16. You have 60 songs to choose from. In how many different ways can you load 5 songs onto your portable media player?​

Answers

Answer 1

The order of choosing doesn't matter, so it's a combination.

[tex]_{60}C_5=\dfrac{60!}{5!55!}=\dfrac{56\cdot57\cdot58\cdot59\cdot60}{120}=5,461,512[/tex]


Related Questions

3. Sophie and Jackie each have a collection of baseball cards, Jackie has 5 more cards than
Sophie, and together they have 30 cards. By writing and solving an equation, find out how
many cards Sophie owns. Show all of your working out.

Answers

Answer:

Sophie has 12.5 cards

Step-by-step explanation:

Let

x -----> number of cards Sophie has

y -----> number of cards Jackie has

we know that

x+y=30 -----> equation A  

y=x+5 -----> equation B

Solve by substitution

Substitute equation B in equation A and solve for x

x+(x+5)=30

2x=30-5

x=12.5 cards

Note I assume the problem was invented without taking into account the result, because the amount of cards should be a whole number


Which value represents |-100|?







A. -100


B. -10


C. 0


D. 100

Answers

Answer:

D. :)

Step-by-step explanation:

I think it’s a because -100 is 100

Which of the following best describes the algebraic expression x/3 -15

Answers

Answer:

A. A number divided by three minus fifteen.

A number is divided by three minus fifteen best describes the given algebraic expression [tex]\frac{x}{3}-15[/tex].

Option A is correct.

What is an algebraic expression?

An algebraic expression is a variable expression described using its terms, and operations on the terms. For example, x + 3 can be described as "3 more than x".

Given algebraic expression

[tex]\frac{x}{3}-15[/tex]

[tex]\frac{x}{3}[/tex] means a number is divided by three and [tex]\frac{x}{3}-15[/tex] means a number is divided by three minus fifteen.

A number is divided by three minus fifteen best describes the given algebraic expression [tex]\frac{x}{3}-15[/tex].

Option A is correct.

Find out more information about algebraic expression here

https://brainly.com/question/19245500

#SPJ2

How do you: Find the 4th term of (x-2y)^6

Answers

To find the 4th term of (x-2y)^6, you can use the binomial expansion formula. The 4th term is 240x^2y^4.

To find the 4th term of (x-2y)^6, we can use the binomial expansion formula. The formula is: (a+b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nC(n-1) * a^1 * b^(n-1) + nCn * a^0 * b^nIn this case, a = x, b = -2y, and n = 6. So we have: (x-2y)^6 = 6C0 * x^6 * (-2y)^0 + 6C1 * x^5 * (-2y)^1 + 6C2 * x^4 * (-2y)^2 + 6C3 * x^3 * (-2y)^3 + 6C4 * x^2 * (-2y)^4 + 6C5 * x^1 * (-2y)^5 + 6C6 * x^0 * (-2y)^6To find the 4th term, we need to find the term with the exponent of x^2 * (-2y)^4. This occurs when nCr = 6C4. Using the formula, we have: 6C4 = 6! / (4! * 2!) = 15

Therefore, the 4th term of (x-2y)^6 is 15 * x^2 * (-2y)^4, which simplifies to 15x^2 * 16y^4 = 240x^2y^4.

Final answer:

To find the 4th term of (x - 2y)^6, we can use the binomial expansion formula.

Explanation:

To find the 4th term of (x - 2y)^6, we can use the binomial expansion formula.


The formula is: (a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn * a^0 * b^n


Where nCk represents the binomial coefficient, which can be calculated as n! / (k! * (n-k)!)

In this case, a = x and b = -2y.

The exponents will go from 6 down to 0, and we need to find the term with k = 4.

Let's substitute these values into the formula:

(x - 2y)^6 = 6C0 * x^6 * (-2y)^0 + 6C1 * x^5 * (-2y)^1 + 6C2 * x^4 * (-2y)^2 + 6C3 * x^3 * (-2y)^3 + 6C4 * x^2 * (-2y)^4 + 6C5 * x^1 * (-2y)^5 + 6C6 * x^0 * (-2y)^6

To find the 4th term, we look at the term with k = 4. Using the binomial coefficient:

6C4 = 6! / (4! * (6-4)!)

= 15

Substituting this back into the formula, we get:

15 * x^2 * (-2y)^4

Make a conjecture about the next item in the sequence.
1, 4, 16, 64, 256
Select one:

a. 1024

b. 1025

c. 4096

d. 1022

Answers

Answer:

Option A is correct.

Step-by-step explanation:

Given terms,

1 , 4 , 16 , 64 , 256.

If we observe the equation, we can easily say that the terms are getting multiplied by 4 to get the next one.

Since this equation has a common ratio, this can be solved by using the properties of geometric progressions.

From the properties of geometric progressions :

nth term = a r^( n - 1 ) , where a is the first term, r is the common ratio between the terms and n is the number of terms.

Here,

Common Ratio ( or r ) = any term( except first ) / previous terms = 64 / 16 = 16 / 4 = 4

First terms = 1

Therefore,

= > Next term should be : 1 x ( 4 )^( 6 - 1 ) { Since next term will be 6th term }

= > Next term = 1 x 4^5

= > Next term = 1024

Hence the required next term is 1024.

Option A is correct.

Or

Here we can see that the terms are written in the form of 4^n where n is any whole number.

Since 246 is 4^4 , and terms are increasing in order of 1, next term should be 4^5 i.e. 1024 .

Thus, option A is correct.

Answer:

A

Step-by-step explanation: you times each one by 4

there are 8 finalist in the spelling bee. The order of the contestants will be determined by a random draw. How many different orders are possible for the spelling bee?​

Answers

Answer: Option  C

(C ) 96

Step-by-step explanation:

The correct answer would be C, which is 96.

                         You're Welcome!

Big Bob’s Pizza is having a special on pizza and is offering two different choices: Choice #1: One slice of pizza from a pizza with a 22 inch diameter and is cut into 8 slices. The cost is $4.95. Choice #2: An entire personal-size pizza that has a diameter of 6 inches. The cost is $3.75. Which choice will give you more pizza for your money? Justify your answer using numbers and words.

Answers

Answer:

Choice #1 is better

Step-by-step explanation:

To find the solution to this problem, we have to compute the are in each case, and divide each value by the corresponding cost in order to find the cost per square. The lower the cost, the better the offer because it will give you more pizza for your money Thus:

CHOICE 1:

Here the offer of Big Bob’s Pizza gives one slice of pizza from a pizza with a 22 inches diameter (then the radius is 11 inches) and is cut into 8 slices, so the area for the first entire pizza is:

[tex]A_{1}=\pi r^2=\pi(11)^2 \\ \\ A_{1}=121 \pi in^2[/tex]

Each slice has an area of:

[tex]A_{slice}=\frac{121 \pi}{8} \\ \\ A_{slice}=47.51in^2[/tex]

Finally, the cost per square inch is:

[tex]C=\frac{4.95\$}{47.51in^2}=0.10\$[/tex]

CHOICE 2:

Here the offer of Big Bob’s Pizza gives: An entire personal-size pizza that has a diameter of 6 inches (then the radius is 3 inches), so the area for the entire pizza is:

[tex]A_{2}=\pi r^2=\pi(3)^2 \\ \\ A_{2}=28.27 in^2[/tex]

Finally, the cost per square inch is:

[tex]C=\frac{3.75\$}{28.27in^2}=0.13\$[/tex]

CONCLUSION: Choice #1 gives you more pizza for your money because the cost per square inch is less than the other option.

The special at Big Bob's Pizza which will give you more pizza for your money is Choice #1. Per square inch, Choice #1 will cost less and give more overall pizza at $0.10 a square inch then Choice #2 at $0.13 per square inch. You can find more pizza for your money, by using the area formula for a circle for each pizza and finding the price per square inch of each serving. This is called a unit rate and is the cost per unit.

Further Explanation

a. Find the radius of each pizza.

Since a pizza is a circle shape, it has a diameter and radius. The diameter is the distance across the pizza and the radius is half the diameter. We use the radius to find the area.

Choice #1: One slice of a pizza with a 22 inch diameter and is cut into 8 slices. Since the diameter is the distance across the pizza, 22 inch diameter means the pizza is 22 inches wide. The area formula uses the radius or half the diameter. The radius of choice #1 is 11 inches.Choice #2: An entire personal-size pizza that has a diameter of 6 inches. Here the radius is half of 6 inches. The radius of choice #2 is 3 inches.  

b. Find the area of each pizza using [tex]A = \pi r^{2}[/tex].

Choice #1: Substitute r = 11 into the formula then divide by 8 to find the area of one slice or serving.

       [tex]A = \pi r^{2} \\A = \pi (11)^{2} \\A = 121\pi \\A= 379.94[/tex]

       The area of one slice is [tex]\frac{379.94}{8} = 47.49.[/tex]

Choice #2: Substitute r = 3 into the formula. This is a personal pizza so the entire pizza is a serving.

       [tex]A = \pi r^{2} \\A = \pi (3)^{2} \\A = 9\pi \\A= 28.26[/tex]

c. Divide each area by the price.

The cost of Choice #1 is $4.95. Since the serving size is 1 slice, use the area of the slice 47.49. Divide it into the price to find the cost per square inch of one serving.

        [tex]\frac{4.95}{47.49} = 0.10[/tex]

The cost of Choice#2 is $ 3.75.  Since the serving serving size is the entire personal pizza, use the area of the pizza 28.26.

       [tex]\frac{3.75}{28.26} = 0.13[/tex]

Learn More Area and Circumference of a Circle Application: https://brainly.com/question/3519879 Cost per unit: https://brainly.com/question/11521316Answer Details

Grade: 8th Grade

Subject: Geometry

Chapter: Applications for Area of Shapes

Keywords: circle, area, radius, diameter, cost, unit rate

Read more on Brainly.com - https://brainly.com/question/12878495

Solve for y.



y – (–19) = 25


A.
–44

B.
–6

C.
6

D.
44

Answers

Answer:

C

Step-by-step explanation:

note that - (- 19) = + 19

Given

y - (- 19) = 25, that is

y + 19 = 25 ( subtract 19 from both sides )

y = 6 → C

Answer:

Answer is C. 6

Step-by-step explanation:

Because:

y -(-19) = 25 (well i always put a 1 infront of parenthesis) so,

y -1(-19) =25 distribute the 1 in the parenthesis and you would get

19=25 minus 19 on both sides and you get y= 6

Hope my answer has helped you!

How do you divide (m^(3)- 13m^(2)+24m+18)div(m-3) using synthetic division step by step?

Answers

Answer:

The quotient is: m^2-10m-6

The remainder is: 0

Step-by-step explanation:

We need to divide m^3-13m^2+24m+18 ÷ m-3 using synthetic division

The division is shown in the figure below.

The quotient is: m^2-10m-6

The remainder is: 0

What are the solution(s) to the quadratic equation x2 – 25 = 0?
O x = 5 and x = -5
OX=25 and x = -25
O x = 125 and x = -125
O no real solution​

Answers

[tex]x^2 - 25 = 0\\x^2=25\\x=-5 \vee x=5[/tex]

Answer:

x = ± 5

Step-by-step explanation:

Given

x² - 25 = 0

There are 2 possible approaches to solving this equation

Approach 1

add 25 to both sides

x² = 25 ( take the square root of both sides )

x = ± [tex]\sqrt{25}[/tex] = ± 5

Approach 2

x² - 25 ← is a difference of squares and factors as

(x - 5)(x + 5) = 0 ← in standard form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 5 = 0 ⇒ x = 5

What is the volume of a rectangular prism that has a length of 9 feet, a width of 5 feet, and a height of 7.5 feet? 300 ft3 150 ft3 337.5 ft3 43 ft3

Answers

Answer:

The answer is 337.5.

Step-by-step explanation:

Srry Im late. :(

Answer: C. 337.5

Hope this helps!

please help quick. thanks ​

Answers

Answer:

The number in the square root is 50.

Step-by-step explanation:

Using the pythagorean theorem, we know that c is 10, so we plug in 2a^2=100, since we know that both of the leg lengths are the same.

Simplifying this equation gives a^2=50, which square rooting both sides gives

a = sqrt(50)

Hope this helps!

What is the surface area of the right cylinder below?

Answers

Answer:

A≈622.04

Step-by-step explanation:

Formula: A=2πrh+2πr²

Answer: A. 622 sq. units

Step-by-step explanation:

The surface area of a cylinder is given by :-

[tex]S.A.=2\pi r(r+h)[/tex], where r is the radius , h is height of the cylinder.

Given : The height of the cylinder : h= 2 units

The radius of the cylinder : r= 9 units

Then , the surface area of a cylinder will be :-

[tex]S.A.=2(3.14159) 9(9+2)\\\\\Rightarrow\ S.A.=622.03482\approx622\text{sq. units}[/tex]

which is greater 5000 g or 10 lb​

Answers

Answer:

5000 g

Step-by-step explanation:

5000 g = 11.02311 lb

10 lb​ = 4535.92

Re-write the equation 3x - y = 4 in slope-intercept form.
a. y = 3x -4
b. y = 3x + 4
C. y=-3x
D. y=-3x+4

Answers

Answer:

a

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Rearrange 3x - y = 4 into this form ( add y to both sides )

3x = y + 4 ( subtract 4 from both sides )

3x - 4 = y OR y = 3x - 4 → a

Final answer:

The equation 3x - y = 4 is rewritten in slope-intercept form as y = 3x - 4, where the slope is 3 and the y-intercept is -4, corresponding to answer option A.

Explanation:

To rewrite the equation 3x - y = 4 in slope-intercept form (y = mx + b), we need to solve the equation for y.

Here are the steps:

Add y to both sides of the equation: 3x = y + 4.

Subtract 4 from both sides of the equation: y = 3x - 4.

Therefore, the equation in slope-intercept form is y = 3x - 4. This represents a line with a slope of 3 and a y-intercept of -4. So the correct answer is option A: y = 3x - 4.

Teagan believes she can use a division expression to find the amount of pizza each of 6 friends will eat if they share 4/5 of a pizza. Which statement best explains why Teagan is correct or incorrect?

Answers

Answer: sorry i meant 7.5 would be incorrect

Step-by-step explanation: she wouldn't be able to do it if it goes over 6 so that is incorrect

Answer:

Teagan is correct.

Step-by-step explanation:

We are given the following information in the question:

Number of friends = 6

Pizza eaten by all friends = [tex]\frac{4}{5}[/tex]

Now, in order to find pizza eaten by each friend, Teagan need to divide pizza eaten by total number of friends.

Formula:

[tex]\text{Pizza eaten by each friend} = \displaystyle\frac{\text{Total pizza eaten}}{\text{Number of friends sharing the pizza}}\\\\= \displaystyle\frac{\frac{4}{5}}{6} = \displasystyle\frac{4}{30} = \displaystyle\frac{2}{15}[/tex]

Thus, each friend had  [tex]\frac{2}{15}[/tex] of a pizza.

What is the area of a regular hexagon if a side is 30

Answers

Answer:

[tex]1350\sqrt{3}[/tex] square units (approximately 2338.26859)

Step-by-step explanation:

The formula for finding the area of a regular hexagon when you know its side length is [tex]A=\frac{3\sqrt{3}*s^2}{2}[/tex], where [tex]A[/tex] is the area and [tex]s[/tex] is the side length.

Substitute in the side length. [tex]A=\frac{3\sqrt{3}*30^2}{2}[/tex]Simplify the exponent. [tex]A=\frac{3\sqrt{3}*900}{2}[/tex]Multiply. [tex]A=\frac{2700\sqrt{3}}{2}[/tex]Divide. [tex]A=1350\sqrt{3}[/tex]

[tex]1350\sqrt{3}[/tex] is as simple as the solution can get without estimating, but you can estimate with a calculator to find that it is approximately 2338.26859.

Can someone please help me out ?

Answers

Answer:

b = 14 units

Step-by-step explanation:

The formula of an area of a parallelogram:

A = bh

b - base

h - height

We have A = 140 units², and h = 10 units. Substitute:

140 = 10b           divide both sides by 10

14 = b → b = 14 units

PLEASE HELP!! WILL MARK BRAINLIEST is y=x^2-3 linear

Answers

Answer:

A linear function is in the form y = mx + b or f(x) = mx + b, where m is the slope or rate of change and b is the y-intercept or where the graph of the line crosses the y axis. ... if your first diffs are the same it is linear. if not it is not linear.

a LINEar equation is an equation with a polynomial of degree 1 and is the graph of a LINE, let's look at this one, y = x² - 3, notice the exponent of ², meaning is a 2nd degree equation, and is a parabola, so is namely a quadratic, not a linear one.

Help! What is the equation on the graph. I have tried x^2+1 and it marks it incorrect

Answers

Answer:

[tex]y=2x^{2}+1[/tex]

Step-by-step explanation:

we know that

The graph is a vertical parabola open upward

The vertex is the point (0,1)

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

substitute the vertex in the equation

[tex]y=a(x-0)^{2}+1[/tex]

[tex]y=a(x)^{2}+1[/tex]

Find the value of coefficient a

Observing the graph

For x=1, y=3

substitute in the equation

[tex]3=a(1)^{2}+1[/tex]

[tex]a=3-1=2[/tex]

The equation on the graph is equal to

[tex]y=2x^{2}+1[/tex]

Mia spent 30 minutes answering the math questions on the exam. This was 1/4 of the total amount of time allotted for this section of the exam. To determine the total amount of time allotted for this section of the exam, Mia set up and solved the equation as shown below.


Which best describes the error that Mia made when solving the equation?

Answers

Answer:

Mia multiplied one side of the equation by 5/3 and the other side by 3/5. This makes the equation unbalanced and untrue. x should be 50

Step-by-step explanation:

Final answer:

Mia made an error when setting up the equation to determine the total time allotted for the math section of the exam. She incorrectly set up the equation as 30 = (1/4) * x, instead of 30 = (1/4) * x. The correct solution is x = 120.

Explanation:

Mia made an error when setting up the equation to determine the total amount of time allotted for the math section of the exam. Since Mia spent 30 minutes answering the math questions, which was 1/4 of the total time, the correct equation should be:

30 = (1/4) * x

To solve for x, we need to multiply both sides of the equation by 4 to undo the division:

4 * 30 = x

x = 120

Therefore, the total amount of time allotted for the math section of the exam is 120 minutes, not 30 minutes as Mia mistakenly calculated.

Enter the amplitude of the function. f(x)=3cosx

Answers

Answer:

amplitude = 3

Step-by-step explanation:

given a cosine function in standard form, that is

y = acosx, then

amplitude = | a |

Hence for f(x) = 3cosx, amplitude = | 3 | = 3

Final answer:

The amplitude of the function f(x) = 3cosx is 3, as the amplitude is the coefficient in front of the cosine function.

Explanation:

The amplitude of a trigonometric function like f(x) = 3cosx can be found by looking at the coefficient in front of the cosine function. In this case, the function f(x) = 3cosx has an amplitude of 3. This is because the amplitude of cosx or sinx is the absolute value of the coefficient multiplied by the cosine or sine function, which dictates how much the wave's peak or valley deviates from the center line of the graph. For example, if the function was f(x) = A cosx, the amplitude would be the absolute value of A. Since there is no negative sign or other function manipulating the 3 in f(x) = 3cosx, the amplitude is simply 3.

What is the range of P=3,000(1/1,000)

Answers

Answer:

p = 3

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  

                    p-(3000*(1/1000))=0  

Step by step solution :

Step  1  :

             1  

Simplify   ————

           1000

Equation at the end of step  1  :

                1  

 p -  (3000 • ————)  = 0  

              1000

Step  2  :

Equation at the end of step  2  :

 p - 3  = 0  

Step  3  :

Solving a Single Variable Equation :

3.1      Solve  :    p-3 = 0  

Add  3  to both sides of the equation :  

                     p = 3

Please mark brainliest and have a great day!

The graph of a function f(x)=(x+2)(x-4). Which describes all of the values for which the graph is negative and increasing?
all real values of x where x<-2
all real values of x where -2

Answers

Answer:

1. (2, -9)

2.  ( 0,-5)

Solve 2(1 – x) > 2x.

Answers

First you must distribute the 2 to the numbers inside the parentheses, which would be 1 and -x...

(2 * 1) + (2 * -x) > 2x

2 + (-2x) > 2x

2 - 2x >2x

Add 2x to both sides (what you do on one side you must do to the other). Since 2x is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.

2 - 2x + 2x > 2x + 2x

2 + 0 > 4x

2 > 4x

Next divide 4 to both sides to finish isolating x. Since 4 is being multiplied by x, division (the opposite of multiplication) will cancel 4 out (in this case it will make 4 one) from the right side and bring it over to the left side.

2/4 > 4x / 4

1/2 > x

or

x < 1/2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

x<1/2

Step-by-step explanation:

Expand.

 ↓

2(1-x)=2-2x

2-2x>2x

First, subtract by 2 from both sides of equation.

2-2x-2>2x-2

Simplify.

-2x>2x-2

Then subtract by 2x from both sides of equation.

-2x-2x>2x-2-2x

Simplify.

-4x>-2

Multiply by -1 from both sides of equation.

(-4)(-1)<(-2)(-1)

Simplify.

4x<2

Divide by 4 from both sides of equation.

4x/4<2/4

Simplify, to find the answer.

2/4=1/2

X<1/2 is the correct answer.

WILL GIVE YOU BRAINLIEST + 22 POINT QUESTION!

which expression is equivalent to sqrt 55 x^7 y^6 / 11 x^11 y^8?

assume x > 0 and y > 0

Answers

Answer:

√55x\11x⁸y⁵

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

Answer: C

Explanation:

√55x⁷y⁶/11x¹¹y⁸

→ 55/11 = 5

→ x⁷/x¹¹= x⁷⁻¹¹= x⁻⁴

→ y⁶/y⁸= y⁶⁻⁸= y⁻²

→ √5/x⁴y²

→ √5/x²y

If the exponent is a negative, the base is the reciprocal of itself with a positive exponent.

Ex: 6⁻² = 1/6² = 1/36

The square root of an exponent with a positive, even power is half of that power.

Ex: √x⁴ = x²

A video game system and several games are sold for $700. The cost of the games is three times as much as cost of the system. Find cost of the system and cost of the games

Answers

Answer:

cost of system is $175 and cost of the games is $525

Step-by-step explanation:

Let us take the cost of the system to be X.The games cost 3 times as much as the system and are therefore given 3X. The total cost of the system and the games is $700.Therefore,we form the equation 3X+X=$700.Meaning that 4X=$700 and X is equal to $175.The cost of the system is X therefore it is $175 and the cost of the games is 3X and is therefore $525.

The cost of the video game system is $175, while the cost of the games is $525,.

The student is asking to find the cost of a video game system and the games sold with it, given that the total cost is $700 and that the cost of the games is three times as much as the cost of the system.

Let's define the cost of the system as 'x'.

The cost of the games would then be '3x'.

The total cost is given as $700, so we can write the equation as:

x + 3x = 700

Combining like terms, we get:

4x = 700

x = 700 / 4

x = $175

So, the cost of the system is $175,

and the cost of the games is three times that, which is:

3 × $175 = $525

A taxicab starts at (1, −2) on the grid. It goes 4 blocks south and 3 blocks east to pick up a passenger. Then it goes 6 blocks west and 5 blocks north and drops off the passenger. How many blocks is the taxicab from its starting position?

Answers

Final answer:

The taxicab, after all its movements, is about 3.16 blocks away from its starting position. It ends up 3 blocks west and 1 block north from where it initially started.

Explanation:

The question asks us to determine the final position of a taxicab relative to its starting position after following a series of movements. The taxicab's starting position in this case is at the coordinate (1, -2).

Initially, it goes 4 blocks south (downwards in the grid, which we'll regard as negative) and 3 blocks east (to the right on the grid, which we'll regard as positive). Therefore, it moves to a point that is (+3, -4) relative to its starting position.

Next, it goes 6 blocks west (left on the grid, which is negative) and 5 blocks north (up on the grid, which is positive). So, this movement's relative position is (-6, +5).

To find out the final position of the taxicab relative to its starting position, we need to add up these movements' relative positions. The final relative position will be (+3-6, -4+5), which equals (-3, 1).

Hence, in terms of blocks, the taxicab is 3 blocks west and 1 block north of its starting position. The direct distance to the start would then be determined using the Pythagorean theorem, where the total distance is the square root of the sum of the squares of the movements in each direction (x and y coordinates). That forms the equation √((-3)² + 1²) = √10 ≈ 3.16 blocks.

Learn more about Coordinate Grid Movement here:

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A pencil bag contains 20 red pencils. 12 pencils, and 10 green pencil, Carrie randomly selects a red pencil followed by a green pencil without replacement.

What is the probability that Carrie selects a red pencil followed by a green pencil?

Write the answer as a percent rounded to the nearest tenth of a percent.

Answers

Answer:

11.6%

Step-by-step explanation:

On the first selection, there are 20 red pencils out of 42 total pencils.

On the second selection, there are 10 green pencils out of 41 pencils left over.

So the probability is:

(20/42) (10/41)

100/861

≈11.6%

Writing a quadratic equation given the roots and the leading coefficient
6,-4,1

Answers

[tex]\bf x= \begin{cases} 6\\ -4 \end{cases}\implies \begin{cases} x=6\implies &x-6=0\\ x=-4\implies &x+4=0 \end{cases} \\\\\\ (x-6)(x+4)=\stackrel{y}{0}\implies \stackrel{\mathbb{F~O~I~L}}{1x^2-2x-24}=y[/tex]

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