Answer:
The correct option is b.) $2.28
Step-by-step explanation:
i) the gas tank is of 15 gallons
ii) there are three gallons left in the gas tank
iii) therefore the tank has to be filled with 15 - 3 = 12 gallons
iv) lower grade of gasoline costs $2.96 per gallon
v) the upper grade of gasoline costs $3.15 per gallon
vi) the cost of filling the tank with the lower grade gasoline
= 12 [tex]\times[/tex] 2.96 = $35.52.
vii) the cost of filling the tank with the lower grade gasoline
= 12 [tex]\times[/tex] 3.15 = $37.80
viii) therefore the difference in the cost of filling your tank between the two grades
= $37.80 - $35.52 = $2.28
Therefore the correct option is b.) $2.28
Final answer:
The difference in the cost of filling the 15-gallon gas tank between the two grades of gasoline is $2.28.
Explanation:
Firstly, let's calculate how many gallons are needed to fill the car's tank completely, since it currently has 3 gallons left in a 15-gallon tank. This means the car requires 15 - 3 = 12 gallons of gasoline to be filled up.
Next, we calculate the cost to fill up the car with the lower grade gasoline that costs $2.96 per gallon. The cost for 12 gallons would be 12 x $2.96 = $35.52.
Then, we calculate the cost to fill up the car with the premium gasoline that costs $3.15 per gallon. The cost for 12 gallons would be 12 x $3.15 = $37.80.
Finally, to find the difference in cost between the two grades of gasoline, we subtract the lower cost from the higher cost: $37.80 - $35.52 = $2.28. Hence, the difference in cost is $2.28, so the correct answer is option (b).
(y^4-y^3+2y^2+y-1)/(y^3+1)
Answer:
Solving by method of factorization ,
(y^4-y^3+2y^2+y-1)/(y+1)(y^2-y+1)
Step-by-step explanation:
A sum of two perfect cubes, a3 + b3 can be factored into :
(a+b) • (a^2-ab+b^2)
here a = y and b = 1
hence , expanding y^3+1 in cubic formula ,
(y^3+1) = (y+1)(y^2-(y)(1)-1^2)
(y^3+1)=(y+1)(y^2-y+1)
putting this value of (y^3+1) in the given expression ,
= (y^4-y^3+2y^2+y-1)/(y+1)(y^2-y+1).
Trinomial cannot be factored , hence the final answer is ,
= (y^4-y^3+2y^2+y-1)/(y+1)(y^2-y+1).
A gas can holds 10liters of gas. How many cans could we fill with 7 liters of gas?
Final answer:
You could partially fill one 10-liter gas can with the 7 liters of gas, as 7 divided by 10 is 0.7, and you cannot have a fraction of a physical can.
Explanation:
To find out how many cans we could fill with 7 liters of gas, when a gas can holds 10 liters, we need to perform a simple division.
The calculation is as follows:
Number of cans = Total liters of gas / Liters each can holds = 7 liters / 10 liters = 0.7.
Since you cannot have a fraction of a physical gas can, you would not be able to completely fill a single can with 7 liters of gas.
Therefore, we could partially fill one 10-liter gas can with the 7 liters of gas we have.
The perimeter of a rectangle is 34 units. Its width is 6.5, point
Answer:
Length = 10.5units,Area = 68.25 unit²
Step-by-step explanation:
Perimeter =34 units
Width =6.5 units
Perimeter = l+l+w+w
Where l= length and w= width
34 = l + l + 6.5+ 6.5
34.= 2l + 13
Subtract 13 from both sides
2l = 34 - 13
2l = 21
Divide both sides by 2
L= 21/2
Length = 10.5units
If we are to find the area.
Area = length x width
Area = 10.5 × 6.5
Area = 68.25 unit²
I hope this was helpful, please mark as brainliest
the quadratic p(x)=.65x squared - .047x +2 models the population p(x) in thousands for a species of fish in a local pond, x years after 1997. during what year will the population reach 66,530 fish
Answer:
2007
Step-by-step explanation:
we have
[tex]p(x)=0.65x^{2} -0.047x+2[/tex]
This is a vertical parabola open upward
The vertex represent a minimum
p(x) is the population in thousands for a species of fish
x is the number of years since 1997
Remember that p(x) is in thousands
so
If the population reach 66,530 fish
then
the value of p(x) is equal to
p(x)=66.53
substitute in the quadratic equation
[tex]66.53=0.65x^{2} -0.047x+2[/tex]
[tex]0.65x^{2} -0.047x+2-66.53=0[/tex]
[tex]0.65x^{2} -0.047x-64.53=0[/tex]
Solve the quadratic equation by graphing
The solution is x=10 years
see the attached figure
therefore
Find the year
Adds 10 years to 1997
1997+10=2007
A gain of 56 points in a game as an integer
Answer:
+56
Step-by-step explanation:
Is one and one half greater than one and four tenth
Answer:
yes
Step-by-step explanation:
1 1/2 is greater than 1 4/10. Wich is 1/10 less then 1 1/2
Answer:
Yes
Step-by-step explanation:
1 1/2 > 1 4/10
Step 1: Covert to Improper Fraction
1 1/2 = 2/2 + 1/2 = 3/2
1 4/10 = 10/10 + 4/10 = 14/10
Step 2: Find Common Denominator
The least common denominator is 10
3/2 * 5/5 = 15/10
14/10 is already good
Step 3: Evaluate
Is 15/10 more than 14/10?
Yes!!!!
So, 1 1/2 is more than 1 4/10
What is the volume of a cylinder of 8in by 0.5 ft in cubic inches
The volume of cylinder is 1205.76 cubic inches
Solution:
We have to find the volume of cylinder
The volume of cylinder is given by formula:
[tex]V = \pi r^2h[/tex]
Where "r" is the radius and "h" is the height of cylinder
Given dimensions are:
Radius = 8 inches
Height = 0.5 feet
Convert feet to inches
1 feet = 12 inches
Therefore,
0.5 feet = 12 x 0.5 = 6 inches
Thus, we have got,
height = 6 inches
Substitute r = 8 inches and h = 6 inches in formula:
[tex]V = 3.14 \times 8^2 \times 6\\\\V = 3.14 \times 64 \times 6\\\\V = 1205.76[/tex]
Thus volume of cylinder is 1205.76 cubic inches
why is this true? the interior angle measures of an isosceles triangle can not be 96°,43°, and 43°
(SAT Prep) In △ABC, AB = BC = 20, DE ≈ 9.28. Approximate BD.
The measure of BD ≈ 5.36
Step-by-step explanation:
The side BC = BD+DE+EC.The measure of BC = 20 and DE ≈ 9.28The angles ∠BD and ∠EC are both equal to 15°If the angles are same, then their sides are equal.Let 'x' be the measure of BD and EC.
BC = x+9.28+x
20 = 9.28 + 2x
2x = 20-9.28
x = 10.72/2
x = 5.36 (approx.)
∴ The measure of BD ≈ 5.36
Chau's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Chau $5.50 per pound, and type B coffee costs $4.20 per pound. This month, Chau made 143 pounds of the blend, for a total cost of $677.30. How many pounds of type B coffee did he use?
84 pounds of Type B coffee is used
Solution:
Let "x" be the pounds of type A coffee
Let "y" be the pounds of type B coffee
Cost per pound of type A = $ 5.50
Cost per pound of Type B = $ 4.20
This month, Chau made 143 pounds of the blend
x + y = 143
x = 143 - y -------- eqn 1
For a total cost of $677.30. Thus we frame a equation as:
pounds of type A coffee x Cost per pound of type A + pounds of type B coffee x Cost per pound of Type B = 677.30
[tex]x \times 5.50 + y \times 4.20 = 677.30\\\\5.5x + 4.2y = 677.30 -------- eqn 2[/tex]
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
[tex]5.5(143-y) +4.2y = 677.30\\\\786.5 -5.5y + 4.2y = 677.30\\\\5.5y - 4.2y = 786.5 - 677.30\\\\1.3y = 109.2\\\\Divide\ both\ sides\ by\ 1.3\\\\y = 84[/tex]
Thus 84 pounds of Type B coffee is used
To determine how many pounds of type B coffee were used in Chau's coffee blend, we set up a system of equations based on the total weight and total cost of the blend. By substituting one equation into the other, we can solve for the quantity of type B coffee.
Calculating the Blend of Coffee:
To solve the problem, let's use a system of equations to determine how many pounds of type B coffee Chau used in his coffee blend. We have two unknowns here: the amount of type A coffee (let's call it A) and the amount of type B coffee (let's call it B). The total weight of the coffee blend is given as 143 pounds, and the total cost of the blend is $677.30.
The first equation comes from the total weight of the blend:
A + B = 143
The second equation comes from the total cost:
5.50A + 4.20B = 677.30
We can use either substitution or elimination to solve this system. If we solve the first equation for A (i.e., A = 143 - B) and substitute it into the second equation, we get:
5.50(143 - B) + 4.20B = 677.30
After simplifying, we can solve for B to find out how many pounds of type B coffee were used.
4. Suppose y varies directly with x. Write a direct variation equation that relates x and y.
v=-10 when χ=2
Ov=-5x
Ov=-1
Π
Ov=5x
Ov=x
Answer:
y = - 5x
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = - 10 when x = 2, thus
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-10}{2}[/tex] = - 5
y = - 5x ← equation of variation
Which one of the following words means most nearly the opposite of RANDOM? (remember,opposite)
Answer:
predictable
Step-by-step explanation:
the opposite of random is predictable
The opposite of 'random' would be a word like 'ordered' or 'systematic', which suggest a set plan or sequence, contrasting with the concept of randomness.
Explanation:The opposite of the word 'random' would be a term that denotes a sense of order, structure, or predictability. In this context, one example of a word that is the opposite of 'random' is 'ordered' or 'systematic'. These words suggest that things are arranged or occur according to a set plan or sequence, thereby contrasting with the concept of 'random', which indicates a lack of any discernible order or pattern.
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Determine whether the statement is true or false.
Let A = {1, 3, 5, 7}
B = {5, 6, 7, 8}
C = {5, 8}
D = {2, 5, 8}
U = {1, 2, 3, 4, 5, 6, 7, 8}
Answer: I think it's True :)
Answer:
I feel like it true. Happy yo help!!!
Step-by-step explanation:
what is 0.8888(non terminal) as a fraction?
Hmmm.... do you mean 0.8888...... or just 0.8888.
If you mean point eight repeating the fraction equivalent is just 8/9.
what are the three first terms of 8-n
Step-by-step explanation:
First term : 8 - 0 = 8
second term: 8 - 1 = 7
third term : 8 - 2 = 6
What is the area of a triangle that has a
base of 9 inches and a height of 10
inches?
A. 45 in B. 45 sq in
C. 90 in D. 90 sq in
Answer:
A. 45 in
Step-by-step explanation:
To find area you multiply length and width so you would multiply 9 and 10 but since it is a triangle you would divide by two
Hope this helps!
Convert z = 9cos200° + 9isin200° from polar form to rectangular form.
-8.46 - 3.08i
-2.09 – 6.84i
8.46 + 3.08i
2.09 + 6.84i
Answer:
z = -8.46 - 3.08i.
Step-by-step explanation:
cos 200 = -0.93969 so 9 * cos 200 = -8.46 to the nearest hundredth.
sin 200 = -0.3420 so 9 * sin 200 = -3.08 to nearest hundredth.
Janice is babysitting this summer she already has $35 in her account before she
begins babysitting. If she makes $25 each week, how much does she have after 3
weeks?
Answer:
$110
Step-by-step explanation:
35+25(3)
A positive integer is 11 more than 18 times another. Their product is 6030. Find the two integers.
Answer:
18 and 335
Step-by-step explanation:
y = 18x + 11
x * y = 6030
x * (18x + 11) = 6030
18x^2 + 11x = 6030
18x^2 + 11x - 6030 = 0
(18x + 335)(x - 18) = 0
18x + 335 = 0 x - 18 = 0
18x = -335 x = 18
x = -335/18
x is gonna have to be a positive number...so x = 18
y = 18x + 11
y = 18(18) + 11
y = 324 + 11
y = 335
so ur numbers are 18 and 335
The two positive integer numbers are 18 and 335
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the two numbers be a and b
Now ,
Positive integer is 11 more than 18 times another
a = 11 + 18b be equation (1)
And , product of a and b is 6030
a x b = 6030 be equation (2)
Now , substituting the value of equation (1) in equation (2) , we get
( 11 + 18b ) x b = 6030
18b² + 11b = 6030
Subtracting 6030 on both sides , we get
18b² + 11b - 6030 = 0 be equation (3)
On simplifying , we get
18b² - 324b + 335b - 6030 = 0
18b ( b - 18 ) + 335 ( b - 18 ) = 0
So ,
( 18b + 335 ) ( b - 18 ) = 0
Now , we got two values for b ,
( 18b + 335 ) = 0
b = -335 / 18
And ,
( b - 18 ) = 0
b = 18
Since , b is a positive integer , the value of b is 18
Now , substituting the value of b in equation (2) , we get
a x 18 = 6030
Divide by 18 on both sides , we get
a = 335
Hence , the two positive integer numbers are 18 and 335
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Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48
paintings to the local museum. Each of the 12 collectors will donate the same number of paintings.
007
How many paintings will Sergio have in his art collection after his donation?
Answer:
P - 4
Step-by-step explanation:
Sergio and the other painting collectors have decided to donate a total of 48 paintings all together.
We know that there are 12 collectors in total and they will each donate the same number of paintings.
48 paintings in total
12 collectors
48 / 12 = 4
We now know Sergio will donate 4 paintings from his collection of P paintings. Sergio will have P - 4 paintings left.
We do not know what "P" is equal to, so we cannot give an exact number for how many paintings he will have left. However, we know he will have 4 fewer paintings after donating.
In a certain card game, for every 4 44 blue cards, there are 3 33 yellow cards. There are a total of 84 8484 blue and yellow cards in the game. How many blue cards are in the game?
The total number of blue cards in the game = 48
Step-by-step explanation:
Total number of blue and yellow cards = 84
let the blue card denote B and yellow card as Y
B = 4
Y = 3
Total number of cards in one round = 7
number of rounds possible = total number of cards / number of cards in one round
= 84/7
= 12
number of blue cards = 12 x 4
= 48
The total number of blue cards in the game = 48
Answer:
48
Step-by-step explanation:
Question 3
Carla plans to invest $9,000 for 10 years. Better Bank offers a 10 year CD at an annual rate of 4% using simple interest.
How much is the investment worth?
$3,600
$9,000
$12,600
$18,000
We have been given that Carla plans to invest $9,000 for 10 years. Better Bank offers a 10 year CD at an annual rate of 4% using simple interest. We are asked to find the amount after 10 years.
We will use simple interest formula to solve our given problem.
[tex]A=P(1+rt)[/tex], where
A = Final amount,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
[tex]4\%=\frac{4}{100}=0.04[/tex]
[tex]A=\$9000(1+0.04\times 10)[/tex]
[tex]A=\$9000(1+0.4)[/tex]
[tex]A=\$9000(1.4)[/tex]
[tex]A=\$12600[/tex]
Therefore, the investment will be worth $12600 in 10 years. and option C is the correct choice.
Question 6 of 10
2 Points
The solution set of an equation of a circle is all of the points that lie in the
circle
O
A
True
O
B. False
SUBMIT
It is true that the solution set of an equation of a circle is all of the points that lie in the circle
How to determine the true statement?The equation of a circle is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where:
Center = (a,b)
Radius = r
The points are represented by (x,y)
The (x,y) can take any value as long as it makes the equation (x - a)^2 + (y - b)^2 = r^2 to be true
Hence, it is true that the solution set of an equation of a circle is all of the points that lie in the circle
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Answer:
False
Step-by-step explanation:
What are the values of a, b, and c in the quadratic equation 0 = 5x - 4x4 - 2?
a = 5, b = 4, c = 2
a = 5, b = -4, C = -2
a= -4, b = 5, C = -2
a = 4. b = -5, C = -2
What is the answer to 5(a-b)?
Answer:
5xA-5xB
Step-by-step explanation:
Answer: 5a-5b
Step-by-step explanation: Distribute the 5 and carry the negative sign over
Select all the equations that are equivalent to−3(x+1)
A.-3x+(-3)
B.x-3
C.-3x+1
D.-3x-3
Step-by-step explanation:
We have,
− 3( x + 1)
= − 3x - 3
A. - 3x + (-3)
= − 3x - 3, is equivalent to − 3( x + 1).
B. x - 3
= x - 3, is not equivalent to − 3( x + 1).
C. - 3x + 1
= - 3x + 1, is not equivalent to − 3( x + 1).
D. - 3x - 3
= - 3x - 3, is equivalent to − 3( x + 1).
Thus, A) - 3x + (- 3) and D) - 3x - 3 are equivalent.
For the following figure, complete the statement about the points.
If U lies on the same line as R and N, what terms describe the relationship that U has with R and N?
Answer:
it would be described as a collinear point as it is on the same line! hope this helps!
The term describing the relationship U has with R and N, assuming they lie on the same line, is called 'collinear'. In this scenario, points U, R, and N all lie on the same straight line.
Explanation:If point U lies on the same line as points R and N in geometry, it means that these points are collinear. The term 'Collinear' refers to points that lie on the same straight line. For example, if we consider the line as a straight road, then points U, R, and N can be visualized as three different spots on this road, which are along the same path.
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18)
Solve for 2 in the diagram below.
100
Answer:
100 ÷ 50 = 2.
One student rewrote the expression 17 x 102 as 17 parentheses 100 + 2 parentheses then 2 simplified to get the expression 1700 + 34. B what property of a number does this demonstrate
The expression demonstrates distributive property.
Explanation:
The given expression is [tex]17 \times 102[/tex]
Thus, solving the expression results in [tex]1734[/tex]
One student rewrote this expression as [tex]17(100+2)[/tex]
Then, simplified the expression as
[tex]1700+34[/tex]
Thus, [tex]17(100+2)=1700+34[/tex]
The expression demonstrates distributive property and the property can be generally written as
[tex]$a(b+c)=a b+a c$[/tex]
The given expression [tex]17(100+2)[/tex] is of the form [tex]$a(b+c)$[/tex]
Hence, The expression demonstrates distributive property.
8. Joe can chop vegetables in 5 minutes, and Rich can chop the same amount of vegetables in 4 minutes. Working together, how long will it take them to chop that batch of vegetables? 9. At Ricardo's Tacos, four tacos and two orders of chips cost the same as two tacos and four orders of chips. If Ricardo's charges $2.00 for a single order of chips, how much does Ricardo's charge for 1 taco? 10. Broccoli is $1.69 per pound. Meg paid $8.45 for broccoli. How many pounds did she purchase?
Answer:
Question 8: 2.22 minutesQuestion 9: $2.00 for one taco
Question 10: 5.00 pounds
Explanation:
8. Joe can chop vegetables in 5 minutes, and Rich can chop the same amount of vegetables in 4 minutes. Working together, how long will it take them to chop that batch of vegetables?
Name v the amount of vegetables
Joe can chop that amount is 5 minutes, then his speed is v/5 (vegetables per minute).Rich can chop the same amount of vegetables in 4 minutes, then his speed is v/4 (vegetables per minute)Working together, the combined speed is the sum of the two speeds: v/5 + v/4
Thus, the speed working together is:
[tex]\frac{v}{5} +\frac{v}{4}=\frac{4v+5v}{20}=\frac{9v}{20}[/tex]
Hence, they can chop 9 times the given amount of vegetables (v) in 20 minutes.
And the time to chop the given amount of vegetables (v) is 20 divided by 9.
[tex]time=amount/speed\\\\time=v/(9v/20)\\\\time=20v/(9v)=20/9=2.22[/tex]
That is 2.22 minutes to chop all the vegetables working together.
9. At Ricardo's Tacos, four tacos and two orders of chips cost the same as two tacos and four orders of chips. If Ricardo's charges $2.00 for a single order of chips, how much does Ricardo's charge for 1 taco?
Use T for the cost of tacos and C for the cost of orders of chips
Cost of four tacos and two orders of chips: 4T + 2C Cost of two tacos and four order of chips: 2T + 4CRicardo's charges the same for those orders:
4T + 2C = 2T + 4CRicardo's charges $2.00 for a single order of chips:
C = 2Substitute C = 2 in 4T + 2C = 2T + 4C and solve:
Substitution:
4T + 2(2) = 2T + 4(2)Do the operations:
4T + 4 = 2T + 8Subtract 4 from both sides
4T = 2T + 4Subtract 2T from both sides
4T - 2T = 4Combine like terms
2T = 4Divide both sides by 2
T = 2Hence, Ricardo's charges $2.00 for one taco.
10. Broccoli is $1.69 per pound. Meg paid $8.45 for broccoli. How many pounds did she purchase?
You must divide the amount paid ($8.45) by the unit price ($1.69/lb)
[tex]\$ 8.45/(\$ 1.69/lb)=5.00lb[/tex]
In the operation, $ appears both in the numerator and the denominator so they cancel out each other. The unit pounds (lb) appears dividing the denominator, thus it passes to the numerator.
Hence, Meg purchased 5.00 pounds
Final answer:
Solving these problems, Joe and Rich can chop vegetables in about 2.22 minutes together. Tacos at Ricardo's cost $2 each, and Meg purchased 5 pounds of broccoli.
Explanation:
Problem Solving in Mathematics
Joe and Rich Chopping Vegetables: Joe can chop vegetables in 5 minutes, while Rich can do the same in 4 minutes. When working together, the rate at which they can chop vegetables combines. This means Joe chops 1/5 of the vegetables per minute and Rich chops 1/4 per minute. Together, they can chop 1/5 + 1/4 = 9/20 of the vegetables per minute. Therefore, working together, they will take 20/9 minutes, or approximately 2.22 minutes, to chop the batch of vegetables.
Cost of Tacos at Ricardo's Tacos: Let's denote the cost of one taco as T. The equation based on the given information is 4T + 2(2) = 2T + 4(2). Simplifying this, we get 4T + 4 = 2T + 8, which reduces to 2T = 4, so one taco costs $2.00.
Meg's Broccoli Purchase: Meg paid $8.45 for broccoli that costs $1.69 per pound. To find out how many pounds she purchased, divide the total cost by the price per pound: $8.45 / $1.69. This calculation results in Meg purchasing 5 pounds of broccoli.