the equation of the line tangent to the curve y at x = 3 is y = 36x - 102. The slope of the tangent line to the curve y at x = 3 is 36.
The equation of the line tangent to the curve y at x = 3 can be written using the point-slope form of a line, which is:
y - y1 = m(x - x1)
where m is the slope of the line, (x1, y1) is a point on the line, and m and (x1, y1) are known. In this case, m = 36 and (x1, y1) = (3, y). Substituting these values into the equation above, we get:
y - y = 36(x - 3)
y = 36x - 102
So the equation of the line tangent to the curve y at x = 3 is
y = 36x - 102.
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is y=3x+1/5 proportional? if so what is the constant of proportionality
Answer:
no
Step-by-step explanation:
You want to know if the equation y = 3x +1/5 represents a proportional relation.
Proportional relationA proportional relation has the equation ...
y = kx
for some constant of proportionality k.
Given equationThe added constant +1/5 in the given equation means the relation is Not Proportional.
<95141404393>
60th term of -7, -1, 5, 11
Answer:
60th term is 347
Step-by-step explanation:
This is an arithmetic sequence with common difference = -1 - (-7) = 5 - (-1) = 11 -5 = 6
The nth term for such a series is given by
aₙ = a₁ + d(n-1) where d = common difference and a₁ is the first term
Here d = 6, a₁ = -7
So
aₙ = -7 + 6(n-1)
aₙ = -7 + 6n-6
aₙ = 6n-13
60th term is
a₆₀ = 6(60) - 13 = 360 - 13 = 347
Find amplitude,period,and frequency
The sinusoidal function have the following features:
Amplitude: 1
Period: 2π
Frequency: ω = 2π / 2π = 1
How to analyze a sinusoidal function
Herein we find an example of a sinusoidal function, whose definition is shown below:
f(x) = A · sin (2π · x / T + Φ) + x'
Where:
x' - MidpointA - AmplitudeT - PeriodΦ - PhaseThe frequency (ω) is equal to the following formula:
ω = 2π / T
If we know that the sinusoidal function f(x) = sin (x + π / 2) - 2, then the amplitude, the period and the frequency, that is, the features of the sinusoidal function, are, respectively:
Amplitude: 1
Period: 2π
Frequency: ω = 2π / 2π = 1
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Use these graphics to answer the question.
A lobbyist for road safety collects data about accident trends for men and women. Assuming both graphics represent data in the same country, about how many women were involved in accidents while riding in a two wheeler in 2010?
about 50
about 250
about 1,000
about 5,000
Therefore , the solution of the given problem of graph comes out to be about 5,000 .
What is a graph?To rationally chart or graphically portray events or quantities, academics use graphs. A chart point is a typical tool for showing how various variables interact. Nodes, also known as vertices and lines, make up the non-linear storage arrangement known as a graph. The borders, also referred to as nodes, should be joined together using glue. (4.5) Visualizations, such as flowcharts, graphs, and bar graphs, that graphically depict explosive development within data.
Here,
Based on the graph,
it appears that in 2010, about 5,000 women were involved in accidents while riding in a two-wheeler.
Therefore , the solution of the given problem of graph comes out to be about 5,000 .
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At a particular restaurant, each onion ring has 40 calories and each pizza roll has 80
calories. A combination meal with pizza rolls and onion rings is shown to have 800
total calories and 4 more pizza rolls than onion rings. Graphically solve a system of
equations in order to determine the number of onion rings in the combination meal,
x, and the number of pizza rolls in the combination meal, y.
As a result, the combo meal includes 4 onion rings and 8 pizza buns.
What is equation?An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
Here,
Let x be the number of onion rings in the combination meal and y be the number of pizza rolls. We can write the following system of equations to represent the given information:
40x + 80y = 800 (the total calories of the meal)
y = x + 4 (the number of pizza rolls is 4 more than the number of onion rings)
We can substitute the second equation into the first equation to solve for x:
40x + 80(x + 4) = 800
40x + 80x + 320 = 800
120x = 480
x = 4
We can use this value to find y:
y = x + 4 = 4 + 4 = 8
So, the combination meal contains 4 onion rings and 8 pizza rolls.
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From a sample with n=12, the mean number of television per household is 3 with a standard deviation of 1 television. Using Chebychev Theorem,determine at least how many of the households have between 1 and 5 televisons
Answer:
9
Step-by-step explanation:
Chebyshev's Theorem states that for any given sample, at least 1 - 1/k^2 of the data falls within k standard deviations from the mean.
Let's use k = 2. Then, at least 1 - 1/2^2 = 1 - 1/4 = 3/4 of the households should have between 3 - 2 = 1 and 3 + 2 = 5 televisions.
So, at least 12 * 3/4 = 9 of the households in the sample have between 1 and 5 televisions.
Développer et réduire (3 − 2)² + (7 + 5)(3 − 2)
[tex](3-2)^2+(7+5)(3-2)=(3-2)(3-2)+(7+5)(3-2)=(3-2)(3-2+7+5)=1*13=13[/tex]
f(x)= 9+√(6+7x-x^2)
how do you find the range algebraically?? Please and thank you if you reply
Answer:
[9, 9+√18.25] ≈ [9, 13.272]
Step-by-step explanation:
You want the range of f(x)= 9+√(6+7x-x^2), determined algebraically.
RangeThe range is the set of values that f(x) may take on. It is the vertical extent of the graph. Here, it will be limited by the possible values the radical may have.
The expression under the radical is a quadratic that opens downward. It will have a maximum at its vertex, and a minimum usable value of 0.
The vertex of the quadratic can be found by putting it in vertex form:
-x² +7x +6 = -(x² -7x) +6 = -(x² -7x +(7/2)²) +6 +(7/2)² = -(x -7/2)² +18.25
The maximum value the quadratic may have is 18.25.
Then the range of values that f(x) may have is ...
9 +0 ≤ f(x) ≤ 9 +√18.25
The range is [9, 9+√18.25] ≈ [9, 13.272].
consider a sample with a mean of 500 and a standard deviation of 100. what are the z-scores for the following data values: 550, 660, 500, 440, and 270?
z-score for value 550 = 0.5
z-score for value 660 = 1.6
z-score for value 500 = 0
z-score for value 440 = -0.6
z-score for value 270 = -2.3
What is the standard deviation?
A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
We are given a sample with a mean of 500 and a standard deviation of 100.
i.e., µ= 500 and s= 100
The z score distribution is given by;
Z = (X-µ)/s ~ N(0,1)
where X represents the data values;
So, z score for value 550 is;
z score =(550-500)/100 = 0.5
So, z score for value 660 is;
z score = (660-500)/100 = 1.6
So, z score for value 500 is;
z score = (550-500)/100 = 0
So, z score for value 440 is;
z score = (440-500)/100 = -0.6
So, z score for value 270 is;
z score = (270-500)/100 = -2.3
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z-score for value 550 = 0.5
z-score for value 660 = 1.6
z-score for value 500 = 0
z-score for value 440 = -0.6
z-score for value 270 = -2.3
What is the standard deviation?
A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
We are given a sample with a mean of 500 and a standard deviation of 100.
i.e., µ= 500 and s= 100
The z score distribution is given by;
Z = (X-µ)/s ~ N(0,1)
where X represents the data values;
So, z score for value 550 is;
z score =(550-500)/100 = 0.5
So, z score for value 660 is;
z score = (660-500)/100 = 1.6
So, z score for value 500 is;
z score = (550-500)/100 = 0
So, z score for value 440 is;
z score = (440-500)/100 = -0.6
So, z score for value 270 is;
z score = (270-500)/100 = -2.3
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man bought a second hand car for $8 500, spent $1 500 on repairs and then sold it for $12 000. what was his percentage profit?
Answer:
20%
Step-by-step explanation:
He spent (8500+ 1500) = 10 000 then sold it for 2000 MORE
Profit = 2000 / 10 000 * 100% = 20%
Ahmad's car insurance last year was $630. This year he had two accidents, so the insurance
company raised his yearly bill to $1,008. What was the percent of increase in Ahmad's car insurance?
please answer the screenshot question
Answer:
sin(H) = 4/5cos(H) = 3/5tan(H) = 4/3Step-by-step explanation:
You want the primary trig functions of angle H in right triangle FGH with sides FG=12, GH=9, FH=15.
Trig ratiosThe mnemonic SOH CAH TOA is intended to help you with problems like this. Its purpose is to remind you that ...
Sin = Opposite/HypotenuseCos = Adjacent/HypotenuseTan = Opposite/AdjacentWith respect to angle H, the sides are ...
Opposite = 12Adjacent = 9Hypotenuse = 15Then the values you want are ...
sin(H) = 12/15 = 4/5
cos(H) = 9/15 = 3/5
tan(H) = 12/9 = 4/3
What number should go in the space?
Multiplying by 0.65 is the same as decreasing by _____%.
Answer: 35%
Explanation:
1 - 0.65 = 0.35
0.35 in percentage is 35%
kevin and sam are having a competition on their bikes to see who can ride at a faster rate. kevin rides 600 meters in 45 seconds while same rides 800 meters in 55 seconds which choice best describes who is the faster rider?
A. kevin he rides 10 second faster than sam
B.kevin he rides 13.33 meters per second
C.Sam he rides 800 meters total which is 200 more than Kevin
D.Sam he rides 14.5 meters per second which is over a meter per second faster than kevin
Answer:
D.Sam he rides 14.5 meters per second which is over a meter per second faster than kevin
Step-by-step explanation:
Kevin:
Distance = 600m
Time = 45s
Speed = Distance/time = 600/45 = 13.33m/s
Sam:
Distance = 800m
Time = 55s
Speed = 800/55 = 14.54m/s
Therefore option D will be the answer
Suppose 2.5 liters of water come out of a faucet each minute. For how many minutes was the faucet on if 38.5 liters of water came out?
Answer:
15.4 min
Step-by-step explanation:
rate = liters/min = 2.5 l/min
time = liters/rate = 38.5 l / (2.5 l/min) = 15.4 min
HELP ME PLEASE I WILL GIVE BRAINLIEST QUICK
Answer:
27 and 13
Step-by-step explanation:
let the second number be x then the first number is x - 14
sum the 2 numbers and equate to 40
x - 14 + x = 40
2x - 14 = 40 ( add 14 to both sides )
2x = 54 ( divide both sides by 2 )
x = 27
x - 14 = 27 - 14 = 13
the first number is 27 and the second number is 13
Jackie and Ken shared a bag of popcorn on a field trip. If Ken ate 2/3 of the bag of popcorn and Jackie ate 1/3 of the bag of popcorn, what fraction of the popcorn is left?
Answer:
4/9
Step-by-step explanation:
If Jackie at 1/3, that means that 2/3 was left
2/3 x 2/3 = 4/9
suppose there is a 19.8% probability that a radomly selected person aged 40 years or older is a smoker.A. What is the probability that a randomly selected person aged 40 years or older is female and smokes?B. Would it be unusual to randomly select a person aged 40 years or older who is female and smokes?
A. The probability that a randomly selected person aged 40 years or older is female and smokes is 0.05841.
B. No, it would not be unusual to randomly select a person aged 40 years or older who is female and smokes.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
When given an event A and an event B, the conditional probability that A will occur given than B has occurred is calculated using this formula -
P(A|B) = P(A and B) / P(B)
Let A be that the person is female and B be that they smoke. It is known that P(B) = 0.295 and let P(A|B) = 0.198.
Use the formula for conditional probability -
0.198 = P(A and B) / 0.295
P(A and B) = 0.198 × 0.295
P(A and B) = 0.05841
The probability that a person aged 40 years or older is female and smokes would happen is 0.05841, which is not less than the usual benchmark of 0.05 to be considered unusual.
Therefore, no, this would not be unusual.
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Suppose there is a 29.5% probability that a randomly selected person aged 40 years or older is a smoker. In addition, there is a 19.8% probability that a randomly selected person aged 40 years or older is a smoker. A. What is the probability that a randomly selected person aged 40 years or older is female and smokes? B. Would it be unusual to randomly select a person aged 40 years or older who is female and smokes?
find the area of a radius of 5 feet use 3.14 for pi
Answer: A=78. 5 [tex]feet^{2}[/tex]
Step-by-step explanation:
Keeping all other criteria the same, add a child to the family you used in part a to determine the monthly expenses. How does an additional child impact the family budget and hourly wage? Which category was least affected by this change? Explain why you think there was little impact to this category
The minimum monthly income of full time worker is $6112.
How to calculate the income?Full time worker = 4 weeks of 40 hour per week.
Part time worker = 2 weeks of 40 hour per week.
The full time hourly wage will be:
= $6112/(4 × 40)
= $6112/160
= $38.2
The part time hourly wage will be:
= $6112/(2 × 40)
= $6112/80
= $76.4
An additional child will impact the family budget as it will lead to lesser amount of money spent by each person.
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In AGHI, m/G = (8x + 14)°, m/H = (3x - 6)°, and m/I = (« + 16)°. Find m/G.
The value of the angle m/G is 118 degrees
How to determine the value of the angleIt is important to note that the sum of the angles in a triangle is equivalent to 180 degrees.
From the information given, we have that;
m/G = (8x + 14)°m/H = (3x - 6)° m/I = (« + 16)°Add the angles, we get;
8x + 14 + 3x - 6 + x + 16 = 180
collect like terms
8x + 3x + x = 180- 14 + 6 - 16
add or subtract like terms, we get;
12x = 156
Make 'x' the subject of formula by dividing both sides by the coefficient
x = 156/12
Divide the values
x = 13
m/G = 8(13) + 14
m/G = 118 degrees
Hence, the angle is 118 degrees
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The graph of the function g(x) = a |x| includes the point (1, 16). What is another point on the graph of the function? What is the value of a?
The graph of the function g(x) = a |x| includes the point (1, 16). (-1, 16) is another point on the graph of the function.
What is function?Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function's domain and co-domain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.
Given that,
g(x) = a |x|
In a absolute value graph the value of y is the same in -x and x.
Then if the coordinates (x,y) one point is (1, 16), the graph have another point in (- 1, 16).
To find the value of a you use one of the points (x,y) in the general form of absolute value:
( 1 , 16) x = 1 f(x) = y = 16
16 = a | 1 |
As, |±a| = a
we get:
16 = a . 1
then, a = 16
The equation for the graph with points (1 , 16) and ( -1, 16) is:
g(x) = 16 |x|
a = 16
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Learning aids, listed along the bottom of the window, are available for most problems on homework assignments and study plan practice but are not available on tests and quizzes. Identify the learning aid described in each part below.
One learning aid that provides an interactive walk-through for solving the particular problem you are working on is "view an example"
What does learning aid offer student?It is also known as teaching aids, which are an essential part of any classroom. Teaching aids can help students improve their reading comprehension skills, illustrate or reinforce a skill or concept, differentiate instruction, and relieve anxiety or boredom by presenting information in a new and exciting way.
Teaching aids also engage students' other senses because there are no restrictions on what aids can be used to supplement a lesson. As technology advances, so do teaching aids, which are now classified as audio aids, visual aids, mechanical teaching aids, audio-visual aids, and more.
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Wendy will have new carpet installed on her rectangular bedroom floor. The floor is 15 feet in length and 12 feet in width. The carpet costs $27.50 per square yard, and installation costs $4.15 per square yard. Which statement about the total cost of the carpet and installation is true?
a. The total cost is $379.80 since $31.65×12 = $379.80.
b. The total cost is $633.00 since $31.65×20 = $633.00.
c. The total cost is $474.75 since $31.65×15 = $474.75.
d. The total cost is $4,950.00 since $27.50×180 = $4,950.00
Answer: The statement "d. The total cost is $4,950.00 since $27.50×180 = $4,950.00" is incorrect.
The first step is to convert the dimensions of the floor from feet to yards. Since 1 yard = 3 feet, the length of the floor is 15 feet / 3 feet/yard = 5 yards, and the width of the floor is 12 feet / 3 feet/yard = 4 yards. The total area of the floor is 5 yards * 4 yards = 20 square yards.
The total cost per square yard for carpet and installation is $27.50 + $4.15 = $31.65.
The total cost for carpet and installation for the entire floor is 20 square yards * $31.65/square yard = $633.00.
So, the statement "b. The total cost is $633.00 since $31.65×20 = $633.00" is correct.
Step-by-step explanation:
y=4 over x + square x + 0.2 - 5x
Answer: The expression Y = 4 / (x + sqrt(x) + 0.2) - 5x represents a mathematical function that maps values of x to values of Y. The input x represents the independent variable and Y represents the dependent variable. For any given value of x, the expression calculates the value of Y.
Step-by-step explanation:
(b)The area of a rectangular window is 6789 cm².
If the width of the window is 73 , what is its length?
Answer:
93cm
Step-by-step explanation:
6789 = 73 * length
length = 6789/73=93
Answer:
The length is 93 cm.
Step-by-step explanation:
We know that area is width times height. So, if we don't know what the length is,
Let x = the length
The equation would be
[tex]73x=6789\\[/tex]
We multiply 73 by x because of the formula talked about previously.
Now, lets divide 73 on both sides
[tex]x = 93[/tex]
A two-digit number is formed using the digits 1, 2 and 3. Repetition of digits is allowed. (a) List the sample space. (b) Find the probability that the two-digit number formed is (i) divisible by 3, (ii) a perfect square, (iii) a prime number, (iv) a composite number.
Answer:
two plus two equals five
Step-by-step explanation:
Let R be the region bounded by y= square root of 25-x^2 and y=0. Find the volume of the solid of revolution obtained by revolving R about the x-axis.
As a result, the volume of the revolution solid is roughly -62.83π cubic units.
What is volume?Volume is the quantity of space in a 3D object in arithmetic. A fish tank, for example, is 3 feet long, 1 foot wide, and 2 feet tall. To calculate the volume, multiply the length by the breadth by the height, which is 3x1x2, which is six. As a result, the fish tank has a volume of 6 cubic feet.
Here,
The region R is the upper half of a circle centered at the origin with a radius of 5. By the method of washers, the volume of the solid of revolution obtained by revolving R about the x-axis can be found by subtracting the volume of a cylinder of height "h" and radius "x" from the volume of a cylinder of height "h" and radius "sqrt(25-x²)".
The volume of a cylinder of height "h" and radius "r" is given by V = πr²h.
So, the volume of the solid of revolution can be expressed as:
V = ∫π(sqrt(25-x²)²- x²) dx from x=0 to x=5
Evaluating this integral, we get:
V = π(∫(25-x²)*0.5 dx - ∫x² dx) from x=0 to x=5
Using substitution and integrating, we can obtain the volume:
V = π * (5 * (2 * sqrt(25 - x²) - x²/2))
Evaluating the expression at x=5, we get:
V = π * (5 * (2 * sqrt(25 - 25) - 25/2))
V = π * (5 * (0 - 25/2))
V = -62.83π cubic units.
So, the volume of the solid of revolution is approximately -62.83π cubic units.
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-9x^0-13 I know the answer is -22 but how is it solved?
Answer:
-22
Step-by-step explanation:
-9x^0-13
=-9×1-13
=-9-13
=-22
Answer:
-22
Step-by-step explanation:
To solve the expression
Let's start by finding the value of 'x'
[tex] - 9 {x}^{0} - 13[/tex]
Hint: Any number raised to power 0 is always 1.
Therefore x⁰ = 1
let's rewrite the expression by substituting where x is with 1
[tex] - 9(1) - 13[/tex]
[tex] - 9 \times 1 = - 9[/tex]
[tex] - 9 -13 = - 22[/tex]
Hope that helps with Your questionA batch of 150 containers for frozen orange juice contains 3 that are defective. Two are selected, at random, without replacement, from the batch. Let A and B denote the event that the first and second container selected is defected, respectively.
(a) Are A and B independent events
(b) If the sampling were done with replacement, would A and B be independent.
A) The events are not independent.
B) The events are independent.
Are A and B independent events?There are 150 containers (the probabilities depend on that number), and we draw two of them.
In event A we draw one, then the number of containers after that will be 149.
Then the probabilities for event B (the second draw) are different, which means that the events are not independent.
B) If the containers are replaced, then the events are independent.
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