Answer:
[tex]\displaystyle \frac{dy}{dx} = 2x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x^2 - 3[/tex]
Step 2: Differentiate
Derivative Property [Addition/Subtraction]: [tex]\displaystyle y' = \frac{d}{dx}[x^2] - \frac{d}{dx}[3][/tex]Basic Power Rule: [tex]\displaystyle y' = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
a 300 gallon tank is initially full and water is being drained at a rate of 4 gallons per minute.
does the intercept involving time have any physical meaning in this problem? explain
Answer:
Yes, it's when the tank is out of water.
Step-by-step explanation:
Michael is debating the two job offers below. Determine which will result in a higher income.
OFFER A
$34,500 ANNUALLY
OFFER B
$2,885 MONTHLY
B
Step-by-step explanation:
In a year, offer B would be more. Since annually is once a year and there are 12 months in a year, multiplying B by 12 would get each to a year.
The Cramer's Rule states that, in a system of equation in two unknowns, in which determinants D is not 0, X=_____and Y=_____.
Answer:
Step-by-step explanation:
[tex]x=\frac{D_{1}}{D} \\y=\frac{D_{2}}{D}[/tex]
Factor Зу2 - 4у.
y(4 - Зу)
y(Зу - 4)
y(4y-3)
What is a 7 - 0.9 = *
Answer: 6.1
Step-by-step explanation:
Answer:
6.1
Step-by-step explanation:
have a good day/night may i please have a branlliest
Charlotte is a customer-satisfaction expert at a large pizza company. She took a random sample of 1,000
delivery orders and constructed a one-sample z interval to estimate the proportion of delivery orders that take
more than an hour to arrive. She decides to repeat this process, but this time she'll use a sample of 4,000 orders.
Assume that the point estimates from each sample are approximately equal.
What is true about the margins of error from these two samples?
The margin of error from the smaller sample will be about
select ratio v
the margin of error from the
larger sample.
Answer:
2 times
Step-by-step explanation:
Khan Academy
You can use the formula for margin of error and the fact that the point estimates of both the samples are same to calculate the ratio of margin of errors of both the samples.
The margin of error from the smaller sample will be about double of the margin of error from the larger sample.
[tex]MOE_1 = 2 \times MOE_2[/tex]
How to calculate the margin of error for a given sample from a population?Let the level of significance be [tex]\alpha[/tex] and the standard deviation of the population be [tex]\sigma[/tex] and the sample size be n, then we have:
[tex]\text{MOE(Margin of Error)} = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
Using the above formula to calculate the margin of errors for two specified samplesFor first sample :
[tex]\text{Sample size} = n_1 = 1000\\\\MOE_1 = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{1000}}[/tex]
For second sample :
[tex]\text{Sample size} = n_1 = 1000\\\\MOE_2 = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{4000}}[/tex]
(since it was given that they have same point estimates, so same standard deviation)
Their ratios are given by
[tex]\dfrac{MOE_2}{MOE_1} = \dfrac{Z_{\alpha/2}\dfrac{\sigma}{\sqrt{4000}}}{Z_{\alpha/2}\dfrac{\sigma}{\sqrt{1000}}} = \sqrt{\dfrac{1000}{4000}} = \dfrac{1}{2}\\\\\\MOE_1 = 2 \times MOE_2[/tex]
Thus,
The margin of error from the smaller sample will be about double of the margin of error from the larger sample.[tex]MOE_1 = 2 \times MOE_2[/tex]
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What is greater 3 or -2.5
Answer:
3
Step-by-step explanation:
I’ll give points + brainalist for correct answer (:
Answer:
C) 2
Step-by-step explanation:
Emma: Range = 8
Arianna: Range = 6
The difference in the range is 2 (8-6)
Answer:
C) 2
Step-by-step explanation:
Emma:
Max = 20
Min = 12
Range = 20 - 12
Range = 8
Arianna:
Max = 18
Min = 12
Range = 18 - 12
Range = 6
Difference between the 2 ranges:
8 - 6 = 2
What is m∠1 in this ixl
Answer:
m<1 = 137
Step-by-step explanation:
Exterior angles thm:
41 + 96 = m<1
m<1 = 137
A large pizza has a radius of 7 in. The pizza is cut into 8 slices of equal size. What is the area of 1 slice, rounded to the nearest whole number? Use 3.14 for π.
Answer:
The area of 1 slice is of 19 square inches.
Step-by-step explanation:
Area of a circle:
The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
A large pizza has a radius of 7 in.
So its area of the pizza, in square inches, is of:
[tex]A = \pi(7)^2 = 49\pi = 49*3.14 = 153.86[/tex]
The pizza is cut into 8 slices of equal size. What is the area of 1 slice, rounded to the nearest whole number?
Area of the pizza divided by 8. So
153.86/8 = 19.2
Rounding to the nearest whole number, the area of 1 slice is of 19 square inches.
ILL GIVE BRAINLEST, find the value of x
Answer:
in my panies
Step-by-step explanation:
Janice is rolling a fair number cube that is numbered 1 - 6. Which statement is true?
Answer:
Where r the statements?
Step-by-step explanation:
Determine if the following relations are functions. If they are functions, also state the domain and range.
Answer:
desculpa mas eu não sei a resposta mais eu vou ver se posso te ajudar taaa
is this right? Please tell me....
Answer:
yes
Step-by-step explanation:
Answer:
YES IT IS!!
Step-by-step explanation:
!!
Darby’s Breakfast table an square tabletop what are your area of 36 ft.²
Answer:
Diagonal length = 8.59
Step-by-step explanation:
To find the diagonal length, we need the length of the sides. We find the length of the sides by finding the square root of 36, which is 6. Then, we use this equation (see attached image)
6 is 30% of _________ .
Answer:20
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
Let N be the number
"Is" in this case is =
"Of" means "multiply"
So we got
6 = .3N divide both sides by .3
6/.3 = 20
N=20
Without using a calculator, match each expression to the correct point.
Answer:
The locations of each irrational number are the following:
[tex]\sqrt{16}[/tex] - Point [tex]a[/tex]
[tex]\sqrt{27}[/tex] - Point [tex]b[/tex]
[tex]\sqrt{32}[/tex] - Point [tex]c[/tex]
Step-by-step explanation:
[tex]\sqrt{16}[/tex] is an irrational number that is also rational, since [tex]4^{2} = 16[/tex]. Then, [tex]\sqrt{16}[/tex] must be point [tex]a[/tex].
Both [tex]\sqrt{27}[/tex] and [tex]\sqrt{32}[/tex] are greater than [tex]\sqrt{25} = 5[/tex] and less than [tex]\sqrt{36} = 6[/tex]. Then, both are between 5 and 6. Since [tex]\sqrt{27} < \sqrt{32}[/tex], [tex]\sqrt{27}[/tex] must be point [tex]b[/tex] and [tex]\sqrt{32}[/tex] must be point [tex]c[/tex].
Find Arc ABC pls I need help
Step-by-step explanation:
Arc AD = 70
< D = 98
So
Arc BC = 2 * < D ( relation between arc and inscribed angle)
= 2 * 98
= 196
Hope it will help :)❤
What is the answer to: 20 - 6x = 4x -15 = ?
Answer:
20 - 6x = 4x - 15
35 - 6x = 4x
35 = 2x
x = 15.5
The solution to the equation 20 - 6x = 4x -15 is x = 3.5.
To solve the equation 20 - 6x = 4x - 15,
20 - 6x = 4x - 15
To isolate the variable terms on one side, add 6x to both sides:
20 - 6x + 6x = 4x - 15 + 6x
20 = 10x - 15
Next, add 15 to both sides to further isolate the variable term:
20 + 15 = 10x - 15 + 15
35 = 10x
Finally, divide both sides by 10 to solve for x:
35/10 = 10x/10
3.5 = x
Therefore, the solution to the equation is x = 3.5.
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Sam and you are going to paint your room together.
Sam takes 10 minutes to paint 25 square feet.
It takes you 5 minutes to paint 25 square feet.
Sam says, "If we paint together, then it will take 15 minutes for us to cover
feet."
TI
of
Give an explanation to convince Sam that she is incorrect.
.
Answer:
Sam is incorrect because you would not add the two times together. Hence there being 2 people working it would take you guys less time. You would actually subtract the times to get 5 minutes
Step-by-step explanation:
Answer:
Sam 's thinking is incorrect.
Step-by-step explanation:
Because If Sam takes 10 minutes to paint 25 square feet, then 5 minutes will be paint 12.5 sf... So if 15 minutes will paint 37.5 square feet. (by Sam)
---For me: if 5 mutes to paint 25 square feet.--->10 minutes will be 50 sf---> then 15 minutes will paint 75 square feet...
So If Same and I paint together will be 12.5 + 75 = 112.5 square feet
---Not 50 square feet...
What Sam says is incorrect....He can't add times together., that' s wrong.
Which of the following is a ray as shown in the drawing?
Solve for x to the nearest degree.
Answer:
Using Pythagoras Theorem, squareroot 15^2 - 5^2.
After you found the opposite length, use the cosine rule to find angle x.
Katie has $600 in a savings account that earns 5% annually. The interest is not compounded. How much interest will she earn in 1 year ?
Answer:
$30
Step-by-step explanation:
The formula for interest is I = Prt
Principal = 600
Rate = 0.05 or 5%
Time: 1 year
600 x 0.05 x 1 = 30
She earned an interest of 30.
Find the properties of each Quadratic Function
Answer:
1.) up
2.) (-2,-5)
3.) x = -2
4.) (-2,-5)
5.) y = -5
6.) -∞ < x < ∞
7.) -5 < y < ∞
8.) (0,0)
9.) (0,0) and (-4,0)
10.) two solutions
Step-by-step explanation:
1.) because the parabola opens upward and the vertex is down
2.) the lowest point of the parabola is (-2,-5)
3.) If a line was drawn through the point x = -2, the two halves of the parabola would look symmetrical ( the same on both sides).
4.) The minimum point on the graph is ( -2,-5), because that is the lowest point on this upward parabola, and we can not determine the maximum.
5.) The minimum value of y is y = -5, because that is the lowest value of y on this graph, and we can not determine the maximum.
6.) Because the arms of the parabola continue traveling through negative infinity and positive infinity on the x-axis, the domain is -∞ < x < ∞.
7.) The arms of the parabola go from y = -5 to infinity, so the range of the parabola is -5 < y < ∞.
8.) The parabola first crosses the y-axis at the point (0,0)
9.) The parabola first crosses the x-axis at the points (0,0) and (-4,0)
10,) The solution to the parabola is the variable x. The solutions (x intercepts) of the parabola are x = 0 and x = -4.
Does this help you?
Hi answer as fast as you
it just says hi answer as fast as you where is the question
Simplify the expression:
3(2+8p)
A. 6+24p
B. 30p
C. 3(10p)
D. 6p+24
Answer:
A. 6+24p
Step-by-step explanation:
=(3)(2+8p)
=(3)(2)+(3)(8p)
=6+24p
=24p+6
1.5 x 0.3 =
i’m desperate pls answer-
Answer:
45
Step-by-step explanation:
Answer:
0.45
Step-by-step explanation:
i need help with this pls 9.1k=63.7
Answer:
k = 7
Step-by-step explanation:
63 ÷ 9 = 7
A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounces. If a sample of 9 cups is selected, find the probability that the mean of the sample will be less than 12.1 ounces.
Answer:
0.9332 = 93.32% probability that the mean of the sample will be less than 12.1 ounces.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 12 ounces and a standard deviation of 0.2 ounces.
This means that [tex]\mu = 12, \sigma = 0.2[/tex]
Sample of 9:
This means that [tex]n = 9, s = \frac{0.2}{\sqrt{9}}[/tex]
Find the probability that the mean of the sample will be less than 12.1 ounces.
This is the pvalue of Z when X = 12.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{12.1 - 12}{\frac{0.2}{\sqrt{9}}}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a pvalue of 0.9332
0.9332 = 93.32% probability that the mean of the sample will be less than 12.1 ounces.
Evaluate the following expression.
6^-3
Answer:
.0046, if you mean the -3 to be an exponent
Step-by-step explanation:
Answer:
[tex]\frac{1}{216}[/tex]
Step-by-step explanation:
If you have any questions feel free to ask in the comments