Final answer:
The student can fill up their gas tank up to 4 times within their $108 budget for gasoline. The inequality used to determine this is 27n ≤ 108, solved by dividing both sides by 27.
Explanation:
To solve the student's question regarding how many times they can fill up their gas tank within a $108 budget, we need to set up an inequality and solve it. Let's define the variable n as the number of times they can fill up their tank.
Step A: Write the Inequality
Since it costs $27 to fill up one tank, and the student has budgeted no more than $108 for gas, the inequality will be:
27n ≤ 108
Step B: Solve the Inequality
To find out how many times the student can fill up the tank, we divide both sides of the inequality by 27:
n ≤ [tex]\frac{108}{ 27}[/tex]
n ≤ 4
Therefore, the student can fill up their gas tank up to 4 times within their budget.
A circle has an area of 78.5 square inches. What is the diameter of the circle?
To determine the diameter of a circle with an area of 78.5 square inches, we solve for the radius using the area formula (A = πr²). We find the radius to be 5 inches, and since the diameter is twice the radius, the diameter is 10 inches.
Explanation:The student has asked how to determine the diameter of a circle if the area is known to be 78.5 square inches. To find the diameter, we first need to calculate the radius using the area formula for a circle, which is A = πr², or area equals pi times the radius squared. Pi (π) is approximately 3.14159, but for most calculations, we can use 3.14 for simplicity.
To solve for the radius, we rearrange the formula to r² = A / π. Plugging in the given area of 78.5 square inches:
r² = 78.5 / 3.14 = 25
Next, we take the square root of both sides to find the radius: r = √25 = 5 inches.
Now that we have the radius, we can determine the diameter by multiplying the radius by 2, as the diameter is twice the length of the radius. Thus, the diameter of the circle is 10 inches.
The cage is 4 feet tall, 22 inches, wide, and 2 yards long. What is the volume of the cage in cubic inches?
The base of a pryramid can be any polygon how many faces does a pentagonal pyramid have ? Describe the shapes of the faces 22 points plz help give a good answer
A pentagonal pyramid has six faces: one pentagonal base and five triangular lateral faces. Each side of the pentagonal base connects to the apex forming five triangular faces. The total number of faces is six.
A pyramid is a three-dimensional geometric shape with a polygon as its base and triangular faces that meet at a single point called the apex.
A pentagonal pyramid has a base in the shape of a pentagon.
The total number of faces in a pentagonal pyramid equals the number of sides on the base (5) plus one more for the base itself, giving a total of six faces.
Thus, a pentagonal pyramid consists of six faces - one pentagonal base and five triangular lateral faces.
Find the product of 2x4(2x2 + 3x + 4)
Answer:
The answer is 4x^6 + 6x^5 + 8x^4
Step-by-step explanation:
2x^4(2x^2 + 3x + 4) Note: You add the exponents for multiplactation
4x^6 + 6x ^5 + 8x^4 Note: the exponent is 5 instead of 4 for the 2nd :) term of the soultion because there is a x on 3
I hope this helps you
HELP ASAP!!
The graph shows one of the linear equations for a system of equations. Which equation represents the second linear equation for the system of equations that has the solution which corresponds to a point at (2, 0)?
A) -x - 3y = 2
B) x + 3y = -2
C) 5x + y/2 = 10
D) 5x + y/2 = -10
Answer:
c
Step-by-step explanation:
6 grade math plz help
C equals 5/9 F32 the nearest whole degree what is the temperature in the degrees Fahrenheit when it is 90 degrees Celsius
The temperature in degrees Fahrenheit when it is 90 °C is approximately 194 °F. Therefore, option d is the correct answer.
Let's use the correct formula [tex]F = \frac{9}{5}C +32[/tex] to find the temperature in degrees Fahrenheit when it is 90 °C.
[tex]F = \frac{9}{5} *90+32[/tex]
Now, let's calculate:
[tex]F = \frac{9}{5} *90+32[/tex]
F=162+32
F=194
Therefore, the temperature in degrees Fahrenheit when it is 90 °C is approximately 194 °F.
So, the correct answer is D. 194 °F.
find the difference. express your answer in simplest form. (5s/s^2-10s+25) - (25/s^2-10s+25)
HELP ME PLEASE!!!!!!
The body of a 154-pound person contains approximately 2 X 10^-1 milligrams of gold and 6 X 10^1 milligrams of aluminum. Based on this information, the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body?
The number of milligrams of aluminium in the body is 300 times the number of milligrams of gold in the body.
Given amount of gold is = g = [tex]2 * 10^{-1}[/tex] mg.
Given amount of aluminium is = a = [tex]6*10^1[/tex] mg.
Let the number of milligrams of aluminium in the body is "k" times the number of milligrams of gold in the body.
So, a = kg
[tex]k=\frac{a}{g}\\k=\frac{6\cdot10^{1}}{2\cdot10^{-1}}\\k=300[/tex]
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The body of a 154-pound person contains approximately 300 times more milligrams of aluminum than milligrams of gold. This is found by dividing the amount of aluminum (60 milligrams) by the amount of gold (0.2 milligrams).
Explanation:To find out how many times the number of milligrams of aluminum is compared to that of gold in a 154-pound human body, we need to divide the amount of aluminum by the amount of gold. The problem states that there are 2 X 10^-1 milligrams of gold and 6 X 10^1 milligrams of aluminum. If we simplify these expressions, we get 0.2 milligrams of gold and 60 milligrams of aluminum.
Next step is to divide the number of milligrams of aluminum by the number of milligrams of gold. Hence, 60 ÷ 0.2 gives us 300.
Therefore, the body of a 154-pound person contains approximately 300 times more aluminum than gold.
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Which statement is true about the parts of this expression?
7.5y - z/9 + 50 +2y
A) The constant is 7.5.B) The coefficients are 7.5 and -9.C) The variables are x and y.D) The like terms are 7.5y and 2y.
Answer:
D
Step-by-step explanation:
a=false
b=false
c=false
d=true
edge.
URGENTAbel uses a probability simulator to roll a six-sided number cube 100 times and to flip a coin 100 times. The results of the experiment are shown below: Number on the Cube
Number of Times Rolled
1 l 12
2 l 18
3 l 30
4 l 22
5 l 10
6 l 8
Heads:34 Tails:66
Using Abel's simulation, what is the probability of rolling a 2 on the number cube and the coin landing on tails?
84/10,000
1,188/10,000
18/100
66/100
What is the simplified form of square root 64x^16?
A. 8x^4
B. 8x^8
C. 32x^4
D. 32x^8
1)you can use any side as the__ of a triangle.
2)An ___ is a region blinded by an arc and the two radii to the arcs endpoints.
3)the distance from the center to a vertex is the ___ of a regular polygon.
4)two arcs of a circle with exactly one point in common are ___.
9) A triangle has legs measuring 5ft and 12ft, and hypotenuse measuring 13ft. What is the area?
13) is the picture above.
17) what is the area of a regular hexagon with a perimeter of 240cm?
I have more questions but will post separately because they are all pictures!!!!
The sum of two numbers is 55. One number is 4 times as large as the other. What are the numbers? PLEASE HELP
Answer:
44 and 11
Step-by-step explanation:
Two cyclists leave town at the same time on the same road going in the same direction. Cyclist a is going 6 miles per hour faster than cyclist b. After 8 hours, cyclist a has traveled three times the distance as cyclist b. Use the equation 24x= 8(x+6) to find how fast cyclist b was traveling.
Answer:
3 mph
Step-by-step explanation:
Two cyclists leave town at the same time on the same road going in the same direction.
Cyclist A is going 6 mph faster than cyclist B
Let speed of cyclist B be x mph
Speed of cyclist A be (x+6) mph
Both cyclist leave town at the same time and traveled 8 hours.
Distance covered by cyclist A in 8 hours= 8(x+6)Distance covered by cyclist B in 8 hours= 8xAfter 8 hours cyclist A has traveled 3 times the distance as cyclist B
Therefore, 8(x+6) = 3(8x)
8x + 48 = 24x
24x - 8x = 48
16x = 48
x = 3 mph
Hence, The speed of cyclist B was 3 mph
a parking garage charges $2.00 for the first hour and $0.50 for each fraction of an hour thereafter. Which statement describes the relationship between the parking fee and the amount of time a person parks in the garage? A. the parking fee depends on the amount of time a person uses the garage B. The amount of time a person uses the garage depends on the parking fee C. the parking fee and the amount of time a person uses the garage are independent D. the relationship cannot be determined
all tickets for a concert are the same price.the ticket agency adds a fixed fee to every order.a person who orders 5 tickets pays $93.a person who buys 3 tickets pays $53
The question can be solved using a system of linear equations. The price of each ticket is found to be $20, and the fixed fee added by the ticket agency is $13.
Explanation:The subject of this question concerns solving a system of linear equations. Given the two scenarios, buying 5 tickets for $93 and buying 3 tickets for $53, we can represent these as equations where 't' represents the price of a ticket and 'f' represents the fixed fee. The equations thus become:
5t + f = 933t + f = 53
To solve this system of equations, we could subtract the second equation from the first, which would eliminate 'f' and yield an equation only in terms of 't'. This would look like:
2t = 40
From here, we can see that t (the price of each ticket) equals $20. We can then substitute 't' into one of the equations to find the fixed fee 'f', which in this case equals $13.
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Which expression is NOT equivalent to 8 times −5 and 1/4?
Drag this expression to the box.
Answer:
Step-by-step explanation:
what is the answer to 5+2x10
We are given expression : 5+2x10.
It can be read as 5 plus 2 times 10.
Now, we need to see, what operation should carry out first.
Please note: We always follow the order of operations.
The order of operations could be follow by the rule PEMDAS.
It stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
We don't have Parentheses, Exponents in the given problem.
So, we would start order of operations: first multiplication and then addition.
So, we need to multiply 2 × 10 first.
2 × 10 = 20.
Now, we need to apply addition operation.
Therefore, 5+2x10 = 5+20.
On adding 5 and 20, we get 25.
So, the final answer is 25.
Answer:
25 (assuming the x means multiplication)
Step-by-step explanation:
Start by using PEMDAS (Parenthesis, exponents, multiplication and division from right to left, addition and subtraction from right to left) you would start with multiplication or 2x10 which is 20 and then you have 5+20 left and that is obviously just 25
Jen makes necklaces by stringing different color beads each necklace is 18 in Long Jen has an 86 inch length of beaded string how many necklaces can she make
Can you please help me with this one please
The volume of this box is indeed 84 in^3. What were you looking for beyond that?
Base: (7 in)(3 in) = 21 in^2
Height: 4 in
volume = (21 in^2)(4 in) = 84 in^3 (answer)
HURRY BRAINLIEST ALREADY TAKEN BUT WOULDN'T IT BE NICE TO KNOW YOU HELPED SOMEONE? :)
Is this right? Problem attached
how much green ooze was carried all??
Answer:
[tex]5[/tex] cups.
Step-by-step explanation:
We have been given a line plot, which represents the cups of green ooze. We are asked to find the total number of cups.
To find the total number of cups, we will add all the given quantities as shown below:
[tex]2\times\frac{1}{4}+2\times\frac{3}{8}+2\times\frac{1}{2}+3\times\frac{5}{8}+\frac{7}{8}[/tex]
[tex]\frac{2\times1}{4}+\frac{2\times3}{8}+\frac{2\times1}{2}+\frac{3\times5}{8}+\frac{7}{8}[/tex]
[tex]\frac{2}{4}+\frac{6}{8}+\frac{2}{2}+\frac{15}{8}+\frac{7}{8}[/tex]
Make a common denominator:
[tex]\frac{2\times2}{4\times2}+\frac{6}{8}+\frac{2\times 4}{2\times 4}+\frac{15}{8}+\frac{7}{8}[/tex]
[tex]\frac{4}{8}+\frac{6}{8}+\frac{8}{8}+\frac{15}{8}+\frac{7}{8}[/tex]
Add numerators:
[tex]\frac{4+6+8+15+7}{8}[/tex]
[tex]\frac{40}{8}[/tex]
[tex]5[/tex]
Therefore, there are [tex]5[/tex] cups of green ooze in all.
A giant pencil, in the shape of a cylinder, has a length of 36 inches and a diameter of 6 inches. On top, it has a cone-shaped tip with a height of 4 inches. What is the volume of the pencil terms of pi?
Which point is a solution to the system of equations graphed below?
Simplify the expression
PLEASE HELP ME 19 POINTS What is the perimeter of quadrilateral MNOP ?
16 units
18 units
22 units
36 units
The value of the perimeter of quadrilateral MNOP is,
= 22 units
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
A quadrilateral MNOP is shown in figure.
M = (- 2, 2)
N = (2, 5)
O = (8, 5)
P = (4, 2)
Now, We can formulate;
MP = 6 units
PO = √(8 - 4)² + (5 - 2)²
PO = √ 25
PO = 5
Thus, The value of the perimeter of quadrilateral MNOP is,
= 2 (MP + PO)
= 2 (6 + 5)
= 2 x 11
= 22 units
So, The value of the perimeter of quadrilateral MNOP is,
= 22 units
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what is the volume of the right prism? ______ft3
Daniel gets a weekly $10 allowance. He has swimming class once a week and pays a $1.50 pool fee. After class, he sometimes goes out to eat with friends and spends $5 to $10. He is saving up for new swim trunks and sets aside $2.50 per week. Every few weeks, he goes to a swim meet in another town and spends $3 to $9 on bus fare.
This month, Daniel went out with friends and spent $8.50 for lunch. He went to 2 swim meets and spent $7 on bus fare each time. What are this month’s totals of his fixed and variable expenses?
fixed expenses total: $ ___
variable expenses total: $ ___
We have been given that Daniel's weekly allowance is $10 and we have to figure out his monthly fixed and variable expenses. To tackle this problem we have to figure out what are fixed expenses and what are variable expenses.
Fixed expenses are not going to vary as they are fixed. We have been given that Daniel has swimming class once a week and pays a $1.50 pool fee. Daniel is also saving for a new swimming trunks and sets aside $2.50 per week.
Variables expenses vary in a given range. We have been given that Daniel sometimes goes out to eat with friends and spends $5 to $10. Daniel goes to a swim meet in another town and spends $3 to $9 on bus fare.
Now let us find monthly fixed expenses first. [tex]1.50+2.50[/tex] are his weekly fixed expenses. To figure out monthly expenses we will multiply weekly expenses by 4 because a month has four weeks.
Monthly fixed expenses=[tex]4\times (1.50+2.50)=4\times 4=16[/tex]$
Now we will figure out monthly variable expenses. We have been given that Daniel has spent $8.50 for lunch and gone for two swim meets costing $7 each.
Monthly variable expenses=[tex]8.50+2\times 7=8.50+14=22.50[/tex]$
4. Rosa plays games at a fair. She can buy 8 game tokens for $ 1. Each game cost 2 tokens. How many games can she play with 120 tokens? Write a rule and complete the table.
Please help with the bottom one too
Answer:
60 tokens and the rule is the number of tokens divided by 2
20 cups of oats and the number of cups of raisins times 2
Rosa can play a total of 60 games with 120 tokens.
Explanation:To determine the number of games Rosa can play with 120 tokens, we need to divide the total number of tokens by the number of tokens required to play a game. Since each game costs 2 tokens, we divide 120 by 2. This gives us the number of games Rosa can play, which is 60.
We can also write a rule to calculate the number of games Rosa can play. Let G represent the number of games, and T represent the number of tokens. The rule would be: G = T ÷ 2. We can substitute T with 120 to find G: G = 120 ÷ 2 = 60.
Here is a table that shows the number of games Rosa can play for different numbers of tokens:
Number of Tokens
Number of Games
2
1
4
2
6
3
8
4
10
5
...
...
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