Applying basic unitary method and time conversion, The answer is 3750 calls annually.
What is Unitary method?The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Why do we use unitary method?The unitary technique is used practically all the time, from problems involving speed, distance, and time to issues with estimating material costs. The technique is applied to determining a product's pricing. It is used to determine how long it takes a person or vehicle to travel a certain distance in an hour.
average length of call= 30 minutes
average travel time=30 minutes
annual working days=250
per day works 8 hours.
call hour in work = 8*60 - 30 = 450minutes.
number of calls made in those hours= 450/30=15 calls daily.
total annual number of calls= 250 * 15 = 3750
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2 balloons and 3 cakes = £16
4 balloons and 4 cakes = £24
Answer:
1 balloon is = £2 and 1 cake is = £4
Step-by-step explanation:
this is true because 2 balloons = £4
and 3 cakes = £12 so 4 + 12 = 16 and also
4 balloons = £8
and 4 cakes = £16 so 8 + 16 = £24
this is one of the possible answers
Answer:
A cake is £3.50
A Balloon is £2.75
Step-by-step explanation:
Let b be balloons and c be cake
2 balloons and 3 cakes = £16 = 2b + 3c = 16
4 balloons and 4 cakes = £24 = 4b + 4c = 25
First times -2 to the first equation
-4b - 6c = -32
4b + 4c = 25
Now let's find c first by adding the two equations together.
-2c = -7
c = £3.50
Now put 3.50 back in the c
4b + 4(3.50) = 25
4b + 14 = 25
4b = 11
b = £2.75
What is the reason or purpose of solving system of equations?
The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.
What is solving system?Solving system can be defined as solution set of a system of equations to the collection of all solutions. Solving the system also means finding all solutions with formulas involving some number of parameters.
There are three methods used to solve systems of equations such as:
GraphingSubstitution EliminationTherefore the main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.
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Exponential functions have the form f(x)= b^x. What type of an exponential function would you have (increasing or decreasing) if the value of b is greater than one?.
An exponential function with a base greater than 1 will be increasing in nature.
This is because when the base of an exponential function is greater than 1, the exponent is raised to a power greater than 1, and the result will always be greater than the original number. This means that as the value of x increases, so too will the value of the function. To illustrate this, the formula for an exponential function with base b can be written as f(x) = b^x. As x increases, b^x will become larger and larger, resulting in a continually increasing function. For example, if b = 2, then f(x) = 2^x. As x increases, 2^x will increase exponentially, resulting in a function that is always increasing.
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please help a mate out aye? 80 points!! :D
Simplify the expression 3x(2x – 7).
(A)15x
(B)6x2 – 21
(C)6x2 – 21x
(D)6x – 21
Answer:
Hey no prob!
We take 3x(2x-7) and we distribute the 3x to both of the terms inside
3x times 2x is 6x^2
and
3x times -7 is -21x
the final answer would be C
6x^2-21x
Answer:
[tex] \sf \: c) \: 6 {x}^{2} - 21x[/tex]
Step-by-step explanation:
Given expression,
→ 3x(2x - 7)
Simplifying the expression,
→ 3x(2x - 7)
→ 3x(2x) + 3x(-7)
→ (3 × 2)x² + (3 × -7)x
→ (6)x² + (-21)x
→ 6x² - 21x
Hence, option (c) is correct.
How many months before you can loan at SSS?
Members who have made at least 36 months' worth of contributions overall and six months' worth within the previous 12 months are eligible to apply for a loan through SSS.
One month's worth of salary is equal to the amount of the salary loan. If you have at least 72 months of posted contributions and six months of contributions during the last 12 months, you may also be eligible to apply for a two-month wage loan.
If you have a job, your employer is responsible for keeping your loan payments and monthly contributions current. Additionally, you need to keep up with payments on all of your other loans.
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11. Solve the Right Triangle.
The sides of the right triangle are as follows:
AC = 3.2 metres
AB = 12.4 metres
How to solve right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right triangle is 180 degrees.
Therefore, the sides of a right triangle can be found using trigonometric ratios.
Hence, let's find AC
tan 15 = opposite / adjacent
tan 15 = AC / 12
cross multiply
AC = 12 tan 15
AC = 12 × 0.26794919243
AC = 3.21539030917
AC = 3.2 metres
Let's find AB
cos 15 = adjacent / hypotenuse
cos 15 = 12 / AB
AB = 12 / cos 15
AB = 12 / 0.96592582628
AB = 12.423314503
AB = 12.4 units
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factor completely? please
By Quadratic Formula factors of [tex]a^2+4b^2[/tex] are [tex](a+2bi),(a-2bi)[/tex].
What is Quadratic Formula?The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic equation. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.
The following general quadratic equation is given:
[tex]ax^2+bx+c=0[/tex]
The quadratic formula is:
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}, \frac{-b-\sqrt{b^2-4ac} }{2a}[/tex];
where x stands for an unknown, a, b, and c are constants, and a≠0.
Each of these two answers is also referred to as a quadratic equation root (or zero). These roots, which are clearly stated as [tex]y = ax^2 + bx + c[/tex], are the x-values at which any parabola crosses the x-axis geometrically.
Calculation:Given;
[tex]y=a^2+4b^2;\\[/tex]
By comparing this with general equation [tex]x=a,a=1,b=0,[/tex][tex]c=4b^2[/tex]
By substituting in the formula;
[tex]x=\frac{-0+\sqrt{(0)^2-4(1)(4b^2)} }{2(1)} =2bi\\(or) x=\frac{-0-\sqrt{(0)^2-4(1)(4b^2)} }{2(1)} =-2bi[/tex]
That gives us;
[tex]y=(a+2bi)(a-2bi)[/tex]
By Quadratic Formula factors of [tex]a^2+4b^2[/tex] are [tex](a+2bi),(a-2bi)[/tex].
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Polygon B is a scaled copy of Polygon A using
a scale
factor of 5.
How many
times as large is the area of Polygon B
compared to the area Polygon A?
Answer:
25 times larger
Step-by-step explanation:
given a scale factor of 5 from A → B
then the scale factor of the area is 5² = 25
area of B is 25 times larger than the area of A
What is the maximum or minimum value of the function y =- 2x 2 32x 12?
The maximum of the equation y = -2x² +32x -12 is 116 and the range of the function is y ≤ 116.
What are the Maxima and the minima of a function?The highest and smallest values of a function, respectively, can either be found inside a specific range or across the entire domain. They are sometimes referred to collectively as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, respectively.
Y= ax² + bx + c is the conventional form of this quadratic equation. The vertex of a quadratic function is its greatest value or smallest value. We locate the axis of symmetry to determine the x-coordinate of the vertex. This is determined by the equation x = -b/2a:
x = -32/2(-2) = -32/-4 = 8
To find the y-coordinate, plug this into the equation y = -2(8²)+32(8)-12
y=-2(64) + 256 - 12 = -128+256-12 = 128-12 = 116
The coordinates of the vertex are (8, 116).
Look at the value of a to see if this is maximum or minimal. It is -2. This indicates that the parabola widens downward and that the vertex is a maximum because it is negative.
Therefore this is a maximum at y=116, which means the range will be less than or equal to this value of 116.
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What is the smallest group of repeating digits in this nonterminating decimal, 0.345345?
he repeating digit is
345.
here, 0.345345 is a
nonterminating and repeating
decimal number.
a nonterminating and repeating decimal is
a decimal with no finite number of digits that repeat. these keep going endlessly.
for example
- 0.333333...... which is 1/3, is also a number that repeats itself endlessly. another example is 0.6.
similarly, the minimum or
smallest group of digits that repeats itself here is 345.
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Answer:
345
Step-by-step explanation:
The smallest group of repeating digits in this nonterminating decimal is 3. This is because the decimal 0.345345 contains three repeating digits, "345".
The smallest group of repeating digits in this decimal is 3, 4, 5. This is because the digits 3, 4, and 5 repeat infinitely in the decimal after the decimal point, forming a repeating pattern.
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What is the equation of the line that passes through the point (5,-5) and has a slope of -1/5
Considering the definition of a line, the equation of the line that passes through the point (5, -5) and has a slope of -1/5 is y= -1/5x -4.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Line in this caseIn this case, you know that:
The line has a slope of -1/5.The line passes through the point (5, -5).Substituting the value of the slope m and the value of the point in the expression of a line, the value of the ordinate to the origin b can be obtained as follow:
-5= -1/5×5 + b
-5= -1 + b
-5 +1= b
-4= b
Finally, the equation of the line is y= -1/5x -4.
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2y+(4+5y) please answer
Answer:
7y + 4
Step-by-step explanation:
2y+(4+5y)
2y + 4 + 5y
combine y terms:
7y + 4
Does the following equation has no real roots 3x² 4 √ 3x 4 0?
Yes, the equation has no real roots.
To solve this equation, we first move the constant terms to the right side and the terms with x to the left side.
3x² - 4√3x = -4
Next, we square both sides of the equation.
(3x² - 4√3x)² = (-4)²
9x⁴ - 24√3x² + 16x = 16
Next, we move the constant terms to the right side of the equation.
9x⁴ - 24√3x² = -16
Next, we factor the left side of the equation.
(3x² - 8√3)(3x² + 8√3) = 0
Finally, we set each factor equal to zero and solve for x.
3x² - 8√3 = 0
3x² + 8√3 = 0
However, these equations have no real solutions, so the original equation has no real roots.
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A pyramid has a square base with sides of length s. The height of the pyramid is equal to 12 of the length of a side on the base. Which formula represents the volume of the pyramid?.
Step-by-step explanation:
The volume of the pyramid with a base area of s² and the height s is [tex]\frac{1}{3} s^{2}[/tex]
The formula for calculating the volume of a square based pyramid is expressed as:
Volume = 1/3 * Base area * HeightSince it is a square-based pyramid, the base area is calculated as:
Base Area = s²
If the height of the pyramid is equal to of the length of a side on the base, hence h = s
Substituting the base area and the height into the formula for the volume, this will give us;
[tex]V=\frac{BH}{3} \\V=\frac{s^{2}Xs }{3} \\V=\frac{s^{3} }{3} \\V=\frac{1}{3 } s^{2} \\[/tex]
Hence the volume of the pyramid with a base area of s² and the height s is [tex]\frac{1}{3}s^{3}[/tex]
Pls mark me brainliest
4x + 6 = 2(3x - 7)
Solve
Answer:
x = 10
Step-by-step explanation:
Method 1: Algebraically
1. 4x+6 = 2(3x-7) - Multiply out the 2
2. 4x+6 = 6x-14 - make x the subject of the formula first by subtracting 4 from both sides
3. 6 = 2x-14 - add 14 to both sides
4. 20 = 2x - divide by 2 to solve for x
5. 10 = x - Answer
Method 2: Graphing
Use a graphing calculator to solve for the answer
1. set one side to y1 and the other to y2
2. set the correct window
3. press 2nd then trace
4. Select option 5 to find the intersection
Is the mean of the following data is 14.7 find the values of P and Q?
The values of p and q are 11 and 3 respectively.
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally.
Given that,
∑f = 40
=> 26+p+q = 40
=>p+q=40-26
=> p+q = 14 .......................(i)
∵ x bar = ∑xf/∑f
=>14.7 = 408+9p+27p / 40 (since, x bar = 14.7)
=>588 = 408+9p+27p
=>588 - 408= 9(p+3p)
=>180= 9(p+3p)
=>p+3q=20......................(ii)
Solving equations (i) and (ii)
=>p+3q -(p+q)=20-14
=>p+3q-p-q=6
=>2q=6
=>q=3
Substituting this value in equation (ii)
∴p+3=14 => p = 11
Hence, the values of p and q are 11 and 3 respectively.
(Refer to the image attached for the missing data)
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∠1 and ∠2 are vertical angles. If m∠1 = (5x + 12)° and m∠2 = (6x - 11)°. Find m∠1.
Answer<2= 127°
Step-by-step explanation:
How do you count 1 in an array?
To count 1 in an array, one can use a looping structure to iterate through each element in the array and increment a counter every time the element is equal to 1.
This can be accomplished using a while loop, a for loop, or a for-each loop. A while loop would use a variable to track the index of the array, and then use a conditional statement to check if the value at the current index is equal to 1. Then, the loop can increment the counter and the index variable. A for loop can be used in the same manner, but with the index variable declared within the loop.
A for-each loop can be used to iterate through the elements of the array, and a conditional statement can be used to check if the current element is equal to 1 and increment the counter if necessary. Whichever looping structure is used, the result should be the same. The counter will hold the number of 1s present in the array after the loop completes.
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A box without a top is made from a rectangular piece of cardboard, with dimensions 25 inches by 20 inches, by cutting out square corners with side length x inches. which expression represents the volume of the box in terms of x?
Answer:
[tex]x(20-2x)(25-2x)[/tex]
Step-by-step explanation:
The length removed from each side is [tex]2x[/tex].
So, the length and width of the box are [tex]25-2x[/tex] and [tex]20-2x[/tex].
The height of the box is [tex]x[/tex], so the volume is [tex]x(20-2x)(25-2x)[/tex].
Is Circumcentre and centroid of a triangle same?
Answer:
no, they are different in their different ways
The diameter of a circle is 6 m. What is the area of the circle to the nearest square meter?
Answer:
To find the area of a circle, we can use the formula A = πr^2, where A is the area of the circle, π is a constant with a value of approximately 3.14, and r is the radius of the circle. To use this formula, we first need to find the radius of the circle. We can do this by dividing the diameter of the circle by 2:
r = Diameter / 2
r = 6 m / 2
r = 3 m
Substituting this value for r into the formula for the area of a circle, we get:
A = πr^2
A = 3.14 * 3^2
A = 3.14 * 9
A = 28.26
Therefore, the area of the circle is 28.26 square meters. Rounded to the nearest whole number, this is equal to 28 square meters.
What is the median of 7 6 4 8 2 5 11?
To find the median of a set of numbers, you first need to put the numbers in order from smallest to largest. Then, if there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.
In this case, the set of numbers is already in order: [2, 4, 5, 6, 7, 8, 11]. There are 7 values, so the median is the middle value, which is 6.
So, the median of the set {7, 6, 4, 8, 2, 5, 11} is 6.
What in math is the median?the middle number, which is obtained by sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: Because the number 4 is in the middle when the numbers are ordered (1, 4, 7), it is the median of 4, 1, and 7.
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In the pair of linear equation a1x b1yc1=0 and a2xb2yc2=0,if a1/a2 i not equal to b1/b2 then the equation have no olution. (True or fale)
The statement is false. In the pair of linear equation, if a₁/a₂ ≠ b₁/b₂ then the equations have unique solution.
Given that,
The pair of linear equation
a₁x +b₁y +c₁=0 and
a₂x +b₂y +c₂=0
We have to prove if a₁/a₂ ≠ b₁/b₂ then the equations have no solution.
We know that,
In the pair of linear equation
a₁x +b₁y +c₁=0 and
a₂x +b₂y +c₂=0
If a₁/a₂ ≠ b₁/b₂ then System is called consistent and have a unique Solution
Lines intersect each other at unique point
a₁/a₂ = b₁/b₂ = c₁/c₂ then consistent (infinite solution) as both Equation represent same line
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ then inconsistent (no Solution) as Lines are parallel and never intersect each other
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Is AAA congruence possible?
Angle-Angle-Angle (AAA) does not work because it can produce similar but not congruent triangles.
There are a few conditions for AAA:
The sides of the triangles may or may not be equal. For two triangles with the same respective angles, the congruence will hold true only if those triangles are similar."AAA" is when we know all three angles of a triangle, but no sides. AAA triangles are impossible to solve further since there is nothing to show us the size.
If two angles and any side of one triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.
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What are the 4 functions of a stem?
The 4 functions of a stem are fruits, flowers, leaves, and branches.
In plants, a stem's primary role is to aid in the transfer of water and minerals from the roots to the leaves and other sections of the plant. Additionally, it supports the buds, leaves, flowers, fruits, and branches of plants.
In a plant, a stem does the following tasks:
(i) It holds up the fruits, flowers, leaves, and branches.
(ii) It moves water and minerals from a plant's roots to its leaves and other areas.
(iii) It transports nourishment from the leaves to various plant sections.
(iv) The plant is kept upright by it.
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a country's postal service will accept a package if its length plus its girth (the distance all the way around) does not exceed 96 inches. find the dimensions (in inches) and volume (in cubic inches) of the largest p
Dialyzer re-use efficiency is largely determined by the fiber bundle volume (FBV).
This estimation is performed after the dialyzer has been pressure cleaned and may underrate the level of coagulated strands a patient really experiences while on dialysis.
The package's dimensions:
length = 32 in
width = level = 16 in
Volume of bundle = 8192 in³
The square-shaped package is depicted in the attached image.
Expect that the length is y in and that width = level = x in (since the base is a square)
This implies that the circumference is 4*x = 4x in
We are given that the greatest amount of length and circumference is 96.
This indicates:
This can be rewritten as: y + 4x = 96
The volume of the package can be calculated as follows: y = 96 - 4x..............> I
Volume is equal to the following: length * width * height * y * x * x = x2y in3 Substitute equation I for the following volume equation:
Volume = x2 (96-4x) = 96x2 - 4x3 in3 to achieve maximum volume:
dV/dx = 0 indicates that:
2(96) x - 4(3) x2 = 0 192x - 12x2 = 0 x (192-12x) = 0
either x = 0.......> This is rejected because the side cannot be zero or 192 - 12x = 0...............> 192 = 12x...............> x = 16 in.......> accepted
In Part (b), y = 96 - 4x = 96 - 4(16) = 96 - 64 = 32: obtaining a volume:
The volume of the package is equal to 32 x 16 x 16 x 8192 in3.
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What is the z-score for a height of 67 inches?
Simply said, a z-score, also known as a standard score, informs you of how much a data point deviates from the mean.
It is not possible to determine the z-score for a height of 67 inches without additional information.
What is mean?The sum of all values divided by the total number of values determines the mean of a dataset.
What is z-score?A z-score, also known as a standard score, informs you of how much a data point deviates from the mean.
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Three sisters have were born in 3 consecutive years. The total of their ages is 30. What is the oldest sibling's age?
The oldest child is a 11-year-old boy.
What exactly is a sequential number?Three sisters have were born in 3 consecutive years. The total of their ages is 30.
Sequential numbers are those that follow one another continually, from lowest to biggest.
Here, assume that the youngest sibling is x years old.
Middle sibling's age will be (x+1) years old.
the oldest sibling's age is (x+2) years.
According to the inquiry,
x + (x+1) + (x+2) = 30
3x + 3 = 30
3x = 30-3
3x = 27
x = 27 / 3
x= 9
The oldest child is therefore (x + 2) years old, or 11 years old.
x+2 = 9+2 =11
The oldest child is a 11-year-old boy.
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What is the median of 4 2 7 3 10 9 13?
Answer: 3
Step-by-step explanation: The median is three (3) because its the middle number
What are the zeros of the function y X² 4x 5?
The zeros of the function y = x^2 - 4x - 5 = 0 are 5 and -1.
The given function is y = x^2 - 4x - 5 = 0
We know that the general form of a quadratic equation is:
ax^2 + bx + c =0
On comparing the given equation y = x^2 - 4x - 5 = 0 with the general form of a quadratic equation ax^2 + bx + c =0 we get that:
a= 1, b = -4, c = -5
On multiplying a and c, we get -5 and the factors of it are 1 and 5.
Hence we can break the equation into:
x^2 - 5x + x - 5 = 0
We can factor it into:
x (x -5) + 1 (x - 5) = 0
(x + 1) (x - 5) = 0
Therefore, the zeros of the equation are -1 and 5.
The question is incomplete, the complete question is:
What are the zeros of the function y = x^2 - 4x - 5?
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