Speed = Distance / time:
Speed = 825 miles / 17 hours
Speed = 48.529 miles per hour. (Round the answer as needed).
Gas mileage = miles traveled / gallons used
Gas mileage = 825 miles / 38 gallons = 21.71 miles per gallon (Round answer as needed).
Unit rate of gas = Total money spend / gallons bought:
Unit rate of gas = $125 / 38 gallons = $3.289 per gallon.
Answer:
[tex]Speed = 48.53mph[/tex]
[tex]Gas.Mileage = 27.7 mpg[/tex]
[tex]Unit.Price = 3.29/gallon[/tex]
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
In order to find the Speed we need to divide the amount of total miles in the trip to California by the amount of time that it took.
[tex]Speed = \frac{Miles}{Hours}[/tex]
[tex]Speed = \frac{825.miles}{17.hours}[/tex]
[tex]Speed = 48.53mph[/tex]
Next we can calculate the Gas Mileage by dividing the amount of total miles by the amount of gallons of gas that the trip wasted.
[tex]Gas.Mileage = \frac{Miles}{Gallon}[/tex]
[tex]Gas.Mileage = \frac{825.miles}{38.gallons}[/tex]
[tex]Gas.Mileage = 27.7 mpg[/tex]
Finally, we can calculate the Unit Price by dividing the total amount of money wasted in the trip by the amount of gallons used in that trip.
[tex]Unit.Price = \frac{Total}{Gallons}[/tex]
[tex]Unit.Price = \frac{125}{38.gallons}[/tex]
[tex]Unit.Price = 3.29/gallon[/tex]
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
The frequency table shows the favorite college football teams of middle school students what fraction of the students choose the Sooners write the fraction as a decimal
what does the table look like
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Lou's car had 5.9 gallons in the 13-gallon tank on the coldest day of the year. Lou filled the tank with gas that cost $3.80 per gallon. How much did Lou spend on gas?
Lou spends the total amount would be $26.98 on gas which is determined by subtracting 13 gallons and 5.9 gallons and multiplying the result by $3.80.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
The following information is provided in the problem :
Lou topped up the tank with $3.80 per gallon of petrol.
Lou's car's 13-gallon tank held 5.9 gallons.
If he filled the tank, you can determine the total amount of money Lou spent by subtracting 13 gallons and 5.9 gallons and multiplying the result by $3.80.
So the total amount would be:
⇒ (13 - 5.9)(3.80)
⇒ (7.1)(3.80)
⇒ 26.98.
Therefore, the total amount would be $26.98
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The gravitational attraction between two masses varies inversely as the square of the distance between them. If the attraction force between them is 75 lbs. when the bodies are eight feet apart, find the attraction when the masses are twelve feet apart.
a) 33 1/3 lbs. b) 50 lbs. c) 168 3/4 lbs.
Answer: Option a) 33 1/3 lbs
Solution:
Be
Attraction force (F) varies inversely as the square of the distance between them:
F=k/d^2
Constant of proportionality: k
Distance between the two masses: d
F=75 lbs when d=8 feet
Replacing in the formula above:
F=k/d^2
75 lbs=k/(8 feet)^2
Squaring in the denominator:
75 lbs=k/(64 feet^2)
Solving for k: Multiplying both sides of the equation by 64 feet^2:
(64 feet^2)(75 lbs)=(64 feet^2)[k/(64 feet^2)]
4,800 lbs*feet^2=k
k=4,800 lbs*feet^2
F=k/d^2
F=4,800 lbs*feet^2/d^2
Find the attraction when the masses are twelve feet apart:
F=?
d=12 feet
Replacing in the formula:
F=4,800 lbs*feet^2/(12 feet)^2
Squaring in the denominator:
F=4,800 lbs*feet^2 / (144 feet^2)
Dividing:
F=(4,800/48)/(144/48) lbs
F=100/3 lbs
F=(99+1)/3 lbs
F=(99/3+1/3) lbs
F=33 1/3 lbs
Final answer:
Using Newton's inverse square law for gravitational force, it is determined that the force of attraction will be a) 33 1/3 lbs when the distance between the masses is increased from 8 to 12 feet.
Explanation:
The scenario described falls under the gravitational force law stated by Isaac Newton, which is a fundamental concept in Physics. The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them (F ∝ 1/d²). We are given that the gravitational attraction is 75 lbs when the bodies are 8 feet apart. To find the force at a distance of 12 feet, we use the inverse square law which indicates that increasing distance reduces gravitational force.
Let F1 be the initial force and d1 be the initial distance, and let F2 be the force at a new distance d2. According to the inverse square law, we have F1/F2 = (d2/d1)². Plugging in the values F1 = 75 lbs, d1 = 8 feet, and d2 = 12 feet, we get 75/F2 = (12/8)² = 2.25. Solving for F2, we find that F2 = 75 / 2.25 = 33.33 lbs.
Therefore, the gravitational attraction when the masses are twelve feet apart is 33 1/3 lbs.
I need help with a question before my test: how do I tell if a graph has rotational Symmetry if it is not an odd function and do all odd functions have point symmetry??
Answer:
If you know that the function is not odd, you know that the graph does not have rotational symmetry
Step-by-step explanation:
There is a theorem that says: "A function is odd if, and only if, its graph is symmetric with respect to the origin, or it has rotational symmetry in 180 ° with respect to the origin"
This statement is equivalent to:
If a function is odd, its graph has rotational symmetry with respect to the origin
If a graph has rotational symmetry with respect to the origin then the function is odd.
Therefore, it is impossible for the graph to have rotational symmetry with respect to the origin and the function is not odd.
Then, if you know that the function is not odd, you know that the graph does not have rotational symmetry
In one week, Altoona, PA, and Bethlehem, PA, Received snowfall every day, Monday through Friday. On which days did Altoona receive over 1 inch more snow than Bethlehem?
Answer:
On Friday Altoona receive over 1 inch more snow than Bethlehem.
Step-by-step explanation:
Consider the provided table.
First convert all the mixed fraction in decimal form.
Monday:
Altoona: [tex]2\frac{1}{4}=\frac{9}{4}=2.25[/tex]
On Monday Altoona received snowfall 2.25 inches
On Monday Bethlehem received snowfall 2.6 inches
Altoona receive Less snow on Monday.
Tuesday:
Altoona: [tex]3\frac{1}{4}=\frac{13}{4}=3.25[/tex]
On Tuesday Altoona received snowfall 3.25 inches
On Tuesday Bethlehem received snowfall 3.2 inches
The difference of 3.25 and 3.2 is 3.25-3.2=0.05
On Tuesday Altoona received over 0.05 inch more snow than Bethlehem.
Wednesday:
Altoona: [tex]2\frac{5}{8}=\frac{21}{8}=2.625[/tex]
On Wednesday Altoona received snowfall 2.625 inches
On Wednesday Bethlehem received snowfall 2.5 inches
The difference of 2.625 and 2.5 is: 2.625-2.5=0.125
On Wednesday Altoona received over 0.125 inch more snow than Bethlehem.
Thursday:
Altoona: [tex]4\frac{3}{5}=\frac{23}{5}=4.6[/tex]
On Thursday Altoona received snowfall 4.6 inches
On Thursday Bethlehem received snowfall 4.8 inches
Altoona receive Less snow on Thursday.
Friday:
Altoona: [tex]4\frac{3}{4}=\frac{19}{4}=4.75[/tex]
On Friday Altoona received snowfall 4.75 inches
On Friday Bethlehem received snowfall 2.7 inches
The difference of 4.75 and 2.7 is: 4.75-2.7=2.05
On Friday Altoona received over 2.05 inch more snow than Bethlehem.
Hence, On Friday Altoona receive over 1 inch more snow than Bethlehem.
Fuaad solved an absolute value inequality and expressed the solution as -12 < x > 7. What is another way to show Fuaad’s solution?
Solution: The another way to show the Fuaad's solution is [tex]x>7[/tex].
Explanation:
It is given that the solution of an inequality is [tex]-12<x>7[/tex].
It can be break in two parts [tex]-12<x[/tex] and [tex]x>7[/tex].
The inequality [tex]-12<x[/tex] means the values of x is greater than [tex]-12[/tex] and the inequality [tex]x>7[/tex] means the value of x is greater that than 7.
When we combine both results we get [tex]x>7[/tex] it means the value of x is greater than 7.
It can also represented by number line as shown in given figure.
The number line shows the values of x and red lines shows the solution of both inequalities [tex]-12<x[/tex] and [tex]x>7[/tex].
The common region shows the combination of both the possible inequalities, therefore the another way to show the Fuaad's solution is [tex]x>7[/tex].
Answer:
C (btw its x less than 7)
Step-by-step explanation:
Becuase the first option represents that the arrows go separate ways to infin.
the second option states that one variable is greater than of equal to and the other is only <
the third correctly shows and represents the inequality
the fourth one has the OR which means a number that is plugged in only needs to satisfy one of the inequalities which is not the point.
Factor the expression, show work
3x^3 - 4x^2 - 15x - 20
It can't be factored due to many reasons.
I hope this helps. :)
3x^3 - 4x^2 - 15x - 20
Cannot be factored.
Hope that helps
2x-1=3/4x +9 please help me solve
Hi!
[tex]2x-1=\frac{3}{4x+9}[/tex]
[tex]2x(4x+9)-1*(4x+9)=\frac{3}{4x+9}(4x+9)[/tex]
[tex]2x(4x+9)-(4x+9)=3[/tex]
[tex]2x(4x+9)-(4x+9)=3[/tex]
[tex]x=\frac{\sqrt{145-7} }{8},x=-\frac{7+\sqrt{145} }{8}[/tex]
[tex]x=\frac{\sqrt[]{145-7} }{8}, or x=-\frac{7+\sqrt{145} }{8}[/tex]
Explanation: First you had to multiply by 4x+9 from both sides. Then simplify, it gave us 2x(4x+9)-(4x+9)=3. Next you can also solve 2x(4x+9)-(4x+9)=3. And the answer it gave us is x=√145-7/8 or x=-7+√145/8 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day. -Charlie
PLEASE EXPLAIN THIS TO ME
it is y cause i just did that with my student
a company produces tables determines that its cost of producing and selling x tables is given by the function C(x)=50x+3000. the company is going to sell the bats for $70 per bat. how many table must be sold for the firm to break even
Cost of producing and selling x tables is given by the function C(x)=50x+3000
x is the number of tables produced
Each table is sold for $70
So selling price of x tables S(x) = 70x
Now we find the number of table must be sold for the firm to break even
Break even occurs when selling price = cost price
That is S(x) = C(x)
70x = 50x + 3000
Subtract 50x on both sides
20x = 3000
x = 150
150 tables must be sold for the firm to break even
The cast of the school play had a party at the drama teachers house.There were 20 cookies and 40 carrot sticks served as refreshments.Each cast member had the same amount of whole carrot sticks. Nothing was left over and the drama teacher did not eat. How many cast members might have been at the party??
60/4=15 and 20/4=5 there were 4 cast members at the party and they each ate 15 carrot sticks, your welcome
The cast members might have been at the party are
20 members – each gets 1 cookie and 2 carrot sticks, or 10 – each gets 2 cookies and 4 carrot sticks, or 5 – each gets 4 cookies and 8 carrot sticks, or 4 – each gets 5 cookies and 10 carrot sticks, or 2 – each gets 10 cookies and 20 carrot sticks, or 1 – gets it all: 20 cookies and 40 carrot sticksWhat is refreshments?Something to eat or drink during an event such as a meeting or party. . A more alert and comfortable state, especially after eating or drinking.
Finally the word "refreshment". While English adapted the term in the 15th century from several Gallic sources, according to the OED it meant the physical refreshment of a person or thing by food, drink, rest, coolness, etc.
Enjoying refreshment is a welcome break in the world of the day, and it also means that we leave working time for social elements, sharing coffee improves the mood and has a uniting effect, we are better able to deal with problems that arise within the team.
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Simplify |x| - |-x|.
0
2x
x2
How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?
they will each get 1/6 pound of chocolate. 1/2 divide by 3 = 1/6
[tex]\frac{1}{2}[/tex] divided by 3
[tex]\frac{1}{2}[/tex] / 3
Each person gets [tex]\frac{1}{6} lb. of chocolate
Evaluate the limit ....
It depends on how t is approaching 2.
In fact, if you consider the right limit, you have
[tex] \displaystyle \lim_{t \to 2^+} \dfrac{2-t}{|t-2|} [/tex]
But since t is greater than 2, t-2 is positive, and thus |t-2| = t-2.
So, the limit becomes
[tex] \displaystyle \lim_{t \to 2^+} \dfrac{2-t}{t-2} = \lim_{t \to 2^+} -1 = -1 [/tex]
On the other hand, if you consider the left limit, you have
[tex] \displaystyle \lim_{t \to 2^-} \dfrac{2-t}{|t-2|} [/tex]
But since t is less than 2, t-2 is negative, and thus |t-2| = -t+2.
So, the limit becomes
[tex] \displaystyle \lim_{t \to 2^+} \dfrac{2-t}{-t+2} = \lim_{t \to 2^+} 1 = 1 [/tex]
So, this limit does not exist, because the left and right limits exist but are not the same.
Determine the largest integer value of xxx in the solution of the following inequality.
−4x−5>-4
Is it 20?? I'm severely confused by this question too lol.
Find the value of x. Then find the measure of each label length.
A package of ground beef costs $6.98. The price per pound is $3.86. How many pounds of ground beef are in the package? Round to the nearest hundredth.
A. 1.81
B. .27
C. 1.80
D. 1.72
How do i write 3x-3y=18 in function notation
Maya works at adventure fun park she notices that the daily number of tickets sold at the park varies with the daily high temperature what is the dependent variable in this relationship
In the given scenario, the dependent variable is the daily number of tickets sold at the adventure fun park where Maya works. This changes based on the independent variable, which is the daily high temperature.
Explanation:In the scenario where Maya works at an adventure fun park and notices a change in the daily number of tickets sold depending on the daily high temperature, the dependent variable is the daily number of tickets sold at the park. This means that the number of tickets sold relies on or 'depends on' another factor, which in this case, is the daily high temperature. The daily high temperatures are the independent variable - the variable that signifies what changes can impact the other variable, the dependent variable.
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-20=-4×-6× what does x equal
If f(x)=x/2+8 what is f(x) when x=10
Hey there,
So the answer is 13.
The explanation is:
We are asked to find f(10), so let's evaluate this function at 10 by plugging this in for x.
So, as we know about the 10, the f(x) is going to be this- f(10).
We put f(10)= 10 over 2 + 8= 5+8 = 13
We have to flip the 8.
So you answer should be 13
Hope this helps...
-Justin0208
complete the solution of the equation. fine the value of y when x equals 4.
-3x+9y=-57
y = - 5
substitute the value of x = 4 into the equation and solve for y
- 12 + 9y = - 57 ( add 12 to both sides )
9y = - 45 ( divide both sides by 9 )
y = [tex]\frac{-45}{9}[/tex] = - 5
-3(-4)+9y=-57
12+9y=-57
9y=-57-12
9y=-69
9y/9=69/9
y=-23/3
how many dots will the the sixth figure in the pattern have
(40 points)
Which expression is equivalent to 3^2 ⋅ 3^−5?
(not giving answer choices for the best result)
Hello, The answer is 90.
because, 3x2 x 3x-5= 90
solve for x x−4.76=−7
Quick I need help
x - 4.76 = -7
Add 4.75 to both sides.
x = -2.24
The value of x for the given expression will be equal to -2.24.
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.
The given expression is x−4.76=−7. The value of x will be calculated as,
x - 4.76 = -7
Add 4.75 to both sides.
x = -2.24
Therefore, the value of x for the given expression will be equal to -2.24.
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Can anyone awnser 32.436÷(-4.24) as a fraction?
Hello, here are the fraction forms for this equation
Irrational fraction form; -153/20
Mixed number form; -7 13/20
Hoped this helped
The answer to 32.436 divided by -4.24 is approximately -7.65. However, the conversion of this decimal to a fraction gives us approximately -77/10.
Explanation:To answer the question, 32.436÷(-4.24) as a fraction, first, we should perform the division operation. The division of a positive number by a negative one will give a negative result. Hence, 32.436 divided by -4.24 is -7.65 approximately.
The answer as a decimal is -7.65. However, translating this decimal to a fraction isn't straightforward while keeping it a meaningful fraction, because 7.65 isn't easily expressed as a fraction. If you needed to express it as a fraction, you might round this to -77/10. But it's important to note it's an approximation, not exact.
Thus, 32.436÷(-4.24) becomes approximately -77/10 when expressed as a fraction.
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Josiah traveled 196 miles on 8 gallons of gasoline.At this rate how many gallons of gasoline would he need to travel 343 miles
it is 14 because if you
choose the word that makes the sentence true. The first digit in the quotient 1,875 ÷9
Hi, I'm Jenny from ExperimentsDIYS and I'm here to help you with your math! :)
I am assuming that you need help with question #1 so we will proceed with that one.
Lets first divide 1,875 ÷ 9.
Using a calculator, this is equal to 208.333333333
We can simplify this number by rounding up.
208.33 would be your answer rounded.
The first digit in this quotient ( Which is the answer to a division problem) is using place value.
The decimal place value chart is attached.
The first digit will be in the hundreds place because it is on the left side of the decimal point.
We are ecstatic to help and if there are any more problems or if we got any answers wrong please tell us! Thank you <3
-ExperimentsDIYS
The correct option is c.
The first digit of the result of the division 1,875 ÷ 9 is in the hundreds place
Explanation:Firstly, let's perform the division operation 1,875 ÷ 9 using long division method. The result of this division operation will be 208.333333.. . In this case, the first digit will be in the place that you are asked to identify.
The first digit, '2', is in the hundreds place. It's in this position because it's the first digit to the left of the decimal point. Further to its right, are the ones place (0) and the tenths place (8).
So, the correct option is 'C - hundreds' to fill in the blank for the sentence 'The first digit in the quotient 1,875 ÷ 9 will be in the hundreds place.'
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The complete question is here;
choose the word that makes the sentence true. The first digit in the quotient 1,875 ÷9
Options a. ones b. tens c. hundreds d. thousands
will be in the _______ place.
What is -8/15 as a decimal
-0.533333333
-hope this helps
2 - 4(x + 7) = 3 + 2 (x + 2)
[tex]2 - 4(x + 7) = 3 + 2 (x + 2)\\\\2-4x-28=3+2x+4\\\\6x=-33\\\\x=-\dfrac{33}{6}=-\dfrac{11}{2}[/tex]