The summation notation of the sum is:
[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]
The total amount is $84.
How to use summation notation to write the sum?Summation notation, also known as sigma notation, is a mathematical notation used to represent the sum of a sequence of numbers. The notation typically uses the Greek letter sigma (∑) to represent the operation of summation.
Since each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job.
Let n represent the number of weeks
Thus, this can be written using summation notation as:
[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]
Thus, the total amount = 4¹ + 4² + 4³ = $84
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if there is an 84% chance of an event happening in an hour, what is the probability that it happens in half an hour?
The probability of an event happening in half an hour cannot be determined simply by multiplying or dividing the probability of the event happening in an hour by a factor of 2.
Probabilities are not linear in that way. The probability of an event happening in half an hour would depend on the specific details of the event and the underlying probability distribution.
The probability of an event happening in half an hour, given an 84% chance of it happening in an hour, cannot be determined without additional information. The probability of an event occurring in half an hour would depend on the specific circumstances of the event and how the 84% probability was determined.
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if there is an 84% chance of an event happening in an hour, then the probability that it happens in half an hour will be 84% = 0.84.
One cannot easily calculate the likelihood of an event occurring in half an hour by multiplying or dividing the chance of the event occurring in an hour by a factor of 2.
In that sense, probabilities are not linear. The likelihood of an event occurring in half an hour is determined by the event's specifics and the underlying probability distribution.
Without further information, the likelihood of an event occurring in half an hour given an 84% chance of occurring in an hour cannot be computed. The likelihood of an event occurring in half an hour is influenced on the event's unique circumstances and how the 84% probability was calculated.
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What is the value of x? (Enter x first) I'll give you brainless please this is due today.
Answer:
X = 37.8
Step-by-step explanation:
Since they stated angle BAC equals angle DEC, makes me believe these sides are just a factor of each other.
Because of that, we can make a proportion, then cross multiply and divide
Making that proportion, you get;
15. 18
---. =. ----
31.5. x
Cross multiply the (15)(x) = (31.5)(18), also known as
15x = 567
Last thing we do is divide both sides by 15 to get that X alone.
567/15 = 37.8
Concluding that x = 37.8
Eric spent $21.88, including sales tax, on 2 jerseys and 3 pairs of socks. The jerseys cost $6.75 each and the total sales tax was $1.03. Fill in the table with the correct prices.
Answer:
Step-by-step explanation:
Help pls
Who will answer will be briniest thanks
Answer: A = shade the square above and below the third square (3 to the right). B = Make a straight line of 4 and put a square below the first square of the line, and above the second square. (Let me know if you need help.)
Step-by-step explanation:
The coldest temperature recorded in a city in Texas was −22.3°F. The coldest temperature recorded at Vostok Station in Antarctica was 4 times as cold. What equation can be used to represent the coldest temperature recorded at Vostok Station in °F?
The equation to represent the coldest temperature recorded at Vostok Station in °F is 4*(−22.3)°F = 89.2°F.
The solution is obtained by using the arithmetic operations.
What are arithmetic operations?
In mathematics, mainly there are four basic operations upon which all the calculations are done. The operations are:
1. Addition(‘+’) wherein the sum of the numbers is obtained.
2. Subtraction(‘-’) wherein the difference of the numbers is obtained.
3. Multiplication(‘×’) wherein the product of the numbers is obtained.
4. Division(‘÷’) wherein the quotient of the numbers is obtained.
We are given that the coldest temperature recorded in a city in Texas was −22.3°F and the coldest temperature recorded at Vostok Station in Antarctica was 4 times as cold.
This means that the coldest temperature recorded at Vostok Station in Antarctica was
4*(−22.3)°F = 89.2°F
Hence, the equation to represent the coldest temperature recorded at Vostok Station in °F is 4*(−22.3)°F = 89.2°F.
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The helping hands student club set a go to raise $4,000 by the end of the school year for a project after 3 months it reaches 42% of its goal how much was raised during the first 3 months
Answer:
group has raised $1680 in the first three months.
Step-by-step explanation:
The students group has raised $1680 in the first three months.
Due of this, The Helping Hands Student Club decided to fundraise $4,000 by the end of the academic year.
How much is a percentage?
A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."
It accomplishes 42% of its goal after three months.
The money raised over the initial three months is
42% of 4000
= 42/100 × 4000
= 42×40
= $1680
Thus, the students' group has raised $1680 in the first three months.
what is the area of a rectangle with a length of 13.8 feet and width of 28.4 feet
Answer: 391.92ft²
Step-by-step explanation:
Answer: 391.92
Step-by-step explanation:
All you simply do in multiply the two numbers together.
what is 8<4x please giv an answer
Answer:
Step-by-step explanation:
7
Shelby recorded the heights
of three different trees in this table. Use mental
math to find how much taller the redwood tree
is than the sequoia tree.
3
DATA
Tree
Sequoia
Tanbark
Redwood
Tree Heights
Height (ft)
173
75
237
Answer:
Step-by-step explanation:
Oohh yeah
A straight line passes through the points (3, k) and (-3, 2k). If the gradient of the line is -⅔. find the value of k. What is the equation of this line?
Answer:
To find the value of k and the equation of the line, we can use the slope-intercept form of a line: y = mx + b, where m is the slope of the line, and b is the y-intercept.
The slope of the line (m) is given as -⅔. To find the y-intercept (b), we can substitute one of the given points and the value of m into the equation.
Let's use the point (3,k) :
y = mx + b
k = -⅔ * 3 + b
k = -2 + b
b = k + 2
Now we have the equation of the line in the slope-intercept form: y = -⅔x + (k + 2)
To find the value of k we can use the other point (-3, 2k) and substitute into the equation:
2k = -⅔(-3) + (k + 2)
2k = 2 + k + 2
k = -2
So the value of k is -2 and the equation of the line is y = -⅔x + (k + 2) = -⅔x - 2
This line is a straight line with the slope of -⅔ which passes through the points (3, k) and (-3, 2k) and its equation is y = -⅔x - 2
Quadrilateral JkLM is similar to quadrilateral NOPQ find the measure of side PQ round your answer to the nearest tenth
The measure of PQ is approximately 57.8 units.
Now, According to the question:
A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.
Quadrilateral JKLM is similar to quadrilateral NOPQ .
We have the sides are:
JK = 9, LM = 13.7, NO = 38,
and To find the measure of PQ.
Corresponding sides in similar figures are proportional in length:
PQ/LM = NO/JK
PQ/13.7 = 38/9
PQ = 13.7(38/9) = 2603/45 ≈ 57.8
Hence, The measure of PQ is approximately 57.8 units.
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Are these system specifications consistent? "Whenever the system software is being upgraded, users cannot ac-cess the file system. If users can access the file system, then they can save new files. If users cannot save new files, then the system software is not being upgraded. "
No, these given system specifications are not consistent.
They present a logical contradiction, also known as a paradox. The first claim claims that "Users cannot access the file system if the system software is changed," while the second claim claims that "Users can store new files if they can access the file system."
The third assertion, which reads, "If users cannot save new files, then the system software is not being upgraded," is in direct opposition to the first. All three of the aforementioned assertions cannot be true at the same time.
Hence, these given system specifications are not consistent.
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Given the points B(-2, 10) and C(8, 7), find one point D that makes both statements true.
The slope of the line connecting B and D is 2. The slope of the line connecting C and D is - 3.
Answer:
D(3.4, 20.8)
Step-by-step explanation:
Given points B(-2, 10) and C(8,7), you want the coordinates of point D such that BD has a slope of 2 and CD has a slope of -3.
SlopeThe equation for the slope between two points is ...
m = (y2 -y1)/(x2 -x1)
Using this formula and the given points, we can find D(x, y) to satisfy ...
2 = (y -10)/(x +2)
-3 = (y -7)/(x -8)
SolutionPutting each of these equations in general form, we have ...
2(x +2) -(y -10) = 0
2x -y +14 = 0
and
-3(x -8) -(y -7) = 0
3x +y -31 = 0
Adding the two equations eliminates the y-variable:
(2x -y +14) +(3x +y -31) = 0
5x -17 = 0 . . . . . . simplify
x -3.4 = 0 . . . . . . divide by 5
x = 3.4 . . . . . . . . . add 3.4
Substituting for x in the first equation gives ...
2(3.4) -y +14 = 0
y = 6.8 +14 = 20.8 . . . . add y
The point D has coordinates (3.4, 20.8).
__
Additional comment
The graph shows the equations of the lines written in point-slope form.
A red balloon costs $0.80. How much do 9 red balloons cost?
If a red balloon costs $0.80, then 9 red balloons costs would be $7.20.
What is an algebraic manipulation?
Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.
To find out how much 9 red balloons cost, you need to multiply the cost of one red balloon by the number of red balloons.
So 9 red balloons cost $0.80 * 9 = $7.20
Hence, If a red balloon costs $0.80, then 9 red balloon costs would be $7.20.
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A rectangle has a length of 9 centimeters. The width of the rectangle is 4 centimeters. What is the area of the rectangle?
Answer:
36 cm²
Step-by-step explanation:
Area=Length*Width
so... 9*4 = 36
36 cm²
solve for m please .
Answer:
m < -1 5/8
Step-by-step explanation:
attached pic
The pizza parlor had 6 pizzas, each cut into fifths. By noon, 2/3 of all the pieces were sold. How many pieces of pizza were left to sell?
Answer:
10 Slices
Step-by-step explanation:
6x5=30
30 slices in total
We are trying to find 2/3 of 30 slices so we multiply them.
(2x30)/3
=60/3
=20
20 slices were sold out of 30 total slices
This means that 10 slices are left
30-20=10
The sequence a0, a1, a2,. Is defined by letting a0 = 1, and for integers n > 0, an = a b n 2c + a b 2n 3 c + n. (A) Find a1, a2, a3, a4, a5, a6, a7 and a8. (B) Use part (a) to find the least integer a so that an > 4n for all integers n ≥ a. (C) Prove by strong induction that an > 4n for all integers n ≥ a where a is the integer you chose in part (b). (D) Use part (a) to find the least integer b so that an > 45 for all integers n ≥ b. (E) Prove by strong induction that an > 5n for all integers n ≥ b where b is the integer you chose in part (d)
The first 8 terms of the sequence are 12, 16, 22, 30, 40, 52, 66, 82 respectively.
(a) The first 8 terms of the sequence are as follows:
a1 = 1 + (1^2) + (2^3) + 2 = 12
a2 = 1 + (2^2) + (2^3) + 3 = 16
a3 = 1 + (3^2) + (2^3) + 4 = 22
a4 = 1 + (4^2) + (2^3) + 5 = 30
a5 = 1 + (5^2) + (2^3) + 6 = 40
a6 = 1 + (6^2) + (2^3) + 7 = 52
a7 = 1 + (7^2) + (2^3) + 8 = 66
a8 = 1 + (8^2) + (2^3) + 9 = 82
(b) Observing the values of a1, a2, a3, a4, and so on, we can see that an > 4n for all n ≥ 3. Hence, a = 3.
(c) We will prove the statement "an > 4n for all integers n ≥ a" using strong induction.
Base case (n=3): a3 = 28 and 28 > 4 * 3 = 12, which is true.
Inductive step: Suppose an > 4n for all integers n = k (k ≥ 3). We need to show that a(k+1) > 4(k+1).
a(k+1) = 1 + (k+1)^2 + (2^3) + (k+1) = 1 + (k^2 + 2k + 1) + (2^3) + (k+1) = an + 2k + 3 > 4k + 3 = 4(k+1)
(d) Observing the values of a1, a2, a3, a4, and so on, we can see that an > 45 for all n ≥ 7. Hence, b = 7.
(e) We will prove the statement "an > 5n for all integers n ≥ b" using strong induction.
Base case (n=7): a7 = 120 and 120 > 7 * 5 = 35, which is true.
Inductive step: Suppose an > 5n for all integers n = k (k ≥ 7). We need to show that a(k+1) > 5(k+1).
a(k+1) = 1 + (k+1)^2 + (2^3) + (k+1) = 1 + (k^2 + 2k + 1) + (2^3) + (k+1) = an + 2k + 3 > 5k + 3 = 5(k+1)
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please help with this question;)
Answer:
6931.73
Step-by-step explanation:
π =3
cone base diameter = 6 so r=3
it's given height is 11
so use formula given V = π/3*3²*11 =99
sphere r =3
so use formula given V = 4/3*π*3³ = 4*81 = 324
total 99+324 =423 cubic INCHES!!!
1" = 2.54 cm
so you'll have to multiply 2.54³ to covert it to
cubic CMS = 6931.73 cubic CMS
4632 divided by 8 try to find the equation
Answer:
4632/8=579
Step-by-step explanation:
MARK ME BRAINLISIST.
Answer: 579
Hope I'm right
Select all ratios equivalent to 3:1
a)12:24
b)26:28
c)1:2
Answer:
a)12:4
Step-by-step explanation:
We know
The ratio is 3:1; we time 4 and get a ratio is 12:4
So, the answer is A
Question content area left
Part 1
Find the measure of one interior angle in the regular polygon.
Question content area right
Part 1
The measure of each interior angle is
enter your response here
(Type an integer. )
The measure of one interior angle in the regular polygon is 180° degrees.
Polygon:
A polygon is a shape that is made of straight line segments that are connected to each other.
The polygons are named according to their properties and the number of sides they have which have a minimum of three sides.
A polygon cannot have curved sides they are all straight line segments and can measure each side equal to one other.
The formula to find the interior angles of a regular polygon is required.
The required formula is [tex]\frac{(n-2)*180}{n}[/tex]
where n = Number of sides of the polygon.
given to measure one interior angle n=1
Substitute the n value in the above formula, and we get
[tex]A=\frac{(2-1)*180}{1}[/tex]
A=180°
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Rewrite the exponential model as a logarithmic model that calculates the number of years, g(x), for the number of infected tree to reach the value of x
The logarithmic model that calculates the number of years, g(x), for the number of infected tree to reach the value of x is-
[tex]g(x)[/tex] = ㏑[tex](x) / 0.4[/tex]
For the number of infected trees f(x) after x years, we are given an exponential function.We find the inverse function by using the natural logarithm to calculate the number of years required for the number of infected trees to reach x.The equation can be written as-
[tex]y = f(x) = e x^{0.4x}[/tex]
The natural logarithm is now applied to both sides of the equality after we have isolated y.
[tex]0.4y = ln x[/tex][tex]y = ln x / 0.4[/tex]
This is how the exponential model as a logarithmic model that calculates the number of years, g(x) can be explained as.
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Math
Multiplying and Dividing by Powers of Ten - Item 2671
Warm Up
Move the decimal 3 places to the right.
Which is the same as dividing a number by 1,000?
Move the decimal 1 place to the right.
Guided
Learning
Practice Post-Quiz
Finish
Move the decimal 3 places to the left.
Move the decimal 1 place to the left.
CLEAR
K
Question 2 of
CHECK
A mathematical operation which is the same as dividing a number by 1,000 include the following: C. move the decimal 3 places to the left.
What is a quotient?In Mathematics, a quotient can be defined as a mathematical expression that is typically used for the representation of the division of a number by another number.
This ultimately implies that, a quotient in terms of numerical data simply refers to a division of a number (numerator) by another number (denominator).
In terms of determining the decimal place after a division of a number by 1000, we have the following:
Number = 1/1000
Number = 0.001 (3 places to the left.)
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Janine bikes 4 mph faster than her sister, Jessica. Janine can ride 24 mi in 3 hr less time than Jessica can ride the
same distance. Find each of their speeds.
Part 1 of 2
Jessica's speed is
Part 2 of 2
Janine's speed is
Jessica's speed is 4 mph and Janine's speed is 8 mph
Let us assume that x represents Jessica's speed.
Janine bikes 4 mph faster than her sister, Jessica.
So, Janine's speed would be (x + 4) mph
We know that the formula for the speed is: speed = distance/time
Here, Janine can ride 24 mi in 3 hr less time than Jessica can ride the same distance.
24/(x+4) = (24/x) - 3
24/(x+4) = (24 - 3x)/x
24x = (24 - 3x)(x + 4)
24x = 24x + 96 - 3x² - 12x
3x² + 12x - 96= 0
After solving above quadratic equation we get.
(x - 4) (x + 8) = 0
x = -8 speed is not possible.
So, x = 4 mph
And x + 4 = 8 mph
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(7x^3-13x^2-23x-5)/(x-3) Synthetic Division
The quotient of the expression is 7x² + 8x + 1
How to determine the quotient of the expression?From the question, we have the following expression that can be used in solving the quotient
(7x^3-13x^2-23x-5)/(x-3)
Express properly
So, we have
(7x³ - 13x² - 23x - 5)/(x-3)
Set the divisor to 0
x - 3 = 0
So, we have
x = 3
Using a synthetic setup, we have
3 | 7 - 13 - 23 - 5
The synthetic division is then carried out as follows
3 | 7 - 13 - 23 - 5
21 24 3
7 8 1 -2
So, we have
Quotient = 7 8 1
Remainder = 2
Introduce the variable
Quotient = 7x² + 8x + 1
Remainder = 2
Hence, the result is 7x² + 8x + 1 remainder 2
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HURRY PLEASE A fifth-degree polynomial function has a zero at z = -3 with a multiplicity of 2. It also has a zero at z = 2 with a multiplicity of 3. The value of the
function is negative when z = -4
Which graph could model this polynomial function?
The graph of the polynomial function is given by the following option:
Not C or D.
How to obtain the graph of the polynomial function?At z = -3, the function has a zero with an even multiplicity of 2, meaning that the graph of the function turns at z = -3, due to the even multiplicity.
At z = 2, the function has a zero with an odd multiplicity of 3, meaning that the graph of the function crosses the x-axis at z = 2, due to the odd multiplicity.
At z= -4, the function is negative, hence it becomes positive at z = 2 and goes towards infinity.
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Write an inequality involving absolute value for the graph. Find the point that is the same distance from 2 as it is from 4.
The inequality involving absolute value is 2 < x < 4 and the graph is attached below.
The term called inequality in math is defined as when two real numbers or two algebraic expressions are represented with symbols like <, > or ≤, ≥.
Here we need to find the inequality involving absolute value for the graph. And here we also need to find the point that is the same distance from 2 as it is from 4.
Here we have consider that x be the number that the inequality is formed than it can be written as
=> 2 < x < 4
And the graph of the inequality is plotted and attached below.
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Samantha stores all of her important paperwork in the file cabinet shown below.
A locker measurement at the bottom as 2 one by 6 ft 2, side as 1 and a half ft, and length as 2 2 by 3 ft.
*Picture not drawn to scale
What is the volume of the file cabinet?
The volume of the cabinet where Samantha stores all her important documents would be given as = 7.2 ft
What is a cabinet?A cabinet is defined as an equipment usually located in offices or laboratory which is used for the storage of documents that are of high importance to an organisation.
The shape of the cabinet is the shape of a cube and the volume of a cube is the product of all the sides given
That is = 2⅙ × 1¼ × 2⅔ ( change to single fraction)
= 13/6 × 5/4 × 8/3
= 520/72
= 7.2 ft
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HELP ASAP!!!
Which relation is not a function?
The correct option is C. ((6, 5), (3,2), (2, 4), (6, 3), (1, 0))
Reason: This relation has two y-values of 6 which violates the vertical line test and therefore is not a function.
What is relation of function?A relation of a function is a set of ordered pairs that satisfy the function's equation. A function is a special type of relation, one in which each input has exactly one output. For example, the function y = x + 2 defines a relation of pairs such as (1,3), (2,4), and (3,5). The relation of a function is also known as its graph. The graph of a function is a visual representation of the relationship between the input and output values. It is a common way to visualize functions and can help to identify patterns and trends. The set of all possible input and output values, as determined by the equation, is called the relation of the function.The relation of a function is useful in understanding the behavior of the function. For example, from the graph of a function, one can determine the domain and range of the function, as well as any maximum or minimum points. Furthermore, the graph of a function can help to identify any symmetries or properties of the function.To learn more about relation of function refer to:
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