Answer:
[tex]12x + 9y \geq = 510\\ y\leq 2x\\ y \geq 25[/tex]
Step-by-step explanation:
If x represents the number of lawns and 'y' represents the number of dogs that Fabio walked then:
The amount of money raised by Fabio plus the amount of money raised by Gwen must be greater than or equal to $ 510.
[tex]12x + 9y \geq = 510[/tex]
The number of dogs that Fabio will walk is less than or equal to twice the number of yards of lawn cleared by Gwen.
[tex]y\leq 2x[/tex]
Fabio will walk at least 25 dogs
[tex]y \geq 25[/tex]
Finally, the restrictions are:
[tex]12x + 9y \geq = 510\\ y\leq 2x\\ y \geq 25[/tex]
The volume ( v) of a gas in a container at a constant temperature varies inversely as the pressure (p). If the volume of a gas is 24 cubic centimeters when the pressure is 16 pounds, what is the volume under a pressure of 30 pounds?
a) 45 cubic cm b) 20 cubic cm c) 12.8 cubic cm
Answer : C) 12.8 cubic cm
The volume ( v) of a gas in a container at a constant temperature varies inversely as the pressure (p)
If y is inversely proportional to x then [tex]y=\frac{k}{x}[/tex]
where k is constant of proportionality
v is inversely proportional to p then [tex]v=\frac{k}{p}[/tex]
the volume of a gas is 24 cubic centimeters when the pressure is 16 pounds
Given : v= 24 and p = 16. We need to find out k
[tex]24=\frac{k}{16}[/tex]
Multiply by 16 on both sides
k = 384
Now we find out the volume under a pressure of 30 pounds
[tex]v=\frac{384}{30}[/tex]
[tex]v=\frac{128}{10}[/tex]= 12.8 cubic cm
Under a pressure of 30 pounds, the gas would occupy a volume of 12.8 cubic centimeters, as determined by applying Boyle's law, which states that volume and pressure are inversely proportional in conditions of constant temperature.
The volume (v) of a gas in a container at a constant temperature varies inversely as the pressure (p). This is a demonstration of Boyle's law, which states that pressure and volume are inversely proportional (P = k/V) when temperature is held constant. To find the new volume when the pressure changes, we can set up a proportion based on the original conditions provided: 24 cm³ at 16 pounds pressure. We set the initial volume and pressure as 24 cm³ and 16 lbs, respectively, and then solve for the new volume when the pressure is 30 lbs.
To find the volume under a pressure of 30 pounds, we use the equation:
V1 * P1 = V2 * P2
Where V1 is the original volume, P1 the original pressure, V2 the new volume, and P2 the new pressure. Plugging in our known values:
24 cm³ * 16 lbs = V2 * 30 lbs
Solving for V2, we get:
V2 = (24 cm³ * 16 lbs) / 30 lbs
V2 = 384 cm³ / 30 lbs
V2 = 12.8 cm³
Therefore, under a pressure of 30 pounds, the gas would occupy a volume of 12.8 cubic centimeters.
A part of a line with endpoints on both ends is a(n):
Answer: line segment
Step-by-step explanation:
This is confusing. Someone help me please
1 a) Yogurt : Orange Juice : milk
50 : 100 : 250
(50 : 100 : 250 ) / 50
ans= 1 : 2 : 5
b) 1 l = 1000 ml of milk
so 1000/250 = 4
ans= 4 regular smoothies.
c) 3 regular and 1 small
(50 : 100 : 250 ) *3 + (50 : 100 : 250 ) / 2
= (150 : 300 : 750 ) + (25: 50: 125)
ans = 175 ml yogurt, 350 ml orange juice, 875 ml milk
simplify (7^3)^8 its a question i dont understand what to do please help asap
Hey coffee merchant want to make 6 pounds of a blend of coffee costing five dollars per pound. The blender is made it and using a six dollar per pound grade at coffee and a three dollar per pound grade of coffee. how many pounds of each of these grades should be used?
uhhhhh, your question seems a bit unclear. could you make it a bit more readable?
Javier had $305 in his bank account. His bank charges a fee of $7.50 each month that a balance is below $500.
If he makes no other deposits or withdrawals, how much money is in Javier’s account at the end of three months?
Enter your answer in the box.
282.50
if his bank charges him $7.50 each month for a balance below of $500
then Javier who did not deposit or withdraw (added or subtracted) but had a total of 305 would be charged 7.50 for those 3 months
305 - 7.50 (3) = X
305 - (22.5)
282.50
Answer: He had $277.50 at the end of 3 months.
Step-by-step explanation:
Since we have given that
Amount he had in his bank account = $305
Bank charges each month = $7.50
Number of months = 3
So, Bank charges for 3 months would be
[tex]7.50\times 3\\\\=\$22.5[/tex]
So, Amount left in his bank account would be
[tex]\$305-\$22.5\\\\=\$277.50[/tex]
Hence, he had $277.50 at the end of 3 months.
The elevation of the basement floor in a building is -14 ft. The elevation of the roof is 36 feet. What is the distance from the basement floor to the roof? A) -50 ft Eliminate B) -24 ft C) 24 ft D) 50 ft
The answer would be D) 50, because you would have to add 14+36 which equals 50
Nolan deposited $2300 into a savings account for which interest is compound weekly at a rate of 2.12%.
How much interest will he earn after 7 years?
Answer:
The answers is 367.87
Step-by-step explanation:
The interest Nolan will earn after 7 years of time lapse, with the given figures, is $4,863,465 approx.
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that simple interest, then the interest amount earned is given by:
[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]
For the considered case, the unit of time is weekly.
In 7 years, there can be at least 1 leap year, and at max 2 leap years.
In 7 years, therefore, the number of days are between [tex]6 \times 365 + 366[/tex] and [tex]6 \times 365 + 366+1[/tex] or say in between 2556 and 2557
Since each week has 7 days, therefore, the number of weeks these days will have is approx [tex]\dfrac{2556}{7} \approx 365.14[/tex] (assumed there are 2556 days in 7 years).
This approximates to 365 weeks (integer quantity)
Thus, we get:
Unit of time is weekRate of interest per week = 2.12%Type of interest applied = Compound interestUnits of week for which interest is applied is approx 365Initial amount deposited = $2300Thus, the amount of interest that Nolan will earn is approx:
[tex]CI = P(1 +\dfrac{R}{100})^T - P\\\\CI \approx 2300(1 + 0.0212)^{365} - 2300 \approx 2300 \times 2115.65 - 2300\\CI \approx \$4,863,465[/tex]
Thus. the interest Nolan will earn after 7 years of time lapse, with the given figures, is $4,863,465 approx.
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6. Solve: A chemist needs 30 ounces of 50% hydrochloric acid solution. In her lab, she has some 80% hydrochloric acid solution, some 60% hydrochloric acid solution, and some 40% hydrochloric acid solution. She must use 2 ounces of the 80% solution. How many ounces each of the 40% and 60% solutions must be mixed with the 2 ounces of 80% to obtain the 30 ounces of 50% hydrochloric acid solution she needs?
Final answer:
To prepare 30 ounces of a 50% hydrochloric acid solution, the chemist must mix 17 ounces of the 40% solution with 11 ounces of the 60% solution and 2 ounces of the 80% solution.
Explanation:
The student needs to mix different concentrations of hydrochloric acid to end up with 30 ounces of a 50% solution. We know that 2 ounces of the 80% solution are used, so the remaining 28 ounces must be a mix of the 40% and 60% solutions.
Let x represent the ounces of the 40% solution and 30 - 2 - x, or 28 - x, represent the ounces of the 60% solution. Setting up the equation based on mass of pure hydrochloric acid:
0.80(2) + 0.40(x) + 0.60(28 - x) = 0.50(30)Solving for x:
1.6 + 0.40x + 16.8 - 0.60x = 15-0.20x + 18.4 = 15-0.20x = -3.4x = 17The chemist needs to use 17 ounces of the 40% solution and 11 ounces of the 60% solution, combining them with the 2 ounces of the 80% solution to obtain 30 ounces of 50% hydrochloric acid.
omar worked 29 hours last month and earned $9 per hour. he spent $18 of his earnings since then. how much money does he have left??
To solve, we must find out how much he earned in the month. To do this, we do 29 x 9. This is done to find out how much was earned. Omar earned $261 in the month. Now we do 261-18 to find out how much is left after spending 18 dollars. We can see that Omar has $243 dollars remaining.
A part of a line with endpoints on both ends is a(n):
I believe it's a segment.
The inequality x _> -5
jjjjjjjjjjjjjjjjjjjjjjjjjjjj
Which inequality represents the graph below?
the answer is x > -2
x is greater then -2 and that is the 3 one
Pls help, pls just only tell me how to solve
To find f(2), look and see where the line crosses the Y axis, when The line is on X 2.
The line is on Y = -2, so the answer would be -2.
a paper coffee filter has a radius of 6 centimeters and a slant of height of 12 centimeters. find the surface area of the filter. round your answer to the nearest whole number.
Final answer:
The surface area of the paper coffee filter with a radius of 6 centimeters and a slant height of 12 centimeters is approximately 339 square centimeters when rounded to the nearest whole number.
Explanation:
Finding the Surface Area of a Coffee Filter
To find the surface area of the paper coffee filter, we need to consider it as a part of a cone because a coffee filter is shaped like a cone with a circular base. The surface area of a cone is calculated by the formula Surface Area = πr(r + l), where r is the radius and l is the slant height. Given that the radius of the coffee filter is 6 centimeters and the slant height is 12 centimeters, the formula should be filled in as follows:
Radius (r) = 6 cm
Slant Height (l) = 12 cm
The calculation will then be:
Surface Area = π x 6 cm x (6 cm + 12 cm)
Surface Area = π x 6 cm x 18 cm
Surface Area = π x 108 cm²
Surface Area ≈ 3.14159 x 108 cm²
Surface Area ≈ 339.29 cm²
Rounding to the nearest whole number:
Surface Area ≈ 339 cm²
The surface area of the paper coffee filter is approximately 339 square centimeters.
what's 347 times 987?
342,489 is your answer.
Solve the equation for y
[tex] \frac{2}{5}x + y = 3[/tex]
multiply both sides of the equation by 3.
2x+3y=9
move variable to the right side and change its sign
2x=9-3y
divide both sides of the equation by 2
x=9/2-3/2y
What is the slope of the line with the equation of y=3/4x that passes through the point (2,1)?
A) 1
B) 2
C) 3/4
D) 4/3
E) 3
C
the equation of a line in ' slope- intercept form ' is
y = mx + c ( m is the slope and c the y-intercept )
y = [tex]\frac{3}{4}[/tex] x is in this form
with slope m = [tex]\frac{3}{4}[/tex] → C
The slope of the line is [tex]m=\dfrac{3}{4}[/tex].
Given,
Equation of line is,
[tex]y=\dfrac{3}{4} x[/tex].
The line is passes through point,(2,1) .
We know that the slope form of equation is,
[tex]y=mx+c[/tex]
here m is the slope of the line and c is its y intercept.
On comparing the given equation of line with the general equation we get,
[tex]m=\dfrac{3}{4}[/tex].
Hence the correct option is C.
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s the line for the equation y = 1 horizontal or vertical? What is the slope of this line? Select the best answer.
The line is horizontal. The slope is 0.
The line is horizontal. The slope is 1.
The line is vertical. The slope is undefined.
The line is vertical. The slope is 0.
It is horizontal and has a slope of 0.
The equation y = 1 is a horizontal line with a slope of zero.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation of the line or linear system is given below.
y = 1
The above equation is a horizontal line with a slope of zero.
Thus, the correct option is A.
The graph is given below.
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A total of 336 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
A total of 336 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold then the number of adult tickets sold = 112
Let's denote the number of adult tickets sold as 'A' and the number of student tickets sold as 'S'.
We are given two pieces of information:
1. The total number of tickets sold is 336: A + S = 336.
2. The number of student tickets sold was two times the number of adult tickets sold: S = 2A.
Now, we can use the second equation to substitute the value of 'S' in terms of 'A' into the first equation:
A + 2A = 336.
Combine the like terms:
3A = 336.
Now, isolate 'A' by dividing both sides by 3:
A = 336 / 3.
A = 112.
So, the number of adult tickets sold (A) is 112.
In summary, to find the number of adult tickets sold, we set up equations based on the given information and then solve for the variable representing the number of adult tickets (A).
By substituting the value of 'A' back into one of the equations, we can also find the number of student tickets sold (S).
In this case, 112 adult tickets and 224 student tickets were sold to make a total of 336 tickets.
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A medium can of tomato juice costs $0.92 and contains 46 ounces of tomato juice. A large can of tomato juice costs $3.60 and contains 144 ounces of tomato juice. Which can of tomato juice the lower unit price? How much lower?
Answer:
The medium-sized can is the cheaper by the oz, and is $0.005 per oz. cheaper.
Step-by-step explanation:
Medium can: $0.92/(46 oz) = $0.020/oz
Large can: $3.60 / (144 oz) = $0.025/oz
Surprisingly, the medium can price per oz. is lower than that of the large can. The difference is $0.005 per oz.
The medium can of tomato juice has the lower unit price at $0.02 per ounce, which is $0.005 lower per ounce than the large can's unit price of $0.025 per ounce.
To determine which can of tomato juice has the lower unit price, we need to calculate the cost per ounce for each can. For the medium can, we divide the cost by the number of ounces:
Medium can unit price = $0.92 / 46 ounces = $0.02 per ounce
For the large can, we perform a similar calculation:
Large can unit price = $3.60 / 144 ounces = $0.025 per ounce
The medium can has a lower unit price of $0.02 per ounce compared to the large can's unit price of $0.025 per ounce. The difference in unit price is $0.025 - $0.02 = $0.005, or half a cent per ounce.
Longfield is at an elevation of -144 1/2 feet. Smallville is 4 times farther below sea level than Longfield.
What is the Smallville’s elevation, in feet? The elevation of Smallville is _____feet.
Show me the work please.
The elevation of Smallville is calculated by multiplying the elevation of Longfield by 4. Longfield's elevation is -144 1/2 feet, which is equivalent to -289/2 as an improper fraction. Multiplying this by 4 gives the elevation of Smallville as -578 feet.
Explanation:To find Smallville's elevation, we first take the elevation of Longfield, which is -144 1/2 feet below sea level. Since Smallville is 4 times farther below sea level than Longfield, we have to multiply the elevation of Longfield by 4.
First, convert -144 1/2 to an improper fraction: -144 1/2 = -289/2.
Now, multiply by 4:
(-289/2) × 4 = -289 × 2 = -578 feet
So the elevation of Smallville is -578 feet below sea level.
If 5/6 gallon of paint covers 1/4 of the house, then how much paint is needed for the entire house?
25/6 hope this helps
The model is 18.5 inches wide and 36.5 inches tall. If the actual building is 370 feet wide, what's its height?
I got 750.278... might be wrong
Answer:
It's 730 feet
Step-by-step explanation:
What interest rate per annum is a fund paying its clients if the third to the last payment of a depositor became Php 1,040.40 from an initial savings payment of Php 1,000.00?
Answer: The rate of interest per annum is 1.3%.
Step-by-step explanation:
Given Principal P= $1000
time period n=3
Amount A=$1040,40
To find rate of interest per annum r
We know that
[tex]A=P(1+\frac{r}{100} )^3\\\Rightarrow\ 1040=1000(1+\frac{r}{100})^3\\\Rightarrow\ 1.040=(1+\frac{r}{100})^3\\\text{taking log on both sides}\\log(1.040)=3log(1+\frac{r}{100})\\\Rightarrow0.039=3log(1+\frac{r}{100})\\\Rightarrow0.013=log(1+\frac{r}{100})\\\\\Rightarrow\ e^{0.013}=(1+\frac{r}{100})\\\Rightarrow\ 1.013=(1+\frac{r}{100})\\\Rightarrow\ \frac{r}{100}=1.013-1=0.013\\[/tex]
⇒ r = 1.3%.
Celina babysat for 5 hours and earned 27
If you're asking how much she got paid per hour, the answer would be $5.40.
27 / 5 = 5.4
Find the area of the large rectangle by finding the area of the two small rectangles and adding them.
The total area is 21 (15+6=21)
Answer:
Area of the given figure is 21 square units
Step-by-step explanation:
Area of the rectangle formula is length times width
Area of the top rectangle
Length = 5 and width = 3
So area of top rectangle =5 times 3 is 15 square units
Area of bottom rectangle
length =2 and width =3
So area of bottom rectangle is 2 times 3 is 6 square units
Total area =[tex]15+6= 21[/tex] square units
Which logarithm equation is equivalent to the exponential equation below?
3^c=27
Answer:
log(bsae(3))27=c
Step-by-step explanation:
a p e x
The logarithm equation is equivalent to the exponential equation is c = log₃27
What is logarithm?A logarithm is the power to which a number must be raised in order to get some other number.
Given that, exponential equation, [tex]3^{c}[/tex]=27
By the exponential form of logarithm:
[tex]x^{a} =m[/tex] then logarithm form is a = logₓ m
Therefore,
[tex]3^{c}[/tex]=27
Taking logarithm both sides,
[tex]3^{c}[/tex]=27
c = log₃27
Hence, the logarithm equation is equivalent to the exponential equation is c = log₃27
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A jug holds 4.8 liters. How many milliliters does it hold? Enter your answer in the box.
Answer:
The jug will hold 4,800 milliliters.
Step-by-step explanation:
Each liter is 1000 milliliters, and 4.8 • 100 = 4,800
The jug holds 4800 milliliters. The conversion factor is that 1 liter is equal to 1000 milliliters.
Explanation:The subject of this question is based on the concept of volume conversion, specifically from liters to milliliters. This falls within the field of Mathematics. In the metric system, volume can be measured in cubic meters (m³), liters (L), and milliliters (mL). These units of volume are used in different scenarios depending on the magnitude of the volume to be measured. One liter (L) is equal to 1 cubic decimeter (dm³), or 1,000 cubic centimeters (cm³).
One common metric conversion is from liters to milliliters. This is because 1 Liter equals 1000 milliliters.
Therefore, if a jug holds 4.8 liters, we can find the equivalent volume in milliliters by multiplying the volume in liters by 1000. In this case, 4.8 liters * 1000 equals 4800 milliliters
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what is the missing length of the square
a = 7
Because we are looking for the area we would times the length times width. What times 6 would be equal to 42? 7!