A vegetable store sold 3 tons of vegetables less on the first day than on the second, and on the third day it sold 5/9 of the amount sold in the first two days. How many vegetables was the store selling every day if it sold altogether 98 tons of vegetables for the three days?
Answers
x---------> quantity (ton) of vegetables sold the first day
y---------> quantity (ton) of vegetables sold the second day
z---------> quantity (ton) of vegetables sold the third day
we know that
x=y-3---------> equation 1
z=(5/9)*(x+y)------> equation 2
x+y+z=98-----> equation 3
substitute equation 2 in equation 3
x+y+[(5/9)*(x+y)]=98----> multiply by 9----> 9x+9y+5x+5y=882
14x+14y=882-----> equation 4
to resolve the equations system formed by
x=y-3
14x+14y=882
using a graph tool
see the attached figure
the solution is
x=30
y=33
x+y+z=98----> z=98-(x+y)----> z=98-63---> 35
the answer is
vegetables sold the first day----> 30 ton
vegetables sold the second day----> 33 ton
vegetables sold the third day------> 35 ton
amount sold on first day = 30 tons
amount sold on second day = 33 tons
amount sold in third day = 35 tons
Explanation:
Assume that the amount of vegetables sold on the second day is x.
We are given that:
Amount of vegetables sold on the first day is 3 tons less that sold on the second day.
This means that:
amount sold on first day = x - 3
Amount of vegetables sold on the third day is 5/9 the amount sold on the first two days.
This means that:
amount sold on third day = (5/9) (x + x - 3)
amount sold on third day = [tex] \frac{10}{9} x - \frac{5}{3} [/tex]
Now, we know that:
Total amount sold is 98 tons.
This means that:
98 = x - 3 + x + [tex] \frac{10}{9} x - \frac{5}{3} [/tex]
Now, we will solve for x as follows:
98 = [tex] \frac{28}{9} x - \frac{14}{3} [/tex]
882 = 28x - 42
882 + 42 = 28x
924 = 28x
x = 924/28
x = 33 tons
This means that:
amount sold on first day = x - 3 = 33 - 3 = 30 tons
amount sold on second day = x = 33 tons
amount sold on third day = [tex] \frac{10}{9} x - \frac{5}{3} [/tex] = [tex] \frac{10}{9} (33) - \frac{5}{3} [/tex] = 35 tons
Hope this helps :)
Related Questions
please help asap 50 pts
Answers
The vertex is always the lowest or highest point:
When a parabola looks like a smiley face, it has a minimum (like this one).
When a parabola looks like a frowning face, it has a maximum.
The coordinate for the vertex is (-2, -3).
So, your answer is C.
Based on the information marked in the diagram, ABC and XYZ must be congruent.
Can somebody help ??
A. True
B. False
Answers
There isn't enough info. We have a pair of hypotenuses that are congruent (AB and XY) based on the single tickmarks they share together. Other than that, we don't know anything about any other pairs of sides. We know that angle C = angle Z because of the square angle markers (they're both 90 degrees), but we don't know anything else about the other angles. The triangles could be congruent, or they may not be. There's no way to tell without more information.
Answer: The answer i false
Step-by-step explanation:
The product of some negative number and 10 less than three times that number is 25. find the number.
Answers
n=2+1/3√111 or n=2+-1/3√111
I have a question about the application of definite integrals. I came up with the following integral:
[tex] \int\limits^5_0 {62.5 * 6 * 2 * x} \, dx [/tex]
This is equal to 9780. Unfortunately, 9780 ft-lb is not an answer, but 9375.0 ft-lb is! Can someone tell me what is wrong with my integral and if 9375.0 ft-lb is the answer to my question?
Answers
The volume of each slice is 6*2*DeltaX cubic feet. So the force pulling down on each slice is 62.5*6*2*DeltaX pounds as this is the weight of the slice.
The work done to move that slice x feet upward is 62.5*6*2*DeltaX*x or 62.5*6*2x*DeltaX as you wrote for your integrand.
Integrating with respect to x will effectively add up all the horizontal slices to get the total work done
See the attached image for the integral and steps leading to the answer of 9375
Which of the following sets of possible side lengths forms a right triangle? 12, 35, and 38 11, 60, and 61 9, 40, and 45 6, 12, and 13
Answers
11, 60, and 61
Let's check it using the Pythagorean theorem.
We have then:
ROOT ((a) ^ 2 + (b) ^ 2) = c
Where,
a = 11
b = 60
ROOT ((11) ^ 2 + (60) ^ 2) = 61
Answer:
11, 60, and 61
Answer:
11,60, and 61
Step-by-step explanation:
The sum of two numbers is 0.25. their quotient is 0.25. find the numbers.
Answers
[tex]n,\ m-the\ numbers\\\\n+m=0.25\qquad(*)\\\\n:m=0.25\to\dfrac{n}{m}=0.25\to n=0.25m\qquad(**)\\\\\text{Substitute}\ (**)\ \text{to}\ (*):\\\\0.25m+m=0.25\\\\1.25m=0.25\qquad\text{divide both sides by 1.25}\\\\\boxed{m=0.2}\\\\\text{Put the value of }\ m\ \text{to}\ (**):\\\\n=0.25(0.2)\\\\\boxed{n=0.05}\\\\Answer:\ \boxed{0.05\ and\ 0.2}[/tex]
A lion’s heart beats 12 times in 16 seconds.how many heartbeats will it have in 60 seconds?
Answers
Here is your answer:
The proper answer to this question is "44 times".
Reason:
You have to solve it this way:
12 heartbeats=16 seconds
16+16=32
36+16=48
48+16=64
16-12=4
12+12=36+8=44
Therefore lions heart beats 44 times every 60 seconds.
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
A town has a population of 13000 and grows at 4.5% every year. What will be the population after 13 years, to the nearest whole number?
Answers
y=13,000(1.045)^t
t=13
You get 1.045 because you add 1+ the percentage in decimal form.
Answer:
population after 13 years is around 23,039
Step-by-step explanation:
A town has a population of 13000 and grows at 4.5% every year.
Population growth is given by [tex]y=a(1+r)^t[/tex]
y is the population after t years
'a' is the initial population= 13000
'r' is the rate of growth=4.5%= 0.045
t is the number of years=13
[tex]y=a(1+r)^t[/tex]
[tex]y=13000(1+0.045)^13[/tex]
y=23,038.54
What is the value of x?
28
47
56
33
Answers
______________________________________________________
→ " x = 47 " .
______________________________________________________
Explanation:
______________________________________________________
Note: The "vertex" is "floating around" inside the circle.
Answer:
47
Step-by-step explanation:
A florist earns a profit of $2.00 on each bunch of carnations, $3.00 on each bunch of lilies and $1.00 on a bunch of roses. On a particular day, she sold 46 bunches of flowers and made a profit of $82.00. She sold twice as many bunches of roses as bunches of lilies.
Answers
jk its b. love yah
An alloy of copper is 10% copper and weighs 25 pounds. A second alloy is 18% copper. How much (to the nearest lb.) of the second alloy must be added to the first alloy to get a 13% mixture.
Answers
The measure of a squares side is 1.2 feet. What is the perimeter of the square in inches?
Answers
perimeter = 4 * 14.4 = 57.6 inches.
Megan consumed 3.5 gallons of water in one day. How many milliliters are equal to 3.5 gallons, if 1 liter equals 1,000 milliliters and 1 gallon = 3.785 liters?
Answers
There are 3,785 milliliters in one gallon.
Then, multiply that by 3.5 3,785 x 3.5 = 13,247.5
There are 13,247.5 ml in 3.5 gallons
Answer:
There are 13,247.5 ml in 3.5 gallon
Graph y ≥ (x + 2)2 Click on the graph until the correct graph appears.
Answers
The graph shows a parabola with a solid line and shading above or on the curve to represent the inequality [tex]y\geq (x+2)^{2}[/tex] This graph visually illustrates the solution set for the given inequality.
To graph the inequality [tex]y\geq (x+2)^{2}[/tex] we first need to plot the parabola [tex]y=(x+2)^{2}[/tex] with a solid line. The vertex of the parabola is at [tex](-2,0)[/tex] and it opens upwards.
Next, we shade all the regions above or on the parabola to represent the inequality [tex]y\geq (x+2)^{2}[/tex] Since the inequality includes "or equal to" [tex](\geq )[/tex] we use a solid line for the graph of the parabola.
By following these steps, we create a graph where the area above or on the parabola is shaded, indicating the solutions to the inequality [tex]y\geq (x+2)^{2}[/tex] his shading represents all the points.
where the y-values are greater than or equal to the corresponding y-values on the parabola. The solid line ensures that points on the parabola itself are included in the solution set.
In summary, the graph shows a parabola with a solid line and shading above or on the curve to represent the inequality [tex]y \geq (x+2)^{2}[/tex] This graph visually illustrates the solution set for the given inequality.
What is the probability of drawing five face cards?
Answers
Total number of face cards = 12
P( 5 face cards) = (12/52)(11/51)(10/50)(9/49)(8/48) = 33/108290
Answer: 33/108290
Martha states that –6 is a rational number. Which is a correct explanation for this statement?
The number –6 is the opposite of 6.
The number –6 is a negative integer.
The number –6 can be written as -6/1
The number –6 is less than 0.
Answers
Martha's statement saying - 6 is a rational number is correct as - 6 can be written as - 6/1.
What are rational numbers?Rational numbers consist of fractions and integers.
Any rational number can be written in the form of p/q, where q ≠ 0.
Any integer can be written in the form of a rational number p/q, where q ≠ 0 and q = 1.
Given, Martha states that - 6 is a rational number.
First, it is a negative integer but it can be written in the form - 6/1 as - 6/1 is equal to 6.
learn more about rational numbers here :
https://brainly.com/question/1310146
#SPJ6
Martha is correct in stating that -6 is a rational number because it can be written as -6/1.
Explanation:Martha is correct in stating that -6 is a rational number because it can be written as -6/1. A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers. In this case, -6 can be written as the fraction -6/1.
will give brainiest if correct
A. 69.1
B. 20.9
C. 22.4
D. 67.6
Answers
sin A/ a = sinB/ b
where A = C or 90 degrees; a = 21
B = ? , b = 8
solving for b;
sin(90) / 21 = sin(B) / 8 ; B = 22.39 degrees
Total angle of triangle = 180
180 - 90 - 22.39 = x
x = 67.607 degrees
The Bright Star Video Club offers the two membership plans described below.
Plan A: $50 yearly membership fee and $2 for each video rental
Plan B: $10 yearly membership fee and $4 for each video rental
Greg is planning to enroll in one of these plans. For how many video rentals would the total cost of Plan A be equal to the total cost of Plan B?
A. 50
B. 20
C. 30
D. 40
Answers
Plan A: y = 2x + 50
Plan B: y = 4x + 10
2x + 50 = 4x + 10
Now solve the combined equation.
2x + 50 = 4x + 10
- 10 - 10
2x + 40 = 4x
-2x -2x
40 = 2x
x = 20
Plan A: y=2x+50
Plan B: y=4x+10
and see where they intersect, and that will give you the answer.
OR
You can substitute each answer for x, like this,
A. 50
Plan A:
y=2(50)+50
y=100+50
y=150
Plan B:
y=4x+10
y=4(50)+10
y=200+10
y=210
So, therefore, A.50 is not the answer.
B.20
Plan A:
y=2x+50
y=2(20)+50
y=40+50
y=90
Plan B:
y=4x+10
y=4(20)+10
y=80+10
y=90
So, B.20 is correct but always check the rest of the answers. Just in case
C.30
Plan A:
y=2x+50
y=2(30)+50
y=60+50
y=110
Plan B:
y=4x+10
y=4(30)+10
y=120+10
y=130
So, C.30 is incorrect.
D.40
Plan A:
y=2x+50
y=2(40)+50
y=80+50
y=130
Plan B:
y=4x+10
y=4(40)+10
y=160+10
y=170
So, in conclusion the correct answer is B.20.
simplify 15r+7r+9r-7s
Answers
12r + 2r
14r
_____________________
12r + 2r = simplified
answer is 14r
______________________
Hope this helps,
QueenBeauty666
Maria is traveling for business. She starts by traveling from Mexico City to Singapore which is about 1.26 x 104 miles. She then travels from Singapore to New York which is approximately 9.53 x 103 miles. What is the total distance that Maria traveled?
Answers
1.26 x 104 = 131.04
9.53 x 103 = 981.59
131.04 + 981.59 = 1112.63
Hope this helps :)
Answer:
D
2.213 x 10^4 miles
Step-by-step explanation:
Took the test
A climber is standing at the top of Mount Kazbek, approximately 3.1 miles above sea level. The radius of the Earth is 3959 miles. What is the climber's distance to the horizon?
Answers
The radius of the earth = OC = OB = 3959 miles
Peak of the Mount Kazbek = A = 3.1 miles
OA = OC + CA
OA = 3959 + 3.1 = 3962.1 miles
As OBA is a right triangle,
[tex] OA^{2} [/tex] = [tex] OB^{2} [/tex] + [tex] AB^{2} [/tex]
[tex] 3962.1^{2} [/tex] = [tex] 3959^{2} [/tex] + [tex] AB^{2} [/tex]
15698236.41 = 15673681 + [tex] AB^{2} [/tex]
[tex] AB^{2} [/tex] = 15698236.41 - 15673681
[tex] AB^{2} [/tex] =24555.41
AB = 156.701659
climber's distance to the horizon is 156.7 miles
K(x)=10x+5 inverse function
Answers
The inverse of the function is k(x) = [tex] \frac{x - 5}{10} [/tex]
You can find the inverse of any function by switching the k(x) value and the x value. After that, solve for the new k(x). The result will be your inverse function. The step-by-step process is below.
k(x) = 10x + 5 ----> Switch the x and k(x)
x = 10k(x) + 5 ----> Subtract 5 from both sides
x - 5 = 10k(x) ----> Divide both sides by 10.
[tex] \frac{x - 5}{10} [/tex] = k(x) ----> Now switch the order for formatting
k(x) = [tex] \frac{x - 5}{10} [/tex]
And this is your new inverse function.
A number cube numbered from 1 to 6 is rolled. what is the probability of the number cube showing a 5 or an even number?
Answers
a bag contains 7 red marbles 6 green marbles 5 yellow marbles and 2 orange. marbles are drawn twice with a replacement. what is p {yellow and green?
a coin is tossed and a number cube is rolled. what is p{h, then prime number?
letter tiles that spell the word happiness are replaced in a bag. a tile is drawn and then a second tile is drawn. find p then vowel p?
Answers
[tex]226[/tex]
Question 1:
We have been given that a bag contains 7 red marbles, 6 green marbles, 5 yellow marbles, and 2 orange. Further we are given that marbles are drawn twice with a replacement. We need to figure out the probability P(Yellow and Green).
Basically, we need to determine the probability that first marble drawn is yellow and second marble drawn is green.
Probability of first marble drawn being yellow is [tex]\frac{5}{20}=\frac{1}{4}[/tex] and probability of second marble drawn being green is [tex]\frac{6}{20}=\frac{3}{10}[/tex].
Therefore, the probability P(Yellow and Green) = [tex]\frac{1}{4}\cdot \frac{3}{10}=\frac{3}{40}[/tex].
Question 2:
We have been given that a coin is tossed and a number cube is rolled and we need to find the probability P(H, prime number).
Probability of getting head on the coin is [tex]\frac{1}{2}[/tex].
Probability of getting a prime number on the cube is [tex]\frac{3}{6}=\frac{1}{2}[/tex].
Therefore, probability P(H, prime number) = [tex]\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}[/tex]
If area of a circle measures 16/25 pi cm square, what is the circumference of the circle in terms of pi
Answers
(16/25)*pi = pi*r^2
16/25 = r^2
rt(16/25) = r
r = 4/5
C = 2pi*r
C = 2pi*(4/5)
C = (8/5) pi cm
Daniel is setting up rows for a concert. He decides to put 9 chairs in each row. There are 45 chairs. Let x represent the number of rows of chairs. Which equation can be used to find the number of rows of chairs Daniel needs to set up?
Answers
*divide 45 by 9 which is 5
x=5
hope this helps!
Simplify the function f(x)= 1/2 (27) 2x/3. Then determine the key aspects of the function
Answers
[tex]f(x)= \frac{1}{2}(27)^{ \frac{2x}{3} } \\ \\ f(x)= \frac{1}{2}((27)^{ \frac{2}{3} })^{x} \\ \\ f(x)= \frac{1}{2}(9)^{x} [/tex]
From the above equation, we can answer all the 4 questions.
a) Initial value occurs when x = 0
So,
[tex]f(0)= \frac{1}{2}(9)^{0}= \frac{1}{2} [/tex]
So, the Initial value of the function is 1/2.
b) Simplified Base:
The base of an exponential function is the term which contains the exponent.
From the simplified equation, we can see that the base has been simplified and is equal to 9.
So, the simplified base is 9
c) Domain:
From the equation we can see that there is no such value which makes the function undefined. So all reall numbers are included in the Domain.
So, Domain is Set of All real numbers.
In Interval notation this can be expressed as: (-∞,∞)
d) Range:
Range is the set of all y values that a function can take. Since the graph is not shifted vertically up or down, the range will be the set of all real numbers greater than zero.
So, Range is equal to All real numbers greater than 0.
In Interval notation, this can be expressed as (0,∞)
Answer:
The last one is y>0
A coin is unbalanced such that it comes up tails 55% of the time.
a.what is the probability that you don't flip a head until the fourth flip?
b.what is the probability that you don't flip a tail until the fourth flip?
c.how many tosses would it take, on average, to flip a head?
d.how many tosses would it take, on average, to flip a tail?
Answers
b. P[HHHT] = .45^4*.55 = .0226
c. 1/.45 = 2.222
d. 1/.55 = 1.818
The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions of the rectangle.
Answers
Answer:
length = 9 kilometres
Width = 12 kilometres
Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.
Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.
The area of a rectangle can be found by using the formula:
A = width × length
Plug in the data from the formula
A = x (2x - 6).
Simplify using rainbow technique.
[tex]x(2x - 6) = 2 {x}^{2} - 6x[/tex]
Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.
[tex]2 {x}^{2} - 6x = 108[/tex]
Subtract 108
[tex]2 {x}^{2} - 6x - 108 = 0[/tex]
Divide by 2.
[tex] {x}^{2} - 3x - 54[/tex]
[tex](x - 9)(x + 6) = 0[/tex]
Rule AB = 0, gives A is 0 or B is 0.
[tex]x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6[/tex]
The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).
Length
[tex]x = 9[/tex]
Width
[tex]2x - 6 = 2 \times 9- 6 = 18 - 6 = 12[/tex]
Answer:
length = 9 kilometres
Width = 12 kilometres
~ Hope this helps you!
F(x)=5x^3-2x^2-3x Polynomial factoring