Using mathematical operations, Betsie should buy the 250 envelopes from Letters2go Shop at a total cost of £319.
How is the total cost determined?To determine the total cost, we first determine the unit cost of an envelope at each shop.
The unit cost is multiplied by the number of envelopes required less the cost of free envelopes at Value World.
The mathematical operations used include division and multiplication.
Deals:
Letters2go
Pack of 25 envelopes for £3.19
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go Value World
Cost per pack £3.19 £1.99
Cost per envelope £0.1276 £0.199
The number of envelopes 250 250
The number of packs 10 (250/25) 25 (250/10)
Cost of free envelopes £24.875 (25/2 x £1.99)
Total cost of envelopes £319 (£3.19 x 10) £472.63 (£1.99 x 250 - $24.875)
Thus, using mathematical operations, the total cost of 250 envelopes at Letter2go is less than the total cost at Value World.
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Which inequality represents the phrase "nine less than two
times a number is no more than 45?"
The expression of the inequality is [tex]9 < 2x\le45[/tex]. It can be obtained using the operations of inequality.
What is inequality?
In matmathematics if two numbers are not equal even then there is a relationship. This relationship can be defined by inequality relationship.
According to the pharase, 9 is less than two times a number. Hence, consider the number is x and its two times means 2x. Now, 9 should be less than this number. Hence, 9<2x. Now, again the number 2x is not more than 45. Means, it can be equal to 45. Hence, it will give the expression [tex]2x\le45[/tex].
Now, combine the two expressions as follows:
9<2x
[tex]2x\le45[/tex]
[tex]9 < 2x\le45[/tex]
Hence, the expression of the inequality is [tex]9 < 2x\le45[/tex].
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Quadrilateral TEAM is rotated-180° about the origin.
Draw the image of this rotation.
The area of the quadrilateral is determined as follows if the diagonal and the length of the perpendiculars from the vertices are known: The formula for calculating the area of a quadrilateral is (12) diagonal length the sum of the lengths of the perpendiculars drawn from the other two vertices.
Explain about the Quadrilateral?A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words Quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. A quadrilateral is shown in the above image as an example. quadrilateral pieces.
Quadrilaterals with four congruent sides, four right angles, and two sets of parallel sides are called squares. Quadrilaterals having two sets of parallel sides are known as parallelograms. All squares are parallelograms because squares must have quadrilaterals with two sets of parallel sides.
Four sides and four angles make up a quadrilateral. Any convex polygon's exterior angles (i.e., no interior angle is less than 180 degrees) sum up to 360 degrees ( 4 right angles).
In the quadrilateral, each point's coordinates change as follows:
(x, y) → (-x, -y)
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In 2001 there were 6680 electric-powered vehicles in use in the United States. In 1998 only 4760 electric vehicles were being used. (Source: U. S. Energy Information Administration)
a. Assume that the relationship between time, x, and number of electric-powered vehicles, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (years past 1998 comma number of vehicles).
An equation of slope-intercept form describing this relationship. Use ordered pairs of the form the equation, y = 640x + 4760
Since there were 4760 electric vehicles in 1998, when x=0 (indicating 0 years have passed since 1998), y=4760. There were 1,920 more electric vehicles on the road after three years. 1920 / 3 = 640 is the average rate of change every year. Between 1998 and 2001, there were 640 more automobiles every year.Our slope measures m=640. By dividing the change in y by 4760, or 1920, we can determine the slope.The y-intercept is just the starting point, or x=0. At this point, x=0. The y-intercept is shown here: (0, 4760). Equation of slope intercept: y = 640x + 4760 where b=4760.
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you cannot remember your 5-digit bike-lock combination. what is the probability that you guess the combination correctly? (enter your probability as a fraction.)
The probability that you guess the combination correctly 0.00001.
We know that the probability of an event is (possible outcome/total outcome)
I will assume that repeats are allowed as in most combination locks so the number of possible codes
= 10⁵ = 100000
We also know that there is only one correct combination so the probability that you guess the combination correctly
= 1/10⁵ = 1/100000 = 0.00001
Orchestrating individuals, digits, numbers, letters in order, letters, and tones are instances of changes. Choice of menu, food, garments, subjects, and group are instances of combination.
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Triangle ABC has vertices A(0, -1), B(6, 5), and C(-4, 3). Which statement about triangle ABC is true?
The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.
What is a right triangle?A right triangle is a triangle that has an interior angle of 90°, and therefore, it has two sides known as the legs that are perpendicular.
The lengths of the sides of the triangle ΔABC can be found using the Pythagorean formula for finding the distance, d, between two points, (x₁, y₁) and (x₂, y₂) on the coordinate plane as follows;
d² = (x₂ - x₁)² + (y₂ - y₁)²
The vertices of the triangle ΔABC are; A(0, -1), B(6, 5), and C(-4, 3), which gives;
[tex]\overline{AB}^2[/tex] = (6 - 0)²+ (5 - (-1))² = 72, AB = 6·√2
[tex]\overline{AC}^2[/tex] = (-4 - 0)² + (3 - (-1))² = 32, AC = 4·√2
[tex]\overline{BC}^2[/tex] = (-4 - 6)² + (3 - 5)² = 104, BC = 2·√(26)
72 + 32 = 104
Therefore; [tex]\overline{AB}^2[/tex] + [tex]\overline{AC}^2[/tex] = [tex]\overline{BC}^2[/tex]
ΔABC is a right triangle
The slopes of the equation of the lines of the sides of the triangle are;
Slope of side AB = (5 - (-1))/(6 - 0) = 1
Slope of side BC = (3 - 5)/(-4 - 6) = 0.2
Slope of side AC = (3 - (-1))/(-4 - 0) = -1
Therefore;
[tex]\overline{AB}[/tex] ⊥ [tex]\overline{AC}[/tex]
Which gives;
A true statement about triangle ΔABC is that ΔABC is a right triangle a nd the lengths of the sides of the triangle are differentLearn more about the Pythagorean theorem in mathematics here:
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a large animal preserve has noticed that an albino panther is born unpredictably once every 8 years; and that can happen at any time of the year. a) what are the expected value and standard deviation of the number of albino panthers which will be born in the next 40 years?
The expected value of the number of albino panthers is 5
The standard deviation of the number of albino panthers is 2.09
Given that albino panther is born once every 8 years, probability p, of one albino to be born in 8 years is 1/8
Expected value=n*p, where n is 40 years, and p=1/8
=40*1/8
=5 albino panthers
Hence, the expected value is 5 albino panthers
Standard deviation=(Expected value*(1-p))^1/2
=(5*(1-1/8))^1/2
=4.375^1/2
=2.09
Hence, standard deviation is 2.09
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If f(x) = 10 - 200 and g(x) = 25x2 + 90, the value of f (4) - g (2) is:
As function f(x) is not completely right i assume it to be like f(x)= 10x-200.
Acc. to which the answer is -350.
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X.
Main Body:
f(x)= 10x-200
f(4)= 10*4-200
= 40-200
=-160
g(x)= 25[tex]x^{2}[/tex]+90
g(2)= 25*(2)² +90
= 25*4+90
=190
So, f(4)-g(2) = -160-190
= -350
Therefore the answer is -350.
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The school art club at a large high school is in charge of designing school T-shirts and getting them printed this year. A local business charges $35 to set up their T-shirt printing machine with the design and $4.25 in materials per T-shirt to print.
1). Create an equation to represent the average cost C(x), in dollars, per T-shirt if x T-shirts are printed by this business.
2). what is the average cost per shirt to print 25 shirts? 100 shirts?
3). what is the cheapest the average cost per T-shirt will get? Explain or show your reasoning.
Total cost includes initial charge for printer set up and material cost.
C(x) = 4.25x + 35 represents the total cost, where C(x) is the cost of x T- shirts.Part 1Average cost per T-shirt is
C(x)/ x = (4.25x + 35)/x = 4.25 + 35/xPart 2Average cost to print 25 T-shirts
4.25 + 35/25 = $5.65Average cost to print 100 T-shirts
4.25 + 35/100 = $4.60Part 3The average cost 4.25 + 35/x depends on the number of T-shirts printed.
The larger the x, the smaller is 35/x. It will be closer to but greater than $4.25.
will give u brainliest!
Answer:
3.46
Step-by-step explanation:
[tex]\sqrt{21-9}[/tex]
[tex]\sqrt{12}[/tex]
3.46
Hopes this helps please mark brainliest
Question
Graph x=−6.
A graph of the given mathematical expression (x = -6) is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
In this scenario, a number line would be used to graph the given mathematical expression because it only contains one (1) variable.
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solve for x and y
picture provided
The value of x will be 15 and the value of y will be 4.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
Here in the image, we have a triangle having sub-triangles. The value of x is calculated by considering two right-hand triangles.
x / ( x + 5 ) = 18 / ( 18 + 6 )
x / ( x + 5 ) = 18 / 24
24x = 18x + 90
6x = 90
x = 15
The value of y will be calculated by considering the two left-hand triangles.
12 / ( 12 + y) = 15 / 20
240 = 180 + 15y
15y = 60
y = 60 / 15
y = 4
Therefore, the value of x will be 15 and the value of y will be 4.
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please help lol I need help
The expression can be expanded as 125/64
Evaluating an ExpressionTo evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
To solve this problem, we need to evaluate the expression given;
For this, we can find the cube of the numerator and cube of the denominator.
(5/4)³ = 125/64
The solution to the problem is 125/64
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A pool takes 3,185 gallons to fill. After 2.5 hours the pool is filled with 1,625 gallons how long will it take to fill the whole thing
[tex]\begin{array}{ccll} hours&gallons\\ \cline{1-2} 2.5 & 1625\\ h& 3185 \end{array} \implies \cfrac{2.5}{h}~~=~~\cfrac{1625}{3185}\implies \cfrac{2.5}{h}=\cfrac{25}{49} \\\\\\ (2.5)(49)=25h\implies \cfrac{(2.5)(49)}{25}=h\implies 4.9=h\qquad \textit{4 hours and 54 minutes}[/tex]
Determine the quadratic function of the form f(x)= a(x - h)² + k whose graph is given on the
right.
The quadratic function will be f(x) = 2[tex]x^{2}[/tex] + 4x + 15
General equation of quadratic is
f(x) = a[tex]x^{2}[/tex] + bx + c
and Standard form is
f(x) =a [tex](x-h)^{2}[/tex] + k
where h , k are coordinates of vertex
and x , y represent some point on the graph.
By replacing f(x) with y in standard equation we get
y = a[tex](x-h)^{2}[/tex] + k
Put value of x , y , h , k from the graph.
h = -2
k = 7
x = 0
y = 9
9 = a (4) + 7
a = 2
Now put value of a in standard equation
f(x) = 2 [tex](x + 2)^{2}[/tex] + 7
f(x) = 2[tex]x^{2}[/tex] + 4x + 15
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Use the distributive property to remove the parentheses.
3c³(7c8 +8c+7)
Simplify your answer as much as possible.
Answer: 21 c^16 + 24c^9+ 21 c^8
Step-by-step explanation: To multiply exponents with the same base, add them.
Answer:
3c^3(7c^8+8c+7)
=(3c^3)(7c^8+8c+7)
=(3c^3)(7c^8)+(3c^3)(8c)+(3c^3)(7)
=21c^11 + 24c^4 + 21c^3
Step-by-step explanation:
Remember.... ^ is for power
f(-10) = 4, ƒ(8) = -5
Answer: f(x)=-.5x-1
Step-by-step explanation:
I believe this is the answer you are looking for. Because if you plug in -10 for x and it gives you 4. Do the same with 8 and you get -5
Hope this helps :)
multiply
(−5 2/5) ⋅ 3 7/10.
a. −19 49/50
b. −15 7/25
c. −9 1/10
d. −1 7/10
Answer: -19 49/50 ==> a
Step-by-step explanation:
(−5 2/5) ⋅ 3 7/10=
(−5 - 2/5) ⋅ (3 + 7/10)=
(−25/5 - 2/5) ⋅ (30/10 + 7/10)= ==> make the terms have like denominators
((-25-2)/5) ⋅ ((30+7)/10)=
-27/5 ⋅ 37/10 =
-27 ⋅ 37 / (5 ⋅ 10) =
-999/50=
(-950-49)/50=
-950/50 - 49/50=
-19 - 49/50=-19 49/50 ==> a
A manager of a fast food chain wants to know how his customers rate their service at the restaurany that day. after randomly picking the 9th customer, he surveys every 5th customer that exits the restaurant. which sampling method? your answer: simple random systematic stratified cluster volunteer
The sampling method used in this scenario is random Systematic random sampling
Systematic random sampling
Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the desired sample size, this interval, also known as the sampling interval, is computed.
If the periodic interval is predetermined and the starting point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.
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Three students ran for class president. lisa got 36 votes for class president. she got six times more votes than lauren. chandler got seven times more than lauren. how many votes did lauren get?
Lauren got 5 votes in class president election.
Number of votes Lisa got = 36
Let the number of votes of Lauren be x. So, forming the equation between the number of votes of Lisa and Lauren.
36 = x + 6x
Calculating the value of x from mentioned equation
36 = 7x
Rewriting the equation with 7 as denominator
x = 36/7
Performing division on Right Hand Side of the equation
x = 5.14
Rounding off the digits as number of votes will be whole number
x = 5
Based on the mentioned information, Lauren got 5 votes.
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What is the solution set for 5 - 5 = 15, given the replacement set {0, 1, 2, 3, 4}? O x = 4 O x = 3 O x = 2 O x = 1 x = 0
The solution set for the given equations is x = 4.
What is a set?
A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.
Here,
we put the value of x in the given equation and justify our answer
when we x=4, we get
5x−5=15
5(4) - 5 = 15
20 - 5 = 15
15 = 15
Hence, the solution set for the given equations is x = 4.
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The angles of elevation of the top of a tower with respect to points A and B are 30° and 75°respectively. Points A and B are 175 feet apart and at equal elevations, and the base of the tower lies on the line between them. Find the height of the tower. Round your final answer to the nearest ten thousandth.
The height of the tower is 87.4870 feet
What is Angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The body of the calculation is contained in the attached file.
In conclusion, the height of the tower to the nearest ten thousandth is 87.4870 feet
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Explain how the equations 2/3m=-4 and -4m=24 are equivalent?
Both 2/3m=-4 and -4m=24 have a solution of 1/6 and are equivalent
What are algebraic expressions?Algebraic expressions are described as expressions that contains terms, variables, coefficients, constants and factors.
They are also known to be made up of some arithmetic operations, such as;
AdditionSubtractionMultiplicationDivisionBracket ParenthesesWe have the equations;
2/3m=4 and -4m=24
Let's solve for m in the first equation
12m = 2
Divide both side by coefficient of m
m = 2/ 12 = 1/ 6
For the second equation
-4m = 24
Divide both sides by - 4
m = 24/-4
m = 6/ -1
Take inverse
m = 1/6
Hence, the equations are equivalent
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Decide whether each equation is true for all, one, or no values of x.
1. 3x + 9 = -4.5x + 20 ; This is true for one value of x.
2. 9(x + 3) = 9x + 12 ; This is true for no values of x.
3. 4(2x + 3) = 12 + 8x ; True for any values of x.
Given,
The equations;
1. 3x + 9 = -4.5x + 20
2. 9(x + 3) = 9x + 12
3. 4(2x + 3) = 12 + 8x
We have to find whether each equation is true for all, one or no values of x.
Here,
1. 3x + 9 = -4.5x + 20
Solve for x;
3x + 4.5x = 20 - 9
7.5x = 11
x = 11/7.5
x = 1.47
Then,
This is true for one value of x.
2. 9(x + 3) = 9x + 12
Solve using distributive property;
9x + 27 = 9x + 12
9x - 9x = 12 - 27
0 = -15
This is true for no values of x.
3. 4(2x + 3) = 12 + 8x
Use distributive property and solve;
8x + 12 = 12 + 8x
8x - 8x = 12 - 12
0 = 0
True for any values of x.
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5
The equation of a line is y=-x+9.
8
(a) What is the slope of a line parallel to it?
(b) What is the slope of a line perpendicular to it?
(a) The slope of a line parallel to it is. (Simplify your answer.)
(b) The slope of a line perpendicular to it is
(Simplify your answer.)
a. The slope of the line that is parallel to y = 5/8x + 9 is: 5/8.
b. The slope of the line that is perpendicular to y = 5/8x + 9 is: -8/5.
What is the Slope of Parallel and Perpendicular Lines?When two lines are parallel to each other, the lines will have the same slope value (m). However, if both lines are perpendicular to each other, they would have slope values that are negative reciprocals, meaning the product of their slope would be -1.
a. Given the equation, y = 5/8x + 9, the slope (m) of the line is 5/8.
Therefore, it implies that the line that is parallel to y = 5/8x + 9 will have a slope that is the same as 5/8.
Thus, the slope of the parallel line to the equation, y = 5/8x + 9, is: 5/8.
b. The negative reciprocal of 5/8 is -8/5.
Therefore, the slope of the line that is perpendicular to y = 5/8x + 9 would be: -8/5.
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9. There is so much water in the world, that we normally measure large bodies of water in cubic
miles or cubic kilometers instead of gallons. Cayuga Lake in upstate New York contains an
estimated 9.4 km³. How many cubic miles of water does Cayuga Lake contain?
Answer:
Step-by-step explanation:
12.5km
i made that up sorry
Find a polynomial function of least degree having only real
coefficients, a leading coefficient of 1, and zeros of 4 and
3 + i.
The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
Given,
In the question:
A leading coefficient of 1, and zeros of 4 and 3 + i.
To find the polynomial function of least degree having only real coefficients.
Now, According to the question;
The function has 4 and 3 + i .
As, i's roots
So, 3 - i is also its root a leading coefficient of 1 .
So, The function of polynomial is :
f(x) = (x - 4) [tex][(x - 3)^2 + 1][/tex]
To solve the function;
f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
Hence, The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
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Determine the slope of the graph of x2 = ln(xy) at the point (1, e).
The slope of the given graph x^2 = ln (xy) at the point (1, e) is e
We have been given a graph x^2 = ln (xy) and a point (1, e)
Differentiate the given graph on both sides
d/dx x^2 = d/dx (ln (xy))
⇒ 2x = 1/xy × d/dx (xy)
⇒ 2x × xy = x.dy/dx + y.dx/dx
⇒ 2x^2y = x.dy/dx + y
⇒ 2x^2y = x.dy/dx + y
⇒ 2x^2y - y = x.dy/dx
⇒ (2x^2y - y)/x = dy/dx … (1)
The slope at the point (1, e)
m = dy/dx at x = 1, y = e
Substitute the values in Equation (1)
⇒ m = (2(1)^2 (e) - e)/1
⇒ m = (2e - e)/1
⇒ m = e/1
⇒ m = e
Hence, the slope of the given graph is e.
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Hannah swims in a swimming pool of 25 metres long.
How many laps does she need to complete for a total distance of 0.5 kilometre?
She needs to complete 20 laps for a total distance of 0.5 kilometer.
1 kilometers = 1000 meters
0.5 kilometers = 500 meters
Length of swimming pool = 25 meters
That means, she covers 25 meters in 1 lap.
Laps to cover 500 meters = 500/25
= 20
Hence, she needs to do 20 laps.
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What is the area of the figure?
17.5 yd2
20.0 yd
19.1 yd
35.0 yd2
The area of the triangle is A. 17.5yd².
How to find the area?Using this formula to find the area
Area = 1/2 ( b × h)
Where:
b = base = 5
h = Height = 7
Hence,
Area = 1/2 (5 ×7)
Area = 1/2 (35)
Area = 1× 35/2
Area = 35/2
Area = 17.5yd²
Therefore the correct option is A.
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Kelly has 97 apples, Jason has 72. How may proportional relationships are there?
There are 6984 inverse proportional relationships and the direct proportional relationships are 97/72.
Given that:
Kelly has 97 apples, and Jason has 72.
The relationship between two variables, X and Y, is directly proportional if it can be expressed in terms of Y/X = k or Y = Xk.
Y/X = k
Substitute the given X and Y values and solve for k.
Suppose, Y = 97, X = 72
then k = 97/72
Distinguish a proportional relationship from other relations, including an inverse relationship (XY = k or Y = k/X).
An inverse proportional relationship is one in which two quantities vary inversely with respect to each other. We say that the variable Y changes inversely with X if
Y = k/X
Substitute the given X and Y values and solve for k.
Suppose, Y = 97, X = 72
then k = 97 x 72
=> k = 6984
Hence, there are 6984 inverse proportional relationships and direct proportional relationships are 97/72 between Kelly which has 97 apples, and Jason which has 72.
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