Answer: Lets rewrite our equation.
x + y + kz - 5z =k
x + y -5z = k(1-z)
k = [tex]\frac{x + y - 5z}{1 - z}[/tex]
so the only problem with the equation is that z can't be equal to one.
but x and y are free, so you have two free variables and one equation,
that means that for any k the system has infinitely many solutions.
Final answer:
To determine the nature of solutions in a system of equations involving k, we can check the determinant of the coefficient matrix. If the determinant is not zero, there is a unique solution; if it is zero, there are infinitely many solutions; and if contradictory, the system is inconsistent.
Explanation:
For which value(s) of k does this system have a unique solution?
To have a unique solution, the determinant of the coefficients of the variables x, y, and z must not be zero.Therefore, for a unique solution, the determinant of the coefficient matrix must not equal zero.For which value(s) of k does the system have infinitely many solutions?
If the determinant of the coefficient matrix is zero, the system has infinitely many solutions.When the determinant is zero, it implies dependent equations, leading to infinite solutions.For which value(s) of k is the system inconsistent?
The system is inconsistent when the determinant is zero, and the system contains contradictory equations.When the determinant is zero and the equations are contradictory, the system is inconsistent.You are driving home from school steadily at 95 km/h for 180 km. It then begins to rain and you slow to 65 km/h. You arrive home after driving 4.5 h. (a) How far is your hometown from school? (b) What was your average speed?
Answer:
(a) 349.34
(b) 77.63 km/h
Step-by-step explanation:
Distance you covered before it rain S = 180 km
Speed v = 95/km
Time taken to cover 180 km = [tex]\frac{S}{v}[/tex]
= [tex]\frac{180}{95}[/tex]
= 1.89473 hrs.
Total time to cover the distance between school to home T = 4.5 hrs.
Remaining time t = T - t
= 4.5 - 1.89473
= 2.60527 h.
Velocity after travel 180 km. v' = 65 km/h
Distance traveled in this velocity S' = v'(t)
= 2.60527 × 65
= 169.34 km
(a) distance of hometown from school = 169.34 + 180 = 349.34 km.
(b) Your average speed V = [tex]\frac{S}{T}[/tex]
= [tex]\frac{349.34}{4.5}[/tex]
= 77.63 km/h
Square EFGH stretches vertically by a factor of 2.5 to create rectangle E′F′G′H′. The square stretches with respect to the x-axis. If point H is located at (-2, 0), what are the coordinates of H′ ? A. (-5, 0) B. (-2, 0) C. (0.5, 0) D. (-2, 2.5)
Answer:
The coordinates of point H' are (-2 , 0) ⇒ answer B
Step-by-step explanation:
* Lets revise the vertical stretch
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, then the graph of y = k • f(x) is the graph of f(x) vertically
stretched by multiplying each of its y-coordinates by k
* Lets solve the problem
- Square EFGH stretches vertically by a factor of 2.5 to create
rectangle E′F′G′H′
∴ k = 2.5
- The square stretches with respect to the x-axis
∴ The square stretches vertically
∴ The y-coordinates of each vertex of the square EFGH are
multiplied by 2.5 to get the vertices of the rectangle E'F'G'H'
∵ Point H located at (-2 , 0)
∵ The image of point (x , y) after stretched vertically by k is (x , ky)
∴ Point H' located at (-2 , 0 × 2.5) ⇒ (-2 , 0)
∴ The coordinates of point H' are (-2 , 0)
∴ Point H' located at (-2 , 0)
Answer:
B. (-2, 0)
Step-by-step explanation:
Please please help me out with this
Answer:
y = [tex]\frac{3}{4}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ( = (0, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line
m = [tex]\frac{5-2}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]
Note the line crosses the y- axis at (0, 2) ⇒ c = 2
y = [tex]\frac{3}{4}[/tex] x + 2 ← equation of line
A ball is dropped from a height of 600 feet. The height of the ball, H, after t seconds can be modeled by the function rule, ()=−4.92+600. What would be the independent quantity?
Answer:
the independent quantity is "t" (time in seconds)
Step-by-step explanation:
The problem statement tells you the function rule gives you H (the dependent quantity) as a function of t seconds. "t seconds" is the independent quantity.
19. While serving, the shuttlecock must land within JLMN, the service box. Find the probability that a shuttlecock will land in the service box, relative to the court. (JUSTIFY)
Answer:
HI! I'M TAKING THE TEST FOR IT! SO I HOPE THIS IS RIGHT! IF NOT, FORGIVE ME! SO THE ANSWER IS 25.094
Step-by-step explanation:
I attached the step by step, so look at it for me!
30 POINTS AND BRAINLIEST PLZ HELP
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.
A. 2
B. 3
C. 4
D. 5
Answer:
B. 3
Step-by-step explanation:
"k" represents the number of units of upward translation between f and g. Since g is translated 3 units upward from f, we must have k=3.
Graph f(x) = x2 + 2x - 3, label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry
The given function : [tex]f(x)=x^2+2x-3[/tex]
Using completing the squares, we have
[tex]f(x)=x^2+2x+1-1-3[/tex] [∵ [tex](x+1)^2=x^2+2x+1[/tex]]
[tex]f(x)=(x+1)^2-4[/tex] (1)
Comparing (1) to the standard vertex form [tex]f(x)=(x-h)^2+k[/tex] , the vertex of function is at (h,k)=(-1,-4)
For x-intercept, put f(x)=0 in (1), we get
[tex]0=(x+1)^2-4\\\\\Rightarrow\ (x+1)^2=4[/tex]
Square root on both sides, we get
[tex]x+1=\pm2\\\\x+1=-2\ or\ \ x+1=2\\\\=x=-3\ \ or\ x=1[/tex]
∴ x intercepts : x= (-3,0) and (1,0)
For y-intercept put x=0 in (1), we get
[tex]f(1)=(1)^2-4=1-4=-3[/tex]
∴ y intercept : (0,-3)
Axis of symmetry : [tex]\dfrac{-b}{2a}[/tex]
In [tex]f(x)=x^2+2x-3[/tex] , a=1 and b=2
Axis of symmetry=[tex]\dfrac{-2}{2(1)}=-1[/tex]
A graph of the quadratic equation [tex]f(x) = x^2 + 2x - 3[/tex] with its key features is shown on the coordinate plane in the image below.
What is the graph of a quadratic function?In Mathematics and Euclidean Geometry, the standard form of a quadratic function is represented by the following equation;
[tex]y = ax^2 + bx + c[/tex]
Where:
x and y represents the data points on the graph.a represents the leading coefficient.Since the leading coefficient (value of a) in the given quadratic function [tex]f(x) = x^2 + 2x - 3[/tex] is positive one (1), we can logically deduce that the parabola would open upward and the solutions are the x-intercepts. Furthermore, the key features of this quadratic function include the following;
The vertex is (-1, -4).The mininum value is equal to -4.The axis of symmetry is x = -1.x-intercepts: (-3, 0) and (1, 0)The parabola opens upward.The y-intercept is (0, -3).Read more on quadratic functions here: brainly.com/question/29499209
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Complete Question;
Graph [tex]f(x) = x^2 + 2x - 3[/tex], label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry
if (fx)=5x, what is f^-1(x)
Answer:
x/5
Step-by-step explanation:
To get the inverse function you need to leave the x alone and then switch variables ( f(x) = y)
f(x) = 5x
y = 5x
y/5 = x
Now that x is alone you switch the x for y and the y for x and you get:
x/5 = y
And this new y is the inverse function of f(x) ( f^-1(x))
f^-1(x) = x/5
Have to bake a lot of brownies to sell! You have plenty of flour, cocoa, milk, and oil, but you only have 6 1/2 sticks of butter. You need to know how many batches of brownies you can bake, based on your limited amount of butter. You can cook partial batches in order to use up every bit of butter, which will also help you to bake the most brownies possible. Each batch needs 3/4 of a stick of butter.
Answer: 8 + 2/3 batches of brownies you can bake.
Step-by-step explanation:
6 1/2 butter = 6 + 1/2 = (2·6 + 1)/2 = 13/2 sticks of butter, we have this
Since we have 13/2 sticks of butter and each batch of brownies needs 3/4 of a stick of butter, we have to divide the amount of butter we have between the amount of butter we use to bake a batch of brownies.
13/2 butter ÷ 3/4 butter/batch = 13·4/2·3 batches = 52/6 batches = 8 + 2/3 batches
Answer: 8 + 2/3 batches of brownies you can bake.
[tex]\textit{\textbf{Spymore}}[/tex]
By dividing the total amount of butter (13/2 sticks) by the amount required per batch (3/4 stick), we find that it's possible to make 8 full batches of brownies with 6 1/2 sticks of butter, with some butter left over.
To determine how many batches of brownies you can bake with 6 1/2 sticks of butter, you have to divide the total amount of butter you have by the amount required for one batch. Since each batch requires 3/4 stick of butter, you calculate as follows:
Total sticks of butter: 6 1/2
Required per batch: 3/4
Now convert 6 1/2 to an improper fraction: 6 1/2 = 13/2.
Next, calculate the number of batches by dividing the total butter by the butter per batch:
Number of batches = (13/2) / (3/4) = (13/2) * (4/3) = 52/6
When you simplify 52/6, you get 8 with a remainder, meaning you can make 8 full batches of brownies, and you will have some butter left over.
Which statement about the figure below is true?
B
they have limited (3) common points where the planes meet.
PLEASE HELP Use the rules of exponents to simplify the expressions. Place a final answer in fraction form. (-1/2)to the power of 3 *(-1/2) to the power of 2
Answer:
-1/32.
Step-by-step explanation:
(-1/2)^3 * (-1/2)^2
= -1/8 * 1/4
= -1/32.
Simplify: (7a − 9c) − (−12a − 33c) − (−21a + 10c)
Answer:
The answer is 40a+14c
Step-by-step explanation:
Step 1: Open the brackets
7a-9c+12a+33c+21a-10c
Step 2: Group all the like terms
Like terms are terms with similar variables, for example;
(7a, 12a, 21a) are all like terms since they have a common variable (a)
(-9c, 33c,-10c) are also like terms since they have a common variable (c)
Step 2: Solve
(7a+12a+21a)+(33c-10c-9c)=40a+14c
The answer is 40a+14c
Someone please help me
Answer:
14. 61.2 mi N, 49.8 mi W
15. 7.3 ft
Step-by-step explanation:
14. The components in the different directions are found using the sine and cosine functions. (Draw yourself a diagram to help see this.)
north distance = (78.9 mi)cos(39°10') ≈ 61.2 mi
west distance = (78.9 mi)sin(39°10') ≈ 49.8 mi
__
15. Let d represent the distance from the observation point to the door. Then ...
8.8 ft = d·tan(56°)
x = d·tan(51°)
Dividing the second of these equations by the first cancels d and gives ...
x/(8.8 ft) = tan(51°)/tan(56°)
Multiplying by 8.8 ft, we can find x:
x = (8.8 ft)(tan(51°)/tan(56°)) ≈ 7.3 ft
Suppose your state lottery has an expected value of
−34%.
If you spend $40 per month on lottery tickets, how much money would you be expected to lose in an average year?
We can expect to lose $
.
Final answer:
With an expected value of −34% for the state lottery and monthly spending of $40 on tickets, a person can expect to lose $13.60 monthly or $163.20 annually.
Explanation:
If the expected value of playing the state lottery is −34%, and a person spends $40 per month on lottery tickets, we can calculate the expected annual loss as follows:
Firstly, an expected value of −34% means that on average, for every dollar spent, you would expect to lose 34 cents. So for $40 spent in one month, the expected loss would be 34% of $40, which equals $13.60.
Next, we can find the expected loss for a year by multiplying the monthly loss by the number of months in a year:
Monthly expected loss: 0.34 × $40 = $13.60Annual expected loss: $13.60 × 12 months = $163.20Therefore, on average, you can expect to lose $163.20 per year if you continue spending $40 on lottery tickets every month.
A test consists of 10 true/false questions. To pass the test a student must answer at least 88 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Round to three decimal places.
Answer:
The probability that the student is going to pass the test is 0.0545
Step-by-step explanation:
The variable that says the number of correct questions follows a Binomial distribution, because there are n identical and independent events with a probability p of success and a probability 1-p of fail. So, the probability of get x questions correct is:
[tex]P(x)=\frac{n!}{x!(n-x)!} *p^{x} *(1-p)^{n-x}[/tex]
Where n is equal to 10 questions and p is the probability of get a correct answers, so p is equal to 1/2
Then, if the student pass the test with at least 8 questions correct, the probability P of that is:
P = P(8) + P(9) + P(10)
[tex]P=(\frac{10!}{8!(10-8)!}*0.5^{8}*(0.5)^{10-8})+(\frac{10!}{9!(10-9)!} *0.5^{9} *(0.5)^{10-9})+(\frac{10!}{10!(10-10)!} *0.5^{10} *(0.5)^{10-10})[/tex]
P = 0.0439 + 0.0097 + 0.0009
P = 0.0545
the following shows the result of a random survey about favorite seasons. you decide to display the information as a pie chart. what percentage would represent each season? round to the nearest tenth. show or explain your work.
Answer:
The answer is below
Step-by-step explanation:
Data
Winter = 234
Spring = 673
Summer = 843
Fall = 425
Total = 2175
Then
Winter 2175 ------------------------- 100%
234 ----------------------- x
x = 234(100)/2175 = 10.8 %
Spring 2175 ------------------------ 100%
673 ----------------------- x
x = 673(100)/2175 = 30.9 %
Summer 2175 ------------------------ 100%
843 ------------------------ x
x = 843(100) /2175 = 38.8 %
Fall 2175 ------------------------ 100%
425 ---------------------- x
x = 425(100)/2175 = 19.5%
Total = 10.8 + 30.9 + 38.8 + 19.5 = 100%
If you give siri 0 cookies and she has 0 cookies but then gives you back a cookie where did she get the cookie from? if You and her had 0 cookies ?
Answer:
Maybe she borrowed a cookie from somone? or maybe bought a cookie?
A wall has been built with two pieces of sheetrock, a smaller one and a larger one. The length of the smaller one is stored in the variable small. Similarly, the length of the larger one is stored in the variable large. Write a single expression whose value is the length of this wall.
Answer:
The answer is: small+large.
Step-by-step explanation:
If the variable of the smaller sheetrock is stored in small:
var small.
And the variable of the larger sheetrock is stored in large:
var large.
The length of the wall will be the sum of the two pieces of sheetrock:
small+largeFor example:
var small = 5;
var large = 10;
small+large = 5 + 10 = 15 is the length of the wall.
Final answer:
To calculate the total length of a wall made with two sheets of sheetrock, use the expression 'small + large'. The correct unit for measuring large objects like walls is often feet, and including units is essential for clarity in measurements.
Explanation:
The question asks for an expression to calculate the total length of a wall built with two pieces of sheetrock with lengths stored in the variables small and large. Since the total length of the wall will be the sum of the lengths of the two pieces of sheetrock, the expression you would write is small + large. This will give you the length of the entire wall when you substitute in the numerical values for the lengths represented by the two variables.
When measuring large objects like walls, the appropriate unit of measure is often feet, as inches would be too small and miles or kilometers would be excessively large. It's important to always include units in your measurements to avoid confusion and to ensure that the measurements are useful for practical applications, such as buying fabric or building materials.
I move east a distance of 4km, south a distance of 2 km, and then west a dostance of 1km. What is the cartesian cordinates relative to my starting point ?
Answer:
In x: 4-1=3
In y: -2
Cartesian coordinates: (3,-2)
Step-by-step explanation:
If we move horizontally we must consider only the x axis, if we move to east it is positive, and if we move to west it is negative.
f we move vertically we must consider only the y axis, if we move to north it is positive, and if we move to south it is negative.
What is the slope for 3x + 2y = 8
Answer:
[tex] -1 \frac{1}{2} = m[/tex]
Step-by-step explanation:
3x + 2y = 8
-3x - 3x
___________
2y = -3x + 8
___ _______
2 2
y = -1½x + 4
↑
rate of change [slope]
I am joyous to assist you anytime.
Sarah begins at a negative position along the x-axis. Sarah moves in the positive x-direction, turns around and then moves in the negative x-direction. Her final position is more negative that her initial position. Is the magnitude of Sarah's displacement greater than, less than, or equal to the distance she travels?
Answer:
he magnitude of Sarah's displacement is less than the distance she travels
Step-by-step explanation:
Hi!
The magnitude of her displacement is just the difference between her final and initial state, however the distance she traveled is two times the distance she moved in the positive x-direction until she turned around, since she had to move back, plus her displacement.
So:
[tex]displacement = |x_{final} -x_{initial}| \\distanceTraveled = 2|x_{return}-x_{initial}| + displacement\\[/tex]
Since all the terms are positive:
[tex]x_{displacement}<x_{traveled}[/tex]
The scale on a map of Virginia shows that 1 inch represents 15 miles. The actual distance from Richmond, VA, to Washington, D.C., is 110 miles. On the map, how many inches are between the two cities? Enter your answer as a mixed number with the fraction in simplest form.
The distance on the map is __ in.
Answer:
The answer to your question is: 7 1/3 inches
Step-by-step explanation:
Data
1 inch --------- 15 miles
Distance from Richmond to Washington = 110 miles
Use a rule of three to solve it
1 inch ----------------- 15 miles
x -------------------- 110 miles
x = 110x 1 /15
x = 110 / 15 simplify dividing by 5
x = 22/3
Convert it to a mix number
22/3 = 7 1/3 inches
Final answer:
On the map, 7.6 inches are between the two cities
Explanation:
To find out how many inches are between two cities on a map given the scale and the actual distance. The scale here is that 1 inch represents 15 miles. Therefore, for an actual distance of 110 miles, we simply divide the actual distance by the scale factor to obtain the distance on the map.
By setting up the proportion:
1 inch / 15 miles = x inches / 110 miles, we cross-multiply and solve for x,
which is the number of inches on the map. The calculation would be:
(1 inch / 15 miles) * 110 miles = 110 inches / 15 = 7 3/5 inches or 7.6 inches.
PLEASE HELP!!!
The area of a triangle is given by the
formula A = 1/2bh Solve this for h.
Answer:
h = [tex]\frac{2A}{b}[/tex]
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex] bh
Multiply both sides by 2 to clear the fraction
2A = bh ( isolate h by dividing both sides by b )
h = [tex]\frac{2A}{b}[/tex]
Answer: h = 2a/b
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! THIS IS THE LAST DAY TO COMPLETE THIS ASSIGNMENT AND I DESPERATELY NEED TO FINISH THIS ASSIGNMENT WITH AN 100%.
Answer: d. 75% of the screen is occupied by the image
Step-by-step explanation:
First we have to find a relation between image area and screen area.
Image area is the product of image dimensions.
Screen area is the product of screen dimensions.
We have to divide the major image dimension between the major screen dimension
Major image dim/Major screen dim = 20/5 = 4
Now we have to multiply this relation by the minor screen dimension
Minor screen dim x 4 = 4 x 4 = 16
Then we have found 5/4 = 20/16
Now we can calculate what percent of the screen area is occupied by the image area.
Major image dim x minor image dim/Major screen dim x minor screen dim
Since major image dim = major screen dim, we have:
Minor image dim/Minor screen dim = 12/16 = 0.75 = 75% of the screen
Answer: d. 75% of the screen is occupied by the image
[tex]\textit{\textbf{Spymore}}[/tex]
A vase contains 7 red flowers, 3 white flowers, and 5 yellow flowers. If George selects a flower from the vase for his wife, what is the probability that he will select a red one.
Answer:
The answer to your question is: P(A) = 0.47
Step-by-step explanation:
Data
7 red flowers
3 white flowers
5 yellow flowers
Probability that he select a red one
Formula
P(A) = Number of favorable cases of A / total number of outcomes
Number of favorable cases = 7
Total number of outcomes = 7 + 3 + 5 = 15
Substitution
P(A) = 7 / 15
P(A) = 0.47
Which word best completes this definition? Two lines are _____ if and only if they lie in the same plane and do not intersect. A parallel B perpendicular C bisectors D transversals
Answer:
Parallel
Step-by-step explanation:
All of the other answers give examples of lines that intersect at some point.
Answer:
transversal
Step-by-step explanation:
The line is called transversal. A transversal is a line which intersects two or more parallel lines
Jessica wants to buy a new team jacket that costs $35. If Jessica saves $5 a week for 4 weeks and $4 a week for 3 weeks, will she have enough money to buy the team jacket? Explain
No, Jessica he will not have enough to buy the jacket. She would have saved $32, not $35.
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.
Lets x represent the number of weeks it will take to save enough money. If she saves $11 each week, then in x weeks she will save 11x dollars.
Also, Add this to the 107 she has already saved, and at the end of 11 weeks she will have 11x + 107 dollars.
We want the amount saved to be equal to the price of the bike, so our equation;
11x + 107 = 173
Now we solve the equation.
Subtract 107 from both sides ;
11x = 66
Divide both sides by 11;
x = 6
No, Jessica he will not have enough to buy the jacket. She would have saved $32, not $35.
Learn more about equations here;
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Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 40 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 6 minutes?
Answer:
30 parts
Step-by-step explanation:
We are given that machine produces 100 parts twice as fast as machine B does.
Machine produces 100 parts in 40 minutes.
We have to find number of parts produces by machine A in 6 minutes.
According to question
Machine A takes time to produce 100 parts =[tex]\frac{40}{2}=20 minutes[/tex]
Machine A and machine B produces parts at constant rate.
Machine A produces parts at the rate=[tex]\frac{100}{20}=5 parts /minute[/tex]
In one minute,Machine A produces =5 parts
In 6 minutes , machine B produces =[tex]5\times 6=30[/tex] parts
Hence, machine A produce parts in 6 minutes=30
Order the function from the least steep slope to the steepest slope.
The functions ordered from the least steep slope to the steepest slope are: logarithmic (log(x)), linear (x), quadratic (x²), exponential (eˣ), and cubic (x³).
Explanation:To compare the steepness of the slopes for different types of functions, we consider the growth or decay rates of each function. The order is determined by the behavior of the functions as x increases.
1. Logarithmic function (log(x)): It grows slowly and approaches infinity as x increases, making it the least steep slope.
2. Linear function (x): It has a constant slope, making it steeper than logarithmic but less steep than quadratic, exponential, and cubic functions.
3. Quadratic function (x²): It increases faster than linear but slower than exponential and cubic functions.
4. Exponential function (eˣ): It grows at an increasing rate, making it steeper than quadratic but less steep than cubic.
5. Cubic function (x³): It has the steepest slope as x increases, making it the most rapidly increasing function.
This order is based on the general behavior of each function type and their rates of growth or decay. Understanding the characteristics of these functions helps in comparing and ordering them in terms of steepness.
Answer: here’s the correct answer
OMG HELP A GIRL OUT !!HELP ME PLEASE I NEED A 70%
1. Translate and solve: What number is 408% of 568? Round to the nearest hundredth.
2.In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the total percent decrease.
3.A cash box of $1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. How many of each bill does it contain?
4.Marquese is making 10 pounds of trail mix from raisins and nuts. Raisins cost $3.45 per pound, and nuts cost $7.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese use for the trail mix to cost him $6.96 per pound?
Answer:
#1. 408% of 568
We get two equations from this
408% = x
568 = 100%
568/x=100%/408%
Solve and you'll get
408% of 568
=2317.44
2. New - Original = % change
712500 - 950000 = -237500
3. 10 at $1, 7 at $5
4. 2.2 lb. of raisins, 7.8 lb. of nuts
As per the given conditions we have
1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).
2. Total decrease in percentage of the population of Detroit is equals to 25%.
3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.
What is equation?
" Equation is defined as the relation between the variables using sign of equality."
What is percentage?" Percentage is defined as the hundredth part of the given number."
According to the question,
1. 'x' represents the number
As per given condition,
x = 408% of 568
⇒ [tex]x= \frac{408}{100} (568)[/tex]
⇒ [tex]x = 2317.44[/tex]
Therefore, the number which is 408% of 568 is equals to 2317.44.
2. Total population of Detroit = 950,000
Population after 10 years = 712,500
Decrease in population = 950,000 - 712,500
= 237,500
Total percentage decrease in population = [tex]\frac{237500}{950,000}(100)[/tex]
= 25%
Therefore, total decrease in percentage of the population of Detroit is equals to 25%.
3. 'x' represents the bill of $1
'y' represents the bill of $5
As per the condition given equation we have,
$1x + $5y = $45 ______(1)
x = y + 3 ______(2)
Substitute the value of equation (2) in (1) we get,
[tex]1(y + 3) + 5y = 45\\\\\implies 6y = 45-3\\\\\implies y \frac{42}{6} \\\\\implies y = 7[/tex]
Substitute the value y in (2) we get,
[tex]x= 7 + 3\\\\\implies x =10[/tex]
Therefore , cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. 'x' represents the pounds of raisins
'10- x ' represents the pounds of nuts
Cost of trail mix from raisins and nuts per pound = $6.96
Therefore,
Cost of 10 pounds of trail mix of raisins and nuts = $(6.96 ×10)
= $69.6
Cost per pound of raisins = $3.45
Cost per pound of nuts = $7.95
Equation formed as per given condition we get,
[tex]3.45x + 7.95(10-x) = 69.6\\\\\implies 3.45x + 79.5 -7.95x = 69.6\\\\\implies -4.5x = 69.6 - 79.5\\\\\implies-4.5x= -9.9\\\\\implies x =\frac{9.9}{4.5}\\ \\\implies x = 2.2 pounds[/tex]
Pounds of raisins = 2.2pounds
Pounds of nuts = 10 - 2.2
= 7.8 pounds
Therefore, pounds of raisins is equals to 2.2 and pounds of nuts is equals to 7.8 for the trail mix.
Hence, As per the given conditions we have
1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).
2. Total decrease in percentage of the population of Detroit is equals to 25%.
3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.
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