If the first bus is boarded at a rate of 15 people per minute, the domain of the function is; (15 ≤ x ≤ 45)
How to solve Inequality word problems?We are told that;
Total number of Juniors at Smithers High School that are taking a class trip = 130
Number of buses taking each student to their destination = 3 buses
Capacity of each bus = 45 people
Now, if the function f(x) describes the total number of people on the first
bus, where x is the number of minutes spent loading the bus.
Then since the maximum number of people on the first bus is 45, then it means that the domain of the function is;
(15 ≤ x ≤ 45)
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Why do we need to flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number?
The statement would no longer be true if you did not flip the signs.
Example: 1 < x < 2 multiplied by (-1) equals -2 < x < -1, because you can't have a number that is greater than -1, and less than -2 at the same time.
If C is the line segment from (5,4) to, (0,0), find the value of the line integral:
The value of line integral of the line segment from (5,4) to, (0,0) is 90.
Given that C is the line segment from (5,4) to (0,0):-
So, our first task is to calculate the line segment
After calculating the line segment, we will be able to calculate the line integral
We know that the equation of line is -
y - y1 = (y1 - y2)/ (x1 - x2) * (x - x1)
So now,
y - 0 = (4 - 0)/ (5 - 0) * (x - 0)
y = 4/5 x
5x - 4y = 0 -----------> (1)
A line integral is used to calculate the area covered by that line
c1 = ∫₀⁴ 5x dx ------> (2)
c2 = ∫₀⁵ -4y dy -----> (3)
c1 = [ 5 x²/2 ]₀⁴ = 5 * ( 4² - 0)/2 = 40
c2= [ -4 y²/2 ]₀⁵ = -4 * ( 5² - 0)/2 = 50
The value of the line integral: c1 + c2 = 40 + 50 = 90
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pls help having trouble!
Answer:
a is 30 degrees.
Step-by-step explanation:
The degree of a triangle is 180, which means that all the degrees in any triangle will always add up to 180. Since CB and DB are congruent, the angles C and D will be the same. This means that to get the answer, just subtract the value we already have from 180 and divide the sum by 2.
[tex]\frac{180-120}{2} = \frac{60}{2} = 30[/tex]
Subtract the expressions.
(7.43n − 2.2) − (6 + 10.5n)
−30.70n − 4.5
−3.07n − 8.2
9.63n − 4.5
17.93n + (−8.2)
The solution to the expression is (b) -3.07n - 8.2
How to subtract the expressions?From the question, we have the following parameters that can be used in our computation:
(7.43n − 2.2) − (6 + 10.5n)
Remove the brackets
So, we have
(7.43n − 2.2) − (6 + 10.5n) = 7.43n − 2.2 − 6 - 10.5n
Evaluate the like terms
(7.43n − 2.2) − (6 + 10.5n) = -3.07n - 8.2
Hence, the solution is (b) -3.07n - 8.2
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Find the principal value of cos[pie/2 -sin inverse (1/2)]
The value of the given expression cos(π/2 - sin⁻¹(1/2)) will be equal to 1/2.
What are Trigonometric functions?The fundamental six functions of trigonometry have a range of numbers as their result and a boundary input value that is the angle of the right triangle.
As per the given information in the question,
cos(π/2 - sin⁻¹(1/2))
Use the formula given below,
cos(π/2 - θ) = sin θ
From the above formula,
sin(sin⁻¹ (1/2))
= 1/2
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The original quantity is 10 and a quantity is 15 what is the percent increase
Mapleton School is having a Thanksgiving food drive to support their local food bank. The food bank is running low on soup, so they asked the students to make soup a large part of their donations. Bernard donated 30 cans, 15 of which were soup. Gwen donated 20 cans, 12 of which were soup. Did Gwen and Bernard donate the same ratio of soup cans to total cans?
Answer: No, Gwen's ratio is 3:5 soup to total, and Bernard's is 1:2 soup to total
Step-by-step explanation:
Bernard donates 30 cans, 15 of which are soup.
15soup/30cans = 1soup/2cans = 1 soup to 2 total cans
Gwen donates 20 cans, 12 of which are soup.
12soup/20cans = 3soup/5cans = 3 soup to 5 total cans
Consider the arithmetic sequence 3, -10, -23, -36
Can someone help me with 3C?
The graph of the first five terms can be seen in the image at the end.
How to graph the first 5 terms of the sequence?We know that we have an arithmetic sequence:
3, -10, -23, -36
The common difference is what we get when we subtract two consecutive terms, we will get:
d = -36 - (-23) = -3
Then the recursive relation is:
a(n) = a(n - 1) - 13
At the moment we know:
a(1) = 3
a(2) = -10
a(3) = -23
a(4) = -36
Then fifth term will be:
a(5) = a(4) - 13 = -36 - 13 = -49
Now to graph it, we use the "n-th" value as the input, then we need to graph the five points (1, 3), (2, -10), (3, -23), (4, -36), (5, -49).
The graph can be seen in the image below:
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What is the domain of this function?
Answer:
all real numbers
Step-by-step explanation:
the graph continues to the left and to the right because there are arrows
Which sentence does NOT contain an error in pronoun-antecedent agreement?
a. A large herd of buffalo thundered across the plain and left a cloud of dust in their wake.
b. When the crowd reached the center of town, the mayor was surprised by their size.
c.Our gymnastics team proved their skills during the individual floor exercises.
Answer:
a
Step-by-step explanation:
Given g(x)=-5x+2 find g(-4)
Answer:_18
replace _4 instead of x
-5*-4=_20
_20+2=_18
Step-by-step explanation:
a pentagon with 5 sides of equal length and 5 interior angles of equal measure is inscribed in a circle. is the perimeter of the pentagon greater than 26 centimeters?
the perimeter of the pentagon greater than 26 centimeters is given by
23.51
Given that a pentagon with 5 sides of equal length and 5 interior angles of equal measure is inscribed in a circle
The circle has area of 16 pi sq cm.
Hence radius of circle = 4 cm
The pengagon each side would be a chord of equal length subtending angle 72 at the centre.
visualize the triangle made by one side of pentagon with centre. This is isosceles with angles 72, 54 and 54
Use sine angle for this triangle.
, where R = radius =4 and s = side of pentagon.
s= 4.702
Perimeter = 5s = 23.5114 cm
Perimeter not greater than 26 cm.
If origin is at the centre then two vertices would be (4,0) (4cos 72, 4sin72),(4cos 144, 4 sin 144) and so on.
Longest diagonal = distance between (4,0) and (4cos 144, 4 sin 144)
= (-3.236, 2.351) and (4,0)
=7.608
Yes greater than 8 cm
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I the ytem of equation conitent and independent conitent and dependent or inconitent
The system of linear equations, y = 2x + 4 ;
2y = x + 6 has a unique solution and it is a consistent system of linear equations.
What is linear System of Equations and it's solution?An ordered pair that satisfies all equations of the system is the solution of the system. A system of linear equations can have one solution, no solution, or an infinite number of solutions. The systems of equations can be classified according to the number of solutions. If a system has at least one i.e unique solution, it is called consistent. We have, the system of equations is
y = 2x + 4 => 2x - y + 4 = 0 --(1)
2y = x + 2 => x - 2y + 6 = 0 --(2)
Comparing the equation (1) with a₁x + b₁y + c₁=0
and equation(2) with a₂x + b₂y + c₂=0
We get, a₁ = 2 , a₂= 1 , b₁ = -1 , c₁= 4 , b₂= -2 , c₂ = 2
Now, compute the ratio of coefficients of variables .
a₁/a₂ = 2/1 , b₁/b₂ = -1/-2 = 1/2 , c₁/c₂= 4/6 = 2/3
=> a1/a2 ≠ b1/b2 ,
here, both lines are intersect at a point and a unique solution exist for pair of linear equations. In such a case , the pair of linear equations is said to be consistent. Thus, system is consistent.
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Complete question:
Is the system of equation is consistent and
independent consistent and dependent or inconsistent?
y = 2x + 4 , 2y = x + 6
Is this a function or not a function?
Image result for vertical line graph
Answer:
not a function. There cannot be mutiple y-values under one x value.
Step-by-step explanation:
suppose you want to encrypt the message 10101111 by encrypting the decimal number that corresponds to the message. what is the decimal number
To find the decimal number that corresponds to the message "10101111", you can convert the binary number to decimal.
By using the following formula:
decimal = [tex]sum(binary[i] X 2^{(n-i-1)})[/tex]
binary = converting binary number
i = index of the current digit in the binary number
n = total number of digits in the binary number
[tex]2^{(n-i-1)}[/tex] is the corresponding power of 2
use the following steps to convert the binary number "10101111"
Calculate the decimal value for each digit in the binary number:
binary[0] = 1, [tex]2^{(8-0-1)}[/tex] = [tex]2^7[/tex] = 128
binary[1] = 0, [tex]2^{(8-1-1)}[/tex] = [tex]2^6[/tex] = 64
binary[2] = 1, [tex]2^{(8-2-1)}[/tex] = [tex]2^5[/tex] = 32
binary[3] = 0, [tex]2^{(8-3-1)}[/tex] = [tex]2^4[/tex] = 16
binary[4] = 1, [tex]2^{(8-4-1)}[/tex] = [tex]2^3[/tex] = 8
binary[5] = 1, [tex]2^{(8-5-1)}[/tex] = [tex]2^2[/tex] = 4
binary[6] = 1, [tex]2^{(8-6-1)}[/tex] = [tex]2^1[/tex] = 2
binary[7] = 1, [tex]2^{(8-7-1)}[/tex] = [tex]2^0[/tex] = 1
Adding decimal values for each digit
Total decimal value = 1128 + 064 + 132 + 016 + 18 + 14 + 12 + 11
= 128 + 0 + 32 + 0 + 8 + 4 + 2 + 1
= 175
Hence, the decimal number that corresponds to the binary number "10101111" is 175.
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A scale drawing of a rectangular park had a scale of 1 cm = 110 m.
7.4 cm
4.2 cm-
What is the actual area of the park in meters squared?
The actual area of the park is 376068 meters squared. If A scale drawing of a rectangular park had a scale of 1 cm = 110 m.
Define area of rectangle.The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the product of its length and breadth.
Given
A scale drawing of a rectangular park had a scale of 1 cm = 110 m.
Length of rectangle,
7.4 × 110
814m
Breadth of rectangle,
4.2 × 110
462 m
Area of rectangle
length × breadth
814 ×462
376068
The actual area of the park is 376068 meters squared. If A scale drawing of a rectangular park had a scale of 1 cm = 110 m.
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(-10, -12), (-8, -8), (-6, -4), (-4, 0)
Find the slope of the line passing through the given points
Answer: the slope is [tex]\frac{4}{2}[/tex] which can be simplified to just 2.
Step-by-step explanation:
You can use the equation [tex]\frac{y2-y1}{x2-x1}[/tex] to find the slope of a line. In this case, I chose to use the coordinates (-4,0) and (-6,-4), it doesn't matter which you choose as the (x1,y1) and (x2,y2) coordinates. So, [tex]\frac{-4-0}{-6-(-4)}[/tex] becomes [tex]\frac{-4}{-2}[/tex] which is the same as [tex]\frac{4}{2}[/tex], which is equal to 2. you can repeat this with the other points given to check your answer.
The slope of the line passing through the given points is equal to 2 .
what is the slope of a line?The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line. The slope of a line is the measure of the tangent of the angle made by the line with the x - axis. It is represented by m: m = y₂-y₁ / x₂ - x₁
Given here, are the points P (-10, -12), Q(-8, -8), R(-6, -4),S (-4, 0)
Now the slope of a line is constant for any two points that lie on a line.
therefore, slope of the line that passes through P,Q,R,S is
m = -8-(-12) /-8-(-10)
= 2
or m= 0-(-4) /-4-(-6)
= 2
clearly the slope is equal to 2 in either case that's because the line passes through all the four points.
Hence, the slope of the line passing through the given points is equal to 2.
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In a board of directors composed of 14 people, how many different ways can one chief
executive officer, one director, and one treasurer be selected?
Answer:
2184
Step-by-step explanation:
This question involves permutations. We can solve it using the formula
[tex]\frac{n!}{(n-r)!}[/tex]
where n=14 (because we are choosing from 14 people)
and r=3 (because we are choosing 3 people)
and we are using the permutation formula because the order or placement in which these 3 people are choosing matters (having a person 1 being a director is different from having person 1 being a chief executive officer)
14!/(14-3)!
= 14!/11!
= 14 x 13 x 12
= 2184
if you use 1 pound of mirepoix in a recipe that yields 1 gallon of soup, how much mirepoix do you need to make 31/2 gallons of soup?
we need 31/2 pounds mirepoix to make 31/2 gallons of soup.
let we need x% (percent) of mirepoix to make 1 gallon of soup
given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup
so total amount of mirepoix that required in the solution is = [tex]\frac{x}{100} *1 pound[/tex]
so x/100 = 1 gallon / pound
we will use this equation for further calculation
let we need y pounds of mirepoix to make 31/2 gallon of soup ans we know that x% of mirepoix is required for this solution.
so [tex]\frac{x}{100} * y = 31/2[/tex]
ans in the above equation x/100 =1 gallon / pound
so 1 * y= 31 /2
and hence y = 31/2 pounds
so we need 31/2 pounds of mirepoix to form requied amount of soup.
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Sarah is 148 centimeters tall. How tall is Sarah in inches? Round to the nearest tenth inch.
Answer:
58.3
Step-by-step explanation:
divide the length value by 2.54
58.2677
Answer:
58,3 inches
Step-by-step explanation:
1 inch = 2.54 cm
[tex]148 \: cm \:*\:\frac{1\:inch}{2.54\: cm} = 58,267716535433070866141732283465\\\\148\: cm=58,3 \:inches[/tex]
Domain: -4
BOOKMARK
Determine the domain and range for the following graph.
Answer:
Domain (interval notation) : [-4,4)
Range (interval notation): [1,4)
Domain (inequality notation): [tex]-4\leq x < 4[/tex]
Range (inequality notation): [tex]1\leq x < 4[/tex]
Step-by-step explanation:
Domain is the x-values of a function
Range is the y values of a function
Which algebraic expression is equivalent to this expression?
A. 135x+147
B. 24x+183
C. 24x+13
D. 24x+147
9(-2) +15(x + 11)
Answer:
15x +147
Step-by-step explanation:
which of the following statement is false ? (a)a triangle has three sides. (b) a triangle has three vertices.(c)a triangle has three angles.(d) a triangle has two diagonals
Answer: D
Step-by-step explanation:
Answer:D
Step-by-step explanation: A triangle has no diagonals
Write a triangle congruence statement
Answer:
1. ΔCDE≅ΔJEH
2. ΔIHG≅ΔIHD
3. ΔIHJ≅ΔIXT
4. ΔIJT≅ΔJIH
5. ΔEFD≅ΔDKJ
6.ΔGWY≅ΔGHI
jane will toss a fair coin two times. if you know that the first coin toss resulted in heads, what would the probability be that both coins would land on heads? explain.
The probability that both coins will land on heads is 50%. In other words, each coin toss is an independent event and each coin has an equal chance of landing on either heads or tails.
This is because the result of the first coin toss does not influence the outcome of the second coin toss, meaning each toss is an independent event with a 50% chance of landing on heads.The probability that both coins will land on heads is 50%. This is because the result of the first coin toss does not influence the outcome of the second coin toss. In other words, each coin toss is an independent event and each coin has an equal chance of landing on either heads or tails. This means that the probability of both coins landing on heads is the same as the probability of either coin landing on heads, which is 50%. Therefore, the probability that both coins will land on heads is 50%.
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consider the proposed proof that all real numbers are equal to 0 below. which is the first line that contains an error?
A. Let x be a real number,B. Add x to both sides of the equation, then C. x - x = 0,D. Therefore, x = 0
A. Let x be a real number - This step states that we are selecting a real number for which we will prove that it is equal to 0. This step does not contain an error.
B. Subtract x from both sides of the equation - This step does not contain an error as it is the first step in the process of proving that the real number is equal to 0.
C. x - x = 0 - This step contains an error, as it doesn't provide enough information to prove that the real number is equal to 0.
D. Therefore, x = 0 - This step also contains an error, as it assumes that the proof is correct without providing any evidence.
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Describe how to write 4x^2 + 8x - 10 = 0 in vertex form
Answer:
(2x + 1)^2 = 7
Step-by-step explanation:
To write the quadratic equation 4x^2 + 8x - 10 = 0 in vertex form, we need to first complete the square. To do this, we need to add and subtract the same value to the quadratic term and the linear term so that the resulting quadratic has the form (x - h)^2 = k.
In this case, we need to add and subtract the square of half of the coefficient of the linear term, which is 8/2 = 4. This gives us the equation:
4x^2 + 8x + 4 - 4 - 10 = 0
This simplifies to 4(x^2 + 2x + 1) - 14 = 0, which can be rewritten as (2x + 1)^2 - 7 = 0.
To put this in vertex form, we need to rewrite the right side of the equation as a perfect square, so we add 7 to both sides to get (2x + 1)^2 = 7.
Then, we take the square root of both sides to get 2x + 1 = ±√7. We can then solve for x to get x = -1/2 ± √7/2.
Therefore, the equation 4x^2 + 8x - 10 = 0 can be written in vertex form as (2x + 1)^2 = 7.
in general, a change in what causes a movement along a curve in the models we have studied? a change in what causes a shift in the curve?
In general, a change in the price of the product causes a movement along the demand curve; and a change in production cost and related factors causes a shift in the supply curve.
What is demand curve?The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time. In a typical representation, the price will appear on the left vertical axis of the graph, and the quantity demanded on the horizontal axis.
What is supply curve?The supply curve is a graphic representation of the relationship between product price and quantity of product which a seller is willing and able to supply. Product price is measured on the vertical axis of the graph, and the quantity of product supplied on the horizontal axis.
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Please helpppp me with thisss
Answer:
d = 0
Step-by-step explanation:
We have the equation
7.5d = 2.5d
We divided both sides by factors and get
d = 0
Value of d is 0.
According to question
7.5d=2.5d
Lin divides each side by 2.5d
∴7.5d÷2.5d=2.5d÷2.5d
⇒3=1
which is not possible and Lin is doing wrong
Elena subtract 2.5d from each side
∴7.5d-2.5d=2.5d-2.5d
⇒5d=0
⇒d=0
So Elena is right and the value of d is 0.
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7. find and describe a case in which the land surface of an area in the u.s. has subsided due to groundwater withdrawal. if possible, give an estimate of how many feet the land surface subsided.
an instance where a region's u.s. land surface has changed subsided due to groundwater withdrawal. The land surface in the Central Valley has subsided by as much as 30 feet in distance some areas due to unsustainable groundwater withdrawals.
The most famous case of land subsidence due to groundwater withdrawal in the United States is the Central Valley of California. The land surface in the Central Valley has subsided by as much as 30 feet distance in some areas due to unsustainable groundwater withdrawals. In addition to land subsidence, the unsustainable withdrawals have caused significant groundwater depletion, surface water contamination, and reduced agricultural productivity.
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