In linear equation, $ 1300 is the cost for 80 employees.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Given that cost of a company picnic varies directly as the number of employees attending the picnic
Let "c" be the company picnic cost
Let "n" be the number of employees attending the picnic
Therefore,
cost ∝ number of employee attending picnic
c ∝ n
c = kn
Where "k" is the constant of proportionality
c = kn ---------- eqn 1
Given that company picnic costs $487.50 for 30 employees
Therefore substitute c = 487.50 and n = 30
487.50 = k(30)
k = 487.50/30
k = 16.25
Substitute n = 80 and k = 16.25 in eqn 1
c = 16.25(80)
c = 1300
Thus $ 1300 is the cost for 80 employees.
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The first term of a sequence is -2, and the common difference is 6.
what are the next three terms?
The next three terms of the sequence will be 4,10,16.
What is a sequence?
A sequence is a list of numbers (or elements) that exhibits a particular pattern. For example, Olivia has been offered a job with a starting monthly salary of $1000 with an annual increment of $500. Can you calculate her monthly salary in the first three years? It will be $1000, $1500, and $2000. Observe that Olivia's salary over a number of years forms a sequence as they follow a pattern where the numbers are increasing by an amount of $500 every time.
Some of the most common examples of sequence are:
Arithmetic Sequences
A sequence in which every term is created by adding or subtracting a definite number from the preceding number is an arithmetic sequence.
Geometric Sequences
A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number is known as a geometric sequence.
Harmonic Sequences
A series of numbers is said to be in harmonic sequence if the reciprocals of all the elements of the sequence form an arithmetic sequence.
Fibonacci Numbers
Fibonacci numbers form an interesting sequence of numbers in which each element is obtained by adding two preceding elements and the sequence starts with 0 and 1. Sequence is defined as, F0 = 0 and F1 = 1 and Fₙ = Fn-1 + Fn-2
Now,
Given first term=-2
difference is =6
Therefore,
The next three terms of arithmetic sequence will be -2+6,-2+6+6,-2+6+6+6 i.e. 4,10,16.
Hence,
The next three terms of the sequence will be 4,10,16.
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If Triangle ABC = Triangle XYZ and AB = 15, BC = 9, and XZ = then what is the length of XY?
The length of the side ZY would be 9.
What is a similar triangle?
Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles and squares of any side length are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and their corresponding sides are in equal proportion.
Given:If Triangle ABC = Triangle XYZ and AB = 15, BC = 9, and XZ =8
As in the given question, they have stated that both triangles are the same.
Then by the property of the similar triangles, their sides are also in equal proportion so
Length of ZY = Length of CB
Length of CB = 9
Length of ZY = 9.
Hence, the length of the side ZY would be 9.
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a boat starts off 172 miles directly west from the city of johnstown. it travels due south at a speed of 30 miles per hour. after travelling 126 miles, how fast is the distance between the boat and johnstown changing? (do not include units in your answer, and round to the nearest hundredth.)
The distance between the boat and Johnstown is changing at a rate of 27.73 miles per hour.
This is calculated by taking the speed of the boat (30 miles per hour) and subtracting the rate of change in the boat's displacement in a southward direction, which is 2.27 miles per hour (calculated by taking the distance travelled (126 miles) and dividing it by the time taken (126/30 = 4.2 hours)).
Distance is a measure of how far something is from a given point, while velocity is a measure of the rate at which something changes its position or moves. Distance is a scalar quantity, meaning it has only magnitude and no direction, while velocity is a vector quantity, meaning it has both magnitude and direction.
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4.860 ÷ 10² =
Please help me!
Answer:
0.04860
Step-by-step explanation:
10^2=100
4.860/100
There are 2 zeroes, and in division, you move the decimal point left, so you move the decimal point 2 places to the left.
one place to the left: 0.4860
two places to the left: 0.04860
given that the current in (ma) flowing through a wire is given by: i(t) = ⎧ ⎪⎨ ⎪⎩ 0 for t < 0 6t for 0 ≤ t ≤ 5 s 30e−0.6(t−5) for t ≥ 5 s, (a) sketch i(t) versus t. (b) sketch q(t) versus t.
The given equation represents the current (i (t)) flowing through a wire in milliamps (ma) over time (t) in seconds (s).
(a) To sketch i (t) versus t, the equation i (t) is first rearranged into three separate parts; i (t) = 0 for t < 0, i (t) = 6t for 0 ≤ t ≤ 5s and i (t) = 30e−0.6(t−5) for t ≥ 5s. The graph is then plotted with the origin (0, 0) and the points (0, 0), (5, 30) and (10, 0). A line is then drawn from (0, 0) to (5, 30) and then from (5, 30) to (10, 0). The resulting plot is the graph of i (t) versus t.
(b) To sketch q (t) versus t, the integral of the equation i (t) is taken. The integral of i (t) = 0 for t < 0 is 0. The integral of i (t) = 6t for 0 ≤ t ≤ 5s is q (t) = 3t2 + C. The integral of i (t) = 30e−0.6(t−5) for t ≥ 5s is q (t) = −30e−0.6(t−5) + C. The graph is then plotted with the origin (0, 0) and the points (0, 0), (5, 75) and (10, -30). A line is then drawn from (0, 0) to (5, 75) and then from (5, 75) to (10, -30). The resulting plot is the graph of q (t) versus t.
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For each graph, f(x) is the parent function and g(x) is a transformation of f(x). Use the graph to determine the equation of g(x).
The equation of g(x) when the parent function f(x) = 3^x is transformed is g(x) = 3^{x - 4} + 5.
The equation of g(x) when the parent function f(x) = 2^x is transformed is g(x) = 4(2)^{x - 3}.
The equation of g(x) when the parent function f(x) = 4^x is transformed is g(x) = -2(4)^{x + 1} + 3.
How to determine the equation of g(x) by using the graph?By critically observing the graph of the exponential function f(x) = 3^x, we can reasonably and logically deduce that f(x) is vertically translated (k) by 5 units up and horizontally translated (h) by 4 units to the right. Therefore, the equation of g(x) is given by:
g(x) = 3^{x - h} + k
g(x) = 3^{x - 4} + 5.
Based on the graph of the exponential function f(x) = 2^x, we can reasonably and logically deduce that f(x) is compressed by a scale factor (a) of 4 units and horizontally translated (h) by 3 units to the right. Therefore, the equation of g(x) is given by:
g(x) = a(b)^x - h}
g(x) = 4(2)^{x - 3}
Based on the graph of the exponential function f(x) = 4^x, we can reasonably and logically deduce that f(x) is reflected across the x-axis and expanded by a scale factor (a) of 2 units, followed by a translation of 1 units left and 3 units up:
where; a = -2, h = -1, and k = 3.
g(x) = a(b)^x - h} + k
g(x) = -2(4)^{x - (-1)} + 3
g(x) = -2(4)^{x + 1} + 3
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Ada' hitory teacher wrote a tet for the cla. The tet i 26 quetion long and i worth 123 point. Ada wrote two equation, where m repreent the number of multiple choice quetion on the tet, and repreent the number of eay quetion on the tet. M=26
3m8=123
There are 9 questions on the test.
Let, the number of multiple-choice questions on the test = m
the number of essay questions on the test = s
m + s = 26 .......(1)
So, We are also told that multiple choice is worth 3 points each, so the total number of points for m questions will be 3m.
As essays are worth 8 points each, so the total number of points for s questions will be 8s.
3m + 8s = 123 .......(2)
Now we will use the substitution method to solve a system of linear equations.
From equation (1) we will get,
m = 26 -s
Substituting this value in equation (2) we will get,
3 * (26- s) + 8s =123
78 - 3s + 8s = 123
5s = 123 -78
5s = 45
s = 45/5 = 9
So, there are 9 questions on the test.
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The complete question is:
Ada’s history teacher wrote a test for the class.
The test is 26 questions long and is worth 123 points.
Ada wrote two equations, where m represents the
number of multiple choice questions on the test, and
s represents the number of essay questions on the test.
m+s= 26
3m + 8s = 123
How many essay questions are on the test?
Aeronautical researchers have developed three different processes to pack a parachute. They want to compare the different processes in terms of time to deploy and reliability. There are 1,200 objects that they can drop with a parachute from a plane. Using a table of random digits, the researchers will randomly place the 1,200 items into three equally sized treatment groups suitable for comparison.
How many unique random numbers need to be selected from the table of random digits?
3
400
800
1,200
From the table of number digits, 400 unique random numbers need to be selected.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Aeronautical researchers have developed three different processes to pack a parachute.
They want to compare the different processes in terms of time to deploy and reliability.
There are 1,200 objects that they can drop with a parachute from a plane. Using a table of random digits, the researchers will randomly place the 1,200 items into three equally sized treatment groups suitable for comparison.
That means,
1200/3 = 400.
Therefore, 400 unique numbers.
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let a be an nn matrix. if is computed, what should a be equal to in order to confirm that has been found correctly?
To confirm that the inverse of a square matrix A has been found correctly, it should be verified that AA⁻¹ = I (identity matrix) .
The Inverse of a square matrix A (denoted by A⁻¹) , is a matrix that satisfies the equation AA⁻¹ = AA⁻¹ = I, where I is the identity matrix.
The identity matrix is a square matrix of size n×n with ones on the main diagonal and zeros everywhere else.
If A⁻¹ has been computed correctly, multiplying it by A should result in the identity matrix. That is, AA⁻¹ = I. This confirms that the inverse has been found correctly and that the inverse property holds for the matrix A.
The given question is incomplete , the complete question is
let A be an n×n matrix. if A⁻¹ = (1/detA)×adjA is computed, what should AA⁻¹ be equal to in order to confirm that A⁻¹ has been found correctly ?
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Please Help Urgent!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.
The city will also put a fence around the playground. The perimeter, P, of the fence includes the gates. To save money, the city wants the least perimeter of fencing for the area of 256 square yards.
With one side 8 yards longer than the other side, what are the side lengths for the least perimeter of fencing?
(blank) yards and (blank) yards
The side lengths of the rectangle for the least perimeter of fencing are 12.49 yards and 20.49 yards.
What is a rectangle?
A rectangle is a type of quadrilateral with four 90-degree-distance vertices and parallel sides that are equal to one another. It is also referred to as an equiangular quadrilateral because of this.
We are given that the area of the rectangle is 256 square yards.
We know that area = length * width
Let the width be 'x'
So, as per the question,
Length = x+8
So,
⇒Area = (x+8)(x)
⇒256 = x^2+8x
⇒x^2+8x-256 = 0
Using quadratic formula, we get
x = [-b ± √(b^2 - 4ac)]/(2a)
= [-8 ± √(8^2 + 4*256)]/2
= (-8 ± √1088)/2
= [-8 ± √(64*17)]/2
= (-8 ± 8√17)/2
= -4 ± 4√17
x = -4 + 4√17 ≈ 12.49
x + 8 = 20.49
Hence, the side lengths of the rectangle for the least perimeter of fencing are 12.49 yards and 20.49 yards.
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What is 35713 in expanded form?
When writing a number in expanded form, the value of each digit's sum must be multiplied.
The expanded form of the number 35713 is 30,000+ 5000+700+10+3.
What is meant by expanded form?When writing a number in expanded form, the value of each digit's sum must be multiplied. A place value chart can be used to determine the value of a number's digits. In its expanded form, a number is written as a sum, where each digit stands in for a distinct term that has been multiplied by its place value.
When we expand a number to include the values of each digit, we say that the number is written in expanded form. Simply stating the importance of each digit when writing numbers in expanded form is sufficient. Except for zeroes, a number's extended form gets longer as it gets bigger.
The entry for the number 35713 in the place value table. As a result, the number 2 is in the lakhs position, the number 7 is in the ten thousand, the number 9 is in the thousand, the number 4 is in the hundred, the number 0 is in the tens, and the number 4 is finally in the one position.
Last but not least, the enlarged form of 35713 is 30,000+ 5000+ 700+ 10+ 3.
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PLS ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!
The possible values of each of the expressions are;
1) 10 ≤ a + b ≤ 14
2) -4 ≤ a - b ≤ 1
3) 24 ≤ ab ≤ 48
4) 3/8 ≤ a/b ≤ 1
How to find the range of a function?The range of a function is defined as the set of all possible output values for which the domain works.
The intervals of the domain we have are;
3 < a < 7
5 < b < 9
1) Maximum value of a + b = Maximum + maximum of b
(a + b)max = 6 + 8 = 14
(a + b)min = 4 + 6 = 10
Interval of a + b is;
10 ≤ a + b ≤ 14
2) Maximum value of a - b = Maximum of a - minimum of b
(a - b)max = 6 - 5 = 1
Minimum value of a - b = Minimum of a - maximum of b
(a - b)min = 4 - 8 = -4
Interval of a - b is;
-4 ≤ a - b ≤ 1
3) Maximum value of ab = 6 * 8 = 48
Minimum value of ab = 4 * 6 = 24
interval of ab is;
24 ≤ ab ≤ 48
4) Maximum value of a/b = 6/6 = 1
Minimum value of a/b = 3/8
interval of ab is;
3/8 ≤ a/b ≤ 1
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Please help me understand? I don't get it.
Answer:
-3
Step-by-step explanation:
1. Distribute
2. Combine like terms
3. SUBTRACT 10 FROM BOTH SIDES WHAT U DO ON LEFT YOU MUST DO ON RIGHT ( always remember this )
then u get -3
The answer to the question is -3
Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for $35, then took 5 hours of group snowboarding lessons. Victor paid $175 in all.
Which equation can you use to find how much Snowy Ridge charges, x, for each hour of group snowboarding lessons?
The equation to to find how much Snowy Ridge charges, x, for each hour of group snowboarding lessons is $28
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given;
Rent of snowboard= $35
5 hours of group snowboarding lessons. Victor paid $175 in all
Now
Let, x be the Snowy Ridge charges for each hour of group snowboarding lessons;
He rented a snowboard for $35, then took 5 hours of group snowboarding lessons. Victor paid $175 in all, therefore;
175 = 5x + 35
5x = 140
x = $28 per hour
Hence, the solution of equation will be 28.
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I need help …………………. Please
Slope of the given graph function is -3/2 while the y-intercept: (0, 1)
What is slope intercept?
Finding the equation of a straight line in the coordinate plane is done using the slope intercept form. The connection that any point's coordinates on the line must satisfy is the equation of a straight line. Any point that is not on the line will not have coordinates that satisfy. The answer to this equation is simple to determine.
To Find : equation of the line, in slope-intercept form
Solution:
Standard/ general form of equation of line in 2 variables is
Ax + By + C = 0
Slope intercept form is
y = mx + c
intercept form is
x/a + y/b = 1
Slope intercept form is
y = mx + c
m = Slope = -3/2
c = y intercept = 1
y = (-3/2)x + 1
equation of the line, in slope-intercept form is y = (-3/2)x + 1.
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For what value of x do the two ratios suggest a proportional relationship?
17 to 8, x to 120
Answer:
255
Step-by-step explanation:
For the ratios to suggest a proportional relationship, they must be equal.
[tex]\frac{17}{8}=\frac{x}{120} \implies x=255[/tex]
Absolute Value Functions:
Determine the value of y, if x is 12.
Answer: y = x + 5
[tex]put \: x \: = 12 \\ y = 12 + 5 \\ y = 17 \: anwer...[/tex]
Answer:
y = 17
Step-by-step explanation:
the absolute value function always gives a positive value, that is
| - a | = | a | = a
given
y = | x | + 5 ( substitute x = 12 into the equation )
y = | 12 | + 5 = 12 + 5 = 17
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $25 and same-day tickets cost
$40. For one performance, there were 40 tickets sold in all, and the total amount paid for them was $1225. How many tickets of
each type were sold?
(49 р 18 к + 7 р 82 к ) : 5
jelani is looking for a linear function that meets the following requirements: has a slope of -7,3 has an x intercept at (-9,0) passes through the point (6,-35)
The equation of the line that has a slope of -7/3, has an x intercept at (-9,0) passes through the point (6,-35) is y = (-7/3)x - 21
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard equation of a straight line is:
Ax + By = C
Where A, B and C are constants
The slope intercept form is:
y = mx + b
Where m is the rate of change and b is the y intercept
Given that the line has a slope of -7/3 has an x intercept at (-9,0) passes through the point (6,-35). Using the slope and y intercept:
y - y₁ = m(x - x₁)
y - 0 = (-7/3)(x - (-9))
y = (-7/3)x - 21
The equation of the line is y = (-7/3)x - 21
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what is the Greatest Common Factor of (48x^(2)-40x)/(56x)
Answer: the GCF of (48x^2 - 40x) / (56x) is 8x.
Step-by-step explanation:
To find the greatest common factor (GCF) of the expression (48x^2 - 40x) / (56x), we can use the following steps:
Factor the numerator: 48x^2 - 40x = 8x(6x - 5)
Identify the monomial that divides evenly into both the numerator and denominator: 8x
Divide out this monomial from both the numerator and denominator. This will simplify the fraction to (6x-5)/7
Therefore, the GCF of (48x^2 - 40x) / (56x) is 8x.
a population has µ = 30 and σ = 10. if 5 points are added to every score in the population, what are the new values for the mean and standard deviation?
If 5 points are added to every score in the population, then new values for mean is 35 and standard deviation is 10 .
If 5 points are added to every score in the population, the mean (µ) of the population will increase by 5 and the standard deviation (σ) will remain unchanged.
The new mean (µ') will be:
⇒ µ' = µ + 5 = 30 + 5 = 35
The new standard deviation (σ') will be:
⇒ σ' = σ = 10
Therefore , after adding 5 points to every score, the mean will be 35 and the standard deviation will remain 10.
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29 of the firt 42 preident of the United State were lawyer what percentage of thee preident were lawyer
To find the percentages of U.S. presidents who were lawyers, we can divide the number of presidents by the total number of presidents and then multiply by 100 to get the answer as a percentage.
Given the information, we have:
Number of presidents who were lawyers = 29
Total number of presidents = 42
So, the percentages of presidents who were lawyers is:
(29 / 42) * 100 = 69%
Therefore, 69% of the first 42 U.S. presidents were lawyers.
A percentage is a number or ratio expressed as a fraction of 100. It represents a portion of a whole and is often used to describe parts of a larger quantity in terms of 100. For example, if a student scored 80 out of 100 on a test, their score can be expressed as 80%, which means they answered 80 out of 100 questions correctly. The symbol for percentage is "%". To convert a fraction or decimal to a percentage, it is multiplied by 100.
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please help me with this and explain plss
Answer: x=-6 y=-8
Step-by-step explanation:
For 1st equation solve for x.
3x-2y=-2
3x=-2+2y
x=[tex]\frac{-2+2y}{3}[/tex]
Then plug in the x found in 1st equation into the 2nd equation.
-7x+6y=-6
-7[tex](\frac{-2+2y}{3})[/tex]+6y=-6
[tex]\frac{14-14y}{3}[/tex]+6y=-6
[tex]\frac{14}{3}[/tex] - [tex]\frac{14y}{3}[/tex] +6y=-6
[tex]\frac{4y}{3}[/tex]=-6-[tex]\frac{14}{3}[/tex]
[tex]\frac{4y}{3}[/tex]=[tex]\frac{-32}{3}[/tex]
4y=-32
y=-8
Then plug in the y value found in the 2nd equation into the 1st equation.
x=[tex]\frac{-2+2y}{3}[/tex]
x=[tex]\frac{-2+2(-8)}{3}[/tex]
x=[tex]\frac{-2-16}{3}[/tex]
x=[tex]\frac{-18}{3}[/tex]
x=-6
Answer:
x = -6 and y = -8
Step-by-step explanation:
These two simultaneous linear equations using elimination method:
For this method to be applied, the coefficients of ‘x’ or ‘y’ in the two equations need to be the same with opposite signs.
The coefficients of ‘x’ will be focused on:
(3x - 2y = -2) Multiplied by 7
(-7x + 6y = -6) Multiplied by 3
21x - 14y = -14
-21x + 18y = -18
In the net total, it can be observed that the two ‘x’ terms will completely cancel each other out:
4y = -32
[tex]y = -\frac{32}{4}[/tex]
y = -8
Substitute this value of y in any of the equations to determine the value of x:
3x - 2(-8) = -2
3x + 16 = -2
3x = -2 - 16
3x = -18
[tex]= x =- \frac{18}{3}[/tex]
x = -6
30/7 times t plus 9/14 if t equals 13/2
Answer:
[tex]\frac{77}{2}[/tex]
Step-by-step explanation:
[tex]\frac{30}{7} \cdot \frac{13}{2}+\frac{9}{14}=\frac{390}{14}+\frac{9}{14}=\frac{399}{14}=\frac{77}{2}[/tex]
1. Ben earns $6/h baby sitting. He is saving his earnings to buy an MP3 player that costs $360.
a) Write a relation to show how Ben's savings are related to the number of hours he baby sits.
-Ben earns $6/h
-Ben is saving to reach $360
360=total money/goal
6=money per hour
x=total number of hours
360=6x
x=60
Ben needs to work for 60 hours babysitting to earn $360 to but an MP3 player.
The interior angles of a pentagon (5 sides) are in the ratio 4:5:6:7:5. Find each angle of the polygon
Answer: The interior angles of the Pentagon are 80° , 100° , 120° , 140° and 100°.
Step-by-step explanation:
Let the angles of the Pentagon be 4x, 5x, 6x, 7x and 5x.
Let 'n' be the number of sides.
In a regular Pentagon, sum of interior angles = (2n - 4) × 90°
= ( 2 × 5 - 4) × 90°
= 6 × 90°
= 540°
Acc. to the ques.
=> 4x + 5x + 6x + 7x + 5x = 540°
=> 27x = 540°
=> x = 540° / 27
=> x = 20°
The interior angles of the given Pentagon -
1) 4x = 4 × 20° = 80°
2) 5x = 5 × 20° = 100°
3) 6x = 6 × 20° = 120°
4) 7x = 7 × 20° = 140°
5) 5x = 5 × 20° = 100°
I hope it helps
HELPP
What is the distance between point P and point Q?
Answer:
I believe the answer is 11 units
Step-by-step explanation:
as point P and Q are 11 horizontal units apart from each other.
square root of 400 pl solve fast
Answer:
20
Step-by-step explanation:
[tex]20^{2} = 400[/tex]
[tex]\sqrt{400} = 20[/tex]
Answer: The square root of 400 is 20.
Step-by-step explanation:
The square root of a number is the value that, when multiplied by itself, gives the original number. To find the square root of 400, you can use the long division method or an electronic calculator.
Alternatively, you can approximate the square root of 400 by finding the nearest perfect square (a number whose square root is a whole number). In this case, the perfect squares closest to 400 are 361 and 441. Since the square root of 361 is 19 and the square root of 441 is 21, you can estimate that the square root of 400 is between 19 and 21. Since 20 is halfway between 19 and 21, you can approximate the square root of 400 to be 20.
Help with this please!
Answer: 115°
Step-by-step explanation:
180° - 65° (angles on a straight line)
= 115° (alternate angle to z)
z = 115°
