Answer:
[tex]a_{n}[/tex] = 1 [tex](5)^{n-1}[/tex]
Step-by-step explanation:
the explicit formula for a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{5}{1}[/tex] = 5 , then
[tex]a_{n}[/tex] = 1 [tex](5)^{n-1}[/tex]
What is the appropriate measure of variation (spread) for these data points? 47234213985132324365 what are q1 and q3 for these data?
The Interquartile Range (IQR) is the appropriate measure of variation for the given data points. Q1 and Q3 are 2 and 5 respectively.
The IQR is a method that gives the value of data at the 25th and 75th percentile. Alternatively, it gives the average of the two values which are nearest to these two percentiles, in case a single value does not exist. These values are called Q1 and Q3.
Because these values are less impacted by outliers than the standard deviation, it is best to use them with skewed data.
For the given data points, Q1 and Q3 are 2 and 5 respectively. Q1 is the average of 5th and 6th values. Q3 is the average of 15th and 16th values.
To learn more about the interquartile range, refer to this link:
brainly.com/question/11647487
The Interquartile Range (IQR) is the appropriate measure of variation for the given data points. Q1 and Q3 are 2 and 5 respectively.
The IQR is a method that gives the value of data at the 25th and 75th percentile. Alternatively, it gives the average of the two values which are nearest to these two percentiles, in case a single value does not exist. These values are called Q1 and Q3.
Because these values are less impacted by outliers than the standard deviation, it is best to use them with skewed data.
For the given data points, Q1 and Q3 are 2 and 5 respectively. Q1 is the average of 5th and 6th values. Q3 is the average of 15th and 16th values.
To learn more about the interquartile range, refer to this link:
brainly.com/question/11647487
#SPJ4
An elementary school is offering 3 language classes one in spanish one in french, if 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?
The probability that atleast one students is taking a language class is 0.7
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Let :
Spanish = S ; French = F ; German = G
SnFnG = 3
(SnF) only = 9 - 3 = 6
(SnG) only = 5 - 3 = 2
(FnG) only = 5 - 3 = 2
S only = 28 - (6+3+2) = 17
F only = 21 - (2+3+2) = 14
G only = 12 - (6+3+2) = 1
Student not taking any of the classes are;
(100 - (17+14+1+2+2+6+3))
100 - 45 = 55
Atleast 1 is taking a language class out of 2 selected
The probability that atleast one students is taking a language class :
(45/100 * 55/99) + (55/100 * 45/99) + (45/100 * 44/99)
= 0.7
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ4
can u help me find the GCF of monomials/ with solution
1). 14, 42
2) 16a, 20
3) 22d,33e,99f
4)21b, 14ab, 49bc
14, 4, 11, 7
1. 14, 42
14 = 2 x 7
42 = 2 x 3 x 7
GCF = 14
2. 16a , 20
16a= 2 x 2x2x2xa
20 = 2 x 2 x 5
GCF = 4
3) 22d,33e,99f
22d = 2 x 11x d
33e = 3 x 11 x e
99f = 3 x3 x 11 xf
GCF = 11
4)21b, 14ab, 49bc
21b= 3 x 7 xb
14ab = 2 x 7 x a x b
49bc = 7 x7xb x c
GCF = 7
To learn more about GCF, refer to https://brainly.com/question/219464
#SPJ9
What values of b satisfy 3(26 + 3)² = 36?
The numeric value of the b is 0.23 which satisfy the given equation.
According to the statement
We have to find that the value of the b.
So, For this purpose, we know that the
The numeric value refers to the worth of each digit depending on where it lies in the number.
From the given information:
The equation is a
3(2b + 3)² = 36
then to find the value of b rearrange the terms then
(2b + 3)² = 12
(2b + 3) = \sqrt{12}
(2b) = \sqrt{12} -3
then
b = \sqrt{12} -3/ 2
b = 3.46 - 3/2
b = 0.46/2
b = 0.23.
So, The numeric value of the b is 0.23 which satisfy the given equation.
Learn more about numeric value here
https://brainly.com/question/24703884
#SPJ9
19
Select the correct answer.
A boat is anchored in the water. At low tide, the boat is floating 20 feet above the seafloor and is a horizontal distance of 40 feet away from its
anchor. At high tide, the boat is a horizontal distance of 35 feet away from its anchor.
low tide
high tide
20 ft
? ft
40 ft
35 ft
Approximately how high is the boat floating above the seafloor at high tide? Assume the anchor rope remains tight, without any slack.
OA 22.5 ft
OB. 27.8 ft
OC
15.6 ft
OD. 35.7 ft
Reset
Next
The height of the boat floating above the seafloor at high tide is 17.5 feet.
In this question, we have been given a boat which is anchored in the water.
At low tide, the boat is floating 20 feet above the seafloor and is a horizontal distance of 40 feet away from its anchor.
And at high tide, the boat is a horizontal distance of 35 feet away from its anchor.
We need to find the distance the boat floating above the seafloor at high tide.
Consider the following diagram.
Let the boat floating m feet above the seafloor when the boat is a horizontal distance of 35 feet away from its anchor.
Since both the triangle are similar triangles, the corresponding sides must be in proportion.
⇒ 20/40 = m/35
We need to find the value of m.
⇒ 20 × 35 = m × 40
⇒ m = 35 / 2
⇒ m = 17.5 feet
Therefore, the height of the boat floating above the seafloor at high tide is 17.5 feet.
Learn more on similar triangles here:
https://brainly.com/question/25882965
#SPJ1
Find an equation in point-slope form for the line having the slope m= -3 and containing the point (6,3).
l...................................................
Lashonda is participating in a 4 day cross-country biking challenge. she biked for 50,51,63 and miles on the first three days. how many miles does she need to bike on the last day so that her average (mean) is 54 miles per day?
Lashonda biked for 50,51, and 63 miles on the first three days, to make average 54 miles per she needs to bike 52 miles on the last day.
As given,
Lashonda biked for first three days = 50, 51, 63 miles
Let x miles she bike last day
Average = 54 miles per day
Average = (50 + 51 + 63 + x) /4
⇒ 54 = (164 + x) /4
⇒ x = 216-164
⇒ x= 52 miles
Therefore, Lashonda needs to bike 52miles last day to make average 54miles per day.
Learn more about average here
brainly.com/question/27646993
#SPJ4
Help please for algebra
in slope intercept form:
y=mx+b.
slope of line:
-3/4
y intercept:
(0, 5/2)
How do I solve this question?
DE is parallel to ST as ∠ EAT = ∠ AED which are alternate interior angles.
∠TAC = ∠ABC (The angle between the chord and the tangent is equal to the angle in the alternate segment)
Since, EDCB is a cyclic quadrilateral,
∠CBD + ∠CED = 180 ----- I
- ∠CED + ∠AED = 180 -----II
----------------------------------------------------
∠ CBD = ∠AED
Also, ∠ CBD = ∠ EAT( A is tangent to the circle)
So, ∠ EAT = ∠ AED ( Alternate interior angle)
So, DE || ST
Therefore, DE is parallel to ST as ∠ EAT = ∠ AED which are alternate interior angles.
Learn more about alternate interior angles here:
https://brainly.com/question/24839702
#SPJ9
Which graph represents the equation y=34x−3?
Answer:
The graph in the top right hand corner.
Hope this helps :)
Step-by-step explanation:
The formula y = mx + b
shows that m is the slope and b is the y-intercept.
m = 34
b = - 3
So to find the equation of the graph I looked at the y-intercept which is -3 and the graph in the right hand corner has a y-inyercept of -3 so that graph represents the equation y = 34x - 3
Reason:
The equation is y = (3/4)x - 3 which is in y = mx+b form
m = slope = 3/4
b = -3 = y intercept
The y intercept of -3 means the point (0,-3) is on the line. Start at this point and go up 3, then to the right 4 to arrive at (4,0) which is the x intercept. The motion "up 3, right 4" is directly from the slope 3/4
slope = rise/run = 3/4
rise = 3 = go up 3
run = 4 = go right 4
Rewrite the expression with rational exponents as a radical expression. 7 times x to the two thirds power 9 times the cube root of x to the power of 2 7 times the square root of x to the power of 3 cube root of the quantity 9 times x to the power of 2 square root of the quantity 9 times x to the power of 3
According to the given statement:
Equation one:
(7x)[tex]\frac{2}{3}[/tex]
Equation two:
√(9x)²
Equation three:
√(7x)³
Equation four:
∛(9x)²
Equation five
√(7x)³
What radical expression would that be?Square-root-containing expressions are known as radical expressions. The radical symbol's "radicand" is a number or expression. A radical equation is one that uses radical expressions as the radicands for variables.
According to the given data:The expression's root is represented by the symbol known as the radical. n√x.
The following radical expression can be used to write the given statement:
Equation one:
(7x)[tex]\frac{2}{3}[/tex]
Equation two:
√(9x)²
Equation Three:
√(7x)³
Equation four:
∛(9x)²
Equation Five:
√(7x)³
To know more about radical expression visit:
https://brainly.com/question/16312248
#SPJ4
I understand that the question you are looking for is:
Rewrite the expression with rational exponents as a radical expression.
7 times x to the two thirds power9 times the cube root of x to the power of 2 7 times the square root of x to the power of 3cube root of the quantity 9 times x to the power of 2square root of the quantity 9 times x to the power of 3Solve the given differential equation by undetermined coefficients. y'' 7y' 6y = 30
The complementary solution is Ус = C₁е¯ + C₂е¯ -6x
Consider the differential equation
=y" + 7y' + 6y = 30...(1)
Rewrite the equation,(D² + 7D + 6)y = 30 where
d /D = dx
Auxiliary equation is,
f(m) = 0
3 m³ +7m+6=0
m² + 6m+m+6=0
m(m+6) +1(m+6) = 0
(m +6)(m + 1) = 0
m = −1, −6 -6
Hence,
The complementary solution is Ус = C₁е¯ + C₂е¯ -6x
To know more about "Differential Equation"
Refer this link:
https://brainly.com/question/14617716
#SPJ4
What is the area of the shaded region?
Answer:
208
Step-by-step explanation:
4*30 = 120
(15-4) * 8 = 88
88 + 120 = 208
Answer:
208 cm
Step-by-step explanation:
Solving right side first. 8*15=120
Take out 8cm from 30. 30 - 8 = 22
22*4= 88
88 + 120 = 208
Check work I found the total area and the white rectangle.
15*30=450 which in total area
15-4=11 11 is the left/right side of the white rectangle
30-8=22 22 is the top/bottom side of the white rectangle.
22*11= 242
208+242=450
someone pls help asap thank u so much
Answer: $16.67
Step-by-step explanation:
8% of $48 = 16.67
The first one would be $ 3.59
Explanation- 15% of 23.95 = 3.5925
Rounded off to max. 2 decimal places:
Percentage of
15% of 23.95 ≈ 3.59
At a fish fry fundraiser, the math club raised $277.50. child plates were sold for $2.25 and adult plates were sold for $4.75. if there were twice as many child plates sold than adult plates, how many adult plates were sold?
The number of adult plates sold are 30.
It is given in the question that:-
Total money raised by math club = $277.50
Cost of a child plate = $2.25
Cost of an adult plate = $4.75
There are twice as many child plates sold than adult plates.
Let the number of adult plates be x.
Hence, according to the question,
Number of child plates = 2x
Using this data, we can form a linear equation,
2.25*2x + 4.75*x = 277.50
4.50x + 4.75x = 277.50
9.25x = 277.50
x = 277.50/9.25
x = 30
Hence, the number of adult plates sold are 30.
To learn more about linear equation, here:-
https://brainly.com/question/11897796
#SPJ4
In a figure, m < a = 15x + 81 and m < c = 10x + 24 if < a and < c are supplementary find the measure of angle c.
The measure of angle c is 54 degrees
How to find the measure of angle c?The given parameters are
a = 15x + 81
c = 10x + 24
Angles a and c are supplementary angles
So, we have
a + c = 180
This gives
15x + 81 + 10x + 24 = 180
Evaluate the like terms
25x = 75
Divide by 25
x =3
Substitute x =3 in c = 10x + 24
c = 10 * 3 + 24
Evaluate
c = 54
Hence, the measure of angle c is 54 degrees
Read more about supplementary angles at
https://brainly.com/question/2046046
#SPJ1
A polynomial function g(x) has a negative leading coefficient. Certain values of g(x) are given in the following table. x –4 –1 0 1 5 8 12 g(x) 0 –3 –1 –2 0 3 0 If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)?
By factor theorem and limits, it is found that the end behavior of g(x) is that it goes to negative infinity.
The values of x and g(x) are
x –4 –1 0 1 5 8 12
g(x) 0 –3 –1 –2 0 3 0
We need to find the end behavior of g(x).
What is Factor theorem?The Factor Theorem states that a function with leading coefficient a and zeros x1,x2,x3...xn is defined by:
g(x)=(x-x1)(x-x2)(x-x3)..(x-xn)
By definition of factor theorem,
g(x)=a(x-(-4))(x-12)
g(x)=a(x+4)(x-12)
g(x)=a(x2-8x-48)
The end behavior is the limit of g(x) as x goes to infinity, thus:
lim[tex]lim \lim_{x \to \infty} g(x)= \lim_{x \to \infty} ax^{2} =a*\infty[/tex]
Since the leading coefficient a is negative:
a*infinity= - infinity
Thus the end behaviour of g(x) it goes to negative infinity.
To learn more on Factor theorem click: https://brainly.com/question/24248193
#SPJ1
Astronauts brought back 500 lb of rock samples from the moon.how many kilograms did they bring back?1 kg = 2.20 lb227 kg227 kg498 kg498 kg500 kg500 kg1,100 kg
Astronauts brought back 500 lbs rock samples from the moon they brought back 227 kilograms of sample. The correct option is D.
Who, in brief, is an astronaut?
A space traveler is referred to as an astronaut. The term "astronaut" is currently used to designate to anyone traveling on a spaceship, including civilians, whereas it was previously reserved for military-trained experts.As the astronaut brought 550 lbs sample,
2.20lbs = 1 kg.
1 lbs = 1/2.20
1 lbs = 0.45
so, 500 lbs nearly implies 227kgs.
Thus, the correct option is D.
Learn more about Astronauts
brainly.com/question/11244838
#SPJ4
solve 2x-9y=14 for y
The value of y in expression is 14-2x/-9
How to calculate the value of y ?The expression is written as
2x - 9y = 14
We are asked to calculate the value of y in the expression
2x - 9y = 14
-9y= 14-2x
Divide by the coefficient of y which is -9
y= 14-2x/-9
Hence the value of y is 14-2x/-9
Read more on expression here
https://brainly.com/question/20790743
#SPJ1
Evaluate the following function when x = -1 and x = 2 and determine the sum of the two results:
Answer:
J. 1
Step-by-step explanation:
Plug the x values into the equation:
f(-1)=3-(-1)^2
f(2)=3-(2)^2
Solve each one, then add.
3-(-1)^2=
=3-1=2
3-(2)^2=
=3-4=-1
Combine the answers together.
2-1=1
The answer is J. 1.
Hope this helps!
Please mark as brainliest if correct!
What is the answer ?
Answer:
xy + z = 16
5(2) = 10 + 6 = 16
(MGSE9-12.N.RN.2) Multiply radical expression and write your answer in the simplest radical form. 2√5 (√6 +2). A) 30√2+4√5 B) 2√30+4√5 C) 2√11+4√5 D) 60+4√5
The simplest radical form. 2√5 (√6 +2).
The Simplification form of 2√5 (√6 +2) is B) 2√(30) + 4√5Given that
2√5 (√6 +2)To find
Simplest radical form of 2√5 (√6 +2) = ........?We know that
Simplest radical form is the expression in radical form that, after rationalizing the denominator, leaves no more square roots, cube roots, fourth roots, or other roots to find
So, according to the question
We have
2√5 (√6 +2)To find the simplest radical form of the given problem, we must first solve those brackets, then multiply under root numbers in root and without root numbers with without root numbers.
So now, let's follow that process
We will get,
2√5 (√6 +2) = 2√5 ×√6 +2√5 ×2
= 2√(5×6) + 2×2×√5
= 2√(30) + 4√5
So the radical form of that given problem is B) 2√(30) + 4√5
To learn more about simplest radical form of any problem, please click on the link:
https://brainly.com/question/7440652
#SPJ9
Roman earns $8.50 an hour as an intern at law firm. Usually he works 30 hours a week. This week however, there is a big case and he worked 47 hours. What is his gross pay for this week? (Standard overtime rules.)
The gross pay for this week after working overtime is $471.75.
What is the overtime pay rule?
The civil overtime vittles are contained in the Fair Labor norms Act, Unless pure, workers covered by the Act must admit overtime pay for hours worked over 40 in a workweek at a rate not lower than time, and That's an illustration of total pay for a hand who worked 42 hours in a workweek Regular pay rate x 40 hours = Regular pay, plus. Regular pay rate x1.5 x 2 hours = Overtime pay, equals.
Usual earning Earning = $8.5 for 30 hours for a week
Overtime = 47 hours-30 =17 hours
Overtime rate = $8.5 + $8.5/2 = $ 12.75 for hour for a week
Gross pay= ($8.5*30)+($12.75*17)
= 255 + 216.75
= 471.75.
The gross pay for this week after working overtime is $471.75.
Learn more about the overtime pay rule here: https://brainly.com/question/788795
#SPJ9
Express this number in scientific notation.
621,000
621,000=
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
Answer:
6.21 × 10⁵
Step-by-step explanation:
move thee decimal from .21000 thats how you get 5
-10+l 6+-17l - - 14 show how you got the answer
The solution to the expression -10 + |6 + -17| -- 14 is 15
How to evaluate the expression?The expression is given as:
-10+l 6+-17l - - 14
Rewrite properly as
-10 + |6 + -17| -- 14
Evaluate the sum and the difference
So, we have:
-10 + |6 + -17| -- 14 = -10 + |-11| + 14
Remove the absolute bracket
-10 + |6 + -17| -- 14 = -10 + 11 + 14
Evaluate the sum
-10 + |6 + -17| -- 14 = 15
Hence, the solution to the expression -10 + |6 + -17| -- 14 is 15
Read more about expressions at:
https://brainly.com/question/723406
#SPJ1
The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function f(x)= 10(0.5)". What
is the multiplicative rate of change of the
function?
0.5
2.5
5
Mark this and retum
/ContentViewers/AssessmentViewer/Activit...
The multiplicative rate of a change of the function is 0.5
To solve this question, look at the y coordinates. To get from 10 to 5, and from 5 to 2.5, you divide them by 2. In other words, you multiply them by 0.5. So, the multiplicative rate will be 0 .5.
if we want to find the multiplication. The rate of change of a function, that just means we need to divide one item by the one that comes before it .
An exponential function is a nonlinear function that has the form of. y=abx,wherea≠0,b>0. An exponential function with a > 0 and b > 1, like the one above, represents an exponential growth and the graph of an exponential growth function rises from left to right,this is the multiplicative rate in exponential function.
You can also calculate exponential growth using the formula f(x) = a(1 + r)x, where:
The f(x) term represents the function.
The a variable stands for the beginning value of your data.
The r variable represents the growth rate.
The x variable is the time interval.
.to know more about multiplicative rate ;
visit;https://brainly.com/question/530552
#SPJ9
Durante un entrenamiento, un ciclista da una vuelta a una pista circular en 105 segundos, mientras que otro tarda 60 segundos. Si ambos inician sus recorridos juntos, ¿en cuántos segundos será la próxima vez que coincidan en el punto de inicio?
Los ciclistas se encuentran aproximadamente 140 segundos después de partir.
¿En cuanto tiempo se encuentran dos ciclistas que se mueve a distintas rapideces constantes por primera vez?
En este problema asumimos que cada ciclista se mueve a rapidez constante, de modo que la rapidez angular de cada uno se define como sigue:
ω = 2π / T (1)
Donde:
ω - Rapidez angular, en radianes por segundo.T - Período, en segundos.A su vez, la posición de cada ciclista es descrita por las siguientes dos ecuaciones paramétricas:
x / R = cos ωt (2)
y / R = sin ωt (3)
Donde:
x, y - Coordenadas del ciclista.R - Radio de la pista circular.Primero, determinar la rapidez angular de cada ciclista:
ω₁ = 2π / 105 s
ω₁ ≈ 0.060 rad / s
ω₂ = 2π / 60 s
ω₂ ≈ 0.105 rad / s
Segundo, procedemos a graficar cada función paramétrica y determinamos el primer punto de intersección. Los resultados se encuentran en las imágenes adjuntas. Nótese que las curvas verde y púrpura se basan en la ecuación (2), mientras las curvas azul y rojo lo son de la ecuación (3).
Los dos ciclistas se encuentran por primera vez si las cuatro ecuaciones tienen el mismo valor t. En consecuencia, los ciclistas se encuentran aproximadamente 140 segundos después de partir.
Para aprender más sobre ecuaciones paramétricas: https://brainly.com/question/9056657
#SPJ1
Suppose a survey of 979 business owners found that more than ought . which part of the survey represents the descriptive branch of statistics? make an inference based on the results of the survey.
Women make up 64% of the sample and are typically the household's main investment.
There is a correlation between American women and being the main provider in their home.
What is Descriptive Statistics?Descriptive statistics, also known as brief informative coefficients, are used to summarize a specific data collection, which may be a sample of a population or a representation of the entire population. Descriptive statistics include measures of variability and central tendency (spread). Measures of central tendency include the mean, median, and mode, whereas measures of variability include the standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.
For instance, the sum of the following data set is 20: (2, 3, 4, 5, 6). A 4 (20/5) is the mean. A data set's mode is the number that appears most frequently, while its median is the value that is in the middle of the range of values. It is the value that separates a data set's higher values from lower values. There are many less common ways to use descriptive statistics, but they are nevertheless essential.
To learn more about the, Descriptive Statistics visit:
https://brainly.com/question/13335435
#SPJ4
The correct question is - Suppose a survey of 580 women in the United States found that more than 64% are the primary investor in their household. Which part of the survey represents the descriptive branch of statistics? Make an inference based on the results of the survey.
answer the question in the photo
Answer: input is h, output is k
Step-by-step explanation: inserting a number into h will give you your outcome of k in the solution
Answer:
Step-by-step explanation:
If f(x) = 24x + 24, find the instantaneous rate of change of f(x) at x = 6
Answer:
168
Step-by-step explanation:
You'd plug 6 in for x
f(x) = 24x + 24
f(6) = 24(6) + 24
f(6) = 144 + 24
f(6) = 168
