33.2 miles per gallon is the unit rate for miles per gallon.
Given, Grace drove 41 1/2 miles.
She used 1 1/4 gallons of gasoline.
So, Grace drove 41 1/2 miles = Grace used 1 1/4 gallons of gasoline
41(1/2) miles = 1(1/4) gallons of gasoline
83/2 miles = 5/4 gallons of gasoline
as, 5/4 gallons of gasoline = 83/2 miles
1 gallon of gasoline = (4/5)×(83/2)
1 gallon of gasoline = (2/5)×83
1 gallon of gasoline = 166/5
1 gallon of gasoline = 33.2 miles
33.2 miles/gallon is the unit rate.
Hence, 33.2 miles per gallon is the unit rate for miles per gallon.
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A 95% confidence interval for the population mean is constructed as 6 ± 2. What is the confidence coefficient?.
Confidence coefficient or confidence level for the interval is 0.95.
What is confidence coefficient?
The proportion of samples of a given size that may be anticipated to contain the true mean is all that the confidence coefficient is.
Confidence level:
Confidence level means the proportion or frequency of acceptable confidence intervals that contain the true value of the unknown parameter.
For example,
A 0% confidence level means you have no faith at all that if you repeated the survey that you would get the same results.
Main Body :
Confidence Interval = 95%
Hence the confidence interval would be 0.95.
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A piece of notebook paper measures 8 1/2 inches by 11 inches. Which of the following metric approximations is the same?
a. 2 m x 2.8 m
b. 3 cm x 4 cm
c. 22 cm x 28 cm
d. 30 m x 40 m
The approximation in meters that is same with a notebook paper measures 8 1/2 inches by 11 inches is
c. 22 cm x 28 cmHow to determine approximationsThe approximation is solved by converting the given unit to metric
The conversion from inches to metric
meters = m
inches = in
The unit conversion factor is given as
1 meter = 39.3701 inches
? meter = 8 1/2 inches
cross multiplying gives
? * 39.3701 = 1 * 8 1/2
? = 8 1/2 / 39.3701
? = 0.2159 m
? = 21.59 cm
? =22
11 inches to metric
? = 11 / 39.3701
? = 27.94 cm
? = 28
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Select the correct answer.
Which equation describes the line graphed above?
A. y=-4x-5
B.y=-1/5x-4
C.y=-5x-4
D.y=-4x-1/5
Answer:b
Step-by-step explanation:slope is -1/5. Rise over run, so you go down 1, and right 5
15) The circumference of a circle is 20π ft. There's a 25% reduction of the circle's radius. What is the area of
the circle are the reduction of the radius?
Answer:
314 cm squared
Step-by-step explanation:
yea think so
$ 1,012,481.37
-926,399.76
Answer: $86,081.61
Step-by-step explanation:
Answer: 986,081.61
Step-by-step explanation:
Which fraction has a value that's equal to 7/8?
A. 15/8
B. 21/24
C. 49/64
D. 56/8
Answer:
B
Step-by-step explanation:
If you divide 7/8 you will get 0.875 which is equivalent to 21/24 which is 0.875.
Solve for x, show all work for full credit.
2^(3x+1)=1/4
For your answer please include these three things: Convert to the same base, write the equation, and solve the equation.
Fake answers will be deleted please answer fully and correctly to get brainliest.
The value of x in the given equation, 2^(3x+1)=1/4, is x = -1
Solving equations: Determining the value of xFrom the question, we are to solve the given given equation.
The given equation is
2^(3x+1) = 1/4
To solve the equation, we will determine the value of x.
Solving for x in the equation
2^(3x+1) = 1/4
Express 1/4 in index form
NOTE: 1/4 = 4^-1 = 2^-2
Thus,
The equation becomes
2^(3x+1) = 2^-2
Now, equate the powers
That is,
(3x + 1) = -2
3x + 1 = -2
Subtract 1 from both sides of the equation
3x + 1 - 1 = -2 - 1
3x = -3
Divide both sides of the equation by 3
3x/3 = -3/3
x = -1
Hence, the solution is x = -1
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What document did Missouri need to become a state?
A) Declaration of Independence
B) lease
C) bill of sale
D) state constitution
Answer:
d) State constitution
Step-by-step explanation:
Missouri needs a state constitution to become a state. It is necessary for every state. Hence, option (d) is correct answer.
I"LL GIVE BRAINLEST! You are skiing down a 1,350-meter ski slope at 60 meters per second. Let t represent your skiing time in seconds and d t( ) represent the distance from the bottom of the ski slope. Write an algebraic function rule that can be used to model the scenario. Then explain what the slope and the vertical intercept mean in the context of the problem
Answer:
d = 1350 - 60t
Step-by-step explanation:
the slope is for every x how y changes so the x would be represented by t (which is the time in seconds in this case) and y would be the distance from the bottom of the ski slope.
the vertical intercept would define when you are gaining distance or losing distance
What is the l and w if the area is 32 and the perimeter is 24
According to the area and the perimeter of the rectangle, the value of l is either 4 or 8 and the value of w is either 4 or 8
Area and perimeter of rectangle:
Area of the rectangle is the region occupied by a rectangle within its four sides or boundaries.
Perimeter of the rectangle is add the lengths of all four sides.
Given,
The area of the rectangle is 32 and the perimeter of the rectangle is 24.
Now, we have to find the value l and w.
When we apply the value on the formula of area of rectangle, then we get,
32 = l x w
It can be rewritten as,
l = 32/w
Now, apply the value of perimeter of the rectangle, then we get,
24 = 2(l + w)
Apply the value of l as 32/w, then we get,
24 = 2(32/w + w)
12 = 32/w + w
12 = (32 + w²)/w
w² - 12w + 32 = 0
When we factorize the polynomial, then we get,
=> (w - 4) (w - 8) = 0
So, the value of w is either 4 or 8.
So, now we have to find the value of l through this value,
=> w = 4 => l = 32/4 = 8
=> w = 8 => l = 32/4 = 4
Therefore, the value of l is either 4 or 8.
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Find the linear function represented by the graph.
The slope of the line is
The y-intercept of the line is at
What linear function is represented by the graph?
Answer:
i am trying to gt points step-by-step explanation:
seeeeeee i gto
Find the final price after a discount of 15% and then a sales tax of 4.67%
a) a PlayStation 5 for 750
b) 3 pairs of Yeezys for 265
the line 2y = 6x +c passes through the point (2, 3). find c
Answer:
-6
Step-by-step explanation:
2y=6x + c
(2 X 3) = (6 X 2) + C
C= - 12 + 6
= - 6
The numbers in bold are the point axes.
Using the slope formula, find the slope of the line through the given points (4,2) (-5,2) and Question content area bottom Part 1 What is the slope of the line? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The slope is zero if the fraction's numerator is 0.
Given,
The line passes through the points;
(x₁, y₁) = (4, 2)
(x₂, y₂) = (-5, 2)
We have to find the slope of the line using slope formula;
Slope formula ;
m = (y₂ - y₁) / (x₂ - x₁)
Here,
m = (2 - 2) / (-5 -4 ) = 0/-9
Slope, m = 0
The slope is zero if the fraction's numerator is 0. If both points' y values are equal, this will take place. The graph would be a horizontal line and show that for all values of x, the y value remains constant.
That is,
The slope is zero if the fraction's numerator is 0.
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Which linear function is graphed on the grid?
A g(x)=15x-6
g(x) = 5x +45
g(x)=x-6
g(x) = 5x +45
1 2 3 4 5 6 7 8 9
The linear function graphed on the grid will be g(x) = (15/2) x + 45. Option D is correct.
First, let us understand the linear equation:
When a graph is exhibited, a relationship between a number of variables results in a linear model. The variable will be of degree one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
From the graph, we are given the x-intercept is - 6, and the y-intercept is 45.
Substitute the given values in the above formula, we will get;
x / (-6) + y / 45 = 1
- 15x + 2y = 90
y = (15/2) x + 45
g(x) = (15/2) x + 45
Thus, the linear function graphed on the grid will be g(x) = (15/2) x + 45. Option D is correct.
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Albert ha y ticker. Latika ha more ticker than Albert. John ha time a many ticker a Latika. Write down an expreion, in term of y, for the number of ticker John ha
The algebraic expression, in terms of y , for the number of stickers John has is given by 4(y + 2)
How to write algebraic expression?
Algebra refers to the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
Number of stickers Albert has = y
Number of stickers Latika has = y + 2
Number of stickers John has = 4(y + 2)
The expression for the number of stickers John has = 4(y + 2)
For instance, if y = 3
Number of stickers Latika has = y + 2
= 2 + 2
= 4 stickers
Number of stickers John has = 4(y + 4?2)
= 4(3 + 2)
= 4(5)
= 20 stickers
Therefore, the expression which can be used to represent the number of stickers John has is 4(y + 2)
Complete question:
Albert has y stickers.
Latika has 2 more stickers than Albert.
John has 4 times as many stickers as Latika.
Write down an expression, in terms of y , for the number of stickers John has.
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What is symmetry and its type?.
Shapes that are symmetrical (or symmetric) have an identical side on each side. A symmetry may be divided into four primary categories: translation, rotation, reflection, and glide reflection.
What is symmetry?Shapes that are symmetrical (or symmetric) have an identical side on each side. When mirrored, rotated, or translated, symmetrical forms retain their original appearance. A symmetry may be divided into four primary categories: translation, rotation, reflection, and glide reflection. The line dividing an animal into two halves is referred to as symmetry. Asymmetry, radial symmetry, and bilateral symmetry are only a few examples of symmetry. Animals are classified according to these symmetries, which are distinct from one another. Rotational symmetry, reflection symmetry, translation symmetry, and glide reflection symmetry are some examples of symmetries. Planar symmetry, which refers to various forms of symmetry on a flat surface, is shown by these four different types of symmetry.
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what is the last term, b if there are 12 terms, the first term is 3 and the SUM, s is 612 S=n/2(a+b)
The last term b of the expression is 99
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP : Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Sum of first n terms of an AP : Sₙ = ( n/2) ( a+b )
where a = first term
b = last term
Given data ,
First term a = 3
Number of terms n = 12
Sum of n terms Sₙ = 612
Let the last term of the AP be = b
Sum of first n terms of an AP : Sₙ = ( n/2) ( a+b )
Substitute the values of a , Sₙ and n in the equation
612 = ( 12/2 ) ( 3 + b)
612 = 6 ( 3 + b )
Divide by 6 on both sides , we get
102 = 3 + b
Subtract 3 on both sides , we get
b = 99
Hence , the last term of the Arithmetic Progression is 99
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Instructions
Type an essay response to the following prompt. Completely explain all parts of your response and use the rubric to determine what you need to include in your essay.
Create and solve a story problem that would use this equation: y=5x+3 Be sure to define x, y, the constant, the coefficient and the variable.
The time taken, t, for passengers to be checked-in for a flight is inversely proportional to the square of the number of staff, s, working. It takes 30 minutes passengers to be checked-in when 10 staff are working. (a) Find an equation connecting t and s. (b) What is the minimum number of staff that must be working so that the time taken is under 60 minutes?
(a) The equation connecting t and s in the proportionality question is t = 300/s .
(b) The minimum number of staff that must be working so that the time taken is under 60 minutes is 20 staff.
What is inverse proportion?Inversely proportional means that the two quantities behave opposite in nature.
(a) To find the equation connecting t and s we use the inverse proportionality technique
From the question,
t ∝ 1/sTo remove the proportionality sign, we intoduce a constant (k)
t = k/sk = ts............ Equation 1Given:
t = 30 minutess = 10 staffSubstite these values into equation 1
k = 30×10k = 300Therefore the equation connecting t and s is
t = 300/s(b) To calculate the minimum number of staff that must be working so that time take is under 60 minutes, we substite the value of t = 60 into the equation above
60 = 300/ss = 300/60s = 20 staff.Hence, the equation is t = 300/s and the minimum number of staff is 20 staff.
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the foreclosure crisis has been particularly devastating in housing markets in much of the south and west united states, but even when analysis is restricted to relatively strong housing markets the numbers are staggering. for example, in 2017 an average of three residential properties were auctioned off each weekday in the city of boston, up from an average of one per week in 2011. what is the probability that no more than two foreclosure auctions occurred on a randomly selected weekday of 2017 in boston?
The probability that no more than two foreclosure auctions occurred on a randomly selected weekday of 2017 in boston is 0.4232
What is probability?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
Calculationcalculation has been attached in the picture below
the probability that no more than two foreclosure auctions occurred on a randomly selected weekday of 2017 in boston is 0.4232
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Fill out the table of values given the system of equations. What
is the solution to the system?
y = 5x + 10
y = 6x-1
10
11
12
The solution to the system is:
Write your answer as an ordered pair, for example: (x,y)
The required solution of the system is shown below,
5x+ 10 6x - 1
10 60 59
11 65 64
12 70 71
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here
We have 2 equations,
y = 5x + 10 - - - - - {1}
y = 6x - 1 - - - ---(2)
Substitute the value 10, 11, and 12 in both the equation to get the values of y as,
5x+ 10 6x - 1
10 60 59
11 65 64
12 70 71
Thus, the solution of the system is shown in the table above.
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What is the numerator of the simplified sum?
StartFraction x Over x squared + 3 x + 2 EndFraction + StartFraction 3 Over x + 1 EndFraction
The numerator of equation (x/(x²+3x+2)+3/(x+1)) in simplified sum is 4x+6.
Here, the given equation is
First, we will simplify this equation
(x/(x²+3x+2)+3/(x+1))
We will take LCM an write the equation as follows.
((x(x+1)+3(x²+3x+2))/((x²+3x+2)(x+1))) -----------(1)
Now, factorize the equation x²+3x+2
So,
x²+3x+2
=x²+2x+x+2
=x(x+2)+1(x+2)
=(x+1)(x+2)
Put this factors in denominator of equation (1)
So, the equation will be written as
=((x²+x+3x²+9x+6)/(x+1)(x+2)(x+1))
=((4x²+10x+6)/((x+1)² (x+2))) -----------------(2)
Factor of numerator in above equation
=4x²+10x+6
=4x²+6x+4x+6
=4x(x+1)+6(x+1)
=(4x+6)(x+1)
Put this value in equation (2)
so, we can write equation (2) as
=(((4x+6)(x+1))/((x+1)^2 (x+2)))
Cancelling (x+1) from numerator and denominator
Then the equation will become,
=((4x+6)/((x+1)(x+2)))
This is the simplified form of given equation
Hence,
The numerator of the simplified sum is (4x+6)
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( HELP ASAP) Using the lists of multiples, determine the least common denominator of 1/4 and 7/8.
Answer:
8
Step-by-step explanation:
because is the smallest multiple that 4 and 8 have in common
twelve hours after being filled, all the balloons have decreased in size. predict which balloon will be the smallest. explain your reasoning.
The balloons which have Helium (He) in them will be the smallest.
Because it has the tiniest molecule when compared to the other gases, helium (he) will leak out the most quickly. Helium molecules can enter the balloon through microscopic pores because they are the tiniest molecules. more quickly than the other gases.
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Determine which set of side measurements could be used to form a triangle.
The set of side measurements that could be used to form a right triangle is √3, √13, and 4 option (D) is correct.
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that:
The side length of the triangle is shown in the option:
As we know,
Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
Using Pythagoras' theorem:
From option(D):
√3, √13, and 4
(√3)² + (√13)² = 4²
3 + 13 = 16 (True)
Determine which set of side measurements could be used to form a right triangle.
4, 8, 11
6, 8, 13
square root of 3, square root of 5, 8
square root of 3, square root of 13, 4
Thus, the set of side measurements that could be used to form a right triangle is √3, √13, and 4 option (D) is correct.
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plssss helpppp meeeee
Answer:
x = -4; y = 2
Step-by-step explanation:
The solution is the point of intersection of the two lines.
The lines intersect at point (-4, 2).
Answer: x = -4; y = 2
Answer:
x = -4; y = 2
Step-by-step explanation:
the are the answers to both of the statements
one out every three boxes of cereal has a prize i it.
Answer: The percentage of a cereal box would be 1/3 or 33.33%.
Step-by-step explanation:
Question 4(Multiple Choice Worth 2 points)
(Operations with Decimal Numbers LC)
What is the quotient of 7.536 ÷ 0.3?
The Answer is 25.12 I know this because I used a calculator. Hope this helped! :)
Answer: 25.12
Step-by-step explanation:
The Answer is 25.12 I did a test and got it right. I hope this helps!
Write 23/6 as a mixed number.
Answer:
[tex]3\frac{5}{6}[/tex]
Step-by-step explanation:
6 can go into 23, 3 times with 5 left over
we write it like this
[tex]3\frac{5}{6}[/tex]
Hopes this helps please mark brainliest
Answer: Its 3 5/6
Step-by-step explanation: 6 goes into 23 3 times. and 5 leftover so
