On solving the provided question, we can say that - the instantaneous rate of change of the function at the given value, by solving the equation y = 11 - 5x, f'(1) = 3-8 = -5
What is an equation ?A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
y = f(x) =
[tex]x^3 - 4x^2 + 7 \\at x =1[/tex]
f(x) = 3-4+7
= 6
F'(x) = [tex]3x^2 - 8x[/tex]
f'(1) = 3-8 = -5
equation = y - 6 = -5(x-1)
y = 11 - 5x
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let x be the set of 2000 correct: your answer is correct. people (the pigeons) and y the set of all 1825 incorrect: your answer is incorrect. possible birthdays (the pigeonholes).
Yes, in a group of 2,000 people, at least 5 must have the same birthday.
This is due to the Pigeonhole Principle, which states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.
In this case, there are 2,000 people (the pigeons) and 365 possible birthdays (the pigeonholes). This means that, since 2,000 is greater than 365, at least 5 people must share the same birthday.
The Pigeonhole Principle states that if you have more items than boxes, then at least one box must contain more than one item. It can also be used to prove that certain problems have no solution.
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Complete Question:
In a group of 2,000 people, must at least 5 have the same birthday? Why? Let X be the set of 2000 people (the pigeons) and Y the set of all possible birthdays (the pigeonholes). Define a function B: X - Y by specifying th B(x) = x's birthday. Now 2,000 > 4.366 = 1,464, and so by the generalized pigeonhole principle, there must be some birthday y such that B-1(y) has --Select- 4 + 1 = 5 elements. Hence at -Select- 5 people must share the same birthday.
Given that A,O & B lie on a straight line segment, evaluate the size of the smallest angle.
The diagram is not drawn to scale.
Based on the definition of the angles of a straight line, the measure of the smallest angle is: are: 40°.
What is the Sum of Angles on a Straight Line?The sum of all the angles on a straight line is equal to 180 degrees.
To find the size of the smallest angle, find the value of a by creating the equation below:
(2a + 62) + (54 - a) + (5a - 20) = 180
Open the parentheses:
2a + 62 + 54 - a + 5a - 20 = 180
Combine like terms
6a + 96 = 180
6a = 180 - 96
6a = 84
6a/6 = 84/6
a = 14
Find the measure of each angles:
2a + 62 = 2(14) + 62 = 90°
54 - a = 54 - 14 = 40°
5a - 20 = 5(14) - 20 = 50°
The size of the smallest angle is 40°.
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A cruise ship traveled to Madagascar and
back. On the trip there it traveled 12 km/h
and on the return trip it went 18 km/h.
How long did the trip there take if the
return trip took six hours?
A) 12 hours
C) 9 hours
B) 10 hours
D) 7 hours
To find the time it took the cruise ship to travel to Madagascar, we need to use the formula for distance, which is distance = speed x time. We are given the distance and the speed of the ship on the trip there, so we can solve for the time by dividing the distance by the speed:
time = distance / speed
We are told that the distance of the trip there was the same as the distance of the return trip, which took 6 hours. We are also told that the ship traveled 12 km/h on the trip there, so the distance of the trip there was 12 km/h x 6 h = 72 km.
Now we can plug this information into the formula to solve for the time:
time = 72 km / 12 km/h = <<72/12=6>>6 hours
Therefore, it took the cruise ship 6 hours to travel to Madagascar. The correct answer is therefore (A) 12 hours.
6. ______ is the transfer of energy by electromagnetic waves.
a.Convection b.Radiation. c.Conduction. d.Contact
A sector with central angle theta is cut froma circle of radius 10 inches and the edges of the secotr are brought toegether to ormnr a cone find the amgnitude of theta such that thte volume of the conbe is a maximum
So, the maximum volume of the cone is approximately 1047.19 cubic inches.
The volume of a cone is given by the formula V = (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone. In this case, the height of the cone is the radius of the circle, which is 10 inches, and the radius of the base is half the length of the circumference of the sector, which is (theta/360) * 2 * pi * 10 inches.
We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.
V = (1/3) * pi * r^2 * h
= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10
= (1/3) * pi * (theta/36)^2 * 100
dV/dtheta = (2/3) * pi * (theta/36) * (100/36)
= (2/3) * pi * theta/36
Setting dV/dtheta = 0 and solving for theta, we get theta = 0.
Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then
V = (1/3) * pi * r^2 * h
= (1/3) * pi * (10)^2 * 10
= (1/3) * pi * 100 * 10
= (1/3) * pi * 1000
= approximately 1047.19 cubic inches
So, the maximum volume of the cone is approximately 1047.19 cubic inches.
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We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.
V = (1/3) * pi * r^2 * h
= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10
= (1/3) * pi * (theta/36)^2 * 100
dV/dtheta = (2/3) * pi * (theta/36) * (100/36)
= (2/3) * pi * theta/36
Setting dV/dtheta = 0 and solving for theta, we get theta = 0.
Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then
V = (1/3) * pi * r^2 * h
= (1/3) * pi * (10)^2 * 10
= (1/3) * pi * 100 * 10
= (1/3) * pi * 1000
= approximately 1047.19 cubic inches
So, the maximum volume of the cone is approximately 1047.19 cubic inches.
The graph below represents a system of equations.
-9 8 7 6
3
-10
Which of the following statements is true?
A. The system has infinite solutions
B. The solutions to the system are (0,1) and (0,-3)
C. The solution to the system is (-4,3)
D. The system has no solution
Answer:
C. The solution to the system is (-4,3) where the 2 lines MEET
Step-by-step explanation:
D. The system has no solution only if the lines are PARALLEL
A. The system has infinite solutions only if both equations give ONE and the same line
minute math
HELP PLSS ILL MARK BRAINLIEST!!!
Select the correct images on the graph.
Identify which shapes on the graph are congruent to shape I by performing these sequences of transformations on shape I:
a reflection across the y-axis, followed by a 90° counterclockwise rotation about the origin, and then a translation 3 units down
. a 90° counterclockwise rotation about the origin and then a translation 2 units up and 2 units left
a 180° rotation about the origin and then a translation 1 unit right
Solve g(x) = 10, if g(x) = 2/x+1
Answer:
x = -0.8.
Step-by-step explanation:
To solve for x in the equation g(x) = 10, we need to find the value of x that makes g(x) equal to 10. Since we are given that g(x) = 2/x+1, we can substitute this expression for g(x) in the equation g(x) = 10 to get:
2/x+1 = 10
Next, we can multiply both sides of the equation by x+1 to get rid of the fraction on the left side:
2 = 10 * (x+1)
This simplifies to 2 = 10x + 10, which we can rearrange to get 2 - 10 = 10x. Subtracting 10 from both sides gives us -8 = 10x. Finally, dividing both sides by 10 gives us the solution: x = -0.8.
Therefore, the value of x that makes g(x) equal to 10 is x = -0.8.
In Jimmy's class 1/3 of the pupils have blue eyes and 2/5 have brown eyes. What fraction of the class do not have blue or brown eyes?
Answer:
4/15
Step-by-step explanation:
1/3 x 5/5 = 5/15, 2/5 x3/3 = 6/15
5/15+6/15= 11/15
15/15- 11/15= 4/15
so 4/15 people don't have neither blue nor brown eyes.
Find the interest rate for a principal of $5305 and charged $39534 in interest for 20 years
Answer:
37.237%
Step-by-step explanation:
Use the Formula I = P x R x T
P = Principal amount (the beginning balance).
R = Interest rate (usually per year, expressed as a decimal).
T = Number of time periods (generally one-year time periods).
Plug in the values
I = 5305 x R x 20
Solve for R by dividing 20 by 5305
I=5305 x R x 20
20 / 5305 = 0.0037
Answer: 10.56 or 10.6 %
Step-by-step explanation:
5305 x x^20 = 39534
39534/5305 = x^20
20√39534/5305 = x
x = 1.1056
1.1056 x 100 = 110.56
110.56 - 100 = 10.56 or 10.6
From her eye, which stands 1.75 meters above the ground, Myesha measures the angle of elevation to the top of a prominent skyscraper to be 19^{\circ}
∘
. If she is standing at a horizontal distance of 337 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary
Answer:
117.79 m
Step-by-step explanation:
You have an observer 337 m from a skyscraper who measures the angle of elevation from a point 1.75 m above the ground to be 19°. You want to know the height of the skyscraper.
TangentThe tangent relation tells you ...
Tan = Opposite/Adjacent
Solving for the side opposite the angle, we get ...
Opposite = Adjacent · Tan
ApplicationIn this scenario, the height of the building above the eye height is ...
height above eyes = (337 m)(tan 19°) = 116.038 m
Then the height of the building is ...
skyscraper height = eye height + height above eyes
skyscraper height = 1.75 m + 116.038 m = 117.788 m
The height of the skyscraper is about 117.79 meters.
Are y = 6 and x = - 1 perpendicular lines?
answer: yes.
since y = 6 and x = -1 are parallel to the y and x axis, respectively, they hit each other at a 90° angle when graphed, making a plus sign. they are perpendicular lines.
Noah has 5 m of rope how many pieces of rope of length 1/2 meter can he cut from it
Answer: 10 pieces
Step-by-step explanation:
Answer:
10 ropes
Step-by-step explanation:
5 divided by 1/2 is 10
Use what you know about multiplying integers to explain why this equation is true:
20 ÷ (−5) = (−4).
Here, in the given equation it is true because two different sign, and the result is negative.
What about multiplying integers?To multiply or divide signed integers, always multiply or divide the absolute values and use these rules to determine the sign of the answer.
When multiply two integers with the same signs, the result is always positive. Just multiply the absolute values and make the answer positive.
When multiply two integers with the different signs, the result is negative.
Here in this equation,
20 ÷ (-5)
= - 4
So, it is true.
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Graph TU with endpoints T(1,2) and U(4,6) and its image after the composition
TU with endpoints T(1,2) and U(4,6) and its images after the composition are T' = (-1, -1) and U' = (2,3) and T'' = (-3, 7) and U'' = (0,11).
What is the image point?Tradition holds that the reflection of point P across the line, denoted by the word P', is the "image" of point P. (pronounced "P prime").
Given, line TU with endpoints T(1,2) and U(4,6).
To find the translation:
In 1:
Translate TU 2 units left and 3 units down.
That means,
T' = (-1, -1) and U' = (2,3)
In 2:
Translate TU 4 units left and 5 units up.
That means,
T'' = (-3, 7) and U'' = (0,11)
Therefore, the image points are T' = (-1, -1) and U' = (2,3) and T'' = (-3, 7) and U'' = (0,11)
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Algebraically find the x-coordinates where the line y=2x+3 intersects the circle (x-3)^2 + (y+6)= 50
The x-coordinates where the line y = 2x + 3 intersects the circle is equal to -2 and -4.
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.From the information provided, we have the following system of equations:
(x - 3)² + (y + 6)² = 50 ......equation 1.
y = 2x + 3 .............equation 2.
In order to determine the x-coordinates at the point of intersection, we would substitute the equation 2 into equation 1:
(x - 3)² + (2x + 3 + 6)² = 50
(x - 3)² + (2x + 9)² = 50
x² - 6x + 9 + 4x² + 36x + 81 - 50 = 0
5x² + 30x + 40 = 0
x² + 6x + 8 = 0
x² + 6x + 9 = 1
(x + 3)² = 1
Taking the square of both sides of the equation, we have;
x + 3 = ±1
x = ±1 - 3
x = -2 and -4
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which equal to cos 74
Answer:
0.27563735723563.
Step-by-step explanation:
74 is an acute angle since it is less than 90° cos (74) = 0.27563735723563. Write cos (74) in terms of sin Since 74° is less than 90, we can express this in terms of a cofunction.
How much would you need to deposit in an account now in order to have $5,000.00 in the account in 27
months?
Assume the account earns 2.01% simple interest.
You would need to deposit ______ in your account now?
The amount needed to be deposited in an account in order to have $5000 in 27 month is $4997.74.
What is simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
To calculate the amount that needed to be deposited, we use the formula below.
Formula:
P = 100A/(RT+100)................. Equation 1Where:
P = PrincipleA = AmountR = RateT = yearsFrom the question,
Given:
A = $5000R = 2.01% = 0.0201T = 27 months = 2.25 yearsSubstitute these values into equation 1
P = (100×5000)/(0.0201×2.25+100)P = 500000/100.045225P = $4997.74Hence, the amount needed to be deposited is $4997.74.
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what is the rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled? place your answer in the box:
The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .
Is the rate of change and slope the same thing?Slope and rate of change are the same thing. The difference is just semantics of the situation.
Typically we use the word “slope” when we are referring to a graph, and we use the phrase “rate of change” when we are referring to a table or a situation in real life.
But that’s not absolute. We can count the slope on a graph, but there’s also a “slope formula” for use when you have two coordinate points or two data points — even though you are not creating a graph.
What do you call "the rate of change of slope"?It is the derivative of of the slope, or the second derivative of the original function.
For example, if you plot position verses time, the slope between two points(change in position per change in time) is the velocity. This is the first derivative.
Take any two points ( 0 , 380 ) and ( 15 , 545 )
slope m = 545 - 380 / 15 - 0
= 165 / 15
= 33 / 3
= 11 / 1
= 11 feet
Hence the slope m is 11 feet .
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After his annual review, Miguel's salary was increased from $32,000 per year to $35,000. What percent increase does this represent? Round your answer to the nearest tenth of a percent.
Answer:
91.4%
Step-by-step explanation:
First do: 32,000/35,000 = X/100
Then multiply 32,000 by 100 which is 3,200,000
Then divide 3,200,000 by 35,000
You will get 91.42857142857143
Find the greatest possible error :19oz
Answer:
0.5 oz
Step-by-step explanation:
You want the greatest possible error associated with the measurement 19 oz.
Measurement errorThe possible error is generally considered to be half the place value of least-significant digit. Here, the least significant digit has a place value of units, so the greatest error is 1/2 unit, or 0.5 ounces.
__
Additional comment
We know that values of 18.5 oz up to 19.4999... oz will round to 19 oz. That is why the greatest error is considered to be 0.5 oz.
In practice, there can be some difficulty associated with knowing that a value is 18.5 instead of 18.49. Hence real-world error may actually be slightly larger than 0.5 oz. In math, we ignore that case.
On January 1, 2019, Marblehead, Massachusetts had a population of approximately 19,800 people. On that date, 1,098 Marblehead residents were living with asthma. Between January 1, 2019 and September 1, 2019, there were 495 newly diagnosed cases of asthma in Marblehead. You can assume that the population (19,800) remained constant throughout 2019.
What was the prevalence of asthma in Marblehead on January 1, 2019?
What was the prevalence of asthma in Marblehead on September 1, 2019?
What was the incidence of asthma in Marblehead between January 1, 2019 and September 1, 2019?
Based on the information provided above, it is NOT possible to calculate asthma incidence rate in Marblehead for the year 2018.
The prevalence of asthma on January 1, 2019 is 0.055, the prevalence of asthma on September 1, 2019 is 0.080, the incidence of asthma between January 1 and September 1 is 0.025, there is not possible to calculate asthma incidence rate for the year 2018.
How to calculate prevalence and incidence asthma?Prevalence is the formula to determine the rate of some case based on population. This can be calculated by divide the case by the population.
Incidence rate is same as prevalence in some factor except it only calculate time range and for this case it have same formula which is we can calculate incidence rate by divide the case by the population.
So, for January 1, 2019 is
Prevalence = 1,098 / 19,800
= 0.055
For September 1, 2019 is
Prevalence = (1,098 + new 495) / 19,800
= 1,593 / 19,800
= 0.080
For incidence of asthma between January 1 and September 1 is
Incidence = 495 / 19,800
= 0.025
For 2018 because we are not provided with data for that year so it is impossible to calculate it.
Thus, the prevalence in January 1 is 0.055, September 1 is 0.080, and incidence between January 1 and September 1 is 0.025, and also there is not possible to calculate asthma incidence rat for the year 2018.
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Find the value of x
Answer:
x is equal to 87
Step-by-step explanation:
42 +51=93
93-180=x
x=87
PLEASE HELP!! I will mark Brainliest
Compare these numbers.
>
<
=
none of the above
An object moving with a speed of 21 m/s and has a kinetic energy of 140 J, what is the mass of the object?
Answer:
0.63 kg
Step-by-step explanation:
KE = 1/2mv²
solve for m:
m = 2(KE)/v²
m = 2(140J) / (21m/s)²
m = 280J / 441 = 0.63 kg
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
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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What is the equation of a horizontal line through (0, -1)?
Choose one 4 points
Oy=0
Ox=0
O y = -1
O x=11
Answer:
(c) y = -1
Step-by-step explanation:
You want the equation of the horizontal line through (0, -1).
Horizontal lineA horizontal line has the same y-value for every x-value. Its equation is ...
y = constant
ApplicationIf you want the line to go through a point with a y-coordinate of -1, then the constant must be -1.
y = -1 . . . . . . . horizontal line through (0, -1)
What is 1 1/2 + 5/7?
A. 2 1/14
B. 2 2/7
C.11/14
D 2 3/14
The fraction 1¹/₂ + ⁵/₇ = 2³/₁₄
What are fractions?Fractions are numbers written in the form a/b where a and b are integers and b ≠ 0.
How to find what 1¹/₂ + ⁵/₇?Since we have the fractions 1¹/₂ and ⁵/₇ and we want to compute the sum
1¹/₂ + ⁵/₇, we re-write the first fraction as an improper fraction.
So, 1¹/₂ = ³/₂
Now, re-writting the equation, we have
³/₂ + ⁵/₇
To find the sum, wetake the L.C.M of both numbers which 2 × 7 = 14.
So, we make both denominators equal to the L.C.M.
So,
³/₂ × ⁷/₇ + ⁵/₇ × ²/₂ = ²¹/₁₄ + ¹⁰/₁₄
= (21 + 10)/14
= 31/14
= (28 + 3)/14
= 28/14 + 3/14
= 2 + 3/14
= 2³/₁₄
So, 1¹/₂ + ⁵/₇ = 2³/₁₄
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K
Determine whether the following statement is true or false, and explain why.
If a function is concave upward on an interval, it must be increasing on the interval.
Is the statement true or false?
A. The statement is true. Functions that are concave upward are always increasing.
B. The statement is false. Functions that are concave upward are always decreasing.
C. The statement is false. Functions that are concave upward are constant and do not increase or decrease.
D. The statement is false. Functions that are concave upward can be either increasing or decreasing.
11
The statement is true. Functions that are concave upward are always increasing.
What is Concave Upward Function?
Where the derivative f′ is growing, a function f is concave up (or upwards). This is equivalent to the derivative of f′, which is represented by the notation f′′f, start superscript, prime, end superscript, positive.
Explanation:
If a function is concave upward on an interval, it must be increasing on the interval. Given statement is true. Functions that are concave upward are always increasing.
A function is said to be concave upward on an interval if f″(x) > 0 at each point in the interval and concave downward on an interval if f″(x) < 0 at each point in the interval.
At interval if function is increasing then functions that are concave upward are always increasing.
Hence, The statement is true. Functions that are concave upward are always increasing.
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