The efficiency of car is 55/2 MPG
• Fuel efficiency is a measure of how much energy in terms of fuel will be converted to kinetic energy to travel by a car. Most nations use miles per gallon to measure fuel efficiency (mpg).
• A good rule for fuel efficiency is that at least you are getting 23 miles per gallon combined city and highway.
• We calculate fuel efficiency by the formula MPG = (No of miles drove since last fill) / Gallons Based on the given conditions, Formula for MPG = (64 1/6 ) / (2 1/3)
Solving this we get= (64 + 1/6 ) / ( 2 + 1/3)= ((384 + 1)/6) / (7/3) = (385/6) / (7/3)= 55/2
Therefore, the vehicle's efficiency is 55/2 MPG.
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the center for disease control and prevention (cdc) states that adults should engage in at least 75 min of vigorous-intensity aerobic activity or 150 min of moderate-intensity aerobic activity weekly. researchers gathered data from a random sample of adults who participated in the 2011–2012 national health and nutrition examination survey (nhanes).
The relative frequency of adults who are engaging in less than the minimum amount of recommended moderate-intensity physical activity weekly is 92.16%.
What is relative frequency?The term 'relative' refers to an event that is being thought of in relation to or in proportion to another event.
The frequency of occurrence of an event is measured using frequency. Relative frequency, in contrast hand, is a method of calculating how frequently a specific event occurs in comparison to total occurrences.The amount of times an event happens divided by the total number of occurrences that occur in a specific scenario is defined as relative frequency.As, per the given question.
The minimum standard for moderate-intensity aerobic activity weekly is 150 min.
All the values which are less than 150 min will be considered as the below specified standard for moderate-intensity aerobic activity.
The relative frequency for 0 - 49 min is 47.54%.
The relative frequency for 50 - 99 min is 32.77%.
The relative frequency for 99 - 149 min is 11.85%.
Thus, the cumulative of all relative frequencies will be;
= 47.54% + 32.77% + 11.85%
= 92.17%
Therefore, the percentage of adults who get less than the recommended amount of moderate-intensity physical activity per week is 92.16%.
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The complete question is -
The center for disease control and prevention (cdc) states that adults should engage in at least 75 min of vigorous-intensity aerobic activity or 150 min of moderate-intensity aerobic activity weekly. researchers gathered data from a random sample of adults who participated in the 2011–2012 national health and nutrition examination survey (nhanes).
What is the relative frequency of adults who are engaging in less than the minimum amount of recommended moderate-intensity physical activity weekly (less than 150 min)? Give your answer to two decimal places.
the sum of three numbers is 111. the first number is less than the third. the second number is times the third. what are the numbers?
The first, second, and third numbers are 11, 80, and 20 respectively.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say the first number is a second is b and the third one is c
Now,
The sum of the three numbers is 111
So,
a + b + c = 111
The first number is 9 less than the third
So.
a = c - 9
And the second number is 4 times third
So,
b = 4c
By substitution,
c - 9 + 4c + c = 111
c = 20
b = 4(20) = 80
a = 20 - 9 = 11
Hence "The first, second, and third numbers are 11, 80, and 20 respectively".
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The given question are incomplete , complete question is ;
The sum of the three numbers is 111. the first number is 9 less than the third. the second number is 4 times the third. what are the numbers?
What number is halfway between -46.3
and 46.31?i
The number that is halfway between the numbers -46.3 and 46.31 will be 46.305.
We are given the two numbers:
- 46.30 and 46.31
Now, we need to find a number that is halfway between the given numbers.
For this, we need to find the mid point between the two numbers that is given to us.
Mid point is calculated as:
| x | + | y | / 2
Substituting the values in the expression, we get that:
46.3 + 46.31 / 2
= 92.61 / 2
= 46.305
Therefore, we get that, the number that is halfway between the numbers -46.3 and 46.31 will be 46.305.
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What is the slope of the following linear equation?
y = 4x - 7
Answer:
The slope is 4
Step-by-step explanation:
This equation is in slope intercept form
y = mx+b
where m is the slope and b is the y intercept
y = 4x-7
The slope is 4 and the y intercept is -7
Suppose a car has 4 gallons in its tank and the tank holds 14.5 gallons. How long does it take to fill the tank?
Answer: 1.75 minutes
Step-by-step explanation:
6 gallons per minute.
14.5-4=10.5
10.5/6=1.75 minutes
Continuing with the expression (x+7), do the following.
(a) By using the Distributive Property twice, show
that this expression is equivalent to
x² +14x+49.
35
(b) Test the equivalency by finding the value of
(x+7)² and x² +14x+49 when x = 3.
x² +14x+49
(x+7)²
(a) Using the distributive property ( x + 7 )² is equal to x² + 14x + 49.
(b) When x = 3, the expressions ( x + 7 )² and x² + 14x + 49 are equal.
Consider the expression ( x + 7 ),
Now when we square the expression we get,
( x + 7 )² = ( x + 7 ) ( x + 7 )
Using the distributive property,
( x + 7 )² = x( x + 7 ) + 7( x + 7 )
Again by using distributive property,
( x + 7 )² = x² + 7x + 7x + 49
( x + 7 )² = x² + 14x + 49
(b) For the expressions ( x + 7 )² and x² + 14x + 49,
When x = 3,
( x + 7 )² = ( 3 + 7 )²
( x + 7 )² = 10²
(x + 7 )² = 100
When x = 3,
x² + 14x + 49 = 3² + 14 × 3 + 49
x² + 14x + 49 = 9 + 42 + 49
x² + 14x + 49 = 100
Hence, the expressions (x+7)² and x² + 14x + 49 are equal when x = 3.
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Lisa and john are bowling. Johns score is three times the difference of Lisa's score and 6. The sum of their scores is 382. Find each students bowling score
Lisa bowling score is 100.
John bowling score is 282.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
Lisa and John are bowling.
Johns score is three times the difference of Lisa's score and 6.
The sum of their scores is 382.
Now, Let Lisa bowling score = x
Then, John bowling score = 3 (x - 6)
Since, The sum of their scores is 382.
Hence,
x + 3 ( x - 6 ) = 382
After solving,
x + 3x - 18 = 382
4x = 382 + 18
4x = 400
x = 100
Hence, Lisa bowling score = x = 100
And, John bowling score = 3 (x - 6)
= 3 (100 - 6)
= 3 × 94
= 282
Therefore, Lisa bowling score is 100.
And, John bowling score is 282.
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Answer:
A) The percentage of the bacteria increasing each hour is 15% per hour
B) When t=0 the population of bacteria is 3000 bacteria
C) After 24 hours the a sensible degree of accuracy in population is about 85875 (since only whole numbers count)
Step-by-step explanation:
A) To find the percentage of the bacteria increasing each hour the growth rate needs to be determined. To find it you need to subtract 1.15 by since the formula for exponential growth is a(1+r)^t one is added to the rate so to inverse it 1.15 needs to be subtractied by one to get 0.15. At this point you found the decimal rate to find the percentage you multiply 0.15 by 100 to make it a whole number and it results in 15%
B) To determine the size if the population when t=0 you substitute the variables t for 0 to get 3000×1.15^0 to get 3000 (remember anything times 0 is 0). Another way is to keep in mind that 3000 is the initial amount because that's the number with no variable with it.
C) To find the population after 24 hours substitute t for 24. After substituting t and multiplying 3000×1.15^24 the exact answer is 85875.52857. To find the answer in a sensible degree of accuracy you would round it to the nearest whole number which is 85876 since the dight in the tenths place is 5 or greater than the answer is rounded up by one.
a real estate agent believes that the value of houses in the neighborhood she works in has increased from last year. to test this claim, she randomly selects houses in this neighborhood and compares their estimated market value in the current year to their estimated market value in the previous year. suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market value of the previous year from the market value of the current year. assume that the values are normally distributed. using a test statistic of t≈7.496, the significance level α
The hypothesis is called the alternative hypothesis test.
According to the statement
We have to explain about the alternative hypothesis.
So, For this purpose, we know that the
The alternative hypothesis is one among ll|one amongst |one in every of} two mutually exclusive hypotheses in a hypothesis test. the choice hypothesis states that a population parameter doesn't equal a specified value.
From the given information:
she randomly selects houses during this neighborhood and compares their estimated market price within the current year to their estimated value within the previous year. suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market price of the previous year from the value of the present year.
Then
the alternative hypothesis test usually suggests that there's an opportunity of variation (difference) within the data observed.
Hence, since we are told the "real real estate agent believes that the values of homes within the neighborhood she works in have increased (the chance of variation) from last year," which "each difference is calculated by subtracting the market price of the previous year from the market price of this year," we are able to reach the conclusion that this can be an example of an alternate hypothesis test.
So, The hypothesis is called the alternative hypothesis test.
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Use graphing technology to approximate the solutions of the equation. x2 + 5x - 12 = | x + 3| + 7
The solution of the given equations is x=-7 and x=3.
The given equation is x² + 5x - 12 = | x + 3| + 7.
What is the solutions of the equation?A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values such that, when substituted for the unknowns, the equation becomes an equality.
Now, x² + 5x - 12 = | x + 3| + 7 can be rewritten as
x² + 5x - 12 = x + 3 + 7
⇒x² + 5x - 12 = x+10
⇒x² + 5x - 12 -x - 10=0
⇒x² +4x -22 =0
From the obtained graph, the solution of equations is x=-7 and x=3.
Therefore, the solution of the given equations is x=-7 and x=3.
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Two friends entered the amusement park at 10:05 AM. With the wait time it took 35 minutes to ride the FLIP-A-Trip. Then, it took 23 minutes to ride the Slippery Slope. What time was it then? Explain how you found your answer.
The computation shows that the time will be 11:05 am.
How to compute the value?The friends entered the amusement park at 10:05 AM, the wait time it took 35 minutes to ride the FLIP-A-Trip and it took 23 minutes to ride the Slippery Slope.
Therefore, the time will be:
= 10.05 + 35 + 25
= 10:05 + 60 minutes
= 10:05 + 1
= 11:05
.It should be noted that 60 minutes= 1 hour. Therefore, you'll add 1 hour to the original time.
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What is 4(3-x)+10 what does that equal
Answer:
22 - 4x
Step-by-step explanation:
4(3-x) + 10 Distribute the 4
4(3) - 4x +10
12 - 4x +10
22 - 4x
-10 plus - 3/4
Hurry please!
Point B is on line segment AC. Given AB = 3x, BC = 4x + 8, and
AC = 5x + 10, determine the numerical length of AC.
Answer: AC
Submit Answer
B
attem
Answer:
AC = 15
AB = 3
BC = 12
Step-by-step explanation:
AB + BC = AC
3x + (4x + 8) = 5x + 10
3x + 4x - 5x = 10 - 8
2x = 2
x = 1
AC = 5x + 10 = 5(1) + 10 = 15
AB = 3x = 3
Bc = 4x + 8 = 12
6) I used 4 packages of printer paper during 10 months. At this rate, how many packages
will I use for the year? (Hint: change months to years)
4.8 packages will need for the use of one year.
No. of used packages of printer paper during 10 months = 4 Packages
As we know that there is 12 months in a year,
To determine the number of packages need for the year, first we have to find the number of package is being use in one month.
S0, No. of used package in 1 month = 4/10 = 0.4 Package
Now, we will determine the number of packages for the use of one year, by multiplying the No. of used package in 1 month with 12.
No. of packages for the use of one year = 12 × 0.4
= 4.8 Packages
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HELPPPP!! Each of 8 students reported the number of movies they saw in the past year. Here is what they reported. 6,14,14,16,14,18,15,6
Based on the number of movies that each of the 8 students saw in the past year, the mean number of movies is 12.875 movies
How to find the mean?To find the mean of a distribution of numbers such as the number of movies seen in the past year, sum up the number of movies watched and then divide it by the number of students.
The mean number of movies watched by the students is therefore:
= Sum of movies watched / Number of students
= (6 + 14 + 14 + 16 + 14 + 18 + 15 + 6) / 8 students
= 103 / 8
= 12.875 movies
Rest of the question is:
Find the mean number of movies that the students saw.
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what is the answer too
5< k-2<11?
The k has interval notation(7,13).
Given that 5< k-2<11
Remove all of the teams from the inequality's center that don't contain k.
Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
So, 5+2<k<11+2
7<k<13
Therefore, The interval notation for k is (7,13).
Equations in mathematics are not always balanced on both sides using a 'equal to' symbol. Sometimes it's a 'not equal to' relationship, as though something is more than or less than the other. In mathematics, an inequality is a relationship that results from a non-equal comparison of two numbers or other mathematical expressions. Inequalities are mathematical expressions that fall within the category of algebra.
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Which numbers are irrational?
11, √15, -14, 20.151155111555...
Answer:
√15, -14, 20.151155111555...
Step-by-step explanation:
it's a square root (not perfect), negative, and never ending decimal
Answer:
It would have to be [tex]\sqrt{15}[/tex].
----------------------------------------------
Hope this helps!
Have a great day and God bless! :)
someone please help me with these 2 :(
Answer:
1. x^-3
2. b^7
Step-by-step explanation:
I am pretty sure those are the answers. I'm not 100%
Determine whether the ordered pair (9, 10) is a solution of y = 2x −8.
Answer:
false
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
to determine if (9, 10 ) is a solution, substitute x = 9 into the equation and if y = 10 then it is a solution.
y = 2(9) - 8 = 18 - 8 = 10
then (9, 10 ) is a solution of the equation
A farmer sells an average of 15 3/5 bushels of corn each day. What integer represents the charge in bushels of corn in his inventory after 6 days?
well, let's convert the mixed fraction to improper fraction firstly, then let's check their difference.
[tex]\stackrel{mixed}{15\frac{3}{5}}\implies \cfrac{15\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{78}{5}}\qquad \impliedby \textit{that's for just 1 day} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\LARGE after 6 days}}{\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} }\implies \cfrac{468}{5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{change in bushels}}{\cfrac{468}{5}~~ - ~~\cfrac{78}{5}}\implies 78\qquad \impliedby \textit{so 6 days later he's got 78 more bushels}[/tex]
HELPPP PLEASE HELP i need helpp asap
Answer:
2
Step-by-step explanation:
2 ^ 9 is already way more than 82 so yea it has to be 2
Please help
Find the slope of the line passing through the given points. how do you know?
The slope of the line passing through the given points is 0.4 or 2/5.
From the table given below, we have (2, 23) and (5, 24.3).
What is the slope of the line passing through the coordinate points?Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y-values over the change in the x-values.
Put the points (2, 23) and (5, 24.3) in the slope formula and find the slope.
That is, m=(24.3-23)/(5-2)
=1.3/3
=0.4
=4/10 = 2/5
Put m=2/5 and the coordinate points (2, 23) in y=mx+c.
That is, 23=2/5 (2)+c
⇒23 - 4/5 =c
⇒111/5 = c
⇒ c=22.2
Now, equation is y=0.4m+22.2
Therefore, the slope of the line passing through the given points is 0.4 or 2/5.
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Please Help
Thanks In advance
Answer:
U = 4
Step-by-step explanation:
We take 3/9 and simplify it, making 1/3.
We multiply both by 12 to eliminate denominators, so the new numbers are 4 and U.
U = 4
2 (1.5c - 2.5) + 7 + 17
pls help
The simplified form of the expression is equivalent to 3c - 19
Simplifying expressionsAn algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as the addition, subtraction, division and multiplication.
Given the expression below;
2 (1.5c - 2.5) + 7 + 17
Expand
2(1.5c) - 2(2.5) + 7+ 17
3.0c - 5.0 + 24
3c - 19
Hence the simplified form of the expression is equivalent to 3c - 19
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Do number 14 please thank you
Answer:
(M U C) ∩ V = {3, 5}
Subsets: { }, {3}, {5}, {3, 5}
Step-by-step explanation:
M = {2, 3, 4, 5}
C = {4, 6, 8, 10}
V = {3, 5, 7, 9}
(M U C) ∩ V =
= ( {2, 3, 4, 5} U {4, 6, 8, 10} ) ∩ {3, 5, 7, 9}
= {2, 3, 4, 5, 6, 8, 10} ∩ {3, 5, 7, 9}
= {3, 5}
Subsets: { }, {3}, {5}, {3, 5}
Which linear function represents the line giving by the point slope equation y-2=4(x-3)
The linear function that represents the line giving by the point slope equation y-2=4(x-3) is f(x) = 4x - 10
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
Also note that f(x) = y
Isolate the y then add 2 from both sides:
y - 2 = 4(x-3)
y - 2+ 2 = 4(x-3)+2
y = 4(x-3) + 2
Note that the equation is : y = 4(x-3) + 2
Now Distribute 4 to all terms within the parenthesis
y = 4(x-3) + 2
y = 4x - 12 + 2
Simplify. Combine like terms
y = 4x - 10 ; or f(x) = 4x - 10.
Hence, The linear function that represents the line giving by the point slope equation y-2=4(x-3) is f(x) = 4x - 10
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a recipe for crispy rice treats results in a mixture that fills a 9-inch by 13-inch pan to a depth of one inch. if a crispy rice treats mixture resulting from 1.5 times the original recipe is poured into a pan that is 10 inches by 15 inches, to what depth will the pan be filled? express your answer as a decimal to the nearest hundredth.
Answer: 117in^3
Step-by-step explanation:
Yossi has a square-shaped garage with 52 square meters of floor space plans to build an addition that will increase the floor space by 50%. What will be the length of one side of the new garage?
The length of the new garage will be approximately 8.83 meters.
The length is referred as the side of a rectangle or a square. Ideally we use length to measure the larger side of a rectangle, but for a square all sides are equal and so can be called length.
The are of a square is given by the square of any side .
Given the area of the square is 52 square meters.
The new are of the square is 50% more.
Increased amount = 50% of 52 = 26 meters²
New area of square = 52 + 26 meters² = 78 meters²
Now we know that the area of a square is given by (side)² .
Therefore (side)²= 78
or, side = √78
or, side = 8.8317...
or, side ≈ 8.83 meters
Therefore the length of the new garage is approximately 8.83 meters.
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for how many bases between two and nine inclusive does the representation of $576 {10}$ have a final digit of 1?
Answer:
Step-by-step explanation:
Convert 576 from base 10 to following bases:
first of all convert 576 from base 10 to base 2 we got this
1001000000_2
now then convert 576 from base 10 to base 3 we got this
210100_3
now then convert 576 from base 10 to base 4 we got this
21000_4
now then convert 576 from base 10 to base 5 we got this
4301_5
now then convert 576 from base 10 to base 6 we got this
2400_6
now then convert 576 from base 10 to base 7 we got this
1452_7
now then convert 576 from base 10 to base 8 we got this
1100_8
now then convert 576 from base 10 to base 9
710_9
Only in base 5 does it end in 1.
referred by www.web2.0calc.com
So only in base 5 does it end in final digit of 1.
A Binary operation can be considered as a function whose input is two elements of the same set S and whose output also is an element of S. S . Two elements a and b of S can be written as a pair (a, b) of elements in S.
So first of all convert 576 from base 10 to following bases:
first of all convert 576 from base 10 to base 2 we will get this 1001000000_2
Then convert 576 from base 10 to base 3 we will get this 210100_3
Then convert 576 from base 10 to base 4 we will get this 21000_4
Then convert 576 from base 10 to base 5 we will get this 4301_5
Then convert 576 from base 10 to base 6 we will get this 2400_6
Then convert 576 from base 10 to base 7 we will get this 1452_7
Then convert 576 from base 10 to base 8 we will get this 1100_8
Then convert 576 from base 10 to base 9 we will get this 710_9
Therefore only in base 5 does it end in final digit of 1.
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