1) The base rate for the empty bus is $120.
2) The variable cost (slope) for each person on board the bus is $2.
3) An equation to show the cost, c, of a bus with x number of people on it is C = 120 + 2x.
How the base rate and slope for the equation are derived:The total charge for taking 30 people aboard = $180
The total charge for taking 50 people on board = $220
The differences in the number of people and charges are 20 and $40, respectively.
Let x = the number of people boarding the bus and n = the fixed rate per bus.
30x + n = 180 ... Equation 1
50x + n = $220 ... Equation 2
Subtract Equation 1 from Equation 2:
20x = $40
x = $2 ($40/20)
The variable cost per person = $2 ($40/20)
The base rate for the empty bus = 30(2) + n = $180, where n is the base rate or fixed cost per bus.
= 60 + n = $180
n = $120
OR:
50(2) + n = $220
100 + n = $220
n = $120
The equation for the cost, c, of a bus with x number of people:
C = 120 + 2x
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Evaluate the function for the given values of a and b then use the intermediate value theorem to determine which of the statements below is true.
a=-1 and b =0
f(x)=6x^3-9x^2-7x+3
a).f(-1) and f(0) have the same sign, therefore the function f has a real zero between -1 and 0
b.)f(-1) and f(0) have opposite signs, therfore the function f does not have a real zero between -1 and 0
c.) f(-1) and f(0) have the opposite sign, therefore the function f has a real zero between -1 and 0
d.) f(-1) and F(0) have the same sign, therefore intermediate value theorem cannot be used to determine wheter the function f has a real zero between -1 and 0
The function f has a real zero between -1 and 0. Therefore, statement c) is true.
To evaluate the function for the given values of a and b, we can plug in the values of a and b into the function and solve.
For a=-1, we get:
f(-1) = 6(-1)^3 - 9(-1)^2 - 7(-1) + 3 = 6 - 9 + 7 - 3 = 1For b=0, we get:
f(0) = 6(0)^3 - 9(0)^2 - 7(0) + 3 = 3Therefore, f(-1) and f(0) have opposite signs (one is positive and one is negative).
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what is 10+40-11+100=
Answer:139 is the answer
Step-by-step explanation:
Solve the system by graphing ツ= 3x ツ = -3x + 6
Answer:
(1, 3)
Step-by-step explanation:
Using a graphing website like Desmos or a graphing calculator, we can figure out the solution: (1, 3)
1. A pharmacy has determined that a healthy person should receive 70 units of proteins, 100 units of carbohydrates and 20 units of fat daily. If the store carries the six types of health food with their ingredients as shown in the table below, what blend of foods satisfies the requirements at minimum cost to the pharmacy? Make a mathematical model for the given problem.
Foods
A
20
B
30
C
Ꭰ
40
40
E
F
45
30
Protein units
Carbohydrates units
50
30
4
Cost per unit
9
235
20
11
25
10
6
50
20
Fat units
9
10
8
According to the information in the graph, the blend of foods that satisfies the requirements at the minimum cost is option A because it would be worth only 10.
How to calculate which is the cheapest blend of food option?To calculate the cheapest blend of food option, we must take into account the amounts of each element (carbohydrate, protein, fat) and identify how many units of each blend we need to cover the minimum quota.
Based on the above information, to identify the blend units we need to cover the minimum quota we must find it by multiplying each of the elements by the number of times we would need to meet the minimum requirement. Once we identify the quantities we need, we must multiply the price by the number of units we need.
Following the previous procedure, we can identify that the best option would be blend A because we must buy it 5 times to cover the minimum requirements. Additionally, its value would be 10, while the others would have a higher value.
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2 3X Find the solution set for each of the following equations. a 20x² + 10x -8=0 b x² − 8x + 15 = 0 3X C
The Solution set of the given quadratic equations are
1. x = 5 or x = 3
2. x= -3/2 or x = 5
What is quadratic equation?A Quadratic equation is an algebraic expression in which highest degree of the given variable is 2.
Formula used as x² +ax + b = (x + c)(x + d)
Where 'a' is the sum 'c' and 'd' and 'b' is the product of 'c' and 'd'
According to the information, Factorize all the given quadratic equations we get;
1. x² - 8x + 15 =0
Now Split middle term of quadratic equation using formula we get,
x² - 5x - 3x + 15 =0
⇒ x(x- 5) -3(x - 5) =0
⇒(x -5)(x - 3) =0
⇒ x- 5 =0 or x - 3 =0
⇒ x= 5 or x = 3
2. 20x² + 10x -8=0
Now Split middle term of quadratic equation using formula we get,
10x² + 5x - 4 = 0
⇒ 2x(x-5) +3(x-5)=0
⇒(2x+3)(x-5)=0
⇒2x+3 =0 or x-5 =0
⇒ x= -3/2 or x=5
Hence, the solution set are
1. x = 5 or x = 3
2. x= -3/2 or x = 5
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given g (x)=4x-4 solve for x when g (x)=0
Answer:
1
Step-by-step explanation:
g(x)=4x-4
g(x)=0
0=4x-4
4=4x
x=1
Using circles to model the ratios, divide both circles into
equal parts.
For the ratio 2 to 7,
parts should be shaded.
For the ratio 5:7,
parts should be shaded.
The ratio 2 to 7 is
the ratio 5:7.
By using circle model the images are attached below:
What is a circle model?A circle with a diameter of one has n firms distributed uniformly around it. In light of this, every company's distance from each of its closest neighbors is 1/n.
We must first create two circles in order to compare the ratios of 2 to 7 and 5:7 using a circle model.
Then, we must divide each circle into seven pieces.
We must shade 2 of the circle's total 7 portions in order to maintain the 2:7 ratio.
We must shade 5 of the circle's total 7 portions in order to maintain the 5:7 ratio.
As a result, the first circle symbolizes a 2:7 ratio, while the second circle a 5:7 ratio.
By using circle model the images are attached below:
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Answer: using circles to model the ratios, divide both circles into
7
equal parts.
For the ratio 2 to 7,
2
parts should be shaded.
For the ratio 5:7,
5
parts should be shaded.
The ratio 2 to 7 is
less than
the ratio 5:7
1. Norah uses an ounce of butter to bake 13 cookies. How many cookies can she bake with 89 ounces of butter?
Answer:
1157
Step-by-step explanation:
You multiply 13 and 89
Answer:
1,157 cookies
Step-by-step explanation:
[tex]\frac{cookies}{butter}[/tex] = [tex]\frac{cookies}{butter\\}[/tex]
[tex]\frac{13}{1}[/tex] = [tex]\frac{x}{89}[/tex] You need to multiply 1 by 89 to get 89, so multiply 13 by 89 and you get 1157 cookies.
What is the solution and how do I solve this step by step?
There are 640 acres in 1 square mile. The area of a forest is increasing at a rate of 1 acre per decade. Which of the following is closest to the rate at which the area of the forest is increasing, in square kilometers per decade? (Use 1 kilometer=0.62mile.)
A.0.0006
B.0.0010
C.0.0025
D.0.0041
The rate at which the area of the forest is increasing, in square kilometers per decade, is 0.0041.
What does the rate of change mean?
How quickly one variable changes in relation to another is known as the rate of change. Speed is an example of a "rate of change." Speed is defined as the rate at which the distance to an object varies in relation to the time spent.
It is given that there are 640 acres in 1 square mile which can also be written as 640 acres= 1[tex]mi^2[/tex].
The area of forest is increasing at a rate of 1 acre/decade.
It is given that 1 km= 0.62mi
By squaring on both sides we will get 1 [tex]km^2[/tex] = 0.3844 [tex]mi^2[/tex].
The rate at which the area of forests is increasing in square kilometers per decade is
[tex]\frac{1acre}{decade} *\frac{1mi^2}{640acre} *\frac{1km^2}{0.3844mi^2} =0.00406478\frac{km^2}{decade}[/tex] .
Therefore the closest value is [tex]0.0041[/tex].
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The area of a rectangle is 9/10 square meter. The width is 2/5 meter. b. How many times greater is the length than the width? Write your answer in simplest form.
Using the area of rectangle formula, w = A/l, determine the width of the rectangle first before determining its length.
How do you find the length and width of a rectangle when given the area?In conclusion, you must divide a rectangle's area by its known width in order to determine its length.If you have an area A and a width w, you can calculate the length w using the formula h = A/w.
If you know the perimeter P and the width w, you can calculate the length using the formula h = P/2w.
Given a diagonal (d) and a width (w), its length is given by h = (d2w2).The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape.
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If the area of square and rectangle is same and the side of the square is 40cm and width of rectangle is 25cm. So what is the total area of rectangle?
Answer:
s² = lw
s = 40 w= 25cm
s² = lh
(40cm)² = (25cm)
1 600 cm² = 25cm L
L = 64 cm
The length is 64 cm
Area of Rectangle = length(width)
Area = 64cm(25cm)
Area = 1 600 cm²
Which is correct because the statement is, the area of a square ( 1 600 cm²) is equal to area of the rectangle ( 1 600 cm²)Therefore the area of rectangle is 1 600 cm²Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-could some one help me with this question please (short answers are fine)
The sum of the exterior angles of the given polygon is 360°.
What is polygon?In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words, poly which means numerous and gon means sides. To create a closed figure, a minimum of three line segments must be connected end to end.
Given that,
There is a polygon that has 4 sides.
Since, a polygon having 4 sides is called a quadrilateral, and the sum of the interior angle of the quadrilateral is 360°.
Implies that, the sum of the exterior angle of the quadrilateral will also be 360°.
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if the price of viva increases from $2.50 to $2.60 and the price of brawny is unchanged, the sales of brawny will?
The sales of Brawny will remain unchanged, as the amount of Brawny has not changed.
Price is one of the factors that influence the demand and sales of any product. Therefore, when the price of a product changes, the sales of that product may be impacted. However, when the price of one product changes, the sales of another product that has not changed in price may remain unaffected. In this case, since the price of Viva has increased from $2.50 to $2.60, while the amount of Brawny has remained unchanged, the sales of Brawny will likely remain unchanged.
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Kara is flying to Hawaii. If her packed suitcase weighs more than 50 pounds
when she checks in at the airport, she will have to pay a fee. Her empty suitcase
weighs 11.3 pounds, and she has to pack all her camera equipment, which
weighs 14.25 pounds. To stay under the weight limit, what is the maximum
possible weight of her other packed items?
the manager of a bank record of the amount of each Time customer spent waiting in the line during peak business hours on Monday the waiting times are shown below find the mean waiting time Roger answer to one Decimal place 6.8 min 7.5 min 7.2 min brainly
Answer:
To find the mean waiting time, you need to add up all the waiting times and divide by the number of customers. In this case, the total waiting time is 6.8 + 7.5 + 7.2 = 21.5 minutes. Since there are 3 customers, the mean waiting time is 21.5 / 3 = 7.17 minutes. Rounded to one decimal place, the mean waiting time is 7.2 minutes.
Step-by-step explanation:
PLEASE HELP ASAP
Three key features of a linear function are described as shown.
• The graph of the function has a y-intercept of (0, 3) .
• The function is increasing over its entire domain.
• The x-intercept of the function is (-4, 0).
Answer:
y = 3/4 x + 3
Step-by-step explanation:
slope of the line :
(0-3)/(-4-0)
-3/-4
3/4
y = 3/4 x + 3
A triangle has its base doubled and its
height increased by 30%. By what percent
has the area of the triangle increased?
(A) 130%
(B) 160%
(C) 230%
(D) 260%
Let the base and height of triangle be b and h.
area of triangle= 1/2*base*height
Area of triangle= bh/2
Now Base is Doubled and Height increase by 30%
New base = 2b
New height = h×130/100 = 13h/10
New area = 1/2 × 2b × 13h/10
New area = 13bh/10
Area increased = New area - area
Area increased = 13bh/10 - bh/2
Area increased= 13bh-5bh/10
Area increased= 8bh/10
Area increased= 4bh/5
ratio increased in % = Area increased/ Old Area × 100
ratio increased in % = 4bh/5 ÷ bh/2 × 100
ratio increased in % = 4/bh × 2/bh × 20
ratio increased in % = 8×20
ratio increased in % = 160%
3. draw the circuit for an sr flip-flop given the characteristic table, equation and state diagram. (8pts)
The logic diagram, characteristic table, and equation of the SR flip-flip are shown. (Refer to the images attached below)
What is SR flip-flop?A gated set-reset flip-flop is an SR flip-flop.
The flip-flop is controlled by the S and R inputs when the clock pulse changes from LOW to HIGH.
Till the clock pulse is on a rising edge, the flip-flop won't alter.
There is a chance that the outputs will be HIGH or LOW when S and R are both HIGH at the same time.
A global flip flop with two inputs, the JK flip flop has the letters "J" and "K."
While J and K are not the reduced abbreviated letters for Set and Reset in the SR flip flop, S and R are.
SR flip-flop equation: Qn+1 = S + QnR'
(Refer to the images attached below)
Therefore, the logic diagram, characteristic table, and equation of the SR flip-flip are shown. (Refer to the images attached below)
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at what time t is the instaneous velocity equal to the averge equal to the equal to the average velocity of the bug on 0,6 is the bug speeding up or slowing down at t
At t = 0.6, the instantaneous velocity of the bug is equal to the average velocity of the bug on [0,6], so the bug is neither speeding up nor slowing down.
The instantaneous velocity of a bug at any particular moment in time is the rate at which the bug is changing its position. The average velocity of the bug over a particular interval (in this case, [0,6]) is the average rate at which the bug changes its position over the entire interval. To compare the instantaneous velocity to the average velocity, the two velocities need to be measured at the same time.
At t = 0.6, the instantaneous velocity of the bug is equal to the average velocity of the bug on [0,6]. That means that the bug is neither speeding up nor slowing down.
The Complete the question is :
at what time t is the instaneous velocity equal to the averge equal to the equal to the average velocity of the bug on 0,6 is the bug speeding up or slowing down at t = 0.6
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Savannah takes a car to a title loan business to borrow some money. Savannah is given $2,900.00. She must pay back the $2,900.00 in addition to a $1,375.00 fee in 8 months.
What simple interest rate is she
being charged?
Round to the nearest tenth of a percent and don't forget to include a percent sign, %, in your answer.
Savannah is being charged a simply interest rate of ______.
Step-by-step explanation:
To find the simple interest rate that Savannah is being charged, we can use the formula for simple interest:
I = P * r * t
where I is the total interest paid, P is the principal (the amount borrowed), r is the interest rate, and t is the time period over which the interest is paid.
Since Savannah must pay back the $2,900.00 principal plus a $1,375.00 fee, the total interest paid is $1,375.00. The time period is 8 months, which is equal to 8/12 = 2/3 of a year. Substituting these values into the formula and solving for r, we get:
$1,375.00 = $2,900.00 * r * (2/3)
r = $1,375.00 / ($2,900.00 * (2/3)) = 0.1429
This is the interest rate that Savannah is being charged. To express this rate as a percentage, we can multiply it by 100% to get:
r = 0.1429 * 100% = 14.3%
Therefore, Savannah is being charged a simple interest rate of approximately 14.3%.
Suppose y varies directly with x, and y=10 when x =-3. What direct variation equation relates x and y? What is the value of y when x =-1?
The relation between 'x' and 'y' will be y = -(3/10)x. Then the value of the variable 'y' at x = -1 will be 3/10.
What are ratio and proportion?A proportion is a gathering of consecutively requested numbers an and b communicated as a/b, where b is never equivalent to nothing. At the point when two items are equivalent, a proclamation is supposed to correspond.
The variable 'y' is directly proportional to the 'x'. Then the equation is given as,
y ∝ x
y = kx
At x = - 3 and y = 10, then the value of the constant 'k' is calculated as,
-3 = k(10)
k = - 3/10
Then the equation is written as,
y = -(3/10)x
At x = - 1, then the value of the variable 'y' is calculated as,
y = - (3/10) (-1)
y = 3/10
The connection between 'x' and 'y' can't avoid being y = - (3/10)x. Then, at that point, the worth of the variable 'y' at x = - 1 will be 3/10.
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What is the greatest common factor of 18 and 27
Answer:
Step-by-step explanation.
The HCF of 18 and 27 is 9
Which statements about the opposite of −12 are true?
Select each correct answer.
Responses
The opposite of −12 is −112.
The opposite of , negative 12, is , negative fraction 1 over 12, .
−12 and its opposite are located the same distance from zero on a number line.
negative 12, and its opposite are located the same distance from zero on a number line.
−12 and its opposite are on located on the same side of zero on a number line.
negative 12, and its opposite are on located on the same side of zero on a number line.
The opposite of the opposite of −12 is −12.?
According to Integers and number line the correct statements are given below
what is Integers and number line?
Including zero, integers are a range of positive and negative numbers. The definition of an integer on a number line is an image of an integer on a number line. We can do several arithmetic operations using integers on a number line.
solution:
The opposite of the opposite of -12 is -12
The opposite of -12 is 12, and the opposite of 12 is -12.
−12 and its opposite are located the same distance from zero on a number line.
negative 12, and its opposite are located the same distance from zero on a number line.
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Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pH, medium pH, or high pH, to the water in the tanks that hold the jellyfish.
Which of the following is the best reason for the random assignment of a treatment level to an experimental unit?
A. Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects. B. Randomization will make up for improper experimental design, data collection, and analysis.
C. Randomization makes the analysis easier since the data can be entered into the computer in any order. D. Randomization is required by statistical consultants before they will analyze the experiment.
E. Randomization means that the experiment would not need to be replicated.
In order to prevent such factors from influencing the treatment's outcomes, randomization tends to reduce the impact of uncontrollable variables like water temperature.
What are variables?
A variable in mathematics is a symbol that designates a mathematical object. A variable can represent any of the following: a number, a vector, a matrix, a function, its argument, a set, or an element of a set. An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed. Because they make up a significant portion of mathematics, variables are crucial.
The impact of water pH on moon jellyfish mating behavior is being studied by researchers. In a scientific experiment, the water in the tanks containing the jellyfish will be randomly assigned to one of three treatments: low pH, medium pH, or high ph.
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The positive variables p and c change with respect to time 1. The relationship between p and c is given by the equation p^2 = (20-c)^3. At the instant when dp/dt = 41 and c = 15, what is the value of dc/dtï¼
The value of dc/dt due to changes in p and c variables is 0.364.
The positive variables p and c change with respect to time 1. The relationship between p and c is given by the equation p^2 = (20-c)^3. Now the dp/dt value is 41 and c is 15.
Differentiate the given equation to obtain the following:
2p dp/dt = 3(20-c)^2 dc/dt
Substitute the given values in the equation to obtain the following:
2p (41) = 3(20 - 15)^2 dc/dt
Simplify the equation to obtain the following:
82 = 225 dc/dt
Divide both sides of the equation by 225 to obtain the following:
dc/dt = 82/225
Simplify the equation to obtain the following:
dc/dt = 0.364
Hence, the value of dc/dt is 0.364.
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A researcher performs three independent hypothesis tests each at the 5% significance level.
Determine the probability of observing at LEAST one Type I Error. (Round your final answer to the nearest hundredth of a percent)
The probability of observing at least one Type I Error is 16.67%.
What is probability?Probability is the likelihood of an event occurring, expressed as a number between 0 and 1. It is a measure of how likely it is that something will happen, given the conditions and information available. Probability is the foundation of statistics, which is the science of making decisions when faced with uncertainty. Probability can be used to make predictions about future events and to help us understand how likely various outcomes are.
A Type I Error, also known as a false positive, occurs when an experiment incorrectly rejects a true null hypothesis. This probability can be calculated by multiplying the probability of a Type I Error occurring in each test (0.05) three times, yielding 0.125 (or 12.5%).
We then add 1 minus that probability, which yields 0.167 (or 16.67%). In other words, the probability of observing at least one Type I Error in the three tests is 16.67%.
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wHAT IS THE NEXT NUMBER IN THE FOLLOWING SERIES OF NUMBERS 1,4,8,13,19
Answer:
26
Step-by-step explanation:
a_n = 1/2 (n^2 + 3 n - 2) (for all terms given)
1, 4, 8, 13, 19, 26, 34, 43, 53, 64, 76, 89, 103, 118, 134, 151, 169, 188, 208, 229, ...
Answer:
26
Step-by-step explanation:
The difference between 1 and 4 is 3
The difference between 4 and 8 is 4
The difference between 8 and 13 is 5
The difference between 13 and 19 is 6
The difference between 19 and 26 is 7
You’re involved in the design of a new facility. It is important for people to move between work stations quickly. Based on the figure below, how many feet would a person need to walk to get from Work Station 1 to Work Station 3?
The distance from work station 1 to work station 3 is 13 feet.
How to find the side of a right triangle?The figure shows the distance between workstation. The figure represents a right angle triangle.
The distance from work station 1 to work station 3 can be calculated as follows:
using Pythagoras's theorem,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore, the distance from work station 1 to work station 3 is the hypotenuse side of the right triangle.
Hence,
5² + 12² = c²
25 + 144 = c²
c² = 169
c = √169
c = 13 ft
The distance between the work stations is 13 ft.
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Suppose continuous random variable Y has cumulative distribution function FY (y), and density
function fY (y) > 0. Let random variable U = FY (Y ), find the density function of U, and identify its
distribution (name and parameter(s)) if possible.
Since, U = FY(Y) is uniform distribution (i.e. U(0, 1)).
In the given question, suppose continuous random variable Y has cumulative distribution function FY (y), and density function fY (y) > 0.
Let random variable U = FY (Y ).
We have to find the density function of U, and identify its distribution (name and parameter(s)) if possible.
A random variable Y has cumulative distribution function FY (y).
A random variable Y has density function f(y).
Let U = FY(Y)
Now we have to find the density function of U using cumulative distribution function method
FU(u) = P(U≤u)
FU(u) = P(FY(Y) ≤ u)
FU(u) = P(Y ≤ F (u))
FU(u) = FY(F (u))
FU(u) = u
fU(u) = F'U(u).1
fU(u) = 1
fU(u) = 1, 0<u<1
Here U = FY(Y) is uniform distribution (i.e. U(0, 1)).
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