Find the first five terms of the sequence..
Answer:
The Next fiver tems are - 2, -2,-8,-12,-16
Step-by-step explanation:
Answer:
2,-6,2,-6,2
Step-by-step explanation:
a1 = 2
an = -an-1 -4
Let n =2
a2 = -a1 -4 = -2-4 = -6
Let n=3
a3 = -a2 -4 = - (-6) -4 = +6 -4 = 2
Let n = 4
a4 = -a3 -4 = -2 -4 = -6
Let n=5
a5 = -a4 -4 = -(-6) -4 = +6-4 = 2
Can somebody help me solve this ?
Step-by-step explanation:
volume of sphere = 288
based on formula, V = 4/3πr³
288 = 4/3(3.14)r³
288 = 4.187(r³)
r³ = 288/4.187
r =
[tex] \sqrt[3]{68.78} [/tex]
r = 4.09
= 4.1
help
What is 5 added to 3 4?
6. 12
Answer:
8.4
Step-by-step explanation:
jjdijendjndoendidnie
PLEASE HELPPPPPPPPPP
Answer:
167/346 or 0.483
Step-by-step explanation:
From the question given above, the following data were obtained:
Number of Tails (T) = 167
Number of Heads (H) = 179
Probability of tail, P(T) =?
Next, we shall determine total outcome. This can be obtained as follow:
Number of Tails (T) = 167
Number of Heads (H) = 179
Total outcome (S) =?
S = T + H
S = 167 + 179
Total outcome (S) = 346
Finally, we shall determine the probability of tails. This can be obtained as follow:
Number of Tails (T) = 167
Total outcome (S) = 346
Probability of tail, P(T) =?
P(T) = T / S
P(T) = 167 / 346
P(T) = 0.483
Thus, the probability of tails is 167/346 or 0.483
Adding Fractions: What is 9/8 + 5/6? I would like an explanation for mebecause I am confused about this problem, it will be nice if someone explained it to me. Thanks!
Answer:
4/3
Step-by-step explanation:
just do the lcm of denomination and after that start solving
9514 1404 393
Answer:
1 23/24
Step-by-step explanation:
Fractions can be added when they have the same denominator. Then the addition is performed by adding the numerators, and expressing the sum over the common denominator.
Here, your fractions have denominators of 8 and 6. Usually, we want to find a "least common denominator" to use to express the fractions. There are various ways to find that value. One of the easiest is to consult your memory of multiplication tables to find the smallest number that both a multiple of 8 and a multiple of 6. That number is 24.
An equivalent fraction is one that has the same value, but a different denominator than the one it is being compared to. Equivalent fractions can be made by multiplying by "1" in the form of "a/a" where "a" is any non-zero value. Here, it is useful to multiply 9/8 by 3/3 to make the equivalent fraction 27/24, which has a denominator of 24.
Similarly, we can multiply 5/6 by 4/4 to get the equivalent 20/24, which also has a denominator of 24.
These two fractions can now be added:
[tex]\dfrac{9}{8}+\dfrac{5}{6}=\dfrac{27}{24}+\dfrac{20}{24}=\dfrac{27+20}{24}=\dfrac{47}{24}[/tex]
If you want to turn this into a "mixed number", you need to find how many times 24 goes into 47: 47÷24 = 1 remainder 23. The quotient is the integer part of the mixed number; the remainder is the numerator of the fractional part. Then the mixed number value of the sum is ...
[tex]\dfrac{47}{24}=1\dfrac{23}{24}[/tex]
_____
Additional comments
The product of the denominators can always serve as a common denominator. That may not be the "least" common denominator. If you use that here, you would have ...
[tex]\dfrac{9}{8}+\dfrac{5}{6}=\left(\dfrac{9}{8}\cdot\dfrac{6}{6}\right)+\left(\dfrac{5}{6}\cdot\dfrac{8}{8}\right)=\dfrac{54+40}{48}=\dfrac{94}{48}[/tex]
This result can be reduced by removing a factor of 2 from numerator and denominator to give 47/24, the sum we had above.
The "least common denominator" (LCD) is the Least Common Multiple (LCM) of the denominators. It can be found by forming the product of the unique factors of the denominators. Here, we have 8 = 2·2·2 and 6 = 2·3. The LCD is the product 2·2·2·3. We recognize that 2³ and 3 are unique factors that need to contribute to the LCD. 2 is subsumed by 2³.
As you can see from the factoring, 2 is a common factor of both numbers. Another way to find the LCD (or LCM of the denominators) is to form their product (8×6 = 48) and divide that by the greatest common factor (GCF), which is 2. (48/2 = 24, the LCD) Sometimes it is easier to find the GCF and compute (product/GCF) than to find the LCM using factoring.
__
If you don't mind the possibility of having to reduce the resulting fraction, the sum of fractions can always be computed as ...
[tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}[/tex]
This formula computes 94/48 as the sum of these fractions, effectively leaving out the middle step (9/8×6/6 +...) shown in the work above. I find this especially useful for adding rational expressions, not just numerical fractions.
3（6x+3）=63 How to do it
Please help I’m really stuck!!
Step 1: Solve for one variable
---I will be using the first equation and solving for a.
a + c = 405
a = 405 - c
Step 2: Substitute into the other equation
---Now that we have a value for a, we can substitute that value into the second equation. Then, we can solve for c.
12a + 5c = 3950
12(405 - c) + 5c = 3950
4860 - 12c + 5c = 3950
-12c + 5c = -910
-7c = -910
c = 130
Step 3: Plug back into the first equation
---We now know one variable, which means we can plug back into our first equation and solve for the other.
a = 405 - c
a = 405 - 130
a = 275
Answer: 275 adults, 130 children
Hope this helps!
Use the substitution methed to solve the system of equations. Choose the correct ordered pair.
2y+5x=13
2y+3x=5
Solve both equations for 2y :
2y + 5x = 13 ==> 2y = 13 - 5x
2y + 3x = 5 ==> 2y = 5 - 3x
Solve for x :
13 - 5x = 5 - 3x
8 = 2x
x = 4
Solve for y :
2y = 13 - 5×4
2y = -7
y = -7/2
As an ordered pair, the solution is then the point (x, y) = (4, -7/2).
Factor 64a^3 -8b^3 Explain all steps.
Answer:
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
Step-by-step explanation:
factor out the 8
then you have the sum/difference of cubes..
look that up SOAP: same opposite, always a plus
[tex]64a^3 -8b^3\\8(8a^3 -b^3)[/tex]
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
True or false?
A function assigns each value of the independent variable to exactly one
value of the dependent variable.
A. True
B. False
SUB
Answer:
This statement would be true.
Step-by-step explanation:
1. Write the polynomial function that models the given situation.A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
Answer:
1. (12 - 2x)(11 - 2x)x
2. 4(11 - 2x)²(x + 1)
3. π(x³ + 15x² + 63x + 81)
Step-by-step explanation:
1. Write the polynomial function that models the given situation.
A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
Since the length of the rectangle is 12 units and its width 11 units and squares of x by x units are cut from its corners, it implies that a length x is cut from each side. So, the length of the open box is L = 12 - 2x and its width is w = 11 - 2x.
Since the cut corners of the rectangle are folded, the side x which is cut represents the height of the open box, h. so, h = x
So, the volume of the open box V = LWh = (12 - 2x)(11 - 2x)x
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
Since the square has sides of 24 units and squares of x + 1 by x + 1 units are cut from its corners, it implies that a length x + 1 is cut from each corner and the length 2(x + 1) is cut from each side. So, the length of side open box is L = 24 - 2(x + 1) = 24 - 2x - 2 = 24 - 2 - 2x = 22 - 2x = 2(11 - x)
Since the cut corners of the square are folded, the side x + 1 which is cut represents the height of the open box, h. so, h = x + 1
Since the area of the base of the pen box is a square, its area is L² = [2(11 - 2x)]²
So, the volume of the open box V = L²h = [2(11 - 2x)]²(x + 1) = 4(11 - 2x)²(x + 1)
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
The volume of a cylinder is V = πr²h where r = radius and h = height of cylinder.
Given that r = x + 6 and h is 3 units more than r, h = r + 3 = x + 6 + 3 = x + 9
So, V = πr²h
V = π(x + 3)²(x + 9)
V = π(x² + 6x + 9)(x + 9)
V = π(x³ + 6x² + 9x + 9x² + 54x + 81)
V = π(x³ + 15x² + 63x + 81)
What three consecutive integers equal -87?
Answer:
What three consecutive integers have a sum of 87? Which means that the first number is 28, the second number is 28 + 1 and the third number is 28 + 2. Therefore, three consecutive integers that add up to 87 are 28, 29, and 30. We know our answer is correct because 28 + 29 + 30 equals 87 as displayed above.
Step-by-step explanation:
Consecutive integers are as simple as 1, 2, 3!
Integers are consecutive if one follows another. How do we "jump" from one integer to the next? We add 1, right? 7, 8 and 9 are three consecutive integers. Add one to 7 to get 8 and add one more to get 9.
Now lets think about this in algebraic terms. Lets name these consecutive integers , x, y and z.
The problem tells us that their sum is -87. (Recall, "sum" is just a fancy word for the answer when we add.)
x+y+z = -87
Here is the trick! We need to rewrite this equation so that we have only one variable. Easy!
y is one more that x, so y= x+1
And z is one more than y, so z= y+1. But y is also equal to (x+1)! So z=y+1=(x+1)+1=x+2
Now we have a problem that we can solve! x+(x+1)+(x+2)=-87.
Combining term.: 3x+3=-87
Subtract 3 from both sides of the equation: 3x=84
Divide each side of the equation by 3: x=28
We have solved for x, but we are not done! We need to find y and z. I know you can do this. Remember y is one more than x and z is one more than y.
Check your work! Make sure these three consecutive numbers do in fact add up to -87.
a. 6
b. 10
c. 7
d. 9
Answer:
6
Step-by-step explanation:
21-20 = 1
20-18 =2
18 -15 = 3
15-11 = 4
We are subtracting 1 more each time
11-5 = 6
(07.03. 07.04 MC)
Part A: The area of a square is (4x2 + 20x + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show
your work (5 points)
Part B: The area of a rectangle is (4x2 - 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work
(5 points)
Answer:
A) 4x^2+20x+25=(2x)^2+2*(2x)*5+5^2=(2x+5)^2
Area=(side)^2, side=sqrt(area)=sqrt((2x+5)^2)=2x+5
B) 4x^2-9y^2=(2x-3y)(2x+3y), these are the dimensions of the rectangle
A) The length of each side of the square is (2x + 5).
B) The dimensions of the rectangle are (2x - 3y) and (2x + 3y).
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that,
Part A: The area of a square is [tex](4x^2 + 20x + 25)[/tex] square units.
Part B: The area of a rectangle is [tex](4x^2 - 9y^2)[/tex] square units.
A) Now the length of each side of the square is calculated by factoring the area expression completely,
[tex](4x^2 + 20x + 25)[/tex]
[tex]4x^2 + (10 + 10)x + 25[/tex]
[tex]4x^2 + 10x + 10x + 25[/tex]
[tex]2x (x + 5) + 5(2x + 5)[/tex]
[tex](2x + 5) (2x+5)[/tex]
Hence the length of each side of the square is (2x + 5).
B) the dimensions of the rectangle are calculated by factoring the area expression completely,
[tex](4x^2 - 9y^2)[/tex]
[tex](2x)^2 - (3y)^2[/tex]
[tex](2x - 3y) (2x + 3y)[/tex]
Therefore, the dimensions of the rectangle are (2x - 3y) and (2x + 3y).
To learn more about the rectangle visit:
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I need help ASAP please
Answer:
5:10
6 (-2,0)
7 (-5,6)
8 (5,3)
9 No, ab=8 CD=6
Step-by-step explanation:
2. In a 100m race, Luke was 2m ahead of Azam. Chandra was 3m behind Luke, Maggie was 7m ahead of Chandra. Luke was 5m behind Darren. Who was in the first place?
Answer:
luke won
Step-by-step explanation:
he is 2 meters ahead of azam witch is in 2dn place
write the greatest and smallest four digit number by using 7,8,0,9 digit
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 2.1yd : 1.4yd
9514 1404 393
Answer:
3/2
Step-by-step explanation:
Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.
[tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]
write 6x10x10x10x10 with an expont
Answer:
6x10^4
Step-by-step explanation:
50T Q12 A man wants to buy bags of gravel to cover his driveway. He decides to work out the area of his driveway. 1 bag of gravel covers 14m2 3m Sketch of driveway Not to scale 3m 8m 6m What is the area of his driveway? How many bags of gravel must he buy?
Answer:
hi amki nai patajjdkfkejd
Map Reading. A map is drawn so that every 3.3 inches on the map corresponds to an actual distance of 120
miles. If the actual distance between the two cities is 440 miles, how far apărt are they on the map?
The two cities are
inches apart on the map.
What is the coordinate of point P?
2.3
2.4
2.375
2.25
A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The coordinate of point p on the given number line is 2.375. The correct option is C.
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
Given that there are 8 divisions between two whole numbers, now since the point P is on the third division. Therefore, the coordinate of point p will be,
Coordinate of point P = 2 + 3/8
=2 + 0.375
= 2.375
Hence, the coordinate of point p on the given number line is 2.375.
Learn more about the Number line here:
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44y + 321x = 0 biết x=30000
Answer:
y= -240750/11
Step-by-step explanation:
44y + 321. 30000 = 0
44y = - 963000
y= -240750/11
PLEASE HELP
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
2y-3x=10
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Hey there! I'm happy to help!
Here is our equation.
[tex]2y-3x=10[/tex]
Let's add 3x to both sides.
[tex]2y=3x+10[/tex]
Divide both sides by 2.
[tex]y=\frac{3}{2}x+5[/tex]
Here is slope intercept form.
[tex]y=mx+b\\m=slope\\b=y-intercept[/tex]
So, we can just find those two things in the equation, and here are our answers.
[tex]y=\frac{3}{2}x+5\\m=\frac{3}{2}\\b=5[/tex]
The graph is down below. If our y-intercept is 5, then one of our points is (0,5). You can then plug a random x-value into the formula to find another point and then draw the line going through the two points.
[tex]y=\frac{3}{2}(2)+5\\y=3+5\\y=8\\(2,8)[/tex]
Have a wonderful day and keep on learning! :D
Find QR. please help I’m so lost on this I’ve done it i don’t know how many times. And got it wrong.
Answer:
Step-by-step explanation:
Using the theorem of the middle in a triangle:
[tex]2x+22=\dfrac{x+20}{2} \\\\4x+44=x+20\ cross\ products\\\\3x=-24\\\\x=-8\\[/tex]
What is the volume of the following rectangular prism?
Answer:
44/3
Step-by-step explanation:
V=L*W*H
WH=22/3
V=2*(22/3)
Please help do in an hour
Answer:
-4
Step-by-step explanation:
a1 = -8
an = an-1 +2
a2 = a1+2 = -8+2 = -6
a3 = a2+2 = -6+2 = -4
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample? Make sure to give a whole number answer.
Answer:
The administrator should sample 968 students.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.88}{2} = 0.06[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.06 = 0.94[/tex], so Z = 1.555.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 300.
This means that [tex]n = 300[/tex]
If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample?
This is n for which M = 15. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]15 = 1.555\frac{300}{\sqrt{n}}[/tex]
[tex]15\sqrt{n} = 300*1.555[/tex]
Dividing both sides by 15
[tex]\sqrt{n} = 20*1.555[/tex]
[tex](\sqrt{n})^2 = (20*1.555)^2[/tex]
[tex]n = 967.2[/tex]
Rounding up:
The administrator should sample 968 students.
In a geometric sequence, t4 = 8 and t7 = 216. Find the value of t2
Question 14 plz show ALL STEPS ASAP
Answer:
8/9
Step-by-step explanation:
Let the geometric series have the first term=a and common ratio=r. ATQ, ar^3=8 and ar^6=216. r^3=27. r=3. a=8/3^3=8/27. t2=ar=8/9
A car is traveling at a constant speed of 60 miles per hour. How many feet does it travel in 10 seconds?
Answer:
880 ft.
Step-by-step explanation:
First! We have to establish how many feet the car travels per hour.
60 (number of miles per hour) x 5280 (number of feet in a mile) = 316,800 (number of feet in an hour)
Next, since we know that there are 60 minutes in an hour we are going to divide our "number of feet in an hour" by 60 to get the "number of feet in a minute"
316,800 ÷ 60 = 5280
Once again, we are going to divide our "number of feet in a minute" by 60 to get the "number of feet per second".
5280 ÷ 60 = 88
Finally! We will multiple our "number of feet per second" by 10 to get how many feet the car can travel in 10 seconds.
88 × 10 = 880
So! Our car can travel 880 feet in 10 seconds.
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
