Answer: 7£
Step-by-step explanation:
1. Firstly, we need to subtract the single sign up fee from the total cost. This would be 141-57 =84 pounds
2. We know that you pay a regular amount every month, so therefore we can divide 84 by 12 as there are 12 months in a year.
3. 84/12 = 7. Thus, the answer is 7 pounds a month.
Answer:
£7
Step-by-step explanation:
Given information:
£141 = Total cost of one-year gym membership.£57 = sign-up fee (included in the annual fee).To find the cost of the monthly payments, find the difference between the total cost and the sign-up fee, then divide the result by 12 (as there are 12 months in one year).
The difference between the total cost and the sign-up fee is:
[tex]\implies 141-57=84[/tex]
Therefore, the cost of each monthly payment is:
[tex]\implies \textsf{Monthly fee}=\dfrac{84}{12}=7[/tex]
multiply the maclaurin series for e z and 1 1 z to obtain the series expansion for e z 1 z up to z 5 . on what disk does it converge?
The series expansion for e z 1 z up to z 5 is obtained by multiplying the Maclaurin series for e z and 1 1 z. For |z| 1, this series converges.
The Maclaurin series for e^z is:
e^z = 1 + z + z^2/2! + z^3/3! + z^4/4! + ...
The Maclaurin series for 1/1-z is:
1/(1-z) = 1 + z + z^2 + z^3 + z^4 + ...
Multiplying these two series together gives:
e^z/(1-z) = (1 + z + z^2/2! + z^3/3! + z^4/4! + ...)(1 + z + z^2 + z^3 + z^4 + ...)
= 1 + (1+z) + (z + z^2/2! + z^2) + (z^2/2! + z^3 + z^3/3!) + (z^3/3! + z^4 + z^4/4!) + ...
= 1 + z + 2z^2 + 3z^3 + 5z^4 + ...
This series converges for |z| < 1
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The function shown models the depth d (in inches) of snow on the ground during the first 9 hours of a snowstorm, where t is the time (in hours) after the snowstorm begins
d(t)=1/2t+6
What is the domain
What is the range
The domain of the function d(t)=1/2t+6 is (-∞, ∞) and the range of the function is (-∞, ∞).
What are Domain and Range?Similar to how we input different numbers into functions, we also receive new numbers as the outcome. The two main characteristics of functions are domain and range.
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A → B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range.
The domain of the function d(t)=1/2t+6 is given by
Domain: (-∞, ∞), {x|x ∈ R}
The range of the function is given by
Domain: (-∞, ∞) , {y|y ∈ R}
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Please help I’ll give 30 pts
The area of the figure created by Brianna is [tex]33\frac{3}{4}[/tex] square feet.
Explain area in mathematics.
Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area or, it can be simply defined as the total amount of space occupied by a flat (2-D) surface or an object's shape.
Solution Explained:
A square with a side of 4 1/2 feet and two parallelograms with bases of 4 1/2 feet and heights of 1 1/2 feet make up the figure.
Therefore, the total area of the figure is
Area of Square + 2 X Area of Parallelogram
= (side)^2 + 2(b X h)
= (4 1/2)^2 + 2(4 1/2 X 1 1/2)
= 81/4 + 27/2
= 135/4
= [tex]33\frac{3}{4}[/tex] square feet
Area of the figure is [tex]33\frac{3}{4}[/tex] square feet.
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A positive integer M divided by six gives a remainder of three. Another positive integer N divided by six gives a remainder of five. What is the remainder when the sum M+N is divided by six?
When the sum M+N is divided by 6 , the remainder is 8
What is Remainder?The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). We always have remainder when the denominator is a factor of numerator.
For example 5/2, diving 5 with 2, 2 is not a factor of 5,
There are 2 2s in 5 with remainder 1.
M/6= x y/6
where is the factor and y is the remainder
therefore m/6= (6x+y)/6
y= 3,. m/6= (6x+3)/6
N/6= (6x+5)/6
therefore dividing both sides by 6
m= 6x+3
n= 6x+5
adding m and n
m+n= 12x+8
dividing m+n by 6
(m+n)/6 = (12x+8)/6
relating (12x+8)/6 with (6x+y)/6
y = 8
Therefore the remainder is 8
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7 The nth term of a sequence is u, = 10 x 3" Write down the first four terms in the sequence.
The first four terms in the sequence are 30, 90, 270 and 810 respectively.
How to determine the termsWe have that the nth term of the sequence is expressed as;
U = 10 × 3 ^n
Where;
n = number of terms
To determine the first terms, let's substitute the value of n as 1, we get;
U = 10 × 3^1
Multiply the values
U₁ = 30
The second terms, n = 2
U₂ = 10 × 3²
U₂ = 10 × 9
Multiply through
U₂ = 90
The third year, n = 3
U₃ = 10 × 3³
Find the cube of the value and multiply the values
U₃ = 270
The fourth year, n = 4
U₄ = 10 × 3^4
U₄ = 10 × 81
Multiply through
U₄ = 810
Thus, the numbers are 30, 90, 270, 810
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find the dimensions of a rectangular box with a square base which has a volume of 12 cubic feet and the smallest possible surface area.
The dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3
Rectangular Box with Square base
Volume v = a²b = 12
S = Surface area = 2a² + 4ab
v = a²b = 12
b = 12/a²
S = 2a² + 4ab = 2a² + 4a(12/a²) =2a² + 48/a
S'(a) = 4a -48/a² = 0
4a³ = 48
a = 12^ 1/3
b = 12/a² = 12/12^ 2/3 = 12^ 1/3
Therefore, the dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3
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help me on this math please!
The function rule for each are:
f(x) = -2x - 6
g(x) = 5x - 4
f(x) is less than g(x), in terms of slope, while in terms of y-intercept, f(x) is greater than g(x).
How to Write the Rule of a Function?The rule of a function can be written in slope intercept form as, f(x) = mx + b, where the slope is m and the y-intercept is the value of b.
To write the function rule for f(x), substitute m = -2 and b = -6 into f(x) = mx + b:
f(x) = -2x - 6
Find the slope of the function g(x) whose graph is given:
Slope of g(x) = rise/run = 5/1 = 5
m = 5
The y-intercept is at y = -4, therefore b = -4.
To write the function rule for g(x), substitute m = 5 and b = -4 into g(x) = mx + b:
g(x) = 5x - 4
In terms of slope, f(x) is less than g(x)
In terms of y-intercept, f(x) is greater than g(x).
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please help ASAP
A toy cannon ball is launched from a cannon on top of a platform.
The function h(t) =-5+ 2 + 20+ + 4 gives the height, in meters, of the ball t seconds after it is launched.
Write and solve an inequality to find the times where the ball is more than 12 meters above the ground.
Round to the nearest hundredth.
Answer:
hello\\
Step-by-step explanation:
if f(x) = 2x - 4 find f(3x)
Answer: the answer would be 2
Step-by-step explanation: f(x) means that for every x you are going to multiply it by the value it gives you in this case it is 3.
2x3=6-4=2
Given the following list of axioms, draw a model to properly represent the information.
a. there exists five points
b. there exists two lines
c. each line consists of at least two points
d. each line contains only these five points.
The model which properly represent the information in given axioms is Cross geometry (+).
In the given question we have following information,
total number of points in model is 5total number of lines in model is 2each line consists atleast 2 pointseach line contains only these five pointsby using the above axioms we draw a geometry of Cross sign Geometry as seen above .
We can draw a line which contains three points and these points are only from given five points another line also follow this . this geometry follows all given axioms . The two lines intersect each other at a point . The point of intersection is one of point from five points . both of lines are linear and consists three points .
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8x - 4y = 16
8x+4y= 16
Answer:
X = 2, Y = 0
Step-by-step explanation:
Add the two equations together to cancel out -4y and +4y
leaving you with:
8x = 16
8x = 16
divide both sides of the equation by 8 to get x on its own (8x/8 = x, 16/8 =2)
leaving you with:
x = 2
substitute the value of x back into the equation to calculate y (it can be either equation, top or bottom):
8(2) - 4 y = 16
8 x 2 = 16
leaving you with:
16 - 4y = 16
subtract 16 from both sides to get 4y on its own
leaving you with:
-4y = 0
so y = 0, and x = 2
the ages of five randomly chose cars in the parking lot are determined to be 7, 9, 3,4, and 6 years old. if we consider these 5 cars in groups of 3, how many groups can be formed?
The number of groups formed is 10 if we consider 5 cars in groups of 3.
Given, 5 cars in groups of 3, we can use the formula,
(5 3) = 5! / 3! × 2!
= 10
Permutation and combination are the various ways in which one can form a set that may be selected without any replacement. When the selection of a subset is where we use the permutation and when the ordering of the subset is there we use a combination.
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Write equivalent fractions for 8/9 and 5/8 using the least common denominator.
Type the fractions, using a slash ( / ) to separate the numerator and denominator.
8/9 =
5/8 =
The equivalent fractions for 8/9 and 5/8 using the least common denominator are 8/9 = 64/72 and 5/8 = 45/72.
What is the Least Common Denominator?
The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator (LCD). The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.
The given fractions are 8/9 and 5/8.
The denominators of these fractions are 8 and 9.
so Least Common Divisor(LCD) of 8 and 9 will be = 8 × 9
= 72.
so the equivalent fraction can be calculated as
for 8/9 = [tex]\frac{8*8}{9*8}[/tex]
= 64/72
and for 5/8 = [tex]\frac{5*9}{8*9}[/tex]
= 45/72
Hence, the equivalent fractions are 64/72 and 45/72.
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Find the number of square tiles of sides 6 cm needed to fit in a rectangular region whose length andbreadth are: a) 9 m and 12 m b) 8 m and 9 m
Number of square tiles that are needed to fit the rectangular region are
(a) 30000 tiles and (b) 20000 tiles .
In the question ,
it is given that
the side of the square tile is = 6 cm
so ,the area of the square tile = 6*6= 36 cm²
Part(a)
the length of the rectangular region = 9m = 900 cm
the breadth of the rectangular region = 12m = 1200 cm
So, the area of the rectangular region = 900 * 1200 = 1080000 cm²
the number of tiles required = (area of rectangular region)/(area of tile )
= 1080000/36
= 30000
hence , 30000 tiles are needed.
Part(b)
the length of the rectangular region = 8m = 800 cm
the breadth of the rectangular region = 9m = 900 cm
So, the area of the rectangular region = 800 * 900 = 720000 cm²
the number of tiles required = 720000/36
= 20000
hence , 20000 tiles are needed .
Therefore ,Number of square tiles that are needed to fit the rectangular region are
(a) 30000 tiles and (b) 20000 tiles .
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each face of a cube is given a single narrow stripe painted from the center of one edge to the center of the opposite edge. the choice of the edge pairing is made at random and independently for each face. what is the probability that there is a continuous stripe encircling the cube?
The probability that there is a continuous stripe encircling the cube is 3/16.
A single, thin stripe is painted from the center of one edge to the center of the other edge on each face of a cube. Each face's edge pairing is selected independently and at random.
For each of the cube's six faces, there are two possible stripe orientations, resulting in a total of 2 x 6 = 64 possible stripe permutations. Since there are three sets of parallel faces, the stripe orientation for the remaining faces is determined uniquely by the pair of faces that does not contribute to the encircling stripe. Additionally, there are two possible orientations for the stripe on each face that is non-contributing.
A continuous stripe surrounds the cube as a consequence of a total of
3 * 2 * 2 = 12 stripe variations.
The necessary probability is 12/64, which equals 3/16.
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Please help, I'm struggling.
I think you would just add 8 + 5, because if NO is the same length as MN, then the length from MN is 5 and NP makes up the rest of the line.
Answer: MP = 13
Complete the statement to describe the expression (a+b+c)(d+e+f)(a+b+c)(d+e+f). The expression consists of 3 factors, and each factor contains terms
The statement about the given expression is described below.
What is expression?A math expression consist numbers, variables and operators its operation addition, subtraction, multiplication, and division. The parts of the expression that are connected with addition and subtraction are considered as terms.
According to given data:Expression, (a+b+c)(d+e+f)(a+b+c)(d+e+f) = (a +b+c)^2(d+e+f)^2
It has factors two which consist of 3 termsEach factor has a multiplicity of 2terms in factor (a+b+c) are a, b, cTerms in factor (d+e+f) are d, e, fThus, given expression has two factors which consist 3 terms.
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Norman wants to figure out how tall a light pole is. he uses his sextant to measure the angle of elevation to be 36 degree and he holding the sextant at his eye level, 5 feet from the ground.if he is 10 feet away from the light pole how tall is the light pole?
Norman will measure the light pole to be 12 feet tall
How to determine the height of the light poleInformation from the question
Norman uses his sextant to measure the angle of elevation to be 36
5 feet from the ground. if he is 10 feet away from the light pole
how tall is the light pole = ?
The height of the light pole is calculated using SOH CAH TOA
The direction of movements describes a right angle triangle of
opposite = height of the light pole
adjacent = 10 feet away from the light pole
The height is is calculated using tan, TOA let the angle be x = 36
tan x = Opposite / Adjacent
tan 36 = opposite / 10
opposite = tans 35 * 10
opposite = 7 feet
this is height 5 feet from the ground, so total height is calculated to be
5 + 7 = 12 feet
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a survey of 398 children given at a local elementary school showed that 175 like chocolate ice cream 150 like pistachio ice cream, and 123 do not like chocolate or pistachio ice cream. how many children like at least one kind of ice cream mentioned in the survey? a) 225 b) 100 c) 325 d) 275 e) 125 f) none of the above.
The number of student like at least one kind of ice cream is given by (d) 275.
Let C be the student who like chocolate ice cream and P be the student who like Pistachio ice cream.
Now given that, n(C) = 145, n(P) = 150
Also given that, 123 students do not like neither chocolate or pistachio ice cream.
So, n(P' and C') = 123
The required number of student like at least one kind of ice cream is given by,
N = 398 - n(P' and C') = 398-123 = 275
Hence the correct option is (d).
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A men’s basketball coach would like to know if there is a relationship between how tall a player is and how high he can jump. Here is a scatterplot of the data.
A graph has height (inches) on the x-axis and vertical jump distance (inches) on the y-axis. The points form a line with positive slope.
Describe the scatterplot.
The relationship between height and vertical jump distance is
,
, and
.
There are
unusual observations.
The relationship between height and vertical jump is High positive correlation.
What is a correlation?
A statistical indicator of the relationship between the relative motions of two variables is the correlation. If the variables are correlated, a line or curve will be formed by the points. The points will touch the line more closely the better the correlation.
Main body:
To find the relation we need to draw a line passing closely to all the points , if we are able to draw such line , it has high positive correlation.
If the line doesn't pass through all points it has low positive correlation.
hence this has high positive correlation .
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Answer:
-positive
-linear
-strong
-no.
Step-by-step explanation:
edge 2023
Expand and simplify (2x + 5)2
Answer: 4x+10
simplified: 2x+5
Step-by-step explanation:
Answer: 4x+10
You multiply 2 by (2x) = 4x
You multiply 2 by (5) = 10
help meeeeeeeeeeeeeee pleaseee
The table of solutions for this quadratic equation (y = -2x²) include the following:
x y_
-2 -8
-1 -2
0 -0
1 -2
2 -8
A graph of the solution of the given quadratic equation has been plotted in the image attached below.
How to determine the solutions?In Mathematics, the graph of any quadratic equation or function always forms a parabola, which simply means a u-shaped curve. In order to determine the correct solutions to the given quadratic equation, we would have to substitute the x-values contained in the table into the quadratic equation.
At point x = -2, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(-2)²
y = -2 × 4
y = -8
At point x = -1, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(-1)²
y = -2 × 1
y = -2
At point x = 0, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(0)²
y = -2 × 0
y = 0
At point x = 1, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(1)²
y = -2 × 1
y = -2
At point x = 2, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(2)²
y = -2 × 4
y = -8
In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.
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Elliot makes and sells key chains. His profit depends on what price he charges for a
key chain.
He writes the expression (x - 10) (60 - 3x) to represent his profit based on the
price per key chain, x.
Enter Elliot's average change in profit for two different sections of the graph.
When charging $15 for a key chain, it is discovered that his maximum profit is $75 using the vertex of the quadratic function.
The vertex of a quadratic equation,
A quadratic equation is given by, [tex]ax^{2} +bx +c[/tex]
The vertex is given by [tex]A (x_{1} ,y_{1} )[/tex]
[tex]x_{1} = \frac{-b}{2a}\\ \\y_{1} = \frac{-b^{2} +4ac }{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.
If a > 0, it will be a minimum point.
The function given is (x -10 ) (60 -3x)
f(x) = (x -10 ) (60 -3x) = 60x -3[tex]x^{2}[/tex] -600 +30x = -3[tex]x^{2}[/tex] +90x -600
So, here a = -3, b = 90 and c = -600
So,
[tex]x_{1} = \frac{-b}{2a}\\ \\x_{1} = \frac{-90}{2*(-3)} = 15[/tex]
[tex]y_{1} = \frac{-b^{2} +4ac }{4a} = \frac{(-90)^{2} + 4*(-3)*(-600) }{4*(-3)} = 75[/tex]
Hence, He can make up to $75 in profit when he charges $15 for a key chain.
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you have 100 feet of fence to make a rectangular play area alongside the wall of your house. the wall of the house bounds one side. what is the largest possible area (in square feet)?
The length and width of the rectangle are 50 feet and 25 feet respectively, the product of which gives the area of the rectangle which is 1250 feet.
Given, 100 feet of fence to make a rectangular play area that is side by side with the wall of your house.
The perimeter of the rectangle is = 2x+2y, since the wall bounds from one side as given in the question perimeter changes to = x+2y.
Perimeter = x+2y
100 = x+2y
100 = 50+2y
2y = 50
y = 25
Using this we found the length and width of the rectangle which is equal to 50 feet and 25 feet respectively. The area which is the final answer comes out to be 1250 feet.
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in a class of 20 students, there are two students a and b. what will be the probability of selecting these two students randomly?
The probability of selecting two students (a and b) randomly is found as 1/380.
What is referred as the word probability?The study of random experiments is what aids in determining the likelihood of an event.The study of probabilities, which are determined by the ratio of favorable cases to possible cases, is known as probability.The formula for evaluating the Probability is-
Probability = Favourable outcomes / Total outcomes.
As, per the given question.
Total number of students = 20.
The probability for selection of 'a' is 1/20.
Now, the total students left is 19.
Thus, the probability for selection of 'b' is 1/19.
The total probability for selection of both is -
Probability(a and b) = 1/20×1/19
Probability(a and b) = 1/380
Thus, the probability of selecting two students ( a and b) randomly is found as 1/380.
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How much of a radioactive kind of bismuth will be left after 8 minutes if the half-life is 2
minutes and you start with 79,360 grams?
grams
an analog signal received at a detector (measured in micro volts) may be modeled as a gaussian random variable n (200, 256) at a fixed point in time. what is the probability that the signal will exceed 240 micro volts? what is the probability that the signal is larger than 240 micro volts, given that it is larger than 210 micro volts?
Given that the signal gets larger than 210 microvolts, there is a 2.335 % chance that it is also larger than 240 microvolts.
Define the term Gaussian random variable?We consider the Gaussian form whenever we need to describe complex valued random variables for whom the distribution is unknown. The Central Limit Theorem (CLT), which deals with the sum of several random variables, is substantially fundamental for this tendency.As, per the given question.
Gaussian random variable n (200, 256)
Part a: Probability that signal will exceed 240 micro volts.
P(x > 240) = 1 - P(x ≤ 240)
P(x > 240) = 1 - P(240 - 200)/16
P(x > 240) = 1 - P(2.5)
See p value for z = 2.5
P(x > 240) = 0.00621
Thus, Probability that signal will exceed 240 micro volts is 0.00621.
Part b: larger than 210 micro volts.
P(x ≥ 240) | x ≥ 210) = P(x ≥ 240) / P(x ≥ 210)
P(x ≥ 240) | x ≥ 210) = 1 - P(240 - 200)/16 / 1 - P(210 - 200)/16
P(x ≥ 240) | x ≥ 210) = 0.00621 / 0.26599
P(x ≥ 240) | x ≥ 210) = 0.02335
Thus, for the signal gets larger than 210 microvolts, there is a 0.02335 percent chance that it is also larger than 240 microvolts.
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HELP PLEASE QUICKLY THANKS
Graph will shift in both horizontal and vertical direction by 4 units.
What is straight line?
An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal.
What is general equation of a Straight Line?
The general equation of a straight line can be given as ax + by + c = 0, where
a, b, c are constants, andx, y are variables.The slope is -a/bWhat do you mean by function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain. The usual way to refer to a function is as fn(x), where x is the input.
We have function,
fn(x) = x + 5
when the graph is translated by 4 units, we can write it as;
g(x) = fn(x) + 4
the graph will shift in both horizontal and vertical direction by 4 units as it can be seen in the graph.
Therefore, graph will shift in both horizontal and vertical direction by 4 units.
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raina swam 8 kilometers against the current in the same amount of time it took her to swim kilometers with the current. the rate of the current was kilometer per hour. how fast would raina swim if there were no current?
The speed at which raina can swim if there is no current is 3 km/hor 3 kilometers per hour.
Given that,
In the same length of time it took raina to swim kilometers with the river, she was able to swim 8 kilometers against it. The current flowed at a kilometer per hour rate.
Distance 1 * (Raina's velocity - current velocity) = Distance2 * (Raina's velocity + current velocity)
16 * (Raina's velocity - 1) = 8 * (Ivan's velocity + 1)
(16 * Raina's velocity) - 16 = (8 * Ivan's velocity) +8
8 * Raina's velocity = 24
Raina's velocity = 3 kilometers per hour
As a result, Raina can swim at a speed of 3 km/hr in the absence of a current.
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I need help asap please now please !!!!!!!!!!!