1

Write the coefficients of the polynomial in descending order, including a zero for any terms not included in the polynomial.

In this case a 0 is required to denote the x- term

Division by ( x + h) is evaluated for x = - h, hence

division by x + 1 is evaluated for x = - 1, hence

- 1 | 1  - 4  0  - 3 ← is the required synthetic division → A

Answer:

1

Step-by-step explanation:

(f °g)(3) = f(g(3)) = f(-13) = 1

Answer:

r<280

Step by step explanation:

Subtract 28 from both sides of the equation r+28<308.

r+28 subtracted by 28 leaves us with r<.

308-28 is 280.

Hence the equation becomes r<280.

The expression or inequality is 28 > r < 308 which represents 28 greater than r is less than 308.

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is:

Write the expression for the word expression "28 greater than r is less than 308"

It is given that:

The statement is:

28 greater than r is less than 308:

Here r is the real number.

Inequality can be defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

28 > r < 308

Thus, the expression or inequality is 28 > r < 308 which represents 28 greater than r is less than 308.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ2

Answer:

[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]

Step-by-step explanation:

We are going to find the slope by lining up the points vertically and subtract, then put 2nd difference over first.

Also you could just use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].  It is the same thing.

(  5  ,   5)

-(  1  ,   3)

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

  4      2

So the slope is 2/4 or 1/2 after reducing.

The point-slope form a line is

[tex]y-y_1=m(x-x_1)[/tex] with a point on the line [tex](x_1,y_1)=(1,3)[/tex] given and with slope [tex]m=\frac{1}{2}[/tex] given.

[tex]y-3=\frac{1}{2}(x-1)[/tex]

We are going to solve this for y and simplify what we can because our goal is y=mx+b; this is slope-intercept form.  It is called that because it tells us the slope,m, and the y-intercept,b.

Distribute:

[tex]y-3=\frac{1}{2}x-\frac{1}{2}[/tex]

Add 3 on both sides:

[tex]y=\frac{1}{2}x-\frac{1}{2}+3[/tex]

Simplify:

[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]

Answer:

c) -20x^2+14x+12

all real numbers

Step-by-step explanation:

So (fg)(x)=f(x)g(x)=(-4x-2)(5x-6).

Need find the expression in standard form we need to use foil:

First:  (-4x)(5x)=-20x^2

Outer: (-4x)(-6)=24x

Inner:  (-2)(5x)=-10x

Last:  (-2)(-6)=12

--------------------------Add like terms:

-20x^2+14x+12

Polynomials have domain all real numbers.

There are no restrictions on what x can be.  For every number you plug in, you will get a number back.  

Answer:

c.-20x^2 + 14x + 12; all real numbers

Step-by-step explanation:

f(x) = -4x - 2

g(x) = 5x - 6

Therefore, -20x^2 + 14x + 12; all real numbers.

Answer:

The second choice

Step-by-step explanation:

The histogram shows the following:

3 children are within the ages of 5-10

7 children are within the ages of 11-13

4 children are within the ages of 14-18

So all you need to do is find the set of data that shows that fit the intervals. So find the data that have three values within 5 to 10; seven values with the 11-13; and four values within 14 to 18.

Answer:

-18a⁷b⁷ + 42a²b⁵

Step-by-step explanation:

  (3a⁵b⁶ - 7b⁴)(-6a²b)

= (3a⁵b⁶)(-6a²b) – (7b⁴)(-6a²b)     Distributed the 6a²b term

= -18a⁷b⁷ - (-42a²b⁵)                     Multiplied and added exponents

= -18a⁷b⁷ + 42a²b⁵                       Removed parentheses

Answer: 190°

Step-by-step explanation:

Angle CAE is 1/2 times the measure of arc CBA, therefore:

95° x 2=190°

The  measure of arc CBA =190°

To understand the relationship between angle CAE and arc CBA, we need to delve into the properties of angles and arcs in circles. Here is a step-by-step explanation:

Step 1: Understanding Inscribed Angles

In a circle, an inscribed angle is an angle formed by two chords that intersect on the circle. The measure of an inscribed angle is always half the measure of the intercepted arc.

Step 2: Relationship between Angle CAE and Arc CBA

Given:

- Angle CAE is inscribed in the circle.

- Arc CBA is the intercepted arc for angle CAE.

According to the properties of inscribed angles:

[tex]\[ \text{Measure of Angle CAE} = \frac{1}{2} \times \text{Measure of Arc CBA} \][/tex]

Step 3: Using the Given Information

Let's denote:

[tex]- \( \angle CAE \)[/tex] as the measure of angle CAE.

[tex]- \( \text{Arc CBA} \)[/tex] as the measure of arc CBA.

From the given information, the measure of arc CBA is 95°. Using the inscribed angle property:

[tex]\[ \angle CAE = \frac{1}{2} \times \text{Arc CBA} \][/tex]

[tex]\[ \angle CAE = \frac{1}{2} \times 95^\circ \][/tex]

[tex]\[ \angle CAE = 47.5^\circ \][/tex]

However, if we are interpreting the problem differently and consider that angle CAE is given as 95°, and we need to find the measure of the arc intercepted by this angle when doubled, then we would calculate:

[tex]\[ \text{Arc CBA} = 2 \times \angle CAE \][/tex]

[tex]\[ \text{Arc CBA} = 2 \times 95^\circ \][/tex]

[tex]\[ \text{Arc CBA} = 190^\circ \][/tex]

Therefore, if angle CAE is half the measure of arc CBA, and given the angle CAE as 95°:

[tex]\[ \text{Arc CBA} = 2 \times 95^\circ = 190^\circ \][/tex]

This shows that the measure of arc CBA is 190°.

For this case we must find the roots of the following equation:

[tex]3x ^ 2-4x + 2 = 0[/tex]

We have that the roots will come from:

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

Where:

[tex]a = 3\\b = -4\\c = 2[/tex]

Substituting the values:

[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (3) (2)}} {2 (3)}\\x = \frac {4 \pm \sqrt {16-24}} {6}\\x = \frac {4 \pm \sqrt {-8}} {6}\\x = \frac {4 \pm \sqrt {-1 * 8}} {6}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 2}} {6}\\x = \frac {4 \pm2i \sqrt {2}} {6}\\x = \frac {2 \pmi \sqrt {2}} {3}[/tex]

We have two complex roots:

[tex]x_ {1} = \frac {2 + i \sqrt {2}} {3}\\x_ {2} = \frac {2-i \sqrt {2}} {3}[/tex]

Answer:

[tex]x_ {1} = \frac {2 + i \sqrt {2}} {3}\\x_ {2} = \frac {2-i \sqrt {2}} {3}[/tex]

Step-by-step explanation:

To prove that two sides are parallel on a graph, we must show that their slopes are the same. Plotting this on Desmos, we get the first image attached.  Finding the slopes of each line, we get

[tex]TOP\\\frac{5-3}{6-1} =2/5\\BOTTOM\\\frac{-1-(-1)}{7-2} =2/5\\RIGHT\\-4\\LEFT\\-4[/tex]

As the top slope is the same as the bottom, and the right is the same as the left, this is a parallelogram.

To prove that two sides are congruent, we must find their lengths. The distance formula is

[tex]\sqrt(x_{1}+x_{2})^2+(y_{1}+y_{2})^2 } \\[/tex]

Finding the distances, we get

TOP: [tex]\sqrt{29}[/tex]

BOTTOM: [tex]\sqrt{29}[/tex]

RIGHT:[tex]\sqrt{17}[/tex]

LEFT:[tex]\sqrt{17}[/tex]

As the lengths are the same, the sides are congruent

Answer:

2[tex]w^{3}[/tex]-6[tex]w^{2}[/tex]+4w=240

Step-by-step explanation:

The length and height are given in terms of the width. Width =w; Length =(2w−4); Height =(w−1); and the Volume is equal to the product of the three. Therefore, we can set up the equation as follows:

w×(2w−4)×(w−1)=240

To finish, we distribute and combine like terms:

(2[tex]w^{2}[/tex]−4w)×(w−1)=240

2[tex]w^{3}[/tex]−2[tex]w^{2}[/tex]−4[tex]w^{2}[/tex]+4w=240

2[tex]w^{2}[/tex]−6[tex]w^{2}[/tex]+4w=240

Therefore, 2[tex]w^{3}[/tex]−6[tex]w^{2}[/tex]+4w=240 is our equation for the dimensions of the dumpster in terms of w.

To find the dimensions of the dumpster given its volume and relationships between dimensions, we express the length and height in terms of the width and substitute these into the volume equation to get 240 = (2W - 4)(W)(W - 1).

The student has been given a problem involving the volume of a rectangular prism, representative of a dumpster, which mathematically belongs to the subject of geometry. The volume is given as 240 cubic feet, and the relationships between the dimensions (length, width, and height) are provided. The length L is described as 4 feet less than twice the width W, and the height H is 1 foot less than the width (W). We can express this information in terms of equations:

L = 2W - 4

H = W - 1

The volume V of a rectangular prism is found using the formula V = LWH. Substituting the given expressions in terms of W into the volume equation, we get:

V = (2W - 4)(W)(W - 1)

Since the volume is given as 240 cubic feet, we can write the equation as:

240 = (2W - 4)(W)(W - 1)

This is the equation in terms of the width W that could be used to find the dimensions of the dumpster.

Answer:

A. 30

Step-by-step explanation:

30*.08=24

Answer:

See below.

Step-by-step explanation:

All the equations are one-step equations.

In each case, see what operation is being done to the variable, and do the opposite operation to both sides.

1.

t + 1.32 = 3.48

1.32 is being added to t.

Subtract 1.32 from both sides.

t + 1.32 - 1.32 = 3.48 - 1.32

t = 2.16

2.

b - 4.22 = 7.08

4.22 is being subtracted from b.

Add 4.22 to both sides.

b - 4.22 + 4.22 = 7.08 + 4.22

b = 11.3

4.

h + 4/9 = 7/9

4/9 is being added to h.

Subtract 4/9 from both sides.

h + 4/9 - 4/9 = 7/9 - 4/9

h = 3/9

h = 1/3

5.

-5/8 = x - 1/4

1/4 is being subtracted from x.

Add 1/4 to both sides.

-5/8 + 1/4 = x - 1/4 + 1/4

-5/8 + 2/8 = x

-3/8 = x

x = -3/8

7.

3.2c = 9.6

c is being multiplied by 3.2.

Divide both sides by 3.2.

3.2c/3.2 = 9.6/3.2

c = 3

8.

-5.04 = 1.26d

c is being multiplied by 1.26.

Divide both sides by 1.26.

-5.04/1.26 = 1.26d/1.26

-4 = d

d = -4

10.

-2/3 = 3/4t

t is being multiplied by 3/4.

Divide both sides by 3/4 which is the same as multiplying both sides by 4/3.

-2/3 * 4/3 = 3/4t * 4/3

-8/9 = t

t = -8/9

11.

w/2.5 = 4.2

w is being divided by 2.5.

Multiply both sides by 2.5.

w/2.5 * 2.5 = 4.2 * 2.5

w = 10.5

Answer:

the answer is A. f(x +1) = -2f(x)

Step-by-step explanation:

every new number in the sequence is multiplied by -2, making it -2f(x).

Answer:

(D) f(x+1)=2f(x)

Step-by-step explanation:

Answer:

Step-by-step explanation:

We will check whether the given pair x = 3 and y = 2 is the solution of the first equation.

4(3) - 5(2) = 12 - 10 = 2 CORRECT

Put x = 3 and y = 2 to the equation 6x + 7y = Q:

Q = 6(3) + 7(2)

Q = 18 + 14

Q = 32

Answer: -16

Step-by-step explanation:

input is x

output is y

9x-7=y

9(-1)-7=y

-9-7=-16

Answer:

The answer is -16

Step-by-step explanation:

input is x

output is y

9x-7=y

9(-1)-7=y

-9-7=-16

Answer:

Draw a line across  the points (6,0) and (0,3)

Step-by-step explanation:

This is the equation of a line, so it is enough to find two points (x,y), locate them and draw a straight line passing trough then,

Having said that, lets start.

The first easy point to find is the one that makes y=0, so we have the following equation: 0=-1/2 x +3, which gives that x=6, this point is (6,0)

The other easy point to find is the one that makes x=0, so we have the following equation y=-1/2 * 0 +3, which gives that y=3, this point is (0,3)

We have two points (6,0) and (0,3)