assume that the maximum speed your car will go is a linear function of the steepness of the hill is going up or down. SUppose the car can go a maximum of 55 mph up a 5 hill and a maximum of 104 down a 2 hill
Answers
The maximum speed of the linear function is y = -7x + 90
Assume that the maximum speed your car will go is a linear function of the steepness of the hill is going up or down?a. we have two points connecting (speed, degree) are (+5,55) and (-2,104) representing (x₁ , y₁) and (x₂, y₂)
Slope = (y₂ - y₁) / (x₂ - x₁)
slope = (104-55) / (-2-5) = 49/-7 = -7 mph/1°
speed = slope x (degree) + b
Solve 'b':
55 = -7 x (5) + b
55 = -35 + b
b = 55 + 35
b = 90
y₁ = -7x₁ + 90
b) What does the speed-intercept equal and what does it represent?
The speed is 90 mph when there is no hill.
c ) What does the degree of steepness-intercept and what does it represent?
Up the hill, the steepness is roughly 12.9 degrees at its maximum. Whenever there is a slope, the car will not move.
d) Interpret the slope in words.
The speed drops by 7 mph for every 1 degree that the hill's steepness increases.
e) If your top speed is 83 mph, how steep is the hill? Be sure to include whether the direction is up or down.
83 = -7 x + 90
83 -90 = -7x
-7 = -7x
x = 1° up the hill
f) How fast could you go down a 7º hill?
y = -7 (-7) + 90
y = 139 mph
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Related Questions
Emily's score for a Mathematics test was 5% higher than her score for an English test. If Emily scored 84 points for the Mathematics test, how many points did she score for the English test?
Answers
Answer:
80 points
Step-by-step explanation:
If score in English is x points and score in math is 5% higher then score in math
y = x + 0.05x
where 0.05 = 5% expressed as decimal
0.05x refers to the 5% increase in score
y = math score
y = x(1 + 0.05)
y = 1.05x
Given score in math = 84 this becomes
84 = 1.05x
x = 84/1.05
x = 80
So Emily's score in English was 80 points
What is the exponential expression for the numerical expression 14⋅14⋅14⋅14?
564
4⋅144
414
144
Answers
It may be 1^4 ............................
seb buys 1 gallon of paint that covers 400 square feet
Answers
The least amount of paint that is needed to paint the walls of a room with a rectangular prism shape is 1. 8 gallons.
How to find the amount of paint ?There would be two walls with 10 x 16 dimensions so the area is :
= 2 x 10 x 16
= 320 square feet
Two walls with 20 x 10 dimensions :
= 2 x 20 x 10
= 400 square feet
The total area is :
= 400 + 320
= 720 square feet
One gallon of paint can cover 400 square feet so the number of gallons needed is:
= 720 / 400
= 1. 8 gallons
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Full question is:
One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 20 feet, a width of 16 feet, and a height of 10 feet? Write your answer as a decimal.
If the graph of y=-x^2 is translated horizontally 10 units to the right and translated vertically 3 units upwards, what is its new
equation?
Answers
Answer:
y=\((x-10)^{2}\)+3
Step-by-step explanation
in order to shift the equation to the right you must subtract a positive number from x (ex: -10)
to shift the equation upwards just add the positive number to the end of the equation (ex: +3)
Determinar cuales de las siguientes frases son proposiciones
a) 3+2 = 0 c) ¡Hola!
b) x + 1 = 4 d) Yo estudio
Answers
The exercise is designed to test the students knowledge of prepositions. The correct answer thus is (Option D) Yo estudio (which translates) "I study".
What is the explanation for the answer above?To understand the answer, you need to know what a preposition is. A preposition, in simple terms, is a word or group of words that comes before a noun.
The function of a preposition (much like an adjective) is to give clarity to the noun that it precedes.
Let us complete the Preposition phrase to give meaning to it:
"I study Mathematics". Where;
"Mathematics" is the noun;
"I Study" is the prepositional phrase. Hence the correction answer to the question above is Option D.
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y=2/5xt 10 the rate of change and y intercept
Answers
Answer:
Below
Step-by-step explanation:
Rate of change (aka the slope) = 2/5
Y Intercept = 10
The radius of a right circular cone is increasing at a rate of 1.6 in/s while its height is decreasing at a rate of 2.2 in/s. At what rate is the volume of the cone changing when the radius is 135 in. and the height is 135 in.
Answers
Answer:
Step-by-step explanation:
let radius=r
height=h
dr/dt=1.6 in/s
dh/dt=-2.2 in/s
volume v=1/3 πr²h
dv/dt=1/3 π[h*2r×dr/dt+r²×dh/dt]
when r=135 in
h=135 in
dv/dt=1/3 π[2×135×135×1.6+135²×(-2.2)]
=1/3 π[135²(3.2-2.2)]
=1/3π135²×1
=6075 π in³/s
If a student (represented by initials) was chosen at random, find P(HHU C).
Answers
Answer:
\(P(HH\ u\ C) = \frac{13}{16}\)
Step-by-step explanation:
Given
The Venn diagram
Required
\(P(HH\ u\ C)\)
This is calculated as:
\(P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}\)
Where:
\(n(U) = 16\) --- count of students
\(n(HH\ u\ C) =13\)
So, we have:
\(P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}\)
\(P(HH\ u\ C) = \frac{13}{16}\)
isabella bought tickets for 84 people. each ticket cost $16.22. how much did isabella spend on tickets
Answers
The total money Isabella spent on tickets will be $1362.48
In the given question, it is stated that Isabella bought a total of 84 Tickets. Each of the tickets she bought cost $16.22. We have to find out the total amount that she spent on buying tickets for everyone. From this given situation we know:
The cost of one ticket: $16.22
Total number of tickets: 84
From this formula, we can calculate the total amount spent
Total Amount = Total ticket * cost of one ticket
Putting values in this formula, we get:
=> Amount = cost*number
=> Amount = 16.22*84
=> Amount = 1362.48
Hence, the Total amount that she spent on Tickets will be $1362.48
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What is the mode of this data set?
{4, 15, 6, 11, 7, 4, 3, 14}
Answers
Answer:
4
Step-by-step explanation:
A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)
Scientists want to test a new pair of running shoes. A speed test is performed with two separate groups of participants. The treatment group will wear the new pair of running shoes, while the control group will not. It is believed that age and height may affect speed. Which of the following would be most effective in controlling the confounding variables, such as age and height, in this study?
a. A completely randomized design experiment
b. A longitudinal observational study
c. A retrospective observational study
d. A matched-pair design experiment
Answers
Answer:
a. A completely randomized design experiment
Step-by-step Explanation:
An experiment that is completely randomised is practically an effective way of controlling and reducing the influence of the confounding variables in a research study, especially when you have a sample that is large enough.
Randomisation will ensure that both the group that will wear the new shoe (treatment group) and the group that will not wear the new shoe (control group) will have averagely the same values for age and height. This will eliminate the chances of these confounding variables of correlating with the independent variable in the study, as there would be no difference, in terms of characteristics, between both groups.
b) In a certain weight lifting machine, a weight of 1 kN is lifted by an effort of 25 N. While the weight moves up by 100 mm, the point of application of effort moves by 8 m. Find mechanical advantage, velocity ratio and efficiency of the machine
Answers
The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.
The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.
The problem has provided the following information:
Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m
We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage
The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;
Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;
Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5
Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.
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Matthew is saving money for a pet turtle the data in the table represents the total amount of money in dollars that he saved by the end of each week.
Answers
Please awnser asap I will brainlist
Answers
Answer:
V = 180 (vans)
S = 90 (small trucks)
L = 40 (large trucks)
Step-by-step explanation:
Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.
Write the equations:
V + S + L = 310 (total number of vehicles)
V = 2S (twice as many vans as small trucks)
35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)
Substitute equation 2) into equation 1):
2S + S + L = 310
3S + L = 310
Simplify equation 3) by substituting V = 2S:
70,000S + 70,000S + 60,000L = 15,000,000
140,000S + 60,000L = 15,000,000
Set up a system of equations:
3S + L = 310
140,000S + 60,000L = 15,000,000
Eliminate L by multiplying equation 1) by 60,000:
60,000(3S + L) = 60,000(310)
180,000S + 60,000L = 18,600,000
Subtract equation 2) from the new equation:
(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000
40,000S = 3,600,000
Solve for S:
S = 90
Substitute the value of S into equation 1) to solve for L:
3(90) + L = 310
270 + L = 310
L = 40
Substitute the values of S and L into equation 2) to solve for V:
V = 2S
V = 2(90)
V = 180
The final answer is:
V = 180 (vans)
S = 90 (small trucks)
L = 40 (large trucks)
Answer:
180 Vans 90 Small trucks and 40 Large trucks
Step-by-step explanation:
Find (a) and I also need to find (b)
Answers
The composite functions when evaluated are (f . g)(1) = 4 and (f - g)(0) = -2
How to evaluate the composite functionsThe composite function 1
In this question, the graph represents the given parameter
To calculate (f . g)(1), we make use of
(f . g)(1) = f(1) * g(1)
Using the readings from the graph, we have
(f . g)(1) = 2 * 2
(f . g)(1) = 4
The composite function 2
In this question, the graph represents the given parameter
To calculate (f - g)(0), we make use of
(f - g)(0) = f(0) - g(0)
Using the readings from the graph, we have
(f - g)(0) = 1 - 3
(f - g)(0) = -2
So, the value of (f - g)(0) is -2
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3. There are five different tables in the class and five students. Each table can be occupied by only onestudent. Their
studying year consists of 200 days. As a small prank on their teacher students would like to sit in a new way every
day, so there are no two days during their studying year such that all students are occupying the same tables.
They would like to see whether this is possible. How many ways are there for them to sit in the class?
Answers
There are 3,125 different places to sit if they don't mind sharing s desk sometimes and there are 120 different places to sit, if they all sit on separate tables.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that there are five different tables in the class and five students
Each table can be occupied by only one student
There are 200 days of studying years.
As a small prank on their teacher students would like to sit in a new way every day, so there are no two days during their studying year such that all students are occupying the same tables.
5×4×3×2×1 = 120
There are 120 different places to sit, if they all sit on separate tables.
5×5×5×5×5 = 3,125
There are 3,125 different places to sit if they don't mind sharing s desk sometimes.
Hence, there are 120 different places to sit, if they all sit on separate tables and there are 3,125 different places to sit if they don't mind sharing s desk sometimes.
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A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
Answers
Answer:
53\(x_{123}\) == 134 cf
Step-by-step explanation:
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
The height of the building is approximately 78.63 meters.
The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.
Draw a diagram of the situation described in the problem to get a better understanding of the problem. The diagram would have a right-angled triangle with angle of elevation of 66° at the bottom left vertex and another angle of elevation of 53° at the bottom right vertex. The object on top of the building is at the vertex of the triangle. Point M and I on the diagram are points on the horizontal line of sight and on the ground respectively. We can label the diagram with the following values:Angle of elevation from point A = 66°Angle of elevation from point P = 53° Length of line segment AM = h Length of line segment MP = x Length of line segment IP = y Length of line segment MT = 50m. We'll use these values to calculate the length of h, which is the height of the building.Use the tangent ratio to find x:tan 66° = h / x => x = h / tan 66°. Use the tangent ratio to find y:tan 53° = h / y => y = h / tan 53°.We know that x + y = 50, so substituting the expressions for x and y from step 3 gives:h / tan 66° + h / tan 53° = 50h = 50 tan 66° tan 53° / (tan 53° + tan 66°) ≈ 78.63 m.Therefore, the height of the building is approximately 78.63 meters.
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A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of 2916 with a mean life of 518 minutes.
If the claim is true, in a sample of 81 batteries, what is the probability that the mean battery life would be less than 526.4 minutes? Round your answer to four decimal places.
Answers
The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.
What is probability?The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.
Given:
The variance = 2916,
The mean life of a battery, m = 518 min,
The total number of samples, n = 81
Calculate the probability of a mean battery life of lower than 526.4 minutes by the following formula,
z = x - m / (σ / √ n)
Here, x is the expected value, σ is the deviation, and z is the probability.
Substitute the values,
z = 526.4 - 518 / (54 / √81) [σ = √ variance = √2916 = 54]
z = 1.4
Consult the cumulative standard normal table
P (z < 526.4) = 0.9192,
But we know that
P (z > 526.4) = 1 - P (z < 526.4)
P (z > 526.4) = 1 - 0.9192 = 0.0808
Therefore, The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.
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Three whole numbers have a sum of 118
The ratio of the first number to the second number is 5:3
The ratio of the second number to the third number is 4:9
What are the three numbers?
show working
Answers
17
18
10
that's the answer
mark me as brainliest please
Answer:
40, 24, 54
Step-by-step explanation:
let the 3 numbers be x, y and z
then
\(\frac{x}{y}\) = \(\frac{5}{3}\) ( cross- multiply )
5y = 3x ( divide both sides by 5 )
y = \(\frac{3}{5}\) x
and
\(\frac{y}{z}\) = \(\frac{4}{9}\) ( cross- multiply )
4z = 9y ( divide both sides by 4 )
z = \(\frac{9}{4}\) y = \(\frac{9}{4}\) × \(\frac{3}{5}\) x = \(\frac{27}{20}\) x
The 3 numbers are now expressed in terms of x , then adding gives
x + \(\frac{3}{5}\) x + \(\frac{27}{20}\) x = 118
multiply through by 20 to clear the fractions
20x + 12x + 27x = 2360
59x = 2360 ( divide both sides by 59 )
x = 40 ← first number
y = \(\frac{3}{5}\) × 40 = 3 × 8 = 24 ← second number
z = \(\frac{27}{20}\) × 40 = 27 × 2 = 54 ← third number
The 3 numbers are 40, 24, 54
Which of the following is the most likely the next step in the series?
Answers
Answer: C is the correct answer!I don't feel like explaining. sorry.Please let me know if I am wrong.
please explain what comparison you can state about the two angles and explain how you can draw that conclusion
Answers
The conclusion about angles B and C is that the angles are equal angles
How to determine the true statement?
The given parameters are:
Angle A and Angle B are supplements
Angle A and Angle C are supplements
Supplementary angles add up to 180 degrees.
This means that
A + B = 180
A + C = 180
Subtract the two equations
So, we have
A - A + B - C = 180- 180
Evaluate the like terms
So, we have
B - C = 0
Add C to both sides
B = C
Hence, both angles are congruent angles
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(a) The perimeter of a rectangular field is 366m m.If the width is 86m, what is its length
(b) The area of a rectangular painting is 7200 cm^2. I’f the length of the painting is 96 cm, what is the width
Answers
We know that the width is 86m and the perimeter is 366m. Substituting these values into the formula, we get:
366 = 2l + 2(86)
Simplifying the right side, we get:
366 = 2l + 172
Subtracting 172 from both sides, we get:
194 = 2l
Dividing both sides by 2, we get:
l = 97
Therefore, the length of the rectangular field is 97m.
(b) The formula for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width.
We know that the length is 96cm and the area is 7200cm^2. Substituting these values into the formula, we get:
7200 = 96w
Dividing both sides by 96, we get:
75 = w
Therefore, the width of the rectangular painting is 75cm.
What is the constant up a proportionally in a equation y=x/g
Answers
Answer:
Step-by-step explanation:
\(y=(\frac{1}{g} )x\)
Constant up a proportionally is \(\frac{1}{g}\).
There is a game at the carnival that costs $20 to play. There are two outcomes: either you win a prize worth $100, or you lose. To play, you roll a number cube. If a 6 appears, you win; all other rolls, you lose. Include the cost of playing the game in the expected value.
What is the mean (or expected value) of the game?
Answers
The expected value for the game is -$3.33, so the correct option is the second one.
How to get the expected value?For an experiment with N outcomes {x₁, x₂, ..., xₙ} each one with probabilities {p₁, p₂, ..., pₙ}
Then the expected value is:
EV = x₁*p₁ + x₂*p₂ + ...
In this case we have two outcomes:
In one you win $80 (the $100 of the prize minus the cost) and you only win if the 6 appears, so the probability is 1/6.
The other outcome is that you lose the $20, here the probability is 5/6.
Then the expected value is:
EV = (1/6)*$80 - (5/6)*$20 = -$3.33
The correct option is the second one.
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w = gm, solve for m.
Answers
Answer:
m = w/g
Step-by-step explanation:
Step 1: Write equation
w = gm
Step 2: Divide both sides by g
w/g = m
Step 3: Rewrite
m = w/g
Answer:
w/g = m
Step-by-step explanation:
w = gm
Divide each side by g
w/g = gm/g
w/g = m
A central angle drawn on a unit circle has a measure of 108°. The radian measure of this angle can be written as kπ. What is the value of k? Express your answer as a fraction in reduced form.
K=
Answers
Answer:
k = 3/5
Step-by-step explanation:
You want the coefficient of π in the radian measure of 108°.
RadiansThere are π radians in 180°, so a fraction of 180° will be that fraction of π radians.
108° = (108°)×(π/180°) = (108/180)π = 3/5π
The value of k in 108° = kπ is 3/5.
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Find the value of x
Answers
Answer:
x = 66
Step-by-step explanation:
Shapes with four sides are always 360 degrees
x + x - 20 + x + 40 + 2x + 10 = 360
combine like terms
5x + 30 = 360
subtract 30 from both sides
5x = 330
divide 5 from both sides
x = 66
2
Steve has 18 blue marbles and 27 red marbles in a bag. What is the ratio of red marbles to
blue marbles?
Answers
Answer:
3 : 2
Step-by-step explanation:
27 : 18 reduce the numbers = 3 : 2
The set of blue lines in the graph below are parallel lines. If the lines are translated, 4 units to the right and 3 units down, what are the new coordinates of points A, B, C, and D? graph listed below. Right answer gets brainliest !!
Answers
Answer:
A(0,-3) B (5,0) C(0,-7)D(5,-4)
Step-by-step explanation:
HELP! 10 POINTS!!!!
Where are the residual values shown on a residual plot?
A) on the y-axis
B) on the x-axis
C) on the line of best fit
D) on the x and y-axis
Answers
The coordinate on which the residual values are shown on a residual plot is: A) on the y-axis.
What is a residual value?A residual value can be defined as a difference between the measured (given or observed) value from a residual plot (scatter plot) and the predicted value from a residual plot (scatter plot).
Mathematically, the residual value of a data set can be calculated by using this formula:
Residual value = given value - predicted value
In Mathematics, the independent variable (fitted values) are generally plotted on the x-axis of a residual plot (scatter plot) while the residual value is plotted on y-axis of a residual plot (scatter plot).
In conclusion, a line of best fit simply refers to a trend line on a residual plot (scatter plot).
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