The next three terms are:
0.9072, 0.54432, 0.326592
So, the sequence is:
7, 4. 2, 2. 52, 1. 512, 0.9072, 0.54432, 0.326592
Geometric sequenceA geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is. a n= a 1 r n – 1. The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.
The sequence is:
7, 4. 2, 2. 52, 1. 512,.
We have to find the next three terms.
To find r divide the 2nd term by the first:
4.2/7 = 0.6
To check if this is the same ratio for each number divide it by the ratio to get the number before it:
2.52/4.2 = 0.6
1.512/ 2.52 = 0.6
To find the next three terms multiply the last number by the ratio then repeat
(1.512)(0.6) = 0.9072
(0.9072)(0.6) = 0.54432
(0.54432)(0.6) = 0.326592
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Elsa is building a fence around her garden. For every 4 feet of fencing, the cost is $2
Complete the table below showing the length of the fence and the cost.
Length of fencing (feet)
Cost ($)
Explanation
Pls help
Answer:
Step-by-step explanation:
4ft : $24 -> 1ft = $6
so 7ft = 6X7 = $42
and 6X10 = $60
A gardener has 600ft of fencing to fence in a rectangular garden. One side of the garden is boarded by a river and so it does not need any fencing.
What dimensions would guarantee that the garden has the greatest possible area?
Shorter side:
Longer side:
Greatest possible area:___ft^2 (square feet)
Answer:
To find the dimensions that would guarantee the greatest possible area, we can use the formula for the area of a rectangle, which is A = l * w, where l is the length and w is the width.
Since one side of the garden is already boarded by a river, we only need to use 600ft of fencing for the other three sides. This means that the length and width of the garden must add up to 600ft. We can write this as:
l + w = 600
Since we want to find the dimensions that would give us the greatest possible area, we want to maximize l * w. Using the formula for the area of a rectangle, we can write this as:
A = l * w = l * (600 - l) = 600l - l^2
To find the maximum area, we can differentiate this equation and set it equal to zero:
dA/dl = 600 - 2l = 0
Solving for l, we get:
l = 300/2 = 150ft
So, the shorter side is 150ft and the longer side is 450ft (600 - 150).
Finally, we can use the formula for the area of a rectangle to find the greatest possible area:
A = 150 * 450 = 67,500ft^2
Therefore, the greatest possible area for the garden is 67,500ft^2 when the shorter side is 150ft and the longer side is 450ft.
Step-by-step explanation:
A square has an area of 64 square meters. What is the lenht of each side
Answer:
8 m
Step-by-step explanation:
All the sides of a square are equal.
let x = length of one side
A = x² = 64 m²
√x² = x = √64 = 8
Juan went to the store to buy a plant for his mother, but forgot to ask which kind to get. Out of 30 plants, six of them are a kind that his mother would want. If Juan chooses one randomly, what is the probability that he will choose a kind that his mother would want? You will need to change your probability to a decimal and then to a percent.
The probability that Juan will choose a kind of plant his mother would want is 6/30, which is equal to 0.2 or 20%
To calculate the probability that Juan will choose a kind of plant his mother would want, out of 30 plants, six of them are a kind that his mother would want, first divide the number of plants his mother would want (6) by the total number of plants (30). This will give you a decimal, 0.2. To turn this decimal into a percent, multiply it by 100. This will give you 20%, or a 20% chance of Juan choosing a kind of plant his mother would want. To summarize, therefore, the probability that Juan will choose a kind of plant his mother would want is 0.2 or 20%.
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last year, 20 percent of all teenagers purchased a new iphone. this year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iphone. to test whether the percentage has decreased, the p-value is:
The p-value is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.
The p-value can be calculated by using a one-proportion z-test. The null hypothesis would be that the percentage has stayed the same from last year, and the alternative hypothesis is that the percentage has decreased.
The formula for the z-score is (x-p)/√(p(1-p)/n), where x is the observed proportion (39/260), p is the expected proportion (0.20), and n is the sample size (260). The p-value is then calculated using the z-score and the cumulative distribution function.
Therefore p-value, in this case, is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.
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Jason purchased a car $22,995. According to his research, this make and model of a car loses all of it's marketable value after 9 years. If this car depreciates in a straight line form, what are the coordinates of the intercepts of the depreciation equation?
The coordinates of the intercepts of the depreciation equation are (9, 0) and (0, 22,995).
What are Intercepts?The x intercept is the x coordinate of a point where the line touches the X axis.
The y intercept is the y coordinate of a point where the line touches the Y axis.
Here, there are two variables.
The independent variable x is the number of years.
The dependent variable y is the value of the car.
x intercept is the year when the value of the car is 0.
Given that, model of a car loses all of it's marketable value after 9 years.
x intercept = 9
y intercept is the value of the car in the 0th year.
Initial value of the car = $22,995
y intercept = 22,995
Hence the intercepts are (9, 0) and (0, 22,995).
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Solve the following
i} p+ 3 = 205 ii} 2x/7 = 4 iii} 3y - 6 = 9
Answer:
[tex]1) p = 205 - 3 = 202 \ 2)2x \div 7 = 4 \\ 2x = 28 \\ x = 14 \\ \\ 3)3y - 6 = 9 \\ 3y = 9 + 6 \\ 3y = 15 \\ y = 5[/tex]
Express the product shown as a fraction in simplest form: -2/5 . 2/5
The simplified product of - (2/5).(2/5) is equal to - 4/25.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
A product of two fractions - 2/5 and 2/5 is given.
We know in the product of fractions numerator is multiplied by the numerator and the denominator is multiplied by the denominator.
Therefore, - (2/5).(2/5).
= - (2×2)/(5×5).
= - 4/25.
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−3/4(x+2)=[tex]-3/4(x+2)=6[/tex]6
The value of x for the equation is -10.
What is simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given equation,
-3/4(x + 2) = 6
both sides multiply by -4/3
-3/4(x + 2) * -4/3 = 6 * -4/3
x + 2 = -8
subtract 2 from both sides
x + 2 - 2 = -8 - 2
x = -10
Hence the value of x is -10.
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a) complete the table of values for y = 2x^2 + x
b) Which of the three curves drean matches the graph of y = 2x^2 + x
Answer:
a)
x y
-2 6
-1 1
0 0
1 3
2 10
b) Curve B matches all the values.
Step-by-step explanation:
See attached worksheet.
a) Enter the x values into the equation to find the corresponding values of y.
b) Mark these x,y values on the graph to identify the curve that matches all points. That is curve B.
Match the exponent expression with it's correct solution.
According to algebra property of power of a power, the following results are listed below:
Case 1: (x⁵)³ = x¹⁵ (Correct choice: 1)
Case 2: (x⁸)⁷ = x⁵⁶ (Correct choice: 4)
Case 3: (x⁷)¹⁰ = x⁷⁰ (Correct choice: 2)
Case 4: (x¹⁴)³ = x⁴² (Correct choice: 3)
How to apply power properties
In this question we find four cases of power of a power, whose solution is described by the following algebra property:
(xᵃ)ᵇ = xᵃᵇ, where x, a and b are real numbers.
Now we proceed to determine the solution to each case:
Case 1
(x⁵)³ = x¹⁵
Case 2
(x⁸)⁷ = x⁵⁶
Case 3
(x⁷)¹⁰ = x⁷⁰
Case 4
(x¹⁴)³ = x⁴²
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help me baaaaaaaaaaaaaaaalls
Answer:
The correct scale faction the first pentagon dilated by to create the second pentagon is 1.25.
Step-by-step explanation:
Since the second pentagon is a dilation of the first pentagon, we can conclude these pentagons are similar, meaning the shape retained all of its previous angles, and all the corresponding sides are dilated by a common scale factor. Since we know the values of a pair of corresponding sides, we can use those to find the scale factor of dilation.
The corresponding side of the original pentagon is 4 units, and the corresponding side of the dilated pentagon is 5 units. Since the first pentagon dilated to become the second, in order to solve the scale factor the pentagon dilated by, we'd have to divide the side given on the second pentagon by the corresponding side of the first, which will be 5 ÷ 4 = 1.25. Therefore, that will be the scale factor the pentagon dilated by.
Have a great day! Feel free to let me know if you have any more questions :)
how far away is the puddle from the house? angle of depression is 40 degree
Answer: 29.8 feet
Step-by-step explanation:
To solve this, the first step is to make the imaginary triangle (look at the picture below). Now, we use the basic trigonometry functions. Since we have to find tge base part of the triangle (which is the adjacent one to the angle, and we already have the opposite to the angle. So, now we know we have to use the tan ratio. We now solve it with the following method:
[tex]tan(Angle) = \frac{Opposite}{Adjacent} \\[/tex]
Now we sub in our values and use the calculator to solve it:
[tex]tan(40) = \frac{25}{x}\\\\x = \frac{25}{tan(40)} \\\\x = 29.8 (1 d.p)[/tex]
find the radius and diameter of a circle whose area is 15400 mm²
Solution:
Area=15400mm^2
Now,
Area=pi×r^2
or,15400=22/7×r^2
or,15400×7=22×r^2
or,107800=22r^2
or,107800/22=r^2
or,4900=r^2
or,r=70
Also,
Diameter (d)=r×2
=70×2
=140
PLEASE HELP !!!!!
Function g is graphed here. If function f is the parent exponential function (). what is the equation of transformed function g in terms of f?
Therefore , the solution of the given problem of function comes out to be f(x) = 1.1f(x + 1) is the solution for the graph.
What is function?The study of mathematics includes looking at numbers, their variables, the world around us, buildings, and both real and imagined places. An illustration of the relation between the quantity of inputs and the appropriate outputs for each is called a function. A function, simply described, is a group of inputs who, when combined, provide distinct outputs for each input. Every function has a city, province, or scope—also referred to as a domain—assigned to it. Functions are usually indicated with the letter f. (x). The input contains an x.
Here,
Given:
The parent function f(x) is translated left by one unit and slightly stretched vertically to form g(x).
=>g(x) is:
=> f(x) = 1.1f(x + 1)
Thus , f(x) = 1.1f(x + 1) is the given function which is graphed here.
Therefore , the solution of the given problem of function comes out to be f(x) = 1.1f(x + 1) is the solution for the graph.
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Gerry is shopping for clothes at the mall. He buys 4 new shirts for $6. 0. What is the unit rate for the shirts
The unit rate of the shirt is $1.50 per shirt.
Unit rate is a measure of the relationship between two quantities, where the second quantity is expressed as a unit of one. It is often expressed as a ratio, with the unit of the second quantity being 1. Unit rate helps us compare different quantities and make sense of their relative sizes.
The unit rate for the shirts can be calculated by dividing the total cost by the number of shirts. In this case, the unit rate would be:
$6.00 ÷ 4 shirts = $1.50/shirt
So, the unit rate for the shirts is $1.50 per shirt.
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Create a flowchart proof of a two column proof. If HG = KG and HI || KJ, prove that HI = KJ
Answer:
Both triangles are congruent by S A S congruent.
Step-by-step explanation:
Congruent triangles:In ΔHIG & ΔKJG,
HG = KG Given
∠GHI ≅ ∠GKJ Alternate interior angles, HI // KJ and KH is transversal
HI = KJ Given
ΔHIG ≅ ΔKJG Side Angle Side congruency
q. The graph shows the change in temperature
in Monterey, CA over several hours. Is the
between the number of hours and
relationship between
temperature linear or non-linear? Explain.
Answer:
Non-linear
Explanation below
Step-by-step explanation:
The relationship is clearly non-linear
If it where a linear relationship then the temperature change per hour would be constant throughout the time period when the observations were made.
The resultant graph would be a straight line
Here the graph rises at a decreasing rate until it almost flattens out. This means the temperature reaches a maximum and stays at that maximum.
HELP WHAT IS THE VALUE OF TAN A
Answer: 4 / 3
Step-by-step explanation:
Soh Cah Toa
In this case, we'll use Toa
Tangent = Opposite / Adjacent
Tan A = 40 (opposite) / 30 (adjacent)
Tan A = 40 / 30 = 4 / 3 (simplified)
Show how 15 + 5n and 5(3 + ) are equivalent
Answer: 5n+30
( The problem was incomplete on my end )
( Hope this helps )
focus (4,-3) directrix y=-3 what’s the equation for the parabola
The equation of the parabola is x² - 8x + 16 = 0
What is the equation of the parabolaTo find the equation of the parabola with focus (4, -3) and directrix y = -3, we can use the definition of a parabola.
A parabola is the set of all points that are equidistant to the focus and the directrix.
The distance from a point (x, y) to the directrix y = -3 is simply the vertical distance between the point and the line, which is |y - (-3)| = |y + 3|.
The distance from a point (x, y) to the focus (4, -3) can be found using the distance formula:
d = √[(x - 4)² + (y + 3)²]
Since the point is equidistant to the focus and the directrix, we have:
d = |y + 3|
Squaring both sides, we get:
(x - 4)² + (y + 3)² = (y + 3)²
Simplifying, we get:
(x - 4)² = 0
Thus, the equation of the parabola is simply:
x² - 4x - 4x + 16 = 0
x² - 8x + 16 = 0
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Laura ha comprado una falda y una blusa por 66 euros ambas tenian el mismo precio pero en la falda le han hecho un 20% de rebaja y en la blusa solo un 15% ¿cuanto costaba cada prenda?
The cost of the skirt and blouse after the discount would be -
$52.8 and $56.1 respectively.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Laura has bought a skirt and a blouse for 66 euros, both had the same price but they have given her a 20% discount on the skirt and only 15% on the blouse.
The cost skirt would be -
${x} = 66 - {20% of 66}
${x} = 66 - {20/100 x 66}
${x} = 66 - {66/5}
${x} = 66 - 13.2
${x} = 52.8
The cost of blouse would be -
${y} = 66 - {15% of 66}
${y} = 66 - {15/100 x 66}
${y} = 66 - {3/20 x 66}
${y} = 66 - 9.9
${y} = 56.1
Therefore, the cost of the skirt and blouse after the discount would be -
$52.8 and $56.1 respectively.
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{Question in english -
Laura has bought a skirt and a blouse for 66 euros, both had the same price but they have given her a 20% discount on the skirt and only 15% on the blouse. How much did each item cost??
Real World Application
Cody and Aliyah are selling wrapping paper for a school fundraise.
Customers can buy rolls of plain wrapping paper and rolls of
holiday wrapping paper. Cody sold 5 rolls of plain wrapping paper
and 8 rolls of holiday wrapping paper for a total of $174. Aliyah
sold 5 rolls of plain wrapping paper and 10 rolls of holiday
wrapping paper for a total of $210. What is the solution to the
system of equations? What is the cost each of one roll of plain
wrapping paper and one roll of holiday wrapping paper?
Roll of plain wrapping paper: $
Roll of holiday wrapping paper: $
Using a system of equations, the unit cost of one roll of plain wrapping paper and one roll of holiday wrapping paper is as follows:
Roll of plain wrapping paper: $6.00Roll of holiday wrapping paper: $18.What is a system of equations?A system of equations is two or more equations solved at the same time, concurrently, or simultaneously.
A system of equations is otherwise known as simultaneous equations.
Plain Wrapper Holiday Wrapper Total Cost
Cody sales 5 8 $174.00
Aliyah 5 10 $210.00
Let the unit cost of Plain Wrapper = x
Let the unit cost of Holiday Wrapper = y
Equations:5x + 8y = 174... Equation 1
5x + 10y = 210... Equation 2
Subtract Equation 1 from Equation 2:
5x + 10y = 210
-
5x + 8y = 174
2y = 36
y = 18
y = $18
Substitute y = 18 in either equation:
5x + 8y = 174
5x + 8(18) = 174
5x +144 = 174
5x = 174 - 144
5x = 30
x = 6
x = $6
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4. VOLUME The volume of one column of the Lincoln Memorial is approximated by the expression (x³ +37x²-110x + 400). If the height of the column is x + 40 feet, find the expression that approximates the area of the base of the column in terms of x and pi.
To find the area of the base of the column, we need to find the expression for the radius of the column, r, in terms of x.
The volume of a column can be calculated as V = πr²h, where r is the radius, h is the height, and π is pi.
Using the given expression for the volume of the column, we can write:
πr²h = x³ + 37x² - 110x + 400
Since h = x + 40, we can substitute to get:
πr²(x + 40) = x³ + 37x² - 110x + 400
Dividing both sides by π(x + 40) gives us:
r² = (x³ + 37x² - 110x + 400) / (π(x + 40))
Finally, taking the square root of both sides gives us the expression for the radius in terms of x:
r = √((x³ + 37x² - 110x + 400) / (π(x + 40)))
So, the expression that approximates the area of the base of the column in terms of x and π is:
A = πr² = π √((x³ + 37x² - 110x + 400) / (π(x + 40)))²
Which expression does not have a solution of 12, if w = 4?
Options :
3 w
w + 8
4 w
16 - w
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Fred and his workout partner are lifting weights together, doing many sets of each exercise.
On a certain exercise, Fred is using a 19-kilogram bar, increasing the amount of weight he lifts by 4 kilograms on each set. His partner, meanwhile, started out using a 15-kilogram bar and is upping the weight by adding 6 kilograms on every set. Eventually, Fred and his workout partner will be lifting the same amount, and will take turns using the same barbell.
How much weight will they be lifting then? How many sets will they have completed?
The system of equations is:
y = 19 + 4*x
y = 15 + 6x
And the solution is x = 2 and y = 27.
How to write and solve the system of equations?
We know that red is using a 19-kilogram bar, increasing the amount of weight he lifts by 4 kilograms on each set. Then after x sets he will be lifting:
y = 19 + 4*x
kilograms.
And his partner, meanwhile, started out using a 15-kilogram bar and is upping the weight by adding 6 kilograms on every set. Here we can write:
y = 15 + 6x
Then we need to solve the system of equations at:
y = 19 + 4*x
y = 15 + 6x
Using substitution, wecan write:
19 + 4x = 15 + 6x
19 - 15 = 6x - 4x
4 = 2x
4/2 = x
2 = x
They will lift the same weight after 2 sets, and the weight is:
y = 19 + 4*2
y = 19 + 8 = 27
They will be lifting 27 kilograms.
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Write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. Use a graphing utility to verify your result.
Vertex: (3, 1); Point: (5, −7)
The required standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point is y = -2x² + 12x - 17.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
To find the quadratic function that has the vertex (3, 1) and passes through the point (5, -7), we can use the vertex form of the quadratic function: y = a(x - h)² + k, where (h, k) is the vertex.
First, we substitute the vertex (5, -7) into the vertex form to find a:
y = a(x - 3)² + 1
-7 = a[2]² + 1
a = -2
Since a = -2, the standard form of the quadratic function is:
y = -2x² + bx + c
Substitute the point (5, -7) into the standard form y = -2x² + bx + c to find b and c:
-7 = -2x² + b(5) + c
-7 = -50 + 5b + c
43 = 5b + c - - - - -(1)
Substitute the point (3, 1) into the standard form y = -2x² + bx + c to find b and c:
1 = -18 + b(3) + c
19 =3b + c - - - - -(2)
Solving equations 1 and 2 we get
43 - 19 = 2b
b = 12 and c = -17
Put a,b and c in the standard equation,
y = ax² + bx + c
y = -2x² + 12x - 17
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What is the arc measure of major arc BAC in degrees? no
Answer: 360 = 7n + 12 + 13x — 16 + 6xx = 146 * 14 = 84°
Consider the error formulas.
|E| ≤
(b − a)3
12n2
[max |f ''(x)|], a ≤ x ≤ b
Trapezoidal Rule
|E| ≤
(b − a)5
180n4
[max |f (4)(x)|], a ≤ x ≤ b
Simpson's Rule
Use these to estimate the errors in approximating the integral, with n = 4, using the Trapezoidal Rule and Simpson's Rule.
6 1 (x − 1)2 dx 2
Trapezoidal Rule: [tex](b-a)^3 / 96n^2,[/tex] Simpson's Rule: [tex](b-a)^5 / 2880n^4\\[/tex]. Both approximations have error of 0.0208.
For the Trapezoidal Rule, the formula for estimating the error is |E| ≤ (b − a)3/12n2[max |f ''(x)|], a ≤ x ≤ b. In this case, the integral is from x=1 to x=3, so b-a = 2. Plugging in all the values, we get [tex]|E| ≤ 2^3/12(4)^2(2)[/tex] or |E| ≤ 0.0208. For the Simpson's Rule, the formula for estimating the error is |E| ≤ (b − a)5/180n4[max |f (4)(x)|], a ≤ x ≤ b. Again, b-a = 2. Plugging in all the values, we get[tex]|E| ≤ 2^5/180(4)^4(2)[/tex] or |E| ≤ 0.0208. Therefore, the error in approximating the integral with n = 4, using the Trapezoidal Rule and Simpson's Rule, is 0.0208.
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PLEASE HELP ME ASAP
Answer:
the answer is E
Step-by-step explanation:
your welcome