The common ratio and the 1st term will be 2/3 and 81. And the least number of terms for which the sum exceeds 240 will be 11.
What is a geometric sequence?Let a₁ be the first term and r be the common ratio.
Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The amount of the first 2 terms of a remarkable grouping is 135 and the amount of the third and fourth terms is 60. Then the equations are given below.
a + ar = 136 ...1
ar² + ar³ = 60
r²(a + ar) = 60 ...2
From equations 1 and 2, then we have
r² x 135 = 60
r² = 60/135
r² = 4/9
r = 2/3
Then the value of 'a' is given as,
a + (2/3)a = 135
a = 81
Then the least number of terms for which the sum exceeds 240 will be given as,
Sₙ > [a₁ (1 - rⁿ)] / (1 - r)
240 > [81(1 - 0.66ⁿ)] / (1 - 0.66)
240 > 243(1 - 0.66ⁿ)
0.9876 > 1 - 0.66ⁿ
0.66ⁿ > 1 - 0.9876
n log 0.66 > log 0.012345
n > 10.57
n = 11
The common ratio and the 1st term will be 2/3 and 81. And the least number of terms for which the sum exceeds 240 will be 11.
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how long the chord of the circle 4x²+4y²-8x-8y+3=0 whose the end point where the curve y=1/x cut the circle?
The length of the chord is 6
What is a circle simple definition?Simply said, a circle is a rounded form without any edges or line segments. It has the geometric form
What is the General Equation of Circle?The circle's general equation is written as follows: x2 + y2 + 2gx + 2fy + c = 0. The center of the circle in this general form of the equation of a circle is (-g, -f), and its radius is given by r = g2+f2cg2+f2c.
What is C in the General Equation of Circle?The circle's general equation is written as follows: x2 + y2 + 2gx + 2fy + c = 0. The coordinates of the circle's center and radius are determined using this general form. The equation in this case represents a circle that does not pass through the origin because c is a constant term.
We possess
4x2+4y2−12x+32y=27…(1)
We shall have y=0 when the specified circle intersects the x-axis, therefore
4x2+4y2−12x+32y=27
=>4x2−12x=27
=>4x2−12x−27=0…(2)
The answers to (2) are:
x1=−3/2
x2=9/2
Thus, the supplied circle intersects the x-axis at the following points:
A(−3/2,0) and B(9/2,0)
The length of the chord we want is defined as the distance d between these sites. The well-known formula for calculating the distance between points A and B is used to calculate the distance d:
d=root((9/2−(−3/2))^2+(0−0)^2)
√=6^2
=6
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2b plus 4a minus a minus 2 plus 12b
The value of the expression 2b plus 4a minus a minus 2 plus 12b is 3a + 14b - 2.
Expression:
An expression is defined as the a combination of operators, constants and variables. And it may consist of one or more operands, and zero or more operators to produce a value.
Given,
Here we have the statement "2b plus 4a minus a minus 2 plus 12b".
Now, we have to find the simplified form of this statement.
In order to find the simplified form,
First we have to convert the statement into expression form, then we get
2b plus 4a minus a minus 2 plus 12b = 2b + 4a - a - 2 + 12b
Now, we have to combine the like terms, then we get,
=> (2b + 12b) + (4a - a) - 2
Perform the appropriate arithmetic operations, then we get the simplified form of the expression as,
=> 14b + 3a - 2
Now, we have to arrange them in order then we get,
=> 3a + 14b - 2
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5 =7/2 (3x + 2)
what is x?
Answer:
x=11
Step-by-step explanation:
What is n 1.8n+0.2=3.2n+1
n = -0.5714
Step-by-step explanation:
[tex]{ \tt{1.8n + 0.2 = 3.2n + 1}}[/tex]
[tex]{ \tt{1.8n = 3.2n + 1 - 0.2}}[/tex]
[tex]{ \tt{1.8n = 3.2n + 0.8}}[/tex]
[tex]{ \tt{1.8n - 3.2n = 0.8}}[/tex]
[tex] { \tt{ - 1.4n = 0.8}}[/tex]
Divide both sides by -1.4 then,
[tex]{ \tt{ \frac{ - 1.4}{ - 1.4}n = - \frac{ 0.8}{1.4}}} [/tex]
Let us convert 0.8 to 8 and 1.4 to 14 by shifting the points. Then,
[tex]{ \tt{n = - \frac{8}{14}}} [/tex]
[tex]{ \tt{n = - \frac{4}{7}}} [/tex]
[tex]{ \blue{ \boxed{ \green{\sf{n = -0.571428571}}}}} [/tex]
question 16 a project has a 60% chance of doubling your investment in 1 year and a 40% chance of losing half your money. what is the standard deviation of this investment? 62% 73% 50% 25%
The standard deviation is 70 %.
What is standard deviation ?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. [1] While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD.A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance. Though in algebra, it is simpler.acc to our question=
To get Standard Deviation (SD), we follow the steps shown below:We need to find the difference of each number from the mean and then square it.Then take the sum of all of these values.Then divide by the number of numbers.Then take square root of that.learn more about sd click here:
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-4 2/3+2 1/2
in mixted number form
In year 2020, a pond had 798 gallons of water. In year 2024, the same pond had only 612 gallons of water. If the rate of change is constant, predict the volume of water in year 2030
If the rate of change is constant, the volume of the water in the pond by the year 2030 will be 147 gallons.
Define volume.
Any three-dimensional solid's volume is just the amount of space it takes up. It can be any shape like a cube, cuboid, cone, cylinder, etc. Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. The SI unit of volume is cubic units.
Solution Explained:
Based on the conditions given in the question, we formulate as follows
(612 X (2024 - 2020) + (612 - 798) X (2030 - 2020) / (2024-2020)
= (612 X 4 - 186 X 10) / 4
= (2448 - 1860) / 4
= 588 / 4
= 147
Therefore, by 2030 the volume of the water in the pond will be 147 gallons.
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Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by the wall street journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes. Use that as a planning value for the standard deviation in answering the following questions. Round your answer to next whole number. A. If we want to estimate the population mean time for previews at movie theaters with a margin of error of seconds, what sample size should be used? assume confidence. B. If we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, what sample size should be used? assume confidence.
If we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, then 56 sample size should be used and if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, then 22 sample size should be used.
In the given question,
A preliminary sample conducted by the wall street journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes.
(a) We have to estimate the population mean time for previews at movie theaters with a margin of error of seconds, what sample size should be used.
Assuming the confidence interval 98% and margin error of 75 seconds.
We can write 98% as 0.98.
So the value of z at 98% confidence interval using the standard table of z is 2.326.
Standard Deviation= 4 minutes
Converting minutes in seconds so,
Standard Deviation= 4*60
Standard Deviation= 240
Margin of error is 75 seconds.
So the sample size = (Value of z * Standard Deviation)/Margin Error
Sample Size = ((2.326*240)/75)^2
Sample Size = (558.24/75)^2
Sample Size = (7.4432)^2
Sample Size = 55.401
Approx value of Sample Size = 56
Hence, if we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, then 56 sample size should be used.
(b) We have to estimate if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, what sample size should be used.
The given margin of error is 75 seconds.
Now converting the error in minute by dividing 60.
Now the margin of error = 75/60=5/6 minute
Standard Deviation= 4 minutes
The confidence interval 98% and margin error of 75 seconds.
We can write 98% as 0.98.
So the sample size = (Value of z * Standard Deviation)/Margin Error
sample size = {(0.98*4)/(5/6)}^2
sample size = {6(0.98*4)/5}^2
sample size = (6*3.92/5)^2
sample size = (23.52/5)^2
sample size = (4.704)^2
sample size = 22.13
Approx value of Sample Size = 22
Hence, if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, then 22 sample size should be used.
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Use the area formula A=lw to write a formula for the length l of a baking sheet that has an A = 117^{2}
The formula to find the length l of a baking sheet that has an area of 117 square units is l = 117/w.
According to the question,
We have the following information:
Formula to find area = lw
Now, l is the length of a baking sheet.
Area of a baking sheet = 117 square units
So, we have the following expression:
lw = 117
Now, in order to find the value of l, we will divide both sides by w:
l = 117/w units
Hence, the formula to find the length l of a baking sheet that has an area of 117 square units is l = 117/w.
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Select the correct answer. For which system of inequalities is (3,-7) a solution? A. x + y < -4 3x + 2y < -5 B. x + y ≤ -4 3x + 2y < -5 C. x + y < -4 3x + 2y ≤ -5 D. x + y ≤ -4 3x + 2y ≤ -5
x + y ≤ -4 and 3x + 2y ≤ -5
======================================================
Explanation:
The given point has coordinates of x = 3 and y = -7.
Let's plug those coordinates into the first inequality of choice A.
x+y < -4
3 + (-7) < -4
-4 < -4
The last statement is false. A number cannot be smaller than itself.
Since the last inequality is false, it causes the first to be false for those x,y values. Therefore, we rule out choice A.
--------------
We'll do the same idea for the first inequality in choice B
x + y ≤ -4
3 + (-7) ≤ -4
-4 ≤ -4
This time we get a true statement at the end. The key difference is the "or equal to" portion.
Let's check the other inequality of choice B
3x + 2y < -5
3(3) + 2(-7) < -5
9 - 14 < -5
-5 < -5
We run into a similar issue as we did with choice A. We have no choice but to cross choice B off the list as well.
--------------
Choice C is eliminated for the same reason choice A was.
Choice D is the final answer because both inequalities involve "or equal to". So the -5 < -5 is now -5 ≤ -5 which is true.
It turns out that (3, -7) is on the boundary of each shaded region. It's at the intersection of the two boundary lines x+y = -4 and 3x+2y = -5.
D. x + y ≤ -4
3x + 2y ≤ -5
To see if (3, -7) satisfies both inequalities.
x + y ≤ -4:
Substitute x = 3 and y = -7 into the first inequality:
3 + (-7) ≤ -4
-4 ≤ -4
Since -4 is less than or equal to -4, the first inequality is true for the point (3, -7).
3x + 2y ≤ -5:
Substitute x = 3 and y = -7 into the second inequality:
3(3) + 2(-7) ≤ -5
9 - 14 ≤ -5
-5 ≤ -5
Since -5 is equal to -5, the second inequality is also true for the point (3, -7).
(✿◕‿◕✿)
PLEASE HELP MATH 36 pointssss
Faris has a box of 150 building blocks.
a) He uses some of the blocks to make a tower.
70 blocks are left over.
How many blocks has he used?
80 blocks
b) He uses the 70 blocks left over to make another two towers.
One tower takes 35 blocks and the other takes 20 blocks.
4
How many of the 70 blocks has he got left?
blocks
The value of the blocks he used is 80 blocks.
What is meant by mathematic expression?The difference is that expressions, which are essentially mathematical "phrases," do not contain an equal sign. Equations have an equal sign and demonstrate that two mathematical expressions are equivalent. An algebraic equation is 2x + b = 14, but 2x + b is an algebraic expression.
Arithmetic operations are the most fundamental type of mathematical expression. Any combination of numbers and a mathematical operation, such as multiplication, addition, subtraction, or division, are considered arithmetic operations.
Given ,
A)How many blocks has he used?
150-70
= 80
B) 35 - 20
= 15
70/15
= 4
Therefore the value of the blocks he used is 80 blocks
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How would you graph y =- 3x 7?.
Any algebraic expression can be represented graphically. The given problem can be solved as shown in the image attached.
A polynomial in one variable is also an algebraic expression. It can be written in the form aˣn. Here, n is a non-negative integer and a is a real number. The a is also called the coefficient of the term.
The given problem also consists of a polynomial in one variable. It can be solved as such.
We have been told that = y = -3x+7
We need to graph this. For this, we plot at least two values for x and y -
x = 0 and y = 7
x = 1 and y = 4
We plot both these coordinates on the graph which has been attached below.
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Aubrie Kincade
Fractions as Quotients and Fraction Multiplication:Question 5
Do the following multiplication:
Enter answer below
Enter your response
1
x 7
The multiplication of the quotient and the fraction is 1 (2/5).
What is a fraction?A fraction is a part of the whole represented by a/b, where a and b are any integers.
The given expression is (1/5) × 7.
Perform the multiplication:
(1/5) × 7
= 7/5
= 1 (2/5)
Hence, the multiplication of the quotient and the fraction is 1 (2/5).
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Andre is solving the inequality 14x+3≤8x+3. He first solves a related equation. 14x+3=8x+3 14x=8x 8=14 This seems strange to Andre. He thinks he probably made a mistake. What was his mistake? Responses Andre made a mistake when he erased the 3 on both sides of the equation. Andre made a mistake when he erased the 3 on both sides of the equation. Andre made a mistake by changing the less than symbol to an equal sign. Andre made a mistake by changing the less than symbol to an equal sign. Andre made a mistake after getting 14x=8x. He divided each side by x, but this is not valid since x may be 0 and dividing by 0 gives an undefined result.
Andre made a mistake after getting 14x=8x. He divided each side by x, but this is not valid since x may be 0 and dividing by 0 gives an undefined result.
Andre should have collected the like terms in order to have all the variables x on one side before taking the difference.
Inequality expression
Given the inequality expression solved by andre expressed as:
14x + 3 ≤ 8x + 3
Simplify to have:
14x - 8x ≤ 3-3
6x ≤ 0
x ≤ 0
Hence andre should have collected the like terms in order to have all the variables x on one side before taking the difference.
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I keep getting the wrong answer
Answer:
Equation: 3x - 4 = 6 - 2x
Solution: x = 2
Step-by-step explanation:
Look at the key.
Left side of the equal sign:
A grey rectangle means x.
There are 3 grey rectangles on the left side, so that is 3x.
A white square means -1.
There are 4 white squares on the left side, so that means -4.
Altogether, the left side is 3x - 4.
Right side of the equal sign:
A black square means 1.
There are 6 black squares, so that means 6.
A white rectangle means -x.
There are 2 white rectangles, so that means -2x.
Altogether, the right side is 6 - 2x.
Put both sides together, and you have
3x - 4 = 6 - 2x
Solve the equation:
Add 2x to both sides.
5x - 4 = 6
Add 4 to both sides.
5x = 10
Divide both sides by 5.
x = 2
Answer:
Equation: 3x - 4 = 6 - 2x
Solution: x = 2
what is
1+3=
A.6
B.10
C.4
D.7
Answer:thhe one on top good
Step-by-step explanation:
Please help me with this, thank you.
Answer:
Step-by-step explanation:
Domain is the input
Range is the output
Function is the equation that is set up by the given information
1)
Domain 2 to 8
Range 1 to 6
Yes, this is a function
2)
Domain 2 to 3
Range 7 to 13
No, this is not a function , b/c functions need a 1 to 1 correspondence
3)
Domain 0 to 4
Range -1 to 5
No, this is not a function , b/c functions need a 1 to 1 correspondence
un envase tiene una capacidad de 2,5 litros. si se agregan 1,3 litros de agua, ¿ qué fracción del envase está vacía.
Ayuda
The fraction of the container that is empty, based on the capacity of the container and the water added, is 12 / 25
How to find the fraction?The fraction of the container that is empty can be found by the formula:
= (Capacity of container - Amount of water added ) / Capacity of container
Capacity of container = 2.5 liters
Amount of water added = 1 . 3 liters
The fraction of the container which is empty is:
= (2 . 5 - 1.3) / 2.5
= 1.2 / 2.5
= (1 . 2 x 10) / ( 2 . 5 x 10)
= 12 / 25
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What is the slope of the line that passes through the points (-2, 2) and (-4, -1)
Answer:
f(x) = 1/2x + 3
Answer:
3/2
Step-by-step explanation:
(y2-y1)/(x2-x1)
(-1-2)/(-4+2)
-3/-2
the slope of the line is 3/2
A hot air balloon rises 1,500 feet in 25 minutes. Which equation represents altitude (h) of the balloon over time (t)?
A) h = 60t
B) t = 1,500h
C) h = 1,500t
D) h = 60/t
The equation that represents the altitude h of the balloon over time.
h = 1500t.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 5 is an equation.
3x + 5x = 5 is an equation.
We have,
A hot air balloon rises 1,500 feet in 25 minutes.
This means,
25 minutes = 1,500 feet
h = altitude
The equation that represents the altitude h of the balloon over time.
h = 1500t.
Thus,
The equation that represents the altitude h of the balloon over time.
h = 1500t.
Option B is the correct answer.
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HELP ASAP DUE TOMORRROW
Based on the box plot, the number of students that gained more than 48 marks is 80 students.
What is a box and whisker plot?In Mathematics, the five-number summary of any box and whisker plot include the following:
MinimumFirst quartileMedianThird quartileMaximumBy critically observing the box and whisker plots which represent the scores of students in a test, we can reasonably and logically deduce that the third quartile (75%) is 70 and the median score is 48. Therefore, we would calculate the total number of students as follows:
Total number of students = 75/100 × T
120 = 0.75T
T = 120/0.75
T = 160 students.
From the median score of 48, the number of students that gained more than 48 marks is given by:
Students = 50/100 × 160
Students = 50/100 × 160
Students = 80 students.
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A spurious correlation is the implied causal relationships between events that are ________ linked.
A spurious correlation is the implied causal relationships between events that are statistically linked.
Spurious correlation;
A spurious correlation (or spuriousness) in statistics is an apparent causal relationship between two variables. Any reported dependencies between variables are solely the result of chance or are both a result of an unidentified confounder when there is misleading correlation.
When the price of higher education and the cost of living both rise, for instance, this doesn't necessarily indicate a causal link between the two factors because higher education tuition isn't always the result of rising living costs.
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Find the Volume (pls help me)
Answer:
Step-by-step explanation:
32
A set of computer science exam scores are normally distributed with a mean of 71. 3371. 3371, point, 33 points and a standard deviation of 333 points. What proportion of exam scores are between 686868 and 77. 9977. 9977, point, 99 points? you may round your answer to four decimal places.
0.86 of the exam scores are between 68 and 77.99 points
Since the set of computer science exam scores are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x-μ)/σ
Where
X = computer science exam scores.
μ = mean score
σ = standard deviation
From the information given,
μ = 71.33 points
σ = 333 points
We want to find the proportion of the exam scores are between 68 and 77.99 points. It is expressed as
P(68 < x ≤ 77.99)
For x = 68,
z = (68 - 71.331)/333 = - 0.01
Looking at the normal distribution table, the probability corresponding to the z score is -0.01
For x = 68,
z = (77.99 - 71.33)/333 = 0.25
Looking at the normal distribution table, the probability corresponding to the z score is 0.25
P(68 < x ≤ 77.99) = 0.25 + 0.01 = 0.26
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A home loan including interest is 166430 to pay off the loan equal payments need to be made over the next 180 months about how much will each payment be per month
Answer:
The answer is 923.6111 because 166430÷180 is 923.6111
Put the following equation of a line into lope-intercept form,implifying all fraction 8x12y=108
The slope of the line from the equation is 2/3.
The line:
A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.
The formula of a line:
y = mx + c
m = slope
c = y-intercept
Here we are provided with the equation:
8x - 12y = 108
12y = 8x - 108
y = 2/3x - 9
So by equating we get the slope:
m = 2/3
Therefore the slope is 2/3.
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What is consumidores primarios?
Answer:Consumidores primarios: comen a los productores. Consumidores secundarios: comen a los primarios. Consumidores terciarios: comen a los carnívoros. Descomponedores: se alimentan de restos de seres vivos.
Step-by-step explanation:Consumidores primarios: comen a los productores. Consumidores secundarios: comen a los primarios. Consumidores terciarios: comen a los carnívoros. Descomponedores: se alimentan de restos de seres vivos.
Hello..!
¿What is consumidores primarios?
They are the ones that eat plants. They are herbivores or are parasites of these.
The lengths of the three sides of a triangle (in inches) are consecutive odd integers. If
the perimeter is 57 inches, find the value of the middle of the three side lengths.
The sides of the triangle are 17, 19 and 21 and 19 is middle of the three side lengths.
What are triangles?
Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. The triangle's three angles add up to a total of 180 degrees.Let the side of triangle = x
x-2, x, x+2 are the three sides and their sum is 3x.
3x = 57
x = 57/3
x = 19.
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What is the absolute value of 4 by 3?.
The absolute value of 4 by 3 would be 3.33
What is the absolute value?
The absolute value or modulus of a real number x denoted |x| in mathematics, is the non-negative value of x regardless of its sign.
We have to find the absolute value of 4/3.
So |4/3| = |3.33|
= 3.33
Hence, the absolute value of 4 by 3 would be 3.33
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