The first five terms of a geometric sequence with first term -100 and common ratio 1/5 are -100, -20, -4, -4/5, -4/25
The given parameters:
a₁ = -100, r = 1/5
r is the common ratio, hence, the given sequence is a geometric sequence.
In a geometric sequence, the formula for the nth term is given by:
a(n) = a(1) . rⁿ⁻¹
We can also find the terms using recursive formula. The nth term of a geometric sequence is equal to the (n-1)th term times the common ratio, r. Mathematically,
a(n) = a(n -1) . r
Let us start from n = 1
a(1) = -100 (given)
a(2) = a(1) . r = (-100) . 1/5 = -20
a(3) = a(2) . r = (-20) . 1/5 = -4
a(4) = a(3) . r = (-4) . 1/5 = -4/5
a(5) = a(4) . r = (-4/5) . 1/5 = -4/25
Therefore, the first five terms are -100, -20, -4, -4/5, -4/25
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A pair of parallel interstate gas power lines run 10 meters apart and are equally distant from relay station A. The power company needs to locate a gas-monitoring point on one of the lines exactly 12 meters from relay station A. Draw a diagram showing the locus of possible locations (there should be two.)
Explanation would be appreciated!
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Use the properties of logarithms to evaluate each expression. 3log₉ 3- 1/4 log₉ 81
The evaluation of each expression is 3/2 , 1/2.
What is logarithms:
Logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation. For example, if 102 = 100 then log10 100 = 2.
Hence, we can conclude that,
Log b x = n or bn = x
Where b is the base of the logarithmic function.
This can be read as “Logarithm of x to the base b is equal to n”.
In this article, we are going to learn the definition of logarithms, two types of logarithms such as common logarithm and natural logarithm, and different properties of logarithms with many solved examples.
What is properties of logarithms:
Properties of logarithms functions are used to solve logarithm problems. We have learned many properties in basic math's such as commutative, associative and distributive, which are applicable for algebra. In the case of logarithmic functions, there are basically five properties.
This are as follows:
The product property
The quotient property
Power rule
Change of base rule
Reciprocal rule
Now,
3log₉ 3 = [(9)^x]^3 = 3
[(3^2)^x]^3 = 3
x = 3/2
Second part,
1/4 log₉ 81
= 1/2
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Suppose the tank is halfway full of water. the tank has a radius of 2ft and is 5 ft long. calculate the force on the ends due to the hydrostatic pressure.
The force on one of the ends due to hydrostatic pressure is 332.8lb.
How is a hydrostatic pressure produced?
The force that is produced by water that is still or at rest is known as hydrostatic pressure. It is the consistent pressure that water puts on the walls of your basement. While runoff pouring down a hill might cause hydrostatic pressure, the soil around the foundation of your home usually causes it.The force on one of the ends due to hydrostatic pressure is 332.8lb
Data;
Density = 62.4 lb/ft^3
length = 4ft
radius = 2ft
Force Due to Pressure
The force due to hydrostatic pressure can be calculated as
From the attached diagram
F = Pressure * area
density = 62.4 lb/ft³
depth of water = 2- y
pressure = ( 2- y ) ( 62.4)
= 124.8 - 62.4
We can proceed as
x² + ( y - 2)² = 2²
x² = 4 - ( y - 2)²
x = ± √4y - y²
this implies that
2x = 2 √4y - y²
The area is given as
δA = ( 2x) * δy
δA = 2√4y - y² δy
The force would be given by
δF = ( 2- y ) ( 62.4) (2 √ 4y - y²)δy
The total force is given by
F = [tex]\int\limits^2_0 {( 2 - y)} \, (62.4) ( 2\sqrt{4y - y^{2} } dy[/tex]
F = 124.8 [tex]\int\limits^2_0 {( 2-y)} \,( \sqrt{4y - y^{2} } dy[/tex]
F = 124.8 [tex][ -\frac{1}{3} y( y- 4 ) ( \sqrt{4y - y^{2} }[/tex]
F = 124.8 [tex][ -\frac{1}{3} (2) ( 2-4) \sqrt{4(2) - 2^{2} }[/tex]
F = 332.8lb
The force on one of the ends due to hydrostatic pressure is 332.8lb
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Dan spends 1/5 of his wages on rent and 2/3 on food. If he makes £495 per week, how much money does he have left?
Dan is left with £66 after the total spending.
What is referred as the total expenses?An expense is the amount of operations incurred by a business in order to generate revenue.
It is simply described as the amount of money required to obtain something. "It costs to make money," as the adage goes.Expenses can be classified in a number of ways. Fixed expenses, including such rent or mortgage, are those that don't change in response to changes in production. Expenses can also be described as variable expenses, which change in response to changes in production. Utilities as well as the cost of selling goods are examples of these.As for the given question;
The total earning per week is £495.
Spending on rent is 1/5.
1/5 of £495 = 495/5 = 99
Spending on rent is £99.
Now, spending on food is 2/3 of £495.
Food spending = (2/3)×495 = £330
Let the money left is 'x'.
Total expenses = Total income
food cost + rent cost + saving = 495
99 + 330 + x = 495
x = 495 - 429
x = 66
Thus, the savings by the Dan is £66.
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Line m passes through points (-1,4) and (5,k). Y-7=-3/2(X+4) is perpendicular to line m. Find the value of K.
Line m passes through the point value of k is -1/3.
Now let us find the slope of the equation using the slope equation of line:
y = mx + b,
From the given slope let’s find y,
y-7= -3/2(x+4)
y-7= -3/2x - 6
y= -3/2x + 1
=-1 / (-3/2)
=2/3
As these two lines are perpendicular the product of the slopes is -1.
m= 2/3 , y=-1
Line m is given as y=2/3 x +b
As the line m passes through the points
(-1, 4) and (5, k)
X=4,
To find b
-1 = 2/3 * 4+b
-1=8/3+b
b=-11/3
By substituting all the values in the formula we get value of k,
Line m : y=2/3*-11/3
When x=5
k=y=2/3*5-11/3
=10/3-11/3
=-1/3
K = -1/3
A perpendicular is a straight line that makes an angle of 90° with any other line. 90° is also known as a right angle and is marked through a little square among two perpendicular lines.
Hence, the value of k is -1/3. The two lines intersect at a right angle, and hence, are stated to be perpendicular to each other.
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Answer: k=8
Step-by-step explanation:
To find the value of k in the equation y-7=-3/2(x+4), we need to determine the slope of the line given by this equation.
First, let's rewrite the equation in slope-intercept form (y = mx + b),
where m is the slope and b is the y-intercept:
y - 7 = -3/2(x + 4) y - 7 = -3/2x - 6 y = -3/2x - 6 + 7 y = -3/2x + 1
Comparing this equation with the general slope-intercept form, we can see that the slope (m) is -3/2.
Since the line y - 7 = -3/2(x + 4) is perpendicular to line m, we know that the slopes of the two lines are negative reciprocals of each other.
The negative reciprocal of -3/2 is 2/3.
Therefore, the slope of line m is 2/3.
We know that line m passes through the points (-1, 4) and (5, k). Using the slope-intercept form, we can write the equation of line m as:
y = 2/3x + b Substituting the coordinates (-1, 4) into the equation,
we can solve for the y-intercept (b): 4 = 2/3(-1) + b 4 = -2/3 + b 4 + 2/3 = b 12/3 + 2/3 = b 14/3 = b Therefore, the equation of line m is: y = 2/3x + 14/3 Substituting the x-coordinate 5 and solving for k: k = 2/3(5) + 14/3 k = 10/3 + 14/3 k = 24/3 k = 8 Hence, the value of k is 8.
Factor the polynomial by its greates
9b³ +24b³
||
Answer:
Step-by-step explanation:
=the highest common factor is [tex]3b^{3}[/tex]
therefore you can divide each and every term of the expression and take it out of the brackets.
[tex]=3b^{3} (3+8)\\=3bx^{3} (11)[/tex]
Although I still see no use of factorising because there are only like times that is what I put on table. Please ask if you have questions
Help please??? Quick
Answer:2.5
Step-by-step explanation:
5/2=2.5
A projectile’s motion can be modeled by the quadratic equation: h left parenthesis t right parenthesis space equals space minus g t squared space plus space v subscript 0 t space plus thin space h subscript 0 g is 16 if in feet and 9 if in meters;; t = time in second elapsed from release of projectile; v0= initial velocity; h0 = initial height. Write the equation for a projectile that is dropped (v0 = 0) from a height of 100 ft. When will it hit the ground? Change the equation to reflect that the object is thrown upward from an initial height of 6 ft at 30 ft/sec. When will the object be back at the starting height? Hit the ground?
The projectile motion equation [tex]h(t) = - g \cdot {t}^{2} + v_{0}\cdot {t} + h_{0}[/tex], gives;
First part;
The object will hit the ground in 2.5 secondsSecond part;
The object will be back at the starting point in 1.875 secondsThird part;
The object will hit the ground in approximately 2.06 secondsHow can the projectile motion information be found?The quadratic equation that represents the projectile motion can be presented as follows;
[tex]h(t) = - g \cdot {t}^{2} + v_{0}\cdot {t} + h_{0}[/tex]
g = 16 ft./s² or 9 m/ s²
First part;
When
[tex] v_{0} = 0 \: and \: h_{0} = 100 \: ft.[/tex]
We have;
h(t) = -16•t² + 100
When the object hits the ground, we have;
h(t) = 0, which gives;
0 = -16•t² + 100
Therefore;
16•t² = 100
t² = 100 ÷ 16 = 25/4
t = √(25/4) = 5/2 = 2.5
The time it takes the object to reach the ground is 2.5 seconds.Second part;
The direction in which the object is thrown = Upwards
Initial height of the object, [tex] h_{0} = 6 \: ft[/tex]
Initial speed of the object, [tex] h_{0} = 30 \: ft/sec[/tex]
The equation of the projectile motion is therefore;
h(t) = -16•t² + 30•t + 6
Which gives;
When the object is at its starting height of 6 feet, h(t) = 6, which gives;
6 = -16•t² + 30•t + 6
-16•t² + 30•t = 0
A solution to the above equation is t = 0
The other solution is found as follows;
-16•t² + 30•t = 0
-16•t + 30 = 0
30 = 16•t
t = 30/16 = 1.875
The object will be back at the starting height at 1.875 secondsThird part;
When the object hits the ground, we have;
h(t) = 0, which gives;
0 = -16•t² + 30•t + 6
Which gives;
t ≈ 2.06
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From 1890 through 1990, the number of men M and women W in the US labor force can be modeled by the following equations, where t is the number of years since 1890. M=0.0016t^2 + 0.315t + 19.467 W= 0.007t^2 - 0.228t + 5.908 Find a model for the total number of people in the US Labor force.
The model for the total number of people in the US Labor force is T = -0.0054t² + 0.087t + 13.559 .
In the given question
the number of men "M" in the US labor force is modelled by the equation ,
M = 0.0016t² + 0.315t + 19.467 ...(i)
and
the number of women "W" in the US labor force is modelled by the equation ,
W= 0.007t² - 0.228t + 5.908 ...(ii)
Let "T" denoted the model for total number of people in the US Labor force.
The total number of people in the US Labor force = Number of Men + Number of Women in US Labor force.
Adding equation (i) and (ii) we get ,
T = (0.0016t² + 0.315t + 19.467) + (0.007t² - 0.228t + 5.908)
Adding the like terms we get ,
T = (0.0016-0.007)t² + (0.315-0.228)t + (19.467-5.908)
T = -0.0054t² + 0.087t + 13.559
Therefore , the total number of people in the US Labor force is modeled by the equation T = -0.0054t² + 0.087t + 13.559 .
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evaluate 16.6 -2.9.........................../
Answer: 13.7
Step-by-step explanation:
First you do 16.6 - 2 = 14.6 then you subtract 0.9 from 14.6, your equation would be 14.6 - 0.9 = 13.7
Hope This Helps!
Answer:
13.7
Step-by-step explanation:
The harmonic mean of two numbers a and b equals 2/ 1/a + 1 / b . As you vary the length of a violin or guitar string, its pitch changes. If a full-length string is 1 unit long, then many lengths that are simple fractions produce pitches that harmonize, or sound pleasing together. The harmonic mean relates two lengths that produce harmonious sounds. Find the harmonic mean for each pair of string lengths.
c. 3/4 and 3/5
The Harmonic Mean for the length of strings 3/4 and 3/5 is 2/3 .
Harmonic mean for 2 numbers "a" and "b" is denoted by
[tex]HM=\frac{2}{\frac{1}{a} +\frac{1}{b} }[/tex].
In the given question ;
Given that ;
the length of the first string is 3/4
Length of the second string is 3/5.
Substituting the values in the formula of harmonic mean
we get,
HM=[tex]\frac{2}{\frac{1}{\frac{3}{4} }+\frac{1}{\frac{3}{5} } }[/tex]
[tex]=\frac{2}{\frac{4}{3} +\frac{5}{3} }[/tex]
Taking LCM of denominator as 3 and solving further we get ;
[tex]=\frac{2}{\frac{5+4}{3} }\\ \\ =\frac{2}{\frac{9}{3} }[/tex]
Rewriting the complex fraction
=2*(3/9)
=6/9
On further simplifying we get ;
=2/3
Therefore , the Harmonic Mean for the length of strings 3/4 and 3/5 is 2/3 .
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A bakery sells an average of 14 dozen cupcakes a day to about 50 customers. what is their average sale rate, in cupcakes per customer?
i also need the answer really quick!!!
Answer:
3.36
Step-by-step explanation:
→ How much is a dozen
12
→ Multiply by 14
168
→ Divide by 50
168 ÷ 50 = 3.36
Compute the mean and variance of the following probability distribution. (round your answers to 2 decimal places.) x p(x) 7 0.10 14 0.20 21 0.25 28 0.45 click here for the excel data file
The mean of the probability distribution is 21.35 and the variance of the probability distribution is 51.3275
Given the probability distribution with values of x and corresponding P(x). We need to find the values of [tex]x^2[/tex], x P(x), [tex]x^2[/tex] P(x) to calculate mean and variance.
x P(x) [tex]x^2[/tex] x P(x) [tex]x^2[/tex] P(x)
7 0.10 49 0.7 4.9
14 0.20 196 2.8 39.2
21 0.25 441 5.25 110.25
28 0.45 784 12.6 352.8
-----------------------------------------------------
∑x P(x) = 21.35
∑[tex]x^2[/tex] P(x) = 507.15
Mean = ∑x P(x) = 21.35
and variance = ∑[tex]x^2[/tex] P(x) - [tex](\sum x\ P(x) )^2[/tex] = 507.15 - 455.8225 = 51.3275
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in a school canteen, a cup of tea costs 80p. Write down an expression for the cost in pence of y cups of tea
The expression is f(y) = 80y.
We have a school canteen.
We have to write down an expression for the cost in pence of y cups of tea.
What is a function in Mathematics?A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.
According to the question -
Number of cups of tea = y
Cost of one cup = 80 pence.
Therefore, the function representing the cost in pence of y cups of tea =
f(y) = 80y
Hence, the expression is 80y.
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2x_____=2x10^1=______ i need help please helpppppppppp
The expression is written as 2 × 10 = 2 x 10^ 1 = 20
What is index form?The index form of a number can be defined as that number written as an exponential expression.
It is also said to be a single number that is raised to another number.
Given the expression;
2x _____ = 2 x 10^ 1 = ______
Note that a number raised to the power 1 is that same number, so we have;
2 × 10
2 x 10^1 = 2 × 10
2 × 10 = 20
Thus, we have the expression to be written as 2 × 10 = 2 x 10^ 1 = 20
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make an outcome tree to show all possible combinations. you have three pairs of shorts four shirts, flip flops, and sneakers
The required number of combinations is 24.
Given that,
To make an outcome tree to show all possible combinations. you have three pairs of shorts four shirts, flip-flops, and sneakers.
In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Here,
flip flops
short 1 short 2 short 3
Shirt 1 shirt 2 shirts 3 shirts 4
Number of combinations = 12
sneakers
short 1 short 2 short 3
Shirt 1 shirt 2 shirts 3 shirts 4
Number of combinations = 12
Total number of combination = 12 + 12 = 24
Thus, the required number of combinations is 24.
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Given g(x) = −4x + 4, identify the domain, range, and x-intercept of the function.
pls ill award u need fast PLEASEEEE
The domain, range and x-intercept of the given function are (-∞,∞), (-∞,∞) and (1,0) respectively.
What is domain, range, and x-intercept of the given function?Given the function in the question;
g(x) = −4x + 4
The domain of the expression is all real numbers except where the expression is undefined.
For -4x + 4, there is no real numbers that makes the expression undefined.
Hence, domain is (-∞,∞).
Also, the range is the set of all valid y-values.
The range is (-∞,∞).
For the x-intercept, substitute 0 in place of y or g(x) in the given function and solve for x.
g(x) = −4x + 4
0 = −4x + 4
4x = 4
x = 4/4
x = 1
Hence, the x-intercept in point form is (1,0)
Therefore, the domain, range and x-intercept of the given function are (-∞,∞), (-∞,∞) and (1,0) respectively.
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Plss help me A scale drawing of a lake has a scale of 2 cm to
100 m. If the actual width of the lake is 1,500 m, what is
the width of the lake on the scale drawing?
The width of the lake on the scale drawing is 30 cm.
Based on the given conditions, formulate 1500*2/100
Cross out the common factor: 15*2 = 30
Get the result as 30 cm
An object is enlarged in a scale drawing. An expansion increases or decreases the size of an object by multiplying each of its lengths by a scale factor. Typically, a ratio is used to describe the scale of a drawing. a representation of a real thing with correct sizes that have been scaled back or blown up slightly (called the scale). The scale is represented by the length in the drawing, a colon (":"), and then the actual length that corresponds to it.
Hence, the width of the lake on the scale drawing is 30 cm.
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What is the value of your total assets if you have a car worth $4,000, you owe $1500 on the car loan, and you have a baseball card collection valued at $750?
The total asset is $4750
How to find the total asset ?The worth of the car is valued at the worth of has $4000 and you he have a baseball card collection valued at $750.
The capital is also know as the equity which means the net worth.
Liabilities are everything a business owes, now and in the future.
Assets are everything a business owns. Assets may be current or fixed assets
Therefore,
Total Assets - Total Liabilities = Capital
Where
Base ball card collection = $750
Total assets = ?
Capital = $4000
Hence,
Total Assets = $4000 + $750
Total Assets = $4750
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Suppose a balloon is filled with 5000 cm³ of helium. It then loses one fourth of its helium each day. How much helium will be left in the balloon at the start of the tenth day?c. How can you write a formula for this sequence?
The sequence can be expressed by the formula: v(n) = 5000 . (3/4)ⁿ⁻¹. Helium left at the start of the 10th day is 375.42 cm³
1st day:
Helium is filled with 5000 cm³ of helium.
We can write v(1) = 5000 cm³
2nd day:
The balloon losses 1/4 of helium volume. In other word, the remaining volume of helium is:
(1 - 1/4) = 3/4 of its initial volume.
We can write:
v(2) = 3/4 . 5000 = 3750 cm³
We can continue this process:
v(3) = 3/4 . 3750 = 2812.5
Notice that each day remaining volume of helium forms a geometric sequence, with v(1) = 5000 and a common ratio (r) = 3/4.
Recall the formula for the nth term of a geometric sequence:
v(n) = v(1) . rⁿ⁻¹
To find the explicit formula, substitute v(1) = 5000 and (r) = 3/4:
v(n) = 5000 . (3/4)ⁿ⁻¹
Tenth day means n = 10. Substitute these parameters into the formula:
v(10) = 5000 . (3/4)¹⁰⁻¹
v(10) = 5000 . (3/4)⁹
= 375.42 cm³
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If Leroy made 9 more penalty kicks than he missed how many penalty kicks did he make
The total number of penalty kicks is 9+ 2y where the penalties made is x and the penalties missed is y
How to determine how many penalty kicks he made?The given parameters are:
Leroy made 9 more penalty kicks than he missed
Represent the penalties made with x and the penalties missed with y
So, we have
x = 9 + y
The total number of penalty kicks is then calculated as
Total = x + y
This gives
Total = 9 + y + y
Evaluate
Total = 9+ 2y
Hence, the total number of penalty kicks is 9+ 2y where the penalties made is x and the penalties missed is y
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A bin of 50 manufactured parts contains 3 defective parts and 47 nondefective parts. two parts are selected randomly without replacement. let a denote the event that the first part is defective. let b be the event that the second part. is defective. find the p(b)
The probability that the event that the second part is defective will be 0.0564.
How to calculate the probability?From the information, the bin of 50 manufactured parts contains 3 defective parts and 47 nondefective
Therefore, the probability of having a defective and non defective parts will be:
= 47/50 × 3/50
= 0.94 × 0.06
= 0.0564
Therefore, the probability that the event that the second part is defective will be 0.0564.
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What is the sum of the polynomials? 1.3t3 t2 â€"" 42t 8 1.3t3 t2 â€"" 6t 8 1.9t3 8.4t2 â€"" 42t 1.9t2 â€"" 42t 8
The sum of the polynomials is [tex]\bold{4.5t^3 + 12.3t^2-132t+24}[/tex].
Given polynomials are:
[tex]1.3t^3+t^2-42t+8\\ 1.3t^3+t^2-6t+8 \\1.9t^3+8.4t^2-42t \\1.9t^2-42t+8[/tex]
To find the sum of the polynomials, add the coefficients of the terms of same degree in each polynomials. That is add the terms containing [tex]t^3[/tex] , then terms of [tex]t^2[/tex], then terms of t and finally the constant terms of the polynomials.
So we get, [tex](1.3t^3+t^2-42t+8)+(1.3t^3+t^2-6t+8 )+(1.9t^3+8.4t^2-42t )+(1.9t^2-42t+8)\\ = (1.3+1.3+1.9)t^3+(1+1+8.4+1.9)t^2+(-42-6-42-42)t+(8+8+8)\\=\bold{4.5t^3 + 12.3t^2-132t+24}[/tex]
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Find the distance between pair of parallel lines with the given equations.
y=2x+3 y=2x-7
The distance between pair of parallel lines with the following equation
y=2x+3 y=2x-7 [tex]2{\sqrt 5}[/tex] units
Definition of parallel linesParallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.
The fundamental characteristics listed below make it simple to recognize parallel lines.
Straight lines which are always the same distance apart from one another are known as parallel lines.No matter how far apart they are from one another, the parallel lines can never intersect.The slope of a line which is perpendicular to both the lines will be [tex]-\frac{1}{2}[/tex].
Check what are the y-intercept of any one of the two lines & write the equation of the perpendicular line through it.
The y-intercept of line y = 2x-7 is (0, -7).
So, the equation of any line with slope [tex]-\frac{1}{2}[/tex] and a y-intercept of −7 is
y = [tex]-\frac{1}{2}x-7[/tex]
The perpendicular intersects or meets the line y = 2x -7 at (0,-7).
Now, to find the point of intersection of the perpendicular & the other line, solve the two equations.
Solve for x:
2x + 3 = [tex]-\frac{1}{2}x-7[/tex]
[tex]\frac{5}{2} x[/tex] = -10 (combine them like terms)
x = -4 (multiply each side by 2\5)
Find y:
y = [tex]-\frac{1}{2}.(-4)-7[/tex]
= -5
so, the point is (-4,-5).
Now using the Distance Formula, find the distance between the points (-4,-5) and (0,−7).
[tex]{\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}[/tex]
[tex]={\sqrt {\left(0-(-4\right)^{2}+\left(-7-(-5\right))^{2}}}[/tex]
[tex]={\sqrt {4^2 +(-2)^2}}[/tex]
[tex]=2{\sqrt 5}[/tex]
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Question is attached, Please help me.
Answer:
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Step-by-step explanation:
Recipe a four minestrone soup requires 4 cups of tomatoes a different recipe recipe be for minestrone soup requires 14 cups of tomatoes which recipe requires more tomatoes how much more
Answer:
The recipe with 14 cups of tomatoes requires more tomatoes. This is because it needs 10 cups more of tomatoes than the recipe with 4 cups.
Find the eighth term of each geometric sequence. 24,-6, 3/2, . . . . .
The eighth term of the given geometric sequence is: [tex]\frac{3}{2048}[/tex]
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 24, -6, 3/2, ...
Here, [tex]\frac{-6}{24}=\frac{\frac{3}{2}}{-6} = \frac{1}{-4}[/tex]
Thus, for the given geometric progression, a₁ = 24, and r = -1/ 4.
The nth term of a geometric progression is given by: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 8, a₈ = 24 ( -1/4) ⁷
=> a₈ = [tex]\frac{6}{(-4)^6} = \frac{6}{64\times64}[/tex] = [tex]\frac{3}{2048}[/tex]
Hence, The eighth term of the given geometric sequence is: [tex]\frac{3}{2048}[/tex].
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can someone help me please
The value in the missing place is 10 after plugging the value of F = 0.833; the answer is 10.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
0.83 = F
0.83 is a repeating decimal
Multiply by 10 on both sides:
10x0.83 = Fx10
8.33 = ? F
Plug F = 0.833
8.33 = ? (0.833)
? = 0.833/0.833
? = 10
8.33 = (10) F
Thus, the value in the missing place is 10 after plugging the value of F = 0.833; the answer is 10.
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Igor has not been skiing in 10 years. however, when he gets on his skis, his body remembers exactly how to ski. the kind of memory that makes it possible for him to remember how to ski is:__________
Igor has not been skiing in 10 years. however, when he gets on his skis, his body remembers exactly how to ski. the kind of memory that makes it possible for him to remember how to ski is procedural.
What is procedural memory?Procedure memory exists a kind of implicit memory (unconscious, long-term memory) that helps people carry out particular tasks without thinking about their previous experiences. It frequently resides below the consciousness level and controls the actions we take. The automatic retrieval and use of procedural memories, which are relied upon when appropriate, is necessary for the execution of integrated motor and cognitive functions, such as tying shoes, reading, and flying an airplane. Procedural memories are recovered and used without any conscious control or attention being needed. Procedural learning, or repeatedly completing a challenging activity until all required brain networks are able to coordinate to complete the job automatically, is how procedural memory is established.To learn more about procedural memory, refer to:
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Answer:
kribble
Step-by-step explanation:
Answer: rftyguhjiomnbvfdswertyio
Step-by-step explanation:
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