The sequence 3/32, 3/16, 3/8, 3/4, 3/2, 3,6, ... is a geometric sequence with common ratio 2.
To determine whether the sequence is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic sequence, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric sequence, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given sequence is:
3/32, 3/16, 3/8, 3/4, 3/2, 3,6, . . . .
Notice that
a(2) : a(1) = 3/16 : 3/32 = 2
a(3) : a(2) = 3/8 : 3/16 = 2
and so on
Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 2
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The expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped. What is the distance the object falls during each time?
0.25 second
If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped then the distance the object falls during 0.25 second time is 1 feet
Given,
The expression of distance in feet that an object falls = [tex]16t^{2}[/tex]
Where t is the time seconds
Then the time = 0.25 second
Substitute the values in the expression = [tex]16(0.25)^{2}[/tex]
=1 feet
Hence, If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped then the distance the object falls during 0.25 second time is 1 feet
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please help me again!! i’m probably not focusing because i’m tired.
Answer: x=14
Step-by-step explanation:
First let's find all the inner angles of the triangle.
124+DCB=180 ==> Angles DCB and 124 lie on a straight line. Straight lines measure 180 degrees and are called straight angles.
124+DCB=180
124-124+DCB=180-124
DCB=180-124
DCB=56 degrees
6x+CBD=180 ==> straight angle
2x+CBD+56=180 ==> total degrees of a triangle is 180 degrees
6x+CBD=2x+CBD+56 ==> they both equal 180
6x+CBD-CBD=2x+CBD-CBD+56
6x=2x+56
6x-2x=2x-2x+56
4x=56
4x/4=56/4
x=14
A store pays $10 for a blanket. The markup is 35%. What do they sell it for?
Write an explicit formula for each geometric sequence. 25,5,1, 1/5, . . .
The explicit formula is [tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
For the Geometric sequence, the explicit formula for the nth term is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
Where,
a = first number of the series
r = common ratio
n = number of series
[tex]a_{1}[/tex] = a
[tex]a_{2}[/tex] = ar
[tex]a_{3}[/tex] = a [tex]r^{2}[/tex]
.....
Therefore the series is a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex],,,,.....
Here we have the series 25, 5, 1, 1/5
Here common ratio = 1/5
and if we want to find the 5th term the formula is
[tex]a_{5}[/tex] = 25 ×[tex](\frac{1}{5} )^{4}[/tex]
= [tex]\frac{1}{25}[/tex]
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if t+t = 0
what is the answer
Answer:
t = 0
Step-by-step explanation:
t + t = 0 , that is
2t = 0 ( isolate t by dividing both sides by 2 )
t = [tex]\frac{0}{2}[/tex] = 0
Answer:
t=0
Step-by-step explanation:
t+t is 0 and since were not given any numbers for t its automatically 0
i can't figure this out
2/3(x-3)+6x
Step-by-step explanation:
Have you understand? please notify when you don't understand
What set of reflections and rotations would carry rectangle ABCD onto itself?
Reflect over the y-axis, reflect over the x-axis, rotate 180°
Rotate 180°, reflect over the x-axis, reflect over the line y = x
Reflect over the x-axis, rotate 180°, reflect over the x-axis
Rotate 180°, reflect over the y-axis, reflect over the line y = x
Answer:
2 line is the answer to the questions
Given:
A={1,2,3,4,5,6,7,8,9,10}
B={2,4,6,8,10}
C={1,3,5,7,9}
1.A ꓵ C=
2.B ꓵ C=
3.A ꓵ B=
4.A U B=
5.B U C=
6.A U C=
7.A - C=
8.B - C=
9.A - B=
10.C - A=
Answer:
The answers are as follows:
A ꓵ C = {1, 3, 5, 7, 9}B ꓵ C = 0A ꓵ B = {2, 4, 6, 8, 10}A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}B U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}A U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}A - C = {2, 4, 6, 8, 10}B - C = {2, 4, 6, 8, 10}A - B = {1, 3, 5, 7, 9}C - A = 0I hope they help21. x ≥-1
y> -2 on a graph
Answer:
perhaps it is 7.09809809876 or it might be 5.437437437, a recursive number.
Step-by-step explanation:
i might be
The area of Miki's room is x²+8 x+12 square feet. A gallon of paint will cover an area of x²+6 x+8 square feet. Which expression gives the number of gallons of paint that Miki will need to buy to paint her room?
F. x+6 / x+4
G. x-4 / x-6
H. x+4 / x+6
J. x-4 / x+6
The expression that gives the number of gallons of paint that Miki will need to buy to paint her room is F. (x + 6) / (x + 4)
Expression:
Expression are the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given,
The area of Miki's room is x²+8 x+12 square feet. A gallon of paint will cover an area of x²+6 x+8 square feet.
Here we need to find the expression that gives the number of gallons of paint that Miki will need to buy to paint her room .
The number of gallons of paint required to paint the room is calculated by dividing the expression.
Then we get,
=> [tex]\frac{x^{2} +8 x+12}{x^2+6x+8}[/tex]
Factor the numerator and the denominator to simplify the fraction.
So, the factors of
=> x² + 8x + 12 = (x+6) (x+2)
and the factors of
=> x² + 6x + 8 = (x+4) (x+2)
When we apply the factors instead of the given expression,
Then we get,
=> [tex]\frac{(x+6)(x+2)}{(x+4)(x+2)}[/tex]
After the simplification we get,
=> (x +6) / (x + 4)
So, the option is F. (x+6) / (x+4) is the correct expression that gives the number of gallons of paint that Miki will need to buy to paint her room .
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if the coffee is hot then you shouldn't drink it
Answer: Yes only if is is so hot it will burn yout tung but you dont want cold coffe so
Step-by-step explanation:
Answer:
Step-by-step explanation:
I agree with the first answer but maybe people like cold brews, i know i do. also people on here be asking the craziest questions bro like i just answered "what are your thoughts about brainly being a dating app" i was like what ;-;
The drying time of one particular paint is approximately normally distributed with a mean of 45
minutes. It is also known that 15% of walls painted with this paint need more than 55 minutes to
dry completely. Find the standard deviation of this distribution.
The standard deviation of this distribution is 9.65 minutes.
Due to its description in terms of the second central moment, the standard deviation naturally arises in mathematical statistics.
Any distribution with finite first two moments can have its standard deviation defined, although the most common assumption is that the underlying distribution is normal.
In the above given question it is stated that:
mean(μ) of the distribution is 45 and let us consider the standard deviation to be σ
We convert this to standard normal as
[tex]P(X < x) = P(Z < \frac{( x - \mu)} {\sigma})[/tex]
We have , P(X > 55) = 0.15 (15%)
This can be simplified as:
P(X < 55) = 1 - 0.15
P(X < 55) = 0.85
[tex]P(Z < \frac{( x - \mu)} {\sigma}) = 0.85[/tex]
From Z table, z-score for the probability of 0.85 is found out to be 1.0364 ,
therefore :
[tex]\frac{( 55 - 45)}{ \sigma }= 1.0364\\\\ \sigma = ( 55 - 45) / 1.0364 \\\\\sigma = 9.65[/tex]
Hence the standard deviation is 9.65 minutes.
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5 Granola bars cost $4.00
b. Fill in the table that shows the
costs for 10, 15, and
20 granola bars. Find the cost for a
single granola bar in each case.
Answer:
1 granola bar =
Step-by-step explanation:
10 granola bars= $4.00 x 2 = $8.00
15 granola bars=$4.00 x 3 = $12.00
20 granola bars=$4.00 x 4 = $16.00
1 granola bar = $0.80p
Suppose you toss a coin four times. What is the probability of getting four tails?
Answer:
1/16
Step-by-step explanation:
Coin toss
probability 1/2×1/2×1/2×1/2 = 1/16
PART 2!!
Topic: Addition and Subtraction of polynomials
Directions: Simplify each rational expressions
Step-by-step explanation:
4.
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{a - b}{a + b} [/tex]
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{(a - b)(a - b)}{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{ {a}^{2} - 2ab + {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab - ( {a}^{2} - 2ab + {b}^{2} ) }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab - {a}^{2} + 2ab - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{7ab - {a}^{2} - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] \: [/tex]
5.
[tex] = \frac{5}{n + 5} + \frac{4n}{2n + 6} [/tex]
[tex] = \frac{5}{n + 5} + \frac{4n}{2(n + 3)} [/tex]
[tex] = \frac{5}{n + 5} + \frac{2n}{n + 3} [/tex]
[tex] = \frac{5(n + 3) + 2(n + 5)}{ {n}^{2} + 8n + 15 } [/tex]
[tex] = \frac{5n + 15 + 2n + 10}{ {n}^{2} + 8n + 15} [/tex]
[tex] = \frac{7n + 25}{ {n}^{2} + 8n + 15} [/tex]
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve these problems ~
Problem 1 ~[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab}{ {a}^{2} - {b}^{2} } - \dfrac{a - b}{a + b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab}{ (a + b)(a - b) } - \dfrac{a - b}{a + b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a - b)(a - b)}{ (a + b)(a - b) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a - b) {}^{2} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a {}^{2} - 2ab + {b}^{2} ) {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - a {}^{2} + 2ab - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{7ab - a {}^{2} - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
Problem 2 ~[tex]\qquad \sf \dashrightarrow \: \dfrac{5}{n + 5} + \dfrac{4n}{2n + 6} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5(2n + 6) + 4n(n + 5)}{(2n + 6)(n + 5)} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{10n +30 + 4n {}^{2} + 20n}{2n {}^{2} + 10n + 6n +30} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{4n {}^{2} + 30n + 30}{2n {}^{2} + 16n + 30} [/tex]
[ taking 2 common out ]
[tex]{ \qquad \sf \dashrightarrow \: \dfrac{2n {}^{2} + 15n + 15}{n {}^{2} + 8n + 15}} [/tex]
if the car continues at the same accerleration meaning the slope of the line does not change how fast would it be going in 15 seconds
The car's velocity after 15 seconds is 60.3 m/s.
What is velocity?Velocity is the directional speed of a moving object as an indication of its rate of change in position as observed from a specific frame of reference and measured by a specific time standard.The linear regression equation obtained by fitting the data using technology is:
y = 3.64x + 5.7x = times(seconds) ; y = velocity(m/s)The approximate velocity at time = 0 and x = 0 is as follows:
y = 3.64(0) + 5.7y = 0 + 5.7y = 5.7 m/sAfter 15 seconds, the velocity is:
At time, x = 15 secondsy = 3.64(15) + 5.7y = 60.3 m/sTherefore, the car's velocity after 15 seconds is 60.3 m/s.
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what can 6 divided by using a -1/2?
Simplify each rational expression. State any restrictions on the variable. c²-8 c+12 / c²-11 c+30
Simplify each rational expression. State any restrictions on the variable.
[tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\frac{(c-2)}{(c-5)}[/tex]
How the rational expression is simplified?
[tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }\\\\= > \frac{(c-2)(c-6)}{(c-5)(c-6)} \\= > \frac{(c-2)}{(c-5)}[/tex]
What are the restrictions on the variable ?
If c= 5 , the denominator becomes,
[tex]c^{2} -11c+30[/tex] =25-55+30=0
⇒ [tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\infty[/tex]
If c= 6 ,the denominator becomes,
[tex]c^{2} -11c+30[/tex] = 36- 66+30=0
⇒ [tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\infty[/tex]
So, the restrictions on the variable are: c≠ 5,6
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2(-4)² + (-4)³ +24 - 18(-12)2
Answer:
-440
Step-by-step explanation:
Simplify
2(-4)^2+(-4)^3+24-18(-12)2
2(16)+(-64)+24-432
32-64+24-432
-440
50 PTS - Functional Notation. Please explain how to do this!
9+6.6x=7x-8.7
Help me solve it please
Answer:
x = 44.25
Step-by-step explanation:
9 + 6.6x = 7x - 8.7
-7x -7x
---------------------------
9 - 0.4x = -8.7
-9 -9
-0.4x = -17.7
÷-0.4 ÷-0.4
-------------------
x = 44.25
Your teacher asks you to find a recipe that includes two ingredients with a ratio of 1/2 over one 1/8 cup . Give an example of two ingredients in a recipe that would meet this requirement
The recipe of flour and sugar can be given as an example where we will get the ratio as 4 : 1.
The example is with flour and sugar
Let
x = the number of cups of flour
y = the number of cups of sugar
We know that:
Ratio means the comparison between the two values.
Ratio = x / y
Now, we can let
x = 1 / 2 cups of flour
y = 1 / 8 cups of sugar
Ratio will be
= 1 / 2 : 1 / 8
= 8 : 2
= 4 : 1
Therefore, the recipe of flour and sugar can be given as an example where we will get the ratio as 4 : 1.
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Need help finding x please
Answer:
[tex]x = \frac{64}{3} [/tex]
Step-by-step explanation:
Based on the given conditions:
[tex] \frac{x}{32} = \frac{12}{12 + 6} ⟹ \frac{x}{32} = \frac{12}{18} [/tex]
Cross multiply the above
[tex]18x = 384 [/tex]
Divide both sides by 18 to find the value of x
[tex]x = \frac{384}{18} [/tex]
Therefore:
[tex]x = \frac{64}{3} [/tex]
Find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of miles per hour. speed (miles per hour) 4245 4649 5053 5457 5861 frequency
47.4 is the mean of the data summarized in the given frequency distribution.
What is a frequency distribution?
The number of times a value appears in a dataset is its frequency. The pattern of frequencies for a variable is known as a frequency distribution. The frequency with which each potential value of a variable appears in a dataset.speed m f m*f
42-45 43.5 22 957
46-49 47.5 14 665
50-53 51.5 7 360.5
54-57 55.5 4 222
58-61 59.5 2 119
Total 49 2323.5
mean = 2323.5/49 = 47.4
The computed mean is not close to the actual mean because the difference between the means is more than 5%.
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The graph shows the cube root parent function. Which statement is true? A. (0, 1) is the x and y-intercept of the function. B. The function has no intercepts. C. (1, 1) is the x and y-intercept of the function. D. (0,0) is the x and y-intercept of the function.
Answer:
D
Step-by-step explanation:
X and y come together at (0,0) right?
Write an equation of each line in point-slope form.
(-4,-3) and (2,7
The equation of the line in point-slope form, which passes through the pair of points located at (-4 , -3) and (2 , 7), is y + 3 = 5/3(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-4 , -3) and (2 , 7).
m = (y2 - y1)/(x2 - x1)
m = (7 - -3)/(2 - -4)
m = 10/6
m = 5/3
Using the point slope form, plug in the values of the slope and Point A to set up the equation.
(y - y1) = m(x - x1)
where m = 5/3 and (x1 , y1) = (-4 , -3)
(y - -3) = 5/3(x - -4)
y + 3 = 5/3(x + 4)
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In the first half football season, Marco ran 4 plays for a gain of 60 yards. During the second half of the season, Marco was responsible for 6 penalties resulting in a loss of 80 yards. What was his total yardage for his football season?
Factor each expression completely.
3 x²-75
If the distance between Earth and the Sun is actually 150,000,000 kilometers, how far apart are Earth and the Sun when using the 1:93,000,000 scale model?
The scaled distance using the given scale factor is; 1.613 units
How to use the scale model?
We are given;
Distance between Earth and the sun = 150, 000, 000 km
Now, we are given that the scale model that represents Distance between Earth and the sun is 1:93,000,000.
This means that 1 unit represents 93000000 kilometers. Thus;
The scaled distance using the given scale factor is;
150,000,000/93,000,000 = 1.613 units
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There are n socks, 3 of which are red, in a drawer. what is the value of if, when 2 of the socks are chosen randomly, the probability that they are both r e d i s 12 ?
n=4 is the value of if, when 2 of the socks are chosen randomly, the probability that they are both r e d i s 12.
What is the probability in simple terms?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.Number of socks = n .
Number of red socks = 3 .
Given
3C2nC2=12
⇒nC2=3×2=6
⇒n=4
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