Use the Binomial Theorem to expand the expression.(x +6)^3

Answers

Answer 1

ok

[tex]\begin{gathered} (x+6)^3=^{}x^3+3(x)^2(6)+3(x)(6)^2+6^3 \\ \text{ = x}^3+18x^2\text{ + 3(36)x + 216} \\ \text{ = x}^3+18x^2\text{ + 108x + 216} \end{gathered}[/tex][tex]\begin{gathered} (a+b)^3\text{ } \\ first\text{ term = a} \\ \text{second term = b} \\ \text{theorem } \\ (a+b)^3=a^3+3a^2b+3ab^2+b^3 \end{gathered}[/tex]

that is the rule

just identify a and b in your problem

a = x

b = 6

Substitute in the theorem, and simplify


Related Questions

A tornado siren begins blaring from the center of town 9.5 seconds after a tornado was spotted. The siren is located 490 meters north of a school. If the siren’s sound wave travels at a constant velocity of 350 meters per second south, how long will it take the sound wave to travel from the siren to the school?

Answers

The relationship between distance, time and velocity is:

[tex]v=\frac{d}{t}[/tex]

The question ask us for the time, we can solve for t:

[tex]v=\frac{d}{t}\Rightarrow t=\frac{d}{v}[/tex]

To find the time that it will take the sound wave travelling at 350 m/s to reach the school at 490m is the distance divided the velocity:

[tex]\begin{gathered} t=\frac{490m}{350\frac{m}{s}} \\ \end{gathered}[/tex][tex]t=1.4s[/tex]

The answer is 1.4s

The parabola f (x) = (x - 2)2 + 1 is graphed in the xy-coordinate plane.8Part ASelect from the drop-down menus to correctly complete the sentence.The vertex of the parabola is 2 units(a)(b) Part BSelect from the drop-down menus to correctly complete the sentence.How does the function f (x+3) compare to f (x)?f (x + 3) has avshift 3 unitsV the origin and 1 unitv f(x).the origin.

Answers

We will have the following:

a) The vertex of the parabola is 2 units right of the origin and 1 unit up from the origin.

b) We will have that:

f(x+3) has vertex shift 3 units left of f(x).

CorrectBob's Golf Palace had a set of 10 golf clubs that were marked on sale for $840. This was a discount of 10% off the original selling price.Step 3 of 4: What was the store's percent of profit based on cost ($390)? Follow the problem-solving process and round your answer tothe nearest hundredth of a percent, if necessary.

Answers

The percent change is given by:

[tex]Percent_{\text{ }}change=\frac{New_{\text{ }}value-old_{\text{ }}value}{old_{\text{ }}value}\times100[/tex]

The old value is $390

Please give steps and explanations to how you get the correct answer I am confused

Answers

To find the area under a function in a given interval you need to find the definite integral of the function in that interval.

For the given function:

[tex]\begin{gathered} P=100(0.4)^t \\ \\ \int_0^8Pdt=\int_0^8100(0.4)^tdt \end{gathered}[/tex]

Use the next properties to find the integral:

[tex]\begin{gathered} \int a\times f(x)dx=a\int f(x)dx \\ \\ \int a^xdx=\frac{a^x}{\ln(a)} \end{gathered}[/tex][tex]\int_0^8100(0.4)^tdt=100\int_0^80.4^tdt=100\times\frac{0.4^t}{\ln(0.4)}\lvert^8_0[/tex]

Evaluate the result for the given interval:

[tex]\begin{gathered} (100\times\frac{0.4^8}{\ln(0.4)})-(100\times\frac{0.4^0}{\ln(0.4)}) \\ \\ =-0.07152-(-109.13566) \\ \\ =109.06 \end{gathered}[/tex]Then, the area under the given function in the interval (0,8) is 109.06

Draw a figure to use for numbers 13 - 15. Points A. B. and C are collinear and Bis the midpoint of AC. 13. If AB = 3x - 8 and BC = x + 4, find the length of AB 14. If BC = 6x - 7 and AB = 5x + 1. find the length of AC 15. If AB = 8x + 11 and BC = 12x - 1. find the length of BCAnswer 13

Answers

13.

Given:

AB = 3x - 8, BC = x + 4

A, B and C are collinear

B is a midpoint of AC

Since B is the midpoint, we can write:

[tex]\text{length of AB = Length of BC}[/tex]

Hence, we have:

[tex]3x\text{ - 8 = x + 4}[/tex]

Solving for x:

[tex]\begin{gathered} \text{Collect like terms} \\ 3x\text{ -x = 4 + 8} \\ 2x\text{ = 12} \\ \text{Divide both sides by 2} \\ x\text{ = 6} \end{gathered}[/tex]

Hence, the length of AB is:

[tex]\begin{gathered} =\text{ 3x - 8} \\ =\text{ 3}\times\text{ 6 -8} \\ =\text{ 18 -8} \\ =\text{ 10} \end{gathered}[/tex]

Answer:

The length of AB is 10 unit

Which decimal represents 8 X 1,000 + 4 X 100 + 7 X7 16 +31,0001,0A 8,004.073C 8,400.703B 8,040.073D 8,400.730

Answers

The given expression:

[tex]8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}[/tex]

Simplify the expression:

[tex]\begin{gathered} 8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}=8000+400+0.7+0.003 \\ 8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}=8400.703 \end{gathered}[/tex]

Answer : c) 8400.703

Write a mathematical sentence that expresses the information given below. Use b as your variable name. If necessary:

type < = to mean

or > = to mean .

If you need to show multiplication, do not use the letter x. Use the asterisk ( * ) symbol instead, or simplify your answer.

Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has.

Answers

The number of books owned by frank is represented as b < 150

What is inequality?

Inequality represents the form of writing expressions where the left hand side of the expression is not exactly equal to the right hand side of the expression

How to represent the required expression

Information gotten from the data include

Emily has 300 books

Frank were to double the number of books that he now owns, he would still have fewer than Emily has.

Let the number of books owned by frank be b and from the information we have that:

2b < 300

b < 150

hence the number of books owned by frank, b less than 150

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A scale drawing of a rectangular park is 4 inches wide and 8 inches long. The actual park is 320 yards long. What is the perimeter of the actual park, in square yards?

Answers

Given:

• Width of scale drawing = 4 inches

,

• Length of scale drawing = 8 inches

,

• Length of actual park = 320 yards

Let's find the perimeter of the actual park.

Let's first find the width of the actual park.

To find the width of the actual park, we have:

[tex]\begin{gathered} \text{ width of actual = }\frac{\text{ length of actual}}{\text{ length of scale}}*\text{ width of scale} \\ \\ \\ \text{ width of actual = }\frac{320}{8}*4 \\ \\ \text{ width of actual = 40 * 4 = 160 yards} \end{gathered}[/tex]

The width of the actual park is 160 yards.

Now, to find the perimeter of the actual park, apply the formula do perimeter of a rectangle:

P = 2(L + W)

Where:

P is the perimeter

L is the length = 320 yards

W is the width = 160 yards

Thus, we have:

P = 2(320 + 160)

P = 2(480)

P = 960 yards

Therefore, the perimeter of the actual park is 960 yards.

ANSWER:

960 yards

What is the value of f(3) on the following graph?

Answers

Answer

f(3) = -2

Explanation

We are asked to find the value of f(3) from the graph.

This means we are looking for the value of f(x) or y on the graph, at a point where x = 3.

From the graph, we can see that at the point where x = 3, y = -2

Hence, f(3) = -2

Hope this Helps!!!

Solve for x and then give the m

Answers

x = 38

Step-by-step explanation:

(x + 6) + (3x - 16) + x = sum of angles in a triangle

(x + 6) + (3x - 16) + x = 180

(x + 3x + x ) + (6 - 16) = 180

5x +(-10) = 180

5x - 10 = 180

5x = 180 + 10

5x = 190

5x/5 = 190/5

x = 38

Answer:

x = 38 and m∠M = 98

Step-by-step explanation:

Angles in any triangle will always add up to 180 :

So angle O + Angle N + Angle M = 180

(x+6)+(3x-16)+(x) = 180

Simplify:

5x-10 = 180

Add 10 to both sides :

5x = 190

Divide both sides by 5 :

x = 38

Angle M will therefore

= 3(38) - 16
= 114 - 16

= 98

Hope this helped and have a good day

Solve the triangle: a = 25, C = 25, B = 25°. If it is not possible, say so.A=25*,b= 25, C = 250A=77.5*,b=10.8, C = 77.5eA=77.5', b = 24.1, C = 77.5This triangle is not solvable.

Answers

We will have the following:

First:

Since we have that sides a & c have the same length by theorem angles A & C are equal, so the following is true:

[tex]A+B+C=180\Rightarrow2A+B=180[/tex][tex]\Rightarrow2A=180-25\Rightarrow A=77.5[/tex]

so, angles A & C have a measure of 77.5°.

*Second: We determine the measurement f the segment b, that is:

[tex]\frac{b}{\sin(25)}=\frac{25}{\sin(77.5)}\Rightarrow b=\frac{25\sin (25)}{\sin (77.5)}[/tex][tex]\Rightarrow b=10.8219807\Rightarrow b\approx10.8[/tex]

So we will have that the measurements are:

A = 77.5°

b = 10.8

C = 77.5°

[Option B]

Number 14. Need help finding the area of the shaded area. Forgot how to solve it. Please help.

Answers

To find the area of the shaded region we need to calculate the area of the square and subtract to it the area of the circle.

The area of a square is calculated as follows:

[tex]A=b^2[/tex]

where b is the length of each side.

Substituting with b = 16 cm (given that the radius of the circle is 8 cm, then the length of the square's side is 2x8 = 16 cm):

[tex]\begin{gathered} A_1=16^2 \\ A_1=256\operatorname{cm}^2 \end{gathered}[/tex]

The area of a circle is calculated as follows:

[tex]A=\pi r^2[/tex]

where r is the radius of the circle.

Substituting with r = 8 cm, we get:

[tex]\begin{gathered} A_2=\pi\cdot8^2 \\ A_2=\pi\cdot64 \\ A_2\approx201\operatorname{cm}^2 \end{gathered}[/tex]

Finally, the area of the shaded region is:

[tex]\begin{gathered} A_3=A_1-A_2 \\ A_3=256-201 \\ A_3=55\operatorname{cm}^2 \end{gathered}[/tex]

What is the solution set of x² + 5x - 5 = 0?

Answers

The solution of x² + 5x - 5 = 0 is  :

x = 0.854 and -5.854 .

Solution:

Here given equation,

x2 + 5x - 5 = 0

To solve the given equation use quadratic formula,

Using the quadratic formula,

x = [-b ± [tex]\sqrt{b2 - 4ac}[/tex] ] /2a

Here,

a = 1, b = 5 and c = -5

By substituting,

x = [-5 ± [tex]\sqrt{52 - 4(1)(-5)}[/tex] ] /2(1)

= [-5 ± √[tex]\sqrt{25 + 20}[/tex]] /2

= [-5 ± √45] /2

= [-5 ± 6.708] /2

So,

x = (-5 - 6.708)/2

= -11.708/2

= -5.854

= (-5 + 6.708)/2

= 1.708/2

= 0.854

∴  the solutions of equation is : 0.854 and -5.854.

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Any equation that can be rearranged in standard form as follows, where x stands for, is referred to be a quadratic equation in algebra.

What constitutes the x2 + 5x - 5 = 0 solution set?

We must figure out the equation's answer. The answers to the problem are thus 0.854 and -5.854. x^2 + 5x - 5 = 0

It is impossible to factor a quadratic equation like this one. It can be resolved either by completing the square or by applying the quadratic formula.

x = (-b +-sqrt(b2 - 4ac))/2a is the quadratic formula, where an is the coefficient of the x2, b is the coefficient of the x, and c is the constant.

a = 1, b = 5, c = -5

x = (-5 +- sqrt(25+20))/2

x = (-5 +- sqrt(45))/2

x = (-5 + - 3 sqt 5))/2

x = (-5 + 3sqrt5)/2 as well as x = (-5 - 3sqrt5)/2.

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URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!

Answers

(-4,2) is your answer

Carl is sewing a quilt. The number of yards of green fabric in the quilt is proportional to the number of yards of bluefabric in the quilt. This equation represents the proportional relationship between the number of yards of greenfabric, g, and yards of blue fabric, b, in the quilt.6 2/3 b = 5 1/3 gEnter the number of yards of green fabric used for 1 yard of blue fabric

Answers

Answer:

1 1/4 yards of green fabric.

Explanation:

The equation representing the proportional relationship between the number of yards of green fabric, g, and yards of blue fabric, b, in the quilt is:

[tex]6\frac{2}{3}b=5\frac{1}{3}g[/tex]

If 1 yard of blue fabric is used: b=1

[tex]\begin{gathered} 6\frac{2}{3}\times1=5\frac{1}{3}g \\ \frac{20}{3}=\frac{16}{3}g \\ \text{ Multiply both sides by }\frac{3}{16} \\ \frac{3}{16}\times\frac{20}{3}=\frac{16}{3}\times\frac{3}{16}g \\ g=\frac{20}{16} \\ g=1\frac{1}{4}\text{ yards} \end{gathered}[/tex]

If 1 yard of blue fabric is used, then 1 1/4 yards of green fabric will be used.

I need to find the equation of a circle I will include picture

Answers

Given,

The center of the circle is (6, -3).

The coordinates of the point, circle is passing through (6,6).

The general equation of the circle is,

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here, x, y are the coordinates of the point.

h and k are the center of the circle.

r is the radius of the circle.

Substituting the value of h, k , x and y in the equation of circle then,

[tex]\begin{gathered} (6-6)^2+(6-(-3))^2=r^2 \\ 0+9^2=r^2 \\ r=9 \end{gathered}[/tex]

So, the radius of the circle is 9.

Substituting the value of h, k and r in the general equation of circle.

[tex]\begin{gathered} (x-6)^2+(y-(-3))^2=9^2 \\ x^2+36-12x+y^2+9+6y=81 \\ x^2+y^2-12x+6y-36=0 \end{gathered}[/tex]

Hence, the equation of circle is x^2+y^2-12x+6y-36=0

Find the time. Round to the nearest day given the following:Principal: $74,000Rate: 9.5%Interest: $2343.33

Answers

Explanation

Simple Interest is calculated using the following formula:

[tex]I=\text{PRT}[/tex]

where P is the principal ( initial amount)

R is the rate ( in decimal)

T is the time ( in years)

so

Step 1

Let

[tex]\begin{gathered} P=74000 \\ \text{rate}=\text{ 9.5\% =9.5/100= 0.095} \\ T=t\text{ ( unknown)} \\ \text{Interest}=\text{ 2343.33} \end{gathered}[/tex]

now, replace

[tex]\begin{gathered} I=\text{PRT} \\ 2343.33=74000\cdot0.095\cdot t \\ 2343.33=7030t \\ \text{divide both sides by 7030} \\ \frac{2343.33}{7030}=\frac{7030t}{7030} \\ 0.3333=t\text{ } \end{gathered}[/tex]

so, the time is 0.333 years

Step 2

convert 0.333 years into days

[tex]1\text{ year }\Rightarrow365\text{ days}[/tex]

so

[tex]\begin{gathered} 0.333years(\frac{365}{1\text{ year}})=121.66 \\ \text{rounded} \\ 122\text{ days} \end{gathered}[/tex]

therefore, the answer is

122 days

I need help on this question

Answers

Answer:

Real zeros are: x = 0, x = 1 and x =2

***Your graph is incorrect. See mine for the correct graph***

Step-by-step explanation:

We have the polynomial
[tex]$\displaystyle \:x^{4}-3x^{3}+2x^{2}\:=\:0$[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}x^2:\\\\[/tex]

[tex]=x^2\left(x^2-3x+2\right)[/tex]

[tex]\mathrm{Factor}\:x^2-3x+2:[/tex]

For an expression of the form ax² + bx + c we can find factors if we find two values u and v such uv = c and u + v =b and factor into (ax +ux)+ (vx+c)

We have here a = 1, b = -3 c = 2

==> u = -1, v = -2

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

So the original expression becomes
[tex]\:x^2-3x+2 = x^2\left(x-1\right)\left(x-2\right)[/tex]

To find the zeros, set this equal to 0 and solve for x

[tex]x^2\left(x-1\right)\left(x-2\right)=0[/tex]

We end up with 3 roots corresponding to the 0 values for each of the three terms

[tex]x^2 = 0 == > x = \pm 0 = 0\\\\[/tex]

[tex](x - 1) = 0 == > x = 1\\\\(x - 2) = 0 == > x = 2\\\[/tex]

Answer real zeros are: x = 0, x = 1 and x =2

**** Your graph is incorrect. Check mine. The zeros happen where the curve intersects the x axis and these are at x = 0, x = 1, x =2

1) The weights of a particular group of show dogs are normally distributed with a mean of 16.6 kg and astandard deviation of 2.2 kg. If a random show dog is selected from the group, what is the probability thatit would weigh less than 15.5 kg?

Answers

In order to determine the probability, first use the followinf formula to calculate the Z factorr:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

where:

x: specific value from the data = 15.5 kg

σ: standard deviation = 2.2 kg

μ: mean = 16.6 kg

replace the previous values to find the Z factor:

[tex]Z=\frac{15.5\operatorname{kg}-16.6\operatorname{kg}}{2.2\operatorname{kg}}=0.5[/tex]

Next, search the corresponding value of the probability in a table of Normal distribution.

The correspondinf value of the probability for Z = 0.5 is P = 19.15%

This can be noticed in the following graph.

In 2000, there were 750 cell phone subscribers in a small town. The number of subscribers increased by 80% per year after 2000. How many cell phone subscribers were in 2010? Round off the answer to the nearest whole number.

Answers

This is an exponential growth. We would apply the exponential growth formula which is expressed as

y = a(1 + r)^t

Where

a represents the imitial number of subscribers

r represents the growth rate

t represents the number of years

y represents the number of subscribers after t years

From the information given,

a = 750

r = 80/100 = 0.8

t = 9 (number of years between 2000 and 2010)

Thus,

y = 750(1 + 0.8)^9

y = 750(1.8)^9

y = 148769.48

Rounding to the nearest whole number, the number of cell phone subscribers in 2010 is

148769

GRAPH each triangle and CLASSIFY the triangle according to its sides and angles.

Answers

Answer:

[tex]\Delta CAT\text{ is an ISOSCELES triangle}[/tex]

Explanation:

To properly classify the traingle, we need to get the length of the sides

To get the length of the sides, we need to get the distance between each two points using the distance between two points formula

Mathematically,we have the formula as:

[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where (x1,y1) refers to the coordiantes of the first point while (x2,y2) refers to the coordinates of the second point

let us get the coordinates of the individual points as seen from the plot shown

C (1,8)

A (5,10)

T (7,6)

So, let us find the distance between each two points

For AC, we have:

[tex]D\text{ = }\sqrt[]{(5-1)^2+(10-8)^2}\text{ = }\sqrt[]{20}[/tex]

For AT, we have:

[tex]D=\sqrt[]{(7-5)^2+(6-10)^2\text{ }}\text{ = }\sqrt[]{20}[/tex]

Lastly, for CT, we have:

[tex]D\text{ = }\sqrt[]{(7-1)^2+(6-8)^2\text{ }}\text{ = }\sqrt[]{40}[/tex]

From our calculations, we can see that AC = AT

If we have a triangle which has two of its sides equal in length (the angle facing these sides would be same too), we call this an isosceles triangle

So, the class of triangle CAT is isosceles triangle

please help me work through this, thank you! it specifies to round to 2 decimal places

Answers

Since they will collide the time taken for both to reach the intersection is the same.

Let the time taken by t.

Recall that for steady motion,

[tex]\begin{gathered} d=st \\ \text{ Where:} \\ d=\text{ the distance covered} \\ s=\text{ the speed} \\ t=\text{ the time} \end{gathered}[/tex]

Substitute d = 4 and s = 442 into the equation:

[tex]\begin{gathered} 4=442t \\ \text{ Dividing both sides by }442,\text{ it follows that:} \\ t=\frac{4}{442} \end{gathered}[/tex]

Therefore, the distance covered by the Coyote in this time is given by:

[tex]d=\frac{4}{442}\times481=\frac{74}{17}[/tex]

Using the Pythagorean Rule, it follows that the distance between Road Runner and the Coyote along the diagonal is given by:

[tex]h=\sqrt{(\frac{74}{17})^2+4^2}[/tex]

Since speed s for a body that travelled distance d in time t is given by:

[tex]s=\frac{d}{t}[/tex]

it follows that the required speed is given by:

[tex]-\sqrt{(\frac{74}{17})^2+4^2}\times\frac{442}{4}=-65\sqrt{101}[/tex]

Therefore, the required rate is -65√101 kph.

What is the answer and how do I solve this

Answers

A parent absolute value function f(x) = |x| is plotted as

We can change the appearance of this absolute value function based on what we add to the absolute value function and the constant accompanied by it.

Let's start with shifting the plot from |x| to |x+1|. If we add +1 to x inside an absolute value function, the parent absolute value function will shift one unit to the left. This shifting is represented by the red dotted plot on the figure below.

We now multiply a constant -3 on the absolute value function |x+1|. Multiplying a negative number to the absolute value function results in mirroring the absolute value function via the x-axis. Then, the plot will be compressed by a factor of 1/3. We now have

Hence, the final plot for the given absolute value function y = -3|x+1| is

Question 6 What is the factored form of the expression below? 7 - 16 O OD (x-8)(x - 8) (x - 4)(x + 4) (x - 4)(x - 4) (x-8)(x + 8) Oo

Answers

If :

[tex]x^2-16[/tex][tex]\begin{gathered} \sqrt[]{x^2}=x \\ \sqrt[]{16}=4 \end{gathered}[/tex]

Then:

[tex]x^2-16\text{ =(x-4)(x+4)}[/tex]

Answer: ( x - 4 ) ( x + 4 )

combine like terms
(x+3)+(9+x)

Answers

Answer:

[tex]x^{2}[/tex]+12x+27

Step-by-step explanation:

First, you need to distribute. You multiply x by 9 and x, and then multiply 3 by 9 and x, which results in 9x +  [tex]x^{2}[/tex] +27 +3x.

Second, you collect like terms. In this case, there is only one like term, which is x. The results of this should be [tex]x^{2}[/tex] + 27 + 11x.

Lastly, reorder the terms properly, and you're done!

Hope this helps.

Identify the slope and y-intercept of equation 5x-3y=9

Answers

To identify the slope and y-intercept, we will take the given equation to its slope-intercept form:

[tex]y=mx+b,[/tex]

where m is the slope and b is the y-intercept.

To take the equation to its slope-intercept form, we add 3y to the given equation:

[tex]\begin{gathered} 5x-3y+3y=9+3y, \\ 5x=9+3y\text{.} \end{gathered}[/tex]

Now, we subtract 9, and get:

[tex]5x-9=3y\text{.}[/tex]

Finally, dividing by 3, we get:

[tex]y=\frac{5}{3}x-3.[/tex]

Therefore, the slope and y-intercept are:

[tex]\frac{5}{3},\text{ and -3 }[/tex]

correspondingly.

Answer:

Slope:

[tex]\frac{5}{3}\text{.}[/tex]

Y-intercept:

[tex]-3.[/tex]

PLEASE help I'll send a picture in later.

Answers

Given

Table of names

Procedure

Names end with an E

Gabe

Steve

The probability would be independent and equal to:

[tex]\begin{gathered} \frac{2}{6}\cdot\frac{2}{6} \\ \frac{4}{36} \\ \\ \frac{1}{9} \end{gathered}[/tex]

The probability would be 1/9

What is the domain, range, and function? {(-3, 3), (1, 1), (0, -2), (1,4), (5, -1)}

Answers

The domain are all the inputs, that is; the x-values

Domain = { -3, 0, 1, 5}

The range are all the output, that is the y-values

Range = { 3, 1, -2, 4, -1}

This is just a relation and not a function, as we have more than 2 same value of x

For her phone service, Mai pays a monthly fee of $19, and she pays an additional $0.04 per minute of use. The least she has been charged in a month is$70.28. What are the possible numbers of minutes she has used her phone in a month?

Answers

We have a phone service fee which can be divided in:

- A fixed fee of $19 per month.

- A variable fee of $0.04 per minute, so that the cost for m minutes is 0.04*m.

We can add the two fees to express the total cost in function of the minutes as:

[tex]C(m)=19+0.04m[/tex]

For a month where the cost is C(m) = 70.28, we can calculate the minutes as:

[tex]\begin{gathered} C(m)=70.28 \\ 19+0.04m=70.28 \\ 0.04m=70.28-19 \\ 0.04m=51.28 \\ m=\frac{51.28}{0.04} \\ m=1282 \end{gathered}[/tex]

Answer: if she pays at least $70.28, she has talked at least m = 1282 minutes per month.

can you help me on the part 2 Heads in a Row:

Answers

Given:

Flipping a coin twice.

Required:

We need to find the likelihood of flipping heads twice in a row.

Explanation:

The sample space = All possible outcomes.

The sample space, S= {TT,TH,HT,HH}

[tex]n(S)=4[/tex]

Let A be the event of flipping heads twice..

The favorable outcomes = flipping heads twice.

The favorable outcomes ={HH}

[tex]n(A)=1[/tex]

Consider the probability formula.

[tex]P(A)=\frac{n(A)}{n(S)}[/tex][tex]P(A)=\frac{1}{4}[/tex][tex]P(A)=0.25[/tex]

The probability of flipping heads twice in a row is 0.25 which is a close value to the number 0.

This event happens least likely.

Final answer:

Flipping heads twice in a row is the least likely.

The probability of flipping heads twice in a row is 0.25.

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