The inequality to model this situation is given by x>60 .
Inequality is defined as the relationship between a variable and a constant or two variables which can be written in the form of an equation using the notations < , > , ≤ or ≥ .
Let us consider the number of bags of lettuce bought be x.
Therefore amount needed to buy x bags from Val's veggies is :
250 + 1.5 x
And the amount needed to buy x bags from Sally's Salads is :
100 + 4 x
Now it is given that Val's Veggies need to be cheaper than Sally 's.
a) Therefore we will write an inequality and solve it for x:
∴ 250 + 1.5 x < 100 + 4 x
moving the variables and constants together
or, 1.5 x - 4 x < 100 - 250
or, - 2.5x < -150
or, x > 60
b) Therefore from the inequality we can conclude more than 60 bags of lettuce needs to be purchased for Val's cost to be cheaper.
c) Set notation: {x ∈ Z | x>60}
interval notation : x∈(60.∞)
Therefore from the inequality , the number of bags to be purchased must be more than 60.
To learn more about inequality visit:
https://brainly.com/question/20383699
#SPJ1
Identify a pattern and find the next three terms in the pattern.
-4,-3,-2,-1, . . .
Pattern of the given terms -4,-3,-2,-1, . . is arithmetic progression and common difference 'd' = 1 , next three terms are 0, 1,2
As given,
Given pattern is -4,-3,-2,-1, . . .
a₁ =-4
a₂ =-3
a₃ =-2 ….
d =a₂ - a₁
=-3 - (-4)
=1
Pattern is arithmetic progression with d=1.
aₙ =a₁ + (n-1)d
a₅ =a₁ + (5-1)d
=-4 +4(1)
=0
a₆ =-4 + 5(1)
=1
a₇ =-4 +6(1)
=2
Therefore, pattern of the given terms -4,-3,-2,-1, . . is arithmetic progression and common difference 'd' = 1 , next three terms are 0, 1,2
Learn more about patterns here
brainly.com/question/14720576
#SPJ4
.
Solve for x to the nearest tenth HELP
The value of x is 4.89 ≈ 5 units
Given,
The figure includes two right angled triangles.
Consider the first right angled triangle:
Hypotenuse = 7 units
Base = 3 units
Altitude = a
By using Pythagorean theorem, we can find a.
That is,
Hypotenuse² = Altitude² + Base²
7² = a² + 3²
49 = a² + 9
a² = 49 - 9
a² = 40
Altitude = [tex]\sqrt{40}[/tex] units
Now consider second right angled triangle:
Hypotenuse = [tex]\sqrt{40}[/tex] units
Altitude = 4 units
Base = x units
Apply Pythagorean theorem:
Hypotenuse² = Altitude² + Base²
([tex]\sqrt{40}[/tex])² = 4² + x²
40 = 16 + x²
x² = 40 - 16
x² = 24
x = [tex]\sqrt{24}[/tex]
Base, x = 4.89 ≈ 5 units.
Therefore, the value of x is 4.89 which is approximately equals to 5 units.
Learn more about Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ1
The man in the video spent 9 minutes and 2 seconds to fill his bathtub before taking a bath. After taking the bath, his partner told him that taking a bath was wasting water, and he should shower instead.
Question: How long would he need to run the shower to use the same amount of water as the bath that he took?
Please respond in one clear, succinct paragraph. Be sure to clearly state your final answer and include all of your mathematical reasoning that led you to your final answer. You will be graded on how accurate your final answer is and how clearly you were able to explain your answer. Make sure you write in complete sentences with proper writing conventions (i.e. grammar, punctuation, spelling).
Answer:
he will take the same time as its the same flow of water so he will spend 9 min and 2 sec
two numbers to multiply to get -120
Answer:
-60 x 2= -120
Step-by-step explanation:
Answer:
-40 * 3
Step-by-step explanation:
Just one example of many
A stereo player is pricer at $1320 plus value added tax at 15% how much does the stereo player actually cost
Answer:
$1518
Step-by-step explanation:
Take the 1320 and multiply it by 0.15 (15% as a decimal) to get 198
Then add the 198 to the 1320 to get 1518
What are the multiplication facts for 5? pls help marking brainly
Answer:
it is as follows:
5x2=10
5x3=15
5x4=20
5x5=25
5x6=30
5x7=35
5x8=40
5x9=45
Step-by-step explanation:
Answer: 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150
Step-by-step explanation:
Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Based on the time that Rex walked and the time that Samir walked, we can say that Samir walked TWO times as many hours as Rex walked.
How many times more did Samir walk?To find out how many times more Samir walked than Rex, divide the number of hours walked by Samir by the hours walked by Rex.
Solving gives:
= 3¹/₃ ÷ 1²/₃
= 10/ 3 ÷ 5/3
= 10/3 x 3/5
= 30/ 15
= 2 times more
In conclusion, Samir walked two times more.
Find out more on comparisons at https://brainly.com/question/25173515
#SPJ1
Answer:
Step-by-step explanation:
Based on the time that Rex walked and the time that Samir walked, we can say that Samir walked TWO times as many hours as Rex walked.
How many times more did Samir walk?
To find out how many times more Samir walked than Rex, divide the number of hours walked by Samir by the hours walked by Rex.
Solving gives:
= 3¹/₃ ÷ 1²/₃
= 10/ 3 ÷ 5/3
= 10/3 x 3/5
= 30/ 15
= 2 times more
In conclusion, Samir walked two times more.
Type the integer that makes the following addition sentence true:
_____+ –3 = –4
The integer that makes the expression, (____ + -3 = -4), true is -1.
According to the question,
We have the following expression:
__ + (-3) = -4
Now, let's take the integer to be filled in the blank as x.
Now, putting x in the given expression:
x + (-3) = -4
x = -4+3 (3 was negative on the left hand side. So, it is positive on the right hand side.)
x = -1
(More to know: when two numbers are given with two different signs then the smaller number is subtracted from the larger number but the sign remains of the number which is larger.)
Hence, the integer that makes the given addition sentence true is -1.
To know more about integer here
https://brainly.com/question/15276410
#SPJ1
Some people think that the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, resembles a golf ball. The building is a sphere measuring 165 feet in diameter. A typical golf ball has a diameter of approximately 1.5 inches.
a. Find the volume of Spaceship Earth to the nearest cubic foot.
The Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, a sphere building measuring 165 feet in diameter, has a volume of 2,352,071 cubic feet.
Volume refers to the amount of space occupied by a three-dimensional object.
Based on the problem, the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida is a sphere building measuring 165 feet in diameter. If radius is half of the diameter, then it has a radius of 82.5 feet.
The volume of the Spaceship Earth geosphere can be calculated using the formula for the volume of a sphere given by:
V = 4/3 π r^3
V = 4/3 π (82.5 feet)^3
V = 4/3 π (561,5151.625 cubic feet)
V = 2,352,071.15 cubic feet
Rounding off to the nearest cubic foot,
V = 2,352,071 cubic feet
To learn more about volume of sphere: brainly.com/question/22807400
#SPJ4
Leroy won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Leroy
a bucket of fish to divide evenly among 5 dolphins. Each dolphin gets 4 fish.
Which equation can you use to find the number of fish f in the bucket before Leroy feeds the
dolphins?
F/5=4
5f=4
F-5=4
F+5=4
Answer:
A. F/5 = 4
Step-by-step explanation:
F is the total of fish so F is divided by the total of dolphins, which is 5
so F/5 = 4
Answer:
F/5=4
Step-by-step explanation:
F is the total amount of fish. Since there are 5 dolphins to feed, you should divide F by 5.
Determine if the conjecture is valid by the law of detachment. given: if tommy made enchiladas tonight, then tommy must have an oven. tommy has an oven. conjecture: tommy made enchiladas tonight.
By determining the conjecture is not valid by the law of detachment.
A statement in mathematics that has not been formally proven is referred to as a conjecture. Observing a pattern that holds true in numerous instances leads to conjectures. But just because a pattern appears frequently, it does not imply that it will appear frequently in all instances. The mathematical observation cannot be fully accepted unless conjectures are proven. A conjecture becomes a theorem if it has been thoroughly proven.
Hypothesis: Tommy makes cookies tonight.
Conclusion: Tommy must have an oven.
Even though the stated statement, "Tommy has an oven," matches the conclusion, the hypothesis is not always true. Tommy might own an oven, but he could bake something other than cookies in it.
Hence, the hypothesis is unfounded.
To learn more about Conjecture, visit:
brainly.com/question/14928435
#SPJ1
PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
also show regular work
pls i need help
Answer:
Step-by-step explanation:
3
2
−
2
3
y+
3
1
y+4=0
Combine −
2
3
y and
3
1
y to get −
6
7
y.
3
2
−
6
7
y+4=0
Convert 4 to fraction
3
12
.
3
2
−
6
7
y+
3
12
=0
Since
3
2
and
3
12
have the same denominator, add them by adding their numerators.
3
2+12
−
6
7
y=0
Add 2 and 12 to get 14.
3
14
−
6
7
y=0
Subtract
3
14
from both sides. Anything subtracted from zero gives its negation.
−
6
7
y=−
3
14
Multiply both sides by −
7
6
, the reciprocal of −
6
7
.
y=−
3
14
(−
7
6
)
Multiply −
3
14
times −
7
6
by multiplying numerator times numerator and denominator times denominator.
y=
3×7
−14(−6)
Do the multiplications in the fraction
3×7
−14(−6)
.
y=
21
84
Divide 84 by 21 to get 4.
y=4
find the L in the cone.
We can use the pythagorean theorem to answer this question.
We know that [tex]l[/tex] is the hypotenuse, and the 2 sides are 7 and 7.
So, we can build the equation:
[tex]7^2+7^2 = l^2[/tex]
[tex]98 = l^2[/tex]
[tex]\sqrt{98} = l[/tex]
Convert 55°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C = (F-32)
9
F-C+32
=
Answer:
search up
Step-by-step explanation:
A
A honeybee queen can lay 2.5 × 103 eggs per day. An army ant queen can lay up to 300,000 eggs per day. How many times more eggs can an army ant queen lay?
Answer:
An army ant queen can lay 299,742 more eggs
The army ant queen will lay 120 times more eggs than the honeybee queen.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a honeybee queen can lay 2.5 × 103 eggs per day. An army ant queen can lay up to 300,000 eggs per day.
The ratio will be calculated as,
Army ant/honeybee queen = 300,000 / (2.5 x 10³)
Army ant/honeybee queen = 300,000 / 2500
Army ant = 120 x ( honeybee queen )
Therefore, the army ant queen will lay 120 times more eggs than the honeybee queen.
To know more about an expression follow
https://brainly.com/question/11791008
#SPJ2
Work out the mean of these numbers 2 √18 √50 Give your answer in the form a√2 where a is an integer.
answer in the form a√2 where a is an integer. √18 √50= 4 root 2
Solution:
Mean
Mean is one of the important and most commonly used measures of central tendency. There are several types of means in mathematics. In statistics, the mean for a given set of observations is equal to the sum of all the values of a collection of data divided by the total number of values in the data. In other words, we can simply add all the values in a data set and divide it by the total number of values to calculate the mean. However, the general method and formulas vary depending upon the type of data given, grouped data, or ungrouped data.
Grouped data is the data set formed by aggregating individual observations of a variable into different groups, while ungrouped data is a random set of observations
Observation :
An observation is a fact or figure we collect about a given variable. It can be expressed as a number or as a quality. An example of a number is the observation "25" for the age of a mother at the birth of her first child.
Using mean formula
Mean = {Sum of Observation} ÷ {Total numbers of Observations}
= [tex]\sqrt{18} +\sqrt{50}[/tex]
=[tex]3\sqrt{2} + 5\sqrt{2}\\ = 5\sqrt{2}[/tex]
sum of observation is 8[tex]\sqrt{2}[/tex]
total number of observation = 2
[tex]8\sqrt{2} /2\\=4\sqrt{2}[/tex]
Answer in the form a√2 where a is an integer. = 4 [tex]\sqrt{2}[/tex]
More details : brainly.com/question/521501
#SPJ9
ans = [tex]4\sqrt{2}[/tex]
Physical science
If a car travels 625 meters 15 seconds, how fast is it going?
There are 4 white and 8 red roses in bouquet. Find the ratios.
Answer:
4/12
Step-by-step explanation:
If the ratio 4:8 is a part-to-part ratio, it means that there are 4 of something and 8 of something else with a total of 12. To convert a part-to-part ratio such as 4:8 as a fraction, you make the left side of the colon the numerator and the total the denominator: 4:8 → 4/12
What is 5/9 + 2/3 ? I need to show all my work
Answer:
1.2
Step-by-step explanation:
Answer:[tex]2/3+5/9= \frac{2x3}{3x3} + 5/9 =6/9 +5/9+\frac{6+5}{9} = 11/9[/tex]
Step-by-step explanation: answer : 11/9
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 9 = 27. In the following intermediate step, it cannot further simplify the fraction result by canceling.In other words - two thirds plus five ninths is eleven ninths.Hope this helps u ; )
-5+9-4-(-4)+(-9)-12+7
Answer:
Step-by-step explanation:
if you multiply a negative number with another negative number, it will be positive: ( - ) x ( - ) = ( + )
and if you multiply a negative number with a positive number, it will be negative: ( - ) x ( + ) = ( - )
so -(-4) = 4 and +(-9) = -9
-5+9-4+4-9-12+7=-10
I hope this helps
Let g(x)=-x^2+6x+2. Find and simplify g(-3)
Helpppp
|x+3| horizontail stretch by a factor of 4
g(x) = |14x + 3| is a function whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.
How do we find the function that was used to create the graph?A graph contains information about which input corresponds to which output.An examination of this leads to the relationships that were used to create it.If a function's graph rises after a certain value of x, the function must have an increased output for inputs greater than that value of x.If we know that the function crosses the x axis at some point, we can use those as polynomial roots for some functions.So, we must write a function g whose graph represents a horizontal stretch of f(x)=|x+3| by a factor of 4.
f(x) = |x+3|Now perform horizontal stretch 4:
g(x) = |¼x + 3|Therefore, g(x) = |14x + 3| is a function whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.
Know more about functions here:
https://brainly.com/question/25638609
#SPJ9
The correct question is given below:
Write a function g whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.
g(x)=
A
Write an equation and solve the scenario
4) The sum of three consecutive even
numbers is 42. What is the smallest of
these numbers?
Step-by-step explanation:
Combine like terms on the right side,
42= 3x+6.
Subtract 6 from each side
36=3x
Divide each side by 3
x=12, which is our lowest integer.
The next two integers we find with 12+2=14 and 12+4=16. Or just simply take the next two even integers. Thus, 12+14+16=42.
Hope this helps.
The art club raised $248 through fundraisers. then they spent $206 to set up an art show. they raised another $316 at the art show. how much money did the art club have after the show?
Using basic mathematical operations such as addition and subtraction, the art club have $358 after the show.
Basic mathematical operations includes addition, subtraction, multiplication, and division.
Addition is combining two or more values to come up with a total or sum. On the other hand, subtraction, the opposite of addition, is removing a value from another resulting to their difference.
If the art club raised $248 through fundraisers, spent $206 to set up an art show, and raised another $316 at the art show, adding the total amount they raised and subtracting the amount they have spent, we can solve how much money they have after the show.
$248 - $206 + $316 = $358
Learn more about basic mathematical operations here: https://brainly.com/question/4721701
#SPJ4
HELPP I WILL MSRK YOU BRAINLIST…
Answer:
< - 9, 11 >
Step-by-step explanation:
consider the end points of the vector
(5, - 2 ) and (- 4, 9 )
x- direction is then - 4 - 5 = - 9
y- direction is 9 - (- 2) = 9 + 2 = 11
then vector in component form is < - 9, 11 >
The profit from selling local ballet tickets depends on the ticket price. Using past receipts, the ballet company determines that the profit can be modeled by the function p = -15x2 + 600x + 60, where x is the price of each ticket. A) What unit price x should be charged to maximize revenue? B) what is the maximum revenue? C) between what two prices is a profit made?
A) x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.
B) The maximum revenue is 6060 dollars.
C) Two prices between which a profit is made are $19 and $21.
What are quadratic functions?f(x) = ax² + bx + c, where a, b, and c are numbers and are not equal to zero, is a quadratic function.A parabola is the shape of a quadratic function's graph.The graph's vertex, which is an extreme point, is one of its key characteristics. The vertex, or lowest point on the graph or minimal value of the quadratic function, is where the parabola will open up. The vertex is the highest point on the graph or, if the parabola opens downward, the maximum value.Given:
profit function P(x)= -15x² + 600x + 60
The value of a is -15, which is negative, so the graph is opening downwards.
The graph of the function is a parabola and it opens downward therefore it has a maximum point. The formula used to find the vertex of the parabola f(x) is given by
x-coordinate of the vertex = -b/2a
y-coordinate of the vertex = f(-b/2a)
We have the x-coordinate of the parabola as:
⇒ -600 / 2(-15)
⇒ -600/-30 = 20
A) x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.
B) y-coordinate of the vertex is given by
f(20) = -15(20)² + 600(20) + 60
= 6060
The maximum revenue is 6060 dollars.
C) f(21) = -15(21)² + 600(21) + 60
= 6045
f(19) = -15(19)² + 600(19) + 60
= 6045
at $21, the profit is $6045
at $19, the profit is $6045
Two prices between which a profit is made are $19 and $21.
To learn more about Quadratic functions visit:
https://brainly.com/question/15434489
#SPJ9
Find the position function x(t) of a moving particle with the given acceleration a(t) a(t)=3t
The position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.
The position is the object can depend on where you are, and the description might also change if it is based on where other objects are.
The velocity is the time rate of change of position of a body in a specified direction. the rate of speed with which something happens.
Acceleration is the act or process of moving faster or happening more quickly: the act or process of accelerating rapid acceleration is the acceleration of economic growth.
a(t) = 3t
d^2/dx^2=(3t)
x(t) = [tex]\int\limits {3t} \, dt[/tex]
= 3 *t^2 / 2
Hence the position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.
For more information on acceleration click on the link below:
https://brainly.com/question/17114771
#SPJ4
How to solve? I tried but I found no answers.
Answer:
x=1
Step-by-step explanation:
Perimeter of the square is 4 times the side = 4*(4x-1)
Perimeter of Rectangle = 2 L + 2 W = 2*(2x+2) + 2*2x
4*(4x-1) = 2*(2x+2) +4x
16x-4= 4x+4+4x
16x-4 = 8x+4
16x-8x = 4+4
8x = 8
x = 8/8
x=1
Hope this helps!^^
2.For each of these cylinders dimensions find:
i. the volume
ii. the curved surface area
Give your answers in terms of π.
A. Base radius 3cm and height 8cm.
B. Base diameter 8cm and height 7cm.
5. A cylinder container is 65 cm in diameter. Water is poured into the container until it is 1 m deep.
how much water is in the container? Give your answer in litres.
2. For the given cylinders, we have that:
A. The volume is of 72π cm³ and the curved surface area is of 48π cm².
B. The volume is of 112π cm³ and the curved surface area is of 56π cm².
5. There are 330 liters of water in the container.
What is the volume of a cylinder?
The volume of a cylinder of radius r and height h is given as follows:
V = πr²h.
What is the curved surface area of a cylinder?
The curved surface area of a cylinder of radius r and height h is given as follows:
S = 2πrh.
For problem 2 item a, we have that the parameters are given as follows:
r = 3, h = 8.
Hence:
V = πr²h = 72π.S = 2πrh = 48π.The volume is of 72π cm³ and the curved surface area is of 48π cm².
For problem 2 item b, we have that the parameters are given as follows:
r = 8/2 = 4, h = 7.
Hence:
V = πr²h = 112π.S = 2πrh = 56π.The volume is of 112π cm³ and the curved surface area is of 56π cm².
For item 5, the parameters are given as follows:
r = 0.65/2 = 0.325m, h = 1m.
Hence the volume is:
V = πr²h = π(0.325)² = 0.33 m³.
Each m³ has 1000 liters, hence:
0.33 x 1000 = 330 liters.
There are 330 liters of water in the container.
More can be learned about the volume of a cylinder at https://brainly.com/question/9554871
#SPJ1
Write an equation of each line in standard form with integer coefficients.
the line through (-4,6) and (2,-2)
The equation of the line in standard form passing through the points (-4 , 6) and (2 , -2) is 4x + 3y = 2.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.
Given two points, (-4 , 6) and (2 , -2), use the two-point form to generate the equation of the line.
y - y2 = [(y2 - y1)/(x2 - x1)] (x - x2)
y - -2 = [(-2 - 6)/(2 - -4)](x - 2)
y + 2 = (-8/6)(x - 2)
y + 2 = -4/3 x + 8/3
To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.
y + 2 = -4/3 x + 8/3
4/3 x + y = 8/3 - 2
4/3 x + y = 2/3
Multiply both sides by 3 to have integer coefficients.
3(4/3 x + y) = 3(2/3)
4x + 3y = 2
To learn more about equation of line in standard form: brainly.com/question/17095050
#SPJ4
