Answer: B. [tex]-7185024p^6q^5[/tex]
Step-by-step explanation:
The (r+1)th term in [tex](a+b)^n[/tex] is given by :
[tex]^nC_r(a)^{n-r}(b)^r[/tex]
The given binomial : [tex](2p - 3q)^{11}[/tex]
For the 6th term, we put r=6-1=5 , we get
[tex]^{11}C_5(2p)^{11-5}(-3q)^5\\\\=\dfrac{11!}{5!(11-5)!}(2p)^6(-243q^5)\\\\=-dfrac{11\times10\times9\times8\times7\times6!}{6!5!}(64p^6)(243q^5)\\\\=-462\times(64p^6)(243q^5)\\\\=-7185024p^6q^5[/tex]
Hence, the 6th term of the expansion of [tex](2p - 3q)^{11}[/tex] = [tex]-7185024p^6q^5[/tex]
Express 8.5454545454... as a rational number, in the form p/q where p and q are positive integers with no common factors.
Marion is observing the velocity of a cyclist at different times. After two hours, the velocity is 18km/h. After four hours, the velocity of the cyclist is 4km/h.
Part A: write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used.
Part B: how can you graph the equations obtained in part A for the first 8 hours?
To solve this problem,
we assume that velocity is a linear function of time:
v(t) = m t + b
where
v = velocity
t = time
m = slope of line
b = y-intercept of line equation
When t = 2 hours, v =
18 km/h, therefore:
2 m + b = 18 (1)
When t = 4 hours, v = 4 km/h, therefore
4 m + b = 4 (2)
Subtract (1) from (2) to obtain
4 m – 2 m = 4 - 18
2 m = -14
m = -7
From (1), calculate
for b:
b = 18 – 2(-7) = 32
Part A. The
equation in standard form is therefore:
v = -7 t + 32
Part B. To graph
the equation for the first 8 hours, we create a table as shown below. Assign
values of t from 0 to 8 hours then calculate the corresponding velocity.
The sum of two numbers is 48. One number is 3 times as large as the other. What are the numbers?
Answer: 12 and 36
Step-by-step explanation: The best way to approach a word problem like this is to break it down sentence by sentence.
We know that the sum of two numbers is 48 so we can move on to the next sentence. Now, let's take a look at the second sentence. One number is 3 times as large as the other.
This sentence tells us what variables we are going to use to represent our numbers.
So if we use x to represent one of our numbers, and one number is 3 times as large as the other, we can use 3x to represent our other number. Also, make sure to always label your variables.
X ⇒ first number
3x ⇒ second number
Now let's look back at the first sentence. "The sum of two numbers is 48". This sentence tells us how we will set up our equation. "The sum" if our variables are X and 3x will be X + 3x = 48.
Keep in mind, the word "is" means equal.
Now we have the following equation and we can solve for X.
X + 3x = 48
We start by simplifying on the left side to get 4x.
Now we have the following equation.
4x = 48
÷4 ÷4 ← divide both sides of the equation by 4
X = 12
So our first number, X, is 12 and our second number will be 3 × 12 or 36.
Therefore, our two numbers are 12 and 36.
What is the name of the shape graphed by the function r^2=9 cos(2 theta)?
The name of the shape graphed by the function r ^ 2 = 9 cos (2 theta) is called the “lemniscate”. A lemniscate is a plane curve with a feature shape which consists of two loops that meet at a central point. The curve is also sometimes called as the lemniscate of Bernoulli.
Explanation:
The period of coskθ is 2π/k. In this case, k = 2 therefore the period is π.
r ^ 2 = 9 cos 2θ ≥0 → cos 2θ ≥0. So easily one period can be chosen as θ ∈ [0, π] wherein cos 2θ ≥0.
As cos(2(−θ)) = cos2θ, the graph is symmetrical about the initial line.
Also, as cos (2(pi-theta) = cos 2theta, the graph is symmetrical about the vertical θ = π/2
A Table for half period [0,π4/] is adequate for the shape in Quarter1
Use symmetry for the other three quarters:
(r, θ) : (0,3)(3/√√2,π/8)(3√2/2,π/6)(0,π/4)
Answer:
lemniscate
Step-by-step explanation:
a p e x
The point (1, -5) is an ordered pair for which function?
A. ƒ(x ) = 3x - 11
B. ƒ(x ) = 2x - 7
C. ƒ(x ) = -x + 9
Wayne needs to drive 470 miles to reach Milwaukee. Suppose he drives at a constant speed of 50 miles per hour. Which function represents Wayne’s distance in miles from Milwaukee in terms of the number of hours he drives?
y = 420x
y = 470 + 50x
y = 50 − 470x
y = 50 + 470x
y = 470 − 50x
Answer:
[tex]y= 470 - 50x[/tex]
Step-by-step explanation:
Wayne needs to drive 470 miles to reach Milwaukee. Suppose he drives at a constant speed of 50 miles per hour.
Let x represents the number of hours he drives and y represents the distance in miles.
constant speed is 50 miles per hour.
Distance =speed x time
speed is 50 miles per hour and time is x
So distance = [tex]50x[/tex]
Wayne needs to drive 470 miles to reach Milwaukee.
To find out y, we need to subtract 50x from 470
[tex]y= 470 - 50x[/tex]
Answer:
the last one
y = 470 - 50x
A cylinder is a type of prism.
true
false
A spinner is separated into 5 equal pieces, as shown below: patrick spins the spinner 9 times. what is the theoretical probability that it stops on the brown sector on the last spin?
To solve this problem, let us first define what probability means in this case. It would be:
Probability = (number of colors to choose from) / (total number of colors)
There are a total of 5 colors on the spinner. The number of colors to choose from spins 1 to 8 would be 5 out of 5, while for the last spin 9 the number of colors to choose from would only be brown so that would be 1 out of 5. The total probability would be the product of the probability of each spins, therefore:
Probability = 1st spin * 2nd spin * 3rd spin * 4th spin * 5th spin * 6th spin * 7th spin * 8th spin * 9th spin
Probability = (5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) * (1/5)
Probability = 0.2
There is a 20% chance to get brown on the last spin.
Answer:
1/5
Step-by-step explanation:
Think of it like this. If there is five spots it can potentially land on, and only 1 brown spot, the answer would be 20 %, or as a fraction, 1/5.
A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?
When a point in quadrant 2 is rotated 180 degrees counterclockwise, it will land in quadrant 4.
A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?
Begin in quadrant 2 (Q2).Rotating 180 degrees counterclockwise leads to the point's final position in quadrant 4 (Q4).Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.
n an
1 | 3
2 | −6
3 | 12
The explicit formula for this geometric sequence is: a_n = 3 (-2)^{n-1}. he common ratio is negative, so the domain is all odd positive integers.
Explicit formula:
The explicit formula for a geometric sequence is of the form: a_n = a_1 r^{n-1}
In this case, the first term is 3 and the common ratio is −2. Therefore, the explicit formula for this geometric sequence is:
a_n = 3 (-2)^{n-1}
Restrictions to the domain:
The domain of a geometric sequence is all positive integers, unless the common ratio is negative. In this case, the common ratio is negative, so the domain is all odd positive integers.
Example:
Using the explicit formula, we can find the fourth term of the sequence as follows:
a_4 = 3 (-2)^{4-1} = 3 (-2)^3 = -24
We can also verify that the domain of the sequence is all odd positive integers by checking the first few terms:
n | a_n
1 | 3
2 | -6
3 | 12
4 | -24
5 | 48
For such more question on geometric
https://brainly.com/question/29632351
#SPJ6
The area of a rectangle is 0.8 square units. The length is 3.2 units and the width is x units.What is the value of x?
You're studying different function tools and begin working with this function:
y=-200-12(x)
Use the equation to answer the question:
What is the y-value when x equals -16?
Answer:
-8
Step-by-step explanation:
Given : [tex]y=-200-12(x)[/tex]
To Find:What is the y-value when x equals -16?
Solution:
We are given that You're studying different function tools and begin working with this function:
[tex]y=-200-12(x)[/tex]
Now we are supposed to find the value of y when x is -16
So, substitute x = -16 in the equation
[tex]y=-200-12(-16)[/tex]
[tex]y=-200+192[/tex]
[tex]y=-8[/tex]
So, Value of y is -8
Hence the y-value when x equals -16 is -8
Ben measures the height of two bottles. one is 12 centimeters, and the other is 15 centimeters. in millimeters, what is the difference of the two heights?
One bottle has a height of 12 centimeters or 12 cm. Let us call this h1, so h1 = 12 cm
While the other bottle has a height of 15 centimeters or 15 cm. Let us call this h2, so h2 = 15 cm
The difference in height can be calculated by subtracting the smaller number from the bigger number, therefore:
difference in height = h2 – h1
difference in height = 15 cm – 12 cm
difference in height = 3 cm
We know that in 1 meter there is:
1 meter = 100 centimeters = 1000 millimeters
Therefore,
difference in height = 3 cm (1000 millimeters / 100 centimeters)
difference in height = 30 mm
Answer:
difference in height = 30 mm
Explain why the absolute value of a number will never be negative
Answer:
The absolute value of a number is the distance the number is from 0 on a number line. Since distance is never negative, absolute value is never negative.Step-by-step explanation:
A paper popcorn cone measures 4 inches in diameter and is 9 inches high. What is the volume of popcorn that can be contained within this cone? Use 3.14 for pi. Round your answer to the nearest hundredth. 37.68 cubic inches 39.45 cubic inches 40.23 cubic inches 41.90 cubic inches
Can a geometry expert help me ASAP Please!!!!!!! and can you show me how you got the answer please
Verify the Pythagorean Identity.
1 + cot^2 0 = csc^2 6
To prove this Pythagorean Identity, we have to know that:
cot = 1 / tan
and we also know that:
tan = sin / cos
Therefore,
cot = 1 / tan = cos / sin
So we can write the given equation in the form of:
1 + (cos^2 θ / sin^2 θ) = csc^2 θ
Expanding the left hand side of the equation:
(sin^2 θ / sin^2 θ) + (cos^2 θ / sin^2 θ) = csc^2 θ
(sin^2 θ + cos^2 θ) / sin^2 θ = csc^2 θ
We know that given a unit circle, sin^2 θ + cos^2 θ = 1. So:
1 / sin^2 θ = csc^2 θ
The equation above is already true basing on the trigonometric identities. Therefore:
csc^2 θ = csc^2 θ
how to solve for -5x^2-2x-6=-2 ?
Name the property that the following statement illustrates. 44 • pie =pie•44
The value of a dirt bike decreases by 15% each year. If you purchased this dirt bike today for $500, to the nearest dollar how much would the bike be worth five years later? $84 $119 $164 $222
The answer is 222
All you do is multiply 500 by 0.15, which gives you 75. Then subtract that from 500 to give you 425. Now multiply this 425 by 0.15 then subtract the product form 425. Continue this process until it is done 5 times. Your answer on the fifth time will be your answer.
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work. Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations.
A cyclist rides a bike at a rate of 24 miles per hour. What is this rate in miles per minute? How many miles will the cyclist travel in 5 minutes? Do not round your answer.
there are 60 minutes per hour
24/60 = 0.4 miles per minute
0.4*5 = 2
they will ride 2 miles in 5 minutes
The table below represents an exponential function.
table represents an exponential function.
What is the interval between neighboring
x-values shown in the table?
What is the ratio between neighboring y-values?
In given table of exponential function,
The interval between neighboring x-values is of 1 unit.
The ratio is 4 between neighboring y-values
Observing given table.
To find interval between neighboring x-values . We have to take difference between consecutive x - values.
[tex]1-0=2-1=3-2=4-3=5-4=1[/tex]
Since, in every consecutive x- values , difference of 1 is present.
So, The interval between neighboring x-values is of 1 unit.
To find ratio between neighboring y-values , we have to take ratio of consecutive y - values.
[tex]\frac{4}{1}=\frac{16}{4}=\frac{64}{16}=\frac{256}{64}=4[/tex]
Thus, The ratio is 4 between neighboring y-values
Learn more:
https://brainly.com/question/10652359
A phone banking password consists of 2 letters followed by 4 digits. The letters B, I, S, and O are not used, and the last digit cannot be 0. How many different passwords are possible?
5,148,000
4,840,000
4,356,000
3,175,524
There are 4,356,000 different passwords are possible.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A phone banking password consists of 2 letters followed by 4 digits.
And, The letters B, I, S, and O are not used, and the last digit cannot be 0.
Hence, We can formulate;
Number of different passwords are possible are,
⇒ 22 × 22 × 10× 10 × 10 × 9.
⇒ 4,356,000
Thus, There are 4,356,000 different passwords are possible.
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ3
Find the 6th term of a geometric sequence with t1=5 and r = -1/2
-5/8
-5/16
-5/32
-5/64
The triangle JKL shown on the coordinate grid below is reflected once to map onto triangle J'K'L': Triangle JKL is drawn on a 4 quadrant coordinate grid with vertices J is at 8, 1. K is at 5, 7. L is at 3, 4. If vertex L' is at (−3, 4), what are the coordinates of vertex J'?
Answer:
The vertex J' is at (-8,1).
Step-by-step explanation:
If is given that the triangle JKL reflected once to map onto triangle J'K'L'.
The vertices of the triangle JKL are J(8,1), K(5,7) and L(3,4). The vertex L'(-3,4).
[tex]L(3,4)\rightarrow L'(-3,4)[/tex]
It is in the form of
[tex](x,y)\rightarrow (-x,y)[/tex]
Since the y-coordinate remains same and the sign of x coordinate is changed. It shows the reflection across the y axis.
The vertices of image are,
[tex]K(5,7)\rightarrow K'(-5,7)[/tex]
[tex]J(8,1)\rightarrow J'(-8,1)[/tex]
Therefore the vertex J' is at (-8,1).
s=5r^2t solve for T please
PLEASE HELP ASAP!!!! WILL GIVE THANKS AND BRAINLIEST ANSWER!!!
A rectangular stained glass window is made up of identical triangular parts as pictured below.
Hence, the area of shaded region is:
72 square inches.
Step-by-step explanation:We have to find the area of the shaded region i.e. we have to find the area of a triangle.
Clearly the shaded triangle is in the shape of a right triangle.
we will firstly find the dimension of the triangle in order to find it's area.
Clearly the base(b) of a triangle is 36/4= 9 inches.
( since the side of the rectangle of length 36 inches is divided into 4 equal parts)
similarly the height(h) of the right triangle is:
48/3=16 inches.
( since the side of rectangle of measure 48 inches is divided into 3 equal parts)
Hence, the area of triangle is calculated as:
[tex]Area=\dfrac{1}{2}\times b\times h\\\\\\Area=\dfrac{1}{2}\times 9\times 16\\\\Area=72\text{square\ inches}[/tex]
Hence, the area of shaded region is:
72 square inches.
Find the measures of the interior angles of a triangle whose two exterior angles equal to 120° and 150°
Three interior angles of the given triangle are 60°, 30°, and 90°.
What is a triangle?A triangle is a two-dimensional geometrical figure that has three sides, three vertices, and three interior angles.
Given, two exterior angles of a triangle are 120° and 150°.
Therefore, the first interior angle is
[tex]= (180 - 120)[/tex] degrees
[tex]= 60[/tex] degrees
The second interior angle is
[tex]= (180 - 150)[/tex] degrees
[tex]= 30[/tex] degrees
The third interior angle is
[tex]= [180 - (60+30)][/tex] degrees
= 90 degrees
Learn more about a triangle here:
https://brainly.com/question/12834063
#SPJ2