Answers
Answer:
\(\frac{1}{5}\)
Step-by-step explanation:
Consider the curve \(y=3x^2-5x\)
Differentiate with respect to \(x\)
\(\frac{dy}{dx} =3(2x)-5=6x-5\)
( Use \(\frac{d}{dx}(x^n)=nx^{n-1}\) )
Slope of normal curve is given by \(\frac{-1}{\frac{dy}{dx} }\)
Slope of normal curve = \(\frac{-1}{6x-5}\)
To find slope of normal curve at point \((0,0)\) ,put \(x=0\) in \(\frac{-1}{6x-5}\)
Slope of normal curve at point \((0,0)\) = \(\frac{-1}{6(0)-5} =\frac{-1}{-5}=\frac{1}{5}\)
Related Questions
4 +2y+m how many terms?
Answers
Answer:
2
Step-by-step explanation:
The equation has 2 terms in it which means 2 is the answer.
Find the equation of the line tangent to the graph of
y = sin^-1 (x/5) at x = 5/2. Show your work.
Answers
Answer:
\(\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}\)
Step-by-step explanation:
We want to find the equation of the line tangent to the graph of:
\(\displaystyle y=\sin^{-1}\left(\frac{x}{5}\right)\text{ at } x=\frac{5}{2}\)
So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:
\(\displaystyle y^\prime=\frac{1}{\sqrt{1-\left(\dfrac{x}{5}\right)^2}}\cdot\frac{1}{5}\)
Simplify:
\(\displaystyle y^\prime=\frac{1}{5\sqrt{1-\dfrac{x^2}{25}}}\)
We can factor out the denominator within the square root:
\(\displaystyle y^\prime =\frac{1}{5\sqrt{\dfrac{1}{25}\big(25-x^2)}}\)
Simplify:
\(\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}\)
So, we can find the slope of the tangent line at x = 5/2. By substitution:
\(\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}\)
Evaluate:
\(\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\dfrac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}\)
We will also need the point at x = 5/2. Using our original equation, we acquire that:
\(\displaystyle y=\sin^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{6}\)
So, the point is (5/2, π/6).
Finally, by using the point-slope form, we can write:
\(\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}\left(x-\frac{5}{2}\right)\)
Distribute:
\(\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}\)
Isolate. Hence, our equation is:
\(\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}\)
In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household.) Among the respondents, answered "none," said "one," said "two," said "three," and responded with four or more. A survey respondent is selected at random. Find the probability that his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in use? Consider an event to be unlikely if its probability is less than or equal to 0.05.
P(four or more cell phones)
(Round to three decimal places as needed.)
Answers
204+287+376+137+130=1134
130/1134= .115
No, because the probability of a respondent with four or more cell phones in use is greater than 0.05.
Devon is 30 years old than his son, Milan. The sum of both their ages is 56. Using the variables d and m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.How old is Devon?
Answers
Let's set d as the age of Davon and m as the age of Milan.
Devon is 30 years old than his son Milan, it is represented by the equation:
\(d=m+30\text{ Equation (1)}\)The sum of both ages is 56, the equation that represents the situation is:
\(d+m=56\text{ Equation (2)}\)To find Devon's age, in equation 1, solve for m in terms of d:
\(m=d-30\)Now, replace in equation 2 and solve for d:
\(\begin{gathered} d+(d-30)=56 \\ 2d-30=56 \\ 2d=56+30 \\ 2d=86 \\ d=\frac{86}{2} \\ d=43 \end{gathered}\)Devon is 43 years old.
PLS HELP ALG 1 DUE TMR
Answers
Answer:
y=x^3 - 10x + 16
Step-by-step explanation:
The lengths of two sides of a triangle are shown.
Side 1: 8x2 - 5x - 2
Side 2: 7x - x2 , 3
The perimeter of the triangle is 4xJ - 3x?
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)
Part B: What is the length of the third side of the triangle? Show your work. (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? justify your answer. (2
points)
Answers
The Total length of two sides based on the information will be 7x²+2x+1
The Length of the third side will be 4 x³-10x²-7.
How to calculate the lengthTotal length of two sides= Side 1 + Side 2
= 8x² − 5x − 2+ 7x − x²+ 3
= 8x²-x²-5x+7x-2+3
= 7x²+2x+1
Length of the third side = Perimeter - Total length of two sides
Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)
= 4x³ − 3x² + 2x − 6-7x²-2x-1
= 4 x³-10x²-7
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Determine if an exponential would be an appropriate model for the data shown in each scatter plot. Select
one that applies.
Answers
Answer:
Yes, No, No
Step-by-step explanation:
The function of an exponential graph is attached below. The first graph fits the look of an exponential graph. The rest do not.
Answer:
Yes, No, No
Step-by-step explanation:
1st graph represents exponential2nd graph represents quadratic3rd graph represents linearFind one third missing . Select the figures that have one third missing
Answers
ANSWER
EXPLANATION
We have to select those figures that are missing one-third of them. Note that all the figures have one missing part, but the only ones that have one-third missing are those that are divided in three equal parts - the last circle is missing one of three parts, but that is not one-third because not all the parts are equal.
7.
Write an equation in point-slope form for the line through the given point with the given slope.
(10, –9); m = –2
A. y – 10 = –2(x + 9)
B. y – 9 = –2(x – 10)
C. y – 9 = –2(x + 10)
D. y + 9 = –2(x – 10)
Answers
Answer:
D. y + 9 = –2(x – 10)
Step-by-step explanation:
GradPoint answer
I also got the answer correct on the quiz.
How do you find the radius of a cylinder when you only know the surface area?
Answers
The surface area of a cylinder with circular bases of radius r and height h is equal to the sum of the areas of the two circular faces and the area of the rectangular lateral surface:
A = 2πr² + 2πrh
If you know the height h, then you can solve the quadratic equation for r.
A local congressman must decide whether or not to vote for a bill to reduce the speed limit.
Supporters of the bill claim that the gas mileage improves at lower speeds! The congressman was given the data about the Toyota Camry gas usage - presented in the table below. (Picture Attached.)
Note: MPG stands for miles per gallon of gas.
IDENTIFY THE INDEPENDENT VARIABLE FIR THIS DATA AND WHY.
Answers
The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.
How to explain the variablesThe dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.
The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.
The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.
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The formula for distance is given as distance = speed x time. Use the formula to find:
b. The distance, in km, of a journey which takes 5 hours at a speed of 120 km/h.
give your answer in km
ASAP PLEASE
Answers
❥\(\Large\pmb {\underline {\tt Answer}}\)
Given :-
Time = 5 hoursSpeed = 120 km/hTo find:
DistanceWe know:-
Distance = Speed × TimeDistance = 5 × 120Distance = 600kmRequired Answer :-
600 km
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\( \large \sf \blue{Find \: the \: H.C.F \: of : }\)
\( \sf \purple{➪ \: 84 \: and \: 156}\)
Answers
Answer:
\( \large \sf \blue{Find \: the \: H.C.F \: of : }\)
\( \sf \purple{➪ \: 84 \: and \: 156}\)
![[tex] \large \sf \blue{Find \: the \: H.C.F \: of : }[/tex][tex] \sf \purple{ \: 84 \: and \: 156}[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/LxOUIGzGAYTIDWSSBrxKh7XIcD0QsFHY.jpeg)
The square pyramid has a base area of 625 square meters and a height of 30 meters. Find the volume. cubic meters
No files
and links
Answers
Answer:
6250
Step-by-step explanation:
V= lwh /3 = 5·125·30 /3 = 6250
Yesterday, 15 guests at a hotel called for room service, and 105 guests did not call for room service. What percentage of the guests at this hotel called for room service yesterday?
Answers
Does anyone know this answer??
Answers
Answer:
96.25%
Step-by-step explanation:
The empirical rule regarding mean and standard deviation is that
Around 68% of scores are between 40 and 60.Around 95% of scores are between 30 and 70.Around 99.7% of scores are between 20 and 80.Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find approximately 95/2 = 47.5% of the values
Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values
Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values
A girl who is flying a kite lets out 200 feet of string which makes an angle of 50° with the ground. Assuming that the string is stretched out, find, to the nearest foot, how high the kite is above ground.
Answers
The height of the kite from the ground when the angle is 50 degrees is 232 feet.
What is trigonometry?The study of the correlations between triangles' sides and angles is the focus of the mathematic branch known as trigonometry. To link the angles of a right triangle to the lengths of its sides, it makes use of trigonometric functions like sine, cosine, and tangent.
Numerous industries, including physics, engineering, and navigation, use trigonometry. It can be used, for instance, to determine a building's height or the separation between two locations on a map, as well as to examine how waves and oscillations behave.
To find the height of the kite above the ground we use the trigonometric identity of tangent.
Thus, we have:
tan(50°) = h/200
Now, using cross multiplication:
h = 200 tan(50°) ≈ 232 feet
Hence, the height of the kite from the ground when the angle is 50 degrees is 232 feet.
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consider the distribution of monthly social security (OASDI) payments. Assume a normal distribution with a standard deviation of $116. if one-fourth of payments are above $1214,87 what is the mean monthly payment?
Answers
Answer:
\(\mu = x - z(\sigma)\)
\(\mu = 1214.87 - 0.67(116) \\\\\mu = 1214.87 - 77.72 \\\\\mu = \$1137.15\)
Therefore, the mean monthly payment is $1137.15.
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
We are asked to find the mean monthly social security (OASDI) payment.
Mean monthly payment = μ = ?
We are given that the standard deviation is $116
One-fourth of payments are above $1214.87
One-fourth means 25%
\(P(X > x )= P(Z > z ) = 0.25\\\\P(X < x )= P(Z < z) = 1 - 0.25\\\\P(X < x )= P(Z < z) = 0.75\\\\\)
From the z-table, the z-score corresponding to 0.75 is found to be 0.67
\(z = 0.67\)
The mean is found by
\(x = \mu + z(\sigma)\)
\(\mu = x - z(\sigma)\)
Where
x = $1214.87
z = 0.67
σ = $116
\(\mu = 1214.87 - 0.67(116) \\\\\mu = 1214.87 - 77.72 \\\\\mu = \$1137.15\)
Therefore, the mean monthly payment is $1137.15.
A rectangle is removed from the middle of a larger rectangular shaped board. What is the area of the remaining board?
Answers
Answer:
The area of the remaining board is [(L × B) - (l × b)].
Step-by-step explanation:
Suppose the bigger rectangle is labelled as ABCD and the smaller rectangle is labelled as PQRS.
Consider that the length and breadth of the bigger rectangle are L and B respectively. And the length and breadth of the bigger rectangle are l and b respectively.
The area of any rectangle is:
Area = Length × Breadth
The area of the bigger rectangle is:
Area of ABCD = L × B
The area of the smaller rectangle is:
Area of PQRS = l × b
Then the area of the remaining board will be:
Area of remaining board = Area of ABCD - Area of PQRS
= (L × B) - (l × b)
Thus, the area of the remaining board is [(L × B) - (l × b)].
Answer:
112
Step-by-step explanation:
Find the value of x
14x-15 and 139 degrees (look at the image)
Answers
Answer: x=4
Step-by-step explanation:
Simplifying
(14x + -15) + 139 = 180
Reorder the terms:
(-15 + 14x) + 139 = 180
Remove parenthesis around (-15 + 14x)
-15 + 14x + 139 = 180
Reorder the terms:
-15 + 139 + 14x = 180
Combine like terms: -15 + 139 = 124
124 + 14x = 180
Solving
124 + 14x = 180
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-124' to each side of the equation.
124 + -124 + 14x = 180 + -124
Combine like terms: 124 + -124 = 0
0 + 14x = 180 + -124
14x = 180 + -124
Combine like terms: 180 + -124 = 56
14x = 56
Divide each side by '14'.
x = 4
Simplifying
x = 4
Suppose that the population of heights of all fully grown male West African giraffes is approximately normally distributed. A recent article published in the Zoology Now journal claims ...
Answers
Based on the information, the confidence interval doesn't contradict the claim.
How to calculate the valueBased on the information, the following vs be deduced:
Mean = 2.87
Sample size = 35
Population standard deviation = 1.36
Critical value = 2.576
Standard error = Standard deviation / ✓Sample size
= 1.36 / ✓35
= 0.2299
The margin of error will be:
= 2.576 × 0.2299
= 0.5922
The 99% confidence interval will be 2.5678 < U < 3.7522
In conclusion, the confidence interval doesn't contradict the claim. Hence, the publication claim of 2.87kg is inside the 99% confidence interval.
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Use a quadratic equation to find two real number that satisfy each situation, or show that no such number exist. Their sum is 4, and their product is -117
Answers
Answer: -25
Step-by-step explanation:
Question a b c, need help to to solve them...
Answers
infinityAnswer:
p(0) = 20
p(5) = 59
Horizontal Asymptote: y = 2400 as t approaches infinity
Explanation:
part C.
To find the horizontal asymptote, we investigate the behaviour of the function p(t) as t approaches infinity.
Now as t approaches inifinty
\(P(t)=\frac{60(1+0.4t)}{0.01t+3}\)the terms 0.04 t and 0.01t become extremely large; so large in fact that we can ignore constant 3 and 1 to get
\(P(t)\approx\frac{60\cdot0.4t}{0.01t}\)\(P(t)\approx2400\)which means at t -> ∞, p(t) = 2400. In the context of insect population this means that if we wait a long enough time, eventually the insect population will stop decreasing and approach 2400. In other words, the population limit is 2400 insects
HELP!!!Joe can type 40 words every 2 minutes. How many words can he type in 5 minutes?
Answers
Answer:100
Step-by-step explanation:
40+40 =80 +20=100
what is 3 x 3 x 9 x 9 x 81 x 81 x 6561 x 6561
Answers
Answer:
205891132094649
Write a scenario that can expressed by 3x
Answers
Answer:
Step-by-step explanation:
makinleymiller10 has 3 times as many experience points as desaikov.
A baker bakes 48 dozen doughnuts each morning. She sells 18 dozen
in her store and fills orders with the rest. Write a fraction to show the
portion of doughnuts the baker sells in her store. Be sure to simplify.
Answers
Answer:
30/48
Step-by-step explanation:
She sells 18 dozen of the 48 dozen in her store
18/48 simplified to 3/8
There are only 6 blue pens, 5 green pens and 8 red pens in a box.
One pen is taken at random from the box.
Write down the probability that this pen is blue.
Answers
Answer:
0.316
Step-by-step explanation:
Probability = (number of outcomes)/(total number of outcomes)
In this case,
the total number of outcomes is 6+5+8 = 19, and
the number of outcomes for getting a blue pen = 6
Hence,
P(blue) = 6/19 = 0.31578947368 ≈ 0.316
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Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup. How much pure sugar is in x grams of 10% syrup?
Answers
Answer:
40 grams
Step-by-step explanation:
........................
Answer: 0.10x grams
Step-by-step explanation:
quadratic regression for (1,-8) (2,-4) (3,6)
Answers
The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7
What is quadratic equatiοn?
A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.
Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.
We can start by using the three given pοints tο set up a system οf three equatiοns:
\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)
SimpIifying each equatiοn, we get:
a + b + c = -8 (equatiοn 1)
4a + 2b + c = -4 (equatiοn 2)
9a + 3b + c = 6 (equatiοn 3)
AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.
SοIving the system using technοIοgy, we get:
a = 5
b = -20
c = 7
Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:
y = 5x² - 20x + 7
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