The required first five terms of the sequence are 2, 10, 50, 250, and 1250.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The first five terms of the sequence, a(n), defined by the recurrence relation a(n+1) = 5a(n) and a(1) = 2, are as follows:
a(1) = 2
a(2) = 5a(1) = 5 × 2 = 10
a(3) = 5a(2) = 5 × 10 = 50
a(4) = 5a(3) = 5 × 50 = 250
a(5) = 5a(4) = 5 × 250 = 1250
Therefore, the first five representations of the sequence are 2, 10, 50, 250, and 1250.
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• Jason runs 8 miles in an hour and bikes 12 miles in an hour.
. This week, he runs a total of 3 hours and bikes a total of 6 hours.
when a positive integer was multiplied by each of its digits, the product was 1995. Find the original number.
Answer:
57
Step-by-step explanation:
You want a positive number that gives a product of 1995 when it is multiplied by each of its digits.
NumberThe prime factors of 1995 are 3, 5, 7, 19. The product of 3 and 19 gives 57, so multiplying 57 by 5 and 7 will result in the product 1995.
The original number is 57.
<95141404393>
What's the equation and solution?
Observing the given figure , It is a balanced balance which signifies both side should be equal, The answer is 2=-8-x and x=-10.
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
What are the methods to solve system of equations?There are three ways to solve systems of linear equations :
GraphingSubstitution methodElimination method2=-8-x is the required balanced equation.
-x = 2 + 8
x= -10
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Angelina has taken 27 of the 36 exams she needs to take to become a nurse. What percent of the exams has she taken?
The percentage of the exam that she has taken is 75%.
What percentage of the exam has she taken?Percentage is a measure of frequency that is used to express the ratio of an amount as a number out of 100. The sign that is used to represent percentage is %.
In order to convert a number to percentage, multiply the number by 100. In order to determine the percent of exams that she has taken, multiply the ratio of exams taken and the total number of exams by 100.
Percent of the exams she has taken = (number of exams taken / total number of exams) x 100
Percent of the exams she has taken = (27 / 36) x 100
Percent of the exams she has taken = 75%
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what is the slope of the table below? 3/8 15/12 9/10 0/7
The slope of the table shown in the image attached below is equal to: D. 1/3.
How to calculate the slope of the given table?Mathematically, the slope of the given table can be calculated by using the following mathematical expression;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the table, we have the following data points:
Points on x-axis = (-2, 2).
Points on y-axis = (-4, -2).
Substituting the given points into the slope formula, we have;
Slope, m = (12 - 8)/(15 - 3)
Slope, m = 4/12
Slope, m = 1/3
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find the value of r so the line that passes through each pair of points has the given slope (5, 3), (r, -5), m=4
Answer:
r=3
Step-by-step explanation:
use slope formula : y2-y1 / x2-x1
-5-3 / r-5
the numerator is -8 which means the denominator has to be -2 in order to have the slope be 4
so r-5 = -2
3-5 = -2
A principal of $3600 is invested at 3.5% interest, compounded annually. How much will the investment be worth after 12 years? Use the calculator provided and round your answer to the nearest dollar. X S
Answer:
$5043
Step-by-step explanation:
To find the value of the investment after 12 years, you can use the following formula:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = principal
r = interest rate
n = number of times the interest is compounded per year
t = number of years
Plugging in the values from the problem, we get:
A = 3600 * (1 + 3.5/100)^(1*12)
Solving this equation, we get:
A = $5043.33
So, after 12 years, the investment will be worth $5043.33.
Question
A scientist wants a 90 ounce acid solution with a concentration of 12%. She has concentrations of 8% and 18%. How
much of each solution must she use to get the desired concentration?
On solving the provided question, we can say that - the percentage value of 12 % of 90 = 10.8
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
12% of 90 = 12/100 X 90
= 0.12 X 90 = 10.8
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
B, C, E
Step-by-step explanation:
Let y = length.
Then, y - 5 = width.
area = length × width
area = y(y - 5)
area = 750
y(y - 5) = 750
y² - 5y = 750
A: y(y + 5) = 750
Since y = length, width must be y - 5, not y + 5, so A does not work.
B: y² - 5y = 750
This is what we got above, so this equation works.
C: 750 - y(y - 5) = 0
750 = y(y - 5)
750 = y² - 5y
This is the same as B and works.
D: y(y - 5) + 750 = 0
y(y - 5) = -750
The area cannot be -750, so this equation does not work.
E: (y + 25)(y - 30) = 0
y = -25 or y = 30
This also works.
Answer: B, C, E
EXAMPLE 3.1.30. Let R be the relation on Z defined by ïRy ⇒ x − y is divisible by 3. Then R is an equivalence relation on Z. Find [0], [1], [2], [4], [-1]
equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is ( y - y1 ) = m( x - x1 ) => y - 7 = 2 (x-8) => 2x - y - 1 = 0
What is slope?A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).
equation is -
y = 2x - 5
since these are parallel to each other,
slope, m= 2
now the equation is -
( y - y1 ) = m( x - x1 )
y - 7 = 2 (x-8)
2x - y - 1 = 0
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What is the answer to 156 x 13
Answer:
2028
Step-by-step explanation:
156 x 13 = 2028
each day you do homework for m minutes and watch tv for 30 minutes. Which expression can you use to find how many minutes you do both activities.
Answer:
Let y be the expression for the minutes you do both activities.then
y=m+30 is the required expression
Bradenton Bakery is baking a cake for a customer's quinceañera. The cake mold is shaped like a cylinder with a diameter of 12 inches and height of 8 inches.
Which of the following shows a correct method to calculate the number of cubic units of cake batter needed to fill the mold? Approximate using pi equals 355 over 113.
V equals 355 over 113 times 12 squared times 8
V equals 355 over 113 times 6 squared times 8
V equals 355 over 113 times 8 squared times 6
V equals 355 over 113 times 8 squared times 12
Therefore , the solution of the given problem of volume comes out to be
V =355/113 * (5)² * 7 thus correct option is V equals 355 over 113 times 6 squared times 8.
Define volume.Volume, which is expressed in cubic units, is a unit of measurement for the 3-dimensional space occupied by matter or encircled by a surface. The SI unit of volume = area * height is the cubic metre (m3), which is a derived unit. A "litre" (L) is the name given to the cubic decimeter (dm3).
Here,
The volume of cylinder = πr²h
Given : Diameter = 12 inches
radius = 12/2 = 6 inches
Height = 8 inches
Thus ,
To find the volume we put the all the above values in the formula:
=> V = πr²h
=> V = 22/7 * 6² * 8
=> V =355/113 * (6)² * 8
Therefore , the solution of the given problem of volume comes out to be
V =355/113 * (5)² * 7 thus correct option is V equals 355 over 113 times 6 squared times 8.
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Answer:
V equals 355 over 113 times 6 squared times 8.
Step-by-step explanation:
Round 0.21545977 to the nearest hundredth
Answer:
0.22
Step-by-step explanation:
Since 5 rounds up, it would be 0.22
Answer:
0.22 Is the answer.
I wish you luck on your assignments.
A company employing 10,000 workers offers deluxe medical coverage (D), standard medical coverage (S) and economy medical coverage (E) to its employees. Of the employees, 30% have D, 60% have 5 and 10% have E. From past experience, the probability that an employee with D, will submit no claims during next year is 0.1. The corresponding probabilities for employees with S and E are 0.4 and 0.7 respectively. If an employee is selected at random;
a) What is the probability that the selected employee has standard coverage and will submit no
claim during next year? b) What is the probability that the selected employee will submit no claim during next year?
c) If the selected employee submits no claims during the next year, what is the probability that the employee has standard medical coverage (S)?
please give full answer
You want to buy a $135,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan at
6.1% interest for the rest.
How much is the loan amount going to be?
What will your monthly payments be?
How much total interest do you pay?
Suppose you want to pay off the loan in 15 years rather than 30. What will your monthly payment be?
On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
total is 500
obtained is 400
so, percentage - 400/500 X 100 = 80%
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Which of the following points is shown in the graph below? Question 5 options:
The point shown on the graph is
(4, -5, 6)
How to find the points shown on the graphAn ordered triplet of lines (the axes) that are pair-wise perpendicular and pass through the same point (the origin) make up a Cartesian coordinate system for a three-dimensional space.
Each axis also has an orientation, and the length of all three axes is equal.
In ordered triplet, the order of the axis is (x, y, z)
z is vertical up positive and down negative
y is horizontal right is positive and left is negative
x is the axis pointing to us which is positive pointing away is negative
Using this information, to trace the point shows that the point marked by a dot is (4, -5, 6).
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Draw a diagram of x + 2, and a separate diagram of 3x, when x is 2.
The graph of the equation x + 2 would be a straight line that starts at the point (-2, 0) and goes up 2 units on the y-axis. So, the line would pass through the point (0,2) and would be parallel to the x-axis.
The graph of the equation 3x when x is 2 would be a straight line that starts at the point (0,0) and goes up 6 units on the y-axis for each 1 unit on the x-axis. So, the line would pass through the point (2,6) and would have a slope of 3.
What is diagram in mathematics?In mathematics, a diagram is a visual representation of mathematical concepts or ideas. Diagrams can take many forms, such as graphs, charts, illustrations, and figures, and can be used to help explain or understand mathematical concepts.
For example, a graph is a type of diagram that is used to represent the relationship between two variables. It is commonly used in algebra and calculus to show the relationship between an independent variable (x-axis) and a dependent variable (y-axis).
A chart is a type of diagram that is used to organize and present data. It is commonly used in statistics to show the distribution of data or to compare different sets of data.
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i really need help with this, i dont get how to identify outliners and gaps stuff, please help?
On solving the provided question, we can say that - the plotting data will be done by 3 to 24 ; 6 to 61 ; 5 to 56; 1 to 15
what is plotting data?A graph that demonstrates the relationship between two or more variables is the most common way to depict a data set using a chart. Both hand-drawn and computer-drawn diagrams are acceptable. Start at the origin and move 2 units to the right before moving 3 units up to draw the coordinates for the point 2,3 on the coordinate plane. Make your points clear. As a result, the pink dot with the letter P on it denotes 2.3. A number line containing each value in your data collection should be first created before making a line chart. Then, on the number line, put an X (or dot) over each value of the data. Put an X over the number for each time a value appears in a record where it does.
so we have to plot data from the given data, we can do by
3 to 24 ; 6 to 61 ; 5 to 56; 1 to 15
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Keshawn is organizing textbooks on his bookshelf. He has a Spanish textbook, a biology textbook, a history textbook, and a writing textbook. How many different ways can he line the textbooks up on his bookshelf?
Answer: four textbooks
Step-by-step explanation:
find the area and circumference of a circle with a radius 5 m. use the value 3.14 for radius, and do not round your answers. Be sure to include the correct units in your answers.
Area and circumference of the circle are 78.5 m² and 31.4 m respectively.
What is a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that, a circle have a radius 5 m
Area of a circle = π × radius²
Circumference = 2π×radius
Area = 3.14 × 5² = 3.14 × 25 = 78.5 m²
Circumference = 3,14 × 2 × 5 = 31.4 m
Hence, area and circumference of the circle are 78.5 m² and 31.4 m respectively.
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Lisette wrote the following algebraic expression to represent “4 times as large as the product of w and 11.”
The translation of the sentence "4 times as large as the product of w and 11" to an expression is 44w
How to translate the algebraic sentence to an expressionFrom the question, we have the following parameters that can be used in our computation:
“4 times as large as the product of w and 11.”
The number is represented with w
So, the statement remains unchanged as follows
“4 times as large as the product of w and 11.”
4 times as large means 4 *
So, we have the following representation
4 times as large as the product of w and 11 ⇒ 4 * the product of w and 11.
the product of means that we multiply
4 times as large as the product of w and 11 ⇒ 4 * w * 11
Evaluate the products
This gives
4 times as large as the product of w and 11 ⇒ 44w
Hence, the expression is 44w
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Which of the following equations represent linear functions? select all that apply
Responses
3x+5y=1
y= -9/x2(2 is an exponent)
y=x2(2 is an exponent)-7
y=1/x
will give brainliest for whoever answers correctly and quickly
A trapezoid has interior angle measures of 95°, 97", 85° and X degrees. Find the measure of angle X in the trapezoid. Enter only the number of degrees in the answer
box.
The solution i:
As a result, you are turning the entire trapezium figure 90 degrees clockwise in order to change the trapezoid LMNQ into L′M′NQ′.
The trapezoid is what?In American and Canadian English, a trapezoid is a quadrilateral with at least one set of parallel sides. In British and other versions of English, the word is a trapezium. A trapezoid is always a convex quadrilateral in Euclidean geometry. The parallel sides of the trapezoid are referred to as its bases.
Given: When (-7,-2) to L, L becomes L' (-2,7)
You will often obtain a rotation of 90 degrees clockwise or 270 degrees counterclockwise around the origin (0,0), as well as a reflection across the x-axis and across the line of symmetry of the image, if you have (x,y) and it becomes (y,-x).
The entire graphic is therefore rotated 90 degrees in a clockwise orientation.
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A piece of hematite contains 72% iron. If the hematite weighed 160g, how much iron would there be?
Step-by-step explanation:
160g=100%
72%=72/160*100
=45
In a school containing 360 children, 198 are girls. What percent of all children are girls? What percent of the children are boys? The number of girls is what percent of the number of boys? The number of boys is what percent of the number of girls?
the number of girls is _____% of the number of boys.
Answer:
1st question :55%
2nd ":122.22%
3rd ":81.82%
3. Candy previously sold for $1.60 per pound is now offered for 48 cents in a 6 ounce
package. What is the ratio of former price to present price??
Answer: 5:3
Step-by-step explanation:
note: 16 ounces= one pound
6 ounces = ?
∴6 ounces = pounds
48 cents = pounds
multiplying both sides by
108 cents = 1 pound in the new price
= $1.08 in the new price
ratio of old price to new price =
therefore ratio of old to the new price = 5:3
find the equation of a line parallel to y=-5x+3 that pases through the point -3,-4
Answer:
y = -5x -19
Step-by-step explanation:
You want the equation of the line parallel to y=-5x+3 through point (-3, -4).
Parallel linesThe equations of parallel lines differ only in their constant. We can find the new constant by using the values at the given point:
y = -5x +b
-4 = -5(-3) +b
b = -4 -15 = -19 . . . . . . subtract 15
The equation is ...
y = -5x -19
Ethan has 3pounds of mixed nuts how many ounces of mixed nuts does Ethan have ?
Answer:
48 ounces of Mixed Nuts
Step-by-step explanation:
You need to convert pounds to ounces to find the answer to this problem.
1 pound is 16 ounces, so multiply 3 by 16 for your answer,
In 2-4, write yes or no to indicate whether the expressions are equivalent. Grade 6 math, please help