Cheryl paid 37.20 for 12 gallons of ice cream for a school picnic. How much would 1 quart of ice cream cost?
Answer:
A quart of ice cream costs $0.775
Step-by-step explanation:
This problem can be solved by a rule of three problem.
Rule of three problem:
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
In this problem, the measures are:
- The number of gallons of ice cream
- The cost
As the number of gallons increases, so will the cost that Cheryl paid. So, the relationship between the measures is direct and we have the following rule of three.
12 gallons - $37.20
1 gallon - $x
12x = 37.20
[tex]x = \frac{37.20}{12}[/tex]
x = $3.1
Each gallon cost $3.1. Each gallon also has 4 quarts, so the cost of 4 quarts is $3.1. To find the cost of a quart of ice cream
4 quarts - $3.1
1 quart - $x
4x = 3.1
[tex]x = \frac{3.1}{4}[/tex]
x = $0.775
A quart of ice cream costs $0.775
Find the equation of the plane which has intercepts of (4,0,0) and (0,−2,0) and no z-intercept.
The equation of the plane which has intercepts of (4, 0, 0) and (0, -2, 0) and no z-intercept is [tex]\frac{1}{4}\cdot x -\frac{1}{2}\cdot y = 1[/tex].
A plane is represented by the following expression:
[tex]A\cdot x + B\cdot y + C\cdot z = 1[/tex] (1)
Where [tex]A,B, C[/tex] are real coefficients.
We need three distinct points to determine all coefficients of the plane. If we know that [tex](x_{1}, y_{1}, z_{1}) = (4,0,0)[/tex], [tex](x_{2}, y_{2}, z_{2}) = (0,-2,0)[/tex] and [tex](x_{3}, y_{3}, z_{3}) = (0, 0, 0)[/tex], then we have the following system of linear equations:
[tex]4\cdot A = 1[/tex] (2)
[tex]-2\cdot B = 1[/tex] (3)
[tex]0 \cdot C = 1[/tex] (4)
Then, the solution of this system is [tex]A = \frac{1}{4}[/tex], [tex]B = -\frac{1}{2}[/tex] and [tex]C = 0[/tex].
And the equation of the plane which has intercepts of (4, 0, 0) and (0, -2, 0) and no z-intercept is [tex]\frac{1}{4}\cdot x -\frac{1}{2}\cdot y = 1[/tex].
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One factor of f(x)= 4x^3-4x^2-16x+16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.
How do I convert 12 ounces into grams. Please help
Luis wants to buy a home priced at $315,000. He plans to finance this amount less the down payment required. His mortgage payment would then be $2100. Luis has an annual income of $91,500 and $65,000 in savings. Luis has a car payment of $370, a student loan payment of $165 and a credit card payment of $45. Use a 20% down payment and the 28/36 ratio to determine if Luis is eligible for a loan. What would you advise him to do if he is not eligible?
Solution:
Annual income of Luis= $ 91,500
[tex]\frac{28}{36}[/tex] ratio states that maximum of 28 % of your gross monthly income should be spent on housing finances and not more than 36% of your total monthly income should be spent on loans.
36% of $ 91,500= 0.36 × 91,500=$ 32,940(Annualy)
Total money that luis can use for loan as a monthly payment =$ [tex]\frac{32940}{12}=2745[/tex] $
Amount that Luis spent on loan Monthly =car payment of $370, a st udent loan payment of $165 and a credit card payment of $45= $ 370 + $ 165 + $ 45=$ 580
Amount that can be used for housing debt = $ 2745 - $ 580= $2165
Down Payment =
20 % of $315,000=0.20 × 315,000 =$ 63,000
Remaining amount for home that Luis has to pay = $ 315,000 - $ 63,000= $252,000 (not given in how many months or years Luis has to pay this amount )
Mortgage payment = $ 2100
Calculated Mortgage payment on $ 91,500 using 28% rule = 0.28 × 91,500=$25620 (Yearly)
Amount that Luis can use for Mortgage payment monthly=$ [tex]\frac{25620}{12}=2135[/tex] $(Calculated) Monthly
So, Money saved = 2135-2100=$ 35
If Monthly income allowable for Debt(i.e if $ 252,000 is divided into months) > or exceeds $ 2165, then Luis is not eligible for Loan.
If Monthly income allowable for Debt (i.e if $ 252,000 is divided into months )< or Less than $ 2165, then Luis is eligible for Loan.
The advise that i will give to Luis is that he should make full payment of his car debt, and stop being Extravagant i.e start saving more money if he wants to Possess a home.
Which is equivalent to (−2m + 5n)2, and what type of special product is it? 4m2 + 25n2; a perfect square trinomial 4m2 + 25n2; the difference of squares 4m2 − 20mn + 25n2; a perfect square trinomial 4m2 − 20mn + 25n2; the difference of squares
A equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]
What is expression?"It is a mathematical statement which consists of numbers, variables and some mathematical operations."
What is trinomial?"It is a polynomial which has only three terms."
What is perfect square trinomial?"When a trinomial can be factored into a binomial multiplied to itself, then its is a perfect square trinomial."
For given question,
We have been given a quadratic expression [tex](-2m + 5n)^2[/tex].
We need to find to find an equivalent expression to given expression.
Consider given expression,
[tex]\Rightarrow (-2m + 5n)^2 = (2m)^2-2(2m)(5n)+(5n)^2\\\\\Rightarrow (-2m + 5n)^2 =4m^2-20mn+25n^2[/tex]
We can observe that a trinomial [tex]4m^2-20mn+25n^2[/tex] is a perfect square trinomial.
Therefore, an equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]
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Michael has a total of 15 bills that are either $1 bills or $5 bills. If the total amount of money he has is $47, how many $5 bills does he have?
A picture shows that 3 cans have the same mass as 9 identical boxes. Each can has a mass of 30 grams. What is the mass, in grams, of each box.
Final answer:
To find the mass of each box in this scenario, calculate the total mass of the cans first, then divide by the number of boxes. Each box weighs 10 grams.
Explanation:
A picture shows that 3 cans have the same mass as 9 identical boxes. Each can has a mass of 30 grams. What is the mass, in grams, of each box.
To find the mass of each box, we first calculate the total mass of the 3 cans: 3 cans * 30 grams/can = 90 grams. Since the 3 cans have the same mass as 9 identical boxes, each box's mass is: 90 grams / 9 boxes = 10 grams per box.
The graph shown is the solution set for which of the following inequalities?
y ≥ x + 1
y ≥ |x| + 1
y ≥ |x - 1|
Answer:
The correct option is C) [tex]y\geq |x+1|[/tex]
Step-by-step explanation:
The graph of [tex]y=|x|[/tex] is shown in figure-1
In option (1) [tex]y\geq x+1[/tex] .....(2)
the graph of equation (2) is shown in figure-2
In option (2) [tex]y\geq |x|+1[/tex] .....(3)
the graph of equation (3) is shown in figure-3
In option (3) [tex]y\geq |x+1|[/tex] .....(4)
the graph of equation (3) is shown in figure-4
As this is shifted 1 unit to right side
So, this figure is correct as it is matches the provided figure
Therefore, the correct option is C) [tex]y\geq |x+1|[/tex]
Luke purchased a motorcycle for $8,765. It depreciates about 5.3% each year. What is the value of the motorcycle after five years?
At sea, the distance D to the horizon is directly proportional to the square root of the elevation E of the observer. If a person who is 36 feet above the water can see 7.4 miles, find how far a person 49 feet above the water can see.
Mr Richards science class is conducting a variety of expirements with projectiles and falling objects DROP DOWN ANSWERS ARE GROUPS A-D
△FSB∼△ZDR .
What is the value of x?
Enter your answer.
How many units?
△FSB∼△ZDR
What is the value of x?
Enter your answer in the box.
____UNITS
Solutions for the system 10x^2 -y=48
2y=16x^2+48
Answer:
Solutions are (x, y) = (-6, 312) and (6, 312).
Step-by-step explanation:
HELP PLEASE! −3.64⋅|−5.3|−1.53
^
Absolute value of -5.3
To solve −3.64⋅|−5.3|−1.53, calculate the absolute value of −5.3, which is 5.3, then multiply by −3.64 to get −19.292, and finally, subtract 1.53 to result in −20.822.
Explanation:You have presented a mathematical expression involving absolute value and multiplication: −3.64⋅|−5.3|−1.53. Let's solve this step by step:
First, determine the absolute value of −5.3, which is 5.3 because absolute value represents the distance of a number from zero without considering direction.Next, multiply −3.64 by the absolute value you just calculated: −3.64 * 5.3.Once you have the result of that multiplication, subtract 1.53 from it to get the final answer.
Now performing the operations:
−3.64 * 5.3 = −19.292−19.292 - 1.53 = −20.822Therefore, the result of the given expression −3.64⋅|−5.3|−1.53 is −20.822.
math hw..................
How many possible outcomes exist when two fair coins are flipped and a three-section spinner is spun?
Answer:
12
Step-by-step explanation:
#8 surface area please explain
A culture started with 6000 bacteria after 3 hours ot grew to 7200 bacteria Predict how many bacteria will be present after 19 hours
Answer:
19038
Step-by-step explanation:
Given : A culture started with 6000 bacteria after 3 hours to grew to 7200 bacteria
To Find: Predict how many bacteria will be present after 19 hours
Solution:
General Form of exponential function: [tex]y=ab^x[/tex]
where y is the amount after x hours
x is the time
a is the initial amount
b is the growth factor
Bacteria initial amount= a = 6000
Time = x = 3 hours
Amount of bacteria after 3 hours = 7200
Substitute the values in the general form
[tex]7200=6000(b)^3[/tex]
[tex]\frac{7200}{6000}=(b)^3[/tex]
[tex]\sqrt[3]{\frac{7200}{6000}}=b[/tex]
[tex]1.06265856918=b[/tex]
Now we are supposed to find how many bacteria will be present after 19 hours
So, Bacteria initial amount= a = 6000
Time = x = 19 hours
Amount of bacteria after 19 hours = y
Substitute the values in the formula:
[tex]y=6000(1.06265856918)^{19}[/tex]
[tex]y=19038.488[/tex]
Hence there will be approximately 19038 bacteria present after 19 hours
what is the factored form of 64g^3+8
Jen has 2 meters of taffy. She wants to give each of her 3 best friends an equal amount of taffy. How many centimeters of taffy will each friend get?
Write your answer as a mixed number in the form a b/c.
Answer:
[tex]66\frac{2}{3}[/tex] centimeters.
Step-by-step explanation:
Jen has 2 meters of taffy.
She wants to give each of her 3 best friends an equal amount of taffy.
First we convert 2 meters to centimeters.
1 meter = 100 centimeters
2 meters = 100 × 2 = 200 centimeters.
Now divide 200 cm to 3 friends
Each friend get = [tex]\frac{200}{3}[/tex]
= [tex]66\frac{2}{3}[/tex]
Each friend will get [tex]66\frac{2}{3}[/tex] centimeters of taffy.
which of the following function is f(x) if f^-1(x)=5x-19
Answer: F(x)=x-19/5
Step-by-step explanation:
suppose a new car that cost 20 000 depreciates by 15% each year. in how many year till the car costs 7500. use the equation 7500=(20,000)(0.85)^x
In the figure below, triangle ABC is similar to triangle PQR, as shown below: What is the length of side PQ?
A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. A similar right triangle; triangle PQR, which is triangle ABC enlarged and reflected across a horizontal line, is drawn near it. The right angle is at Q. Angle A is congruent to angle P and angle C is congruent to angle R. The length of QR is 12.
Answer:
Line PQ is 24
which best describes your ability to calculate the volume of prisms, cylinders, pyramids, and cones?
A.I know the correct formulas to find the volumes of a ll of these figures.
B.I know the correct formulas to find the volume of at least half of these figures.
C.I can find the volume of these figures when the formulas are given to me.
I know the correct formulas to find the volumes of a ll of these figures. best describes to calculate the volume of prisms, cylinders, pyramids, and cones
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Volume of prism is Surface area multiplied by height, or more simple:
V=1/2×(l×w×h)
Volume of cylinder = πr²h
where r is the radius of cylinder and h is the height of the cylinder
Volume of pyramid = 1/3×l×w×h
Where l is length of pyramid, w is width of pyramid and h is height of the pyramid.
Volume of cone = 1/3πr²h
r is the radius of cone and h is the height of the cone
Hence, I know the correct formulas to find the volumes of a ll of these figures. best describes to calculate the volume of prisms, cylinders, pyramids, and cones
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Tyrone’s hourly wage is $18 and his net pay is 72% of his earnings. Tyrone spends about $1,800 on his monthly expenses. If Tyrone works 40 hours per week and has no other sources of income, what is his total monthly cash inflow? (Hint: Assume that there are 4 pay periods per month.)
a. $273.60
b. $1,080.00
c. $1,800.00
d. $2,073.60
Would It Be D?
Answer:
Yes the Answer is
"D" $2,073.60
Step-by-step explanation:
Correct on edg. 2021
find the length of arc ac, cb=60degrees, ab=12ft(diameter)
The function f(x)=15000(0.96)^x represents the value in dollars of a vehicle x years after it has been purchased new. What is the average decrease in value per year between years 5 and 10? Please show all work!
To find the average decrease in value per year between years 5 and 10 of a vehicle, we plug in x=5 and x=10 into the given function, subtract the values, and divide by 5.
Explanation:To find the average decrease in value per year between years 5 and 10, we need to calculate the difference in value between those two years and then divide it by the number of years.
First, we find the value of the vehicle in year 5 by plugging in x = 5 into the function:
f(5) = 15000(0.96)^5
solving this equation gives us the value of the vehicle in year 5.
Next, we find the value of the vehicle in year 10 by plugging in x = 10 into the function:
f(10) = 15000(0.96)^10
solving this equation gives us the value of the vehicle in year 10.
Finally, we subtract the value in year 10 from the value in year 5 and divide by 5 (the number of years) to get the average decrease in value per year.
One is dollar is currently worth 84.1 Japanese yen. If you exchange 4,205 for US dollars, how much will you have?
Two cylinders are similar. The radius of cylinder A is 5.6 inches. The radius of cylinder B is 1.4 inches. If the height of cylinder B is 4 inches, what is the height of cylinder A
Answer:
C ✔️
Step-by-step explanation:
"16 inches"