The ninth term of the geometric sequence is 2048.
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.This ratio is known as a common ratio.Geometric sequence is defined as : a, ar, ar², ar³, .... , aⁿ.The nth term of a geometric sequence with initial value {a = a₁} and common ratio {r} is given by : a{n} = ar ⁿ ⁻ ¹.Given is the geometric sequence as -
8, -16, 32, -64, .....
We can write the 9th term as -
a{9} = ar ⁹ ⁻ ¹
a{9} = ar⁸
a{9} = 8 (-2)⁸
a{9} = 8 x 16 x 16
a{9} = 2048
Therefore, the ninth term of the geometric sequence is 2048.
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A line's slope is 4. The line passes through the point (5, 22). Find an equation for this line in both slope-intercept form and point-slope form using the given point.
Answer:Find the equation of a line.whose slope is 4 and which passes through the point (5, - 7) Class 11. >> Applied Mathematics. >> Straight lines. >> Various forms of the equation of a line. >> Find the equation of a line.whose slope. Question. Find the equation of a line.
Step-by-step explanation:
A bag contains 31 red blocks, 46 green blocks, 22 yellow blocks, and 26 purple blocks. You pick one block from the bag at random. Find the indicated theoretical probability.
The theoretical probability for each event is given below.
What is a probability? Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates complete certainty.Given is that a bag contains 31 red blocks, 46 green blocks, 22 yellow blocks, and 26 purple blocks.
Total number of blocks = n{T} = 31 + 46 + 22 + 26 = 125
Probability that a red block is selected is : 31/125Probability that a green block is selected is : 46/125Probability that a yellow block is selected is : 22/125Probability that a purple block is selected is : 26/125Therefore, the theoretical probability for each event is given above.
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As part of a weight reduction program, a man designs a monthly exercise program consisting of bicycling, jogging, and swimming. He would like to exercise at most 30 hours, devote at most 7 hours to swimming, and jog for no more than the total number of hours bicycling and swimming. The calories burned by this person per hour by bicycling, jogging, and swimming are 200,415 , and 295 respectively. How many hours should be allotted to each activity to maximize the number of calories burned? What is the maximum number of calories he will burn?
Answer:
Jogging = 10 hours
Swimming = 7 hours
Cycling = 3 hours
9.
Allen's water bill contains the following information:
He used 1600 cubic feet of water.
. The total cost for the water he used is $34.80.
دا2
31
Which price is closest to the cost per gallon of water that Allen
used?
3100
[1 cubic foot of water = 7.48 gallons of water] +
10
5
A. $0.0029 B. $0.0218 C. $0.1627 21 D. $0.2908
C
The cost per gallon of water is A)$0.0029.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here According to the question ,
Cost of 1600 cubic feet of water = $34.80
Now Here 1 cubic feet = 7.481 gallon then,
Then 1600 cubic feet = 11968.83 gallon
Cost of 1 gallon of water = [tex]\frac{34.80}{11968.83}[/tex] = $0.0029
Hence the cost per gallon of water is A)$0.0029.
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PLEASE HELP I'M DESPERATE
Answer the question below.
Solve the equation -22 = q + 7(2q - 1)
and verify the solution. Show all work.
The solution of the equation -22 = q + 7(2q - 1) is as follows:
q = -1How to solve equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Let's solve the equations as follows:
-22 = q + 7(2q - 1)
The variable in the equation is q. A variable is an letter use to represent number in an equation.
-22 = q + 7(2q - 1)
-22 = q + 14q - 7
-22 = 15q - 7
add 7 to both sides of the equation
-22 + 7 = 15q - 7 + 7
-15 = 15q
divide both sides by 15
q = -15 / 15
q = -1
Therefore,
q = -1
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Answer:
-22 = q + 7(2q - 1)
-22 = q + 14q - 7
-22 = 15q - 7
add 7 to both sides of the equation
-22 + 7 = 15q - 7 + 7
-15 = 15q
divide both sides by 15
q = -15 / 15
q = -1
Step-by-step explanation:
DUE SOON PLEASE HELP!
QUESTION DOWN BELOW!!
Answer:
To find the scale factor between the two similar figures, we can use the ratio of their surface areas. Similar figures have the same shape but different sizes, so their surface areas will be in proportion to the scale factor.
We are given that the surface area of the first figure is 169 cm² and the surface area of the second figure is 121 cm².
The scale factor is the ratio of the surface area of the first figure to the surface area of the second figure.
The ratio can be found by dividing the surface area of the first figure by the surface area of the second figure:
169 cm² / 121 cm² = 13/9
So, the scale factor between the two similar figures is 13/9
Therefore, the answer is 13:9.
A fast-food worker works Monday through Friday, 8 hours per day. Daily, the worker receives a -hour break in the morning, a -hour break for lunch, and a -hour break in the afternoon. How many hours of break time does the worker receive per day?
The worker recieves 3 hours of break time per day.
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 a a fast-food worker works Monday through Friday, 8 hours per day. Daily, the worker receives a hour break in the morning, a hour break for lunch, and a hour break in the afternoon.
The worker recieves three breaks, meaning it recieves 3 hours of break time per day.
Therefore, the worker recieves 3 hours of break time per day.
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write the first 5 terms whose geometric sequence is 9 and whose common ratio is 3
The Geometric Sequence if first term is 9 and common ratio is 3 is 9,27,81,243,729 .
What is Geometric Progression ?
Geometric Progression can be defined when in a sequence of numbers , if the ratio between consecutive numbers is same than it is said to be in Geometric Progression.
Given
The first term is 9
and common ratio is 3
So, we need to find the geometric sequence ,
Geometric sequence, An = a * r^(n-1)
so here a=9
r = 3
a1 = 9
a2 = 9 * 3^(2-1)
a2 = 9*3
a2 = 27
a3 = 9 * 3^(3-1)
a3 = 9 * 3 * 3
a3 = 81
a4 = 9 * 3^(4-1)
a4 = 9 * 27
a4 = 243
a5 = 9*3^(5-1)
a5 = 9 * 81
a5 = 729
Hence, The Geometric Sequence if first term is 9 and common ratio is 3 is 9,27,81,243,729 .
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Rewrite the following equation in slope-intercept form.
19x − 3y = –9
y = 5x - 9 X =y + 5
how dobi solve this?
The two equations given, "Y = 5x - 9" and "X = y + 5", are a pair of linear equations. We can solve for the values of x and y by using substitution or elimination method.
How do solve this?Here's how to solve using the substitution method:
Substitute the value of y from the second equation into the first equation:Y = 5x - 9
Y = (y + 5) + 5 - 9
Simplifying the equation and solving for y:5x - y - 4 = 0
y = 5x - 4
Substitute the value of y from the above equation into the second equation:X = y + 5
X = (5x - 4) + 5
X = 5x + 1
Solving for x:5x + 1 = X
5x = X - 1
x = (X - 1) / 5
Substitute the value of x into one of the equations to find the value of y:y = 5x - 4
y = 5((X - 1) / 5) - 4
y = X - 1 - 4
y = X - 5
So, the solution to the system of equations is (x, y) = ((X - 1) / 5, X - 5).
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Cate started with $0 in her account. After one week Cate saved $1; after two weeks she saved $4; after three weeks she saved $9; and after four weeks she saved $16.
The answer is neither. Option C
How to determine if the number pattern is linear or exponentialA linear number pattern is a sequence of numbers whose difference between all the terms is the same. When you count, the difference between each successive number is 1. You start with 1, then you add 1 to get 2. Then you add another 1 to get 3. And you keep repeating this addition of 1 process to get the rest of the terms.
Exponential notation is used to represent very large numbers and very small numbers. When representing very large numbers, the exponential notation will have a positive exponent; when representing a really small number, the exponential notation will contain a negative exponent.
From the question, the pattern of the number takes non of the pattern or neither linear or exponential
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Using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $72,550? (use a dollar sign and 2 decimal places)
Using the standard 28/36 guidelines, the maximum mortgage payment allowed for someone with an annual salary of $72,550 is: $1,692.83.
How to find the Maximum mortgage payment allowed ?First step is to find the monthly gross income
Monthly gross income = $72,550 /12 months
Monthly gross income = $6,045.83
Now let apply the standard 28/36 guidelines so as to find the maximum mortgage payment allowed
Maximum mortgage payment allowed = $6,045.83 × 28%
Maximum mortgage payment allowed =$1,692.83
Therefore the Maximum mortgage payment allowed is $1,692.83.
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The points (2, 5) and (–3, 5) fall on a particular line. What is its equation in slope-intercept form?
Equation in slope-intercept form is y=5.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Slope of line passing through points (2, 5) and (–3, 5)
m=5-5/-3-2=0
So the slope is 0
Y intercept is 5=0(2)+b
b=5
Hence, equation in slope-intercept form is y=5.
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If b = -2, what is 3b-7 ?
On Wednesday evening Sonto spent hour doing homework, 45 minutes doing housework, 1 hour visiting friends and 1 hours watching television. Write this information as a ratio.
Answer:
hablas espanol para ayudarte
Alonso is going to drive from his house to City A without stopping. Let DD represent Alonso's distance from City A tt hours after leaving his house. The table below has select values showing the linear relationship between tt and D.D. Determine how long Alonso has been driving the moment he was 225 miles away from City A.
tt DD
0.50.5 275275
22 200200
55 5050
The equation of line is y = -50x + 300 , where the slope is m = -50 and the time t when Alonso was 225 miles away was t = 1.5 hours
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 2 , 200 )
Let the second point be Q ( 5 , 50 )
Now , the slope of the line between the points is ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 200 - 150 ) / ( 2 - 5 )
Slope m = -150/3
Slope m = -50
And , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 200 = -50 ( x - 2 )
On simplifying the equation , we get
y - 200 = -50x + 100
Adding 200 on both sides of the equation , we get
y = -50x + 300
So , when Alonso is at 225 miles away ,
Substitute the value of y = 225 miles , we get
225 = -50x + 300
Subtracting 300 on both sides of the equation , we get
-50x = -75
Divide by -50 on both sides of the equation , we get
x = 75/50
x = 3/2
x = 1.5 hours
Hence , the equation of line is y = -50x + 300
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David has $540 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $298.79. He buys 3 bicycle reflectors for $8.13 each and a pair of bike gloves for $21.79. He plans to spend some or all of the money he has left to buy new biking outfits for $79.43 each. Which inequality can be used to determine xx, the maximum number of outfits David can purchase while staying within his budget?
The inequality that can be used to determine x, the maximum number of outfits David can purchase at the bicycle store while staying within his budget is 344.97 + 79.43x ≤ 540.
What is inequality?An inequality is a mathematical statement that shows that two or more mathematical expressions are unequal.
Inequalities are represented as either:
Greater than (>)Less than (<)Greater or equal to (≥)Less than or equal to (≤)Not equal to (≠).David's total spending budget at the bicycle store = $540
Tax-inclusive Prices:
New Bicycle = $298.79
3 Bicycle reflectors = $24.39 ($8.13 x 3)
A pair of bike gloves = $21.79
Total for the three items = $344.97
The remaining amount of the budget after the three items = $195.03
The cost of new biking outfits per unit = $79.43
Let the maximum number of outfits = x
Inequality:$344.97 + $79.43x ≤ $540
344.97 + 79.43x ≤ 540
79.43x ≤ 540 - 344.97
79.43x ≤ 195.03
x ≤ 2
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Which number is greater: 3 x 10-¹² or 9 x 10-¹¹? How many times as great
The 9 x 10⁻¹¹ is greater number than 3 x 10⁻¹².
What is an absolute value?The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.
We have two numbers:
3 x 10⁻¹² or 9 x 10⁻¹¹.
To find the greater number;
Divide both numbers by 10⁻¹¹.
That means,
3 x 10⁻¹² becomes 3/10.
And 9 x 10⁻¹¹ becomes 9.
The absolute value,
9 > 3/10.
Therefore, 9 x 10⁻¹¹ is greater number.
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39
ultiplying Fractions (NF 4)
In which equation is the product greater than 3? (Do all the math for each answer ch
a.
3/4 x2
b.
3/6 x4
C.
3/10 x 10
d.
2/3 x 18
Answer:
Step-by-step
look at the pic for the problem lol
Answer:jrifigjitgjtigjijijiij
Step-by-step explanation:
jjfijjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj
7) If the radius is 10 ft, what will be the area of the circle?
Answer:
100π
Step-by-step explanation:
Area of the circle is [tex]\pi r^2[/tex]. r is 10. So, the area is 100π
8. During the first year, the average depreciation for new cars is around 30 to 40 per cent, according to an article in the Globe and Mail. What is the depreciation range for the following 2021 models in their first year? • 2021 RAV 4 LE FWD at $28,590 • 2021 BMW Coupe 2-series at $45,500
The depreciation range ( Depreciated price) for 2021 RAV 4 LE FWD at $28,590 will be $17154-$20013 and for 2021 BMW Coupe 2-series at $45,500 will be $27300-$31850.
What is depreciation?
Almost everything we see around us has a useful life because it is being used up little by little every day or will become outdated as technology changes. Think about the computer you are using. You probably expect it to last only about five years because every time you access it, the components inside it get used up a little bit, and improved technology will eventually make it obsolete. This 'using up' is called depreciation, and that five years is considered the computer's useful life.
Now,
As given that average depreciation for cars is between 30% and 40%
that means their depreciated price will be between 60% and 70%.
Hence,
For 2021 RAV 4 LE FWD at $28,590
Depreciation range will be 60/100*28590 to 70/100*28590
i.e. $17154-$20013
For 2021 BMW Coupe 2-series at $45,500
Depreciation range will be 60/100*45500 to 70/100*45500
i.e. $27300-$31850
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Amy counts butterflies for a science project.
She wants to know how many more butterflies she saw this month than in the past 4 months.
First she adds the number of butterflies she saw in the past 4 months.
She calls this number b. What should Amy do next?
Answer: After adding the number of butterflies she saw in the past 4 months and assigning it to the variable "b", the next step for Amy would be to add the number of butterflies she saw in the current month.
Once she has both the current month and the past 4 months total number of butterflies, she can then subtract the past 4 months total from the current month total.
The result will be the number of butterflies seen this month than in the past 4 months.
Amy can then record and analyze her data.
Regene
Step-by-step explanation:
A=8 and b=24
What is (a+b) squared
The value of the expression (a + b)² at a = 8 and b = 24 will be 1,024.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ (a + b)²
The value of the expression at a = 8 and b = 24 will be calculated as,
⇒ (8 + 24)²
⇒ (32)²
⇒ 1,024
The value of the expression is 1,024.
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Please show me how to work out these math problems. Only the ones with stairs next them please. Thank you. Don’t understand how to work it out. Try to give me a good and simple step by of how to do this. Thanks .
Answer:
Here
Step-by-step explanation:
To find the area of a composite figure, you need to determine the areas of all the individual shapes that make up the composite figure and add them together.
The result will be the total area of the composite figure, expressed in square units.
Here are some steps you can follow:
Identify all the shapes in the composite figure and label them.Find the area of each individual shape. The formula for the area of different shapes such as a rectangle, triangle, circle, etc.Add the areas of all the individual shapes to find the total area of the composite figure.Express the answer in square units.Example: If the composite figure is made up of a rectangle with area 36 square units and a triangle with area 18 square units, the total area A would be 36 + 18 = 54 square units.
In this case, figure number 1, consists of two rectangles. To find the area of a rectangle, use the formula width x height. Follow these steps:
Step 1: determine the formulas needed. In this case, since there are two rectangles, use the formula width x height.Step 2: break down the composite figure into simpler shapes to solve.Step 3: use the formulas to find the area of each rectangle. For the first rectangle, the width is 8 and the height is 2, so the area is 8 x 2 = 16. For the second rectangle, the height is 4 and the width is 5, so the area is 4 x 5 = 20.Step 4: finally, add the areas of all the rectangles together to find the total area. In this case, the total area is 16 + 20 = 36.Learn more about composite figure here: brainly.com/question/30292204
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Each morning Daniel runs 5 miles in 45 minutes. If he keeps the same pace, how long will it take him to run 8.5 miles?
Answer:
Approximately 57 minutes.
Step-by-step explanation:
5 ÷ 45 = 1/9
1/9 · 8.5 = 17/18
An hour = 60 mins so
60 ÷ 18 = 10/3
10/3 · 17 = 56.6666667
also known as 56.67 minutes if rounded to hundreds, 56.7 minutes if rounded to the tenths, and 57 minutes if rounded to a whole number.
Which situation can be modeled by the inequality 7x+6<30?
The correct question which can be modeled by the inequality
7x + 6 < 30 is,
⇒ Dai must complete a project in less than 30 days. He work on a project 7 days each. To date, 6 days have already passed. What is greater number of weeks Dai has left to complete the project.
The correct option is c,
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
The inequality is,
⇒ 7x + 6 < 30
So, For the given inequality, the correct question is,
⇒ Dai must complete a project in less than 30 days. He work on a project 7 days each. To date, 6 days have already passed. What is greater number of weeks Dai has left to complete the project.
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Full Question ;
Which situation can be modeled by the inequality 7z+6 < 30?
A .A landscaper needs at least 30 pounds of fertilizer for lawns. Each lawn uses 7 pounds of fertilizer. What is the greatest number of lawns the landscaper can work on?
B. Miranda can spend no more than $30. She spends $7 for lunch and $6 for a subway fare. What is the greatest amount Miranda can spend on coffee?
C. Dai must complete a project in less than 30 days. He works on the project 7 days each week. To date, 6 days O have already passed. What is the greatest number of weeks Dai has left to complete the project?
D. A chef serves less than 30 steaks during dinner time. For 6 hours he serves the same number of steaks each hour. Then he serves 7 more steaks. What is the greatest number of steaks the chef served per hour?
PLEASE HELPP It took Andrea 2.7 hours to drive to her mother's house on Wednesday morning. On her return trip on Thursday night, traffic was heavier, so the trip took her 3 hours. Her average speed on Thursday was 7 mph slower than on Wednesday. What was her average speed on Thursday?
The Average speed of Andrea on thursday is 63 mph and on wednesday was 70 mph.
What is Speed and Distance ?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route. In other words, velocity is a vector, whereas speed is a scalar number.
The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The length of the entire journey taken to go from one point to another is the distance traveled.
The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.
Let the average speed on thursday be x mph
Average speed on wednesday was x+7 mph
The distance covered is the same on both journey so
3 * x = 2.7 * (x + 7)
⇒3x - 2.7x = 18.9
⇒x = 63
The Average speed of Andrea on thursday is 63 mph and on wednesday was 70 mph.
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If cosA=3/5 and sinB=7/25, where A is acute and B is obtuse find without using tables, the value of cos(A+B)
The value of cos(A+B) is -4/5.
What is the expansion of sum for cosine of sum of two angles?Suppose we've got trigonometric cosine of angle A and B measurements.
Then, we have:
[tex]\cos(A+B) = \cos(A)\cos(B) - \sin(A)\sin(B)[/tex]
If we get A = B, then:
[tex]\cos(2A) = \cos^2(A)- \sin^2(A)[/tex]
Given;
cosA=3/5
sinB=7/25
Now,cos(A+B) = cos A cos B - sin A sin B
for angle A 3^2+4^2 = 5^2
cos A = 3/5 so sin A = 4/5
for angle B 24^2 + 7^2 = 25^2
cos B = -24/25 and sin B = 7/25 because B is obtuse
Substituting the values in cos(A+B)
=3/5*-24/25-4/5*7/25
=-72/125-28/125
=-100/125
=-4/5
Therefore, the value of trigonometric identity will be -4/5.
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Out of 50 Students that patronized Christis resturant on a certain day, 23 ordered meat pie and 34 ordered fried rice while 6 ordered neither meat pie nor fried rice
(a) How many students ordered both food
(b) how many students ordered meat pie but not fried rice
Using Venn Diagram formula, 13 students ordered both food, 10 students ordered meat pie but not fried rice.
A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not. Venn diagrams help to visually represent the similarities and differences between two concepts.
Using Venn diagram formula,
n(A U B) = n(A) + n(B) – n (A ⋂ B)
Given,
n(A U B) = Total students = 50
n(A) = 23 ordered meat pie
n(B) = 34 ordered fried rice
6 ordered neither meat pie nor fried rice
As 6 students ordered neither meat pie nor fried rice,
Total students = 50 - 6 = 44
According to n(A U B) = n(A) + n(B) – n (A ⋂ B)
⇒ 44 = 23 + 34 - n (A ⋂ B)
⇒ 44 = 57 - n (A ⋂ B)
⇒ - 57 + 44 = - n (A ⋂ B)
⇒ n (A ⋂ B) = 13
13 students ordered both food.
students ordered meat pie but not fried rice = n(A) – n (A ⋂ B) = 23 - 13 = 10
10 students ordered meat pie but not fried rice
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