The rate of gas usage, in miles per gallon, is 35.4 miles/gallon.
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
Given that, A table below shows that the number of miles driven by Hakeem is directly proportional to the number of gallons he used.
According to the table,
There are 36, 41, 45 gallons of gas are used for 1274.4 mile, 1451.4 and 1593 miles respectively,
So, for finding unit rates, we will divide the total mile to total gallons used, in one journey,
unit rate = 1593/45 = 1274.4/36 = 1451.4/41 = 35.4
Hence, The rate of gas usage, in miles per gallon, is 35.4 miles/gallon.
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the value in dollars of recycling varies with the type of material. what is the weighted mean of this mixture of recyclables if compost is now worth twice as much?
The weighted mean of the mixture of recyclables would be (4 x $1 + 2 x $2) / 6 = $1.33.
To calculate the weighted mean of the mixture of recyclables, first identify the number of each material and their respective values. In this case, there are 4 items worth $1 each and 2 items worth $2 each. To calculate the weighted mean, multiply each item's value by the number of items and then divide by the total number of items
In this case,
4 x $1 + 2 x $2 = $6
and 6 items total, so the weighted mean is
$6 / 6 = $1.33.
This means that if compost is now worth twice as much, the weighted mean would be
(4 x $1 + 2 x $2) / 6 = $1.33.
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Juan claims that y=4x^3+1 is a function, but not a linear function. Select the statement that supports Juan's claim.
A. The function does not contain the point (0,0)
B. The coefficient of x^3 is not 1
C. The graph of the function does not form a straight line
D. The function increases
Answer:
C. The graph of the function does not form a straight line
Find two number uch that one of them i five time the other and their difference i 200
Based on the relation between two numbers considering their difference and multiple, the numbers are 50 and 250.
Let the one number be x. So, the other number, according to the information in question, will be 5x. Now representing the equation depending on the stated details -
5x - x = 200
Performing subtraction on Left Hand Side of the equation
4x = 200
Writing the equation again to find the value of x
x = 200/4
Performing division on Right Hand Side of the equation
x = 50
First number = 50
Another number = 50×5
Performing multiplication on Right Hand Side of the equation
Second number = 250
The two numbers according to multiple and difference are 50 and 250.
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Solve using a matrix.
2x-6y=22
-5x+y=1
can you please give me something I can copy-paste?
IT is found that the value of x is 4 and value of y is 5.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given system of equations are
2x-6y=22
-5x+y=1
The matrix form is
[tex]\left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}22\\1\end{array}\right][/tex]
Let as assume
[tex]A = \left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right]\\ \\X = \left[\begin{array}{ccc}x\\y\end{array}\right] \\B = \left[\begin{array}{ccc}22\\1\end{array}\right][/tex]
WE know that AX = B
Then we have;
[tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4\\5\end{array}\right][/tex]
Therefore, the value of x is 4 and value of y is 5.
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The area of a sector is 135π and the arc measure is 216°. What is the radius of the circle?
The radius of the sector of area 135π is 15.
What is a sector?A sector is a geometric figure bounded by two radii and the included arc of a circle.
To calculate the radius of the sector, we use the formula below
Formula:
r = √(360A/π∅).............. Equation 1Where:
r = Radius of the sectorA = Area of the sector∅ = Angle of the arc at the center of the circleπ = pieFrom the question,
Given:
A = 135π∅ = 216°Substitute these values into equation 1
r = √(360×135π/π×216)r = √225r = 15Hence, the radius of the sector is 15.
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© {2, 4, 6, 8}
(3, 4, 5, 6}
(2, 3), (4, 4), (6, 5), (8, 6)
{2, 3, 4, 5, 6, 8)
X
2
4
6
8
у
3
4
5
6
Let P(n) be the statement that 13 +23 +···+n3 = (n(n+1)/2)2 for the positive integer n.a) What is the statement P(1)?b) Show that P(1) is true, completing the basis step of the proof.c) What is the inductive hypothesis?d) What do you need to prove in the inductive step?e) Complete the inductive step, identifying where you use the inductive hypothesis.f) Explain why these steps show that this formula is true whenever n is a positive integer.
P(n) = 1³ +2³ +···+n³ = (n(n+1)/2)²
P(1) = 1³ = 1
According to statement P(n) = (n(n+1)/2)²
Checking for n = 1,
(n(n+1)/ 2)² = (1(1+1)/ 2)²
P(1) = (1 × 2/ 2)²
P(1) = 1² = 1
P(1) = 1³ = 1
So P(n) holds for n = 1.
The inductive hypothesis is that the statement holds for P(n). To prove this the inductive step under the assumption that the inductive hypothesis is true, we prove it is true for P(n + 1)
Let us assume P(n) = 1³ + 2³ + ... + n³ = (n(n+1)/ 2)²
Then P(n + 1) = 1³ + 2³ + ... + n³ + (n + 1)³ = (n(n+1)/ 2)² + (n + 1)³
P(n + 1) = (n(n+1)/ 2)² + n³ + 3n² + 3n + 1
P(n + 1) = ((n + 1)((n + 1) + 1)/ 2)²
As assuming P(n) holds, it is also true for P(n + 1) so it will be true for all values of n as it is proved already that P(1) is true.
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in class a there are 20 students 14 of them are girls in class b there 25 students 15 of them are girls (a) find the percentages of girls in each class
To find the percentage of girls in class A, we need to divide the number of girls by the total number of students and then multiply by 100. This gives us:
14 / 20 * 100 = 70%
To find the percentage of girls in class B, we need to divide the number of girls by the total number of students and then multiply by 100. This gives us:
15 / 25 * 100 = 60%
Thus, the percentage of girls in class A is 70%, and the percentage of girls in class B is 60%.
Please help me it’s asap
Answer:
215
Step-by-step explanation:
218+212/2
11. Define the range of the following:
Answer:
The answer is B.
Step-by-step explanation:
Looking at the points gives you a x-axis and y-axis.
(x , y)
(-2 , 3) ,
(0 , 5) ,
(1 , 5) ,
(2 , 4) ,
(8 , -2)
Focus on the y-axis instead of the x-axis and list them.
{3 , 5 , 4 , -2}
It takes 73 pounds of seed to completely plant an 11 -acre field. How many pounds of seed are needed per acre?
Step-by-step explanation:
It takes 73 pounds of seed to completely plant an 11 -acre field. How many pounds of seed are needed per acre?
73 / 11 = 6.6363636 pounds per acre
rounded to two decimal places: 6.64 pounds per acre
how many additional groups would be required to conduct a 3 x 2 x 3 factorial design compared to a 3 x 2 x 2 design?
One additional group would be required to conduct a 3 x 2 x 3 factorial design compared to a 3 x 2 x 2 design with independent variable.
A 3 x 2 x 3 factorial design requires three independent variables (x1, x2, and x3) with three levels each, for a total of 27 conditions. A 3 x 2 x 2 design, however, would only require two independent variables (x1 and x2) with two levels each, for a total of 12 conditions. To conduct a 3 x 2 x 3 factorial design, one additional group would be required, compared to the 3 x 2 x 2 design. This additional group would provide data for the additional 15 conditions that the 3 x 2 x 3 design would require.
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10. What is the side length of a regular
36-gon that has an area of 164,592
square meters and an apothem of
228.6 m?
Answer:
39.95m
Step-by-step explanation:
To find the side length of a regular 36-gon with a given area and apothem, we need to use the formula for the area of a regular polygon and the formula for the apothem of a regular polygon.
The formula for the area of a regular polygon is given by:
A = (1/2) * a * p
where A is the area of the polygon, a is the apothem of the polygon, and p is the perimeter of the polygon.
The formula for the apothem of a regular polygon is given by:
a = r * cos(180/n)
where a is the apothem of the polygon, r is the radius of the polygon, and n is the number of sides of the polygon.
In this case, we are given that the area of the 36-gon is 164,592 square meters, the apothem of the 36-gon is 228.6 m, and the number of sides of the 36-gon is 36.
We can use these values to solve for the side length of the 36-gon. First, we can use the formula for the area of a regular polygon to solve for the perimeter of the 36-gon:
A = (1/2) * a * p
164,592 = (1/2) * 228.6 * p
164,592 = 114.3 * p
p = 1438.3
Next, we can use the formula for the apothem of a regular polygon to solve for the radius of the 36-gon:
a = r * cos(180/n)
228.6 = r * cos(180/36)
r = 561.8
Finally, we can use the formula for the perimeter of a regular polygon to solve for the side length of the 36-gon:
p = n * s
1438.3 = 36 * s
s = 39.95
Therefore, the side length of the 36-gon is 39.95 meters.
a company has the following information regarding its forecast performance in the past three periods. icture what is the mean absolute deviation (mad)? question 26 options: 225 -66.7 1200 200
The mean absolute deviation over three period of time is 200
The absolute value of error in period 1 = 300
The absolute value of error in period 2 = 200
The absolute value of error in period 3 = -100
Total absolute value of error = The absolute value of error in period 1 + The absolute value of error in period 2 + The absolute value of error in period 3
Substitute values in the equation
Total absolute value of error = 300 + 200 + 100
= 600
The mean absolute deviation = Total absolute value of error / 3
Substitute the values in the equation
The mean absolute deviation = 600 / 3
= 200
Therefore, the mean absolute deviation is 200
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A number is such that it is as much greater than 112 as it is less than it. find the number.
Answer:
Answer. it is -111 because it is greater than 112 and in positive form it is smaller and in negative it is bigger .
Which of the following rational functions is graphed below? 5 -5 5 -5
Answer:
b
Step-by-step explanation:
Infer from domain and range
Find the value of k that would make the left side of the equation a perfect square trinomial.
9x² - kx + 4 = 0
Answer: k=±`12
Step-by-step explanation:
[tex]ax^2-bx+c=0\\\\9x^2-kx+4=0\\\\D=b^2-4ac\\\\a=9\ \ \ \ b=-k\ \ \ \ c=4\\\\D=0\\\\Hence,\\\\D=(-k)^ 2-4(9)(4)=0\\\\k^2-144=0\\\\k^2=144\\\\k^2=12^2[/tex]
Extract the square root of both parts of the equation:
[tex]k=б\sqrt{12^2} \\\\k=б12[/tex]
Answer:
k = - 12 or k = 12---------------------------------------------
A perfect square trinomial is:
(a ± b)² = a² ± 2ab + b²Given trinomial:
9x² - kx + 4 = 0Show this as:
(±3x)² - kx + (±2)² = 0Compare and find possible values of k:
k = - 2(±3)(±2) = ± 12Use the marginal tax rate chart to answer the question.
Marginal Tax Rate Chart
Tax Bracket
Marginal Tax Rate
$0-$10,275
10%
$10.276-$41.175
12%
$41.176-$89.075
22%
$89,076-$170.050 24%
$170,051-$215,950 32%
$215,951-$539,900 35%
$539,901
37%
Determine the amount of taxes owed on a taxable income of $49,652.
Answer choices
$4,735.38
$6,600.44
$7,709.92
$10,293.44
The amount of taxes owed on a taxable income of $49,652 is $10,293.44.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Are the tax percentages for various amounts of income.
Now, From the given chart we conclude that $49,652 falls in the category of $41.176-$89.075 is 22% tax.
So, the Tax owed is 22% of $49,652.
∴ (22/100)×$49,652.
= $10,293.44.
So, an income of $49,652 owed 22% tax of the income which is $10,293.44.
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Answer:THE ANSWER IS B)6,600.44
Step-by-step explanation:
I got it right :)
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PLEASE HELP!!!
The simple interest is $2160 and the amount after 30 years is $6160.
Given that, principal =$4000, rate of interest =1.8%, and time period =30 years.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
a) Now, S.I =(4000×1.8×30)/100
= 40×1.8×30
= $2160
b) Amount = Principal + Interest
= 4000 + 2160
= $6160
Therefore, the simple interest is $2160 and the amount after 30 years is $6160.
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34) An airplane pilot is planning a flight to Hawaii. In his flight plan, he will include fuel estimates for the trip.
Explain the way he can use estimates in his plan without causing any danger to the flight
The airplane pilot should include and follow the relation y > [D][x] for his fuel estimates.
What is a mathematical function, equation and expression?
Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is that an airplane pilot is planning a flight to Hawaii. In his flight plan, he will include fuel estimates for the trip.
Assume that the distance of Hawaii from the initial location of pilot is [D] miles. If the amount of fuel burnt per miles is [x] liters/miles. Let the total amount of fuel needed to reach Hawaii is [y] liters. Than, his estimates should include and follow the given relation as -
y > [D][x]
Therefore, the airplane pilot should include and follow the relation y > [D][x] for his fuel estimates.
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the spread of a rumor in a town can be modeled as n equals 500 square root of t, where n is the number of people who have heard of the rumor, and t is time (in days). how long will it take until 2000 people know about the rumor? 12 days 4 days 8 days 16 days
The time it take until 2000 people know about the rumor is 16 days.
The square root of a variety of is described because the value, which offers the variety while it's miles increased with the aid of using itself. The radical symbol √ is used to suggest the square root. Radical is any other call given to the square root symbol. It is likewise called the surds. While Radicand is the variety gift beneath neath the square root symbol.
Find t, when N=200
N=5OO t^1/2
2000=500 t^1/2
t^1/2=4
t=16 days
Thus, the time it take until 2000 people know about the rumor is 16 days.
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Use the given information to find the new price. Round to the nearest cent Original Price: $28 Discount Rate: 25%
Answer:
To find the new price after a discount, you can use the formula: new price = original price * (1 - discount rate). In this case, the new price would be $28 * (1 - 0.25) = $28 * 0.75 = $<<28*0.75=21>>21. So the new price, rounded to the nearest cent, would be $21.
Step-by-step explanation:
if a line equation 2x +y =4 what is the gradie value
The gradient value of the line 2x + y = 4 is 2. This can be found by rearranging the equation into slope-intercept form, which is y = -2x + 4. The coefficient of the x term, -2, is the slope of the line.
if the value of x is 3 and the value of y is 5, what is displayed as a result of executing the code segment?
The result of executing the code segment is -2
How to determine the result of executing the code segment?The complete question is added at the end of this solution as an attachment
The code in the question is given as
IF X > Y
DISPLAY X + Y
ELSE
DISPLAY X - Y
Given that
X = 3 and Y = 5
When x and y are compared, we have the truth value to be
Y > X
This means that the executed segment is
DISPLAY X - Y
So, we have
DISPLAY 3 - 5
Evaluate
DISPLAY -2
Hence. the displayed result is -2
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(2+√-4) (3 +5i)(-4-i)
Answer:
[tex]32-60i[/tex]----------------------------------------
Simplify the expression in below steps:
[tex](2+\sqrt{-4} ) (3 +5i)(-4-i)=[/tex][tex](2+\sqrt{-1*4} ) (3 +5i)(-4-i)=[/tex][tex](2+2i ) (3 +5i)(-4-i)=[/tex][tex]2(1+i ) (3 +5i)(-4-i)=[/tex][tex]2(1+i ) (3(-4) -3i+5i(-4)-5i*i)=[/tex][tex]2(1+i ) (-12 -3i-20i-5(-1))=[/tex][tex]2(1+i ) (-12 -23i+5)=[/tex][tex]2(1+i ) (-7 -23i)=[/tex][tex]2(-7 -23i -7i-23i*i)=[/tex][tex]2(-7 -30i +23)=[/tex][tex]2(16 -30i)=[/tex][tex]32-60i[/tex]Answer:
[tex]32-60i[/tex]
Step-by-step explanation:
Given expression:
[tex](2+\sqrt{-4})(3 +5i)(-4-i)[/tex]
[tex]\textsf{Rewrite $\sqrt{-4}$ as $\sqrt{4 \cdot -1}$}:[/tex]
[tex]\implies (2+\sqrt{4 \cdot -1})(3 +5i)(-4-i)[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies (2+\sqrt{4}\sqrt{-1})(3 +5i)(-4-i)[/tex]
[tex]\implies (2+2\sqrt{-1})(3 +5i)(-4-i)[/tex]
[tex]\textsf{Apply imaginary number rule} \quad \sqrt{-1}=i:[/tex]
[tex]\implies (2+2i)(3 +5i)(-4-i)[/tex]
Multiply:
[tex]\implies (6+16i+10i^2)(-4-i)[/tex]
[tex]\implies -24-6i-64i-16i^2-40i^2-10i^3[/tex]
[tex]\implies -24-70i-56i^2-10i^3[/tex]
[tex]\textsf{Apply imaginary number rule} \quad i^2=-1:[/tex]
[tex]\implies -24-70i-56(-1)-10(-1)i[/tex]
Simplify:
[tex]\implies -24-70i+56+10i[/tex]
[tex]\implies 32-60i[/tex]
Select the graph of the solution. Click until the correct graph appears.
|x| + 1 < 3
Answer:
Graph B
Step-by-step explanation:
First, simplify by subtracting 1 on both sides.
|x| + 1 - 1 < 3 - 1
|x| < 2
Using the absolute value definition, we know the inequalities are:
x < 2
-x < 2
Divide both sides by -1.
x < -2
If you multiply or divide both sides of an inequality by a negative number, you must flip the sign.
x > -2
x<2, x>-2
Graph B
Answer:
Graph A
Step-by-step explanation:
if x ≥ 0
x + 1 < 3
x < 3 - 1
x < 2
0≤ x < 2
if x < 0
-x + 1 < 3
-x < 3 - 1
-x < 2
x > -2
-2 < x < 0
Final solution
-2 < x < 2
The figure shows a loading dock and a side view of
an attached ramp, whose run is 12 feet and whose
rise is 39 inches. Joaquin is wondering whether a
long rectangular box can be stored underneath the
ramp, as suggested by the dotted lines. The box is
2 feet tall and 5 feet long. Answer Joaquin's question.
The area of the triangular dock is 19.5 square feet and the area of the rectangular box is 10 feet. The box will fit under the dock.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.
Calculate the area of the triangle first,
Area = 1 / 2 x B x H
Area = 1/2 x 12 x 3.25
Area = 19.5 square feet
Calculate the area of the rectangle,
Area = L x W
Area = 2 x 5
Area = 10 square feet
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Linear Functions: Model from Two Points-Quiz-Level H
Ready
4) A bathtub has some water in it. Mia turns on the faucet to add more water. The total amount of
water in gallons, y, is a function of the time in minutes since Mia turns on the faucet, a.
4) The graph of the linear function passes through the points (4, 24) and (6, 30).
What is the equation of the function?
?
The equation of function for the given problem is y = 3x + 12.
What is point slope form of the line?
For linear equations, the general form is y - y1 = m(x - x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
Given:
A bathtub has some water in it. Mia turns on the faucet to add more water.
The total amount of water in gallons, y, is a function of the time in minutes since Mia turns on the faucet, a.
The graph of the linear function passes through the points (4, 24) and
(6, 30).
We have to find the equation of function.
Let the linear function passes through the points (4, 24) and (6, 30).
First to find the slope of equation using given points.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{30-24}{6-4} = \frac{6}{2} = 3[/tex]
Now to find the equation of function.
Consider the point slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug the values of m = 3 and [tex](x_1,, y_1) = (4, 24)[/tex]
⇒
[tex]y-24=3(x-4)\\y-24=3x-12\\y=3x-12+24\\y=3x+12[/tex]
Hence, the equation of function for the given problem is y = 3x + 12.
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Every other weekend, Bronwyn’s brother Daniel mows the lawn. He can mow 15,000 ft2 in 3/4 fourths hour. Who mows the lawn in less time? Explain. PLEASE HELP ME
The person who mows the lawn in less time is given as follows:
Daniel.
How to decide who mows the lawn in less time?To obtain who mows the lawn in less time, we calculate the hourly rates for each person, applying the proportion, which is the division of the amount of area mowed by the time needed.
Daniel can mow 15,000 ft³ in 3/4 = 0.75 hours, hence his hourly rate is calculated as follows:
Daniel hourly rate = 15000/0.75 = 15000 x 4/3 = 20,000 ft² per hour.
Bronwyn can mow 12,000 ft² in hour, hence her rate is of:
12,000 ft² per hour.
20,000 > 12,000, hence Daniel can mow the law in less time, as he has a higher rate.
Missing InformationThe missing sentence is of:
"Bronwyn can mow 12,000 ft² in hour".
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as the sample size increases, the distribution of the sample proportion becomes more normal. this fact is due to
the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal.
The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal. This means that the mean of the sample will be closer to the mean of the population, and the variability of the sample will be smaller. Since the sample proportion is just the mean of the sample, as the sample size increases, the distribution of the sample proportion will also become more normal. The larger the sample size, the more likely it is that the sample will accurately represent the population, and the more normal the distribution of the sample proportion will be. In other words, the sample proportion will be closer to the true population proportion, and the variability of the sample proportion will be smaller.
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